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NIST BUILDING SCIENCE SERIES 170

Seismic Performance of

Circular Bridge Columns

Designed in Accordance With

AASHTO/CALTRANS Standards

-TA

U.S. DEPARTMENT OF COMMERCE • TECHNOLOGY ADMINISTRATION

^ NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY

,U58

//1 70

1993
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'At Boulder, CO 80303. ^Some elements at Boulder, CO 80303.
NIST BUILDING SCIENCE SERIES 170

Seismic Performance of

Circular Bridge Columns

Designed in Accordance With

AASHTO/CALTRANS Standards

William C. Stone

Andrew W. Taylor

Structures Division

Building and Fire Research Laboratory

National Institute of Standards and Technology

Gaithersburg, MD 20899

Issued February 1993

U.S. DEPARTMENT OF COMMERCE, Ronald H. Brown, Secretary

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY

Raymond G. Kammer, Acting Director
National Institute of Standards and Technology Building Science Series 170

Natl. Inst. Stand. Technol. Bldg. Sci. Ser. 170, 129 pages (Feb. 1993)

CODEN: NBSSES

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1993

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402-9325
ABSTRACT

Limitations of present procedures for the design of bridge columns to withstand

seismic loads are discussed. An integrated seismic design procedure is

developed which 1) allows the automatic selection and scaling of design

earthquakes given the earthquake magnitude, the distance from the site to the

fault, and the type of overlying soil strata; 2) predicts the inelastic behavior of

reinforced concrete bridge columns when subjected to random lateral loads up

to and including failure; and 3) calculates cumulative damage which can be

directly correlated to observed states of damage in laboratory tests of bridge

columns. Techniques for achieving the above capabilities are described and

new design criteria, based on acceptable damage indices as functions of

earthquake magnitude, distance, and structural importance, are proposed. Using

the proposed procedure and criteria the performance of 72 representative bridge

columns designed in accordance with 1992 CALTRANS specifications is

analyzed. Analysis parameters included earthquake magnitude, distance from

epicenter, subsurface soil characteristics, column aspect ratio, and normalized

column axial load. Design charts, based on allowable damage index versus

earthquake magnimde, are developed and retrofit strategies are discussed for

those designs which do not meet the proposed design criteria.

Key words: circular bridge columns; damage index; design; dynamic analysis;

earthquakes; hysteretic damage model; inelastic modeling;

reinforced concrete; seismic loads; site specific response; soil

amplification; spiral reinforcement.

iii
On the cover: Proposed envelope for acceptable damage index, as a function of earthquake magnitude and distance, for bridge piers deemed

moderately important to seismic lifelines. See Chapter 6.

Disclaimer

Certain commercial equipment, instruments, or materials are identified in this paper

in order to specify the experimental procedure adequately. Such identification is not intended to imply recommendation or endorsement by the National Institute of

Standards and Technology, nor is it intended to imply that the materials or equipment identified are necessarily the best available for the purpose.

iv
ACKNOWLEDGMENT

This project was funded in part by the Federal Highway Administration, Office of

Research and Development. The authors gratefully acknowledge this support. The

authors would also like to thank James Cooper of the Federal Highway

Administration, James Gates of CALTRANS and Roy Imbsen of Imbsen and

Associates for their helpful comments.

V
List of Symbols

a = Peak ground acceleration, g's

as = Cross section area of spiral bar, cm^

Ac = Spiral core cross section area, cm^

Ag = Gross cross section area, cm^

ARS = Response spectrum factor in CALTRANS design

procedure, dimensionless

db = Diameter of longitudinal bar, cm

ds = Diameter of spiral bar, cm

D = Overall diameter of pier, cm

Dc = Diameter of spiral core (out to out), cm

D.I. = Damage index

fc = Concrete cylinder strength, MPa

fya = Longitudinal reinforcement yield stress, MPa

fys = Spiral reinforcement yield stress, MPa

F = Cumulative error between predicted and experimentally

observed differential energy absorption for each

point in an experimental record

L = Length of pier, from base to first point of contraflexure, cm

M = Earthquake moment magnitude

N = Number of longitudinal bars in cross section

p

_

2asf ygD^ ~

S

Per = Lateral load which causes first cracking of the column

Pfaii = Lateral load which causes complete collapse of the column

Puit = Maximum lateral load carried by the column

Py = Lateral load which causes observable yielding of the longitudinal

column reinforcement

Pe = Axial load applied to pier, kN

Q = 4p,Vf7V<^o -0.1 [Q = Oifa, <0.1]

Ra

Rd

Ac

_S

D

VI
Rf

Rl

Rs

Rt

Ry

Rn

f

D

S

f^ ys f^ ys f~"

ya

Pa

S = Spacing (pitch) of spiral hoops, cm

Sa = Response spectral acceleration, g's

t = Thickness of steel retrofit shell, mm

o

T = ——— (in regressions equations for a, P

and y)

T = Fundamental period of structure (in CALTRANS design procedure)

W = Superstructure dead weight in CALTRANS design

procedure, kilo pounds

Z = Risk and ductility factor in CALTRANS

design procedure, dimensionless

a = Stiffness degradation parameter for hysteretic

failure rules, dimensionless

P = Strength degradation parameter for hysteretic

failure rules, dimensionless

Y = Pinching behavior parameter for hysteretic

failure rules, dimensionless

pa = Axial reinforcement content, areal %

ps = Spiral reinforcement content, volumetric %

o = Standard deviation of spectral acceleration

for target response spectrum

lOP

Oo = ^—^ (kN , MPa and cm^ j Normalized applied axial load

f^Ag

vii
List of Acronymns

AASHTO = American Association of State Highway and

Transportation Officials

CALTRANS = State of California Department of Transportation

EARTHGEN = NIST interactive graphics program for selection and

scaling of design earthquake records

IDARC = Program for Inelastic Damage Analysis of Reinforced

Concrete Frame-Shearwall Structures (Park et al., 1987)

ISDP = NIST Integrated Seismic Design Procedure

NIDENT = NIST interactive graphics program for system identification

of cyclic behavior of reinforced concrete elements

NIST = National Institute of Standards and Technology

SAS/STAT = Commercial statitistical analysis package (SAS/STAT, 1987)

viii
Table of Contents

1.0 Introduction 1

1 . 1 Background (Current CALTRANS Design Procedure) 2

1.2 Integrated Seismic Design Procedure (ISDP). 4

1 .3 Scope of Present Study. 1

1 .4 Limitations and Assumptions 1

2.0. Modeling Inelastic Reversed Lateral Response of

Circular Bridge Columns 15

2. 1 Inelastic Dynamic Analysis Codes 15

2.2 Development of Hysteretic Failure Models 1

2.3 Digital Database 16

2.4 System Identification Procedures (NIDENT) 16

2.5 Closed-Form Equations for Hysteretic Parameters 20

2.6 Summary. 23

3.0 Selecting Design Earthquakes 24

3 . 1 Introduction 24

3.2 Earthquake Record Selection and Scaling Method 24

3.3 Target Response Spectrum and Attenuation Relationships 25

3.4 Demonstration Computer Program. 28

3.5 Discussion, 32

3.6 Bedrock Acceleration Records Selected for Trial Bridge Column

Designs 32

4.0 Damage State Prediction. 33

4.1 Introduction 33

4.2 Damage States 35

4.3 Determination of Threshold Damage Indices 38

4.4 Variability of Threshold Damage Indices 41

4.4.1 The Bootstrap Method 41

4.4.2 Apphcation of the Bootstrap Method to Threshold Damage

Indices 42

5.0 Analysis of CALTRANS Columns. 43

5.1 Selection Criteria 43

5.2 Design of Columns 44

5.3 Inelastic Dynamic Analyses of CALTRANS Designs 47

5.3.1 Overview. 47

5.3.2 Analyses on Bedrock Substrate. 48

5.3.3 Analyses on 37 m Sand Substrate 49

ix
6.0 Performance of CALTRANS-Designed Columns 52

6. 1 Development of Relationships for Acceptable Damage 52

6.2 Summary of Critical State Failures for CALTRANS Columns 59

6.2.1 Damage Index as a Function of Magnitude and Epicentral

Distance 60

6.2.2 Column Performance Charts 73

7.0 Retrofit Analysis 84

7 . 1 Introduction 84

7.2 Retrofit Procedure 85

7.3 Results of Steel Jacket Retrofit Analyses 91

7.4 Discussion 94

8.0 Conclusions 97

8.1 Integrated Seismic Design Procedure 97

8.2 Acceptable Damage Limits 98

8.3 Deficiencies in Current CALTRANis/AASHf6 Designs 99

8.4 Retrofit Procedures Based on ISDP. 100

9.0 References. 102

10.0 Appendix A: Table of Available Digital Test Records 107

11.0 Appendix B: Table of Earthquakes Selected for Analyses 1 1

1

12.0 Appendix C: Table of Damage States for Column Tests 1 14

X
SEISMIC PERFORMANCE OF CIRCULAR BRIDGE COLUMNS

DESIGNED IN ACCORDANCE WITH AASHTO/CALTRANS STANDARDS

1.0 Introduction

Research on the design of bridge structures to resist seismic loadings has

traditionally been driven by the inadequate performance of constructed facilities

under actual earthquakes. The catastrophic collapse of the 1-880 Cypress

Freeway, and the significant damage sustained by other elevated highway

structures in the Oakland-San Francisco region during the Loma Prieta

earthquake of 1989 [Lew 1990] initiated a research project at the National

Institute of Standards and Technology (NIST) to develop a rational procedure

for the design of ductile bridge columns. Strong emphasis was placed on the

creation of an integrated design tool which followed from fundamental physics

and took advantage of advanced computational tools developed over the past

decade to study various aspects of transient response prediction.

Of particular interest to practicing bridge designers is the state of existing

infrastructure immediately following an earthquake: Has the structure been

damaged, and if so, how badly? Should it be repaired? Can it be repaired?

Even more pressing is the question whether existing bridges should be

retrofitted now, before the next, more severe earthquake arrives. What should

a "design" earthquake be for the purposes of retrofit analysis? What level of

damage should be considered "acceptable" for a given structure in light of its

importance and the energy content of a particular earthquake? How is damage

to be quantified? All of these questions have been heretofore answered only

subjectively by committees of consultants from various fields. As a result, no

standard procedure exists for site- specific design.

This paper describes the fundamental concepts used in an integrated seismic

design procedure (ISDP) being developed at NIST for bridge columns. The

procedure is then employed to investigate the performance of a series of 72

representative bridge columns designed in accordance with 1990 California

Department of Transportation [CALTRANS 1990] seismic provisions. Since

these represent a more rigorous implementation of the American Association of

State Highway and Transportation Officials (AASHTO) design specifications

for highway bridges [AASHTO 1989] they can be considered the current stateof-the-art for the seismic design of bridge columns in the United States.

It must be recognized that the vast majority of bridges in use in the United

States were constructed more than 40 years ago. Given the enormous capital

invested in this existing infrastructure there is strong interest, both at the federal

1
and state levels, to improve the survivability of these bridges during

earthquakes. While it is not possible to address the entire field of bridge

retrofitting techniques in this paper the potential power and utility of an

integrated seismic design procedure (ISDP) in this field is demonstrated by

means of a case study.

1.1 Background (Current CALTRANS Design Procedure)

Before discussing what constitutes a "rational" design procedure, it will be

useful to summarize the current generally accepted design procedure for single,

cantilevered bridge columns employed by the California Department of

Transportation [CALTRANS 1990]. The CALTRANS procedure, summarized

in fig. 1.1, requires the selection of a maximum expected bedrock acceleration

at the bridge site from a seismicity contour map; the calculation of the

anticipated fundamental period of the structure; and the selection of an

appropriate response spectrum (the so-called ARS spectrum) based on generic

soil conditions. The designer then reads a static equivalent lateral design

acceleration from the ARS response spectrum, from which a design base shear,

which accounts for presumed ductility based on a generic structural

classification, can be calculated. This procedure, while lending itself to a codified standard, suffers from several drawbacks:

• A single peak acceleration value for a regional area ignores important

localized phenomena associated with distances from active faults, variations in

earthquake magnitudes and their effects on frequency content, and attenuation

and frequency shifting with distance from the active faults (or in the case of the

Eastern and Central United States, where active fault locations are often

unknown, the estimated probable distances, measured in any direction, from

earthquake epicenters).

• A sample of representative response spectra for homogeneous soil conditions

for a few depth ranges will not necessarily yield a realistic measure of the

lateral surface excitation force as experienced by the structure, particularly if a)

the frequency content of the earthquake rock motion is other than assumed in

the generation of the generic design charts, and b) if there are multi-layered

sedimentary deposits.

• There is no basis for the prediction of the post-earthquake damage status for

the structure. Thus, the design codes for lifeline structures presently include

arbitrary modifiers to the static equivalent lateral design load based on the level

of "importance" and the presumed post-elastic ductility capacity of a particular

structure. Because of this, there is no ability to perform an effective

2
optimization study which would result in the least-cost design solution to meet a particular survival requirement.

• Current retrofit assessment procedures [e.g., FHWA 1983, and FHWA 1987j

rely on a capacity/demand approach which involves the use of single mode or multi-mode linear spectral analyses, again followed by modifications to account

for presumed ductility capacity. As with the design of new bridges, there is no

means for assessing the effectiveness of the proposed retrofit nor to predict the

state of damage that might exist following any particular seismic event.

Current Design Approach: CALTRANS

1. Estimate Period of Structure

T = 0.32V(W/k)

(W = weight; k = stiffness)

2. Linear elastic, lumped-mass space

space frame model, subjected to

response spectrum acceleration.

2. Determine Risk & Ductility Factor, Z

1.0 2.0 3.0 PERIOD OF STRUCTURE, T, sec

3. Compute Lateral Load

F = (ARS)(W) / Z

'0 2.0 4.0 6.01 PERIOD OF STRUCTURE, T, sec

(Note: 1 foot = 205 mm)

Figure 1.1. Schematic of current CALTRANS seismic design approach.

3
1.2 Integrated Seismic Design Procedure (ISDP)

Rational structural design requires 1) the definition of functional requirements

for the structure, and 2) the use of appropriate analysis techniques to determine

if a proposed design meets the functional requirements. When considering the

seismic design of a highway bridge the functional requirements are most

concisely stated by defining the design loads and the acceptable structural

behavior in response to those loads. In this paper the design loads are defined

by "suites" of likely events (acceleration time histories) which cover a broad

range of energy contents (as defined by magnitude and distance from the

earthquake epicenter). The specific procedures by which such design suites are selected and/or created are described in Chapter 3. There are several reasons

for using this approach, the most important of which is that it explicitly

accounts for the transient nature of earthquake loading, rather than reducing it to a simplified static force. The reason for employing a suite is that no single

earthquake record can characterize the randomness that will be exhibited in

nature at a particular construction site. Thus, given a particular energy content

(as defined by magnitude and distance) a group of distinctly different (from a frequency content viewpoint) time histories has a higher likelihood of capturing

the worst case response for any given structure at a particular job site.

For any given time history a performance standard is required to determine if

the structural response is acceptable. In this paper a significant departure is

made from traditional load and resistance factor design procedures by

introducing the concept of acceptable damage. It is generally recognized in

seismic design (as opposed to design for live loads) that economical

construction excludes designs based on elastic response to the anticipated

maximum design earthquake. One can envision that elastic response is both

desirable, and feasible, for relatively low energy events. Between this condition

and total collapse in a high energy event will be a sliding relationship between

energy content and acceptable behavior, which necessarily will involve inelastic

performance.

Only recently [e.g.. Park, Reinhom, and Kunnath, 1987] have researchers begun

to develop practical quantitative analytical models for cumulative damage to

reinforced concrete structures under reversed cyclic loading. Research is active

in this area and models are being refined. The eventual utility of such models is

clearly evident. Since there are no existing quantitative standards for acceptable

seismic damage an initial model is proposed by the authors in Chapter 6, that

will hopefully be the nucleus of a more refined AASHTO Specification.

4
To determine if the functional requirements described above are met, the

designer must employ models that traditionally have belonged to the fields of

structural engineering, seismology, and geotechnical engineering. These are

structural analysis models, attenuation relationships, and wave propagation

models, respectively. Transient seismic analysis begins with the definition of

an anticipated attenuation relationship based on historic bedrock motion data,

which for a geographic region relates frequency content and amplitude to

magnitude and distance. Using this relationship, suites of design bedrock

motions can be developed either by scahng recorded time histories or through

synthetic generation techniques. Given a knowledge of the soil profile at a particular construction site wave propagation models may be used to determine

the altered time history that would be perceived by the structure at the surface.

Given a realistic time history, the inelastic response of the structure must be

determined. Inherent in the structural analysis phase is the need to realistically

model the hysteretic, inelastic behavior of the concrete; to determine a cumulative damage "index"; and to account for any nonlinearities and damping

imposed by soil-structure interaction. Each of the above tools is predicated on

the existence of certain knowledge bases which include, for example, laboratory

tests of bridge substructures and elements; strong motion instrument records

made at bedrock sites; strong motion records made at soft soil sites; and boring

logs which describe the soil column properties at a particular site.

If properly integrated the above tools and requirements (each of which will be

described below) can lead to a rational seismic design, retrofit, and repair

procedure which is far more general, effective, and economical than the current

AASHTO and CALTRANS approaches (see fig. 1.2).

5
Structural Bedrock Soft Soil

Experimental Earthquake Earthquake

i Data Records Records

rTom laDoraiory lesis ouong-mouon Strong-motion on reinforced concrete instrument records instrument records elements, bridge made at bedrock made at soft soil subassemblies, sites. sites. and foundations.

Structural

Analysis

Models

Experimental data is used to calibrate

inelastic dynamic

analysis codes,

(e.g.. Park etal. 1987)

1

Attenuation

Models

Attenuation relationships

for acceleration response

spectra as a function of

magnitude, distance and

geology.

(e.g., Joyner and Boore

1988)

Wave

Propagation

Models

Methods for propagating bedrock

motions to the ground surface,

(e.g., SHAKE91 1992)

OJ

xn

OX) -a

o

t/3

o

%

y

<

Reinforced concrete bridges

which meet specific seismic

functional requirements,

designed using the best

available analytical tools.

Design

Earthquakes

Suite of likely events in region over design life of structure: distances and earthquake

magnitudes

(geological

considerations)

Acceptable

Damage Levels

Degree of damage

deemed acceptable, as a

function of earthquake

magnitude, distance to

fault, and importance of

bridge

(building code-related

considerations)

03

Figure 1.2. Overview of development of integrated procedures for the seismic

design, retrofit, and repair of concrete bridges.

6
Figure 1.3 shows a computer program flow chart for the integrated seismic

analysis procedure. The approach is modular. It is based on recent advances in

methods for acquiring data on appropriate design earthquakes, and on the

development of reliable models for the prediction of hysteretic behavior in

reinforced concrete structures. Because the concept requires the integration of

seismological, subsurface soil, and structural analysis components, the input

data upon which the analyses are based are necessarily site- and structurespecific.

Presently there is no national data base from which one might, for example,

obtain a set of representative acceleration-time histories for a particular region

which might then be used for design. To limit the scope of the required data

base generation a demonstration project is presented, using the State of

Califomia as an example. Similarly, because there are many possible variations

to superstructure architecture, the initial scope of the project is limited to the

performance and design of circular, spirally reinforced, single cantilevered

columns which are monolithically cast with continuous longitudinal

reinforcement through the potential plastic hinge regions. These criteria are applicable to a large number of elevated highway systems presently in use in

Califomia and elsewhere in the United States.

There are eight separate, but interrelated, elements governing the design of a bridge column with specified performance under given levels of seismic

excitation. These are as follows:

• Structural System and Performance Definition

• Subsurface (Soil Column) Definition

• Bedrock Motion Definition

• Site (Surface) Motion Calculation

• Hysteretic Failure Model Selection

• Soil-Structure Interaction Modeling

• Inelastic Dynamic Analysis

• Cost Optimization

7
Q START ^

1: Column Height, h

2: A;(ial Load, P

3; Concrete Str.. fc

4; Steel yield, Fy

5: Column Dia., D

6: steel rat., rhoa

7. con1. rat .rtios

I Solution ^2

Construction site on bedrock? No

C/)

Soil Records Database

Auto Contour

1 , Graphical Rck o1 Site location from

regional map

1.1 Layer Depth (1) 1.2 Layer(l) Properties

N.I Layer (N) Depth

N.2 Layer (N) Properties

Depths (N) Properties (N) Depths (N) Properties (N)

Bedrock Motion

1 : Site tocation pick from digitized regional map determines design suite

of a(t) htstones for a specific magnitude earthquake

(t) .... a (t) ml

3 (t) In mn m = # of Magnitudes

n = number ol hist, compnsing suite

a. Updated empiricaJ models relating response

spectra to Magnitude &

distance from source

(attenuation relationships)

b. Where available, select &

scale bedrock

records matching cnterion (a) for specific regional sites,

c. Where records are not available stochasticaily generate

artifida) earthquakes to match cntenon (a).

User supplied acceleration time Nstory. a(t) m = 1 , n = 1

Soil Column Propagation Code: Generate Surface

a(t)'s. SHAKE91 FEM Codes

Hysteretlc Failure Model

User Data

Polynomial

Select:

1 Strength Degradation

2: Stiffness Degradation

3; Rnching

Based on

regression fit to experimental

bridge column data. Cydic

Rule only,

[Polynomial Y | |3-ParamGtGr|

Select:

1 : alpha

2: beta

3: gamma

Based on regression

fit to experimental

bridge column data

a: Fixed Parameters

b: Cydic Rule

NIDENT 1.0

Interactive Structural

Identification Code

Solution Flag = 1,2

Solution Flag = 1 Solution Rag = 2

Initial Estimates:

fc. D, fy. rhos, rhoa. h, P. m, n

Magnitude

Suite Number

Do J = 1 ,

N

optimized

Store: Cost, f c, fy. D. rhos, rhoa. m, n

IDARC 2 2

Inelastic Dynamic

Structural Analysis Code

New Estimates:

fc. D, fy, rhos. rhoa

Delta (t) E(m.n,k)

Etot {m,n)

Dl (m.n) Deltamax (m.n) Mmax (m.n)

Optimization

Optimization Code:

Minimize: Construction Cost C = F(fc,fy.h.D.rhos,rhoa)

Subject to the constraint: Dl = x1. x2. x3, x4

= allowable damage

indices for Magnitude(M)

Dl =; F(fc,fy, D. rhos, rhoa)

Figure 1.3. Flow chart of seismic design procedure.

8
In considering the first element, Structural System and Performance Definition,

the engineer would prefer to enter as few pieces of information into a design

procedure as necessary, hi the case of geometry and loads, the minimum data

required are the height of the column, L, and the effective axial load, Pe, from

the superstructure. In addition the engineer would also like to specify the level

of acceptable damage following an earthquake of a given magnitude. A bridge

column which is required to be totally functional, with no damage at all,

following a Magnitude 6.5 earthquake, may demand a more robust design than

the same column which would be required to remain marginally standing (and

require subsequent demohtion) following a Magnitude 7.5 earthquake. Since

these criteria will depend on site-specific characteristics, the engineer would

also want to provide the computer program with a geographical location

(longitude and latitude) of the construction site, from which, ultimately, design

loadings would be automatically generated. Obviously, this design approach

represents a significant departure from current design practices, particularly in

the explicit inclusion of performance based on earthquake magnitude (energy

content). Its implementation is predicated upon a number of developments

taking place and on the integration of what are presently disparate research

software packages into an automated system.

The issue of structural input loadings is addressed in the second, third, and

fourth elements listed above. The seismic excitation function (acceleration-time

history) is dependent upon the following parameters, among others:

1 . The magnitude of the earthquake.

2. The local tectonics which affect the generation and propagation

of seismic waves.

3. The distance from the earthquake source to the structure.

4. The underlying soil conditions between the foundation of the

structure and bedrock.

Given these parameters the development of an appropriate "design" earthquake

loading is a comphcated process which is presently the subject of considerable

research. The authors envision, ultimately, a national database which would

permit the user, by specifying a geographic location for the construction site, to

automatically develop a best estimate for the soil column profile from surface to

bedrock level; and automatically generate a suite of design bedrock

acceleration-time histories, with varying magnitudes and frequency contents

which would be representative of that site. Existing wave propagation software

[e.g., SHAKE91, 1992] can then be used to automatically generate surface-level

acceleration-time histories which would serve as the input loading for the

structural design. Initially, it is clear that the scarcity of available boring logs to

9
bedrock will relegate such automated soil selection procedures to preliminary

analyses, pending availability of specific construction site logs. However, with

required filing of boring logs to bedrock at all construction sites in seismic

regions with a national organization, such as the United States Geological

Survey, the completeness of such a soils database would gradually improve.

