NBS SPECIAL PUBLICATION 523

y

U.S. DEPARTMENT OF COMMERCE / National Bureau of Standards

WIND AND SEISMIC EFFECTS

Proceedings of the

Ninth Joint UJNR

Panel Conference
NATIONAL BUREAU OF STANDARDS

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: Some divisions within the center are located at Boulder, Colorado, 80303. The National Bureau of Standards was reorganized, effective April 9, 1978.
National BurWJ " ! sw"""' WIND AND SEISMIC EFFECTS

^ ^ m

Proceedings of the Ninth Joint Panel Conference of the U.S.-Japan

Cooperative Program in Natural Resources

May 24-27, 1977 Tokyo, Japan

H.S. Lew, Editor

Center for Building Technology

National Engineering Laboratory

National Bureau of Standards Washington, D.C. 20234

U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

Dr. Sidney Harman, Under Secretary Jordan J. Baruch, Assistant Secretary for Science and Technology

\jb NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Issued September 1978
Library of Congress Catalog Card Number: 78-600082

National Bureau of Standards Special Publication 523

Nat. Bur. Stand. (U.S.), Spec. Publ. 523, 518 pages (Sept. 1978) CODEN: XNBSAV

U.S. GOVERNMENT PRINTING OFFICE WASHINGTON: 1978

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402

Stock No. O03-003-O1979-8 Price $6.75 (Add 25 percent additional for other than U.S. mailing).
The Ninth Joint Meeting of the U.S. - Japan Panel on Wind and Seismic Effects was held

Ln Tokyo, Japan on May 24-27, 1977. This panel is a part of the U.S. - Japan Cooperative

Program in Natural Resources (UJNR) . The UJNR was established in 1964 by the U.S. - Japan

Cabinet-level Committee on Trade and Economic Affairs. The purpose of the UJNR is to exchange

scientific and technological information which will be mutually beneficial to the economics

and welfare of both countries. These proceedings include the program, the formal resolutions, and the technical papers

presented at the Joint Meeting. The texts of the papers, all of which were prepared in English, have been edited for obvious errors and clarity.

It should be noted that throughout the proceedings certain commercial equipment, instruments or materials are identified in order to specify adequately experimental procedure. In

no case does such identification imply recommendation or endorsement by the National Bureau

of Standards, nor does it imply that the material or equipment identified is necessarily the

best for the purpose. Publication of these proceedings is partially supported by the National Science

?oundation.

H. S. Lew, Secretary

U.S. Panel on Wind and Seismic Effects

iii
SI Conversion Units

In view of present accepted practice in this technological area, U.S. customary units of measurements have been used throughout this report. It should be noted that the U.S.

is a signatory to the General Conference on Weights and Measures which gave official status

to the metric SI system of units in 1960. Conversion factors for units in this report are:

Customary Unit International

(SI), UNIT

Conversion

Approximate Length inch (in) meter (m) a

1 in=0. 0254m* foot (ft) meter (m) 1 ft=0. 3048m* Force pound (lbf) newton (N) 1 lbf=4.48N

kilogram (kgf) newton (N) 1 kgf=9.807 Pressure pound per square

Stress inch (psi) newton/meter 21 psi=6895N/m2 kip per square

inch (ksi) newton/meter 2

1 ksi=5895xl0 6N/m2 Energy inch-pound (in-lbf) joule (J) 1 in-lbf=0.11 30 J

foot-pound (ft-lbf) joule (J) 1 ft-lbf=1.3558 J

Torque

or Bending Moment

pound- inch newton-me ter ( N-m

)

1 lbf-in=0.1130 N-m pound-foot (lbf-ft) newton-me ter ( N-m ) 1 lbf-ft=1.3558 N-m

Weight pound (lb) kilogram (kg) 1 lb=0.4536 kg

Unit Weight pound per cubic foot

(pcf) kilogram per cubic meter (kg/nr)

1 pcf=16.018 kg/m3

Velocity foot per second

(ft/sec) meter per second

(m/s)

1 fps=0.3048 m/s

Acceleration foot per second per second (ft/sec2

) meter per second

per second (m/s ) 1 ft/sec2=0.3048 m/s:

aMeter may be subdivided. A centimeter (cm) is 1/100 m and a millimeter (mm) is 1/1000 m.

iv
ABSTRACT

The Ninth Joint Meeting of the U.S. - Japan Panel on Wind and Seismic Effects was held

in Tokyo, Japan on May 24-27, 1977. The proceedings of the Joint Meeting include the program

the formal resolutions, and the technical papers. The subjects covered in the papers include

(1) characteristics of strong winds, (2) wind loads on structures and design criteria, (3) earthquake prediction, (4) earthquake ground motions and soil failures, (5) seismic loads

on structures and design criteria, (6) design of special structures, (7) earthquake hazard

reduction program, and (8) quantitative evaluation of damages caused by winds and earthquakes

Key Words: Accelerograph; codes; design criteria; disaster; earthquakes; earthquake hazards; ground failures; seismicity; solids; standards; structural engineering; structural responses; wind loads; and winds.

CONTENTS

Page Preface iii

SI Conversion iv Abstract v Program of the Joint Meeting x List of Members xiv

Formal Resolutions xviii Themes and Technical Papers

Theme I: CHARACTERISTICS OF STRONG WINDS

Distribution Models of Pressure and Wind over Stationary Typhoon Fields . . . 1-1 Shigemi Fujiwhara and Kiyoshi Kurashige

Extreme Winds in the United States 1-10 Thomas D. Potter and Michael Changery

Theme II: WIND LOADS ON STRUCTURES AND DESIGN CRITERIA

Aerodynamic Stability of a Long-Span Suspension Bridge at Construction

Stage II-l

T. Kunihiro, N. Narita and K. Yokoyama

Theme III: EARTHQUAKE PREDICTION (STATE-OF-THE-ART REPORTS) Present Situation of Earthquake Prediction Research in Japan III-l Kazuo Hamada, Hiroshi Takahashi, Hiroshi Sato and Akira Suwa

The Complementary Importance of Earthquake Prediction and Structural Response Estimation in Seismic Design and Planning Decisions 111-20 Robin K. McGuire

Research and Development of Permanent Ocean-bottom Seismograph Observation

System Off the Pacific Coast to Central Honshu, Japan 111-30 Akira Suwa, Norio Yamakawa and Tatsuto Iinuma Vertical Distribution of the Seismic S-Wave Velocities at the Site of the Iwatsuki Deep Borehole Observatory of Crustal Activities 111-44 Fumio Yamamizu, Hiroshi Takahashi, Noritoshi Gotoh, Yutaka Ohta and Keiji Shiono

Research on Active Faults in the Metropolitan Area 111-55 Hiroshi Sato and Toshihiro Kakimi

Theme IV: EARTHQUAKE GROUND MOTIONS AND SOILS FAILURE Characteristics of Vertical Components of Strong-Motion Accelerograms .... rv-1 Tatsuo Uwabe, Setsuo Noda, Eiiehi Kurata and Satoshi Hayashi Developments in Strong-Motion Data Management IV-20

A. Gerald Brady On A Method for Synthesizing the Artificial Earthquake Waves by Using the Prediction Error Filter IV-28 Keiichi Ohtani and Shigeo Kinoshita Statistical Analysis of Strong-Motion Acceleration Records IV-48 Masamitsu Ohashi, Toshio Iwasaki, Susumu Wakabayashi, Ken-ichi Takida

vii
Research on Design Earthquake IV-78 Makota Watabe Determination of Wave Propagation Velocities in Subsurface Soil Layers. . . . IV-96 Yukitake Shioi and Toshio Iwasaki Studies on Soil Liquefaction Related to Earthquake Resistant Design of Structures IV-115 Masamitsu Ohashi, Toshio Iwasaki and Fumio Tatsuoka

Earthquake Resistant Designs Based on Ground Motions at Base-Rock rv-158 Eiichi Kuribayashi, and Kazuhiko Kawashima

Theme V: SEISMIC LOADS ON STRUCTURES AND DESIGN CRITERIA

Basic Earthquake for Dam Design V-l Jerry S. Dodd Study on Regional Distribution of Maximum Earthquake Motions in Japan .... V-14 Masakazu Ozaki, Yoshikazu Kitakawa and Sadaiku Hattori Treatments on Seismic Force in Designing Earth Structures V-45

Kenkichi Sawada

Studies on the Aseismic Properties of Underground Pipes V-53 Keiichi Obtani, Nobuyuki Ogawa and Chikahiro Minowa Observation of Dynamic Behavior of Kinuura Submerged Tunnel during Earthquakes V-69 Shigeo Nakayama, Osamu Kiyomiya and Hajime Tsuchida A Proposal for Earthquake Resistant Design Methods V-80 Kiyoshi Nakano and Masamitsu Ohashi

On the Object Postulate for Earthquake-Resistant Code . V-102

Kiyoshi Nakauo, Yuji Ishiyama, Yoshitsugu Aoki and Kazumasa Watanabe

Theme VI: DESIGN OF SPECIAL STRUCTURES

The Earthquake Response of Hysteretie Structures VI-1

W.D. Iwan and N.C. Giates Earthquake Resistant Design of High-rise Buildings in Japan VI-15

Keiichi Ohtani

Racking Strength of Wood-frame Walls VI-25

Roger L. Tuomi Theme VII: EARTHQUAKE HAZARD REDUCTION PROGRAM

Examination for an Evaluation Method of Damage to Existing Wooden Houses

Caused by Earthquakes VTI-1 Kaoru Ichihara, Eiichi Kuribayashi, Tadayuki Tazaki, and Takayuki Hadate Relationship Between Modified Mercalli Intensity and Wood Frame Dwelling Earthquake Insurance VI 1-16 Karl V. Steinbrugge and S.T. Algermissen

viii
Theme VIII: QUANTITATIVE EVALUATIONOF DAMAGES CAUSED BY WINDS AND EARTHQUAKES

(INCLUDING TECHNICAL COOPERATIONS IN DEVELOPING COUNTRIES) Warrants for Retrofitting Highway Bridges VIII-1 Anatole Longinow, Ernest Bergmann and James D. Cooper Criterion on the Evaluation of Seismic Safety of Existing Reinforced

Concrete Buildings VIII-22

Kiyoshi Nakano, Masaya Hirosaua and Shin Okamoto

Transferring the Technology for Wind-resistant Buildings to Developing Countries VTII-42

Noel J. Raufaste, Jr.

ix
NINTH JOINT MEETING

OF THE

U.S. -JAPAN PANEL ON WIND AND SEISMIC EFFECTS MAY 24-27, 1977 AT THE

KEIDANREN KAIKAN

TUESDAY-May 24 OPENING SESSION

9:30 Call to order by Dr. Tadayoshi Okubo, Head Planning and Research Administration Division, Public Works Research Institute Remarks by Mr. Takashi Inoue, Engineer General, Ministry of Construction

Remarks by Mr. Justin Bloom, Acting Counselor for Scientific and Technolgical Affairs, U.S. Embassy Remarks by Mr. Kimio Fukushima, Chief, International Division, Promotion

Bureau, Science and Technology Agency

Remarks by Dr. Chester R. Benjamin, Assistant Director, International Program Division, Agricultural Research Survey, Department of Agriculture Remarks by Dr. Kaoru Ichihara, Director, Public Works Research Institute, Ministry of Construction

Remarks by Dr. E.O. Pfrang, Chief, Structures, Materials and Safety Division, Center for Building Technology, NEL, National Bureau of Standards Introduction of United States Panel Members by U.S. Chairman and Japan Panel Members by Japanese Chairman Election of Permanent Chairman Adoption of Agenda

1:00 p.m. On Distribution Models of Pressure and wind over Stationary Typhoon Fields —

Shigemi Fujiwhara, and Kiyoshi Kurashige 1:25 Extreme Winds in the United States — T.D. Potter 1:50 Aerodynamic Stability of a Long-span Suspension Bridge at Construction

Stage — Tetsuo Kunihiro, Nobuyuki Narita, and Koichi Yokoyama

2:15 Discussion

2:40 Present Situation of Earthquake Prediction Research in Japan — Kazuo

Hamada, Hiroshi Sato, Hiroshi Takahashi, and Akira Suwa

3:05 The Complementary Importance of Earthquake Prediction and Structural Response Estimation in Seismic Design and Planning Decisions — R.K. McGuire

3:30 Discussion

3:50 Recess 4:05 Research and Development of Permanent Ocean-Bottom Seismograph Observation

System Off the Pacific Coast of Central Honshu, Japan — Akira Suwa, Norio

Yamakawa, and Tatsuto Iinuma

x
4:30 Vertical Distribution of the Seismic S-wave and Response Characteristics at

the Site of the Iwatsuki Deep Bore Hole Observatory of Crustal Activities — Fumio Yamamizu, Hiroshi Takahashi, Yutaka Ohta, Noritoshi Gotoh,

and Keiji Shiono

4:55 Researches of Active Faults in the Metropolitan Area — Hiroshi Sato, and Toshihiro Kakimi

5:20 Discussion

5:45 Adjourn

WEDNESDAY-May 25 9:00 a.m. Characteristics of Vertical Components of Strong-Motion Accelerograms —

Tatsuo Uwabe, Setsuo Noda, Eiichi Kurata, and Satoshi Hayashi 9:25 Developments in Strong-Motion Data Management — A.G. Brady

9:50 On a Method for Synthesizing the Artifical Earthquake Wave by Using Prediction Error Filter — Keiichi Ohtani, and Shigeo Kinoshita

10:15 Discussion

10:45 Recess 10:55 Statistical Analysis of Strong-Motion Acceleration Records — Masamitsu

Ohashi, Toshio Iwasaki, Susumu Wakabayashi, and Kenichi Tokida 11:20 Research on Design Earthquake — Makoto Watabe

11:45 Discussion

0:05 p.m. Recess (Lunch) 1:00 Properties of Superficial Layer for Vibration — Yukitake Shioi, and Toshio

Iwasaki 1:25 Studies on Soil Liquefaction Relating to the Earthquake Resistant Design of Structures — Masamitsu Ohashi, Toshio Iwasaki, and Fumio Tatsuoka

1:50 Earthquake Resistant Design Based on Ground Motions at Base-Rock — Eiichi Kuribayashi, and Kazuhiko Kawashima

2:15 Discussion

2:40 Basic Earthquake for Dam Design — J.S. Dodd

3:05 Study on Regional Distribution of Maximum Earthquake Motion in Japan —

Masakazu Ozaki, Makoto Watabe, Yoshikazu Kitagawa, and Sadaiku Hattori

3:30 Discussion

3:50 Recess

4:05 Treatments on Seismic Force in Designing Earth Structures — Kenkichi Sawada

4:30 Studies on the Aseismic Properties of Underground Pipes — Keiichi Ohtani, Nobuyuki Ogawa, and Chikahiro Minowa

4:55 Observation of Dynamic Behavior of Kinuura Submerged Tunnel During Earth- quakes — Shigeo Nakayama, Osamu Kiyomiya, and Hajime Tsuchida

xi
5:20 5:45

Discussion Adjourn

THURSDAY-May 26 9:00 a.m. A Proposal for Earthquake Resistant Design Methods — Kiyoshi Nakano,

and Misamitsu Qhashi 9:25 On the Object Postulate for Earchquake-Resistant Code — Kiyoshi Nakano,

Yuji Ishiyama, and Yoshitsugu Aoki

9:50 Discussion

10:10 10:25 The Earthquake Response of Hysteretic Structures — W.D. Iwan 10:50 Earthquake Resistant Design of High-Rise Buildings in Japan — Keiichi Ohtani

11:15 Racking Strength of Wood-Frame Walls — Roger L. Tuomi 11:40 Discussion

0:05 p.m. Recess (Lunch) 1:00 Expanded Role of the National Science Foundation Earthquake Engineering Program — J.B. Scalzi 1:25 Examination for an Evaluation Method of Damage of Existing Wooden Houses

Caused by Earthquakes — Kaoru Ichihara, Eiichi Kuribayashi, Tadayuki

Tazaki, and Takayuki Hadate

1:50 Modified Mercalli Intensity Relationships to Wood Frame Dwelling Earthquake

Insurance — K.V. Steinbrugge, and S.T. Altermissen

2:15 Discussion

2:40 Recess

3:00 Discussion of Task Committee

5:00 Adjourn

FRIDAY-May 27 9:00 a.m. Warrents for Retrofitting Highway Bridges — J.D. Cooper

9:25 Criterion on the Evaluation of Seismic Capacity of Existing Reinforced Concrete Buildings — Kiyoshi Nakano, Masaya Hirosawa, and Shin Okamoto

9:50 Transferring Wind Technology to Developing Countries - N.J. Raufaste 10:15 Discussion

10:40 Recess

* Special Presentation 10:55 * Investigation Report of the Earthquake in Rumania, March 4, 1977 - Seiji

Nakano, Eiichi Kuribayashi, and Masaya Hirosawa

xii
11:55 Recess (Lunch) 1:00 p.m. Report of Task Committee

2:20 Resolution

2:50 3:00

3:30 Closing Session

xiii
U.S. Panel on Wind and Seismic Effects

May

Dr. Edward 0. Pfrang Chairman

Chief, Structures, Materials and Safety Division

Center for Building Technology, NEL

National Bureau of Standards Room B368, Bldg. 226 Washington, D.C. 20234

Dr. S.T. Algermissen Office of Earthquake Studies

Denver Federal Center Branch of Earthquake Tactonics

USGS

Stop 978, Box 25046

Denver, Colorado 80225 303-234-4014

Mr. Billy Bohannan Assistant Director

Wood Engineering Research Forest Products Laboratory USDA

P.O. Box 5130 Madison, Wisconsin 53705 608-257-2211

Dr. Roger t D. Borcherdt Office of Earthquake Studies

Branch of Earthquake Hazards USGS

345 Middlefied Road Menlo Park, California 94025 415-323-8111 (FTS 467-2755)

Dr. Charles G. Culver Disaster Research Coordinator

National Bureau of Standards Room B212, Bldg. 225 Washington, D.C. 20234 301-921-3126

Mr. Jerry Dodd Bureau of Reclamation

Mail Code 230

P.O. Box 25007 Denver Federal Center

Denver, Colorado 80225

Dr. Michael P. Gaus

Head, Engineering Mechanics Section Engineering Division

National Science Foundation

1800 G. Street, N.W. Washington, D.C. 20550

ihip List

1977

Mr. John J. Healy Department of the Army DAEN-RDM

Washington, D.C. 20314 202-693-7287

Dr. William B. Joyner

Office of Earthquake Studies Branch of Earthquake Hazards USGS

345 Middlefield Road Menlo Park, California 94025

413-323-8111 (FTS 467-2754

Mr. John W. Kaufman Aerospace Environment Division ES42-Space Science Laboratory

National Aeronautics and Space Administration

Marshall Space Flight Center Alabama

35812, 205-453-3104

Dr. Noel E. LaSeur Director National Hurricane and Experimental Meteorology Laboratory

National Oceanic and Atmospheric Administration

P.O. Box 248265

Coral Gables, Florida 33134 305-350-4150

Dr. Richard D. Mc Connell Office of Construction Veterans Administration

811 Vermont Ave., N.W. Washington, D.C. 20234 202-389-3103

Dr. Richard D. Marshall

Research Structural Engineer National Bureau of Standards

Room B168, Bldg. 226 Washington, D.C. 20234 301-921-3475

Dr. R.B. Matthiesen

Chief, Branch of Seismic Engineering Office of Earthquake Studies USGS

345 Middlefield Road Menlo Park, California 94025 415-323-8111 (FTS 467-2881)

xiv
Mr. Howard L. Metcalf

Staff Engineer Construction Standards and Design

Directorate

Office of the Assistant Secretary

of Defense

Room 3E763

The Pentagon

Washington, D.C. 20301 202-695-2713

Mr. Keith 0. O'Donnell

Assistant Chief, Structrual Branch

Engineering Division, Civil Works Directorate

Office of The Chief of Engineers

I ATTN: DAEN-CWE-D

Washington, D.C. 20314

Dr. Thomas D. Potter

Director

National Climatic Center Environmental Data Service

National Oceanic and Atmospheric

Administration

Federal Building

Asheville, North Carolina 28801

I 704-258-2850 x 236

Dr. Bonn B. Scalzi

Program Manager, Earthquake Engineers

Division of Advanced Environmental Research and Technology

National Science Foundation

1800 G Street, N.W. Washington, D.C. 20550

Mr. Charles Scheffey

Director

Office of Research

HRS-1 Federal Highway Administration

Department of Transportation

Washington, D.C. 20590 202-426-2943

Mr. Lawrence C. Shao

Chief, Structural Engineering Branch

Nuclear Regulatory Commission

Washington, D.C. 20555 202-492-8035

Dr. Warren A. Shaw

Head, Civil Engineering Department

Civil Engineering Laboratory

Naval Construction Battalion Center

Port Hueneme, California 93043

Mr. William J. Werner

Energy Building Technology and Standards Department of Housing and Urban Development

Room 8158

451 7th Street, S.W. Washington, D.C. 20410 202-755-0642 ALTERNATIVES

Dr. A. Gerald Brady

Physical Scientist Office of Earthquake Studes USGS

345 Menlo Park, California 94025 415-323-8111 (FTS-467-2881)

Dr. James D. Cooper Structures & Applied Mechanics Division

Federal Highway Administration

Office of Research HRS-11 Washington, D.C. 20590

Mr. G. Robert Fuller Architectural and Engineering Division Department of Housing and Urban Development

Room 6176, 451 7th Street, S.W. Washington, D.C. 20411

Dr. H.S. Lew Secretary

Structures, Materials and Safety Division

Center for Building Technology, NEL

Washington, D.C. 20234 301-921-3158

Dr. Charles T. Thiel Deputy Director Divison of Advanced Environmental Research

and Technology

National Science Foundation

1800 G. Street, N.W. Washington, D.C. 20550 202-632-5734

Mr. Drew A. Tiedemann

Bureau of Reclamation

Engineering and Research Center

Denver Federal Center

P.O. Box 25007

Denver, Colorado 80225 303-234-3029

xv
Japanese Panel on Wind and Seismic Effects Membership List May 1977

Dr. Kaoru Ichihara, Chairman

Director Public Works Research Institute Ministry of Construction

Mr. Shigemi Fujiwhara, Member

Head, Typhoon Research Division

Meterological Research Institute

Dr. Satoshi Hayashi, Member Vice Director Port and Harbour Research Institute Ministry of Construction

Mr. Toshio Iwasaki, Member

Chief Researcher, Building Research Institute Ministry of Construction

Mr. Toshio Iwasaki, Member

Chief, Ground Vibration Section Earthquake Disaster Prevention Division

Chiba Branch Public Works Research Institute Ministry of Construction

Dr. Tetsuo Kunihiro, Member

Head, Structure and Bridge Division Chiba Branch Public Works Research Institute Ministry of Construction

Mr. Eiichi Kuribayashi, Member

Chief, Earthquake Engineering Section Earthquake Disaster Prevention Division

Chiba Branch Public Works Research Institute Ministry of Construction

Mr. Tatsuro Murota, Member

Chief, Structure Section Structure Division

Building Research Institute Ministry of Construction

Dr. Keikichi Naito, Member

Head, Meterological Satellite Division

Meterological Research Institute Meterological Agency

Dr. Kiyoshi Nakano, Member Assistant Director

Building Research Institute Ministry of Construction

Mr. Nobuyuki Narita, Member

Chief, Structures Section Structure and Bridge Division

Chiba Branch Public Works Research Institute Ministry of Construction

Dr. Masamitsu Ohashi, Member

Head, Earthquake Disaster Prevention

Division, Chiba Branch

Public Works Research Institute Ministry of Construction

Mr. Keiichi Ohtani, Member

Chief, Earthquake Engineering Laboratory

National Research Center for Disaster Prevention

Science and Technology Agency

Dr. Michio Chtsuka, Member Acting Director, International Institute of Seismology and Earthquake Engineering (I.I.S.E.E.) Building Research Institute Ministry of Construction

Dr. Tadayoshi Okubo, Secretary-General

Head, Planning and Research Administration

Division Public Works Research Institute Ministry of Construction

Dr. Hiroshi Sato, Member

Chief, Research Division

Crustal Dynamics Department

Geographical Survey Institute Ministry of Construction

Mr. Kenkichi Sawada, Member

Chief, Soil Dynamics Section Construction Method and Equipment Division Chiba Branch Public Works Research Institute Ministry of Construction

Mr. Akira Suwa, Member

Head, Seismological Laboratory

Meteorological Research Institute Meteorological Agency

Mr. Hiroshi Takahashi, Member

Head, Second Research Division

National Research Center for Disaster Prevention

Science and Technology Agency

xvi
Dr. Tsutomu Terashima, Member

Chief, Seismology Section

International Institute of Seismology and Earthquake Engineering (I.I.S.E.E.) Building Research Institute Ministry of Construction

Mr. Hajime Tsuchida, Member

Chief, Earthquake Resistant Structures Laboratory

Structure Division Port and Harbour Research Institute Ministry of Transport

Dr. Makoto Watabe, Member

Head, Structures Division

Building Research Institute Ministry of Construction

Mr. Kaname Yahagi, Member

Chief, Foundation Engineering Section Structure and Bridge Division, Chiba Branch

Public Works Research Institute Ministry of Construction

Dr. Masami Hukuoka, Honorary Member Professor of Tokyo Univ.

Dr. Shiro Ibukiyama, Honorary Member

An Executive Director

of Japan Road Company, Ltd.

Mr. Mitsuru Nagao, Honorary Member

Director of Japan International Cooperation Agency

Mr. Kenji Kawakami, Honorary Member

An Adviser of Kubota, Tekko, Ltd.
RESOLUTIONS OF THE JOINT MEETING

U.S. -JAPAN PANEL ON WIND AND SEISMIC EFFECTS

U.J.N.R. May 24-27, 1977

The following resolutions for future activities of this Joint Panel are hereby resolved:

1. The Ninth Joint Meeting was an extremely valuable opportunity to exchange technical infor- mation which was beneficial to both countries. In view of the importance of cooperative programs on the subject of wind and seismic effects, the continuation of Joint Panel Meetings is considered essential.

2. The exchange of technical information, especially revised codes and specifications rele- vant to wind and seismic effects shall be encouraged.

3. The cooperative research programs including exchange of personnel and equipment should be promoted

.

4. Considerable advancements in various Task Committees were observed. These activities

should be encourage and continued. Correspondence between Task Committee Chairmen should be encouraged, and additional meetings should be held as required.

5. Program agenda for future Joint Meetings should be developed to encourage a balanced

number of presentations dealing with wind and seismic effects on structures.

6. The Tenth Joint Panel Meeting will be held in May 1978 in Washington, D.C. The specific date and itinerary of the Meeting will be determined by the U.S. Panel with concurrence

by the Japan Panel.

xviii
DISTRIBUTION MODELS OF PRESSURE AND WIND OVER

STATIONARY TYPHOON FIELDS Shigemi Fujiwhara and Kiyoshi Kurashige

Meteorological Research Institute ABSTRACT

For pressure and wind distributions on the sea surface over typhoon and hurricane

jirea, many trials have been proposed in order to adapt distribution models for observational data. These models have been utilized widely in many scientific and technical

applications. For example, theoretical analysis, storm surge, disaster evaluation, protective measurement against typhoon damage, and so on. The above models proposed are simple models. Unfortunately,- however , the better

adaptation for observed data requires more complicated models. However, the advent of

jthe electronic computer has brought about the methods which can shorten the computational

time tremendously. Therefore, the models no longer have to be simple.

In this paper, several new models are introduced and their characteristics are discussed. Then, basic differences between the formulas by various models are pointed out

clearly. In order to increase the accuracy of model adaptation, a technique of revising

the formulas is discussed. Taking into account the computation time of the electronic

computer, a new model formula is presented and examined by comparing it with other formulas.

KEYWORDS: Distribution Models; Pressures; Sea Surface; Stationary Typhoon
INTRODUCTION Pressure and wind distributions on the sea surface over typhoon or hurricane area

seem to be complex in performing detailed analysis. However, they can be considered

simply as circularly symmetric. Therefore, many trials have been proposed in order to adapt distribution models for observational data. These models have been utilized widely

in many scientific and technical applications. For example, theoretical analysis, storm

surge, disaster evaluation, protective measurement against typhoon damage, and so on. These models were introduced by many researchers in Japan, the United States and Philippines

The above models were proposed for the purpose of simplification. Unfortunately, the better adaptation for observed data requires more complicated models.

However, with the recent development of the electronic computer, the shorter computa- tion time has come to be realized. Therefore, the necessity of simplifying the models is no longer a problem. This paper attempts to reevaluate the distribution models from the above standpoint.

We have never had this sort of discussion, because these models have been considered as conventional formulas and also there have been many difficulties in computing the distances between the typhoon center and every data position at each weather map time. The advent of the electronic computer has brought about new concepts into these distribution models. Also, the current practices require greater accuracy of adaptation

for observed data. CHARACTERISTICS OF PRESSURE DISTRIBUTION FORMULA

Among typhoon models proposed to date, several representatives are as follows: Schloemer (1954) P = P

c + AP exp (-YQ

/Y) (D

Takahashi (1939) P = P^ - AP/]1 + (Y/YQ

) 1 (2) Bjerknes (1921) P ~ P - AP/[1 + (y/Y ) 2

] (3)

oo O

2 1/2 Fujita (1952) P = P - AP/[1 + (Y/YJ J (4)

P at the typhoon center, P^ means the average pressure value along the outer edge of the typhoon area, and AP = P^ - T?^. and P^ are calculated statistically from weather

analysis maps. Parameter YQ

is defined individually in the above formulas: in (1), Y

Q

i equal to the radius Y„ where the maximum wind velocity is observed, in (2) and (3) Y M O means Y where P = (P^ + P

c >/2, and in (4) Y

Q

is equal to ty/STl Wind velocities within typhoon area are expressed in the following equation (the gradient wind law)

:

1-2
where f is Coriolis factor 2 U) sin U) the rotating angular velocity of the earth, latitudinal degree, p the density of the atmosphere, v the gradient wind velocity. We can estimate v from Eq. (5) if we know the pressure distribution. Therefore, Eqs. (1) through

(4) involve distribution formulas of wind implicitly. Their characteristics are shown as follows:

Eq. (1) is very convenient with respect to theoretical arrangement as far as the adaptation for data is concerned. It has a good response over the outer regions of the typhoon area, but it is too flat to fit with observed data over the inner regions. (See Fig. 1)Eq. (2) has also a good adaptation over the outer regions, but at the center, the pressure gradient becomes discrete. Therefore, the calculated wind velocity at the center

comes to be unreasonable.

Eq. (3) is introduced basically under the rotating fluid assumption, so that it has a good adaptation over the inner regions and a bad adaptation over the outer regions.

Eq. (4) is similar to Eq. (2) over the outer regions and also similar to Eq. (3) over the inner regions, because it was designed so as to include excellent features of

Eqs. (2) and (3). However, it is hard to deal with Eq. (4) practically.

In addition to the above individual deficiencies, they have some common weak points. For example, a general typhoon has several stages; the developing stage, the mature stage, the decay stage, and the warm cyclone stage. When a typhoon changes its stage from one to another, the time variance of its pressure distributions has usually come to be remarkable.

But, unfortunately, the stage variation was not taken into account in the above formulas.

If we introduce the following equation as a general type of Eqs. (2) and (3)

,

P = !>„ - AP/[1 + (Y/YQ

) a

] (6)

where a is determined so as to fit Eq. (6) into the observed data. It might be impossible

for us to express a typhoon involving many stages by Eq. (6)

.

Now in order to eliminate the above weak points, it is necessary to make the problem

more distinct. Namely, let us treat Eqs. (1) through (4) in the following way.

Eq. (1) is considered as an integral form of the following differential equation,

dP

dx -Y (P - P ) ; x = 1/Y (7) In the same manner, for Eq. (2) , fr af (p

oo - p) < p - V ; x = ln (Y/V (8) Also, for Eq. (3) , dP _ _2

dx AP

Also, for Eq. (4)

,

dP _ _1 dx AP

In (Y/Yj (9)

4— = T^r (p„ - p) (p - p_) • f (x) (10)

f (x) = 1 + (1 + p 2x )" 1/2

; x = ln( YA )

1-3
Eqs. (7) through (10) correspond to Eqs. (1) through (4) respectively.

In Fig. 2, characteristics of Eqs. (7) through (10) are shown schematically. Eq. (10) (Fujita type) approaches to Eq. (8) (Takahashi type) over the outer typhoon regions and

it also approaches to Eq. (9) (Bjerknes type) over the inner typhoon regions. On the contrary, Eq. (7) (Schloemer type) does not show such a good approach over the inner

regions. These characteristics are the same as those shown in Fig. 1. However, Fig. 2 gives us information about an advanced formula which should be a hyperbola having two asymptotes, Eq. (8) and Eq. (9) . Eq. (10) (Fujita type) is quite

similar to such an advanced model, but it is not a hyperbola. Rather, it is a transcendental

curve having some restrictions. It is desirable that the advanced model should be a more general type of hyperbola with less restrictions. In this Figure, the cross point T of two asymptotes shows the transitional point between the inner and outer regions of the typhoon.

In these formulas mentioned above, there are two main restrictions: positions of T and gradient of asymptotes. However, if we assume a new model in which those restrictions are taken off and some freedoms are given so as to determine those values statistically by using observational data, the above problem may be solved. Namely, an introduction of new

parameters (determined by data) causes an increase of freedom number and finally a better adaptation for data may be expected.

A NEW DISTRIBUTION FORMULA

A new formula is basically similar to Eq. (10). Instead of f(x), ^ is introduced. That is £ = af <£» (p

co - p >

< p - p

c

>; x ln (y/y0

) (id

where y means a hyperbola, which we want to obtain. Therefore, dy/dx shows its gradient.

By integrating Eq. (11)

,

P = P - AP/[1 + g(x)]

g(x) = Y ^/(Yo'Yp^ * exP {-K^y1

' ln Y/Y

p

)-C'] V2

} (12) where new parameters a, Yp

and C are referred to gradient of asymptote over the inner regions of typhoon, position of the transitional point and curvature of the hyperbola, respectively. Adding to the previous parameter Y

Q

» the new constants can be determined

statistically by observational data (the least square method) . This new technique is proposed by Kurashige (1977) . The method of determining these constants is shown in Appendix. RELATIONSHIP BETWEEN THE NEW MODEL AND THE OTHERS

As revision of the above formulas (1) through (4) , Fujita (1952) and Haraguchi (1976) have also presented their models (besides Kurashige). Therefore, we have to discuss the relationship or differences between these models and Kurashige' s one. Fujita 's model,

1-4
Eq. (4) , as mentioned above, contained two individual distribution forms for the inner and

outer regions of the typhoon. Kurashige's Eq. (12) also adopted the same concept. However,

the position of T in Eq. (4) is apriori defined. Syono (1958) pointed out that the amount

of negative vorticity over the outer regions in Eq. (4) was less than actual. The relationship between the vorticity C and wind velocity v is explained as follows:

So that Syono 's speculation is related to the second order derivative of y in the pressure distribution formula. (See Eq. (5)) On the other hand, Haraguchi's model is one where two individual distribution formulas

are connected empirically. Therefore, the adaptation for data shows a better result as well

as Kurashige's. However, if we want to obtain characteristic values in his model, it is necessary to get a smoothed distribution curve defined previously by some other methods, and moreover the position of maximum wind velocity must be well-defined. The above conditions

are unsuitable for use of the electronic computer. Recently, Mitsuta and others (1974, 1975) examined statistically adaptations between

models and observations. They reported that, on the average, each model had a rather good adaptation and there was no remarkable difference between the above models, but the deviation

was rather large in an individual case. However, Haraguchi's and Kurashige's models have

been proposed more recently, so that they were not included in Mitsuta 's test. Even in Kurashige's model, some uncertain problems still remain. One of them is whether the other curve besides hyperbola is convenient or not. For example, tanh x and irrational function may be taken into consideration, but unfortunately, they are so complicated that their integral forms may face difficulties. At present, the hyperbola

is the most convenient one. Another of them is that the gradient of asymptote over the outer regions is apriori determined to be Takahashi type. If a sufficient data coverage

is available, the above gradient should be obtained by the least square method. As a conclusion, Kurashige's formula is apparently complicated, but its main points

are the same as those in the previous models, and, moreover, it has larger freedoms than previous ones in order to get a better adaptation for data. Therefore, as far as the use of electronic computers is concerned, it does not take so much machine time as usual

Also, a moving typhoon field is not circularly symmetric. However, as it is possible

to divide the typhoon field into two parts (the general current and a stationary typhoon

field) , we have no problem about that. APPENDIX

How to determine YQ

is shown as follows. At first, data position y and observed

value P are given by data. If we take an arbitrary constant y^, we can compute as

x = In (y/fj) , y = In | (P - P

C >/(P00 - P) I

1-5
Next, we consider a hyperbola with two asymptotes (y^ = x + y , = ax + 8) as follows:

2 * 2 ax -(a+l)xy + y + 2gx + 2fy + C=0 (14) where 2g = a-y + 6, 2f = - (y+8) , c = yB + e and a > 1. Using the above x and y, we can determine a, g, f and C statistically by the least square method. The cross point T is defined as

xT

= [2 (a + 1) f + 4g]/(a - l)

2

yT

= [2 (a + 1) g + 4af]/(a - l)

2

Now, the asymptote of outer regions y^ is moved according to the parallel transformation so as to pass through the origin. Then, Eq. (14) becomes

ax' - (a + Dx'y' + y'

2 - 2f'x' + 2f'y' + C' = 0 where x' = x - x , y' =y,

o

X

o

= XT

" yT

= (2f + 2 9 )/(1 -

a) 2f = [4 a f + 2g(a + l)]/(a - 1)

2 C'=ax -2xg+C o o and the cross point of two asymptotes becomes

If we convert them into (y, P) system,

, , ,2f + 2g % y

o

= Yl exp(x

o

) = Yl exp ( ± _ fl

) and the transitional point Y

p between the inner and the outer regions is replaced as, Y

p = YQ exp (2f)

REFERENCES

Bjerknes, V. (1921) : On the dynamics of the circular vortex with applications to the atmospheric vortex and wave motions. Geophysiske Publikationer , Vol. 2, pp. 1-81. Fujita, T. (1952): Pressure distribution in typhoon. Rep. Met. Lab., Kyushu Inst. Tech.

2, No. 1-2. Haraguchi, K. (1976) : On a pressure distribution model applicable for various type cyclones. Tenki Vol. 23, pp. 615-623 (in Japanese).

Kurashige, K. (1977) : On a new pressure distribution model over stationary typhoons. Pap. Met. Geophys. (to be published)

Mitsuta, Y. and others (1974): Model of severe typhoon (1). Kyoto Univ. Dev. Lab. Rep. Vol.

17, pp. 227-234 (in Japanese).

(1975) : Studies on severe typhoon model (2) . Kyoto Univ. Def . Lab. Rep. Vol. 18-B,

pp. 227-243 (in Japanese)

Schloemer, R. W. (1954) : Analysis and synthesis of hurricane wind patterns over Lake Okeechobee, Florida, Hydrometeorological Report, No. 31, pp. 1-49, U.S. Weather Bureau.

1-6
Syono, S. (1958): The structure of typhoon near the ground surface. The general theory of

meteorology. Chijin-Shokan, pp. 252-255 (in Japanese)

.

Takahashi, K. (1939): Distribution of pressure and wind in a typhoon. J. Met. Soc

. Japan,

17, pp. 417-421 (in Japanese).

1-7
Y sfP-PcJ/lPje-Pc)

ure 1. Comparison of pressure distribution formulas The origin shows the center of typhoon. The additional figure in SE corner is a magnification near the center. The cross point between Bjerknes' and

Takahashi's is located at x = 1.0, y = 0. 5. Over inner regions of typhoon, Schloemer'6 formula shows

flat and Takahashi's becomes discontinuous at the center.

1-8
Figure 2. Comparison of formulas characteristics

Fujita type shows a transcendental curve with two asymptotes

of Takahashi type and Bjerknes one. T is the cross point between the above two asymptotes. Schloemer type shows to approach to Takahashi's over outer regions, but to be far from

Bjerknes' over inner regions.

1-9
EXTREME WINDS IN THE UNITED STATES Thomas D. Potter and Michael Changery Environmental Data Service National Oceanic and Atmospheric Administration ABSTRACT

Each year extreme winds in the U.S. cause extensive property damage and occasionally

the loss of lives. This paper will first review the patterns of extreme winds in the U.S. and the associated wind damage. The types of maximum wind speed data currently available

are then discussed. Finally, problems associated with using these maximum wind speed data

in U.S. design standards are considered.

KEYWORDS: Design requirements; design standards; extreme winds; hurricanes; property

damage

.

1-10
INTRODUCTION

A large portion of the United States is subject to damage caused by wind-induced

stress on structures. Many of the earliest records from explorers nearly 500 years ago refer to the occurrence of hurricanes along the Atlantic and Gulf coasts. The great heartland of the United States is well known for the large frequency of tornadoes (some- times over 1000 per year) which often leave total destruction along their path. Other

areas of the United States also suffer wind damage from various types of storms. Until recently, however, wind has not been considered an important factor in building

design. The climatologist has had little input into the problems created by winds on structural design. This is due partially to a lack of information on the characteristics

of the wind and on the interaction between the wind and the structure. It is due also to

the lack of a long-period homogeneous set of standard wind measurements from which design

values can be obtained. This paper will examine the patterns of extreme winds and wind

damage in the United States, the types and volume of maximum wind speed data currently

available, and the problems in using these wind data in the current United States design

standards. WIND AND DESIGN REQUIREMENTS

Buildings and structures are now commonly being designed to heights not even con- sidered 10 or 20 years ago. One of the most important of the loads acting upon these structures is that due to the wind. The level of safety built into these structures is directly related to the accuracy with which the wind and its effects can be determined.

In the past, the highest wind recorded in an area or location was used as the design

value. Among the various problems apparent with this approach was the fact that all meteorological records are eventually broken. Thus a station with a longer period of record had a higher probability of observing an extreme wind speed - a fact which would

obscure the true climatic similarity among a number of stations in an area. A second problem was the possible loss of data due to instrument failure at high wind speeds. Finally, an instrument with a better response time would record speeds higher than those recorded by a more "sluggish" system. These problems led to the adoption of a statistical

estimate of design speeds. For various engineering and meteorological reasons, wind loads are best considered in terms of a steady applied force together with a factor describing gust effects. The spectrum of horizontal velocity measured by Van der Hoven (1) showed two most prominent

peaks. One peak occurs in the gust region and a second peak occurs at a period reflecting

large-scale atmospheric fluctuations of no concern to the engineer. Between the two peaks

is a gap ranging from 5 minutes to 5 hours which is useful for obtaining stable speed measurements. Structurally, it is not desirable to rely on only the peak gust for design purposes because this ignores the influence of a sequence of gusts which may be resonant with the structure.

1-11
In addition to being highly dependent on instrument response, gusts alone provide an uncertain estimate of the wind environment since a number of samples with similar mean

speeds may all have varying peak gust values. In some instances, however, it is the gust superimposed on the load caused by a high mean speed which causes extensive damage to the surface of many structures. For example, most of the damage from Hurricane Celia at Corpus Christi, TX, in 1970 was caused by the extremely high gusts rather than the prevailing strong winds. So a knowledge of both the mean wind and gusts (determined from measure- ments or theory) is required to evaluate wind loads on a structure. WIND REGIMES AND WIND DAMAGE IN THE UNITED STATES

In the United States, wind damage results from extreme winds caused by four meteorological systems: extratropical cyclones, hurricanes and other tropical cyclones, tornadoes, and severe thunderstorms. The extratropical cyclones produce their highest speeds in the winter months deriving their energy from the large thermal contrasts available in this season. Generally, the West Coast, mountain and inter-mountain areas of the Rockies, some areas of the Northern Plains and the Great Lakes receive their highest winds from these

systems. Maximum wind speeds are usually less than 75 knots but may reach 100 knots in very severe extratropical cyclones. The area along and within 200 miles of the Atlantic

and Gulf coasts receives its highest winds from hurricanes in which wind speeds sometimes reach 200 knots. Tornadoes produce the strongest winds observed in the United States; precise values of maximum speeds are not well established because wind instruments are usually destroyed in tornadoes but there is evidence to show that values above 300 knots

are sometimes reached. The Great Plains experiences the highest frequency of tornadoes but every State in the United States (except Hawaii) has experienced at least one tornado. Occasionally, widespread outbreaks of tornadoes produce extensive structural damage and loss of life, such as in the tornadic storms of April 3-4 in 1974 (2) . Portions of the United States not already mentioned usually receive their strongest winds from severe thunderstorms. A few notable exceptions to this generalization exist such as the Chinook winds in the lee of the Rockies and the Santa Ana winds of Southern California. These are usually localized in extent but may produce very strong winds which cause considerable

damage.Wind damage statistics have been collected for many years. Current statistics

indicate that damage from hurricanes and other tropical storms, severe thunderstorms, and extratropical storms average approximately $750 million per year. This figure varies, of

course, from year to year and may be as high as $2 billion in years with exceptionally

severe hurricanes such as Camille in 1969. Tornado damage amounts to two-thirds the value obtained by larger scale storms - on the order of $400 to $500 million per year. Again, large fluctuations in annual damages may occur in years with severe tornado outbreaks. Average damage from large-scale storms and tornadoes has been increasing year to year. This is attributed to the general population increase in the United States and the corresponding increase in area covered by dwellings and other structures, resulting in more damage even though the annual number of storms remains relatively the same on a long1-12
term basis. Although damage statistics may be tempered by building design considerations,

the annual loss likely will continue to increase in future years. Much of this damage

loss occurs along the East Coast with its high population density. Although the West

Coast is heavily populated, the probability of extreme winds is rather low so the wind

damage losses are relatively small. Finally, even though the population density is low in

the mid-portions of the country, substantial damage occurs from the high incidence of tornadoes

.

WIND MEASUREMENTS AND DATA AVAILABILITY

The United States currently has available the following four basic wind measurements

in the archives:

(1) Fastest Mile : This type of wind observation has been extracted since 1887 at approximately 200 locations. For these locations an additional 20 years of data could be obtained from the original records. For about 300 additional stations a limited period

(10 to 25 years) could also be extracted. Daily data for nearly 150 sites are on tape for the period since 1965. Three problems are apparent in using this data set. First - at high wind speeds, the estimate of the fastest mile becomes very inexact due to the extremely

small increment to be measured on the chart. Second - most locations experienced a change

in instrument exposure 30 to 40 years ago when the weather office moved from a city to airport site. Suitable methods to obtain a homogeneous data set have not been developed. Current design estimates then are obtained only from the airport data. Finally, any attempt to reference the city office data to a standard height faces the problem of the change in urban profile over a period of years.

(2) Five-minute maximum : Daily values of the five-minute maximum have been taken

since 1872 at the same locations mentioned previously. Beginning in 1956, it was no longer extracted from the original records. A period of 10-25 years of data can also be extracted for an additional 300 locations. None of these data have been placed on magnetic tape. The problems of mixing city and airport data mentioned for the fastest mile

apply also to this measurement.

(3) Peak gust : The daily peak gust has been extracted from strip charts for approximately 450-500 stations for the past 20 to 30 years. The majority of these data are on

magnetic tape. Peak gust data have not been the basis for design speeds due to the problems mentioned previously.

(4) Hourly average : This measurement, taken at approximately 3,000 locations, is presently available on tape for 800 of these locations. The hourly average is not a true value for an hourly period but a subjective assessment by the observer of the winds for a few minutes on the hour and considered representative of the entire hour. This measurement has been digitized hourly since the late 1940 's and 3-hourly since 1965. A few sets of data from special tall observation towers exist for various locations

throughout the United States. Some of these data sets contain high frequency observations

which permit calculations of spectral properties of the turbulent wind structure. Panofsky

1-13
(3) summarizes these special data sets which are not generally available for most locations

in the United States.

In the United States the fastest mile is used for design purposes because (a) it generally falls in the gap in the energy spectrum and hence is representative of load inducing winds and (b) the parameter has been measured for a long number of years. Many investigators believe a better estimate can be obtained from a 15 or 20 minute average. Unfortunately, the cost of obtaining such averages from old records is prohibitive. At

present, then, only data already extracted from the original records can be used to obtain

a design speed. THE UNITED STATES DESIGN STANDARDS

The currently accepted United States design standards are the result of the application by Thorn (4) of extreme value theory to a set of annual fastest mile values. These data were all taken at airport locations for a 15-20 year period ending in the mid-1960' s. Since then an additional 10 years of data have been collected. Utilizing the earlier work

of Davenport (5) , Thorn converted these data to a standard 30 foot height by using an exponent of 1/7 in the familiar power law. This value is considered to be representative

of the surface roughness for an open, uncluttered environment, and ranges to 1/3 for a heavily urbanized area. This roughness is the drag of the wind on the earth's surface, vegetation, and manmade structures. One of the primary difficulties in developing a standardized set of city data is the unknown change in surface roughness characterizing the gradual urbanization of

a site over a period of time. There are a number of problems with the currently accepted design standard maps used

in the United States.:

(1) The period of data used is generally less than 20 years. For many areas, especially the coastline, the representativeness of the design values has been questioned. Greater confidence could be achieved by including the 10 additional years of data avail- able or developing some method of integrating the 40-60 years of city data with the air- port data used.

(2) Many of the airport locations have gradually become urbanized or industrialized

and the l/7th power law may no longer be accurate. An approach based on an exponent varying with the roughness characterizing the fetch in various directions may better describe the environment at a location.

(3) It has been recognized that under high wind speed episodes in flat terrain, the l/7th power law is suitable for the neutral atmosphere characterizing large-scale mature storm systems. However, in the strongly unstable and mixing environment of a thunderstorm,

the exponent can become very small - perhaps approaching zero. For those areas of the United States receiving maximum winds from thunderstorms, the measured speed values should probably be used unchanged. *

1-14
CONCLUSIONS

To summarize, wind damage in the United States is greater than one billion dollars

per year. With increasing population, the damage should continue to increase in the future. Although some measurement other than the fastest mile might be used to derive the design wind, the costs to extract these data are currently prohibitive. Better design

values could be obtained by including additional years of data at airport locations, developing methods to include the long period of city office data, or ensuring that the power law exponent used reflects the character of the surrounding terrain or stability of the air mass. Research is underway to overcome these limitations in current wind data to use in structural design. However, for the next few years the fastest mile wind data will

continue to be used for most design purposes. REFERENCES

(1) Van der Hoven, I. (1957) : Power Spectrum of Horizontal Wind Speed in the Frequency

Range from 0.00007 to 900 Cycles Per Hour. J. Meteorology, Vol. 14, p. 160.

(2) Fujita, T. T. (1975): Super Outbreak Tornadoes of April 3-4, 1974. University of Chicago.

(3) Panofsky, H. A. (1974): The Atmospheric Boundary Layer Below 150 Meters. Annual Review of Fluid Mechanics, Vol. 6, pp. 147-177.

(4) Thorn, H. C. S. (1968): New Distributions of Extreme Winds in the U.S. Jour. Struct.

Div. , Proc, ASCE Paper 6038, pp. 1783-1801.

(5) Davenport, A. G. (1960): Rationale for Determining Design Wind Velocities, Jour. Struct. Div., ASCE Paper 2433, pp. 39-68.

1-15

AERODYNAMIC STABILITY OF A LONG-SPAN SUSPENSION BRIDGE AT CONSTRUCTION STAGE

T. Kunihiro

N. Narita

K. Yokoyama

Public Works Research Institute, Japan ABSTRACT

Wind accidents on bridge structures have so far occurred at their construction stage, and this necessitates confirming the safety of a structure under construction as well as after completion. The aerodynamic safety of a suspension bridge at construction stage

is especially important, because the rigidity and the relevant dynamic characteristics of

the structure alter gradually as the construction work proceeds.

The aerodynamic stability of suspension bridges at construction stages for the Seven

Bridge (1) , the Kanmon Bridge (2) , the Honshu-Shikoku Bridge (3,4) and the Narrows Bridge

(5) has already been examined by others. These studies demonstrated the importance of

the problem.

However, the erection method of a bridge depends largely on the conditions that, how

much clearance is necessary for navigation during construction period and what kinds of erection machines are available, etc. Therefore, the results of this study can not be applied directly to other bridges. This paper describes the design wind speed and the aerodynamic stability of suspended

structure of the Hirado Ohashi Bridge.

KEYWORDS: Aerodynamic stability; suspension bridge," construction stages

II-l
INTRODUCTION

1.1 Wind Problems on a Suspension Bridge During Erection Stage Much consideration should be given to the wind induced oscillation of a free standing tower of the main cables not being spanned, and of a suspended structure under constructioi A free standing tower is prone to be put in oscillation by the effect of synchronizing

lateral force originated in the wake vortex. This type of oscillation, called Aeolian

oscillation, often occurs in a high-rise structure with low rigidity and small damping.

In the wind tunnel investigation for the free standing tower of the Hirado Ohashi Bridge, i- was suggested that the oscillation might happen at the wind speed of 11.4 m/s and the maximi vibrational amplitude at the top of the tower was expected to reach 2.35 meters. A mechanical device using a sliding concrete block, which was connected with the tower top by wire rope, was installed to suppress the oscillation. The device was found successful in suppressing violent oscillation.

On the other hand, a large deflection and a catastrophic vibration like flutter may happen when the suspended structure is erected. The deflection can be prevented easily by reinforcing the structure or by installing a special device for cramping the deflection.

However, the catastrophic oscillation must be prevented as it is fatal to the structure, anc it is necessary to confirm the safety against strong wind through wind tunnel tests.

1.2 Erection Plans of Suspended Structure

The Hirado Ohashi Bridge, which is constructed over the Hirado Seto Straits and links Hirado Island to Kyushu Island, is the second largest suspension bridge in Japan. It has a center span length of 460 meters. The suspended structure carrying two-lane traffic and sidewalk is stiffened by a truss girder six meters high and 14.5 meters apart. The clear- ance is 30 meters above the sea level at the center span. The cross-sectional shape of the stiffening girder was selected through wind tunnel tests. The location, general view, and dimensions are shown in Fig.-l, Fig. -2, and Table-1. The following erection method was proposed after studying the site condition, amount of work, construction machinery, economical efficiency, and so on;

1) The construction of stiffening girder starts from both ends near the tower, and it proceeds gradually to the midpoint of the span as shown in Fig. -3.

2) The unit of suspended structure in erection work is 40 meters in length and 200 tons in weight except the starting stage.

3) The concrete blocks in the barge are hoisted by a lifting crane set on the main

cables. The state of erection work is shown in Photo-1.

4) The field connection of blocks are fixed immediately after lifting. But the temporary hinges are installed at the sixth point to minimize the erection stress.

By using this erection method, the construction period of suspended structure was reduced to three months, and the floor deck (I-beam grid deck without concrete slab and

pavement) was erected together with stiffening truss. Three types of deck shape shown in

Fig. -4 were proposed for erection stage. Crane cars can be driven on the deck in Plan-Ill, and this is convenient for construction work. However, Plan-Ill may make the aerodynamic

II-2
stability worse, so Plan-I and Plan-II were also proposed as supplementary methods. The major subject of the research was to examine aerodynamic characteristics of these three deck

plans for erection through wind tunnel test. Photo-2 shows the sectional model for wind

• tunnel testing (6)

The natural frequency varies as the construction work proceeds. Fig. -5 shows how the vertical bending and torsional frequencies vary in accordance with the stage of construction.

The natural frequency in bending mode does not shift so much, but one in torsional mode

increases a ter the middle of steps. DESIGN WIND SPEED FOR ERECTION STAGE Wind load acting on a structure under construction is different from one acting on a

, completed structure. Namely, the expected wind speed for shorter periods may be used to evaluate the design wind speed, because the construction period is usually short. The relation between a return period (R in years) , a probability of the annual extreme wind

speed not exceeding a design value (q) , and a life time of the structure (T in years) is

i given by the following formula;

q = (1 - 1/R) T

It is reasonable that T is defined to be equal to the erection period. The erection

period of suspended structure was estimated as three months, and the total duration from starting tower construction to finishing the construction of the suspended structure as fifteen months. Assuming that T = 2 years and q = 0.6, the return period R becomes 4.4 years

in the case of the Hirado Ohashi Bridge. The monthly maximum wind speed for the last thirty-five years at the Hirado Meteorological Observatory near the bridge site is given in Fig. 6. It suggests that there are few

occasions of strong wind in the period from January to June. Hence this period was

supposed to be the best time for erecting the suspended structure. Fig. -7 shows the relation

between the return period and the expected wind speed. It follows from the figure that the expected wind speed in this period with a return period of 4.4 years (R = 4.4) is very low, and therefore, the following wind speed based on the return period of twenty years was

used in the design; Basic wind speed 20.2 m/s Design wind speed 32 . 2 m/s Critical wind speed for catastrophic oscillation 38.6 m/s WIND TUNNEL TESTS

3.1 Wind Tunnel Test Method for Suspension Bridge Under Construction

Generally speaking, a sectional model, which is a rigid, geometrical copy of a typical section of a full-scale structure, is used for the aerodynamic stability test in

the case of a completed bridge, because the uniformity of longitudinal mass distribution

can be assumed. But a sectional model can not be used directly for a suspension bridge

under construction, because the assumption can not be held valid.

II-3
Wind tunnel test methods for a suspension bridge under construction are classified as follows:

1) Sectional model test method making use of reduced mass parameters. A typical length of a full structure is modeled, and it is rigged up in the tunnel by helical springs with required stiffness, and the weight of the model is simulated in accordai with a reduced mass, which represents the whole structure.

2) Analytical method making use of aerodynamic coefficients. The response of whole structure can be obtained by using non-steady aerodynamic force coefficients which are measured through win tunnel tests on a two-dimensional model.

3) Full-model test method. The response can be obtained by the use of a full-model with mechanically and geo- metrically simulated characteristics.

In the present study, methods 1) and 2) were used.

3.2 Stability Test

3.2.1 Test Procedure

The following similarity conditions were satisfied in order to replace a full-scale structure to a two-dimensional model.

1) Mass parameter

n

f

o M

c*cdt + t M

t*tdt + j Vtdt t *Jdt + & *t

dt

where M : reduced mass M

c

, M^_: mass of the prototype structure

$ , <J> : mode function

c t and the subscripts c and t denote cable and suspended structure, respectively. The reduced moment of inertia can be calculated in a similar manner.

2) Vibration mode

The model is mounted by helical springs and it permits both vertical translatory and pitching motion. The natural frequencies in fundamental asymmetric modes (both bending and

torsional) were observed for modelling, and no coupling between symmetric oscillation and asymmetric one was considered in the test. The test conditions are given in Table-2. The vibration of cable is so dominant at

the earlier construction steps, that the reduced mass becomes very large and the similitude

law can not be maintained in the test. For this reason the stability test for the thirteenth

step only can be carried out.

3.2.2 Test Results

Fig. -9 shows the relation between angle of attack a (vertical angle between wind

direction and the reference axis of structure and it is taken as positive when wind blows

upward) and the critical wind speed of flutter v^. II-4
The effect of deck shape on wind stability is clarified through the test on the thirteenth step. Model-I, having an opening at the middle of the deck, is stable up to

50 m/s at the angle of attack, a = -6° - +6°. On other other hand, Model-Ill, having a solid deck, showed instability at a = 5°, but the critical wind speed is much higher than the design wind speed. The variation of stability characteristics with construction steps cannot be obtained

by this test. The reduced mass for 5th to 12th steps becomes so large that the stability

in these steps seems to be guaranteed. The effect of frequency ratio r (the ratio of torsional frequency to bending frequency) on the stability was examined. The test was carried out at r = 1.65 in the thirteenth

step. The type of oscillation is a stall flutter, and the critical wind speed v

c is pro- portional to reduced wind speed (see Fig. -9. 3 and 9.4).

3.3 Response Analysis Using Aerodynamic Forces

3.3.1 Measurement of aerodynamic forces

The aerodynamic force acting on a model was measured by a forced oscillation method

in order to supplement the stability tests. In the case of driving the model, great care must be taken to balance out the inertia forces of the model so that only purely aerodynamic

forces are measured (7)

.

The aerodynamic force coefficients measured are shown in Fig. -10. CMTI, imaginary part of the coefficient of pitching moment in pure pitching oscillation, at a = 5° in Model-Ill is positive for almost the whole range of wind speed, and, on the other hand,

it is negative in Model-I and Model-Ill except a = 5°. When CMTI is positive, the vibration

system with one degree of freedom in torsional mode becomes unstable.

3.3.2 Estimation of Flutter Wind Speed Flutter wind speed for each step of erection stage are estimated by the use of aerodynamic force coefficients. In the computer program, the motion of both cables and sus- pended structures is considered. The number of modes in torsional and bending oscillation

is five at maximum, and the number of aerodynamic forces along the span is three at maximum. It was found that flutter may not occur at whole angle of attack in Model-I and ModelIll (except a = 5°) . The critical flutter speed at a = 5° in Model-Ill is as follows

(torsional flutter)

5th and 8th step not present

11th step 73.6 m/s

13th step 52.4 m/s

The estimated wind speed is noted in Fig. -9. 2 to compare with ones out of the sectional model test. Both results agree fairly well with each other, and it is found that the estimation method using aerodynamic force coefficients is reliable. When the coupled

flutter is assumed, the estimated critical wind speed decreases slightly as shown in Table- 3.

II-5
CONCLUSION

A study has been carried out to confirm the aerodynamic safety of the Hirado Ohashi Bridge under construction. In conclusion the following can be pointed out:

1) The design wind speed for construction work is estimated by the use of wind

record in the last thirty-five years at the Hirado meteorological Observatory. Assuming

the return period of twenty years, the expected basic wind speed, the design wind speed, and the critical wind speed for flutter are calcualted as 20.2, 32.2, and 38.6 m/s, respectively.

2) The wind tunnel test on sectional models shows that Model-I with opening in the middle of the deck is stable for whole angle of attack and Model-Ill with solid deck is unstable for the angle of attack more than four degrees. The critical wind speed at a = 4° is fairly high, i.e., over 50 m/s, so that Model-Ill is judged to have sufficient aerodynamic stability in practical use.

3) The responses calculated with the aerodynamic force coefficients give good corre- lation with the test results on sectional models, and this proves that the test methods

are reliable. The instability of bridge can occur in torsional flutter, and the effect of coupling of bending and torsional vibration seems to be negligible.

4) The variation of flutter wind speed with the progress of construction work is derived, and it is shown that the flutter wind speed is high at the first stage, and then

it decreases gradually as the stage proceeds. This result is different from those of the Seven Bridge and the Kanmon Bridge.

5) As stated above, it is concluded that Plan-Ill, in which the stiffening truss and solid deck are constructed altogether, has sufficient aerodynamic stability. In the study, only aerodynamic stability tests are performed, and no attempt is done about the large deflection of suspended structure due to wind action in construction stage. ACKNOWLEDGEMENT

The field work started in February, 1976 and ended in May of the same year. During

the field work, the results of the study were fully applied. The structure, though it has a solid deck, showed no harmful vibration during erection. The authors would like to acknowledge the staff of Structure Section of P.W.R.I. for their valuable assistance. The work described in the paper has been carried out as part of

a research program on the Hirado Ohashi Bridge Design and Construction. The authors are much indebted to the staff of the Hirado Ohashi Bridge Construction Office for their earnest

cooperation. REFERENCES

(1) Smith, I. P.: The aerodynamic stability of the Seven Suspension Bridge, NPL Aero Report

1105, May 1964

(2) Shiraki, K. et al.: Aerodynamic Instability in Suspension Bridge under Erection, Mitsubishi Heavy Indusries Tech. Review, vol. 7, No. 7 December 1970.

(3) Ito, M. et al.: Aerodynamic stability of a suspension bridge during erection, Proc. National Meeting of JSCE, October 1974

II-6
(4) Shiraishi, N. , Urata, A., and Sakai, J.: A study of wind stability on a long span suspension bridge during erection, Proc. JSCE, No. 250 June 1976

(5) Davenport, A. G. et al. : A study of wind action on a suspension bridge during erection

and on completion. Res. Rep. BLWT-3-69, Fac. Eng. Sci., Univ. of Western Ontario, London , Canada

(6) Narita, N. and Yokoyama, K. : Wind tunnel test on the Hirado Ohashi Bridge, Tech. Memo. P.W.R.I., No. 1102, December 1975

(7) Okubo, T. , Narita, N. and Yokoyama, K. : Some approaches for improving wind stability

for cable-stayed girder bridges, Proc. Fourth Int. Conf . on Wind Effects on Buildings

and Structures, London September 1975

II-7
II-8
II-9
11-10
(zh) Xouanbajj

11-11
11-12
Return P«riod

11-13
Fig. 8 Model system

11-14
11-15

Table-1 Dimension of Hirado-Ohashi Bridge

Item Unit Plan-D

Span length m 465.40

Effective span length m 460.00

Sag m 45.00

Backstay (lateral) right . m 105.00

Hirado Island m 139.00 Backstay (vertical) right . m 53.37 HiraZ Island 61.37 Cross sectional area (cable) m2 /bridge 0.170

Dead load (whole structure) t/m/bridge 11.02

" (floor deck) t/m/bridge 6.99

" (stiffening truss) t/m/bridge 2.50

" (cable, hanger) t/m/bridge 1.53 Width of truss m 14.50 Height of truss m 6. 00 Panel length of truss 5.00

of lateral brae ing 10.00 Width of floor deck 11.30 Moment of inertia of area of truss nrVbridge 1.649

Table-2.1 Reduced mass density

Mode

Step

5 8 11 13

Torsional os. Asymmetric, 1st 861,544 8,232.13 123.746 30.1326

ton sec2 Symmetric, 1st 63,012 24,701 2,200.6 32.950 Bending os. ton 8ec 2 /m2 Asymmetric, 1st 1.8804 0.8459 0.7151 0.6837

11-17
Table-2.2 Test condition with sectional model

" ~~~~ ^ Step Mode —1 5 8 11 13

Scale 1:37.59 1:37.59 1:37.59 1:37.59 Mass density (kg/model) 20.867 9.387 7.935 7.586

Polar moment of inertia

(AS1) 69.041 659.7 9.916 2. 415

(SI) 5.050 1.979 176.3 2.640

Table-2.3 Frequency ratio — Step Mode — 5 8 11 13

Na(ASl)/NTl 1.71 3.28 3.55 2.85 Na (S i)/Nn 1.58 1.14 1.90 2.59

11-18
Table-3 Critical Flutter Wind Speed

at C*=5° in Model-Ill (m/s)

Step

Type

14 14* 13 11 8

Torsional Flutter 50.8 49.1 45.8 75.6 Not occur

Coupled Flutter 49.0 47.3 44.2 73.8 Not occur

'without pavement

11-19

PRESENT SITUATION OF EARTHQUAKE PREDICTION RESEARCH IN JAPAN

Kazuo Hamada, National Research Center for Disaster Prevention

Hiroshi Takahashi, National Research Center for Disaster Prevention

Hiroshi Sato, Geographycal Survey Institute Akira Suwa, Meteorological Research Institute ABSTRACT

An outline of the Japanese National Program of Earthquake Prediction is introduced

here. First, the progress up to date of the national program of earthquake precition;

second, the organizations related to the prediction, their main roles, and the organizational

structure; third, the strategy of earthquake prediction by the Coordinating Committee for Earthquake Prediction (CCEP) ; fourth, the activities of the CEEP; fifth, the present state

of earthquake prediction; sixth, the promotion of the prediction program, including the

authors' points of view and finally, the following items of research and observations

are introduced:

1. GEODETIC SURVEY

2. TIDAL OBSERVATION

3. CONTINUOUS OBSERVATION OF CRUSTAL MOVEMENT

4. SEISMIC OBSERVATION

5. VELOCITY CHANGE OF SEISMIC WAVES

6. ACTIVE FAULTS AND FOLDING

7. GEOMAGNETIC AND GEOELECTRIC OBSERVATIONS

8. LABORATORY EXPERIMENTS

9. WORKS RELATED TO GROUND WATER

10. DATA PROCESSING AND MONITORING SYSTEM

KEYWORDS: Earthquake prediction; Japan National Program; present state

III-l
PROGRESS OF EARTHQUAKE PREDICTION RESEARCH

The present research of earthquake prediction goes back to 1962, when the publication

"Earthquake Prediction - Progress to Date and Plans for Future" was issued by a research

group for an earthquake prediction program consisting of Japanese seismologists. This planning had drawn much attention in the world, especially in the United States. As a result, the first Japan-United States Conference on Research Related to Earthquake Pre- diction was held in Tokyo and Kyoto in 1964, under the auspices of the Japan-United States Cooperative Program, which still continues up to the present. In Japan, the Science

Council of Japan and Geodesy Council in the Ministry of Education established some committee meetings and made recommendations and/or authorized proposals to the Prime Minister and other related Ministers with respect to promotion of earthquake prediction. Table 1 summa- rizes the main events related to the promotion of earthquake prediction up to the present. A national program of earthquake prediction was launched in 1965 with the financial support of the Government. The funding and planning of the program have been in 5-year

increments. The program is now in the third 5-year segment and will be 13 years old by

the end of the fiscal year 1977. As a result of the progress, the number of research

scientists and technicians involved in the national program exceeds four hundred and several

tens, and the total funding in 1977 amounted to 3.7 billion yen (approximately $13 million,

Fig. 1). During these years, approximately 130 additional positions for scientists and technicians were created, and a total of 15 billion yen will have been allocated by 1977. This budget is the largest of all projects in solid-earth science in Japan. Since the Japanese funding excludes salaries and the costs of construction of observatories, the size

of the Japanese program is not small in comparison with that of the United States whose

funding was $11 million in 1976, including salaries (National Academy of Science, 1976)

.

ORGANIZATIONS RELATED TO THE PREDICTION PROGRAM

Organizations related to the earthquake prediction program and their main roles are shown in Fig. 2. All sorts of information of up-to-date research and observations concerning the earthquake prediction are gathered into the CCEP for judgments with respect to the earthquake occurrence in and around Japan. Main courses of information flow to the CCEP

are illustrated in Fig. 3. There are about 9 organizations of universities which have their unique programs. Most requirements of budgets and new positions from these organizations

are approved by the concerned ministries or agencies (Science and Technology Agency, Ministries of Education, International Trade and Industry, Transportation, and Construction) through ordinary administrative procedures. There are no review panels made up of scientists assisting a responsible agency in selecting the research projects and other requirements

to be supported, unlike the United States. Nor is there a responsible lead agency which is responsible for the whole program concerning the earthquake prediction, like the State Sesimo logical Bureau of China. In Japan, however, deep regard is given to the proposals

by the Geodesy Council.

III-2
STRATEGY OF EARTHQUAKE PREDICTION BY THE CCEP

The CCEP designated some areas as the "area of specific observation, area of intensified observation, and area of concentrated observation" as the target of a strategy of earthquake prediction. The designation of an "area of specific observation" is given to areas

of historically disastrous earthquakes, active faults, high seismicity in a limited area, and

an important area from social and economic aspects, like a densely populated area. Whenever

anomalous phenomena, such as land uplift, are observed by either nationwide observations

like geodetic survey, seismic observations and tide-gauge observations or other observations

in the "area of specific observation," the region of anomaly is designated as an "area of intensified observation." If the anomalous phenomena are later suspected precursory to an impending earthquake, the designation will be changed to an "area of concentrated observation," and all types of observations will be concentrated there. And, if the precursor is later more positively ascertained, all efforts will be concentrated to predict an earthquake. As illustrated in Fig. 4, the Tokai area and the southern part of the Kanto area

are "areas of intensified observation." However, there is no "area of concentrated observation" up to the present. ACTIVITIES OF THE CCEP

The CCEP has not yet issued any prediction of an earthquake, in contrast with the examples of the United States and China. However, after its establishment in 1969, the CCEP

released a series of information related to an earthquake to the society in the form of general warnings; uplift in the Boso and Miura Peninsulas, no chance of a large earthquake

in the Kanto region for the time being, possibilitv of a large earthquake in the Tokai

area, the recent uplift in the lower reaches of the Tamagawa river, Kawasaki city, and most

recently, the uplift in the Izu Peninsula. Thus, the CCEP also plays the role of a mediator

between the scientist and the society besides the judgment of earthquake prediction. Although any prediction of earthquake has not yet been issued in Japan, if we take "prediction" in a wide and general sense, such predictions were issued twice. A coordinating committee issued the first one to the local people through JMA (Japan Meteorological

Agency) when the Matsushiro Earthquake Swarm (1965-1967) by judging from microearthquake

activities preceeding the occurrence of medium-size earthquakes. The second prediction in

a wide and general sense was made by the CCEP before the Off-Nemuro Earthquake of 1973 by judging from the seismicity gap and the accumulated crustal deformation. THE STATE OF EARTHQUAKE PREDICTION

Predictions of earthquakes should specify the time, magnitude, and place with the probabilities. However, neither the present state nor the present distribution of instrumentation permits useful predictions to the society on a routine basis. An earthquake prediction theory (e.g., Rikitake, 1976) or a formula to predict an earthquake

is not completed, but is at the developing stage. Also, a final network of observations

for the prediction on a routine basis is not made clear. What is certain is: any kind of

III-3
the present observations is not sufficient yet and we have to monitor not only one or two but several kinds of observations in order to select a phenomenon really precursory to earthquakes, rejecting all the disturbances from other sources. And a final synthetic judgment is required from observational, experimental, and theoretical aspects. Although

the present state of prediction is not at an advanced, satisfactory stage, if a precursory

phenomenon to a large earthquake appears very strong in a wide area, we could recognize

the precursors from the present network of instrumentation. Therefore, construction of an integrated system of data gathering/release, analyses, and judgments is urged especially

for the Tokai area. PROMOTION OF EARTHQUAKE PREDICTION

The Japanese National Program of Earthquake Prediction, since it was launched in 1965, has been gradually strengthened by mutual cooperation of different organizations. The present organizational structure, however, is no longer adequate for the growing program with

increasingly wide variety of observational data, larger continuous monitoring systems, broadening areas of research, and synthetic judgments from all kinds of data and research

at the same time. Serious problems in the program are the chance for studying social aspect: of prediction and the absence of a responsible lead agency. Under these circumstances,

the Headquarters for Promotion of Earthquake Prediction was established in October, 1976, with purposes of interministrial adjustment and communication, and of promotion of compre- hensive and systematic planning with respect to the national programs. This Headquarters is of the highest level of its kind in Japan and is expected to influence the state of earth- quakes very much.

ITEMS OF OBSERVATIONS AND RESEARCH

Items of research and observations for the prediction program are outlined as follows:

1. GEODETIC SURVEY. A nationwide triangulation (recently, tirlateration) network

consists of 6000 first-order and second-order triangulation points which are surveyed by GSI (Geographycal Survey Institute) by means of geodimeters at 5-year intervals (Fig. 5) . Also, nationwide levellings of first order, 20,000 km in total length, are conducted by GSI every

5 years (Fig. 6) . In a special region like the Capital area, GSI has a planning of accurate geodetic measurements at the resurvey intervals of 2.5 years and other temporary

geodetic measurements on occasion. Gravity surveys are conducted by GSI and universities

occasionally.

2. TIDAL OBSERVATION. There are about 100 tide-gauge stations along the coast at approximately 100-km intervals. These stations belong to JMA, GSI, and HD (Hydrographic

Department) primarily (Fig. 7), but their observational data are gathered into the Coastal Movement Data Center of GSI and released from this center.

3. CONTINUOUS OBSERVATION OF CRUSTAL MOVEMENT. There are various types of strain and tilt meters for continuous observation of crustal movements, but they are still at the developing stage. They are silica-bar strain meters, wire strain meters, volumetric strain

III-4
meters of buried type, tilt meters of borehole type and of tunnel type, and water-tube

tilt meters. Most of them belong to universities, JMA, and CDP (National Research Center

for Disaster Prevention) and are distributed at about 30 sites illustrated in Fig. 8. Recently, emphasis is placed on the continuous monitoring of crustal movements in the Tokai

area as seen in the figure.

4. SEISMIC OBSERVATION. JMA has a nationwide network, consisting of about 120 stations, for large, moderate, and small earthquakes of M>3 (Fig. 9) , and regularly publishes a bulletin of the earthquake. Furthermore, JMA is now constructing additional 20 high-sensitive stations. Micro- and ultra- microearthquakes are observed at about one hundred and several tens stations which belong to approximately 20 observatories of several

universities, CDP, and JMA (Fig. 10) . Seven universities have their mobile parties for temporary observations of micro- and ultra-microearthquakes

.

CDP installed deep-borehole seismometers and tilt meters in a 3500-m well at the Iwatsuki

city about 30 km north from the center of Tokyo, so as to overcome artificial noises in the Tokyo area. And other two deep-borehole observatories will be completed in a few years

also in the Tokyo area. There are three types of ocean bottom seismometers (OBS) , an anchored buoy type, a free-fall pop-up type by the University of Tokyo, and a submarine cable type by JMA. JMA

intends to set several OBSs of submarine cable type off the shores of Tokai area for continuous observation on a routine basis.

5. VELOCITY CHANGE OF SEISMIC WAVES . In cooperation with universities and CDP, GS (Geological Survey) has repeatedly conducted the explosion experiment at Izu-Oshima Island

since 1968 at intervals of approximately one year, with the aim of monitoring the velocity

change of seismic P waves propagating beneath Sagami Bay, which was the epicentral area of

the great Kanto earthquake of 1923. No velocity change exceeding 0.1% has been observed

up to the present (Fig. 11)

.

6. ACTIVE FAULTS AND FOLDINGS. By mutual cooperation of universities, GS , and CDP

the research of active faults and foldings over the country were summarized and published

(e.g., Research Group for Quaternary Tectonic Map, 1973). Matsuda's work (1972) is a classification of active faults based on an average dislocation (Table 2) , and it includes

his studies with respect to a recurrent interval of earthquakes along the fault. Recently,

a research group of Kaizuka and his colleagues investigated the distribution of active

faults, their activities, and seismic risk all over the country.

7. GEOMAGNETIC AND GEOELECTRIC OBSERVATIONS. Much emphases are placed on geomagnetic

secular variation. There is a nationwide array of accurate proton-precession magnetometers

as shown in Fig. 12. The natural noises contaminate the observed values of the total

intensity of the geomagnetic field unexpectedly so much that it might not be easy to detect

significant changes associated with an earthquake. First-order geomagnetic surveys are conducted every 5 years by GSI at about 300 sites all over the country. Continuous monitoring of the earth's resistivity changes has been carried out at Aburatsubo about 60 km

south of Tokyo. Some precursors and coseismic changes have been reported (e.g., Yamazaki,

1975)

.

III-5
8. LABORATORY EXPERIMENTS. Apparatus for the experiments of rock failure, which sim- ulates the circumstances prevailing within the earth's crust, were installed at five univer- sities and GS. This kind of investigation is represented by Mogi's series of experiments.

9. WORKS RELATED TO GROUND WATER. Research on ground-water level, chemical analysis, and radon content as well as other water-related research from the viewpoint of earthquake prediction belong to the scientific fields where Japan was behind other countries.

Recently, the University of Tokyo and GS, however, investigated such water-related problems

(e.g., Wakita, 1976). Also, CDP is going to start on such works with a newly created research group.

10. DATA PROCESSING AND MONITORING SYSTEM. Various centers for specific activities were established: the Crustal Activity Monitoring Center in GSI; the Seismicity Monitoring Center in JMA; the Earthquake Prediction Observation Center in ERI (Earthquake Research

Institute) ; and the Local Center of Earthquake Prediction Observation in each of five main universities. These centers are gathering and processing the widely growing variety of observation data. Most of the data are gathered and sent by a telemetering network to these centers. Furthermore, at present, a coordinated system of synthetic and rapid judgments, analyses, and data gathering/release from/to all the centers and organizations all over the country is under discussion. To promote the short-term prediction in the Tokai area, which

is publicly suspected to be dangerous, a judgment committee is going to start the work

under the supervision of the CCEP. REFERENCES Geomagnetic Research Group on Earthquake Prediction (1974) : Observation of Geomagnetic

Total Intensity under the Project of Earthquake Prediction Research, 1972-1973, Report of the CCEP, 12, 151-160, in Japanese. Geological Survey (1977): Data submitted at the 36th meeting of the CCEP of Feb., 1977,

in Japanese.

Matsuda, Tokihiko (1972) : Earthquakes and faults from geological standpoints, Proc. 12th Conf . Earthquake Engineering, Comm. Earthquake Engineering, Japan Society of Civil

Engineers, Tokyo, 7, in Japanese.

Mogi, Kiyoo (1974) : Roch Fracture and Earthquake Prediction, Journal of the Society of Materials Science, Japan, 23, 2-13, in Japanese. National Academy of Science (the United States, 1976) : Predicting Earthquakes A Scientific

and Technical Evaluation—With Implications for Society. Research Group for Quaternary Tectonic Map (1973): "Quaternary Tectonic Map of Japan," National Research Center for Disaster Prevention.

