NONLINEAR RESPONSES OF HIGH-RISE BUILDINGS IN
GIANT SUBDUCTION EARTHQUAKES

Thesis by
Jing Yang

In Partial Fulfillment of the Requirements for the
Degree ofDoctor of Philosophy

CALIFORNIA INSTITUTE OF TECHNOLOGY
Pasadena, California
2009(Defended Dec.10, 2008)© 2009
Jing Yang
All Rights Reserved

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Acknowledgements
I cannot overstate my deep gratitude to my PhD advisor, Professor Tom Heaton for his full
support and great guidance. It is hard to count how many times I came into his office full ofconfusion or even frustration, and came out of his office with excitement and confidence.
Professor Heaton’s office is like a magic box and he is more like a loving father. Working
with Professor Heaton has been a great and cherished experience in my life.
I also wish to thank the members in my thesis defense committee. Thanks to Professor Jim
Beck and Swami Krishnan who had spent much of their time to modify my thesis carefully
and gave me many precious suggestions. Thanks to Professor Hiroo Kanamori for his
encourage and precious time drawing from his busy schedule. I want to especially thankProfessor Hall for providing me the building designs and models. His patient and detailed
explanations helped me a lot in understanding the building modeling.
This research was supported by the NSF and the Gordon & Betty Moore Foundation. The
teleseismic data used in this study is obtained from IRIS, and strong ground motion
recordings are obtained from websites of K-Net and KiK-Net. Data from SHIP02
experiment was generously provided by Professor Thomas Pratt at the University ofWashington. High-sample GPS data was provided by Prof Kristine Larson at the Universityof Colorado. Building responses were calculated at SCEC High Performance Computing
Center.
My many thanks go to my fellow graduate students, Anna Olsen, Masumi Yamada, Matt
Muto, Case Bradford, Georgia Cua and John Clinton for helping me with research andiv
candidacy exams. Thank you to Carolina Oseguera and many graduate students fromSeismolab for lots of help.
Above all, I would like to express my gratitude to my family. Without the support from myfather and my mother-in-law, I would not have finished this thesis. My little son Aaron
makes my life busy but enjoyable. Finally, I would like to give my deepest thanks to myhusband Ke Wang, for his support and encouragement. I wish that my loving mother would
see my achievements in heaven.

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Abstract
With the exception of the 2003 Tokachi-Oki earthquake, strong ground recordings fromlarge subduction earthquakes (Mw > 8.0) are meager. Furthermore there are no strong
motion recordings of giant earthquakes. However, there is a growing set of high-quality
broadband teleseismic recordings of large and giant earthquakes. In this thesis, we use
recordings from the 2003 Tokachi-Oki (Mw 8.3) earthquake as empirical Green’s functions
to simulate the rock and soil ground motions from the 2004 Sumatra-Andaman earthquake
and a scenario Mw 9.2 Cascadia subduction earthquake in the frequency band of interest to
flexible and tall buildings (0.075 to 1 Hz). The effect of amplification by the Seattle basin
is considered by using a basin response transfer function, which is derived fromdeconvolving the teleseismic waves recorded at rock sites from basin sites at the SHIP02
experiment. These strong ground motion time histories are used to simulate of the fully
nonlinear response of 20-story and 6-story steel moment-frame buildings designed
according to both the U.S. 1994 Uniform Building Code and the 1987 Japanese building
code. We consider several realizations of the hypothetical subduction earthquake. The
basin amplification and the down-dip limit of rupture are of particular importance to thesimulated ground motions in Seattle. At rock sites, if slip is limited to offshore regions, thebuilding model responses are mostly in the linear range. However, if rupture is extended
beyond the Olympic Mountains, large deformations occur in the high-rise buildings models,
especially those with brittle welds. At basin sites, our simulations indicate the collapse of
all building models for a source model with rupture beyond the Olympic Mountains,
whereas buildings with perfect welds avoid collapse for simulations based on a source

vimodel with rupture limited to offshore. The synthetic ground motions all have very long
durations (more than 5 minutes at basin sites), and our building simulations should beconsidered as a low estimate since we the degradation model used in our simulation did notconsider local flange buckling.

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Contents

Acknowledgementsiii

Abstractv

Contents

vii

List of Figuresxi

List of Tables

xvii

Introduction

1

1.1 Motivation........................................................................................................................1
1.2 Previous Work .................................................................................................................4
1.2.1 Strong Ground Motions in Earthquakes ................................................................4
1.2.2 Performance of Steel Moment-Resisting Frame Buildings in Earthquakes.........5
1.3 Our Work and Outline of Chapters.................................................................................7
Computational Building Models

10

2.1 Computational Method..................................................................................................10
2.1.1 Beam-Column Elements ......................................................................................112.1.2 Panel Zone ............................................................................................................12

viii
2.1.3 Weld Fracture .......................................................................................................142.1.4 P-Delta Effects .....................................................................................................16
2.1.5 Limitations of Frame-2D .....................................................................................16
2.2 Buildings Considered ....................................................................................................172.2.1 General Characteristics ........................................................................................172.2.2 Pushover Analysis ................................................................................................23
2.2.3 Discussion.............................................................................................................23
26 September 2003 Tokachi-Oki, Hokkaido, Earthquake Mw 8.1

27

3.1 Introduction....................................................................................................................27
3.2 Recorded Strong Ground Motions and Site Condition on Hokkaido Island ...............29
3.3 Nonlinear Performance of Buildings ............................................................................35
3.4 Relations Between Responses of Buildings and Ground Motions ..............................49
3.5 Collapse Factor ..............................................................................................................52
Empirical Green’s Functions Method

61

4.1 Empirical Green’s Functions Technique ......................................................................63
4.2 Choosing Records From the 2003 Tokachi-Oki Earthquake (Mw 8.1) as EmpiricalGreen’s Functions........................................................................................................65
December 2004 Sumatra-Andaman, Indonesia, Earthquake Mw 9.2

70

5.1 Introduction....................................................................................................................71
5.2 Rupture Fault Models....................................................................................................71
5.3 Teleseismic P-wave Simulation ....................................................................................74
5.4 Strong Ground Motion Simulation ...............................................................................81
5.4.1 Choosing Empirical Green’s Functions...............................................................81
5.4.2 Results and Discussion.........................................................................................85
5.5 Nonlinear Performance of Buildings ............................................................................92
5.5.1 20-Story vs. 6-Story Buildings ............................................................................95
5.5.2 Buildings with Brittle Welds vs. Perfect Welds..................................................96
5.5.3 Stiffer vs. More Flexible Buildings .....................................................................97

ix
5.5.4 Responses of Buildings for Different Site Conditions........................................98
5.5.5 Comments on Long Duration Effects..................................................................99
The Scenario Cascadia Subduction Earthquake Mw 9.2

103

6.1 Introduction..................................................................................................................104
6.2 Rupture Fault Models..................................................................................................105
6.3 Teleseismic P-wave Simulations ................................................................................108
6.4 Strong Ground Motion Simulations............................................................................110
6.4.1 Rock Sites...........................................................................................................110
6.4.2 Site Amplification ..............................................................................................116
6.4.2.1
Data....................................................................................................117
6.4.2.2
Method...............................................................................................117
6.4.2.3
Results................................................................................................119
6.5 Nonlinear Performance of Buildings ..........................................................................128
6.5.1 20-Story vs. 6-Story Buildings ..........................................................................131
6.5.2 Buildings with Brittle Welds vs. Perfect Welds................................................131
6.5.3 Stiffer vs. More Flexible Buildings ..................................................................134
6.5.4 Responses of Buildings for Different Site Conditions......................................135
6.5.5 Response of Buildings to Motions from Different Fault Width Models..........135
Determining Broadband Displacements by Combining Inertial Seismic Records andHigh-Sample Rate GPS Records
136
7.1 Introduction..................................................................................................................136
7.2 Correction Scheme ......................................................................................................138
7.2.1 Seismic Data.......................................................................................................138
7.2.2 GPS Data ............................................................................................................139
7.2.3 Correction Scheme .............................................................................................142
7.3 Error Analysis..............................................................................................................145
7.4 Results..........................................................................................................................148
7.5 Conclusions..................................................................................................................152
Concluding Remarks

153x
8.1 Summary of Research .................................................................................................153
8.2 Conclusions..................................................................................................................154
8.3 Future Directions .........................................................................................................156
References

158

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List of Figures
2.1 Segment layout and fiber layout for beams and columns ...............................................13
2.2 Backbone curves and the axial stress-strain hysteresis relation for beam or column steel
fiber. ..................................................................................................................................14
2.3 Fracture strain distribution of different connections for brittle welds ............................15
2.4 Illustration of P-Delta effects on a steel MRF and the definition of interstory drift ratio(IDR) and roof displacement (RD) ..................................................................................16
2.5 Floor plan and frame elevations of the 20-story building designed according to the
UBC94 (U20) ...................................................................................................................19
2.6 Floor plan and frame elevations of the 20-story building designed according to theJapanese building code (J20)............................................................................................20
2.7 Floor plan and frame elevations of the 6-story building designed according to the
UBC94 (U6)......................................................................................................................21
2.8 Floor plan and frame elevations of the 6-story building designed according to theJapanese building code (J6)..............................................................................................22
2.9 The definitions of ductility, yield strength and ultimate strength of a building on a
pushover curve..................................................................................................................24
2.10 Pushover analysis of the 6- and 20-story steel moment frame buildings designed to the
UBC94 and Japanese code with brittle welds and perfect welds....................................24
2.11 Pushover curves for the 20-story buildings with yield stress = 42 ksi and = 50 ksi.....26
2.12 Pushover curves for the 6-story buildings with yield stress = 42 ksi and = 50 ksi.......26
3.1 Historic large and giant earthquakes on Hokkaido region ..............................................28
3.2 The distribution of PGA, PGV and PGD.........................................................................30

xii
3.3 The distributions of pseudo spectral acceleration at periods of 1.5 sec and 3.5 sec for
5% damping ......................................................................................................................31
3.4 Contours of the average shear wave velocity in the upper 30 meters.............................32
3.5 Locations of 276 K-Net and KiK-Net stations that recorded the 2003 Tokachi-Oki
earthquake (Mw 8.1) on Hokkaido Island ........................................................................34
3.6 Contour maps of Peak IDR for U20B and U20P ............................................................38
3.7 Contour maps of Peak IDR for J20B and J20P ...............................................................39
3.8 Contour maps of Peak IDR for U6B and U6P.................................................................40
3.9 Contour maps of Peak IDR for J6B and J6P ...................................................................40
3.10 Contour maps of MRD for U20B and U20P .................................................................42
3.11 Contour maps of MRD for J20B and J20P....................................................................43
3.12 Contour maps of MRD for U6B and U6P .....................................................................44
3.13 Contour maps of MRD for J6B and J6P ........................................................................45
3.14 Contour maps of percentage of the total welded moment-resisting connections thatfractured for U20B and J20B ...........................................................................................46
3.15 Contour maps of percentage of the total welded moment-resisting connections thatfractured for U6B and J6B ...............................................................................................47
3.16 Combination of the pushover curves for 20-story buildings and station distribution forroof displacements............................................................................................................48
3.17 Combination of the pushover curves for 6-story buildings and station distribution forroof displacement .............................................................................................................49
3.18 Relationships between peak inter-story drift of U20 and ground motion intensity
measures............................................................................................................................52
3.19 Relationships of P pseudo spectral velocity (5% damped) to peak IDRs for 3 sets of
20-story building models..................................................................................................53
3.20 Relationships of pseudo spectral velocity (5% damped) to peak IDRs for 3 sets of 6story building models .......................................................................................................54
3.21 Contour maps of collapse factor for U20B and J20B....................................................57

xiii
3.22 Contour maps of collapse factor for U20P and J20P ....................................................58
3.23 Contour maps of collapse factor ratio between J20 and U20........................................59
3.24 Contour maps of collapse factor ratio between 20P and 20B .......................................60
4.1 Illustration of empirical Green’s function method ..........................................................64
4.2 Smoothed teleseismic P-wave Fourier acceleration spectra for large shallow subduction
earthquakes (Mw ≥ 7.6) that occurring in 1990 to 2007 ..................................................67
4.3 Smoothed teleseismic P-wave Fourier displacement spectra for large shallow
subduction earthquakes (Mw ≥ 7.6) occurring in 1990 to 2007 ......................................67
4.4 Cross sections of the approximate geometry of the rupture surfaces for Hokkaido,
Sumatra and Cascadia subduction zones. ........................................................................68
5.1 Geometries of the rupture fault models used to simulate the 2004 Sumatra-Andaman
earthquake.........................................................................................................................73
5.2 Locations of Global Seismograph Network stations (Δ = 30º ~ 90º) which had recorded
teleseismic data from the 2003 Tokachi-Oki earthquake and the 2004 SumatraAndaman earthquake........................................................................................................76
5.3 Teleseismic P-wave seismograms recorded at Global Seismograph Network stations (Δ= 30º to 90º) from the 2003 Tokachi-Oki earthquake .....................................................77
5.4 Teleseismic P-wave seismograms recorded at Global Seismograph Network stations (Δ= 30º to 90º) from the 2004 Sumatra-Andaman earthquake ...........................................78
5.5 Four teleseismic P-wave seismograms recorded at the 2003 Tokachi-Oki earthquake
used as empirical Green’s functions to simulate the 2004 Sumatra earthquake.............79
5.6 Distributions of empirical Green’s functions used to simulate teleseismic P-waves from2004 Sumatra earthquake. ................................................................................................79
5.7 Comparison of simulate teleseismic P-waveforms at distance 60o from 8 models withobserved recordings at station YSS (Δ = 60.5º) in Sumatra event..................................80
5.8 Comparison of smoothed Fourier spectra of teleseismic P-waveforms from different
models and records at station YSS (Δ = 60.5º) in Sumatra event ...................................81
5.9 Peak ground velocities versus distance from stations to the center of the fault .............84
5.10 Simulated accelerations for six models in BAC ............................................................87

xiv
5.11 Simulated velocities for six models in BAC..................................................................88
5.12 Simulated displacements for six models in BAC ..........................................................89
5.13 Pseudo-velocity spectra for simulated data with 5% damping .....................................90
5.14 Comparing PGA and PGV for different models ...........................................................91
5.15 Peak interstory drift ratio and maximum roof displacements of 20- and 6-story
buildings at rock and soil sites for wide and narrow models ..........................................93
5.16 Roof displacement time histories for U20B for 6 models in east-west component .....94
5.17 Roof displacement time histories for U20B for 6 models in north-south component..95
5.18 Distribution of peak IDRs along the height for U20 with brittle welds, perfect welds
and elastic elements ..........................................................................................................97
5.19 Comparing roof displacements between flexible U20 and stiff stronger J20 in Model
S-Wide-24 Soil .................................................................................................................99
5.20 An example of hysteresis loop obtained from the SAC experiment...........................100
5.21 Examples of moment-rotation response (hysteresis loop) in an end of a beam to thesimulated ground motions ..............................................................................................101
6.1 Rainer Tower in downtown Seattle................................................................................105
6.2 Geometry of rupture fault models used to simulate the Scenario Cascadia Earthquake
Mw9.2 ..............................................................................................................................107
6.3 Distribution of empirical Green’s functions used to simulate teleseismic P-waves fromthe expected Cascadia earthquake..................................................................................108
6.4 Comparison of simulate teleseismic P-waveforms at distance 60o from 3 models withobserved recordings at station YSS (Δ = 60.5º) in the Sumatra event..........................109
6.5 Simulated accelerations for nine models at rock sites in SEA ......................................112
6.6 Simulated velocities for nine models at rock sites in SEA............................................113
6.7 Simulated displacements for nine models at rock sites in SEA ....................................114
6.8 Pseudo-velocity spectra for simulated data at rock sites in SEA with 5% damping ....115
6.9 Resulting Green's functions time history deconvolved teleseismic S-waves recorded inrock site 7295 from basin site 7335 in the 2002 Taiwan M7.1 earthquake..................121

xv
6.10 Convolve transfer function with simulated ground motions at rock sites to get motions
at basin sites in frequency domain .................................................................................122
6.11 A pair of simulated velocities and accelerations in rock sites and basin sites............123
6.12 Simulated accelerations for nine models at the Seattle basin......................................124
6.13 Simulated velocities for nine models at the Seattle basin ...........................................125
6.14 Simulated displacements for nine models at the Seattle basin....................................126
6.15 Pseudo-velocity spectra for simulated data at the Settle basin with 5% damping......127
6.16 Comparing simulated PGA and PGV for nine models at rock sites and at the Seattle
basin at station SEA........................................................................................................128
6.17 Peak interstory drift ratio and maximum roof displacements of 20- and 6-story
buildings at rock and basin sites for Med Models .........................................................130
6.18 Compare roof displacement time histories for U20B and U20P to six Med Models ineast-west component ......................................................................................................132
6.19 Compare roof displacement time histories for U20B and U20P to six Med Models innorth-south component...................................................................................................133
7.1 Horizontal displacements from GPS station 124 and double-integrated seismic station
HKD084 during the 2003 Tokachi-Oki earthquake ......................................................138
7.2 Amplitude spectra of east-west preevent noise at GPS and K-Net stations .................141
7.3 Amplitude spectra of displacements from GPS and seismic stations ...........................141
7.4 Derived acceleration baseline offsets and the final velocities and displacements results
processed by different corner frequencies .....................................................................144
7.5 Generate typical seismic recordings by adding baseline offset to the original data .....146
7.6 Generate typical GPS recordings by adding GPS noise to the original displacement data.........................................................................................................................................146
7.7 Processing error using corner frequency equals 0.02 Hz ..............................................147
7.8 The acceleration baseline offsets and displacement error derived by different cornerfrequencies ......................................................................................................................148
7.9 Distribution of colocated seismic and GPS station pairs on Hokkaido ........................149

xvi
7.10 Derived baseline offsets from GPS station 521 and K-Net station HKD095.............150
7.11 Original and corrected velocities and displacements from GPS station 521 and K-Net
station HKD095..............................................................................................................150
7.12 Derived baseline offsets from GPS station 136 and K-Net station HKD129.............151
7.13 Original and corrected velocities and displacements from GPS station 136 and K-Net
station HKD129..............................................................................................................151

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List of Tables
2.1 The stress-strain parameters of the steel used in this study..........................................12
2.2 Building types................................................................................................................18
2.3 The natural periods of buildings (in elastic range) .......................................................22
3.1 Maximum PGA, PGV, PGD, PSA1.5 and PSA3.5 in the 2003 Tokachi-Oki
earthquake....................................................................................................................32
3.2 Summary of response for each type of buildings in the 2003 Tokachi-Oki earthquake......................................................................................................................................37
5.1 Parameters for each model in Sumatra event ...............................................................74
5.2 Strong ground motions chosen to be empirical Green’s functions to simulate motions
at Banda Aceh (BAC) in the 2004 Sumatra earthquake ............................................85
5.3 PGA and PGV of simulated strong ground motions at station BAC and performanceof 20- and 6-story buildings shaken by these motions...............................................92
6.1 Parameters for each model in Cascadia event ............................................................106
6.2 Strong ground motions chosen to be empirical Green’s functions to simulate motionsof the Scenario Cascadian earthquake experienced at rock sites in Seattle (SEA) .111
6.3 PGA and PGV of simulated strong ground motions at station SEA and performanceof 20- and 6-story buildings shaken by these motions.............................................129

1

1

CHAPTER 1

Introduction
Great earthquakes (Mw > 8.0) are rare but occur on the average about once a year on theplanet. If they happen to be close to urban areas, they could be catastrophic. Tremendous
loss of life and widespread damage would have a long-lasting impact on the affected areas.
The 2004 Sumatra-Andaman earthquake with more than 230,000 dead or missing and the2008 Wenchuan earthquake with about 90,000 dead or missing surprise and remind us of
the great power of earthquakes. Many of the deaths in the earthquakes were caused by thecollapse of buildings. And modern designed high-rise buildings did collapse in the pastmoderate to large earthquakes (1985 Michoacan earthquake, 1995 Kobe earthquake, 1999
Chi-Chi earthquake). With the tremendous rise in world population and the mass humanmigration to cities, urbanization has been rampant and tall building construction has
boomed. Today, there is a great possibility of some of these buildings being shaken by
great earthquakes.