Procedures are currently available [e.g., Joyner and Boore 1988, Idriss 1985,

and Taylor and Stone 1991] for the selection and scaling of earthquake records

at a given site, provided information on local geology and tectonics are

available. For any given site, and any given structure, a single accelerationtime history is nearly as insufficient for proper analysis as a single equivalent

static lateral load. Because some structures may respond more strongly to a

particular segment of a response spectrum, it is important to develop, for each

site, a suite of acceleration-time histories which, taken together, span the entire

target response spectrum, and taken individually, span discrete portions of the

target response spectrum. Likewise, because different magnitude earthquakes

may occur from different sources, a separate suite of design acceleration-time

histories for each magnitude under consideration must be generated. Given

these data, one may then develop a suite of surface -level time histories suitable

for subsequent structural analysis. An interactive graphics-driven system which

employs the above principles has been developed at NIST and will be the

subject of a forthcoming paper. Portions of this system are used for the

analyses reported in the present paper. The details of design earthquake suite

generation are presented in Chapter 3.

The techniques used for inelastic dynamic analysis (steps 5 through 7 in the

proposed design procedure) are described in detail in Chapters 2 and 4, Briefly,

the approach subjects a column with known geometry and material properties to a suite of independent earthquakes and for each time step in the earthquake

record, tracks the top of column lateral displacement as a function of lateral

load. These load-displacement (or moment-curvature) histories may then be

analyzed to determine a damage index at any point in time. The damage index

is a composite, dimensionless number which is a function of both maximum

displacement (curvature) ductility and normalized absorbed hysteretic energy.

As will be shown in Chapter 4, these damage indices can be correlated to

physical states of damage observed in laboratory tests of bridge columns. This

then completes the analysis cycle which starts with the definition of a design

earthquake based on magnitude and proximity to the earthquake origin, and

ends with an assessment of probable damage caused by a given seismic event.

There is thus a means for directly assessing the cumulative damage to a column

subjected to a series of events, since any given analysis of a column could

simply be extended in time by attaching a subsequent earthquake record to the

10
input time history. This leads naturally into the subject of retrofit analysis

which is discussed in Chapter 6.

In the present study no attempt was made to address the issue of optimized

structural design other than to say that it is a logical and straightforward

extension of the analytical package (ISDP) presently under development at

NIST. As described in figure 1.3 and graphically in fig. 1.4, automated design

is possible using the ISDP approach, figure 1.4 shows one possibility in which

there are two optimization constraints. The damage constraint is provided by

means of a closed form equation which relates acceptable structural damage to

earthquake energy and structural importance (see Chapter 6). The second

constraint is the construction cost of the column. Using this approach the

practicing designer will ultimately be able automatically to determine the lowest

cost design which meets the acceptable damage criteria.

1.3 Scope of Present Study

Chapters 2-4 describe the analysis tools used to assess bridge column

performance. Beginning in Chapter 5 these techniques are used to study the

specific question of how bridge columns designed in accordance with current

CALTRANS specifications would perform when subjected to various design

earthquakes, hi all, three column geometries (L/D = 3,6, and 9), three axial

load levels (Pe/f'cAg = 0.05, 0.10, and 0.15); and four epicentral (fault)

distances (D = 10, 20, 30, and 40 kilometers) were investigated, comprising 36

separate design scenarios. Each design scenario was subjected to a suite of four

automatically generated earthquakes for four earthquake magnitudes (M=

5,6,7,8) for a total of 16 inelastic transient analyses per scenario or a total of

576 analyses for each subsurface condition investigated.

In order to assess the importance of soil amplification two subsurface

conditions were considered: a) column founded on bedrock; b) column founded

on 37 m (120 foot) layer of alluvium (sand) underlain by bedrock. For each of

these cases (representing a total of 1152 analyses) design charts are constructed

relating cumulative column damage as a function of earthquake magnitude.

These charts also include, based on the work presented in Chapter 4, 90th

percentile probability limits representing damage states corresponding to three

discrete conditions: a) yield of axial reinforcement; b) ultimate load capacity;

and c) complete column failure.

11
Begin Desi

Earthquake

Suite

quake

Inelastic

Dynamic

Analysis

Hysteretic

Failure

Mode!

Damage

Index

No Lowest

Cost?

Yes

I

h Ma

ilium Co.

1

No

Meets Required

Damage Index?

Yes

Figure 1.4. Schematic of automated inelastic design algorithm.

The design and analysis procedures used to investigate the CALTRANS

columns are described in Chapter 5. Chapter 6 presents first a brief treatise on

the subject of acceptable damage and then reduces the concept to a closed form

equation suitable for inclusion into the integrated seismic design procedure.

The performance of the CALTRANS columns analyzed using the procedures

identified in Chapter 5 is then discussed. Two types of design charts are presented, each of which has specific practical application. The first chart

series relates the total damage that would occur to a particular column at a

particular construction site (located a specified distance from a likely fault or earthquake source) as a function of earthquake magnitude. This is a highly

useful tool for examining the effect of column axial load and aspect ratio (L/D =

height/diameter) on damage avoidance. The second series of charts aUows for

12
quick assessment of the anticipated performance of a column whose geometric

properties and axial loading are known but the variance of damage is desired as a function of both magnitude and location.

On the basis of the material presented through Chapter 6 a column retrofit

design example is solved for a specific case in which the predicted performance

of a column designed to current CALTRANS specifications is unacceptable.

The procedure described is general and can be used to analyze a broad class of

existing circular bridge columns in any area of the United States. Chapter 7

summarizes the implementation of the damage index design procedure for

retrofit problems and discusses the effectiveness and limitations of steel

jacketing procedures presently in use by CALTRANS.

1.4 Limitations and Assumptions

Because of the reliance of the NIST method on direct calibration of analytical

tools to empirical test data the results described in this paper are limited in

scope to the design of circular, spirally reinforced bridge columns, for which a

substantial digital database has been established at NIST. It is anticipated in the

future that the method will be extended to handle other cross section

geometries, as well as multiple column bents.

Although the present ISDP package can handle any soil profile (including

clays), the analyses presented were limited to those for which direct

comparisons could be made with the existing simplified CALTRANS column

design procedures, as defined by the available ARS spectra charts. The intent

was to demonstrate the potential of the ISDP procedure and to caU attention to

certain shortcomings in existing simplified design approaches.

In an effort to limit the scope of the present study, the influence of soil-structure

interaction was neglected. Generally, bridge foundations will fall into three

categories: piles, battered piles, and spread footings. Each of these substructure

systems will react inelastically with surrounding soil media during an

earthquake with the general effect of damping, to varying degrees, the

superstructure response. The results presented in the present paper can

therefore be considered conservative for bridge foundations constructed on deep

soil deposits. There is significant active research in the area of soil-structure

interaction. Those analytical models which have thus far been developed, and

those likely to be developed to characterize this phenomenon, reduce the effects

of soil interaction to a series of frequency-dependent nonlinear springs which

are, in essence, boundary conditions that can be directly assimilated at some

future date into the structural analysis models presently used in the ISDP

package.

13
Finally, in Chapter 7, the retrofit analysis example is solved by considering, for

various seismic loadings, the effects on damage of changing design parameters,

specifically the confining reinforcement ratio (as determined by the thickness of

a steel jacket). Retrofitting is a global process and once the column retrofit has

been determined to be acceptable, a revised analysis must be performed on both

the foundation as well as the superstructure systems to ensure that the point of

failure has not merely been displaced from the column plastic hinge zone to

some other point in the bridge.

14
2.0 Modeling Inelastic Reversed Lateral Response of Circular

Bridge Columns

2.1 Inelastic Dynamic Analysis Codes

Several computer programs presently exist including SAKE [Otani 1974],

SARCF-II [Rodriguez-Gomez, Chung, and Meyer 1990], DRAIN-2DX

[Allahabadi 1987], and IDARC [Park, Reinhom, and Kunnath 1987], among

others, which have achieved some measure of success in analytically predicting

the dynamic response of reinforced concrete structures, not just to their elastic

hmits, but to complete failure. All are "research codes" and to date are hmited

to the analysis of two dimensional structural systems. At the heart of these

programs are hysteretic rules to idealize the inelastic behavior of reinforced

concrete under dynamic or quasi-static loading. Such models attempt to capture

overall behavior of the structural element based on load-displacement (or

moment-curvature) predictive algorithms cahbrated to experimental data. The

output of these programs lends itself to the computation of absorbed hysteretic

energy and displacement ductility, both of which have been shown to be

correlated to a quantifiable measure of the state of damage sustained by the

structure following a seismic event [Park, Ang, and Wen 1984]. In the present

study a multi-linear hysteretic model, known as a "Three Parameter Model,"

was employed. This same algorithm is presently used in the program IDARC

[Park, Reinhom, and Kunnath 1987].

2.2 Development of Hysteretic Failure Models

It is common practice to describe the envelope curve of the force-deformation

relation of reinforced concrete components by a multi-linear function with three

turning points, e.g., cracking, yield, and ultimate strength. The tri-linear

approximation to the envelope curve is known as the "skeleton" curve. Procedures have been developed to extract this curve from an equivalent

monotonic load-displacement envelope curve that has been fitted to

experimental data for columns tested under reversed cyclic loading [Park,

Reinhom, and Kunnath 1987]. A variety of hysteretic properties can be

obtained through the combination of the tri-linear skeleton curve and three

characteristic parameters, a, P and y- Complete definitions of these variables

may be found in Stone and Taylor [1991]. Briefly, the parameter a controls the

degradation (softening) in the unloading stiffness that is generally observed in

reinforced concrete members as they degrade under reversed cyclic loading.

The parameter (3 determines the rate of strength deterioration, and is commonly

a function of cumulative absorbed energy and maximum displacement.

Pinching behavior is controlled by the parameter y. The introduction of such a

15
pinching parameter causes constriction of the hysteresis loops, and an overall

reduction in the cyclic energy absorbed by the structural element.

These three parameters, together with the skeleton curve information described

above, are the variables required for implementation of the hysteretic rule

described in Park, Reinhom, and Kunnath [1987]. El-Borgi, White, and

Gergely [1991] wam that proper implementation of this type of model requires

calibration of the variables to a specific type of structural element if reliable

results are to be obtained. It was for this reason that the initial project scope

was restricted to circular, spirally reinforced, single bridge columns. The first

task was thus to assemble a suitable digital database of tests of spirally

reinforced, circular concrete bridge columns subjected to reverse cyclic loading

combined with axial load. The process of determining the relationship between

the hysteretic parameters a, (3, and y and the column geometry and materials is

known as "system identification."

2.3 Digital Database

An extensive literature search identified several sources of bridge column test

data. Digitized records were available from Stone and Cheok [1989]; Cheok

and Stone [1990]; Lim and McLean [1991]; and McLean and Lim [1990].

Additional records, generally in the form of lateral load-displacement plots,

were obtained from Ang, Priestley, and Park [1981]; Mander [1984]; Munro,

Park, and Priestley [1976]; Priestley and Park [1984]; Zahn, Park and Priestley

[1986]; Petrovski and Ristic [1984]; Wong, Paulay, and Priestley [1990]; Ang,

Priestley and Paulay [1985, 1989]; Davey [1975]; Ng, Priestley and Park

[1978]; Kenchiku Kenkyu Siryo [1975, 1978]; and Watson [1989]. All of the

analog data were digitized from large scale precision photo enlargements of the

analog records.

2.4 System Identification Procedures (NIDENT)

The term "System Identification" is generally associated with the experimental

acquisition of such dynamic characteristics of a structure as its mode shapes,

frequencies, and damping coefficients. In this report we use the term to refer to

the determination of the three parameters a, (3, and y, which best characterize

the hysteretic behavior of a given test specimen. The system identification

procedure used in this study consists of a three dimensional trial and error search with bounded limits on a, P , and y subject to the constraint of

minimizing the cumulative error between predicted and experimentally

observed differential energy absorption for each point in the experimental

16
database. In equation form, we seek to minimize the function F, where F is defined as follows:

n

i=l

S0.5|6ii+l 5i-,|(Pexp(i)-P*eo(i))

n

where:

3i+l

ai-1

Pexp(i)

Ptheo(i)

displacement of next point in load-displacement record

displacement of previous point in load-displacement record

experimentally observed load at current point

predicted load at current displacement, calculated using the multi-linear

hysteretic rule and the currently selected values of a, p, and y

.

n number of data points in the experimental record

Following the initial identification of the parameters a, p, and y, the predicted

load-displacement record was superimposed graphically, in a different color, on

top of the experimental record. Using a high performance graphics workstation

it was then possible to interactively adjust any of the three model parameters by

means of a dial-box while viewing the results in real time on the graphics

screen. This visual-feedback approach proved effective in arriving at a "best

fit." As a final check, the absorbed energy was calculated for the experimental

and predicted data for each cycle and compared in a histogram plot. When the error between the theoretical and experimental sums of the cyclic absorbed

energies was reduced to a level of a few percent, the final values of a, (3, and y

were recorded. The above tasks were carried out using NIDENT 3.0, the NIST

graphics-based system identification package, running on a Silicon Graphics

4D-420 workstation.

Examples of the fit between the analytical model and experimental data are shown in figures 2.1 and 2.2. Several details of these figures bear discussion.

The first, as evidenced, for example, in figure 2.1, is that as the column begins

to fail, there is a tendency for the predicted loads to overshoot the

experimentally observed load at the maximum observed displacements for each

cycle. This is an expected consequence of using a tri-linear skeleton curve

where the post-yielding stiffness for such a model is defined to be positive for

reasons of numeric stability. Second, as evidenced in the associated cyclic

absorbed energy histograms (see figures 2.1-2.2), there is a tendency for the

predicted absorbed energy to overestimate the experimental data for low values

of lateral displacement and to underestimate the experimental data for high

displacement ductility. Despite these shortcomings, the Three Parameter model

is able to generally predict both overall absorbed cyclic energy and

displacement ductility to within a few percent error, which was considered

acceptable for the purposes of dynamic behavior studies involving reinforced

concrete.

17
B

90

70

50

30

10

-10

-30

-50

-70

-90

Alpha 12.01 Beta 0.005

Gamma 1.00

Energy Error -1.2 %

-70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70

Lateral Displacement (mm)

8.00 10-"

I

7.00 10^

S 6.00 10^

^

5.00 10^

«-( ^

4.00 10^ ^ 3.00 10^

-P 2.00 10"* 5on < 1.00 10"*

0

Experimental

Theoretical

N cycles g . g

Cumulative Error = (

!!iL^xlOO = -1.2%

0.00 10 , „ ^ , ^ ^ ^

1 2 3 4 5 6 7

Cycle Number

Figure 2.1. Experimental and analytical results for specimen Nl of Cheok and Stone [1990].

18
5.00 10"

4.00 10-

(J U 3.00 10^

15

2.00 10"^ aW

"I 1.00 10^

X)

<

0.00 10,0

Experimental

Theoretical

N cycles g _ g

Cumulative Error = 2^ ^xl 00 = -0.5%

i = 1

4 5

Cycle Number

Figure 2.2. Experimental and analytical results for specimen 3 of Ng.

19
2.5 Closed-Form Equations for Hysteretic Parameters

Given best-fit values of the parameters a, p, and y for many different column

tests, the next objective is to ascertain if there is any correlation between these

parameters and the physical properties and dimensions of the test specimens

which were modeled A stepwise linear regression analysis was conducted

using 65 digital test records. The regression analysis was carried out using the

commercial software package SAS/STAT [SAS/STAT, 1987]. R2 (square of

the regression correlation coefficient) values of 0.79, 0.85, and 0.80 were

obtained for the estimates of the parameters a, p, and y. It would be possible to

find a model which would explain a larger percentage of the total scatter in the

data, but at the expense of a significant number of additional terms. The

regression equations associated with the three parameters are given below.

= Cross sectional area of spiral bar, cm^ = Spiral core cross section area, cm^

Ag = Gross cross section area, cm^

db = Diameter of longitudinal bar, cm

d^ = Diameter of spiral bar, cm

D = Overall diameter of pier, cm

D^. = Diameter of spiral core (out to out), cm

fJ. = Concrete cylinder strength, MPa

fy3 = longitudinal reinforcement yield stress, MPa

f = Spiral reinforcement yield stress, MPa

L = Length of pier, from base to first point of contraflexure, cm

N = Number of longitudinal bars in cross section

Pg = Axial load applied to pier, kN

S = Spacing (pitch) of spiral layers, cm

P3 = Axial reinforcement content, %

p5 = Spiral reinforcement content (volumetric), %

Let

20
then

a = 135-0.0439A/f

0.0646

1000 - 0.0178— + 6.14R, - 1.02f

22.0

[lOOO - 0. 1 14AJ

- 104. 5Ry - 198R, + —- 28700T +

+ 230R,Rf[l + 1.09oJ

1 12700T

-l-683Rf + 2.84S - 62.8Rd - 108(0.1)'''

P = 2.53 +

1470

30i:^-f I 8.81x10^ 4750p,

P. f..X f.RL

l_ri_i7,oc l-^+^+Pitt-M.M

96000T^ °^ 21.9 3260 2.76 f ys P

Y = 4.29 + 0.204Vf

g„ 4660 12.8

+- 627 N R,

7700

+

1

+ 0. 2 19p3 [r, - 1. 85(0. 3)"'

] - 769T - 1. 1 2d,

1 1 87.2

83.0 8.13 133Rd 41.5a„ 21.2Rf D

The above equations were subsequently used to derive calculated estimates for

each hysteretic model parameter given the geometry and material properties for

each test specimen. Scatter plots for each parameter (values determined by

system identification on the x-axis; values calculated from the regression

equations on the y-axis) are shown in figures 2.3-2.5. In the case of the

parameter p it should be noted that negative predicted values are not valid (and

a zero should be substituted). (3 values must be positive, and are normally less

than 1.0. A practical upper limit on P, based on the experimental data, is 1.75.

Predicted y values greater than 1.0 are not valid (and 1.0 should be substituted).

A perfect model for a, P and y would cause all of the data in figures 2.3-2.5 to

fall on a 45-degree line intersecting the origin. Actually there is moderate, but

not unreasonably large, scatter, which is characterized by the values of 0.79,

0.85, and 0.80. We anticipate that the expansion of the column test database

will extend the range of applicability of the regression equations. However, as the limits of scatter are likely controlled by the variability of response that is

typical of reinforced concrete, it seems unlikely that the quality of correlation

between the parameters derived via system identification and those calculated

using closed form equations will improve significantly, and that the scatter

cloud will simply become more dense. For the purposes of conservative

inelastic dynamic-based design it should be possible to shift a and y downward

and p upward by some multiple of the standard deviation, much as strength

21
adjustment factors are incorporated in traditional design codes to account for

workmanship and material variability.

5 10 15 20 25 30 35

alpha experimental

Figure 2.3. Predicted and experimental values of a.

1.4

1.2

1.0

I 0.8

uB

0.6

0.4

0.2

0.0

-0.2

> B m-rmrrmm

\ :^ i • •

wwvyvwwwwvvwv> \

•

t m

-0.2 -0.0 0.2 0.4 0.6 0.! 1.0 1.2 1.4 Beta experimental

Figure 2.4. Predicted and experimental values of p.

22
0.0 0.2 0.4 0.6 0.8 1.0 1.2 gamma experimental

Figure 2.5. Predicted and experimental values of y.

2.6 Summary

Within the bounds of the available test data for circular, spirally reinforced

concrete bridge columns subjected to cyclic lateral loading, it was found that

the Three Parameter model was able to generally predict the observed

experimental load-deflection histories, and more importantly to produce an

estimate of the cumulative absorbed cyclic energy within an error bound of

several percent. Preliminary regression equations, which are functions of the

physical properties of the bridge columns, were developed for the parameters a,

p, and y. The availability of closed form equations for these failure model

parameters permits an a priori inelastic dynamic solution for a large class of

bridge columns which employ circular cross-sections and spiral confining steel.

This was one of three critical factors which needed to be addressed in order to

create the integrated seismic design procedure (ISDP) described in Chapter 1

.

The remaining two factors - damage model correlation to experimental data and

the development of a closed-form model for acceptable damage - are described

in Chapters 4 and 6, respectively.

23
3.0 Selecting Design Earthquakes

3.1 Introduction

A critical step in the implementation of any time-step analysis is the selection of

appropriate earthquake motions to drive the analysis. In order to design a new

bridge, evaluate the potential for seismic damage to an existing bridge, or

evaluate the effectiveness of earthquake protection systems, it is first necessary

to obtain a prediction of the seismic forcing function. In the case of the NIST

integrated seismic design procedure (ISDP), the desired earthquake motions are bedrock acceleration-time records: the motions at the ground surface are obtained by employing the shear wave propagation model SHAKE91

[SHAKE91, 1992] to filter the bedrock motions upward through the overlying

soil layers. This chapter describes a method for selecting site-specific bedrock

motions for the seismic design or evaluation of bridges.

3.2 Earthquake Record Selection and Scaling Method

There are in general two approaches to the generation of site-dependent

earthquake bedrock motions. First, synthetic ground motions can be generated.

These motions are normally computed on the basis of parameters derived from

probabilistic studies of seismicity in the region of interest. The parameters not

only account for earthquake magnitude but also distance from the causative

fault. In many cases an historically-recorded ground motion, or some

"standard" fictitious record, is selected to serve as a basis for the synthetic

motion. This record is then altered (sometimes radically) in frequency content,

duration and intensity to arrive at a synthetic motion which satisfies the

statistical model.

With the second approach, a "design" or "target" acceleration response

spectrum is established, and "natural" response spectra, from historicallyrecorded ground motions, are matched to it. The target spectrum is derived

from statistical studies of response spectra, calculated from all available

historically-recorded ground motions in the region of interest. Attenuation

relationships are derived to adjust the target spectrum for earthquake magnitude

and distance from the causative fault. The natural response spectrum, or

spectra, which best match the target spectrum are chosen for design purposes.

If no natural spectra match the target spectrum closely, the natural spectra can

be altered to some degree. Amplitude scaling is accomplished by multiplying

the ordinates of the entire natural response spectrum by a constant scale factor.

24
The second approach has been chosen for use in the NIST seismic design

procedure for several reasons. First, the NIST study has focused initially on the

Northern California region. Since there is a relative abundance of historic

earthquake data from the West Coast of the United States it is possible to derive

relationships for the target response spectrum and attenuation equations in the

region of interest. Second, the method relies mainly on natural earthquake

records which are minimally altered to match the target response spectrum. It is preferable to make use of natural earthquake records whenever possible, rather

than synthetic records, as the natural records may reflect aspects of the ground

motions which are not accounted for in the synthetic record generation

procedures. Finally, the use of a suite of three to five natural earthquake

records, which together span the target spectrum, provides a more realistic

loading history than a single synthetic record, which is forced to match the

entire target spectrum. In reality, a structure is subjected to a series of

earthquakes over its lifetime. Taken together, these earthquakes tend to cover

the entire range of the target response spectrum. A single synthetic earthquake

record which covers the entire target response spectrum represents an

unrealistic agglomeration of earthquake effects.

3.3 Target Response Spectrum and Attenuation Relationships

A number of methods for computing site-dependent target response spectra

have been proposed [e.g., Campbell 1981, Idriss 1985, Joyner and Boore 1988,

and Youngs et al. 1988]. In the present study, the spectral equations developed

by Idriss [1985] were employed. This is because the development of the

equations was based exclusively on seismic data from California (the initial

area of interest in this study), and because the equations have been recently

updated to reflect the seismic data collected from the 1989 Loma Prieta

earthquake. Figure 3.1 illustrates schematically how the target response

spectrum is computed, as a function of magnitude and distance. This method is

summarized briefly below.

The method begins with a basic normalized spectral shape for a magnitude 6.75

earthquake. The ordinates of this curve, shown in table 3.1 below, were

determined from a statistical study of historically-recorded earthquake bedrock

motions in California.

25
M = 6.75

a

1.0

Period

-ij exp[ A + B X ln(T)] =(—

?

^M=6.75 ^ ^M=M'

Empirically Derived Basic

Normalized Spectral Shape

for Magnitude = 6.75

(A and B functions of M')

Altered Spectral

Ordinates for a New Magnitude M = M'

Target Response Spectrum

Compute Peak Acceleration

as a Function of

Magnitude, M' and Distance, D

a = exp [a (M') - p (M') x ln(D + 20)]

Figure 3.1. Calculation of Target Response Spectrum.