Rikitake, Tsuneji (1976): Theory of Earthquake Prediction in "Earthquake Prediction,"

Elsevier, 245-301. Science and Technology Agency (1976): "Handbook of Earthquake Prediction," edited by the Coordinating Committee to Promote Earthquake Prediction Research, in Japanese.

Wakita, Hiroshi (1976): The Kawasaki Uplift, Kagaku, 46, 573-579, in Japanese. Yamazaki, Yoshio (1975) : Precursory and Coseismic Resistivity Changes, Pure and Applied

Geophysics (PAGEOPH) , 113, 219-227. III-6
Table 1. Progress to Date of Earthquake Prediction

Y. M. 1961 4 The first meeting of the research group for earthquake prediction program.

1962 1 "Earthquake Prediction Progress to Date and Plans for Future" was issued from

the above research group.

1963 6 The Sectional Meeting of Earthquake Prediction was established in the Geodesy

Council in the Ministry of Education.

10 The Science Council of Japan recommended the Government to promote earthquake prediction research.

1964 6 The Geodesy Council proposed to the Ministries of Education, International Trade

and Industry, Transportation, and Construction on planning of earthquake pre- diction research.

1965 3 The Sub-Committee Meeting for Earthquake Prediction was established in the Coordinating Committee for Geophysical Research in the Science Council of Japan.

4 Beginning of financial support to the program of earthquake prediction research.

6 Yearly schedules of earthquake prediction research were made by the Sub-Committee Meeting for Earthquake Prediction.

1966 6 The yearly schedules were modified, considering the experience of the Matsushiro

earthquake swarm. 1968 5 Acknowledgement at the Cabinet Council on application of earthquake prediction

research, in consideration of damages caused by the 1968 Off-Tokachi Earthquake.

7 The Geodesy Council proposed to the related Ministers on application of earthquake prediction research.

1969 4 The Coordinating Committee for Earthquake Prediction was established in the Geo- graphical Survey Institute, for exchanging information and overall judgments concerning earthquake occurrences.

1973 7 Agreement to promote earthquake prediction at the Central Conference for Disaster Prevention in the Prime Minister's Office.

1974 11 The Coordinating Committee to Promote Earthquake Prediction Research was established for administrative adjustment among the Ministries and Agencies.

1976 10 The Headquarters for Promotion of Earthquake Prediction was established in the Cabinet and the above coordinating committee to promote earthquake prediction

research was displaced by this headquarters.

1977 A Judgment Committee of the Tokai Area will be established to promote short-term prediction in the Tokai area.

III-7
Table 2 Main active faults in Japan (Matsuda, 1972)

A; the mean rate of movement = 1-10 m/lOOOyears

B; ".. 0.1-1

C; " less than 0.1 "

Location Name of faull Typo Length Class (km)

Akita Pref. Rikuu reverse fault GO B

Iwate Prof. Morioka reverse fault 40 B

Fukushima Pref. Fukushima basin reverse fault 50 B

Fukushima Pref. Aizu basin reverse fault 40 B

Niigata Pref. Nagaoka plain reverse fault 30 B

Nagano Pref. Zenkoji basin reverse fault 70 B

Nagano Pref. Itoigawa—Shizuoka left-lateral 80 A

Shizuoka Pref. North Izu left-lateral 30 A

Toyama and Gifu Pref. Alolsu gav/a right-lateral 60 A

Gifu Pref. At era lert-laterat 70 A

Gifu Pref. Neo valley left-lateral 70 A

Aichi Pref. Fukozu reverse fault 10 C

Kyoto Pref. Tango left-lateral 20 C

Hyogo Pref. Rokko reverse fault 50 B

Hyogo Pref. Yamazaki left-lateral 50 A

Tottori Pref. Tottori right-lateral 15 C

Southwest Japan Median tectonic line right-lateral 800 A

III-8
1965 1970 1977

Fig. 1. Yearly budget related to the prediction program

in billion yen (Science and Technology Agency,

1976)

III-9
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111-10
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III-LL
Fig. 4. Designation of area by the Coordinating Committee for Earthquake Prediction

111-12
Fig. 5. Nationwide network of a first-order triangulation.

111-13
Fig. 6. Nationwide first-order levelling routes

20,000 km in total length.

111-14
Fig. 7. Tide-gauge stations registered at the Coastal Movement Data Center.

111-15
111-16

111-18
111-19
The Complementary Importance of Earthquake Prediction

and Structural Response Estimation in Seismic Design and Planning Decisions

ROBIN K. MCGUIRE

U.S. Geological Survey, Denver, Colorado, U.S.A.

Abstract

The present uncertainty in estimating the responses of manmade and natural structures

to earthquake threats is translated into cost penalties reflecting costs associated with

possible failure of the structure due to underestimated response, and costs associated with overdesign of the structure (or over-conservative reaction to a hazard) due to overesti- mated levels of motion. The important uncertainties for seismic design and planning decisions are those associated with the size, location, and time of future earthquakes, and those associated with estimating ground motion and structural response during these events.

It is shown that reducing the uncertainties in one part of the problem has only a minor effect on reducing the (social and economic) cost of earthquakes unless significant and complementary advances are also made in reducing the uncertainties of the other part. KEYWORDS: Seismic risk; Design decisions; Minimum cost. Introduction

Long-term earthquake design and planning decisions are made daily and will continue

to be made as earthquake prediction capabilities develop and as new theories are tested

to estimate ground motions and responses of structures (natural and manmade). These decisions include choosing seismic design levels, zoning land for different types of development depending on the earthquake hazard, and condemning existing low-strength

buildings. The uncertainties associated with earthquake occurrence and with the ground motion and structural response generated by the event lead to cost penalties associated with these decisions. The purpose of this paper is to examine simple, typical cost penalty functions and to estimate the penalties associated with present uncertainty and with various advances in earthquake prediction capability and in ground motion and structural response estimation.

III-2C
Cost penalties can be associated with the two possible outcomes of a design or planning decision regarding earthquake hazards: failure of the structure or system of interest, or survival of the structure or system because of over-design. The rare instances

in which a structure experiences exactly the design response during its lifetime can be regarded as a trivial case of the second type of outcome. For the purposes of this brief

study, the "earthquake demand" as well as the "structural capacity" will be measured by random-variable Y, which may (as in the example to follow) be peak ground acceleration

or some other ground motion measure, or it may be a structural response measure (inter- story displacement, percent liquefaction of an earth-fill dam, etc.). The failure cost penalty C_(y,,Y) is a function of the design capacity y, and the

h a a demand on the structure Y (this demand may, in the general case, be the result of one earthquake, the maximum of a series of earthquakes, or the cumulative effect of a series

of earthquakes). Let y be a specific observation of Y; then failure is defined as y

> y(j- A possible function for C p is shown in Figure 1. For ySyd there is no failure; as y in- creases above y, , C„ increases from zero to a maximum value CL which may represent the

a r K replacement cost of the structure or the maximum life loss possible.

The cost of over-design Cg is equal to the cost of earthquake design provided in the structure cD

(y^)' minus the cost of earthquake design which would have just met the earthquake demand y, CD

(y). A typical increase in cost of earthquake resistance as a function of capacity y^ is shown in Figure 2. The over-design penalty cost Cg is thus

the "extra" capacity which is designed into the structure and which, in retrospect after having observed a seismic demand value y, is not used. Cg is obviously defined only when the observation y of Y is <y^. The penalty cost functions presented here may easily be interpreted as dollar costs associated with repairing and designing a specific structure. The failure penalty function may also be interpreted as the cost of life loss or loss of service of some facility;

the overdesign penalty function may be considered the cost of non-development of some area of potential soil failure, or the cost of needless condemnation and razing of buildings. Capacity y

d might be chosen by optimization to minimize a total cost function

(not the penalty functions) . The optimum design could imply some structural repair or

111-21
casualty cost even when y exactly equals y^ (for instance, non-structural partitions

might be allowed to crack in a building during the design earthquake demand) ; in this case the penalty functions represent increases in costs for cases in which y>y, or y<y,.

d d The expected penalty for a given design capacity y^ can be calculated as the over- design cost (a function of y) times the distribution function of Y given y<y,, integrated

d over all values, plus the failure cost (also a function of y) times the distribution

function of Y given y

> y, > integrated over all values. Mathematically,

where f^ is the density function and the cumulative distribution function for Y. This expected penalty can be interpreted as the average penalty for a group of structures (with the same cost penalty functions) subjected to what is ostensibly the same earthquake risk, or as the expected penalty for a single structure. The advantage with working with penalty functions (over expected cost functions) is that they derive entirely from our lack of perfect knowledge of the processes governing earthquake occurrence, ground motion generation and transmission, and structural response. If there were no uncertainties in any of these processes, we would simply predict the design earthquake, calculate y, design the structure (presumably for minimum cost), and incur no penalty. Since there are uncertainties, we can calculate (through equa- tion (1)) the associated costs, and can estimate how these costs decrease with reduced uncertainty (better theories) about physical phenomena.

A simple hypothetical problem has been chosen to illustrate several points. A building site is threatened by an earthquake source located 25 km away; the source produces earthquakes in the magnitude range 5-7.5, with a Richter b value of 0.88, at an average rate of one per year. Ground acceleration y is chosen as the intensity measure of interest (it is assumed for simplicity that y is a good estimator of

o

(1)

Simple Example

111-22
building damage and is a good measure to estimate design costs) . The attenuation equa- tion used is In y=6. 16+. 65M-1 . 3 ln(R+25) , where M is magnitude and R is source-to-site

distance (25 km in this example). This attenuation equation 1 is typical of most for

the range in which there is plentiful data; dispersion of observed values about the regression estimates indicates that the standard deviation of In y is 0.51, which is a typical dispersion for California acceleration data. A lognormal distribution of y is used, corresponding to conclusions reached by many researchers.

The failure cost penalty function chosen is

0 y<y

d

which corresponds to the simple situation that the cost of replacement is incurred if the design intensity is exceeded. (No increase in replacement cost with seismic design

level is assumed in this simple analysis.) For the over-design penalty, the following function is used:

(«(yd-y) y<y

d

C

s (y,yd )= (3)

lo y>y

d This corresponds to a linear increase in design cost with y^. The total expected

penalty is calculated using equation (1). The penalty associated with current technology (no earthquake prediction methods

available, typical dispersion in ground motion intensity estimation) will be calculated

and will be compared with the (reduced) penalties associated with various advances in prediction technology and in ground motion estimation. It is assumed that, with present technology, designing the building under consideration to survive earthquake motions during its lifetime with 90-percent reliability, i.e., F^(y^)=0.9, results in minimum total cost. The choice of design motion assuming advances in prediction tech- nology and/or ground motion estimation is also made using a minimum cost criterion. A risk of some size is inherent in any choice of design intensity, either explicitly or implicitly, and will remain until all uncertainties in earthquake prediction, ground motion estimation, and building response estimation are eliminated or at least bounded.

1 R. K. McGuire, "Seismic Structural Response Risk Analysis, Incorporating Peak Response

Regressions on Earthquake Magnitude and Distance," M.I.T. Dept. of Civil Eng., Research

Report R74-51, 371 (August 1974). 111-23
Distributions of Ground Motion

Figure 3 shows the distribution of intensity y during the structure's lifetime

using the assumptions and properties presented above, and using a typical state-of-the- art risk analysis 2

. From the Poisson distribution there is a probability of 0.37 that

no earthquake occurs at all, resulting in the spike of height 0.37 at y=0. According

to the 10-percent risk design rule assumed, the value chosen for y^ is 22-percent g. The penalty associated with this procedure can straight-f orwardly be calculated via equation (1), using Figure 3 for f^(y) • Performing this calculation gives a penalty

of 13.8a+0.1 C R

, the first term due to over-design (because no earthquake occurs or because the earthquake (s) which occurs produces an intensity yly^) and the second term due to possible failure. The assumption that this a minimum cost design means that a=0.0125 CR

, and this relationship is used for subsequent cases. Let us hypothesize first that a perfect positive earthquake prediction capability

is available, i.e., that precursors have been identified which are sufficient to predict all earthquakes during a structure's lifetime, but which are not known to be necessary, so that the absence of earthquakes cannot be predicted. This is an optimistic

goal for an earthquake prediction program to achieve in 5 to 10 years; we would be happy if precursors can be identified which will allow reliable predictions of the size, location, and time of the next event on a section of fault. Those faults which do not exhibit the precursory behavior would be suspected of being aseismic (during the lifetime of a structure) but, until more detailed investigations and data gathering, no specific aseismic prediction would be made. The distribution of ground motion from the predicted event depends upon its size; distributions of y for three events (magnitude 5, 6, and 7) are shown in Figure 4. The minimum cost criterion is used, and it is assumed

also that only one event is predicted during the structure's lifetime. The expected penalty for each design depends on the magnitude of the predicted event (it increases with magnitude) and this penalty can be calculated with equation (1) . To determine an expected penalty for a single structure before the earthquake is predicted (or equi- valently to calculate the average penalty for a large number of structures to be affected

2 R. K. McGuire, "Fortran Computer Program for Seismic Risk Analysis," U.S. Geological

Survey Open-File Report 76-67, 90 (1976).

111-24
by a range of predicted magnitudes) we use the exponential magnitude distribution and integrate over all values between M=5 and M=7.5. Performing this calculation gives an

expected over-design penalty, for cases in which earthquakes can be predicted, of 11.1

a. The expected failure penalty, calculated by weighting according to the exponential

magnitude distribution, is 0.077 CR

. Using the relationship between a and described

above, the total xpected penalty is 80 percent of that for the risk analysis case. It must be concluded that the expected cost penalties associated with long-term earthquake design and planning decisions will not be reduced greatly by a positive earthquake pre- diction capability.

If a perfect positive and negative prediction capability is available (i.e., we can predict earthquakes and no earthquakes) , the expected penalties are reduced because

there are no penalties (and no costs) for structures which will not be shaken. Assuming (from the Poisson distribution described above) that this happens 37 percent of the

time, the penalties associated with a positive prediction capability are reduced 37 percent, to 50 percent of the penalty calculated for risk analysis. We are thus faced with the interesting conclusion that, given present uncertainties in ground motion

estimation, more benefits in long-term planning decisions will be realized in an earth- quake prediction program by identifying faults and areas where earthquakes will not occur, rather than where they will occur.

To determine the effect on cost penalties of advances in ground motion estimation,

the three cases above (no earthquake prediction capability, positive capability, positive and negative capability) were repeated assuming first that uncertainty in ground motion is reduced by one-half (a of In y=0.25), and second that it is reduced to zero. The cost penalties were calculated in a manner identical to that described above. Table 1 summarizes the expected penalties under various hypothesized advances in pre- diction technology and/or ground motion estimates, as percentages of the expected penalty under present technology (first row, first column). Table 2 indicates a similar comparison for the total expected cost for each case, calculated as the design cost

plus the failure cost times the probability of failure, i.e., ay

d+C

R

(l-FY

(yd

) )

, inte- grated over the various possibilities where applicable.

It can be seen from the first column of Table 1 (or 2) that (as discussed above)

the reduction in expected penalty is small when going from present technology to a 111-25
positive prediction capability, primarily because of the large uncertainty in ground motion given the prediction. Similarly, reading across the first row of Table 1 (or

2) the reduction in expected penalty due to reducing uncertainty in ground motion is small, primarily because of the large uncertainty in earthquake size, location, and

time of occurrence. It is only when advances in both earthquake prediction and ground motion estimation are made, that substantial reductions in expected penalties and total costs are achieved.

Conclusions

It is shown by this simple study that advances must be made in both earthquake prediction capability, and in ground motion and structural response estimation tech- nology, for the costs associated with long-term design and planning decisions to be significantly reduced. Large reductions in these costs will not be achieved by an

earthquake prediction capability alone, nor will they be achieved solely by more ad- vanced theories to estimate ground motion and structural response. This is the case whether one examines the expected cost penalties due to uncertainties in estimating structural responses during future earthquakes, or whether total expected design and failure costs are used as the criterion for comparison. Design and planning costs will be reduced somewhat by a perfect positive prediction capability (meaning that earthquake precursors have been identified which are sufficient but not necessary for prediction purposes); more cost reduction will occur when a perfect positive and negative prediction capability is available (meaning that faults can be identified which

can be assumed to be aseismic in the future, for planning and design purposes).

111-26
Table I

Expected Cost Penalties as Percent of Present Penalty due to Uncertainties in Earthquake Occurrence and in Ground Motion

Ground Motion Uncertainty

Present 1/2 of Present No Uncertainty

None 100% 60% 56% Earthquake prediction

capability

Positive*

capability Positive and negative

capability

80%

50%

33%

21%

0%

0% *Analysis only for sites where events are predicted.

Table II Total Expected Costs as Percent of Present

Cost of Earthquake Design and Failure

Ground Motion Uncertainty

Present 1/2 of Present No Uncertainty None 100% 82% 76% Earthquake prediction

capability

Positive* capability Positive and negative

capability

94%

60%

66%

42%

38%

24% *Analysis only for sites where events are predicted.

111-27
FAILURE COST c

| PENALTY

CAPACITY y d EARTHQUAKE DEMAND Y

FIG. 1- FAILURE COST PENALTY AS FUNCTION OF EARTHQUAKE DEMAND

.

EARTHQUAKEwcD

(y)

C

s =C

D(y )-C

d

(y)

y yd CAPACITY yd AND DEMAND Y

FIG. 2- DESIGN COST AS FUNCTION OF CAPACITY.

111-28
0.38

1

0.37-

.06-

.05-

ACCELERATION y (%g)

FIG. 3- DISTRIBUTION OF ACCELERATION, RISK ANALYSIS.

ACCELERATION y (%g)

FIG. 4- DISTRIBUTION OF ACCELERATION, 3 PREDICTED EARTHQUAKES.

111-29
RESEARCH AND DEVELOPMENT OF PERMANENT OCEAN-BOTTOM SEISMOGRAPH OBSERVATION SYSTEM

OFF THE PACIFIC COAST TO CENTRAL HONSHU, JAPAN Akira Suwa, Head, Seismology & Volcanology Division Norio Yamakawa, Chief, 1st Laboratory of the Division

Tatsuto Iinuma, Chief, 3rd Laboratory of the Division Meteorological Research Institute Japan Meteorological Agency ABSTRACT

Eighty to ninety percent of all the earthquakes in the world occur in the sea area. However, there is not a single permanent ocean-bottom seismograph yet; this is the weakest point in seismic activity monitoring and earthquake prediction. The Seismology and Volcanology Division of the Meteorological Research Institute has been engaged in the devel- opment of a permanent ocean-bottom seismograph observation system off the Pacific coast of Tokai District, central Honshu, which is one of the major items included in the 3rd Five-Year

Plan of the National Program of Earthquake Prediction Research in Japan (1974-1978)

.

The observation system being developed consists of the combination of submarine and land equipment. The submarine equipment consists of one terminal apparatus and several intermediate apparatus, i.e., pressure vessels containing seismograph and tsunami-meter

sensors, and signal transmitters, which are connected in series by a submarine co-axial

cable. This equipment is laid one hundred and twenty kilometers off Omaezaki, Shizuoka

Prefecture, at the ocean-bottom down to 3,000m below sea level. On the other hand, the land equipment consists of receiving and repeating apparatus in the shore station (Omaezaki Weather Station) , and receiving and data processing apparatus at the Earthquake and Tsunami Center (Japan Meteorological Agency in Tokyo)

.

This development project has been progressively implemented. Trial layings of the submarine equipment have been carried out already and actual layings are planned in 1978.

KEYWORDS: Cables; development of submarine equipment; earthquake prediction; ocean-bottom

seismograph.

111-30
MAJOR AIMS OF THIS OBSERVATION SYSTEM DEVELOPMENT

Two-thirds of the globe's surface is covered with sea water, and accordingly, 80 to 90%

of all the earthquakes take place in the sea area. Ten to fifteen percent of the world's earthquakes occur in and near the Japan Archipelago. And the Japan Meteorological Agency is responsible for permanent monitoring of large, moderate, and small earthquakes (M _> 3) which occur in this area. It is estimated that the number of these earthquakes is approximately 10,000 per year. Moreover, it is also estimated

that the number of micro- and ultra micro-earthquakes (M < 3) in this area is more than

10,000,000 per year. The observation of these earthquakes is significant for realizing

earthquake prediction, though they have no direct influence on our daily life. Most of these numerous earthquakes have their hypocenters under the sea bottom near the

Japan Archipelago. Remarkably, all the recorded great earthquakes with a magnitude of M ^ 8, which caused huge damages, occurred in the sea bottom off the Pacific coast between the coastline and the Japan Trench, Nankai Trough and so on, with the single exception of the Nobi

Earthquake in 1891. Whil the Japan Meteorological Agency is always carrying out permanent observations at

130 locations or more together with a number of university laboratories conducting their

local observations, the concerned seismographs are all land based ones and not a single

piece of permanent observation equipment is located at the sea bottom. Consequently it has not been determined exactly how many and in which areas minor earthquakes occur in the sea bottom. Moreover, even for major earthquake occurrences, concrete and

precise data on the location of the epicenter, the depth of the hypocenter and the magnitude

have not been available.

This means a lack of monitoring devices for seismic activities in the sea bottom, producing serious obstacles in processing tsunami warnings and earthquake informations,

as well as realizing earthquake prediction and forecast. The monitoring devices are indispensable for disaster prevention.

Under such circumstances, the Japan Meteorological Agency is going to implement a program for the immediate application of land observation data combined with permanent sea

bottom observation data which are obtained by seismographs connected in series at the sea bottom down to thousands of meters, the deepest part, under the sea level, off Sanriku

District, Sagami Bay to the Boso Peninsula, Tokai District, and Shikoku, all of which are

the locations with frequent earthquake occurrences.

The development of the on-line and real-time system of permanent ocean-bottom

seismograph observation off the Pacific coast of central Honshu, Japan, is presently

being implemented by the Meteorological Research Institute as one of the major items

included in the 3rd Five-Year Plan of the National Program of Earthquake Prediction

Research in Japan (1974-1978). The system is transferred to routine observation by the

Japan Meteorological Agency after completion of the Plan.

The sea area, off the Pacific coast of central Honshu, was selected because it was

around this area where great earthquakes of the M8.5 class occurred at least four times

111-31
in history with intervals of 145 to 402 years. 123 years have already passed since the last occurrence of such a great earthquake and there is a seismicity gap, as shown in Figure 1, even when small earthquakes are taken into consideration. Such being the case, the Coordinating Committee for Earthquake Prediction of Japan also specifically designated

Tokai District of central Honshu, as an "Area of Intensified Observations." Studying the data from a large earthquake that occurred in 1854, the last case observed

in the past in this area, it is well anticipated that, if such a large-scale earthquake takes place again, not only Tokai District will suffer very serious damages but also Tokyo, Kanasawa, Kobe, etc. will be subjected to damages as well. Although the existence of a seismicity gap does not in itself reflect the imminent sign of a large scale earthquake, we cannot deny the existence of the ominous silence usually observed before a storm. In this respect, further change in seismic activity within this

sea area requires a special attention. Furthermore, a large budget is required for the development of this system, and even with such a budget and the most up-to-date sophisticated technology, there still remains various risks. Fortunately, the depth of the water in this area is not so deep as the other

three areas. The authors together with Hideteru Matsumoto, senior researcher, and other staff

members, Yasuo Nagayama, Akio Takayanagi, Michio Takahashi and Toshimitsu Tsukakoshi, have been making every effort to carry out the research and development of this system at the Research Division. However, research and development activities are not being carried out solely by the Meteorological Agency. Nippon Telegraph and Telephone Public Corporation, the Faculty of Science and the Earthquake Research Institute of Tokyo University, and the Hydrography Department of the Maritime Safety Agency have extended special cooperation.

As to the production of equipment the Nippon Electric Company, Ltd., and related companies

have been engaged in this project. CONSTITUTION OF A SUBMARINE SYSTEM

The observation of ocean-bottom earthquakes using the submarine cable system has only been attempted once in the past by the U.S.A., and this system was less complicated than that which is now being developed by the authors, et al. In 1965, the Lamont-Doherty

Geological Observatory of Columbia University installed a cable in the Pacific Ocean approximately 180km (100 nautical miles) off Point Arena, California, to a depth of nearly 4,000m and equipment such as seismographs were attached only at the tip of the cable. Staff members including the authors were successively dispatched to the above observatory in order to acquire knowledge of their valuable techniques and experiences.

However, the Lamont-Doherty Geological Observatory was forced to give up their research

after only several years of study mainly due to frequent trouble, which resulted from wire breaks in the cable and slight water leakage in the pressure vessel, caused by geographical and geological features.

The series type system now being developed by the Meteorological Research Institute

of the JMA is more intricate, therefore, precise studies on the geographical and geological

111-32
features of the sea bottom are required in order to select the best route for the cable

laying. The laying work must be carried out with extra caution because modifications after

the completion and replacement of broken components are almost impossible with this kind of

system.The system is composed of a submarine system which is installed at a depth of nearly

3,000m in the sea approximately one hundred and twenty kilometers off the coast of

Omaezaki, Tokai District, and a land system. The submarine system consists of one terminal

apparatus and several intermediate apparatus of high reliability, i.e. , pressure vessels

containing seismograph and tsunami-meter sensors, and signal transmitters, which are connected

in series by the co-axial submarine cable. The land system consists of the receiving and repeating apparatus in the shore station (Omaezaki Weather Station) , and of the receiving

and data processing apparatus at the Earthquake and Tsunami Center (Japan Meteorological

Agency in Tokyo)

.

Figure 2 indicates the above mentioned system. The submarine transmitting system is an application of the transmitting techniques of the ocean-bottom co-axial cable used for the most recently developed long-range submarine telephone and telegram lines. In other words,

of the two types of real-time and on-line transmitting systems, one is multi-cable systems in which components are divided into several channels and electric power is transmitted through

a different channel, and the other is the co-axial cable system in which all components

are combined in one channel through which electric power is also transmitted. The co-axial

cable system has been employed for our observation system. All components of the observation equipment installed at the tip of the cable and at intermediate points transmit signals

using the ocean-bottom co-axial cable by way of an FM-FDM system. An electric current

is fed by way of a constant current feeding system in which electric currents run through the center conductor of the co-axial cable, and are released into the sea water from th§ terminal

equipment attached to the ocean-bottom earth and then sent back to the coastal station

through shore earth. We have developed large size pressure-resistance containers for the terminal equipment

(inner diameter 300m; inner length 820m), as a large variety of sensors needs to be incorporated. However, the largest of the pressure-resistant containers (inner diameter 204m; inner length 700mm) currently being used for ocean-bottom relaying equipment will be employed for intermediate apparatus. This will enable cable ships available in Japan to carry out the laying work. The pressure vessels are incorporated with 3 directional

short-period (seismograph) sensors on gimbals (natural frequency 4.5Hz), an equalizing

amplifier, signal transmitter, etc. The terminal equipment will also be equipped with a medium-period seismograph and pinger which is used for measuring the actual laying position of

the equipment at the ocean-bottom.

A tsunami-meter is installed in order to contribute directly to the improvement of tsunami warning activities which are essential for the prevention of natural disasters.

Sensors will be installed at the sea bottom to measure the change in hydraulic pressure

and thereby detect tsunami. A quartz pressure transducer of the sensor which is used for this system (manufactured by the Hewlett-Packard Co., the U.S.A.) records changes in

111-33
frequency when there is a pressure change. This tsunami -meter sensor is covered with oil filled rubber to insulate it from brine.

The advantage of using this tsunami-meter has been confirmed through evaluation of its characteristics in a pressure chamber, thermostatic chamber, etc., and also by continuous

test observations in the sea for five months at the marine observatory tower of the Meteorological Research Institute off the coast of Ito City, Shizuoka Prefecture. Although

this tsunami-meter is a total pressure type which detects the overall pressure from the sea surface to the bottom, its resolvability is approximately 1 cm even at a depth of 3,000m, and has the comprehensive characteristic of being able to release sufficiently strong signals compared to other surrounding noise, when a 10cm change in terms of water depth occurs. Furthermore, observation errors of a 10m high tsunami are 10cm or less. The prerequisites for the apparatus to be used for this submarine system, both sensors and transmitters, are that they be highly efficient, reliable, and safe, and in addition, extremely compact. RESEARCH AND DEVELOPMENT PROGRESS

The research and development of this permanent observation system for submarine seismic observation have been making steady progress in accordance with the annual program as shown

in Table 1. In 1974, the initial year of the program, the system design of the total system

including the land part was conducted, and as an integral part of this, various tests using

a breadboard model were also carried out. Then, hardware was developed on the basis of

1 the system design, and various tests have been conducted on the characteristics of these developed products and evaluated.

No damage should be incurred on any of the submarine system equipment while loading it on the cable ship or during the construction work. A route which meets the geographical

and geological requirements must be carefully determined prior to the construction work. Geographical and geological conditions must have little possibility of sea-bottom land- slides and wire breaks, and a small gradient, and also they must be as flat as possible to avoid a cable bridge. It is esepcially important that the intermediate apparatus are not left hanging in the water as a result of the geographical and geological features of the sea-bottom. Also, one end of the cable of this submarine system is placed a few thousand meters at the deep sea-bottom, whereas in the case of a submarine cable for telephone

and telegram, both ends are at the two coastal stations. The above-mentioned points make it necessary to first conduct elaborate studies on the geographical and geological features of the sea area to be used. Since the work also involve construction of heavy terminal equipment (the weight in water is approximately 1 ton including the cage) , special methods will have to be employed in order to accomplish the work

successfully, and trial layings of the terminal equipment are indispensable.

In view of the above-mentioned conditions, a bathymetric chart and a submarine structural chart of the sea bottom to be used, which are the results of a detailed survey conducted in 1974 by the Hydrography Department of the Maritime Safety Agency, were made available by the same Department to the Meteorological Research Institute; and four proposed

111-34
routes for submarine cable installation were determined on the basis of such charts and

the bathymetric record of the same survey, and also by taking into consideration the opinions of the experts in the Hydrography Department and the Nippon Telegraph and Telephone Public Corporation. Furthermore, in 1975 and 1976, the Meteorological Research Institute commissioned the Corporation to carry out research on geographical and geological features concerning sea- bottom of the proposed routes, and had a private land survey company perform surveys of

the sea bottom along the coastal area south of the Omaezaki Weather Station. The Corporation

was also commissioned to implement trial operations aiming at establishing a laying system

of the sea bottom terminal equipment.

The Corporation carried out bottom sampling and sounding along all the proposed

routes on board the Kuroshio-Maru (3,344.9 tons), the newest cable ship, employing a multi-beam bathymeter (which is capable of simultaneous sounding and inclination measurement

in a transverse direction to the course) , the NNSS (U.S. Navy Navigation Satellite System)

,

and a computerized automatic control system. As a result, among the four proposed routes which run from NNE to SSW along the zone between the Suruga Trough to the Nankai Trough

and the submarine canyon off the Tenryu River, the central route was determined to meet

the necessary geographical and geological conditions, while others did not. The Corporation, in 1976, carried out a trial laying and refloating of the terminal

and intermediate equipment by use of a dummy system on board the Kuroshio-Maru. The

laying of the sea-bottom system is planned to start from the terminal. The terminal will

be lowered to the sea-bottom from the bow of the cable ship, and then the laying of the intermediate equipment will take place from the stern by operations in the ship. The lowering of the terminal will be performed by adopting the so-called single wirehanging

process which ties the heavy terminal equipment and the ocean-bottom earth with 1,000m

long cable ( approx. 500m in the trial) to the signal transmitting co-axial cable. However,

since the conventional type non-armored co-axial cable has a 7-ton tensile strength and therefore presented large risks, a high tension non-armored co-axial cable (15-ton tensile

strength) was newly developed and used. This new cable endured well at the maximum tensile

strength, i.e., 9 tons, at the time of refloating.

In this co-axial cable of the sea bottom system, a section of approximately 40km

which was to be laid in the shallow sea-bottom (down to approximately 500m) adopts a single or double armored co-axial cable in order to avoid any trouble in relation to the operation of dragnet fishing. In the very shallow sea-bottom (down to 50m) along the sea

shore, various kinds of trouble tend to occur due to wave action and tidal currents. Therefore, the double armored co-axial cable guarded by a steel protector is adopted and furthermore, the cable is buried in the sea-bottom mud. The sole manufacturer of the submarine

co-axial cable in Japan is the Ocean Cable Company.

The research and development project of this permanent sea-bottom earthquake observation system has been steadily progressing with the support of the earnest people concerned.

While numerous difficulties have been encountered and overcome, there still remains a lot of problems to be analyzed and solved in the coming days. The practical laying of the submarine

system is planned to be implemented in summer or fall of 1978, and preparations are now being
Figure 1. Distribution of Epicenters of Shallow Earthquakes off the Tokai District (1926-72) and the Permanent Ocean-Bottom Seismograph Observation System

111-36
111-37
111-38
111-39
C

o

Coil o m

Magnet

$6 0 Figure 4. Seismometer Sensor

Lead

- 852 Figure 5-1. Tsunami-meter Sensor

QPT : Quartz Pressure traedueer

T C .' Thermal compensator Figure 5-2. Tsunami-meter Block Diagram

111-40
111-41
111-42
Figure 10 Trial Layings of the Terminal Apparatus

111-43
VERTICAL DISTRIBUTION OF THE SEISMIC S-WAVE VELOCITIES AT THE SITE OF THE IWATSUKI DEEP BOREHOLE OBSERVATORY OF CRUSTAL ACTIVITIES

Fumio Yamamizu and Hiroshi Takahashi National Research Center for Disaster Prevention Noritoshi Gotoh, Yutaka Ohta and Keiji Shiono Hokkaido University ABSTRACT

From the earthquake engineering point of view, in-situ velocity measurement of the seismic S-wave was carried out down to a depth of 3500 meters at the site of the Iwatsuki Deep Borehole Observatory constructed by the National Research Center for Disaster Prevention. S-waves were produced mainly by ordinary small chemical explosions in a shallow borehole and supplementarily by an SH-wave generator (an S gun) firmly pressed on the ground

surface. A set of three-component seismometers of moving-coil type with natural frequency

of 4.5 Hz was installed in a capsule which could be fixed at any depth in the borehole. Repeated measurements were made at 16 different depths from the surface to the bottom. The S-wave by the S gun was clearly recorded down to the depth of 1500 m. Identification of the S-wave onset on the record of the explosion was unexpectedly easy, even for depths deeper than 1500 m, because very good phase correspondence between the S phase from the S gun and the S phase from the explosion was obtained. Therefore, the reading of the S-wave onset was most reliable. The estimated S-wave velocity structure was 0.44, 0.76, 1.3, 1.6 and 2.6 km/sec with

the boundary depths of 300, 1000, 2000 and 2800 m, respectively, from the surface to the bottom of the borehole. The boundary at 2000-m depth was uncertain unlike the other three boundaries. This boundary may not exist, or the velocity may change gradually with depth. The P-wave velocity structure was estimated at the same time, and the velocity values were 1.8, 2.1, 2.9 and 4.7 km/ sec with the boundaries very close to those of S-wave

velocity. But the 2000-m depth boundary was not found.

KEYWORDS: Deep borehole; earthquake, in-situ velocity measurement; S-wave; vertical dis- tribution of seismic wave.

111-44
INTRODUCTION With the recent increase of large size structures, it has become essential that the response characteristics related to the sub-surface structure at depth, probably several kilometers deep, should be evaluated; in other words, the existence of a thick sedimentary

layer is indispensable for the earthquake resistance of high and/or long structures (Seis. Expl. Group of Japan, 1976)

.

As a first step to understand the response characteristics of a thick, deep sedi- mentary layer, the velocity of S-waves was directly measured in-situ down to the depth of

3500 meters, at the Iwatsuki Deep Borehole Observatory of Crustal Activities constructed

by the National Research Center for Disaster Prevention. Since there has been no direct

S-wave measurement made for the depths over several hundred meters, the present measurement

over 3500 m depth was the first trial in Japan, probably even in the world. Firstly, the detection and identification of S-waves are emphasized and then the general trend of their velocities is properly evaluated.

To produce S-waves, we used small chemical explosions in a shallow borehole and we

also used a specially designed SH-wave generator, called an S gun. The SH-wave predominantly generated by the S gun (Jolly 1956, Komaki 1959, Shima and Ohta 1967) was recorded

clearly down to the depth of 1500 m. Through the comparison of records from the explosion

and the S gun, it was possible to extract S-wave characteristics contained in the record

from the explosion. Therefore, the S-wave identification at depth by simple detonations

has become unexpectedly easy and the reading of the S-wave onset is reliable. OBSERVATION

The Iwatsuki Deep Borehole Observatory of Crustal Activities fronts on the Moto- Arakawa River, Iwatsuki-city , Saitama-ken, Japan. Four shot holes were drilled on this riverbed about 100 meters southeast from the observation well, and the S gun was firmly pressed on the surface of the same bed about 50 m east from the well. A set of instruments was well designed with the purpose of efficient task of the observation and easy operation not to miss recordings. The block diagram of the observation system is shown in Fig. 2. The apparent dynamic range of this recording system is over 70 db, including the effect of the analog voltage divider. All seismometers used

were of the moving-coil type, with natural frequency of 4.5 Hz for the underground use, and 1.0 Hz for the surface use. A set of seismometers on the surface was also operated in order to determine the attenuation of S-wave energy by comparing the records at varying

depths and at the surface. The measurement was sequentially carried out at the following 16 depths, 100, 200,

300, 500, 750, 1000, 1500, 2000, 2500, 3000, 3482, 3249, 2745.3, 2245, 1750 and 1250

meters.

111-45
ANALYSIS

The analysis proceeded along a line in which the priority was given to detection and identification of S-waves, and then the general trend of S-wave velocities were evaluated. This was also inevitably required because the interval between depths of measurement was rather rough, namely 100 or 250 m. In the determination of the S-wave velocity structure on the basis of the obtained

travel-time diagram, any other data concerning the observation well (for example, the

sonic, the density logging) were not taken into account. All efforts were concentrated on determining the objective S-wave structure from the travel-time only. After that, all the data were compared with each other, and the harmony between them was examined. PROCESSING OF RECORDS Along the line stated above, at first, the record from the S gun which predominantly produced the SH-wave was processed (Fig. 3) . Traces shown in Fig. 3 were resynthesized by

the analog signal converter shown in Fig. 4. Since the horizontal direction of the seismometers in the borehole was not known, this converter was used, so that the expected SH-wave could be emphasized. The result was very clear especially for the trace of 1500m

depth. This converter was also applied to records of the explosion, but the result was not improved. Probably, the reason was that the explosion produced both SH- and SV-waves. Accordingly, the S/N ratio was improved primarily by various digital filtering. Filtered

traces are shown in Fig. 5. Comparing Fig. 3 with Fig. 5, relatively long-period wave groups are clearly recognized on the record of the explosion at the time of appearance of the SH-wave on the record of S gun. The records in Fig. 5 were made by various filterings, so that this relatively long- period wave group could be emphasized, because these wave groups are taken as S-waves. The solid circle in the figure shows the S-wave onset. Only the onset at 3250 m is less objective

Next, the trace of the vertical seismometer is drawn up (Fig. 6) so as to determine

the P-wave velocity structure. There are almost three wave groups: the first wave group

is the precursor with small amplitudes, appearing at the depths as deep as 2500 m, the second is the true P-wave group, and the third group following the P waves has large amplitudes. Judging from a rough estimation of their velocities, they correspond to the dilatational wave propagating through the cemented zone around the observation well protected by the wall and through the water filled in the well. Especially, from the fact that in the large-amplitude wave group those reflected by the well bottom are recognized,

it is obvious that the third wave group has propagated in the well water. TRAVEL-TIME DIAGRAM AND VELOCITY STRUCTURE

The onsets of S and P waves were read with the precision of 1/100 sec. After that, the travel- time was corrected, as if the source were just above the well at the surface.

In the correction, detailed velocities of S and P waves near the surface were used and

111-46
these were the results of the P, S velocity loggings as deep as the depth of 120 meters, which were carried out at an area close to the observatory.

In Fig. 7, the corrected travel- times were plotted and straight lines were drawn through the plots. All the points except one or two are on the lines, and furthermore, even those exceptional points are away from the lines by only 3/100 sec. Therefore, straight lines seemed to be very reasonable. From this travel-time diagram, we can directly determine the velocity structures of S and P waves. It is summarized in Fig. 8 together with the structure near the surface. The S-wave velocity structure consists of four layers, and the velocity structure consists of three layers to the deep basement, excepting the vicinity of the surface. The boundaries

at the depth of 300, 1000 and 2800 m coincide with each other in both the S- and P-wave

structures. The only discrepancy occurs in the boundary at 2000 m. Since the ratio of S velocity at this boundary is 1.3/1.6=0.8, it is not significant. On the other hand, the travel-time of that interval seems to be increasing gradually with increase in the depth, and so it is also possible that the two layers are taken as one mirage layer. Accordingly, both the structures of S and P waves are in good agreement with each other. COMPARISON WITH OTHER DATA Other data concerning the Iwatsuki Deep Borehole, that is, the sonic wave (P wave),

the density and the electrical loggings and the geologic columnar section, etc. had been examined (Takahashi and Hamada, 1975) . The sonic logging was basically a continuous

measurement. Although the variation of velocity was very complex and scattering, the general tendency of the sonic logging and the absolute values are in good agreement with

the present estimated structure. Two discontinuities at depths of 1000 and 2800 m are clearly seen in the sonic logging, and also obvious in the columnar section, corresponding

to the boundary of Pleistocene-Miocene and Miocene-Pretertiary , respectively. In the sonic logging, velocities are almost constant or slightly increasing between 1000 and

2800 m depths except small scatterings near a depth of 1200 m. They also agree with the results shown in Fig. 8. Such general tendency is also shown in the density and electrical

loggings. Accordingly, the resultant S- and P-wave velocity structure are reasonable and in harmony with all the other data of the observation well. CONCLUSION

Measurements of velocities of S and P waves were carried out down to a depth of 3500m at the Iwatsuki Deep Borehole Observatory. The results are summarized in Fig. 8. And

they are in good harmony with all other data of observation well. Except at the ground

surface, the S-wave velocity structure consists of four layers, and the velocity structure

of P wave three layers. If we regard the intermediate depth layers as a mirage layer, the boundaries for S and P waves are consistent with each other. The S gun plays an important role for detection of an S wave contained in the simple detonation, and so the reading of S-wave onset has become more reliable and accurate. 111-47
This is one of the good harvests of the present measurement, and also suggests a technical method of the deep S wave in-situ velocity measurement for the future research.

In conclusion, the experiment was carried out under the cooperation of five groups, NRCDP, Hokkaido Univ., Teikoku Oil Co., Akashi Seisakusho Co. and Allaround Consultant of Geological Survey Co. We want to express our gratitude to the scientist and technicians who participated in this experiment, especially to Mr. Suzuki at NRCDP who partly conducted

the experiment. Also we would like to express our sincere thanks to Dr. Hamada who was a member of the planning team at the early stage of this experiment and kindly read the manuscript making valuable suggestions and encouragements.

Jolly, R. N. (1956): Investigation of Shear Waves. Geophysics, 21, 905-938. Komaki S. (1959): Fundamental Experiments on Generation of Shear Waves. Journ. Seis. Ex- ploration Group, 18, 19-100. [in Japanese]

Shima, E. and Y. Ohta (1967) : Experimental Study on Generation and Propagation of S-waves

I, Designing SH-wave Generator and its Field Tests. Bull. Eartq. Res. Inst., 45, 19-

32. Takahashi, H. and K. Hamada (1975): Deep Borehole Observation of the Earth's Crust Activities Around Tokyo - Introduction of the Iwatsuki Observatory. Pure. & Appl. Geophys. 113, 311-320. The Seismic Exploration Group of Japan (1976) : Experimental Studies on Generation and Propagation of Seismic Waves, Chapt. 5, Sec. 6. [in Japanese]

.

111-48
SHOT HOLES

Fig. 1 Arrangement of the observation well, shot-holes and the SH-wave generator.

DATA REC.

Fig. 2 Block diagram of the observation system.

111-49
SH-WAVE GENERATOR

—^~-^v/v~—wv---y^yv\yy\/w\/vv^—vw*

TRAVEL TIME ( »»c

)

Fig. 3 Resynthesized records of the SH-wave generator. Solid circles show the onset of S waves.

H 2

Input

Hi- cos 2

rVsinG

H2«sin 9

Ho-cos 0

Co-ordinate Conversion

Circuit

H 10

H 20

Output

(rotated

by 0 )

Fig. 4 Block diagram of an analog signal converter.

111-50
EXPLOSION

Horizontal component, filtered.

3250 >

/|

3500 > -~>^\A^\vVW\^/v

n^a/—

*^-^^vv^\^y\/^

Fig. 5 Records of the horizontal component seismometer with

the suitable filtering. Solid circles show the detected

onset of S wave.
EXPLOSION

Vertical component, no filtering.

0 1 (sec) 2 3 DEPTH I I I L

( m )

200 -~3WH+*/

300

500 ^|MH^ —*|4ft* —4#

iyw —

Fig. 6 Records of the vertical seismometer without filtering. Solid circles show the true P wave. ^

111-52
TRAVEL TIME (sec.)

1.0 2.0 (S-wave) 3.0

0.5 1.0 (P-wave) 1.5

Fig. 7 Travel-time diagram of S and P waves

111-53
S and P wave Velocity [ km/sec

1.0 2.0 2.0 (S-wave) 3.0 4.0 (P-wave) 6.0

0.44

0.76

! 1.8 0 Velocity %g

(

( g)

0.16 -

2.1 0.125

1.30 50

2.9

— S-wave — P-wave

0.3 3 1.65

0.37 J

[

0.325

0.41

0.36

1.60

4.7 2.50

Fig. 8 Velocity structure of S and P waves.

111-54
RESEARCH ON ACTIVE FAULTS IN THE METROPOLITAN AREA

Hiroshi Sato, Geographical Survey Institute Toshihiro Kakimi, Geological Survey of Japan ABSTRACT

The present state of research on active faults in the metropolitan area is discussed.

The paper describes the discovery of two active faults, the Tachikawa Fault and the Arakawa

Fault, in the Kanto plain. The paper also points out that at present there is no definitive method (s) to detect active faults covered by thick sediment. The geophysical methods

commonly employed in underground research work present problems when the methods are used

for research on active faults in urban areas. Geochemical methods should be considered.

KEYWORDS: Detection of active faults; earthquake prediction; research on active fault

111-55
INTRODUCTION

It is well known that a sudden movement of a fault results in an earthquake. Fault which had moved in geologically recent time, namely Ouartenary, is considered to move in the future. Such a fault is called an active fault and it is possible to estimate the magnitude and the mean recurrence time by knowing its length and displacement. Research

on active fault are important for earthquake prediction and earthquake hazard mitigation.

However, active faults in urban areas have not been well understood yet because of the many difficulties in performing research on active faults. Recently, importance of counter- measure for earthquake hazards in urban areas is emphasized, and research on active faults under metropolitan areas have been urged. This paper describes the present state of the research on active faults in the metropolitan area. EARTHQUAKE DISASTER IN THE METROPOLITAN AREA

Since 1603 when the Shogunate was established in Edo, the metropolis of Japan has been attacked by destructive earthquakes more than thirty times, and those of intensity 6 or more in JMA scale have been recorded eight times. The earthquakes that caused severe damages to the metropolis can be classified into two categories, that is, major earthquakes in the Sagami Bay and destructive earthquakes

under the urban area. More than half of the earthquakes that attacked Edo are considered

to be the latter type. Nowadays, the possibility of the occurrence of a major earthquake

in the Sagami Bay in the near future is considered small and that of a destructive earth- quake in the inland is considered not so small, as we have not had large earthquakes in the metropolitan area since the Nishisaitama earthquake occurred in 1931. The mean time interval of destructive earthquakes in this area is nearly 30 years, so the occurrence of

a destructive earthquake under Tokyo is very apprehensive today. Earthquakes that caused damages to Edo or Tokyo are divided into two groups from their focal depth. The Ansei Edo earthquake of 1854 is estimated (from the distribution

of damages) to be a shallow earthquake whose focal depth was 30 Km or less, and the Tokyo earthquake of 1894 is considered to be a relatively deep one. In the southern Kanto

district, there is an active seismic zone in the depth of 40 - 60 Km and the Tokyo earth- quake of 1894 is estimated to be in this zone. Though the likelihood of occurrence of

a relatively deep earthquake is larger than that of a shallow earthquake, the latter may

give more severe damages to the Tokyo area. The distribution of destructive earthquakes in Kanto appears to be closely related with the tectonic line extending from the northwestern part of the Kanto plain to the southeastern part. So, the studies of the tectonic structure are important for the evaluation of seismic hazards in the metropolis of Japan. (Fig. 1)

.

GEOLOGICAL STRUCTURE AND ACTIVE FAULTS IN THE KANTO PLAIN

The geological structure of south Kanto is characterized by thick sediment of Neogen

and Quartenary and also by active seismicity zone of 50 - 60 Km in depth. In such thick

111-56
sediment areas, it might be possible to estimate a linear structure of base rocks, namely

fault, from the discontinuity in the thickness of sediment, but it is difficult to know

j whether the fault had moved or not in geologically recent time. (Fig. 2) The known or estimated active faults at present in the southern Kanto district are

shown in Fig. 3. As seen in the figure, the faults are located mainly in the western part

of the plain, and their strikes are prominent in the direction from northwest to southeast.

Some active foldings are estimated to be in the central and eastern part of the plain. These foldings might be considered a faulting in deep layer, resulting foldings in

I the upper layer. Among the active faults in the metropolitan area the most important ones

; on the hazard mitigation are the Tachikawa fault and the Arakawa fault. Tachikawa Fault

This is the active fault running from Oome city to Tachikawa city (west of Tokyo) and

its length is estimated to be 20 Km or more. It was very recently that the existence of

\ this fault became definitive from the interpretation of air photographs and field investigations, and this poses a problem for land use in this area. The fault pass under the Tachikawa airdrome of the U.S. air force and the airdrome will be turned over to the Japanese government in the near future. Its mean vertical displacement rate is estimated

j to be 0.2 mm/year, resulting in the present total displacement of about 4 m to the Tachikawa plain which was formed nearly 20,000 years ago. Any historical earthquake originated from the Tachikawa fault is not known, but at least one earthquake resulted from the fault within the last 10,000 years, when it dis- placed a sedimental layer formed nearly 10,000 years ago. If we assume that the displacement of the fault is about 1 m during one earthquake, the mean recurrence time of the

j earthquakes originated from the fault is estimated to be about 5,000 years.

Arakawa Fault

This fault is estimated from investigations of tectonic movements of late Quartenary

in the Kanto plain. A clear boundary of tectonic blocks has been found along the Arakawa

River, and an active fault should be considered to be there to explain the discontinuity

in the movements. Although its existence is not confirmed yet by field investigations,

the fault is estimated to be west down reverse fault of B class, that is, mean displacement rate in the order of 0.1 - 0.2 mm/year. Recently a clear gap of about 400 m in the depth of base rock was found at the north

of Tokyo by the artificial explosion at Yumenoshima in Tokyo Bay. Some researchers suppose

that this gap is a part of the Arakawa fault. Considering the estimated strike of the

fault and the distribution of the historical earthquake, the Arakawa fault might be considered as a part of the medium line in the Kanto district. Exact location and length of the Arakawa fault are not known, but it is the nearest

fault to the central part of the metropolis of Japan, therefore, research of the Arakawa

fault is greatly needed.

111-57
RESEARCH OF ACTIVE FAULTS IN THE METROPOLITAN AREA

The first synthesis research of active faults in the metropolitan area have been

conducted by the Committee for Disaster Prevention of Tokyo. The committee emphasized the importance of active faults on the hazard mitigation, and compiled a map of active faults

and foldings. However, present information about active faults in the southern Kanto plain is not sufficient because of many difficulties encountered in the research. Recently, a research project on active faults under sedimental layer has been initiat under the promotion by the Science and Technology Agency of Japan. The project is aimed

to explore a new way of investigating active faults covered by thick sediment by using many kinds of geophysical methods. Although these geophysical methods are commonly used

for geophysical prospectings of underground structure some problems remain when they are used for the research on active faults under young sediment. It is important to know the amount of displacement in the young sediment due to faulting, but physical property of the young sediment is much affected by the amount of included water, then it is difficult to detect the displacement from the difference of the physical property of the sediment. The present project is to search effective ways to apply these geophysical methods for the studies of active faults under thick sediments with the cooperation by governmental

institutes related to the research for earthquake prediction.

The following is a short summary of the present research. Gravity Survey Areal distribution of gravity anomaries reflects the geological structure of the underground, so it is possible to know the depth of base rock and its fall-off by sur- veying the gravity values minutely. Therefore, the Geographical Survey Institute is now doing gravity surveys with the alloting of one point at every 1 Km in the metropolitan

area. Fig. 4, is the preliminary result of the survey. The figure is made by filtering out long wave component in the bouguer anomary. As seen in the figure, a linear structure

of the bouguer anomary extending in the west-east direction is remarkable in the northern part of the Kanto plain.

As mentioned previously, the strikes of the active fault known in the southern Kanto district are NW-SE direction, so the line like anomary found by the gravity survey is noteworthy. Micro Earthquakes

In western Japan where the depth of base rock is very shallow, the activity of micro

earthquakes has a close relation with active faults, that is, many micro earthquakes along active faults are observed. Such phenomena, however, have not yet been known in eastern

Japan. Recently, a linear distribution of micro earthquakes of shallow depth was found by

the observations of very high sensitivity at Iwatuki in the area where an active folding

is estimated, and the distribution of the micro earthquakes is well accordant with this active folding.

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At present, any micro earthquake activity is not known along the Techikawa fault and

the Arakawa fault, but there is a possibility that micro earthquakes might be observed

there when the observation net is well established. Elastic Wave Prospecting

Elastic waves are effective means to prospect underground structures, buc there are problems when it is applied for the research on active faults in the urban area, that is,

f it is difficult to use gunpowder as a source of elastic wave, so it is necessary to search

for another source usable in the urban area. Another problem is that physical property of shallow sedimental layer is much affected by the ground water and also contrasts between

the sediments are very small. It is, therefore, necessary to develop a new receiving

system of high resolving power and the way of data analysis. The Geological Survey of Japan is now developing a new system of elastic wave sounding for active fault under

sedimental layer. Electrical Method

This is an effective way to research active faults from the difference of electric property such as resistivity in the sedimental layers, but there are many artificial disturbances in the measurements of the resistivity in urban areas, so it is necessary to eliminate artificial noises in the measurement. The Geomagnetic Observatory of Kakioka is now studying a method to search an active fault by the measurement of ground resistivity

and other electric properties of the ground. Conclusive Remarks At present, there is no definitive method to detect active faults covered by thick

sediment. The geophysical methods are useful ways to search ground structure through the sediment, but they have difficult problems to solve when they are applied for the reserach on active faults, and geochemical methods should be considered. Aside from these geo- physical and chemical methods, geological drilling and topographical research have to be conducted by a new approach for the research. We expect much progress in the research on active faults, as well as in earthquake hazard mitigation in the metropolitan area, by

synthesizing the studies from the present project.

111-59
Fig. 1 Destructive earthquakes and estimated

tectonic line in the metropoitan area

Fig. 2 Contour lines of the base of Neogene sediment

T

"rr"Active fault

-T-r-rnTr estimated active fault block boundary

Name

1. Tachkawa

2. Fukaya

3. Arakawa

Strike N 45 W

N 50 W

N 50 W

Length

20 Km

10 Km

Mean Displacement

Velocity 0.2/1000 0.2/1000

0.1 0.2/1000

Fig. 3 Active faults and block boundaries in the Kanto District

111-60
Fig. 4 Tachikawa fault

Fig. 5 Distribution' of gravity anomany in the metrolitan area

111-61
m$ 1974^12 H -1976^1 B A 0 — 5 km focal depth O 0 -30km O30 -40km

Fig. 6 Distridution of micro-earthquakes in Kanto District.

111-62
CHARACTERISTICS OF VERTICAL COMPONENTS

OF STRONG-MOTION ACCELEROGRAMS

Tatsuo Uwabe

Setsuo Noda Eiichi Kurata

and Satoshi Hayashi Port and Harbour Research Institute ABSTRACT

Characteristics of vertical components of the 574 strong-motion accelerograms were

studied in order to determine the effects of vertical ground motions on dynamic stability

of structures. The following were made clear.

1) According to accelerograms with the maximum acceleration of over 50 gals the ratio of the maximum acceleration on the vertical component to that on the horizontal

component was less than 1/2.

2) The occurrence time of the maximum acceleration on the horizontal component was different from that on the vertical component. At the time when the safety factors against sliding and overturning were the smallest, the ratio of the vertical acceleration

to the horizontal acceleration was less than 1/3.

3) The stability analysis of the gravity type quaywalls based on a current design method of port facilities was performed considering the vertical seismic coefficient. Consequently, the vertical seismic coefficient was found to have little influence on the safety factor for gravity type quaywalls.

KEYWORDS: Design; horizontal acceleration; seismic coefficients; stability; strong-motion

accelerogram; structures; vertical acceleration.

IV-1
INTRODUCTION

A ground motion during an earthquake consists of a vertical component besides horizontal components. It is generally recognized that vertical accelerations usually have smaller amplitude and higher frequency components as compared with horizontal accelerations, hence the vertical accelerations have little influence on stability of civil engineering

structures and buildings. However, it is pointed out from the case studies of damage records that the vertical motion might have severe influence on the stability of structures

in some cases. According to the present methods of earthquake resistant design, the vertical motion

is considered as a vertical seismic coefficient in some cases, and in other cases it is not clearly provided but indirectly included in design conditions. Because of insufficient

data on the vertical motions during earthquakes, the effects of the vertical motion in the design procedures are not based on enough information on amplitude and frequency charac- teristics of the motion but are decided from a sort of empirical knowledge on dynamic characteristics and stability of structures as a whole.

In order to collect more reliable data for a seismic design, such engineering features

of vertical motions as amplitude, predominant frequency, ratio of vertical acceleration to horizontal ones are investigated by using strong-motion accelerograms. Furthermore, for the purpose of clarifying the effects of vertical motion on stability of structures, gravity type quaywalls which are typical type among harbour structures are analyzed by present design procedures based on a seismic coefficient method (1)

.

STRONG-MOTION ACCELEROGRAMS Strong-motion accelerograms used in this paper are drawn from "Annual Report on Strong-Motion Earthquake Records in Japanese Ports" (2) published annually by the Port and Harbour Research Institute, Ministry of Transport and also from "Strong-Motion Earthquake

Records from Public Works in Japan" (3) by the Public Work Research Institute, Ministry of Construction. Maximum amplitude of accelerograms used herein is over 10 gals in either of

the two horizontal components. The 294 records during May 1963 to December 1974 are selected from the publications by PHRI and the 280 records during January 1968 to December

1973, from the publications by PWRI. Table 1 shows the number of records in each maximum acceleration range. Additionally, most of these were recorded by SMAC-B

2 accelerograph,

of which specifications are listed in Table 2. Because of limited time for analysis, only

25 records published already by PHRI are used in the study based on the digitized vertical

components. The digitized accelerograms are listed in Table 3. INVESTIGATION ON CHARACTERISTICS OF VERTICAL ACCELERATION

Ratio of Maximum Vertical Acceleration to Maximum Horizontal Acceleration

As shown in Fig. 1 maximum vertical acceleration (A ) is compared to the maximum ^ vmax horizontal accelerations (Aj^^ for a11 574 records. In this figure ratios of the former

to the latter (A /A, ) are also indicated by straight lines. Fig. 2 shows a frequency vmax hmax

IV-2
distribution of the ratios A /A, for all records and also shows the frequency in vmax hmax

each acceleration range. In these records the 3 records show particularly large ratios, that is, 1.30, 1.60 and 1.67. According to Fig. 1 the ratios A /A, are less than * a vmax hmax

1/2 for most records of which maximum horizontal accelerations are over 50 gals. In this case the maximum horizontal acceleration means the larger one in the two horizontal components. But the real horizontal acceleration in each instant must be the resultant of these components, and the maximum resultant acceleration in the horizontal direction is always

larger than the maximum horizontal acceleration and becomes 2 times in the largest case. Therefore, the ratio A /A, becomes smaller, if the maximum resultant acceleration is vmax nmax

used instead of the maximum horizontal acceleration. Factors Having Influence Upon Ratio of Maximum Vertical Acceleration to Maximum Horizontal Acceleration

As shown in Fig. 1 the ratios A /A, are widely scattered. If it is made clear vmax hmax what factors have influence upon the ratio, it may give useful information for the earthquake resistant design. Since phenomena of ground motion during earthquakes are very complicated, mathematical and statistical studies are desirable for estimating the factors

correctly. Prior to such approach, the influence of various factors including maximum

horizontal acceleration, epicentral distance, magnitude of earthquake, subsoil condition

and others on the ratio A /A, are preliminarily investigated hereinafter, vmax hmax

(1) Maximum Horizontal Acceleration

In Fig. 1 the ratios A /A, are fairly scattered in case of small maximum hori- vmax hmax

zontal accelerations and decrease to almost less than 1/2 in case of large maximum horizontal acceleration.

(2) Epicentral Distance

Fig. 3 shows the distributions of the ratios A /A, in relation to the epicentral vmax nmax distance for all records, and Fig. 4 also shows the ratios for the records with the maximum

horizontal acceleration of over 50 gals. Both in Fig. 3 and Fig. 4 the ratios tend to scatter and show no definite correlation with the epicentral distance. But, for extremely

short distance the ratios become over 1, and this fact may be worthy of attention for considering the near epicentral area.

(3) Magnitude of Earthquake

In Fig. 5 the ratios A /A, which are obtained from records with the maximum

vmax hmax

horizontal acceleration of over 50 gals are against the magnitude of earthquakes. It is shown in Fig. 5 that there is no particular feature in the relationship between the ratio

and the magnitude of earthquakes.

(4) Subsoil Condition

Accelerograms which were collected by the Port and Harbour Research Institute are used for investigation on subsoil conditions. As shown in Table 4 the sites of the obser- vation stations are classified into three groups which were already reported in the study on the average response spectra of the horizontal components of the accelerograms at the sites (4). The relationship between A and A. in each group is shown in Figs. 6 to

IV-3
is no significant difference in characteristics among these groups.

(5) The Others Wakayama zi-S station in the observation network of the PHRI and Kinokawa-ohashi

station (Station No. 112) of the PWRI observation network are only 1.4 km away from each other and succeeded to record the ground motions during the same earthquakes. Fig. 9 shows the observation results from these stations. In the figure the results are respec- tively numbered in sequence of date of earthquake events for each station but the same numbers are used for records by the same events. In the case of the epicentral distance

of 5.2 km the ratios A /A, which are obtained from earthquake magnitude of 3.6 to vmax nmax

5.0 are fairly well scattered. Comparing the results at both stations from the same earthquakes, the ratios are similarly over 1.0 for the event No. 5 and less than 0.5 for the event No. 9. Fig. 10 shows the observation results at several stations during a great earthquake (1968 Tokachi-oki earthquake, Magnitude: 7.9). In the figure the ratios A /A, tend to scatter, even though they were recorded at stations of similar epi- vmax hmax

central distance. Phase Difference Between Maximum Vertical Acceleration and Maximum Horizontal Acceleration

According to the strong-motion accelerograms, it appears that the occurrence time of the maximum horizontal acceleration does not usually coincide with that of the maximum

vertical acceleration. Therefore, discussion based on the maximum accelerations of both

components is to be presented toward the most extreme case in which both of the maximum

accelerations occur at the same time. This assumption is on the safe side from the view- point of design. But, for rational earthquake resistant designs it is desirable to make

clear by the observed data whether both the maximum accelerations occur at the same time

or not. The following investigation is performed on the ratio of the vertical acceleration

to the horizontal acceleration (A /A, ) when the structure becomes the most unstable. v h

In order to make the problem simpler, a stability of a rigid block on a solid plane

is analyzed by the seismic coefficient method. A resultant force due to gravity and seismic force, and its direction are expressed by the following equations, 7

(i±v 2+ R = mg / (1+kJ +kvv

(1)

K = tan 9 = Y^k~ (2) — v

R = resultant force acting on the block m = mass of the block

g = acceleration of gravity

k = seismic coefficient in the vertical direction

seismic coefficient in the horizontal direction K = resultant seismic coefficient

8 = angle between directions of resultant force and gravity

IV-4
The block becomes more unstable with increase of the resultant seismic coefficient. From

the digitized records listed in Table 3 the resultant accelerations of the two components

in the horizontal direction are calculated and the resultant seismic coefficients at each

instant are obtained from the equation (2) , in which the resultant acceleration in the

Ihorizontal direction and the vertical acceleration are introduced. When the resultant

seismic coefficient becomes maximum, the block is in the most unstable condition against

sliding and overturning. Fig. 11 shows the vertical acceleration (A^) and the horizontal

acceleration (A^) for this maximum condition. Usually maximum resultant seismic coefficient

occurs when the horizontal acceleration is almost maximum but the corresponding vertical

acceleration is not so large. If the difference of the occurrence time between A and vmax Vis taken into consideration, the ratios A /A, become almost less than 1/3. ax vmax hmax Frequency Characteristics of Vertical Acceleration

Fourier spectra and response spectra of the digitized records are calculated. In this case the minimum epicentral distance is 14 km, and then the records from the near

epicentral area are not included. Judging from Fourier spectra of 20 records out of total

25 records, it was not found that the vertical motion may contain higher frequency components in comparison with the horizontal motion. As an example of the results the spectra

of the three components having similar shape are shown in Fig. 12. Response spectra for relative displacement, relative velocity and absolute acceleration are also calculated. According to the calculation the spectra of the vertical component and the horizontal

components are almost similar in shape exept 6 records out of 25. Fig. 13 shows a typical example of the absolute acceleration spectra similar in shape and Fig. 14, an example of

the spectra different in shape. Owing to the limited number of records available, it is not recognized that there were any particular influences by subsoil conditions and earthquakes on spectra. Accelerograms at Wakayama Port on March 30 , 1968 Strong-motion accelerograms shown in Fig. 15 were recorded at Wakayama port (epicentral

distance: 5.2 km, Subsoil condition: group B) in Wakayama city during a local earthquake

(magnitude: 5, focal depth: 0 km) on March 30, 1968. The maximum acceleration of N-S component was 176 gals, 253 gals in E-W component and 405 gals in vertical component. Notable feature of the record was very large vertical acceleration in comparison with the horizontal acceleration. Although the principal part of the vertical component did not

come out clearly in Fig. 15, it consisted of fairly high frequency components of about 20

Hz. The maximum accelerations both in the vertical and the horizontal directions occurred

at different instants, that is, the horizontal acceleration was about 25 gals when the maximum vertical acceleration occurred and the vertical acceleration was about 40 gals when the maximum horizontal acceleration occurred. What is specially noteworthy is the fact that none of the facilities at Wakayama port

were damaged by the earthquake in spite of the fairly large acceleration on the vertical

component and the relatively large acceleration on the horizontal components. It is con- sequently recognized that the earthquake motion with fairly high frequency components and

IV-5
the different occurrence time on the maximum accelerations both in the horizontal and in I

1,

vate

slic

vert

the vertical direction do not have so much influence on the stability of the structures. INFLUENCE OF VERTICAL ACCELERATION ON STABILITY OF GRAVITY TYPE STRUCTURES

Influence on Safety Factor Against Sliding for Rigid Block When both the horizontal and the vertical accelerations exist, a safety factor against

sliding for such a rigid block as concrete caisson on a firm ground is expressed by the following equation,

(1-k )

where SF = safety factor against sliding

= coefficient of friction between block and ground

k^ and k^ = seismic coefficients in horizontal and in vertical direction, respectively

Three kinds of situations are considered for the calculation of safety factors against

sliding for block. In the first situation, only the horizontal seismic coefficient corresponding to is taken into consideration. The second situation is when the safety factor is the minimum value by the equation (3) in which the seismic coefficients

are equivalent to the resultant horizontal acceleration and the vertical acceleration in each instant. In the third situation, the safety factor is calculated by the equation (3) in terms of the seismic coefficients corresponding to A, and A . For the comparisons hmax vmax

of safety factors in three situations, Aj^^ is normalized as 250 gals and the coefficient

of friction is assumed to be 0.6 for all cases.

If the safety factor in the second case is assumed to be rational for the stability

analysis of structures during earthquake, the safety factor in the first case is over- estimated about 4% and is underestimated about 5% in the third case. These results, though obtained in the particular conditions will provide some information on the influence

of the vertical acceleration on the stability of structures. Influence on Stability of Gravity Type Quaywall Referring to the investigation mentioned above, the influence of the vertical acceleration on the stability of gravity type structures will be discussed with the aid of the present design procedures. The gravity type quaywalls are selected for discussion. In the present design procedures of port facilities (5) the seismic coefficient in the vertical direction is not considered. This conception is not based on the investigation

of the earthquake records but on the empirical judgment that the effects of the vertical acceleration on the stability of structures will be compensated by applying a proper value of seismic coefficients in the horizontal direction. Therefore, safety factors considering

the vertical seismic coefficient will be examined using the present design procedures. Model quaywalls are shown in Figs. 16 and 17. One is a common size of wall with a water depth of -5.5 m, the other is a relatively large wall with a water depth of -12 m. In the stability analysis the horizontal seismic coefficient are changed as 0.15, 0.10 and

IV-6
0.05, and the vertical seismic coefficients are fixed as one half of the horizontal one in both the upward and downward directions. Such design conditions as crown height, sea water level, angle of friction of backfill soil, surcharge, ratio of width to height of caisson and residual water level are also changed in several ways. Safety factors against

sliding and overturning, and bottom reaction are calculated, and their changes due to the vertical seismic coefficient are also examined. According to the analysis, the vertical seismic coefficient acting in the upward direction reduces the safety factors and the rate of reduction of the safety factors increases proportionally with increase in the horizontal seismic coefficient. For example, safety factors in which the vertical seismic coefficient are considered decrease 1.5% in the case of the horizontal seismic coefficient of 0.05 and 10% in the case of 0.20 in comparison with the cases in which the vertical seismic coefficient is not considered.

These rates of the reduction of safety factors remain unchanged, even if the design parameters except the horizontal seismic coefficient are changed. It is indicated that bottom reactions vary complicatedly with the direction of the vertical seismic coefficient

and other design parameters. The rate of change of the safety factors is commonly within

several percents, but in special cases it changes up to 20% for the structure with a safety factor of 1.0 against sliding. This discussion is limited to the particular condition in which the vertical seismic coefficient is one-half of the horizontal one. But the influence of the vertical motion

on safety factors and bottom reaction will certainly decrease in the case when the difference of occurrence time between A, and A is taken into consideration. From the hmax vmax

analysis above, it will be concluded that the vertical component of earthquake motion may

give only a small variation, less than several percents, in safety factors for gravity

type structures, and in the practical design it is possible to compensate this degree of

small variation by applying a proper value of horizontal seismic coefficients. CONCLUSIONS

1) According to the accelerograms of the maximum horizontal acceleration of more

than 50 gals, the ratio of the maximum acceleration on the vertical component to that on

the horizontal component (greater acceleration on the resultant of two horizontal components) is less than 1/2.

2) Any significant relationship can not be found between the ratio of the maximum

vertical acceleration to the maximum horizontal acceleration and the factors such as maximum horizontal acceleration, epicentral distance, magnitude of earthquake and subsoil conditions at the sites.

3) The ratios of the maximum vertical acceleration to the maximum horizontal acceleration are fairly scattered in the accelerograms which are recorded at stations during

earthquakes with almost the same epicentral distance and the same magnitude.

4) The occurrence time of the maximum acceleration on the horizontal component is different from that on the vertical component. At the time when the safety factors against

IV-7
sliding and overturning for gravity type structures are the smallest, the ratio of the vertical acceleration to the horizontal acceleration is less than 1/3.

5) Fourier spectra and response spectra of the vertical component and the horizontal components of the earthquake motions in which epicentral distances are more than 14 km show almost similar frequency characteristics.

6) During a local earthquake near Wakayama city on March 30, 1968, the accelerogram

with the vertical component of 405 gals was recorded at Wakayama port with the epicentral distance of 5.2 km. Inspite of the fairly large vertical acceleration, none of the facilities at the port were damaged.

7) Using the present design method for harbour structures, the stability analysis

for gravity type quaywalls was performed in order to examine the effect of the seismic coefficient in the vertical direction. So far as the quaywalls investigated herein are concerned, the vertical seismic coefficient has not so considerable influence on the stability. ACKNOWLEDGEMENT

This report is indebted to the fruits of projects on observation of strong-motion

earthquakes. The authors wish to express their thanks to persons concerned in the networks on the Port and Harbour Research Institute and the Public Work Research Institute. REFERENCES

(1) Tatsuo Uwabe, Setsuo Noda and Eiichi Kurata: Characteristics of Vertical Components of Strong-Motion Accelerograms and Effects of Vertical Ground Motion on Stability of Gravity Type Quay Walls, Report of the Port and Harbour Research Institute, Vol. 15, No. 2, June 1976, pp. 289-317.

(2) Annual Report on Strong-Motion Earthquake Records in Japanese ports, Technical Note

of the Port and Harbour Research Institute, Ministry of Transport, No. 10, No. 15, No. 55, No. 62, No. 64, No. 80, No. 98, No. 100, No. 116, No. 136, No. 160, No. 181, No. 202.

(3) Strong-Motion Earthquake Records from Public Works in Japan, Technical Memorandum of Public Work Research Institute, Ministry of Construction, No. 430, No. 641, No. 718,

No. 815, No. 913, No. 967.

(4) Satoshi Hayashi, Hajime Tsuchida, Eiichi Kurata: Average Response Spectra for Various

Subsoil Conditions, Third Joint Meeting, U.S. -Japan Panel on Wind and Seismic Effects,

UJNR, May 1971.

(5) Design Manual of Harbour Structures in Japan, The Japan Port and Harbour Association, April 1967.

IV-8
Table 1 Number of Accelerograms

Max. acceleration

range in gals Number of accelerograms

PHRI

(Mar. 1963 - Dec. 1974) PWRI

(Jan. 1968 -Dec. 1973) Total

10 - 20 135 103 238

20 - 50 106 114 220 over 50 53 63 116 Total 294 280 574

Table 2 Specifications of SMAC-B2 accelerograph

Number of elements

Na tura

1

period of pendulum

(sec)

Damping

constant Sensitivity

(gal /mm) Max. recording

accelera tion

(gals)

2 in horizontal

1 in vertical

0.14 critica

1

damping

12.5 500

Recording

system Recordingspeed

(mm/ sec)

Recording

time

(min)

Timing

(sec)

Dimension

of instrument

(cm) Scratching

stylus paper10 3 1 54 x 54 x 37

Table 4 Stations classified by subsoil condition

Group Subsoil condition Station

A Rock, very dense granular

layer with N value of over 50

Miyako-S, Kashima-S, Kushiro-S, Koken-S, Ofunado-bochi-S , Akita-S

B Sandy, silty and clayey

layer with medium density

except group A and C

Muroran-S, Hachinohe-S, Shiogama-S, Tomakomai-S, Shiogamako jo-S , Onahama-S,

Chiba-S, Keihinji-S, Shinagawa-S, Yamashitahen-S , Tagonoura-S, Shimizuko jo-S

,

Kinuura-S, Nagoyazokan-S , Yokka ichi j i-S

,

Yokaichichitose-S , Kobeji-S, Hiroshima-S,

Kochi-S, Hososhima-S, Kanazawa-S, Sakata-S, Wakayama ji-S , Tsuruga-S, Ofunado-S, Kashina ji-S , Okitsu-S

£ j Loose sandy layer with N value of less than 5. Aomori-S, Kagoshima-S

IV-9
O 00 <J -i o

o o o o o

O O lo o

m o vo <r

(N N (M H

<f <r <r oCO IT\ \0 ^ n n m 4 r-- i— r^- I—. i~~ O C7> O 0\ On CT* 0> CT*

cn to [/i in w

co o m o

nO

05 O) to to co to

IV-10
200 300400500 1000 Fig. 1 Relationship between max. vertical acceleration (A^,^) and max. horizontal acceleration (Au m.„)

1 1 Vx ^ 10 gal

r ,',,'] Vvw 2 50 gal \mx 2 100 ?al

Fig. 2 Frequency distribution of ratios of

max. vertical acceleration to max. horizontal acceleration (Aynax/A^gx)

IV-11
°I67

1

1

I 1

-

-

;

•

•

'

' .**•••.' *

°

2 5 10 20 30 40 50 100 500 Id

Epicentral distance (km) Fig. 3 Distribution of ratios of max. vertical acceleration to max. horizontal acceler- ation (Aymax/Ahmax) to epicentral distance

'

1

' Mil

llll

1

j

Epicentral distance (km) Fig. h Distribution of ratios of max. vertical acceleration to max. horizontal acceler- ation (Ayroax/Ahjnax) to epicentral distance, Ahmax ^50 gals

IV-12
4 5 6

Mmnitide Fig. 5 Distribution of ratios of max. vertical acceleration to max. horizontal acceler- ation (Avmax/Ahmax) to magnitude of earthquake

Group A

1

:

i i i

/ a*

f \

I 5 10 50 100 500 1000 W (6AL) Fig. 6 Relationship between max. vertical

acceleration (Ay^y) and max. horizontal acceleration (Ahmax ) , for Group A

IV-13
1000

500

' 5 10 50 100 500 W (GAL) Fig. 7 Relationship between max. vertical acceleration (Ay^y) and max. horizontal acceleration (Ahmax ), for Group B

I0O0

500

Group 'INc

1

! '

\\

t 50

Fig. 8 Relationship between max. vertical acceleration (A^,^) and max. horizontal acceleration (A^.^), for Group C IV-14
Wakayama-S station (PHRI)

KlNOKAWA-OHASHI STATION (r\fll)

5 10 50 100 500 1000

Epicentral distance ( km) Fig. 9 Ratios of max. vertical acceleration to i horizontal acceleration (A^*/

hmax ) at Wakayama-zi-S station

1 1 1 1 1 1

1 1 1

1

1 1 II 1

1 111!

Subsoil condition

* Group A

x Grou B a Group C • by PW Rl

•

•

*• .1

1 1 1 1 1

•

1 1 Li. 2 5 10 50 100 500 1000

Epicentral distance ( km

)

Fig. 10 Ratios of max. vertical acceleration to max. horizontal acceleration (Ay^x/Ah^x) during Tokachi-oki earthquake in 1968

IV-15
I 5 10 50 100 500 1000

A, (GAL) Fig. 11 Relationship between vertical acceleration (Ay) and resultant horizontal acceleration (A^) corresponding to max. resultant seismic coefficient

S-578 N-S S-578 E-W S-578 U-D

2 3 4 S FREQUENCY (HZ)

fig. 12 An example of Fourier 6pectra similar

in shape

IV-16
IV-17
gal r250 £

125 h,.

1 sec

125 L 25o i w

gal250

125 t

125 "«

( S—2 6 5, WAK AY AM A J I — S. 0 4 .0 4 ..n MARCH 30.1968

Fig. 15 Accelerograms recorded at Wakayama port

IV-18
McdelA

0=30"

Fig. 16 Cross section of gravity type quaywall,

sea water depth of -5.5 m

Model B

Fig. 17 Cross section of gravity type quaywall,

sea water depth of -12 m

IV-19
Developments in Strong-Motion Data Management

A. GERALD BRADY

U.S. Geological Survey, Menlo Park, California

ABSTRACT

Some recent developments in the procedures for digitization and subsequent analysis of strong-motion earthquake accelerograph records are described. The standard digitizing and analysis procedures of the California

Institute of Technology's Earthquake Engineering Research Laboratory have been

well documented for several years now and apply well to the long-duration, high-amplitude recordings that were the main content of the project. This paper provides further descriptive material dealing with the care needed in using standard analysis procedures on records which cannot be described as standard. In particular, short duration records, where except for a few peaks the amplitudes are low, have noise problems that can only be reduced

by considerable reduction of the frequency range containing valid data. The Seismic Engineering Branch of the U.S. Geological Survey, in continuing

the digitization and analysis of significant records, has modified the standard procedures where experience has shown such adjustments are necessary,

and plans to make further modification where appropriate.

INTRODUCTION Strong-motion earthquake accelerograph records have been digitized with various techniques since significant ones were first recorded. A detailed description of the methods used over the years up to the present day would show the gradual improvement in digitizing during this time, indicative of the concern amongst users of this data for the extraction of the maximum amount of information. This quest continues, and indeed it is obvious that any report describing "current" techniques under such circumstances must be expected to appear immediately out of date to some readers. The digitizing of records

has been carried out, in the main, in order to analyse them more thoroughly then can be KEYWORDS: Accelerograms, Digitization, High Frequencies, Low Frequencies

IV-20
done by visual study. Of interest has been the time history of ground velocity and displacement, the frequency content of the different bursts of energy in the record, and

the effects on simple idealized structures assumed to be excited by the ground motion,

and portrayed in response spectra.