1.1 Motivation
In order to limit the stresses encountered in beams and columns during earthquake groundshaking, modern moment-resisting frame tall buildings (midheight 15 to 30 story range）
are designed to be quite flexible relative to many other types of building designs (e.g., shear

2wall); Steel moment-resisting frame is the most popular type of construction in the areas ofhigh seismicity (FEMA-354, 2000). To date, this strategy has largely been successful inthat flexible high-rise buildings have generally performed well in past earthquake groundshaking (Yanev, Gillengerten J.D. et al., 1991), even for ground motions with large
accelerations such as those that occurred at tall buildings site during the 1995 Kobe
earthquake. The one notable exception (at the time of this thesis) was the catastrophic
collapse of many 10- to 20-story buildings in Mexico City during the 1985 Michoacan
earthquake (M8.2) (Hall and Beck, 1986; Rosenblueth and Meli, 1986). The Mexico City
catastrophe has been attributed to a serious underestimation of the importance ofresonances of ground shaking in the ½ Hz band caused by the lacustrian deposits beneath
Mexico City (Anderson, Bodin P. et al., 1986; Beck and Hall, 1986). Ironically, theMichoacan rupture was approximately 350 km from Mexico City and consequently tens of
thousands of stiff brittle buildings were undamaged by the ground shaking in Mexico City.
Thus, while tall flexible buildings may perform well in high-frequency ground motions thatare damaging to many types of buildings, their unique dynamic characteristics make themvulnerable to large amplitude long-period ground shaking.
Most great earthquakes occur at subduction zones and seismic waves from theseearthquakes are rich in long-period waves that may be especially large in regions with local
site amplification. Subduction earthquakes occur at the interface of two converging plates
jerk past one another examples include the 2004 Sumatra-Andaman earthquake and the1985 Michoacan earthquake. In a video taken during the Sumatra event at Banda Aceh,people had difficulty in maintaining their balance while keep standing and some weresitting on the curb swaying back and forth at a slow rate. Nance (1988) also described asimilar phenomenon in the giant 1964 Alaskan earthquake (Mw9.3). Hundreds ofkilometers of Alaskan coastline was horizontally displaced by 20 meters during the minutesof shaking that occurred in that event (Plafker, 1965). This implies that even if theseearthquakes may occur at a large distance, they are rich in long-period seismic waves
which attenuate more slowly and can travel long distance as a result. Soft soil sites may
further amplify these motions. Unfortunately, there are no strong motion records from giant

3
subduction earthquakes. So it raises the question: what will happen to the high-rise steel
moment frame buildings in a large coastal city if a great subduction earthquake occurs
offshore? This question is especially critical in the Cascadia subduction zone of the PacificNorthwest.
In the 1980s, the potential of great subduction earthquakes along Cascadia area was first
proposed by Heaton et.al (1984). Later Atwater (1987) found geologic evidence of great
subduction earthquakes; the most recent one is estimated to have occurred 300 years ago.
This earthquake also explained the mysterious tsunami documented in Japanese historical
documents (Atwater, Satoko et al., 2005) and in native Indian legend (Heaton and Snavely,1985). It is now apparent and widely agreed upon that such an earthquake will reoccur,
resulting in severe shaking of the modern cities of Seattle, Portland and Vancouver. In thisstudy, we focus on Seattle because a number of sites have been investigated (Frankel,
Carver et al., 2002; Pratt, Brocher et al., 2003) in that area. Large site amplification fromthe Seattle basin was found by these investigations and future great subduction earthquakes
would pose a serious threat to the flexible buildings in Seattle.
The Mw8.1 2003 Tokachi-Oki subduction earthquake is the largest event recorded by awealth of modern networks densely-deployed on Hokkaido Island in Japan. The abundant
high-quality strong shaking data can extend our knowledge of ground motions from large
earthquakes. Furthermore, these motions constitute a good source of empirical Green’s
functions to simulate strong ground motions from giant subduction earthquakes.
All of the above issues motivate us to simulate the strong ground motions from ahypothetical Cascadia earthquake and use these motions to check the nonlinear
performance of high-rise buildings in the city of Seattle.

4

1.2 Previous Work1.2.1 Strong Ground Motions in Earthquakes
Since the first good records of ground shaking in 1880 by Ewing at the University ofTokyo (Agnew, 2002), more and more strong or weak ground motions have been recorded
worldwide. It provides a principal research tool for seismologists to analyze earthquake
mechanism through interpreting and matching these seismic waves. It is also useful forearthquake engineers to computationally simulate or experimentally test the seismic
performance of structures. To date, many dense seismic networks have been deployed inJapan, California and Taiwan. Their recordings can be easily accessed through websites
open to the public. These seismic networks, the features of their instruments, and dataprocessing technique are described elsewhere (Clinton, 2004).
Although a lot of progress has been made in installing seismic instruments, strong groundmotion from great earthquakes has not been recorded yet due to the rarity of theiroccurrence, and the difficulty in anticipating the corresponding regions of strong shakings.
The 1985 Michoacan earthquake (M8.2) used to be the largest earthquake, strong groundshaking from which was recorded at several stations (Anderson, Bodin P. et al., 1986).
Now, the largest well recorded earthquake is the 2003 Tokachi-Oki earthquake with amagnitude 8.1. To date, no strong ground motions from moment magnitude 9 earthquakes
have been recorded. In order to estimate these motions, earthquake engineers have beenscaling the amplitude of motions from smaller earthquakes (Bolt and Abrahamson, 2002).
There are two serious limitations to this approach. First, the frequency content of shaking
from large earthquakes is different from that in smaller events. Second, the peak groundaccelerations saturate at larger magnitudes (Cua and Heaton, 2007; Yamada, 2007). As aresult, scaling of ground accelerations based on attenuation characteristics of groundaccelerations may severely underestimate the velocities and displacements in large events.

5With an increased understanding of earthquake sources, propagation paths, local geology,
site conditions. Seismologists have begun to simulate strong ground motions from historicand hypothetical scenario earthquakes. Examples include the simulation of the 1923 Kanto
earthquake (Takeo and Kanamori, 1997; Sato, Graves et al., 1999), the 1906 San Francisco
earthquake (Aagaard, Brocher et al., 2008), an 1857-like San Andreas fault earthquake(Krishnan, Ji et al., 2006; Olsen, Day et al., 2006) and others (Saikia and Somerville, 1997;
Hartzell, Leeds et al., 2002). However, all of these earthquakes are moderate to large
crustal earthquakes. Not many simulations of strong ground motions from giant subduction
earthquakes (Mw > 9.0) have been performed (except Heaton and Hartzell, 1989) until
recently because of the lack ofknowledge of the earthquake sources and the non-availability of recordings. The 2004 Sumatra-Andaman earthquake provides a good
opportunity for understanding giant earthquakes. Sørensen et al. (2007) and Mavroeidis etal. (2008) have used hybrid processing in different frequency bands to simulate the strong
ground motions for the 2004 Sumatra event Mw9.3 and the 1964 Alaskan earthquake
Mw9.2, respectively. Olsen et.al. (2008) have used a 3D finite difference method tosimulate the fully synthetic strong motions for a Cascadia earthquake with magnitude 9.0
using a source model from the Sumatra event. These simulated strong ground motions were
gradually introduced to earthquake engineers in dynamic analysis of structures.

1.2.2 Performance of Steel Moment-Resisting Frame Buildings inEarthquakes
The performance of structures in earthquakes is known through computational simulation,
experimentally tests as well as the experience in past earthquakes. Among these ways,
experience in past earthquakes has had the greatest impact. Almost every destructive
earthquake would lead to a modification of a current building code in that area and disclose
some unknown phenomena. Olsen (2008) gave a detailed description the performance ofsteel moment frame buildings in historic earthquakes. Although steel buildings performed
relatively well in comparison to other types of buildings at first glance in these moderate

6earthquakes, the Northridge and the Kobe earthquake revealed the susceptibility of moment
connections in steel buildings to fracture. This mode of failure significantly reduced theductility and strength of the steel moment-resisting frame (SMRF) buildings. Learning
lessons from past earthquake and improving structural design is valuable, but rather slow.
Most importantly, engineers noticed that “satisfactory building performance in a moderate
earthquake does not imply satisfactory performance in a great earthquake” (Olsen, 2008).
No high-rise SMRF building has experienced a giant subduction earthquake (Mw > 9.0).
Instead of waiting for the next giant earthquake to cause another disaster, we should better
predict the performance of SMRF and do some retrofits in advance.
Computational simulation is a powerful tool to understand the performance of buildings
and reduce the loss in earthquakes. The simplest conceptual method is to use single- or
multiple-degree-of-freedom oscillators to model the linear elastic response of buildings.
The response spectrum is widely used in earthquake engineering research for this purpose
and plays an important role in elastic analysis. Along with the rapid increase ofcomputational power, the finite element method (FEM) was introduced to earthquake
engineering field. Many commercial software packages such as ETABS, SAP2000 and
Staad pro were developed. The finite element method allowed engineers to include
nonlinear plastic behavior of structural members. Frame-2D developed by Hall (1995) is a
powerful program to simulate the nonlinear performance of planar SMRF buildings. It
includes material and geometric nonlinearities and has the ability to simulate collapse
mechanisms. Krishnan (2003) later extended it to three-dimensions.
Using Frame-2D, Hall and others (1995) simulated the nonlinear response of 20-story
SMRF buildings to ground motions that would be expected to occur in the near-source areaof a M 7.0 blind thrust earthquake. These ground motions were characterized by pulse-like
displacements exceeding 1 m and with velocities exceeding 1 m/s. They found that theselarge directivity pulses caused large plastic strains that were often localized within several
stories, and in some instances the simulations indicated the collapse of the buildings due to
P-Delta instability. Olsen and others (2008) simulated the responses of 20-story SMRF

7
buildings to the synthetic ground motion of the 1989 Loma Prieta and the 1906 San
Francisco earthquake and also found significant damage occurring in these long-periodbuildings.
Using Frame-3D, Krishnan and others (2006) simulated the responses of 18-story steel
moment frame buildings in Southern California from ground motion simulations for a M
7.9 earthquake on the San Andreas fault along the segment that last ruptured in 1857. They
demonstrate that large amplification of the seismic waves occurs as they propagate throughthe deep sedimentary basins on which much of urban Los Angeles is constructed. Thesesimulated large ground motions cause very large inelastic deformations within manybuildings and simulated collapse occurs in some regions more than 30 km from the fault
trace.
The studies of Hall et.al.(1995), Olsen et.al.(2008) and Krishnan et.al.(2006) indicate
potential problems with flexible tall moment-frame buildings in large crustal earthquakes.
However, far larger earthquakes have occurred at subducting boundaries than haveoccurred in crustal ruptures; the largest crustal earthquakes are approximately M 8.0,
whereas giant subduction earthquakes can be as large as M 9.5, which corresponds to afactor of almost 200 in terms of seismic moment (Kanamori, 1977). It is important tosimulate the response of SMRF buildings under this type of earthquakes.

1.3 Our Work and Outline of Chapters
In this study, we use the empirical Green’s function approach to simulate the strong groundmotions for the 2004 Sumatra-Andaman earthquake and a scenario Cascadia earthquake
Mw 9.2. These synthetic motions are used to simulate the nonlinear performance of 6- and20- story steel moment-resisting frame buildings. The Seattle basin amplification ismodeled by a transfer function as well.
Steel moment-frame buildings are chosen for our analysis since their material properties
and moment-connection mechanism are better understood than for other building types.

8Moreover, they are widely used for many of the nation’s most important facilities andcommercial office buildings. FEMA354 (2000) reported that most high-rise buildings
constructed in the U.S. in the last 30 years incorporate this type of construction.
In Chapter 2 of this thesis, we briefly introduce the characteristics and limitations of thefinite element model Frame-2D used in our analysis. Then we discuss eight steel moment
frame building models used in this study. They are 6- and 20-story buildings designed
according to both UBC94 and the 1987 Japanese building code. For each code, we consider
buildings with both perfect welds and brittle welds similar to those observed in the 1994
Northridge earthquake (FEMA-354, 2000).
In Chapter 3, we analyze the ground motions recorded at 276 stations from the 2003
Tokachi-Oki earthquake Mw8.1 and simulate the fully nonlinear dynamic performance of
SMRF buildings in this event. Although the low-rise buildings in Japanese coastal villages
performed well in this earthquake, the inherently rich long-period ground motions would
have exposed many high-rise buildings there to a high potential of damage. A newparameter called the “collapse factor” is introduced to describe the collapse safety marginof structures to a certain ground motion.
In Chapter 4, we briefly describe the empirical Green’s function (EGF) method and thereasons to choose this method as our tool. and to choose the 2003 Tokachi-Oki event as
empirical Green’s functions to simulate the strong ground motions for giant earthquakes.
The 2004 Sumatra-Andaman earthquake Mw9.2 was recorded by global broadband
seismometers. The source parameters were determined through these recorded data. The
tectonic setting of the Sumatra subduction zone and the size of this earthquake are similar
with the earthquake that can be expected to occur at the Cascadia subduction zone.
Therefore, we use the source model from this event as the source model for our scenario
Cascadia earthquake.

9
In Chapter 5, we use EGF method to simulate the strong ground motions at Banda Aceh
from the 2004 Sumatra-Andaman earthquake and estimate the response of SMRF buildingsin that event. Rupture models with wide and narrow fault width and motions at rock andsite sites are considered. The simulated strong motions are validated by the local damage in
Banda Aceh.
In Chapter 6, we use the EGF method to simulate the strong ground motions in Seattle
from the scenario giant Cascadia subduction earthquake and estimate the response of
SMRF buildings in that event. Rupture models with wide, median and narrow fault widthand motions at rock and basin sites are considered. The Seattle basin amplification ismodeled by a basin Green’s function through deconvolving teleseismic motions at rocksites from basin sites.
In Chapter 7, we develop a data processing method to obtain broad-band displacements bycombining inertial seismic records and high-sample rate GPS records. It is found that some
important ground motion intensity measures such as peak ground displacements are
sensitive to the data processing techniques. We also found that the performance ofbuildings sometimes is sensitive to certain data-processing schemes. To faithfully reflect
the real ground motions is important not only for seismologists but also for earthquake
engineers.

10

CHAPTER 2

Computational Building Models
Steel Moment-Resisting Frame (SMRF) is a very popular structural system for many lowand high-rise buildings in seismic regions. The absence of diagonal braces and structural
walls in this type of buildings allows complete freedom for interior space layout andaesthetic exterior expression (FEMA-354, 2000). Their construction is economical and fast.
Most importantly, many reports concluded that SMRFs performed well in the 1906 San
Francisco earthquake (Himmelwright, 1906) as well as in the 1971 San Fernando
earthquake (Steinbrugge, Schader et al., 1971). Therefore, the SMRF system is the mostcommon type of structural system used in tall buildings in the 10-30 story range in regionswith high seismic activity, such as Los Angeles, San Francisco, Portland and Seattle.
In this chapter, we first discuss the advantages and limitations of finite element models
used in our dynamic time history analysis and then discuss the design of steel momentresisting frame (SMRF) buildings used in this analysis.

2.1 Computational Method
To assess the potential performance, including collapse of high-rise SMRF buildings tolarge ground motions, the computational model we used must have the capacity to capture
the nonlinear large lateral deformation. Frame-2D, a seismic nonlinear structural simulation
program developed by Hall (1997), meets this requirement. This program is based on a

11planar-frame fiber-element model that includes both material nonlinearities as well as
geometric nonlinearities. Most importantly, Frame-2D updates buildings’ configuration foreach time step. This automatically accounts for the P-Delta effects (AISC 2005) and allows
the analysis to follow a building's response well into collapse. In the following, the mainfeatures of this model are briefly described. Hall (1997) contains a thorough discussion of
the structural behavior assumptions and other details of this program.

2.1.1 Beam-Column Elements
Beam-column elements are the primary component of a moment-resisting frame system.
There are many beam-column mathematical models that could account for material andgeometric nonlinearities. These models can be classified into two main categories: plastic
hinge model and fiber model. Frame-2D employs fiber model.
The plastic hinge model is the earliest and most widely used method in structural analysis
to incorporate material nonlinearity of a frame structure. It concentrates plastic hinges on adiscrete cross-section and the rest of the member between hinges is assumed to remain
elastic. Although this model is computationally efficient and easy to apply, it includes
strain hardening and moment-capacity reduction in a crude way. Moreover, residual
stresses can not be included. When residual stress or details of the yielding process become
important, plastic hinge model is inadequate (Hall and Challa, 1995).
The fiber model is a distributed plasticity method and could accurately capture the gradualspread of yielding within the cross section and along the member length. In addition, thismethod can naturally include residual stress, stress hardening and moment-capacity
reduction which are important features for modeling cyclic loading. Hall and Challa (1995)
gave a detailed comparison of these two methods.
In Frame-2D, beam-column elements are subdivided into eight segments along their length.
Their cross sections are divided into eight to ten fibers (figure 2.1). Each fiber has an axial
stress-strain hysteretic relation shown in figure 2.2. The parameters that is used to define

12
the skeleton curve is listed in table 2.1. Notice that in this hysteresis model, the yield stressremains constant until strain reaches a very large value. However, in real experiment, theyield stress would gradually decrease when local flange buckling is developing (figure5.19).

Table 2.1. The stress-strain parameters of the steel used in this study
Parameters

English Units (ksi)Metric(ton/cm2)

E

Initial elastic Young’s modulus

29,0002040

ESH

Initial modulus at strain hardening

580

40.8

σY

Yield stress

42

2.96

σU

Ultimate stress

50

3.52

Residual stress

6

0.42

τY

Shear yield stress for panel zone

24.0

1.69

G

Shear modulus for panel zone

11,600

816

σRES

εSH

Strain at strain-hardening

0.012

εU

Strain at ultimate strength

0.160

ν

Poisson’s ratio

0.3

2.1.2 Panel Zone
Connections are the medium through which moments and forces are transferred from one
structural member to another. They are the other essential elements in modeling MRF
system besides beam-column elements. Their participation in the cyclic energy dissipationis also important.
In the earlier research, connections are idealized as zero dimensional points. Later, finite
rigid joints and finite flexible joints are introduced gradually. In Frame-2D, finite-size
panel zones are modeled. They have similar hysteresis model as steel fiber (figure 2.2)
(Hall, 1997). Double plates can be modeled in this panel zone element. However, thestrength degradation contained in the hysteretic model also is relatively simple.

13

Figure 2.1. Segment layout (top) and fiber layout (bottom) for beams and columns used inthis study. Fibers 9 and 10 in the strong axis orientation are used only for beam to represent
composite action with a metal deck and concrete slab (Hall, 1997).

14

Figure 2.2. The top figure shows the backbone curves for beam or column steel fiber andthe bottom figure shows the axial stress-strain hysteresis relation for this fiber. Panel zone
hysteresis is similar to that of the fiber. The stress-strain parameters of the steel skeleton
curve used in this study are listed in table 2.1 (Hall, 1997).

2.1.3 Weld Fracture
Frame-2D also has the capability to model welds fracturing. Prior to the 1994 Northridge
earthquake, it was commonly assumed that welded connections had significantly stronger
plastic yield strength than other structural elements and that steel frames would only yield
because of plastic deformation of the structural steel. However, numerous welded
connections were found to fracture along steel MRF’s in the near-source area of theNorthridge earthquake (SAC Joint Venture, 1996). Emergency code change was
implemented in 1995 to correct this problem in the US. (FEMA, 1995) and in Japan (JASS
1996). However, the vast majority of existing buildings probably have connections

15
susceptible to fracture which would dramatically lower the lateral force-resisting capacity
and the ductility of the building.
In Frame-2D, each fiber in the end-segment of beams and the segment where column
splices would be located is assigned a fracture strain εf using a randomized process. Whenthe strain in the fiber reaches this fracture strain εf, fiber fractures and loses its ability tosustain tension in the future, but it can carry compression when contact is regained. The
distribution of fracture strain εf is user defined. Figure 2.3 gives the detailed fracture strainprobability distribution density used to model our brittle welds building. This distribution iscompatible with the observations of welds in the 1994 Northridge earthquake (Hall, 1998).
For example, the bottom flange of beams has a median εf = εy , while the top flange ofbeams has a median εf = 10 εy (Hall, 1997), where εy is the yielding strain. This guarantees
that the bottom flange of beam is easier to fracture than the top flange. For buildings withperfect welds, fracture strain for all the connections are set to be infinity.

0.5

Beam bottom flanges and column splices
0.5

0.4

0.4

Assigned distribution

Assigned distribution

Beam top flanges

0.3
0.2
0.1
0

1

10

εf / εy

100

0.3
0.2
0.1
0

0.71

10

50 100εf / εyFigure 2.3. Fracture strain distribution of different connections for brittle welds used in thisstudy. The left panel shows the set for top flanges of the beams and the right panel shows
the set for bottle flanges of the beams and column splices.

16

2.1.4 P-Delta Effects
P-Delta effect refers to the 2nd order over-turning moment resulting from the weight of thestructure acting through the lateral displaced configuration of the structure (figure 2.4). For
low-rise structures with small deflection, this effect is small and can be ignored. However,for high-rise structures experienced large ground motions, this effect can significantly
reduce the buildings’ lateral force-resisting capacity and trigger collapse (Challa and Hall,
1994; Gupta and Krawinkler, 2000).
In Frame-2D, P-Delta effects are included by geometrically updating the global nodal
translation and rotation at each time and satisfying the equations of dynamic equilibrium inthe updated configuration of the structure

Figure 2.4. Illustration of P-Delta effects on a SMRF and the definition of interstory drift
ratio (IDR) and roof displacement (RD).