Table 3.1. Bedrock accelerations, normalized spectral ordinates for M=6.75

Normalized Normalized

Period, Spectral Period, Spectral

seconds Ordinates seconds Ordinates

Sa Sa

a a

0.03 1.000 0.50 2.170

0.05 1.275 0.55 2.020

0.075 1.635 0.60 1.875

0.10 1.920 0.65 1.724

0.11 2.022 0.70 1.600

0.13 2.210 0.75 1.481

0.15 2.375 0.80 1.375

0.18 2.525 0.85 1.280

0.20 2.610 0.90 1.200

0.22 2.666 1.00 1.065

0.25 2.720 1.50 0.648

0.27 2.769 2.00 0.452

0.30 2.755 3.00 0.266

0.32 2.751 4.00 0.180

0.35 2.690 5.00 0.130

0.37 2.630 6.00 0.1

0.4 2.530 8.00 0.065

0.45 2.340

26
The next step is to alter this basic normalized spectrum to account for a magnitude other than 6.75. This is accomplished using equation 1 below,

which was derived from a statistical study of earthquakes in California, and

accounts for the variation of spectral amplitude as a function of magnitude, M,

and period, T, in seconds (Idriss 1985).

The peak acceleration, "a", is computed using equation 2, which is a function of

magnitude, M, and the distance from the earthquake source, d, in kilometers.

a = exp[a(M) - P(M) hi(d + 20)] (Eqn. 2)

where a(M) = exp[2.261 - 0.083M] for M < 6.0

a(M) = exp[3.477 - 0.284M] for M > 6.0

P(M) = exp[1.602-0.142M] for M< 6.0

P(M) = exp[2.475 - 0.286M] for M > 6.0

Finally, the normalized spectral ordinates are multiplied by the peak

acceleration to obtain the absolute spectral ordinates, as shown by equation 3.

(Eqn.l)

where a(M) = -7.427 + 1.654(M) - 0.082(m2)

and b(M) = -3.224 + 0.718(M) - 0.036(m2)

x(a) (Eqn. 3)

27
3.4 Demonstration Computer Program

The method of selecting and scahng bedrock motions outlined above is well

suited for implementation in a computer program on a work station with

interactive graphics capabilities. Such a program called EARTHGEN was

written at NIST for a Silicon Graphics IRIS 4D/410VGX work station.* It is

anticipated that EARTHGEN will make up one module of the comprehensive

seismic design procedure for bridge piers currently under development at NIST.

A block diagram of EARTHGEN is shown in figure 3.2, and the operation of

EARTHGEN is summarized below.

^START^

Designer Enters the Distance From the Fault, D, and Five Earthquake Magnitudes Ml,M2,M3,M4and M5

EARTHGEN Updates and Displays the Most Recent

1 ) Magnitude

2) Target Response Spectrum

3) Scaled Natural Response Spectra

4) Scale Factors

Designer Selects an Earthquake Magnitude

Ml,M2,M3,M4orM5

EARTHGEN Computes

the Target Response

Spectram for That Magnitude

Designer Selects an

Acceleration Record From

the Available Data Base

EARTHGEN Computes

the Natural Response

Spectrum for That Acceleration Record

c

STOP

EARTHGEN Multiplies Each Acceleration Record by its Corresponding Scale Factor and Sends all Data to a File

YES

Designer Selects a New

Scale Factor for a Natural Response Spectrum

EARTHGEN MultipUes the Natural Response Spectrum Times the Scale Factor

Is Operator Satisfied With the Agreement

Between the Target Spectra and

Natural Spectra for all Five magnitudes?

Figure 3.2. Block diagram of the program EARTHGEN.

Initially, EARTHGEN displays a menu and prompts the designer to enter the

distance of the bridge site from the fault of interest, and up to five earthquake

magnitudes. EARTHGEN then displays the target response spectrum for the

first magnitude value. The 84th and 16th percentile limits (the target spectrum

plus and minus one standard deviation) are also displayed (fig. 3.3). The

designer may then select, from a list, the name of an historically-recorded

bedrock motion. EARTHGEN retrieves the corresponding acceleration-time

record from a data base, computes the response spectrum, and overlays this

natural response spectrum on the target response spectrum already displayed

* EARTHGEN could have been written for any work station with high resolution graphics capabilities.

28
(fig. 3.4). (As part of this study some 60 recorded bedrock acceleration records

for the state of California were compiled and incorporated into the

EARTHGEN data base). The designer may then alter the vertical scale of the

natural response spectrum by adjusting a valuator dial (fig. 3.5). EARTHGEN

continuously updates the display to reflect, in real time, this scaling of the

natural response spectrum.

The designer may repeat the record selection and scaling procedure for up to

five other historically recorded bedrock motions, all of which are displayed

simultaneously on the screen (fig. 3.6). When the designer is satisfied that this

suite of scaled natural response spectra adequately covers the target spectrum, a new magnitude value is chosen and the record selection and scaling process is

repeated. The designer may re-display and adjust the scaling of the spectra for

any of the five magnitudes at any time. An automated scaling option is also

incorporated in EARTHGEN. When invoked, this routine determines the scale

factor for each natural response spectrum which results in the least total

difference between the natural spectra and the target spectrum. The designer

may use this feature to provide an objective measure of the agreement of the

natural and target spectra.

Finally, when records have been selected and scaled for all five magnitude

values, the designer terminates the interactive session, and data are written to an

output file. These data include the initial input data (distance and magnitudes),

and up to 25 historically recorded bedrock motions and their scale factors (up to

five records for each of five magnitudes). The scaled bedrock motions may

then be used for later non-linear analyses of the bridge structure subjected to

five-earthquake suites of varying magnitude.

29
raJii)-Maii.f NniuFinL Hcapohsc specihh twamfudo 6. no nUTO-SCLCCT Efl(lTHflUflK£ BCCanOS MosiiHuilB 6,50

EXIT HHO Ewr omn ii,-,. - . -

-

i/ni«i¥^-iMi'it.f.-

Figure 3.3. EARTHGEN display of target spectrum and 84th and 16th

percentiles.

.1 cdi'oR

I stsur CfKioii!

time or 'tiiimiu i , ~1

0.0-«,0 6,0-8.0

1 ^9

UNSCALED

NATURAL

SPECTRUM

ID. D

H.Ur IBDGET lltSWKSf SPrCISUtl .ciqqnfiuda S.S0 -

nuio-sCTLC NBrUBin, ficapohBi: spcciwi Jlosfiiiuiia COii

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emitiisT.s? ^ suiiuiST. 3or

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rntiviTfts.aze ^ SRHTPHK. im

|^ LKHI1£H54. lit Bl.ltHl«HS1.2Dl IP IKMUfillSS.Jt tS LKHUGHSS.ZSt [g PtJDO-UBH.SS m IIUMt-ain. 925 g§ pncaiiiii. iE4'

II LIST rwinaiuiKiiij

Figure 3.4. EARTHGEN display of natural response spectrum before scaling.

30
Kl.CUHU Mlhi; i coirik I Ki.nl ( I (n;n)K

"i. Jim

'

I , (JUU

5-,uni; IK" nyijiiHt c ii; i I'ltiin:-, 1

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(lit 20II2I)«. lis ^ 2ail2DNl.2UII P JDJIIIinK.O n8naLiM(,?ra il «2Mfwa.I27 ^ «2»HfO,2l7

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US Mwuim.wr

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llUI0-6CTiC KflTUnni. BfaPOflSt SHIXTFUI rtaoniludn C.nfl nUTO-SELECT EnBIII(lUm<£ RtCOnOS Honti[(uJo 8.50

Figure 3.5. EARTHGEN display of scaled natural response spectrum

^ o.r>o

Sims or sMunBES or ermirs o.Qi-n.o 0,0-8.0 8.0-fl.a COLOR HBI B. 1283 a.paoo

'U. IHJllU u.uuua

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NATURAL SPECTRA

conniiLiT.aii ; Ig'coAinLiT.aEa 9 DinnoHTS.o uianoHis.sa gimoy-i.ao Hi cimov-i.asii B HICIFHIS.Sn

PIIClfKre.360 HI PRESiom.o 01 PlieSIDID.90 B RINCONHL.O

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[UAH IfWKfcl fltSPONSE SPfCTfttm

ftUTO-SELECl EmiTHqUfiK£ itCCOROS MinwiltiMU 4.5

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EKiT UNO stwr onrn Mosj^'tuds ?,5a

^ure 3.6. EARTHGEN display of multiple scaled natural response spectra

31
3.5 Discussion

A method has been presented for selecting and scaling bedrock

earthquake motions for the seismic design and evaluation of bridges. The

method lends itself well to implementation on a computer with interactive

graphics capabilities. A demonstration program, EARTHGEN, has been

described. EARTHGEN allows a designer to rapidly view response spectra

from a large number of historically recorded ground motions, then select and

scale the records which are most appropriate for a particular site and structure.

EARTHGEN has been initially configured for Northern California region, but

could easily be re-configured for other localities. To do so it is only necessary

to supply attenuation relationships (such as those developed in the studies of

Campbell 1981, Idriss 1985, Joyner and Boore 1988, and Youngs et al. 1988)

and specify a data base of bedrock motion records which are appropriate for the

geology of the region of interest.

3.6 Bedrock Acceleration Records Selected for Trial Bridge Column

Designs

EARTHGEN was used to select and scale suites of bedrock acceleration records

for use in the trial bridge column designs of this study. A total of 64 records

were selected and scaled: (suite of 4 records) x (magnitudes 5.0, 6.0, 7.0, and

8.0) X (distances 10 km, 20 km, 30 km and 40 km) = 64 records. These records

are listed, along with their amphtude scale factors, in Appendix B. In all cases,

records were selected which required the minimum amplitude scale factor to

match the target response spectrum. However, for some of the high magnitude

events at close distances the scale factors were comparatively large, out of

necessity, since very few near-field records exist for large magnitude

earthquakes.

32
4.0 Damage State Prediction

4.1 Introduction

It was shown in Chapter 2 that the inelastic response of a spiral-reinforced

bridge column when subjected to random lateral loading can now be

analytically predicted with reasonable accuracy. The present availability of

empirical closed-form equations for the hysteretic model parameters a, p, and y

allows the extension of this type of analysis to practical seismic design, where

the engineer has available beforehand only the geometry and material properties

of a bridge column and a suite of appropriate design earthquakes (the selection

of which was described in Chapter 3).

Given that we can predict the response of the bridge to an earthquake

characterized by magnitude and distance, the next question is: "would the

column be damaged, and if so, how severely?" For practicing engineers who

must perform post-earthquake assessments of highway structures, the

quantification of damage is a subjective process. The determination of when a column is serviceable; when it is not serviceable but can be economically

repaired; or when it must be destroyed, based solely on an extemal inspection

inherently involves a high degree of variability.

In this chapter we discuss an altemative approach to damage assessment. It is a two step process involving first the analytical calculation of a damage index,

and second a comparison of this value with a statistical damage state model.

The latter, as will be discussed in greater detail below, is based upon extensive

empirical correlation studies with existing laboratory data from tests of fullsc^e and model bridge columns.

Briefly stated, a damage index is a dimensionless quantity generated by a mathematical algorithm during the course of an inelastic dynamic analysis.

Many damage algorithms have been proposed over the last two decades. All

have the common feature of equating the damage index to parameters believed

to be related to the overall state of a structural element, as observed in

laboratory tests of beams, columns, bents, multi-story frames, etc. The original

models were primarily based upon a ratio of the maximum observed lateral

displacement and the calculated ultimate displacement of the structure under

monotonic loading. Later improvements recognized that strength degradation

also occurred during consecutive cycles at the same displacement ductility.

This additional cyclic damage was presumed to be caused by energy absorbed

by the structural element, as measured by the area bounded by a hysteresis loop

for one cycle of reversed loading.

33
The damage index model employed in the original release of IDARC [Park,

Ang, and Wen 1985] is given by:

where:

dm - Maximum deformation under seismic loading

3u = Ultimate deformation under monotonia loading

Py = Yield load under monotonia loading

Eabs - Absorbed cyclic energy under seismic loading

(3 = Strength deterioration parameter

a.,p.

This equation may be evaluated at any successive displacement step (if the

analysis is simulating a displacement-controlled test) or at any discrete time

step in a transient (earthquake) analysis. The first component represents a

ductility ratio whereas the second component is a strength deterioration term

which is tied to the cumulative normalized energy absorbed by the column.

Although damage indices calculated using this equation generally run between

0 and 1.0, values of D.I. can be significantly higher depending on confining

reinforcement details.

The 1992 release of IDARC, which was modified extensively for work specific

to this report, employs an alternative formulation of the damage index equation

which is more versatile. Direct application of the original model to structural

systems requires determination of an overall member deformation. Since

inelastic behavior is confined within plastic zones near the ends of a member,

the relationship between overall member deformation, local plastic rotations,

and the damage index is difficult to correlate. The 1992 IDARC damage index

equation, based on moment and curvature, rather than loads and deflections, is

34
r A

D.L = + P

y J

where:

Om = Maximum curvature attained during seismic loading = Ultimate curvature capacity of section

Or = Recoverable curvature at unloading

My = Yield moment of section

At = Total area contained in M-O loops

P = Strength deterioration parameter

The term At does not correspond to the original energy term in Park's model.

However, it does represent an implicit measure of energy, and when normalized

as indicated above, was found to correlate well with the original strength

deterioration parameter, (3. As described above, the moment-curvature model

is more versatile, particularly where complex indeterminate structures are involved. For the case of a cantilevered bridge column, however, the results are essentially the same as for the load-displacement formulation and either model

could be used effectively (the previous model being more intuitive). For the

sake of continuity with future, more sophisticated, analyses of indeterminate

multiple-pier bridge bents, we have used the moment-curvature formulation for

the work presented in this paper. Because the damage index equations are in a non-dimensional format, they permit comparisons between columns of different

sizes as well as columns with different loading histories.

4.2 Damage States

Figure 4.1 shows a typical inelastic cyclic test of a bridge column under

displacement control through failure of the column. In this figure three discrete

conditions relating to the structural integrity of the column are called out: yield,

ultimate, and failure. Although cracking and "spalhng" might also be useful,

these were not considered as limiting states for the following reasons. First,

except in special prestressed situations, service load cracking is normal in

reinforced concrete and does not always represent a cause for concern, nor does

it constitute the sole cause for repair of a structure in the wake of an earthquake.

35
NIST Test Column: Model-N2

-80

-80 -60 -40 -20 0 20 40 60 80

Lateral Displacement (mm)

Figure 4.1. Damage states of a laboratory test column.

Damage Index vs. Load Step Number

NIST Test Column Model N2

Load Step Number, N

Figure 4.2. Increase of damage index with load step.

36
Yielding of longitudinal steel, on the other hand, is a signal of the onset of real

structural distress. Spalling of cover concrete in the plastic hinge region will

generally occur following extensive yielding but prior to reaching the ultimate

load (moment) capacity of the section. It is therefore a symptom of extensive

yielding, and not the cause. Ultimate load (moment) capacity of the section is

simply the maximum observed lateral load (moment) capacity of the column.

Beyond this point the stiffness of the column is negative and continued

application of the ultimate load would lead to complete failure of a single,

isolated column. However, a bridge column is usually part of a larger structural

system, and, depending on the structural configuration, can often be restrained

from lateral collapse by other structural elements. In displacement-controlled

tests it is possible to track the behavior of the column in this regime. It has

generally been accepted that once the lateral load capacity has fallen off to less

than 80% of the ultimate load the column will completely fail in an actual

earthquake, due to high moments created by its own axial load (P-3 effects).

This has been labeled in figure 4. 1 as the failure state of the column.

The above three states form useful delimiters for four possible damage

conditions that might exist in a bridge column following an earthquake. These

are:

1) No Damage: the column has not yielded. Although cracking may have

occurred it will likely not be extensive and will not

compromise the serviceability of the structure.

2) Repairable: the column has yielded but has not reached ultimate load.

Extensive spalling may have occurred but inherent stiffness

remains and economics will likely dictate that the structure

should be repaired rather than replaced.

3) Demolish: the column has been loaded beyond ultimate load but

remains standing. Complete failure is likely pending

another severe earthquake and the column, at least, and

possibly the entire bridge structure must be replaced.

4) Collapse: the column has completely failed and will likely contribute

to collapse of the entire bridge.

As described above, the model employed in IDARC produces a quantitative

estimate of deterioration under cyclic loading, namely the damage index. As an

example of how this index is cumulative throughout the loading history for a

particular column figure 4.2 shows the damage index at each displacement load

step for the same column depicted in figure 4.1.

37
While the damage index provides a convenient relative measure of degradation

under cychc loading, in a practical sense the damage index is useless unless it can be calibrated against experimentally observed states of column damage.

Therefore, it was necessary to investigate the correlation between the observed

states of damage in cyclic lateral load tests of spirally-reinforced bridge piers

and the calculated damage indices produced by IDARC. Furthermore, for the

purpose of establishing seismic design guidelines, it is advantageous to

establish threshold damage indices which indicate the likely occurrence of three

damage states: onset of yielding (Py); attainment of maximum lateral load

capacity (Pult); and complete failure (Pfail).

4.3 Determination of Threshold Damage Indices

Threshold damage indices for the yield, ultimate and failure damage states were

conservatively estimated by examining the statistical distribution of calculated

damage indices from laboratory tests of 82 spiral-reinforced bridge piers (a

digital database for these tests has been established at NIST). The procedure for

the determination of the damage indices is outlined below.

For each of the 82 tests listed in table A.l and A.2 the points in the

experimental loading history at which the yield, ultimate and failure damage

states occurred were determined by inspection of the load-displacement

histories, as illustrated in figure 4.1. Three separate IDARC analyses were then

carried out for each test specimen: the first analysis produced a calculated

damage index resulting from the load-displacement history applied up to the

observed point of yielding; in the second analysis the damage index was

calculated for a virgin column subjected to the load-displacement history from

its beginning up to the observed point of ultimate load; and in the third analysis a virgin column was subjected to the load-displacement history from its

beginning up to the observed failure point.

Table C.l presents a summary of the damage analyses, indicating the number of

displacement steps ("Number of Data Points") from the laboratory tests used in

the analysis, the observed damage state, the deformation (curvature) damage,

the energy (M-O) damage, and total damage. The yield state could not be

determined for one test, the ultimate state did not occur for one test, and the

failure state did not occur for 16 tests. Thus, the available populations were 81,

81, and 66 tests for estimating threshold damage indices for yield, ultimate, and

failure damage states, respectively.

38
Histograms of calculated damage indices for each of the three damage states are shown in figures 4.3, 4.4, and 4.5. In all three cases the distributions have a pronounced mode (peak value) and are skewed strongly to the left. An estimate

of the most frequently occurring threshold damage index would be the mode of

the distribution, and a conservative estimate of the threshold damage index

would lie somewhat to the left of the mode. After close examination of the data

it was determined that the tenth percentile of each of the three distributions

provides threshold damage index estimates which are close to the mode, but are

fairly conservative. That is, in all three cases the tenth percentile threshold lies

close to the most frequently observed value of the threshold damage index, and

at the same time 90% of the calculated damage indices lie above the tenth

percentile. The tenth percentile threshold damage indices for the three damage

states are discussed in Section 4.4, and shown in table 4.1.

Yield State Damage Indices (Closeup of Range 0.0 to 2.5)

20

o

I

o

o

o

o

c

Tenth Percentile 81 Observations

Histogram

category size 0.1 Minimum recorded damage index 0.05

Maximum recorded damage index 12.66

Tenth percentile 0.11 Tenth percentile

90% confidence

interval

(0.08,0.17)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 Computed Damage Index

Figure 4.3. Histogram of observed yield state damage indices.

39
Ultimate State Damage Indices (Closeup of Range 0.0 to 5.0)

16

enth Percentile

81 observations

0.0 0.5

Histogram

category size 0.1

Minimum computed

damage index 0.19

Maximum computed

damage index

54.12

Tenth percentile 0.40

Tenth percentile

90% confidence

interval

(0.32,0.43)

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 Computed Damage Index

Figure 4.4. Histogram of observed ultimate state damage indices.

Failure State Damage Indices (Closeup of Range 0.0 to 5.0)

<—Tenth Percentile 66 observations

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Computed Damage Index

Figure 4.5. Histogram of observed failure state damage indices.

40
4.4 Variability of Threshold Damage Indices

The proposed threshold damage indices discussed above were derived from a diverse experimental database. Thus, in a qualitative sense one could be fairly

confident that the proposed tenth percentile threshold values will not change

dramatically in light of future experimental results. However, it is desirable to

have a quantitative measure of the variability of the tenth percentile values. In

other words, one would like to know how precisely the tenth percentile values

have been determined. If there is wide variabiHty in the tenth percentile values,

then further experimentation might be required to establish reliable damage

index thresholds. If there is narrow variability, then the proposed values could

be used with reasonable confidence.

4.4.1 The Bootstrap Method

As described in section 4.3 above, estimates of the threshold damage indices

were made, using as a database of all the known experimental results from

cyclic lateral load tests on spirally-reinforced bridge piers. Since this database

is of finite size, it would appear that an estimate of the variability of any single

statistical parameter (such as the tenth percentile) could only be made if a large

number of additional databases of similar size became available. Specifically,

in order to determine the variability of the tenth percentile estimates made

above, one would need to collect a large number, say 500, additional sets of

tests on 82 bridge piers, compute the tenth percentile of each set of 82 tests,

then find the mean and standard error terms of the 500 resulting tenth percentile

values. Clearly, it is very unlikely that such a large number of tests on spirallyreinforced bridge piers will ever be carried out. However, using a statistical

technique known as "resampling" or "the bootstrap method," one can simulate a very large data set and obtain estimates of the variability of the statistical

parameters that characterize the original, smaller, data set.

Overviews of the bootstrap method, its theory and applicability are presented by

Efron and Gong (1983), Diaconis and Efron (1983), and Efron and Tibshirani

(1986). The fundamental requirement for valid apphcation of the bootstrap

method is that the available data set be a representative subset of a much larger

population. In the case at hand, it is reasonable to assume that the 82 column

tests, performed by a number of different researchers working in separate

laboratories, and employing a variety of experimental methods, is a representative random sample of the very large number of column tests which

could be (but probably wiU not be) performed in the future.

41
The steps of the bootstrap method may be described conceptually as follows.

First, the original data set of size n is randomly sampled, with replacement of

each value after sampling, to obtain a new set of n variables. Because

sampling is done with replacement, the probability of sampling any one value

from the original data set is always 1/n, and there may be multiple occurrences

of the same value in the new data set. Once the new data set is obtained, the

statistical parameter of interest (mean, variance, percentile, etc.) is computed.

Sampling of new data sets with n values is carried out a sufficient number of

times (on the order of several hundred to several thousand) to obtain a histogram which shows the variability of the parameter of interest. Once this

histogram has been constructed, indicators of the variability of the parameter,

such as the standard error term and confidence intervals, can be computed.

4.4.2 Application of the Bootstrap Method to Threshold Damage Indices

The bootstrap method was applied to the tenth percentile threshold damage

indices, derived earlier, by carrying out sampling with replacement of data sets

with 81 values (or 66 values in the case of the failure damage index) 10,000

times. Tenth percentile damage indices were computed for each of these 10,000

data sets. Subsequent analyses of the 10,000 damage indices resulted in

standard error terms and 90% confidence intervals for each of the three

threshold damage indices (yield, ultimate and failure damage states). Table 4.1

summarizes the estimates of the threshold damage indices obtained from the

original data sets, and the standard error terms and 90% confidence intervals

obtained from the bootstrap method. The threshold damage indices in the table

can be interpreted as the best available empirical estimates of the tenth

percentile thresholds, and the 90% confidence intervals can be interpreted as the

estimated variability in the threshold damage indices, based on a large

bootstrapped data set.

Table 4.1. Threshold Damage Indices for Spiral-Reinforced Bridge Piers, and

Estimates of Their Variability

Damage

State

Threshold

Damage Indices

Standard

Error Term

90% Confidence

Interval

Yield 0.11 0.03 (0.08,0.17)

Ultimate 0.40 0.03 (0.32, 0.43)

Failure 0.77 0.05 (0.71,0.86)

42
5.0 Analysis of CALTRANSrolnmn.

5.1. Selection Criteria

To demonstrate the seismic design approach described in this report, a series of

representative spiral-reinforced single column bridge bents was selected for

analysis. These columns were designed according to the seismic design

procedures currently published by CALTRANS [CALTRANS 1990], which

are an extension of AASHTO standards [AASHTO 1989] , and are generally

considered to be the most stringent seismic design standards for bridges in the

United States. This series of CALTRANS-designed columns was then analyzed

using the procedures outlined above in Chapters 1 through 4, and the

performance of the columns was evaluated. The series of columns chosen for

analysis had geometries, material strengths and axial loads typical of those

found in practice. However, due to the hmited scope of this study, it was not

possible to perform a comprehensive set of analyses encompassing all common

design parameters. That is, the series of analyses addresses a sampling of

columns, and further study is required to fully evaluate the adequacy of the

CALTRANS approach to seismic design.