By the early 1960's it was realized that the results of most analyses of digitized

records depended to an appreciable extent on the individual technique of the people doing

the digitizing and planning the subsequent computer analysis. A comparative digitizing

effort, carried out by research staff at Caltech, U.C. Berkeley, the University of

Michigan and the University of Illinois, clarified a number of points pertaining to the digitizations and analyses. 1 At that time parabolic corrections were made to the accelerations, and calculations of displacement showed up the dependence of these displacements on the details of the computing techniques. Response spectra calculations

were also shown to depend on such parameters as the integration step length and the record duration, as well as the obvious basic dependence on the digitizer of the original

record.

In 1968 Caltech's Earthquake Engineering Research Laboratory embarked on a digitization and analysis project whose main goal was to provide data in digital form

by standard procedures developed over the early stages. Reports2 and magnetic tapes containing the data from 381 digitized records were distributed throughout the country

and to some overseas destinations, and their use attest to their acceptance. Procedures

are fully described in the reports for digitization of the various types of records making up the total, and for routine analyses. These standard analysis procedures

include the following:

1. Preparation of uncorrected scaled data by making use of time marks and fixed traces where available.

!a. G. Brady, "Studies of Response to Earthquake Ground Motion,'' EERL Report,

Calif. Inst, of Tech., Pasadena, Calif. (1966)

2 "Strong Motion Earthquake Accelerograms," Vol. 1, Part A (Report No. EERL 70-20),

Vol. II, Part A (Report No. EERL 71-50), Vol. Ill, Part A (Report No. EERL 72-80),

Vol. IV, Part A (Report No. EERL 72-100), Calif. Inst, of Tech., Pasadena, Calif. (1970-1972)

IV-21
2. Preparation of corrected data by making use of the instrumental constants in an instrument correction, and by removal of high frequency and low frequency

noise in a band pass filtering operation.

3. Calculation of response spectra for five different values of damping and over

a frequency range equal to that of the pass band used in the correction stage.

4. Calculation of the Fourier amplitude spectrum of the record by use of Fast Fourier Transform techniques.

Many countries in seismic areas of the world have similarly embarked on the planning and installation of instrumentation networks and have subsequently developed analysis techniques for use on those significant records that they have recovered and digitized.

The Caltech project has frequently been used as a standard guide for these endeavors and

has served well in this capacity when care has been exercised in transferring the procedures to the users particular circumstances.

DIGITIZATION

An appreciable amount of information can be obtained from the record before any digitization attempt. Peak values of acceleration can be scaled off, using the sensitivity of an individual transducer's mechanical and optical properties. The total duration of the instrumental record can be determined from the time marks. The duration of various levels of strong-motion can be determined, such as the length of time between

the first and last amplitudes of 100 cm/sec 2 (or O.lg). In some cases where the instrument has been triggered by the first vertical accelerations reaching it, (P waves),

and the horizontal components show S wave arrivals clearly, then S-T times can be read off for use in epicenter determinations and other travel time calculations. Engineering uses of accelerogram records prior to digitizing is limited to the investigation of upper story records where modal vibrations of a structure become apparent, particularly after the first transient motions have dissipated. Some preliminary estimates of mode shapes, depending on the number of records throughout the height of the structure, and of their natural frequencies, can be made. This allows calculation of base shears and overturning moments during normal mode vibrations as they occur during earthquake excitation.

IV-22
For computer analysis of the dynamic behavior of buildings during base input motion,

ground motion records must first be digitized. The records from upper levels of structures must be digitized if a detailed computer investigation is required of building

motions, stiffnesses and mode shapes. Also, for investigations that require the integration of carefully prepared accelerations, for velocity and displacement time histories, the original accelerations need digitization.

High Frequency Considerations of Hand Digitizing

Hand digitizing refers for the time being to moving a cross-hair by hand, following

a trace, and selecting individual points whose coordinates are recorded automatically

'when signalled by the operator. Subsequent computer programs, which assume that the traces are straight lines between elected points, demand that among the points chosen are

! all the local peaks and all changes of slope. In order that the same control on high frequency noise can be maintained throughout the duration of the digitized record the average density of selected points must be kept up in the weak-motion portions to the

i level maintained in the strong-motion portions. 3 The following line of reasoning can now be applied to the further analysis of this

raw data. Suppose for the sake of an example that the average digitizing rate of a particular trace corresponded to 50 points per second of record time, chosen because

25 Hz content was seen to be present and capable of digitizing. Portions of the record

that contained 20-25 Hz signals would be digitized just at the peaks, i.e., two points

per cycle, while signals at the 10 Hz frequency level would be identified with approximately 5 points per cycle. Lower frequency content, appearing smoother in the record,

would be well-defined with many points per cycle. For analyses that required the highest

accuracy, i.e., maintaining the accuracy already present, equal-step interpolation must

be performed at a Aac equal to the least count of the digitizing machine. Otherwise,

peaks will be missed during interpolation. However, a compromise must be reached because

data of this density is too large in volume to handle. The compromise must consider the

fact that the final data, in order to portray accurately the 25 Hz content originally

3 J. B. Berrill and T. C. Hanks, "High Frequency Amplitude Errors in Digitized Strong

Motion Accelerograms," in "Analyses of Strong Motion Earthquake Accelerograms", Vol.

IV, Parts Q, R, and S, Report No. EERL 74-104, Calif. Inst, of Tech., Pasadena,

Calif. (1974)

IV-23
seen, must be at a density that offers approximately 6 points per cycle, and therefore

150 points per second. The 25 Hz content could be satisfactorily represented with 50 points per second only if each time the 25 Hz waves appeared they were always in phase with each other and their peaks occurred at multiples of 0.02 sec. This of course is never the case.

If 25 Hz is the highest frequency that can be seen and digitized, the digitization

at an average density of 50 points per second will contain unacceptable digitization

noise at frequencies above 25 Hz and low-pass filtering at 25 Hz is called for. Main- tenance of a final data density of 150 points per second is still required.

The compromise between data density and the accuracy of peak values leads to some confusion when comparisons are made^ between the maximum acceleration of a record when scaled off the original (or off the raw digitized data) and the maximum acceleration

after correction. If the correction procedures have required interpolation at a density

with Ax greater than the least count of the machine, then it is probable that this scaled peak will be lost, and a lower peak value will result. As an example, with

records containing 12-16 Hz components, whose peak accelerations occur in this frequency

range, corrected data with At = 0.02 sec have had peak values in the range of 0.75 to 0.3 of the uncorrected peak values.

High Frequency Considerations for Machine Digitizing

Various other possibilities of selecting points are available and in use on some digitizing systems. Although the cross-hair is moved by hand along the trace in question,

the automatic relaying of points into some storage device can take the form of a set number of points transferred each cm in the X-direction (i.e., Ax , or At kept constant)

or a set number of points transferred each second of real time (in which case Ax or At

depends on the speed of the operator following the trace). Totally automatic digitizing can be of two principle types. The first consists of automatically scanning the entire recorded film and measuring the greyness at each matrix

element location, followed by computer analysis to recover the traces. The second consists ^"Strong Motion Earthquake Accelerograms," Index Volume, Report No. EERL 76-02,

Calif. Inst, of Tech., Pasadena, Calif. (1976)

IV-24
of automatically following a particular trace having been given a starting position, and recording X and Y coordinates according to some fixed procedure.

In all of these cases, the procedure can be compared with the description in the previous section on hand digitizing and appropriate measures taken to insure that the quality of the high frequency content remaining in a record is accurately known.

LONG PERIOD ANALYSIS

The baseline correction procedure of the Caltech standard data processing project

removes from the accelerogram all Fourier components with periods longer than an upper

period limit chosen on the basis of careful tests. For the particular equipment used at Caltech, and for the typical records used in the project, namely with sensitivities of 7 to 14 cm/g and with record speeds of the order of 1 cm/sec, this upper limit was about

14 seconds. A filter was developed with a cut-off period of 14 sec and roll -off term- ination at 20 sec - the corresponding frequencies are 0.07 and 0.05 Hz. Subsequent

investigations confirmed that for this typical Caltech data the errors in the 14 or 16 second components could be up to 4 cm of displacement, while errors in the 8 second components were of the order of 1 cm of displacement. 5 Shorter periods had correspondingly smaller errors. These displacement errors were apparent irrespective of the acceleration amplitudes, which for most of the records in the project were relatively

high - the selection of the records had been originally made on the basis of peak accelerations being greater than O.lg. It has recently become clear that for records of

low acceleration amplitudes, or of accelerations of large amplitudes but corresponding

to small displacement pulses as in records close in to small shocks, or in short records,

some further adjustment of the long period limit is required.

Short Records

Recent experience with records shorter than approximately 60 sec has shown that the upper limit for long periods must be selected with due consideration to record length.

It is not advisable to assume that a satisfactory quantitative measure of the Fourier

5 T. C. Hanks, "Strong Ground Motion of the San Fernando, California, Earthquake:

Ground Displacements," Bull. Seis. Soc. America, 65, 1, p. 193 (1975)

IV-25
components with periods longer than 1/4 or 1/3 of the total record length can be obtained

from any record. Consequently, for records shorter than 60 sec, revised cut-off and

roll -off termination periods must be used. A suitable choice has been found to be the restriction of periods retained in the corrected data to 15 seconds or 1/4 of the record

length, whichever is smaller.

Records With Small Displacements Treatment of the long period limits in this case is rather obvious, after a few trials are run on any particular record. The long period limit must be chosen so that

the errors in the displacement at this long period are negligible when compared to the actual displacements expected when the accelerogram is integrated twice. For an 8 cm/g sensitivity, use can be made of a table such as the following in order to estimate the longest period to retain: longest period retained (sec) 16 8 4 2 1 Expected errors in displacement (cm) 4 1 .25 .06 .015 The required ground displacements from a filtered accelerogram should be, say, 10 times

these expected errors in order that the displacements retain an acceptable signal to noise ratio. Adjustments to these figures can be made for instruments with different sensitivities, and recorder speeds different from 1 cm/sec, and further adjustments of the long period limit can subsequently be made if desired in order that resulting displacements compare favorably, in amplitude and frequency content with actual displacements predicted on the basis of seismological studies.

CONCLUSIONS

This paper has discussed the areas in which it is appropriate to make some changes

in the standard data processing of strong-motion earthquake records. Included have been

the following conclusions:

Hand digitization of records, (trace following by hand, and points selected individ- ually), in which the highest frequency capable of being examined and digitized is 25 Hz, should be accompanied by computer analyses which treat the data at a density of 150

IV-26
points per second. Careful considerations along similar lines must be given to any digitization that is more automated.

The long period limit for corrected data must, in general, be reduced for accelerograms that are shorter than 60 sec, for accelerograms that have short duration, high amplitude pulses, corresponding to small displacement pulses, and for accelerograms with

generally low amplitudes.

IV-27
ON A METHOD FOR SYNTHESIZING THE ARTIFICIAL EARTHQUAKE WAVES

BY USING THE PREDICTION ERROR FILTER

Keiichi Ohtani and Shigeo Kinoshita National Research Center for Disaster Prevention, Science & Technology Agency

i ABSTRACT

|| Several methods for synthesizing the artificial earthquake waves have been reported

for the purpose of dynamic analysis and earthquake-resistant design of structures. In the present report, the authors discuss a method by using "the prediction error filter," in which there are less numbers of the required parameters than those in other methods and also these parameters are more easily estimated. This method is based on the linear prediction model for the earthquake wave in the time domain. Therefore, parameters by which the prediction error filter is constructed are computed from the sequence of co- variance matrices that represent the characteristics of earthquake waves in the time domain.

I As compared with the methods using the finite Fourier expansion by harmonic functions, this method uses the finite Fourier expansion by uncorrelated random variables, and the filter is designed in the time domain. Also, the number of terms of this expansion is automatically determined by using "An Information Criterion" (AIC) proposed by Akaike. The relationship introduced by the authors for synthesizing correlated multi-dimensional waves show an example of synthesis by using an observed strong-motion accelerogram.

KEYWORDS: Accelerogram; artificial earthquake; covariance; filter; finite Fourier expansio prediction error; random variables; synthesis; wave

; t:

j ti

- it

i tl

t st

i a

s si

ti

'( Ml

f H

ta

i

III

I isi

> itf

1 K

IV-28
INTRODUCTION Mathematical processes of the simulation of various random phenomena have growing

applications. In the field of earthquake engineering, the simulation for strong-motion

earthquake waves provides a valid starting point for the dynamic analysis and the earth- quake-resistant design of structures in seismic regions, and also in playing an important

role in the shaking table tests. Accordingly, several methods for synthesizing artificial

waves have been already reported (1) . The present report discusses a simple method for synthesizing artificial waves by using the prediction error filter, in which required

parameters are fewer than those in other methods and also they are easily estimated. The suggestion that the application of prediction error filter to earthquake wave would be efficient was made in two references (2,3). In the authors' method by using the prediction error filter, a filtered white noise

model is used for generating the artificial earthquake waves as shown in Fig. 1. The procedure is to use the digital computer for generating a random number, to multiply this

by a gain function (i.e., a function of the covariance matrix of final prediction error),

and then to pass the resultant sequence through a linear filter (i.e., the prediction

error filter with the sequence of covariance matrices of a given earthquake wave) . Matrices

F(n,n), B(n,l), in which n=l,...,p, are referred to as the filter parameters, and are required in order to design this filter and to describe the characteristics of the filter.

Also, the covariance matrix S_(p) of final prediction error is required in order to describe

the characteristics of input for the filter. The induction of those matrices and the construction of the prediction error filter are discussed in sections 2 and 3, respectively.

Generally, there are two difficulties associated with the simulation of earthquake

waves. One is that the two horizontal components and the vertical component of observed

earthquake waves are not statistically independent. However, this difficulty is probably

out of the question in this method, because correlations between these components are taken into account by designing the filter from the sequence of covariance matrices. The other difficulty is the nonstationarity of observed earthquake waves, especially because

this method is based on a theory of stationary stochastic process. Assuming the frequency

stationarity , the amplitude nonstationarity is induced by passing the input random number through the time-dependent function of covariance matrix of prediction error, i.e., a shape function in matrix form. On the other hand, the simulation of the frequency nonstationarity is difficult. Putting the filter parameters as time-dependent matrices, the nonstationarity representation of frequency characteristics is theoretically possible.

But, generally, the the time constant of prediction error filter composed from observed

earthquake waves is so large that the simulated waves can not run after the variation of

the original waves. However, a simulation of one dimensional nonstationary process by

using the prediction error filter and the Kalman filtering technique was reported in reference 2. In the present report, the object of the author's study, i.e., the simulation

of multi-dimensional artificial earthquake wave, is bound within the stationary case.

IV-29
INDUCTION OF FILTER PARAMETERS AND COVARIANCE MATRIX OF PREDICTION ERROR

When a linear subspace M(q) is given, the forward prediction of X(k) can be defined

as the projection of X(k) on this subspace. Then, the forward prediction of X(k), _ q

X(k;q) = Z F(q,n)X(k-n) (2.1) n=l

is estimated by solving the so-called forward Yule-Walker equations. q E[{x(k)- Z F(q,m)X(k-m) }x' (k-n) ] m=l

q

= R(n) - Z F (q,m) R (n-m) m=l

= 0, n=l, . . . ,q (2.2) Prediction matrices F(q,n), where n=l,...,q, in Eq. (2.1) are the solution of the above simultaneous equations. Also, the forward prediction error is,

X(k;q)=X(k)-X(k;q) (2.3)

Similarly, the backward prediction of X(k-(q+D),

q

X(k-(q+l) ;q)= E B(q,n)X(k-n) (2.4) n=l

the backward Yule-Walker equations, q E[{x(k-(q+D- Z B(q,m)X(k-m) }x' (k-n) ] m=l

q

= R(n-(q+l)J- Z B(q,m)R(n-m) m=l

= 0, n=l,...,q (2.5) and the backward prediction error

X(k-(q+l) ;q)=X(k-(q+l))-X(k-(q+l) ;q) (2.6)

are obtained as corresponding to (2.1), (2.2) and (2.3) in the forward prediction scheme, respectively. Furthermore, the forward Yule-Walker equations with regard to the subspace M(q+1) are partitioned into the following relations,

IV-30
q+1

R(n) - E F(q+l,m)R(n-m) m=l

R(n) - E F(q+l / m)R(n-m)-F(q+l,q+l)R(n-(q+l))

m=l

= 0, n=l, . . . ,q+l (2.7)

From (2.2), (2.5) and (2.7), we have

q q q

{ E F (q,m)R(n-m) }-{ E F (q+l,m) R(n-m) }-F (q+1 ,q+l) { E B (q,m) R(n-m)

}

m=l m=l m=l

= 0, n=l, . . . ,q+l (2.8)

i.e.,

F(q+l,m)=F(q,m)-F(q+l,q+l)B(q,m) , m=l,...,q (2.9)

Analogously, following relations are obtained in the backward scheme:

B(q+l,m+l)=B(q,m)-B(q+l,l)F(q,m) , m=l,...,q (2.10)

As shown in the next section, the prediction error filter is constructed by using matrices

{F (q+1, q+1), B(q+l,l), q=0,...,p-l} which appeared in relations (2.9) and (2.10). That

is, these matrices are required to construct the filter and are referred to as the filter

parameters. The filter parameters are computed by using the recursive formulae which are

due to Whittle (4)

.

The stochastic characteristics of input for this filter is governed by the covariance

matrix S^(p) of the final prediction error X(k;p) . Although the final prediction error

does not necessarily become a white noise, in general the spectral structure of this error

is so flat that the white noise approximation for this error is possible from engineering

viewpoints. Therefore, the stochastic characteristics of input for the filter is governed

by S (p)

,

S(p)=E [X(k;p)X' (k;p)]

=E[{x(k)-X(k;p) }X' (k)

]

P

= R(0)- E F(q,n)R(-n) (2.11) n=l

IV-31
Actually, the square root of diagonal component of matrix S_(p) is used as a gain function

in the direction corresponding to the diagonal component. Analogously, the covariance matrix of background prediction error is computed. Especially, the covariance of forward prediction error and that of backward one are equivalent in one dimensional case. CONSTRUCTION OF PREDICTION ERROR FILTER

In this section, we will consider the construction of the prediction error filter. As the prediction error filter is based on the wave matching in the time domain, the filter is constructed by using the filter parameters induced in the foregoing section and

the delay operator D. First, the following notations are defined as follows:

F(n,0)=-I, B(n,n+1)=-I, n=l,...,p

By using these notations and the delay operator D, (2.1) and (2.4) become (3.1) and (3.2) respectively.

q X(k;q)=- E F(q,n)Dn

x(k) (3.1) n=0

q+i

X(k-(q+l) ;q)=- E B(q,n)DX(k) (3.2) n=l

From (2.9), (2.10), (3.1) and (3.2), we have the following two relations,

q+1 X(k;q+1)=- E F(q+l,n)D

n

x(k) n=0

=-F(q+l;0)+ E {F(q,n)-F(q+l /q+ i) B (q,n) }Dn+F(q+l,q+l)Dq+1

]X(k) n=l

=X (k; q) -F (q+1 , q+1) X (k- (q+1) ; q)

TV-32
and

q+2 X(k-(q+2) ;q+l)=- E B (q+1, n)

D

n

x (k) n=l

=-D(B(q+l,l)- E {B(q,n)-B(q+l,l)F(q,n) }Dn+D

q+1

]X(k) n=l

=D[X(k-(q+l) ;q)-B(q+l,l)X(k;q)] (3.4)

where X(k;0)=X(k) and X(k-l;0)=DX(k)=X(k-l)

.

Employing Eqs. (3.3) and (3.4) recursively from q=0 to q=p-l, three-dimensional prediction

error filter is constructed as shown in Fig. 2. In this figure, the diagonal component of filter parameters represents the characteristics of the corresponding direction and the off-diagonal one represents the degree of correlation between the two coresponding directions

.

FREQUENCY CHARACTERISTICS OF PREDICTION ERROR FILTER

The more the filter's order increases, the more the spectral structure of the original

wave is absorbed into the filter. In the final order p, the filter has the spectral envelope of the original wave as the characteristics of the filter. The remaining spectral

fine structure is the frequency characteristics of the final prediction error X(k;p)

.

' Namely, if the final order p is determined as such, the final prediction error becomes a

! white noise, and then a white noise with the covariance matrix S_(p) could be used as the input of the filter in this stochastic model. The autoregressive spectrum estimation procedure is used in order to represent the

I frequency characteristics of the filter. Forward prediction matrices, i.e., regression

matrices F(p,n), where n=l, — ,p, are obtained from the filter parameters by using (2.9) and (2.10). From these matrices and the covariance matrix of the final prediction error,

' the spectral envelope of the original wave, i.e., the spectral density matrix P(g), is estimated in the following form (5)

P(g) = ^ A

_1

(z)S(p) [A 0 (z)] _1

, |g|<TT (4.1)

where p

A(z) = I - E F(p,n)z z=exp(ig) (4.2) n=l

The resonance frequency and the damping coefficient of each vibration mode appeared

in every direction components are computed by solving the algebraic equation A(z)=0 in one-dimensional case. In the complex s plain, the frequency response function of the second order system has

IV-33
By the transformation z=exp (sT) =exp ( ig) , (4.3) becomes (6)

H (z)=K exp -huT '- — —

n n n n (z-z ) (z-z*)

cp{ (-h tu +iw /l-h

2 )T}

(4.6)

Accordingly, the transfer function of this system has

|Hn(z)|

2=H

n

(z)H

n

(z1

)

(z-z ) (z-z*

" 1

) (z-z*) (z-(z*)*

1

) n n

(4.7)

In the actual ground motion, each of the direction components of recorded wave has the spectral density function having the product of this type of transfer function. Therefore, taking out the factor of fourth order such as (4.7) from the power spectrum density

function, the resonance frequency and the damping coefficient of each vibration mode are computed. In one dimensional case, the roots of the characteristic equation A(z)=0 are denoted with z , n=l,...,p. Then, (4.1) becomes

S(p) P(g)

2v n |l-z_1

z | 2

(-irs (p)

2TT II Z* (Z-Z ) (Z-Z* ) n n n n n=l

IV-34
Therefore, if the roots of A(z)=0 are z and z*, the factor of fourth order such as (4.7) n n is extracted. Namely, when A(z) is decomposed with the factor of second order and that of first order, the resonance frequency and the damping coefficient of each vibration mode

are computed by using the relation (4.5) and the root of the factor of second order. Solving the characteristic equation A(z)=0, the Bairstow's method is convenient in the numeric computation. In this method, the resonance frequency is exactly estimated, but

the stability and the estimation of the damping coefficient are not expected to be as accurate as the estimation of the resonance frequency. MATHEMATICAL MEANINGS OF PREDICTION ERROR FILTER

By repeated application of (3.3), we have

X(k)=X(k;0) P

= E F(q,q)X(k-q;q-l)+X(k;p) (5.1) q=l

This is a basic equation of the prediction error filter. In this section, a mathematical

meaning of this equation is discussed. By applying the Gram-Schmidt orthonormalization process to a sequence of X(k-n), n=l,...,p and finally X(k), an orthonormal sequence is obtained. The first p orthonormal

random variables are

X(k-n;n-l)

V(n) = ~, n=l,...,p, (5.2)

| |x(k-n;n-l) | |

where

X(k-n;n-l)=X(k-n)-X(k-n;n-l) (5.3)

and _ n-1 X(k-n;n-l)= E (X(k-n) ,V(m) )V(m) (5.4) m=l

Before the final step of the Gram-Schmidt orthonormalization process is applied, it is necessary to find the following relations. Namely, as X(k;n-1) is the projection of X(k) on the n-1 dimensional subspace M(n-l) spanned by the sequence of X(k-m), m=l,...,n-l and

X(k;n-1) is the orthogonal component of X(k) to this subspace, we have the following

relations.

IV-35
n-1 X(k;n-1)= E (X (k) ,V (m) ) V (m)

m=l

i.e.

(X(k;n-1) ,V(m) )=0, m=n,...,p (5.5)

and

X(k;n-l)=X(k)-X(k;n-l)

i.e.

X(k;n-1) ,V(m) )=0, m=l f ...,n-l (5.6)

Applying the final step of the Gram-Schmidt orthonormalization process to X(k), a relation

is obtained,

P

X(k) = E ( (X(k)-X(k;n-1)) ,V(n))V(n)+X(k;p)

n=l

p (X(k;n-1) ,X(k-n;n-D)

= E

- X(k-n;n-l)

n=l | |x(k-n;n-l) |

This expression is the finite Fourier expansion of X(k) by an uncorrelated sequence of vector valued random variables X(k-n;n-l), n=l, ,p and X(k;p)

In one-dimensional case, the norm of X(k-n;n-l) and that of X(k;n-1) are equal, i.e., the covariance of X(k-n;n-l) and that of X(k;n-1) are equal. Then, Fourier coefficients

are equivalent to partial correlation coefficients, i.e.,

X(k)=X(k;p)+X(k;p)

P

= E (X(k) ,V(n))V(n)+X(k;p)

n=l

(5.7)

By using (5.6), this relation is expanded as follows:

(X(k;n-1) ,X(k-n;n-D)

r(n) = (5.9)

| |x(k;n-l) | |x(k-n;n-l) |

IV-36
That is, r(n)=F(n,n) is the partial correlation of X(k) and X(k-n) after the effect of

X(k-m) , m=l,...,n-l has been removed by regression. Also, from (5.9) and Schwartz

inequality, the absolute value of r(n) is less than one and this is the stability condition

of the prediction error filter in one-dimensional case. NUMERICAL EXAMPLE

We first consider how to determine the final order p of the prediction error filter.

In order to determine the order p, the "An Information Criterion" (AIC) proposed by Akaike

is used (7) . The AIC is a criterion for obtaining the maximum information about the dis- tribution of future value obtained from the model. The degrees of freedom for the model's

parameter is determined by using the AIC. In this case, a second order process with zero mean is treated. Therefore, an identical Gaussian process is considered. Then, the AIC

is

AIC (n)=N'ln[det{s (n) }]+2M2n (6.1)

where M is the number of dimension (8) . The order p is the value of n for which the

AIC(n) is minimized.

As an original record for simulation, we used the strong-motion accelerogram at the Golden Gate Park site of San Francisco earthquake (1957.3.22). A numerical computation

was done in two-dimensional case, i.e., X^(k) and X^ (k) which represent the N-S component

and the U-D one, respectively. We employed 300 (=N) samples with 20 msec(=T) from the main

part of accelerogram. Grasping the characteristics of this part, the sample spectral density matrix Kg)

was estimated by the following relation (5)

Kg) = ~ Z(g)Z» (g), |g|<ir (6.2)

where Z(g) is the sample Fourier transform: N

Z(g) = E x(nT)exp(-ign) (6.3) n=l

As the spectral density matrix is a Hermitian matrix, the contents are represented by two diagonal components, and the real part and the imaginary one of the off-diagonal component.

They are shown in Figs. 3-6. In these Figs., the transverse axis is expressed in g/

(

2ttt) Hz. Among these four Figs., Fig. 3 (N-S component), Fig. 5 (co-spectrum) and Fig. 6 (quadrature spectrum) show the distinguished spectral peaks. But, Fig. 4 (U-D component)

shows almost flat spectral structure so that the difficulty of simulation for this component

is expected. A two-dimensional prediction error filter is shown in Fig. 7. The final order p

which was computed from (6.1) was 12 within n=14. Table 1 is the list of the filter

IV-37
parameters obtained by using the recursive formulae which are due to Whittle. The relations

1 <n)-b

1 1 (n), f

3 3^ n ^~b3 3^' n=1 ' 'P are found from this table. In one- dimensional case, this relationship is r(n)=f^ ]_^ n ) =b

j_ -^M > n=l,...,p. Introducing a mathematical model of multi-reflection type, these parameters r(n), n=l , ,p play the role of reflection coefficients. The off-diagonal components of matrices F(n,n), B(n,l), n=l,...,p are so small compared with unity that the degree of correlation between two direction components is not conspicuous. Corresponding to the components of the matrix Kg), those of the estimated spectral density matrix P (g) which represents the characteristics of the prediction error filter, are shown in Figs. 3 to 6. As a whole, the matrix P(g) envelopes the matrix Kg). But, the final order p=12 is so small that the separation of spectral peaks is not sufficient

in the high frequency region. The input for this filter is synthesized by using a sequence of random numbers between

zero and one, i.e., e(n), n=l,.... By using this sequence, two-dimensional independent Gaussian white noise with zero mean and one variance is obtained by the following relations

(9) ,

u(n) = /21n[e(n)] sin (2iTe (n+1) ) , (6.4)

v(n) =V21n[e(n)] cos ( 2ire (n+1 ) ) (6.5)

Taking the covariance matrix £(12) into consideration, the input for this filter is

X

3 (n;p) = /{S(12))

2 2v(n), (6.6)

3^ (nip) = /{S(12)} -{s(12)} 2

2 {S(12) }~ 1

2 u(n) (6.7)

+ {S(12)}

lf2 {s(12)}

2 ^ 2x

3 (n;p)

Fig. 8 shows a sample of synthesized two-dimensional wave during the first four seconds.

In the following four figures, the components of the sample spectral density matrix of the synthesized wave between the five second and the ten second, are shown. As a whole, these components envelope the characteristics of the corresponding components of the estimated

spectral density matrix P(g). CONCLUSION

In the present report we developed a method for synthesizing the artificial earth- quake waves. The method uses a finite Fourier expansion by uncorrelated random variables, while the other methods use the finite Fourier expansion by harmonic functions. As an advantage of this method, the characteristics of the strong-motion earthquake waves are represented by a smaller number of parameters. Therefore, this method would be convenient

to file a large number of strong-motion records.

IV-38
REFERENCES

(1) Hoshiya, M. (1974) : Probabilistic analysis of structural vibration, Kaj ima-Shuppan

.

[in Japanese]

.

(2) Matsui, E., T. Nakajima, T. Suzuki and H. Omura (1972): An adaptive method for speech analysis based on the Kalman filtering theory, Report of the Electrotechnical

Laboratory, 36,3,42-51. [in Japanese].

(3) Riley, D. C. and J. P. Burg (1972): Time and space adaptive deconvolution filters, Presented at the 42nd annual meeting of the SEG.

(4) Whittle, P. (1963) : On the fitting of multivariate autoregressions , and the approximate

canonical factorization of a spectral density matrix, Biometrika, 50,129-134.

(5) Parsen, E. (1968): Multiple time series modeling, Technical Report No. 12, Department

of Statistics, Stanford University.

(6) Jury, E. I. (1964): Theory and application of the Z-transform method, John Wiley & Sons, 298.

(7) Akaike, H. (1974): A new look at the statistical model identification, IEEE Trans. A.C., 19,6,716-723.

(8) Jones, R. H. (1974): Identification and autoregressive spectrum estimation, IEEE

Trans. A.C., 19,6,894-898.

(9) Gold, B. and C. M. Rader (1969): Digital processing of signals, McGraw-Hill, 144-146. GLOSSARY OF SYMBOLS

T: Sampling time

N: Number of sample points

x(n*T), n=l,...,N: Sequence of observed acceleration vectors which are samplized with

the sampling time T

X(n), n=l, ,N: Sequence of vector valued Gaussian random variables with zero mean

M(q): q-dimensional linear subspace spanned by the sequence of X(k-n), n=l,...,q

X(k;q): Projection of X(k) on M(q) X(k;q)=X(k)-X(k;q) : Prediction error of X(k) which is orthogonal to M(q)

E [ ] : Expectation operator

X' : Transpose of X

p: Final order of the prediction error filter

D: Delay operator; d"x (k) =X (k-n)

I: Unit matrix

R(n)=E[X(k)X' (k-nQ, n=0,l,...: Sequence of covariance matrices

S_(q) : Covariance matrix of the prediction error J((k;q) F(p,n), n=l,...p: Forward prediction matrices

B(p,n), n=l,...,p: Backward prediction matrices

F(n,n), B(n,l) n=l,...,p: Prediction error filter parameters

f. ,(n), b. (n) : (j,k) components of F(n,n) and B(n,l), respectively

1 1 k j , k

U: Circular frequency

IV-39
g=coT: Normalized circular frequency, | g |_<TT P(g): Spectral density matrix

z*: Complex conjugate of z A": Adjoint matrix of A

(X,Y)=E[X'Y] : Inner product of X and Y

| |x| |=/(X,X) : Norm of X V(n), n=l,...,p: Sequence of orthonormal vector valued random variables

r (n) , n=l,...,p: Sequence of partial correlation coefficients

AIC ( ) : An information criterion Kg): Sample spectral density matrix

Z (g) : Sample Fourier transform

{u(n) , v(n)}, n=l,...: Sequence of two dimension Gaussian vectors with zero mean

IV-40
f 11 (n) h] | (n) b n

(n) b

31 (n) 0.124 0.5 38 0.749 0.032 0.529

i 1 -0.380 0.183 0.035 -0.264 -0.387 0. 120 0.072

5— -0,112 -0.002 0.015 0,069. -0.116 0.044 -0.007 0.068

-0.098 -0.179

11 -0.02 3 0.117 0.011 -0.077 -0.027 0.033 0.051 -0.080

12 0. 303 -0.017 -0.171 0. 183 -0.079 0.131 -0.181

Table 1 Parameters of two dimensional prediction error filter

white

noise x(k;P) x(k)

gain filter >

t t s(p) F(n,n),B(n,1),

n=1 p

Fig. 1 Filtered White Noise Model

IV-41
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3V-43
IV-44
IV-45
3V-46
IV-47
STATISTICAL ANALYSIS OF STRONG-MOTION ACCELERATION RECORDS Masamitsu Ohashi, Head, Earthquake Disaster Prevention Division

Toshio Iwasaki, Chief, Ground Vibration Section, Earthquake Disaster Prevention Division

Susumu Wakabayashi, Research Engineer Ken-ichi Takida, Research Engineer

All of the Public Works Research Institute, Ministry of Construction ABSTRACT

This paper briefly discusses the present status of strong-motion observation for engineering structures in Japan. Next, it presents the results of the multiple regression

analysis of 301 strong-motion acceleration records to evaluate the effects of earthquake

magnitude, epicentral distance and subsoil condition on characteristic variables of ground accelerations such as maximum horizontal acceleration, time duration of major motion, ratio of vertical to horizontal accelerations, etc. The paper also shows the results of a quantification analysis of average response accelerations obtained from 277-component horizontal acceleration records to clarify the effects of seismic and subsoil conditions on average response spectra. From the analysis performed, empirical formulas which can statistically estimate maximum horizontal acceleration, duration of major motion, and number of zero-crossing in terms of earthquake magnitude, epicentral distance, and subsoil condition, are proposed. Frequency characteristics of horizontal motions and ratios of vertical to horizontal accelerations are evaluated and averaged depending on subsoil conditions. Furthermore, various average response spectrum curves for a linear single-degree-of-freedom system are proposed in terms of earthquake magnitude, epicentral distance, and subsoil condition.

KEYWORDS: Design; earthquake magnitude; epicentral distance; statistical analysis; strong-motion acceleration records.

IV-48
INTRODUCTION

In establishing reasonable procedures for earthquake resistant design of structures,

it seems essential to properly evaluate characteristics of ground motions and structural

behavior during strong earthquakes. A number of strong motion accelerographs are installed

at various engineering structures and on their neighboring grounds in Japan to understand

dynamic properties of ground motions and structural responses. The strong-motion observation network for engineering structures in this country has progressed significantly

after experiencing the Niigata Earthquake of 1964 and the Tokachi-oki Earthquake of 1968. At the present time more than 1,000 sets of strong-motion accelerographs are equipped at structures and on grounds near the structures, and many meaningful acceleration records

are already available. Although the records triggered include those of structural responses,

only the records on ground surfaces are employed in the present analysis. Characteristic variables of acceleration records and response spectral accelerations

of a linear single-degree-of-freedom system computed from ground accelerations are statistically investigated. Records used are classified into four groups, depending on the subsoil

j conditions at the observation stations, from rocky ground to soft alluvial ground. Although there will be a number of factors which affect characteristics of ground

motions, three principal factors might be: earthquake magnitude, geographical situation

of the focal area of a concerned earthquake related to the structural site, and subsoil condition at the site. Accordingly, in this study, characteristic variables of ground

accelerations are statistically analyzed in terms of these three factors. It is expected

that the results of the analysis will give the designer invaluable information when performing seismic design of structures.

The study shown in this paper was performed as one of comprehensive work done in the Aseismic Technology Development Committee established at the Technology Center for National

'j Land Development with a commission from the Public Works Research Institute. The results

from the study are utilized as basic materials in standard design seismic forces and seismic loads of "New Criteria of Earthquake Resistant Design (Draft)," (1,2) proposed by

the Ministry of Construction in March, 1977. OBSERVATION OF STRONG-MOTION EARTHQUAKES AT ENGINEERING STRUCTURES IN JAPAN

In Japan the observation of strong-motion earthquakes for engineering structures was

initiated when SMAC-type accelerographs were developed in 1953. The observation network

has gradually advanced since the experiences of severe structural damages due to the Niigata Earthquake of 1964 and the Tokachi-oki Earthquake of 1968. As of March, 1976, the total number of SMAC accelerographs installed on various structures and neighboring grounds

; is 1048, as shown in Fig. 1 and Table 1. It is believed, however, that additional accelerographs are needed in order to obtain reliable records for major earthquakes which might

take place in any areas of ;this country. At the present time about one third of the installed accelerographs are on the ground

surfaces, and the rest on structures. Fig. 1 illustrates the present network of strongIV-49
motion observation for various structures. These instruments are generally installed by individual organizations such as governmental agencies and private companies which are in charge of construction and maintenance of the structures.

In addition to the stations with strong-motion accelerographs , there are a number of stations where electromagnetic-type seismographs are equipped. Moreover, dynamic behavior of subsoils during earthquakes is also being studied using downhole seismometers at several points (some at depths greather than 100 m) as well as using standard seismometer and SMAC accelerograph measurements on the surface. These studies will provide pertinent information

for establishing seismic design methodology of engineering structures. Records obtained from these field study programs have been published periodically by institutions concerned (3) . Records obtained at port and harbor structures are digitized, analyzed and published at the Port and Harbour Research Institute. Records triggered at highway bridges, tunnels, dams, and embankments are processed mainly at the Public Works Research Institute. Furthermore, records at building structures are treated mostly at the Building Research Institute. Incidentally, in order to promote the strong-motion observation program in Japan, the Strong-Motion Observation Council is established at the National Research Center for Disaster Prevention, Science and Technology Agency, with the cooperation of universities, governmental organizations, public corporations, and private companeis. The council has been preparing a nationwide strong-motion observation program, and also has been publishing

important acceleration records collected from all field studies covering the above-mentioned

structures and others. ANALYSIS OF ACCELERATION RECORDS

A statistical analysis of measured acceleration records was attempted to quantitatively

express characteristic variables of ground motions as functions of seismic conditions and subsoil properties at the observation point. Records analyzed were extracted from the publications issued by the Earthquake Research Institute of the University of Tokyo, the National Research Center for Disaster Prevention of Science and Technology Agency, Port

and Harbour Research Institute of the Ministry of Transport, the Public Works Research

Institute of the Ministry of Construction, and the Railway Technical Research Institute of

the Japanese National Railways.

The present analysis employed those records which were obtained during earthquakes with the Richter magnitude of 5.0 or higher and the hypocentral depth of 60 km or shallower,

and also those records which include at least one record with the maximum acceleration of

50 gals or higher for an earthquake. Records with the maximum acceleration less than 10 gals were excluded. The total number of the records used is 301 (the number of components treated is 3 x 301 = 903) for 51 earthquakes. Factors considered in the analysis are as follows:

(1) Seismic properties: Richter magnitude M, epicentral distance A (km)

(2) Subsoil conditions: Observation stations are classified into the following four groups depending on subsoil conditions, with reference to the stipulation in "Specifications for Earthquake Resistant Design of Highway Bridges," Japan Road Association (5,6). IV-50
1st Group: Rock

2nd Group: Diluvium

3rd Group: Alluvium (Except the 4th Group) 4th Group: Soft Alluvium

The definition of this classification is described in Table 2. Characteristic variables of acceleration records:

(a) Absolute maximum horizontal acceleration (larger value of two perpendicular

horizontal motions): Hmax

<gals)

(b) Period of vibration about the time when acceleration becomes H : T, (sec) max 1

(c) Duration of major motion: T,(sec)

a

(d) Ratio of vertical to horizontal accelerations: v=V /H max max

(e) Number of zero-crossing during the time interval of T^:

(f) Mean period of vibration during the time interval of T,: T =2T/N

d m d z The determination of the above characteristic variables are illustrated in Fig. 2. Each of the characteristics values (expressed as X below) was assumed to be represented

by the following two types of expressions:

Type-1: X = a

1 «10b

lM«A

C

l (1)

(2)

where X = characteristic value (namely, H , T, , T , , N , and T ) max 1 d z m

M = earthquake magnitude on the Richter scale

A = epicentral distance (km) a

l' ^1' °1' a

2' ^2' °2 = constants f°r eacn characteristic value

The analysis was conducted for five different cases, namely four groups of subsoil conditions plus the average subsoil conditions including the entire data. In determining

the expressions for H , only eq. (1) was investigated and the term A in eq. (1) was

max

substituted by (A+A

Q

) , where A

Q was taken as 0, 10, 20, 30 and 40 km. Table 3 indicates the distribution of 301 records used in the analysis. Table 4 shows formulated regression equations and correlation coefficients. These are obtained

from the analysis based on the multiple regression analysis. The table shows the results

for three characteristic values H , T, and N , and it is seen that multiple correlation max d z coefficients are greater than 0.5. Since correlation coefficients for expressions of Type-1 were generally greater than those for Type-2, the results for only Type-1 were

generally greater than those for Type-2, the results for only Type-1 are shown in the

table. Although the correlation coefficient was the largest in the cases of A

Q=10 km among the five cases analyzed (Table 3), Hmax

equations in Table 4 were for the cases of

A =0 for simplicity. Figs. 3(A) to (E) illustrate the expressions for H in the cases

0 max

of Ag=0 as functions of M and A for the four groups of subsoil conditions and the average

subsoils.

IV-51
As for the other three characteristic values T, , v and T , the multiple correlation

1 m

e coefficients are found to be less than 0.5. This means that there is no distinct relation

among these values and M and A. For these variables the mean values and the standard deviations are evaluated, and are listed in Table 5. The results of the analysis described above may be summarized as follows:

(1) The maximum horizontal acceleration (H ). the duration of major motion (T,), and the max * d number of zero-crossing (N^) can be approximately expressed as functions of earthquake magnitude and epicentral distance, as shown in Table 4.

(2) The maximum horizontal acceleration ( H

maj{

) becomes larger as the earthquake magnitude

(M) increases and the epicentral distance (A) decreases. The average values of Hmax

for M=8 and A=50 km are estimated to be 130, 270, 200 and 400 gals for rock, diluvium,

alluvium, and soft alluvium, respectively. The corresponding values of Hmaxfor M=8

and A=100 km are estimated to be 85, 150, 110 and 200 gals. The decrease in Hmax values with increase in the epicentral distance is not considerable for rock compared with the other three subsoils.

(3) The duration of major motions (T^) defined in Fig. 2 becomes greater as the earthquake magnitude (M) increases and as the epicentral distance (A) increases. Fig. 4 (A) and

(B) show the relation between A and T„ for M=8, and the relation between M and T, for

d d A=100 km, respectively. It is seen from those results that the duration of major motions is between 10 and 30 seconds for ground motions of earthquakes with the Richter magnitude between 7 and 8 at the epicentral distance of 100 km.

(4) The relation between the number of zero-crossing (N^) and the epicentral distance (A) is considerably affected by subsoil conditions. The value of increases with

increase in A for harder grounds such as rocky and diluvial soils. For softer soils,

it seems that N

z is affected by M, but not by A. The number of repetitions of major motions (N) , which can be approximately N

z/2, is 30 to 100 for various subsoil conditions

(5) The period of vibration about the time of H occurrence, T, , the ratio of vertical max 1

to horizontal acceleration, v, and the mean period of vibration during the major

motion, T , are not clearly related with M and A. The following two points, however, m

can be seen from Tables 4 and 5.

(a) The mean values of T, and t become larger as the subsoil condition becomes

1 d softer. This tendency is obvious for soft alluvial soils. The ratio of T^ to T varies from 1.20 to 1.26, and these ratios are nearly constant irrespective m

of the subsoil conditions.

(b) The mean values of v being 0.32 to 0.34 are not strongly affected by the subsoil conditions. Since the standard deviation is in the range of 0.15 to 0.21, it may be reasonable to assume that the vertical acceleration is equal to one-half of the horizontal acceleration for design purposes. Fig. 5 illustrates an example of the relationship between A and v. In the figure the mean value of v

is equal to 0.32.

IV-52
ANALYSIS OF EARTHQUAKE RESPONSE SPECTRA

The Port and Harbour Research Institute, the Ministry of Transport and the Public

Works Research Institute, the Ministry of Construction have been conducting response

spectrum analysis for major ground motions obtained at various ground conditions during

moderate to strong earthquakes (7,8). The present analysis discusses the results of the response spectra analysis performed at the two Institutes for 277 horizontal components of

ground motions, which were triggered during 68 earthquakes with the Richter magnitude

between 4.5 and 7.9 and the hypocentral depth of 60 km or shallower. Factors considered in the analysis are as follows:

(1) Seismic properties: Earthquake magnitude on the Richter scale M, and epicentral

distance A km.

(2) Subsoil conditions: Observations are classified into four, in the same manner as they were in the previous section. (See Table 2 for the definition of the classification of subsoils.)

(3) Characteristic variables of acceleration records and their response spectral values:

(a) Maximum horizontal acceleration (two perpendicular components for one record)

:

A (gals) max

(b) Absolute response acceleration: S^ (gals), which is computed from digitized

values of triggered records by assuming a linear viscously damped single-degree-of- freedom system with the natural periods T of 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4,

0.5, 0.6, 0.7, 0.8, 0.9, 1, 1.5, 2, 2.5, 3, and 4 seconds and the damping ratio h of 5% of critical.

the analysis assumes the following:

Lysis can be applied to the estimat: of earthquake magnitude M, epicentral distance A, and subsoil conditions S, by assuming an expression as

log.. S = C(M) + C (A) + C(S) (3)

C(M), C (A) , and C(S) = weighting functions depending on M, A, and S, respectively.

terms of the three factors used above by assuming an expression,

IV-53
where

C (M) , C (A), c' (S) = weighting functions depending on M, A, and S, respectively. Classification of 277-component records employed in the analysis is shown in Tables 6 and 7. Magnitudes M in the tables are irregularly divided into five groups with consideration of the scatter in the data used and also convenience of practical application of the results. Table 8 shows the results of the quantification analysis for S^, and lists the ranges

of the weighting functions C(M), C(A), and C(S) in Eq. (3). The table also gives the multiple correlation coefficients of these three functions. Furthermore, Figs. 6 to 9

estimated from the quantification analysis are tabulated. From these two types of information, the acceleration magnification factor 8 (= S /A ) can be evaluated. The values of A max

: be used for the estimation of the absolute maximum

but for the estimation of 8, these values may be used, the results described in the previous section may be employed.

5ffects of the three factors (M, A, and S) on S

ft are shown in Fig. 10, by indicating the variation of the ranges of C(M), C(A), and C(S) with T. On the other

hand, Fig. 11 shows an example of frequency distribution for 277 values of SA

/SA

(the ratio of response spectral accelerations computed directly from the measured records to those estimated by the results of the quantification analysis) for the natural period of T=0.6 seconds. Shapes of frequency distribution of SA

/SA

f°r tne other natural periods

are found to be similar to that of Fig. 11. From the analysis shown above, the following significant points can be made:

(1) magnitude.

(2) Values of for the same earthquake magnitude decrease as the epicentral distance becomes smaller.

(3) As for the effects of subsoil conditions on S^, the effect on rock ground is considerably different from those on the other three subsoil conditions

are smaller than those for the other subsoils, except for the subsoils with the natural periods shorter than 0.3 seconds. For the range of comparatively longer periods, the values of tend to become larger for softer subsoils.

(4) The shapes of T vs. curves do not change much with the variations of M and A. It

is supposed from Figs. 6 to 9 that for the range of longer natural periods the values of 6 will increase as M becomes greater, and as A becomes longer.

(5) Among the effects of the three factors, earthquake magnitude (M=4.5 to 7.9), epicentral distance (A=6 to 405 km) , and subsoil condition (rock to soft alluvium) , the effects

of M are found to be the greatest for the entire range of natural periods. The

IV-54
effects of A are close to those of M for the shorter period range, and become small

for the longer period range. The effects of subsoil condition are small in comparison with those of M and A for the entire period range. This may be reasonable from the fact that the ranges of M and A are both considerably large. It is noted, however, that for the range of the periods between 0.5 and 2 seconds the effects of subsoils become rather great.

(6) Multiple correlation coefficients in the quantification analysis of vary between

0.53 and 0.72. The coefficients generally become larger as the natural periods become longer. Multiple correlation coefficient in the analysis A is approximately

max

0.6.

(7) Frequency distribution of SA

/SA does not vary much with the change in natural periods.

In view of this, it may be possible to stochastically assess design seismic forces in consideration of the importance of structures. The results described so far are for the case of the damping ratio of h=0.05 only. Values of S^ for damping ratio other than 0.05 can be approximately estimated by multiplying

the values of for h=0.05 by shown in Fig. 12, which are derived from the previous

investigation (9,10). As an example of use of the results shown above, let us estimate the average response

of a structure with the natural period of T = 0.35 seconds and the damping ratio of h = 0.1, when subjected to an earthquake with the Richter magnitude of M=7.5 to 7.9 and the epicentral distance of A=60 to 120 km. From Fig. 9(C) and Fig. 12,

S, = S, (T=0.35 sec, h=0.5) x a (h=0.1) A A h

= (200 ~ 308) x 0.78 = (156 ~ 240) gals

The value of varies depending on the subsoil conditions at the site of the structure,

being 156 gals for rock, 211 gals for dilluvium, 240 gals for alluvium, and 234 dais for

soft alluvium. Response accelerations of structures with different dynamic properties can

be estimated in the similar way, depending on the earthquake magnitude, the epicentral

distance, and the subsoil condition.

It should be noted that in the above analysis the structures are assumed as linear

systems with viscous dampings. A similar analysis for nonlinear structures may be necessitated in the succeeding steps. CONCLUSIONS

The following remarks may be made as the conclusions of the statistical analyses of

strong motion records measured in Japan.

(1) The absolute maximum horizontal acceleration, the duration of major motions, and the number of zero-crossings can be approximately evaluated as functions of the earth- quake magnitude and the epicentral distance, and the subsoil conditions.

(2) The mean value of the ratio of vertical to horizontal accelerations is found to be around 1/3. The ratio may be conservatively taken as 1/2, for design purposes.

IV-55
(3) Response spectral curves, by which structural response accelerations can be estimated

in terms of earthquake magnitude, epicentral distance, and subsoil conditions, are proposed.

(4) Among the three factors, the earthquake magnitude M, the epicentral distance A, and

the subsoil condition S, which affect the response acceleration of a structure during

an earthquake, the effects of M are found to be the greatest. The effects of A are close to those of M for the range of shorter natural periods, and become smaller for the range of longer natural periods. The effects of subsoil conditions are compara- tively small, but become comparatively large for the range of natural periods between

0.5 and 2 seconds. It is remarkable that response accelerations for the range of the natural periods between 0.5 and 2 seconds become larger as the subsoils become

softer.

(5) The results presented in this paper would be useful in evaluating the characteristics

of seismic forces and seismic loads for the earthquake resistant design of structures. ACKNOWLEDGMENTS

This study has been performed as one of comprehensive research projects done in the Aseismic Technology Development Committee which was established at the Technology Center

for National Land Development with a commission from the Public Works Research Institute, Ministry of Construction. The authors express their thankful appreciation to Professor

Shunzo Okamoto (President of Saita University and the Chairman of the Committee) , Professor Keizaburo Kubo (Chairman of the Subcommittee on Seismic Forces and Subsoils) , Professor

Motohiko Hakuno and Kenji Ishihara (Vice-chairman of the Subcommittee) , and Professor

Tsuneo Katayama (Member of the Subcommittee) for their helpful guidance. The authors also thank Mr. Mitsuaki Saeki (Japan Engineering Consultants, Co.) for his strenuous work in processing a great deal of strong-motion records. REFERENCES

(1) Ministry of Construction, "New Criteria of Earthquake Resistant Design (Draft)," March, 1977 (in Japanese) ; and Masamitsu Ohashi, Kiyoshi Nakano, "A Proposal for Earthquake Resistant Design Methods," Ninth Joint Meeting, U.S. -Japan Panel on Wind

and Seismic Effects, U.J.N.R. , Tokyo, Japan, May 24-27, 1977.

(2) Public Works Research Institute, "Report on Research and Development of Aseismic Technology," March, 1977 (in Japanese)

(3) E. Kuribayashi, H. Tsuchida and M. Watabe, "On the Maintenance of the Strong-Motion Accelerograph and the Data Processing of the Records," Seventh Joint Meeting of Wind

and Seismic Effects, U.J.N.R., May, 1975

(4) Strong-Motion Earthquake Observation Council, "The Project for Observation of Strong- Motion Earthquakes and its Results in Japan," National Research Center for Disaster

Prevention, Science and Technology Agency, Tokyo, Aug., 1972.

(5) Japan Road Association, "Specifications for Earthquake-Resistant Design of Highway

Bridges," Jan., 1971 (in Japanese)

IV-56
(6) T. Iwasaki, "Earthquake-Resistant Design of Highway Bridges in Japan," Bulletin No.

29, Public Works Research Institute, May, 1972

(7) M. Saeki, T. Katayama and T. Iwasaki, "On Characteristics of Earthquake Acceleration

Records and Response Acceleration Spectra Obtained on Grounds in Japan," Proceedings

of 31st Annual Meeting of JSCE, Oct., 1976 (in Japanese)

(8) T. Iwasaki, T. Katayama, "Statistical Analysis of Strong-Motion Earthquake Response

Spectra, "Japan-U.S. Seminar on Earthquake Engineering Research with Emphasis on Lifeline Systems, Tokyo, Japan, Nov. 8-12, 1976

(9) E. Kuribayashi, T. Iwasaki, Y. Iida and K. Tuji, "Effects of Seismic and Subsoil Conditions on Earthquake Response Spectra," Proceedings of International Conference

on Microzonation for Safer Construction, Research and Application, Seattle, Washington,

Vol. II, October-November, 1972

(10) E. Kuribayashi, T. Iwasaki, K. Tuji, "Several Factors Affecting Earthquake Response

Spectra," JSCE Meeting on Earthquake Engineering, July, 1971 (in Japanese).

IV-57
Table 1 Number of Strong-Motion Accelerographs (SMAC-Type)

(as of March, 1976) ^~^~^Number of Accelerograph6

Installed at

' At Structures On Grounds Total

Buildings 424 48 472 Highway Bridges 89 79 168 Railways 38 57 95 Ports 5 51 56 Telephone Offices 94 0 94 Power Plants 27 11 38 Nuclear Power Plants 21 20 41 Dams 9 10 19 River & Coastal Dykes 15 28 43 Storage Tanks 3 4 7

Others (Tunnels, Subways, Pipelines, etc.)

5 10 15

Total 730 318 1,048

Table 2 Definitions of Classification of Subsoil Conditions

Category Definitions Abbreviation

I

(1) Ground of the Tertiary era or older defined

as bedrock hereafter in this table

(2) Diluvial layer with depth less than 10 meters

above bedrock

Rock

II

(1) Diluvial layer with depth greater than 10 meters above bedrock

(2) Alluvial layer with depth less than 10 meters

above bedrock

Diluvium

(Dil.)

III Alluvial layer with depth less than 25 meters, which has soft layer with depth less than 5 meters

Alluvium

(All.)

IV Softer than the above

Soft Alluvium

(Soft All.)

IV-58
Table 3. Classification of 301 Records Analyzed

Magnitude Subsoil Epicentral Distance A (km) Total

M Condition

20<A 204A<60 60SA<120 120£A<200 200£A Rock 2 3 5

5.0£M<6.0

Dil. 3 12 3 18

65 All. 4 16 5 2 2 29 Soft All. 2 5 7 1 15 Rock 3 6 3 1

6.0SM<6.5

Dil. 7 8 2 1 18 81 All. 12 13 8 1 34 Soft All. 3 6 6 1 16 Rock 1 2 1

6.5£M<7.0

Dil. 1 6 6 13 62 All. 1 5 10 10 1 27 Soft All. 1 4 9 4 18 Rock 1 3 4

7.0*M<7.5

Dil. 2 12 14 40 All. 2 14 16 Soft All. 1 1 5 7 Rock 1 2 3

7.5iMi7.9

Dil. 3 8 11

50 All. 2 6 16 24 Soft All. 1 11 12 Total 12 69 74 64 82 301

Note. 1) Numbers of records for four subsoil conditions are 29 for rock, 74 for diluvium, 130 for alluvium, and 68 for soft alluvium.

IV-59
Table 4 Regression Equations for Hmax, Td and N z

Characteristic Subsoil Empirical Equations

Partial Correlation

Coefficient Multiple Correlation Value

Condition Magnitude Epicentral

Distanc e Coefficient

r

1 Rock Hmax

= 28.5 x 10°.207MX A -0.598 0.33 -0.47 0.48

Oil. Hnax = 13.2 x 10°-"0Mx A -0.806 0.50 -0.59 0.59 Umax All. Hmax = 32.1 x 10°-254MX A -0.757 0.47 -0.61 0.61

Soft All. Hmax = 6.5 x 10°-"3»x A -0.977 0.65 -0.72 0.72

Total Hmax = 18.4 x 10O-3O2M, A-0.800 0.51 -0.62 0.62

Rock Td

= 3.89 x 10-4 x 10°- 4 °<»!x A 0.589 0.59 0.40 0.89

Dil. Td

= 1.37 x 10-2 x 10°-262MX A 0.485 0.29 0.26 0.71

Td All. Td

= 2.75 x 10-2 x i 0 0.291Mx A 0.265 0.37 0.17 n.61

Soft All. Td = 2.28 x 10" 1 x 10°- ^"x A 0.233 0.25 0.16 0.52 Total Td = 2.08 x 10-2 x ioO-274^ A 0.394 0.32 0.23 0.65

Rock N 2 = 1.43 x 10- 2 x loO-^OMx fiO.444 0.41 0.22

- 0.75

Dil. N Z = 4.23 x 10" 1 x 10°- 0974Mx A

0 - 681 0.11 0.35 0.66

All. N 2 = 6.28 x 10- 1 x 10°-272MX A 0.0313 0.39 0.02 0.54

Soft All. N z = 4.05 x 1 00-190MX A -0.0646 0.22 -0.04 0.29

Total N Z = 4.68 x 10-1 x ioO.243^ A 0.195 0.30 0.12 0.54

Table 5. Averages and Standard Deviations

of Ti, v, and Subsoil Tm

Subsoil Condition

Rock Diluvium Alluvium jj??

1

. Alluvium

Ti (sec) Average 0.36 0.43 0.49 0.75

S.D. 0.52 0.39 0.30 0.42 Average 0.34 0.33 0.34 0.32

S.D. 0.15 0.18 0.18 0.21 0.30 0.34 0.39 0.61

S.D. 0. 36 0.22 0.22 0.35 Tl/Tm 1.20 1.26 1.26 1.23

Note: 1) S.D. - Standard Deviation

IV-60
Table 6. Classification of 277-Component Records for the Response Spectrum Analysis

Magnitude M

Subsoil Condition Epicentral Distance A (km) Total A<20 20^A<60 60iA<120 120^A<200 200^A

4. 5£M<5.4

Rock 6 4 10

Dil. 4 10 14 All. 12 8 8 2 30 Soft All. 6 6

5.4*M<6.1

Rock 4 2 6

48

Dil. 4 4 4 12 All. 2 12 6 20 Soft All. 4 2 4 10

6.UM<6.8

Rock 4 6 10

102

Dil. 4 4 2 10

All. 4 32 22 8 2 68 Soft All. 6 4 2 2 14

6.8*M<7.

5

Rock 4 3 2 9

1

29 Dil. 2 4 2 8 All. 4 4 8 Soft All. 4 4

7.5£M*7.9

Rock 2 2 4

38 Dil. 6 2 8 All. 2 6 4 2 14 Soft All. 2 10 12 To tal 42 92 72 39 32 277

Note: 1) Numbers of components for four subsoil conditions are 39 for rock,

52 for diluvium, 140 for aluvium, and 46 for soft alluvium.

IV-61
Table 7 Classification of 277-Component Records and Mean Values in Each Category

Factor Numberof Components

Mean Value

Category Peak

Ground Acc. Ac (gals) Magnitude

M Epicentral

Distance

A (km)

Magnitude

(M)

I 4.5^>£5.4 60 66.0 5.0 31 II 5.4i>£6.1 48 67.5 5.8 A3 m 6.UMS6.8 102 63.6 6.3 76 IV 6.8±Mi7.5 29 58.1 7.1 194

v 7.5^MS7.9 38 112.4 7.7 197

i 6SA<20km 42 110.6 5.3 12

Epicentral

Distance

(A)

ii 20^A<60km 92 68.2 5.8 38 u 60±A<120km 72 59.1 6.2 83 IV 120^A< 200km 39 56.2 7.0 159

V 200£A*405km 32 71.3 7.3 271

Subsoil

Conditions

(S)

I Rock 39 59.9 6.2 j 87 II Diluvium 52 69.4 6.2 86 Alluvium 140 73.2 6.1 74 IV Soft Alluvium 46 75.1 6.4 143 Total 277 70.9 6.2 90

IV-62
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3 3

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3:3 3 [3 3;3

3 3 S|Si3|3;2

3 313 3 3 5

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: 3 3 3 S3 2 3 3 3 3'3 3

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3^2

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d d d !!! TT76 6 3 3 3

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-1

9UIM!? ? 1 ?

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IV-63
Fig. 1 Strong-Motion Observation Network in Japan as of March, 1976

IV-64
Maximum acceleration

Period near the time when Amax occurs

Td : Duration of major motion

(= Time interval between

the initial time and the last time when A is equal to the half of Amax) N z

: Number of zero-crossing within the time of Td (n=12 for the case shown)

Fig. 2 Definitions of Ti, Td and N z

IV-65
XDUJ H

' uoijojaiaDoy iojuozuoh wnwixo^

IV-66
IV-67
IV-68
IV-69
300

50 100 200

Epicentrol Distance A

500 1000 km

Fig. 3(E) Epicentral Distance versus Maximum Horizontal Acceleration

for Average Subsoils

o

50 100 150 200 km

Epicentral Distance, D

(A) Epicentral Distance versus Duration of Major Motion

for Magnitude of 8 Fig. 4 Duration of Major Motion Defined by Fig. 2

IV-70
5 6 7 8 Magnitude

(B) Earthquake Magnitude versus Duration of Major Motion at Epicentral Distance of 100 Km

Fig. A Duration of Major Motion Defined by Fig. 2

j Soft A 1 1 u v i u"mj x 5 0SM< 60 I O 6 0§M< 7.0 | • 7 OSM S 79 I

g o

0<n) o

o v o

oo o

o <£>• *

50 10 200

Epicentral Distance, A

500 1000

Fig. 5 Example of Ratios of Vertical to Horizontal Accelerations

IV-71
IV-72
Fig. 7(A) -(D) Response Spectrum Curves for Maximum Response Accelerations i Case of 6.1 4 M < 6.8

IV-73
IV-74
IV-75
2.0

0.01 1 1—

i 1—ii i

,

- i 0.1 0.2 0.5 1.0 2.0 5.0 sec No turol Period, T Fig. 10 Natural Period versus Ranges of Coefficients for

the Three Factors (Magnitude, Epicentral Distance,

and Subsoil Condition)

Noturol Period T= 0.6 sec |

( Tolol Number = 2 77)

1.0 2.0 Sa /S a Fig. 11 Distribution of S./S

A A

IV-76
3.0

(2.33)

(0.36)

0 l_J 1 1 1 1 1 0 0.02 0.05 0.1 0.2 0.3 04 Damping Ratio, h

Fig. 12 Effect of Damping Ratio (Ch) on Response Spectrum

Values (Ch =1.0 when h = 0.05)

17-77
RESEARCH ON DESIGN EARTHQUAKE

Makoto Watabe Building Research Institute Ministry of Construction ABSTRACT

The maximum values of accelerations, velocities and displacements of the ground motions due to earthquakes are first discussed utilizing the historical data as well as some theoretical approaches. Then, duration time and the deterministic intensity function

of the accelerograms are introduced. The predominant periods and spectral shapes of the strong motion accelerograms are also reported. Historical earthquake data were utilized

to assess the earthquake risks in Japan. Finally the explanation of proposed "design earthquake" concludes this report.

KEYWORDS: Design earthquake; deterministic intensity function; historical data; maximum

values; random characteristics; seismic zoning; spectral shapes; theoretical

analysis.

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INTRODUCTION

One of the essential factors for aseismic designs of structures is to estimate the intensity and characteristics of ground motions. Numerous research on this matter has been carried out and the results are summarized here. Recognizing that seismic waves are initiated by irregular slippage along faults followed by numerous random reflections,

refractions, and attenuations within the complex ground formations through which they

pass, the stochastic modelling of strong ground motions is a realistic form which can be applied in practice. Noting the above fact, stochastic quantities are induced as much as possible in this report. MAXIMA OF EARTHQUAKE GROUND MOTIONS

(1) Evaluation by overturning of the tombstones

:

Fig. 1 illustrates the relation between the epicentral distance (km) and the maximum

acceleration estimated by overturned tombstones, based on the earthquake data with the magnitudes greater than 7 since 1927 in Japan. According to this figure, the maximum

acceleration may exceed the value of 0.4g and the upper bound of the maximum acceleration

at ground surface appears to be around 0.6g.

(2) Evaluation by the records of the strong motion seismographs:

The maximum accelerations measured by the strong motion accelerographs on the hard

subsoil layers are tabulated in Table 1. In Fig. 2, the relation between the epicentral

distances and the maximum velocity values measured by the strong motion seismographs are indicated with the parameter of the magnitude (1) . It may be noticed that the maximum

velocity ever recorded by the seismographs is approximately 35 kines as seen in Fig. 2.

(3) Estimation of upper bound from the critical strain level of the rocks (2)

:

-4 Assuming the critical maximum strain of the fracture of the rocks (£ ) as E =10

* cr cr and shear wave velocity value in the rock (Vs) as Vs=3km/sec, the maximum velocity value

is estimated as 30 kines by the following equation,

M<..*Hf<t - £ HXaxHff^L^S^ z where y = amplitude of seismic wave in terms of time,

z = coordinate along the wave propagation,

t = time, V

g = shear wave velocity,

e = strain

From the above estimation, it is suggested that there is little change for the maximum

velocity to exceed the value of 30 kines.

(4) Proposal by Professor K. Kanai: With his vast experience on earthquake engineering, Professor Kanai proposed the following equation for the relationship between the hypocentral distance (x) and the

IV-79
, J3.61M - (1.66 + —) log x - (0.631 + ^-^-)

10 x x

the maximum velocity on the surface of the bed-rock (kine) M = the magnitude of the earthquake

x = the hypocentral distance (km)

Also, the radius (D km) of the spherical volume within which hypocenters of after-shocks of the earthquake exist can be expressed in terms of the magnitude (M) followingly (4) ;

Assuming that the above value D is the depth of the hypocenter and using Kanai's equations of maximum velocity, the relationship between the maximum velocity and the epicentral distance can be expressed as illustrated in Fig. 3 with the parameter of the magnitude. The intersection of the relevant magnitude line and the dotted line indicate

the radium (D km) in the above equation or, let us say, the depth of the hypocenter. Fig.

3 suggests that the maximum probable velocity value will never exceed the value of 60 kines.

(5) The ratio of the maximum acceleration to the maximum velocity: From the 75 sets of the strong motion accelerograms and the corresponding velocity records obtained in both Japan and the United States, the mean value of these ratios is 9.95 in horizontal components and the standard deviation of those ratios is 1.7, while in the vertical component, the above accelerograms and the corresponding velocity records do not coincide in the time domain. However, these maxima will be regarded as closely correlated if the above time difference of the peaks is limited within one second. Selecting such records, the mean value of the ratios of the maximum acceleration to the maximum velocity is 11.0 in horizontal components and the standard deviation of those ratios is 1.8. In vertical component, the mean value and the standard deviation of those ratios are 13.8 and 1.7, respectively. Incidentally, for the horizontal components, the mean value of the ratios of the maximum acceleration to the corresponding maximum displacement is 20.6 and the standard deviation of those ratios is 3.3. In the case of vertical component, the mean value and the standard deviation of those ratios are 18.0 and 1.9, respectively. Using the same materials including vertical components as well, a stochastic analysis is also made on the cross-correlations between the maximum values of acceleration, velocity, displacement and Housner's spectral intensity with zero and 0.2 dampings. The results are indicated in Table 2 from which it may be suggested that "measures" to represent intensity

of ground motions such as values mentioned above are extremely cross-correlated. Therefore

the choice of these "measures" can be rather arbitrary. This analysis also provides

linear relations between these maxima. The results are indicated in Table 3, and suggest reasonable ratios between two values of maxima such as horizontal and vertical acceleration

IV-80
velocity, displacement and spectral intensity. The ratios indicated in Table 3 give

closer values which are proposed by M.D. Trifunac and A. G. Brady (5) as follows,

A

H

= 5.89V/' 2

1 2 V = 0.4V V H

where A and V represent maximum acceleration and velocity, respectively, and the suffixes

H and v represent horizontal and vertical components, respectively. RELATIONS BETWEEN HORIZONTAL AND VERTICAL COMPONENTS OF EARTHQUAKE GROUND MOTIONS

(1) The ratio of the maximum acceleration in vertical component to those in the corresponding two horizontal components: From the same sets of the strong motion accelerograms mentioned previously (5)

,

ratios between horizontal and vertical components are obtained. It might be reasonable to associate the epicentral distance with these ratios of the vertical maximum accelerations

to the horizontal accelerations. The results suggest that the shorter the epicentral

distance is, the larger this ratio becomes. This ratio of the maximum acceleration in vertical component to those in the corresponding two horizontal components, R(d) , can be approximated as follows,

R(d) = e-0.0022(^ + 300)

:ra (2) Random characteristics of the accelerations ratios (horizontal and vertical components)

.

In spite of the above results, this ratio of the maximum acceleration in vertical

components to those in the corresponding two horizontal components follows the complete

characteristics of Gaussian random process as may be observed in Fig. 4, in which the probability distribution of variables as logarithms of the above ratio are plotted with solid

lines and the reference plots (in dotted line) of true Gaussian distribution. As previously

introduced, Table 3 suggests stochastically reasonable ratios between horizontal and vertical components (diagonal elements in Table 3) . It should be noted that the ratio of

intensity between horizontal and vertical components is rather stable, whatever intensity

scale may be chosen such as acceleration, velocity, displacement or spectral intensity. DURATION TIME AND DETERMINISTIC INTENSITY FUNCTION From 76 accelerograms obtained by 56 strong motion earthquakes during the years

between 1968 and 1971 in Japan, the duration time (t) of accelerograms determined by the engineering judgment can be expressed in terms of the magnitude of the earthquake (M)

,

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t = 10M-2.5

, 3.23

(sec.

According to research work on length (L,km) and displacement (D,m) of the active faults, the following relationships are known (6)

log D=0.60 M-3.91 log L=0.6 M-2.91 R=D/S

where S = average displacement velocity (m/year) M = magnitude of caused earthquake

R = period of earthquake occurrence (year)

With the rupture velocity of 3 km/ sec. along the fault, total rupture duration of the earthquake can be calculated using the above relation. The results are also indicated in Fig. 5.Figs. 6(a) and 6(b) are the deterministic intensity functions determined from the actual accelerograms by smoothing the oscillatory irregular waves. If a(t) is the accelerogram, £(t) is the deterministic intensity function and a' (t) is the stationary random process of the accelerogram, a(t) is expressed as,

If real £(t) is to be obtained, a' (t) must satisfy the condition of the stationary random process such as the Gaussian distribution of probability and run's test. Thus true £(t) can be obtained by step-by-step smoothing techniques through checking the stationary random process of a' (t) . Figs. 6(a) and 6(b) suggest the deterministic intensity function of ideal model (7) , and the generalization of this pattern is somewhat controversial, but desirable from an engineering point of view. It also should be noted that the deterministic

intensity functions for the vertical components are not identical to those for the hori- zontal components as seen in Fig. 6. Another approach to obtain the pattern of deterministic intensity function was shown by J. Penzien and T. Kubo (8)

Spectral shape of the accelerograms on the surface of the bed-rock:

The transfer function to transmit the seismic wave around the bed-rock layers might

be regarded uniform in frequency domain, i.e., the spectral shape of the transfer function

is "White." The spectral shape of the accelerograms on the surface of the bed-rock may be subjected to the influence of the spectral shape of source mechanisms and the surroundings of the hypocenters. The velocity response spectrum Sv(T,h) at free field bed-rock is assumed to be the function of magnitude M and hypocentral distance x in addition to period

T and damping ratio h,

a(t) = £(t) a' (t) a' (t) = a(t)/C(t)

SPECTRAL CHARACTERISTICS

Sv(T,h) = 10a*M-b logx-c

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Using 27 accelerograms obtained at free field bed-rock, coefficients a, b and c for every

period of spectrum are determined by least square sum techniques . The results are shown

in Fig. 7(a) and Fig. 7(b) as examples. It can be clearly seen in Fig. 7(a) that higher

frequency components are predominant in response spectrum for smaller magnitude while

lower frequency components are predominant in response spectrum for larger magnitude. By

these figures, Fig. 7(a) and Fig. 7(b), any response spectra at free field bed-rock can be

obtained. CONCEPT OF PRINCIPAL AXES OF THE ACCELEROGRAMS

In this paper, only the outline of the concept of principal axes of ground motions is introduced. Details are explained in reference 9. First, 3 components of accelerograms

along three orthogonal coordinate axes are defined through the relations,

ax(t) = £(t) b

x

(t), a

y

(t) = C(t) by(t), a^t) = £(t) b^t)

where b (t) , b (t) and b (t) are stationary random processes and £(t) is the deterministic

x y z intensity function giving appropriate non-stationarity to the ground motion process. If

a^(t) , a^(t) and ^(t) are considered to be zero-mean non-stationary random processes, the covariance functions

E[a

i (t)a

j (t+T) ] = £(t) 5(t+T) E[b

i (t)b

j (t+T)] i,j = x,y,z

where E denotes ensemble average, it can be used to characterize the ground motion process.

Since random processes b

x

(t), b

y

(t) and b

z

(t) are stationary, all ensemble averages on the right side of the above equation are independent of time t; therefore, showing dependence

only upon the time difference T. Since real earthquake accelerograms demonstrate a very

rapid loss in correlation with increasing values of |t|, the influence of coordinate

directions on the covariance functions can be investigated by considering the relations,

E(a

i (t)a

j (t)] = C(t)

2E(b

i (t)b

j (t) ] i,j = x,y,z

Defining covariance matrix _3 as

~3 3 3 xx xy xz

3 = 3 3 3 i - y* yy yz

; 3 3 3 ^ zx zy zzj

where 3. .=E [b. (t)b . (t) ] , the total covariance matrix can be written in the form u(t)=?(t)

2

3.

3-D i : -

By coordinate transformation of a^ft), a^(t) and a

z

(t) along new three orthogonal coordinate

IV-83
6^=0; ij^j. Such new axes which satisfy the above conditions are defined as principal

axes where no cross-term of covariance exists and 3 variances of diagonal elements become

the maximum, minimum and intermediate. Using the defined orthogonal transformation, principal axes of ground motion have been located for six different earthquakes. Variano

and covariances of the recorded accelerations a (t) , a (t) and a (t) along the three

x y z accelerograph axes x, y and z respectively, were obtained. By selecting successive

intervals over the entire duration of motion, the changes in direction of principal axes with time can be checked. Fig. 8 shows the horizontal directions of one principal axis

for the above mentioned six earthquakes using sufficiently long time intervals to reasonal I stabilize the principal coordinate directions. The corresponding variances are indicated by arrow lengths applied to the radial scale. In most cases the principal axis shown in Fig. 8 is the major principal axis; however, in some cases, usually for intervals near th< ends of the motions when intensities have decreased considerably, the major principal axis is at right angles to the directions shown. The minor principal axis is in each case nearly vertical. When averaging over the entire duration of motion and averaging for the six earthquakes, the resulting ratios of intermediate and minor principal variances to the major principal variance are approximately 3/4 and 1/2, respectively, i.e., (u ,,/U )

J. J. 2.2. avg ^ 3/4 and (T-^A1 -^) * !/ 2 - Using these numerical values to obtain principal covariances,

the principal cross-correlation coefficients become

Finally it is suggested that the potential use of the concept of principal axes to explore physical phenomena, such as tracing the center of energy release, should be investigated. SEISMIC ZONING IN JAPAN

In Japan, history of earthquakes from the 7th century up to the present time extendin

over 1300 years can be available. The total number of destructive earthquakes with mag- nitudes more than 6 amount to 600. Fig. 9 shows epicenters and magnitudes of earthquakes

in and around Japan during these 1300 years. For instance, applying Professor Kanai's

equation, introduced in the previous section, to all historical earthquakes, frequency

where T is the length of historical years of earthquake.

IV-84
By integration,

/V

probability distribution function P

(

vmax Q

) can be obtained, which represents the probability

of such an earthquake whose maximum velocity, at this specific site, is larger than (V ) max , 0 in a year. Inverse of such probability, 1/P (v"max q) is termed as "return period (Tr)

of (V ) . If some specific return Tr is chosen, say 200 years (P (V )=0.005), then max ,0 max ,

0

the corresponding (V „) can be evaluated. According to Poisson's distribution, the

max, 0 probability P(t) of experiencing the ground motions, the maximum velocity of which exceeds

(V -) the corresponding return period Tr during the lifetime of a building t, can be

max, 0 evaluated,

P(t) = L^Ar

Taking t/Tr=0.1, P (t) equals 0.095. Assuming the chance of experiencing more than ( vmax Q

) earthquake during the lifetime of building t is 0.3, then t/Tr becomes 0.36. Various

researchers proposed seismicity maps in Japan applying similar analyses introduced here. The entire map of Japan is divided into rectangles, the dimensions of which are 20' in both longitude and latitude. Then seven different seismicity maps of Japan (10,11,12,13) of return period 100 years are normalized to assign unity (1.0) for the rectangular division

of the maximum value in each map. Using these normalized maps, the mean value of these

seven different maps, the mean value plus two standard deviations of these maps and the maximum value of these maps in each rectangular division are obtained. The results are shown in Fig. 10(a), Fig. 10(b) and Fig. 10(c), which are considered to be the appropriate

seismic zoning coefficients for aseismic design of structures. DESIGN EARTHQUAKE Now let the deviation of estimating intensity of ground motions in terms of magnitude

and hypocentral distance be considered. Applying the best fit method to estimate intensities

(for instance, maximum velocities) in terms of magnitudes and hypocentral distances of 75 earthquakes, coefficients of deviation for intensity of ground motions are obtained. 0.8

is the smallest possible value for the coefficients of deviation to assess the intensity

of ground motions in terms of given magnitude and hypocentral distance. Some other research

paper on the coefficient of deviation also suggests the similar value (14)

.

SUMMARY

(i) As for the maximum velocity value, Fig. 3 might be regarded reasonable, considering

the results of critical maximum strain. Also, the maximum velocity ever recorded is 35 kines as seen in Fig. 2 and the upper bound area in Fig. 3 is obtained by extrapolating

the values actually recorded. It is quite controversial to define the maximum acceleration

IV-85
value. However, in a stochastic sense, this value can represent a reasonable measure for thi intensity parameter. This may mean to exclude a single peak value of the acceleration with frequency higher than 20 Hz for the stochastically significant value. The values indicated in Table 4 can be regarded as the "mean value of the maximum," therefore, in actual cases, many of the maximum values may exceed the values in the table, which indicate the values for vertical components, as well, by applying linear coefficients shown in Table 3. (ii) Total duration of design earthquake may be calculated by the equation introduced

in Chapter 4, in terms of magnitude of earthquake. As for the duration of the stationary part of ground motions the following equation was derived from fault length of rupture, with assumption of rupture velocity of 3 km/sec,

I t- 10

0 ' a4 - 3 - 38 (sec.)

where M is the magnitude of assumed earthquake and t is the duration in second of stationary part which can be applied to the deterministic intensity function.

(iii) The deterministic intensity function for design earthquake may be determined by applying an ideal model proposed in reference 7. This ideal model assumes deterministic

intensity functions which increase linearly or parabolically for the stationary part and then decay exponentially.

(iv) Fig. 7(a) and Fig. 7(b) may be recommended as response spectra of design earth- quake on bed-rock.