2.1.5 Limitations of Frame-2D
There are two main limitation of the Frame-2D. The first one is that this is a 2-dimentionalmodel. For regular symmetric buildings, this model is sufficient. Since the center of gravity
and rigidity are the same for these buildings, no torsional eccentricity would be generated,

17
so steel MRF buildings can be simplified as several separated planar frames in the narrowdimension of the building, which has larger stress than the wide dimension of the building
due to the smaller stiffness. For simpler irregular SMRFs, this 2-dimensional model canstill be used by placing the moment frames in a three dimensional setting with correct
location and orientation (Hall, 2002). However when plastic deformation occurs in thebuilding, the stiffness symmetry may break. This may cause discrepancy of results from 2dimensional and 3-dimensional models. Moreover, for more complicated irregular SMRFs,
three-dimensional treatment is necessary. FRAME3D developed recently by Krishnan(http://www.virtualshaker.caltech.edu/), can be used in such cases.
The other limitation is slightly simple strength and stiffness degradation model in Frame2D for basic elements. Strength degradation can be caused by many factors such as local
flange and lateral-torsional buckling, temperature increasing, weld fracture, column tension
splice rupture, etc. However, weld fracture is the only degradation mechanism modeled in
Frame-2D. In other words, in our simulation, there is no strength degradation for buildings
with perfect welds. Many studies have revealed that when the structure members are
exposed to repeated reversal inelastic deformation for a long time, accumulated developed
damages have a high potential to cause structural collapse (Villaverde, 2007). To
incorporate these degradations in the dynamic modeling is a challenge research topic and isout of scope for this thesis. Almost all these modeling limitations indicate that the true
behavior of SMRFs could be worse than the simulations undertaken here.

2.2 Buildings Considered

2.2.1 General Characteristics
In this study, we consider four types of SMRF buildings. They are 20- and 6-story
buildings designed by Hall according to two codes: the 1994 Uniform Building Code(UBC94) assuming seismic zone 4 and soil site S2 (corresponding to soil type B in UBC97)

18
and the Japanese building code updated in 1987. Two weld conditions: brittle and perfect(refer section 2.1.3) are considered. The notations of these buildings are listed in table 2.2.
For example, U20B represents a 20-story SMRF building designed according to UBC94
with brittle welds. And J6P represents a 6-story SMRF building designed according toJapanese code with perfect welds. Overall there are eight building models. All of these
SMRFs are symmetric and their floor plans and planar frames elevations participating inmodeling are shown in figure 2.5 to 2.8. Detailed design parameters can be found in Hall
(1997).
The main difference between buildings designed according to U.S. and Japanese codes isthat Japanese buildings have more moment connections at the middle frame (Frame C infigure 2.6) than U.S. buildings which use simple connections for all joints in the middle
frame. As a result, the Japanese model has greater strength and stiffness than the U.S.
model, which can be easily seen from the pushover curves in figure 2.10. The reason
behind this difference is that the Japanese code prefers stronger buildings while the U.S.
code prefers long period buildings which can avoid resonance during moderate earthquakes.
The natural period of each model are listed in table 2.3.
The height above the ground is 77.88 m for our 20-story buildings and is 24.54 m for the 6story buildings. These two models will be assumed to be representative of high-rise andlow-rise SMRFs in the US and in Japan. In this study, 20-story building is the main type ofbuilding that we are interested in and 6-story building is used mainly for comparison.

Table 2.2. Building types
The 1st letter

The 2nd letter
The 3rd letterU

20

buildings designed according to the 1994 Uniform Building Code (ICBO 1994).
buildings designed according to the Japanese building provision published at1987 (IAEE 1992).
20-story steel moment-frame buildings

6

6-story steel moment-frame buildings

Bbuildings with brittle welds at connections

Pbuildings with perfect welds at connections

J19

Figure 2.5. Floor plan and frame elevations of the 20-story building designed according to
the UBC94 (U20) (Hall, 1997).

20

Figure 2.6. Floor plan and frame elevations of the 20-story building designed according to
the Japanese building code (J20) (Hall, 1997).

21

Figure 2.7. Floor plan and frame elevations of the 6-story building designed according to
the UBC94 (U6) Reproduce from Hall (Hall, 1997).

22

Figure 2.8. Floor plan and frame elevations of the 6-story building designed according to
the Japanese building code (J6) (Hall, 1997).

Table 2.3. Characteristic values of the buildings
Building Type
Elastic Natural Period (in the
narrow direction)
Pushover Yield Strength %Pushover Peak Strength %Pushover Yield Displacement(cm)
Ductility

U20B

U20P

3.5 sec

J20B

J20P

3.05 sec

U6B

U6P

1.5 sec

J6B

J6P

1.17 sec

4.9

9.5

8.2

12

9.5

17.0

20.1

31

6.6

10.5

8.3

14.6

16.8

22.8

24.5

39.7

30

65

35

65

10

20

12

24

1.9

3.6

1.8

3.5

2.0

9.6

2.1

8.4

23

2.2.2 Pushover Analysis
To qualify the actual strength and ductility of buildings, pushover analysis is applied.
Pushover curves relate the base shear strength which can be carried by structures (given asa percentage of the building weight) to the lateral roof displacement. To generate this curve,a building is subjected to a slow, ramped, horizontal ground acceleration that increases at
the rate of 0.3g per minute. Stiffness, yield base shear, peak base shear and ductility ofbuildings can be obtained from pushover curves. The definitions of these parameters areillustrated in figure 2. 9 and their values are listed in table 2.3.
Hall (1997) contains a detail discussion about pushover analysis. Here, we compare thepushover curves for all the eight models in figure 2.10. Solid lines correspond to buildings
with brittle welds whereas dashed lines correspond to buildings with perfect welds. From
this figure, we can find that the 6-story buildings are stiffer and can carry much higher
loads than the 20-story buildings. The ductility for the 6-story buildings is also much larger
than the 20-story buildings because P-Delta effects are greater in high-rise buildings. As wealready mentioned, the Japanese buildings are stiffer and stronger than the U.S. buildings. It
is apparent that the presence of brittle welds could significantly reduce the pushover yieldstrength and ductility of the buildings.

2.2.3 Discussion
The models used in this study seem slightly out of date: designing according to pre-1995
codes and using yield stress = 42 ksi (Nowadays much stronger steels are used which haveyield stress around 50 ksi). Recently, there were some concerns about the satisfaction of
U20 to the drift limit of UBC94 and its reasonable representative of UBC-94 design. Halland Krishnan (Oct. 2008) reran the analysis by different programs and contradicted thesearguments. They showed that the U20 is an appropriate design under UBC94. Since there
are numerous existing SMRF buildings built before the 1994 Northridge earthquake in24most seismic regions in the US, these models could be considered representative of thecurrent building stock.

Pushover Curve

Figure 2.9. The definitions of ductility, yield strength and ultimate strength of a building ona pushover curve. Ultimate displacement is the place where pushover curve began to drop
dramatically.
Pushover Curves

40

U20B
U20P
U6B
U6P
J20B
J20P
J6B
J6P

Base Shear (frac of building weight) %

35

30

25

20

15

10

5

0

0

50

100
150
200
Lateral Roof Displacement cm

250

300

25
Figure 2.10. Pushover analysis of the 6- and 20-story steel moment frame buildings
designed to the UBC94 and Japanese code with brittle welds and perfect welds.

Hall (1998) compared the building models used in this study to the UBC97 seismic
provision. After the 1994 Northridge earthquake, there have been many improvements
adopted in the building codes and construction practice. The main difference between
UBC94 and UBC97 seismic design is that UBC97 uses near-source factors and requires
lateral force resisting systems to resist larger earthquake force if located in a region close toactive faults. The results show that J6 satisfies UBC97 and J20 satisfies only the nearsource factor less than or equal to 1.2 which corresponds to the location 10km from aseismic source with strong seismic activity.
If A572 steel (σy = 50 ksi and σu = 65 ksi) is used in our buildings, it also could increase theglobal strength of buildings. Figures 2.11 and 2.12 compare the pushover curves of thebuildings using steel which has a yield stress σy = 42 ksi to those using steel with yieldstress σy = 50 ksi. We can find that U20-50 is upper bounded by J20.
Above all, the current designed buildings are stronger than our building models, however,strengthening existing high-rise buildings is not an efficient method and in some groundmotions, stronger and stiffer buildings perform even worse than more flexible buildings,
which was discovered in section 5.5.3 and discussed in detail in section 6.5.3. Therefore,
we still use σy = 42 ksi in this study for all the buildings unless stated otherwise.

26
Pushover curves for 20-story buildings

20

Base Shear (frac of building weight) %

18
16
14

U20B
U20P
J20B
J20P
U20B-50
U20P-50
J20B-50
J20P-50

12
10
8
6
4
2
0

0

50

100
150
200
250
Lateral Roof Displacement cm

300

Figure 2.11. Comparison of pushover curves of the 20-story buildings using steel withyield stress σy = 42 ksi to those buildings using steel which has yield stress σy = 50 ksi.
Pushover curve for 6-story buildings

50

Base Shear (frac of building weight) %

45
40
35

U6B
U6P
J6B
J6P
U6B-50
U6P-50J6B-50J6P-50

30
25
20
15
10
5
0

0

50

100
150
200
250
Lateral Roof Displacement cm

300

Figure 2.12. Comparison of pushover curves of the 6-story buildings using steel with yieldstress σy = 42 ksi to those buildings using steel which has yield stress σy = 50 ksi.

27

CHAPTER 3

26 September 2003 Tokachi-Oki, Hokkaido,
Earthquake Mw 8.1
The 2003 Tokachi-Oki earthquake Mw8.1 is the largest well-recorded earthquake till now
and was recorded by various densely distributed seismic and GPS networks in Japan. It was
the first time that large amplitude, long-period ground motions, which are characteristics oflarge subduction earthquakes, were densely recorded at many sites in Japan. The strong
ground motions recorded at this event are good sources for us to study giant subduction
earthquakes. In this chapter, we simulate the fully nonlinear responses of buildings
mentioned in Chapter 2 from 276 strong motion stations located on Hokkaido Island. The
results are analyzed and a new parameter called the “collapse factor” is introduced todescribe the collapse safety margin of structures to a certain ground motion.

3.1 Introduction
On September 26, 2003 at 19:50 (GMT), a moment magnitude (Mw) 8.1 subduction
earthquake occurred along the Kuril trench off Tokachi, Hokkaido, Japan. The hypocenter
was at 41.78° N, 143.90° E, about 80 km east-southeast of Cape Erimo, at a depth of 27 km(USGS report). The Kuril trench is a highly active subduction zone where the Pacific plateis subducted toward N60°W beneath Hokkaido region at a rate of about 80 mm/year(Demets, Gordon et al., 1990). Figure 2.1 gives the locations of the largest historic

28
earthquakes along this subduction interface during the past half a century (Yagi, 2004). By
using teleseismic body waves, Yamanaka et al. (2003) estimated the main source
parameters as follows: (Strike, dip, rake) = (230°, 20°, 109°), fault area is 90 × 70 km2, themaximum slip is 5.8 m, the average slip is 2.6 m and the source duration is 40 sec. The
geometry cross section of this region is shown in figure 4.4. The detailed structure of thisregion can be found in Iwasaki et al. (1989).
Despite the proximity of this large event to the island of Hokkaido, damage was relatively
mild. There are numerous coastal towns in southeastern Hokkaido, but there are no large
cities within the region of heaviest shaking. The short, stout buildings of Japanese coastal
communities performed well in this long-period shaking. The most serious damage was due
to sloshing in petroleum storage tanks located about 150 km west of Cape Erimo, which isthe peninsula that juts out over the rupture surface (ABS Consulting Inc, 2003). This
sloshing was undoubtedly caused by the large long-period ground motions generated bythis event.

Figure 3.1. Historic large and giant earthquakes happened on Hokkaido region. The
contours represent the source area for each event (Yagi, 2004). 1952 (Ms 8.2), 1958 (Ms
8.1), 1969 (Ms 7.8), and 1973 (Ms 7.4).

29

3.2 Recorded Strong Ground Motions and Site Condition on Hokkaido
IslandThe strong ground motions of 2003 Tokachi-Oki earthquake were recorded by various
densely distributed seismic networks (K-Net, KiK-Net, H-Net etc) and geodetic networks
in Japan. The raw data can be downloaded from the websites of Japanese National
Research Institute for Earth Science and Disaster Prevention (NIED). Clinton (2004)
contains a comprehensive description of these networks and their data. Both networks use
K-NET95 accelerometers, with 144dB dynamic range and a clip of 2g. Frequency
bandwidth is from about 20Hz to DC, so there is no need to remove instrument responses.
Sampling frequency is 100 Hz for K-Net and 200 Hz for KiK-Net. In this chapter, we use
records from 276 K-Net and KiK-Net stations located on Hokkaido Island (figure 3.2).
To show the ground motion intensity of this event, peak ground acceleration (PGA),
velocity (PGV) and displacement (PGD) are calculated. It is unfeasible to recover the real
ground displacements for all the stations in this event (discussed in page 33), so a zerophase 4th-order Butterworth filter at frequency 0.02 Hz is applied to all the records before
these ground motion intensity measures are calculated. Pseudo spectral accelerations (PSA)
for all the stations are also calculated at periods T=1.5 sec and 3.5 sec for 5% damping.
These periods are about the natural periods of U6 and U20 respectively. PSA = ω2|x(t)|max,
where |x(t)|max is the maximum displacement of a mass in a one dimensional spring-masssystem with a fixed natural period subjected to ground motion. The bigger values of the twohorizontal components (EW and NS) are chosen as our ground motion intensities. Table
3.1 lists the maximum values and figures 3.2 to 3.3 show the distributions of these values.
This ground motion dataset shows the significant spatial variation of shaking on Hokkaido
Island. Hatayama et.al., (2007) carefully investigated the spatial variation of long period
strong ground motions within the Yufutsu basin (figure 3.3) and concluded that the
thickness of near-surface (<1 km) soft sediments rather than bedrock depth governs thespatial variation of amplitudes of the long period (7 to 8 second, natural period of oil
storage tank). His study also showed that the Yufutsu basin not only amplified the ground30
motion amplitude but also elongated the strong shaking from 20 sec to more than 100 sec(figure 2 in Hatayama et.al.).

Figure 3.2. The distributions of PGA, PGV and PGD. Locations which have the largest
values are labeled on maps. Zero-phase 4th-order Butterworth filters at frequency 0.02 Hz
are applied. The largest PGA is 0.97g, the largest PGV is 0.96 m/s and the largest PGD is
0.6 m.

31

Figure 3.3. The distributions of pseudo spectral accelerations at periods of 1.5 sec (natural
period of U6) and 3.5 sec (natural period of U20) for 5% damping. The largest PSA1.5 is
1.4g and the largest PSA3.5 is 0.45g. Comparing with PGA, PGV and PGD, the distributionof PSA is more consistent with the topography of Hokkaido Island at these long periods.
Stations with larger PSA are concentrated at Tokachi Basin and Yufutsu Basin

32
Table 3.1 Maximum PGA, PGV, PGD, PSA1.5 and PSA3.5
Maximum peak value

Location

Ground Acceleration

0.97 g

HKD100Ground Velocity

96.6 cm/s

TKCH07Ground Displacement

63.6 cm

HKD0981.422 g

TKCH07452 cm/s2

HKD098

Pseudo Spectral Acceleration at 1.5 sec (natural periodof U6) for 5% damping.
Pseudo Spectral Acceleration at 3.5 sec (natural periodof U20) for 5% damping.

Figure 3.4. Contours of the average shear wave velocity in the upper 30 meters. The siteclassification criterion used in UBC97 and IBC is listed in the upper part of the figure. Soiltype E (basin) is show in red colors. Soil type D is in green. Soil type C is in blue. Most
stations are located at site C, D and E.

Engineers are used to describing local site condition in terms of Vs30. It is the average shearwave velocity in the upper 30 m (~100 ft) of the deposit. UBC97 and IBC both use thisparameter as the primary basis to classify site categories. For each K-Net station, soil

33
condition has been investigated down to a depth of 10 to 20 meters. This information
allows us to approximately estimate the Vs30 by assuming the velocity of the remaining
deeper soil equals the deepest measured velocity. It should be noticed that this assumption
would underestimate Vs30 and give a lower limit. The Vs30 is calculated from the following
formula:n

V s 30 =

∑ d
i=1
n

i

di
∑
i = 1 V si

(3.1)

where Vsi is the shear-wave velocity of the ith soil layer and di is its thickness. The siteclassification criterion and the contour map of Vs30 can be found in figure 3.4. It could
roughly capture the basin areas but some areas in Tokachi Basin are classified as soil class
C. It indicates that Vs30 alone is not enough to represent the site conditions.
Although accelerometer K-NET95 is capable to capture the ground motion over a wide
range of frequencies, sometimes even can provide reliable static displacements after theearthquake ceases, displacement time series obtained from double integration ofacceleration recordings are often plagued with unrealistic baseline drifts and growdramatically with time (most commonly as t2). Many issues can induce this drift:
instrument tilt, baseline offsets and other unknown sources of long-period noise.
Researchers have also proposed numerous data processing techniques to eliminate thedisplacement drift (USGS data; Caltech EERL report 1974-1976; Iwan, Moser et al., 1985;
Boore, 2001; Zhu, 2003; Shakal, Huang et al., 2004). Unfortunately, all of them require thespecification of processing parameters that strongly affect the derived grounddisplacements. We developed a scheme (Chapter 7) to better estimate the broadband
ground displacements by combining the seismic records with high-sample rate GPS records.
This methodology is easy to implement and is consistent and robust for all stations.
However, it requires colocated seismic and GPS stations. In this seismic event, only a few
seismic stations have colocated GPS stations. Therefore, using Boore’s method (Boore,
2001), we carefully ansalyzed each record in an attempt to recover the static grounddisplacement and show horizontal radial (parallel to the trench) ground displacements at

34
selected stations in figure 3.5. The largest displacement was about 1.5 m and occurred atstation HKD098.
The accelerograms corrected only for preevent means are used in this study to simulate theresponse of buildings. Although acceleration is insensitive to data processing in most cases,
it generates different responses for the same building model when processed by different
correction schemes (Yang and Heaton, 2005). To avoid the potential artificial effects, we
use raw accelerations (corrected for preevent means) as our input to Frame-2D.

Figure 3.5. Locations of 276 K-Net (black triangle) and KiK-Net (red square) stations thatrecorded the 2003 Tokachi-Oki earthquake (Mw 8.1) on Hokkaido Island. The approximate
surface projection of the rupture is given by the black rectangular box (Yagi, 2004). The
radial components of ground displacements for selected stations are also shown. The redstar is the epicenter of this event. The largest recorded displacement was 1.5 meters.

35

3.3 Nonlinear Performance of Buildings
Although short, stiff buildings performed well in this earthquake, an obvious question israised by this event. How well would tall, flexible structures perform in these long-period
ground motions? In order to answer this question, we simulated the responses of four tallbuildings described in Chapter 2 (U20, J20 with brittle welds and perfect welds) using 276
ground motions recorded on Hokkaido Island. Their responses are compared against the
low-rise U6 and J6 buildings, also described in Chapter 2. The results are presented in theform of contour maps.
In this study, we use the peak interstory drift ratio (IDR) as the main quantity to evaluate
the performance of buildings. Other parameters such as roof displacement relative to theground and percentage of fractured welds among all beam-to-column connections are also
provided to assist the response evaluation. Interstory drift ratio is the relative horizontal
displacement of adjacent floors divided by the story height. For steel moment frame type ofstructure which can be modeled by a shear beam, interstory drift ratio basically is the shear
strain of one story. Roof displacement is defined as the relative horizontal deflection
between roof and foundation. These definitions are graphically illustrated in figure 2.4. The
responses of buildings located at 276 stations are illustrated on contour maps. Figure 3.6 to
3.9 map the peak interstory drift ratio in the U20, J20, U6, and J6 with brittle and perfectwelds. All the peak values and the corresponding location are listed in table 3.2.
The peak IDR of U20B is 3.8% at station HKD098. This value is very close to collapse,
which will be discussed in next section. Many stations along the coastal area have peak
IDRs exceeding 1.5% and they have more than 15% connection welds fractured. It reflects
the large deformation and yielding occurring in the buildings.
The contour maps show clearly that the strong ground shaking would affect 20-story
buildings in a larger region than 6-story buildings. High-rise buildings in Yufutsu andIshikari basin (shown in the bottle map in figure 3.3) would experience more deformation
than low-rise buildings in these areas.

36
The contour maps also confirm that buildings with perfect welds perform much better thanbuildings with brittle welds. The regions with peak IDR exceeding 1.5 % is much smaller
for 20P than 20B. This improvement is much higher than that getting from strengthening
buildings (from the U.S. buildings to the Japanese buildings) especially for buildings withperfect welds. The collapse factor introduced in section 3.5 could confirm this argument ina quantitative way.
From these figures, we find that the roof displacements of buildings designed to theJapanese code are greater than these of the U.S. buildings although the peak IDR are
smaller for J20/J6 than for U20/U6. The reason is that the higher yielding strength requiredby Japanese code results in stiffer building (as can be seen from pushover curves in figure3.2), so the deformation is distributed more evenly to each story instead of localized inbottom or weak story. This also explains the same phenomena for buildings with brittle
welds and perfect welds that larger maximum interstory drift ratios associated with smaller
roof displacements.
Figures 3.16 to 3.17 combine the pushover curves with the histogram of maximum roof
displacements for 20- and 6-story buildings respectively. They provide another way toshow how many buildings would yield on Hokkaido during this event. It is easy to find thatthe existing brittle welds would cause buildings yielding in much more stations.
Furthermore, in some stations, the amount of lateral force carried by structures with brittle
welds begins to decrease and the damage caused is irreparable. The similarity between
histograms of U20 and J20 also confirms that increasing the strength of building alone(from U to J) does not change the station distribution much. However, the 6-story buildings
remain elastic in more stations than the 20-story buildings.
Figures 3.6 to 3.9 show that buildings located to the northeast and to the southwest (around
IBUH03) suffered strong shaking even though they are almost 200 km away from theepicenter. The disaster investigation team from ABS Consulting Inc. also reported that in
the area around station IBUH03, large petroleum storages tanks were serious damaged bysloshing (ABS Consulting Inc. report 2003). Another feature is that ground motions

37
directly above the rupture at Cape Erimo caused less simulated damage than stations
located in a band just to the northwest. Comparing with contour map of Vs30 (figure 3.4),
both of these facts are effects of the local site geology. The basin areas indicated by red
color in figure 3.4 have apparent site amplification effects in figures 3.6 to 3.9.
In general, the whole coastal region would have been strongly shaken by the 2003 TokachiOki earthquake if there had been high-rise buildings. Although none of the buildings
collapsed in these simulations, the peak IDRs in some stations (eg. HKD098) were very
close to collapse level. This indicates that if there existed a 20-story steel moment framebuilding of pre-Northridge earthquake type, it would have had very high potential ofcollapse. We will discuss this issue in more detail in section 3.5.