The general characteristics of the series of columns analyzed in this study are summarized in table 5.1 below.

Table 5.1. General characteristics of CALTRANS columns analyzed in this

study

Column Characteristic Values Investigated

Diameter, D 122 cm

Length/Diameter ratio, L/D 3,6,9

Concrete cylinder strength, fc 27.6 MPa

Axial reinforcement yield, ultimate stress 414, 724 MPa

Spiral reinforcement yield, ultimate stress 414, 724 MPa

Axial load level = Pe/(fc*Ag) 0.05, 0.10, 0.15

Clear cover to spiral bars 5.1 cm

Diameter of spiral reinforcing bar 1.59 cm

Soil overburden none (bedrock), 37 m sand

Distance from causative fault 10, 20, 30 and 40 km

The column diameter in all cases was fixed at 122 cm, and the length was

varied to obtain length-to-diameter ratios of 3, 6, and 9. Concrete and steel

material properties were assigned the typical values shown in table 5.1. The

43
axial load levels of 0.05, 0.10, and 0.15 cover the range of values commonly

found in practice. The spiral bar diameter and concrete clear cover dimensions

also have typical values. Two soil overburden conditions were selected for

analysis: no soil overburden (construction on bedrock, or less than 3 m of

alluvial deposits), and 37 m of sand. Distances of 10, 20, 30, and 40 km from

the causative fault were investigated, in order to explore the effects of distance

attenuation effects on column behavior. A total of 72 columns were designed

by the CALTRANS procedures [(3 L/D ratios) x (3 axial load levels) x (2 soil

conditions) x (4 distances to causative fault) = 72 cases].

5.2. Design of Columns

The currently published CALTRANS seismic design procedures permit an

equivalent static lateral load analysis for most ordinary bridge structures. This

procedure is summarized in figure 1.1, and its essential features are outlined

below.

The first step of the procedure is to estimate the fundamental period of the

elastic, undamaged structure by means of a simple function:

T = 0.32VW/k

where W is the axial dead load of the bridge, and k is the lateral stiffness of the

substructure, in compatible units. An empirical factor, Z, is then read from a graph. Z accounts for the approximate ductility of the member being analyzed,

and the risk associated with failure of that member. Next, knowing the

geographic location of the proposed bridge, a value of peak bedrock

acceleration is read from a series of acceleration isoclines plotted on a map of

California. This map accounts for the locations of known active faults in

Califomia, the maximum credible earthquakes associated with those faults, and

the attenuating characteristics of the subsurface geology. Once the period of the

structure and the peak bedrock acceleration have been determined, an "ARS

factor" is read from a curve which corresponds to one of four soil overburden

conditions: 0-3 m alluvium, 3-24 m alluvium, 24-46 m alluvium, or over 46 m

alluvium. These ARS curves are pseudo-acceleration response spectra, which

have been adjusted for peak bedrock acceleration and soil amplification effects.

Finally, the equivalent static lateral load, F, for which the structure is to be

designed is found from the equation

^ (ARS)(W)

44
Sizing and detailing of the pier then proceeds as it would for a static design,

with certain additional constraints imposed on reinforcement contents to insure

adequate ductility under cyclic loading.

The distance of the bridge from the causative fault is not an explicit factor in the

CALTRANS design procedure; rather, distance is considered implicitly by

means of the peak bedrock acceleration map for California. Since the design

method described in this report accounts explicitly for distance, a means of

explicitly entering distance in the CALTRANS designs procedure was required.

This was accomplished by surveying the California peak acceleration map and

extracting peak acceleration values from the map for distances of 10, 20, 30,

and 40 km from major active faults. A total of 15 locations were examined near

major faults throughout the state. The maximum peak acceleration values from

any of these 15 locations (conservatively rounded up to the nearest O.lg) are shown in table 5.2 below. These acceleration values represent the worst

possible peak ground accelerations required under the CALTRANS design

procedure, and should result in conservative, or at least acceptable, designs at

any location in the state.

Table 5.2. Maximum CALTRANS bedrock accelerations for various distances

from fault

Distance of bridge from

causative fault

Maximum peak bedrock

acceleration from CALTRANS

km design map, g's

10 0.6

20 0.4

30 0.4

40 0.3

It was found that for all 72 designs the spiral reinforcement content was

controlled by the CALTRANS requirement for minimum confining steel, so #5

spirals spaced at 12.1 cm are used in all cases. The calculated longitudinal

reinforcement contents for the 72 designs are shown in tables 5.3 and 5.4 below.

45
Table 5.3. Longitudinal reinforcement contents for CALTRANS designs on

bedrock

L/D Pe/(fc*Ag) = 0.05 Pe/(fc*Ag) = 0.10 Pe/(fc*Ag) = 0.15

Distance =10 km, amax = 0.6 g

3.0 18 - #9 bars 18 - #9 bars 18 -#10 bars

6.0 18- #9 bars 18- #9 bars 18 -#10 bars

9.0 18- #9 bars 18- #9 bars 25 - #10 bars

Distance = 20 km, amax = 0.4 g

3.0 18- #9 bars 18- #9 bars 18- #9 bars

6.0 18- #9 bars 18- #9 bars 18- #9 bars

18- #9 bars 18- #9 bars 21 -#10 bars

Distance = 30 km, amax = 0.4 g

3.0 18- #9 bars 18- #9 bars 18- #9 bars

6.0 18- #9 bars 18- #9 bars 18- #9 bars

9.0 18- #9 bars 18- #9 bars 21 -#10 bars

Distance = 40 km, amax = 0.3 g

3.0 18- #9 bars 18- #9 bars 18- #9 bars

6.0 18- #9 bars 18- #9 bars 18- #9 bars

9.0 18- #9 bars 18- #9 bars 21 -#10 bars

46
Table 5.4. Longitudinal reinforcement contents for CALTRANS designs on

37 m sand

L/D Pe/(fc*Ag)=0.05 Pe/(fc*Ag) = 0.10 Pe/(f'c*Ag)=0.15

Distance =10 km, amax = 0.6 g

3.0 18- #9 bars 18 - #9 bars 18 - #9 bars

6.0 18 - #9 bars 21 -#11 bars 22 - #14 bars

9.0 18 -#10 bars 20 - #14 bars 31 -#14 bars

Distance = 20 km, amax = 0.4 g

3.0 18- #9 bars 18- #9 bars 18 - #9 bars

6.0 18 - #9 bars 18 -#10 bars 25 -#10 bars

9.0 18 - #9 bars 21 -#10 bars 20 - #14 bars

Distance = 30 km, amax = 0.4 g

3.0 18 - #9 bars 18 - #9 bars 18 - #9 bars

6.0 18- #9 bars 18 -#10 bars 25 - #10 bars

9.0 18- #9 bars 21 -#10 bars 20 - #14 bars

Distance = 40 km, amax = 0.3 g

3.0 18 - #9 bars 18- #9 bars 18 - #9 bars

6.0 18 - #9 bars 18 - #9 bars 20 - #10 bars

9.0 18 - #9 bars 18- #9 bars 19 -#11 bars

5.3. Inelastic Dynamic Analyses of CALTRANS Designs

5.3.1. Overview

In Chapter 3 the selection and scaling of bedrock acceleration records for

seismic design of bridges was discussed. This method is briefly summarized

below.

The approach taken in this report is to utihze, to the greatest extent possible,

suites of three to five natural bedrock acceleration records which were recorded

under conditions similar to the specified design conditions for the bridge.

Suites of records, rather than a single record, are used to account for the natural

variabihty in frequency content of seismic events. If the design requirements

for the bridge call for a certain minimum level of performance when the bridge

47
is subjected to a magnitude 7.0 event at a distance of 20 km, then the preferred

suite of bedrock motions for input to the inelastic analyses procedure would be,

of course, bedrock motions recorded under similar geological conditions, from

magnitude 7.0 events at a distance of 20 km. However, lacking such a suite of

recorded bedrock acceleration records, minimal amplitude (but not frequency)

scaling is carried out on records obtained from events which are as close as possible to the desired event. The amplitude scaling factor for each record in

the suite is determined by comparing the acceleration response spectrum of

each record to a "target" response spectrum, which is calculated for the desired

event.

Experience has shown that a sufficient number of recorded bedrock motions are currently available to make this approach within the realm of possibility for

Califomia, and possibly for much of the West Coast region of the United States.

However, for the Central and Eastern regions of the United States, it may be

necessary to make use of synthetic acceleration records. While the validity of

using synthetic records is open to debate, they may be the only available option

in some cases.

Once a suite of design bedrock motions is determined, whether the suite is

natural, amplitude scaled, or synthetic, the bridge design under consideration is

subjected to each record in the suite individually (not sequentially). The single

record which causes the greatest damage to the structure determines the worstcase damage index expected for the bridge under the design-level earthquake at

the design distance. This worst-case damage index is then compared with

acceptable levels of damage, discussed in Chapter 6, to determine whether or not the design is adequate.

The suites of design-level earthquakes derived for use in this study are listed in

Appendix B. A suite of four records was developed for each of magnitudes 5.0,

6.0, 7.0, and 8.0, at distances of 10 km, 20 km, 30 km, and 40 km, making a

total of 64 records.

5.3.2. Analyses on Bedrock Substrate

A schematic of the analysis of a single spiral column bridge bent situated on

bedrock is shown in figure 5.1. Each inelastic dynamic analysis of a column

results in a plot of damage index vs. time for the column. Examples of such

plots (for the same column with three different L/D ratios) are shown at the top

of figure 5.1. It can be seen that for each analysis the damage index rises to a certain value, then levels off as the ground shaking subsides. This terminal

value of damage index is used to characterize the performance of the column

design, when subjected to the given seismic event.

48
As discussed in Section 5.2 above, 36 sample columns were designed using

CALTRANS procedures, assuming the columns were situated on bedrock (table

5.2). Each of these designs was subjected to 16 bedrock acceleration records:

four suites consisting of four records, each suite containing four earthquakes of

the same magnitude and distance. The highest of the four terminal damage

index values obtained from each suite was used to characterize the performance

of the column when subjected to the given magnitude earthquake at the given

distance. The numerical results of these analyses are presented in Section 6.2.

5.3.3. Analyses on 37 m Sand Substrate

A schematic of the analysis of a single spiral column bridge bent situated on an

alluvium substrate is shown in figure 5.2. The process of computing the

damage index is exactly the same as describe above, except for the intermediate

step of propagating the bedrock acceleration record to the ground surface. As

explained in Section 1 .2, this was accomplished in the present study using the

program SHAKE91.

Thirty-six sample columns were designed assuming they were situated on a 37

m thick layer of sand overlying bedrock (table 5.4). The results of these

analyses are presented in Section 6.2.

49
-0.25 LL = = = ' 0 5 10 15 20

Time, sec Bedrock Acceleration Record

Figure 5.1. Calculation of damage index for bridges on bedrock substrate.

50
D

\ \ S X \ s f f f f f f

N S \ S \ -J yyyfyy/yfyyyyyyyyyyfyff\

/yyy////f/yyfyy/yyyfyy \ \ \ \ \ \

s \ \ s s \ s \ s X \ \

//////

ALLUVIUM |s\\s\\ f///x///x////////////x//l

'////////X///////////'//'/ /•////•//////////////x/// Iv. xxxxxxxxxxxxxxxxxxxxxxx \ s. s \ \ \ \ \ s s N S \ S \ S \ \ X \ \ x s. \ \ \ \ xxxxxxxxxxxxxxxxxxxxx// rxxxxxxxxxxxxxxxxxxx/xxx Ixxxxxxxxxxxxxxxxxxx/xxx xxxxxxxxxxxxxxx/x/x/xxx i.SXS\\\S\\S\.\\\S\\\\\S\' xxxxxxxxxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxxxxxxxx S X \ s X X X \ X X X X xxxxxxxxxxxxxxxxxxxxxxx

X X X X X X X xxxxxxxx X X X X X X xxxxxxxxxxxxxxxxxxxxxxx sXXXXXXXXXXXX xxxxxxxxxx

xxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxxxxxxxx

xxxxxxxxxxxxxxxxxxxxxxx

BEDROCK

co

•a

C3

o

co

1-1 o

o<

Time (seconds)

Damage Index vs. Time

I 5 10 15 Time, sec Surface Acceleration Record

20

0.60

0.40

0.20

0.00

-0.20

-0.40

-0.60

a.S

O 1/5 Oh

0 5 10 15 Time, sec Bedrock Acceleration Record

Figure 5.2. Calculation of damage index for bridges on alluvium substrate.

20

51
6.0 Performance of CALTRANS-Designed Columns

6.1. Development of Relationships for Acceptable Damage

In this section relationships are proposed for acceptable levels of seismic

damage to spiral reinforced bridge piers. In this study damage is quantified in

terms of the damage index, and acceptable values of the damage index are expressed in terms of earthquake magnitude, distance of the structure from the

causative fault, and the importance of the structure.

Acceptable levels of structural performance (e.g., minimum strength, allowable

deflections) are normally determined by code writing organizations, and local,

state and national government agencies. However, no guidelines for acceptable

levels of seismic damage currently exist. Because the notion of employing a "damage index" to gage the seismic performance of reinforced concrete

structures is relatively new, code writing bodies have not yet addressed the

issue of determining an "acceptable" damage index for a given structure

subjected to a given seismic event. Therefore, a proposed model for acceptable

damage level was derived in this study, and is described below. While the

model was developed specifically for spiral-reinforced concrete bridge piers,

with minor modifications the model could be applied to other types of

reinforced concrete members and structures.

The level of seismic damage deemed "acceptable" for a given structure is

mainly a function of two conditions: the severity of the seismic event, and the

importance of the stmcture. In tum, the severity of the seismic event depends

on a number of subsidiary factors, including the magnitude of the event, the

distance of the causative fault from the structure, and the ground motion

attenuation characteristics of the local geology. Likewise, the importance of the

structure depends on several subsidiary factors, such as the threat to hfe-safety

posed by the structure, the role of the structure in maintaining essential lifeline

services (transportation, communication, utilities delivery, medical care, and

governance) following a major earthquake, and the potential cost of repair or replacement of the structure. (For further discussions of evaluating the

structural importance of bridges, see Maroney 1990, FHWA 1983, and FHWA

1987).

Thus, many factors figure into the determination of an acceptable level of

damage for a specific structure at a specific location subjected to a specific

seismic event. For example, extensive damage of an unimportant and

inexpensive structure in a minor seismic event might be tolerated, but a highly

important structure might be required to remain fully operational following a

52
severe earthquake. Along these lines, a number of guiding principles can be

stated which shape the development of a model of acceptable damage. First,

regardless of the characteristics of the seismic event or the importance of the

structure, total collapse of the structure must be avoided, as total collapse

would likely result in loss of life. Second, for small events at large distances

from causative faults the damage suffered by any structure should be minor.

Depending on the importance of the structure, this minor level of damage

should lie somewhere between the state of no perceptible damage and the state

of first yield. Third, for very large, extraordinary, seismic events (on the order

of magnitude 8) extensive damage is unavoidable even at moderate distances

from the causative fault (say 40 km). Therefore damage indices approaching

(but less than) the failure damage state must be allowed in some cases. Finally,

allowable damage levels should in general be lower for important structures

than for unimportant structures.

Using the guiding principles outlined above, matrices of acceptable damage

indices could be constructed, which are functions of earthquake magnitude,

distance to fault and structural importance. Although the precise level of

acceptable damage at a given magnitude, distance and structural importance

level is somewhat open to interpretation, the approximate levels of acceptable

damage are generally evident. In this study, three damage index thresholds

have been defined: yield, ultimate, and failure, as discussed in Chapter 4.

Acceptable damage index matrices are constructed in terms of those threshold

values.

An example of a matrix of acceptable damage indices is illustrated by the bar

chart in figure 6.1. The proposed values shown are for bridge piers which are deemed moderately important to seismic lifelines, that is, for piers in bridges

which are judged to have a secondary role in sustaining transportation routes

and emergency services following an earthquake. Notice that for earthquakes

near magnitude 8.0 a high level of allowable damage is proposed for all

distances up to about 50 km. This reflects the difficulty and impracticality of

limiting damage of moderately important bridges subject to massive, extremely

rare events, even at considerable distances from causative faults. Similarly, a

fairly high level of damage is allowed for moderate magnitude earthquakes at

small distances, up to about 30 km. Very low levels of damage are permitted

for low magnitude earthquakes at moderate-to-large distances.

53
0.40 = ultimate

0.11 = yield

Figure 6.1. Estimated acceptable damage indices, as functions of

magnitude and distance, for bridge piers deemed moderately

important to seismic lifelines.

Figure 6.2 shows a matrix of proposed allowable damage indices for piers in

bridges which are highly important to seismic hfelines. High levels of damage

are acceptable only for very large events at small distances, and the allowable

damage index decreases rapidly as distance increases and magnitude decreases.

This would permit most important lifeline bridges - except those very close to

the causative fault - to remain in limited operation following a major

earthquake. At moderate-to-small magnitudes and moderate-to-large distances

little or no damage is allowed, since under those conditions important lifeline

bridges should remain completely serviceable.

54
Figure 6.2. Estimated acceptable damage indices, as functions of

magnitude and distance, for bridge piers deemed highly important

to seismic lifelines.

The process outlined above can be extended another step by fitting smooth,

three-dimensional surfaces to the discrete values shown in the bar charts of

figures 6.1 and 6.2. In this way acceptable damage levels for moderately

important and highly important bridge piers can be expressed as simple,

continuous functions of magnitude and distance. Continuous functions have the

advantage of being easily usable by design engineers, and, unlike tables of

discrete values, continuous functions provide unambiguous values of acceptable

damage at any magnitude and distance. A simple surface with a shape

appropriate to the data of figures 6.1 and 6.2 is a hyperbolic trumpet, which has

an equation of the form

55
where D.L = D = M =

damage index

distance, km

earthquake moment magnitude

a,b,c = coefficients

and 0<D.L <0.77

5 < D < 50

5.0 <M<8.0

The valid range of the surface is limited by the three conditions on damage

index, distance, and magnitude, as shown above. The first condition reflects the

fact that damage indices greater than the failure damage index, determined in

this study as 0.77 for spirally reinforced bridge piers, are not possible. The

second and third conditions are imposed by limitations on the ranges of distance

and magnitude investigated in this study.

Figures 6.3 and 6.4 show surfaces which, in general, fit conservatively (that is,

generally provide a lower bound to) the bar graphs of figures 6.1 and 6.2.

These surfaces have equations of the form shown above. The equations of the

curves in figures 6.3 and 6.4 were found by selecting three mathematical control

points for each curve, which in turn were used to solve for the coefficients a, b

and c. The control points used in this study are shown in table 6.1 below.

Although some of the control point values are outside the normal ranges

considered in design, they do serve to mathematically constrain the smoothed

curves of figures 6.3 and 6.4 so that they generally form lower bounds to the bar

graphs of figures 6.1 and 6.2, over practical ranges of magnitude and distance (5

km < distance < 50 km and 5.0 < magnitude < 8.0).

56
Table 6.1. Control points used to solve for curves of figures 6.3 and 6.4

Magnitude Distance Damage Index

Structures of Moderate Importance to Seismic Lifelines (figure 6.1)

Control Point 1 6.5 0 0.77

Control Point 2 9.0 65 0.40

Control Point 3 9.0 50 0.77

Structures of High Importance to Seismic Lifelines (figure 6.2)

Control Point 1 7.0 0 0.4

Control Point 2 9.0 50 0.0

Control Point 3 4.0 0 0.0

The equation of the surface in figure 6.3, for moderately important bridge piers,

is

D.L =

1 ^(9-M)'

- 0.14

2300 5.7

where D.L = damage index

D = distance, km

M = earthquake moment magnitude

a,b,c = coefficients

and 0 < D.L < 0.77

5 < D < 50

5.0 < M < 8.0

57
.1

0J7 = failure

0.40 = ultimate

0.11 = yield

distance D, km

magnitude M

Figure 6.3. Proposed envelope for acceptable damage index, as a function of magnitude and distance, for bridge piers deemed

moderately important to seismic lifelines.

The equation for the surface in figure 6.4, for highly important bridge piers, is

1 D.I.=

(9-M)^

190 1.9

- 0.08

0 < D.I. < 0.77

5 < D < 50

5.0 < M < 8.0

58
0.77 = failure

0.40 = ultimate

0.11 = yield

distance D, km

magnitude M

Figure 6.4. Proposed envelope for acceptable damage index, as a function of magnitude and distance, for bridge piers deemed highly

important to seismic lifelines.

Further refinement of these acceptable damage level surfaces is possible, and

other surfaces could be constructed for other types of members and structures

and other levels of structural importance. The presentation here of the steps

followed in deriving these surfaces is intended as a demonstration of a rational

procedure. Such a procedure could be followed by code-writing bodies, and by

government agencies, to derive similar curves for the types of structures under

their jurisdiction.

6.2. Summary of Critical State Failures for CALTRANS Columns

In Chapter 5 a series of example analyses of CALTRANS-designed 122 cm

diameter spiral-reinforced bridge columns was described, hi this section the

results of those analyses are presented, and the performance of the CALTRANS

designs, as compared with the proposed acceptable damage index functions

derived in Section 6.1, is discussed.

59
6.2.1. Damage Index as a Function of Magnitude and Epicentral Distance

Below, 24 plots are presented showing calculated damage indices for the

example CALTRANS-designed columns as a function of magnitude and

distance. Twelve plots are for the example CALTRANS designs situated on

bedrock, and twelve are for the example CALTRANS design situated on 37 m

of sand overlying bedrock. Also shown, by heavy lines on each plot, are the

proposed acceptable damage level curves for bridges which are moderately

(upper curve) and highly important (lower curve) to seismic lifelines. (These

curves may be visualized as "slices" through the three-dimensional plots of

figures 6.3 and 6.4, parallel to the Magnitude axis). Horizontal shaded bands on

each plot show stages of degradation of the column, determined from analyses

of experimental data, as described in Chapter 4. Each plot presents results for a

single soil condition (bedrock or 37 m sand overburden), a single distance from

the causative fault (10 km, 20 km, 30 km, or 40 km), a single axial load level

(5%, 10%, or 15%) and three L/D ratios (3.0, 6.0, and 9.0).

Due to limitations on the scope of this study, the plots shown are only

representative of a much larger set of design charts which could in principle be

derived. Such a set of charts would allow the design engineer to estimate, in

advance of or following an earthquake, the level of damage a particular column

design suffers when subjected to a specific magnitude earthquake at a specific

distance. This estimate of damage could then be compared with specified

acceptable damage levels, such as the suggested curves shown by heavy lines in

each plot.

It is important to note that only those column performance curves that fall

entirely beneath a particular acceptable damage curve, up to the maximum

credible earthquake magnitude for the region, are considered to have met the

requirements of the proposed acceptable damage provisions. If the actual

column performance curve rises above the acceptable damage curve at a magnitude less than the maximum credible earthquake for the region, then

retrofitting should be considered. For example, referring to figure 6.9, the

design with L/D = 9.0 would be unacceptable in much of the Westem U.S., but

might be acceptable in parts of the Central United States and Eastem United

States, where in many localities maximum credible earthquake magnitudes are

less than 7.0.

60
1.0

0.8

V

XJ 0.6

at) a

B^ 0.4

0.2

0.0

122 cm diameter CALTRANS column, 5% axial load

10 km from fault, 37 m sand overburden

L/D = 3.0 L/D = 6.0 L/D = 9.0

bridge moderately important

to seismic lifeline ""Will

>^ Acceptable damage curv

bridge highly impxjrtant

to seismic hfeline me '-^^f'^-^^k I Demolish]^

5.5 6 6.5 7 7.5 Magnitude

Figure 6.5. Damage index 122 cm dia., 10 km, 37 m sand, 5% axial load.

8

1.0

0.8

O 0.6 B

OAs

0.2

0.0

122 cm diameter CALTRANS column, 10% axial load

10 km from fault, 37 m sand overburden — L/D = 3.0 — L/D = 6.0 — L/D = 9.0

M554_'i_'i *5 1 1,1 < 15,1 .1 11 11.'

Collj^psed

ii«miiini4<mmni«4«i-iniiiigmiiii«imiiiMm4'

Acceptable aamagt . bridge moderately important

to seismic lifeline

't. Acceptable damage curve

bridge highly important ; ^

to seismic lifeline

5.5 6 6.5 7

Magnitude

Figure 6.6. Damage index 122 cm dia., 10 km, 37 m sand, 10% axial load.