(v) The concept of principal axes may be quite useful for multi-dimensional ground

motions.

(vi) It must be fully considered that earthquake ground motions are so random natured

that they are not to be permitted to give any explicit values but to give values with mean

and deviation. Proposed procedures to obtain design earthquake are discussed below.

(1) Time history of design earthquake:

a) Assume magnitude and hypocentral distance and then calculate the maximum velocity

using Kanai's equation and the equation for radius (D) of spherical volume.

b) Use Table 3 to obtain maximum acceleration and spectral intensity (SI) , both in horizontal and vertical directions.

c) Calculate total and stationary duration of the assumed earthquake by equations introduced in summary (ii) . Then, assume an ideal model of deterministic intensity

if necessary.

d) Determine spectral characteristics using Fig. 7(a) or Fig. 7(b) if necessary.

e) Produce accelerograms either through simulated earthquake or modification of

real accelerograms and then establish multi-dimensional time history ground motions if necessary.

f) Principal axes accelerograms are strongly recommended for design earthquake.

IV-86
g) Multiply 1.8 (mean plus 1 standard deviation) to accelerograms derived above

for important structure and 2.6 (mean plus 2 standard deviation) for very important structures or very dangerous structures.

h) If the time histories of design earthquake on the ground surface is necessary, apply conventional or non-linear wave propagation techniques.

(2) Response spectrum for design earthquake:

a) Assume a maximum possible earthquake ground motion, for instance magnitude 8 and hypocentral distance 50 km and then by Fig. 7(a) or Fig. 7(b) establish response spectrum for the maximum possible ground motions.

b) According to the importance factor of structure, choose Fig. 10(a) for less important structures , Fig. 10(b) for general structures or, Fig. 10(c) for important structures . For the response spectrum in any districts, multiply

seismic zoning coefficients of relevant districts to the response spectrum derived in (i) as the maximum possible one.

c) Apply linear coefficients indicated in Table 3 to obtain response spectrum for vertical component if necessary.

d) Multiply 1.8 (mean plus 1 standard deviation) to the spectral values in (ii) and (iii) for important structures.

e) Amplification spectrum of subsoil layers may be multiplied for the design response spectrum on the ground surface.BIBLIOGRAPHY

(1) Watabe, M. and Kitagawa, Y., 1973, Characteristics of Strong Motion Earthquake Obtained

in Japan, 5th U.J.N.R.

(2) Muramatsu, I. et al. , 1963, Observation of Micro-Earthquake in Mino District in Gifu

Prefecture, General Japan Journal of Phys. of the Earth.

(3) Kanai, K. , 1966, Improved Empirical Formula for Characteristics of Strong Earthquake

Motions, Proc. Japan Earthquake Symposium, (in Japan) , pp. 1-4.

(4) Iida, K. , 1963, A Relation of Earthquake Energy to Tsunami Energy and the Estimation

of the Vertical Displacement in a Tsunami Source, Journal of Earth Science Nagoya

Univ. Vol. 11, pp. 49-67.

(5) Trifunac, M. D., and Brady A. G. , 1975, On the Correlation of Seismic Intensity

Scales with the Peaks of Recorded Strong Ground Motion, B.S.S.A. Vol. 65, 139-162.

(6) Matsuda, T. , 1975, Magnitude and Recurrence Interval of Earthquakes from a Fault, Zishin Vol. 28, pp. 269-283.

(7) Jennings, P. C, Housner, G. W. , and Tsai, N. C, April 1969, Simulated Earthquake

Motions, Earthquake Engineering Research Laboratory, California Institute of Technology, Pasadena.

(8) Penzien, J., and Kubo, T. , 1977 Characteristics of Three-Dimensional Ground Motions

Along Principal Axes, San Fernando Earthquake, WCEE.

(9) Penzien, J., and Watabe, M. , 1975, Simulation 3-Dimensional Earthquake Ground Motions, International Journal of Earthquake Engineering, McGraw-Hill.

IV-87
(10) Goto, H. , and Kameda, H., November 1968, A Statistical Study of the Maximum Ground Motion in Strong Earthquakes, Dobokugakkai , No. 159

(11) Takanashi, K. , July 1974, Risk Analysis for Earthquake, Saigaikagaku-Kenkyu-kai

(12) Omote, S., and Muramatsu, S., Acceleration Expectancy in Japan Derived from Up-toDate Data.

(13) Hattori, S., and Kitagawa, Y. , 1974, On the Regional Distribution of Earthquake

Danger in Japan, Bull. I.I.S.E.E. Vol. 112, pp. 83-102.

(14) O'Brien, L. J., et al. , March 1976, The Correlation of Peak Ground Acceleration

Amplitude with Seismic Intensity and Other Physical Parameters, Computer Science

Corporation.

IV-88
Table 1 : Max. Acceleration by Strong Motion Accelerographs on Hard Subsoil

Earthquake Date M Location Epicentral

Distance

Subsoil Max. Acceleration

(gal) MatBushiro 1966. 4.S 6.1 Hoshina A 8.0 550

1966. S.28 4.9 Matsushiro B 3.5 370 1966. 8.8 -

Hoshina B 390 Tokachioki 1968. 5.16 7.9 Miyako 115 Hard 118 Horomanbashl 69 Higashi- 1968. 7.1 6.4 HibiyaDenden 50 Gravel 27 matsuyana Shintonebashl 32 Hard 75 Sakaigawa- 48 55 bashi

Hidaka- 1970. 1.21 6.7 Horomanbashl 20 Rock 182 Sankei Table 2 : Coherence Among Measures to Represent

the Intensity of Ground Motions

A V D Sl o.o

SI 0.2 A 0.905 0.841 0.587 0.830 0.902 V 0.892 0.798 0.876 0.957 0.986

D 0.739 0.888 0.7Q2 0.826 0.770

sio.o 0.815 0.923 0.786 1 0.924 0.970

SI0.2 0.911 0.960 0.791 0.960 0.897

A half above the diagonal : Horizontal and horizontal

A half below the diagonal : Vertical and vertical

Diagonal matrix : Horizontal and vertical

A : Maximum acceleration V : Maximum velocity

D : Maximum displacement SI : Housner's intensity

: Damping ratio) Table 3 : Linear Relations Between Maxima V X A V D SI o.o

SI 0.2 A

1.669

(0.532) 0.0961

(8.701) 0.0389

(15.98) 0.579

(1.429) 0.227(3.945) V 9.921

(0.0880) 1.753

(0.448) 0.440(2.000) 5.921

(0.162) 2.242"(C.431) D

L7.67

(0.0406) 1.839

(0.476) 1.555

(0.468) 11.81(0.0710) 4.290(0.181)

SI o.o 1.551

(0.511) 0.157

(5.821)

. 0.0741

(10.63) 1.887(0.489) 0.371

(2.610)

SI 0.2 4.819

(0.186) 0.469

(2.035) 0.216

(3.614) 2.855

(0.334) 2.038(0.435) H : Horizontal Components V : Vertical Component

A half above the diagonal : Horizontal and horizontal

A half below the diagonal : Vertical and vertical

Diagonal matrix : Horizontal and Vertical

X(row) = coef. Y (column) Inside parenthesis ; Y (column) = coef. X(row) example ; Ah = 1.669 Av = 8.701 Vh Av =, 0.532 • Ah = 9.921 Vv

IV-89
Table 4 : The Mean Maximum Values

Horizontal Vertical

(epicentral distance within 20km)

Max. acceleration

(gals) 573 356.8

Max. velocity

(kines) 55 31.4

Max. displacement

(cm) 24.2 17.1 Spectral intensity

(cm) h=0.2 123.3 67.0

g 0 8

c

.21

0-4

(J

<Jtoa

• M=8

°M = 7

oo

•

•

1 . 10 , j . 100., . 1000

epicentral distance (knrv) Fig.-l Max. Acceleration Estimated by Overturning of Tombstones

IV-90
\-

BOUNDARY

x THE

OF SOURCE EARTHQUAKEOF

0 40 80 120 160 EPICENTRAL DISTANCE Fig. -3 Epicentral Distance and Max. Velocity

Fig. -4 Probability Distribution Fig. -5 Duration and Magnitude Proposed

Plots of Variables as by Various Researchers Logarithm of Ratio (Vertical

VS. Horizontal Housner's

Intensity with 20% Damping)

XV-91
15^..6983.(GQLS)

CHI SOUARE TEST STANDEPD DEVIATION - O- 989H27D

MEAN VALUE =-0.0025559

X*- 39. i221975<»'= >46. ,2ii000S4

HUN "tEST NUMBER OF PUNS

TIME POP . 1. F EOkJflVE NAME 0URAT10N T

1 ME TIME INTERVAL EQWBYE NUMEER Fig. -6a Deterministic Intensity Function (Horizontal Components)

CHI 'jCUAPF test OTANDEPD DEVIATION - 1 0328SS mean valof - o. discs;

32 73^23 76 '-»•- M6.21CC05''

RUN 'EST NUMBER OF PUNS

TIME F OR D. 1. F tCJAVc NAME DURATION T

1 ME

T

1 ME 1N T EPVAL 10UAVE NUMBER

3 7. 620C (SEC1

0. 020C (SEC I 3 Fig. -6b Deterministic Intensity Function (Vertical Component)

IV-92
Sv(kine)

6jO MAGNITUDE =8.08.0 10.0 PERKXXs^c.) Fig. -7a Velocity Response Spectrum of Ground Motions at Hard-rock due to Earthquake with Magnitude 8.0 (Fraction of Critical Damping : 0.05)

Fig. -7b Velocity Response Spectrum of Ground Motions at Hard-rock due to Earthquake of 50km Hypocentral Distance

(Fraction of Critical Damping : 0.05)

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E-EPICENTER DIRECTION

Fig. -8 Principal Axis Directions for 3 Different Recorded Earthquake

Ground Motions.

Fig. -9 Magnitude and Location of large Earthquakes in and Around Japan

IV- 9 4
IV-95
DETERMINATION OF WAVE PROPAGATION VELOCITIES IN SUBSURFACE SOIL LAYERS Yukitake Shioi, Chief, Civil Engineering Section International Institute of Seismology and Earthquake Engineering

Building Research Institute, Ministry of Construction

Toshio Iwasaki, Chief, Ground Vibration Section Earthquake Disaster Prevention Division

Public Works Research Institute, Ministry of Construction ABSTRACT

Activities of the Committee on Earthquake Observation on Soil-Structure Interaction

have been described. One of the committee's research activities is the research involving

the construction of a model structure, soil investigations, dynamic tests and analysis of dynamic soil-structure interaction. This paper discusses the results of forced vibration tests conducted on a model

structure with a vibrator which generated harmonic waves. These waves were then compared with the Rayleigh and Love waves.

KEYWORDS: Harmonic wave; Love waves; model structure; Rayleigh waves; soil-structure

interaction; vibrator.

IV-96
INTRODUCTION

It is empirically and theoretically well known that the vibration of structures on the ground by such energy as an earthquake principally depends on the properties of the superficial layer. In other words it is possible to presume the main ground motions to the structures if we can relate the physical properties of layers to the variables of the vibratory characteristics. Substituting the superficial waves with the Rayleigh and Love

waves, we have attempted to obtain the values of coefficients relevant to the ground

vibration with the observed records of the harmonic wave propagation generated artificially

on a small surface base. Also, the characteristics of these data were examined. As a matter of fact, we took measures to study these characteristics on the propagation waves

by means of a high frequency vibrator based on the surface. This test was a part of the forced vibration tests conducted under the direction of

the Committee on Earthquake Observation on Soil-Structure Interaction presided by Professor

Yutaka Osawa at the Tokyo University in a comprehensive research project for the Establishment of New Aseismic Design Method. This testing method is somewhat similar to the methods

employed by Jeukelon, Foster and Fry at the Waterways Experiment Station (1)

.

We expect that the accumulated results from these vibratory tests may serve as an exploratory calculation method on the ground movement under various conditions of aseismic

design of underground structures and, of countermeasures against the vibration by circulations, etc. ACTIVITIES OF THE COMMITTEE ON EARTHQUAKE OBSERVATION ON SOIL-STRUCTURE INTERACTION (4) The research theme commenced since the fiscal year of 1974. During the past second

year the Technology Center for National Land Development established a committee on earthquake observation on soil-structure interaction (Chairman: Professor Yutaka Osawa) , under

the authority of the Building Research Institute, Ministry of Construction. The committee

attempted to make a research plan covering all the necessary stages for the future.

In the fiscal year of 1975, construction of an upper structure, dynamic tests on a soil-structure model, and observation of earthquake motions on and around the foundation

structure have been accomplished. In addition, theoretical and experimental procedures to analyze dynamic behavior of soils and structures have been investigated.

The research includes construction of a model structure, soil investigations, instrumentation, measurement of seismic motions, dynamic tests and analysis of dynamic soilstructure interaction. The research is expected to be completed in three years. The work accomplished or to be accomplished in the middle of the year is as follows: (See Fig. 1)

a) Forced vibration test: The forced vibration test using a vibrator was made to study

the dynamic characteristics of the model structure, of the neighboring building, and

of the wave propagation.

b) Construction of upper model structure: An upper structure having four steel columns

(4-0 267.4 x 6.) and one reinforced concrete slab, 4m long, 4m wide and lm high, was constructed in Fuchinobe, Sagamihara City, Kanagawa Pref. IV-97
c) Earthquake observation: Four transducers were installed in the model foundation structure and six transducers were placed around the model. Six observational data were obtained to determine the dynamic behavior of the subsoil foundation system.

d) Analysis of dynamic soil-structure interaction: Analytical evaluation of dynamic behavior of the simply shaped structure may be done. For a detailed and complicated

system, however, it seems that quantitative investigations and experimental procedure

are more significant.

This report discusses the work listed in a) above. PROPERTIES OF SURFACE WAVE

The vibration of the superficial layers becomes maximum at the surface wave during earthquake from the viewpoint of energy. Among the surface waves, the Rayleigh and Love waves are typical. Their formulas are shown as follows (3) , (Fig. 2)

Rayleigh Wave (See Fig. 3)

u=A*n[exp(-Y*z) sin (tot - nx) - (2 y/n's/n) / (1 + s

2 /n2

) exp (- sz)

sin (tot - nx)

2 2 w=A [2y/ (1 + s /n ) •exp(-sz)-yexp (-yz) ] cos (oot - nx)

Love Wave

v = [B cos ( qz) + C sin (qz) ] cos (pt - fy)

v' = D exp (-q'z) cos (pt - fy)

u = displacement in x direction

v = displacement in y direction (at upper layer)

v' = displacement in y direction (at lower layer) w = displacement in z direction

A, B, C, D = arbitrary constant

to = circular frequency on x - z plane

p = circular frequency on x - y plane

n = wave number

f = frequency

2 2 2 ,2

Y = n - u /v

2 2 2.X

s = n - co /v

H v^ = velocity of p wave

v

H

= velocity of S wave

q

2 = (P/vv

) 2 - f

2

, o 2 2 2 q"4 = f - (p /V

' H

) (prime means of lower layer)

IV-98
The phase velocities of each surface waves are shown as follows:

v„ = k v = U)L_/2ir

(1 - 2u) / (2 - 2y) = G / (2G + X) p / f = V„ (1 + q

2L2

T / 4^ 2 )l/2 = p

L

L

7 2V

where

,

vR

= velocity of Rayleigh wave

v

L

= velocity of Love wave

LR

= wave length of Rayleigh wave

= wave length of Love wave

y = Poisson's ratio of subsoil

G = shear modulus of subsoil

X = Lame 1 s constant OUTLINE OF THE TEST

The vibration tests were performed to research the above mentioned subjects in December, 1975 at which time we installed a high frequency vibrator on a model of reinforced concrete footing (4m

x 4mx im

) . The layout of the model, the fixed observatory

instruments and so on, are shown in Fig. 1, but the superstructure of the model was not

yet constructed at that time. The site is on the complex of Sagamihara Engineering Center of Nippon Steel Co. /LTD

1 at Fuchinobe, Sagamihara City, Kanagawa prefecture (See Fig. 4) . The geological structure

ij consists of Nakatsu layer in the tertiary period, Sagami layers in the dilluvial epoch, Sagamino gravel layer, Musashino and Tachikawa loams and subsoil from the bottom, and the

ij upper layers are shown in Fig. 5. The results from the standard penetration tests, seismic prospectings, and so on at the site are given in Fig. 6. The most important layer

in this test is the loam extending 14m down. Its physical constants from Fig. 6 and from

other existing reports are assumed to be 0.5 to 1.11 km/sec. for the velocity of the P wave,

0.15 to 0.30 km/sec. for the velocity of the S wave, and 0.33 to 0.45 for Poisson's

ratio. The predominant frequencies of micro-tremor at this site are recognized at 0.7,

; 2.1 and 5 Hz. The specifications of the vibrator are shown on Table 1 and it is possible

l to change continuously the vertical and horizontal frequencies. The frequency range in the test is distributed at 8 to 30 Hz for the vertical, axial, and transverse directions.

To measure the ground vibrations, "pickups" were placed to observe the types of velocity and displacements at constant intervals on the axial direction and we used a

|l master control system for operation and recording at the station (See Fig. 1). The measurement in velocity type was adopted for ground vibration and measurement in displacement

type was adopted for soil-structure interaction and vibration of neighboring buildings.

The latter results may be introduced again for further studies in the future.

IV-99
RESULTS

The wave lengths and shear moduli given by substituting the measured frequencies and phase velocities into the equations in article 3 are shown in Table 2 and 3. The vibration test was mainly carried out at the range of frequency around 20 Hz, being relatively

stable, because higher frequency was limited in order to protect the vibrator itself and lower frequency could not give clear waves owing to insufficient existing force. The phase velocities on the horizontal and vertical directions were measured with

various pickups. As a result, these differences do not affect the observed values of phase velocity. On the other hand, the dynamic behavior of the ground as seen in Figs. 7 and 8, shows such aspect as the Rayleigh wave at the propagation of the vertical wave but

it does not look as clearly as the Love wave at the propagation of the horizontal waves

(5) . Assuming that the velocities and shear moduli in Table 2 and 3 represent dynamic

properties of the layer in depth of a half wave length, it is possible to express this relation in Figs. 9 and 10. Although it is difficult to indicate the corresponding layer,

it seems reasonable from Figs. 3 and 7 that the layer in depth of 0.4 to 0.5 wave length shares the most severe deformation.

The above mentioned results have good corredpondence with soil test results and seismic prospecting results. This fact makes us believe that this method of determining

dynamic properties of the ground from phase velocity with a vibrator is practical and useful. Now we can point out the merits of this method,

(1) availability of any type of pickups and of any component of waves.

(2) continuous measurment of properties of layers downward, depending on different

frequencies.

(3) detailed measurement for shallow layers.

(4) simple and economic measurement with a vibrator, pickups and recorders. The disadvantages of this method are:

(1) requirement to improve the accuracy of the measured phase velocity.

(2) necessity of electric power.

(3) difficulty to apply it to the ground under some obstacles, up and down surface, deep layers and so on. -4 On account of the deformation level in this test, approximately 2 x 10 , the resulting values are not directly applicable to such a big vibration as an earthquake but useful to the vibrations caused by circulations, construction works, factories, and so on. CONCLUSIONS AND ACKNOWLEDGMENT

It is found that if we want to know the dynamic properties of the ground, we can easily obtain comparatively accurate values from shake tests on the ground with a vibrator. Now there still remain some problems to pursue such as expansion of frequency range, minimization of the base, more comparisons with other methods, device for simpler operation,

and so on.

iy-ioo
We would like to express our grateful thanks to Professor Osawa and the members of

the committee and to the persons who cooperated with this field test. REFERENCES

1. Vibrations of Soils and Foundations, by Richart, Hall and Woods, Prentice-Hall.

2. Ditto, translated in the Japanese by T. Iwasaki and A. Shimazu, Kashima Shuppankai

.

3. Vibration Manual for Civil Engineer (in Japanese) , The Japan Society of Civil Engineers.

4. Earthquake Observation on Soil and Structure I, II, III, March in 1975, 1976, 1977

(in Japanese) , Building Research Institute.

5. Bulletin of the International Institute of Seismology and Earthquake Engineering,

Vol. 14, 1977. Surface Waves Generated by a Vibrator, by S. Hattori.

IV-101
IV-102
/' L wave aa/v

I

ft. wave

Fig. 2 Modes of Rayleigh and Love waves

IV-103
IV-104
point WO 2 reference

title Survey for dynamic properties of soil U i o

P : Pressureneter

2-2-24 Fuchinobe, Sagamihara, Kanagawa

date 20 - 25 March, 1^75 altitude i//S*2<)0 ] standard TP

me thpri

Rotary boring

manner N. Yamada | chief | S. Miyaji

in. it

110 44

-tin

106 74

standard penetration test

lb lows/ 10cm"

103 <?* //. 85

101.54 1215

light brown 3i?I

db^h

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Of5 £=JL

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:layeybrown 12 - mp0

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medi- um

soft

medi

urn soft

hard

gravel |dia . of grave 1 with brown3m/m ~P5m/m very

Fig. 5 Result from geological survey

IV-105
IV-106
Fig. 7 (a) Amp. distribution

(Rayleigh wave; Ver. comp.)

00 0-5 10

Q.

a> Q

10

15

20

1. 25-2 cps

2. 20-6 cps

3. U-9 cps

k 12 2 cps

5, 10 0 cps

6, 8-0 cps

7, 6-6 cps

IV-107
IV-108
Fig. 8 Amp. distribution

(Love wave)

606

805

U QU cps

2196

1009

12-75

1500

1, 2U cps

2 15 2 cps

3, 12-6 cps

4, 10 1 cps

5, 8 0 cps

6, 6 0 cps

7, 5 3 cps

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Content

Convertable

velocity

induction

motor

in

air

ventilation

type

5.5

kW 3

phase

A.C.

200/220

V

50/60

Hz 0

-

1100/0

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1300

rpm

Control

by

thyrister

system

Item

(Motor) Type

Out-put Power

Rotational frequency

Control system

Content

Simultaneous

reversal

rotation

system

with 3

-

unbalanced

weight

and 3

horizontal

axes

1

-

250 kg

-cm

(continuously

changeable)

3000

kg(

>

17

Hz)

1-20,

2-40

Hz

+1%

against

Max.

value.

1020

(mm)

in

width

880

(mm)

in

length

880

(mm)

in

height

900 kg

(incl.

motor)

Item (Vibrator) Exiciting systemExiciting

moment

Max.

force

Frequency Accurancy

Dimension

Weight

IV-112
Values

on

horizontal

shaking

by

displacement

vlbrograph

Refer- ence

Elici- tingforce It Exici- ting

force O.ltExici- tingforce It ditto Exici- tingforce O.lt

o kg/

cm 2

735 474 848 876 832 419 00 <£> 00 <r <r

cr 00 CA >» CA <j

a

e

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tH to

00 r- 00 r- 00 r- tH tH tH tH tH tH

L/2 o> vo o> <r os *3" J m 15.4 9.2

18.1 12.6 16.6 8.4

18.9 12.6 18.8 8.6

19.4 8.6

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33 co 00 cm 00 CO 00 12.0 18.1 12.1 18.1 12.0 18.0

*>

m/sec 208 167 217 227 215 156

r— r-- \D CO vo

cm cm cm m co m

CM CM CM tH CM tH

3 rad/sec 85

113 77

113 82

116 co v£ co so co r~ tH tH tH

tH tH tH

Sec- tion m 0

tH co r~ S ml O 1 ml

m

tH O ml 0 co m r^* CM 1 1

Direc- tion Axial Vertical

Values

by

velocity

vlbrograph

Refer- ence

Exici- ting

force lt,2t

kg/

cm 2

1250 1050 545 430 404 327

2218 1114 734 607 463

sured

60 § S .Ad-^OOr-r^vOvC OOr-*r-»r^ E

| U CM CM tH tH tH tH CM CM tH tH fH * O 0) •H to

L/2 in cm m co co cm n h <o 4 ci g tH tH CM tH

m 31.2 24.2 10.6 7.2 6.4 5.1

45.0 23.6 13.5 9.4 7.2

•K "3 m r-. <r <r N 00 <y> vo cm m 00 r~ 0 m © co

SB tH CM CM CM tH tH CM CM >

m/sec 250 230 179 159 159 143 333 236 208 189 165

3

rad/sec

Love wave 50 60

105 138 157 176

Rayleigh

wave 46 63 97

126 144

IV-113
Values

on

Vertical

shaking

by

displacement

vlbrograph

Reference

Exiclting

force

It

ditto ditto ditto ditto ditto ditto ditto ditto ditto ditto ditto

o kg/cm 2

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1235 521 398

1140 521 452 1140 845 707

a

8

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21.4 9.7 6.6

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20.5 13.5 8.5

sured

*3

Hz 12.0 18.1 23.0 12.0 18.0 23.0 12.0 18.1 21.1 12.0 18.1 24.0 *

mea

> ml

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r- vo <f cn o CM tH tH CM CN CM

3

red/

sec 75

114 145 75

113 145 m m vo m sr <H

tH cn r— tH ui

Section

u-i O tH C-> e i i m Ocm

5-15 20

- 30

Direction Axial

Vertical

IV-114
STUDIES ON SOIL LIQUEFACTION RELATED TO EARTHQUAKE RESISTANT DESIGN OF STRUCTURES Masamitsu Ohashi, Chief, Earthquake Disaster Prevention Division

Toshio Iwasaki, Chief, Ground Vibration Section Fumio Tatsuoka, Research Engineer, Ground Vibration Section

All from the Public Works Research Institute, Ministry of Construction, Japan ABSTRACT

In order to evaluate dynamic behavior of structural foundations and embedded structures

during earthquakes, it is essential to estimate the effects of the surrounding soils on

j these structures. The authors have conducted a literature survey on the effects of liquejfied soils on bridge foundations and also conducted laboratory experiments using models of

pile foundations including surrounding soils. Furthermore, a simplified method to evaluate liquefaction potential of sand deposits

was investigated on the basis of numbers of blows (so called N-values) by the standard

penetration test. Proposed herein are the critical N-values which can be used in determining liquefaction potential. This method can estimate whether the sand deposit may likely

liquefy or not during future severe earthquakes by means of comparing N-values measured at

Ithe site of interest with the critical values proposed. These critical values were

{determined on the basis of dynamic triaxial tests on undisturbed sand samples and N-values

measured at the points where the undisturbed samples were obtained. These studies are to clarify the effects of liquefied soils on pile foundations and

to establish design methodology of pile foundations considering the effects of soil liquefaction.

KEYWORDS: Bridge foundations; dynamic triaxial tests; liquefaction; model tests; pile

foundations; sand; standard penetration test; shake table.

J

IV-115
INTRODUCTION

In order to appropriately evaluate dynamic behavior of pile foundations or embedded

structures during earthquakes, it is essential to estimate the effects of the behavior of

the surrounding soils on these structures. It can be supposed that the surrounding soils do not move severely in normal cases and normally resist movements of the structures, but

sometimes the surrounding soils cause large movements of the structures when the soils vibrate severely as a result of resonant state of the soils and furthermore in special cases the surrounding soils do not support these structures at all when soil liquefaction

takes place.

To provide a proper solution to this problem, it seems necessary to precisely analyze

the behavior of the structures considering the effects of soil-structure interactions. When the surrounding soils liquefy during earthquakes, the problem becomes more complicated

In this case, the effects of liquefied soils on the structures will be much more severe. The authors have conducted a literature survey on the effects of liquefied soils on bridge foundations and also conducted laboratory experiments using models of structures including surrounding soils. This attempt was to clarify the effects of liquefied soils on pile foundations, and to establish design methodology of pile foundations considering

the effects of soil liquefaction. Another problem to be considered in the aseismic design of bridges with pile founda- j tions in sand deposits with high liquefaction potential is the evaluation of liquefaction

potential of sand deposits. In the simplified procedures for evaluating liquefaction

potential generally used in Japan, the N-value obtained from the standard penetration

tests are used in evaluating the liquefaction potential of the sand deposit.

If the N-value of the sand deposit of interest is lower than a critical value, say

N=10, it is judged that this sand deposit will liquefy during severe earthquake motions.

In this study dynamic triaxial tests on undisturbed sand samples were conducted and at the | same time N-values were measured at the points from where undisturbed samples were secured.; Then the appropriate critical N-values were determined on the basis of the relationship

among dynamic shear strength, N-value and insitu effective overburden pressure. It was

found that even in the case where the dynamic shear strengths are identical, the N-values may vary according to the variation of soil properties which can be represented by the content of fine soils and the mean diameter of soil particles.

The results of this study are summarized as follows

1) The supporting capacities of surrounding soils may become considerably smaller when liquefaction takes place.

In some cases, dynamic forces of soils acting on piles may become considerably larger

in the course of liquefaction. When the complete liquefaction takes place, both the supporting capacities and the dynamic forces can be approximately estimated by assuming that a liquefied sand layer is heavy water.

2) In the course of liquefaction, soil-pile foundation systems may resonate to the I input motions, and may vibrate severely.

IV-116
3) Critical N-values for evaluating the liquefaction potential should be determined

by taking into account the facts that the N-values decrease with increase in the content

of fine soils in sand deposits. Also, the dynamic shear strength does not decrease much

as compared with the decrease in the N-values. DAMAGE TO BRIDGE FOUNDATIONS DUE TO LIQUEFACTION

It has been recognized that one of the main causes of damage to bridges which were

constructed in alluvial deposits and reclaimed lands is an unstable performance of ground

soils. It is also well known that liquefaction of sandy soils induce catastrophic movements

of ground and loss of bearing capacities of ground. A number of damages to bridge structures

with pile foundations were observed during the Niigata Earthquakes of 1964 in Japan (Iwasaki

(1973)) and during the Alaska Earthquake of 1964 in the United States (Kachadoorian (1968)). Similar damages were also reported for other earthquakes in Japan (Iwasaki (1973)) and for

the San Francisco Earthquake of 1906 (Youd and Hoose (1976) ) . Liquefactions have been

observed in alluvial deposits and reclaimed lands during major earthquakes including the

above earthquakes. In Japan, 44 earthquakes induced liquefaction phenomena during the period from 1872 to 1968 (Kuribayashi and Tatsuoka (1974)). In viewing damages to engineering structures caused by soil liquefaction, numerous

studies on evaluation of liquefaction potential of sandy deposits have been conducted by

using dynamic soil testing equipment such as dynamic triaxial apparatus and a dynamic

simple shear apparatus. Furthermore, studies have also been conducted with shaking table

tests to determine the effects of the loss of bearing capacities caused by liquefaction on

the behavior of heavy structures (Yoshimi et al. (1975), Ishihara, et al. (1975)). However,

little effort has been made on the study of the effects of soil liquefaction on the dynamic

behavior of pile foundations (Shikamori, Sato and Hakuno (1973) , Yoshida and Uematsu

(1975), Iwasaki, Tatsuoka and Sakaba (1976)). Accordingly methodology of aseismic design

of pile foundations considering the effects of liquefaction is still in the process of

formation. Intending to establish a rational aseismic design criterion of pile foundations which

are constructed in soil deposits with high liquefaction potential, a series of shaking

table tests of pile foundations placed in liquefying sand deposits was performed. EXPERIMENT ON DYNAMIC BEHAVIOR OF PILE FOUNDATION MODELS

Test Arrangements - In this experiment small models of pile foundations were prefabricated on a shaking table. Five different tests listed in Table 1 were conducted. Typical

test arrangements for Test 1 and Test 2 are illustrated in Figs. 1 and 2, repsectively . A

saturated loose sand layer including a small model of a pile foundation was placed in a container on a shaking table. To actuate the shaking table an electro-magnetic actuator

was used for Test 1. A displacement controlled hydraulic actuator was used for Tests 2 to

5. Sand layers were prepared by pouring air-dried sand into water. Initial relative

densitites of the sand layers ranged from 24 to 40 percent. The water level coincided

IV-117
with the sand surface at the beginning of shaking. As shown in Figs. 1 and 2, acclerometers

and strain gauges were installed to measure movements of the shaking table, sand layers

and pile foundation models. Earth pressure cells and pore pressure cells were also equipped

to measure earth pressures acting on piles and excessive pore water pressures. Sinusoidal

table motions were applied in all tests (Tests 1 to 5) . Wave form of acceleration measured

at the table was of triangular form in the case of Test 1, as shown in Fig. 3 where the table acceleration is denoted as Al. However, in the other tests (Test 2 to Test 5) where a hyraulic actuator was used, the measured table acceleration was close to sinusoidal

motion, as shown in Figs. 4 and 5. Several motions with different frequencies were employed

as input motions. Frequencies were selected on the basis of the natural frequencies of pile foundation models submerged in water. The base acceleration was determined in view

of outbreak of gradual increase in excessive pore water pressure in sand layers. Actuators

used in the experiments were not sufficient enough to keep an accurately constant base acceleration during a test run. This is due to a great change in rigidity of sand layers, which are caused by soil liquefaction. Actually, the base acceleration changed somewhat

in the course of liquefaction of sand layers, as shown in Figs. 3 through 5. Four different pile foundation models were examined (see Table 1) . Their natural frequencies when submerged in water are 3.8, 4.0, 10 and 14 Hz, respectively. Their natural frequencies in air are slightly higher than those in water. Each of these models

consists of several solid aluminum bars with 2 cm in diameter and a top mass. The values

of the natural frequencies of models were adjusted by choosing the number of bars and the weight of the top mass. These models were fixed at the bottom, as shown in Figs. 1 and 2 to facilitate the boundary condition. The degree of fixity would be considered to be larger than that in actual cases. Principles of Similarity - Frequencies of input motion and natural frequencies of pile foundation models submerged in water were determined in the following manner. Model

tests in the field of soil mechanics can be classified into two groups by their objectives. The first group is to find fundamental parameters required to be taken into account when

analyzing the behavior of the prototype by an analytical method. This analytical method

can be, of course, applied to the model test. In this case, the rigorous satisfaction of principles of similarity is not of first importance. The second group is to quantitatively

estimate the behavior of the prototype from the results of model tests. In this case the principles of similarity should be determined and satisfied. At present, it is of first importance to find the controlling factors in the behavior of structures in liquefying

soils. Therefore, reported herein is the result of tests of the first category. Accordingly,

the similitude between the prototype and the model was satisfied in terms of the following

(but others such as the permeability of sand layers could not satisfy the principles of similarity)

(i) Length (L) : Scale ratio considered for length was on the order of 1:10 to 1:30. Therefore, model sand layers with the height of 70 cm correspond to actual sand deposits

of 7 to 21 m in depth.

(ii) Density of sand layer (MLT ): Since actual sands were used, the ratio of density of soils was on the order of 1:1. IV-118
Since body force induced by gravity is the same between

models and prototypes, the ratio for body force induced by horizontal motions should be on

the order of 1:1. And the ratio for horizontal acceleration was also on the order of 1:1.

(iv) Time (T) : From (i) and (iii) the ratio for time is determined as

1 : /l"= 1 : /lO to 1 : /30" = 1:3.2 to 1:5.5.

(v) Natural frequencies of model pile foundations submerged in water (f ) , frequencies

. P

of input motion (f.), and fundamental natural frequencies of sand layers with the excessive

1 -4 -1 porewater pressure of zero and the shear strain level of T = 10 or less (f ), (T )

111 g These scale ratios are determined from (iv) as 1:— = 1:— to 1 :-g—

g- = 1:0.32 to 1:0.18. Estimated frequencies f^ for model sand layers were around 18 and 24 Hz as shown in Table 1. These values correspond to the natural frequencies of the prototype sand layers,

3.2 to 7.7 Hz. On the other hand, the fundamental natural frequency of a soil deposit f^

(Hz) can be approximately estimated by:

f

l = i (HZ) (1)

in which V

g denotes the average shear wave velocity (m/sec) and H means the depth (m) of

soil deposit of interest. Since the usual values of for shallow alluvial sand deposits

range from 150 to 250 m/sec, the fundamental frequency of sand deposit with the depth of 7 to 21 m ranges from 150/(4x21) = 1.8 Hz to 250/(4x7) = 8.9 Hz. These values corresond

well to the values derived from scale ratios and the fundamental frequencies of model sand

layers (=3.2 to 7.7 HZ)

.

Since predominant frequencies of strong earthquake motion observed on the actual sand

deposits are estimated to be less than the above values, the frequency of input motion in model tests f^ should be less than the natural frequencies of model sand layers f^ (18 and 24 Hz). Therefore, as the values of f. in the model tests, 12 Hz for Iruma sand and

l 10 Hz and 20 Hz for Toyoura sands were selected. Furthermore, it can be estimated that the fundamental natural frequencies of ordinary

bridges with pile foundations, f^, are less than the predominant frequency of strong

• earthquake motion observed on shallow sand deposits when the value of f^ are determined on

the assumption that liquefied sand layer with the depth of 7 to 2imare removed. Therefore,

three of the five model tests conducted were cases where the natural frequencies of model

pile foundations submerged in water, f , are less than the frequency of input motion, f^, which correspond to actual ordinary cases. In addition to these cases where f^ < f^, other two cases where fpi= f . and f > f . were examined in order to evaluate the importance

p l of the relationship between these two values, f^ and f^ in assessing the dynamic behavior

of pile foundations in liquefying sand layers. Test Records - For Test 1, acceleration records at the table at three positions in

the sand layer and at three positions of the model pile foundation are shown in Fig. 3. Excessive porewater pressure in the sand layer and earth pressure acting on the pile

foundation are also illustrated in the figure during the elapsed time of 8 to 14 seconds

IV-119
counting from the beginning of shaking. Similar records in the cases of Test 2 and Test 4 are shown in Figs. 4 and 5, respectively. One of the most peculiar performances observed

in these tests is non- stationary behavior of the sand layer and the pile foundation, and non-stationary dynamic interaction between them, while the table movement is almost stationary Furthermore, it can be noted that the responses of different pile foundation models are not similar to each other. Especially, the variation of the response of the pile foundation

in Test 4 is quite different from those in Test 1 and Test 2. In order to clarify the dynamic behavior of the sand layer and the pile foundation, envelopes of dynamic amplitudes recorded were illustrated in Fig. 6 for Test 1. Since in the case of Test 1 excessive porewater pressures reached their maximum stationary values

at the elapsed time between 11 and 12 seconds and the acceleration in the entire sand layer decreased to almost zero at the same time, it could be estimated that liquefaction

in the entire sand layer initiated at the elapsed time between 11 and 12 seconds in the case of Test 1. It should be noted in the case of Test 1 that the maximum response of the pile foundation occurred at the elapsed time of about 10 seconds when excessive porepressure

did not reach the maximum value yet and the sand layer was vibrated in ordinary fashion. And at t=10 seconds, dynamic earth pressure acting on the pile foundation and strains in the pile also had their maximum values. In addition to this, it is also noted in the case of Test 1 that the response (acceleration) of the pile foundation decreased to the small value after the entire sand layer had liquefied. Corresponding to this decrease in accelerat: of the pile foundation, earth pressure acting on the piles and strains in the pile also decreased to the small values. Following this, recovery from liquefaction started at the elapsed time of about 30 seconds, and after this moment the response of pile foundation increased again. Although this recovery phenomenon is also very interesting, this will not be discussed herein because such a phenomenon is unlikely to take place in the prototype during severe ground shaking in an actual earthquake. In this test, the ratio of time in the model and that in the prototype is considered on the order of 1:3.2 to 1:5.5. Therefore, the elapsed time of 30 seconds in the model corresponds to 96 to 165 seconds in the prototype. This duration time seems longer than the duration of major ground motion

during a strong earthquake. Furthemore, it is recognized that recovery from liquefaction began after the cease of earthquake motion in the actual earthquakes experienced. From

these reasons, only phenomena observed before the recovery from liquefaction will be discussed in this report. Variations of Responses of Pile Foundation Models in the Course of Liquefaction - In Fig. 7 shown is the variation of response ratio 3^ of the pile foundation with respect to frequencies of input motion in the case of Test 1. The response ratio is defined as KJ (2)

where |<*A1 I represents the amplitude of the acceleration at the base and \®^\ represents

the amplitude of the acceleration at the bottom of the top mass of the pile foundation. The solid curve in Fig. 7 represents the response curve of the pile foundation model

IV-120
measured when submerged in water and the black solid circles denote the response ratio of

the pile foundation model measured in liquefying sand layer at several increments of elapsed

time. Numbers near the black solid circles represent the elapsed time in seconds from the beginning of shaking. It is seen from this figure that the response ratio of the pile foundation model, 3 i once increased before t=10 seconds and then decreased abruptly to a smaller

P

value of 0.2 at t=12 seconds. Also illustrated in Fig. 7 are the response ratio of sand

layer 3 =

l a l/l a

A1 l' excessive pore water pressure ratio u/umax

anc^ the amplitude of dynamic

earth pressure acting on the pile foundation Ip^I- These values are illustrated in relation

with 3p- It is clearly seen from this figure that at the moment of the maximum response of

the pile foundation model, sand layer had not liquefied yet and the dynamic earth pressure

had the maximum value and also that after the occurrence of liquefaction in the entire sand

layer the response of pile foundation and the dynamic earth pressure also decreased to smaller values. Similarly Figs. 7, 8, 9 and 10 represent the variation of responses of pile foundation

models in the cases of Test 2, Test 4 and Test 5, respectively. In these figures, squares

denote responses of pile foundation models at the moment when liquefaction is not initiated

in any part of the sand layer, triangles show responses at the moment when liquefaction is taking place in the upper part of the sand layer, and circles represent responses when

liquefaction is taking place in the entire sand layer. It can be noted from these figures

that while the variation of the response of the pile foundation model in the case of Test

2 is quite similar to that in the case of Test 1, those in the case of Test 4 and in the

case of Test 5 are considerably different from that in the case of Test 1 or that in the

case of Test 2. The cause for these differences among these tests will be discussed later.

Fig. 11 illustrates instantaneous positions of the sand layer and the pile foundation

model at several instants of time (t=8.0 to 12 seconds) in the case of Test 1. In this

figure, each stage (a) through (d) in each column represents the variation of positions of

the sand layer and the pile foundation model with a short interval during the half of the vibration period (=1/24 second). In each figure, circles represent the value of ~a/l a

A1 l in which a denotes the instantaneous value of acceleration recorded by the accelerometers

A2 through A4 equipped in the sand layer, and l a

Al l represents the amplitude of the base

acceleration. In an ideal sinusoidal movement, _ot/l a

A

jl can ke an index representing the displacement modes. And solid circles represent those for the pile foundation model.

Arrows represent the instantaneous directions of the movements at each point and the short

vertical straight lines represent the maximum values of -ct/l a

Al l at each point during the

half of the vibration period. Triangles denote the instantaneous values of earth pressures

acting on the pile. The positive sign corresponds to the increase of earth pressures

sensed by the earth pressure cell which faced to the right in these figures. At the bottom

of Fig. 11 shown are the excessive pore pressure ratio u/u . It is seen from this max

figure that at the elapsed time of 8 seconds when excessive pore water pressures were

very small, movements of the sand layer and those of the pile foundation model are close

to each other during the half of the vibration period. Then, as time goes on and excessive

pore pressures increase, the difference between the movement of the sand layer and that of

IV-121
the pile foundation model increases gradually. This would mean that the capability of the sand layer to support the pile foundation model is decreasing with decrease in the effecti

stress in sand layer (which corresponds to increases in excessive pore water pressure)

As seen in Figs. 3 through 11, liquefied parts in the sand layer expand from the surface toward the bottom. Therefore, the free length of the pile foundation model which are not 1 supported by the surrounding sand layer increased with increase in excessive pore pressure

in the sand layer. This means that the natural frequency of the pile foundation in the sand layer, which is defined as f , decreased with increase in the free length of pile

foundation.

Then, it would be beneficial to examine the response of the pile foundation model

from the viewpoint of structural dynamics. First, let's suppose a single-degree-offreedom vibrating system which corresponds to the pile foundation model in the sand layer. The maximum value of the response ratio 3 = 3.6 of the pile foundation model, which took

P place at the elapsed time of 10 seconds, could be regarded as that of the vibrating systen which resonates to the sinusoidal input motion with the frequency of f^ = 12 Hz. Then, the apparent damping ratio (h) of the vibrating system could be derived as,

htr ^br^ 0 - 14 (3)

In Fig. 12 shown are the response curve of the equivalent single degree-of-freedom vibrating system with the damping of 0.14 and are the phase relation between the input

force and the motion of the system. Using this response curve, the apparent natural frequency of the pile foundation model embedded in the sand layer f^* in the case of Test

1 was obtained as follows. It could be supposed that the natural frequency of the pile

-4 foundation embedded in non-liquefied sand layer at the strain of around 10 is similar tc the natural frequency of the sand layer, that is, f = 18 Hz in the case of Test 1. g Therefore, just after the beginning of shaking the natural frequency of the pile foundatic embedded in the sand layer, f * would be around 18 Hz. This means then f./f * (=12/18) <1. P i P

Therefore, the approximate value of f./f * at the elapsed time of t=8.0 seconds can be

i P obtained from the intersection point between 3 =2.1 (3 at t = 8.0 seconds ) and the P P response curve for f./f * < 1.0. By the same procedure, the values of f./f * were obtains

1 P 1 P

for the following elapsed time t = 10.0, 10.8, 11.3, 12.2 seconds as shown in Fig. 12. 11 is seen from this figure that the ratio of the frequency of input motion to the natural : frequency of the pile foundation model embedded in the sand layer, f^/f^*, increased with

time and eventually approached the value in the case of the pile foundation model submerge; in water, f./f = 12/3.8 = 3.2. Since the value of f. was kept constant as 12 Hz,

l p l the increase of f./f * means the decrease of f *. Also shown in Fig. 12 is the phase

l p p relation 0 between the motion at the bottom of the top mass and the motion at the base.

In this figure, the values of 0 were obtained from Fig. 11 and the values of f^/f * were ! obtained from the procedure described above. The general coincidence of the measured phase relation with that of the single-degree-of-freedom vibrating system with damping

ratio h = 0.14 means that the variation of the response of the pile foundation, 3 , in

IV-122
liquefying sand layer was caused by the variation of the apparent natural frequency of the pile foundation model in the sand layer, f *. As a next step, the effects of the response of the sand layer on the response of the

pile foundation model should be taken into account, because the response of sand layer varied in the course of liquefaction as shown in Figs. 3 thorugh 11. In the case of the pile foundation with a very small rigidity, the response of this pile foundation would be completely affected by the response of the sand layer before effective stress in the sand reduces to zero. On the other hand, this effect would be rather small in the case of the pile foundation with a relatively large rigidity. This would be the cases of these tests

(Tests 1 to 5) . For example, in the case of Test 1, the maximum response ratio of the pile foundation 3^, is about 3.6 at t = 10 seconds and at this moment the response ratio

of the sand layer near the surface was about 1.9 which is less than 3.6 (=3 ). This means

P

that the large response of the pile foundation model at t = 10 seconds was caused mainly

i by the resonance of the pile foundation model embedded in the sand, as illustrated in Fig.

12. A Summary of Model Tests of Pile Foundation Tests

A summary of the whole test results in Fig. 13 shows the relationship between the response ratios (3^) of the pile foundation models and the ratios (f^/f^) of frequencies

of input motions to the natural frequencies of the pile foundation models submerged in water. This figure indicates clearly that a comparative relation among the frequencies of

input motions f^, the natural frequencies of the pile foundation models submerged in water

(f ) and the initial natural frequencies of the sand layer (f ) is fundamental in determining

P g the dynamic behavior of the pile foundation models in liquefying sand layer. Since all of

the tests shown in Fig. 13 are the cases where f is larger than f. or f , these tests can

g

y

i P

be divided into the following three groups:

(a) f^ > f^ > fp (Tests 1 to 3) : In these tests, the response ratios of the pile

foundation models, 3^r are small at the beginning of shaking as indicated by hollow squares

in Fig. 13, and as the sand layer begins to liquefy, 3 starts to increase, reaching its maximum value as indicated by black triangles. At this moment, the sand layer has not liquefied completely. And following this moment, 3^ begins to decrease and eventually 3^ becomes a small value as indicated by hollow circles in Fig. 13. These small values of 3P

correspond well to those of the response ratios of the pile foundation models submerged in

water. The phenomenon described above could take place in the prototype as one of the worst cases. Therefore, the maximum value of 3 in the course of liquefaction in sand P

deposits should be estimated accurately in the case of the prototype so that this phenomenon

can be taken into account in aseismic design of pile foundations.

(b) f > f. = f (Test 4): In this test, 3 simply increases from the beginning of

g l p p shaking to the state of the liquefaction in the entire sand layer. The eventual response

ratio in the completely liquefied sand layer is as large as the value at the resonance of

the pile foundation model submerged in water. If there could be such a case where f. = f i P

in the prototype, severe damages could take place, because the response might become quite

large.

IV-123
(c) f > f > f. (Test 5): In this test, the tendency of the variation of 8 is

g P i p similar to that of Test 4. However, unlike in Test 4, the eventual value of 6 in the P completely liquefied sand layer is rather small, because the response ratio of the pile foundation model submerged in water is small due to the fact that the value of f ,/f is

i P much less than 1.0. In this case, the damage to the pile foundation would be minor. However, this case would be unlikely to exist in the prototype, because the value of fP would be smaller than in most cases in the prototype. SIMPLIFIED PROCEDURES IN EVALUATING LIQUEFACTION POTENTIAL

Present Status

In the specifications for Earthquake Resistant Design of Highway Bridges (Japan Road Association - 1971) , a special attention is given to the design of highway bridges con- structed in sandy layers vulnerable to liquefaction during earthquakes and in very soft cohesive layers. The bearing capacities of these layers are neglected in the design, in order to assure high earthquake resistance of structures built in these layers. An artic

"Sandy Soil Layers Vulnerable to Liquefaction" states: saturated sandy soil layers which

are within 10 meters below the actual ground surface, have a standard penetration test N- value less than 10, have a coefficient of uniformity less than 6, and also have a D^Q-val of the grain size accumulation curve between 0.04 mm and 0.5 mm, shall have a high potent

for liquefaction during earthquakes. Bearing capacities of these layers shall be neglect

in design. Saturated sandy soil layers which have a D^-value between 0.004 and 0.04 mm or between 0.5 and 1.2 mm may liquefy during earthquakes, and shall be given an attention. Estimation in the case shall be made in accordance with the available information on liquefaction problems. When a special investigation is performed, the above article may not be required to apply.On the other hand, it is well known that standard penetration N-values may vary considerably due to the variation of the grain size of sand deposits. For example, it is

a general tendency that in so-called alluvial sandy deposits, N-values are considerably

large for gravelly sand deposits and are quite small for silty sand deposits. Therefore,

it can be easily supposed that N-values do not hold a constant value even for the cases where the dynamic shear strengths are constant. The difference of N-values in the two cases would be caused by the other soil properties such as the grain size rather than the dynamic shear strengths. Accordingly, if an identical critical N-value, say 10, is appli

to all types of sand deposits in evaluting liquefaction potential, this critical N-value may be too small for gravelly sand deposits and may be too large for silty sand deposits. For these reasons, it is specified in the above-mentioned specifications that the uniform coefficient U and D„ -value should be taken into account in the evaluation of liquefacti

c 20 potential in addition to the N-value. However, it has become clear recently that there i no evidence that the U -values of sands have a definite relation to liquefaction potentia

c Furthermore, it seems that the D -value specified in the above-mentioned specifications '

IV-124
are not always proper as an index representing grain size for the evaluation of liquefaction

potential. For these reasons, the present study discusses the relationship among standard penetration N-values, grain size distribution characteristics and dynamic shear strengths

which were obtained from dynamic triaxial tests on undisturbed sandy samples. It was

found from the relationship that the critical N-value in the evaluation of liquefaction

potential could be smaller for sand deposits with small grain sizes. Dynamic Triaxial Tests on Undisturbed Sandy Samples Sampling of undistrubed sand samples and standard penetration tests were performed at

two sites, i) Akebono - Tatsumi Site and ii) Haneda Site. Both sites are along the Eay of

Tokyo. A typical boring log at Akebono-Tatsumi Site is shown in Fig. 32. Undistrubed

samples were secured by a reformed Bishop sampler in which the inner diameter of the sampler is 5.4 cm and the length of the sampler is 65.0 cm. Sand samples with low contents

of fine soils were frozen at site by dry ice to avoid disturbances which may be caused

during the transportation from the site to the laboratory for testing. Silt samples were

not frozen to avoid the disturbance due to volume expansion caused by freezing. Figs. 15 through 18 show typical grain size analysis curves. Almost all sand samples secured are

Dynamic triaxial tests were conducted on samples with the diameter of 5.0 cm and the height of 10.0 cm. Applied isotropical effective confining pressures were equal to insitu

effective overburden pressures and enough back pressures were applied to make the Skempton's

B-value larger than 0.96 (Fig. 19) . Figs. 20 and 21 show typical test results which

describe the relationship between the applied stress ratio and the number of repetitions

in both cases of undisturbed samples and disturbed samples. Disturbed samples were made

by pouring completely disturbed de-aired saturated soils which were made from undisturbed

samples into a mold. It is seen from this figure that the strength of disturbed samples

is smaller than those of undisturbed samples for the same density. In this study, the dynamic shear strength in dynamic triaxial tests was defined as

K io' 'a

a

d the stress ratio (^7") when the simple amplitude

of axial strain Ae (§A) becomes 3%, at the number

a of repetitions.

The value of R„ were read off from the relationship between a / (20 ) and the number of

x, dp c repetitions. Fig. 22 indicates a relationship between dynamic shear strength of undisturbed

samples and that of disturbed samples (obtained from Figs. 20 and 21). Dynamic Shear Strength ( T/°^)£ Comparable With Dynamic Shear Stress Ratio ( T/°v

) e Dynamic shear stress ratio (T/a^,)^ which are induced in grounds by earthquake motions

were defined as the maximum shear stress ratio in the computed time history of shear

stress ratio T/a^, at the depth of interest. Earthquake response analysis of grounds were

performed by the wave propagation theory with the equivalent linearization method with

IV-125
respect to deformation properties of soils. In this study, underground acceleration records were used as input base motions. The maximum acceleration in the computations was taken as j 150 gals at the base (assumed at the depth of 127 m)

In evaluating liquefaction potential, the dynamic shear strength should be compared with the dynamic shear stress ratio due to earthquake motions (See Fig. 14) . In this procedure, to obtain the dynamic shear strength ( T/°v

')£ which is compared with the computed dynamic stress ( T/°

v

') e' some corrections should be made on the dynamic shear strength R^, which are obtained from dynamic triaxial tests. These corrections are expressed as,

(T/V} *

C

l

• °2 * S * C

4

* °5 * h (5)

(i) C^: This is the correction factor for confining pressure. In this study, the insitu earth pressure at rest, K

q

, was estimated to be around 0.5. In this case, the effective mean principal stress in the insitu stress condition becomes (1+2 K )

• O ,/3 where a , o v v

is the effective overburden pressure. On the other hand, the effective mean principal

stress in dynamic triaxial tests is O^, as shown in Fig. 19. As it was shown by Ishihara

and Li (1972) that dynamic shear strength of samples under stress conditions with different

K

Q values should be evaluated for the same effective mean principal stress, the correction

factor C. becomes,

c lt2K

° 2 (6)

^1 3 3 (ii) C_: This is the correction factor for wave form of loading. While actual earthquake

2 motions are random with respect to time, the loading wave forms used in dynamic triaxial

tests were sinusoidal with constant amplitudes. According to Ishihara and Yasuda (1972)

the value of C

2 ranges from 1/0.55 to 1/0.7, in which has a larger value for a shocktype earthquake motion and has a smaller value for a vibration type one. In this study, a moderate value equal to 1.5 was adopted.

(iii) C^: This is the correction facte able in the processes of sampling, freezing, transportation and testing procedures in dynamic triaxial tests. It can be supposed that the dynamic shear strength of soils may decrease due to these disturbances. Fig. 22 shows the relationship between the values of

R^ of undisturbed samples defined by Eq. (4) and those of completely disturbed samples. It

is clearly seen from this figure that the difference between two values is too large to be neglected. Therefore, it seems that the value of C

3 should be larger than 1.0. However,

at present, the precise value of can not be evaluated.

(iv) C.: This is the correction factor for the effect of the densif ication, which are

4 also inevitable during the above-mentioned operations. In fact, some densif ications were observed in samples. As denser sand samples have larger dynamic shear strengths, can

be, in general, less than 1.0. Considering that densif ications of samples are caused by disturbances during operations, it was estimated in this study that * = 1.0.

(v) C^: This is the correction factor for compensating the effects of directions of excitation. Although the precise value of can not be evaluated, here it is assumed that

IV-126
Eventually, the product of all the correction factors became about 1.0. Therefore,

in this study the dynamic shear strength were obtained as

(7)

To estimate the value of ( T /°

v

')£ at the P°int where only the N-values or both the N- values and other soil properties such as mean grain size and contents of fine soils were

obtained but no undisturbed samples were available, the relationship among (T/O^,

) ^-values, N-values and soil property parameters should be established. In this study, it was supposed

that (T/G^,

) ^-values can be represented as

(8)

in which N means the standard penetration test N-value, S denotes the content of fine soils

(< 74y) in percentage and D^^ denotes the mean grain size in mm. As a great deal of dynamic

triaxial tests on clean sands have been conducted at various laboratories, it is necessary

to establish the method of evaluation of clean sand deposits as the first step. For this

purpose, insitu relative density should be evaluated. As an indirect method, Meyerhof (1957) proposed the following equation:

(9)

where is relative density in percentage, N is the standard penetration N-value and o^, is

j the effective overburden stress in kg/cm2

. This equation was proposed on the basis of the

test results on clean sands by Gibbs and Holtz (1957). Figs. 23 and 24 represent the comparison between the relative density obtained from eq. (9) and that obtained directly by

D = fe -eVfe -e . where the values of void ratio e were obtained from undisturbed sand

r * max ' max min

samples by a reformed Bishop sampler. These samplings were performed at Kawagishi-cho,

Niigata City by the Japanese Society of Soil Mechanics and Foundation Engineering (1976)

.

The values of e and e . were obtained on completely disturbed air-dry samples. These max min e J 1 c

figures indicate that the value of the relative density D

r obtained by eq. (9) is almost

identical with that obtained directly1 by1 D = (e -e)/(e -e . ) . Fig. 25 shows the relar max max mm 3

j tionship between the dynamic shear strength from dynamic triaxial tests on clean sands with

, no fine soils less than 0.074 mm and the relative densities D = (e -e)/(e -e . ) . These

r max max min

tests were conducted at various laboratories as listed in Table 2. The average relationship among data plots in Fig. 25 can be represented by

R

£ = 0.0042 D

r

(10)

j.where D denotes (e -e)/(e -e . ) in percentage. If there is not a large difference

r max max min

between the strength of an undisturbed clean sand and that of a completely disturbed clean

sand, the dynamic shear strength (t/o ,)j can be estimated by the following procedure:

IV-127
/ N

(N,0"v

,) -> D

r = 21 /-

Q 7 (eq. (9)) -> R£ = 0.0042 Dr

(eq. 10))

v' > (T/Ov

,) £ = R

£

(eq. (7)) (11)

Fig. 26 shows the relationship between (T/O ,)„ obtainted by dynamic triaxial tests

v X, , undisturbed samples which were conducted in this study and the value of = 21/N/(a

v

, +

It can be clearly seen that the (t/o^,) ^-D^ relationship of silty find sands -:. which were tested in this study is quite different from the average ( T /av

'^£~D

r relationship of clea sands. Therefore, it seems that the direct application of eq. (11) to this case gives coj siderably under-estimated values of (T/a^,)

£

. Estimation of (x/a ,

£

- Values at Akebono-Tatsumi Site

The values of ( T/°

v

'^£ at tne site of Akebono-Tatsumi were estimated by the followin procedure, because it was found that eq. (11) could not be applied directly to this case.

(a) (T/Ov

,

) £-values were obtained as ( T/°v

'^£ = R£ at tne points where undisturbed sampl were obtained and the values of R

£ were obtained by dynamic triaxial tests.

(b) (T/a^,

) g-values at the points where only N-values were measured and no other informs

is available were estimated as follows:

(eq. (9)) 0.7

v + R

£ = 0.21 + 0.0021 D

r

(eq. (13) (T/O ,) £ = R

£

(eq. (7))

R

£ = 0.21 + 0.0021 • D

r

(13)

Eq. (13) represents the average relationship of the test data from this study and the average relationship is shown in Fig. 26.

(c) (T/Ov

,

) ^-values at the points where N-values and grain size analysis curves of the samples were obtained were estimated as follows. First, it was supposed that the reason why the (T/0 ,) .-values of sands tested in this study are larger than those of clean sane for the same value of D

r = 21/n/{O

v

, + 0.7) is that sands tested in this study are fine sands and include fine soils less than 0.074 mm to some extent. Therefore, DR

£ was defirc as the difference in the dynamic shear strength (T/a^,)^ = R^for the same value of D

r between the value of the data obtained in this study and the average value of clean sands This definition is illustrated in Fig. 27. As almost all of the samples tested in this study were fine sands where the mean grain size D^

0 were less than 0.3 mm, only the correlation between the DR

£-value and the content of fine soils were examined as shown

in Fig. 28. While there is a wide scattering in the plots, it may be seen from this figi that DR

£-values increase with increase in the content of fine soils (S) . This relations)- may be expressed as,

(14) IV-128
Therefore, the ) ^-values in this case were estimated as follows:

(T/0v

,) £ = {( T /°

v

') £ by eq- (ID > + fD(T/Ov

,) A by eq. (14)} (15)

Comparison Between ( T/°

v

') e

anci ^ T//°v

'^£ at Akebono-Tatsuln:'- Site Firstly, the critical N-value = 10 specified in the specifications for the EarthquakeResistant Design of Highway Bridges were evaluated as follows. In Fig. 30 shown is the

value of ( T/av

') e which was calculated for a point at Akebono-Tatsumi site. In this calculation, the maximum acceleration at the base was taken as 150 gals and four different earthquake motions recorded at the depth of 127 m near this site were utilized. Also shown in : this figure are the values of (T/o^)^ which were obtained from eq. (11) on the assumption

that the N-values at this site were 10 irrespective of depth and the sands in this point were

clean. Therefore, the dynamic shear strength R^ of these sands can be obtained from eq. (10)

.

It can be seen from Fig. 30 that the value of ( T /°

v

') £ obtained as above are almost

identical to the value of (T/0 ,) for the entire depth of interest. Therefore, it was

v e evaluated that the critical N-value of 10 is a proper value for clean sand deposits with the

value of ( T/av

') e which were estimated in this study. Secondly, the values of ( T/°

v

')£ obtained by eq. (11) using the measured N-values and

0 , were compared with the calculated values of (T/a ,) as shown in Fig. 31. It can be

v v e seen from this figure that the overall values of ( T /°

v

')£ are less than those of (T/a^,)

g

. This means that this deposit may liquefy during severe earthquake motions. However, as eq.

(11) is based on the test results on clean sands, this conclusion may not be proper. Therefore, (t/o"v

* ) ^-values were estimated by the three methods (a), (b) and (c) presented earlier. In Fig. 32, black squares represent the (t/0v

,

) ^-values obtained by the method (a), hollow circles and triangle circles represent the (X/O^,

)

^-values obtained by the

method (b) and horizontal lines represent the ranges of (t/o*v# ) ^-value obtained by the method (c) . And the hatched zone shows the estimated range of (t/0^,)^. It can be seen

from this figure that the estimated values of ( T/°

v

»)£ are, in general, larger than the estimated values of (T/0 ,) . This conclusion is rather different from that which can be

v e derived from Fig. 31. This means that when the liquefaction potential of sand deposits are

evaluated on the basis of dynamic triaxial tests, these tests should be conducted on undisturbed samples if these samples include much fine soils. An additional survey was performed at the Haneda site. The data obtained from this

survey were added to those of the Akebono-Tatsumi site as shown in Figs. 33 and 34. In these

figures, data with letters A means those of the Akebono-Tatsumi site. It is seen from

these figures that the general trend is almost similarfor both sites.

The Critical N-values Based on Dynamic Triaxial Tests on Undisturbed Sand Samples

Fig. 33 shows the relationship between the dynamic shear strength of undisturbed samples

R^ and the relative density D

r = 21 / N/O^,, + 0.7 obtained by using N-values and insitu

effective overburden pressures 0^, . On the basis of this relationship, the critical N-values

were determined for fine sands with different content of fine soils as follows. It should

be noted that the almost mean grain diameter D of sands tested are less than 0.3 mm.

IV-129
Therefore, the following discussions can be applied only for sands with D^q less than 0.3mm. While there is a large scatter in the data shown in Fig. 34, the average relationship of these plots can be represented conservatively as

(16)

where S denotes the content of fine soils in percentage. The value of R 0 is represented

= 0.0042 x 21 /

^ Q 7 + 0.0035 S

= 0.0882 /-

+ Q 7 + 0.0035 S (17) v' To obtain the relationship in fine sands with D

5Q less than 0.3 mm between the critical N-value for the evaluation of liquefaction potential and the content of fine soils, the critical N-value of 10 was selected as the value for clean sand deposits with O

1 =0.5

2 kg/cm . This value was evaluated from the above-mentioned specifications. In the specifi- cations, it is specified that saturated sandy soil layers within 10 m of the actual ground

surface and with a standard penetration test N-value less than 10 may be vulnerable to liquefaction. Therefore, as the mean value of O^, for this sandy soil layer, 0.5 kg/cm2 was selected. If this critical N-value of 10 can be applied to clean sand deposits like those at Niigata City, the standard value of R^, R^, can be obtained by substituting

N=10, O^, =0.5 and S=0 into eq. (17) as

(18)

Next, by substituting R^= 0.255 and O^, = 0.5 into eq. (17), the relationship between

the critical N-value for sands including fine soils and the content of fine soils S can

be expressed as:

N = 0.00189 (72.9 - S)

2 (19)

From eq. (19), the critical N-values for various values of S can be obtained as,

N = 10 for S = 0%,

N = 7.5 for S = 10%,

N - 5.3 for s = 20%,

N = 3.5 for s = 30% and

N

~- 2 . 0 for s = 40%.

IV-130
From these values, the design critical N-values for sand deposits whose D^-values are less

than 0.3 mm can be tentatively proposed as,

N = 10 for S = 0

- 10%, N = 7 for S = 10 - 20%, N = 5 for S = 20 - 40% and

N = 3 for s = 40 - 60%.

Since these values were obtained from the small number of field data, more research

is necessary. Therefore, the critical N-values recommended for design purposes should be determined after more field data are accumulated. CONCLUSIONS

Dynamic behavior of pile foundations in liquefying soil deposits is considered to be

one of soil-structure interaction problems during earthquakes. As this problem is very

complicated, only qualitative results can be derived from the experimental tests conducted

in this study. The following remarks can be made.

(1) Since liquefaction phenomena progress with respect to time and with respect to

space, the effects of liquefied sands on the piles vary as functions of time and sapce.

It can be normally recognized that the response of a pile foundation with a normal rigidity

is small during earthquakes before liquefaction initiates. The response increases abruptly

after liquefaction begins, and decreases when complete liquefaction takes place. During

the complete liquefaction, soils behave as heavy liquid, and piles are subjected to hydrodynamic pressures due to the liquefied soils.

(2) The relationship among the natural frequency of the pile foundation supported by

the surrounding soil deposits before liquefaction initiates, the natural frequency of the

pile foundation submerged in completely liquefied soils and the predominant frequency of

input motion is the most important factor. Dynamic behavior of pile foundations in the

course of liquefaction of sand layers will be considerably affected by this relationship.

(3) While the complete liquefaction continues, the soil-pile foundation system behave

as a submerged structure. Since its natural frequency becomes smaller, it may resonate

when subjected to seismic motion with longer periods. Accordingly it will be important to

assess the components of longer periods involved in induced seismic motions.

For simplified procedure in evaluating liquefaction potential, critical N-values are

proposed on the basis of dynamic triaxial tests on undisturbed samples and the standard

penetration tests. While additional research works are necessary, the tentatively proposed critical

N-values for sands whose D^-values are less than 0.3 mm are:

N = 10 for the content of fine soils S = 0 to 10%

N = 7 for S = 10 - 20%,

N = 5 for S = 20 - 40%,

N = 3 for S = 40 - 60%. IV-131
I

ACKNOWLEDGEMENTS

The studies described in this paper were greatly assisted by Messrs. Susumu Yasuda, Makoto Hirose, Seiichi Yoshida, Masahide Ikemoto, Yoshio Sakaba and Hironobu Noma. Their experimental works are especially appreciated. The field soil surveys at the Akebono-Tatsumi site and Haneda site were conducted by ; Kawasaki National Road Construction Office, Kanto Regional Bureau, Ministry of Constructio: with a cooperation of the Public Works Research Institute. Mr. Koji Miyata, Director of Kawasaki National Road Construction Office gave the authors an invaluable opportunity to investigate insitu dyanmic soil properties with emphasis on liquefaction potential. The authors express their cordial appreciation to him and the staff members at the above offic REFERENCES

Gibbs, H. J., and Holtz, W. G. , (1957), "Research on Determining the Density of Sands by Spoon Penetration Tests," Proc. of 4th ICSMFE. London, Vol. 1. Ishihara, K. , and Li, S., (1972), "Liquefaction of Saturated Sand in Triaxial Torsion Test! Soils and Foundations, Vol. 12, No. 2, June. Ishihara, K. , and Yasuda, S., (1972), "Sand Liquefaction Due to Irregular Excitation,"

Soils and Foundations, Vol. 12, No. 4., Dec. Ishihara, K. , and Matsumoto, K. (1975), "Bearing Capacity of Saturated Sand Deposits

During Vibration," Proc. of the 4th Japan Earthquake Engineering Symposium, 1975. Iwasaki, T. (1973), "Earthquake-Resistant Design of Bridges in Japan," Bulletin of Public Works Research Institute, No. 29. Iwasaki, T. , Tatsuoka, F. , and Y. Sakaba (1976), "A Shaking Table Test on Dynamic Behavior

of Model Pile Foundations Embedded in Sand Layers," Proc. of 14th Annual Meeting of Earthquake Engineering, JSCE (in Japanese)

Japan Road Association (1971) , "The Specifications for Earthquake Resistant Design

of Highway Bridges." Kachadoorian, R. (1968), "Effects of the Earthquake of March 27, 1964, on the Alaska

Highway System," Geological Survey Professional Paper 545-C, U.S. Department of

the Interior. Kuribayashi, E., and Tatsuoka, F. (1975), "Brief Review of Liquefaction During Earthquakes'

in Japan," Soils and Foundations, Vol. 15, No. 4., Dec. Meyerhof, G. G. , (1957), "Discussion of Gibbs and Holtz Ppaer," Proc. of 4th ICSMFE, London, Vol. III. Shikamori, M. , Sato, Y. , and Hakuno, M. (1973), "Effects of Noncomplete Liquefaction of

Soils on Embedded Structures," Proc. of Annual Meeting of JSCE (in Japanese).

Yoshida, T. , and Uematsu, M. (1973), "A Model Test of Piles in Liquefying Sand," Proc. of Annual Meeting of JSCE (in Japanese)

Yoshimi, Y. and Tokimatsu, T. (1975), "Liquefaction of Sand Deposits during Earthquakes Ne Structures," Proc. or 4th Japan Earthquake Engineering Symposium, 1975 (in Japanese).:

Youd, T. L. , and Hoose, S. N. (1975), "Liquefaction During 1906 San Francisco Earthquake," Journal of the Geotechnical Division, ASCE, Vol. 102, No. GT5. IV-132
TEST

CASE SAND

(%) Number4 ) of Piles

Head Weight

(kg)

5) fp

(Hz)

6)

f i (Hz)

7)

| u All

(gal)

Shaking

Per iod (sec .

)

Sj fg

(Hz i Tl lruma 1 ' 40 9 44 3.8 12 40 - 100 60 18 T2 27 53 4 10 60 - 80 30 __T3 _ 2) 34 . 6 1. 10 20 80 - 130 15 T4 Toyoura

24 6 18 10 10 60 - 80 30

24 T5 40 9 13 14 10 60 - 120 30

1) lruma Sand (G s =2.88, D5 0=0.52mm, U c =1.52, emax =0.93, emin=0.66)

2) Toyoura Sand (C s =2.64, D5 0 =0.16mm, U c =1.46, emax =0.96, emin=0.64)

3) Relative Density

4) Each Pile is made of aluminum bars with 70cm in length and 2cm in diameter.

5) Natural Frequency of Pile Foundation in Water

6) Frequency of Input Motion

7) Amplitude of Base Acceleration before Perfect Liquefaction

8) Estimated Natural Frequency of Non-liquefied Sand Layer (y=10~ 4

) Table 1. List of Test Cases

Fig. 1 Test Arrangements for Test 1

IV-133
Fig. 2 Test Arrangements for Test 2

excessive

pore pressure

ACCELERATION 1 Of PILE FOUNDATION

EARTH PRESSURE ON

PILE FOUNDATION vmwvVi/V\M/vV^ —1—

elapsed time isec i Fig. 3 Typical Test Records (Test 1) (See Fig. 1)

IV-134
0.2 mm _n

Ba,c nispuconcn. in,,

0 ? mm —^ A-^/V A A A A n - -

100 gol. ^ \y \j \j \j \s w

100901.

lOOjal.

Acceleration in Sand Layer [a:i

509/cm

50 Ibt

209/cm jn

0-0 0.5 Fig. 4 Typical Test Records (Test 2) (See Fig. 2)

0.2""" Base Displacement (Dl )

[ up

ioo r'

Relative Displacement to Base at Tc w

100«=l _n w

AAA?—

AcccUranon ,„ Sand Lav, - A.IA. a. Ia. a. A /V

100 «*l _n

E.O»tm- Jl T

hxccssive Tore Pressure at Base P

i

, , r Sand Layer P3

0 o asmo.4 o 6 0.8 1 0 1 2 1 4 1 6 1 8

' ft .0 10 .a Fig. 5 Typical Test Records (Test 4) (See Fig. 2)

IV-135
IV-136
,—y% nos obtointd at this Itvi / „ g _

^ f, = 12 Hz, Fnqutncy of input motion FREQUENCY . f I Hz) Fig. 7 Variation of Response of Pile Foundation in the course of Liquefaction of Sand Layer (Test 1)

IV-137
IV-138
50

Fig. 9 Variation of Response of Pile Foundation in the course of Liquefaction of Sand Layer (Test 4)

IV-139
50

20 14 Hz

iO -

0 5

Response curve of pile

foundation in water

Estimated response curve

of sand layer before liquefaction

0 0.5 1.0 0 2 4 U/Umox |Pd! (g/cm2

)

05

02

Response at entire liquefaction

Response at partial liquefaction

Response before liquefaction

0 1 5 10 20

Frequency f (hz)

50 100

Fig. 10 Variation of Response of Pile Foundation in the course of Liquefaction of Sand Layer (Test 5)

IV-140
Fig. 11 | Instantaneous Positions of Sand Layer and the Pile Foundation Model

1 (Test 1)

IV-141
Fig. 12 Estimation of Apparent Natural Frequency of Pile Foundation Model Embedded in Liquefying Sand Layer (Test 1)

IV-142
2

10 -

Estimated range of response of pile foundations in non- liquefied sand layers

LEGEND

fj : Frequencies of input motions

f«: Natural freqencies pile of foundations in water

: Response of pile foundations in non- liquefied sond layers a a : Response of pile foundation in partiolly liquefied sond loyers o • : Response of pile foundation in perfectly liquefied sond loyers • : The maximum response in the

course of liquefaction of sond

loyers TI.--.T5. : Test coses

i.2 05 1 2 5 10 FREQUENCY RATIO ; f ( /f p

Fig. 13 Summary of Whole Tests

IV-143
JSoil Exploration

| Density"] | N-value~| Shear^Wave Velocity |

| Undisturbed Samples

|

Model of Ground for Earthquake Response Analysis

Underground Seismic

Ground Motion Records

G/G

Earthquake Response Analysis ~1

(T/ffvO e,

Dynamic Shear Stress due to Earthquake Motion (r/<V) = (r/(r v ')e maY

NO LIQUEFACTION

Dynamic Soil Tests

Tests for Shear Moduli

and Dampings Tests for Dynamic Shear Strength (Dynamic Triaxial

Tests)

q d D

2 a c

' N/; Relation

[R^ at =20 for Ae a (SA)=3%

| Dynamic Shear Strength

- C r

C

2 .C3 .C4 .C

5 .R^ Correction Factors

l + 2Kf C2:C.F. for Loading wave form

C^rC.F. for Sampling Disturbance

C.:C.F. for Densification

C

5 :C.F. for Other Factors

- Relation

(S: the content of fine soils)

]

LIQUEFACTION

Fig. 14 Flow Chart of Precise Evatuation of Liquefaction

Potential

IV-144
Fig. 15 Typical Grain Size Accumulation Curves

(Akebono, Reclaimed Sand Layer)

0 074mm J Grain size (mm) Fig. 16 Typical Grain Size Accumulation Curves

(Akebono, Alluvial Sand Layer)

Tatsumi -2.9-~-6.45m Reclaimed

Uc = 50.0 ~ 2.9 If/ / a; o 20 = 0.04 ~o.5 mfn If / B ; D 20 = 0.004 ~ 1.2mm

——

0.001 0.01 Toi 1 10 100 O.OMTM- Grain size (mm) Fig. 17 Typical Grain Size Accumulation Curves

(Tatsumi, Reclaimed Sand Layer)

IV-145
Grain Size (nun) Fig. 18 Typical Grain Size Accumulation Curve

(Tatsumi, Alluvial Sand Layer)

5 cm

— (Tc = (Tc

1

°c' (Effective confining pressure ) = OV (insitu effective overburden pressure) °BP(Back pressure) aBP § J> (Insitu static porepressure)

All of the tests were performed on samples with Skempton's B-value larger than 0.96.

Fig. 19 Stress Condition in Dynamic Triaxial Tests

IV-146
AVphonn-1' 2 ' ' "2 80 ~ -3 811 m ) f O u : (Tc

( 0"[ -o

)

{.. i€ Q (SA ) : 1 %

Af 0 <SA ) ; 3%

Undisturbed Samples ^

V y- U = Oc 0V - O. 4 kg /err

2 -- 3 % 0 = 4,0 kg /cm 2 \ A£ a (SA):

Dr = 76.4 %*

-

Disturbed Samples N, y- fl€a (SA) = l% —*• a^vv /— Ae0

( SA ) : 3%

OY - 0.4 kg/cm 2

\ 0=0.0 ^ I

U;Crc

Or =76.4 %

* Mean relative density

(Content of Fine

i i i

Soils ; 20%)

2 5 10 20 50 100 200 500 Number of Repetitions

Fig. 20 Typical Dynamic Triaxial Test Results (Akebono)

Pi

.2 0.2

Tatsumi T-2

r i

( - 4.96 ~ -5 409m ) f • O u = ac

i Oc' = o

)

A£0 (SA)= 1 %

i O A£„ (SA)= 3%

Undisturbed Samples ^

u =rjc ^ Ae„(SA ) = 3% > A A£ 0 (SA)= 5 %

fje

' ; 0.6 kg/cm 2 (SA )

-- 5 %

0"

BP = 1.3 kg/cm 2 ^ A€ Q

tSfl )= i%

Dr = 72.6%*

" Disturbed Samples

0"c' =0.6 kg /cm 2 U=CTC 0> =0.0 * A£o (SA) : i % y 3D- A€0 (SA) = 3%

Or = 66.8 %*

* Mean relative density (Content of Fine Soils; 11%)

10 20 50 100 Number of Repetitions

500 1000

Fig. 21 Typical Dynamic Triaxial Test Results (Tatsumi)

IV-147
IV-148
Grading

llt.clay Sand Gravel Relative Density D (%)

10 20 30 40 50 6 0 70 8 0 90

. \

V . \

i

. i _. .1

P i 8

1 <—

• 7

1 /1 .1

1 .

• 1 \ \

i

' 1.

1 J • 7 —1- i —

-8—

• 1 i

V

\

. 1\ 9

i

' t

• * / / -4 —

a / \V

i

. i > »n

i

i .» -9- "I

/T • 22 —V— o Me H

asured

// ^24-

• V

V\ M— \ V

V f (TV + 0.7 N \

»

0. i

i ).84" m

N-value

10 20 30 40

Fig. 23 Comparison between Measured Relative Density Dr = e max~ e x 100 and Dr

e max-emin

at Kawagishi-cho, Niigata

Z1]°v' + 0.7

IV-149
Gr ad i ng

\ m m m

Silt and clay Sand Grave!

3 20 40 60 80 00

Relative Density Or (%

10 20 3 0 4 0 50 6 0 70 80

Fig. 24 Comparison between Measured Relative Density Dr = e max-e x 1QQ and Dr = ^ / N

e max / 0 v + 0. 7 at Kawagishi-cho, Niigata

IV-150
0.5

0.4

p.3

0.2

0.