Table 3.2. Summary of response for each type of buildings
Building Type

Peak IDR %Max RD cm

Fractured welds %

U20B

3.8

93

38

J20B

3.4

103

36

U20P

2.1

129

J20P

2.5

144

U6B

5.5

79

55

J6B

4.8

75

58

U6P

4.0

70

J6P

2.8

49

38

Figure 3.6. Peak interstory drift ratio (IDR in percent) for U20B and U20P. The maximum
value is 3.8% and 2.1% respectively, and both occurred at station HKD098.

39

Figure 3.7. Peak interstory drift ratio (IDR in percent) for J20B and J20P. The maximum
value is 3.4% and 2.5% respectively, and both occurred at station HKD098.

40

Figure 3.8. Peak interstory drift ratio (IDR in percent) for U6B and U6P. The maximum
value is 5.5% and 4.0% respectively, and both occurred at station TKCH07.

41

Figure 3.9. Peak interstory drift ratio (IDR in percent) for J6B and J6P. The maximum
value is 4.8% at IBUH03 and 2.8% at TKCH07 respectively.

42

Figure 3.10. Maximum roof displacement for U20B and U20P. The maximum value is 93
cm and 129 cm respectively, and both occurred at station HKD098.

43

Figure 3.11. Maximum roof displacement for J20B and J20P. The maximum value is 103
cm and 144 cm respectively, and both occurred at station HKD098.

44

Figure 3.12. Maximum roof displacement for U6B and U6P. The maximum value is 79 cm
and 70 cm respectively, and both occurred at station TKCH07.

45

Figure 3.13. Maximum roof displacement for J6B and J6P. The maximum value is 75 cm
at IBUH03 and 49 cm at TKCH07 respectively.

46

Figure 3.14. Percentage of the total welded moment-resisting connections that fractured for
U20B and J20B. The maximum value is 38% and 36% respectively, and both occurred atstation IBUH03.

47

Figure 3.15. Percentage of the total welded moment-resisting connections that fractured for
U6B and J6B. The maximum value is 55% and 58% respectively, and both occurred atstation IBUH03.

48

Figure 3.16. Combination of the pushover curves for 20-story buildings and the histogramof roof displacements to show the number of stations with elastic and inelastic performance.
Left y-axis is the number of stations in terms of maximum roof displacements (MRD).
Right y-axis is the base shear force in the buildings in terms of MRD. Dash lines indicate
the onset of yielding. It is easy to find that the existing brittle welds cause more buildings
yielding. Furthermore, in some stations, the amount of lateral force carried by structureswith brittle welds begins to decrease and the damage caused is irreparable. Increasing thestrength of buildings alone (from U20 to J20) does not change the station distribution much.

49

Figure 3.17. Combination of the pushover curves for 6-story buildings and station
distribution for roof displacements to show the number of stations with elastic and inelastic
performance. Left y-axis is the number of stations in terms of maximum roof
displacements (MRD). Right y-axis is the base shear force in the buildings in terms of
MRD. Dash lines indicate the onset of yielding. The same trend is found that existing
brittle welds cause more buildings yielding. And increasing the strength alone (from U6 toJ6) does not change the station distribution much. However, comparing with the 20-story
buildings, the 6-story buildings remain elastic in more stations.

3.4 Relations Between Responses of Buildings and Ground Motions
The extensive simulations for all the recorded stations on Hokkaido Island discussed in theprevious section not only give a detailed picture of regional performance of high-risebuildings in a quantitative manner, but also provide an opportunity to seek the correlations
between the building responses and ground motion intensity measures. Although using
scalar measures characterizing the shaking intensity of earthquakes are known to be50
inadequate in predicting the response of buildings, nevertheless, they are widely used inmany deductions, reasoning, conclusions and design because of their simplicity. Several
intensity measures have been proposed such as PGA, PGV, PGD and response spectra but
there is no consensus on the one that can best predict SMRF response. So it is important tochoose the most appropriate single parameter to represent earthquake hazard.
Comparing the contour map of these parameters (figures 3.3 to 3.4) with contour maps ofbuildings’ peak IDRs (figures 3.6 to 3.9) gives us a rough pattern. It is found that the
distribution of response spectra is most similar to that of peak IDRs. On the other hand, thecontour map of PGA gives a surprisingly bad match of peak IDRs. For example, station
HKD100 has the highest PGA, but it is associated with relatively small deformation for 20story buildings. With regard to PGD, the exact values are sensitive to data processing
schemes. Therefore, among PGA, PGV and PGD, PGV is the best parameter to predict theperformance of SMRF buildings.
To cement this argument, the peak IDRs as functions of ground motion intensity measuresfor U20 are compared in figure 3.18. All the data is separated roughly into linear (peakIDRs < 0.25%) and nonlinear cases (peak IDRs > 0.25%). In the linear range, the linear
relationships of PSV to peak IDRs or PGV to peak IDRs are apparent and can be
represented by a straight line, whereas there is a big scatter in terms of PGA to predict theperformance of buildings. Although PSV fits the linear trend very well, it is worth to notethat when buildings with brittle welds become nonlinear, their peak IDRs are larger thanthe value predicted by the trend line. This is reasonable because the response spectra
method is based on a SDOF linear model analysis. Once buildings become inelastic, thestiffness of the structures would decrease and damage would localize at certain stories. So
PSV can not accurately reflect the behavior of buildings with nonlinear effects. In otherwords, a single degree of freedom model no longer works in that case. On the other hand,
PSV is good at predicting the response of buildings with perfect welds for both linear andnonlinear ranges. This could also be seen in figure 3.19 where peak IDRs for U20P
increase relatively smoothly as PSV increases.

51

Figure 3.18. Relationships between peak IDRs of U20 and ground motion intensity
measures: PGA, PGV, PGD and PSV. PSV = ω|x(t)|max, where |x(t)|max is the maximum
displacement of a mass in a one dimensional spring-mass system with a fixed natural
period subjected to ground motion. In linear range, the linear relationships of PSV to peak
IDRs or PGV to peak IDRs are apparent and can be represented by a straight line, whereas
there is a big scatter in terms of PGA to predict the performance of buildings.

52

3.5 Collapse Factor
It is difficult to use ground motion intensity to predict the nonlinear response of buildings
with brittle welds. To illustrate this, a perfect elastic building model (U20E, U6E) was
added to show purely linear response vs. nonlinear response of buildings with brittle andperfect welds. In the elastic model, the elements would never yield (achieved by using
infinite yield stress but the same mass and stiffness). All three building models were
subjected to ground motions which were obtained by multiplying the recorded groundacceleration by a sequence of constants. The response results of 20- and 6-story buildings
at five stations are given in figures 3.19 and 3.20. The top x-axis shows the scalarmultipliers for the ground motion and the bottom x-axis gives PSV of the scaled groundmotion at natural period of the corresponding building. The linear relationship between
PSV and peak IDRs is apparent for elastic models, however the peak IDRs of the brittle
welds model are larger than the value predicted by PSV when peak IDRs exceed 0.25%.
Furthermore, there is no apparent relationship between the response of elastic models to the
response of brittle welds models. Notice that peak IDR in U20B does not monotonicallyincrease as PSV increases at stations HKD105 and HKD117. Other stations have similarfeatures. We can find that when the peak IDR approaches 4%, U20B is very close tocollapse, whereas U20P has a larger collapse peak IDR. This means that the ductility of
U20B is much smaller than U20P. The collapse peak IDR for U6B is larger than 6%
because of the smaller P-Delta effects. The most interesting thing appears in figure 3.20.
An station HKD105, when PSV reaches 250 cm/s, U6B collapses. However, when PSV
increases to 300 cm/s, U6B does not collapse and its peak IDR is around 6%. This highdegree of nonlinearity indicates that response spectra can not predict the performance ofbuildings when large deformations occur in the buildings. Time history analysis isnecessary for design purposes.

53

Figure 3.19. Relationships of pseudo spectral velocity (5% damped) to peak IDRs for 3
sets of 20-story building models (blue solid line is for U20 with brittle welds, red dash-dot
line is for U20 with perfect welds and black dashed line is for elastic U20). The top x-axis
shows the scalar multipliers for ground motions and the bottom x-axis gives thecorresponding 5% damp 3.5 sec pseudo spectral velocity. It shows that when the peak IDR
approaches 4%, U20B is very close to collapse, whereas U20P has a larger peak IDR whenapproaching collapse.

54

Figure 3.20. Relationships of pseudo spectral velocity (5% damped) to peak IDRs for 3
sets of 6-story building models (blue solid line is for U6 with brittle welds, red dash-dot
line is for U6 with perfect welds and black dashed line is for elastic U6). The top x-axis
shows the scalar multipliers for ground motions and the bottom x-axis gives thecorresponding 5% damp 1.5 sec pseudo spectral velocity. The peak IDR for U6B
approaching collapse is larger than 6% because of the smaller P-Delta effects

55
Extending the previous idea further, we use a parameter to quantify the collapse possibilityof simulated buildings. We named it the “collapse factor” and it is defined to be the scalarmultiplier of the recorded ground motion that is required to cause collapse of the model.
That is, we simply multiplied the recorded ground motion by a constant and then re-ran thebuilding simulation. When the multiplying constant was large enough to cause simulated
collapse, then we called that multiplier the collapse factor. For example, collapse factor of
U20B is 1.06 at HKD098 and 5.5 at HKD117 which can be figured out in figure 3.19. Thisparameter is good at describing the collapse safety margin of structures to a certain groundmotion.
We map the collapse factors for U20B and J20B in figure 3.21. From this figure, we foundthat although no building shown simulated collapse, increasing the ground motion
amplitude recorded at station HKD098 only by 6% caused collapse for U20B. This is wellwithin the uncertainty of this type of calculation. Since Frame-2D does not consider local
failure which is possible to occur along the column flanges once fracture developed in the
beam-column joints, in reality, U20B has a high potential to collapse at station HKD098 in
the Tokachi-Oki event. The contour maps of collapse factors for U20P and J20P are given
in figure 3.22. As expected, buildings with perfect welds have larger collapse factors thanbuildings with brittle models. Some of the ground records are so small that they cause
simulated collapse only when the collapse factors are very large. This is out of our interest.
Collapse factors larger than 20 are not calculated in this study and these areas were coveredby blue color in figures 3.21 and 3.22.
The contour maps of collapse factor indicate some interesting phenomena. In general, thecontour maps of collapse factor (figures 3.21 and 3.22) have the same regional pattern as
the contour maps of peak IDRs (figures 3.6 to 3.9). However, there are conspicuous
discrepancies in some areas. For example, the peak IDRs for U20B at areas around station
HKD016 (around 0.2%) are much smaller than the peak IDRs at areas around station
HKD105 (around 1 to 2%). However the collapse factors are almost the same for these twoareas (about 3.6). That means increasing the ground motions at these areas by the same

56
scale would cause collapse although buildings at areas around HKD105 was shaken muchheavier than these at areas around HKD016. It might be due to the soft soil amplification
caused by the Teshio basin underneath HKD016 (refer figure 3.4). Notice, the low collapse
factor at station IKRH02 is also due to the local site amplification at Ishikari basin.
Figure 3.23 shows the collapse factor ratio between J20 and U20. In general, J20 is safer
than U20 by a factor 1 to 1.4. However for station close to collapse (e.g. HKD098), thecollapse factor of J20B is only 6% larger than that of U20B. This difference is muchsmaller than their strength difference (20%). In addition, for perfect welds models, thecollapse factors of J20P are surprising smaller than these of U20P in some areas whichwere believed to experience strong shaking (covered by red color). In other words, whenwelds in the building do not fracture in violent shaking, the performance of stiffer andstronger Japanese buildings is not as good as that of relatively flexible and weak U.S.
buildings. This demonstrates the crucial roles of connection welds played in theperformance of buildings. It also shows that evaluating the advantages of stronger andstiffer high-rise buildings should be more done cautiously.
Figure 3.24 shows the collapse factor ratio between 20P and 20B. Again, the ratios
corresponding to the collapse factor greater than 20 were not calculated and these areas
were covered with white color. As expected, in most areas, 20P is safer than 20B by afactor of 1.2 to 2.0 which is larger than the ratio between J20 and U20. Therefore, fixing thewelds is a more efficient way to increase the collapse factor than strengthening existingbuildings.

57

Figure 3.21. Contour maps of collapse factor for U20B and J20B. The minimum value is
1.06 and 1.125 respectively at station HKD098. This means that increasing the amplitudeof HKD098 only by 6% (12.5%) caused simulated collapse of U20B (J20B). The collapse
factor in purple areas is larger than 16. Their exact values are out of our interest.

58

Figure 3.22. Contour maps of collapse factor for U20P and J20P. The minimum value is1.98 at station HKD098 for both buildings. This means that doubling the amplitude of
HKD098 caused simulated collapse of U20P (J20P). The collapse factor in blue areas islarger than 20. Their exact values are out of our interest.

59

Figure 3.23. Contour maps of collapse factor ratio between J20 and U20. The ratios at
white areas are not calculated because the exact collapse factor values are not available andout of our interest. In most areas, strengthening buildings increases the collapse factor. But
comparing with figure 3.22, the increase is smaller. The advantage of stronger Japanesebuildings is not apparent.

60

Figure 3.24. Contour maps of collapse factor ratio between 20P and 20B. The ratios at
white areas are not calculated because the exact collapse factor values are not available andout of our interest. In most areas, fixing the welds increases the collapse factor.

61

CHAPTER 4

Empirical Green’s Functions Method
Estimating the strong ground motions for great historic and future earthquakes is an active
and challenging research topic because of the meager recorded data. These synthetic strong
ground motions could provide insight to seismologists in understanding the special
characteristics associated with great earthquakes. Additionally, they also provide guidance
to earthquake engineers in designig flexible structures located in seismic regions with thepotential for great earthquakes.
Current ground motion simulation techniques can be grouped into three main categories.
The first one is fully theoretical modeling where the ground motion is numericallycomputed by the finite element method. In this approach, simulated waves are generatefrom a fault with proposed temporal and spatial slip time history, and propagated through arealistic 3-D earth structure model (Komatitsch, Liu et al., 2004). The second category isempirical method. This method was originally proposed by Hartzell (1978). It uses
recordings of small earthquakes as empirical Green’s functions and convolves them with asource model. The third category is a combination of these two schemes individuallyprocessed at different frequency bandwidth (Heaton, Hall et al., 1995).
Empirical Green’s functions (EGF) method is more suitable to simulate the strong groundmotions from great earthquakes than the theoretical method. In the fully theoretical method,
researchers have to assume the spatial and temporal evolution of slip for each grid on thelarge fault. They also have to assume the rupture velocity for each subfault. Although some62
progress has been made recently to understand the source parameters in giant earthquakes
thanks to the Sumatra event, it is still far away to understand well the physics of the rupture
process based on our current level of knowledge. For a giant earthquake, there are morethan 10,000 subfaults according to the popularly used grid dimension (2 to 5 km). The little
knowledge about giant earthquakes would cause large uncertainty in the resulting
synthetics. This makes us not confident to accept the simulated results from more than
10,000 assumed spatio-temporal slip histories. Furthermore, the theoretical method also
needs to assume the three-dimensional earth structures in shallow and deep part. The elastic
structure of the real earth is very complex, with oddly shaped bodies of low velocity
materials that can be of first order importance to wave propagation. It is hard to obtain thisdetailed information for a region more than 1000 km long. Last, but not the least, even if
we obtain all the detailed information, the computation is too expensive for current
supercomputers to solve the fully 3-dimensional dynamic continuum problems at mostfrequencies of engineering interest. On the other hand, the previous issues do not cause
problems for the empirical Green’s function method. In this method, the ground motions
recorded in real earthquakes are used as Green’s functions. If motions from a larger
earthquake are chosen to be the EGFs, the heterogeneous caused by the slip variations intime and space are inherently included. Furthermore, if the waves from the smaller andlarger events travel through similar seismic velocity structures in a similar manner, theunknown soil structures can be removed. Finally, the computation cost is much lower.
Therefore, we choose the empirical Green’s functions method to estimate strong groundmotions for great subduction earthquakes.
In this chapter, I briefly discuss the empirical Green’s function technique and show the
self-similarity for the 2003 Tokachi-Oki and the 2004 Sumatra event. Tectonic settings ofthe Hokkaido, Sumatra and Cascadia subduction zones are compared. We show that it isreasonable to use records from the 2003 Tokachi-Oki earthquake as empirical Green’s
functions to generate the 2004 Sumatra earthquake, as well as simulate a hypothetical giant
Cascadia earthquake.

63

4.1 Empirical Green’s Functions TechniqueEmpirical Green’s functions (EGF) method is based on the assumption that larger
earthquakes can be considered to be a linear combination of smaller ones. It originally used
aftershock records as empirical Green’s functions (Hartzell, 1978) and later was
generalized to use records from earthquakes with similar tectonic settings (Kanamori, 1979;
Hartzell and Heaton, 1985; Heaton and Hartzell, 1989). A Brief discussion of thistechnique is provided in this section. A detailed deduction can be found in Appendix B of
Heaton and Hartzell (1989).
The ground motion U(t) (either teleseismic data or strong ground motion recordings) can be
represented as a finite source model convolving with Green’s functions, that is,
L W

U (t ) = ∫ ∫ D ( x, y, t ) * G ( x, y, t )dydx ,
0

0

(4.1)

where D(x,y,t) is the dislocation time histories for the larger earthquake; G(x,y,t) is the
double-couple impulse response of the medium; L and W are length and width of the planar
fault respectively. Modeling the earth as a linear system, U(t) can be represented as asummation of the motions from subfaults,
l

m

l

m

U (t ) = ∑∑U ij (t ) = ∑∑ ∫i =1 j =1

i =1 j =1

iΔL

∫

jΔW

( i −1) ΔL ( j −1) ΔW

D( x, y, t ) * G ( x, y, t )dydx .

(4.2)

The ground motions uij(t) from a smaller earthquake that ruptured the ij-th subfault would
be given byuij (t ) = ∫

iΔL

∫

jΔW

( i −1) ΔL ( j −1) ΔW

d ( x, y, t ) * G ( x, y, t )dydx ,(4.3)

where d(x,y,t) is the dislocation time histories for the smaller earthquake. AssumeD( x, y, t ) = Fij (t ) * dij ( x, y, t ) ,

(4.4)

64
n

t
Fij (t ) = ∑ δ (t − Tij − τ k ) and τ k = (k − χ k ) d ,
n
k =1

(4.5)

where Tij is the delay time for the rupture front to travel from the hypocenter to the ij-th
subfault; τk is a simple distribution of times between zero and the dislocation rise time; td isthe duration of the dislocation of the large event and χk is a uniform random number
between 0 and 1. Combining all these equations together, we obtain
l
m
l
m n
t ⎤
⎡
U (t ) = ∑∑ Fij (t ) ∗ uij (t ) = ∑∑∑ uij ⎢t − Tij − (k − χ k ) d ⎥ .
n⎦⎣i =1 j =1
i =1 j =1 k =1

(4.6)

That is, the ground motions U(t) for a larger event is the summation of the empiricalGreen’s functions uij(t) recorded at smaller earthquakes. I use a schematic figure 4.1 toillustrate this method.
near field or far field stationlm

U (t ) = ∑∑ Fij (t ) ∗ uij (t )i =1 j =1

l
m n
t ⎤
⎡
= ∑∑∑ uij ⎢t − Tij − (k − χ k ) d ⎥n⎦⎣i =1 j =1 k =1

Figure 4.1. Illustration of empirical Green’s function method. Red triangle represents a station andgreen rectangular represents the rupture fault for a large earthquake and purple rectangular is a
subfault. The ground motion recorded at stations is a summation of subfaults motions convolving
with a comb function with some time delays.