61
1.0

0.8

•O 0.6 c

OA

122 cm diameter CALTRANS column, 15% axial load

10 km from fault, 37 m sand overburden

0.2

0.0

— L/D = 3.0 — L/D = 6.0 — L/D = 9.0

, X .•• jr <.<:>m*?5!

Acceptable damage curve

bridge moderately miportant

to seismic lifeline Acceptable damage curve

bridge highly important

to seismic lifeline

Repairable

Functional

5.5 6 6.5 7 7.5 Magnitude

Figure 6.7. Damage index 122 cm dia., 10 km, 37 m sand, 15% axial load.

8

1.0

0.8

o 0.6

DOE

0.2

0.0

122 cm diameter CALTRANS column, 5% axial load

20 km from fault, 37 m sand overburden

L/D = 3.0 — = L/D = 6.0 — L/D = 9.0 Collapsed

Acceptable damage curve

bridge moderately important

to seismic lifeline

Acceptable damage curve

bridge highly important

to seismic lifelme 4 \.y<r..

5.5 6 6.5 7 7.5 Magnitude

Figure 6.8. Damage index 122 cm dia., 20 km, 37 m sand, 5% axial load

8

62

page 62
OAs

1.0

0.8

0.6

0.4

0.2

0.0

122 cm diameter CALTRANS column, 10% axial load

20 km from fault, 37 m sand overburden

L/D == 3.0 — L/D == 6.0 L/D == 9.0

>»>»»»»»»»»»»»»»*»> >l»»»»»l>»» >iyn»tt>t>t»mmm*t

Acceptable damage curve

bridge moderately important

to seismic lifeline

Acceptable damage curve

bridge highly important

to seismic lifeline

5.5 6 6.5 7 7.5 Magnitude

Figure 6.9. Damage index 122 cm dia., 20 km, 37 m sand, 10% axial load

8

1.0

0.8

o 0.6

s

61)

0.2

0.0

122 cm diameter CALTRANS column, 15% axial load

20 km from fault, 37 m sand overburden

>t>>k»»t>tk»)>>>>»>>>>t>>>»>0»tt»»>^>>>»t>>lt>t>»>l>>>»>fi>»l>>>»>>>tt>l»>»>>t»>»>t»>>>^>»>»»»»>»>l>>>l>»>>»>»>>>>>K

— L/D = 3.0 — L/D = 6.0 — L/D = 9.0

Acceptable damage curve

bridge moderately important

to seismic lifeline

Collapsed

Acceptable damage curve y'

bridge highly important

5.5 6 6.5 7 7.5 8

Magnitude

Figure 6.10. Damage index 122 cm dia., 20 km, 37 m sand, 15% axial load

63
1.0

0.8

"O 0.6

B

122 cm diameter CALTRANS column, 5% axial load

30 km from fault, 37 m sand overburden

0.2

0.0

— L/D = 3.0 — L/D = 6.0 — L/D = 9.0 Collapsed

Acceptable damage curve

bridge moderately important

to seismic lifeline

'

L'SiioTOlrii

j... Acceptable damage curve i. bridge highly important

Repairable

to seismic lifeline

i Functional

5.5 6 6.5 7 7.5 Magnitude

Figure 6.11. Damage index 122 cm dia., 30 km, 37 m sand, 5% axial load

8

1.0

0.8

"O 0.6 c

V

OX) CO£

0.2

0.0

122 cm diameter CALTRANS column, 10% axial load

30 km from fault, 37 m sand overburden — L/D = 3.0 — L/D = 6.0 — L/D = 9.0

Acceptable damage curve

bridge moderately important

to seismic lifeline

1/

Acceptable damage curve

bridge highly important

to seismic lifeline

IEc01 lapsed

[jjcrnolislf

fable

5.5 6 6.5 7 7.5 8

Magnitude

Figure 6.12. Damage index 122 cm dia., 30 km, 37 m sand, 10% axial load

64
1.0

0.8

Vo 0.6 c

DAE

0.2

122 cm diameter CALTRANS column, 15% axial load

30 km from fault, 37 m sand overburden

0.0

-- LA) = 3.0

- L/D = 6.0 — L/D = 9.0 Collapsed

Acceptable damage curve ; bridge moderately important [ «

to seismic lirelme r*r~^,i:^y»

i /

^

/

[Pcmojjs??'

Acceptable damage curve

bridge highly important

to seismic lifeline

pairable

Functional

5.5 6 6.5 7 7.5 8

Magnitude

Figure 6.13. Damage index 122 cm dia., 30 km, 37 m sand, 15% axial load.

a>e

a>

OX) 03 Q

LO

0.8

0.6

0.4

0.2

0.0

122 cm diameter CALTRANS column, 5% axial load

40 km from fault, 37 m sand overburden

L/D = 3.0 L/D = 6.0 L/D = 9.0

'yk>»»»>y>»>»»»>vk>>:

Collapsed

vkt>»t>bt»t»>»h)>>>kky>>»&)>>)>>vi>»>>>y)»k>>t>kt>>v>>>l>>k>>>>>>>»>>>»>t >>)>>>>>>>>•>>>>»>>>>>>»>>>»>>»>>>>>>>>>:

Acceptable damage curv e bridge moderately important

to seismic lifeline Demolish

ReJJaTrable ^4" Acceptable damage curve <<ri

^

.

•

i bridge highly important

: to seismic lifeline

i— \ fcjnctional

5.5 6 6.5 7 7.5 8

Magnitude

Figure 6.14. Damage index 122 cm dia., 40 km, 37 m sand, 5% axial load

65
1.0

122 cm diameter CALTRANS column, 10% axial load

40 km from fault, 37 m sand overburden — L/D = 3.0 — L/D = 6.0 — L/D = 9.0 Collapsed

0 8

^<<<<<<<<<<i<'f<^<<<''<^'f<''<^<<<<^''<^<^<<^<<<<<<<<<<<<<<<<<<<<<<?'<<<<<<<<<<<<<<<<<<<<<<<<<'-'

"2 0.6

c

at« 0.4

0.2

0.0

Accepiable dai'iiagi curve

bridge moderately important

to seismic lifeline

Acceptable damage curve

bridge highly important

to seismic lifeline

Repairat^

5.5 6 6.5 7 7.5 8

Magnitude

Figure 6.15. Damage index 122 cm dia., 40 km, 37 m sand, 10% axial load.

« 0.4 I

122 cm diameter CALTRANS column, 15% axial load

40 km from fault, 37 m sand overburden — L/D = 3.0 — L/D = 6.0 — L/D = 9.0 Collapsed

Acceptable aaiaage ^ui've bridge moderately important

to seismic lifeline olish

Acceptable damage curve

bridge highly important

to seismic Ufeline

i j. *tf1£tiflflgL

5.5 6 6.5 7 7.5 8

Magnitude

Figure 6.16. Damage index 122 cm dia., 40 km, 37 m sand, 15% axial load

66
1.0

0.8

O 0.6

B

B« 0.4

0.2

0.0

122 cm diameter CALTRANS column, 5% axial load

10 km from fault, on bedrock

L/D = 3.0 - L/D = 6.0 — L/D = 9.0

» „ fAw/.&^/yjyj^j^/'.jVy//j/y/yW^f//*y.jyvy^^,.^.,,

Acceptable damage curve

bridge moderately important

to seismic lifeline Acceptable damage curve ::mm bridge highly important

to seismic lifeline

5.5 6 6.5 7 7.5 Magnitude

Figure 6.17. Damage index 122 cm dia., 10 km, bedrock, 5% axial load.

LO

0.8

"2 0.6

eg« 0.4

0.2

0.0

122 cm diameter CALTRANS column, 10% axial load

10 km fronri faulto on bedrock — L/D = 3.0 — L/D = 6.0 — L/D = 9.0 I Collapsed

Acccpiaolc damage curve

bridge moderately important

to seismic lifeline # Acceptable damage curve • 'fvtvff^fl^ bridge highly important : ^ ^mm

to seismic lifeline ,jwf<f J Demolish

5.5 6 6.5 7 7.5 8

Magnitude

Figure 6.18. Damage index 122 cm dia., 10 km, bedrock, 10% axial load.

67
1.0

0.8

o 0.6

e

01) eaE« 0.4 Q

0.2

0.0

122 cm diameter CALTRANS column, 15% axial load

10 km from fault, on bedrock

Collapsed

IT!??!!!??!?!??!?!!!??! _ „ _ MM^^M-^^M...

>r»>»>»>»»»»»>»»»»>l»>l>D>l»l»»»l>l»>»»>r»»»M>i&>»»>»>>»r»>i>M>f»»>f» »'r> » r rtf t >| >. * -w >rf t i> t t it at ttt »>»>»»>»»>»»>»>»»»>f »>

Acceptable damage curve

bridge moderately important

to seismic lifeline

--- L/D = 3.0 - L/D = 6.0 — L/D = 9.0

Acceptable damage curve mm bridge highly important

to seismic lifeline

5.5 6 6.5 7 7.5 Magnitude

Figure 6.19. Damage index 122 cm dia., 10 km, bedrock, 15% axial load,

8

1.0

0.8

V

"2 0-6 B

hH

OX) E

0.2

0.0

122 cm diameter CALTRANS column, 5% axial load

20 km from fault, 37 m sand overburden — L/D = 3.0 — L/D = 6.0 — L/D = 9.0 I Gbllapsed

Acceptable damage curve

bridge moderately important

to seismic lifeline

5 4

Acceptable damage curve

bridge highly important

to seismic lifeline

5.5 6 6.5 7 7.5 Magnitude

Figure 6.20. Damage index 122 cm dia., 20 km, bedrock, 5% axial load

8

68
1.0

0.8

Vo 0.6 s

a

B« 0.4

0.2

0.0

122 cm diameter CALTRANS column, 10% axial load

20 km from fault, on bedrock — L/D = 3.0 — L/D = 6.0 — L/D = 9.0

Acceptable damage curve mm. bridge moderately important

to seismic lifeline ~**-t»^» s / i

I

Demolish

Acceptable damage curve bndge highly important

to seismic lifeline

1

-y"-

5.5 6 6.5 7 7.5 Magnitude

Figure 6.21. Damage index 122 cm dia., 20 km, bedrock, 10% axial load.

8

1.0

0.8

•o 0.6

E« 0.4

0.2

0.0

122 cm diameter CALTRANS column, 15% axial load

20 km from fault, on bedrock — L/D = 3.0 — L/D = 6.0 — L/D = 9.0 Collapsed

m»i)

Acceptable damage curve bndge moderately important

to seismic lifelme

2

Demolish

,

• * Acceptable damage curve

bridge highly important

to seismic lifelme -—^^•pairable ^

5.5 6 6.5 7 7.5 Magnitude

Figure 6.22. Damage index 122 cm dia., 20 km, bedrock, 15% axial load

8

69
1.0

0.8

o 0.6

B

V

U)

S5 0.4

0.2

0.0

122 cm diameter CALTRANS column, 5% axial load

30 km from fault, on bedrock

L/D = 3.0 L/D = 6.0

L/D = 9.0

?

Collapsed

Acceptable damage curve bndge moderately important

to seismic lifeline

Acceptable damage curve

bridge highly important

to seismic lifeline

RepajraWe

5.5 6 6.5 7 7.5 Magnitude

Figure 6.23. Damage index 122 cm dia., 30 km, bedrock, 5% axial load,

8

1.0

0.8

•O 0.6

s

DAB

0.2

0.0

122 cm diameter CALTRANS column, 10% axial load

30 km from fault, on bedrock

L/D = 3.0 L/D = 6.0 L/D = 9.0 Collapsed

Acceptable damage curve

bridge moderately important

to seismic lifeline

Demolish

Acceptable damage curve

bridge highly important

i to seismic Hfeline

RefJmrable

5.5 6 6.5 7 7.5 8

Magnitude

Figure 6.24. Damage index 122 cm dia., 30 km, bedrock, 10% axial load

70
1.0

0.8

•O 0.6

a>

E

122 cm diameter CALTRANS column, 15% axial load

30 km from fault, on bedrock — L/D = 3.0 — L/D = 6.0 — L/D = 9.0

0.2

0.0

Acceptable damage curve : bridge moderately important I to seismic lifeline

»»»..><»>».»' /

; » s * Demolish

^ 0

Acceptable damage curve ....

1 bridge highly important

.= to seismic lifeline

Repairable

5.5 6 6.5 7 7.5 Magnitude

Figure 6.25. Damage index 122 cm dia., 30 km, bedrock, 15% axial load.

8

1.0

0.8

•O 0.6 c

V

E

0.2

0.0

122 cm diameter CALTRANS column, 5% axial load

40 km from fault, on bedrock

L/D = 3.0 L/D = 6.0 L/D = 9.0 Collapsed

Acceptable damage curve

bridge moderately important " ""

to seismic lifeline Demolish

Acceptable damage curve

j bridge highly important

j to seismic lifeline

Repairable

5.5 6 6.5 7 7.5 Magnitude

Figure 6.26. Damage index 122 cm dia., 40 km, bedrock, 5% axial load

8

71
1.0

0.8

122 cm diameter CALTRANS column, 10% axial load

40 km from fault, on bedrock

L/D = 3.0 L/D = 6.0 L/D = 9.0 Collapsed

•O 0.6

M

eiB

S

0.4

0.2

0.0

r'':|!':??55i;i':>:i:r;! bridge moderately important

i to sejsmic hfeliiT' Demolish]

..[... Acceptable damage curve .....I

I bridge highly important ^j ,i- to seismiclifeline

Repairable

rJ

; —r

' j j^POS^iOSi^i

5.5 6 6.5 7 7.5 Magnitude

Figure 6.27. Damage index 122 cm dia., 40 km, bedrock, 10% axial load.

1.0

0.8

o 0.6

«

B« 0.4

0.2

0.0

122 cm diameter CALTRANS column, 15% axial load

40 km from fault, on bedrock

L/D = 3.0 L/D = 6.0 L/D = 9.0 Collapsed'

Acceptable damage curve

bridge moderately important

to seismic lifeline 'cmoMsh

i /.1 *

| Repairable

Acceptable damage curve |

i bridge highly important

j to seismic lifeline

5.5 6 6.5 7 7.5 8

Magnitude

Figure 6.28. Damage index 122 cm dia., 40 km, bedrock, 15% axial load.

72
6.2.2. Column Performance Charts

Below, 18 plots are presented which show three damage states for a particular

column as a function of earthquake magnitude and distance. The three damage

states shown are the onset of significant yielding of longitudinal reinforcement,

the attainment of ultimate lateral load (moment) capacity, and the overall failure

(collapse) of the column. The data for these plots was extracted from the

figures of Section 6.2.1: each of the curves shown in Section 6.2.1 crosses the

yield, ultimate and failure damage threshold states at certain values of

earthquake magnitude, and these three values form one vertical row of data

points in the figures below. Nine of the plots below are for the example

CALTRANS-designed columns situated on bedrock, and the remaining nine are for the CALTRANS-designed columns situated on 37 m of sand overlying

bedrock. Each plot shows data for a single axial load level (5%, 10%, or 15%)

and a single L/D ratio (3.0, 6.0, or 9.0).

As with the plots in Section 6.2.1, the plots below are useful for evaluating the

future performance of proposed designs, or for estimating the need for repair or

retrofit of a particular column after a particular seismic event at a specific

distance. While the plots below do not indicate specific values of damage

index, they do illustrate clearly how a column is expected to perform in terms of

laboratory-calibrated damage states. This type of plot is useful to the design

engineer in giving an overall sense of the performance of a class of columns,

and for suggesting changes in design parameters which will improve seismic

performance. Examination of these plots leads to a number of observations,

which are outlined below.

General Observations:

For a given magnitude, distance. Go [where Cq = Pe/(fc*Ag)], and soil

condition, lower values of L/D result in greater damage.

For a given magnitude, L/D ratio, Oo, and soil condition, smaller values of

distance result in greater damage (obviously).

For a given L/D ratio, Cq, soil condition, and distance, greater values of

magnitude result in greater damage (obviously).

For a given L/D ratio, distance, Oo, and magnitude, 37 m of granular soil

overburden results in greater damage than bedrock alone. This

supports the generally accepted hypothesis, as demonstrated by the

performance of engineered structures during the 1985 Mexico City and the

73
1989 Loma Prieta Earthquakes, that soil amplification can occur in thick

overburden deposits and will result in higher forces imparted to the

structure.

For a given L/D ratio, distance, magnitude, and soil condition, greater

values of Oq result in greater damage.

Specific Observations for Columns Founded on Bedrock:

a) At axial load levels of 5%, all columns analyzed performed acceptably,

regardless of aspect ratio.

b) At axial load levels greater than 10% but less than 15%, columns with

aspect ratios of three or less can be expected to suffer total failure under

a magnitude 7.0 earthquake at 10 kilometers from the epicenter and for a magnitude 8.0 earthquake at 30 kilometers from the epicenter.

Although results are not available in this study for axial load levels

greater than 15% it seems clear that increases in this variable would

lead to deteriorated column performance.

Specific Observations for Columns Founded on37 m ofAlluvium:

c) At axial load levels as low as 5%, failure of columns with aspect ratios

of less than 3 is indicated for a magnitude 6.6 event at 10 kilometers

and for a magnitude 8.0 event at 40 kilometers.

d) At axial load levels of 10%, total failure of columns with aspect ratios

of less than 3 is indicated for a magnitude 5.5 event at 10 kilometers

and for a magnitude 6.7 event at 40 kilometers. Total failure of

columns with L/D ratios of 6 are indicated for a magnitude 7.5 event at

less than 20 kilometers.

e) At axial load levels of 15%, total failure of columns with aspect ratios

of less than 3 is indicated for a magnitude 5.3 event at 10 kilometers

and for a magnitude 6.4 event at 40 kilometers. Total failure of

columns with L/D = 6 is indicated for a magnitude 7.2 earthquake at 10

kilometers.

It may be gathered from the above discussion that short, stubby CALTRANS

columns as well as columns carrying high axial loads are particularly

susceptible to failure, despite what might be considered to be a significant

amount of confining reinforcement (as compared with pre-1971 standards). In

most cases only columns with axial loads of less than 10% and L/D ratios of at

least 9 the acceptable damage criteria for important structures presented earlier

in this chapter.

74
122 cm diameter CALTRANS column

15 20 25 30 35

Distance From Fault, km

45

Figure 6.29. Damage states for 122 cm dia. column, = 0.05, LTD = 3, on bedrock.

122 cm diameter CALTRANS column

3

*5

CD

10 15 20 25 30 35

Distance From Fault, km

Figure 6.30. Damage states for 122 cm dia. column, = 0.05, L/D = 6, on bedrock.

75
122 cm diameter CALTRANS column

8.5

8.0

/.J

7.0

•o3

6.5 *C

&£

6.0

5.5

5.0

4.5

4.0

Yield

a =0.05

o L/D = 9

On bedrock

10 15 20 25 30 35

Distance From Fault, km

40 45

Figure 6.31. Damage states for 122 cm dia. column, a = 0.05, L/D = 9, on bedrock.

122 cm diameter CALTRANS column

15 20 25 30 35

Distance From Fault, km

40 45

Figure 6.32. Damage states for 122 cm dia. column, ct^ = 0.10, IVD = 3, on bedrock.

76
122 cm diameter CALTRANS column

15 20 25 30 35

Distance From Fault, km

40 45

Figure 6.33. Damage states for 122 cm dia. column, = 0. 10, L/D = 6, on bedrock.

122 cm diameter CALTRANS column

8.5

8.0

7.5

7.0

6.5

6.0

5.5

5.0

4.5

4.0

Ultimate '

Yield <

a =0.10

o L/D = 9

On bedrock

10 15 20 25 30 35

Distance From Fault, km

40 45

Figure 6.34. Damage states for 122 cm dia. column, = 0.10, I7D = 9, on bedrock.

77
122 cm diameter CALTRANS column

10 15 20 25 30 35

Distance From Fault, km

40 45

Figure 6.35. Damage states for 122 cm dia. column, = 0.15, L/D = 3, on bedrock.

0^ o

8.0

7.5

7.0

.t: 6.5 e

on

"5 6.0

5.5

5.0

4.5

4.0

Yield ^

122 cm diameter CALTRANS column

a =0.15

o L/D = 6

On bedrock

10 15 20 25 30 35

Distance From Fault, km

40 45

Figure 6.36. Damage states for 122 cm dia. column, = 0.15, L/D = 6, on bedrock,

78
122 cm diameter CALTRANS column

8.5

8.0

7.5

7.0

6.5

6.0

5.5

5.0

4.5

4.0

• Yield i

o =0.15

o L7D = 9

On bedrock

10 15 20 25 30 35

Distance From Fault, km

40 45

Figure 6.37. Damage states for 122 cm dia. column, a = 0. 15, L/D = 9, on bedrock.

122 cm diameter CALTRANS column

10 15 20 25 30 35

Distance From Fault, km

Figure 6.38. Damage states for 122 cm dia. column, = 0.05, L/D = 3, on 37 m sand,

79
122 cm diameter CALTRANS column

8.5

8.0

7.5

T33

.r 6.5 aS

6.0

5.5

5.0

4.5

4.0

" Failure

Ultimate i

1

Yield *

CT =0.05

o L/D = 6

37 m sand overburden

10 15 20 25 30 35

Distance From Fault, km

40 45

Figure 6.39. Damage states for 122 cm dia. column, = 0.05, L/D = 6, on 37 m sand.

122 cm diameter CALTRANS column

8.5

8.0

7.5

7.0 3

6.5 'c

6.0

5.5

5.0

4.5

4.0

Ultimate ^!r-^ \

Yield

'

a =0.05

o L/D = 9

37 m sand overburden

10 15 20 25 30 35

Distance From Fault, km

40 45

Figure 6.40. Damage states for 122 cm dia. column, = 0.05, L/D = 9, on 37 m sand.

80
122 cm diameter CALTRANS column

15 20 25 30 35

Distance From Fault, km

40 45

Figure 6.41 . Damage states for 122 cm dia. column, o = 0. 10, L/D = 3, on 37 m sand.

122 cm diameter CALTRANS column

8.5

8.0

7.5

7.0

6.5

6.0

5.5

5.0

4.5

4.0

Failure <

•

i i >—'

Ultimate i

Yield <

a =0.10

o L/D = 6

37 m sand overburden

10 15 20 25 30 35

Distance From Fault, km

40 45

Figure 6.42. Damage states for 122 cm dia. column, = 0.10, L/D = 6, on 37 m sand.

81
8.5

8.0

7.5

7.0

6.5

6.0

5.5

5.0

4.5

4.0

Ultimate

Yield

122 cm diameter CALTRANS column

a =0.10

L/D = 9

37 m sand overburden

10 15 20 25 30 35

Distance From Fault, km

40 45

Figure 6.43. Damage states for 122 cm dia. column, = 0. 10, L/D = 9, on 37 m sand.

122 cm diameter CALTRANS column

8.0

7.5

7.0

6.5

6.0

5.5

5.0

4.5

4.0

a =0.15

o L/D = 3

37 m sand overburden

Ultimate Yield

10 15 20 25 30

Distance From Fault, km

35 40 45

Figure 6.44. Damage states for 122 cm dia. column, o =0.15, L/D = 3, on 37 m sand.

82
122 cm diameter CALTRANS column

8.5

8.0

7.5

7.0

6.5

6.0

5.5

5.0

4.5

4.0

Failure *

Ultimate ^

Yield <

a =0.15

o L/D = 6

37 m sand overburden

10 15 20 25 30 35

Distance From Fault, km

40 45

Figure 6.45. Damage states for 122 cm dia. column, = 0. 15, L/D = 6, on 37 m sand.

122 cm diameter CALTRANS column

8.5

8.0

7.5

7.0

6.5

6.0

5.5

5.0

4.5

4.0

Failure <

Ultimate t

Yield ^-""'''l

a =0.15

o L/D = 9

37 m sand overburden

10 15 20 25 30 35

Distance From Fault, km

40 45

Figure 6.46. Damage states for 122 cm dia. column, = 0.15, L/D = 9, on 37 m sand.

83
7.0 Retrofit Analysis

7.1 Introduction

According to a recent Federal Highway Administration memorandum [Cooper,

1992],

"There are more than 7 million kilometers of roads and highways in the

United States of America and approximately 575,000 bridges, ranging

from 7 m in length to 40 km. Tlie bridge inventory varies from single,

simple-span structures to multispan suspension bridges. About one-half are State-owned and 47,000 are on the hiterstate System. Approximately

72 percent of the bridges in the U.S. were constructed prior to 1935 with

little or no consideration given to seismic resistance."