1

0

N/ - 20 L/i63.n ocLnas

yS^— Rg^ 0.0042 Dr (%)

0 50 100 Relative Density n = ema*-e , „ , (%

)

1 J 8mo» - emin

Fig. 25 B,£ - D. Relationship of Clean Sands

IV-151
IV-152
0.5 (Akebono-Tatsumi

)

(0 V

': kg/cm2

) Fig. 26 D^- Relationship of Sands of Akebono-Tatsumi Site

Average R^ - D

r Relation

of Clean Sands

Fig. 27 Definition of DR/

"

0 20 40 60 Content of Fine Soils. S(%) Fig. 28 S-D Relationship

IV-153
Akebono

r/<rv

' OJ) OJ 02 03 M

Fig. 30 Comparison of <j/o v

> ) of Clean Sand for N = 10 with (r/(j /) A

e

IV-154
Akebono

IV-155
1st Boring 2nd Boring

RS : a

ASa: RSiSa ASiSa

ASi:

Reclaimed Sand Alluvial Sand

Reclaimed Silty Sand

: Alluvial Silty Sand Alluvial Silt

r/ffV

0 0 0.1 0.2 0.3 0.4

Upper Bound of Estimated (T/a ,) Lower Bound of Estimated (r/o

v

,)^

O {T/a v

<)g

. value from eq. (13) for Nj A (t/Uv')^ - value from eq. (13) for N

2 (x/av

>)£

- value of undisturbed samples

|__| Ran ge of <?/<>?) # - value from eq. (IS)

R/ = 0 0882 J-=

f0.0O22S 1 (-0.0075SJ

(£0.1751

Fig. 32 Comparison of (T/°v' ) Based on Dvnamic Triaxial Tests on Undisturbed Samples with (t/"v' ) e

IV-156
o

0.4 -

(f> 20 40 60 80 100 Content of Fine Soil.S {%) Fig. 34 S

- DR£ Relationship of Sands of Two Sites

IV-157
EARTHQUAKE RESISTANT DESIGN BASED ON GROUND MOTIONS AT BASE-ROCK

Eiichi Kuribayashi, Chief, Earthquake Engineering Section Kazuhiko Kawashima, Research Engineer, Earthquake Section

Public Works Research Institute ABSTRACT

It is generally known that dynamic behaviors of structures are influenced by their ground conditions and that earthquake ground motions recorded are dependent on their ground conditions. In order to specify common input earthquake motions for design of every structure on and under ground, it is useful to select base-rocks in ground, where effects of grounds near surface are small enough to be ignored, as an input terminal where earth- quake motions are to be specified. In order to improve such seismic designs, discussions

on necessary conditions of base-rock and on accuracies of base-rock motions estimated by theoretical calculations are presented. Earthquake responses of bridges are also presented

as a numerical example. KEYWORDS : Analytical method; base-rock; bridge foundations; deconvolution procedure; earthquake records; ground conditions; ground transfer functions; shear wave.

IV-158
INTRODUCTION

Advances in technology would make it possible to construct huge structures with deeply

embedded foundations. In the current seismic designs of structures the usual practice is to specify earthquake motions at a gravity center as an input even in huge structures. However, based on observations of underground earthquake motions, the earthquake motions are not uniform in grounds. Therefore, it is necessary to take into account such trends in the seismic design of structures. On the other hand, it is generally recognized that earthquake

motions recorded are appreciably influenced by local ground conditions. It is, therefore, inadequate to employ the recorded earthquake motions directly, disregarding the differences

of ground conditions in the seismic design. One of the approaches to consider such problems

is to select a suitable widespread formation of the ground (base-rock) , where effects of

ground near the surface (subsurface ground) are small enough to be ignored, as a common

input terminal of earthquake motions. When the earthquake motions at the selected formation

are found to be independent of the properties of the subsurface ground, their characteristics

can be directly compared with each other among various sites. By specifying input earthquake

motions at the base-rocks, the subsurface ground motions can be determined based on the assumptions of upward shear wave propagations in the grounds. The earthquake responses of structures can then be determined by appropriate analytical models. Although the base-rocks are generally selected based on their geological and soil conditions, it should be noted that they are essentially selected in accordance with the characteristics of earthquake motions specified there (base-rock motions) . The base-rock

motions are expected to be compared on the same basis among various sites as an index expressing seismic intensities considered in design and we can appropriately incorporate

the subsurface ground conditions so as to specify input motions for every structure constructed on and underground (Pig. 1-1)

.

When the base-rock motions have such conditions, the remaining significant factors which influence the base-rock motions would be magnitudes (Richter scale) and epicentral

distances. Fig. 1-2 shows earthquake motions classified in terms of such factors. From

an engineering point of view, it is considered desirable to apply earthquake motions in design which lie on the dotted line in Fig. 1-2. The level of intensity will depend on

the factors determined based on the dynamic behaviors, magnitudes, shapes of the structures,

etc. For instance, earthquake ground motions used for seismic analyses of suspension

bridges in Japan are shown in Fig. 1-3. This paper presents the conditions of base-rocks to improve seismic designs based on base-rock motions and discusses the accurate base-rock motions estimated by theoretical

calculations. Also, earthquake responses of bridges are presented as a numerical example

to estimate base-rock motions.BASE-ROCKS AND BASE-ROCK MOTIONS Assuming propagations of shear waves in horizontally stratified two elastic layers as shown in Fig. 2-1, equations of motion can be expressed disregarding damping terms as

IV-159
where

,

suffix expressing j th formation (j = 1, 2) shear modulus of j th formation mass density of j th formation

(2-2)

Fourier transformation of Eq. (2-1) gives 9Ti twhere,

v

,

: written as,

in which A. and B. are arbitrary constants and express amplitude of downward and upward

shear waves at x.. = 0, respectively. Determinations of the constants A_. and B.. based on boundary conditions give the solution in the form as,

cos —

Jcos : (2-5) 2B2 cos (-^r + «5 ) <~ lS V5

where

,

a = PtVi /Pi V*

5 = tan (atari——

)

y i

From Eqs. (2-4) to (2-6) two types of ground transfer functions can be defined, i.e. suppose the ground transfer function H^B

2 (to) be defined as ratio between ground motions

IV-160
in the first or second layers (v.. or v ) and the amplitude of upward (incidental) motions

'<<"> "

! WH

~V H a>H , . ,">» 7 cos'— + «'sin1 -—

(2-9) (2nd layer) 0/v

and suppose the transfer function H 20 (w) be defined as ratio between ground motions in the first or second layers (v^ or v^) and ground motions at the interface x

2 = 0 (v^ = 0)

,

then it can be written as

(1st layer)

(2nd layer)

The ground transfer functions defined by Eqs. (2-9) and (2-10) change in accordance with

the parameter a as shown in Table 2-1. It is obvious from Table 2-1 that both types of transfer functions in the second layer are unconditionally independent with properties

of the first layer when a = 0, i.e., the shear modulus of the second layer is infinitely

large compared with that 0 f the first layer. It implies that both the incidental and

ground motions in the second layer are independent of the properties of first layer in

such conditions. Even in the case when a ^ 0, no reflections and refractions of propagating

shear waves develop in the second layer, provided that the second layer is uniform continua

in grounds. In such conditions the incidental motions in the second layer are independent

of the first layer.

It is recognized therefore that the second layer can be selected as base-rock in either case when the second layer is infinitely stiff as compared with the first layer or

when the second layer is uniform continua in the ground. In the former condition, both the

incidental and ground motions in the second layer can be selected as base-rock motions while

in the latter condition, only the incidental motions can be selected as base-rock motions.

The ground with the above conditions do not exist in practice. It is required therefore to relieve the above conditions from practical point of view in accordance with

objectives and accuracies needed in the analyses. For example, in the former condition,

influences of the first layer (subsurface ground) on the ground motions in the second layer

(base-rock motions) would be controlled to be small, provided that the second layer is considerably stiff comparatively to the first layer, and, in the latter condition, incidental

motions in the second layer would be considered as base-rock motions as long as the second

layer continues almost uniformly with the depth where shear waves propagate for a period of predominant motions.

IV-161
ACCURACY OF BASE-ROCK MOTIONS ESTIMATED

In order to obtain base-rock motions from recorded motions it is required to incorporate effects of local subsurface conditions. A one-dimensional analytical model based on vertically propagating shear waves with equivalent linear materials is currently established

for such purposes. An accuracy of base- rock motions calculated theoretically by the decon- volution procedures was correlated with the recorded underground motions. Three underground motion accelerations observed at Ukishima Park near Tokyo (Table 3-1) were employed for this purpose. Three motions were the most significant ones recorded up to the present. Underground Transfer Functions Estimated from Observations

Soil profile at Ukishima Park (Fig. 3-1) consists of upper alluvium soft formations and lower diluvial hard formations which lie 50 m beneath the ground surface. Earthquake motion: were recorded at four points, i.e., at the ground surface, 27 m, 67 m and 127 m beneath

the ground surface. Power spectra were calculated to estimate predominant frequencies as shown in Figs. 3-2 to 3-4 and it was found from these results that they are approximately

4-7 c/s for A-earthquake motion and 0-1 c/s for B- and C-earthquake motions. The former motion was obtained from small earthquake in magnitude with relatively short epicentral distance while the latter motions were obtained from large earthquakes in magnitude with

long epicentral distances. Ground transfer functions (amplitude) between each recording point were calculated

as shown in Fig. 3-5. It is noted from the result that although the ground motions have significant differences in their predominant frequencies, the ground transfer functions obtained from the motions are almost independent of such characteristics. Theoretical and Estimated Ground Transfer Functions

The ground transfer functions were theoretically determined by calculations based on

the deconvolution procedures. An analytical model was formulated based on the soil profile of Fig. 3-1. The shear moduli of soils were evaluated by estimated shear wave velocities

v

g (m/sec) based on a relationship with the N-values obtained by field tests as

v

g = 60 /FT (3-1)

The shear moduli of soils G

q determined based on Eq. (3-1) correspond to the value at low amplitude strain level. Since the ground motions studied were very small, it was found appropriate to analyze them by using G

q

. Fig. 3-6 shows the comparisons of theoretical and observed underground transfer

functions. A damping ratio of 2% of the critical was assumed in the theoretical calculations Theoretical and Measured Underground Motions

The underground motions were computed for C-earthquake theoretically by specifying the recorded surface motion. The deconvolution procedure was applied using the analytical

model formulated in the preceding paragraph. Fig. 3-7 shows comparisons between computed

IV-162
I and recorded underground motions. Both motions are considered to be in fairly good agreei ment. It would be possible to improve the computed motions by formulating more accurate

analytical models based on precise investigations of ground. Based on the results presented it was recognized that the deconvolution procedures

based on shear wave propagations are effective in taking account of local ground conditions

into recorded earthquake motions. NUMERICAL EXAMPLES FOR CALCULATION OF BASE-ROCK MOTIONS AND EARTHQUAKE RESPONSES OF BRIDGE

Analytical Model

A discrete analytical model as shown in Fig. 4-1 was formulated to calculate earthquake

i responses of the embedded foundation. The equation of motions of the system can be written

; as

(M + M)ii + C u + K u -p -e -p -p -p -p -p +C (u - u ) + K (u - u ) = 0 (4-1) -e -p -g -e -p -g -

where,

M : mass matrix of structure -P

M^ : mass matrix of surrounding soils

C^ : damping matrix of structure

K : stiffness matrix of structure -P

C^ : damping matrix expressing radiational dampings

K^ : stiffness matrix expressing springs between structure and surrounding soils u . u , u : absolute displacement, velocity and acceleration vectors of structure -P TP ~P

u^, u^: absolute displacement and velocity vectors of subsurface ground

in which the subsurface ground motions of u^ and u^ are assumed to be specified. Denoting

M = M + M - -p -e

C = C + C (4-2) - -p -e

K = K + K

[. (4-1) can be written as

IV-163
(4-4)

The vector u can be conveniently decomposed into a quasi-static displacement vector u and

a dynamic displacement vector i.e.,

u = u , + u -p -pd -ps

By definition of quasi-static displacement in the form as Ku+K u =0 (4-5)

u = - K

_1 K u = - K u -ps — —e -g —s —

g

Substitutions of Eqs. (4-4) and (4-6) into Eq. (4-3) gives

KJ ^ (4-7)

Usually the damping term on the right hand side of Eq. (4-7) is less significant comparing with the inertia terms so that it can be dropped from the equation without introducing

significant errors. Then Eq. (4-7) can be written as

(4-8)

Eq. (4-8) can be solved by mode-superposition procedures provided that the damping matrix on the left hand side of the equation is assumed to be triangularized in the same manner as the mass and stiffness matrices in the form of damping ratio of critical. Numerical Example

The Itajima Bridge is a composite steel girder bridge with five simple spans as shown

in Fig. 4-2. In this numerical example, earthquake response of second pier-foundation

of the bridge from right hand side was investigated based on earthquake motions recorded

on ground surface near the bridge (approximately 400 m apart from the bridge, refer to Fig.

4-3) . An earthquake motion acceleration selected was induced by Hyuganada Earthquake

(April 1, 1968, M - 7.5, A - 100 Km) and had the maximum amplitude of 185 gals as shown

in Fig. 4-4. Based on soil investigations conducted near the pier-foundation (Fig. 4-5) it was

found that the soil profile consists of upper soft loan formations with an averaged N-value

of 7 and lower stiff gravel formations with averaged N-values of 30 or more. Assuming the relation of Eq. (3-1), the relative stiffness a defined by Eq. (2-7) between the loam

and gravel formations was estimated approximately as 0.48 for low amplitude ground vibrations and 0.34 for high amplitude ground vibrations. It was expected therefore that ground motions in the gravel formations would be less significantly influenced by the loam

IV-164
! formations during high amplitude ground vibrations. Then, based on the relieved criteria

of base-rocks in the preceding chapter it was judged that the gravel formations underlying

10 m below the surface could be selected as base-rock at this site. On the other hand, ground conditions had not yet been investigated enough at the recording site. Based on topography of the sites it was assumed that the gravel formations existed at the bridge

site continues to the recording site and underlies 20 m below the surface. This assumption

coincided with the evidence that predominant frequency of the ground was approximately

3-4 c/s in field microtremor observations at the site. The ground motion and incidental motion at the top face of gravel formations were

theoretically calculated as shown inFigs. 4-6 and 4-8, respectively, by the deconvolution

procedures taking into account the shear moduli of loam formations with their strain

dependences. Fig. 4-7 shows comparisons of response acceleration spectrum between the recorded surface motion and theoretically calculated base-rock motion (Fig. 4-6) . The pier-foundation and surrounding subsurface ground were modeled as shown in Fig. 4-9 by the analytical model described in the preceding paragraph. The loam formations were idealized

by one dimensional shear column model with equivalent linear soil properties. The weight of

girder supported by the pier was treated as an additional lumped mass at the pier top. The

mass of surrounding soils defined by Eq. (4-1) was disregarded in the analyses. Vibration

modes and natural periods (1st - 3rd) calculated for the subsurface ground and pier-foundation are shown in Fig. 4-10. Earthquake responses of the pier- foundation were calculated based on Eq. (4-8) by

j applying the base-rock motion displayed in Fig. 4-6 at the base of shear column model. The

damping ratio of 5% of the critical was assumed in the calculation. The maximum responses

of displacements and accelerations are shown in Fig. 4-11 and representative response time

histories at the top of pier are displayed in Fig. 4-12. CONCLUSIONS

Based on the results presented, the following conclusions can be deduced:

(1) In order to specify common input earthquake motions for design of every structure

I on and underground at various sites, the useful approach is to select base-rocks in ground,

; where effects of ground near surface (subsurface ground) are small enough to be ignored, as common input terminals where earthquake motions, independent of subsurface ground

properties, are to be specified.

(2) Formations considered can be selected as base-rocks at the site either when they

are infinitely stiff as compared with the overburden subsurface grounds (a = 0) or when they

are uniform continua in ground. In the former condition, both the incidental motions and the

j ground motions in those formations are selected as base-rock motions, while in the latter

condition, the incidental motions in those formations are selected as base-rock motions. It

is required to relieve the above conditions, however, from practical points of view in accordance with objectives and accuracies needed in design.

IV-165
(3) Based on the correlative studies conducted for the underground earthquake motions, deconvolution procedures based on vertically propagating shear waves with equivalent linear material properties were effective in incorporating local subsurface ground conditions into earthquake motions recorded on grounds.

(4) The seismic analyses based on base-rock motions were successively applied to the Itajima Bridge. ACKNOWLEDGEMENT

The authors wish to express their sincere appreciation to Mr. Toshio Iwasaki and Mr. Susumu Wakabayashi, Chief and Research Engineering of PWRI, in making digitized ground motion records available to us. Special thanks are also due to Mr. Matuo Shibata and Mr. Tadaaki Miyata, Engineers of PWRI, for their cooperation in the present investigation. REFERENCES

1) Kanai, K. , Relation Between the Nature of Surface Layer and Amplitude of Earthquake

Motions, (I) BERI, 30 (1952), pp 31-37 (II) BERI , 31 (1953, pp. 219-226, (III) BERI

,

31 (1953), pp. 275-279, (IV) BERI, 34 (1956), pp. 167-184.

2) Kanai, K. , et al., Comparative Studies of Earthquake Motions on the Ground and Underground, (I) BERI, 37 (1959), pp. 53-87, (II) BERI, 44 (1966), pp. 609-643.

3) Kagami, H. and Kobayashi, H. , A Numerical Analysis of the Propagation of Shear Waves

in Multi-Layered Ground, Proceedings of Japan Earthquake Engineering Symposium,

Oct., 1966, pp. 15-20.

4) Public Works Research Institute, Locations of Strong Motion Accelerometers (No. 3), Ministry of Construction, 1973.

5) Kuribayashi, E., Iwasaki, T. and Takagi, Y., Digitized Strong Motion Acceleration

Records (No. 1 to No. 3), Technical Report No. 876, Public Works Research Institute, Ministry of Construction, 1974.

6) Iwasaki, T. , Wakabayashi, S. and Horiuchi, S., Digitized Underground Strong Motion Acceleration Records, Technical Report No. 1103, Public Works Research Institute, Ministry of Construction, 1976.

7) Penzien, J., Scheffey, C. F. and Parmelee, R. A., Seismic Analyses of Bridges on Long

Piles, Proc. ASCE, Vol. 90, No. EM3, 1964, pp. 223-254.

8) Kuribayashi, E. , Kawashima, K. and Miyata, T. , Earthquake Resistant Design Based on Ground Motions at Base-Rock, Technical Report No. 1192, Public Works Research Institute Ministry of Construction, 1977.

9) Kuribayashi, E. , Kawashima, K. and Miyata, T. , Stress Analyses of Piles Due to Shear Deformation of Subsurface Ground in Earthquakes, Technical Report No. 972, Public Works Research Institute, Ministry of Construction, 1974.

IV-1 66
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OOw to

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§

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Off

Hachijo

Island 1

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CT> 1 1

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a1

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jII

ii

s Iks'

1>"

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8

n - "1*

s|>-

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- tit

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a|>- 8 1

s

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oI

1

j

3|>-

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ft 11

il

a

?

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! ill [ n i

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IV-167
IV-168
Fig, 1-2 GROUND MOTIONS USED FOR SEISMIC ANALYSES

MAGNITUDE CM]

400 -

Fig. 1-3 GROUND MOTIONS USED FOR SEISMIC ANALYSES

OF SUSPENSION BRIDGES CONSTRUCTED OR PLANED TO CONSTRUCT

IV-169
GROUND SURFACE

Fig. 2-1 SUBSURFACE GROUND MODEL

Fig 3-1 SOIL PROFILE AT UKISHIMA PARK [6]

IV-170
010

008

|

0 2 4 6 6 FREQUENCY [Hz]

Fig 3-2 POWER SPECTRUM OF A -EARTHQUAKE GROUND MOTION

I 0

0 2 4 6 6 FREQUENCY [Hzl

Fig. 3-3 POWER SPECTRUM OF B- EARTHQUAKE GROUND MOTION

20

FREQUENCY (.Hz)

Fig 3-4 POWER SPECTRUM OF C- EARTHQUAKE GROUND MOTION

IV-171
FREQUENCY (Hz)

Fig 3-5(a) TRANSFER FUNCTION OF GROUND

BETWEEN GROUND SURFACE AND

27m BNEATH GROUND SURFACE

(0 m / 27m)

100

FREOUENCY ( Hz) Fig 3-5 (b) TRANSFER FUNCTION OF GROUND BETWEEN 27m AND 67m BENEATH GROUND SURFACE [27m/ 67m]

-A- EARTHOUAKE

-8- EARTHOUAKE

- C- EARTHQUAKE

FREOUENCY [Hz) 3-5 (: ) TRANSFER FUXT10N OF GROUND BETWEEN

6 7^ AND 127m BENEATH GROJND SURFACE [67m/i27m ]

IV-172
10 0

IV-173
IV-174
LUMPED MASS

OF SOILS

LUMPED MASS

OF EMBEDDED

STRUCTURE

Fig. 4-1 DISCRETE ANALYTICAL MODEL OF DEEPLY EMBEDDED STRUCTURE

Fig. 4-2 GENERAL VIEW OF ITAJIMA BRIDGE (4]

Fig. 4-3 LOCATIONS OF ITAJIMA BRIDGE AND ACCELEROMETER ON

GROUND SURFACE [4]

IV-175
^

200 < 100 ill J III liJlflJIM Aft A A

6 8 10 12 16 18 20 22 24 26

TIME [ SECONDS]

Fig 4-4 EARTHQUAKE GROUND MOTION ACCELERATION [GALS] RECORDED ON GROUND SURFACE

30 32 34 36 38 40

DEPHTA

AT ITAJIMA BR Cm] N- VALUE

20 40 80 80 Kj»

DEPTH AT

HIGH^ SCHOOL

0

SURFASE GROUND

CLAYEY LOAM

3

5

SANDY LOAM

10-

3ILT WITH GRAVELS

12

SILT WTTH COBBLES

15-

GRAVEL WITH COBBLES

17

20-

CLAY WITH GRAVELS i\

23

SLT WTTH GRAVELS CLAY WTH GRAVELS 27

25- GRAVEL

WITH COBBLES

Fig. 4-5 SOIL PROFILE AT ITAJIMA BRIDGE [4)

I

0 I -ic y -2 0a Li^tM^\^)^lhL)ifotJM\\ii\\\l\ mJill

Fig. 4-6 CALCULATED BASE-ROCK ACCELERATION

IV-176
IV-177
BRIDGE PIER

CAISSON

PIER

SOFT LAYER

MEADIUM LAYER

iiiiiiniiMjiiiiiiiii

(a) BRIDGE COLUMN AND

PIER OF ITAJIMA BRIDGE

PIER-CAISSON MODEL

(b) ANALYTICAL MODEL

Fig. 4-9 ANALYTICAL MODEL OF BRIDGE FOUNDATION WITH SURROUNDING SUBSURFACE GROUND

W-I78
(a) ACCELERATION AT THE TOP OF PIER

(c) BASE- ROCK INPUT ACCELERATION

Fig 4-12 CALCULATED RESPONSE ACCELERATION AND DISPLACEMENT AT TCP OF PIER

IV-179

BASIC EARTHQUAKE FOR DAM DESIGN Jerry S. Dodd

U.S. Bureau of Reclamation, Denver, Colorado ABSTRACT

Modern computational techniques permit mathematical dynamic analysis of concrete and

embankment dams. Steps in the analysis are: (1) specify location, depth, and magnitude

jof critical specifically located earthquakes, (2) attenuate seismic waves to site, (3) deter- mine site response to seismic waves, (4) analyze response of structure, (5) evaluate

jresults. This discussion addresses the first step and proposes the establishment of a linimum earthquake — the basic earthquake — for damsites in the western United States.

KEYWORDS: Earthquakes, Dams; Dynamic Analysis

V-1
INTRODUCTION Modern computational techniques permit mathematical dynamic analysis of concrete and embankment dams. Steps in the analysis are: (1) specify location, depth, and magnitude

of critical specifically located earthquakes, (2) attenuate seismic waves to site, (3) deter- mine site response to seismic waves, (4) analyze response of structure, (5) evaluate

results. However, with respect to the first step, there should be a small earthquake which is independent of location and which does not control or dominate the design of a dam, and therefore, should be a basis of comparison for specifically located earthquakes

to determine if their effects will exceed those of a small earthquake. Also this approach permits during the design of a dam a rational means for the consideration of small earthquakes, which are difficult to define as specifically located earthquakes. The following evaluation is based on information about western United States. RELATIONSHIP OF EARTHQUAKE MAGNITUDE AND INTENSITY

No direct relationship exists between magnitude and epicentral intensity. However, a general correlation does exist and has been studied by many investigators. Derived rela- tionships of three investigations (Gutenberg and Richter, 1956; Toppozada, 1975; Krinitzsky

and Chang, 1975) are shown in Fig. 1. Without violating the precision of these equations

the relationship between magnitude and epicentral intensity can be more simply stated as: M = 2 + 1/2 or1=2 (M-2) where M = Richter magnitude

I = Modified Mercalli intensity

A comparison of three common Intensity scales is shown in Fig. 2. EARTHQUAKE CLASSIFICATION

A classification of earthquakes for engineering seismology incorporating the above relationship is shown in Table I. TABLE I Engineering Classification of Earthquakes Classification Magnitude Range Epicentral Intensity Micro Up to 2.0 Very Minor 2.1 to 2.9 I Minor 3.0 to 4.4 II, III, IV Moderately Strong 4.5 to 5.9 V, VI, VII Strong 6.0 to 6.9 VIII, IX Major 7.0 to 7.9 X, XI Great 8.0 and Up XII
"Strong," "Major," and "Great" have been used for some time by the United States Geological Survey to describe the magnitude of earthquakes. The remaining classification

nomenclature is also employed by the Geological Survey (W. Person, personal communication)

The intensity relationship is from the above equation. "Micro" earthquakes are not felt

and are detected only with instruments. "Very minor" earthquakes are on the threshold of human perceivability. The classification of "Minor" is used for those earthquakes with a magnitude range of 3.0 to 4.4. These are felt earthquakes but inflict at most only slight

damage in the United States and correspond to epicentral intensities of II, III, and IV. The "Moderately strong" earthquake is that classification between minor and strong. Minor earthquakes can be considered as not having associated surface rupture of the ground surface, see Fig. 3. An exception may be smaller earthquakes which occur on faults capable of producing creep and moderately strong or larger earthquakes. The magnitude 3.5 earthquake shown on Fig. 3 is an earthquake on the Imperial fault in California, which

earlier ruptured at the ground surface in 1940 as the result of a magnitude 7.1 earthquake

Whether this 3.5 magnitude earthquake actually caused surface rupture is still open to discussion. Shallow moderately strong earthquakes may produce ground rupture on the fault generating the earthquake. Shallow strong and larger earthquakes are very likely to produce ground rupture on the source fault. From the study by Krinitzsky and Chang (1975), it is reasonable to assume that minor

earthquakes do not possess near field effects, see Fig. 4. That is, higher frequency

content and complicated wave forms generated near the earthquake source are filtered out

of the seismic signal by the time it reaches the ground surface. A reasonable conclusion

is that a minor earthquake results only in far field vibrations at the ground surface. BASIC EARTHQUAKE

The basic earthquake is defined as the minimum earthquake considered in the design of

a dam. It yields the maximum ground motion which can be expected for a minor earthquake. Because of uncertainties with respect to the location and occurrence of minor earthquakes primarily because of the lack of good historical and instrumental data — it is prudent in dam design to assume a ubiquitous nature for minor earthquakes. In many areas of the western United States it is likely that imposing the basic earthquake will be more severe than the resulting site ground motions determined from specifically located earthquakes. The bedrock characteristics of the basic earthquake are:

1. Peak acceleration of .10 g.

2. Maximum duration (g > .05 g) of 8 sec.

3. No surface fault rupture.

4. No near field effects. Krinitzsky and Chang (1976) show that for far field the limit of observed data for peak acceleration for an intensity between IV and V is .10 g (Fig. 5). Correspondent^

,

Gutenberg and Richter (1956) correlated an acceleration of . 10 g with an intensity VII

(Fig. 6). Employing the limit of observed data from Krinitzsky and Chang is conservative.

V-3
For rock the upper bound of duration for accelerations exceeding .05 g for intensities between IV and V is 8 sec. as shown by Krinitzsky and Chang (1976) (Fig. 7) . This also appears conservative. Bedrock can be assumed to be rock. Studies by Duke, et al. (1972) found that peak accelerations during the 1971 San Fernando earthquake in southern California

were higher in rocks than surficial deposits (alluvium) for 40 to 60 km from the epicenter. An engineering geologic description of the three primary earth materials is: Bedrock - A generic term that embraces any of the continuous and generally indurated

or compact earth material that makes up the earth's crust and is exposed at the earth's surface as outcrops or is covered by surficial deposits or topsoil. Surficial Deposits - The young, generally loose and normally unstratified earth material occurring at or near the earth's surface as a bedrock cover and of two major

classes: (1) dislocated and generally eroded or weathered bedrock materials transported

by water, wind, ice, gravity, and man to another place, and (2) sedentary deposits formed

in situ as a result of weathering and chemical processes or by the accumulation of organic

matter.Topsoil - The darker colored upper portion of a soil profile, the organic layer and organic rich A layer. GOVERNING EARTHQUAKE Using the data from Krinitzsky and Chang (1975) , as shown in Fig. 8, a general guideline can be developed indicating when the basic earthquake will govern or when a specifi- cally located earthquake will dominate. This is shown on Fig. 9. Also shown is a curve

for a peak acceleration of .10 g developed from seismic wave attenuation studies of others and depicts the most moderate attenuation characteristics expressed in these studies

(Gutenberg and Richter, 1942; Housner, 1965; Blume, 1965; Kanai, 1966; Esteva, 1970; Schnabel and Seed, 1973; Duke, et al. 1972; Donovan, 1973; Trifunac and Brady, 1976). The actual attenuation employed in the dynamic design of a dam is more likely to generate a curve to the left of this curve rather than between this curve and the Krinitzsky and Chang curve. This means generally that specifically located earthquakes need to be evaluated only within 125 km of the damsite. Also the controlling epicentral distances for governing

specifically located earthquakes for earthquake classifications greater than magnitudes

4.4 can be estimated. REFERENCES

Barosh, P. J., "Use of Seismic Intensity Data to Predict the Effects of Earthquakes and Underground Nuclear Explosives in Various Geologic Settings," Bulletin 1279 , U.S. Geological Survey, Washington, D.C., 1969. Blume, J. A., "Earthquake Ground Motion and Engineering Procedures for Important Installations Near Active Faults," Proceedings of the Third World Conference on Earthquake Engineering , New Zealand, Vol. IV, pp. 53-67, 1965. Bonilla, M. G. , "Surface Faulting and Related Effects," Earthquake Engineering , R. H. Wiegel, ed., Prentice Hall, Englewood Cliffs, Chapter 3, pp. 47-74, 1970.

V-4
S Donovan, N. C, "A Statistical Evaluation of Strong Motion Data Including the Feb. 9, 1971 San Fernando Earthquake , " Proceedings of the Fifth World Conference on Earthquake Engineering , Rome, Italy, 1973.

la ^Duke, C. M., Johnsen, K. E. , Larson, L. E. , and Engman, D. C. , "Effects of Site Classification and Distance on Instrumental Indices in the San Fernando Earthquake," UCLA Eng- 7247 , University of California, Los Angeles, June 1972. Esteva, L. , "Seismic Risk and Seismic Design Decisions," Seismic Design for Nuclear Power Plants , R. J. Hansen, ed. , M.I.T. Press, Cambridge, Massachusetts, 1970. Gutenberg, B. , and Richter, C. F. , "Earthquake Magnitude, Intensity, Energy, and Acceleration," Bulletin, Seismological Society of America , Vol. 32, pp. 163-191, 1942. Gutenberg, B. , and Richter, C. F. , "Earthquake Magnitude, Intensity, Energy, and Acceleration (Second paper)," Bulletin, Seismological Society of America , Vol. 46, pp. 105-

145, 1956. Housner, G. W. , "Intensity of Earthquake Ground Shaking Near the Causative Fault," Proceedings of the Third World Conference on Earthquake Engineering , New Zealand, pp. 94-111, 1965. Kanai, K. , "Improved Empirical Formula for Characteristics of Strong Earthquake Motions," Proceedings of Japan Earthquake Symposium , 1-4 (in Japanese) , 1966. Krinitzsky, E. L. , and Chang, F. K. , "Earthquake Intensity and the Selection of Ground Motions for Seismic Design" State-of-the-Art for Assessing Earthquake Hazards in the United States - Report 4, Miscellaneous Paper S-73-1 , U.S. Army Engineer Waterways Experiment Station, 1975.

[ Krinitzsky, E. L. , and Chang, F. K. , "Design Earthquakes," Unpublished, U.S. Army Engineer, Waterways Experiment Station, 1976. Linehan, D. , "Geological and Seismological Factors Influencing the Assessment of a Seismic Threat to Nuclear Reactors," Seismic Design for Nuclear Power Plants , R. J. Hansen,

ed. , M.I.T. Press, Cambridge, Massachusetts, 1970. Schnabel, P., and Seed, H. B. , "Accelerations in Rock for Earthquakes in the Western United States," Bulletin, Seismological Society of America , Vol. 63, pp. 501-516,

1973. Toppozada, T. R. , "Earthquake Magnitude as a Function of Intensity Data in California and Western Nevada," Bulletin, Seismological Society of America , Vol. 65, pp. 1223-1238,

1975.

1 Trifunac, M. D. , and Brady, A. G. , "Correlations of Peak Accelerations Velocity and Dis- placement with Earthquake Magnitude, Distance and Site Conditions," Earthquake Engineering and Structural Dynamics , Vol. 4, pp. 455-471, 1976.

V-5
iy y si sn ys rx z n

INTENSITY (MODIFIED MERC1ULI SCALE ) Comparisons of several curves relating magnitude and intensity values in the western United States (Gutenberg and Richter

curve from Krinitsky and Chang, 19 75).

V-6

I 5 10 SO 100 500 1000 DISPLACEMENT (cm) FIGURE 3. Magnitude versus maximum displacement on main fault at surface

(after Bonilla, 19 70).
0.4.

TTT TZ ~SL 21 VTT VIII TT INTENSITY (MODIFIED MERCALLI SCALE)

FIGURE 5. Acceleration values for MM intensity in the far field (after Krinitzsky and Chang, 19 76).

V-9
v-io
1 1 I l i i i i r UPPER BOUND DURATION FOR HARD ROCK

LEGEND

INSTR COMPONENT

HORIZONTAL

VERTICAL HORIZONTAL

VERTICAL HORIZONTAL

VERTICAL

SITE CONDITION

SOFT

INTERMEDIATE

J i L TV 3 3Z1 T7TT VTTT TT INTENSITY (MODIFIED MERCALLI SCALE)

FIGURE 7. Durations for MM intensity in the far field (after Krinitzsky

and Chang, 1976)

V-ll
V-12
SP6CI ICALLY LOCATED EARTHQUAKE

S 6* I

o / / i

1

'

L iru» KRINITZSKT «»0 CHANC,

1 (1973) Omo» = 1 Dg

BASIC CARTHOUAIC

1

j

! 1

1

1

j 1 O.I I 10 SO 1 00 lOOO EPICCNTRAL DfSTANCC (km) FIGURE 9. Governing earthquake - magnitude versus epicentral distance.

V-13
STUDY ON REGIONAL DISTRIBUTION OF MAXIMUM EARTHQUAKE MOTIONS IN JAPAN Masakazu Ozaki, Head, Str. Div. , B.R.I. , Ministry of Const, Japan Yoshikazu Kitagawa, Res. Memb. , Str. Div., B.R.I. , Min. of Const., Japan Sadaiku Hattori, Res. Memb., I.I.S.E.E., B.R.I. , Min. of Const., Japan ABSTRACT

Research activities in the earthquake danger have been critically reviewed. Many researchers concentrated on the study of the past earthquake data and statistical analyses

of these data. This paper presents an application of Gumbel's theory of extremes for the prediction

of the intensity of future earthquakes. The paper concludes with a new regional seismic coefficient map of Japan.

KEYWORDS: Earthquake danger; Gumbel's theory of extremes, literature review; regional

seismic coefficient map; statistical analysis.

V-14
1 . INTRODUCTION

One of the most important problems in earthquake engineering is to predict statistically

the intensity of future earthquakes from the past earthquake data, since at the present

time the precise earthquake forecast is difficult. In the process of the prediction, the selection of the past earthquake data and statistical method of analysis are most important, because the available earthquake data are not sufficiently large. Many investigations have been carried out in these two subjects in Japan. However,

there has been no research on the prediction of the intensity of future earthquakes based

on the theory of extremes developed by Gumbel. This paper deals with the expected values

of the intensity of future earthquakes on base rock as well as on the surface of ground by introducing Gumbel 's Theory of Extremes.

2. GENERAL REVIEW ON THE EARTHQUAKE DANGER IN JAPAN The earthquake danger in a certain place may be defined by the seismic activity in the vicinity and the characteristics of the soil-layers. In order to clarify the earthquake danger more reliably, it is necessary to investigate the regional distribution or variation of the seismic activity and the characteristics of soil-layers. General reviews indicate that some research has been conducted considering seismic activity only, i.e., magnitude frequency distribution and focal distribution, disregarding

the regional difference of soil characteristics. A few investigations seem to be performed

considering the influence of the soil characteristics, but not sufficiently.

Since Dr. H. Kawasumi published his regional map on the earthquake danger in 1951, the research activities have increased in number as many as 10 in Japan. The outline of the research conducted on the earthquake danger in the vicinity of Japan is as follows:

Dr. H. Kawasumi"*"* observed the following relation between the seismic intensity I in J.M.A. and the maximum acceleration amplitude a on the ground,

a (gal) = 0.45 x

10°* 51

(1)

Taking into account the fact that the regional distribution of the intensity is closely

related to the epicentral distance and the magnitude of an earthquake, he also determined

the relation between the epicenters and his magnitudes for the earthquakes in the olden

times (A.D. 679-1925) when no observed data had been given, utilizing the descriptions in ancient documents. Kawasumi also defined the relation among M^, I, and the epicentral distance A. Taking Eq. 1 into consideration, the relation is represented in terms of M, a and A as follows:

*The superscript numerals refer to the corresponding numerals in Table 1.

V-15
= M-0.540-log (r/rQ

) - 0.00834 (r-rQ) for r<r

Q

= 100 km (2)

/ 2— 2~ where r means the hypocentral distance, A

Q = 100 km, rQ = /100 + 18 . Using the data for the period 679-1948 and Eq. 2 , the expected maximum acceleration was calculated at arbitrary points for the return period T years and was determined by the following equation,

E n (a) a=a

where n (a) and T are the frequency of maximum acceleration amplitude and the data period

in year. He obtained finally the regional distribution of the expected maximum acceleration

amplitude for the return periods (T = 50, 75, 100 and 200 years) at every half degree point

in latitude and longitude.

Dr. I. Muramatsu^ analyzed the destructive earthquakes in latitude and longitude since

1926 and obtained the following equations as the relation among M, r and maximum velocity

amplitude V,

-1 -r/r (M) V (cm/sec) = C(M)r e c

log C (M) = 0.655M - 1.719 (4)

log rc (M) = 0.145

Dividing the earthquake data into two periods A.D. 679-1867 and A.D. 1868-1956 and

using these data in each period, he made the same analysis as Dr. Kawasumi and pointed

out that the distribution of the expected maximum acceleration amplitude resembled each

other, but the absolute values were fairly different between both cases. So that the regional distribution of the expected maximum velocity amplitude Vo for the return period

(T = 50 years) using Eq. 4 and the data between 1868-1964 years was obtained by the following equation,

£ n(V) =f--i

where n (V) is the frequency of the maximum velocity amplitude.

V-16
After analyzing the seismic records observed underneath the ground at the depth of

00 m, Dr. K. Kanai and T. Suzuki 3 concluded that the amplitude of the velocity spectrum V

f earthquake motions at base rock was nearly constant with regards to period t as follows:

(6)

ind that amplitude is determined by the following equation:

log V = 0.61M - (1.66 +

•3-^) log r - (0.631 + i^3

-) (7)

So that using Eqs. 5 and 7 and the earthquake data with damages for the period 599-1964,

they obtained the regional distribution of the expected maximum velocity spectral amplitude

(at the base rock for the return periods (T = 75, 100, 200 years).

; H. Goto and H. Kameda4 applied a certain probabilistic model to make up for insufficient

earthquake data in ancient time. They assumed the occurrence of earthquakes to be independent

jevents and defined that the records in the period were the sample values of n times Bernoulli trials, in which H^'

intensities I,, II . ... I 1 2 r jfor the period B^ in the whole records, and the earthquake danger in each period was

estimated with P^. At that time, the seismic acceleration amplitude X(t) was indicated as 3f(t;T)g(t) and the mean maximum acceleration amplitude relating to the parameter g was

given as a(V) = 50 T

~1 " 316

, a (VI) = 320(To/

Q 4

) _1 " 316 and a (VII) = 470 (To/

Q A )~1 ' 316

, where

f(t;T), g(t) and g are a deterministic time function, a non-dimensional stationary stochastic process and a constant with dimension of acceleration, and To means a predominant

period. Taking these into consideration, the probability distributions of the maximum

acceleration amplitude ¥

f

(a

f

) and the maximum velocity amplitude ^ (Vmf) at arbitrary

points for a certain period were given as follows:

(8) ^f(^f)-g„ ...^{^s^fJij)^ b-(K a ;n B ;Pf)]}

I

nil nim m

*f •••£Lo< l3

:1 tYs(Vmf;ij)

Klj ;1, ;*f

>]}J

and the regional distributions of the expectation E[a

f

], E[Vmf ] were calculated in the following equations:

(9) E [Ctf [ s { a-*f

(af

) } daf

E [Vmf ] s 7{l-Tf (Vmf )} dVmf

0 where the return period T is 75 years and the predominant period is 0.5 sec.

V-17
T. Okubo and T. Terashima"' modified the expected maximum acceleration amplitude pro- posed by Dr. Kawasumi on the distribution of earthquake intensity in the major earthquakes

after the Kwanto Earthquake in 1923. In their map, Japan was divided into four divisions

by recombining Kawasumi ' s map and the distribution of intensity V or more.

K. Takahashi^ defined that a mean annual accumulative intensity frequency f (a) at the observatories of J.M.A. could be shown in the following equation as the first approximation,

f fo

f (ot) = a( 1 + a/25)

= a(l + o.002aF) (10)

where a = 0.8 x lO

0 ""^ 1

, fQ and F are a regional coefficient and times of felt earthquake

respectively.

He estimated the expected maximum values at any point with the following data: (a) the times of felt earthquakes for the period 1884-1970 year, (b) the mean annual frequency of earthquakes with Intensity III or more for the period 1884-1970 year, (c) the mean annual frequency of Intensity V or more for the period 1506-1970 year. So that final regional distribution of the expected maximum acceleration amplitude was obtained by means of weighted mean values as the result of the above-mentioned method.

S. Hattori and Y. Kitagawa7 applied Ishimoto-Iida's formula

n(A)dA = k A dA (11)

to the maximum displacement amplitude at each observational station of J.M.A. , using

the observed data for the period 1967-1972.

In Eq. 11 n(A) is the frequency of the maximum displacement amplitude A, k and m are constants at each observational station. At that time, m and k were determined

as follows:

m = —i S

„ l0

;! f — + 1.0, log k = log N (A>A . ) + log (m - 1) + (m - 1) log A.,

3 log A.-S log A. = 3 3 I

3 3 i=l where S, A_. , A.^ and N (A>A.) are the total number of the data, the smallest maximum

amplitude, the i-th maximum amplitude counted from the largest one and accumulative fre- quency of A^A_. , respectively. Taking these values and the data period into consideration,

the regional distribution of the expected maximum displacement amplitude was obtained for the return periods (T = 25, 50, 100 years)

.

S. Omote and K. Matsumura

8 obtained the regional distribution of the expected maximum

acceleration amplitude using the data for the period 1885-1973. At that time, magnitude M in J.M.A. for the period after 1926 was transformed into M

k by ^ = 2M - 8.7. The method

of analysis was almost the same as that of Dr. Kawasumi except the following equation was

used instead of Eq. 1)

.

a = 0.253 x 10

0 " 51

(12)

V-18
Moreover, S. Omote, H. Hanai and S. Nagamatsu made the regional distribution of the expected earthquake motions at the base rock using Eq. 7 and a probability model of earthquake occurrences represented by a Poisson process. At that time, they used the earthquake

data from the periods 679-1972 and 1741-1972 for the same return periods (T = 50, 200 years).

S. Nagahashi defined the expected maximum velocity response amplitude SV

q

as follows:

log SV

q

= a M - b log r - c (13)

where a, b and c are the functions of natural period modified by the characteristics of the observational site from the strong-motion records.

And he obtained the regional distribution of the expected SV

q values having 0.3, 1.0 and 3.0 sec. in natural period and 0.05 in the damping of response system for the return

I period 50 years, using the data for the period 1885-1975. At that time, M^ for the period

1885-1925 was transformed into M by Muramatsu's equation = 0.88M + 1.2. The research described above is summarized in Table 1.

3. THEORY OF EXTREME VALUES

3-1. Gumbel's First Asymptotic Distribution

The simplest method by which the extreme values of a variate can be predicted is known as that of the First Asymptotic Distribution of Gumbel (1958) ^ . Whether the dis- tribution is a reasonable one to employ in a specific application is a matter of judgment. Such a judgment can be exercised by considering how well the inputs fit the distribution

and by taking into account any factor which may tend to influence the trend toward the extreme values. While the goodness of fit is a statistical problem, the cirterion by which it is judged depends on the intended application and no priori rule can be formulated

in its regard. The deviation in trend to extreme is usually a physical problem and its prediction cannot always be made on a purely statistical basis but may require insight into the nature of the phenomenon to be predicted.

1) INPUTS

The prediction of extreme values is made by carrying out certain statistical operations

on a set of maximum values of the variate to be predicted. Such a set is obtained either

by sampling subsets of a totality or by the sequential measurement of a process over specific intervals of time suitably spaced. The method is the same in either case, but since the environmental phenomena of interest are essentially time-dependent, the exposition that

follows is expressed in the parlance pertinent to time functions.

Thus, the inputs required are:

a) A compilation of set maxima, x

b) The total number of set maxima, N

2) ORDERING OF INPUTS When N is large, the set maxima (adjusted) are ordered by magnitude, either ascending

or descending. In what follows, the ascending order is used. The generic value of the ranking index of the set maxima is denoted by xm

, thus:

V-19
x

x < x

2 < < X < m

3) ORDINAL FREQUENCY 0m

To each set maximum x corresponds the ordinal frequency

4) INPUT STATISTICS

The mean value of x

'I

The variance

2 1 N

2 a

2 = ± • Z [x - x r N ^ m

The corresponding dispersion

a = /7~

5) REDUCED VARIATE ym

The set maximum is plotted at the position given by the reduced variate

y = -in [-in (0 )]

The slope is calculated by the least square technique as

1 l Um~ Xm

) " V

7) MODE U The mode is calculated by the least square technique as

V-20
8) EXPECTED MAXIMUM VALUE x(y) The regression line of expected maxima is

x(y) = U + J

3-2. Gumbel's Second and Third Asymptotic Distributions

The First Asymptotic Distribution of Gumbel predicts extreme values of a variate

approaching infinity as the return period approaches infinity. In most applications to forecasting, this tendency of growth does lead to predictions of reasonable accuracy. This

is obtained when the observed values ranked by magnitude and related to a probability

of occurrence crowd the regression line of the expected values. There exist, however, cases

for which there is, indeed, a marked tendency of the observed values to deviate increasingly from the regression line as the return period increases. Such cases occur when

physical causes operate to impose constraints of ever greater severity as the variate tends

to grow in magnitude.

The reliable treatment of such problems requires extremal probability distributions

to be somewhat more flexible than the First Asymptotic Distribution. A convenient one is Gumbel's Second or Third Asymptotic Distribution. As against the First, which is a two- parameter distribution (mode and slope) , the Second or Third is a three-parameter distribution

(asymptote, characteristic value, and exponent). However, the enhanced flexibility intro- duced by the third parameter is paid for in increased complexity, and a relatively simple

and direct determination of parameters, as in the case of the First Distribution, is not

quite in hand. The way out is to have recourse to a computer and derive the parameters

by iteration. A method for accomplishing this is outlined herein. The cumulative probability corresponding to Gumbel's Second Asymptotic Distribution

is given by

20 (x) = exp (-[V

x ~_

£

£

] K) m

where x is the variable, e its limiting value, V its characteristic value and K an exponent. The problem is to derive them from the input data. The inputs are a set of maximum values measured over a specific interval. The cumulative probability corresponding to Gumbel's Third Asymptotic Distribution

is given by W " X

n, V

30 (x) = exp (-[——] )

where x is the variable, W its limiting value, i.e., the expected maximum value that the variable is likely to attain in the infinitely long run, V its characteristic value and K an exponent. The set of maximum values x is arranged in ascending order and plotted against the m

corresponding ordinal frequency

V-21
- I" m

_ N + 1 where N is the total number of data points. The mean value, variance and dispersion

x^, °N

2

» 0 are obtained as for the First Asymptotic Distribution.

The reduced variate

2 Zm for the Second Asymptotic Distribution when introduced onto

the expression

n x - e

W

n W - V

will plot as a straight line against

Note that in the outline that follows the subscript m is employed to define either an input x or a value directly related to inputs y , 0 , etc. m mm

Note also that the characteristic value is that value of x which corresponds to the cumulative probability 0 = ~ = 0.368, i.e., to y = 0. In the First Asymptotic Distribution

such a value is termed the mode.

1 ) VARIANCE O

2 N

2 Variance 0 (V, £, K) for the Second Asymptotic Distribution can be obtained as

0

N

2 (V, C, K) -±j ( 2 Zm -ym)

:

2 Variance (V,W,K) for the Third Asymptotic Distribution is as follows:

i= ( -K4ntinr ] -ym

)

2) EXPONENT K Using the least square method, the exponent K for the Second Asymptotic Distribution

can be expressed in terms of £ and V.

V-22
3K

N v

.) ]

1 *m e N w

1 *>

The exponent K for the Third can also be expressed in terms of W and V

N

. V - x

K

1 m ' " W -V

N W - v Eft (- ^5_)} 2

Then the variance a

2 (v,£) and c? 2 (V,W) are

N N N

2,. ..i; f . i and Vomo = |

e [ -k (v,w) . M^Hr-> " y-

]2

3) PARAMETRIC SEQUENCE OF THE CHARACTERISTIC VALUE V

The characteristic value V is obtained by iteration. A new characteristic value

Vp

+ ^ is related to its previous value through recurrence relation Vi = v

p

+ [ - i

]Cp,Av

where p is an interation index and Av is an arbitrary incremental value. Note that the characteristic value V corresponds to the mode U of the First Distribution. Therefore, an approximate characteristic value V

q

is obtained by letting = Mode of First Distribution.

The exponent C appearing in the recurrence relation denotes the number of times the inequality sign changes in step 2.6. The initial value of C^ is zero.

4) PARAMETRIC SEQUENCE OF THE ASYMPTOTES £ AND W

The asymptote E or W is also obtained by iteration. A new value of the asymptote

E , or W , is related to the previous value E or W through the recurrence relation

q+1 q+1 * q q

V-23
Vl (V) £ q

(V> + [ " I

10"

C w (v) = w (v) + [- -] q • Aw

q+1 q 2

where q is a sequential index and Ae or Aw is an arbitrary incremental value whose selectic should be based, if possible, on physical reasoning.

The exponent C denotes the number of times the inequality sign changes in Step 5)

.

The initial value of C is zero. q

a

2 (V . e J_. ) < a2 (v , e ) N P q+1 N p q

N p q+1 N p q

the sign change count is

N p q+1 N p q

cr 2

(v , w _,_.) > a

2 (v , w ) N p q+1 N p q

the sign change count is

2 Repeat e calculation from C „ until C = 3, 4, or 5 and find the minimum value of a . q=0 q N The selection of = 3, 4, or 5 depends upon the nature of the problem.

6) CRITERION FOR THE CHARACTERISTIC VALUE V (FOR ALL POSSIBLE VALUES OF £ OR W)

2 2 If the minimum value of a (V , , e) or a (V , , W) is smaller than that of

2 2 TM P ^ " P ' a , (V , e) or a„ (V , W) the sign change count is N p N p

C ^ = C p+1 p

V-24
2 If the minimum value of O (V , , £) or 0

0 N p+1 N p+1 , W) is larger than that of

a.N

(V , £) or a (V , W) the sign change count is

Repeat calculation from C = 0 until C = 3, 4, or 5 and find the smallest value of

2 P P 2 O (V , E) for all possible combinations of V and e or 0 (V , W) for all possible

N p N p comginations of V and W by iteration. The selection of = 3, 4, or 5 also depends

on the nature of the problem. The exact solution of V, £ and K for the Second Asymptotic Distribution or V, W and K

2 2 for the Third corresponds to the smallest value of a (V, £) or a (V, W)

.

N N Note that the value of exponent K is a function of V and £ or V and W for which the

2 2 variance Cf„ (V, e) or a„ (V, W) is the smallest and is calculated for each step of V and N N p

e or V and W . q p q

The earthquake data considered to be available at present in Japan can be divided into

five periods as follows:

(I) Period 416-1872 - Magnitude Mk and epicenters were determined by Dr. Kawasumi

using the descriptions in ancient documents. These values are shown in the Science Calendar . No data except damages are included.

(II) Period 1885-1925 - Both Mk and M are shown in such a relation as Mk = M + 0.5

in the Science Calendar. No data except damages are included.

(III) Period 1885-1925 - Both Mk and M are shown with the same relation as the data

(II) in the Science Calendar. Moreover the data in the major earthquakes above are included in the Catalogue of Major Earthquakes by J.M.A.

13

(IV) Period 1926-1960 - The results of instrumental observations are reported in the Catalogue of Major Earthquakes by J.M.A. , in which all the earthquakes with the magnitude M>5.0 are considered to be included.

(V) Period in and after 1961 - The data in this period are reported in the Catalogue

of Major Earthquakes or the Seismological Bulletin of J.M.A., in which almost all the earthquakes with the magnitude M>4.0 are considered to be included because of advanced instruments comparing with those in the period 1926-1960.

It is generally assumed that the seismic activity has been or will be nearly as con- stant in an area as in the whole vicinity of Japan. If the assumption above is made and the data of the earthquakes occurred in the period are completely included, such phenomena should

be recognized for any data as follows; (1) the gradient of the accumulative energy curve, that is, the mean annual energy released by earthquakes is nearly constant and (2) the mean annual accumulative magnitude frequency distribution is similar for any period of data. Mean annual magnitude frequency distribution and mean annual energy released by the earthquakes for the data period of (I) - (V) are shown in Figs. 1 and 2. As seen in these figures, the data (I) - (V) can be classified into two parts, data A (I, II) and

EARTHQUAKE DATA

V-25
data B (III, IV, V) , and there are remarkable differences between the data in A and the data in B. It is necessary to pay attention for the data A as follows: (1) the data A were made according to the descriptions in the ancient documents and (2) the distribution of popula- tion in the time when the documents were made had to be very uneven. The reason is easily

inferred why the data A are not only small in quantity and low in accuracy but also uneven

regionally. On the other hand it is doubtful whether the period of the data B is long eno\ for the seismic activity to be regarded as being constant. After considering the facts above, two kinds of data are used in the present paper as follows

:

1. The data B with modified magnitude - The data B are examined and modified in the following. The accumulative energy curves using the original magnitude and modified mag- nitude are shown in Fig. 3. As seen in Fig. 3 the gradient of energy curve before 1925 is larger than that after 1926.

It seems necessary to modify the magnitude for the period 1885-1925, because the magnitude for the period 1885-1925 was Kawasumi's magnitude and the magnitude for the period

thereafter has been determined based on the instrumental observation. Assuming that the gradient of the accumulative energy curve is nearly constant and that the gradient value

for the period 1926-1973 is representative in the vicinity of Japan, three types of modification for the magnitude are made as follows: (1) M-0.5 for the period 1885-1925,

(2) M-0.6 for the period 1896-1915 and M-0.5 for the periods 1885-1895 and 1916-1925, and

(3) M-0.7 for the period 1896-1915 and M-0.5 for the periods 1885-1895 and 1916-1925.

In Fig. 3, it is seen that the resultant accumulative energy curve makes almost a straight

line in the modification (2) . The mean annual magnitude frequency distribution for the period 1885-1925 after the above modification is compared with that for the period

1926-1973 in Fig. 4. As seen in Figs. 3 and 4, the modification (2) seems to be most

suitable for data B.

2. The data after the period 1946 when the distribution of population was relatively even - As for the data before 1926, the following treatments with characteristics of acceleration

were applied.

(1) The major earthquakes having 100 gals or more were estimated from the destructive

earthquakes in the Science Calendar.

(2) Considering the annual magnitude frequency distribution curves in Fig. 4, it is assumed for the small or medium earthquakes less than 100 gals that the frequency

of earthquakes occurrence was the same as that after 1926 year. The magnitude

before the period 1885 was estimated from Mk.

5. EXPECTED VALUES OF EARTHQUAKE INTENSITY BY THE THEORY OF EXTREMES

5-1. PRESUMPTION OF EARTHQUAKE INTENSITY Many empirical formulae concerning the relationship of intensity, magnitude and epi- central distance have been proposed by many investigators in addition to those mentioned

in Chapter 2; Gutenberg and Davenport (1942), Blume (1965), Housner (1965), Milke and

V-26
Davenport (1969), Esteva (1970), Watanabe (1971), Donovan (1972), Soknabel and Seed (1973), Katayama (1974) , Trifunac and Brady (1975) . Fig. 5 shows the relationship between the

4 imaximum acceleration and epicentral distance in the case of magnitude M=6.5 . Good agreement can be seen among these empirical formulae in the range of epicentral distance

20-250 km except those by Gutenberg and Richter, and by Blume.

In this paper, Kanai's formula (7) which indicates velocity spectrum on the base rock

was utilized for the presumption of earthquake intensity.

imax

on the surface of ground can be obtained as follows:

- nn o.6iM-(i 6 6"<—5 ) logio r + Co. 1 6 7 - * 8 3 ) . 1 a r max ~, r r t

_ in o.6iM-d >6 6+ * °

) logior- (o .631+

1 ' 83 v

) n max ~ LU r r • l» u;

10°- 61 M-( 1 . 6 6+ ——)LOgio r ( l.iso + )

• T • G(T)

where G (T) is dynamic characterisitcs of the ground and is approximated by

1

T: Predominant period of earthquake motion

of the ground are approximated as follows:

- = _J_ . 100.61M-(1.66+ -

3 ^-°) logior + (0.167- I -i 3 ) 3X

/

TG

r r SVt" • 10°- 61 M-0. 66 + i^l0 )logior-( 0>63 i +

i, 83 •) G r ^

= 5/TG

3

. 10°

6 l M-(l .66 + lil ) logior - (i.hsi

V-27
jl 5-2. EXPECTED VALUES OF EARTHQUAKE INTENSITY

.V 1) Expected Values of Maximum Acceleration and Velocity in Tokyo

The expected values of maximum acceleration and velocity on the surface of ground at the center of Tokyo (35.7°N. 139. 8°E) are predicted using the past 326 year earthquake data

(magnitude and epicentral distance) mentioned in Chapter 4.2. Fig. 6 shows the expected

values of maximum acceleration on the surface of the ground, of which the predominant period

T is 0.3, 0.5, 0.8 and 1.2 sec, obtained by Gumbel Asymptotic Distribution.

G

The expected values of maximum velocity are shown in Fig. 7 obtained by Kanai's

formula (7) . Tables 2 and 3 show the calculated values of maximum acceleration for each

year and the expected maximum acceleration and velocity vs. return period on the surface of the standard ground (TQ =0.3 sec.) at the center of Tokyo, respectively.

2) Regional Distribution of Expected Maximum Acceleration on the Surface of Standard Ground

The expected maximum acceleration on the surface of the standard ground (TQ

= 0.3 sec.)

is calculated at the location of every 0.5° in latitude and longitude by Kanai's formula

and Gumbel' s Asymptotic Distribution. The past earthquake data used are described in Chapter 4.2. Regional distribution maps of the expected maximum acceleration corresponding

to the return periods of 50, 100 and 200 years are shown in Figs. 8, 9 and 10, respectively. | 3) Regional Distribution of Expected Maximum Velocity in Bedrock

The expected maximum velocity at the base rock is obtained at the location of every

0.5" latitude and longitude by Kanai's formula and Gumbel Asymptotic Distribution.

The past earthquake data since 1885 are used as described in Chapter 4.1. Regional distribution maps of the expected maximum velocity corresponding to the return periods of

50, 100 and 200 years are shown in Figs. 11, 12 and 13, respectively.

Figs. 14 and 15 show the expected maximum acceleration and displacement at the base

rock corresponding to the return period of 100 years, respectively.

6. PRACTICAL APPLICATION ON THE EARTHQUAKE DANGER

As is clear from Table 1, the periods of the data used and of the analyses in the respective research vary from a scientific point of view. For practical purposes, that

is, especially the regional seismic coefficients for aseismic design of structures, these results may not be available directly, because it is disagreeable to say that the results express the regionality of seismic activity in the vicinity of Japan completely and objectively. Moreover it seems not ot be always desirable in aseismic design that there are many kinds of the regional distribution of the expected values. So a new regional seismic coefficient map was made after examining all results from the following standpoints: (i) the! accuracy of each value in earthquake data, (ii) the regional evenness of data information,

(iii) the quantity or the period length of data, (iv) the method to calculate the maximum

earthquake motions from M and r, (v) the method to determine the expectation of the maximum

earthquake motions and (vi) the representative method to obtain the results. The regional distribution maps of the expectation values based on the regionality of seismic activity only were selected from various maps and normalized to assign unity for the

V-28
maximum value in each map at the point of every half degree in both longitude and latitude.

The regional distribution of seismic coefficients was determined by means of the weighted

mean values by multiplying each normalized one by each weight determined from the six items

above.The final results are shown in Fig. 16, which are considered to be the appropriate

regional seismic zoning coefficients for aseismic design of structures. As seen in Fig. 16, Japan is divided into three divisions by the criterion of seismic activity, that is, A) area with high earthquake danger, B) medium danger area and C) low danger area. ACKNOWLEDGEMENT

This study was partially supported by the project of Establishment of New Aseismic

Design Method monitored by Ministry of Construction, Japan. The authors wish to express

their thanks to Professor St. Denis, University of Hawaii, for introduction of Gumbel's

Second and Third Asymptotic Distribution by iteration method; to Dr. Otsuka, Head of I.I.S.E.E. and Dr. M. Watabe, Head of Str. Div. at present, for valuable discussion on regional seismic/zoning coefficient; to Mr. Y. Serizawa, member of B.R.I. , for drawing of figures.

V-29
V-30
Table - 2 Calculated Values of Maximum Acceleration (gal) for Each Year in Tokyo (TQ =0.3 sec.) A.D.

Fnicpntrnl distance tude ama*(TG =Q3) A.D.

Epicentral distance tude <WTg=Q3)

1G7C jyzo 4o.lU / om A 9 O- Z

ftQ7fi O3./0 iocn iyou O/ oc o4.yb c c b.o C1 1Q b 1. 1 o 192/ 1/1 cc 1 41bb c n

b.u 1 / no 14.UO 1QC 1 lyoi 00.60 C 7 b.z CO 7C boob

/b.lU c ft 0.0 9fi ft7 zo.o/ 1QC7 iyoz 1 A/ / 1 1 U4.4

1

c c 0.

0

1 1 n7 l I.U/ 1Q9G iyzy /UJU fi 1 O. I 4fiQ1 1Qfi9 iyoj 99fi ft9 ZZb.CZ fi fi b.b 1 C 7C I o. /b 1QOA iyou QQ 7Q

yo.zo 7/•Un QQfil 33.0 I iyo4 1 9fi On I ZOlOU fibn/ 7Q 7C zy.zo

1Q91 l3o I 7 1 71 7 fi 1I fi7 O /.3o 09 IQfifi lyoo 7/ 97 fiO 9o

1 9 77 lyoZ I ZU03 1 90 fi9 IQfifi iyoo en 07 ou.oz fi n o. u C7 00 bZoo

1077 1 1 A 91 I 1 4Z

1

C c 0.0 111/ II . 14 1QC7 lyo/ 1CC £7 loo.oJ c n

o.U 7 OD

107/ 1934 CO DC OaOb C 9 o.z 1 C CQ l b.bo 1OC0 iy do / 7 QC 4J. 30 / / 4.4 o no ouy

1Q7C 1 / oon I4yzu C 7 b.3 1 Q 07 i y.oo 1QCQ iyoy 177 n7 c c

o. b

c\ on 930

1936 1/7 QC

1 42.85 C 7 6.3 7 1 10 2 1.19 1960 177.37 5.9 866

1097 1 1QQQ c c b.b / 9 19 *tZ. IZ 1QC1 iyb i 1/7 7C 14/.Z0 c o

o.y

1 1 C7 1Q7Q 193o 1 1 900 l layy c c b.b 9fifi9 1QC9 iybz 70 7C /y.zo / o

4.9 7 1C Alb

iyoy C7 99 0 /.ZZ C 9 0. J

1 R Q1 I 0.3

1

1QC9 iybo 1 9C /C l3b.4o C 1 b. 11 7 1C

I /.lb io/n 1 17 79 1 1 J.Li fi 1 b. i 91 47 Z I.H/ 1Qfi/ iy Oh 199 /f\ 1JZ.4U fi 7 b.Z on co zO.bo

10/ 1 iy4i TC 7C

/ 0.J0 fi n b.u 9fi no 1QCC iybo ic.9 en lOZ.ou C 7

b. / 7 7 C7 1Q/7 iy4z 1 / 1 1C 14 1. 10 fiDofi 99 on iybb C7 m 0/.1U / Q 4.9 1 1 /7

1 1.42

1 O / 7 1943 1 C 1 C7 Ibl.bz c c b.b 70 / Q z9.4o 1QC7 iyb/ 07 TO 87. do c c

O.b 1 £ A / 16.04 1944 o *2 cn c c 0.0 D7 on oz.yu 19bo 7n70-10m C 1 6.1 46.09 1945 ^ O A1 68.01 C 7

0./ 17 / / 27.44 1969 65.84 4.5 5.33 19A6 71.17 6.3 59.73 1970 84.05 5.1 8.70 1947 11830 6.0 18.52 1971 7Q85 4.9 8.41 1948 74.03 5.4 15.94 1972 5a60 5.1 1458

1949 114.38 6.7 52.90

Table - 3 Expected Maximum Acceleration and Velocity Values vs Return Period

in Tokyo Return Period (years)

Unit 50 100 200

Amax 162.7 217.0 287.7 gal. Vmax 7.77 10.4 13.7 cm/sec

V-31
1000. r

100.

10.

0.1

0.01

O Data I •A Data D o Data III • Data IV a Data V

0.001 00

I —' —' —' — I ... I — I —I —I —I —I 40 5.0 6.0 7.0 8.0 9.0 Magnitude

Fig. 1. Frequency Distribution of Mean Annual Magnitude

for Data I to V.

V-32
J I I I I I I ' Data i n m rv v

Fig. 2. Mean Annual Energy Released by Earthquake Data (I to V)

V-33
,-23 -10 erg

500r

200 1

• 1885- 1926 :M=M o 1885-1926:M=M-Q5

o 1885-1896,1916-1925: M=M-Q5

1896-1915:M=M-Q6 * 1885-1896,1916-1925:M=M-Q5

1896- 1915 :M=M- 0.7

1900 1910 1920 1930 1940 1950 1960 1970

Fig. 3. Accumulative Energy Curves of Original and Modified Data

V-34
• 1926-1973 O 1885-1925:M=M O 1885-1896,1916-1925:M=M-Q5 nOi 1896-1915:M=M-Q6 oA % ° ^

A

1885-1896,1916-1925.M=M-05 °&®1b&>s.J> 1896-1915: M=M-Q7

1.0

0.1

0.01

oX2" Ox> .

OOA <*> •fiAoA O O

O e«0oA O

F ?a „<> ^Oa <>o

oA Vo

H o

#

AOA O0O

o • •• •

OA •••<> OOO O

I I I I I I I I I I I I II I 1 I I I I I I I I I I I I I 1 I I 11 1 I I I I I I I I I I I I I I I n en c r\ n r\ on at 4.0 5.0 6.0 7.0 8.0 9.0 — Magnitude

Fig. 4. Frequency Distribution of Mean Annual Accumulative Magnitude

V-35
HORIZONTAL PfcAKS

AVERAGE OF PEAK ACC E L ERATION FOR"o" AND I SITE CLASSIFICATIONS AND FOR Mr6.5(THIS STUDY)* •SCHNABEL ft SEED (1973) Mr6.g

KANA1*(1966) M = 6 5

o USES HYPOCENTRAL DISTANCE USES EPICENTRAL DISTANCE

400 6C0

kilometers ? 20.0 *Q0, . .ippjo

1 2 LOG (DISTANCE - KM) Fig. 5. Comparison of the Correlations of Maximum Acceleration and - Distance

in Case of M=6.5 (After Trifnac, M. D. and Brady, A. G.

)

V-36
gal

600

1 5 10 50 100 500 1000 years

Fig. 6. Expected Maximum Acceleration Values (gal) vs. Return Period in Tokyo

30

25

20

15

10

TM2 T*=Q8 T*=Q5

/,TrQ3

1 5 10 50 100 500 1000 years

Fig. 7. Expected Maximum Velocity Values (cm/sec.) vs. Return Period in Tokyo

V-37
V-38
V-39
V-40
V-41
V-42
V-43
130°

Fig. 16. Regional Seismic Zoning Coefficient for the Aseismic Design

V-44
TREATMENTS ON SEISMIC FORCE IN DESIGNING EARTH STRUCTURES Kenkichi Sawada, Chief, Soil Dynamics Section

Public Works Research Institute ABSTRACT

Treatment of earthquake forces in the design of retaining walls and of embankment

slopes is discussed. The discussion centers around the philosophy and considerations given

when Japan Road Association revised its Earth Work Manual in Road Construction.

KEYWORDS : Culverts; design principle; fill slope; earth structure; earthwork manual; priority; retaining wall; seismic forces

V-45
1 . PREFACE Statistical analysis of damages to earth structures, preservation of records and other treatments on the damages were discussed in my previous report. This paper will analyze

the actual circumstances by considering the very basic problems in designing particular

earth structures.

The earth structures have been built for many years by trial and error method with accumulated knowhow rather than by so-called design process, thus the process of design

was not particularly required in these years.

It is considered that the design procedure for earth structures becomes particularly

important only when constructing a large structure or construction of a structure in a minimum time was a prerequisite. It may be said that the design of stable slope and retaining wall became important becuase the height of the slope was large and also because consolidation of soft ground became important when a high construction speed was needed. Recently, the Japan Road Association revised its Earth Work Manual in Road Construction

in which an important problem was the treatment of the seismic force in the design after

the social movement toward incorporation of the seismic force in designing the earth

structures. This also may be considered a new prerequisite as stated in the above example.

In this manual, influence of seismic force has become more important when designing

especially retaining walls, embankment on soft ground, and culvert. This subject will be outlined below.

2. CONSIDERATION FOR RETAINING WALLS

Seismic force on retaining wall is now treated in a manner stated below in design. The retaining walls exceeding eight meters in height will be now designed for earthquake. For retaining walls lower than eight meters, those resisting forces or abilities that are not taken into account in normal computations, such as the passive earth pressure at front face

or design under the worst condition of the rear earth fill (that is, loss of cohesion that may occur only during a long period of use) , are considered resistive against increased

loads due to earthquake. That is, the lower walls require no particular consideration for earthquake and they are considered to be safe for seismic forces. The next problem is in the area of calculations for retaining wall exceeding eight meters in height with seismic forces. The previously mentioned Earth Work Manual employs equations for earth pressure principle proposed by Mononobe-Okabe during earthquakes.

The Mononobe-Okabe equations propose to tilt a retaining wall imaginarily forward by an angle corresponding to seismic coefficient in order to statically calculate a seismic

force applied to the wall during an earthquake. This type of equation is also used in many other manuals. However, one of the characteristics of the road embankment is its sloped

surface at the rear of the retaining wall instead of horizontal surface. Therefore, especially when a retaining wall is required at the bottom of a long sloped ground, these equations may often result in an overdesigned wall. In order to provide horizontal friction

forces sufficient to resist the forces such as earth pressure, inertia force assumed to be

V-46
applied to main portion of retaining wall, and seismic earth pressure, the length of

bottom slab required is enormously large. To solve this type of problem in design, various design manuals for retaining walls

are responding in many different approaches. For example, the design manual prepared by

the Japan Highway Public Corporation simply clarifies this problem by employing Terzaghi 1 s aquations for earth pressure with proportional increase of (1 + k) corresponding to coefficient k. With this modification for the equations, the use of excessive earth

pressure in design can be prevented. For retaining walls for structures other than road

construction, this kind of problem is not likely to occur since the rear top of most

retaining walls is considered to be associated with horizontal ground surface. Depending upon the angle of friction assumed on slip surface of soil back to the wall,

the direction of earth pressure force will vary greatly, resulting in a serious influence

Ion the stability. Value of this angle is normally assumed to be zero at the time of an earthquake, but it is inconsistent to make its static value simply zero since it may still

have statically a fractional value of internal friction angle of the earth. Also the equations proposed by Mononobe-Okabe do not consider the cohesion force, but it may be agreeable to consider the effect of cohesion force in some way since an earthquake and

loss of cohesion force of earth next to wall are not likely to occur at the same time. The

Earth Work Manual qualitatively discusses the effect of cohesion force in the hope of

limiting the size of slip surface. With these various approaches employed in the Manual, the Manual establishes a rational design method that offers dimensional ranges acceptable in the actual practices.

However, it is widely said that the studies on soil mechanics start and end in coping with

the problems of the earth pressure, so that step by step improvement of the design method

for the retaining walls stated in the Manual is likely to be expected but problems will

never be completely solved.

3. CONSIDERATION FOR EMBANKMENT SLOPE Various types of problems are also pointed out for the stability of the earth fill

slope, as in the case of the retaining wall. Not only for retaining walls but also for

the earth fill slopes the need for encountering the effect of earthquake by some method

was strongly discussed in the process of hearing for the Earth Work Manual. Conventionally the stability of the slope has been analyzed by the use of the slip

surface method which is equivalent to seismic coefficient method. However, justification

for accurately computing the safety factor in dynamic design was questioned in the hearing

even if the method itself was valid for static design problems, since the test method for

soil dynamics did not completely reproduce job site conditions, failure models were

oversimplified and soil properties of job site varied too much from one location to another. For this reason, the committee for the Manual once concluded that the statical calculations

with simply increased safety factor would be adequate for earthquake. This approach was

identical to that of retaining wall. Since the earth fill slope had no extra resisting

abilities uncounted in the calculations, the value of safety factor had to be increased in V-47
the actual practices. Then, the safety factor as extra room for strength was in question but it was once set to be about 0.5 by a majority of the committee members. However, in the final stage, this method was abandoned since it was not well grounded to take up as a method to be specified in the Manual.

In the end, the soil was classified into the clayey soil and sandy soil, and they were specified separately in the Earth Work Manual. The former has a reocvery of strength

after construction, and the increase of strength after construction is expected to provide ' an extra stability to the slope, as in the case of retaining walls. Thus, no special consideration was given to the earthquake. However, for the sandy soil, only a basis for determining possibility of liquefaction of poor soil was described without including detailed requirements. It seems to be very important to examine the dynamic properties

of clay, but no requirements are provided for examining strength properties since it was

simply agreed in the committee that the earth structures would gain strength required for safety after their construction. It was found that a dynamic test method capable of producing results clear as these by dynamic triaxial test used for checking poor sandy soil was not available at this time. Thus, methods for analyzing the sliding of slope were not positively stated in the Earth Work Manual. It should be noted that some manuals are using the circular arc slip surface methods. However, many variations can be expected in details in the method of the Manual where the sliding plane of various forms is combined with the seismic coefficient

method. A few examples will be described hereinafter, but some of them are somewhat identical to those already reported as "earthquake-resistive properties of earth fill" at

the 5th joint meeting. There are three methods in the linear sliding plane approaches: (1) sliding plane

is treated as infinitely long slope as employed by National Railway Laboratories and

others; (2) resistance at the bottom edge of the slip surface is compensated in the method

used by Seed and Goodman; and 3) sliding plane passing through the toe of the slope is used by the Design Standards for Harbour Structures. The circular arc slip surface methods are: (1) standard method applying seismic

force to center of gravity of each slice; (2) design criteria for earth fill dam applying

seismic force on slip surface; (3) design standards for Harbour Structures where influence

of seismic force is not applied to resistance term; (4) report of research by National Railway and proposed design criteria for an artificial island of Tokyo Bay by Japan Road Association where the seismic coefficient is applied only to earth fill in providing

resistance to earthquake; and (5) so-called folded line method where a special form is assumed for the sliding mass of earth fill. The latter methods (circular arc type) are employed when the results of the computations by standard methods are unable to assure stability due to exceptionally large sizes

of structure or unusual form or to provide basis for calculations by accurately studying mechanism of phenomenon with various devices and by various types of simplifications. By this approach, each of these phenomena is examined in detail for evaluating its contribution

to resistance, and thus extra forces hidden in the calculations will be reduced accordingly.

V-48
4. DESIGN BY DISPLACEMENT CRITERIA

In the design of a retaining wall, one problem is the value of the destructive dis- placement to be used, and this is not the problem concerned with the earthquake alone. It was tried to make provisions for displacement in the Manual. As reported previously, there

will be a number of different types of failure in earth structures caused by actual earthquakes. However, a type of failure similar to that modeled in an analysis is hardly found.

In fact a slight projection of retaining wall after an earthquake may be found, but complete overturning or sliding is rarely found. Most of the failures stop after a certain degree

of progress. Even if an overall failure occurs it is usually made as a part of overall slope

failure instead of its own independent failure. Also in the case of earth fill, overall

failure rarely occurs unless a liquefaction is present.

All of these phenomena are called "failure" so that various types of recognitions for

the failure become unclear. A number of phenomena existing in reality are all cast in the limited number of forms, resulting in a shortage of useful information. It may be natural

to find this kind of problem in old references investigated but a complete record may not be obtained in earthquake damage investigation conducted in recent years unless the problem

stated above is reformed in investigation. When an actual damage is seen, each person

may classify it differently from others. Also, a damage may look as if it can be classified

into certain types at a glance, but an engineering method for quantitatively determining

the damage by a survey has not been studied consciously.

Slip failure of road embankment caused by earthquake in the middle district of Oita

Prefecture may be a good example of this problem. At a glance or from photographs of damage,

the contents of damage look very clear but it is extremely difficult to record it quantitatively as a prototype. It seems very difficult to imagine a real state of a damage

from drawings of data gathered only from Survey of Soil Property for Disaster Restoration

Work. Regardless of the consequences, it may be an only way to produce drawings according

to a pattern. Because of this uncertainty, many people are used to thinking that consideration for failure of earth structures by earthquake is unnecessary. However, this is mainly

because conventional analytical models cope with a boundary condition where a failure may

start, but it should be understood that a structure can be utilized even after this boundary

state is exceeded. The discussion may be advanced with such a view in which the use of structures is precluded taken as a limit. For this purpose, also an effort to adopt a design method determining a failure by displacement criteria may be required. However, this method has not been adopted in the recent revision of the Manual.

5. PROGRESS OF DESIGN PRINCIPLE

Empirical techniques of design for earth structures have been useful for the design of structures with limited sizes. But, uncontrollable factors will appear when the sizes of structures increase. At first, the difficulty in design is overcome by modifying values expressing the characteristics of soils used in design. When this approach becomes no more appropriate to design, other mechanical or qualitative development must be expected. V-49
The problem in evaluating the influence of earthquake may be the same as that stated

above. This problem can't be solved simply by increasing the accuracy of the same analyticc method. This problem requires a certain new method. As presently done so often, resorting

to the strength characteristics such as "c" and "0" (which are not related to strain) as a result of analysis of soil properties is an accustomed method in normal approaches of

mechanics. However, possibility of solving problems within this conventional area of approach is becoming very small.

6. CONSIDERATION FOR CULVERTS

Lastly, the influences of earthquakes are not taken into consideration in the design

principle for culverts in the Manual. However, in the design of gate type culverts, one paragraph of the Manual requires an analysis with earth pressures acting only on one side during earthquake even if the earth pressures may be acting on both sides in reality. In this case, the method for computing the earth pressures during the earthquake is not designated.

7. IMPRESSIONS

(1) Revision

Subjects related to earthquake in the revised Earth Work Manual have been described

above, and now my impressions will be stated below. An important point is that major changes covering a wide area of subjects may be required instead of conventional type revisions in the sense of narrow area if a design

manual for earth structures is to be revised in the future. Methods used in many

revisions up to now are to revise parametric values of earth mechanics while maintaining

the same qualitative mechanism. This traditional approach may be limited in its effects

even if the accuracy of the values of parameters is improved by means of many experiments

since the approach is not considering non-uniformity of the quality of earth structures.