Once the framework is set up, the most difficult question left is how many empiricalGreen’s functions (N=lmn) are needed to add together. Heaton and Hartzell (1989)
proposed to use the short-period teleseismic waveforms as constraints to find this number N.
One natural choice is that N equals the ratio of the seismic moments of the larger event M0
to the smaller event M0΄. However, results in Section 5.3 imply that the predicted

65
teleseismic P-waves using this ratio are much larger than the corresponding recorded P-

waves in most cases. Another choice is that N equals the ratio of the rupture surface areasof the larger event to the smaller event. As mentioned before, high-frequency motions fromlarge earthquakes are of interest for engineers. Many researchers found that near-sourcehigh-frequency ground motions saturate as a function of magnitude (Kanamori and
Jennings, 1978; Cua and Heaton, 2007). That is to say, they are independent of theamplitude of slip and are proportional to the rupture surface areas (Boatwright, 1982;
Yamada, 2007). Our result in section 5.3 indicates that this ratio did a good job to matchthe recorded teleseismic P-waves. A third choice is proposed by Joyner and Boore (1986)
in order to make empirical Green’s function techniques consisting with Brune’s (1970) ω-2
spectral scaling law. They summed N4/3 records and scaled the final results by N-1/3.
However, the synthetic motions simulated by this method led to underestimates of theteleseismic P-waves (refer to section 5.3). Although Brune’s spectral scaling law is very
popular, there are still some debates about its constant spectral slope ω-2 (Hartzell and
Heaton, 1985). Finally, the ratio of rupture areas is chosen in this study to determine thetotal number of the summed Green’s functions.

4.2 Choosing Records From the 2003 Tokachi-Oki Earthquake (Mw 8.1) as
Empirical Green’s Functions
The empirical Green’s function technique basically is an extrapolation from smaller
earthquakes to larger earthquakes. To get reasonable results, this extrapolation should be
kept as small as possible. It is ideal for two events to be self-similar. Although it is a hard
problem to determine whether two events are self-similar with each other, we know thatlarger subduction earthquakes have much higher possibility than smaller earthquakes to be
self-similar with great subduction earthquakes. Hartzell and Heaton (1988) found that the
self-similarity failed for large earthquakes (Mw > 8¼) to smaller one (Mw < 8¼). Therefore,
it is better to choose an earthquake as large as possible to be the EGF to simulate a giant
earthquake. Furthermore, if a Mw 6 earthquake was chosen to simulate a Mw 9 earthquake,

66
we would need more than 30,000 EGFs based on seismic moment ratio and 400 EGFs

based on rupture size ratio. There is a large variation in N and in the final results comparedwith using a Mw 8 earthquake to simulate a Mw 9 earthquake which needs 20 to 50 EGF.
The 2003 Tokachi-Oki earthquake is the largest well recorded earthquake. It provides anadequate set of records to use as Green’s functions and needs the least extrapolation by the
EGF method. The response spectra of teleseismic P-waves are similar for the Tokachi-Oki
event with the Sumatra event. In figure 4.2 and 4.3, we compare the smoothed teleseismic
P-wave Fourier amplitude spectra for all the large shallow subduction earthquakes (Mw ≥7.6) that occurred from 1990 to 2007; 22 events are considered. Figure 4.2 plots
acceleration spectra to focus on comparing the short period components whereas figure 4.3
plots displacement spectra to focus on comparing the long period components. For each
event, the smoothed Fourier spectrum is the average of all the recorded teleseismic Pwaves corrected to a distance at 60o and the frequency band is 0.0033 to 9 Hz. Although theslopes are different from one to another, it is clear to see that the slopes of the Sumatra andthe Tokachi-Oki events are very similar with each other. It provides insight to the similarity
between the Tokachi-Oki event and the Sumatra event.
In order to get reasonable results from empirical Green’s function method, two eventsshould also have similar wave propagation paths. In other words, impulse response of themedium G(x,y,t) in equation (4.1) should be the same for two events. The subduction zone
where the 2003 Tokachi-Oki Earthquake occurred shares many similar characteristic with
the Sumatra and Cascadia subduction zones. Figure 4.4 displays the cross sections of thesethree subduction zones. The references used to plot these cross sections are: Iwasaki et al.
(1989); Katsumata et al. (2003); Subarya et al. (2006); Fisher et al. (2005). The interfacesof one plate subducting beneath the other are all gently sloping. The similarity is especiallyhigh for subduction zones with a potential for giant earthquakes such as Sumatra andCascadia. In these subduction zones, the trench is followed by an outer-arc ridge, an outerarc basin, a trench-parallel strike-slip fault system and volcanoes. Although the Hokkaido
subduction zone is slightly different from the other two zones, to date the 2003 Tokachi-

67
Oki event is the best earthquake we can find to provide empirical Green’s functions. In

figure 4.4, we also provide the extents of sources for hypothetical Cascadia earthquake withdifferent rupture faults (wide and narrow) which are introduced in Chapter 6.

68

Figure 4.2 Smoothed teleseismic P-wave Fourier acceleration spectra for large shallow subduction
earthquakes (Mw ≥ 7.6) occurred in 1990 to 2007. The 2004 Sumatra and 2003 Tokachi-Oki
events are represented by blue and red lines respectively. Although the slopes are different from
one to another, the slopes of the Sumatra and the Tokachi-Oki events are very similar with eachother. It provides insight to the similarity between that 2003 Tokachi-Oki event and the 2004
Sumatra event.

Figure 4.3. Smoothed teleseismic P-wave Fourier displacement spectra for large shallow
subduction earthquakes (Mw ≥ 7.6) occurred in 1990 to 2007.

69

Figure 4.4. Cross sections of the approximate geometry of the rupture surfaces. The top
panel is for of Hokkaido subduction zone, the middle panel is for Sumatra subduction zone
and the bottom panel is for Cascadia subduction zone. There is no depth exaggeration used
to plot these cross sections. The blue, green and red lines in the bottom figure represent thewide, middle and narrow rupture models used in Chapter 6 respectively. The tectonic
settings of these subduction zones are very similar with others.

70

CHAPTER 5

December 2004 Sumatra-Andaman, Indonesia,
Earthquake Mw 9.2
The 2004 Sumatra-Andaman earthquake (Mw 9.2) is the third largest earthquake since theinstallation of seismometers. It generated more than 0.2 million people dead or missing andone million people displaced. Although much of the damage was caused by theaccompanying tsunami, it is still not clear how much of the damage was associated withstrong ground shaking. Unfortunately, there are no seismic records on scale at close
distances. The nearest station recording this event was the PPI station of the JISNET
network which is about 650 km from the epicenter (Sørensen, Atakan et al., 2007). On theother hand, the teleseismic data of this event was recorded globally by substantial highquality broadband seismometers and we know much more information about this event
than any other historic giant earthquakes (Mw > 9.0). Since the rupture size of thisearthquake is at the same scale to the event that we expect in the Cascadia area, it provides
a good source model for that scenario event.
In this chapter, I briefly introduce the 2004 Sumatra-Andaman earthquake. Then the strong
ground motions from two rupture models (wide and narrow rupture width) for two site
conditions (rock and soil) are estimated by empirical Green’s functions method. Nonlinear
dynamic responses of 20- and 6-story steel moment-frame buildings are simulated for thisevent.

71

5.1 Introduction
The 2004 Sumatra-Andaman earthquake ruptured the Sunda Trench subduction zone along
which the Indo-Australian plates are subducted northeastward beneath the Sunda shelf at aconvergence rate 45 to 60 mm/year (Menke, Abend et al., 2006). The hypocenter was atlatitude 3.3oN, longitude 96.0oE, at a depth of 28 km (Harvard CMT). The rupture length of
this event was initially estimated to 400 km and later modified to 1200 to 1300 km (Sieh,2005). Most researchers agree that rupture occurred in two broad phases. The rupture
velocity was 2.8 km/s for the southern 500 to 600 km of the rupture and lasted 200 seconds.
It reduced to 2.1 km/s for the northern part of the rupture fault (Menke, Abend et al., 2006).
The source duration was more than 480 seconds. The estimates of seismic moment varied
from 3.95×1022 to 1.17×1023 Nm for different researchers using different data sets andassumptions. Kanamori (2006) gave an explanation about the difference. The estimates of
average slip along the fault also varied from 5 to 10 m because of the complexity of thisevent.

5.2 Rupture Fault Models
Like the variability in estimating seismic moment, the rupture model sizes proposed bydifferent investigators are different. The rupture length is estimated to be 1300 to 1600 km(Lay, Kanamori et al., 2005; Subarya, Chlieh et al., 2006). For the rupture width, Lay et. al.
(2005) proposed that it is around 240 km along the northwestern Sumatra and 160 to 170
km along the Nicobar and Andaman Islands. However, Subarya et. al. (2006) estimatedthat the rupture width is less than 150 km and Ammon et. al. (2005) proposed 240 km allalong the rupture length. Choosing a geometric rupture model is a primary aspect inempirical Green’s function scheme. So, in this chapter, we use two geometric rupture faults
with different widths as our simulation basis because we found that the final strong motion
predictions are sensitive to the width instead of length of the rupture fault.

72
Figure 5.1 gives the geometry of the rupture faults used in our empirical Green’s function

method. The first geometric model is named S-Wide where “S” represents the Sumatra
event and “Wide” represents that the width of rupture fault is wider. It has a rupture width
250 km in the first segment (south part of the fault) and reduces to 200 km in the second
segment (north part of the fault). The second geometric model is named S-Narrow where“Narrow” represents the narrower width rupture fault. It has a rupture width 175 at the first
segment and 200 km at the second one. The rupture size of the 2003 Tokachi-Oki
earthquake which is used to tile the Sumatra rupture fault is around 130 ×100 km2. Because
there are some overlaps in the tiling, the average fault width of the Tokachi event is about
85 km, a value similar with Yamanaka’s model (2003). The subfaults in the adjacent rows
are staggered to reduce the artificial pattern in the simulated results.
As for how many Green’s functions should be summed together, we propose three criteria
to determine N. The first one is based on the seismic moment ratio of larger and smaller
events. The second one is based on the ratio of the rupture fault size. The last one is basedon the Joyner and Boore’s method (1986) as mentioned in Chapter 4. It is easy to figure out
from figure 5.1 that rupture size ratio is 24 for wide models and 20 for narrow models.
Therefore, each subfault would rupture only once if N was determined from the rupture size
ratio. However, if N was determined from the moment ratio, each subfault would rupture atleast three times since the seismic moment ratio is about 50 to 70 for Sumatra event toTokachi event. Although there is a big variation in estimated seismic moments, we cancalculate the seismic moment ratio with respect to the rupture size ratio in another way.
Since it is well known that Mo=μSD, assuming μ is the same for two events,

M oS S S DS=,
M oT ST DT

that is the seismic moment ratio is the product of the rupture size ratio with the average slip
ratio. The average slip is 2.6 m for the Tokachi event and 5 to 10 m for the Sumatra events.
If we choose the median value, thenM oS
S
= 3 × S that is, N=72 for wide models and 60
M oT
ST

for narrow models. Recall from Chapter 4, if we use Joyner and Boore’s method, weshould sum N4/3 records and reduce the amplitude by N1/3.

73
Considering all these possibilities, we propose eight models to predict teleseismic data.

Their source parameters are listed in table 5.1. There are two segments along the fault withdifferent strike, dip and rupture velocity values. And the source parameters within eachsegment are assumed the same. Recommended models can be chosen to best match theobserved recordings. Slightly change of strike, dip and rupture velocities have muchsmaller effects to the final results than the number change of EGFs.

Figure 5.1. Geometries of the rupture fault models used to simulate the 2004 SumatraAndaman earthquake. Red star represents the hypocenter of this event. Red dot represents
observe station at Banda Aceh (BAC) where strong ground motions would be estimated.
Each box represents a subfault whose response is simulated by summing the groundmotion from the 2003 Tokachi-Oki earthquake. Letters in each box denotes the name foreach subfault. The size of each subfault is 130 × 100 km2. Left figure (a) shows S-Widemodels which have wide fault width. Right figure (b) shows S-Narrow models which havenarrow fault width.

74
Table 5.1. Parameters for each model
Model Code

StrikeDip

No. ofadded
EGF

S-Wide-24

24

S-Narrow-20

20

S-Wide-72

72

S-Narrow-60
S-Wide-24-JB

315º
/**
342º

12º
/
15º

No. ofrupture60
72

S-Narrow-20-JB

60

S-Wide-72-JB

288

S-Narrow-60-JB

240

RuptureVel(km/s)

L
(km)

1

3

12

2.8
/
2.5

650
/
650

W
(km)

m*

n*

250 / 200

3/2

175 / 2002

250 / 200

3/2

175 / 200
250 / 200

5/5

2
3/2

175 / 2002

250 / 200

3/2

175 / 2002

*m is the number of subfaults along the fault length; n is the number of subfaults along the fault width;** The parameters for two segments are separated by ‘/’.

5.3 Teleseismic P-wave Simulation
Teleseismic P-waves simulated from EGF technique provide an important constraint on themodel parameters of our strong ground motion models. Recorded teleseismic P-waves fromthe 2003 Tokachi-Oki earthquake are used as EGFs to simulate the teleseismic P-waves atabout 60 degrees in the 2004 Sumatra earthquake. All the teleseismic time histories were
downloaded from the website of IRIS (Incorporated Research Institutions for Seismology).
Their sampling frequency is 20 Hz. To avoid nyquist side effect and to remove very long
period motions which are out of our interest, a Butterworth filter at a period band of 0.11 to
300 sec is applied to all the records. Figure 5.2 illustrates the locations and recordings of all
stations between 30 to 90 degrees for Tokachi and Sumatra events. Figure 5.3 and 5.4 orderthese waveforms by distance for easy comparison.
Recordings from station YSS (Δ=60.5o) in Sumatra event (circled in the bottom of figure5.2) is our simulation target since its location is far away from nodes as you can see fromfigure 5.2. Recordings from four stations KBS (Δ=55.9o), KEV (Δ=59.3o), ABKT
(Δ=63.0o) and OBN (Δ=65.1o) in Tokachi event are chosen to constitute our EGFs
teleseismic database (circled in the top of figure 5.2). All of these stations are far awayfrom nodes and close to simulated distance 60o. This database requires the smallest

75
spherical spreading correction and avoids the final results depending on a single record.

Figure 5.5 plots their waveforms. Comparing with other stations around 60o (e.g., CTAO,
WRAB) shown in Figure 5.3, it is clear to see that these four recordings have similar
waveform shapes and their amplitudes are at the same scale. Each Green’s function was
assigned a code to represent its recorded station. These codes are listed in the left column infigure 5.5.
Eight source models listed in table 5.1 are simulated. These models are grouped into twocases: wide and narrow models. Their Green’s functions are randomly distributed and thesets that used in our simulation are shown in figure 5.6. Different distributions only slightly
change the resulted peak amplitudes and the discrepancy can be ignored.
The simulated results from eight models at distance 60o are compared in figure 5.7. The
records from station YSS are all plotted in the last row in each panel. The peak value islisted on the top left for each trace. By comparing the peak values, we find that waveforms
generated by Model S-Wide-72 and S-Narrow-60 which are based on the seismic moment
ratio overestimate the observed waveforms. On the other hand, Model S-Wide-24-JB andS-Narrow-20-JB which apply Joyner and Boore’s method to the rupture size ratio
underestimate the observed waveforms. Model S-Wide-72-JB and S-Narrow-60-JB which
apply Joyner and Boore’s method to the seismic moment ratio could well estimate
accelerations; however they underestimate the velocities and displacements which are more
important than accelerations in teleseismic signals. If the whole envelopes of the waves arecompared, S-Wide-24 and S-Narrow-20 give the best fit. Smoothed Fourier spectra ofteleseismic P-waveforms from different models and records at station YSS (Δ = 60.5º) in
Sumatra event are compared in figure 5.8. Overall, Model S-Wide-24 and S-Narrow-20
which are based on the rupture size ratio give comparable results to the recorded P-waves
in terms of velocities and displacements although overestimate the accelerations. Fromthese comparisons, we conclude that the total Green’s functions number N is best
determined by the rupture size ratio.

76

Figure 5.2. Locations of Global Seismograph Network stations (Δ= 30º to 90º) which hadrecorded teleseismic data from the 2003 Tokachi-Oki earthquake (top) and the 2004 SumatraAndaman earthquake (bottom). Teleseismic P-wave seismograms are shown for each station andfocal mechanisms of these events are also shown. The amplitude scale is different for two eventsin order to show them clearly. Four stations whose records are used as EGFs are circled by red
ellipses in the top figure. The station YSS whose record is used to compare with predictedmotions is also circled in the bottom figure. Notice that their relative azimuths with event strikes
are similar for two events.

77

Figure 5.3. Teleseismic P-wave seismograms recorded at Global Seismograph Network
stations (Δ = 30º to 90º) from the 2003 Tokachi-Oki earthquake. They are ordered bydistance. Four stations whose seismograms are used as our empirical Green’s functions arelabeled in red.

78

Figure 5.4. Teleseismic P-wave seismograms recorded at Global Seismograph Network
stations (Δ = 30º to 90º) from the 2004 Sumatra-Andaman earthquake. They are ordered bydistance. Station YSS whose seismograms are used to compare with our simulation islabeled in red.

79

Figure 5.5. Four teleseismic P-wave seismograms recorded at the 2003 Tokachi-Oki
earthquake used as empirical Green’s functions to simulate the 2004 Sumatra earthquake.
Notice that their waveforms are very similar with each other, only with slightly different
amplitudes.

Figure 5.6. Distributions of empirical Green’s functions used to simulate teleseismic Pwaves from 2004 Sumatra earthquake. Each box represents a subfault. Letters in the box
refer to figure 5.5 and designate which records from the 2003 Tokachi-Oki event are used
as Green’s functions. These records are chosen randomly from the four stations.
Difference choices would only slightly affect the resulted peak amplitudes. Star represents
the hypocenter of Sumatra event. The top figure is for rupture model with wide width andthe bottom figure is for rupture model with narrow width.

80

Figure 5.7. Comparison of simulate teleseismic P-waveforms at distance 60o from eightmodels with observed recordings at station YSS (Δ = 60.5º) in Sumatra event.
Accelerations are shown at top left, velocities are shown at top right and displacements areshown at bottom left. These data are highpassed at 0.05 Hz. Displacements without filters
are listed at the bottom right. Maximum value for each waveform is shown on the left.
Detailed parameters for each model can be found in table 5.1. Green’s functions
distributions for these models are shown in figure 5.6.

81
As to which one is preferred between S-Wide-24 and S-Narrow-20, teleseismic P-wave

could not provide enough information to decide. Although we found that in strong groundmotion simulation, results are very sensitive to the rupture width, simulating teleseismic Pwaves could not give a constraint on how much down dip a fault would rupture. Based on
our current understanding on the physical of earthquake, we could not decide either.
Therefore, considering the similarity with the records as well as the simplicity of method,
we choose both S-Wide-24 and S-Narrow-20 as our rupture fault models for simulating
teleseismic and strong ground motions waves.
Smoothed Fourier Spectra of teleseismic P-waves
-1

10

-2

10

S Wide 24
S Narrow 20
S Wide 72
S Narrow 60
S Wide 24 JB
S Narrow 20 JB
S Wide 72 JB
S Narrow 60 JB
Recorded at YSS

-3

10

-4

10

0.01

0.1
Frequencv Hz

1.0

Figure 5.8. Comparison of smoothed Fourier spectra of teleseismic P-waveforms fromdifferent models and records at station YSS (Δ = 60.5º) in Sumatra event.

5.4 Strong Ground Motion Simulation

5.4.1 Choosing Empirical Green’s Functions
Rupture model S-Wide-24 and S-Narrow-20 are used to simulate strong ground motions at
Banda Aceh (BAC). For doing this, we need to choose appropriate records from Tokachi-

82
Oki event as a Green’s function for each subfault in our models. In principle, the Green’s

functions were chosen such that the difference in distance between that required by themodel geometry and that at which they were observed is smaller than a range, say 10 km.
According to this criterion, there are several stations with scatted amplitudes within that
distance range, because K-Net and KiK-Net are densely deployed at Hokkaido Island. This
fact can be clearly found from figure 5.9 which relates peak ground velocities with thecentral distances (from the station to the center of the fault) for all the stations.
These qualified signals were recorded at stations with different site conditions. Generally
speaking, signals recorded at soil sites are more sensitive to the local geology condition andhave large spatial variations. On the other hand, site effects are much smaller for signals
recorded at bedrock sites. Therefore, it is ideal to use Tokachi-Oki rock records to simulate
Sumatra rock synthetics and then amplify the synthetics based on the local site condition in
Banda Aceh area. However, to date, there have been few studies on local soil structure in
Sumatra area. The site amplification information is not available for us. In order to consider
the shaking on soil sites in Banda Aceh, we directly use soil records in Tokachi event as
our EGFs to simulate strong motions. Although processing excludes the site condition ofBanda Aceh completely, it could shed some insight on motions at soil sites.
To classify rock and soil sites, we can use the parameter Vs30 introduced in section 3.2. Soiltype B and C belong to rock sites whereas type D and E belong to soil sites. Recall that
there are no soil structure investigations for KiK-Net, site conditions are unknown for KiKNet stations. This fact limited our main source of Green’s functions to K-Net. Figure 5.9
shows the attenuation trends for rock K-Net stations, soil K-Net stations and KiK-Net
stations. We use a simplest attenuation relationship which has the form log (PGV) = a – blog(R) to address the amplitude difference for rock and soil site conditions, where R is the

distance from the center of the fault to the station. As expected, soil sites generally givestronger shaking than rock sites. Site condition is not classified for KiK-Net stations, so theslope of its trend (b =1.4 to1.5) is slightly different from that of the K-Net stations (b =1.9

83
to 2.0). We noticed that PGV is much smaller than that predicted by the trend when station

is close to the fault (R ≈ 50 to 70km).
In the following, rock synthetics are simulated using rock record which has a median PGV
for a given central distance as an EGF for the corresponding subfault. At the same time,soil synthetics are estimated using soil record which has a median PGV for a given central
distance as an EGF for the corresponding subfault. The important parameters of the record
chosen for each subfault as EGF are listed in table 5.2. To estimate ground motions atregions rather than Banda Aceh, all these EGFs should be chosen correspondingly toachieve the smallest scaling and best results.
Recall from Chapter 3 that signals recorded at KiK-Net station IBUH03 in Yufutsu basin
contain a lot of long period motions (large petroleum storages tanks were serious damaged
in this region). Its PGV is 90 cm/s, substantially larger than the median PGV (around 20cm/s) for that central distance. Although this record seems like an extreme case, we areinterest in the results from which this record was included in our EGF data base. Soil-L
model which uses IBUH03 recording as an alternative EGF choice for subfault D2 (others
are the same as Soil model) is considered for comparison. In the model name, L represents
long-period motions.