"Historically, bridges have proven to be vulnerable to earthquakes,

sustaining damage to substructures and foundations and in some cases being destroyed as substructures fail or superstructures are unseated from

their supporting elements. In 1971 the San Fernando earthquake

damaged more than 60 bridges on the Golden State Freeway in

California. This 1971 earthquake is estimated to have cost the State

approximately $100 million to repair these bridges, including the indirect

costs due to bridge closures. In 1989, the Loma Prieta earthquake in

Northern California damaged more than 80 bridges in a five-county

region, and caused the deaths of more than 40 people in bridge-related

coUapses alone. The cost of the earthquake to the transportation system

was $1.8 billion of which the damage to State-owned viaducts was about

$200 miUion and to other State owned bridges about $100 million."

Given the above statistics there is a clear need for the development of improved

vulnerability assessment techniques, as well as retrofit procedures which can be

used to improve the seismic resistance of older bridges. During the 1970's,

particularly in the State of Califomia, emphasis was placed on the development

of improved design procedures for new bridges, with particular attention paid to

reinforcement requirements for new columns. The focus shifted in the 1980's

towards implementation of a multi-phase retrofitting program. This effort was

largely concerned with improving connections between bridge elements. Cable

restrainers and other motion-limiting devices were installed to prevent

unseating of spans during an earthquake. Two useful reports, "Seismic Design

and Retrofit Manual for Highway Bridges" (FHWA, 1987) and "Seismic

Retrofitting Guidelines for Highway Bridges" (FHWA, 1983) contain in-depth

84
discussion of these procedures. Most engineers familiar with retrofit restrainers

point to their use in California as one of the little-recognized success stories of

the Loma Prieta earthquake; without them the damage toll would likely have

been far greater.

Nonetheless, much work remains to be done on seismic retrofitting of existing

bridges. Only a few retrofitting schemes (as described above) have actually

been used in practice and given the present state of knowledge, retrofitting is still an art requiring a considerable amount of engineering judgment. While it is

beyond the scope of this report to address all aspects of bridge retrofitting (see

FHWA 1987 for a global perspective on the complexity of the problem) the

specific problem of vulnerability assessment and retrofit design for RC column

substructures is highly amenable to solution using the ISDP procedure

described in this report. In the remainder of this chapter ISDP first will be

employed to investigate the performance of an existing RC column when

subjected to a range of earthquake intensities. These responses will then be

compared to the design standard proposed in Chapter 6, and the effectiveness of

a common retrofit strategy will be analyzed.

7.2 Retrofit Procedure

Figure 7.1 depicts a box girder bridge cross section at a single column bent, as might be typically employed at an elevated interchange. The column is circular

with a diameter of 122 cm and a height of 732 cm giving an aspect ratio of L/D

= 6. Hence flexural effects are expected to dominate the behavior of the

column. Axial reinforcement consists of 18 #10 bars (da = 3.2 cm). Confining

reinforcement is provided by 1.6 cm diameter bars at a pitch of 12.1 cm. The

yield stress for both types of reinforcement is 414 MPa. The nominal concrete

cylinder strength is 27.6 MPa. The axial load is 3220 kN, producing a normalized axial stress level, CJo, of 0.10. Concrete cover is presumed to be 5.1

cm to the centerline of the confining steel. The structure is situated 20 km from

a known fault (i.e., the most likely source of a future earthquake that would be

of sufficient energy to damage the bridge). The bridge is considered a critical

lifeline structure which must remain fully operational following a severe

earthquake.

85
i

D

Column Specification:

fc = 27.6 MPa

fy = 414 MPa

fu = 725 MPa

Pe = 3220 kN

D = 122 cm

cover = 5.1 cm

ds, spiral bar dia. = 1.6 cm

s, spiral pitch = 12.1 cm

L = 732 cm

da, long, bar dia. = 3.2 cm

# long, bars = 18 (#10)

Design Earthquake

[ Loma Prieta '89, Telegraph Hill, 0-degrees

scaled to magnitude 7.0 at 20 km, and filtered through 37m alluvium

u

o<

-0.6-f

0 10 15 20

Time (seconds)

Figure 7.1. Retrofit design example - initial conditions and design earthquake.

86
The column described above was designed in accordance with current

CALTRANS seismic design procedures [CALTRANS 1990] for a structure

founded on 37 m of alluvium. As was demonstrated in Chapter 6, it is possible

using ISDP to generate continuous curves representing the damage sustained by

the column when subjected to earthquakes of increasing energy content

(increasing magnitude). For the purposes of retrofit analysis it will be useful to

initially look at the response of the column to a specific earthquake, and then to

expand the parametric analysis to examine various levels of retrofit.

Figure 7.2 shows the response of the column to a magnitude 7.0 earthquake

(shown at the bottom of fig. 7.1). The acceleration-time history shown in figure

7.1 was obtained by first scaling the Loma Prieta Telegraph Hill 0-degree

record to magnitude 7.0 (as outlined in Chapter 3) and then filtering the record

through 37 m of alluvium using SHAKE91, which was embedded as a subroutine in ISDP. In a general retrofit analysis each magnitude level will be

accompanied by a suite of time histories, selected in accordance with the

principles set out in Chapter 3. The record shown in figure 7.1 was shown

through analysis to produce the greatest damage of the four-record suite

generated for that magnitude. The damage response shown in figure 7.2

indicates that, at a final damage index value of approximately 0.34, the column,

subjected to this particular earthquake, would have sustained loading

approaching its ultimate capacity but would remain standing and could possibly

sustain emergency traffic. At a damage level of 0.34 substantial yielding will

have taken place as well as extensive spalling but none of the confining steel

would have fractured. Below the trace of the damage-time history in figure 7.2

is a shaded area indicating the zone of acceptable damage for important lifeline

structures, in accordance with the principles presented in Chapter 6. This

indicates that the damage sustained by the column in this particular event is

nearly double the desired maximum for important structures. The worst-case

response for all time-history suites for all magnitudes is plotted in figure 7.6. It can be seen that the as -built column fails to meet the maximum allowable

damage design criteria for important structures, as detailed in Chapter 6, at all

earthquake magnitudes. Thus, some form of column retrofit is required.

87
Damage vs. Time

0.3S

0.3-

X

1

^

sQ 0.1

O.OSt

K-; 0-tt

As-Built Column

Kesponse

Allowable Damage Limit: Important

8lr<ic:tttres j t

i

i

0 5 10 15 20 25 30

Time (seconds)

Figure 7.2. Retrofit design example - predicted response of the as-built column

to the design earthquake shown in figure 7.1.

88
For the specific class of columns investigated in this report (single circular

column, cantilevered construction, stiff box girder superstructure) failure occurs

in the plastic hinge region at the base of the column. In this type of

construction the foundations are generally designed with significant

conservatism. It is thus assumed in the following discussion that failure is

constrained to occur in the column and will not be permitted to migrate into the

foundation. Since any retrofit to the column will necessarily increase the

loading on the foundation, a follow up study would be required to determine if

subsequent strengthening is required of the foundation.

A number of bridge column retrofit schemes have been investigated in recent

years, including cast-in-place concrete jackets; welded or bolted cylindrical

steel plate jackets; wrapped epoxy-fiberglass jackets; and tension-wound

prestressed confining steel. A useful report on the merits of these various

techniques is presented by Priestley and Seible [1991]. The latter two

approaches listed above must still be considered experimental as only a few

laboratory tests have been conducted. The first two techniques have seen

limited apphcation in the United States, Japan, and elsewhere. Of these, steel

jacketing appears to be the most effective technique and will be used in this

report as the basis for parametric retrofit analyses. It should be noted that, with

appropriate constitutive modeling, all of the aforementioned retrofitting

schemes could be incorporated into ISDP, both for the purposes of routine

design and for automated parameter sensitivity studies.

Figure 7.3 surrmiarizes the retrofit approach used for the present example. This

procedure maintains the as-built column diameter and adds successively thicker

cylindrical jacketing plates to the zone of high predicted damage. These plates are presumed to be rolled to form a close match to the column surface and are welded in place in the field. A narrow gap of a few millimeters is permitted

between the shell and column to allow for cement-based pressure grouting to

ensure integrity with the column. Generally, the height of the jacket should

extend a significant distance above the plastic hinge region, to a height of

approximately 2D or greater to ensure that a localized hinge is not simply

translated to the top of the jacket. In the retrofit analysis described below the

participation of the existing spiral reinforcement is included together with the

enhancement provided by the jacket. The jacket is presumed to be effective in

providing confinement only and not to act as additional longitudinal

reinforcement.

89
1: Maintain D

2: Vary (increase) jacket

plate thickness, t. 3: L remains a fixed parameter.

4:H> 2D

\ J

Figure 7.3. Retrofit design example - steel jacket retrofit configuration.

90
It is assumed in the above procedure that the column height is a fixed parameter

and that, for reasons of economy, complete replacement of the column or a reduction in the diameter of the column is not feasible. Depending on the likely

frequency content of the earthquakes in a given region it may actually be

desirable to increase the fundamental period of the structure by making the

column more flexible. This could only be achieved through complete

replacement of the column (to achieve an increase in the L/D ratio) or possibly

by removal of selected longitudinal reinforcement. These techniques are both

rather extreme, and would only be warranted where critical structures could not

be retrofitted by more conventional methods.

7.3 Results of Steel Jacket Retrofit Analyses

Figure 7.4 shows a series of damage index versus time plots for various

thickness jackets in response to the magnitude 7.0 earthquake shown in figures

7.1 and 7.4. As can be seen, the addition of even a relatively thin steel casing

significantly improves the survivability of the column.

There is, apparently, a point of diminishing returns, beyond which there is no

significant decrease in damage index for an increase in shell thickness. Figure

7.5 shows the response of the retrofitted column to all 16 design earthquakes (a

four-record suite for each of four earthquake magnitudes) as a function of the

shell thickness. This clearly indicates that the maximum benefit afforded by

this type retrofit approach is achieved by the time the jacket shell has reached

about 5 mm. Indeed, auxiliary analyses indicated that for very thick shells

(greater than 10 mm) there may in fact be a loss of performance. This is

because the increase in concrete strain capacity afforded by the thicker shell is

ultimately offset by tensile fracture of the longitudinal reinforcement. This

phenomenon is accounted for in the fiber model employed in IDARC, which

presently forms the analysis core of ISDP.

91
Damage vs. Time

10 15 20

Time (seconds)

Acceleration Record

[ Loma Prieta '89, Telegraph Hill, 0-degrees

scaled to magnitude 7.0 at 20 km, and filtered through 37m alluvium 0.6

n W

i 7 "J

-0.6

10 15 20 25 30

Time (seconds)

Figure 7.4. Damage accumulation for various steel jacket thicknesses.

92
Damage vs. Jacket Thickness

Retrofit of Existing Column

M = 5

2 3

Jacket Thickness (mm)

Figure 7.5. Cumulative damage vs. retrofit jacket thickness for example

column.

93
7.4 Discussion

Figures 7.6 and 7.7 summarize the retrofit analyses described in this chapter.

Given the as-built specifications and material properties for any column it is

possible using ISDP to predict the damage-vs.-time response of the column to

any acceleration-time history. By compiling the worst-case response of the

column to suites of design records appropriate for a particular construction site,

it is possible to construct a damage profile for the colunm as a function of

earthquake energy content (as expressed by magnitude at a particular distance

from the likely source of the earthquake). In cases where there are many

possible sources for earthquakes at a certain construction site, similar damage

response analysis sets should be performed for each likely source distance, to

ensure that all possible scenarios are reasonably accounted for. Although this

may sound complex, using ISDP it is a straightforward matter to analyze a wide

range of design cases.

1.0

0.8

e 0.6

Retrofit of 122 cm dia. CALTRANS column, 10% axial load

20km from fault, 37 m sand overburdern

7

Acceptable damage curve

juridge moderately importantii to seismic lifelin

original column,

without retrofit

cceptable damage curve

bridge highly important

to seismic lifeline

j Repairable

Functional

6.5 Magnitude

7.5

Figure 7.6. Original state of example CALTRANS column before addition of

extemal steel jacket.

94
1.0

0.8

1 0.6

^7

Retrofit of CALTRANS column, 10% axial load

20km from fault, 37 m sand overburdern

= zone of acceptable damage

for bridges highly important

to seismic lifeline

Acceptable damage curve

bridge moderately important

to seismic lifeline

<<<<<<«<<<4

6.5 7 Magnitude

Figure 7.7. Effect of external jackets on example CALTRANS column.

In figure 7.6 the overall response for the as-built column is shown as a function

of earthquake magnitude together with the two limiting design criteria set forth

in Chapter 6 for highly important and moderately important structures. Since

the initial criteria for this particular retrofit problem was that the bridge must be

serviceable under even the most severe event, the lower criteria corresponding

to important structures is the one of interest. From this perspective it is clear

that the as-built column does not satisfy the criteria for any magnitude.

In contrast, figure 7.7 shows the effectiveness of the steel jacket retrofit. It is evident from this graph that a jacket thickness of 3 mm will be sufficient to

bring the column up to specification. However, it is also important to recognize

the issue of constructability. Bridge columns of the type described in this report

will generally vary in diameter from 100 to 300 cm. Retrofitting of such

columns using steel jackets means handling relatively large thin shell structures

at the job site. These shells may, if abused, be subject to buckling during

95
transport and placement, which could compromise the ability of the shell to

provide the necessary column confinement. It may be more reasonable in such

cases to use a slightly thicker shell, for example using the 5 mm jacket in the

present example instead of the 3 mm jacket, to avoid problems in the field.

Furthermore, although there is presently no known experimental or field data to

support it, there is the possibility of localized tearing of particularly thin jacket

plates during an earthquake, at such locations as weld lines or bolt holes. Such

tearing would appear to be less likely for thicker plates. For these reasons a 4

mm or 5 mm thick jacket would be the recommended retrofit for the column

used in this example.

As was mentioned above, the present analysis was limited to retrofitting

procedures which employ a steel jacket. Further research is required to develop

appropriate constitutive models for other retrofit strategies and substructure

configurations, hi this way ISDP could be become a design tool capable of

assessing the relative merits of a number of retrofit techniques for both singleand multiple-column bridge bents.

96
8.0 Conclusions

8.1 Integrated Seismic Design Procedure

The authors have proposed an alternative procedure for the seismic design of

reinforced concrete bridge columns, which is in their opinion more rational than

the codified techniques presently in use in seismically active regions of the

United States. The approach, referred to as the Integrated Seismic Design

Procedure (ISDP), is in essence a unification of many disparate aspects of

advanced seismic design which heretofore have existed separately within the

various fields of seismology, geotechnical engineering, structural design, and

structural engineering research. It has been shown that the data and techniques

utilized in these fields (e.g., reinforced concrete test results; earthquake time

histories both at bedrock and at the top of soil overburden; soil boring records;

site geographic location; and the like) can be included either in computer codes

or in knowledge databases. Using these computer codes and knowledge

databases it is possible to approach the seismic analysis problem in rational

stages, arriving ultimately at specific columns designs (cross section geometry,

L/D ratio, material properties and reinforcement contents) which meet specific

levels of performance for specific seismic events.

The implementation of ISDP necessarily involves the use of a very high

performance computer with fast, sophisticated graphics capabilities. The

reasons for this are obvious when one considers, first, that database

manipulation requires processing of hundreds of earthquake time histories (each

of which generally consists of some 10,000 data points); hundreds of

experimental test records (which also may consist of several thousand data

points) and second the computational burdens of wave propagation analyses and

full non-linear transient dynamic analyses associated with each trial case in a parametric column design (of which there may easily be hundreds or thousands

of runs involved in the design matrix of variables of interest). Until recently,

with the advent of RISC-based desktop workstations which are both compact

and affordable to the average design office, such a large, computationally

intensive program as ISDP would have been intractable, except on a few

supercomputers operating at industry or govemment laboratories.

That such an integration of all the various pieces necessary for advanced

seismic design is feasible was demonstrated through the results of the ISDP

analyses presented in Chapters 6 and 7. At the inception of the research

described in this report three necessary components of the ISDP did not exist in

any form. These were a) a set of closed-form equations which, given material

97
and geometric properties for a prospective column design, could be used to

calculate an appropriate set of hysteretic failure model parameters for

subsequent use in the non-linear time history analysis module; b) a realistic

damage assessment model that could relate an intangible (but analytically

tractable) damage index to a specified level of observed damage in laboratory

tests of a wide variety of bridge columns; and c) an acceptable damage-based

design criteria which preferably could be reduced to a set of closed form

equations relating allowable damage to earthquake energy content and the

importance of the structure. The first two of these components were based on

extensive system identification analyses of empirical test results, including fullscale column tests, and are believed to be relatively accurate over the range of

parameters within which the models were developed. The third element was

based on a systematic study of damage states, and could serve as a model for

future development of damage-based performance criteria.

8.2 Acceptable Damage Limits

The acceptable damage model developed in Chapter 6 presents an initial

attempt by the authors to address the complex, socio-economic-technological

topic that is summarized by the question: "What cost are we willing to pay in

order for a particular bridge to survive a given earthquake?" The authors have

proposed a non-linear scale which relates allowable damage level to earthquake

intensity and structural importance. The criteria were developed, somewhat

subjectively, by considering limiting cases in a three-dimensional space defined

by allowable damage, distance from the earthquake epicenter, and earthquake

magnitude. From these discrete values parametric equations were developed to

model the three-dimensional surfaces of acceptable damage. Equations for two

classes of bridges were presented: bridges deemed moderately important to

seismic lifelines, and bridges deemed highly important to seismic lifelines.

This was largely done in an effort to maintain consistency with existing design

procedures, which also recognize two levels of importance.

Refmement of the acceptable damage models beyond the ones presented by the

authors will necessarily involve probabilistic analyses on the likelihood of a

particular earthquake occurring during the useful lifetime of a bridge, as well as the estimation of the cost to society of repair/retrofit/replacement of the bridge

following a particular earthquake. While these tasks are well-defined, they are beyond the scope of the present study. The important distinctions between this

approach and the approach presently employed by the model code agencies are

that a) the concept of acceptable damage, as a calculable quantity, replaces

ambiguous safety factors and base shear coefficients and b) the acceptable

98
performance is tied specifically to two engineering quantities: the earthquake

magnitude and the distance of the construction site from the earthquake source.

8.3 Deficiencies in Current CALTRANS/AASHTO Designs

Using the ISDP and the aforementioned acceptable damage criteria a large

number of parametric analyses were conducted to investigate the performance

of a certain class of circular, spirally-reinforced concrete bridge columns such

as would be designed in accordance with current CALTRANS specifications

and procedures. The parameters investigated included column aspect ratio

(L/D), normalized axial load (ao), the type of subsoil deposit (either bedrock or 37 m of alluvium), the earthquake magnitude (M), and the distance of the

bridge from the causative fault (d).

The detailed results of these analyses were presented in Chapter 6. However,

several notable points are worth summarizing here:

For columns founded on bedrock:

a) At axial load levels of 5% of ultimate, all columns analyzed performed

acceptably, regardless of aspect ratio and distance from the causative fault.

b) At axial load levels greater than 10% but less than 15%, columns with

aspect ratios of three or less can be expected to suffer total failure under a magnitude 7.0 earthquake at 10 km from the epicenter and for a magnitude

8.0 earthquake at 30 km from the epicenter.

For columns founded on 37m of alluvium:

c) At axial load levels as low as 5%, total failure of columns with aspect

ratios of less than 3 is indicated for a magnitude 6.6 event at 10 km and for a magnitude 8.0 event at 40 km.

d) At axial load levels of 10%, total failure of columns with aspect ratios of

less than 3 is predicted for a magnitude 5.5 event at 10 km and for a magnitude 6.7 event at 40 km. Failure of columns with L/D ratios of 6 are indicated at magnitude 7.5 and distances less than 20 km.

e) At axial load levels of 15%, failure of columns with aspect ratios of less

than 3 is indicated for a magnitude 5.3 event at 10 km and for a magnitude

6.4 event at 40 km. Failure of columns with L/D = 6 is indicated for a magnitude 7.2 earthquake at 10 km.

It may be concluded from the above summary that short, stubby CALTRANS

designed columns as well as columns carrying high axial loads are particularly

99
susceptible to failure, in spite of what is currently considered to be a significant

amount of confining reinforcement (as compared with, for example, pre-1971

design standards).

In most cases only columns with axial loads of less than 10% and L/D ratios of

at least 9 met the acceptable damage criteria for important structures presented

in Chapter 6. Presuming such an acceptable damage criteria were to become

part of a future AASHTO Code it is fortunate that steel jacketing procedures, as discussed in Chapter 7, appear to be particularly effective at improving the

behavior of columns to acceptable levels.

8.4 Retrofit Procedures Based on ISDP

For existing columns that have been identified (through analyses such as ISDP)

as being highly susceptible to seismic damage, there are a number of methods

which can be used for retrofitting. These include a) complete replacement; b)

jacketing; c) base isolation; d) use of energy dissipaters (e.g., lead extruders)

and e) active damping. Of these techniques jacketing will almost always be the

most cost-effective provided it can be demonstrated that the necessary increase

in performance can be achieved using this technique.

Within the jacketing subset there are four approaches presently under

consideration by the seismic design community: cast-in-place concrete jacket;

steel plate jacket; fiberglass-epoxy jacket; and prestressed, wire-wound jacket.

Steel plate jacketing was investigated in Chapter 7. The analyses assumed that

the steel jacket was rolled to form a co-axial split cylinder that effectively

matched the radius of the column in the field, plus a few millimeters to permit

high pressure grout placement to insure integrity with the column. Field

installation was assumed to have been either by welding or bolting of the split

cylinder. A parametric investigation revealed that even a relatively thin steel

jacket can have a pronounced effect on the seismic behavior of a circular bridge

column. There is, however, a point of diminishing returns, beyond which

increased plate thickness will not yield improved performance. For the 122 cm

diameter column investigated in the Chapter 7 retrofit study it was found that

this point of diminishing returns was reached at a jacket thickness of

approximately 5 mm. However, the application of that 5 mm jacket reduced the

predicted column damage by about 75%.

These results clearly indicate the beneficial effects of steel jacketing. However

certain precautionary notes are in order. First, while steel jacketing can

significantly improve the seismic performance of a circular column, retrofitting

100
of columns may simply divert damage to other elements of the bridge, such as the foundation or superstructure. Second, it is possible that thin steel jackets

may be susceptible to tearing when subjected to high internal pressures and

cyclic lateral loads. Along these same lines, the methods of installing thin steel

jackets (e.g., welding or bolting) should be adequate to maintain the integrity of

the jacket under these severe conditions. Further studies of the toughness and

durability of thin steel jackets subjected to seismic loads may be required before

they then can be used with complete confidence.

101
9.0 References

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Edition," The American Association of State Highway and Transportation

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Allahabadi, Rakesh (1987), "Drain-2DX, Seismic Response and Damage

Assessment for 2D Structures," doctoral dissertation. Department of Civil

Engineering, University of Cahfomia, Berkeley, March 1987.

Ang Beng Ghee; Priestley, M. J. N.; and Park, R. (1981), "Ductility of

Reinforced Concrete Bridge Piers Under Seismic Loading," Report 81-3,

Department of Civil Engineering, University of Canterbury, Christchurch, New

Zealand, February 1981.

Ang Beng Ghee; Priestley, M. J. N.; and Paulay, T. (1985), "Seismic Shear

Strength of Circular Bridge Piers," Report 85-5, Department of Civil

Engineering, University of Canterbury, Christchurch, New Zealand, July 1985.

Ang Beng Ghee; Priestley, M. J. N.; and Paulay, T. (1989), "Seismic Shear

Strength of Circular Reinforced Concrete Columns," ACI Structural Journal,

January-February 1989, pp 45-59.

CALTRANS (1990), "Bridge Design Specifications," State of California,

Department of Transportation (CALTRANS), Office of Structure Design,

Sacramento, California, August 1986 (with revisions up to June 1990).

Campbell, K.W. (1981), "Near Source Attenuation of Peak Horizontal

Acceleration," Bulletin of the Seismological Society ofAmerica, Vol. 71, No. 6,

1981, pp 2039-2070.

Cheok, G.S.; and Stone, W.C. (1990), "Behavior of 1/6-Scale Model Bridge

Columns Subjected to Inelastic Cyclic Loading," ACI Structural Joumal, Nov.-

Dec. 1990, Vol. 87, No. 6, American Concrete Institute, Detroit, Michigan, pp

630-638.

Cooper, James (1992), "High Priority National Program Area: Seismic

Protection," Structures Division, HNR-10, Research Plan 1992-1996, Federal

Highway Administration, Tumer-Fairbank Highway, McLean, Virginia, July

1992.

102
Davey, B.E. (1975), "Reinforced Concrete Bridge Piers Under Seismic

Loading," Master of Engineering Report, Civil Engineering Department,

University of Canterbury, Christchurch, New Zealand, February 1975.