As a result, this may raise a question whether properties of earth structures can be expressed by accumulation of minor items as expressed in normal mechanics. Normally,

in research activities, more details are investigated as the research progresses. But the entire picture can be more exactly understood if macroscopical view is taken as long as the magnitudes of disturbance of the properties are identical. A solution might be to employ a probabilistic approach. But, simply using the probability concept is not desirable to us since solutions by considering soil mechanics are more important at this stage

of the development. Now let us examine these subjects in more detail. As long as we try to understand a phenomenon by the use of data and anlaysis, contradictions between requirements for analytical accuracy and actual state will go non-reversibly towards more contradictory direction. In such a case, a proper compromise may be necessary. Usually the compromise is considered to be passive, but, in this case, it should be more positive in nature and this can be achieved

if it solves the problem. The use of slip surface method may be a kind of compromise to the present state of mechanics, but it is very pracitcal especially for producing proper

V-50
compromise now is response to the present needs. However, it should not be limited only

in an area where values of coefficients are prepared unless it contains wider mechanical

area.

(2) Renovation

It must also be considered that the problem of renovation in earth structures is very particular compared to other structural materials. With other materials, renovation

of a failed structure means that broken portions are completely replaced by new materials,

though it may be sometimes very difficult to determine a limit of broken portion. This is quite different from the earth structures since broken portions of soils are rarely

replaced by other new soils. This phenomenon is rather quantitative in nature since a form

is rearranged by adding soils to the broken, deformed portions. On the other hand, there

is an example of rather qualitative renovation. A final renovation work is executed directly

on an emergency work made immediately after a failure of earth structure. Thus, in earth

structures, wear rather than failure is often more adequate expression to use. As long as the failure of earth structure is treated as stated above, it may be very difficult to expect a complete answer to the design. That is why a consistent description

in a limit of a system will give a justification as stated previously.

But, it is understood that this type of system must experience a qualitative improvement of the method at a certain stage. Research and design are mutually combined in such

types of relationships. In earth structures, however, this kind of stage is long overdue,

and the result is slow progress. Though only these kinds of findings are useful for design,

they are not all of the present fruits. A great number of .data resulted from various

types of enormous in-house analytical experiments must be totally integrated to utilize them

for the improvement of the method.

(3) Terms

We are accustomed to the use of existing concepts when observing something. Especially

in soils engineering, concepts developed in other fields of science are often used without

modification since analytical soil dynamics is very slow in its progress. The present

approach may be handy for an approximate understanding but chance for true understanding can't

be achieved simply by this borrowing of concepts. Also a significant progress can't be achieved as long as a chaos exists in the technical terms. The chaos also exists in the magnitude of sizes and forces but more importantly in the areas of social demand for quality and changes in environmental conditions.

(4) Priority

In the discussions held for revisions of the Earth Work Manual, a concept of priority

in design of earth structures was once taken into consideration in an attempt to prevent

the failure of structures having top priorities. It will be very hard for me to understand

if this concept is brought to an attention only for compensating the design method employing "c" and "0". It is not sufficient to use the priority concept only for immediately

solving discrepancy that has not been resolved by "c" and "0". This gives an impression that all unclear subjects are to be approached with the priority concept. It may be possible to establish the priority concept to restrict the

V-51
designs for high priority structures for preventing the failure, but it is very difficult

to determine the priority for actual structures agreeable to people. Also the priority

or value is not a constant factor in nature. Changes in the priority or value are normal

and it is not a simple phenomenon. The changing state doesn't mean dimensions or shapes

of structure itself but means social demands.

If the priority is understood in this way, it may be a type of an expression for indicating social importance. As stated above the priority concept was brought to an attention as an important concept in the design of earth structures but its meaning failed

to obtain the common understanding.

(5) Postscript

Lastly I consider conditions where structures made of earth can be produced. If only

the probability of failure during earthquake is taken into account, production of structures

by soil may become impossible. Exposure to any other type of disaster must also be taken into consideration. Also, it may be possible to discuss a difference in human senses between products made of earth and those made of steel as a factor in considering earth structures.

V-52
STUDIES ON THE ASEISMIC PROPERTIES OF UNDERGROUND PIPES Keiichi Ohtani, Chief, Earthquake Engineering Laboratory Nobuyuki Ogawa, Research Member, Earthquake Engineering Laboratory Chikahiro Minowa, Research Member, Earthquake Engineering Laboratory

National Research Center for Disaster Prevention, Science and Technology Agency ABSTRACT

This paper describes the experiments of underground pipes by using the large-scale

shaking table of the National Research Center for Disaster Prevention, the analysis

results of dynamic water pressure on pipelines caused by earthquake motions, and the problem of the slip between the surface of pipe and the soil. Two kinds of experiments were executed. In the first experiment a linear pipeline

(steel) was buried in the ground at the vicinity of this shaking table. The test pipeline

was excited by the waves which were generated from the shaking table and transmitted

through the ground. The behaviors of this pipeline and the ground would not always be similar because of the differences in the rigidities between pipe and soil and in the boundary conditions of pipeline ending. In this experiment, slight differences were measured between the behaviors of the test pipeline and the ground.

In the second experiment, a steel pipeline with a branch pipe was set on this shaking table and one end of the main pipe was clumped in the shaking table foundation. And this pipeline was buried in the sand pit. The bending strains and restoring forces

of this pipeline were measured. The dynamic strains had the values similar to those of

static strains for the same displacements. The hysteresis loops, drawn by the restoring

force and displacement at the clumped end, had the energy absorption. The necessity for the second experiment was based on the slip which had grown around the pipe surface in dis- astrous earthquakes. The slip values of the infinite length pipeline with a branch pipe

were calculated for sinusoidal ground waves.

In addition to these problems concerning water supply pipelines, etc., the water pressure

in the pipelines has to be considered. In this paper, the procedure for estimating the distributions of dynamic water pressures caused by earthquakes without the so-called water

hammer has been developed. For example, the dynamic water pressures for model pipelines

are calculated.

KEYWORDS: Dynamic water pressure; shaking table; underground pipes; vibration experiments.

V-53
1. INTRODUCTION

In the cases of damaging earthquakes, such as the 1923 Kanto Earthquake and the 1974 Izuhanto-oki Earthquake and so on, the underground pipelines were severely damaged. Some

of the damage happened to be brought about by landslides and falling stones accompanied with earthquakes. But in most cases damages would be brought about by the ground motions

during earthquakes. There would be many pipe breaks in the vicinities of structures, and

the boundaries of different ground properties would be more vulnerable than in general

sites. Almost all of the pipes would be broken by the axial and bending deformations,

and the increase of water pressure would occur during earthquakes. The damage patterns

of pipes would vary in accordance with the types of pipe materials, the ages of being

buried, the methods of pipe joints and pipe sizes.

The aseismic properties of underground pipe lines were already studied by many researchers - A. Sakurai, and the Ministry of Construction, and so on, and many valuable

results were brought by them. In the present paper, the experiments using the large-scale

shaking table, the vibration experiment of an underground pipeline of finite length and

the forced displacement experiment of T-shaped underground pipelines are discussed. In addition, the dynamic water pressure caused by earthquake are calculated.

The ground vibrations around the shaking table amount to 3-10 gal during the shaking

table excitations with the heavy loading weight. This level of vibration corresponds to the earthquake of Intensity III of Japan Meteorological Agency scale. These ground vibrations were used for the underground pipeline experiments. The steel pipeline 6.5m

long and 139.8 mm in diameter was buried in the depth of about 40 cm, parallel with the direction of this shaking table excitation. Accelerations and strains measured were only

in the axial direction component of this test pipeline. Also, the ground acceleration

of this component was measured. The ground acceleration measured was about 3 gal, and the apparent transmitting velocities were supposed to be 150-800 m/s with the dispersion by another experiment. The axial strain values of the test pipeline during the excitations

-6 were 4x10 in maximum. According to Figs. 2 and 3, differences in behaviors of this test pipeline and the ground were found to be small. The displacement equation in the axial direction component of the underground pipeline, using the coefficient of subgrade reaction, is expressed as follows:

where E = Youngs modulus of the pipeline, A is cross section area of pipeline, p is the unit length mass of the pipeline, k is the interaction spring between ground and pipega

line, x is the co-ordinate in parallel with axial direction, u

g is the absolute ground

displacement, u is the absolute pipe displacement, k would be obtained approximately

ga

as follows:

2. THE VIBRATION EXPERIMENT OF AN UNDERGROUND PIPELINE OF FINITE LENGTH

EA U) (1)

V-54
The pipeline was assumed to be buried in the infinite depth for convenience. The wavelength in the axial direction was also assumed to be infinite. Thus, this problem was reduced to two-dimensional procedure. The equation for obtaining k by the use of polar

ga co-ordinate r-6 was given as follows:

9r 2 r

9r r

2 36 2 G

8t 2

where G is the shear modulus of the ground, u^ is the ground displacement for the axial direction (perpendicular to the r-9 plane) , p

Q is the unit volume mass of ground. The solution of this equation would be assumed as u =e

ia)t *R(r) "6 (0) . It would be

x sufficient to assume the uniform radiation wave only, because of infinite medium. The boundary forces and displacements along the pipe surface would be assumed to be continuous.

Therefore, the displacements along the pipe surface are written as follows:

ux

(a,t) =

(3) H

(2) wa

1 V

force acting on the pipeline, CO is the circular frequency, (~^) H ^ ^ (^") is tne Hankel function of the 2nd kind. u

x

(a,t) corresponds to u -u in the first expression,

follows:

(4)

where k is expressed in complex numbers, and the values of k /(2ttG) are shown in Table

ga ga

1. Because this problem was analyzed in two dimensions, the static value of k^

a would be

equal to zero. The solution of the first expression for the stationary sinusoidal waves with the boundary conditions of the free ends is written as follows:

io>t kga e u(x,t) =

'Va

2 (EA + iCa )—-+ (kqa -pto2

) va z a Va \a. SINH(X a £)

COS(^) SINH(Xax) (5) Va A a COSH(X a S.)

V-55
where

EA + icai» (5 cont'd.)

Va is apparent transmitting velocity of the ground excitation, Ca is the damping of the pipeline, and 2l is the length of the pipeline.

Besides, another solution for the first expression with the use of modal analyses would be expressed as follows:

(6)

where 3 is the nth modal participation factor, 0 (x) is the nth natural function, and

n n qn

(t) is the nth normal co-ordinate. V * n

2

tt 2 2_ - P

(

)

( + ) (7)

4tt 2 4 I

2 p EA

^ p

) (8)

where V is the transmitting velocity of longitudinal waves along the pipeline, k

s is the spring between the pipe and the ground, and is the damping of the ground. Supposing the sinusoidal ground excitation u

g=e*

a) ^ t X//Va ' as the input wave for the underground pipeline, 6^ would be expressed as follows:

n £ 0 n

£ 0

. SIN + -2-) SIN 7r£ - —

)

a - 1_[ 2 L . ,_u n ? h \ (9) Wl

2 L

; l 2 L

;

where £Q is the length of the pipeline and L is the wavelength. According to these considerations, if the input ground wave have sufficiently long wavelengths in comparison with the pipe length, the pipeline would give almost the same behaviors to the ground. However, in the short wavelength input waves, the pipeline would give complicated behaviors.

The slight differences between the test pipeline and the ground in this measurement

will be explained by these reasons.

V-56
3. THE FORCED DISPLACEMENT EXPERIMENT OF T-SHAPED UNDERGROUND PIPELINE

In the disastrous earthquakes, the pipelines are supposed to slip along the boundary

of the pipe and ground. In this case, the axial spring between the pipe and the ground is assumed to be represented by the bilinear loop. Supposing the sinusoidal ground waves, kga

may be expressed with the first term of Fourier series for the bilinear loop a 3 follows:

kga - *i(C + iS ) (10) where,

C = -(A - i- SIN(2<M) (l-ct)+a, S = -(l-a)SlN2

(<f>)

IT 2 u 27m k 8 W h

k =2Tr?G kr , <J> = COS (1-

-^f

)

f Ue =

a is the bilinear coefficient, U is the relative displacement between the pipeline and the ground, k^ is the elastic spring between the pipeline and the ground, £ is the decrease

coefficient of G, h is the thickness of the backfill soil over the pipeline, W is the unit

volume weight of the backfill soil, k^ is the coefficient of dynamic friction between

the pipe surface and the soil.

^

If the sinusoidal ground wave

qU e"""^

1" is applied to the T-shaped pipeline, parallel

with the axial direction of the main pipe, the displacement of the pipeline at the junction

would be given in the condition of infinite length for each pipe as follows:

Xb

d I b (1 + 6) kbb

<Am

Am + A b

3 I b

(1 +6)) (kbb - p b

W

2

) kga ^

+ 2 (Xm Bj,, + Xb

3 lb (l + 6)) ((E Am + iCm w) — + kga - pm a> 2

)

kbb - Pb w

2 ~ H Abo

- E Im

+ i Cbb 0) E Im + i Cbm u

kga

- Xm 2 Xbo

2

Im

i 2 _ 6 = - Am + i Cm to 2 *bo

2

Im + Xb

2 Ib

where I and I, stand for section moments of inertia of the main pipe and branch pipes, m b and stand for unit length masses of the main and branch pipes, C^ and C^ stand for

the damping factor of the main and branch pipes attributed to bending vibrations, Cmstands

for the damping factor of the main pipe attributed to the axial vibrations, Jc^^ and k

fab mean

the ground springs for the bending displacements of the main and branch pipes, Va means the apparent transmitting velocity of the input ground wave in the direction of the main pipe

axis. V-57
Figs. 8, 9 and 10 are the calculation results of the expression (11) for the parameter

2 3 values of U

e=0.2cm, U=10cm, kbm=kbb=28kg/cm , W=1.9g/cm , h=120cm. In the calculations, the damping factors of the pipes were neglected. Judging from Figs. 8, 9 and 10, the relative displacements (slips) between the ground and pipe at the junction would increase if input waves have short wavelengths. The pipeline with branch pipes would have small relative

displacements. As a result of this relative displacement, the concentrated bending moments would occur at the junction points.

To examine these concentrated bending-moment strains, the experiment illustrated in

Fig. 5 was executed. The steel pipeline with the same pipe section as in the first experiment was set on the shaking table. One end of this main pipe was clumped in the shaking table foundation. And this test pipelines of T-shape was buried in the sand pit. The bending strains and restoring forces caused by the shaking table displacements were

measured. The dynamic strains excited by the 1Hz sinusoidal waves were found to have the value similar to the static strains for the same displacements. The hysteresis loops at the clumped end showed the absorption of energy, as illustrated in Fig. 7.

4. DYNAMIC WATER PRESSURE OF PIPELINE CAUSED BY EARTHQUAKE MOTION

Dynamic water pressure of pipeline caused by earthquake motion is one of the design

factors of water supply system. On this subject Nakagawa (Ref. 7) performed theoretical

studies and offered some practical conclusion on maximum water pressure at the stop end, bend, junction, etc. of pipeline due to sinusoidal earthquake motion. We made an attempt

to approach more actual conditions, that is, to estimate the dynamic pressure distribution

in the pipeline system. Basic assumptions are as follows:

(1) Any part of the pipeline is forced to have the same motion as the ground around

it during the earthquake.

(2) Earthquake motion is stationary sinusoidal wave at any place.

(3) Only the dynamic water pressure due to axial motion of pipeline is considered.

(4) Propagation of pressure wave in the pipeline is considered to be one dimensional.

(5) Pipeline system is in the horizontal plane.

Then, considering the earthquake motion, the equations of motion and continuity of water in

a pipe element are k«« -a-* <•?>, :J

si -p »

2 Sx«v &

where x is the co-ordinate along the axis of pipe, t the time, P the pressure change from stationary value, v the particle velocity of water caused by earthquake motion (relative velocity of vibration to pipe) , £ the ground displacement along the axis of the pipe

(component in axial direction of the pipe) , a the velocity of pressure wave propagation,

p the density of water, and Q the linearized resistance.

V-58
Put £(x,t)=£e^

Wt kx *

f anci considering stationary solution v=V (x) e^"^ , and p=P(x)e _ we get: -sx jw(a 2 k

2 -to 2

) V(x)=VA c SX

+ V„e sx

re 3Kx jwQ + a

2 k2 -«.2 pa 2

toQk jwQ + a

2 k2

-co 2

(1 3)

where P

A# Pg, etc. are constants to be determined by boundary conditions, s=j(i)k/a, k=l-j (Q/W) and j=v^T. Considering that a is constant in pipeline system for simplicity, and using the boundary

condition (equality of pressure and continuity of flow) for bend, T-junction, etc., we can express a general formula for dynamic pressure amplitude as follows: Pressure amplitude = Velocity amplitude of ground motion (jwfjx (14) Wave impedance in pipeline (pak)xB where B is determined by 0), Q and network system of pipeline considering the direction of

the ground motion.

In order to obtain pressure distribution in general pipeline systems, we can use numerical computations based on solution (13) as follows. Considering a network system of pipeline including N-nodal points (stop end, bend, etc.), which have linear boundary condition

on pressure and flow, the boundary condition at a nodal point i=l,2,...,N is written in matrix form:

[Wil' W

i2 ] [ V

1] =

( V (15)

i Supposing a two-dimensional horizontal ground motion, and substituting the solution (13) of

each pipeline, we will have a simultaneous linear equation including the boundary conditions

of all nodal points and ground motions.

[W] (P) = (S) (16) Solving this equation, we may obtain P^, Pg, and the pressure distribution of pipeline system.

Fig. 11 shows an example. In this example it is assumed that the frequency of ground

motion f=1.4Hz, propagation velocity of ground motion (apparent velocity at ground surface) Vg=100m/sec .

, and damping Q=0. Ten nodal points are shown by No. 1-10, where No. 1, 8, and 10 may be infinite points which absorb pressure energy and have no reflection waves. In this figure, the pressure distribution is normalized by paoo£=0. 9kg/cm so as to show the effect of infinite points. From some computations as shown above (Ref. 8) we can say that,

1) Dynamic water pressure in the pipeline to be caused by earthquake motion has frequency characteristics which will depend on pipeline system and ground.

2) Water pressure is considerably damped at infinite points in pipeline system, but considerably high pressures may arise in some parts of the pipelines which have many stop ends. V-59
3) Pressure distribution in pipeline system shows some difference depending on the ground motion, but it seems to have a specific mode depending on the structure

of pipeline system, and the maximum pressure amplitude does not always appear at

a stop end or junction point.

5. CONCLUSION

The behavior of underground pipelines during earthquakes is expected to give smaller vibrations in comparison with that of the ground, because of the difference in the stiffness. In the cases of the pipelines with branch pipes, the earthquake loads would be con- sidered to be concentrated in the junction points. In the design of water supply system, great care must be paid to the distribution of pipelines where large dynamic water pressures might be caused by earthquakes. The properties of earthquake ground motions should be clarified for the aseismic design

of underground pipeline as well as for the other structures. Considering the input earthquake waves to the pipeline, the apparent transmitting velocities should be an important

factor because of their wavelengths. For the purpose of investigations for the apparent transmitting properties of earthquake ground motions, it is necessary to intensify the earthquake observations oh the surface.

6. REFERENCES

1) Sakurai, A., et al, (1970): Dynamic stresses of underground pipelines during earthquakes 2, Technical Report: C69087, Central Res. Inst. Electric Power Industry, etc.

2) Public Works Research Institute (1975) : Technical Memorandum of Public Works Research

Institute No. 1037.

3) Hohjo, S., et al . (1974): Earthquake and pipe lines (2), Ductile Cast Iron Pipe No.

16.

4) Miyajima, N. , et al. (1975): Stress on the underground pipeline during earthquakes, Proceedings of the Fourth Japan Earthquake Engineering Symposium.

5) Ishimaru, S., et al. (1973): Ductility factor control method, Transactions of the Architectural Institute of Japan, No. 174.

6) Minowa, C. (1976) : Dynamic experiment of an underground pipeline, The Report of the National Research Center for Disaster Prevention, No. 16.

7) Nakagawa, Y. (1969) : Theoretical research on the dynamic water pressure of water

supply system during earthquakes, Journal of Japan Water Works Association, No. 416.

8) Ogawa, N. (1976) : Study on the dynamic water pressure of water supply system during

earthquakes, Journal of Japan Water Works Association, No. 501.

V-60
V-61
PIPE STRAIN

1 1 0-5 sec GROUND ACCELFig. 2 Measured Waves by an Impulse

V-62
3.03H0"6 PIPE ACCEL. 5Hz

4 0.2sec. GROUND ACCEL 5Hz

Fig. 3 Measured. Sinusoidal Waves

V-63
ig. 4 Participation Factor of a Finite Length PipePLAN

J2m_

: .'.pit-

•

'

. 5AND-

'

pipe ANCHOR

FORCE DIRECTION Er T. • • .-*^-*.-| ANCHOR J^P

^aking' table

Fig. 5 The Outline of Second Experiment

V-64
STATIC STRAIN

A125xA125

0 -'200X1CT6

DYNAMIC STRAIN OF BRANCH PIPE

A125 A125xAl25

1 Hz 3waves

A. 2mm A.2ton 1A0mm A.5ton 190mm A3 ton

;600xi0"6

A125 FORCE

Fig. 6 Strain Distribution

V-65
1Hz

V-66
Fig. 9 Slip of a Junction Point
I Numerical Example"]

Distribution of Normalized Value

in model pipe line

Table 1 . k ga /2ng

toaV Real Imaginary

0 00001 0 0845 0 011

0 00005 0 0974 0 015

0 0001 0 1043 0 017

0 0005 0 1244 0 025

0 001 0 1356 0 030

0 005 0 1705 0 049

0 01 0 1907 0 063

0 05 0 2576 0 129

0 1 0 2970 0 189

V-68
OBSERVATION OF DYNAMIC BEHAVIOR OF KINUURA SUBMERGED TUNNEL

DURING EARTHQUAKES

Shigeo Nakayama, Chief of Subaqueous Tunnels and Pipe Lines Laboratory Osamu Kiyomiya, Member of Subaqueous Tunnels and Pipe Lines Laboratory

Hajime Tsuchida, Chief of Earthquake Resistant Structures Laboratory

All of Structures Division, Port and Harbour Research Institute Ministry of Transport ABSTRACT

Kinuura Submerged Tunnel, which is located at Kinuura Port and Aichi Prefecture, is equipped with a number of instruments comprising of accelerometers , strain meters, bar

stress transducers, and a displacement meter, which are intended to serve the purpose of

the tunnel maintenance and to provide data for studying the behavior of the submerged

tunnel during earthquakes.

The measurement of earthquake response of the tunnel has been carried out since August,

1973 when the tunnel was opened to traffic. Fifteen earthquakes have been recorded up to January, 1977. A part of the data thus obtained and its analysis have already been reported

by the authors (1) . This paper describes the analysis of the data and the result of earthquake response calculations carried out by using these earthquake records.

KEYWORDS: Accelerometer ; axial force; bar stress transducer; bending moment; displacement

meter; dynamic behavior of tunnel; power spectrum; strain meter; submerged

tunnel

.

V-69
1. SUMMARY OF THE TUNNEL AND INSTRUMENTATION Kinuura Submerged Tunnel which connects the cities of Handa and Hekinan is a two- lane highway tunnel having a total length of 1,560 m. The submerged portion of the tunnel

is 480 m in length and consists of six reinforced concrete elements, 80 m long. The soil conditions at the tunnel site consist of a well compacted sandy gravel layer below a depth

of -17 to -18 m and a filled-up layer to the depth of -5 to -10 m from the surface. Intervening layer in Handa side between the foregoing two layers is a very soft, unconsolidated, clay layer, however, the intervening layer in Hekinan side is hard clay with N-value

9-13. The arrangement of instruments installed in the tunnel is shown in Fig. 1. A total

of 19 accelerometers is installed, one each in the axial and normal directions to the tunnel axis at the ground surface on both sides of the tunnel, thus totalling four; two each at the top and bottom of each of the two ventilation towers and two more for vertical acceleration measurement at the top of the ventilation tower on Handa side to catch rocking

motion, totalling ten; and five in the submerged elements. A pair of strain meters are installed at three sections of the tunnel under the navigation channel, totalling six. A

total of eight bar stress transducers, at each junction of the ventilation towers and the submerged tunnel elements is installed.

Bar stress transducers were initially used for the execution control. Also, one dis- placement meter is installed in the middle of the submerged tunnel. The trigger level for the starter of these instruments is set at three gals and the system is so designed as to take the records for three minutes. The recording systems are located in the ventilation

towers.

2. EARTHQUAKE DATA AND ANLYSIS Earthquake data obtained and analyzed are given in Table 1. Earthquake Nos. KUWT-4 through KUWT-6 were omitted in the tabulation because they were recorded only in some instruments. All of the earthquakes recorded were medium scale (not exceeding magnitude 6) , and the intensities at Kinuura were Scale II-III in the Japan Meteorological Agency Scale. Shown

in Fig. 2 are some of the records during the earthquakes. A study of the data obtained by accelerometers indicates that the values of the maximum acceleration on the ground surface

of Hekinan side were in most cases greater than those on the ground surface of Handa side, and this appears to be attributable to the difference in the soil properties between the ground at both sides of the tunnel. Unlike the foregoing difference, however, almost

identical values were shown on both sides in the case of the maximum accelerations recorded

at the ventilation towers. From this point of view, it is presumed that the ventilation

towers have responses to earthquake different from those of the tunnel elements. At the tunnel section under the navigation channel, the record of KUWT-1 and that of KUWT-2 showed

little difference in the values of the maximum acceleration. As for KUWT-3 and KUWT-7, however, the values of maximum acceleration increased as the location became closer to Handa

V-70
side. At the approach portion of the tunnel, the values of the maximum acceleration were

somewhat greater than those for the tunnel elements. In the ventilation towers, the maximum

acceleration at the top was greater than that at the bottom.

The Fourier analysis of waveforms indicates that the predominant periods of KUWT-1

and KUWT-2 are significantly different from those of KUWT-3 and KUWT-7. This difference

is considered to be attributable to the difference in the characteristics of these earthquakes. The earthquake waveform at the bed layer was calculated by the theory of multiple

reflections using the ground surface records obtained in KUWT-7. Shown in Fig. 3 are the maximum accelerations for each stratum as calculated from the records obtained at Handa side

and also the maximum acceleration as measured at the ventilation tower (P-5, -6, -14 and -15) and at the on-ground portion (P-3) of the tunnel. It can be seen from the figure that the maximum acceleration of the structure in the ground was almost equal to or slightly smaller

than that of the ground itself.

3. EARTHQUAKE RESPONSE CALCULATIONS Using the earthquake records, earthquake response calculations were carried out and compared with the measured values. The method of these earthquake response calculations

was proposed by TAMURA and HAMADA (2,3), i.e., the method in which the responses of the ground and structure are obtained by replacing the ground and the structure by an idealized

system composed of mass, spring and dashpot. As input records, P-2 and P-9 in KUWT-2, and P-l,

P-2, P-8 and P-9 in KUWT-3, were used. The input records were gained by the theory of multiple reflection. Table 2 shows the bending moments and axial forces as calculated from the measured

values by the bar stress transducers and strain meters. Fig. 4 to 9 shows the results of earthquake response calculations. For these calculations, the damping constant was taken as

0.0 except for some cases. Black dots in these figures represent the bending moments and axial forces calculated from the measured values given in Table 2 and the measured values

of acceleration. As for the bending moments, the values calculated from the strain meters

agreed fairly well with those obtained by earthquake response calculations as shown in

Fig. 4.The values obtained by the bar stress transducers were somewhat lower than the calculated moments. This disagreement may have been caused by the fact that the bar stress

transducers, having been primarily intended for the execution control, were not designed for high precision measurement. According to the results of earthquake response calculations in other cases, the maximum bending moments generally occurred at the tunnel proximate to the shore protection structures. However, the calculated maximum moments from the measured

values occurred at the same point and also at the middle of the tunnel section under the navigation channel. In view of this, further studies will be made as to the cause of this

result.

In the case of axial forces, the measured values agreed well with the corresponding

calculated values where the damping constant was taken as 0.0 as shown in Fig. 5. When

the damping constant was taken as 0.1, the sectional forces were 1/2 or 1/3 of the value as shown by dash lines in Fig. 5. V-71
As shown in Figs. 5 and 6, the maximum axial forces occurred on the opposite side to the place where the input record had been obtained. When the power spectrum of the earth- quake waveforms were compared with the predominant period of the ground obtained from the measurement by microtremor, it was found that the period of earthquake record of P-2 in KUWT-2 are close to the predominant period of the ground on Hekinan side, but are not close

to that of the ground on Handa side. What can be considered in this respect is that the assumption of the soil conditions made

in the ground modelling might have been somewhat inadequate. From this point of view, the tunnel was divided into halves at the midpoint under the navigation channel , the earthquake

response calculation of each half of the tunnel was made with the earthquake record obtained

on that side, and then the two results were superposed.

In consequence, the peak of the sectional force, which was conspicuous in the opposite

side to the one in which the input was made, disappeared, and a comparatively flatter curve of axial force distribution as shown in Fig. 7 was obtained.

Fig. 8 was plotted by using the earthquake record of P-3 in KUWT-3. The maximum response accelerations turned out to be greater in the submerged portion of the tunnel. As to P-3, P-ll, and P-16 in the submerged portion and P-l and P-8 at the ground surface, the calculated

values agreed fairly well with the measured values.

Fig. 9 is plotted by using the earthquake record of P-2 in KUWT-3 which was in axial

direction. Slightly differing from the case of P-l, the acceleration in the navigation

channel was smaller, but the calculated values were approximately in accord with the measured

values. There were cases where the maximum response acceleration of the navigation channel portion was greater than those on both sides or where the measured values were substantially

lower than the calculated values. This will have to be clarified by future studies. It is to be noted in Table 2 that, except for the measured values in KUWT-3 by the strain meters of S-l and S-2, the axial strains were greater than the bending strains. The maximum axial strains measured

by the bar stress transducers of K-l and K-3 in KUWT-3 was 3.75x10 ^. Since the corresponding maximum axial strain obtained from the earthquake response calculations was 3.78x10 6

, there was a fair agreement between them. The measured bending strain was 0.92x10 ^ which was about a quarter of the axial strain, but the maximum bending strain as obtained by the earthquake response calculations was 5.78x10

6

, which is about six times as great as the measured bending strain. Although the calculated bending strain curve was of such

a shape that its amplitude became large gradually, the measured and the calculated values agreed well with each other in respect with the predominant period in the power spectrum.

Figs. 10 and 11 show the axial and bending strains, and the power spectrum, respectively,

Of KUWT-3. Predominant periods in the measured bending strain were 0.79 and 0.60 second and those

in the calculations were 0.79 and 0.68 seconds, respectively. As for the axial strains,

1.02, 0.85 and 0.60 seconds, and 0.93, 0.85 and 0.57 seconds were predominant for the measured and the calculated values, respectively.

V-72
4. CONCLUSIONS

While the epicenters of KUWT-1 and KUWT-2 were at a long distance from the submerged

tunnel site, those of KUWT-3 and KUWT-7 were proximate to the tunnel site. All of these

earthquakes were of comparatively small scale but each had its own characteristics. The

fact that they had different characteristics clarifies that the ground as well as the sub- merged tunnel had behaviors depending on the earthquake characteristics. It was also found

ithat, in the earthquakes originated far from the tunnel site, the long period components

(were predominant in ground motion, and the tunnel had almost the same behaviors as the

ground. On the contrary, where the epicenters are located near the tunnel site, the ground

motion was governed by the short period components, and the behaviors of the tunnel differed slightly from those of the ground. The vibration of the submerged tunnel as a whole was governed by the surrounding soil conditions at respective sections of the tunnel, and the ground vibration characteristics

along the axis of the tunnel were different from those in direction normal to the tunnel

axis. It is, therefore considered necessary to investigate topography and soil properties

both in the direction of the tunnel axis and in the direction normal to the tunnel axis in order to determine the natural period of the ground. The greatest value of the maximum acceleration was found at the ground surface. The

values of the maximum accelerations in the ventilation towers and the submerged section of

the tunnel were almost equal to or slightly smaller than those at the ground surface. At

the upper part of the ventilation tower, the maximum acceleration was found to be smaller

than that at the ground surface. As for the strains which occurred in the submerged tunnel, the axial strains were found

to be predominant over the bending strains in all cases except one record in KUWT-3,

and the maximum axial force calculated by the measured strain was about 1,100 tons. In view of the results of earthquake response calculations, it is very important to determine

J soil condition, spring constant, damping constant, etc.. Since the moduli of elasticity of

soils vary with the levels of the ground strain during earthquakes, the value of spring

constant should be determined on the basis of elastic-plastic analysis or triaxial vibration

tests, particularly if the strong earthquakes are to be considered. In these calculations,

there were cases wherein the measured strains showed fairly good agreement with the value

by the earthquake response calculations. In such cases, it was found that the power spectrum

for both had also similar predominant periods. Values of the calculated accelerations

were somewhat larger than the measured values. This was particularly so under the navigation

channel where the calculated accelerations were large. Unfortunately, there was no case

in the present observations where perfect record of strains was obtained at all of the

three sections of the submerged tunnel.

Thus, the distribution of the sectional forces with respect to the submerged tunnel axis should be taken up as the subject of the future research studies.

V-73
REFERENCES

1) Shigeo Nakayama, Osamu Kiyomiya and Hajime Tsuchida, "Observation of Dynamic Behavior

of the Kinuura Submerged Tunnel during Earthquakes," Summary of Lecture at 13th Earthquake Engineering Conference.

2) Masanori Hamada, "Computations of Earthquake Response of Submerged Tunnel," Proc. of 26th Annual Research Conference of Japan Society of Civil Engineers.

3) Choshiro Tamura, Shunzo Okamoto and Masanori Hamada, "Dynamic Behavior of a Submerged

Tunnel during Earthquakes," Report of the Institute of Industrial Science, the Tokyo

University, Vol. 24, No. 5. 4) Osamu Kiyomiya, Shigeo Nakayama and Hajime Tsuchida, "Observations of Dynamic Response

of Kinuura Submerged Tunnel During Earthquakes and Dynamic Response Analysis," Technical Note of Port and Harbour Research Institute, No. 221.

V-74
% Re

e

5

15

4

80»6=4 80

5-2 S-4 S-6 AK

3 O <^

K - ,A7 «

K-8 A

AK

AK

11 12 20

-1 to<x>e«

Off) o

K-5 A

13 K-6 A eo

S-1 S-3 S-5

,6 ,7<J

100 ,1

HEKINAN

ACCELEROMETER G (AXIAL DIRECTIN) © (NOMAL DIRECTIN) (UP-DOWN DIRECTIN) • DISPLACEMENT METER A BAR STRESS TRANSDUCER

OSTRA1N METER

Fig-1 Arrangement of meters

S-liT £ ilS m & B 0

Fig. IS Location of Tunnel

KUWT-3 P-1 (GAL ) 5

0

5 KUWT-3 P-8

(GAL ) 40

6 0 8 0 10 0(SEC)

Fig. 2 EARTHQUAKE RECORDS

234 3 26J.3 800(36 = 480.0

4QQ.Q.

25Q.Q

CHANNEL

SUBMERGED TUNNEL

2 51.9 234.3

CAST-IN -SITU TUNNEL

Fig. 2S Longitudinal Section of Tunnel

V-75
Table - 1 EARTHQUAKE RECORDS

Earthquake

No. Date Location

of Origin Magnitude Depth

(km) Epicentral distance

KUWT - 1 1973.11.25

N 33° 51'

E 135° 25' 5.9 60 185 KUWT - 2 1973.11.25

N 33° 53'

E 135° 23' 5.8 60 185 KUWT - 3 1974. 2.10

N 35° 2' E 136° 56' 5.3 40 30 KUWT - 7 1974. 8.16

N 35° 15' E 136° 11' 4.9 50 50

V-76
MEASURED BENDING MOMENTS

AND AXIAL FORCES Earthquake

No. Axial Strain

(10*)

Axial

Force

(ton)

Bending

Strain

(lO

-*)

Bending

Moment

(t-m) KUWT-2

K-1 & K-3

1.84 239 0.33 110 KUWT-2

K-2 & K-4 6.34 823 2.09 696 KUWT-2

K-5 & K-7 2.55 331 1.15 383 KUWT-2

K-6 & K-8 8.65 1,123 5.80 1,931 KUWT-2

S-l & S-2 6.5 844 1.5 703 KUWT-3

S-l & S-2

0.37 324 5.66 2,655 KUWT-3

K-1 & K-3

3.75 487 0.92 306

80 0®6 ^80 0 HEKINAN

4000

3000

2000

1000 J

Fig-4 Maximum bending moment (KUWT-3 P-l)

r n

INI 111

-

Fig-5 Maximum axial force (KUWT-3 P-2) h=0.1

V-77
ma

-co:

3000

2000

1000

Fig-6 Maximum axial force (KUWT-3 P-9)

Fig-7 Maximum axial force (KUWT-2 P-2 P-9)

SllR rACE (iRC 'JND

V,

SI BMEF GEO

Fig-8 Maximum response acceleration (KUWT-3 P-l)

SL RI M E

3 d£BS EJL

,4

Fig-9 Maximum response acceleration (KUWT-3 P-2) h=0.0

V-78
( 10-6j KUWT-3 K1 K3 BENDING STRAIN

5

"

(10°)

5

-5

KUWT-3 K1 K3 AXIAL STRAIN

2 0' % .0 6.0 8 0 100

Fig-10 Bending & axial strain KUWT-3 (K2-K3)/2 BENDING

L 2 0 3 0

KUWT-3 (K1*K3)/

2

AXIAL

KUWT-3 P-1 BENDING

AT TRANSDUCER

0 2D 30 4.0 50

(hz;

KUWT-3 P-2 AXIAL AT TRANSDUCER

1.0 2.0 3 0 4.0 5.0(H Z) Fig-11 Power spectrum

V-79
A PROPOSAL FOR EARTHQUAKE RESISTANT DESIGN METHODS

Kiyoshi Nakano, Assistant Director, Building Research Institute, Ministry of Construction

and Masamitsu Ohashi, Head, Earthquake Disaster Prevention Division, Public Works Research Institute, Ministry of Construction ABSTRACT

This paper describes the outline of a Proposal for Earthquake Resistant Design Method which was completed by the Ministry of Construction in March, 1977.

KEYWORDS: Coefficients in aseismic design; design method; proposed earthquake resistant

design method; seismic hazard zonging map.

V-80
1 . INTRODUCTION

A Proposal for Earthquake Resistant Design Methods owes a great deal to the results

of the investigations of a major ministrial project on new technology for synthesized

earthquake resistant design in the Ministry of Construction, which were carried out from

1972 through 1976. The proposal also had absorbed the results of investigations by universities, public and private laboratories. The purpose of the proposal is to establish

a practical and rational earthquake resistant design method.

2. OUTLINE OF A PROPOSAL FOR EARTHQUAKE RESISTANT DESIGN METHODS

Damages of the structures caused by the Niigata Earthquake (1964) , Tokachioki Earthquake (1968) , and San Fernando Earthquake (1971) stimulated to improve and rationalize the earthquake resistant design methods. For this purpose, a new major ministrial project was conducted from 1972 through 1976 and a Proposal for Earthquake Resistant Design Methods

was presented by the Ministry of Construction in March, 1977. This project consisted of 6 themes and 20 sub-themes as shown in Appendix I. The proposal has been divided into 3 parts. In part I, a fundamental conception

commonly applied to bridges, soil structures, underground structures and buildings is proposed. In part II, practical calcualtions excluding buildings are advanced based on Part

I. Part III deals with the calculation methods for buildings. The contents of the proposal are shown in Appendix II. The proposal is compiled according to the following principles:

(1) Standardization of Fundamental Conception

Each earthquake resistant design method has its own background. It has improved by

itself by studying the damages of structures caused by past earthquakes, analyzing the earthquake ground motions which were obtained by the strong motion observation network,

and investigating the characteristics of structures and their members. Consequently, the design methods have been diversified in accordance with the uses and types of each structure.

In the project, existing earthquake resistant design methods were reviewed and a fundamental conception for designing bridges, soil structures, underground structures and

buildings was proposed.

(2) Clarification of Design Procedure

Until recently, the earthquake resistant design has been apt to concentrate on the calculation methods. The fundamental design procedure has not satisfactorily been clarified.

The proposal clarifies the fundamental design procedure considering characteristics of earthquake ground motion, seismic performance, and safety.

(3) Systematization of Design Procedure

Earthquake resistant design is required to follow a proper procedure in accordance with

the characteristics of subgrounds and structures.

The proposal presents a fundamental conception for the earthquake resistant design in order to indicate correct procedures to follow.

V-81
3. PART I, FUNDAMENTAL CONCEPTION

3.1 Fundamental Conception of Aseismic Design

In the earthquake resistant design, following items should be considered:

(1) Characteristics of structures

(2) Uses of structures

(3) Types of structures

(4) Scales of structures

(5) Circumstances of structures

(6) Damages of structures and surrounding grounds caused by past earthquakes.

Fig. 3.1 shows a fundamental procedure of aseismic design. In the procedure, the process

to calculate seismic force or earthquake response is classified into 4 methods as below:

(1) Seismic coefficient method

(2) Modified seismic coefficient method

(3) Seismic deformation method

(4) Dynamic analysis method

The method to be selected among these is determined by considering the characteristics

of structures.

3.2 Standard Seismic Loadings for Aseismic Design

Seismic zoning is presented herein in order to indicate the characteristics of earth- quake ground motion at each site. The occurrence of past earthquakes, the records of strong-motion earthquakes and the earthquake activities in relatively wide areas were taken

into account in the zoning.

To determine the intensity of earthquake ground motion at a certain site, the seismic zoning as stated above and the characteristics of ground should be taken into consideration. Seismic loadings for aseismic design is evaluated by the coefficients concerning the seismic zoning and the characteristics of grounds according to the particular method of earthquake resistant design.

3.3 Ground Examinations and Seismic Performance of Grounds Investigating the documents about the damages of grounds caused by past earthquakes is important in the earthquake resistant design of structures. If it is necessary, the characteristics of grounds and soils at the construction site should be examined. Seismic loadings are determined considering the results of investigations and examinations stated

above.The proposal presents herein soil and ground examinations and stability of grounds. It also systematizes the methodology for examination and confirmation regarding the stability

of grounds.

3.4 Seismic Performance of Structural Members

The proposal has aimed at systematizing the methodology to evaluate and promote the seismic performance of structural members in reinforced concrete, steel and reinforced

concrete composite, prestressed concrete, steel and other structures.

V-82
4. PART II EARTHQUAKE RESISTANT DESIGN OF CIVIL ENGINEERING STRUCTURES

1.1 General Current seismic design specifications for construction excluding buildings have been

formulated on the basis of experiences gained through earthquake damage in the past and investigations on seismic design criteria. The seismic design criteria introduced in this

chapter were established based on the fundamental conceptions presented in the previous

chapter (Part I) in difference to the current seismic design specifications. In the case

of designing special types of structure, it is recommended to make use of this aseismic

design specification selectively according to the structural properties considered.

4.2 Coefficients in Aseismic Design

In the case of estimating the seismic loadings specified in Part I, the coefficients

in aseismic design shall not be lower than the values allowed in the following provisions.

4.2.1 Design Coefficients in the Seismic Coefficient Method

The horizontal design seismic coefficient can be determined by the following formula:

*H = A

l

• A

2

' A

3

* K

o

(4 - 15

(1) The standard horizontal design seismic coefficient K can be taken as 0.2. o

(2) Seismic zone factor is shown in Table 4.1 by referring to the seismic zoning map displayed in Fig. 4.1.

(3) Ground condition factor A

2 is shown in Table 4.2.

(4) A factor A^ dependent on other conditions can be determined through considerations on uses and types of structures. The structural type factor is shown in Table 4.3.

.2 Design Coefficients in the Modified Seismic Coefficient Method

The horizontal design seismic coefficient can be determined by the following formula:

(1) The standard horizontal design seismic coefficient K^, seismic zoning factor A^, and ground condition factor can be the same values employed in the seismic coefficient method.

(2)

(3)

for four groups of ground conditions in Fig. 4.2. In the case when natural period

case when the allowable stress design procedure is to be applied. However, in the case when the ultimate strengths of structure are to be checked in design,

a factor A^ can be properly determined in accordance with the ductilities expected

in plastic zone of structural members.

A factor A^ dependent on other conditions can be properly determined through con6 siderations on uses and types of structures and so on. When it is considered not necessary to pay special attentions to these matters, a factor A

g can be taken as V-83
4.3 Principal Features of Aseismic Design Criteria

4.3.1 Development of New Seismic Zoning Map and Intensity of Design Earthquake Motions

The seismic zoning maps and intensities of design earthquake motions applied in the current seismic design specifications are not necessarily uniform. There are slight differences among these according to the types of structure considered. It has been, therefore, requested to establish a unified seismic zoning map.

In the proposal, a unified seismic zoning map applicable for all types of structure

is presented.

4.3.2 Development of New Aseismic Design Criteria for Foundations

It has been pointed out that the design criteria employed in the current seismic design

of foundations are not necessarily uniform since they have been formulated separately.

In the proposal, a unified criteria for aseismic design of spread foundations, caisson

foundations, pile group foundations, steel-walled-pipe pile foundations, and multi-column

foundations are presented.

4.3.3 Development of New Seismic Design Criteria for Reinforced Concrete and Steel Structures Evaluation systems of ductilities are presented for reinforced concrete structures.

The results of investigation concerning the buckling effects on seismic stability are introduced into the design of thin walled steel structures.

4.3.4 Development of New Seismic Design Criteria for Soil Structures

The basic principles for aseismic design criteria of soil structures are presented. An empirical seismic design criterion, in which a seismic design calculation can be omitted

as long as the structure has standard shape, material, size and construction procedure,

is also presented. Technical means to improve soft subsurface soil layers are presented.

4.3.5 Development of New Seismic Design Criteria for Underground Structures

The seismic design criteria for important underground structures such as water, gas, electricity and communication facilities, which are often called as life lines systems, are presented as well as the seismic design criteria for petroleum pipe lines and submerged

tunnels. 4.3.6 Development of New Criteria for Restoration Systems of Existing Structures Evaluation systems of seismic performance and restoration systems of existing structures are presented.

4.3.7 Improvements of Design Details

Design details are presented so that detailed devices, which help improve seismic performance of structures, are adequately provided.

5. PART III BUILDING CONSTRUCTION

5.1 Introduction

In this part, an aseismic design method for the building structures, non-structural

elements, foundations, and retaining walls is introduced.

V-84
Compared with the conventional design method, the proposed method is based on the most

recent research in seismology, earthquake engineering and structural engineering. One of the important characteristics of this method is that the appropriate design procedure can be applied according to the structural properties and the occupancy of the building.

5.2 Characteristics of the Proposed Design Method

5.2.1 Design Procedures and Steps

This aseismic design method involves six design procedures and each procedure has two

steps

.

One or more of the six procedures would be selected, according to the structural properties and the occupancy of the building, materials, seismic resisting system, height,

use or occupancy, etc. The step 1 of these design procedures should satisfy the condition that the response

of the structural members as well as the non-structural elements due to frequent earthquakes

should not exceed the elastic range of the materials and the damages caused should be small enough that the repair would be scarcely required due to such earthquakes.

The step 2 which follows step 1 should satisfy the condition that the building

structure would not collapse due to the maximum possible earthquakes such as Great Kanto

Earthquake in 192 3. The schematic chart of these design procedures and steps are set forth in Table 5.1. 5.2.2 Seismic Force

The total lateral seismic force is basically determined by the following formula:

F = C • W (5.1)

where C is the seismic design coefficient given by formulas (5.2a), (5.2b), (5.3a) or

(5.3b), and W is the total dead load of the building and applicable portions of other

loads

.

The seismic design coefficient for step 1 shall be determined in accordance with the following formula:

C

1 = Z • Go(T) -eCo (5.2a)

where Z is the seismic hazard zoning factor prescribed in section 5.2.3, Go (T) is the soil profile spectrum for approximation as given in section 5.2.4, T is the fundamental natural

period of the building in seconds, and eCo = 0.2 is the standard base shear coefficient

for step 1. In the procedure I-A or I-B in Table 5.1 the height of the building concerned is low

and the value of T is small. Accordingly, Go(T) is considered to be constant and 1.0. Therefore, formula (5.2a) is reduced to (5.2b)

C

1 = Z-eCo (5.2b)

V-85
The seismic design coefficient for step 2 shall be determined in accordance with eithe: of the following formulae:

where Go(T) is the soil profile spectrum as specified in section 5.2.4, pCo = 1.0 is the standard base shear coefficient for step 2, and and K

2 are the structural coefficients

as given in section 5.2.5. 5.2.3 Seismic hazard zoning factor Sesimic hazard zoning factor Z was determined by the seismicity and by applying the theory of extremes, statistics and engineering judgment. The values of Z are given in

Fig. 5.1 Seismic Hazard Zoning Map. 5.2.4 Soil Profile Spectrum

The effects of the soil profile properties and the natural period of the building

are expressed as the soil profile spectra given in Fig. 5.2. One of these spectra, Go (T) , is for approximation and the other four G

1

(T) correspond

to four soil profile types. The soil profile types are defined as follows: Soil profile type 1 is a profile with rocks, stiff and well consolidated sands, etc. Soil profile type 2 is a profile with sands, stiff clays, stiff loams, etc. Soil profile type 3 is a profile which would not belong to other types. Soil profile type 4 is a profile with soft clays, loose sands, etc. 5.2.5 Structural Coefficient

It is a well known fact that the ductile structure could absorb more energy

than the brittle structure and it is not practical to design the building to be completely

elastic when subjected to the maximum possible earthquake motion. Accordingly the struc- tural coefficients and are calculated and they would be denoted as the response modification factors which depend on the energy absorption capacity of the building during

the earthquakes. The values of these factors are given in Table 5.2, according to the structural materials and system, and ductility level and K

2 in procedure II-B, III-A and III-B, as shown in Table 5.1 5.2.6 Seismic Hazard Exposure Factor According to the use or the character of the occupancy of the building, the appropriate

design procedure could be elected or the seismic hazard exposure factor could be adopted for use in step 1 or 2. The value of the factor is not specified in this method, because the reliable theory to determine the value is not developed yet. But it can be suggested that

the probability of failure, the dispersion of the seismic resistant capacity as well as the dispersion of the seismic force, social utilities and the acceptable level of human risk

should be studied to determine the value of the seismic hazard exposure factor.

V-86
eitijj , 3 Concluding Remarks

The proposed aseismic design method has been founded on the principle that make

ossible the application of new theory and research as well as the use of new materials and

ew structural sysatems. If one of the six design procedures would be selected properly,

he building designed might be safe enough for the earthquakes with a minimum design effort

nd a minimum volume of structural materials.

But, the details of the design method might not be complete yet, therefore, the followng studies would be necessary in the near future:

i) re-examination of various parameters

ii) case study for different types of buildings

iii) simplification of the method for practical use

(SUPPLEMENT)

In Part II, the seismic design coefficient is denoted as the following formula:

This formula corresponds to the following formula in Part III.

C

1 = Z-Go(T) -eCo or

C

1 = Z-eCo

And the following correspondences would be given:

A

3 = seismic hazard exposure factor

K = eCo

o

The modified seismic design coefficient in Part II is denoted as the following formula:

K = A • A

2

• A

4

• A

5

• A

6

• K

o

In Part III:

C_ = Z-Go(T) • K -pCo

V-87
here, we have:

Ag = seismic hazard exposure factor K = pCo

o APPENDIX I - Themes of Research Project on New Criteria for Earthquake Resistant Design

of Structures

I Research on Earthquake Ground Motions

1. Characteristics of Earthquake Ground Motions on Baserock

1) Seismic Records obtained

2) Source Mechanism and Propagation of Seismic Waves

3) Earthquake Ground Motions on Various Subsoils

4) Earthquake Ground Motions of Long Period Components

2. Evaluation of Standard Seismic Inputs Depending on Subsoils

1) Standard Design Seismic Inputs

II Research on Dynamic Properties of Soils

1. Failure Mechanism and Strength of Soils

1) Behavior of Loose Sands and Soft Clayey Soils

2) Dynamic Strength of Soils

3) Seismic Damage to Embankments and Slopes

III Dynamic Properties and Dynamic Strength of Structural Members

1. Dynamic Strength of Structural Members

1) Plastic Properties of Bridge Piers

2) Dynamic Behavior of Bridge Piers

3) Dynamic Strength of Building Members

1) Reinforced Concrete Columns

2) Reinforced Concrete Walls

3) Steel Reinforced Concrete Columns

2. Dynamic Strength of Structural Joints

1) Dynamic Strength of Structural Joints for Prefabricated Buildings

2) Dynamic Strength of Steel Structural Joints

3) Dynamic Strength of Structural Joints for Prestressed Concrete Buildings

and Steel Reinforced Concrete Structures

4) Dynamic Strength of Structural Joints of Reinforced Structures

IV Research on Vibrational Characteristics and Earthquake Response Analyses of Structures

1. Dynamic Interactions of Soils and Structures

1) Sesimic Measurements at Structures and Surrounding Soils

1) Bridges

2) Buildings
2) Dynamic Analyses of Soil-Building Systems

3) Dynamic Interactions of Soil-Bridge Foundation Systems

2. Failure Mechanism of Structures

1) Failure Mechanism of Wooden Building Structures

V Establishment of Criteria on Earthquake Resistant Design of Structures

1. Establishment of New Criteria on Earthquake Resistant Design

1) Civil Engineering Structures

2) Building Structures

2. Establishment of New Earthquake Resistant Design of Various Structures

1) Establishment of Prefabricated Building Structure

2) Establishment of Buried Pipes

3) Establishment of Non-Structural Members

VI Research on Countermeasures Against Earthquake Disaster

1. Procedures for Assessing Earthquake Resistance for Existing Structures

1) Criteria on Evaluating Earthquake Resistance of Reinforced Concrete Buildings

2. Rehabilitations of Existing Structures

1) Strength and Deformation of Structural Members for Reinforced Concrete Buildings and Steel Reinforced Concrete Buildings

3. Establishments of Procedures for Preventing Earthquake Disaster

1) Development of Procedures for Predicting Seismic Risk

APPENDIX II - Contents of a Proposal for Earthquake Resistant Design Methods

Introductory Remarks

Part I. Fundamental Conception

1 . Scope

2. Definition of Terms

3. Fundamental Conception of Aseismic Design

3-1. Fundamental Procedure of Aseismic Design

3-2. Methods of Calculation for Aseismic Design

3-2-1. Classification

3-2-2. Selection

3- 2-3. Precaution

3- 3. Safety

4. Standard Seismic Loadings for Aseismic Design

4- 1. Past Earthquakes

4-2. Engineering Characteristics of Earthquake Ground Motions

4- 2-1. Characteristics of Earthquake Ground Motions

4-2-2. Seismic Zoning

4-2-3. Intensity of Earthquake Ground Motions at Construction Site

4-3. Design Seismic Loadings

4-3-1. General Remarks

4-3-2. Design Coefficients in the Seismic Coefficient Method

4-3-3. Design Coefficients in the Modified Seismic Coefficient Method V-89
4-3-4. Design Coefficients in the Seismic Deformation Method

4- 3-5. Seismic Loads in the Dynamic Analysis Method

5. Ground Examinations and Seismic Performance of Grounds

5-1. General

5-2. Soil Examinations

5- 2-1. General Remarks

5-2-2. Examinations for Dynamic Properties of Soils

5-3. Ground Examinations

5-3-1. General Remarks

5-3-2. Examinations for Dynamic Characteristics of Grounds

5-3-3. Dynamic Analysis of Grounds

5-3-4. Examinations for Classification of Grounds

5-4. Stability of Grounds During Earthquakes

5-4-1. General Remarks

5-4-2. Examinations for Stability of Sandy Grounds

5- 4-3. Examinations for Stability of Clayey Grounds

6. Seismic Performance of Concrete Members

6- 1. Properties of Concrete and Steel Materials

6- 1-1. Concrete

6-1-2. Reinforcements

6-2. Seismic Performance of Reinforced Concrete Structural Members

(Excluding Buildings)

6-2-1. General Remarks

6-2-2. Fundamentals for Design

6-2-3. Ultimate Strength and Ductility

6-3. Seismic Performance of Reinforced Concrete Structural Members for Buildings

6-3-1. General Remarks

6-3-2. Fundamentals for Design

6-3-3. Ultimate Strength and Ductility

6-4. Seismic Performance of Steel and Reinforced Concrete Structural Members for Buildings

6-4-1. General Remarks

6-4-2. Fundamentals for Design

6-4-3. Ultimate Strength and Ductility

6- 5. Seismic Performance of Prestressed Concrete Structural Members for Buildings

6-5-1. General Remarks

6-5-2. Fundamentals for Design

6- 5-3. Ultimate Strength and Ductility

7. Seismic Performance of Steel Members

7- 1. Properties of Steel Materials

7-2. Seismic Performance of Steel Structural Members (Excluding Buildings)

7- 2-1. General Remarks V-90
7-2-2. Fundamentals for Design

7-2-3. Ultimate Strength and Ductility

7- 3. Seismic Performance of Steel Structural Members for Buildings

7-3-1. General Remarks

7-3-2. Fundamentals for Design

7- 3-3. Ultimate Strength and Ductility

8. Seismic Performance of Other Members

8- 1. General

8-2. Seismic Performance of Wooden Structural Members for Ordinary Wooden Houses

8- 2-1. General Remarks

8-2-2. Ultimate Strength and Ductility

8-3. Seismic Performance of Non-Structural Members for Buildings

8-3-1. General Remarks

8-3-2. Fundamentals for Design

8-3-3. Ultimate Strength and Ductility

8-4. Seismic Performance of Underground Pipes

Part II. Earthquake Resistant Design of Civil Engineering Structures

1. General

1-1. General Remarks

1-2. Usage and Classifications of Structures in Aseismic Design

1-3. Coefficients in Aseismic Design

1-3-1. Outline

1-3-2. Design Coefficients in the Seismic Coefficient Method

1-3-3. Design Coefficients in the Modified Seismic Coefficient Method

1-3-4. Design Coefficients in th Seismic Deformation Method

1-3-5. Seismic Loads in the Dynamic Analysis Method

1- 4. Effects of Earthquakes During Construction

2. Aseismic Design of Foundations

2- 1. General Remarks

2-2. Effects of Earthquakes

2-3. Foundation Grounds and Allowable Bearing Forces

2-4. Methods of Calculation of Stress, Displacements and Stability

2-4-1. Outline

2-4-2. Spread Foundations

2-4-3. Caisson Foundations

2-4-4. Pile Group Foundations

2-4-5. Steel Walled pipe Pile Foundations

2-4-6. Multi-Column Foundations

3. Aseismic Design of Concrete and Steel Structures

3-1. General Remarks

3-2. Effects of Earthquakes

3-3. Methods of Calculation of Stress and Displacement V-91
3-3-1. Bridges (Reinforced Concrete Pier and Abutments)

3-3-2. Bridges (Steel Piers)

3-3-3. Concrete Dams (Gravity, Hollow Gravity and Arch Dams) 3-3-4. Tanks

3- 3-5. Others

4. Aseismic Design of Soil Structures

4-1. Effects of Earthquakes

4-2. Methods of Calculation for Stability

4- 2-1. Outline

4-2-2. Fill-Type Structures

4-2-3. Artificial Island

4-2-4. Artificial Ground

4- 2-5. Cutting Slope

4-3. Improvement of Ground

4-4. Safety

5. Aseismic Design of Underground Structures

5- 1. Effects of Earthquakes

5-2. Stability of Surrounding Ground

5-3. Methods of Calculation of Stress and Displacement

5- 3-1. Outline

5-3-2. Underground Pipes

5-3-3. Submerged Tunnels and Common Ducts

5- 4. Safety

6. Seismic Performance of Existing Structures

6- 1. System for Evaluating Seismic Performance

6- 2. System for Retrofitting Existing Structures

7. Design Details

7- 1. Foundations

7-2. Substructures and Devices for Preventing the Fall of Superstructures

7-2-1. Reinforced Concrete Piers and Abutments

7-2-2. Devices for Preventing the Fall of Superstructures

7-3. Soil Structures

7-4. Underground Structures

7-4-1. Outline

7-4-2. Joints Part III. Building Construction

1. General

1-1. Scope

1-2. Object of Aseismic Design

1-3. Fundamental Method of Aseismic Design

1-4. Design Procedures of Aseismic Design

V-92
1-4-1. Kinds of Design Procedures

1-4-2. Selection of Design Procedures

1-5. Methods of Aseismic Design

1-5-1. Design Procedure I-A 1-5-2. Design Procedure I-B

1-5-3. Design Procedure II-A

1-5-4. Design Procedure II-B

1-5-5. Design Procedure III-A

1-5-6. Design Procedure III-B

1- 6. Parameters for Aseismic Design

1-6-1. Seismic Hazard Zoning Factor

1-6-2. Standard Base Shear Coefficient

1-6-3. Soil Profile Types

1-6-4. Fundamental Natural Period

1-6-5. Vertical Distribution of Lateral Force

1-6-6. Seismic Hazard Exposure Factor

1-6-7. Limitation of Structural Discontinuities

1-6-8. Story Drifts Limitation

1-6-9. Structural Coefficient

1-6-10. Ultimate Load Carrying Capacity

1-6-11. Allowable Stresses and Allowable Load Carrying Capacity

2. Aseismic Design Method for Reinforced Concrete Buildings

2- 1. General

2-2. Design Procedure

2-3. Structural Ceofficient

2-4. Ultimate Story Shear Capacity

2- 5. Design of Building Elements and Structural Design Requirements

3. Aseismic Design Method for Steel Reinforced Concrete Buildings

3- 1. General

3-2. Design Procedure

3-3. Structural Coefficient

3-4. Ultimate Story Shear Capacity

3- 5 Design of Building Elements and Structural Design Requirements

4. Aseismic Design Method for Steel Buildings

4- 1. General

4-2. Design Procedure

4-3. Structural Coefficient

4-4. Ultimate Story Shear Capacity

4-5. Design of Building Elements and Structural Design Requirements

4- 6. Story Drifts Limitation

5. Aseismic Design Method for Prestressed Concrete Buildings

5- 1. General

5-2. Design Procedure

V-93
5-3. Structural Ceofficient

5-4. Ultimate Story Shear Capacity

5- 5. Design of Building Elements and Structural Design Requirements

6. Aseismic Design Method for Conventional Wooden Buildings

6- 1. General

6-2. Design Procedure

6-3. Structural Coefficient

6-4. Ultimate Story Shear Capacity

6- 5. Design of Building Elements and Structural Design Requirements

7. Aseismic Design Method for Non-Structural Elements

7- 1. General

7-2. Required Aseismic Consideration for Non-Structural Elements

7-3. Load and Story Drifts

7- 4. Selection of Construction Methods and Design of Elements

8. Aseismic Design Method for Foundations and Retaining Walls

8- 1. General

8-2. Design of Foundations

8- 3. Design of Retaining Walls

9. Safety Against Earthquakes of Existing Buildings

9- 1. System for Evaluating Earthquake Resistant Capacity

9-2. System for Reinforcing Existing Buildings

V-94
V-95
Table k.l Seismic Zone Factor z±\

Zone Value of A]

A 1.0

B 0.85

C 0.7 Table U.2 Ground Condition Factor

Group Definitions'^ Value of Zi x

1

(1) Ground of the Tertiary era

or older (defined as bedrock hereafter)

(2) Diluvial layer ^ with

depth less than 10 meters

above bedrock

0.9

2

(1) Diluvial layer ^with

depth greater than 10 meters above bedrock

(2) Alluvial Layer SJ with

depth less than 10 meters above bedrock

1.0

3 Alluvial layer ^with depth less than 25 meters, which has soft layer ^with depth less than 5 meters

1.1

h Other than the above 1.2

(Notes)

1) Since these definitions are not very comprehensive, the classification of ground conditions shall be made with

adequate consideration of the bridge site. Depth of layer indicated here shall be measured from the actual ground surface.

2) Diluvial layer implies a dense alluvial layer such as .

a

dense sandy layer, gravel layer, or cobble layer.

3) Alluvial layer implies a new sedimentary layer made by a landslide.

V-96
Table k. 3 Structural Type Factor ^ ]

Definitions Value of <c± 3 Steel Structures Concrete Structures

Steel Reinforced Concrete Structures

1.0

Huge Massive Structures Soil Structures

0.5

Table 5.1 SEISMIC DESIGN COEFFICIENT AND DESICN METHOD ACCORDING TO DESIGN PROCEDURES AND STEPS

DESIGN PROCEDURE SCOPE STEP 1 STEP 2

I-A CONVENTIONAL

WOODEN BUILDINGS

C-y = Z-eCo

ELASTIC DESIGN WITH STRUCTURAL DESIGN REQUIREMENTS

REINFORCED CONCRETE

BUILDINGS WITH SHEAR WALL SYSTEM, etc.

SEISMIC DESIGN COEFFICIENT

AND ALLOWABLE STRESSES

II-A

ORDINARY BUILDINGS

C

1

= Z-Go(T)-eCo

ELASTIC DESIGN WITH APPROXI- MATE MODIFIED SEISMIC DESIGN

C2

= Z-Go(T)-Ki.pCo

PLASTIC DESIGN WITH APPROXIMATE MODIFIED SEISMIC COE- FFICIENT AND APPROXIMATE ULTIMATE STORY SHEAR CAPACITY

II-B

C 2 Z-GitTl-Kg-pCo

PLASTIC DESIGN WITH MODIFIED SEISMIC COEFFICIENT AND ULTIMATE STORY SHEAR CAPACITY

III-A HIGH RISE BUILDINGS COEFFICIENT AND ALLOWABLE

STRESSES

C 2 = Z-Gi(T)-K2 -pCo DYNAMIC DESIGN WITH MODAL ANALYSIS

III-B

SUPER HIGH RISE

BUILDINGS

C

2

= Z-Gi.(T)-K2 -pCo DYNAMIC DESIGN WITH MODAL ANALYSIS AND TIME HISTORY ANALYSIS SEISMIC DESIGN COEFFICIENT FOR STEP 1 SEISMIC DESIGN COEFFICIENT FOR STEP 2 SEISMIC HAZARD ZONING FACTOR SOIL PROFILE SPECTRUM FOR APPROXIMATION

SOIL PROFILE SPECTRUM

FUNDAMENTAL NATURAL PERIOD OF BUILDING

V-97
130°

S

Fig. Jf.l Seismic Zoning

V-98
Table 5.2 STANDARD STRUCTURAL COEFFICIENT

STRUCTURAL COEFFICIENT

DUCTILITY LEVEL

A B c

REINFORCED CONCRETE BUILDINGS PRESTRESSED CONCRETE BUILDINGS

K

l O.U 0.5 0.6

K2 0.3 0.1. 0.5

STEEL REINFORCED

CONCRETE BUILDINGS

Kl 0.3 O.U 0.5

K2 0.3 0.3 o.i.

STEEL BUILDINGS

Kl 0.3 0.5 0.6

K

2 0.3 0.1* 0.5

WOODEN BUILDINGS

Kl O.U

K2 0.3

DUCTILITY LEVEL A : DUCTILE BUILDINGS DUCTILITY LEVEL B : INTERMEDIATE BUILDINGS DUCTILITY LEVEL C : BRITTLE BUILDINGS

\

d Dm id a y

S

•\

GROl

GROl

GR 01

P3 ' \

JP2 y

s \

\

PI '

0.5 I 2 3 4 5sec

Fig. U.2 Factor

V-99
V-100
(0.55) (10)

0 5

GIT)

/Go(T ) for approximation (035) > / ^ r,. ( T 1 In, / «i i u toi soil profile type 4

/— Gi ( T ) • ,3 \\ > \/ r G| (T) • .. 2 TV ,Gi IT) • •, 1

Tlsec) 10 2 0 3.0 4 0

Fig. 5.2 Soil Profile Spectra

V-101
ON THE OBJECT POSTULATE FOR EARTHQUAKE-RESISTANT CODE Kiyoshi Nakano, Assistant Director

Yuji Ishiyama, Chief Research Engineer

Yoshitsugu Aoki, Research Engineer Kazumasa Watanabe, Research Engineer

Building Research Institute, Ministry of Construction ABSTRACT

What the object of the earthquake-resistant code should be and how to define the object are the concerns of the object postulate. Since the seismic forces and the earth- quake-resistant capacity of the buildings have certain dispersions, it is necessary to introduce the concept of the reliability to define the object postulate. This report deals with research on 1) dispersions, 2) relation between the earthquake-resistant capacity and

the construction cost, 3) acceptable level of human risk, and 4) principle of social utility to optimize the importance factor, in order to define the object postulate for the earthquake-resistant code.

KEYWORDS: Acceptable level of human risk; construction costs; earthquake resistant code; expected seismic force; object postulate; reliability theory; social utility.

V-102
1 . INTRODUCTION Any design process is implicitly or explicitly constructed on a design system which is sometimes called a design code. It was shown by Niels C. Lind (1) that present structural

design codes could well be understood by searching for basic eight principles or postulates.

In his earlier paper, Kiyoshi Nakano (2) proposed an important postulate concerned with the probability of the death of occupants caused by the failure of structures.

The authors propose some postulates in addition to the above postulates, and classify

the postulates, and examine their relations to structural codes. Furthermore, the object

postulate, one of the most important postulates, is considered extensively.

2. CLASSIFICATION OF STRUCTURAL DESIGN POSTULATES

The following eight postulates which are included in several design codes were shown

by Niels C. Lind.

1) Load postulate

2) Strength postulate

3) Design method (postulate)

4) Principle of constant reliability

5) Postulate of data sufficiency

6) ISO format

7) Cornell's format

8) Linearized factor format

The authors proposed the following postulates in addition to the above postulates (2,3),

9) Earthquake load postulate proposed in AIJ draft (4)

r

< b > 5 r

< 1 H - 125 ' r

iE 6r 1

(c) r=l

< — , i = number of stories,

i —

E H r=l r

where,y^ = ductility factor of the r-th story,

y = permissable ductility factor which is fixed in accordance with the kind of structures (such as steel structures, reinforced concrete structures, etc.),

I = importance factor which is fixed in accordance with the occupancy of structures

and with the structural importance of structural members,

6^ = inter-story deformation (inter story drift) of the r-th story, which is caused by elasto-plastic response,
= story height of the r-th story.

10) The postulate for optimizing monetary expenses

8L

3n " °' (2-1J

where

,

L = I + pF, (2-2) L = expected value of losses

I = initial expenses, p = probability of failure,

F = losses caused by the failure = otl, (2-3) n = (I - A

Q )/A

1 (2-4) = central safety factor = (R*/S*)

,

R* = expected value of resistance,

S* = expected value of load effect,

Aq, A^ = constants corresponding to the kind of structures.

11) Starr's postulate (2,5),

pf = p (R* < S*) <_ r cr

• e • A, (2-5)

where

,

pf = probability of failure,

r = cr

9 = probability of the death of occupants caused by the failure of structures,

A = factor which is fixed in accordance with occupancies (1.0 for housings and office buildings which are indispensable for life, 1000 for leasure facilities)

12) Nakano's postulate (2),

pr

< r • © (1 + b • g) • A, (2-6)

r — cr

where,b = coefficient of density (number of occupants per unit floor area)

,

g = coefficient of evacuation (constant fixed in accordance with easiness of evacuation

in case of emergency)

.

The combination of the postulates in various design codes are shown in Table 2-1. Furthermore, we have attempted a classification of the postulates as shown in Table 2-2. That is, the traditional design processes are governed by three kinds of postulates: load strength postulate, comparison postulate, and object postulate. The object postulate is concerned with design philosophy on social needs for structural safety, therefore we shall consider the object postulate more extensively.

V-104
3. SURVEY ON EARTHQUAKE-RESISTANT CAPACITY AND ITS DISPERSION

It is almost impossible to measure the earthquake-resistant capacity of each building

is a total system. Accordingly, we tried to evaluate it by an expert survey which would

lake use of the intuition of the experts most effectively. About two hundred experts from

four different fields of structural engineering; 1) constructors, 2) administrators,

3) designers and 4) researchers or educators, participated in this survey. From the result

of this survey, the earthquake-resistant capacity and its dispersion of buildings are given

n Fig. 3-1. In Fig. 3-2, the weighted factors are set forth depending on seven major

actors; 1) designer, 2) design cost, 3) design term, 4) constructor, 5) construction cost,

6) construction term, and 7) material. From Fig. 3-1, it can be seen that the cast in situ reinforced concrete wall buildings,

super high rise steel buildings and high rise steel buildings are considered to have good earthquake-resistant capacities. On the contrary, the reinforced concrete block buildings,

conventional wooden buildings and prefabricated wooden buildings seem to have rather

small resistant capacity against earthquakes.

As to the dispersions of earthquake-resistant capacity, the super high rise buildings, prestressed concrete buildings and prefabricated H-steel reinforced concrete buildings have

small variance and the value of c.o.v. (coefficient of variance) is about 0.25. The cast

in situ reinforced concrete buildings, conventional wooden buildings and low rise steel buildings have large variance and the value of c.o.v. is about 0.45. From Fig. 3-2 we can assume that among seven major factors concerning earthquakeresistant capacity, the level of the designer and the level of the constructor are the most

influential factors. From the result of this survey, it was also found that the administrators and the constructors take an optimistic view of earthquake resistant capacity of buildings, and

that the designers and the researchers or educators have a pessimistic one.

4. RELATION BETWEEN EARTHQUAKE-RES I S TANT CAPACITY AND CONSTRUCTION COST

It is evident that the construction cost of the building would be influenced by the seismic design coefficient which is one of the main factors controlling the earthquakeresistant capacity. In this chapter, the relation between the seismic design coefficient

and the construction cost is discussed. To analyze the problem, the following assumptions

are adopted.

1) Elastic design with seismic design coefficients and allowable stresses is used.

2) The range of seismic design coefficient is from 0.2 to 1.0.

3) Two cases of construction cost ratio; i) columns and girders, and ii) column, girders, beams and slabs, are considered. The construction cost of foundations, other non- structural members and finishings are not included in both cases.

4) The costs of columns and girders are dependent on the seismic design coefficient, but the beams and slabs are independent of it.

5) The costs of columns and girders are approximated by the formula proposed by Nakagawa

(6). V-105
6) Two structural systems; i) steel frame buildings and ii) reinforced concrete buildings,

are considered. The numbers of stories are five and ten.

Under these assumptions the cost ratio is given in accordance with following formula;

Y

= 1 + R (C - 0.2) (4-1)

where

,

cost ratio = cost bv seismic design coefficient equals C

^ Y - cos ra 10 - CQst by se i smi c design coefficient equals 0.2

R = cost coefficients as given in Table 4-1

C = seismic design coefficient (0.2 <_ C < 1.0) Two examples of Eq. (4-1) are shown in Fig. 4-1- (1) for steel frame buildings and

Fig. 4-1- (2) for reinforced concrete buildings.

5. ACCEPTABLE LEVEL OF HUMAN RISK

The point of view of the security of human lives may be considered as one of the most

important criteria for structural design.

In the domain of the security of human lives, we find some discussions that propose

several criteria; such as those of David E. Allen, of H. G. Otway, of Starr, of K. Nakano

and of K. Watanabe. But we cannot find any proposition that achieves the practical level. We dared to attempt to overcome such a difficult state, and this report proposes an acceptable level of human risk, observing the fluctuations in the evolution of the ordinary

death rate and assuming the existence of insensible range of the fluctuations in the death

rate.

1) The sense of average risk level is supposed to be based on the average death rate

d for a period of several years which preceed the point of time for this sense. This average death rate may be considered as the basic death rate for the sense of risk.

2) Taking the standard deviation a, in the evolution of death rate for the same period

a as that of the average death rate, the rate of fluctuation of death rate Ad is obtained as Ad = 0 Vd . d

3) The observation through a sufficiently long term of the rates of fluctuation, each of which is calcualted on the same period of time, permits to suppose that the rate of fluctuation is nearly constant. So that if the mean level of the rates of fluctuations

Ad is obtained,

V-106
As for the acceptable level of human risk, this report proposes the acceptable death

rate from earthquake, dsac

It may be considered that the average death rate d includes a part of the death rate from earthquakes in certain proportion e. The death rate from earthquakes, d

g

, included in the average death rate is obtained as d = e • d.

s The acceptable death rate from earthquake, dsac

, is proposed as the sum of the part of

the death rate from earthquakes included in the average death rate d

g and the insensible

range of fluctuation of death rate 0 , . : d =d +0,. = e-d + 0 . dins sac s dins dins On the supposition that the number of deaths from earthquake is proportional to the number of destroyed buildings, a proposition is established that the acceptable rate

of destruction from earthquake, ? fac » is to be obtained as a proportional value to the acceptable death rate from earthquakes, 3

sac;

:

P = d

5 , fac sac Y'N^'f

where

,

P = population of the area concerned

Y = probability of deaths in case of destruction of a building (the number of deaths/the number of destroyed buildings)

N, = number of buildings in the area concerned.

Id f

g = frequency of earthquakes on the area concerned.

6. PRINCIPLE OF SOCIAL UTILITY TO OPTIMIZE IMPORTANCE FACTOR

The object postulate is concerned with social utilities, that is, we assume that the value of structure is comprised of the construction cost (negative utility) and the social- human utilities. We are going to establish an object postulate which formulates the value of importance factor corresponding to the maximum total utilities. The following concepts are used in this discussion,

(1) Load means a scalar having an expected value s and a coefficient of variance fi g

. (2) Strength means a potential of structures corresponding to a certain limit state designated in design. The strength is also a scalar having an expected value R and a coefficient of variance

(3) Magnifying factor of strength means the ratio defined by the following equation

e = r/r

0

, where,R = actual strength of structure,

V-107
Particularly, we shall distinguish the value of magnifying factor for ordinary buildings

from that for public buildings. The ratio of magnifying factors is called an importance

factor, and it may be defined as follows:

where,

{ (4) Probability of reaching limit state is defined as follows:

p = P (QqRq < S) (6-3)

(6-4)

Equation (6-3) is applied to ordinary buildings and equation (6-4) is applied to public buildings such as hospitals, public facilities, public halls, and so on.

(5) Social utilities are presented by four utilities, U.^, U

2

, U

3 and as shown in Table 6-1. Table 6-1 Social utilities

STATE OF PUBLIC BUILDINGS STATE OF ORDINARY BUILDINGS : (1) Undamaged (2) Damaged

0R„ > S 6R < S

(1) Undamaged State (6 e R 0 > S) u i u

3

(2) Damaged State (9 0 R0 < S) U2 UM

(6) Construction cost means the present value of initial construction cost. We define CQ/ construction cost in the payment time, and T

Q

, time lag between the payment time and

the time of putting the building in use. The construction cost can then be shown by the following equation with the interest rate r, T

C = C

Q

(1 + r) (6-5)

With the above conception, we can examine the social utilities for the building. In the first year, the expected value of social utility is as follows:

U

(1) = (1-p) (l-p_) U + p (l-p») U 0 + (1-p) Po U, + pp 0 U„ (6-6)

V-108
The present value of social utility in the second year is

U

(2> =^U(1) (6-7, Similarly, the present value in the nth year is

1 " Po

1 + r Consequently, the sum of the social utility in life span of the building T is obtained

as follows:

U

g = I U

(i) =U (1) T

Z (^V (6-9)

S i=l i=0 r

The total utility is represented by the following equation,

U = U

s - C (6-10)

We must maximize the value of U from a viewpoint of social safety or urban safety. Therefore, we obtain the following postulate by differentiating Eq. (6-10) with respect 9,

- *r = ^ / ^ 1 (6" 11) The optimum value of importance factor can be obtained from the above equation when

the distribution functions of random values S and R are given. Actually, if the distribution functions of load effect and strength are normal distributions N[S, 0^] , N[R, 0R

] respectively, the optimal values of magnifying factor and importance factor are expressed approximately by the following equations respectively:

±- + 6/21n ( _^L_ ) , (6-12)

H o /2TTk6 ±r + jf- /21n ( * ) , (6-13)

/O 2 02 / R + S (6-14) 3C0 k =( ^Q- / C

o

) (6 "15)

V-109
(6-16)

The auxiliary parameter 6 and k are called synthetic coefficient of variance and cost performance sensibility, respectively, and the parameter T# means the turnover year of

the buildings. The relation among the optimal values of magnifying factor 9, synthetic

c.o.v. 6 and the cost performance sensibility k is shown in Fig. 6-1.

7. CONCLUDING REMARKS From Chapters 3 to 6, we have suggested several approaches to settle the object postulate for the earthquake-resistant code. The details of each chapter should be investigated more extensively and intensively. Though more suitable ways to determine the object postulate might be discovered in the future, the following items are the most

influential factors to settle the object postulate from the surveys we have conducted.