84

Figure 5.9. Peak ground velocities versus distance from stations to the center of the fault.
K-Net stations at rock sites are represented by blue triangles, K-Net stations at soil sites are
represented by red circles and KiK-Net stations are green crosses. Their linear trends for
loglog scale are represented by corresponding colored solid lines. Notice that the site
condition is unknown for KiK-Net stations, so the slope of its trend (b =1.4~1.5) is slightly
different from that of the K-Net stations (b =1.9~2.0). These figures are useful for choosing
maximum, median or minimum empirical Green’s functions for a certain distance. The top
figure is for east-west component and the bottom figure is for north-south component.

85
Table 5.2. Strong ground motions chosen to be empirical Green’s functions tosimulate notions at Banda Aceh (BAC) in the 2004 Sumatra earthquake.
Rock Model

Soil Model (Soil-L Model*)Subfault
Code

Dist
(km)

Sta Name

Dist
(km)

PGA
cm/s/sPGV
cm/s

Sta Name

Dist
(km)

PGA
cm/s/sA1

309

HKD175

298

27.1

6.8

AOM025

307

23.0

7.8

A2

297

HKD047

292

20.8

4.6

AOM020

298

30.3

7.2

A3

226

HKD041

234

45.1

6.9

HKD127

221

104.9

17.7

B1

259

HKD131

257

82.4

6.2

HKD052

260

47.7

15.4

B2

218

HKD124

231

49.5

20.2

HKD127

221

104.9

17.7

B3

130

HKD096

128

200.1

30.5

HKD077

136

407.4

40.3

C1

233

HKD124

231

49.5

20.2

HKD053

226

100.4

12.7

C2

172

HKD083

163

192.9

29.3

HKD079

175

188.3

28.1

C3

119

HKD096

128

200.1

30.5

HKD085

131

277.8

53.4

D1

281

HKD177

281

25.3

6.9

D2

204

HKD101

195

45.8

8.1

D3

224

HKD041

234

45.1

6.9

HKD156
HKD072(IBUH03)
HKD127

280
197
(206)
221

33.9
293.8
(374.9)
104.9

3.7
19.8
(89.6)
17.7

E1

386

IWT015

390

6.6

0.9

AKT005

382

9.6

5.1

E2

316

IWT017

316

16.3

1.0

HKD143

322

20.5

6.0

F1

524

MYG016

512

4.3

0.8

FKS001

512

9.4

0.7

F2

449

MYG009

459

4.3

0.8

MYG006

443

12.3

2.2

G1

657

TCG006

690

3.7

0.7

TCG005

658

3.2

0.9

G2

591

FKSH13

610

3.8

0.2

FKS024

593

5.9

1.0

PGV
cm/s

H1

787

NGNH27

777

0.6

0.4

CHB014

782

3.6

0.8

H2

718

TCG012

713

3.7

1.2

IBR011

716

5.0

1.2

I1

911

SZOH34

887

0.6

0.2

SZOH39

903

0.5

0.2

I2

848

YMNH10

855

0.4

0.2

NGNH21

849

0.5

0.2

J1
1016 SZOH34
887
0.6
0.2 SZOH39
903
0.5
0.2
J2
957 SZOH34
887
0.6
0.2 SZOH39
903
0.5
0.2
*using station in the blanket as an empirical Green’s function. It is for Soil-L model, where L represents long period
records.

5.4.2 Results and Discussion
Considering different rupture fault widths and site conditions, there are totally six models
simulated. They are S-Wide-24 Rock; S-Narrow-20 Rock; S-Wide-24 Soil; S-Narrow-20
Soil; S-Wide-24 Soil-L and S-Narrow-20 Soil-L. Their simulated accelerations, velocities,
displacements and response spectra (with 5% damping) at station BAC are compared in

86
Figure 5.10 to 5.13. And peak amplitudes are compared in figure 5.14. All of thesesynthetics are highpassed at 0.075 Hz (~13.3 sec) to avoid unstable displacements.
We estimate that PGA is around 0.15 to 0.25 g in rock site at Banda Aceh. It is consistent
with the damages caused by strong shaking in that area (Somerville, Thio et al., 2005).
PGA at soil sites is estimated to be 0.3 to 0.4 g which is about 1.5 to 2 times larger than thatin rock site. Estimated PGV in rock site is around 30 to 40 cm/s. This is smaller than PGV≈ 80 cm/s which is estimated from the empirical relations between PGV and intensity(Sørensen, Atakan et al., 2007). On the other hand, PGV estimated from Soil-L model is inthat range. But it should be pointed out that this relationship was achieved from California
earthquake database whose signals were mostly recorded at moderate to large crustal
earthquakes. From our simulation, the amplification in low-frequency components fromRock model to Soil model is relatively small (smaller difference of PGV between rock andsoil model). It may be caused by the underestimation of Vs30 as discussed in section 3.2. In
fact, the so called soil sites are firmer than the real soil sites.
Response spectra in figure 5.13 provide frequency distributions of the ground shaking. The
peaks occur at period 1 to 3 seconds for all the models. And the Soil-L model has a striking
peak at 2 sec due to records at IBUH03.
By comparing these waveforms, we found that the soil site synthetics have longer duration
than the rock site synthetics and Soil-L models give the longest shakings. The strong
shaking duration is about 150 sec in rock sites and is more than 200 sec in soil sites. It isalso similar to the value estimated by Sørensen (2007).
Motions estimated from wide rupture width models (S-Wide) generally are stronger thanthese from narrow rupture width models (S-Narrow). However, this is not true for Soil-L
models because the velocity from one EGF (record of IBUH03 included in both wide andnarrow models) significantly larger than EGFs at other subfaults.

87
Accn EW Highpass at 0.075 Hz

500

EW: 246.4 S-Wide-24 Rock

0
-500
500

EW: 179.5 S-Narrow-20 RockAccn cm/s 2

0
-500
500

EW: 402.7 S-Wide-24 Soil

0
-500
500

EW: 303.5 S-Narrow-20 Soil

0
-500
500

EW: 422.9 S-Wide-24 Soil-L

0
-500
500

EW: 358.4 S-Narrow-20 Soil-L

0
-500
0

50

100

150

200
Time sec

250

300

350

400

Accn NS Highpass at 0.075 Hz

500

NS: 196.8 S-Wide-24 Rock

0
-500
500

NS: 158.5 S-Narrow-20 Rock

0
-500
500

NS: 332.6 S-Wide-24 Soil

Accn cm/s 2

0
-500
500

NS: 233.4 S-Narrow-20 Soil

0
-500
500

NS: 332.5 S-Wide-24 Soil-L

0
-500
500

NS: 276.6 S-Narrow-20 Soil-L

0
-500
0

50

100

150

200
Time sec

250

300

350

400

Figure 5.10. Simulated accelerations for six models in BAC. A highpass filter at 0.075 Hz
is applied. Maximum value for each waveform is shown in front of the model name. The
top figure is for east-west component and the bottom figure is for north-south component.

88
Vel EW Highpass at 0.075 Hz

100

EW: 41.4 S-Wide-24 Rock

0
-100
100

EW: 28.0 S-Narrow-20 Rock

0
-100
100

EW: 65.0 S-Wide-24 SoilVel cm/s

0
-100
100
EW: 26.9 S-Narrow-20 Soil

0
-100
100

EW: 98.2 S-Wide-24 Soil-L

0
-100
100

EW: 86.3 S-Narrow-20 Soil-L

0
-100
0

50

100

150

200
Time sec

250

300

350

400

Vel NS Highpass at 0.075 Hz

100

NS: 37.5 S-Wide-24 Rock

0
-100
100

NS: 29.6 S-Narrow-20 Rock

0
-100
100

NS: 47.7 S-Wide-24 SoilVel cm/s

0
-100
100

NS: 29.8 S-Narrow-20 Soil

0
-100
100

NS: 69.7 S-Wide-24 Soil-L

0
-100
100

NS: 83.2 S-Narrow-20 Soil-L

0
-100
0

50

100

150

200

250

300

350

400

Figure 5.11. Simulated velocities for six models in BAC. A highpass filter at 0.075 Hz isapplied. Maximum value for each waveform is shown in front of the model name. The top
figure is for east-west component and the bottom figure is for north-south component.

89
Disp EW Highpass at 0.075 Hz

50

EW: 25.8 S-Wide-24 Rock

0
-50
50

EW: 18.4 S-Narrow-20 Rock

0
50
-50

EW: 36.9 S-Wide-24 Soil

Disp cm0-50
50
EW: 19.9 S-Narrow-20 Soil

0
-50
50

EW: 39.8 S-Wide-24 Soil-L

0
50
-50

EW: 41.1 S-Narrow-20 Soil-L

0
-50
0

50

100

150

200
Time sec

250

300

350

400

Disp NS Highpass at 0.075 Hz

50

NS: 21.9 S-Wide-24 Rock

0
-50
50

NS: 19.6 S-Narrow-20 Rock

0
-50
50

NS: 27.2 S-Wide-24 Soil

Disp cm0-50
50

NS: 18.2 S-Narrow-20 Soil

0
-50
50

NS: 42.5 S-Wide-24 Soil-L

0
-50
50

NS: 49.9 S-Narrow-20 Soil-L

0
-50
0

50

100

150

200
Time sec

250

300

350

400

Figure 5.12. Simulated displacements for six models in BAC. A highpass filter at 0.075 Hz
is applied. Maximum value for each waveform is shown in front of the model name. The
top figure is for east-west component and the bottom figure is for north-south component.

90
3

10

Pseudo Veloctiy Spectra EW 5% dampling

2

cm/s

10

S-Wide-24 RockS-Narrow-20 RockS-Wide-24 Soil
S-Narrow-20 Soil
S-Wide-24 Soil-L
S-Narrow-20 Soil-L

1

10

0

10
0.1

3

10

1
Period sec

10

Pseudo Veloctiy Spectra NS 5% dampling

2

cm/s

10

S-Wide-24 RockS-Narrow-20 RockS-Wide-24 Soil
S-Narrow-20 Soil
S-Wide-24 Soil-L
S-Narrow-20 Soil-L

1

10

0

10
0.1

1

10
Period sec

Figure 5.13. Pseudo velocity spectra for simulated data with 5% damping. The top figure isfor east-west component and the bottom figure is for north-south component.

91
PGA EW

500

400
Accn cm/s/s

Accn cm/s/s

400
300
200
100
0

Rock

Soil

200
100

100
80
Vel cm/s

80
Vel cm/s

3000Soil-LPGV EW

100

60
40
20
0

PGA NS

500

Rock

Soil

Soil-LPGV NS
S-Wide-24
S-Narrow-20

60
40
20

Rock

Soil

Soil-L

0

Rock

Soil

Soil-L

Figure 5.14. Comparing PGA and PGV for different models. The left column is for eastwest component and the right column is for north-south component.

In our strong motion simulation, results are sensitive to some parameters in the modeling.
The first one is the number of subfaults close to the observation point. Since the central
distances (from center of subfaults to station BAC) are extremely large for subfaults suchas I1 and J1 in the far north end of rupture fault, their corresponding EGFs are very small
and contribute little to the final waveforms. The final results are contributed mainly by
EGFs from nearby subfaults such as A3, B3 and C2. Therefore, rupture width is far more
important than rupture length to affect results. If the fault rupture extended down dip
further, the subfaults were closer to the observation point, larger EGFs would be chosen forthese subfaults. Overall, these facts all indicate the importance of choosing empiricalGreen’s functions. Choosing different sets of Green’s function would generate waveforms
with different peak ground motions. In this chapter, we choose median records as our EGFs
and in Chapter 6 we choose maximum, median and minimum records as EGFs separately
to consider the large uncertainty associated with the hypothetical Cascadia earthquake.

92

5.5 Nonlinear Performance of Buildings
All of the strong ground motions obtained from above models are used to simulate thenonlinear responses of 20- and 6-story buildings as discussed in Chapter 2. As mentioned
in section 3.3, we retrieve peak interstory drift ratio (IDR %) and maximum roof
displacements (MRD cm) to get an insight to the performance of buildings. Their values
are exhibited in table 5.3 and figure 5.15.

Table 5.3. PGA and PGV of simulated strong ground motions at station BAC andperformance of 20- and 6-story buildings shaken by these motions
Rock

Model Name

Soil

Direction

S-Wide-24
EW
NS

PGA cm/s2

246

197

180

159

403

333

304

233

423

333

358

277

PGV cm/s

41.4

37.5

28.0

29.6

65.0

47.7

26.9

29.8

98.2

69.7

86.3

83.2

MRD

43.5

51.9

42.0

46.9

74.4

52.7

46.5

45.5

77.7

72.0

68.6

72.3

IDR

1.2

1.0

0.9

0.9

2.1

1.3

1.1

1.4

2.4

2.2

1.7

2.1

MRD

52.0

57.9

53.9

64.4

71.3

68.5

55.5

59.3

120

81.1

108

106

IDR

0.6

0.6

0.5

0.7

1.3

0.8

0.6

0.7

1.9

0.9

1.6

1.3

MRD

47.3

52.0

36.8

56.9

71.2

57.3

51.5

53.7

71.2

72.4

66.5

75.9

IDR

1.2

0.9

0.6

1.2

2.4

1.5

1.0

1.2

2.3

2.1

2.1

2.1

MRD

63.6

74.8

40.0

67.7

82.2

72.9

65.7

58.6

106

128

81.4

135

IDR

0.6

0.7

0.4

0.7

1.0

0.9

0.7

0.6

1.6

1.5

1.0

1.8

MRD

29.9

18.3

11.6

13.2

26.8

34.9

13.9

11.9

79.6

88.6

54.7

73.2

IDR

2.1

1.1

0.7

0.8

1.6

2.4

0.9

0.7

4.8

5.1

3.7

4.3

MRD

26.6

20.2

11.5

12.8

26.4

30.0

12.6

13.4

59.4

62.4

59.1

75.5

IDR

1.5

1.0

0.6

0.6

1.5

1.7

0.6

0.6

3.6

3.6

3.6

4.4

MRD

14.3

11.7

5.8

8.2

30.5

28.0

7.1

9.6

68.2

54.5

66.1

56.2

IDR

0.7

0.5

0.3

0.3

1.9

1.6

0.3

0.4

4.3

3.4

4.2

3.5

MRD

11.3

11.2

5.8

8.2

28.9

28.5

7.1

9.7

31.2

28.4

29.8

33.4

IDR

0.5

0.5

0.3

0.3

1.7

1.5

0.3

0.4

1.7

1.5

1.6

1.7

U20B
U20P
J20B
J20P
U6B
U6P
J6B
J6P

S-Narrow-20
EW
NS

S-Wide-24
EW
NS

Soil-LS-Narrow-20
EW
NS

S-Wide-24
EW
NS

MRD represents Maximum Roof Displacements (cm). IDR represents peak interstory drift ratio (%).
Yellow cells denote buildings experienced large deformation and damaged.

S-Narrow-20
EW
NS

93

1

2

0

150

20-story Buildings EW

100

50

0

100

60
40
20
0

WR NR WS NS WSL NSL

100

WR NR WS NS WSL NSL
6-story Buildings NS
U6B
U6P
J6B
J6P

WR NR WS NS WSL NSL
20-story Buildings NS
U20B
U20P
J20B
J20P

50

0

6-story Buildings EW

U20B
U20P
J20B
J20P

2

150

WR NR WS NS WSL NSL

80

4

0

WR NR WS NS WSL NSL

20-story Buildings NS

1

6

100
Max Roof Disp cm

Max Roof Disp cm

6-story Buildings EW

4

2

0

WR NR WS NS WSL NSL

Peak IDR %Peak IDR %6

3Peak IDR %2

0

Max Roof Disp cm

20-story Buildings EW

Max Roof Disp cm

Peak IDR %

3

80
60

WR NR WS NS WSL NSL
6-story Buildings NS
U6B
U6P
J6B
J6P

40
20
0

WR NR WS NS WSL NSL

Figure 5.15. Peak interstory drift ratio (top) and maximum roof displacements (bottom) of
20- and 6-story buildings at rock and soil sites for wide and narrow models. x-axis lists themodel names. Since space is limited, we abbreviate wide model as W, narrow model as N,
rock model as R, soil model as S and soil model with long period motions as SL.

94
For 20-story buildings, the peak IDR is less than 1% for rock model and is around 2% forsoil model. Comparing with their performance in Tokachi-Oki event (Chapter 3), thesevalues would have caused buildings yielding but no collapse. The conclusion is similar for
6-story buildings. It should be pointed out that our soil model may underestimate the site
amplification since not much site condition information available in Sumatra area. The roof
displacement time histories from U20B are plotted in figures 5.16 to 5.17 as an example.
We find that motions from rupture down dip further (S-Wide model) would have caused
U20B large permanent deformation with peak IDR above 2%. Detailed discussions arepresented later according to different models.
U20B Roof Displacements EW

100

43.5 S-Wide-24 Rock

0
-100
100
42.0 S-Narrow-20 Rock

0
-100
100

74.4 S-Wide-24 Soil

0
-100
100
cm

46.5 S-Narrow-20 Soil

0
-100
100

77.7 S-Wide-24 Soil-L

0
-100
100

68.6 S-Narrow-20 Soil-L

0
-100
0

50

100

150

200
250
Time sec

300

350

400

Figure 5.16. Roof displacement time histories for U20B for 6 models in east-westcomponent. The maximum value is shown on the top right of each trace. Large permanent
roof displacement (around 0.5 m) occurs for U20B in Model S-Wide at soil sites. It
indicates lot of damage occurred along U20B.

95
U20B Roof Displacements NS

100

51.9 S-Wide-24 Rock

0
-100
100
46.9 S-Narrow-20 Rock

0
-100
100
52.7 S-Wide-24 Soil

0
-100
100
cm

45.5 S-Narrow-20 Soil

0
-100
100

72.0 S-Wide-24 Soil-L

0
-100
100

72.3 S-Narrow-20 Soil-L

0
-100
0

50

100

150

200

250

300

350

400

Time sec

Figure 5.17. Roof displacement time histories for U20B for 6 models in north-south
component. The maximum value is shown on the top right of each trace. Permanent roof
displacement is around 0.25 m for U20B in Model S-Wide Soil-L.

5.5.1 20-Story vs. 6-Story Buildings
From table 5.3 and figure 5.15, it is clear to find that 6-story buildings have larger peak
IDRs than 20-story buildings. However, they are much stronger than 20-story buildings as
discussed from pushover curves in section 2.2. The peak IDR for 6-story buildings closing
to collapse is much larger than that for 20-story buildings because of less P-Delta effects
and larger lateral force-resisting capacity. Therefore, directly comparing peak IDRs for thetwo types of buildings is meaningless.

96
More attention should be paid to the much larger deformations of 6-story buildings in Soil-

L model. It is induced by a striking response spectrum peak at 2 sec for Soil-L model(figure 5.13) when IBUH03 record is included in EGF database. This peak is close to thenatural period of U6 which is about 1.5 sec. J6P has a natural period of 1.15 sec which is at
the down hill of this peak, so its performance is much better than U6. Although J6B has thesame natural period with J6P, its performance is much worse than J6P with larger
deformation and more damage in strong motions. It is due to the greater nonlinearity
associated with welds fracturing and the building’s natural period increases during theshaking. Therefore, its performance can not be predicted obviously from response spectra.
It confirms the conclusion drawn in section 3.4.

5.5.2 Buildings with Brittle Welds vs. Perfect Welds
Table 5.3 and figure 5.15 also provide performance comparison between buildings withbrittle welds and with perfect welds. The peak IDRs of buildings with perfect welds are
significantly smaller than these of buildings with welds which are prone to facture. Thisdecrease of peak IDRs is significant larger than the decrease from Japanese buildings to
U.S. buildings, as we will discuss further in the next section. On the other hand, 20-story
buildings with perfect welds (20P) have larger maximum roof displacements (MRD) thanbuildings with brittle welds (20B). This opposite trend discloses that once the high-risebuildings yield under strong shaking, the deformation distribution patterns are different forbuildings with different welds condition. 20B concentrates deformation on weak floors
whereas 20P tries to extend the deformation to the whole buildings more evenly. To
illustrate it more clearly, the peak IDRs distributions along the height of the buildings areshown in figure 5.16 for U20B, U20P and U20E for one strong record. U20E refers to thebuilding in which material nonlinearity is removed. As a result, it would never yield asmentioned in section 3.4. Different from U20P and U20E whose peak IDRs changesmoothly above the 3rd floor, the peak IDR for U20B drops significantly from the 8th floor
to the 10th floor as shown in the figure. Most deformations are concentrated in story 6 to 8
of U20B. For low-rise buildings, this concentration is not so significant. As we can see

97from the pushover curves in figure 2.10, 20P has larger yielding displacements than 20B.