Diaconis, Persi; and Efron, Bradley (1983), "Computer-Intensive Methods in

Statistics," Scientific American, Vol. 248, No. 5, May 1983, pp 116-130.

Efron, Bradley; and Gong, Gail (1983), "A Leisurely Look at the Bootstrap,

the Jackknife, and Cross-Validation," The American Statistician, Vol. 37, No. 1,

February 1983, pp 36-48.

Efron, Bradley; and Tibshirani, R. (1986), "Bootstrap Methods for Standard

Errors, Confidence Intervals, and Other Measures of Statistical Accuracy,"

Statistical Science, Vol. 1, No. 1, 1986, pp 54-77.

El-Borgi, S.; White, R.N.; and Gergely, P. (1991), "Analytical Modeling of

Pinching and Degrading Hysteretic Systems and System Identification of

Parameters: Progress Report to NIST," Department of Structural Engineering,

School of Civil Engineering, Cornell University, Ithaca, New York, 14853,

January 1991, NIST Contract #50SBNB1C6543.

FHWA (1983), "Seismic Retrofitting Guidelines for Highway Bridges," report

FHWA/RD-83/007, Office of Research and Development, Federal Highway

Administration, U.S. Department of Transportation, Washington, D.C., 20590,

December 1983.

FHWA (1987), "Seismic Design and Retrofit Manual for Highway Bridges,"

report FHWA-IP-87-6, Office of Implementation, HRT-10, Federal Highway

Administration, 6400 Georgetown Pike, McLean, Virginia, 22101, May 1987.

Idriss, I.M. (1985), "Evaluating Seismic Risk in Engineering Practice,"

Proceedings, Xlth Intemational Conference on Soil Mechanics and Foundation

Engineering, San Francisco, California, August 1985, pp. 255-320.

Joyner, W.B.; and Boore, D.M. (1988), "Measurement, Characterization, and

Prediction of Strong Ground Motion," Earthquake Engineering and Soil

Dynamics II - Recent Advances in Ground-Motion Evaluation, Proceedings of

the specialty conference sponsored by the Geotechnical Engineering Division of

the American Society of Civil Engineers, Park City, Utah, 1988, pp 43-102.

Kenchiku Kenkyu Siryo (1975), "Aseismic Analysis of Building Structural

Members: A List of Experimental Results on Deformation Ability of

103
Reinforced Concrete Columns under Large Deflection (No.2)," Building

Research Institute, Ministry of Construction, Japan, March 1975.

Kenchiku Kenkyu Siryo No.21 (1978), "Aseismic Analysis of Building

Structural Members: A List of Experimental Results on Deformation Ability of

Reinforced Concrete Columns Under Large Deflection (No. 3)," Building

Research Institute, Ministry of Construction, Japan, February 1978.

Lew, H.S. (ed.) (1990), "Performance of Structures During the Loma Prieta

Earthquake of October 17, 1989," NIST Special Pubhcation 778, Center for

Building Technology, National Engineering Laboratory, National Institute of

Standards and Technology, Gaithersburg, MD, 20899, January 1990.

Lim, Kuang Y.; and McLean, David I., (1991), "Scale Model Studies of

Moment-Reducing Hinge Details in Bridge Columns," ACI Structural Joumal,

Vol. 88, No. 4, July-August 1991, pp 465-474.

McLean, David I.; and Lim, Kuang Y. (1990), "Moment-Reducing Hinge

Details for the Bases of Bridge Columns," Report No. WA-RD 220.1,

Washington State Department of Transportation, Planning, Research and Public

Transportation Division, October 1990.

Mander, J.B. (1984), "Seismic Design of Bridge Piers," Research Report #84-

2, Department of Civil Engineering, University of Canterbury, Christchurch,

New Zealand, February 1984.

Maroney, Brian (1990), "CALTRANS' Seismic Risk Algorithm for Bridge

Structures", Seismic and Structural Analysis, Division of Structures, Cahfomia

Department of Transportation, Sacramento, California, 94274-0001, June 30,

1990, 23 pages.

Munro, L R. M.; Park, R.; and Priestley, M. J. N. (1976), "Seismic

Behaviour of Reinforced Concrete Bridge Piers," Report 76-9, Department of

Civil Engineering, University of Canterbury, Christchurch New Zealand,

February 1976.

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104
Otani, S. (1974), "SAKE, a Computer Program for Inelastic Response of R/C

Frames Subject to Earthquakes," Civil Engineering Studies, SRS No. 413,

University of Illinois, Urbana, November 1974.

Park, Y.J.; Ang, A. H-S.; and Wen, Y.K. (1984), "Seismic Damage Analysis

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Damage Analysis of Reinforced Concrete Frame-Sheai-wall Structures, (1987)"

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Petrovski, J.; and Ristic, D. (1984), "Reversed Cyclic Loading Test of Bridge

Column Models," Institute of Earthquake Engineering and Engineering

Seismology, University "Kiril and Metodij," Skopje, Yugoslavia. Report #

IZnS 84-164, September 1984.

Priestley, M. J. N.; and Park, R. (1984), "Strength and Ductility of Bridge

Substructures," Report 84-20, Department of Civil Engineering, University of

Canterbury, Christchurch, New Zealand, December 1984.

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Retrofit of Bridges," Report SSRP-91/03, Department of Applied Mechanics

and Engineering Sciences, University of California, San Diego, San Diego,

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User's Guide: Seismic Analysis of Reinforced Concrete Frames," Technical

Report NCEER-90-0027, National Center for Earthquake Engineering

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Conducting Equivalent Linear Response Analysis of Horizontally Layered Soil

Deposits," I.M. Idriss, Joseph I. Sun, and Peter Dirrim, Department of Civil

Engineering, University of Califomia, Davis, Califomia, March 1992.

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Bridge Columns Subjected to Cyclic Loading," NIST Building Science Series

105
166, National Institute of Standards and Technology, Gaithersburg, Maryland,

20899, January 1989.

Stone, W.C.; and Taylor, A.W. (1991), "System Identification of Spirally

Reinforced Circular Bridge Columns Subjected to Cyclic Lateral Loading,"

Wind and Seismic Effects; Proceedings of the 23rd Joint Meeting UJNR, NIST

SP 820, National Institute of Standards and Technology, September 1991.

Watson, Soesianawati (1989), "Design of Reinforced Concrete Frames of

Limited Ductility," Report 89-4, Department of Civil Engineering, University of

Canterbury, Christchurch, New Zealand, January 1989.

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Bridge Piers Under Multi-Directional Seismic Attack," Report 90-4,

Department of Civil Engineering, University of Canterbury, Christchurch, New

Zealand, October 1990.

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Motions on Rock for Large Subduction Earthquakes," Earthquake Engineering

and Soil Dynamics 11 - Recent Advances in Ground-Motion Evaluation,

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Engineering Division of the American Society of Civil Engineers, Park City,

Utah, 1988, pp 445-462.

Zahn, F. A.; Park, R.; and Priestley, M. J. N. (1986), "Design of Reinforced

Concrete Bridge Columns for Strength and Ductility," Report 86-7, Department

of Civil Engineering, University of Canterbury, Christchurch, New Zealand,

March 1986.

106
10.0 Appendix A: Table of Availahle Digital Test Records

Table A. 1 (part 1 of 2). Spiral column database used in this study, data group I

1

' fc fy Column Cover C-to-C No. of Diameter Diameter

Test Name Mra Mra OD mm long. long. long.bars hoop bars mm bars mm bars mm mm

iiiun /onui oozU OAZU 1 Qlo o

o

11^ / oIlUZ jj.i ZjU 1

01 1 zi 11 (\ 1

1

J

4

J J.U 904 zjU 1 o Zl J

11 0Iz A4

rw^t7Qnr\ 1 \A)l / 7llU 1 '^ni JVJ 9*^ Zj J lO lO 94zt 1

0

lU

put / J Z.O.O DUU 9^Zj '^1 A lO 94ZH 11 0u

rv-\t-'7Qnrwl jyjj 9SZJ S16 16lO 94Zn 10lU

pui f ZflnJJCl "^9 5 j\j ^071 98zo JUH S04 16lO 94ZH 16lO

"^9 S ^07 fiOO 98Zo JUH S04 16lO 94ZH 1

6

1 u

all^O iUlllLX ^08 400 1^^ 16lO 16lO D

QfifTx 1 unit/ cUI^^O iUIULZr 98 S 400 11 ao 1^8 JJO 16lO 161 o 10lU

z.aiiiiO\JUiiiL^ ^9 JJ / 400 181 o JJo 16lU 16lU 10lU

ZdllllOOUIlUO 97 n 117 400 1 alo 118 JJO 1610 16ID 1

0

lU moucin I 94 1 101 jyj 9'nO Z3U 1

0

lU 990 ZZU O'n Zj 7 1J niodcln2 1Q1 jyj zjU 1

OOA zzU o<ZJ 1 1J modcln3 0< /I ZJ.4 101 jyj zjU 1 n 00 1 zzl O's ZJ 1 1

J modeln4 Z4.4 1Q1 jyj zjU 1 A OOA zzU o<ZJ 1 J

iTiOQeinj 94 1 1Q1 jyj zjU 1 AlU OOA ZzU 0^ZJ 1 1J

IIIOUCIIIO 9^ZJ.Z9 jyj 9*^0 ZJU 10 991 ZZ

9SZJ 7/ 1J IICAIICW 47 S 11 JZU S90 1 '^44 9*5 ZJ 4'^

*T J 16lU

5I1C<U new '^4 47 S 11 JZW S90 ^iO 1 JJ 1 9*^ ZJ 4^^ HJ 1Q1 y alaKawal 98zo.o8 Z / J 90zw 9nZl J 19 161 u \j 9Qzy. J J\Jk) 97S Z / J 90zw 9nZl J 19 16 AVJ 9Q 8 97S Z / J 90Z\7 9n 19 16 6VJ 98 ft 275 20 213 ^ J. ^ 12 16 6

366 975 20 213 12 16 6

^66 975 Z / J 90 913 16 16 6VJ ^0 9 "^66 975 Z / J 90 913 aO 16 6VJ

5ir!ilr!iwii 1 1 98zo.7/ "^66 975 Z / J 90 913 12 16 0

dTdKdWd 1

97z a / .o jOO 97S Z / J 90ZU 9nZl J 19iz 16lU u

oTalvaWal J JU.J 97S Z / J 90ZU 9nZ 1

J

19 161 VJ 6VJ

dJ dJvdWa 1

H- 97S Z / J 90ZU 9nz u 19 16X VJ 6VJ dldKaWdlj 19 n 97'n Z / J 90ZU 91"^ Zl J 19iz 161 Kj VJ dldKaWdlO 11 1 1*^1 97S Z / J 90ZU 91Zl J 19iz 161 u

AVJ araKawai / 11 1 IK^I 97'n Z / J 90ZU 911 Zl J 19iz 16lU AVJ araKawai o

1 1 1 l^^l 97^ Z / J 90ZU 911 Zl J

19iz 16lO

arakawal9 31.2 363 275 20 213 12 16 6

arakawa20 29.3 363 275 20 213 12 16 6

arakawa21 30.5 363 275 20 213 12 16 6

arakawa22 20.5 363 275 20 213 12 16 6

arakawa23 42.2 363 275 20 213 12 16 6

arakawa24 31.1 363 275 20 213 12 16 0

arakawa25 29.7 363 275 20 213 12 16 6

arakawa26 30.9 363 275 20 213 12 16 6

arakawa27 18.9 363 275 20 213 12 16 6

arakawa28 41.3 363 275 20 213 12 16 6

107
Table A. 1 (part 2 of 2). Spiral column database used in this study, data group I

Test Name fc fy Column Cover C-to-C No. of Diameter Diameter

MPa MPa OD mm long. long. long.bars hoop bars —— mm bars mm bars mm mm

ang85umt2 5 1 .1 zyo 4UU 1 o •2/1i4Z OAZU lo 6

ang85unit4 jU.o 4UU OAzu 11A 334 OAZU lo 1 AlU

ang85unit6 iU.l /I 4UU 1 0lo Q/l o 34Z OAZU 1lo 6

ang85unit7 448 /I AA 4UU 1 Qio 1/1 0 34Z OAZU lo o

ang85unit9 Zy.y AAQ 44O

/I AA 4UU 1 816 1/10 34Z OAZU 1 <lo 0

angojuniiiu jl .z 44o 4nA 4UU 01Zl 11A OAZU 1 fi 10 1 oIZ angojuniii J jO.Z 4JO 4UU 1loa 140 j4Z onzu 1lO fi0

angojuniii4 DD. 1 4Z4 /! AA 4UU 1 8io 11/1 334 Qy

0/1 Z4 0

angojuniii J 4jO 4UU 1loa j4Z 140 1IZ 1lOfi o

angojunui.0 4jO 4UU 1loa 140 j4Z onzu 1 fi lO o angojunui

'i.A 'X HjO 4.An 4UU 1loa 140 j4Z onzu 1lOfs o

angojuniiio JJ.U A7.fi, 4j0 4AA 4UU 1 alo 140 j4Z OAzu 1 fi 10 0

ang85unitl9 4jO /i AA 4UU 1 8lo 1/10 34Z OAzu 110 0

f\r%rxQ Clival fl-O^ angojunitzu DO. 1 A4oZeo /I AA 4UU 1 816 1/10 J4Z OAzu 10 0

angojunitzz 4io /I K /I AA 4UU OAzu 11/1 334 OAzu lo 1 AlU angojunitzj 3z.3 4jo /I AA 4UU O 1 Zl 11A 33U OAzu lo 1 oIZ ang55unit24 33.1 436 /I AA 4UU OAZU 334 OA2U 1 A

lU

angojunitzS 32.0 296 4UU 18 0 /t o 34Z OAzu 16 u

oaveyTSunitl 33.2 373 CAA SOU OA20 /lie 435 OA2U 1 olo / davey75unit2 34.5 371 CAA 50U OAZU A^ Z 43 J OAzu lo 1 aavey/Duniti 33.0 3/3 CAA 300 OAzU /I '3 c 435 OAzU lo 1 wong90unitl 4zi yl AA 4UU OAZU 11/1 334 OAzu 1io 1 AlU

wong90unit2 J / .U 4 / J 4AA 4UU 1 a16 140 j4Z OAzu 1lOf\ O

wong90unit3 J /.u 4 / J

/I AA 4UU OAZU 114 Jj4 OAzu in 10 watson 1

4U.U 4 /4 4AA 4UU 1

1 / 140 j4Z 10IZ 1 o

oo waison 1

Dy.yj 4 /4 4nA 4UU 1loa iia 1

IZ lO inlU

peiroviTi lei JO.O 04n Z4U jU / jO 017 Zl / 10IZ 1IZ0 o petrovm le2 JO.Z Z4U J\J 1 JO 017 Zl /

1 0IZ 1 0IZ 0

peirovrnzei ^a a JO.O 040 Z4U 'XCM jO 017 Zl / 12 12 o peuovinzez jO.Z 04^ Z4U 'XfYl jU / jO 017 Zl / 12 12 o mc isniii 448 44o 1 JZ 1

lU 11^ 11

8 13 4

mc2shift 34.5 448 152 10 115 8 13 4

mcBshift 34.5 448 152 10 115 8 13 4

bri2spbaal 26.5 399 250 40 151 4 10 9

bri3ws21bs 26.5 375 250 40 151 8 10 9

bri3ws22bs 31.6 375 250 38 158 81 10 6

bri3ws25bs 26.5 381 250 40 148 8 1 13 9

bri3ws26bs 31.6 381 250 37 159 8 13 4

bri3ws27bs 31.6 345 250 40 145 8 16 9

108
Table A.2 (part 1 of 2). Spiral column database used in this study, data group II, and

measured hysteretic model parameters

1 CdL INalllC —

Hoop —

—— Axial ———

Column rOSl- I icia

T /^aH mm kN mm alpha beta Reduction

Ratio

mun76nol 34 26.4 2730 14.00 0.001 1.00 0.05(X)

ng78no2 14 16.9 1340 14.00 0.001 1.00 0.0988

ng78no2 10 550 930 5.00 0.120 0.95 0.0271

pot79nol 75 1920 1200 8.75 0.100 1.00 0.0329

pot79no3 50 4300 1200 13.00 0.030 1.00 0.0411

pot79no4 70 3785 1200 10.50 0.240 1.00 0.0320

pot79no5a 55 3385 1200 5.00 0.310 1.00 0.0511

pot79no5b 55 6770 1200 14.00 0.001 1.00 0.1283

angSlunitl 40 680 1600 8.00 0.080 1.00 0.0256

ang81unit2 55 2111 1600 14.00 0.001 1.00 0.0800

zahn86unit5 135 555 1600 10.50 0.250 1.00 0.0563

zahn86unit6 75 2080 1600 14.00 0.001 1.00 0.0834

modelnl 9 120 750 12.01 0.005 1.00 0.0110

modeln2 9 239 750 10.50 0.320 1.00 0.0402

modelnS 15 120 1500 10.50 0.170 1.00 0.0489

modeln4 9 120 750 12.01 0.230 1.00 0.0463

modelnS 9 239 750 10.50 0.280 1.00 0.0452

modeln6 15 120 1500 14.00 0.180 1.00 0.0724

flexnew 89 4450 9140 7.50 0.065 1.00 0.0326

sheamew 54 4450 4570 10.50 0.250 1.00 0.0311

arakawal 100 0 600 2.00 0.850 0.30 0.0850

arakawa2 50 0 600 2.00 0.600 0.25 0.0562

arakawa4 100 215 600 3.50 1.200 0.85 0.0572

arakawa6 50 215 600 4.00 0.980 0.26 0.0708

arakawaS 35 215 600 3.00 0.900 0.40 0.0741

arakawa9 50 215 600 3.32 1.100 0.60 0.1020

arakawalO 50 215 600 2.87 0.850 0.42 0.0925

arakawall N/A 430 600 4.53 2.400 0.93 0.0813

arakawal 2 100 430 600 2.60 1.100 0.65 0.0274

arakawal 3 50 430 600 2.55 0.980 0.65 0.0482

arakawal 4 35 430 600 3.20 0.900 0.65 0.0722

arakawal 5 75 0 900 1.90 0.470 0.20 0.0467

arakawal 6 35 0 900 6.00 0.260 0.98 0.0856

arakawal 7 75 215 600 2.80 1.000 0.26 0.0974

arakawal 8 N/A 215 900 3.00 2.000 0.60 0.0968

arakawal 9 75 215 900 1.90 0.700 0.50 0.0870

arakawa20 35 215 900 2.50 0.120 0.65 0.0507

arakawa21 75 215 1200 2.25 0.120 0.75 0.0245

arakawa22 75 215 900 1.90 0.750 0.18 0.0753

arakawa23 75 215 900 1.52 0.520 0.30 0.0736

arakawa24 N/A 430 600 2.95 0.820 0.40 0.0818

arakawa25 75 430 900 1.60 0.640 0.36 0.0718

arakawa26 75 430 1200 1.80 0.200 1.00 0.0665

arakawa27 75 430 900 2.30 0.700 0.25 0.0632

arakawa28 75 430 900 2.00 0.950 0.20 0.0792

109
Table A.2 (part 2 of 2). Spiral column database used in this study, data group II, and

measured hysteretic model parameters

Tfst Name Hoop

Spacing

mm

Axial

Load

kN

Column

Height

mm

Measured

alpha

Measured

beta

....

Measured

gamma *-*

Post-Yield

Stiffness Reduction

Ratio

anff85unit2 60 0 800 25.00 0.030 1.00 0.0246

ang85unit4 165 0 800 6.00 0.290 0.51 0.1068

ang85unit6 60 0 600 20.00 0.728 0.92 0.3175

angSSunit? 80 0 800 12.50 0.490 0.45 0.4421

ang85unit9 30 751 1000 18.00 0.070 1.00 0.0483

ang85unitlO 120 784 800 30.00 0.002 1.00 0.1164

ang85unitl3 30 455 800 5.00 0.090 0.70 0.0385

ang85unitl4 60 0 800 4.50 0.160 0.50 0.0384

ang85umtl5 60 0 800 9.00 0.140 0.72 0.0442

ang85unitl6 60 420 800 1.40 0.350 0.90 0.0960

ang85unitl7 60 431 1000 2.25 0.220 0.70 0.1193

ang85unitl8 60 440 600 2.90 0.300 0.98 0.0743

ang85unitl9 80 432 600 12.50 0.400 0.60 0.3047

ang85umt20 80 807 700 12.50 0.380 0.98 0.1385

ang85unit22 220 0 800 2.50 0.380 0.76 0.1962

ang85unit23 160 0 800 5.20 0.240 0.60 0.0180

ang85unit24 110 0 800 5.00 0.080 0.44 0.0152

ang85unit25 N/A 0 600 5.00 0.380 0.70 0.0886

davey75unitl 65 380 2750 12.50 0.375 1.00 0.0442

davey75unit2 65 380 1750 7.03 0.250 1.00 0.0705

davey75unit3 65 380 3250 12.50 0.780 1.00 0.0780

wong90unitl 60 907 800 5.00 0.100 1.00 0.0361

wong90unit2 65 1813 800 0.38 0.120 1.00 0.0907

wong90unit3 60 1813 800 2.10 0.080 1.00 0.0827

watsonlO 84 2652 1600 9.50 0.290 1.00 0.0630

watsonll 57 3620 1600 19.00 0.002 1.00 0.1595

petrovmlel 75 145 1910 7.50 0.100 1.00 0.0730

petrovmle2 75 254 1910 7.00 0.040 1.00 0.0595

petrovm2el 75 145 900 12.50 0.075 0.96 0.0857

petrovm2e2 75 254 895 9.00 0.180 1.00 0.0440

mcl shift 22 151 1140 9.00 0.120 1.00 0.1827

mc2shift 22 151 570 15.50 0.005 1.00 0.1168

mc3shift 22 220 570 12.50 0.048 1.00 0.1417

bri2spbaal 50 184 375 1.35 0.020 0.60 0.0240

bri3ws21bs 33 322 250 4.00 0.280 0.80 0.0429

bri3ws22bs 63 322 500 3.00 0.180 0.50 0.0592

bri3ws25bs 45 161 250 5.00 0.705 0.20 0.0770

bri3ws26bs 37 161 500 2.50 0.064 0.58 0.0678

bri3ws27bs 42 322 500 7.99 0.200 0.75 0.0726

110
11.0 Appendix B; Table of Earthquakes Selected for Analyses

Table B.l shows the bedrock acceleration record database that was used in this

study. From this data base acceleration records were selected and scaled, using

EARTHGEN and the procedures outlined in Chapter 3. Table B.2 shows the

suites of four records that were selected for each magnitude and distance, and

the amplitude scale factor applied to each record.