1) earthquake-resistant capacity of buildings

2) expected seismic force

3) earthquake-resistant capacity and construction cost

4) acceptable human risk

5) social utility

8. REFERENCES

(1) Niels C. Lind, Consistent Partial Safety Factors, Journal of the Structural Division, Proceedings of ASCE, June, 1971, pp. 1651-1669.

(2) Kiyoshi Nakano, State-of-the-Art Report on Safety of Building Structures. Report

of the Building Research Institute, No. 73, March, 1976.

(3) Kiyoshi Nakano, Yoshitsugu Aoki and Kazumasa Watanabe, A Proposal for a Rational Aseismic Structural Design Process. BRI Research Paper No. 68, Building Research

Institute, September, 1976.

(4) Committee Report, Architectural Institute of Japan, 1975.

(5) Chauncey Starr, Social Benefit versus Technological Risk. Science, Vol. 165, September

19, 1969, pp. 1232-1238.

(6) Atsushi Nakagawa, Structural Cost Planning of High Rise Buildings. Kenchiku Gitjutsu

No. 238, June, 1971.

(1 + r)

U3 /Uj

1 + Pu2 /u. r(l + r) T-T

V-110
Table 2-1 Postulates included in strucutral design codes

Name of Code

1 2 3 4 rub LUld L fc: 5 6 7a 7b 8 9 11 ISO draft * * * * AIJ RC code * * * AIJ earthquake load

draft

* * *

NORDIC CODE

(A-Type)

* * * * * * * NORDIC CODE

(B-Type)

* * * * 0 -*

Proposal of Lind

* * * Proposal of Cornell

* * * * * Proposal of Ravindra

* * * * * * FIP-CEB Code * * * *

Table 2-2 Classification of postulates

The first Group: LOAD-STRENGTH

POSTULATE

Main Postulates:

1, 2 Sub Postulates:

6, 8, 7b

The main postulates are basic postulates for design system. The sub postulates are the modification of the main postulate for the purpose of facilitating probabilistic treatment

of design variables.

The Second Group: COMPARISON

POSTULATE

Main Postulates:

3, 4 Background

Postulates:

5, 7a Sub Postulates:

9, 10, 11,

12

The main postulate 3 is representing the classical design

procedure. The main postulate

4 is representing probabilistic concepts. The background postulates supplies logical

support for the postulate 4. The sub postulates are used together with the postulate 3 to introduce considerations of deformat ion. The Third Group: OBJECT POSTULATE

Main Postulates:

3, 9, 10, 11, 12

The postulate 3 is an object postulate as well as the comparison postulate. The postulates 10, 11, and 12 are used together with the postulate 4.

V-lll
V : mean value

01,02: standard deviation

CONVENTIONAL WOODEN

BUILDINGS

PREFABRICATED WOODEN

BUILDINGS

CAST IN SITU REINFORCED

CONCRETE BUILDINGS

CAST IN SITU REINFORCED CONCRETE WALL BUILDINGS PREFABRICATED REINFORCED CONCRETE WALL BUILDINGS

STEEL REINFORCED CONCRETE BUILDINGS

PREFABRICATED H-STEEL REINFOCED CONCRETE

BUILDINGS

SUPER HIGH RISE

STEEL BUILDINGS

HIGH RISE STEEL BUILDINGS LOW RISE

STEEL BUILDINGS LARGE SPAN STEEL BUILDINGS PRESTRESSED CONCRETE

BUILDINGS REINFORCED CONCRETE

BLOCK BUILDINGS

0.0 0,5 1.0 1.5 2.0 25 (Normalized by the mean value of cast in situ reinforced concrete buildings)

Fig. 3-1 RELATIVE EARTHQUAKE-RESISTANT CAPACITY AND ITS DISPERSION OF BUILDINGS

V-112
Factor (1) : Level of Designer

(2) : Design Cost

(3) : Design Term

(A) : Level of Constructor

(5) : Construction Cost

(6) : Construction Term

(7) : Material

CONVENTIONAL

WOODEN BUILDINGS

1 1 1 1 1 1 1 1 1

(1) (2) (5) (4) (5) 21.5* 9.9* 84* 20.9* 1 57* 10.7* 12.V--1

CAST IN SITU REINFORCED

CONCRETE BUILDINGS III 1 1 1 I 1

0) (2) (3) (4) (5) (6> 22.1* 9.5* 9.3* 20.6* 157* 11.7* 1 Ji^r

1 1 I I I I I PREFABRICATED REINFORCED CONCRETE WALL BUILDINGS 0) (2) (5) (4) (5) (61 (7. :21.4* 9.2* 9.4* 22D* 127* 1 144 1iV«

1 1 1 1 1 1 1 ! I STEEL REINFORCED CONCRETE BUILDINGS (D (2) (4) (5) 22.6* 9.5* 9.4* 209* 15.5* 11.4*

HIGH RISE

STEEL BUILDINGS (1) (2) (5) (4) (5) (tl 25.2* 9.4* 94* 21.6* 13.5* 107*

Fig. 3-2 WEIGHTED FACTORS OF EARTHQUAKE-RESISTANT

CAPACITY

V-113
Table A-l-(l) Cost Coefficients of Steel Frame Buildings

N

n R X y y = 1.0 y = 0.6 y = 0.5

5 3 2.0 1.2 1.0

5

5 5 2.0 1.2 1.0

00 5 2.0 1.2 1.0

oo . 2.0 1.2 1.0

5 3 2.0 1.2 1.0

10

5 5 2.0 1.2 1.0

5 2.0 1.2 1.0

2.0 1.2 1.0

Table 4-l-(2) Cost Coefficients of Reinforced Concrete Buildings

N

n R X y U = 1.0 P = 0.4 U = 0.3

5

5 3 3.2 1.25 0.95

5 5 3.0 1.22 0.92

5 3.1 1.23 0.93

3.1 1.24 0.93

* oo 3.7 1.43 1.10

10

5 3 4.0 1.60 1.17

5 5 3.8 1.53 1.13

5 3.8 1.55 1.15

00 A.O 1.60 1.17

N : number of stories

n : number of spans

y : cost ratio of columns and girders to total structural cost

(y= 1.0 means that cost of columns and girders is total structural

cost)

* : aseismic shear wall, columns and girders system

V-114
0.0

V-115
5.0

CD

4J

Synthetic c.o.v.6

Fig. 6-1 Relation among k, 6 and 6

V-116
The Earthquake Response of Hysteretic Structures W. D. IWAN and N. C. GATES

California Institute of Technology, Pasadena, California

ABSTRACT

The earthquake response of a broad class of hysteretic structures

is investigated. Inelastic response spectra are determined. Based on

these spectra, an effective linear period and damping are defined for each type of hysteretic structure as a function of ductility. A simple

empirical formula is presented which may be used to estimate the response of a general hysteretic structure given the linear response spectrum of the excitation. The predictions obtained from this formula are compared with those of another frequently used scheme

for estimating the response of hysteretic structures. INTRODUCTION

Most modern building structures are designed to respond in a ductile manner

during a major earthquake. In a steel structure, ductility is associated with the

local yielding of steel structural elements. For cyclic loading, the resulting load- deformation behavior is hysteretic and the hysteresis loops are quite stable with successive loading. In reinforced concrete structures, ductility arises both from

the yielding of the steel reinforcing and the cracking and crushing of the concrete. The resulting load- deformation behavior is again hysteretic. However, in this case,

the hysteresis loops tend to degrade in both energy dissipation and stiffness with successive loading. It is important for the safe design of structures that the response of both degrading and nondegrading hysteretic structures be well understood. There have been numerous studies of the earthquake response of simple non- degrading hysteretic structures. Based on studies of the most elementary systems,

it has been suggested that for moderate to long structural periods, the peak amplitude

of response of the hysteretic system is very nearly the same as that of a linear system with the same nominal period and viscous damping independent of the ductility ratio of the response [1]. There have been relatively few studies of the earthquake response of degrading structures and no general design guidelines have yet been

VT-1
proposed. However, the equal displacement rule is often employed for this type of structure as well [2]. The purpose of the present investigation is to examine the earthquake response

of a general class of single-degree-of-freedom hysteretic structures and to evaluate

the merit of certain simplified methods for estimating the response of such structures INELASTIC RESPONSE SPECTRA

It is assumed that the equation of motion of the structure or a particular mode

of the structure can be written in the form

x + 2C o

co qx + co o

2f[x(t)]/k0

= a(t) (1)

where x is the generalized relative displacement, Q Q

is the fraction of viscous damping, co 0

is the natural frequency, f[x(t)] is the generalized restoring force, kQ

is the nominal stiffness, and a(t) is the excitation acceleration. In what follows, it is assumed that C Q

= 2%. The nominal period of the system is TQ

= 2n/wQ

. The generalized restoring force f(x) is assumed to be hysteretic. In this investigation, the particular form of f(x) is derived from a combination of linear

elastic and coulomb slip elements as indicated in reference [3], The restoring

force model incorporates the major features associated with linear, simple hysteretic and degrading hysteretic behavior. Six specific systems are considered and the restoring force diagrams for these systems are shown schematically for cyclic loading with monotonically increasing amplitude in Figure 1. The symbol BLH denotes the bilinear hysteretic restoring force model. The

other systems are designated by a three number code. The first set of two digits specifies the ratio of the strength of the simple hysteretic component of the model

to that of the degrading component with 1.0 denoted by 10. The second set of two

digits specifies the ratio of the generalized yield displacement of the simple hysteretic

component to that of the degrading component with 1.0 denoted by 10. The third set

of two digits specifies the ratio of the failure loads associated with tensile and compressive failure for the basic degrading component of the model with 0. 1 denoted by

10. In reinforced concrete, the simple yielding component of the model would be

representative of the behavior of the reinforcing steel and the degrading component

VI-2
would be representative of the behavior of the concrete. In this case, the third set of digits would be roughly proportional to the ratio of the cracking to crushing strength

of the concrete. The limiting fully yielded stiffness for each case is taken to be 5%

of the nominal stiffness kQ

. The ductility ratio of the response is defined as

V> = xmax/x

y ( 2 )

where xmax is the maximum amplitude of response and Xy is the generalized yield displacement of the simple yielding component of the system.

In the present investigation, the structural model described by equation (1) is excited by an ensemble of twelve earthquake acceleration time histories a(t) which

are chosen to be representative of a variety of different types of earthquake excitation. An effective peak acceleration level A* is determined for each earthquake by

finding the scale factor necessary to minimize the mean square difference between

the 2% damped response spectrum of the earthquake in question and the NRC 1.60 design response spectrum [4] in the period range of 0.2 to 4.0 seconds. The latter spectrum is adjusted to a mean value spectrum by subtracting one o- from the published spectrum. The twelve earthquakes and their effective peak accelerations are

given in Table I. The response of each structural model to each earthquake of the ensemble is calculated numerically. The yield level of the structural model Xy is varied until a desired ductility ratio |i is obtained and the resulting maximum generalized displace- ment xmax is recorded. In the present investigation, this is done for nine different nominal structural periods ranging from 0.4 to 4.0 seconds and ductility ratios of

2, 4 and 8. The resulting values of xmax are used to construct inelastic response

spectra for each hysteretic system. In order to minimize the effects of the local variations in the spectral content of each earthquake, the inelastic response spectra are normalized by A* and averaged over the twelve earthquakes. This defines a family of normalized averaged inelastic response spectra for each structural model. A typical family of inelastic pseudo-velocity response spectra is shown in Figure 2 for the highly degrading system 02-10-00. Also shown for comparison are the averaged linear response spectra for 2, 5 and 10% viscous damping.

VT-3
OPTIMAL EFFECTIVE LINEAR PARAMETERS

An examination of Figure 2 reveals that the overall shape of the averaged

inelastic spectrum for a given value of |i closely resembles that of some linear spectrum except for a translation along a line of constant spectral displacement

(a line with slope of minus one on the log-log PSV diagram). For example, a linear spectrum for £ = 5% may be translated to fit very closely the inelastic spectrum for

\i = 2. This fact may be used to define a linear system which gives very nearly the same spectral response as a given hysteretic system. Let SD

n

^(EQ(j), SYS(k),p,, Tit Q Q ) be the spectral displacement of the k

th hysteretic system SYS(k) with nominal period and damping T^ and Q Q

at ductility \s, to the j**1 earthquake, EQ(j). Let SD^(EQ(j), T, £) be the spectral displacement of a linear sys- tem with period T and viscous damping Q to the earthquake EQ(j). Then, consider

a shifted linear spectrum defined by SD^(EQ(j), T^(Te/T0 ) , C Q+C e

). In this way, Te/TQ represents a period shift ratio and £ e an added damping with respect to the linear spectrum. Let 6.., be the difference between the nonlinear inelastic spectral dis- placement and the shifted linear spectral displacement defined by

SD^(EQ(j), T.(Te/T0), £ Q+ C e) 5 ijk

= SD

n

^(EQ(j), SYS(k), n, Tif C Q

) "

1

" (3)

Then, a measure of the overall difference or error between the averaged nonlinear and averaged shifted linear spectrum will be

i2

(4)

€(k) will be referred to as the root mean square (rms) averaged spectral error. An optimal period shift and added damping can be defined for each hysteretic

system by minimizing c (k) with respect to T

e/T

Q and C g

. Let the optimal parameters

be noted by T /T and £ and let c (k) be the minimum value of c(k). Then

e m °

e m m

T(k) =7m

(k), a minimum , when T /T = T /T and C = C (5) e o e m o e em

This defines an optimal effective linear system for any particular nonlinear system.

€(k) 1Z E6ijkSD Ul\j= l

J / J = l

12E sdnl

VI-4
The optimal period shift and added damping for the six hysteretic systems con- sidered herein is presented in Table II along with the minimum rms averaged spectral error e m as a function of ductility ratio. It is observed that the averaged spectral error is in no case greater than 6%. Hence, it is concluded that the optimal effective linear parameters are capable of providing an excellent description of the averaged

inelastic response spectrum for hysteretic structures of the type considered. As a general trend, it will be noted that both the optimal period shift and damping tend to increase with increasing ductility |i for all systems. It will also be noted that the more degrading systems tend to have greater period shift particularly at the largest

ductilities. The effective added damping is in the range of 6 to 12% for all cases. A SIMPLE EMPIRICAL MODEL

If graphed as a function of p, without regard to system, the results presented

in Table II suggest a simple empirical formula for approximating T /T and £ em °

e m

This may be expressed in the form VT

o

= 1 + T^- 1 * (6)

C e (%) = 6(u.-l)^ .

This formula may be used to predict the response of a nonlinear hysteretic structure

given the linear response spectrum of the excitation. This is accomplished by shifting the period from its nominal value by an amount T

g/To and introducing an additional viscous damping Q q

. The accuracy of this formula will now be examined and compared with another simple prediction method. EVALUATION OF RESPONSE PREDICTIONS

The merit of any scheme for predicting the earthquake response of a hysteretic

structure may be measured by the magnitude of the error between the actual and

predicted response over the period range of interest. The ability of a given scheme

to predict gross response features can best be seen with reference to a smooth or averaged response spectrum as shown in Figure 2. In this case, the root mean

square averaged spectral error J(k) defined by equation (4) is an appropriate error measure. The ability of a scheme to predict the finer details of the response can

VT-5
best be seen with reference to a particular earthquake with all of its spectral variations. For this purpose, an unaveraged root mean square spectral error e(k) will be an appropriate error measure where

€(k)

i 9 12

TTJs ^ £ 5ijk i=l j=l

(7)

In this investigation, the response predictions of the empirical formula will be compared with those of the optimal parameters and those of the Newmark-Hall

method [1]. The Newmark-Hall method was originally formulated as a technique for generating an inelastic response spectrum from a smooth linear design spectrum. In

this method, the linear spectrum is modified according to different rules depending

on period range. For periods greater than or equal to some value T', the method

follows the equal displacement rule and the inelastic displacement or pseudo- velocity spectrum is identical to the linear spectrum. For periods in an interval slightly less than some value T", the inelastic spectral displacement is obtained from the linear spectral displacement by multiplying by a factor of \i/\fZ^-l where p, is an

effective ductility ratio. Between T and T" the spectral behavior changes

c ontinuou sly

.

In order to obtain a direct comparison with the empirical formula, the NewmarkHall method is herein applied directly to the averaged linear 2% damped spectrum or

to the corresponding spectrum of an individual earthquake as required rather than to a smoothed or bounding spectrum. Use of a bounding spectrum has been found to give response results which are considerably over conservative. The values of T

and T" are taken to be 0.5 and 0.4 seconds respectively and the effective ductility ratio [i is taken to be equal to p, . This latter assumption has very little effect since

the method gives results which are independent of over most of the period range

considered. Table III gives the rms spectral error c(k) and the rms averaged spectral error c(k) resulting from response predictions based on the optimal parameters

presented in Table II, the effective parameters from empirical formula (6) and the Newmark-Hall method. It is seen that all of the methods considered give better response predictions for an averaged or smoothed response spectrum than for the VT-6
spectrum of a particular earthquake. This is evident from the much lower values for

the averaged spectral error c as compared to the unaveraged spectral error c. For the optimal parameters, the ratio of e to 7 is approximately four and for the two predicting schemes, the ratio is approximately two. This particular feature of the data

is not at all surprising in light of the variations in frequency content associated with any particular earthquake of an ensemble. An important observation from Table III is that for given ductility, the spectral errors resulting from either the empirical formula or the Newmark-Hall method are comparable for all of the systems considered. Hence, it may be concluded that very marked differences in hysteretic behavior of the type considered herein have only a secondary effect on the accuracy of a given response prediction technique. This does

not imply that there are no systematic differences in the response of one system

versus another, but it does imply that these differences are of the order of the error

inherent in the two simple prediction schemes. For all ductilities considered, Table III indicates that the spectral error e resulting from the empirical formula is comparable to that resulting from use of the optimal parameters. This error is typically of the order of 20% which would be

satisfactory for most design purposes. The error resulting from the Newmark-Hall

method is generally more than twice that of the empirical formula. Even for the simple bilinear hysteretic system, the spectral errors resulting from the NewmarkHall method are of the order of 50%. Overall, for all systems and ductilities, the unaveraged spectral error c is 18.3%> for the optimal parameters, 20.9%> for the empirical formula and 54.5% for the Newmark-Hall method.

Additional insight into the merit of the two simple prediction schemes considered

in Table III may be gained from an examination of the distribution of the individual spectral errors ^j^.* For this purpose, all of the different systems, earthquakes,

periods and ductilities are taken together. The results are shown in Figure 3. Figures 3(a), (b) and (c) give the results of the empirical formula and Figures 3(d),

(e) and (f) the results of the Newmark-Hall method. It will be seen that the mean

spectral error associated with the empirical formula is substantially smaller than

that associated with the Newmark-Hall method for all values of ductility. The mean

error for the empirical formula is always less than 2% while that for the

VI-7
Newmark-Hall method ranges from 17% to 32%. In addition, the standard deviation of the error for the empirical formula is roughly one-half that for the Newmark-Hall

method. It is true that the Newmark-Hall method is more conservative than the empirical formula. However, this conservatism is often excessive and is offset by

the fact that the results of the Newmark-Hall method show considerably greater

scatter than those of the empirical formula. As an illustration of the ability of the simple empirical formula to predict the response of a given hysteretic structure to a particular earthquake, the predicted

inelastic response spectra for two different systems are shown in Figures 4(a) and

(b) along with actual response data. Also shown are the predicted spectra given by

application of the Newmark-Hall method. In each case, the excitation is the scaled accelerogram for 8244 Orion Blvd., 1st floor, San Fernando, 1971, NOOW (HOL).

This accelerogram was chosen because of the presence of several pronounced peaks and valleys in its response spectrum. This helps to demonstrate the effects of local variations in spectral content.

It will be seen from Figure 4 that the predictions of the empirical formula are

generally in good agreement with the data over the range of periods considered while

the Newmark-Hall method tends to be somewhat overly conservative. This is consistent with the results of Figure 3. Even more significant, however, is the fact that the empirical formula appears to be capable of accounting to some extent for local variations in spectral content. For example, at a nominal period of 1 second, there

is a marked valley in the linear and Newmark-Hall inelastic spectrum but this is not reflected in the behavior of the numerical integration results which, for the system

BLH, actually exhibit a maximum. The inelastic spectrum predicted by the empirical formula possesses a local maximum at this period. On the other hand, from a nominal period of 3 to 4 seconds there is a sharp increase in the value of spectral displacement as predicted by the linear or Newmark-Hall inelastic spectrum while

the numerical results show a local decrease. The empirical formula also predicts

a decrease in spectral displacement. The superiority of the empirical formula in predicting detailed spectral behavior may be attributed in part to the fact that this method takes into account a shift in the effective period of oscillation of the structure while the Newmark-Hall method does not.

VT-8
CONCLUSIONS

Based on the results of the present investigation of a class of single-degree-of- freedom hysteretic systems, the following conclusions are made.

(1) Over the midperiod range of 0.4 to 4.0 seconds and for ductility ratios in the range of 2 to 8, it is possible to approximate the response of both simple and

degrading hysteretic structures from a linear response spectrum by using an

effective period shift and added damping. The use of optimal parameters leads

to root mean square averaged spectral errors of less than 5% and unaveraged

root mean square spectral errors of less than 20%.

(2) A simple empirical formula for the effective period shift and added damping is capable of providing response predictions which are quite acceptable from a design point of view. The overall root mean square averaged spectral error

for all systems and ductilities considered is of the order of 11% and the unaveraged root mean square spectral error is of the order of 21%.

(3) The differences in hysteretic behavior considered herein have only a secondaryeffect on the accuracy of the results of the empirical formula.

(4) The response predictions resulting from the empirical formula represent a

significant improvement over the results obtained using currently accepted

criteria for estimating the response of ductile structures. ACKNOWLEDGMENT

The authors wish to thank Mr. C. Krousgrill for his assistance in the computational aspects of this investigation. This research was sponsored by Grant No. ATA 74-19135 from the National Science Foundation, Research Applied to National Needs. Any opinions, findings, and conclusions or recommendations expressed in

this paper are those of the authors and do not necessarily reflect the views of the National Science Foundation. REFERENCES

*N. M. Newmark and W. J. Hall, "Procedures and Criteria for Earthquake

Resistant Design," Building Practices for Disaster Mitigation , Building Science

Series 46, NDS, February 1973, pp. 209-237.

VI-9
'Applied Technology Council, "An Evaluation of a Response Spectrum Approach to Seismic Design of Buildings," A Study Report for the N. D. S . , Washington, D.C.,

September 1974.

'"W. D. Iwan, "Response of a Simple Stiffness Degrading Structure," Proceedings of the Sixth World Conference on Earthquake Engineering , New Delhi, India, 1977, Volume III, pp. 121-126 (preprint).

''U.S. Atomic Energy Corrirnission, Regulatory Guide 1.60, "Design Response Spectra

for Seismic Design of Nuclear Power Plants," 1973.

VT-10
Tabic I Ensemble of Earthquakes Employed In Investigation with Effective Acceleration Level

Earthquake Actual Peak Effective Peak

Accel, (g's) A (g "

Vernon, Long Beach, 1933, S82E 0 154 0 169 Helena, Montana, 1935, N90E 0 145 0 123 El Centro, Imperial Valley, 1940, S00E 0 348 0 410 Olympia, Washington, 1949, S04E 0 165 0 236

Taft, Kern Co., 1952, S69E 0 179 0 218 Eureka, 1954, N11W 0 168 Array No, 8, Parkfield, 1966, N50E 0 237 0 140 Borrego Mountain, 1968, S90W 0 057 125 Pacoima Dam, San Fernando, 1971, S14W 1 170 0 952 8244 Orion Blvd., 1st Fl. , San Fernando, 1971, N00W 0 255 0 415

445 Figueroa St., San Fernando, 1971, S38W 0 119 0 174 Smoothed Golden Gate Park (artificial), S80E 0 150 0 264

Table II Optimal Effective Linear System Parameters T e /TQ

, C e and Associated Root Mean Square Averaged Spectral Error c.

System

Ductility, u = 2 Ductility, u = 4 Ductility, m. = 8 T em

/T0 Cem (%) £ m (%) T em/T0 Cem (%) <m <%) T em/T

o Cem (%) Cm (%) BLH 1. 130 6.06 5.3 1.317 8.75 3.9 1.573 10. 25 5.7 02-06-10 0.979 5.93 1.7 1. 281 11.44 3.5 1.594 11.66 3.2 50-06-10 1. 128 7.68 5. 3 1.328 10.88 2.8 1.574 11.06 4.7 02-10-10 1.068 6.53 3. 1 1.449 10.76 4. 1 1.850 12.00 6.0 02-10-00 1.082 2. 37 5.0 1.559 7.88 3.6 2.050 11.00 5.4

10-10-00 1. 202 6. 15 4.5 1.434 9.75 4.0 1.692 9.80 5.9

Table III Root Mean Square Spectral Error c and Root Mean Square Averaged Spectral Error (7) for Different Response Models in Percent

System

Optimal Parameters Empirical Formula (6) Newmark-Hall Method [1]

u = 2 H = 8 H = 2 H

= 4 u = 8 u = 2 H = 8 BLH 19.6

(5.3) 22.0(3.9) 23.3

(5.7) 19.2(6.3) 22.0(4. 2) 23.0(8. 1) 47.7

(30.0) 59.0(37.4) 56.7

(36.7) 02-06-10 6.4

(1.7) 13.7(3.5) 18.3(3.2) 22.8

(15.6) 18.3

(9.9) 19.5(7.9) 59.8

(52.7) 69.4

(52.2)

65. 1 (43.4) 50-06-10 15.9

(5.3) 19.4

(2.8) 21.2(4.7) 18.3

(7.8)

22. 3 (4.9) 22.2

(8.6) 55.0

(41. 1) 65.3

(44.0) 60.2

(39.8) 02-10-10 13.6

(3.1) 16.3(4. 1) 17.4

(6.0) 15.4

(6.5) 19.5(7.6) 19.4

(8.4) 52.4

(39.8) 56.0

(34. 1) 50.4

(29.3) 02-10-00 19.4

(5.0) 18.8(3.6) 20.6

(5.4) 22.4

(18. 1) 26. 1 (19.9) 25.2

(18.0) 31.3

(12.5) 46.2

(21.6) 46.8

(26.8) 10-10-00 16.9

(4.5) 17.4(4.0) 22. 2 (5.9)

17. 1 (9.9) 20.3

(8.6) 20.5

(7.6) 39.8

(23.8)

56. 1 (32.9) 49.5

(29.8)

All systems 15.9

(4.4)

18. 1 (3.7) 20.6

(5.2) 19.4

(11.6) 21.6

(10.6) 21.7

(10.4) 48.6

(35.8) 60.7

(38.2) 55.2

(34.8)

VI-11
VI-12
Empirical Formula

Mean error = O.I %

Std. dev. = 19.4 %

-60 -40 -20 0 20 40 60 80 100 120 140 160 Spectral Error , Sjj k (%) (a)

Mean error = -1.9%

Std. dev. = 21.5 %

•60 -40 -20 0 20 40 60 80 100 120 140 160 Spectral Error , S ijk (%)

Mean error = 0.1 %

Std. dev. = 21.7 %

50 -40 -20 0 20 40 60 80 100 120 140 160 Spectral Error , S ijk (%)

(c)

Newmark-Hall Method

Mean error = 31.7%

Std dev. = 36.8%

40 60 80 100 120 140 160

(e)

to 12-

-40 -20 0 20 40 60 80 100 120 140 160 Spectral Error , S ijk (%)

( f

)

Figure 3

VI-13
VI-14
EARTHQUAKE RESISTANT DESIGN OF HIGH-RISE BUILDINGS IN JAPAN Keiichi Ohtani, Chief, Earthquake Engineering Laboratory National Research Center for Disaster Prevention

Science and Technology Agency ABSTRACT

In January, 1964, the building height limitation which had been stipulated in the

Structural Standard Law of Japan since 1921 was replaced with the building volume limitation,

-lumber of high-rise buildings exceeding 45 meters in height came out to be about 300 cases.

These buildings are examined thoroughly for the aseismic safety by dynamic analysis instead

3f static analysis, and received judge-and-rating as to the propriety of structural design

from the committee consisting of specialists.

In this report, I discuss the present state of design, especially of dynamic analysis,

using the design specification presented to the above committee. The number of data

used in this report is 78 for SRC (composite steel and reinforced concrete structure)

and 160 for S (steel structure) omitting special type structures such as high chimneys,

towers, etc. As this study is the research of materials based on the actual design

specification, I refer to the problems of aseismic design or the future subjects of research

and development by considering the trend of design.

KEYWORDS: Building height limitation; building volume limitation; f lexural-shear model; earthquake resistant design; high-rise buildings; histogram for building uses; shear model.

I

VT-15
1. INTRODUCTION

The building height in Japan was limited to 31 meters since the Kanto Earthquake. The study of possibility of realization of the hihg-rise buildings was started by the Building Constructor Society with trust from the Ministry of Construction. In September, 1963, the Architectural Institute of Japan published the original draft of the "Guide Line for Aseismic Design of Tall Buildings" ("Guide Line") , and in January, 1964, the Structural Standard Law

of Japan was altered from the building height limitation to the building volume limitation.

It is certain that the rapid developments in the techniques of the response analysis of structure for earthquakes (the dynamic analysis of structure) along with a recent remarkable progress of electronic computers were the background of this alteration of the law. Although we had been annoyed by the absolute deficiency of land and overcrowded state

of buildings in the city region of Japan, we took the interest to raise the open space ratio

of the city, and to rearrange the city for more green spaces by consideration of the building volume limitation.

In order to assure the structural safety of tall buildings exceeding 45 meters in height, an Examination Board was set up in the Ministry of Construction in September, 1964. The Board was transferred to the Evaluation Committee of High-Rise Building Structures,

the Building Center of Japan, in August, 1965. The structural designs of high-rise buildings are carried out generally in accordance j with the "Guide Lines," usually employing dynamic response analysis. Documents and drawings

'

of the structural design are presented to the Building Center of Japan by a structural engineer and he explains the outline of design to all members of the committee. After this

' hearing, a sub-committee consisting of appropriate number of the committee members and several other specialists, if necessary, is organized to investigate the design in detail. The sub—committee reports its conclusion to the main committee, and the decision on approval!

is made by the vote of all committee members. Detailed explanation on the function of the Evaluation Committee appears in the literature. Finally it is subjected to approval of the Ministry of Construction. Number of high-rise buildings which have been approved by either the Examination

Board in the Ministry of Construction or by the Evaluation Committee of High-Rise Building i Structures in the Building Center of Japan is about 300 cases from March, 1963 to February,

1977. Omitting special type structures such as high chimneys, towers, etc., from these i cases, and classifying them into S (steel structure for the main parts) and SRC (composite i steel and reinforced concrete structure for the main parts) types, their general trend of current earthquake resistant design are briefly discussed in this report.

2. USE AND SIZE OF BUILDINGS Numbers of data which have been used in this report are 78 cases for SR and 160 cases for S. These numbers are all the data available to the author, and form 95% of the , pertinent data. The histograms for the use of buildings are as follows:

it VI-16
for SRC (see Fig. 1-a) office (include those of stores and halls) 36 cases (46%) hotel (include those of offices) 12 cases (15%) apartment house (include those of offices) 16 cases (21%) bank 7 cases ( 9%) hospital 7 cases ( 9%)

> (see Fig. 1-b) office (include those of stores and halls) 101 cases (63%) telephone station and broadcasting station 13 cases ( 8%) hotel (include those of offices) 23 cases (14%) store and department store 10 cases ( 6%) apartment house (include those of offices) 9 cases ( 6%) other use 4 cases ( 2%) From the trend of use, it is noted that the buildings, which are adopted into SRC, are used

in many cases for the apartment house, hospital and bank. It seems to be all right to consider that the reason for this adoption into SRC are to raise the rigidity of structure

and to restrain the deformation. On the other hand, about 2/3 of the high-rise buildings,

jwhich are constructed with S, are used for the office. The histograms for number of stories are illustrated in Figs. 2-a,b,b'. When the number of stories is distributed 10 to 60 stories, its peak is 14 to 18 for SRC, 14 to 30

(for S. The basements ranged 0 to 5 storeis for SRC, 0 to 6 for S. It has a trend that the

S structure is 4 or 5 stories taller and 1 story deeper than the SRC.

J The total floor area of the buildings is distributed from 5,000 to 220,000 m and is

2 2 concentrated on 30,000 to 40,000 m . The typical floor area occupied 1,000 to 1,500 m for

the most part. Though the height of the highest building in Japan is 226.2 m, the heights

are 50 to 75 m for most buildings. Although the deepest foundation bed sets on GL-43 m,

the depths of the foundation bed are located GL-12 ^ 20 m for most cases.

3. VIBRATION CHARACTERISTICS

)-l Modeling of Structure

The structure is so complex for space or plane and the mechanical property of

materials is not so simple that it is impossible to analyze the structural characteristics

fhich remain intact. In the case of dynamic analysis, the model constructed in mathemat-

.cally simple forms is necessary. A general method of modeling is the method that concentrates the mass at each floor

Level and connects some springs from floor to floor, so called the idealized lumped mass

'ibration system. The shear model and the f lexual-shear model are used for elastic response

alysis, but the employment of the f lexual-shear model is more widely used than the shear

del in recent years. A general method of the use of springs for inelastic response analysis is as follows:

he force-deformation curves of the open frame (Rahmen) and of the quake resisting wall

re determined respectively as shown in Fig. 3, and then the curve of the story is obtained

VT-17
by cumulating these curves. And simplifying the curve of the story, the story spring is approximated to the polygonal line as bi-linear or tri-linear.

The shear model is used for inelastic response analysis. If the f lexural-shear model

is used for elastic analysis, the equivalent shear model which is constructed with the same fundamental period and vibrational mode of the above model is used for inelastic analysis.

The histograms of the viscous damping ratio for the fundamental period (h^) are shown

in Figs. 4-a, b where its peak is 5% for SRC and 2% for S. The results of vibration tests, indicated that the actual structure did not have the damping mechanism which was in proportion to the frequency. In the structural designs, a method which increases the damping for the higher modes as the type of frequency proportion, assuming constant values for the funda mental and the 2nd modes (for the 3rd mode and so on, if necessary) , has been more and more employed.

3-2 Natural Periods and Design Base Shear Coefficients

The relationships between the fundamental period (T^) and the number of stories (N) are plotted in Figs. 5-a,b, 6-a,b where N in Fig. 5 denotes the number of all stories including

the basements and penthouse and, N in Fig. 6 the number of stories above ground only (except the basement and the penthouse). In these figures, one-dot-dash-line is for T^=0.1N from

the formula proposed in the SEAOC code, and the region sandwiched between one-dot-dash-line

and the two-dots-dash- line is for T^= (0.06^0. IN) from the formula recommended in the "Guide

Line." The relation between "T^" and "N" is approximated by a formula T^-0.06N for SRC, T^O.OSN for S in Fig. 5, and T^O.OSN for SRC, T^O.IN for S in Fig. 6. Since the relation between the 2nd order period (T^) and the fundamental period (T^) has small dispersions, a linear equation T

2=0.364T1 for SRC and T^O.354^ for S by the method of least squares passing through the zero point can be found as shown in Figs. 7-a,b. The difference in both approximate expressions is so little that it would be almost adequate

to consider a relation T

2=0.36T^ as the approximate expression.

The relation between "T

1

" and "CB" are plotted in Figs. 8-a,b where C

B

is the design

base shear coefficient. The "Guide Line" has recommended C^= (0 . 18^0. 36) /T^ and 0.05^^0.2,

and has advanced an opinion that the decreases from above formula to (0. 15V). 30) /T^

.

From the actual state of designs, most of them are in the range of C

B

= (0. 24^0.42) /T^ and

the designers have attempted to design structures using the more severe criterion than the "Guide Line." This is because they expect that the satisfactory structural safety is to

be achieved only specifying the sufficient capacity of section, even if it means a little wasteful design, since the high-rise buildings have had no experience of greater earthquakes and their safety has not been sufficiently proved in practice.

4. INPUT EXCITATIONS AND THE MAXIMUM INPUT ACCELERATIONS

The histograms of the employed earthquake accelerograms are shown in Figs. 9-a,b where its trend are alike for both cases of SRC and S. El-Centro NS is used in almost

all designs as the standard excitations and Taft EW is used in the cases of 80 ^ 90 percents. It is hoped truly that the high-rise buildings are going to be designed by El-Centro

VI-18
NS and Taft EW in Japan. The accelerograms observed in Japan, Tokyo 101 NS, Sendai 501 NS, Osaka 205 EW, etc. are employed. It is pointed out in a few cases that Hachinohe EW, which gives large responses of the structure with longer fundamental period, and El-Centro

EW, which has large effects on the structures with fundamental period of about 2 sec, are

also employed.

Figs. 10-a,b give the maximum input accelerations for elastic or inelastic response

analysis, generally 200 ^ 250 gal for the former, and 350 ^ 400 gal for the latter.

In the design methods based on the maximum input acceleration, even if several waves

(are employed, only one wave of them gives the maximum response because that they all have

individual frequency characteristics. Namely, in practice it is equivalent to the design

employing one wave, and therefore in several cases, the design method based on the maximum input velocity is employed. For the value of the maximum velocity corresponding with the

!ir.aximum acceleration, 25 kine for elastic analysis and 40 kine for inelastic analysis

lare used. For the scale for estimation of the response of structure, its standard value has been

used as follows: The maximum angle of story deformation:

1/250 ^ 1/200 for elastic analysis, 1/150 ^ 1/100 for inelastic analysis.

The ductility factor: y <2_ for inelastic analysis.

5. PROBLEMS OF THE DESIGN FOR HIGH-RISE BUILDINGS

Using the value of the design for high-rise buildings, studying the present state of

the design and dynamic analysis, I raise several points with regard to the design and future

subjects of research as follows:

1) Institution of Input Excitation

As the "Guide Line" has recommended that a suitable input excitation must be chosen

in consideration of site or foundation condition, the actual states of the design has hardly

taken into consideration the aforementioned condition. The development of the "Standard

Excitation" and the method that takes into account the seismicity and dynamic characteristics

of ground at the site of the structure are necessary.

2) Level of Input Excitation

In the present design method, 250 gal for elastic analysis and 400 gal for inelastic

analysis are widely employed, though there has been no investigation on the safety of structure when the greater earthquake than the designed one occurs. It is necessary to consider the criteria to be used to perform the abovementioned investigation.

3) Establishment of the Restoring Force Characteristics

In the case of establishing the restoring force characteristics of the building stories,

ibhe method that sums up the force-deformation curves of the frame and quake resisting wall

i«?hich is individually calculated is employed. Although the propriety of this method is not

/et verified, it is necessary to prove the structural behavior by large-scale experiments,

vibration test, etc. VI-19
4) Treatment of Quake Resisting Wall Using the method by which the reinforced concrete wall such as a boundary wall of the room at hotel or a wall of the surrounding core are designed, the non-resisting wall are designed by the treatment of detail and the most cases are designed for the open frame structure. It is necessary to reconsider how the method of this treatment is to aim the correct direction of the structural design.

VI-20
SRC

SRC

Fi 9- 1-a Fig. 2-a

3 ES S H II s II I £

s l! l

TOh n I I m D m n Fig. 2-b Histogram for number of stories

S

K E STORY

2 3 4 5 6

Fig. 2-b"

s«V-"7

S&Y 6 Fig. 3 Relation between displacements and forces

Fig. 1-b Histogram for use of buildings

VI-21
r iFig. 4-a Histogram for damping factor

2 3 4 6 OTH.

/•: . '/

t.-o.in/

<• —hi:

y :

/ /

/ /

;::

'

//vo /

06N

N

0 3 Fig. 5-a

Fig. 4-b

——

.

r 1 2 3 4 6 h,C«0

: min 4

MV'.

40 JO Fig. 5-b Fundamental period vs. number of stories —i . .•:/

• 'A J.

•/^r,-ao6N

/

! : v

K":

/./

// r

10 JO 3 Fig. 6-a

WIN

/

• /

V

m TfOMN

Fig. 6-b Fundamental period vs. number of stories

VI-22
Fig. 7-a Fig. 7-b Relation between fundamental and second order periods

V:«*> - -v.

0^)8^*-.

Fig. 8-a Fig. 8-b Fundamental period vs. design base shear coefficient

10 20 30 40 50

Fig. 9-a Fig. 9-b Employed earthquake accelerograms

VT-23
s

1 2 3 4 5 6 GAL (X100) Fig. 10-b Maximum input accelerations for elastic or inelastic response analyses

VI-24
Racking Strength of Wood-frame Walls

ROGER L. TUOMI Forest Products Laboratory, Madison, Wisconsin

ABSTRACT

Evaluation of the racking strength of wall systems has generally been limited to performance testing. Acceptance criteria for ultimate racking strength of sheathed walls

are based on the strength of a wall with a let-in corner brace and horizontal board sheathing.

An analytical method for predicting racking performance has been developed that appears promising. It is independent of panel size, and small-scale tests can be used to augment the more costly standard tests. A small-scale loading apparatus was designed for rapid testing of wall sections.

Let-in corner braces using today's construction methods and materials no longer meet

even the minimum level of acceptance. This is due to the elimination of horizontal board sheathing and the reduction in actual lumber sizes which took place since the racking performance standards were established.

Racking stiffness is an important performance consideration that has not been investigated. New testing apparatus has been designed that will make possible future evaluations

of racking stiffness.

KEYWORDS: Racking strength; Windloads; Inplane shear forces; Corner brace; Racking stiffness

VT-25
INTRODUCTION

The racking strength of a wall system is defined as its ability to resist horizontal

inplane shear forces. These forces arise primarily from wind, but are also present under earthquake loadings. Current design procedures in the United States for calculating wind

forces are published by the American National Standards Institute (1) .—

Evaluation of wood-frame wall systems has generally been limited to performance

testing. This technique has been used because no analytical method for predicting racking performance has yet been accepted.

BACKGROUND

For the first half of this century, wood-framed walls were typically built with horizontal board sheathing with let-in corner braces. With the development of plywood and fiberboards, the building industry abandoned the traditional board sheathing in favor of

the more labor-efficient sheet products.

In 1949, the Federal Housing Administration (FHA) established minimum performance

standards (2^ as the basis for accepting new sheathing materials. The original standard was intended as an interim measure until a permanent one could be introduced. None has yet been developed, but a standard racking test procedure was approved by the American Society

for Testing and Materials (ASTM) (3). With this procedure, the standard test panels are 8- by 8-foot (2.4- x 2.4-m) wall sections, fabricated with nominal 2- by 4-inch (50- x 100-

mm) lumber and covered with two sheets of 4- by 8-foot (1.2- x 2.4-m) sheathing. This construction simulates conventional platform construction with studs spaced 16 inches

(400 mm) apart.

Considerable wall testing, conducted prior to 1949, indicated that horizontal board sheathing with let-in corner bracing provided a minimum racking strength of 5,200 lbf

(23 kN) for the 8-foot (2.4-m) square wall sections. Experience with existing houses

ll Underlined numbers in parenthesis indicate references listed at end of this report.

VT-26
showed this to be an adequate level of performance. All structural sheathing materials

were required to meet this standard.

With the new emphasis on energy-efficient construction, many nonstructural sheet products are appearing on the market. This has forced many builders to revert to mechanical bracing systems, such as let-in lumber or metal straps.

STRUCTURAL SHEATHING Development of Theory After testing several standard wall panels at the Forest Products Laboratory (FPL) , it became apparent that racking strength was controlled by fastener capacity rather than by

the shear strength of the sheet material. FPL then developed a theory to predict racking

strength of sheathing materials mechanically fastened to a stud frame. The equation was

derived by an energy formulation whereby the externally applied load is resisted by the internal energy absorbed by the fasteners. The frame is assumed to distort like a parallel- ogram while the sheathing remains rectangular. The structural analog is shown on figure 1. The equation for the resistance provided by the perimeter nails of a single sheet of sheathing is:

sr sin a

2 / n

2 - 1 2 A n + m - — | -— cos a + (1)

where

R is racking strength of one sheet of material (lbf or N)

,

sr is product of slip times resistance of a single fastener (ultimate lateral load)

(lbf or N), a is arctan (base of sheet divided by its height), n is number of nail spaces on one horizontal edge, and m is number of nail spaces on one vertical edge.

The total racking strength provided by the perimeter nails of a wall assembly is then

the above result times the number of sheets of material plus the strength of the stud

f rame

.

VI-27
However, this relationship is complicated by the fact that most sheets also have interior or field nails. These field nails, being closer to the centroid of the sheet, offer far less resistance than the perimeter nails (5 to 10 pet), but their contribuiton

should nonetheless be considered.

The above equation can be modified to include the contribution of the interior fasteners, and racking coefficients calculated for standard sheet sizes. A Forest Products Laboratory report, "Lightframe Walls—A Theoretical Solution for Predicting Racking," will

be available later this year. It will cover the development of this theory in detail and will include racking coefficients in table form.

Small-Scale Tests The theoretical equation considers the geometry of the sheathing, the number of horizontal and vertical nails, and the lateral resistance of the fasteners, but is independent

of panel size. Figure 2 shows the correlation between theoretical and actual racking strength of both 2- by 2-foot (0.6- x 0.6-m) and 8- by 8-foot (2.4- x 2.4-m) test panels.

Since the full-scale 8- by 8-foot (2.4- x 2.4-m) tests are cumbersome and expensive tc run, FPL designed a small-scale loading apparatus. It consists of a pantograph frame whicl

is pinned at four corners. The lower member can swing freely but will always remain horizontal. The two structural members and the pinned-connector straps form a parallelogram at all times, eliminating the need for hold-down devices at the corners. The principal advan- tage in this arrangement is that the applied load direction can be reversed to study the effect of cyclic loading.

Deflection readings are obtained by measuring the change in diagonal length between opposite corners of the test specimen. The current ASTM Standard (3) requires three simul- taneous measurements: gross horizontal corner deflection, slip, and rotation. The net racking deflection must then be calculated for each load level. With the diagonal dis- placement method, loads and net deflections are obtained directly.

VI-28
Lateral Nail Tests

Since the lateral nail strength of fasteners is a parameter needed for predicting

racking strength, it is important that the lateral nail tests represent the actual wall

construction.

Two standard nail tests are used in the United States—ASTM D 1037 (4) and ASTM D 1761

(5). ASTM D 1037 was designed for evaluating the properties of wood-base fiber and particle

panel materials. With this method, the nail shank is supported by a steel stirrup and is pulled through the edge of the sheet material. This method is adequate for lower strength

materials, but may not indicate the mode of failure in actual racking joints.

With stronger materials, such as plywood, the joint failure may occur in the lumber rather than the sheathing. To better simulate the actual joint for higher strength sheathing, a modified version of the ASTM D 1761 test procedure is recommended. This test was designed for conducting lateral nail tests in wood. The modification recommended is that the cleat is a piece of sheathing material and the block is an actual piece of framing

lumber taken from the test panel. Thus, the actual materials from the racking tests are mated in the lateral nail tests.

The distance between the nail and the edge of the sheathing is also very important.

The effect of edge distance on lateral nail strength is shown in figure 3. A 3/4-inch

(19-mm) end distance was selected for the value used in equation (1) because it best represents the displacement of the tension corner nails, which are the critical ones. Nails along a vertical joint, where two sheets butt together, are closer to the edge, but their displacement direction is essentially parallel to the edge rather than toward it. Half the nails have displacement components toward the center and are not affected by edge

distance.

LET-IN CORNER BRACES Many changes in construction practice have occurred since FHA established the minimum

performance standard. Horizontal board sheathing is no longer used, and the actual size of dimension lumber has been reduced. Some building codes currently accept the let-in corner

VT-29
brace when nonstructural sheathing is used. However, few tests have been made on walls with let-in corner bracing since the performance standard was developed.

FPL conducted a few tests to determine the capacity of let-in corner braces with

today's materials. The first tests did use horizontal board sheathing to reaffirm the FHA

requirements, and 5,200 lbf (23 kN) was attainable. The horizontal board sheathing supports

the brace against outward buckling and also reinforces the stud frame. This was not the

case, however, when the horizontal boards were eliminated.

Let-in corner braces are generally 1- by 4-inch (25- x 100-mm) .boards cut into the frame and secured with two nails per stud crossing. They can act either in tension or compression depending upon the load direction. Figure 4 shows a typical brace under com- pression loading. Braces loaded in this manner failed violently in buckling like a slender

column, or else the stud frame slowly came apart. The strength of compression braces was calculated by the following equation for an ideal column:

2 P = —~— sina (2) L

in which

P is applied racking force (lbf or N)

,

a is angle between brace and vertical member,

a is end condition coefficient (use a = 1 for pinned),

E is modulus of elasticity of the brace (psi or kPa)

,

4 4

I is moment of inertia of the brace (in. or mm )

, and

L is unsupported clear distance between studs along the brace (in. or mm).

This approach worked fairly well for braces with a modulus of elasticity up to about

1.6 million psi (11,000 MPa) , but beyond that stiffness the stud frame simply came apart. The ultimate load when good quality braces are used is controlled by the stud wall and is around 3,600 lbf (16 kN)

.

When loaded in tension, racking strength is provided primarily by the lateral nail strength of the nails which secure the brace to the studs. The maximum racking load is VT-30
lower for braces loaded in tension. Further discussion on braces is presented in an upcoming FPL Report, "Racking Strength of Let-in Corner Bracing, Sheet Materials, and the Effect

of Rate of Loading." This report should be available in a few months.

FUTURE RESEARCH

One important consideration that has not been resolved for racking performance is that

of racking stiffness. Traditionally, racking tests have been run essentially to failure without much attention to the shape of the load-deflection curves. The initial loading

produces a parabolic curve with no well-defined stiffness value or limit of proportionality.

However, in the few cases where cyclic loading was performed, the load-deflection

curve became fairly linear and reproducible. This was true for lateral nail tests, wall

racking tests, and full-scale house tests. Figure 5 is an example of a wall racking test

' cycled five times prior to loading to failure. The first loading does produce a degree of

j set or seating of the fasteners, but it appears to be a constant value for a given load

level.

In equation (1), the lateral fastener strength was given as sr, the product of slip

j times resistance or stiffness. If this stiffness property can be better defined, then it would be possible to predict racking resistance for any level of deformation.

II f|; l %f:FPL recently built a new racking frame that is capable of cyclic load reversals. It

j can be programmed to cycle between desired limits of displacement or load level. Also, the frequency can be adjusted to simulate earthquake excitation or dynamic wind response. Load-deflection data can be monitored after 1, 10, 100, 1,000, or any desired number of cycles. A study is scheduled for later this year to use this new apparatus in an attempt

to develop racking stiffness information.

SUMMARY

A relationship between theoretical and actual racking strength has been developed that appears quite promising. Small-scale tests can be used to augment the more cumbersome and

J

VI-31
expensive standard tests. The small-scale tests should provide a quick and easy way to estimate the racking properties of new sheet materials.

The actual performance of let-in corner braces, without the horizontal board sheathing,

is well below the 5,200 lbf (23 kN) level required by FHA. Although the strength and stiffness of the brace are important, a level is reached where the stud frame controls ultimate strength.

Racking stiffness is an important performance consideration that has not been investigated. A new test apparatus has recently been designed that should enable researchers to study the stiffness properties of wall systems under cyclic loading. These tests, together with a theoretical design approach, should provide a means for predicting racking resistance

at various levels of load or deflection below ultimate strength.

REFERENCES CITED

1. American National Standards Institute (1972). American national standard building

code requirements for minimum design loads in buildings and other structures. ANSI A58

1-1972.

2. Federal Housing Administration (1949). A standard for testing sheathing materials for I resistance to racking. FHA Tech. Cir. No. 12. Washington, D.C.

3. American Society for Testing and Materials (1968). Standard methods of conducting strength tests of panels for building construction. ASTM E 72-68. Philadelphia, Pa.

4. American Society for Testing and Materials (1964). Standard methods of evaluating the j properties of wood-base fiber and particle panel materials. ASTM D 1037-64. Philadelphia, Pa.

5. American Society for Testing and Materials (1968). Standard methods of testing metal

fasteners in wood. ASTM D 1961-68. Philadelphia, Pa.

VI-32
m, spaces

ORIGINAL PANEL DISTORTION UNDER LOAD

Figure 1. Original panel shows parameters necessary to calculate racking strength. Under load, the frame distorts like a parallelogram while the sheathing remains

rectangular. The direction and relative magnitude of the nail displacements are shown under load.

^ 6,000

. . 5.000

4,000

% 3,000 %

^ 20OO 1^ IfiOO

1 O y

P-- 0.995

R

/--- 0.986 / O —

• SMALL SCALE TESTS

0 FULL SCALE TESTS

0 0 /

8 o"/ 0 <y so

r

° _ 00 -

•yBf S 1 1 1 1 1 0 1,000 2,000 3J000 4jOOO 5,000 6fi00 7,000 THEORETICAL RACKING STRENGTH, R(LB) Figure 2. The relationship between theoretical

and actual racking strength for both

full-scale and small-scale test specimens

.

O i-IN. INTERMEDIATE DENSITY FIBERBOARD D g-IN. REGULAR DENSITY FIBERBOARD

Oj-IN. REGULAR DENSITY FIBERBOARD

I I

EDGE DISTANCE IIN. I Figure 3. Lateral nail strength at various

edge distances for four types of fiberboard sheathing.

VT-33
Figure 4. Schematic diagram of a let-in corner brace being loaded in compression.

CORNER BROKE

DEFLECTION (IN) Figure 5. Typical load-deflection pattern for cyclic loading of wall panel. Curve becomes fairly linear after the first cycle seats the fasteners.

VI-34
EXAMINATION FOR AN EVALUATION METHOD OF DAMAGE TO EXISTING WOODEN HOUSES CAUSED BY EARTHQUAKES

Kaoru Ichihara, Director

Eiich Kuribayashi, Chief, Earthquake Engineering Section Tadayuki Tazaki, Research Member

and Takayuki Hadate, Research Member

All of Public Works Research Institute ABSTRACT

In an effort to help draft an earthquake disaster mitigation program, an evaluation method for damages of structures by earthquakes is proposed. Concepts of the ratios of razed houses and probability theories with number of razed houses have been employed in the method.

KEYWORDS: Damages of structure by earthquake; disaster mitigation; probability theory; ratio of razed houses; wooden houses

VTI-1
1 . INTRODUCTION

A consideration in the evaluation of damages of structures by future earthquakes is proposed herein. This wouH help in drafting an earthquake disaster mitigation program. Prior to evaluating the losses of lives and damages to the structures, the damages of houses were assigned an index in terms of the whole losses and damages. For instance, H. Mizuno and S. Horiuchi presented relationships between the ratios

of outbreak of fires and those of totally destroyed dwelling houses caused by past earth- quakes since the Great Kanto Earthquake in 1923 as shown in Fig. 1 (1) . And relationships between the losses of human lives and those of razed houses in the Fukui Earthquake in 1948 are presented as shown in Fig. 2 (2)

.

The equivalent ratio of razed house (defined in Chapter 2) , which could be considered

as an index of principal damage, is assumed as follows.

(1) The equivalent ratio of razed houses normally expresses a seismic intensity

even in the vicinity subjected to severe earthquakes, where data on ground motions are rarely obtained.

(2) Wooden houses are common dwellings in this country, and much data on damages of wooden houses by earthquakes have been reported.

In this report, the equivalent ratio of razed houses at a respective site by a strong earthquake was estimated by applying statistical relationships among the equivalent ratios, epicentral distances and magnitude (Richter Scale) of the earthquakes reported at the last Joint Meeting (3,4). Furthermore the results of

the evaluation were compared with actual damages at the site caused by the earthquakes.

2. DEFINITIONS OF DISTRIBUTION OF DAMAGE RATIOS OF EXISTING WOODEN HOUSES CAUSED BY PAST EARTHQUAKES (3) Using the statistics of disaster documents on short distant earthquakes, Fukui Earthquake (M = 7.3, 1948), Izuhanto Oki Earthquake (M = 6.8, 1974), and Ebino Earthquake

(M = 6.1,1968), relationships among ratios of razed houses, epicentral distances and mag- nitudes of earthquakes were reported (3) . The equivalent ratio of razed houses is defined

as: D % _ Number of Razed Houses + 0.5 x Numbers of Half Razed Houses ^

1' ' Total Number of Existing Houses Conclusively, the ratio in the area of diluvium or tertiary is given as and D^^ in the area of alluvium is given as D^jj'

, /-,,-„ , rt 0.625M + 0.025AM - 0.272A ... D

lx

= 1/164 x 10 (1)

, ,„0.576M + 0.026AM - 0.248A (2) = 1/73 x 10 where A = epicentral distances

M = magnitudes of earthquakes (Richter Scale)

VII-2
AN EVALUATION METHOD OF DAMAGE TO WOODEN HOUSES

razed houses, epicentral distance, and magnitude are given in Eq. (1) and (2) . In order

to estimate the distribution as for the equivalent ratios in Tokyo, Kawasaki and Yokohama

districts, the earthquake is assumed as follows: magnitude = medium class as 6 to 7, focal depth = less than 50 km, epicenter = assumed as the same point located at the epicenter of Ansei-Yedo

Earthquake (1855), i.e., E139.8 0

, N35.8°.

In general, wooden houses behave elastically with relatively small amplitudes of deformation induced by ground motions, and elasto-plastically with relatively large

amplitudes. H. Umemura proposed critical seismic lateral force coefficients at a point from

elastic to elasto-plastic states as 0.4 for one story houses and as 0.6 for two story

houses. M. Mononobe proposed the relationship between the ratio of razed houses and seismic coefficient K as Eq. (3) assuming a Gaussian Distribution, J*/ e dK (3)

where Ko = average resistivity

a = the parameter expressing uniformity of resistivity

Fig. 3 shows the estimated results by applying Eq. (3) to Noubi Earthquake (Ko = 0.40,

a = 0.053), Fukui Earthquake (Ko = 0.40, a = 0.071, Kanto Earthquake (Ko = 0.45, 0 = 0.071), and Sempoku Earthquake (Ko = 0.47, O = 0.105). According to this figure, the original ratios of razed houses D

2

* corresponding to the critical seismic coefficient

of 0.4 and 0.6 are 20 to 50% and 90 to 100%, respectively. So the multiplier 6 for the original ratio of razed houses of two stories normalized by those of one story becomes

1.8 to 5.0. In this report, 6 is assumed to be 1.8. In Eq. (2) , the average depth of alluvial deposits is assumed to be 10 to 30 m. The equivalent ratio of razed houses at the area of thicker alluvium will be greater. Fig.

4 shows the " relationship between the equivalent ratio of razed houses and the depths of

alluvial deposits in Tokyo and Yokohama districts during the Kanto Earthquake. The data

from the investigations by H. Kawasumi, Y. Ohsaki, S. Omote and S. Miyamura are used in this estimation. According to this figure, the multipliers y for the equivalent ratio in

the area with various depth of alluvial deposits are evaluated as shown in Table 1. These

multipliers are normalized by the ratio at alluvial deposits 10 to 30 m deep.

} _ number of razed houses

2 total numebr of existing houses VTI-3
Fig. 5 shows the deviations of the equivalent ratio of razed houses in subground type

II for the Fukui Earthquake. The numbers on the abscissa in this figure correspond to those equivalent ratios of razed houses in Table 2. The deviations shown in Fig. 5 are relatively

large. Comparing the deviations in Fig. 5 with the numbers of existing wooden houses N in Table 2, it can be assumed that 'N' also affects the equivalent ratio. In this report, the deviation is assumed to be a binomial distribution. Risk Indexes, RI, which means upper control limits for three standard deviations of the equivalent ratios are introduced as follows: V?

(4) D

1 ±3 Y

D

1 (100-D

1

) /N in %

= upper limit of the deviation of the equivalent ratio of razed houses.

of epicentral distance. A binomial distribution can be approximated to a normal distribution when N is sufficiently large and is sufficiently small. The difference between these distribution

functions is given by Eq. (6)

,

r!0

R! (N -R)! (c+l/2-N.D

1 )/ 7 N.D

1 (1-D

1

) du ... (6) 2r The relationship of Pb_ n and R* is shown in Fig. 6. According to this figure, a binomial distribution approximates to a normal distribution having an error of 2% when N exceeds

100. If RI is greater than 10, which means that the actual equivalent ratio exceeds D^, RI can be considered being affected by other factors than earthquake intensity, i.e., sub- ground condition.

*R = number of razed houses + 0.5 x number of half razed houses.

= number of equivalent razed houses. VTI-4
Ill considering the difference of resistivity between the houses of two stories and those of one story, the depth of alluvial deposit and the sample size of the existing houses in the areas are given as follows:

= in % ( 7) B

in

= e ' RI ' DiS i" % (8) in which

6 + y

i - Dn

+ 3 i

Dn < 100 - Dn>

/N

6 -

J 1.00 in the area where most houses are one floor

I 1.80 in the area where most houses are two floor

Y ; given in Table 1 hn

RI ; given by Eq. (5)

The procedure stated above was applied to Tokyo, Kawasaki and Yokohama districts and

Fig. 7 shows the results. In this estimation, the values of RI were obtained from the Fukui Earthquake data. The value of <S was assumed to be 1.80, because most of the existing

wooden houses are two stories. The average depth of alluvial deposit in ward k was estimated as follows:

h. = I ( M t Ai / Z A. (9) i=l 2 i=l 1

in which

hi = the depth of alluvial deposit

Ai = the area in which depth is between h^ and

In Fig. 7, upper, middle and lower numerals in each ward correspond to the estimated

equivalent ratios of razed houses destroyed by the assumed earthquake of magnitude 6.0, 6.5 and 7.0, respectively.

4. CONSIDERATION

Based on the examination described herein for the evaluation method of damage to existing wooden houses by earthquakes, the estimated ratio of razed houses and the actual VTI-5
ratio reported in the document of razed houses in the Ansei-Yedo Earthquake (1855) com- prehensively agree with each other except minor errors.

Here, one of the evidences of the evaluation method for the damage ratios as well as their distributions could be given. Using these, it would be possible to totally evaluate

the losses and damages by the earthquakes.

5. ACKNOWLEDGEMENTS

The author appreciates their cooperation listed below:

1) Prime Minister's Office, Statistics Bureau, National Census Department

2) Tokyo Metropolis, General Affair Bureau, Disaster Countermeasures Division

3) Fukui Pref., Fire and Disaster Prevention Department

4) Fukui Prefectural Library

5) Ishikawa Pref., Statistics Department

6) Kagoshima Pref., Fire and Disaster Prevention Department

7) Yebino City Office, lino Branch and Shinko Branch

6. REFERENCES

1) H. Mizuno, S. Horiuchi, Study on the Estimation of Fires in Earthquakes, Proceedings

of the Japan Society of Architects, 250, 1976.

2) H. Mizuno, S. Horiuchi, Study on the Relationship Between the Ratio of the Outbreak of Fires and That of the Totally Destroyed Dwelling Houses Caused by the Earthquakes, Proceedings of the Japan Society of Architects, 247, 1976.

3) E. Kuribayashi, T. Tasaki and T. Hadate, Relationships Between Earthquake Damage of Existing Wooden Houses and Seismic Intensities, U. S. Japan Panel on Wind and Seismic

Effects, Eighth Joint Meeting, UJNR, May 18-26, 1976.

4) E. Kuribayashi, T. Hadate, Y. Hoshiba, Characteristics of Distribution of Damages Caused by Earthquakes, Journal of the P.W.R.I., Ministry of Construction, 18-9, 1976.

5) H. Unemura, Research on the Estimation of Architectural Damages by Earthquakes, Tokyo Metropolis Disaster Prevention Committee, 1970.

6) T. Mochizuki, Research and Earthquake Response Analysis to Estimate the Damage of Wooden Houses in Tokyo, Proc. of the Japan Society of Architects, 230, 1970.

7) N. Mononobe, Earthquake Engineering in Civil Engineering Structures.

8) Investigations on the Damages of Hokuriku Earthquake, Report of Public Works Research

Institute, Ministry of Construction, No. 78, 1949.

9) H. Kawazumi, Damage Distribution and Earthquake in Tokyo, Architecture Magazine, 773, 1951.

10) Y. Ohsaki, Earthquake Damage of Wooden Buildings and Depth of Alluvial Deposit,

Proc, of Japan Society of Architects, 72, 1962.

11) S. Omote, S. Miyamura, Relationships Between Damage Distribution in Earthquake in Yokohama and Nagoya City, and Subground Conditions, Architecture Magazine, 773, 1951.

12) Memorandum of the Statistics on Houses, Prime Minister's Office, Statistics Bureau, National Census Department.

VII-6
13) Subgrounds around Tokyo Bay, 17, Planning Bureau, Ministry of Construction, edited by Tokyo Bay Development Committee.

14) Tokyo Metropolis, Documents of Ansei-Yedo Earthquake, 1973.

15) N. Koiwai, K. Miyawaki, Determination of Earthquake Hazards in Densely Populated Areas and Preventive Measures to be Considered in Urban Planning, Proc . of 5th Joint Meeting, U.S. and Japan Panle on Wind and Seismic Effects, UJNR, Tokyo, May 14-16,

197 3. 16) K. Kanai, Damages of Wooden Houses Caused by Earthquakes, Bulletin of Earthquake

Institute, 29, 1951.

17) Tokyo Metropolis Disaster Prevention Committee, Research for Short Distant Earthquakes,

Vol. 1, 2, 3, 1974 to 1975.

18) Classified Maps of Subground, Land Planning Agency.

19) J. Fukuda, Introduction to the Applied Statistics, Nikkankogyo Shimbunsha.

q Center of Tokyo O Suburbs of Tokyo V Yokohama . Yokosuka A Suburbs of Kanagawa Pre

K Kita-Tajima Eq. • Tango Eq. ^ Tottori Eq.

<u Tonankai Eq. A NankaidoEq.

Fukui Eq. Tokachi-oki Eq. (1952) B Niigata Eq. ~ Ebino Eq. Tokachi-oki F.o

K anto Eq.

f."

•

•l

• <

•

• O •

joT

• °—

c Izu-ok l Eq. (1974) —

;

o

1

Dy, 03 e

e

»

a>

0.0005 s0.001 0.005 0.01 0.05 0.1 0.5 1 5 10 50 100

Fig.

VII-7
Table 1 Multiplier for Depthes of Alluvial Deposits.

-—— District

Depth of Y ~~~~

. Alluvial Deposit

Tokyo Yokohama

40 in > 30 m 3.60 1.17

AO m 8.80 1.23 Table 2 Equivalent Ratio of Razed Houses in Fukui Earthquake

Epicentral Number of Equivalent

Index Town or Village Distance Existing Ratio of Razed

(Km) Houses Houses

(%)

1 —LI 4 .1 4Q , 9J! i Maruoka —1.680 2P. £_lZ —2 ,418 95 j Hvogo 2.0 320 1 00 Higashijugo Li^ 904 99 °h* s h* 568 100

0 T~7

§ ±L2 iii 11 None 780 §J . —rl Natsume 9j_2 ^21 Vi — Nakafujl9hima 6^5 806 » ...... MM?

TT r — 1^ 770 ?J —i— Hamashigo 508 8J) —— Honsyo 5.6 7 60 92

1 4 Morita 5.2 _ 1 , 7 7 3 97 Kanazee —t\ —I'll!

7-| A vara - 8 —T 2° —

i

7

- Kauaal - . 5 1 6 692 99

18 Higashif uj ishima 9 .

0

74 7

_ 100

19 Isobe 6 . 8 880 99 Goryogashima 300 90^ Takahoko 5.6 1,366 . . 96. —*A— Nlshifuj Ishima

Shln — ±1° 2° 24 Uzura 7.5 756 50

25 Yashiro 13.0 911 58 Fukui 10,5 17 ' 805 —— ^1

27 Matsuoka 10. 2 1,501 56 —28 Yosti l zaki LLi2 159 90

29 Kltagata 11.7 844 88

30 Tsuboe 10.

1

703 73

31 Rokujo 14 .

7

563 94

32 Okabo 11 .6 644 91

33 Yoshino 13.7 262 75

34 Daishoji 18.5 3,353 39

35 Shioya 15.4 741 88

36 Mlki 16.

1

431 40

37 Segoe 15.6 115 35

39 Shimomonju 17.0 565 94 40 Sakau 15.9 708 62 41 Tatematsu 17.7 856 2 42 Nlshiago 17.5 448 10 43 16.3 647

44 Nango 18.8 565 30

45 Sandani 15.2 284 3 46 Togo 17.3 813 49

47 Yoshikawa 21.9 591

48 Katayamazu 24.4 1,416 14 49 Klta Nakayama 25.0 828 31 50 Nakagaua 23.3 780 23

51 Katagami 22.3 397 11

52 Yutaka 24.7 486 1 53 Shlzu 21.8 570 5 54 Iburibashi 24.0 491 3 55 Kuritabe 27.0 865 6 56 Klta Shlnlo 25.5 519 2 57 Kunltaka 26.5 947 2 58 Minami Nakayama 26.0 566

59 Yatano 2 . 0 604 1 60 Neagarl 40.0 1,598

61 Mi rial o 42.2 279 2 62 Hlsachune 42.0 375 1 63 Yoshida 41.5 336

VII-8
Ratios of Death and Injured

O "tio of burnt houses is less than 1% A ratio of burnt houses is greater than or equal to 1 %

( ) ratio of burnt houses

Ratios of death

Maruoka 4 170%)

Nlshffuzishima

Kanazu

i 124 72%)

Fukul 1(1352%)

Harue * (5%)

Morlta (243*/!

Harue (5% )

Maruoka

k (70%)

Kanazu

> 124 72%)

Morita a (2 43%)

Fukul ° (1352%) ° „

0

_o° 1° 2_

20 30 40 50 60 70

Equivalent Ratios of Razed Houses

90 100 %

Fig. 2 Relationships between Equivalent Ratio of Razed Houses

and Losses of Lives in Fukui Earthquake3)

VII-9
Mil / @ Nobi Earthquake J // [/ - ruhui Lai 57 —1—

-In

i / -H-

///© Kanto Earthquake // 4 Se pok u Earthquake

! 1 0 0.1 0-2 0.3 0.4 05 06 07 0.8 0.9 Seismic Coefficient (K) Fig. 3 Relationships between

Original Ratio of Razed Houses and Seismic Coefficient by N.Mononobe'

Fig. A

Multiplier 0 S.Omote. S.Miyamura (Dj'V' H)

Depth of Alluvial Deposit (H) (m) Relationships between

Equivalent or Original

Ratio of Razed Houses and Depthes of Alluvial

Deposits

Fig. 5 Equivalent Ratio of Razed Houses and Its Deviation in Fukui

Earthquake.

VII-10
Table 3 Equivalent Ratio of Razed Houses in Ansei-Yedo Earthquake

Group ^^^^ Equivalent Ratio ^~~^\of Razed Houses Equivalent Ratio of Razed Houses Obtained

from Documents^)

Estimated Equivalent

Ratio of Razed Houses

(Chiyoda Ward) 46% 35%

2 V^llUU WclIU^ g 26

3 (Minato Ward) 80 34 (Bunkyo Ward) 68 46

5 (Taito Ward) 51 54

6 (Sumida Ward) 80 100

7 (Koto Ward) 76 84

^b-n (Binominal Probability — Normal Probability)

15 R (Number of Equivalent

Razed Houses)

(a) N = 10, 50 D t = 10 % Fig. 6 Influence of Number of Existing Houses on Binominal and Normal Distributions

VII-11
Pb-n

0.020

(Binominal Probability — Normal Probability)

-o : N = 500

~b : N = 100

25 30 35 40 45 R (Number of Equivalent Razed Houses)

0 02

0 00

(b) N = 100, 500, Di = 10%

-n (Binominal Probability — Normal Probability)

(c) N = 1000, D2

Fig. 6 Influence of Number of Existing Houses on Binominal and Normal Distributions

VII-12
j'

/^ltabashi '

2.5 <

0.8

2.5

8.4

Kita , \36l2 r

», ^-113 Nakano.

. SuriiuniK. _ , , Shimuku

x-s^ » ^Tama ^ 0 I J'

C.V.- Midori

' 0

I n

N ' Asahi '

Setagaya 0.2 0.8

3.1

1.3 u;

•"Shibuya

1 Adachi

18.2 43.3 I00D -

' "v88.E yArakawa ^ Katsushika^

Toshima.'"o !««)»_ / \ 36.2 !

*' ":^Q |^99I »'

/0

's U mida ea- 6

;

I c 3I.3CQ x.65.8/ 752"--^ ^.3/Chiyoda ;-< lOOOKc

O.B'Minato 'VS/Oi'V i 00*0*

0.9

2. 1?

Takatsi^V

Nakahara v.?

Shinagawaf

', 4.0,-; 0.3

'

. v 1.0 . "\'Ohta '-3.9. 0.3

Asahi Seya\ 0

Kohoku

0.2 , s\0.8 •' N

3 6

/'Tsurum ''o^-"^ 0.6

\ cKanagawa 2 71 Hodogaya '^'y- --^Q^

Assumed Epicenter Ward Border

Prefectural Border

Fig. 7 Estimated Equivalent Ratio of Razed Houses at Each Ward in Tokyo, Kawasaki and Yokohama

hi; Depthes of Alluvial Deposit

Ai; Aiea involving Depth of Alluvial Deposit between hi and h ;j .

Fig. Determination of Average Depthes of Alluvial Deposits in k Ward.

VII-13
Fig. 9 Distribution of Eauivalent Ratio of Razed Houses Obtained from Documents

of Ansei-Yedo Earthquake 14)

VII-14
Table A Documents on Damages in Suburbs of Tokyo Caused by Ansei-Yedo

Earthquake

.

Hlgashlohmorl

Kirigaya

Ikeganl

Shlmoikegiunl

Yuklgaya

Nakanobe

Kimonya

Kamimeguro

Shimojagakubo

Karaijagakubo Togoshi

Taniyama

Kamiohsaki

Shimoohsaki

Irukibashi Futsukai

Damaged 15n lfcO, Tota

Totally

WarehouS'

Partly

Damaged Warehouses

Yedoeawa Ward Nakaguki Book

Wounded Ke»r

Sasagasaki Village, Number of Houses; 48, Population; 245, Totally Dam

Totally Damaged ; 11, Half Damaged ; 45

umber of Houses ; 1726, Totally Damaged ; 21, Half Damaged ; 21 chiba Village, Number of Houses ; 130, Totally Damaged ; 1, Half Damaged

Ushiohda Village, Num Half Damaged

ushika Ward

mjchi, Ichiba- Tsurumi Ward.

VTI-15
RELATIONSHIP BETWEEN MODIFIED MERCALLI INTENSITY AND WOOD FRAME DWELLING EARTHQUAKE INSURANCE

Karl V. Steinbrugge

Insurance Services Office, San Francisco, California, U.S.A. and

S. T. Algermissen

U.S. Geological Survey, Denver, Colorado, U.S.A. ABSTRACT

Traditionally, earthquake insurance rates have been based on business judgment tempered by engineering input obtained from analyses of observed earthquake damage. The development of loss simulation techniques has provided important new input for improvement of the basis for earthquake insurance rates. Some important loss simulation results are reviewed. Modified Mercalli intensity can be directly related to dwelling loss and is an important parameter in dwelling loss simulation studies. Careful additional study of existing

dwelling loss data (such as is available for the 1971 San Fernando, California, earthquake) together with well planned damage studies after future earthquakes will lead to greatly

improved loss estimates. Probabilistic loss models should also be developed for dwelling

loss studies and the effects of parameter uncertainties taken into account.

KEYWORDS: Earthquake losses; Earthquake insurance; Loss simulation; Intensity- loss relationships

VII-16
INTRODUCTION

The traditional property insurance method is to establish rate levels based on insurance

loss experience gained over the years. Unfortunately, earthquake insurance loss data do not exist in any meaningful way. In the United States, earthquake insurance was not written on dwellings at the time of the 1906 San Francisco shock. Practically no earthquake insurance was carried by homeowners prior to the 1925 Santa Barbara earthquake, the 1933 Long Beach earthquake, and the 1952 Kern County earthquake. Little was carried in the most heavily shaken areas of the 1971 San Fernando shock. Dwelling loss data from elsewhere in the world do not exist in an insurance loss sense and are usually complicated

by non-relevant construction. Over the years, earthquake insurance rates have been generally based on business

judgment which was tempered by engineering judgment in turn based on observations of damage in earthquakes. There were no alternate methods. In recent years, simulation

studies on dwelling earthquake losses tend to confirm the appropriateness of long established dwelling rates — this newer methodology will be discussed in more detail in the next section of this paper. The judgment procedures which were used for over half a century are adequate for small volumes of business. In recent years, however, there have been an increasing number

of inquiries and statements from Federal and California state authorities regarding the possibility of mandation of earthquake insurance for dwellings. In California alone, dwelling values at risk in a single major event are in terms of many billions of dollars.

This, in turn, has made research economically feasible for dwelling insurance rates as well as a need to examine possible industry capacity problems. It follows that it has become appropriate to develop alternate loss determination methodologies. Methods for estimation of losses to wood frame dwellings are discussed in this paper; however, the techniques discussed here are generally applicable to other classes of construction, if the building units are widely distributed in the affected area. ECONOMIC CONSTRAINTS Any kind of basic earthquake insurance study, whether for the private or public

sector, requires an understanding of monetary loss associated with specific earthquakes. Monetary loss, usually expressed as a percentage of value, must be relatable to (a) earthquake magnitude, (b) nature and duration of ground motion, and (c) a practical classification of buildings according to damage patterns. Historic records of Modified Mercalli

intensities have important functions in these earthquake insurance loss studies since

these intensities may, in many cases, be equated to monetary loss. The detail and refinement of any earthquake loss estimates intended for practical

insurance application will be limited principally by costs. In actuality, the engineering

costs involved in field examining dwellings, identifying them by class or damage type, and recognizing local geologic hazards must be borne by the insurance purchaser. To these

costs must be added overhead and taxes. In the private sector's competitive marketplace,

VII-17
a complex dwelling classification system will substantially increase total costs and, while better results are obtained in an engineering-science sense, normally will make the entire process economically unfeasible. For example, the current class rated earthquake insurance premium (i.e., rate manual basis) for a $50,000 wood frame dwelling in San Francisco or Los Angeles would not exceed $100 annually for the usual case. If individual engineering inspections and analysis were made and periodically updated (say not exceeding 10-year intervals) these engineering costs plus overheads of accounting, filing, etc., would probably substantially exceed $10 per year. Assuming a minimum of $10 per year, this would amount to a 10 percent increase in premium over class rating (i.e., no inspections) — probably enough to lose a competitive edge in the private sector. Unfortunately,

it has yet to be shown that the cost-benefit would be sufficiently favorable to all con- cerned to warrant inspections. Indeed, based on fire insurance experience, specific rating of single family dwellings is quite unwarranted. Alternative to all of the fore- going, cost differentials probably would remain the same even if insurance were issued by the public sector, unless subsidized (eventually being paid by the public through taxes)

.

In past practice, the approach has been to group all single family wood frame dwellings into one class and disregard construction varients, thereby eliminating high cost engineering field inspections and reducing paperwork to that which can be readily processed by the homeowner, his agent, and office clerks. It has been practical to map principal structurally poor ground areas and apply a rate penalty in major communities where insurance may be commonly carried. Practical dwelling sub-classes could include age approximations and story height. Date of construction determined or estimated to the nearest decade is useful since age

reflects, in a general way, earthquake resistive construction practices and the possible amount of deterioration over time. Microzonation has not yet been developed to a state where it can be applied on a uniform and consistent basis from city to city and is relatable

to usable loss figures, and therefore is not part of present insurance rating programs.

In summary, economics dictates that wood frame dwellings be simply classed, with possible

rating varients being based on easily determined factors such as age, story height, geo- graphic location by political boundaries, and location in major structurally poor ground

areas. SIMULATED LOSS TECHNIQUES

A fundamental advance in improving the basis for earthquake insurance rates has been

the development of earthquake loss simulation techniques. Several important dwelling loss

VII-18
simulation studies have been published in recent years1 ' 2 ' 3 ' 4

, in addition to general discussions of the simulation technique 5

. Direct economic losses resulting from earthquakes depend upon: (1) the distribution

and kinds of property at risk, (2) the ground shaking and ground failures of various types associated with earthquakes, and (3) the relationships between (1) and (2) that result in economic loss. In loss simulation studies, the distribution of property at risk is estimated in some manner. The seismicity of the area considered is modeled either deterministically or probabilistically and losses are computed using damage-ground motion and damage-ground failure relationships. As an example, consider the San Francisco area. In the San Francisco area, earthquakes have damage patterns that are related to and can be quantified with respect to earthquake magnitude, length of fault displacement, geographic

damage distribution throughout the affected area by class of construction, and other

similar measurable characteristics. Using the earthquake history of the area, it is possible to simulate the damage and losses for any postulated or known distribution of buildings by construction class for any given earthquake or set of earthquakes. The total

; losses for each class of construction for the entire historic record can be developed by summation. In other words, the total dollar loss for any class of construction and for

I any geographic distribution can be computed for any given earthquake in the San Francisco

area. It then follows that the total loss for all earthquakes listed in the historic

record can be determined and the simulated average annual loss established. Alternately,

a probabilistic simulation model may be constructed, incorporating uncertainties in inventory, seismicity, ground motion, and resulting losses to buildings. Isoseismal maps and

the related intensity data play a key role in simulation studies. Of paramount importance

i is the need to relate intensity to monetary loss. While the concepts are simple, the

1,2, 3,4 computational details can be complex; the cited references , describe the methodology

preferred by the authors. Some important results from simulation studies in California

are given in Table 1. The losses in Table 1 are losses associated with ground shaking and

do not include losses associated with ground failure. Losses to dwellings from ground

Anonymous, "Summary and Recommendations," in Studies in Seismicity and Earthquake

Damage Statistics, 1969, U.S. Coast and Geodetic Survey, 23 (1969).