Therefore larger MRD in 20P does not imply that its performance is poor compared to 20B.

Figure 5.18. Distribution of peak IDRs along the height for U20 with brittle welds, perfectwelds and elastic elements (never yield at in strong shaking as discussed in section 3.4).
Curve marked with blue circles is for buildings with brittle welds. Curve marked with pinksquares is for buildings with perfect welds. Curve marked with green triangles is for elastic
buildings which are designed to be never yields in strong shaking. Unlike U20P and U20E
whose peak IDRs change smoothly above the 3rd floor, peak IDRs for U20B drop
significantly from the 8th story to the 10th story.

5.5.3 Stiffer vs. More Flexible Buildings
From table 5.3 and figure 5.15, we find that stiffer, stronger 20-story buildings which aredesigned according to Japanese building code (J20) do not perform as well as we expect. It
is surprising that in some models, J20 had greater damage than those designed according to
UBC94 (U20). For example, in Model S-Wide-24 Soil, J20B has larger peak IDR than
U20B although J20P has smaller peak IDR than U20P. The roof displacement time
histories for these building models are compared at figure 5.17. They also confirm that theadvantage of J20 over U20 is not universally suitable for all the ground motions. Thisphenomenon appears not only for Soil model, but also for Rock model and Soil-L model.

98Comparing with significant deformation reduction from retrofitting the fracture-prone

welds as discussed in the pervious section, increasing the strength capacity and stiffness are
not as efficient as fixing welds in this type of earthquakes.
For low-rise buildings, the advantage of J6 to U6 is striking. Table 5.3 and figure 5.15
show that 6-story Japanese buildings with perfect welds (J6P) have much smaller
deformation either in terms of peak IDR or in terms of MRD. It may imply thatstrengthening buildings is a powerful way to improve the earthquake resistance for low-risebuildings.

5.5.4 Responses of Buildings for Different Site Conditions
As expected, the deformation of all type of buildings at soil site is generally larger than thatat rock site especially when IBUH03 record with large PGV is used as an EGF. Since theresponse spectrum of records at IBUH03 has a peak at 2 sec (close to the natural period of
6-story buildings), motions from Model Soil-L could shake 6-story building more violently
than motions from other site condition.
Because the soil condition is unknown for the Sumatra area, soil synthetics in this study
depend completely on the stations recording Tokachi-Oki event. Therefore, it should be
more cautious to explain the simulated results for soil sites in the Sumatra event.

99
Roof Displacements EW

100

74.4 U20B

50

0

cm

cm

50

-50

cm

cm

0

0

-50
0

100

200
300
Time sec

400

-100

Roof Displacements EW

100

071.3 U20P

50

50

0

0

-50

100

200
300
Time sec

400

Roof Displacements NS

100

cm

cm

57.3 J20B

50-50

68.5 U20P

-50

-100
100

-100
100

82.2 J20P

50

50

0

0

cm

cm

0

-100
100
71.2 J20B

50

-50
-100

52.7 U20B

-50

-100
100

-100

Roof Displacements NS

100

72.9 J20P

-50
0

100

200
300
Time sec

400

-100

0

100

200
300
Time sec

400

Figure 5.19. Comparing roof displacements between flexible U20 and stiff stronger J20 inModel S-Wide-24 Soil. In this case, many J20 give larger roof displacements than U20
although in some other cases, J20 could give smaller roof displacements than U20. The
MRD value is listed on the top right for each trace. The advantage of stiffer high-risebuildings to flexible buildings can not be found here.

5.5.5 Comments on Long Duration Effects
Although our simulation did not show the collapse of building in this event, it is hard toconclude the none-collapsing for the real high-rise steel moment-frame buildings whichhave more deterioration mechanisms than our model. Recall in section 2.1.5, our FEM

100
building model did not consider any local buckling in the elements. This limitation may not

be significant for moderate crustal earthquakes (such as the 1994 Northridge earthquakeand 1995 Kobe earthquake) whose durations are around 10 to 30 seconds. However, for
giant subduction earthquakes strong shaking duration is very long. Our simulation presents
more than 3 minutes strong shaking in BAC for the Sumatra event (section 5.4.2) and morethan 5 minutes strong shaking in the Seattle basin for the Cascadia (section 6.4.2). Their
contribution could not be ignored. Because once structural damage is initiated, it tends toprogressively worsen as the number of large-amplitude cycles increases, for longer shaking,more damage will accumulate.
For low-rise buildings, the advantage of J6 to U6 is striking. Table 5.3 and figure 5.15
show that 6-story Japanese buildings with perfect welds (J6P) have much smaller
deformation either in terms of peak IDR or in terms of MRD. This tells us thatstrengthening buildings is a powerful way to improve the earthquake resistance for low-risebuildings.

Figure 5.20. An example of hysteresis loop obtained from the SAC experiment Test No.
UCSD-3R (SAC 1996). This is a steel specimen of beam with local flange buckling
occurred.

101
4

Left End of the Middle Beamin the 2nd Floor U20B

4

2

1.5

1.5

1

1

Moment M (kips-in)

Moment M (kips-in)

2

x 10

0.5
0
-0.5
-1

Left End of the Middle Beamin the 3rd Floor U20P

0.5
0
-0.5
-1
-1.5

-1.5
-2
-0.02

x 10

-0.01

0
0.01
Rotation θ

0.02

0.03

-2
-0.02

-0.01

0
0.01
Rotation θ

0.02

0.03

Figure 5.21. Examples of moment-rotation response (hysteresis loop) in an end of a beam
to the simulated ground motions. The left figure is for U20B. Since some fibers fractured
duration the shaking, resisting moment decreased suddenly. The right figure is for U20P.
Since local buckling is not considered in this model, stiffness and yielding strength are kept
constant after so many cycles. There is no degradation mechanism involved in the figure.

Figure 5.20 shows an example of a hysteresis loop for a beam obtained from the SAC testwith Test No. UCSD-3R (SAC 1996). This is a typical loop for the specimen with local
flange buckling and web distortion but no welds fracture occurring during the test. Its
yielding strength and stiffness were reduced as cyclic loading continued. For comparison,
figure 5.21 gives examples of strength-deformation response (i.e. hysteresis loop) of beams
for building model U20B and U20P to our simulated ground motion. The figure shows
clearly that there is no other degradation mechanisms involved in U20P during this long
shaking. Our simulation shows that buildings are heavily yielded during shaking but
continue to sway back and forth for the remaining one to two minutes (and three to four
minutes for the Cascadia event in section 6.4.2.). If more deterioration mechanisms are
considered in our model, the yield stress and stiffness of elements would decrease gradually
after plastic hinges are formed. With so many cycles after yielding, the roof displacements
may not be as stable as we show in figures 5.16, 5.17, 5.19 for 20-story buildings withperfect welds. And the real high-rise buildings would have performed significantly worse
than our simulation.

102This long duration also bring out the possibility of the stress decreasing because of thetemperature raise. As we know, most of the energy generated by plastic deformation of amaterial would transfer to the heat if there is no other energy exchange in the system. The
shaking from earthquake happens too quickly to allow heat transition. The heat could
concentrate on the connections and increase the steel temperature locally. To obtain theamount of temperature increase, we need to first calculate the plastic energy generated
duration the shaking. The amount of plastic energy can be classified as the area under the
stress-strain diagram up to a specified strain. This can be roughly expressed as:
ΔE (t ) =σ (τ )dε (τ )dV dτ
∫∫∫
τ

(5.1)

V , = 0 →t

At the same time, energy can be represented as the following equation in terms oftemperature change,
ΔE = mCΔT = ρVCΔT ,(5.2)

where C is the heat capacity of steel. So the temperature change can be roughly calculated
as

ΔT =

σ (τ ) dε (τ ) dV dτ∫∫∫τV , = 0→t

ρVC

.

(5.3)

Using this simplified method, we get that the temperature increase is no more than 100ºC
after 200 seconds strong shaking. It does not reach the threshold which would reduce steel
yield stress. However, it provides an idea to include deterioration mechanism in terms ofenergy in FEM model. Detailed description and applications are beyond the scope of thisthesis and can be regarded as future work.

103

CHAPTER 6

The Scenario Cascadia Subduction Earthquake Mw 9.2
Researchers have found that Cascadia subduction zone generated a giant earthquake (Mw>9.0) three hundred years ago and has a potential to generate another one in the future(Atwater, 1987; Heaton and Hartzell, 1987). The strong ground motions from this type ofearthquake will shake the inland cities such as Seattle, Portland and Vancouver where morethan 900 modern high-rise buildings exist. These modern designs have never been
examined by such large earthquakes except the 1985 Michoacan earthquake (M8.2) where
many 10- to 20-story modern designed buildings collapsed in Mexico city which is 400 km
away from epicenter (Anderson, Bodin P. et al., 1986; Hall and Beck, 1986). To
understand the performance of high-rise buildings under this scenario earthquake is of great
importance for earthquake engineers as well as residence in these areas.
In this chapter, the scenario Cascadia subduction earthquake is assumed to have the similarsource model as the 2004 Sumatra earthquake. Based on this assumption, we apply
empirical Green’s function method to estimate the strong ground motions in the city of
Seattle. We calculate the Settle basin amplification and simulate the responses of 20- and 6story steel moment frame buildings in this expecting event.

104

6.1 Introduction
The Cascadia subduction zone is a very long sloping fault that stretches from Brooks
Peninsula on Vancouver Island to Cape Mendocino in northern California. The recognitionof great earthquakes associated with Cascadia subduction zone began in the early 1980s.
Heaton and Kanamori (1984) firstly proposed this idea although scientists had longassumed that there is no great-earthquake potential in the Cascadia area. This argument
spurred a lot of debate until Atwater (1987) found geologic evidence of an great subduction
earthquake occurred 300 years ago. This earthquake also explained the mysterious tsunami
documented in Japanese historic literatures (Atwater, Satoko et al., 2005) and in native
Indian legend (Heaton and Snavely, 1985). For a detailed historic story, reader can refer
Nance’s book: On Shaky Ground (Nance, 1988). Nowadays, researchers have achievedconsensus that a giant earthquake (Mw >9.0) has rupture the Cascadia subduction zone in1700 from northern California to British Columbia and would return in the future.
More than half of the 900 existing high-rise buildings in the Cascadia area were constructed
before the great-subduction earthquake threat was reflected in the seismic design code in
1997 (Atwater, Satoko et al., 2005). Even for the newly constructed high-rise buildings, thelocal crustal earthquakes instead of the subduction earthquakes control the design (Whiteand Ventura, 2004). In this study, we focus on Seattle because there are lots of site
investigation results available (Frankel, Carver et al., 2002; Pratt, Brocher et al., 2003) inthis area. Although this great subduction earthquake would occur offshore and be morethan 250 km away from city of Seattle, long-period waves would attenuate slowly and may
get trapped and significantly amplified in the Seattle basin. A series of SHIPS
investigations were conducted (Pratt, Brocher et al., 2003; Pratt, 2006) and Pratt found thatthe amplifications of 0.3 to 0.8 Hz seismic waves can be as large as a factor of 6 to 8 in the
Seattle basin. Many engineers do not realize this and frame the Seattle seismic building
codes similar to California seismic building codes although they are threatened by very
different types of earthquakes. Therefore, numerical simulation of building’s response isnecessary to quantify the seriousness of this issue. Figure 6.1 shows an example of the105
modern high-rise buildings in downtown Seattle. Its unusual appearance in the foot basemay not be a good lateral force-resisting system for seismic purpose. If a future giant
subduction earthquake occurs in weekday, the collapse of these high-rise buildings would
generate a large death toll.

Figure 6.1. Rainer Tower in downtown Seattle. It is a 40-story building constructed at 1977.

6.2 Rupture Fault Models
The Cascadia subduction zone separates the Juan de Fuca and North America plates where
the Juan de Fuca plate is subducted beneath the North American plate along this 1300 kmlong zone at a convergence rate of 3 to 4 cm/year. Figure 4.4 has shown the cross section ofgeometry of this subduction zone. The Cascadia subduction zone shares many
characteristics with other subduction zones such as southern Chile where giant subduction
earthquakes have occurred (Heaton and Hartzell, 1987). A magnitude 9 earthquake would
occur if the whole subduction zone ruptured. Therefore, we use the source model from the2004 Sumatra-Andaman earthquake to estimate the hypothetical Cascadia subduction
earthquake.

106
In this study, three rupture models with different widths were proposed (figure 6.2). It isfound in Chapter 5 that the results are sensitive to the rupture width, considering different
widths cases would include this uncertainty in our modeling. The wider model extends
beyond the Olympic Mountain with a maximum rupture width 250 km. It is the same as thewide model used in the Sumatra event. The Olympic Mountain can be regarded as an outerarc ridge. Its counterpart in the 2004 Sumatra event is the Simenulue Island. The narrowmodel has a maximum rupture width 150 km and rupture extends to the coastline. This
coastline is approximately along the hinge line where rupture fault ends in elastic rupture
modeling. The intermediate model has a maximum rupture width 175 km. It extends moreinland than the narrow model but has not reached the Olympic Mountain.
The number of EGFs summing up together for each model is determined from the rupture
size ratio as recommend in Chapter 5. The wide model has 23 subfaults; the median modelhas 15 subfaults and the narrow model has 13 subfaults. Each subfault ruptures once. Theirgeometries are shown in figure 6.2. Notice that the overlap areas increase in narrow modelin order to better fit the shape of the Cascadia subduction zone. And the rupture length isaround 1200 km. Source parameters are listed in table 6.1. Again, results are not sensitive
to the slight changes of strike, dip, fault length and rupture velocity.

Table 6.1. Parameters for each model
Model Code
C-Wide-23
C-Med-15
C-Narrow-13

Strike
310º
/
** 0º

Dip

No. ofadded
EGF

No. ofruptureRuptureVel(km/s)

L
(km)

1

2.5
/
2.8

390
/
780

23
8º

15
13

W
(km)
175 ~ 250
100 ~ 175
100 ~ 150

m*

n*

3
/
6

2~3

*m is the number of subfaults along the fault length; n is the number of subfaults along the fault width;** The parameters for two segments are separated by ‘/’.

107(a) C-Wide-23(b) C-Med-15

Figure 6.2. Geometry of rupture fault
models used to simulate the Scenario
Cascadia Earthquake Mw9.2. Red
star represents the hypocenter of thisevent. Red dot represents thelocation where strong groundmotions would be simulated. Eachbox represents a subfault whose
response is simulated by the groundmotions recorded corresponding
station from the 2003 Tokachi-Oki
earthquake. Letters in each box
denote the subfault code. (a) shows
the wide rupture width model. (b)shows the median rupture widthmodel. (c) shows the narrow rupture
width model.

(c) C-Narrow-13

108

6.3 Teleseismic P-wave Simulations
Teleseismic P-waves are simulated for the above three models using four records from
Tokachi-Oki event as our empirical Green’s functions. These four records are shown in
Figure 5.5 and the method is completely the same as that discussed in section 5.3.
Distribution of EGFs is randomly assigned to the subfaults and the sets that used in our
simulation are shown in figure 6.3. Difference choices would only slightly affect theresulted peak amplitudes.
The simulated teleseismic P-waveforms at distance 60 o are exhibited in figure 6.4. Signals
recorded at station YSS in the Sumatra event are compared with our simulation. It indicatesthat estimated velocities and displacements are slightly smaller than the observed data for
all the three models but in the same scale. And the estimated accelerations are similar withrecordings. However, if the envelopes are compared, we found that model C-Wide-23
gives a best estimation.

Figure 6.3. Distribution of empirical Green’s functions used to simulate teleseismic P-waves fromthe expected Cascadia earthquake. Each box represents a subfault. Letters in the box refer tofigure 5.5 and designate which records from the 2003 Tokachi-Oki event are used as Green’s
functions. These records are chosen randomly from the four stations. Difference choices would
only slightly affect the resulted peak amplitudes. Star represents the hypocenter of the Cascadia
event. The top figure is for rupture model with wide width; the middle figure is for rupture modelwith intermediate width and the bottom figure is for rupture model with narrow width.

109
-4

-4

x 10

5

3.4e-004

C-Wide-23

-4

x 10

2.6e-004

0C-Med-15

-4

x 10

-5
5

2.5e-004

0

C-Narrow-13

-4

x 10

-5
5

2.8e-004

0
0

100

-4

x 10

-5
5
Vel m/sAccn m/s 2-5
5

200 300 400
Time sec

500

1.7e-004

0

x 10

-5
5

-5

-4

x 10

0

x 10

3.0e-004

0

0
-5
5
0
-5
5

C-Wide-23-2
2

C-Med-15-4x 10

2.5e-004

C-Narrow-13

-4

x 10
3.7e-004

Recorded at YSS

0
-5

0

100

200 300 400
Time sec

x 10
1.6e-003

0

-4

x 10

2.6e-004

100

500

600

-3

2

200 300 400
Time sec

500

600

Disp m (No Highpass)

Disp m-5
5

Recorded at YSS

2.3e-004-4

5

C-Narrow-13

1.7e-00400600

C-Med-15-4-5
5

Recorded at YSS

C-Wide-23

2.0e-004

0

0

-5

x 10

5

0
-2
2
0
-2
2

C-Wide-23

-3

x 10

1.1e-003

C-Med-15-3x 10

1.1e-003

C-Narrow-13

-3

x 10
1.4e-003

Recorded at YSS

0
-2

0

100

200 300 400
Time sec

500

600

Figure 6.4. Comparison of simulate teleseismic P-waveforms at distance 60o from threemodels with observed recordings at station YSS (Δ = 60.5º) in the Sumatra event.
Accelerations are shown in the top left, velocities are shown in the top right anddisplacements are shown in the bottom left. Data is highpassed at 0.05 Hz. Displacements
without filters are listed in the bottom right. Maximum value for each waveform is shownon the left. Detailed parameters for each model can be found in table 6.1. The distributionsof Green’s functions for these models are shown in figure 6.3.

110

6.4 Strong Ground Motion Simulations

6.4.1 Rock Sites
As discussed in section 5.4.1, we use strong ground motion recordings from the 2003
Tokachi-Oki event as the database for EGFs. The same as before, we first simulate thesynthetics at rock site in Seattle (station SEA) using data recorded at rock sites.
Classification of rock sites and soil sites were discussed in section 5.4.1. For each subfault,
there are several records within that central distance range and they are suitable to be an
EGF. Unlike the Sumatra event, this future giant Cascadia subduction earthquake has alarger uncertainty. Three sets of EGFs are chosen for each subfault to consider thisuncertainty. If a record which gives the maximum PGV is chosen as an EGF for thatsubfault, we call this model Max Model. If a record which gives the median PGV is chosen
as a Green’s function, we call this model Med Model. If a record which gives the minimum
PGV is chosen as a Green’s function, we call this model Min Model. Table 6.2 lists therecords chosen for each subfault in these three models. The reason to use PGV as achoosing criterion is that buildings’ response can be better predicted by PGV than PGA and
PGD which is discussed in section 3.4.
Considering different rupture fault widths and different EGF sets, there are nine models
simulated in total. They are C-Wide-23 Max; C-Med-15 Max; C-Narrow-13 Max; C-Wide23 Med; C-Med-15 Med; C-Narrow-13 Med; C-Wide-23 Min; C-Med-15 Min and CNarrow-13 Min, where “C” represents the Cascadia event. The simulated accelerations,velocities, displacements and response spectra (with 5% damping) at station SEA are
compared in figures 6.5 to 6.8, respectively. All of these synthetics are highpassed at 0.075
Hz (13.3 sec) to avoid displacements drift and be consistent with reliable frequency rangeof the transfer functions representing the Seattle basin amplification. This would be
discussed in more detail in the next section.