Table B.l (part 1 of 2). Database of recorded bedrock acceleration records used in this study

No.

v^riciiidiiuii Deg. CWAgency

1 Golden Gate Park 10 CALTECH San Francisco 1957

2 Golden Gate Park 100 CALTECH

3 201 1 Zonal Avenue 118 USGS San Fernando 1971

4 2011 Zonal Avenue 208 USGS

5 3838 Lankershim 0 USGS

6 3838 Lankershim 270 USGS

7 420 South Grand Avenue 127 USGS

8 420 South Grand Avenue 217 USGS

9 455 South Figueroa Street 218 USGS

10 455 South Figueroa Street 308 USGS

11 800 West 1st Street 37 USGS

12 800 West 1st Street 307 USGS

13 Santa Anita Reservoir Dam abutment 3 USGS

14 Santa Anita Reservoir Dam abutment 273 USGS

15 Caltech Seismic Laboratory 180 USGS

16 Caltech Seismic Laboratory 270 USGS

17 Fairmont Reservoir Dam 56 USGS

18 Fairmont Reservoir Dam 326 USGS

19 Santa Felicia Dam, outlet works 172 USGS

20 Santa Felicia Dam, outlet works 262 USGS

21 Griffith Park Observatory 180 USGS

22 Griffith Park Observatory 270 USGS

23 Lake Hughes Array #4 111 USGS

24 Lake Hughes Array #4 201 USGS

25 Lake Hughes Array #9 21 USGS

26 Lake Hughes Array #9 291 USGS

27 Puddingstone Reservoir Dam abutment 55 USGS

28 Puddingstone Reservoir Dam abutment 325 USGS

29 Pacoima Dam Abutment 164 USGS

30 Pacoima Dam Abutment 254 USGS

31 Superstition Mountain 45 USGS Imperial Valley, 1979

32 Superstition Mountain 135 USGS

* CALTECH = California Institute of Technology; USGS = U.S. Geological Survey; CDMG = California Division of Mines

and Geology

111
Table B.l (part 2 of 2). Database of recorded bedrock acceleration records used in this study

Kecora

No

L/rieniaiion Agency* Event Name

0 Whittipr williuci, 1087 lyO / 00 V^L-'IVIO JJ LJCAjWcL V alley IT J nV V^i^lVlO —_ _

jO ixond V alley #

j

on V^UIVIO

'XI j->eond vdiicy #o u V^UJVllj

DO lyeona vaiicy ffo on V^UIVllJ 1Qjy jviouni Wilson, L-aiiecn oeismic oiauon u

jviouni wiison, i^auccn oeismic otaiion ony\J 41 Pacoima, Ka^^el Canyon u

404Z Pacoima, Kagel Canyon on

V^lUl nUUsC, IUtU rUlIll l^UuOa nu k_iylVlVJ Tl^OIIId r»mQ T>rif>tQ rTlCia, 1080 1707

Pliff HniiQp 1000 Point T nhns 00

4*5 i^r\fTQl 1 tr\o 1 4'7'^ T-?iir^*lrQ i^n\ir\T\ Pr\QH \^UIIallLUo, IH / J HUICKa V_.aJiyUII ixUaU 00y\j 4A ^^r\rTQl 1 fr\c 1 TniirAl^Q (~^*^n\rr\n Pr\oH v_-uiraiiLUi>, It /J cureivd \_-aiiyuii ixuau JUVJ V^i-ZlVlVJ 47H / L/idiTionu ricij^nu>, ou i-'if^oy oiicci U V^iylVlVj ________ ____

48 00yyj y^LJLvLKJ 4Q vjuruy if a, vjdviidii i^uucj^c wdicr laiiK 00yyj oiiroy ffi, vjdvudn x^oiicj^c wdier laruc jOU V^L^lVlvJ J

rdLUl^ neij^iiia 970 V^-L'IVIVJ Po/^iTi^ 1-1^^1 fTrlfc V^i-'iVlO rTcalUlO V^l^iVHJ 54 Presidio 90 CDMG

55 Rincon Hill 0 CDMG

56 Rincon Hill 90 CDMG

57 Santa Cruz 0 CDMG

58 Santa Cruz 90 CDMG

59 Telegraph Hill 0 CDMG

60 Telegraph Hill 90 CDMG

61 Verba Buena Island 90 CDMG

62 Verba Buena Island 360 CDMG

112
Table B.2. Suites of design bedrock accelerations and amplitude scaling factors for

magnitudes 5.0, 6.0, 7.0, and 8.0, and distances of 10 km, 20 km, 30 km, and 40 km.

Magnitude 5.0 Magnitude 6.0 Magnitude 7,0 Magnitude 8.0

Record Amplitude Record Amplitude Record Amplitude Record Amplitude

No. Scale No. Scale No. Scale No. Scale

Factor Factor Factor Factor

Distance

10 km

23 0.755 16 1.169 59 7.259 7 4.187

37 2.488 30 0.256 30 0.518 10 4.288

57 0.198 27 3.390 48 3.477 59 12.570

50 0.228 5 1.627 21 2.214 48 6.117

Distance

23 0.374 16 0.636 59 4.575 7 2.960

37 1.233 30 0.139 30 0.327 10 3.031 20 km 57 0.098 27 1.844 48 2.191 59 8.886

50 0.113 5 0.885 21 1.396 48 4.324

Distance

30 km

23 0.217 16 0.396 59 3.198 7 2.262

37 0.715 30 0.087 30 0.228 10 2.316

57 0.057 27 1.150 48 1.532 59 6.790

50 0.066 5 0.552 21 0.975 48 3.304

Distance

40 km

23 0.139 16 0.270 59 2.387 7 1.815 57 0.037 27 0.781 48 1.143 10 1.859 38 0.384 31 0.405 62 3.755 59 5.450

50 0.042 5 0.375 21 0.728 48 2.652

113
12.0 Appendix C: Table of Damage States for Column Tests

Table C.l (part 1 of 6). Damage indices for test columns at critical damage states

Analysis Run: Number

of Data

Points

Damage

State DeformationDamage

Index

Energy

Damage

Index

Total Damage

Index

niun76nol 1 121 yield 0.17 0.04 0.2 mun/onol 2 376 ultimate 0.69 0.56 1.25 ng78no2_l 241 yield 0.26 0.11 0.37

ng78no2_2 AO t 481 ultimate 0.53 A C 1 0.51 1.04 ng78no3_l 61 yield 0.19 A AO 0.03 0.23 ng78no3_2 421 ultimate 0.85 A

0.56 1 A 1 1.41 pot79nol_l 121 yield 0.40 A 1 U.12 A CO 0.52

pot7ynol_2 241 ultimate 0.88 r\ Af\ U.4U 1 OO 1.28 pot7yno3_l 61 yield 0.33 A OA 0.39

pot79no3_2 181 ultimate 0.70 A0.25 A A^ 0.96

pot7ync>4_l 121 yield A ^A 0.60 A 1 O 0.12 A TO U.72

pot79no4_2 241 ultimate 1 1 o 1.18 A /I /I 0.44 1.63 pot7yno5a_l 1 o 1 Izl yield A 1 O 0.18 A A/1 0.04 A

0.22

pot7ynoja_2 z41 ultimate A

0.37 A 1 0 0.13 A /I A

0.49

poi/yno!)D_l n 1 IZl yield U.4o U.zU A A< U.oo poi/ynojD_z 1 Q 1 181 ultimate u.oy A 1Q U.3o 1 .U / ang81unitl_l IZl yield U. 14 U.U3 AIT u.l / angoiunui_z Z41 ultimate u.zy All U.l 1 A /1A U.4U

angoiuniLZ_i mIzl yield AIT U. 1 / A Al U.U3 A 1 Q U.19

angoiuniLZ_z Z41 ultimate AnU.lz A <1 U.51 ang81unit2_3 3oi failure U.JO All U.31 A QO U.89

zahn86no5 1 69 yield A0.23 A {\A 0.04 A o^ 0.z6

zann8onoj z 121 ultimate n AO 0.48 A 1 O

O.lZ A <A 0.60

zann86no5 3 361 failure 1 CA 1.50 A OO 0.88 O OO 2.3 / zannSonoo 1 68 yield 0.15 A AO 0.02 AIT 0.17

zannSonoo 2 121 ultimate A 1 O 0.38 A A'T 0.07 0.46

zannSonoo 3 361 failure 11.26 0.76 AO 2.02

modem1 1 121 yield 0.43 A 1 O 0.13 A C C 0.55 modem 1 2 241 ultimate A an 0.97 0.44 1 /I o

i.4z modern 1 3 421 failure 1 C A

1.50 1 11.30 O OA 2.80

modelnz 1 121 yield 0.34 A AA 0.09 A y1 O 0.4z

modeln2 2 Z41 ultimate A HA0. /4 A 1f\ 0.30 1 Ayl 1.U4 modeln2 3

/CAT 6U1 failure z. 11 1.85 3.95 modeIn3 1 61 yield All 0.11 A Al 0.01 A 1 0 0.13 modeln3 2 121 ultimate 0.38 0.10 0.48

modeln3 3 421 failure 0.80 0.66 1.46 modeln4 1 121 yield 0.21 0.06 0.26

modeln4 2 241 ultimate 0.46 0.20 0.66

modeln4 3 721 failure 1.32 1.71 3.04 modelnS 1 121 yield 0.27 0.06 0.34 modelnS 2 241 ultimate 0.57 0.23 0.80

modelnS 3 661 failure 1.52 1.69 3.21 modeln6 1 61 yield 0.09 0.01 0.10

modeln6 2 121 ultimate 0.28 0.07 0.35 modeln6 3 841 failure 0.60 1.13 1.73

114
Table C.l (part 2 of 6). Damage indices for test columns at critical damage states

Analysis Run: Number

of Data

Points

Damage

State

Deformation

Damage

Index

Energy

Damage

Index

Total Damage

Index

flexnew 1 121 yield 0.36 0.09 0.45 flexnew 2 241 ultimate 0.56 0.25 0.81 flexnew 3 1201 failure 1.18 2.4? 3.65 sheamew 1 121 yield 0.25 0.09 0.33 sheamew 2 289 ultimate 0.?6 0.4? 1.23 sheamew 3 529 failure 1.2? 1.50 2.?? arakawal 1 121 yield 0.32 0.04 0.35 arakawal 2 181 ultimate 0.50 0.08 0.5? arakawal 3 421 failure 1.22 0.36 1.59 arakawa2 1 181 yield 0.52 0.08 0.60

arakawa2 2 241 ultimate 0.69 0.13 0.82

arakawa2 3 481 failure 1.50 0.48 1.9? arakawa4 1 61 yield 0.1? 0.01 0.18 arakawa4 2 181 ultimate 0.5? 0.12 0.69 arakawa4 3 301 failure 1.02 0.32 1.34 arakawa6 1 121 yield 0.1? 0.02 0.18 arakawa6 2 181 ultimate 0.26 0.04 0.30

arakawa6 3 361 failure 0.5? 0.14 0.?2

arakawaS 1 61 yield 0.04 0.01 0.05 arakawaS 2 181 ultimate 0.16 0.03 0.19

arakawaS 3 421 failure 0.43 0.14 0.5? arakawa9 1 61 yield 0.08 0.01 0.08 arakawa9 2 181 ultimate 0.2? 0.05 0.32

arakawa9 3 361 failure 0.60 0.19 0.?9 arakawal 0 1 121 yield 0.16 0.02 0.18 arakawalO 2 241 ultimate 0.34 0.0? 0.41 arakawal 0 3 421 failure 0.60 0.22 0.81 arakawal 1 1 13 yield 0.31 0.01 0.33 arakawal 1 2 61 ultimate 0.65 0.05 0.?1 arakawal 1 3 121 failure 1.04 0.15 1.19 arakawal 2 1 61 yield 0.23 0.01 0.25 arakawal2 2 121 ultimate 0.53 0.0? 0.60

arakawal 2 3 181 failure 0.8? 0.15 1.03 arakawal 3 1 61 yield 0.11 0.01 0.11 arakawal 3 2 181 ultimate 0.38 0.0? 0.45 arakawal 3 3 301 failure 0.69 0.19 0.88 arakawal4 1 121 yield 0.15 0.02 0.18 arakawal4 2 241 ultimate 0.34 0.08 0.43 arakawal4 3 361 failure 0.53 0.18 0.?2

arakawal 5 1 301 yield 0.38 0.0? 0.45 arakawal 5 2 421 ultimate 0.56 0.13 0.69 arakawal 5 3 601 failure 0.90 0.2? 1.18 arakawal 6 1 241 yield 0.22 0.06 0.28 arakawal 6 2 361 ultimate 0.34 0.16 0.50

arakawal? 1 121 yield 0.2? 0.03 0.30

arakawal? 2 181 ultimate 0.42 0.06 0.48 arakawal? 3 361 failure 0.91 0.22 1.14

115
Table C.l (part 3 of 6). Damage indices for test columns at critical damage states

Analysis Run: Number

of Data

Points

Damage

State

Deformation

Damage

Index

Energy

Damage

Index

Total Damage

Index

arakawalS 1 73 yield 0.28 0.02 0.30

arakawalS 2 121 ultimate 0.35 0.03 0.38

arakawalS 3 181 failure 0.59 0.07 0.66

arakawal9 1 181 yield 0.18 0.02 0.20

arakawal9 2 301 ultimate 0.34 0.07 0.40

arakawal9 3 541 failure 0.64 0.22 0.86

arakawa20 1 241 yield 0.10 0.02 0.12

arakawa20 2 421 ultimate 0.18 0.07 0.25 arakawa21 1 301 yield 0.19 0.05 0.24

arakawa21 2 541 ultimate 0.35 0.17 0.53 arakawa22 1 181 yield 0.15 0.01 0.16

ara]kawa22 2 361 ultimate 0.34 0.06 0.40

arakawa22 3 541 failure 0.57 0.14 0.70

arakawa23 1 181 yield 0.17 0.02 0.19

arakawa23 2 361 ultimate 0.39 0.08 0.47

arakawa23 3 601 failure 0.74 0.25 0.99

arakawa24 1 61 yield 0.48 0.03 0.51 arakawa24 2 181 ultimate 1.67 0.28 1.95 arakawa24 3 301 failure 2.97 0.73 3.70

arakawa25 1 181 yield 0.27 0.03 0.29

arakawa25 2 301 ultimate 0.50 0.09 0.59

arakawa25 3 541 failure 1.02 0.30 1.33 arakawa26 1 241 yield 0.22 0.04 0.26

arakawa26 2 541 ultimate 0.51 0.24 0.75

arakawa27 1 181 yield 0.19 0.02 0.20

arakawa27 2 301 ultimate 0.37 0.06 0.42

arakawa27 3 481 failure 0.64 0.15 0.80

arakawa28 1 181 yield 0.18 0.02 0.20

arakawa28 2 301 ultimate 0.34 0.05 0.40

arakawa28 3 481 failure 0.60 0.14 0.73 ang85no2_l 361 yield 0.56 0.46 1.02 ang85no2_2 961 ultimate 1.06 1.78 2.84

ang85no2_3 1981 failure 1.87 6.44 8.31 ang85no4_l 314 yield 0.77 0.37 1.14 ang85no4_2 361 ultimate 0.88 0.42 1.30 ang85no4_3 721 failure 1.32 1.11 2.43 ang85no6_l 11 yield 0.57 0.14 0.70

ang85no6_2 61 ultimate 0.85 0.27 1.12 ang85no6_3 361 failure 1.27 1.08 2.35 ang85no7_l 13 yield 0.58 0.12 0.69

ang85no7_2 61 ultimate 0.72 0.16 0.87 ang65no7_i 361 failure 0.94 U.66 1.6U ang85no9_l 361 yield 1.03 0.85 1.88 ang85no9_2 915 ultimate 1.92 3.18 5.11 ang85no9_3 1381 failure 2.78 7.10 9.89

ang85nolO_l 61 yield 1.13 0.39 1.53 ang85nol0_2 361 ultimate 1.56 1.99 3.54 an585nol0_3 721 failure 2.30 5.33 7.63

116
Table C.l (part 4 of 6). Damage indices for test columns at critical damage states

Anjilv^i^ Run* NiimKpr

of Data

Points

State

r^pfr\fTn t i r\n Damage

Index

energy

Damape

Index

Tntnl Damage

Index

ang85nol3_l 361 yield 0.41 0.21 0.63 ang85nol3_2 961 ultimate 1.13 1.05 2.18 ang85nol3 3 1201 failure 1.13 1.73 2.86

ang85nol4 1 361 yield 0.90 0.39 1.29 ang85nol4_2 661 ultimate 1.22 0.89 2.11 an?8Snol4 3 961 mil failure ui \/ 2 31 1 80 4.11 ang85nol5 1 361 yield 0.38 0.21 0.59 ang85nol5 2 961 ultimate 1.02 1.01 2.03 ang85nol5 3 1201 failure 1.05 1.69 2.74

ang85nol6_l 314 yield 0.61 0.24 0.85 ang85nol6_2 361 ultimate 0.70 0.26 0.97 ane;85nol6 3 721 failure 0.95 0.74 1.69 ang85nol7_l 361 yield 0.51 0.19 0.70

ang85nol7_2 661 ultimate 0.67 0.47 1.14 ang85nol7_3 961 failure 1.02 0.88 1.90 ang85nol8_l 361 yield 1.16 0.60 1.77 ang85nol8_2 661 ultimate 1.70 1.47 3.17 ang85nol8 3 721 failure 1.74 1.73 3.47 ang85nol9_l 61 yield 0.92 0.20 1.12 ang85nol9_2 361 ultimate 1.50 0.91 2.41 ang85nol9_3 421 failure 1.55 1.16 2.71 ang85no20 1 314 yield 1.29 0.73 2.02

ang85no20 2 361 ultimate 1.63 0.92 2.55 ang85no20 3 421 failure 1.68 1.21 2.89 ang85no22 1 61 yield 0.57 0.08 0.64 ang85no22 2 361 ultimate 1.01 0.44 1.45 ang85no22_3 421 failure 1.01 0.57 1.58 ang85no23_l 361 yield 1.22 0.47 1.69 ang85no23_2 661 ultimate 2.42 1.34 3.76 ang85no23_3 721 failure 2.42 1.64 4.06

ang85no24_l 361 yield 1.03 0.41 1.44 ang85no24_2 661 ultimate 2.11 1.18 3.30 ang85no24_3 721 failure 2.16 1.41 3.57 ang85no25 1 61 yield 1.39 0.3 1.68 ang85no25_2 361 ultimate 2.30 1.27 3.58 ang85no25_3 421 failure 2.35 1.57 3.92 davey75nol_l 181 yield 0.20 0.03 0.23 davey75nol_2 241 ultimate 0.53 0.14 0.66

davey75nol_3 361 failure 1.04 0.37 1.41 davey75no2_l 61 yield 0.16 0.02 0.17

davey75no2_2 241 ultimate 1.18 0.44 1.62 davey75no3_l 61 yield 0.05 0.00 0.05 davey75no3_2 181 ultimate 0.23 0.03 0.27 davey75no3_3 361 failure 0.53 0.27 0.80

117
Table C.l (part 5 of 6). Damage indices for test columns at critical damage states

Analysis Run: Number

of Data

Points

Damage

State

Deformation

Damage

Index

Enerev

Damage

Index

Total

Damage

Index

wong90nol_l 301 yield 0.31 0.14 0.45 wong90nol 2 1199 ultimate 0.87 0.80 1.68 wong90no2_l 301 yield 0.23 0.04 0.26

wong90no2_2 1199 ultimate 3.58 1.33 4.91 wong90no2 3 1559 failure 4.70 2.15 6.84

wong90no3 1 661 yield 0.30 0.21 0.51 wong90no3_2 1261 ultimate 1.03 0.98 2.01 wong90no3_3 1621 failure 1.37 1.94 3.31 watsonlO 1 241 yield 0.33 0.05 0.38 watsonlO 2 361 ultimate 0.54 0.17 0.71 watsonlO 3 661 failure 0.97 0.74 1.71 watsonll 1 68 yield 0.08 0.00 0.08

watsonll 2 241 ultimate 0.51 0.15 i 0.66

watsonll 3 316 failure 0.77 0.32 1.09 mclshift 1 181 yield 0.15 0.02 0.16

mclshift 2 421 ultimate 0.45 0.18 0.63 mclshift 3 781 failure 0.93 0.92 1.85 mc2shift 1 181 yield 0.30 0.06 0.36

mc2shift 2 541 ultimate 1.33 1.14 2.47 mcBshift 1 301 yield 0.72 0.27 0.99

mc3shift 2 421 ultimate 1.15 0.66 1.81 mc3shift 3 856 failure 2.39 3.73 6.12

bri2spbaal 1 121 yield 2.95 0.55 3.50

bri2spbaal_2 2701 ultimate 22.35 34.98 57.33

bri2spbaal 3 2761 failure 24.22 38.21 62.43

bri3ws21bs 1 121 yield 3.37 1.01 4.38

bri3ws21bs 2 781 ultimate 6.34 6.02 12.37 bri3ws21bs 3 1501 failure 9.63 18.59 28.21

bri3ws22bs 1 121 yield 1.22 0.24 1.46 bri3ws22bs 2 721 ultimate 2.50 1.47 3.98 bri3ws22bs 3 2641 failure 7.78 14.16 21.94

bri3ws25bs 1 121 yield 1.23 0.28 1.51 bri3ws25bs 2 721 ultimate 2.60 1.33 3.93 bri3ws25bs 3 1441 failure 3.67 4.81 8.48 bri3ws26bs 1 121 yield 0.39 0.08 0.47

bri3ws26bs 2 1381 ultimate 1.28 1.56 2.85 bri3ws26bs 3 2881 failure 3.48 7.26 10.74 bri3ws27bs 1 121 yield 0.64 0.19 0.82

bri3ws27bs 2 721 ultimate 1.27 1.08 2.35 bri3ws27bs 3 1561 failure 2.03 3.95 5.98

118
Table C. 1 (part 6 of 6). Damage indices for test columns at critical damage states

Analysis Run: Number

of Data

Points

Damage

State Deformation

Damage

Index

Energy

Damage

Index

Total Damage

Index

petlel_l 420 yield 0.04 0.01 0.05 petlel_2 1201 ultimate 0.31 0.16 0.48 petlel_3 1561 failure 0.52 0.55 1.07 petle2_l 485 yield 0.05 0.01 0.06

1 0fii'y 1Z.OJ 1 1 1 f 1 rvi ofA uiiimdie U.J / U. lO U. Jt petle2_3 1565 failure 0.56 0.51 1.07 pet2el_l 961 yield 0.25 0.26 0.51 pet2el_2 1201 ultimate 0.50 0.50 1.01 pet2el_3 2041 failure 1.56 3.07 4.63 pet2e2_l 601 yield 0.23 0.15 0.39 pet2e2_2 1141 ultimate 0.86 0.88 1.74 pet2e2_3 1501 failure 2.01 2.20 4.21

*US GOVERNMENT PRINTTING OFFICE 1 9 9 3 -s",! - 9 3 1/8 2 6 2 0

119

N'ST-114A U.S. DEPARTMENT OF COMMERCE

(REV. 3-90) NATIONAI IN^^TITlfTF DF •^TANnARDC; AND TFPHNIOI Df^V

BIBLIOGRAPHIC DATA SHEET

1. PUBLICATION OR REPORT NUMBER flIST/BSS-170

2. PERFORMINQ OROAMIZATIOH REPORT NUMBER

X PUBUCATIOH DATE February 199 3

4. TITLE ANO SUBTITLE SEISMIC PERFORMANCE OF CIRCULAR BRIDGE COLUMNS DESIGNED IN ACCORDANCE WITH

AASHTO/CALTRANS STANDARDS

5. AUTHOR(S)

WILLIAM C. STONE AND ANDREW W. TAYLOR

6. PERFORMINQ OROANIZATION (IF JOINT OR OTHER THAN NIST, SEE INSTRUCTIONS)

U.S. DEPARTMENT OF COMMERCE

NATIONAL INSTITUTE OF STANDARDS ANO TECHNOLOQY

OAITHERSBURO, MD 20609

7. CONTRACT/QRANT NUMBER

a. TYPE OF REPORT ANO PERIOD COVERED

Final

9. SPONSORING OROANIZATION NAME ANO COMPLETE ADDRESS (STREET, CITY, STATE, ZIP) NIST (National Institute of Standards and Technology, Gai thersburg , MD 20899)

FHWA (Federal Highway Administration, Turner-Fairbank Highway, 6300 Georgetown Pike,

McLean, VA 22101-2295)

10. SUPPLEMENTARY NOTES

11. ABSTRACT (A 200-WORD OR LESS FACTUAL SUMMARY OF MOST SIGNIFICANT INFORMATION. IF DOCUMENT INCLUDES A SIQNIFICANT BIBUOQRAPHY OR

LJTERATURE SURVEY, MENTION IT HERE.) Limitations of present procedures for the design of bridge columns to withstand seismic

loads are discussed. An integrated seismic design procedure is developed which 1) allows

the automatic selection and scaling of design earthquakes given the earthquake magnitude,

the distance from the site to the fault, and the type of overlying soil strata; 2) predicts

the inelastic behavior of reinforced concrete bridge columns when subjected to random lateral

loads up to and including failure; and 3) calculates cumulative damage which can be

directly correlated to observed states of damage in laboratory tests of bridge columns.

Techniques for achieving the above capabilities are described and new design criteria,

based on acceptable damage indices as functions of earthquake magnitude, distance, and

structural importance, are proposed. Losing the proposed procedure and criteria the

performance of 72 representative bridge columns designed in accordance with 1992 CALTRANS

specifications is analyzed. Analysis parameters included earthquake magnitude, distance

from epicenter, subsurface soil characteristics, column aspect ratio, and normalized

column axial load. Design charts, based on allowable damage index versus earthquake

magnitude, are developed and retrofit strategies are discussed for those designs which do

not meet the proposed design criteria.

12. KEY WORDS (6 TO 12 ENTRIES; ALPHABETICAL ORDER; CAPITALIZE ONLY PROPER NAMES; AND SEPARATE KEY WORDS BY SEMICOLONS)

circular bridge columns; damage index; design; dynamic analysis;

earthquakes; hysteretic damage model; inelastic modeling;

reinforced concrete; seismic loads; site specific response; soil

amplification; spiral reinforcement.

13. AVAILABIUTY 14. NUMBER OF PRINTED PAGES XX UNUMITEO

FOR OFFICIAL DISTRIBUTION. DO NOT RELEASE TO NATIONAL TECHNICAL INFORMATION SERVICE (NTIS). 129

XX

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