2K. V. Steinbrugge, F. E. McClure and A. J. Snow, "Appendix A," in Studies in Seismicity

and Earthquake Damage Statistics, 1969, U.S. Coast and Geodetic Survey, 142 (1969).

3 S. T. Algermissen, J. C. Stepp, W. A. Rinehart, and E. P. Arnold, "Appendix B," in Studies in Seismicity and Earthquake Damage Statistics, 1969, U.S. Coast and Geodetic

Survey, 68 (1969)

.

4W. A. Rinehart, S. T. Algermissen, and Mary Gibbons, "Estimation of Earthquake

1 Losses to Single Family Dwellings," U.S. Geol. Survey Open-File Rept. 76-156, 57 plus appendices (1976)

.

5D. C. Friedman, "Computer Simulation of the Earthquake Hazard," Proc. Conf. on

Geologic Hazards and Public Problems, May 27-29, 1969, U.S. Govt. Printing Office, 153-181

(1970)

.

VII-19
shaking have been shown to be far more important than losses from ground failure in the San Francisco Bay area

6

, and this is believed to be true throughout California. Other interesting results have also been obtained for dwellings in California. Figure 1 is a map of California with the state somewhat arbitrarily divided into a northern, middle, and southern portion. Using the known historical seismicity of the state from 1801 to 1967, average dollar losses to dwellings in northern, middle, and southern California were found to be in the ratio of 1.00:0.19:1.25. The distribution of dwellings units taken from the 1960 United States Census (updated to 1967) was used as inventory. Figure 1 also shows seismic risk zones in California as defined by Algermissen

7

. Assuming the same seismicity

and inventory as above, average dollar losses per dwelling in seismic risk zone 3 (Figure

1) were found to be approximately 100 times the losses per dwelling in zone 2. Using the historical earthquake record 1801-1967 in California and the 1967 distribution of dwellings in California, dwelling losses as a function of earthquake magnitude may also be obtained. Figure 2 shows the distribution of dwelling loss with magnitude in California6

. Note that because of the exponential distribution of earthquakes with mag- nitude and the nature of the damage to dwellings, the larger earthquakes in California do not account for the greatest losses. One inherent weakness of all known simulation studies involves the need to accurately know the actual monetary losses to dwellings as a function of each intensity. This loss information should be known by construction component*, by age, by height, and by local surficial geologic characteristics if_ the results are to be transferable to other regions.

It is also necessary to carefully define loss (personal vs. impersonal, building vs. content, etc.) and value (cash vs. replacement for older buildings, etc.). It would be wrong to apply loss figures derived from older rotten foundation houses to new earthquake resistive ones, for example. A specific instance of the detail required, the average loss to painted gypsumboard partitions for MM=VIII should be known as a percentage to dwelling market value (or other value) by building age, height, etc. Techniques exist to answer

these kinds of questions, but all techniques involve varying degrees of judgment based on appropriate experience by engineers, architects, contractors, etc. Obviously, tabulated

actual loss experience data would be better than value judgments. Good progress in simulation studies, then, will come from appropriately gathered

actual loss experience in order to supplement or revise current judgmentally determined

S. T. Algermissen, W. A. Rinehart, and J. C. Stepp, "Techniques for Seismic Zoning: Economic Considerations," Proc. Intl. Conf. on Microzonation for Safer Construction,

Seattle, Washington, Vol. II, 943-956 (1972).

7 S. T. Algermissen, "Seismic Risk Studies in the United States," Proc. 43, World

Conf. on Earthquake Eng., Vol. 1, 14-27 (1969). Construction component is defined as an assembly of materials within a dwelling which

is readily identifiable and has a recognizable damage pattern. Painted gypsum on interior wood stud partitions is one such example.

VTI-20
monetary values. A review of past and current literature has shown practically nothing of substantial value beyond that cited in the references of this paper. POST-EVENT ANALYSIS: SAN FERNANDO 1971 CASE STUDY The first major post-earthquake study which related monetary losses to intensity was conducted after the 1971 San Fernando, California earthquake. The Pacific Fire Rating

Bureau surveyed the damage to approximately 12,000 single family wood frame dwellings

located in the most heavily shaken areas. Their survey form identified the following

items, among others: Location by city block. Age group: (a) pre-1940, (b) 1940-49, and (c) post-1949. Number of stories. Floor construction. Degree of damage to: (a) foundations, (b) wood frame, (c) interior finish by

type of finish, (d) exterior finish by type of finish

(including veneer) , and (e) chimney. Ground disturbance, if any, including faulting. Improved loss data for input to simulation studies is best obtained from information

carefully gathered shortly after an earthquake. When these loss data are related to intensity, then the loss relationships may be applied to isoseismal maps of other earth- quakes or directly to simulated loss studies. Some work in progress is worth reviewing. Intensity-Loss Correlations: Figure 3 is an isoseismal map of the most heavily shaken dwelling areas. This map

was based on a literal reading of the definitions of the Modified Mercalli scale with

respect to dwellings. The base map for Figure 2 (i.e., map without isoseismal lines) is Figure 16 from reference 8; each tract includes a number of city blocks and has boundaries

selected to enhance sample consistency (i.e., similar values, similar age of construction,

etc.). Three different vibrational intensities are shown: VII, VIII, and IX. Additionally, some faulting and related ground breakage areas are, by definition, Intensity X. However, adjacent to and comingled with Intensity X areas are vibrational intensities of

VII, VIII, and IX. In Figure 3, the "average dwelling loss" for each tract may be interpreted as an equivalent of an average intensity for that tract. This suggests correlating Modified

Mercalli intensity in terms of percent loss. A crude but reasonable correlation based on Figure 3 plus extensive personal knowledge of the area is as follows: MM VII: 2 percent to and including 5 percent dwelling loss MM VIII: 6 percent to and including 10 percent dwelling loss MM IX: 11 percent and greater dwelling loss

K. V. Steinbrugge, E. E. Schader, H. C. Bigglestone, and C. A. Weers, "San Fernando

Earthquake, February 9, 1971," Pacific Fire Rating Bureau, 93 plus map (1971). VII-21
For the purposes of this paper, this correlation will be used as a tentative relationship between intensity and dwelling loss. This correlation is restricted to vibrational damage, and therefore excludes the geologic effects in MM VII-X areas. It should be recognized that

the foregoing relationship between dwelling loss and intensity is partially judgmental since there is no other way to relate the subjective wording in the Modified Mercalli definition

to numerical loss values. In any event, it is a rational correlation. A possible improvement in the San Fernando intensity- loss correlations is to re-examine

the basic data for the 12,000 dwellings by sub-dividing the tracts into smaller units. The isoseismal lines may vary somewhat but the correlations are expected to stand. The loss-intensity correlations as given above are not transferable to most other

communities. They are only transferable to communities having comparable amounts of dwelling construction as to story height, age of construction finishes, etc. For example, the dwelling age distribution in the San Fernando study area was: Pre-1940 5.3 percent

1940-49 38.2 percent

Post-1949 56.5 percent

with 94.2 percent of the study area being one story. The identical ground motion striking a community of predominately older two story dwellings would cause much larger losses than those

in San Fernando; thus the intensity-loss correlations for San Fernando would not be transferable to the other community discussed below.

If, however, the damage surveys for 12,000 dwellings were sorted (sub-classed) by age, height, and other factors, then the resulting intensity-loss correlations for each item could

be transferable to many other communities. For an over-simplified example, a California

community consisting of 50 percent 1940-49 one-story dwellings plus 50 percent one-story

post-1949 dwellings (all other construction features identical) would have computable losses

for MM VII, VIII, and IX. In summary, it is possible to synthesize the potential dwelling

loss for MM VII, VIII, and IX for any community if the number and distribution of appropriate

dwelling sub-classes are known and if loss-intensity correlations for these sub-classes are

known. Damage Factors: An important item in detailed simulation involving insurance deductibles is a knowledge

of damage distribution among "identical" dwellings or among "identical construction components" of dwellings. For example, in a tract of 100 identical homes having 4 percent

average dwelling loss, the actual loss distribution might be: Under 1 percent loss 40 homes 6 percent - 10 percent loss 5 homes

1 percent - 3 percent loss 30 homes 11 percent - 20 percent loss 3 homes

4 percent - 5 percent loss 20 homes Over 20 percent loss 2 homes Assume a 5-percent insurance deductible, the actual loss over the deductible is not zero,

i.e., the average loss (4 percent) minus the deductible (5 percent). Thus, average values cannot be used. This introduces the need for a loss distribution function which in previous studies has been termed "damage factor."

3t

pi

ad

tog

VTI-22
Damage factor is defined as the ratio of the number of structures having a specified

degree of loss for a given construction component to the number of structures in the tract

under study. For the 1971 San Fernando earthquake, the damage factors were computed and grouped according to intensities with results as shown in Table 2. This information is transferable to other communities having similar construction component characteristics.

While detailed sophisticated studies on earthquake insurance rate levels and affects

of insurance deductibles on aggregate losses may give a feeling of confidence, in many

ways these studies are no better than their data base. Any studies involving the losses

over time must be based on, or be consistent with, losses over the historic record. The

use of Modified Mercalli intensities and their resulting isoseismal maps becomes inescapable

in retrospective insurance simulation loss studies since, for better or worse, these are

the best available data. Substantially improved loss information from the 1971 San Fernando earthquake plus

that expected to be obtained after future shocks, is expected to greatly improve the quality of the numerical output. Concurrently, simulation studies should continue to be conducted, particularly with the view towards simplification. Probabilistic loss models

should also be developed and compared with loss estimates obtained using historical

seismicity as input.

PROSPECT

VII-23
TABLE 1 CALIFORNIA EARTHQUAKE LOSS SUMMARY

Lose In Dollars (1968 base) (From Table 3 of Reference 3)

San Francisco, 1906

Total affected area Nine Bay Area Counties3 $1,156,370,424

1,013,524,447

$250 Deductible

$ 863,129,283 772,763,546

Per Damaged

Dwelling1

$916

992

Per Dwelling

Unit2

302 870 Long Beach, 1933

Total affected area 597,520,100 412,586,399 750

100 Year Period

Entire state 6,539,698,400 2,766,142,200 385

Nine Bay Area Counties3 2,328,105,900 1,137,936,900 436 Los Angeles and Orange Counties 2,752,299,700 1,090.291,000 377

1,216

1,997 1,285

Dwellings sustaining some damage were used. For the 100 year period, dwellings may be repeatedly damaged.

! All dwellings (damaged and undamaged) within the geographical area considered for the IV isoseismal of the earthquake. 'Marin, Sonoma, Napa, Solano, San Francisco, Santa Clara, Contra Costa, Alameda and San Mateo Counties.

VTI-24
TABLE 2 DAMAGE FACTORS FOR 1971 SAN FERNANDO EARTHQUAKE

From Steinbrugge, et al (1971) data (reference 8)

Damage Factor (%) for MM Intensity Degree of (% of Dwellings Having C ven Degree of Damage)

Construction Component Damage* vn VIII IX Vll-X

Structural — foundation None 98. 7% 88. 4% 6L4% 82. 8%

Slight 0.8% 9.4% 29. 3% 9- 0%

Moderate 0.4% 1. 8% 6.0% 4.7%

Severe 0. 1% 0. 4% 3. 3% 3. 5%

100. 0% 100. 0% 100. 0% 100. 0%

Structural — frame None 94. 0% 67. 6% 39. 9% 72. 8%

Slight 5. 1% 25. 6% 45. 3% 15. 5%

Moderate 0. 5% 4. 9% 8. 7% 7. 1%

Severe 0. 4% 1 9£ 6. 1% 4. 6%

100. 0% 100. 0% 100. 0% 100. 0%

Exterior — stucco None 26.3% 6.7% 2. 9% 31. 9%

Slight 72. 6% 87. 3% 81. 4% 55.7% Moderate 1. o% 5. 1% 10. 3% 9. 0%

Severe 0. 1% 0. 9% 5. 4% 3. 4%

1 00. 0% 1 00. 0% 1 00. 0% 1 00. 0%

Exterior -- wood None 87.1% 55. 6% 35. 7% 63.7%

Slight 8-7% 36. 2% 37. 0% 23. 3%

Moderate 3.7% 4. 2% 15. 6% 7.8%

Severe a 5% 4. 0% 11.7% 5. 25? 100.0% 100. 0% ion. o~ 100. 0%

Exterior ~ other None 90.7% 71. 5% 37.7% 83. 4%

Slight 7. 2% 11. 2% 27. 5% 10. 0% Moderate 2.1% 7. 8% 11. 6% 3. 35; Severe 9. 5% 23. 2% 3.35; 100.0% 100. 0% 100. 0% 100. 05; Chimney (1 chimney) None 84. 9% 58. 5% 29. 9% 66. 7%

Slight 5.1% 22. 4% 39. 1% 13.55=. Moderate 6.8% 6. 6% 8.3% 9. 6%

Severe 2.5% 8. 9% 19. 6% 5. 8=* Total 0. 7% 3. 6% 3.1% 4.45=

1 00. 0% 100. 0% 1 00. 0% 100. 0^

*See Steinbrugge, et al (1971), page 20, for summary definitions (reference 6). Field inspectors used this terminology which, in turn, was related to percent loss.

VTI-25
Figure 1. —Seismic risk zones in California (after Reference" 1) . The hatchured area represents zone 2 and the remainder of the state, zone 3. The heavy black lines divide the state into northern, middle, and southern California as used in this report.

VII-26
(VI 3 6 4.3 5.0 5.6 6.3 7.0 7.6 83

Figure 2. —Estimated dollar losses to wood frame dwellings in California as a function

of maximum Modified Ilercalli intensity (I.) and equivalent mean magnitude (H)

.

Historical earthquakes in California for the period 1801-1967 were used as the seis- micity input. The spatial distribution of dwellings and their characteristics were assumed constant at the 1967 level for the loss simulation study. (Adapted from Reference 6).

VII-27
Figure 3. —Modified llercalli intensities based on observed dwelling damage, San

Fernando, California, earthquake of 1971.

VII-28
Warrants for Retrofitting Highway Bridges

Anatole Longinow

and Ernest Bergmann

IIT Research Institute, Chicago, Illinois

and James D. Cooper Federal Highway Administration, Washington, D.C.

ABSTRACT

A methodology for determining whether or not to seismically retrofit an existing bridge is presented. The method is based on the concept of identifying and comparing

the importance of the bridge to its structural integrity. Criticality factors which

are expressed in terms of bridge classification and its importance to the social, medical, economic, and security needs of a geographical area following a natural di- saster are developed. Structural factors, which estimate a bridge's ability to withstand an earthquake, are determined analytically or by inspection. The criticality

and structural factors are compared to determine if a bridge warrants retrofitting. The method is demonstrated by example.

KEYWORDS: Earthquake; Bridges; Retrofit decision

VIII-1
INTRODUCTION

A bridge is a vital link in any road network. If a disaster occurs, a bridge may

be destroyed or damaged to the extent that it cannot sustain traffic or it blocks an intersecting road. A method is presented to identify and quantify the criticality, or worth, of a bridge in relation to the road, the road network, the community, and the national defense/security system. The criticality is then compared to the capability

of the structure to withstand the disaster and a method is established to determine whether or not retrofit is warranted.

Specifically, the worth of a bridge can be evaluated in terms of:

. Administration/Transportation System Effects . The City, County, State, and Federa

highway organizations classify roads and streets. These classifications are based

on plans which relate the importance of the roads and streets to the normal emergency transportation needs of the community and the nation.

. Social/Survival Effects . Social/survival effects involve the ability of the community to meet its short term emergency needs following a disaster. Normally

the social/survival effects are considered in the administration/transportation

system plans for the roads and streets. There are instances, however, in which

those plans have been dated by changes within or near the community (e.g. , a subdivision was added, a hospital was built, etc.), or the effect on the community was not considered in the original plan.

. Security /Defense Effects . Security /defense effects concern the importance of the bridge in regard to its ability to move troops and equipment to, and within, an area to maintain law and order or to meet a threat to the security of the area,

region, or Nation.

. Economic/Personal Effects . Following a disaster, the recovery process begins. The economic/personal effect relates the community need for the bridge to return

to its predisaster social and business status.

VIII-2
Each measure of worth (e.g. , Social/Survival Effects) has measures of effectiveness

(e.g. , Medical Support) which relate to the need for the bridge. The measures of effectiveness can be grouped, quantified, or qualified to allow an engineer to make a relative

assessment of the worth of the bridge.

The measures of worth for each effect can be interrelated to allow overall assessment

of the need for the bridge. After all bridges within an area of interest are analyzed,

they can be separated into two categories: 1) retrofit is required to enable the bridge

to withstand the earthquake, or 2) retrofit is not required because either the bridge

can withstand the earthquake or the loss of the bridge does not justify the retrofit

expense. Since highway budgets are finite, it is probable that some additional priority

system will be needed to rank the bridges in the first category. The ranking can be achieved by applying a cost-benefit analysis and the retrofit budget can then be allocated

according to this ranking. A discussion of the cost-benefit analysis is not included in

this report. The state-of-the-art of evaluating the worth of the bridge, in terms of the effects identified, does not allow the worth to be graded rigorously enough to permit

a meaningful cost-benefit analysis.

It is noted that a significant amount of research is required to identify and quantify each of the effects which are briefly described above. Therefore, only a brief discussion of the basic methodology, the elements of the methodology, preliminary weightI ing of criticality factors, and sample calculations to illustrate the methodology are

presented.

METHODOLOGY

The procedure for assessing the worth of a bridge is described in this section. It represents a sequential evaluation of worth by considering the resulting effects caused

by the loss of the bridge.

VIII-3
Procedural Flow Diagram

A decision diagram for evaluating whether or not a bridge warrants retrofit is illustrated in Figure 1. Each block or diamond in the procedural flow diagram is an element; the work elements are rectangular and the decision elements are diamonds. The

measures of worth are evaluated in sequence (Elements 1, 3, 5, and 7). The output of each work element is a criticality factor (CF) , rated from 0 through 3, which relates

the worth of the bridge to the particular measure of worth. The higher the criticality

factor the more the bridge is worth to that particular element. As an illustration, the bridge may be evaluated in terms of its worth to the social/survival effects (Element 3). A criticality factor of 3 indicates that the bridge is critical (e.g., it is the only ambulance route); a factor of 2 indicates that the bridge is desired; a factor of 1 indicates that it is convenient; and a factor of 0 indicates that it is expendable.

Decision points (Elements 2, 4, 6, and 10) are inserted between work elements. These decision points act as filters to reduce the effort needed to make a retrofit decision. At each of the first three decision points (Elements 2, 4, and 6), a criticality

factor of 3 (CF=3) indicates that the bridge is of sufficient worth to merit an evaluation. If a criticality factor of less than 3 is selected, the evaluation process is continued until work Element 8 is reached.

In work Element 8, the highest criticality factor of the four measures of worth

(Elements 1, 3, 5, and 7) is selected. Similarly, a structural factor (SF) is selected

(Element 9) which relates the capability of the bridge to survive damage from the disaster.

The structural factors are graded over the same range as the criticality factor. A

structural factor of 3 indicates that the bridge is sound; SF=2 indicates the bridge is probably sound; SF=1 indicates the bridge is probably unsound; and SF=0 indicates that the bridge is unsound.

Next, the criticality and structural factors are compared (CF - SF). If the difference is less than or equal to zero, retrofit of the bridge is not warranted.

VIII-4
n

EVALUATE BRIDGE WORTH

TO ADMINISTRATION /TRANSPORTATION

SYSTEM EFFECTS

3.EVALUATE BRIDGE WORTH TO SOCIAL/ SURVIVAL EFFECTS

5.EVALUATE BRIDGE WORTH TO SECURITY/ DEFENSE EFFECTS

YES.

7.EVALUATE BRIDGE WORTH TO ECONOMIC/

PERSONAL EFFECTS

8.SELECT THE HIGHEST CRITICALITY FACTOR

12. RETROFIT

Figure 1 Bridge Retrofit Warrant Procedural Flow Diagram

VIII-5
If the difference is greater than or equal to 1, then retrofit is warranted. Table I lists the retrofit decision elements. This table, or the criteria illustrated in Figure 1, can be used as the basis for determining whether or not a bridge warrants retrofit.

Table I RETROFIT/NO RETROFIT DECISION TABLE

Criticality

Factor (CF)

S t rue t u 1 Factor (SF) CF - SF Subjective EvaluationRetrof it Decision

3 3 0 Critical/Sound No

3 2 1 Critical/Probably Sound Yes

3 1 2 Critical/Probably Unsound Yes

3 0 3 Critical/Unsound Yes

2 3 -1 Desired/Sound No

2 2 0 Desired/Probably Sound No

2 1 1 Desired/Probably Unsound Yes

2 0 2 Desired/Unsound Yes

1 3 -2 Convenient /Sound No

1 2 -1 Convenient/Probably Sound No

1 1 0 Convenient/Probably Unsound No

1 0 1 Convenient /Unsound Yes

0 3 -3 Expendable/Sound No

0 2 -2 Expendable /Probably Sound No

0 1 -1 Expendable/Probably Unsound No

0 0 0 Expendable /Unsound No

Structural

Factor (SF) Criticality

Factor (CF)

3 = Sound 3 = Critical

2 = Probably Sound 2 = Desired

1 = Probably Unsound 1 = Convenient

0 = Unsound 0 = Expendable

VIII-6
ADMINISTRATION/TRANSPORTATION SYSTEM (ATS) EFFECTS

Highway systems are grouped into a number of different classifications for administrative, planning, and design purposes. At least three different types of systems exist which affect the administration and operation of highways. These are State-countylocal administrative systems, commercial-industrial-residential-recreational systems, and

the Federal-Aid System. However, they all serve to develop a complete integrated highway

system.

The most basic classification system for administration purposes groups highways and streets into two broad classes: systems serving rural areas or connecting urban areas, and streets or highways serving urban areas.

The rural area classification system contains following levels of road classes:

. Interstate,

. Primary (excluding interstate),

. Secondary roads with volume greater than 1,000 vehicles per day

. Secondary roads with traffic less than 1,000 vehicles per day (may be subdivided into 500-1,000, 100-400, under 100),

. Feeder roads (same as secondary roads under 1,000), and

. Tertiary roads.

A quantitatively similar system for urban areas includes:

. Expressways,

. Arterials,

. Collectors, and

. Local roads and streets.

The classification criteria for rural roads are possibly more self-explanatory than the criteria for urban streets. Table II lists the major function of each type of urban

road.

VIII-7
Table II URBAN ROADWAY FUNCTIONS

Syst(

Expressway System (Including

freeways and parkways)

Major Arterial System

Collector Street System

Local Street Systems

Provides for expeditious movement

of large volumes of through traffic between areas and across the city, and not intended to provide landaccess service. Provides for through traffic movement between areas and across the city and direct access to adjoining

property; subject to necessary control

of entrances, exits, and curb use. Provides for traffic movement between

major arterial and local streets, and

direct access to adjoining property. Provides for direct access to adjoining land and for local traffic movement

.

The classifications carry with them a set of suggested minimum design standards which

are in keeping with the importance of the system and are related to the specific trans- portation services the system is to perform. The functions of the rural road system heirarchy are essentially similar to the urban road system.

It is likely that exceptions to the classifications described above occasionally will occur and adjustments in assigned values could be made. Such differences are most likely to be the result of radically altered transportation patterns which have rendered portions of the system obsolete or of recent demands which outstrip the ability of the administrative system to provide an adequate roadway.

More specific information on classification criteria may be found in reference 1.

Criticality Factors

A procedure for determining the criticality factor for ATS effects is outlined

VIII-8
1. Get Federal-Aid Highway Map of region of interest from Federal Highway Administration (FHWA) or from State Department of Transportation.

2. Identify the bridge on the map.

3. Identify the road or street leading to and from the bridge.

4. Identify the road or street (if any) passing under the bridge.

5. Identify the classification of the two roads or streets from

the legend on the map.

6. Select a criticality factor from Table III based on the highest of the two road or street classifications.

Table III CRITICALITY FACTORS FOR ATS EFFECTS

Criticality

Factor (CF) Road or Street

Rural Classification

Urban

3 Interstate Expressway

2 Primary Major Arterial

1 Secondary Collector

0 Tertiary Local

SOCIAL/ SURVIVAL (S/S) EFFECTS

Evaluation of the social/survival effect is based on the need for roadways immediately following a disaster. It is possible to use roadways with degraded levels of performance

as long as continuous routes can be established. When evaluating the S/S effects on a system, the primary requisite should be identifying a system which can facilitate the emergency services listed in Table IV as rapidly as possible.

It is obvious that the evaluation of the worth of a bridge in the social/survival

related context is compounded by the uncertainty of where the disaster might strike and the complexity of the transport network. However, a subjective approach is presented for consideration.

vTII-9
Obtain a detailed map of an area and determine the extent to which the locality has developed disaster plans. Bridges of interest can be readily identified, the population

density estimated, the road network illustrated, and important service facilities (e.g.

,

hospitals, fire stations, etc.) identified on the map. After the local departments in- volved in disaster related operations are interviewed, a disaster scenario can be developed. The significance of the transport network, particularly bridges, can be subjectively established and appropriate criticality factors selected.

Criticality Factors

A procedure for determining the criticality factor for S/S effects is outlined below.

1. Get detailed map of area.

2. Identify bridges of interest on the map.

3. Identify segment of community or area which would be affected by the disaster.

4. Identify hospitals, fire stations, police stations, reservoirs, and power stations.

5. Identify preferred fire and police route by telephone

calls or visits to the respective departments.

6. Identify alternate routes in the event that the bridge

of interest is destroyed.

7. Identify utilities carried by bridge.

8. Select criticality service from Table IV.

9. Record the associated criticality factor.

VIII-10
Table IV CRITICALITY FACTORS FOR S/S EFFECTS

Criticality Criticality

Factor Service Services

(CF) (Subjective Evaluation) Considered

3 Survival Related . Communications

2 Health Related . Energy

1 Comfort Related . Evacuation

0 Insignificant . Medical Support

. Food

. Water

• Law Enforcement

. Fire and Disaster

SECURITY/DEFENSE (S/D) EFFECTS

The 1973 Federal-Aid Highway Act requires that a revised plan for defense highways

be developed by each individual State. The plan will include, as a minimum, the Interstate

and the Federal-Aid primary routes, although some routes may be deleted if this is con- sidered appropriate by the State. The defense highway network will provide connecting

routes to important military installations, industries, and resources not served by the primary routes and will include locations of the following:

. Military bases, national guard installations, supply depots, etc.

. Hospitals, medical supply centers, emergency depots, etc.

. Major airports

. Defense industries including those that could easily or logically

be converted to such

. Refineries, fuel storage and distribution centers

. Major railroad terminals, railheads, docks, truck terminals

. Major power plants including hydroelectric centers at major

dams

VIII-11
. Major communications centers

. Other facilities that the State considers important relating

to national defense or natural disaster emergencies.

Bridges are considered a part of the Security/Defense Road Network data bank and can be classed in terms of critical, noncritical, nonbypassable, and bypassable. Infor- mation on the administration and operation of this data bank can be found in reference 2.

Criticality Factors

A procedure for determining the criticality factor for S/D effects is outlined below.

1. Determine bridge location.

2. Obtain:

. Road Section No.

. Miles from beginning of section

. Bypass Code

. Average Daily Traffic

. Criticality (this information is sometimes available)

3. With criticality and bypass data enter Table V.

4. Record criticality factor.

Table V CRITICALITY FACTORS FOR S/D EFFECTS

Criticality Bridge Criticality/ Factor Alternate Route

(CF)

3 Critical Structure/Nonbypassable

2 Critical Structure/Bypassable

1 Noncritical Structure/Nonbypassable

0 Noncritical Structure/Bypassable

VIII-12
ECONOMIC /PERSONAL (E/P) EFFECTS

The measure of worth of a bridge, during the recovery period, relates to: (1) the amount of traffic which normally passes over the bridge; and (2) the somewhat rare In- stances in which a severed bridge isolates a community from its primary source of business.

The average annual daily traffic, AADT , listed in Table VI, as it relates to the criticality factors, is in general agreement with the road or street classifications

listed in Table III. Some adjustment can be made by the investigator to characterize the importance of a particular bridge within the environment of a particular community. For instance, the AADT over a bridge in a rural environment may be significantly below the

top category (AADT > 80,000), but the bridge, as the only link between two communities,

may have a higher level of importance than would be indicated by the AADT alone. A weighting factor, then, could be applied to the AADT which provides the adjustment. It is important, however, to maintain consistency when applying the weighting factors to each bridge in the geographical area of interest so that the relative importance of each bridge is characterized.

Criticality Factors

A procedure for determining the criticality factor is outlined below.

1. Identify the road and the road section (intersection, town, milepost, etc.) on which the bridge is located.

2. Determine the estimated average annual daily traffic over

the bridge.

3. Enter Table VI at the appropriate level of traffic.

4. Select and record the criticality factor.

i

VIIM3
Table VI CRITICALITY FACTORS FOR E/P EFFECTS

Criticality Average Annual Daily Traffic* (AADT) Factor Over Bridge

(CF)

3 80,000 - Up

2 25,000 - 79,999

1 5,000 - 24,999

0 0 - 4,999

*AADT is the total yearly volume (number of cars passing a particular

point) divided by the number of days in the year.

EARTHQUAKE EFFECTS ON BRIDGES

To better understand seismic effects on structures, seismic damage to bridge abutments,

piers, girders and supports has been documented. Damage typically occurs to bridges having

the following inherent weak details: 1) bearings, 2) substructures, and 3) foundations. Types of failure most often observed are: tilting, settling, sliding, cracking, and

1 overturning of substructures; displacement, cracking, and dislodging of girders at supi ports; shearing or pulling out of anchor bolts and crushing of concrete at supports;

. I; crushing of concrete columns; pulling out of reinforcing bars at column caps or footings; and settlement of approach roads and slippage of wingwalls from abutments.

A study entitled "Seismic Retrofitting of Existing Highway Bridges," reported in the Proceedings of the Sixth Joint UJNR Panel Conference, was conducted to identify and define through structural analyses practical techniques and criteria for retrofitting existing bridges to increase resistance to seismic forces. Simplified mathematical models of seven existing highway bridges representing predominant types of construction were used for developing general retrofit concepts. Each bridge was analyzed for dynamic structural

VIII-14
response when subjected to an analysis earthquake. Failure mechanisms which correspond

closely to observed failure mechanisms described above were identified for each of the bridges, and five preliminary general retrofit concepts were identified, including the following:

1. Superstructure horizontal motion restrainers for hinges, expansion

joints, bearings, etc.

2. Bearing restrainers - vertical.

3. Bearing area widening techniques.

4. Column or pier strengthening.

5. Foundation strengthening.

Several alternatives were developed for each concept.

No simple , straightforward, totally reliable method exists to determine the susceptibility of a bridge to damage. Time, location, and magnitude of an earthquake can- not be predicted. Therefore, mathematical analysis of a large number of bridges in a geo- graphical region becomes impractical because of prohibitive cost and excessive time.

The procedure outlined below represents an initial attempt to quantify a structural

factor (SF) to be used in making the decision on whether or not to retrofit. It relies heavily on engineering judgment and is based solely on observed damage caused by past

earthquakes. Additional thoughts should be given to quantification of the structural

factor.

Structural Factors

The procedure for determining the structural factor is:

1. Determine the structural type.

2. Examine the structure for known vulnerable details.

3. Enter Table VII.

4. Select and record the structural factor.

VIII-15
Table VII

STRUCTURAL FACTORS FOR EXISTING BRIDGES

Structural

Factor Bridge Type - Details

(SF)

0 Simply supported single and multiple

span bridges or Reinforced concrete slab bridges with

two hinges or hangars in any one span

or in adjacent spans.

1 Continuous span bridges with at least

one hinge or Concrete bridges with expansion joints

on one or both sides of inverted T caps.

2 Simply supported spans with continuous, composite slabs or Long, continuous, composite reinforced

concrete slab bridges without expansion

joints in adjacent spans having a hinge

orOne, two, or three span bridges with

high backfilled or bin type abutments.

Single span, rigid frame bridges or Continuous, multiple span bridges

without expansion joints.

The State of California relies solely on recognition of bridge type, identified

in Table VII, to determine whether or not retrofit is warranted. Structures having a structural factor equal to 0 or 1 are considered for retrofit while those having a structural factor equal to 2 or 3 are not considered for retrofit.

VIII-16
Evaluate the two-span, simply supported bridge on U.S. 45 over Des Plainea River, near Chicago, Illinois.

Criticality Factor Based on ATS Effects (Element 1, Figure 1)

1. A map of the area containing the bridge indicates:

. U.S. 45 leads to and from the bridge

. There is no road or street passing under the bridge

. The road crossing the bridge is classed as "major arterial" - the road is a four-lane highway in an urban area

2. From Table III the criticality factor is 2, (CF) = 2.

3. From Figure 1, Element 2, the next point of evaluation is Element 3.

Criticality Factor Based on S/S Effects (Element 3, Figure 1)

1. If the bridge is down, the communities of Hickory Hills and Justice would be isolated from Hodgkins.

2. Alternate routes between those communities would be the toll road

bridge, Wentworth Avenue Bridge, Route 171 Bridge, and the Harlem

Avenue Bridge.

3. The route (U.S. 45) is a preferred police and fire department route; however, the bridge is not critical to emergency services.

4. Hospitals, police, and fire services exist on both sides of the bridge.

5. The bridge is considered insignificant and from Table IV a criticality factor of 0 (CF = 0) is selected.

6. From Figure 1, Element 4, the next point of evaluation is Element 5.

VIII-17
Criticality Factor Based on S/D Effects (Element 5, Figure 1)

1. From the Planning Department of the Illinois Department of Transportation,

Springfield, Illinois, the following data on the bridge was obtained.

. Road Section No. [Kind 2, designation 1, No. 12]

1 Item 679

2

. Miles from beginning of section 0.5

. Bypass Code 6?

. Average annual daily traffic 44, 300

. Criticality NC

2. From Table V, the criticality factor is 1 (noncritical structure/

nonbypassable) , CF = 1.

3. From Figure 1, Element 6, the next point of evaluation is Element 7.

Criticality Factor Based on E/P Effects (Element 7, Figure 1)

1. Average annual daily traffic over bridge is 44,300 (from Regional State Department of Transportation, Planning Department).

2. From Table VI, the criticality factor is 2, (CF = 2).

3. From Figure 1, Element 7, the next point of evaluation is Element 8.

1. Indicates type of road (conformity to Federal code not yet completed).

2. Indicates the location of bridge (State code).

3. Indicates number of miles of bypass required if bridge is out.

VIII-18
Selection of Highest Criticality Factor (Element 8, Figure 1)

Criticality Factor ATS 2 S/S 0 S/D 1 E/P 2

1. The highest criticality factor is 2 (CF = 2).

2. Select structural factor (Element 9), Figure 1.

Structural Factor (SF) Element 9, Figure 1

. From Table VII, the structural factor for the bridge is 0 (SF - 0). The bridge is unsound in the event of an earthquake.

(A separate analytical study, not reported herein, conducted for the bridge verified that the bridge is unsound in the event of a strong earthquake.)

. From Figure 1, the next point of evaluation is Element 10.

Comparison of Highest Criticality Factor with

Structural Factor (Element 10, Figure 1)

. CF - SF = 2 - 0 - 2.

. From Figure 1, the final point in the process is Element 12.

Based on the foregoing methodology, a bridge retrofit is warranted.

CLOSING STATEMENT

A new procedure has been presented which may help administrations decide which, if any, highway bridges situated in seismically active areas should be structurally upgraded

to resist future earthquake induced damage. This represents the first attempt to identify,

VIII-19
prior to the occurrence of an earthquake, what the worth or loss of a bridge means to

a community. It is recognized, however, that the method has shortcomings, particularly when used to evaluate a group of bridges in a given geographic area. Undoubtedly, funds will not be available to upgrade those structures which warrant retrofitting. This will require further analysis, probably a yet-to-be-developed cost-benefit analysis. Also, a structural factor (SF) which is based on current bridge inspection reports should be developed and included in the methodology. And finally, the weighting of criticality

factors (CF) should be examined—perhaps more effects than the four discussed should be considered.

Although the methodology was developed specifically for the purpose of identifying

those existing bridges which warrant seismic retrofitting, it can be modified and used

as a tool to identify those existing structures vulnerable to damage caused by other

types of natural disasters.

VIII-20
REFERENCES

1. Standards for Street Facilities and Services, Procedural Manual 7A, National

Committee on Urban Transportation, Public Administration Service, Chicago,

1958.

2. U.S. Department of Transportation, Federal Highway Administration—Federal-Aid Program Manual, Volume 4, Chapter 7, Section 2, Washington, D.C.

3. Cooper, J. D., Robinson, R. R. , and Longinow, A., "Seismic Retrofitting of Existing Highway Bridges," Proceedings of the Sixth Joint UJNR Panel Conference,

NBS Special Publication 444, U.S. Department of Commerce, Washington, D.C,

April 1976.

4. "Seismic Retrofitting Measures for Highway Bridges," Contract DOT-FH- 11-8847 with

IIT Research Institute, Office of Development, Federal Highway Administration,

Washington, D.C, 1977.

VIII-21
CRITERION ON THE EVALUATION OF SEISMIC SAFETY

OF EXISTING REINFORCED CONCRETE BUILDINGS Kiyoshi Nakano, Masaya Hirosawa and Shin Okamoto Building Reserch Institute, Ministry of Construction ABSTRACT

The outline of "Criterion on the Evaluation of Seismic Safety of Existing Reinforced

Concrete Buildings" by the Ministry of Construction is discussed in detail. The evaluation method consists of three steps with use of various seismic indices.

KEYWORDS: Evaluation method of seismic safety; non-structural elements; reinforced con- crete buildings; structural elements; seismic safety index.

VTII-22
1. INTRODUCTION

This report describes the outline of "Criterion on the Evaluation of Seismic Safety

of Existing Reinforced Concrete Buildings" which was compiled by the joint committee chaired

by Dr. H. Umemura, Professor of Tokyo University, with the commission by the Ministry of Construction, Japanese Government. The buildings which this criterion covers are low-and medium-rise reinforced concrete

buildings constructed by ordinary construction methods, and items for evaluation are not only super- structure itself but also non-structural elements such as exterior finish

elements. Further, these evaluation methodologies consist of three steps, from simple first screening to complicated third screening.

The result of evaluation is expressed by the continuous numerical values but the result shall be judged by the engineer who uses this criterion considering individual and social impacts caused by presumed damages. Moreover, the results by this criterion on damaged and un-damaged buildings in the Tokachi-oki earthquake (1968) are shown as a reference for the judgment.

2. THE CONSTITUTION OF THE SYNTHESIS INDEX REPRESENTING SEISMIC SAFETY

2.1 Definition of Seismic Index The seismic safety of a building is represented in the following two numerical indexes

and the larger value means the higher seismic safety. Seismic Index of Structure: Ig Seismic Index of Non-Structural Elements: I — — N

2.2 Constitution of I^Index

I g-index shall be calculated by Eq. 1 for both the longitudinal and ridge directions

at each floor of the building under consideration.

However, the following G-Index, T-Index and S D~Index in the first screening are the constants to a particular building independent of the floor location and direction.

I = E„ x G x S x T (1) s 0 D where

,

E

Q = Seismic Sub Index of Basic Structural Performance

G = Seismic Sub Index of Ground Motion

Sp = Seismic Sub Index of Structural Design

T = Seismic Sub Index of Time-Depended Deterioration

2.3 Calculation of Seismic Index of Structure I s

1) General

In order to calculate the value of I g-Index, any one of the first, the second and the third evaluation method may be used. However, the value of G-Index may be taken as 1.0

for all cases.

2) The First Evaluation Method

E

Q-Index is calculated from the horizontal strength of a building, based on the sum

of the horizontal area of columns and walls and on their assumed unit strength.

VIII-23
and section of the building. T-Index is evaluated, based on the age of the building and the observed results of the distortion and cracks in columns and walls.

3) The Second Evaluation Method

E

Q-Index is calculated from the ultimate horizontal strength, failure modes and duc- tility of columns and walls with the assumption of infinitely strong floor system.

SD~Index is evaluated based on the results of calculated horizontal rigidity distribut:

and vertical mass and rigidity distribution in addition to the results of the check points

in the first evaluation method. T-Index is evaluated from the investigated quantitative results on structural crackings, distortion, changes in quality and deterioration of the building.

4) The Third Evaluation Method

E

Q-Index is calculated from the ultimate horizontal strength, failure modes and flexi- bility of columns and walls, based on failure mechanism of frames with consideration of strength of beams and overturning of walls.

3. DETERMINATION AND CONSTITUTION OF SEISMIC SUB INDEX

OF BASIC STRUCTURAL PERFORMANCE, E

Q 3.1 General

E

Q-Index in each evaluation method is expressed as function of sub-index of strength

C (bearing capacity of the building) and of sub-index of ductility F (deformation ability

of the building) and so on. 3.2 The First Evaluation Method

1) General After dividing the vertical members of the frame into the following three categories,

0follows:

Eq.

a. column: column with clear height (hQ

) equal to or shorter than the depth

of column (D)

.

b. extremely short column: column with h

Q equal to or shorter than twice D.

c. wall: reinforced concrete wall with or without surrounding framing members.

2 ) Eg-index of buildings without the extremely short columns

E. = — (C + a • C ) x F (2) where

,

0 n+i

= total number of stories of the building

= number of stories of the floor under inspection counted from the first story

VIII-24
= C-index of wall, calculated by Eq. 6 C

c = C-index of column, calculated by Eq. 7 = (Sum of the lateral shear forces beared by columns in the displacement at the ultimate strength of walls)/ (Sum of the ultimate strength of the columns); may

be taken as equal to 0.7, except in case of = 0 where may be taken as equal to 1.0. F^ = F-index of walls; may be taken as equal to 1.0.

3) E

Q -index of buildings with extremely short columns

E

Q -index of buildings with extremely short columns shall be equal to the larger of

two following values of E

Q

; E

Q calculated from Eq. 2 neglecting the extremely short columns

and E

Q calculated by Eq. 3. However, in case that the extremely short columns are the secondary seismic elements

defined below, E

Q -index shall be computed by Eq. 3. The structural elements whose vertical

loads can not be sustained by surrounding structural elements such as beams, walls, and

columns, after having reached to their maximum capacity under lateral seismic loads, are defined as the secondary seismic elements.

E. = (C + a. • C + a, • C ) x F (3) 0 n+i sc 2 w 3 c sc where

,

C sc

= C-index of extremely short columns, calculated by Eq. 8. C^ = C-index of walls, calculated by Eq. 6 C

c = C-index of columns not including extremely short columns, calculated by Eq. 7.

Ct 2 = (Sum of the lateral shear forces beared by walls in the displacement at the ultimate strength of extremely short columns) / (Sum of the ultimate strength of

the walls); may be taken as 0.7. a ^ = (Sum of the lateral shear forces beared by the ordinary columns in the displace- ment at the ultimate strength of the extremely short columns) / (Sum of the ultimate

strength of the ordinary columns); may be taken as 0.5. F^

c = F-index of extremely short columns; may be taken as 0.8.

3.3 The Second Evaluation Method

1) General Vertical structural members, that is, columns and walls, are classified into the five following categories: a) flexural columns, b) flexural walls, c) shear columns, d) shear

walls, and e) extremely brittle columns. These classifications are made by comparing the load carrying capacity of each member

for flexure with that for shear. Shear columns may be classified as extremely brittle

columns, provided that its clear height is less than twice its depth.

The ultimate strength of each member subjected to flexure and shear may be determined

in accordance with Eqs. (9) to (14) in Section 4.2. The F-index of flexural columns and flexural walls may be determined by Eqs. (20) to

(23). The F-index of the other members is fixed to the following values:

VTII-25
F 1.0 for shear columns and shear walls

F = 0.8 for extremely brittle columns

Having determined the F-values of all columns and walls , they are grouped into three or less, and then C- index of i group may be obtained as follows: = (Sum of the ultimate

strength of the members belonging to i-group)/£W (= total weight of the portion above the floor under inspection) . E

Q-index will thus be obtained in accordance with the following articles 2) and 3)

.

2) E

Q-index of buildings without extremely brittle columns

E

Q-index of buildings without extremely brittle columns may be determined as the larger

of two values computed by Eq. 4 and by Eq. 5. However, in the case that the shear columns

are classified as the secondary seismic elements, E -value should be determined by Eq. 5.

= C-index of the members classified into the 1st group, which have relatively low value of F-index

= C-index of the members classified into the 2nd group, which have medium value of F-index

C

3 = C-index of the members classified into the 3rd group, which have relatively high

value of F-index.

F^ = F-index of 1st group, taken as the least value of F-indexes of the members classified into the 1st group

F

2 = F-index of the 2nd group, taken as the least value of the F-indexes of the members classified into the 2nd group

F

3 = F-index of the 3rd group, taken as the least value of the F-indexes of the members classified into the 3rd group.

E

0 = Si (C1 + V2 + W X F

l

(5) where

,

a

2 = (The sum of the lateral shear forces beared by the 2nd group members, corresponding to the displacement at the ultimate strength of the 1st group members) / (The sum of the ultimate strength of the 2nd group members) ; may be taken as the values shown in Table 1. = (The sum of the lateral shear forces beared by the 3rd group members, corresponding to the displacement at the ultimate strength of the 1st group members) / (The sum of the ultimate strength of the 3rd group members) ; may be taken as the values shown in Table 1.

3) E

Q-index of the buildings with extremely brittle columns

E

Q-index of the buildings with extremely brittle columns should be the highest of the following three values:

a) The value computed by Eq. 4, neglecting the extremely brittle columns,

b) The value computed by Eq. 5, neglecting the extremely short columns, and

(4)

where,

VTII-26
c) The value computed by Eq. 5 considering the extremely short column as the first

group. However, when the extremely short columns are the secondary seismic elements, E

Q-values

should be computed based on the condition c)

.

3.4 The Third Evaluation Method

1) General

The lateral load carrying capacity and failure mode of vertical structural members may

be determined from consdieration of the flexure or shear failure of beams and overturning

I capacity of walls. The vertical structural members are then calssified into the following

eight categories: a) flexural columns, b) flexural walls, c) shear columns, d) shear walls,

e) extremely brittle columns, f) beam yield type columns (columns whose lateral load carrying capacity depends on the flexural yield of beams) , g) beam shear failure type columns (columns of which lateral load carrying capacity depends on the shear failure of

beams) , and h) overturning type walls (walls of which lateral load carrying capacity

depends on their overturning capacity)

.

F- index for the members classified into a) and b) may be determined by the equations

shown in Section 5 and for others the F-index may be fixed to the following values.

F = 1.0 for shear columns and walls

F = 0.8 for extremely short columns

F = 3.0 for beam yield type columns

F = 1.5 for beam shear failure type columns

F = 2.0 for overturning type walls

2) Grouping of vertical structural members and determination of E -index

The grouping of vertical structural members in accordance with their F-index and the determination of E -index may be performed as in the 2nd evaluation method.

4.1 First Evaluation Method

The C-index for the 1st evaluation method at a floor may be determined by the following equations using the cross sectional areas of columns and walls at the floor and the assumed ultimate strength in terms of mean shear stress.

CALCULATION OF STRENGTH INDEX, C, AND DETERMINATION OF FAILURE MODE

C = (T , 'At w w*EA

f wl wl

+ Tw2AlW2 Tw3

• A ,) w3

(6)

T A

sc

(7)

C

T A

sc

(8) sc

VIII-27
where

,

C = C-index of walls w

C = C-index of columns

c Csc

= C-index of extremely short columns

T

1 = Mean shear stress of walls at their strength, with surrounding columns at both

2 ends. It may be assumed as equal to 30 kg/cm

Tw2

= Mean shear stress of walls at their strength, with columns at one end. It may

be assumed as equal to 20 kg/cm

2 T = Mean shear stress of walls at their strength, without columns. It may be

w3

2 assumed as equal to 10 kg/cm

T = Mean shear stress of columns at their strength. It may be assumed as equal to

C

2 2 10 kg/cm , except in the case of 7 kg/cm for columns whose h

Q/D are equal to or exceed 6.0. T^^ = Mean shear stress of extremely short columns at their strength. It may be assumed as equal to 15 kg/cm

2 A n = Sum of the horizontal sectional area of walls, with surrounding columns at both

2 ends, which are effective in the direction under inspection at the floor (cm ) A

w2

= Sum of the horizontal sectional area of walls with surrounding column at one

end, which are effective in the direction under inspection at the floor (cm

2

) A = Sum of the horizontal sectional area of walls without surrounding columns, which

2 are effective in the direction under inspection at the floor (cm ) A_ = Sum of the horizontal sectional area of columns at the floor in which the

Sri and A

w2 A = The sum of horizontal sectional area of extremely short columns at the floor (cm ) SC

2 A

f = Total floor area above the floor under inspection (cm ) w = [Total weight (including dead and live load) above the floor under inspection]/

EA

f 4.2 Second Evaluation Method

1) The strength index, C for the second evaluation method is obtained from the ultimate strength of the vertical structural members based on the assumption of the infinitively stiff horizontal diaphram.

2) The flexural strength of section of the members, may be calculated from the following equations.

a) The flexural strength of section of rectangular columns, may be obtained

from Eq. 9

VIII-28
For Nmax. >N>0.4 bDF

M = {0.8 a • 0 * D + 0.12b • D

2

• F }( NmaX-=-g ) u t y c Nmax - 0.4bDF For 0.4 bDF >N>0

M = {0.8 a.

For 0>N>Nmin.

Ty

• D + 0.5N D (1 -^r »

where

,

Nmax. = Ultimate strength of columns under axial compression = b'D-F + a '0 (kg) g y Nmin. = Ultimate strength of columns under axial tension = -a .0 (kg) N = Axial load of column (kg) a = Area of tension reinforcement of column (cm

2

) 2 a = Gross area of longitudinal reinforcement of column (cm ) gb = Width of column (cm) D = Depth of column (cm) Yield strength of reinforcement (kg/cm ) Compressive strength of concrete (kg/cm

2

) b) The ultimate flexural strength of section of a column with wing walls at both

sides may be obtained from Eq. 10

For N<{0.5 a (0.9 + $) - 13p ) b*D*F — e t c 0.5N-D {l + 2$ - a -a „ N

For N>{0.5 Cte (0.9 + 6) - 13p

fc } b'D'F^ M

y may be calculated also by Eq. 10 supposing

a = A/l , e wb

A = total sectional area

1 = total horizontal length measured out-to-out of wing wall w

B = (Length of compression zone)/D

The other notations are the same as in Eq. 9.

c) Ultimate flexural strength of walls with surrounding columns at both ends may be calculated by Eq. 11

VIII-29
(11)

where,

Area of longitudinal reinforcement of tension side column

b = Width of compression side column (cm) 1 = Length of wall, measured center to center of column, w

3) The ultimate shear strength of section of members may be determined by the following equations

a) Utlimate shear strength of section of rectangular columns may be obtained

by Eq. 12. 0.053p

°" 23 (180+F ) , Q = { *

a — ° + 2.7 /p • a + O.la } xbxj (12) *su M/Q-d +0.12 ^w s wy o

J

1<M/Q*d<3

where

,

Pt = Tensile reinforcement rario (%) p = Shear reinforcement ratio. When p exceeds 0.012, p should be taken as w w *w

equal to 0.012.

O = Yield strength of shear reinforcement (kg/cm^)

s wy

2 2 0 = Axial stress of column (kg/cm ) . When O exceed 80 kg/cm , a should be

o 2 ° ° taken as equal to 80 kg/cm

d = Effective depth of column, = (D-5) cm M/Q = May be taken as equal to h

Q

/2, where, h

Q

is clear height of column.

b) The ultimate shear strength of section of a column with wing walls may be calculated by Eq. 13.

1 t(1w"D) Q = 0.8 (t—) EA + 0.5 {p * 0 + p "a —r—-—} b-D+0.1N (13) *su c h w wy s sy b*D

o where,

p = Shear reinforcement ratio of column W

2 a = Yield strength of shear reinforcement of column (kg/cm ) wy

p = Lateral reinforcement ratio of wing wall, = a /t's

s

2 Where a = Sectional area of a pair of lateral reinforcement of wing wall (cm )

VTII-30
S = Spacing of lateral reinforcements (cm) t = Depth of wing wall

2 0gy

= Yield strength of lateral reinforcement of wing wall (kg/cm ) N = Axial force of column (kg) hQ

= Clear depth of column (cm)

c) The ultimate shear strength of section walls with surrounding columns at both

ends may be obtained by Eq. 14. 0.053p

t

°' 23 (180+F ) . 2su " { M/(Q-1) + 0.12

+ 2 - 7 ^we'sV + °- l0o

} x be ^ (14)

where

,

be = Equivalent depth of wall, = A/1 (cm) A = Sum of sectional area of wall and column (cm

2

) 1 = End-to-end distance between columns

p = 100 x a./(be-l) (%) 2 a

fc = Total sectional areas of axial reinforcement of tension side column (cm ) p = Equivalent lateral reinforcement ratio of wall, = a /(be'S)

2 Where, a = Sectional areas of lateral reinforcement of wall (cm ) w

S = Spacing of lateral reinforcements (cm)

2 a = Yield strength of above reinforcement (kg/cm ) s wy

0

q

= EN/(be'l) (kg/cm ) Where EN represents the total axial force sustained by wall and columns

j = May be taken as 1 or 0.8 x 1 w

In the case of walls with opening, the ultimate strength of section may be obtained by multiplying the following reduction factors, to the strength obtained by Eq. 14.

T = 1 - (Equivalent opening peripheral ratio) (15)

where

,

(Equivalent opening peripheral ratio) h = Story height

_ /Area of opening

h x 1

4) Determination of the failure mechanism and lateral strength of each member.

a) In the case of columns, lateral strength can be taken as the smaller one out

VIII-31
Determination of the failure mechanism and the lateral strength of a column at the mechanism can be performed as follows.

M + M , c uu c ub *****

c2Mu = h < 16 >

h

Q

= Clear height of column

b) In case of walls, the shear force at the ultimate flexural strength of sec- tion of a member, w

QMu

may be obtained by Eq. 17. Then the failure mechanism and the lateral load carrying capacity at the mechanism may be determined as follows:

at the mechanism, Q may be taken as Q

c u

J w^

hw

= Total height of the wall measured from the floor under consideration

0 =2 (when the top portion of vertically continuous wall is under consideration, 9 may be taken as equal to 1.0.)

4.3 Third Evaluation Method

1) General

The lateral load carrying capacity of each vertical structural elements may be obtained, based on the following three failure mechanisms in addition to the mechanisms

considered in the 2nd evaluation method; a) beam yield type columns, b) beam shear type columns and c) overturning type walls.

2) Flexural and shear strength of beam sections

The flexural and shear strength of beam sections may be computed by Eq. 10 and Eq. 11, respectively, substituting N = 0<or 0" = 0 into these equations. Here, the effect of the

VTII-32
reinforcements in slabs, may be considered for the computation of the flexural strength of beams. For the computation of the flexural strength of beam sections the following simple equation is also applicable.

(18)

t Area of tensile reinforcement

0^ = Yield strength of tensile reinforcement

d = Effective depth of a beam cross-section

3) Determination of the lateral load carrying capacity of vertical memebers and the failure mode of the members .

a) Columns

Columns are classified into the following four types; flexural failure column, shear failure column, beam yield type column and beam shear type column. Based on the ultimate strength of columns and beams, the maximum end moments of all members at all nodal points are determined. Comparing the sum of the end moments of beams with that

of columns at each nodal point, the ultimate moment distribution of columns is determined by the nodal limit analysis. Considering the above moment distribution,

may be computed by Eq. 19.

height of column) (19)

b) Walls Walls are idealized by cutting off from the other framing members at the mid-span

of connecting beams. The lateral load carrying capacity of the idealized walls may be taken as the least of the three following lateral loads determined under inverse triangular distribution of lateral loads; resultant lateral loads acting above the floor under inspection (at which the walls reach their flexural yield strength) , shear strength or overturning capacity. The failure mode of walls corresponds to the mech- anism on which the determination of their lateral load carrying capacity is based.

5. DETERMINATION OF SUB- INDEX OF DUCTILITY F

5.1 General

The sub-index of ductility of members except flexural columns and flexural walls is fixed to the constant values shown in Article 1) of 3.4. F-index of flexural columns and flexural walls may be determined as follows.

5.2 Determination of F-index of Flexural Columns and Flexural Walls.

a) F-index of flexural columns may be obtained by equation 20, based on the ductility factor of the columns determined by Eq. 22 in 5.3.

VIII-33
b) F-index of flexural walls is obtained by Eq. 21 using their shear strength,

= F = 1.0

(21) when Q / Q > 1.4 =F=2.0 w su w u =

^ when 1.3 < Q / Q < 1.4 = F = -12.0 + 10 x w su w u Qw

xu 5.3 Determination of Ductility Factor y of Flexural Columns. Ductility factor y of flexural columns may be computed by Eq. 22. However, F should

be 1.0 provided that any one of the conditins described in Eq. 23 are corresponded.

(22)

here 1 £ y < 5 Q where, y = 10 ( , 5U

- 1) o Q

c u

k = 2.0 (k n may be zero provided that shear reinforcement spacing is less than

eight times the diameter of longitudinal reinforcement.)

T k

2 = 30 (~ - 0.1) > 0

b = Width of column

j = Distance between compressive resultant forces and tensile resultant forces.

F^ = Compressive strength of concrete Conditions in which F should be 1.0; Ns/bDF^ > 0.4, (N^ corresponds to axial forces of columns at their failure mechanism)

(23)

)

.

h /D <^ 2.0, where h is clear height of columns.

VTII-34
6. 6.1 General

This index becomes effective only in combination usage with EQ-index for evaluating

the effect of the structural profile and the distribution of mass or stiffness for the seismic safety of buildings,

building in the 1st screeni direction in 2nd screening.

6.2 Judgment Items

a) For the 1st screening the following items may be examined. Items concerning plan profile; i) irregularlity of plan, ii) length-width ratio

in plan, iii) clearance of expansion joints, iv) presence of open hall and v) other

special profiles in plan.

Items concerning elevation profile; vi) presence of underground stories, vii) uni- formity of story height, viii) presence of piles, and ix) other special profiles in section.

b) In the second screening the following items may be examined in addition to the items considered in the 1st screening.

i) Eccentricity of the center of gravity and the center of rigidity in plan,

ii) Weight-stiffness ratio at a story to that at the story directly above.

The influence factor, which represents the degree of influence of each judgment item

may be computed using the grading factor, G^, which varies 1.0 to 0.8 in accordance with

| the situations of each item and the adjusting factor for the range of the influence of each

item, R^. Then, the S^- index is obtained by the mutual multiplication of C

i as shown in

Eq. 24.

(24) C

i = 1 - (1 - GJ x R±

7. SEISMIC SUB-INDEX OF TIME DEPENDED DETERIORATION

7.1 General

This index aims to evaluate the effect of the structural defects, such as cracks, excessive deflections , superannuations, and so on for the seismic safety of the buildings.

Only single value for a building is determined in both the 1st and 2nd evaluation methods, respectively.

7.2 First Evaluation Method

T- index for the 1st evaluation method may be taken as the minimum value of reduction

factors determined by checking the prepared questionnaire in accordance with the degree

of the structural defects as cracks, deflections , superannuations , and so on observed in structural members.

VIII-35
7.3 Second Evaluation Method

T- index for the 2nd evaluation method may be calculated by Eg. 25, where p^ and p^

Eq. 25 are the sum of the demerit points concerning about structural cracks and deflecti. and deterioration and superannuations, respectively. These demerit points are obtained ] checking the prepared guestionnaire at each story and T-factor is taken as the average o: T\ determined at i-story.

. + T )/N

n

(25)

where

,

T\ = T-index of i-story

N = Number of stories examined

p^^ = The sum of the demerit points at i-story concerning about structural cracks

and deflections.

p^_^ = The sum of the demerit points at i-story concerning about deterioration and superannuation

.

In the third evaluation method, the same value of T-index as the value determined in the second evaluation method may be used.

8 «1 General

This index aims to evaluate the dangerousness in earthquakes caused by the collapse

or the fall of non-structural elements such as the finish of exterior walls. For this

index, screening methods from 1st to 3rd are also applied. I^-index is determined for every wall surface in every story.

8.2 Outline of Determination of I -index

N The constitution of the sub-indexes used for determination of I -index is shown on N

the following page. The values of sub-indexes, g

s

, gN , g^, g , e and c are given in tables. Sub-index

f and t are given as matrix of g

g and gN and of g

H and gy

, respectively. The other

sub-indexes are calculated by given equations.

26. w a IB-WH-L. {f+(l-f)-t} • {0.5 + ^} (Ze-OL

1 = ! ! 1

VIII-36
Seismic index

of non-structural { elements, I N

Sub-index of structural

type (B)

Sub index of flexibility (f)

Grade of flexibility

of structures (gs )

Grade of flexibility

of non-structural

elements (g^) Sub-index of the actual condition (t) Grade of the trouble hystory of non-structural elements (g„)H

rade of years passed (gy

) Sub-index of wall surface area (w) (Length of wall; Li, height of wall; hi standard story height; hs)

Sub-index of degree

of influence (H) Sub-index of environments (e,

Sub-index of the arrest of falls (c,

9. SEVERAL FEATURES OF CRITERION

9.1 Adoption of Seismic Index of Non-structural Elements

The seismic safety of buildings should be examined not only from a viewpoint of the safety of structural elements from collapse, but also from the viewpoint of the safety

of non- structural elements such as finishing materials of exterior walls directly facing

to streets from their fall. Because the reinforced concrete buildings in Japan have relatively large lateral strengths, the structures themselves seldom fall instantaneously

even under the strong earthquake motions. Actually, the experience of past earthquake

damages indicates that most buildings survived from catastrophic destructions. Even in the cases of buildings which were unfortunately destroyed and fell, the residents of the buildings had enought time to escape from the buildings.

Therefore, it becomes important to protect people from injury due to the fall of the non-structural elements such as finishing materials of exterior walls. Though there is not sufficient experimental and empirical information concerning the performance of non-structural elements under earthquake loads, the safety evaluation of non- structural elements by I N~index is attempted in this criterion taking into account the relative flexibility of structure itself and non-structual elements.

VTII-37
9.2 Adoption of Screening Method

The structural safety evaluation considered in this criterion consists of a sequence of

steps from 1st to 3rd evaluation. This procedure is repeated in successive cycles, the assumptions and details of the calculations being refined in each successive cycle when nec- essary for a reliable estimate of structural performance. The repetitive procedure is called

"Screening," and is believed to be the fastest and the most practical method for reasonably evaluating the structural adequacy of a large number of buildings subjected to strong earthquake motions.

9.3 Evaluation and Judgment of Seismic Safety

The evaluation of the seismic safety in a broad sense is taken more precisely in the following senses:

1) Evaluation of seismic safety; to express the seismic safety of structures with con- tinuous quantity such as seismic index proposed in this criterion.

2) Judgment of seismic safety; to judge the adequacy of buildings for seismic safety taking into account various conditions such as their use, their importance and their age, based on the seismic index obtained by the evaluation seismic safety. This criterion aims to evaluate the seismic safety as defined above and the judgment

is left to the engineers who use this criterion. The results by this criterion applied on damaged and un-damaged buildings in the Tokachioki earthquake of 1968 are summarized in the appendix of this criterion. These results will be helpful in performing the judgment of the seismic safety.

9.4 Adoption of Seismic Sub-indexes, S^, T and G to Seismic Index, I g Seismic sub-indexes, S^ and T which represent the quality of structural design and time depended deterioration, respectively, are taken into account in this criterion as the sub- indexes of synthesis index representing seismic safety, I g

, in addition to the seismic sub- index of basic structural performance E

Q which is related to the lateral load carrying ca- pacity and the deformation capacity of structures. In this criterion, the quantitative eval- uation of such sub-indexes are attempted using a check list system. Moreover, the sesimic

sub- index representing the intensity of input ground motions to the base of a building, which

depends on the seismicity of its location and on the relationship between its dynamic char- acteristics and the type of soil, is defined as G in this criterion. The standard value of

this sub-index is taken as equal to 1.0 and decreasing value with increase of the earthquake danger in the location is assumed. However, G-index is fixed to 1.0 in this criterion

because of the difficulty of the evaluation of the earthquake danger at present.

9.5 Consideration of Seismic Sub-index of Ductility, F to Seismic Sub-index of Basic Structural Performance, E . o

In the basic sub-index representing the earthquake resistant ability of structures, E

q

, not only strength but also deformation capacity are considered as follows.

1) Critical conditions defined by the failure of brittle members. The lateral load carrying capacity of a building depends on the failure of brittle

structural members, provided thatthe building consists of structural members with various deformation capacity, and, therefore, is not always the sum of the ultimate lateral strength

of every structural member. In general, critical displacements at the ultimate strength

VIII-38
of brittle structural members are small because of their high stiffness, and then the ductile members which have relatively low stiffness might not reach their ultimate strength

at the critical displacements.

Moreover, the brittle members show significant reduction of load carrying capacity

after they reach their ultimate strength. Therefore, the failure of brittle structural members becomes one of critical conditions

for evaluating the seismic performance of buildings. In this criterion, such critical conditions are expressed in Eqs. 2, 3 and 5. In these equations, a means one of the reduction factors of the strength for ductile members considering the compatibility of the displacement at the failure of brittle members. The value of a which is taken as 0.5 to

0.7 in these equations is determined empirically, based on many test results on the yield

displacements

.

On the other hand, the failure of brittle members causes often the local collapse

of buildings because they become ineffective in sustaining vertical loads. Therefore, in this criterion, the failure of brittle memebrs is considered to be one of the critical conditions on the safety of buildings even if the lateral load carrying capacity of the buildings as a whole is not affected by it. Such a critical condition is considered in

Eq. 3 or 5.

2) Critical condition of buildings consisted of the structural members which have various deformation capacity.

It is not always easy to evaluate the seismic safety of the buildings consisted of the structural members which have various deformation capacities. In the case of a building

consisted of structural members which have nearly the same deformation capacities, it is possible to evaluate its earthquake resistance, based on the assumption of the equal energy

concept proposed by Blume, et al., which implies that the potential energy stored by the elastic system at maximum deflection is the same as that stored by the elasto-plastic

system at maximum deflection. In the case of a building consisted of, for example, some brittle shear walls and ductile columns, its seismic resistance abilitiy changes with change

of the ratio of the load carrying capacity of walls to that of columns or change of deformation capacity of framing members. For evaluating the seismic safety of such type

of structures, Eq. 4 is proposed, based on many non-linear dynamic analyses of combined

structures of brittle shear walls and ductile frames responding to ground motions recorded

during severe earthquakes.

3) Relation between required ductility factor of non-linear system and seismic

sub- index, F. Non-linear dynamic analyses of structures responding to earthquake motions have shown

that the required ductility factor of the elasto-plastic systems whose yield shear factor

is Cv may be estimated from the elastic spectral response acceleration, C^. Blume, et al.,

for example, have shown that the required ductility factor of reinforced concrete structures

is given by the following equation

VIII-39
c

E/c

y

= /Tv-^T

Yield shear factor of elasto-plastic system. Spectral response acceleration of elastic system. Required ductility factor of elasto-plastic system.

This equation is based on the equal energy concept as mentioned in Article 2) . Com- paring the above equation with the results obtained from dynamic analyses on single degree

of freedom systems with elasto-plastic and degrading stiffness load-deflection relationship,

it is evident that the above equation may be an upper bound. For determining the seismic sub-index, F, given in Eq. 20, the same approach as mentioned above has been applied, based on the non-linear dynamic analyses responding to the ground motions recorded during severe earthquakes carried out on the single degree of freedom oscillator having degrading tri-linear load-deflection relationship which seemed to be a typical load-deflection relationship of reinforced concrete structures.

The reciprocal of the seismic sub-index, 1/F, in this criterion is one of the upper bound for the ratio of the yield shear factor of degrading tri-linear system to the elastic

spectral response acceleration.

4) Determining the required ductility factor of structural members of multistory

frames from the response ductility factor obtained from non-linear dynamic analyses of one mass system. The ductility demand obtained from the non-linear dynamic response analyses on one mass system cannot be claimed to give an accurate assessment of the ductility demand of each structural member of the multistory frame responding to non-linearly strong earthquakes. In this criterion, however, it is supposed that the ductility demand of each structural member is assumed to be the same as the response ductility factor obtained by

the non-linear dynamic analyses of one mass system. Many experimental studies have been carried out recently on the ductility behavior

of the flexural yield type structural members. However, there are still a lack of information concerning about the quantiative estimation of allowable ductility in accordance with structural details of the members. The equation 22 is proposed provisionally for estimation of the allowable ductility of flexural columns with some restricting conditions

in which ductile behavior can not be expected.

In the cases of walls, even the experimental studies on the ductility behavior have

not been performed sufficiently. Therefore, the F-index is directly given by Eq. 24 for walls for safe-side estimation instead of the estimation of F-index from the allowable ductility factor as in the case of columns.

9.6 Recommendations for repairs to improve the earthquake resistant characteristics of buildings

When insufficient seismic safety of buildings comes into question as a result of the application of this criterion, appropriate repairs may be required for improving the

VIII-40
earthquake resistant characteristics of the buildings. The recommendations for repairs

are also provided for this purpsoe. These recommendations deal with the procedures of repairs in accordance with strength requirements or ductility requirements of the structural members. The method of evaluating the seismic safety for the repaired buildings,

some attention for the practice of repairs, and some design details for repairs are also provided in these recommendations.

Table 1. Value of <* 2 and a

? in E1« 5 ^T\0Jhe 1st 2nd or ^\

3rd group

gr0^

Extremely

short column

Shear column

or shear wall Plexural column 0.5 0.7 Flexural wall 0.7 1.0 Shear column or

0.7 shear wall

VIII-41
TRANSFERRING THE TECHNOLOGY FOR WIND-RESISTANT

BUILDINGS TO DEVELOPING COUNTRIES

Noel J. Raufaste, Jr. National Bureau of Standards, Gaithersburg, Maryland

ABSTRACT

The National Bureau of Standards project to develop improved design criteria for low- rise buildings to better resist high winds was recently completed. It contained two essential parts. The first included developing technology to reduce wind damage to buildings through improved building practices. The second part centered around making sure these improved building practices actually reached the individuals who construct and live

in buildings. The latter has traditionally received minimum attention. This paper presents

a method for getting the results of the NBS wind research to the building community which

includes building owners and users who need it most. A 3-level approach to this method is described. The method used can be a model for other research projects aimed at technical, semi-technical, or even semi-literate audiences.

KEYWORDS: Buildings, design criteria, developing countries, technology transfer, windloads

VTII-42
INTRODUCTION

This paper discusses efforts in transferring the technical results on the effect of wind on low-rise buildings in developing countries to the local building community and to homeowners and low-technology craftsman who often build their dwellings from local materials. The homeowner and craftsmen group generally do not understand the highly technical results produced by this project; but they want a method to keep their home from collapsing in a storm. One component of this project attempted to do just that — to transfer project

information to the general public. Actual use of this technology by the general public

will demonstrate the real payoff of the research. The Center for Building Technology, of the U.S. National Bureau of Standards (NBS)

,

recently completed this three and a half year study of the effect of wind on low-rise

buildings. The project sponsored by the Agency for International Development was aimed at improving building practices — in high wind-prone developing nations worldwide. Two previous papers discuss the technical aspects of this study — "High Wind Study in the Philippines," and "Wind Loads on Low-Rise Buildings," published in the NBS Special Publi- cations 470 and 477, both titled Wind and Seismic Effects . The papers were presented at the 7th and 8th joint meetings of the US/Japan Panel on Natural Resources, respectively. Most of the data collection activities (full-scale and wind-tunnel experiments) were

centered in the Philippines. This was the host country; its environment provided a natural wind laboratory. There was a significant technical contribution by the local Philippine building community, represented by the projects local coordinating group known

as the Philippine Advisory Committee; (high level officials from the private and govern- ment building organizations) in all phases of the study. Also, the other participating

countries (Jamaica, Bangladesh) constantly asked about the relevance of our research to local codes and standards, building materials, and socio-economic aspects of their countries. The project team recognized that the research results be consistent with, sensitive

to, and relevant to improving local building practices. The project developed improved design criteria for wind loads on buildings; provided

technical material to serve as the basis for better building practices; produced a method

to estimate extreme wind speeds; and documented essential information in the areas of design wind speeds and pressure coefficients, economic forecasting, socio-economic and architectural concerns, and construction detailing practices. These results are described

in the next section. PROJECT RESULTS

Three levels of information were developed to reach three major audience classes. At

the first level, highly technical information is aimed at technical groups responsible for producing similar complementary research and for implementing disaster mitigation programs.

VTII-43
For this group a 5-volume report, Building to Resist the Effect of Wind1

, was produced which detailed the research progress and technical outputs. The second level of information is aimed at local builders and home owners who hand- craft houses on a limited scale. For them, guidelines were produced, 43 Rules - How

2 Houses Can Better Resist High Wind . These 43 rules were designed to make the technical

results more understandable and useable for those concerned with implementing only general building practices.

The third level of information is aimed at the general public. The medium is a 2- color poster that illustrates through simple and bold graphics, wind hazards, and presents

four methods to reduce damage and injury — and most important — tells where to go for more information. As with the 43 Rules it was designed to be reprinted in local languages. Level-One Information: Highly Technical Audience

Technical results were published in five companion volumes. Contents of each volume

are summarized. "Estimation of Extreme Wind Speeds and Guide to the Determination of Wind

Forces," reviews probabilistic techniques for the analysis of existing data and the selec- tion of design wind speeds. Simplified procedures for the calculation of wind pressure

acting on building surfaces were developed. These procedures and associated design criteria provide building professionals with more reliable design loads. The data can form the basis for wind load design codes and standards in developing countries.

"A Guide for Improved Masonry and Timber Connections in Buildings," presents recommen- dations for good construction practices and details, especially for countries experiencing

extreme wind. The report serves as a reference for improving building practices. "Forecasting the Economics of Housing Needs: A Methodological Guide," presents a method for a nation's planners, economists, public officials, and other decision makers to assess housing needs for up to 20 years into the future. Information on the cultural and socio-economic factors that affect building practices

was developed as, "Housing in Extreme Winds: Socio-Economic and Architectural Considerations." The report discusses how strong, inexpensive, locally available building materials

can be integrated with good building design. The report addresses the Philippines, Jamaica and Bangladesh. An "Overview" volume containing an executive summary serves as an introduction and background to the technical material. It was developed for the decision maker who may not have the time to read the substantive technical material of the other four volumes yet is sufficiently familiar with the project to direct his staff to particular volumes of

interest.

The Building Science Series 100, Building To Resist The Effect of Wind , Volumes 1-5 may be purchased from the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402.

2This report may be ordered as NBSIR 77-1197 under its title from the National Technical Information Service, 5285 Port Royal Road, Springfield, VA 22161.

VTII-44
As the technical results were being developed emphasis was placed on: 1) producing

data that could be developed into performance criteria (focuses on user requirements and

• the attributes necessary to satisfy them) and 2) producing reproducible models. Level-Two Information: Semi-Technical Audience

A second or intermediate level of material was developed for local housing agencies,

builders, and building owners. This material, 43 Rules - How Houses Can Better Resist

High Wind , is a guide presenting ways to better design new and existing buildings. The information is presented in a manner for translation into a local country's language.

The audience can be considered the middle level of the housing trade, such as the local builder, contractor, designer, housing authority. For them, especially in developing

nations, code enforcement is not the problem, just simple, safe practices are. This

report provides suggestions to improve building practices. For example, local housing

authorities and lending institutions will learn from 43 Rules that houses with lengthy

3 roof overhangs will need special precautions such as tie-downs and learn that buldings

with long roof overhangs should be designed in a manner that permits wind to pass through.

Also, they will find that roofs should be designed with slopes approaching 30 degrees

since this angle minimizes wind damages. Another intended target of this publication is the leader (often unofficial) of local political units, called in the Philippines, "barrios" — although such units occur on a

- worldwide basis. If this individual reads the 43 Rules he is in a good position to encourage his jurisdiction to adopt appropriate recommendations to improve building

practices for new buildings and the use of certain retrofit practices for use on existing

buildings. To reach this rather special audience, 43 Rules could be printed in local

languages. Likewise, 43 Rules can be used by squatter and nonsquatter settlements and

also can be used to improve public buildings (such as schools and community centers) and multi-family dwellings. A 1976 award-winning 16 mm, 18 minute color movie 3

, also was produced by NBS to educate the audience that information is available to reduce wind damages to buildings and inform the audience about how the information was developed.

Level-Three Information: Lay Audience

A poster was produced that graphically depicts damages due to wind. It is based on information learned during this three and a half year research project. The idea to develop this poster was based on information learned from frequent discussions with members

of the various participating countries and on feedback from two regional conferences where

draft project results were communicated and discussed (Manila, Philippines and Kingston,

Jamaica)

.

Available on free loan from Association Sterling Films, 600 Grand Avenue, Ridgefield,

NJ 07657 or may be purchased from the National Audio-Visual Center, General Services

Administration, Washington, DC 20409.

4Copies of the poster are available from the author at the National Bureau of Standards,

Center for Building Technology, Washington, DC 20234.

VTII-45
The conference audiences were composed of representatives of the building community

(architects; engineers; regulatory, codes and standards officials; academia; manufacturers; builders and contractors; government agencies; and building users) . They believed if research (any research) is to have a significant impact on the entire country, each citizen must be able to benefit directly from it and be able to implement the research results. The poster was designed as an educational tool to illustrate critical principles of improved building practices and most importantly to identify a local contact for additional

information. It is printed in two sizes; the smaller size for internal office use and the larger one for hanging on fences or telephone poles. CONCLUSION

In the United States, Japan and other developed countries, the building codes and standards systems are aimed at protecting the public health, safety, and general welfare

as they relate to the construction and occupancy of buildings. Results from this project

will have an impact on those codes and standards dealing with wind loads. When building

research takes place in developed countries, its results normally find their way into practices by way of the law. In developing countries, this usually is not the case. The research covered by this project (applicable to both developed and developing

countries) dealt in part with apsects that in developing countries has little code enforcement. Thus, for these users to implement the research, they must be made aware of the information, learn how to obtain the data, and be informed how to initiate improving their building practices. This phase of the project addressed the traditional role of "technology transfer."

However, it was aided by classifying the audience into three levels and then carefully tailoring the results to meet each audience's needs.

VIII-46
NBS-114A (rev. 11-77) U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBS SP-523

2. Gov't Accession

No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE WIND AND SEISMIC EFFECTS

Proceedings of the Ninth Joint Panel Conference of the

U.S. -Japan Cooperative Program in Natural Resources

May 24-27, 1977, Tokyo, Japan

5. Publication Date

6. Performing Organization Code

7. AUTHOR(S)

n. o. .Lew, LQitor

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS NATIONAL BUREAU OF STANDARDS DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work: Unit No.

11. Contract/Grant No.

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP) National Bureau of Standards Department of Commerce

Washington, D.C. 20234

13. Type of Report & Period Covered Final

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES Library of Congress Catalog Card Number; 78-600082

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant bibliography or literature survey, mention it here.) The Ninth Joint Meeting of the U.S. -Japan Panel on Wind and Seismic Effects was

held in Tokyo, Japan on May 24-27, 1977. The proceedings of the Joint Meeting

include the program, the formal resolutions, and the technical papers. The subjects

covered in the paper include (1) characteristics of strong winds; (2) wind loads on structures and design criteria; (3) earthquake prediction; (4) earthquake ground motions and soil failures; (5) seismic loads on structures and design criteria; (6) design of special structures; (7) earthquake hazard reduction program; and (8) quantitative evaluation of damages caused by winds and earthquakes.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons) Accelerograph; codes; design criteria; disaster; Earthquakes; earthquake hazards; ground failures; saismicity; solids; standards; structural engineering; structural

responses; wind loads; and winds.

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