111
Table 6.2. Strong ground motions chosen to be empirical Green’s functions tosimulate motions of the scenario Cascadian earthquake experienced at rock sites in
Seattle (SEA).
Subfault
Code

CW23

CM15

CN13

A2
A3
B2
B3
C2
C3
D1
D2
D3
E1
E2
E3
F1
F2
F3
G1
G2
G3
H1
H2
H3
I2
I3
A2
B2
C2
D1
D2
E1
E2
F1
F2
G1
G2
H1
H2
I1
I2
A2
B2
C2
D2
E2
F1
F2
G1
G2
H1
H2
I1
I2

Dist
(km)
665.6
708.6
536.6
576.3
406.8
438.1
388.6
283.0
303.9
277.5
185.1
176.1
224.2
164.1
94.4
246.7
247.1
152.4
340.2
357.2
269.6
468.4
384.9
699.2
568.8
437.8
409.2
305.6
295.0
192.8
225.8
152.9
237.3
224.5
326.6
333.6
432.4
446.8
686.8
562.4
436.4
314.0
217.2
247.2
187.4
254.3
259.7
333.9
367.0
434.7
481.3

Max Model

Med Model

Sta Name

PGA
cm/s/sPGV
cm/s

FKS014
IBR006
MYG016
FKS007
IWT015
MYG003
IWT025
HKD020
HKD017
HKD020
HKD129HKD054
HKD117
HKD105
HKD084
HKD176
HKD176
HKD105
AOM018AOM018
HKD022
MYG011
AKT021
IBR006
FKS005
MYG003
IWT015
HKD017
HKD169
HKD129
HKD117
HKD105
HKD176
HKD117
HKD171HKD171
MYG002
MYG003
TCG006
FKS005
MYG003
HKD017
HKD130
HKD176
HKD129
HKD175
HKD022
HKD171
AKT003
MYG002
YMT002

2.5
6.5
4.3
5.1
6.7
10.9
6.5
7.6
9.7
7.6
86.7
54.0
27.6
141.6
353.8
47.2
47.2
141.6
11.1
11.1
34.2
29.5
3.6
6.5
6.8
10.9
6.7
9.7
29.6
86.7
27.6
141.6
47.2
27.6
6.7
6.7
22.5
10.9
3.7
6.8
10.9
9.7
58.0
47.2
86.7
27.2
34.2
6.7
8.1
22.5
3.2

0.7
1.0
1.3
0.9
1.4
1.0
1.3
6.8
9.5
6.8
39.8
16.2
12.5
43.3
50.7
9.3
9.3
43.3
4.5
4.5
10.1
1.3
1.3
1.0
1.1
1.0
1.4
9.5
6.8
39.8
12.5
43.3
9.3
12.5
2.9
2.9
1.3
1.0
0.8
1.1
1.0
9.5
20.6
9.3
39.8
9.2
10.1
2.9
3.9
1.3
2.1

Min Model

Sta Name

PGA
cm/s/sPGV
cm/s

Sta Name

PGA
cm/s/sPGV
cm/s

FKS014
IBR006
MYG016
FKS007
IWT015
MYG003
IWT025
HKD020
HKD018
HKD020
HKD124
HKD054
HKD131
HKD123
HKD095
AOM008AOM008
HKD088AOM029AOM029
HKD146
MYG011
AKT021
IBR006
FKS005
MYG003
IWT015
HKD018
HKD169
HKD124
HKD131
HKD088
HKD177
HKD131HKD171HKD171
MYG002
MYG003
TCG006
FKS005
MYG003
HKD018
HKD117
AOM008
HKD124
HKD030
HKD175
HKD171
AKT003
MYG002
YMT002

2.5
6.5
4.3
5.1
6.7
10.9
6.5
7.6
9.4
7.6
50.2
54.0
81.9
34.2
192.5
55.6
55.6
162.9
11.8
11.8
27.5
29.5
3.6
6.5
6.8
10.9
6.7
9.4
29.6
50.2
81.9
162.9
25.2
81.9
6.7
6.7
22.5
10.9
3.7
6.8
10.9
9.4
27.6
55.6
50.2
11.6
27.2
6.7
8.1
22.5
3.2

0.7
1.0
1.3
0.9
1.4
1.0
1.3
6.8
6.1
6.8
19.7
16.2
7.7
14.5
41.0
7.6
7.6
19.6
2.6
2.6
8.0
1.3
1.3
1.0
1.1
1.0
1.4
6.1
6.8
19.7
7.7
19.6
7.9
7.7
2.9
2.9
1.3
1.0
0.8
1.1
1.0
6.1
12.5
7.6
19.7
6.7
9.2
2.9
3.9
1.3
2.1

FKS014
IBR006
MYG016
FKS007
IWT015
MYG003
IWT025
AOM022
HKD170
AOM022
HKD035
HKD041
AOM004
HKD038
HKD096
AOM009AOM009
HKD101
IWT016
IWT016
AOM002
MYG011
AKT021
IBR006
FKS005
MYG003
IWT015
HKD170
AOM028
HKD035
AOM004
HKD101
HKD031
AOM004
HKD171HKD171
MYG002
MYG003
TCG006
FKS005
MYG003
HKD170
AOM004
AOM009
HKD035
HKD045
HKD045
HKD171
AKT003
MYG002
YMT002

2.5
6.5
4.3
5.1
6.7
10.9
6.5
26.1
6.4
26.1
14.1
45.0
26.2
192.0
200.3
35.4
35.4
47.0
15.1
15.1
22.8
29.5
3.6
6.5
6.8
10.9
6.7
6.4
28.4
14.1
26.2
47.0
11.9
26.2
6.7
6.7
22.5
10.9
3.7
6.8
10.9
6.4
26.2
35.4
14.1
10.0
10.0
6.7
8.1
22.5
3.2

0.7
1.0
1.3
0.9
1.4
1.0
1.3
2.8
2.3
2.8
7.0
8.0
3.8
12.5
34.5
4.6
4.6
11.8
1.6
1.6
2.9
1.3
1.3
1.0
1.1
1.0
1.4
2.3
3.8
7.0
3.8
11.8
5.5
3.8
2.9
2.9
1.3
1.0
0.8
1.1
1.0
2.3
3.8
4.6
7.0
4.0
4.0
2.9
3.9
1.3
2.1

112
Accn EW Highpass at 0.075 Hz Rock500

428.4 C-Wide-23 Max
0
-500
500

152.5 C-Med-15 Max

0
-500
500
87.5 C-Narrow-13 Max

0
-500
500

266.6 C-Wide-23 Med

Accn cm/s 2

0
-500
500

152.6 C-Med-15 Med

0
-500
500
50.3 C-Narrow-13 Med

0
-500
500

207.8 C-Wide-23 Min

0
-500
500
47.3 C-Med-15 Min

0
-500
500

35.0 C-Narrow-13 Min

0
-500

0

50

100

150

200
Time sec

250

300

350

400

350

400

Accn NS Highpass at 0.075 Hz Rock500

416.3 C-Wide-23 Max
0
-500
500
134.1 C-Med-15 Max

0
-500
500

101.5 C-Narrow-13 Max

0
-500
500

229.8 C-Wide-23 Med

Accn cm/s 2

0
-500
500
160.9 C-Med-15 Med

0
-500
500

76.7 C-Narrow-13 Med

0
-500
500

180.8 C-Wide-23 Min
0
-500
500
51.4 C-Med-15 Min

0
-500
500

37.6 C-Narrow-13 Min

0
-500

0

50

100

150

200
Time sec

250

300

Figure 6.5. Simulated accelerations for nine models at rock sites in SEA. A highpass filter
at 0.075 Hz is applied. Maximum value for each trace is shown in the front of the model
name. Top figure is for east-west component and bottom figure is for north-south
component.

113
Vel EW Highpass at 0.075 Hz Rock50

60.1 C-Wide-23 Max

0
-50
50

38.7 C-Med-15 Max

0
-50
50

39.0 C-Narrow-13 Max

0
-50
50

54.6 C-Wide-23 Med0

Vel cm/s-50
50

21.4 C-Med-15 Med

0
-50
50

20.2 C-Narrow-13 Med

0
-50
50

32.2 C-Wide-23 Min

0
-50
50

20.4 C-Med-15 Min

0
-50
50

5.3 C-Narrow-13 Min

0
-50
0

50

100

150

200
Time sec

250

300

350

400

300

350

400

Vel NS Highpass at 0.075 Hz Rock50

78.1 C-Wide-23 Max

0-50

38.5 C-Med-15 Max

50
0
-50

38.4 C-Narrow-13 Max

50
0
-50

43.0 C-Wide-23 Med

50
0Vel cm/s-50
50

13.8 C-Med-15 Med

0
-50
50

17.6 C-Narrow-13 Med

0
-50
50

23.9 C-Wide-23 Min

0
-50
50

16.2 C-Med-15 Min

0
-50
50

6.3 C-Narrow-13 Min

0
-50
0

50

100

150

200
Time sec

250

Figure 6.6. Simulated velocities for nine models at rock sites in SEA. A highpass filter at
0.075 Hz is applied. Maximum value for each trace is shown in the front of the model
name. Top figure is for east-west component and bottom figure is for north-south
component.

114
Disp EW Highpass at 0.075 Hz Rock50

36.8 C-Wide-23 Max

0
-50
50

30.1 C-Med-15 Max

0
-50
50

36.9 C-Narrow-13 Max

0
-50
50

35.5 C-Wide-23 Med0

Disp cm-50
50
20.6 C-Med-15 Med

0
-50
50

19.2 C-Narrow-13 Med

0
-50
50

17.2 C-Wide-23 Min

0
-50
50

18.8 C-Med-15 Min

0
-50
50

7.3 C-Narrow-13 Min

0
-50

0

50

100

150

200
Time sec

250

300

350

400

350

400

Disp NS Highpass at 0.075 Hz Rock50

35.2 C-Wide-23 Max

0
-50
50

23.6 C-Med-15 Max

0
-50
50

28.6 C-Narrow-13 Max

0
-50
50

35.5 C-Wide-23 Med0

Disp cm-50
50
14.3 C-Med-15 Med

0
-50
50

17.2 C-Narrow-13 Med
0-50
50
16.1 C-Wide-23 Min

0
-50
50

16.3 C-Med-15 Min

0
-50
50

8.6 C-Narrow-13 Min
0
-50

0

50

100

150

200
Time sec

250

300

Figure 6.7. Simulated displacements for nine models at rock sites in SEA. A highpass filter
at 0.075 Hz is applied. Maximum value for each trace is shown in the front of the model
name. Top figure is for east-west component and bottom figure is for north-south
component.

115

Figure 6.8. Pseudo spectral velocities for simulated data at rock sites in SEA with 5%
damping. The top figure is for east-west component and the bottom figure is for northsouth component. If two extreme cases (C-Wide-24 Max and C-Narrow-13 Min) areexcluded, the pseudo spectral velocity are concentrated on a belt (shaded by grey lines)
where C-Wide-23 Med gives the upper limit and C-Narrow-13 Med gives the bottom limit.
The peaks appear at 2 to 5 sec. Red lines are for wide models, blue lines are for medianmodels and green lines are for narrow models.

116
Large variation can be found in the results. Since there are so many unknowns, it is hard todetermine which one is the best. However, from statistical point of view, two extreme cases:
Model C-Wide-24 Max which gives very large results and Model C-Narrow-13 Min which
gives very small results, could be excluded. After this exclusion, the pseudo spectral
velocity are concentrated on a belt in figure 6.8 where C-Wide-23 Med gives the upper
limit and C-Narrow-13 Med gives the lower limit. Therefore, we can focus more attention
on models using median PGV.
If Med Model is considered, the estimated PGA is around 0.25 g for wide model, 0.15 g formedian model and 0.05 g for narrow model. The estimated PGV is around 50 cm/s for widemodel and 20 cm/s for median and narrow model. The same as before, wide models givelarger values than narrow models. These values are comparable to the results from Sumatra
event. Pseudo spectral velocity has a peak around 2 to 5 sec.

6.4.2 Site Amplification
The city of Seattle is located in Puget Sound. This region is home to the majority ofWashington State citizens. Beneath the sound, there are three major sedimentary basins:
Everett, Seattle and Tacoma. The deepest and most studied is the Seattle basin which is 70
km by 30 km, 7 to 9 km deep (Johnson, Potter et al., 1994; Pratt, Johnson et al., 1997;
Brocher, Parsons et al., 2001). Portions of the city of Seattle are also underlain by artificial
fill created by hydraulically sluicing dirt from downtown hills onto the nearby tide flats(Galster and LaPrade, 1991). Vs30 is investigated to be 140 to 680 m/sec in Seattle(Williams, Stephenson et al., 1999).
Recently, many researchers have found the large seismic amplifications in the Seattle
region. Analysis of arrivals from local Nisqually earthquake M6.8 (Frankel, Carver et al.,2002), regional Denali earthquake Mw7.9 (Barberopoulou, Qamar et al., 2004) andteleseismic Chi-Chi earthquake Mw7.6 (Pratt, Brocher et al., 2003) all indicated that the
Seattle basin amplifies seismic waves with peak amplifications in the 0.2 to 0.5 Hz range.

117
Forward computer models also predict the amplification of low-frequency seismic waves(Frankel and Stephenson, 2000; Pitarka, Graves et al., 2004). At higher frequency ranges,
the effects are variable but most sites show decreasing amplification with increasing
frequency (Pratt, Brocher et al., 2003).
Fortunately, Seattle area has considerable more information of site condition than theSumatra region. In this study, we use teleseismic S-waves collected by the SHIPS02 (the2002 Seismic Hazard Investigation of Puget Sound) study to estimate the transfer functionof the Seattle basin. Frequency domain analysis has been widely used to reveal site
amplification because it could clearly show the amplification factor for a certain frequency
range. However, it disregards the phase information and could not disclose the longer
duration caused by basin effects that is crucial for building’s response. To overcome thesedisadvantages, we propose a time domain analysis. In this empirical analysis, the main
target is to achieve a transfer function which transfers rock records to basin records. Thismethod is based on an assumption that the site response is linear. Most nonlinearity of site
response is generated by shallow soil structure and would deamplify the high-frequency
motions. However, for long-period motions (<1 Hz), the nonlinearity can be ignored andlinear assumption is reasonable. Therefore, we can extrapolate site amplification derived
from weak motions to site amplification for strong motions.
6.4.2.1 Data

The SHIPS project consisted of a series of studies designed specifically to help characterize
the seismic hazard in the region. In SHIPS02, 85 seismometers were installed throughout
the central Puget Lowland to record ground motions between January and May, 2002 (Pratt,2006). Four teleseismic earthquakes with magnitude 7.1 to 7.5 were recorded with clear Swave arrivals (table 2 in Pratt’s paper 2006). The sites were classified into 5 sets based on
the underlying geologic structures and shallow deposits. Teleseismic S-waves (withduration = 100 sec) from bedrock sites and the Seattle basin sites are used in our analysis.
6.4.2.2 Method

118
The purpose of our method is to find transfer functions which satisfy,
Rock (t ) * G (t ) = Basin(t ) ,(6.1)

where Rock(t) is a teleseismic S-waves recorded at bedrock site, Basin(t) is a teleseismic Swaves recorded at the Seattle basin site and G(t) is a transfer function. A band-pass filter at
0.075 to 1 Hz is applied to all Rock(t) and Basin(t) recorded at SHIPS02 experiment.
Amplifications for high-frequency (>1 Hz) motions is not considered because of the large
varied amplification ratio and nonlinearity associated with the site response. Very lowfrequency (< 0.1 Hz) signals are not reliable because of the low signal-to-noise ratio for 2
Hz sensor used in SHIPS02 experiment (Pratt, 2006). Therefore, we define the frequency
band 0.075 to 1 Hz in our calculation.
Basin(ω )G(t) can be deconvolved in frequency domain by Gˆ (ω ) =. However, exactRˆ ock (ω )deconvolution would contaminate important characteristics of transfer functions byrecovering the noises. Therefore, this inversion problem is widely solved by linear leastsquares methods in time domain. The jth component of Basin(t) can be written as,N

b j = (r * g ) j = ∑ rk g j −k

(6.2)

k =1

where rj is the jth component of Rock(t) and gj is the jth component of G(t); N is the total
length of the signal. In order to remove the end effects, we pad N zeros at the beginning of
the rock and basin recordings. The matrix form of this equation can be written as,
⎡ r1
⎢r
⎢2
⎢ r3
⎢
⎢
⎢
⎢
⎣⎢rn

rn
r1
r2

rn−1

rn−1 … … r2 ⎤ ⎡ g1 ⎤ ⎡ b1 ⎤rn … … r3 ⎥⎥ ⎢⎢ g 2 ⎥⎥ ⎢⎢b2 ⎥⎥r1 … … r4 ⎥ ⎢ g 3 ⎥ ⎢b3 ⎥⎥⎢ ⎥ ≅ ⎢ ⎥ ,… …
⎥⎢ ⎥ ⎢ ⎥⎥⎢ ⎥ ⎢ ⎥… …
⎥⎢ ⎥ ⎢ ⎥rn−2 … … r1 ⎦⎥ ⎣⎢ g n ⎦⎥ ⎣⎢bn ⎦⎥

(6.3)

119
where n=2N because of the zero padding. This matrix form can be denoted as
Ax ≅ b where x is deconvolved by least squares methods. In general, the solution isunstable because A is an ill-conditioned matrix that means a small change in the data results
in a large change in the solution. This problem can be stabilized by appending linear
stability constraints generated through singular value decomposition. That is,
⎡ A⎤
⎡ b ⎤
x
≅
⎢⎣ λF ⎥⎦⎢⎣ λd ⎥⎦ .

(6.4)

Decompose singular values of A as A = USV T where U and V are orthogonal matrices, S isthe diagonal matrix of singular values and T indicates the transpose of the matrix. Then
F=VHVT and d = 0, where⎧ H ii = 0 i ≤ k⎪
H = ⎨ H ii = 1 i > k .
⎪H = 0 i ≠ j
⎩ ij

(6.5)

This stability constraint is basically a highpass filter to the singular values of A matrix. Fora detailed description, readers can refer to Olson and Apsel (1982). We choose k = 150 for
the 1000×1000 matrix H in this study. Final results are not sensitive to k changing from 100
to 300. λ(t) is a weight function. To concentrate the main components of transfer function
at the beginning, we use an exponential decay function for the first 90 sec in weightfunction and set λ(t>90) = 0.
6.4.2.3 Results

A transfer function can be obtained from each pair of rock and basin records. Figure 6.9
shows an example. Once a transfer function is determined, it can be convolved with therock synthetics to predict the strong ground motions in basin sites. The results vary whenusing transfer functions obtained from different pairs of rock basin sets. To simplify our
method in a statistical way, the transfer function which could give a median PGV of basin

120synthetics is chosen as our standard transfer function to represent the Seattle basin effects.

Figure 6.9 shows this representative transfer function.
The representative transfer function convolves with strong ground motions simulated atrock sites to estimate the motions in the Seattle basin. Figure 6.10 shows the Fourier
spectra of the rock synthetics, transfer function and basin synthetics. We assume that there
is no amplification in high-frequency range. So the frequency components larger than 1 Hz
are set to be 1 for the transfer function. Figure 6.11 shows the time histories of the rock andbasin synthetics. It can be found that the amplification is much more significant forvelocities than for accelerations. This is reasonable because amplification in highfrequency components is not considered here. As we expected, the transfer function not
only amplifies the amplitude of rock motions by 2.5 to 6 times but also significantly
elongates the duration of strong shakings by 150 to 200 sec.
Figures 6.12 to 6.15 plot the simulated strong ground accelerations, velocities,
displacements and pseudo spectral velocity with 5% damping at the Seattle basin in SEA
for nine models discussed in the previous section. The same as the results for rock sites,
there is a substantial variation for motions generated from different models. North-south
direction has stronger motions than east-west directions because of the large transfer
function in north-south direction. Excluding two extreme cases (C-Wide-23 Max and CNarrow-13 Min), PGA is estimated around 0.1 to 0.4 g for east-west direction and 0.2 to
0.6 g for north-south direction. PGV is around 50 to 120 cm/s for east-west direction and
80 to 300 cm/s for north-south direction. PGD is around 30 to 100 cm for east-west
direction and 50 to 150 cm for north-south direction. The variable range is about 3 times.
The pseudo spectral velocities show peaks at 1, 3 and 8 sec for east-west direction and 2 to
6 sec for north-south direction. Figure 6.16 compares the simulated PGA and PGV for ninemodels at rock sites and at the Seattle basin at station SEA.

121

Vel cm/s

1
0
-1
1

x 10

-3

Records
Recoverd

EW Rock site: 7295
x 10 RockEW Basin site: 7335
-3

0

Basin

10
-1

Transfer function EW

0
-10
0
10

50

100
Time sec
Amplified transfer function EW

0
-10

0

5
-3

Vel cm/s

1
0
-1
1

15

20
Records
Recoverd

x 10 RockNS Basin site: 7335
-3

Basin

10
-1

Transfer function NS

0
0

10
0
-10

200

x 10
NS Rock site: 7295

0

-10

10
Time sec

150

0

50

100
Time sec
Amplified transfer function NS

5

10Time sec

150

200

15

20

Figure 6.9. Resulting transfer functions time history (the 3rd trace) deconvolved teleseismic
S-waves recorded in rock site 7295 (the 1st trace) from basin site 7335 (the 2nd trace) in the2002 Taiwan M7.1 earthquake. This transfer function is chosen to represent the Seattle
basin effects since it results median basin motion PGV. It is shown in large scale in the 4th
trace. The top figure is for east-west component and the bottom figure is for north-south
component. Station names are listed in table 1 in Pratt’s paper (2006).

122

Figure 6.10. Convolve transfer function (middle column) with simulated ground motions atrock sites (left column) to get motions at basin sites (right column) in frequency domain.
For transfer function, frequency larger than 1 Hz is set to be 1. This assumes that there is
no amplification in high-frequency range. The top figure is for east-west component andthe bottom figure is for north-south component.

123
EW C-Med-15 Medvel cm/s

100

Rock Vel: 21.4

0
-100
100
Basin Vel: 51.8 GF:7295-7335
0
-100

0

accn cm/s 2

200

50

100

150

200

250
300
Time sec

350

400

450

500

350

400

450

500

350

400

450

500

350

400

450

500

Rock Accn: 152.6

0
-200
200

Basin Accn: 172.3 GF:7295-7335

0
-200

0

50

100

150

vel cm/s

250
300Time sec

NS C-Med-15 Med

100
Rock Vel: 13.8

0
-100
100

Basin Vel: 84.1 GF:7295-7335

0
-100

0

200
accn cm/s 2

200

50

100

150

200

250
300
Time sec

Rock Accn: 161.0

0
-200
200

Basin Accn: 202.8 GF:7295-7335

0
-200

0

50

100

150

200

250
300
Time sec

Figure 6.11. A pair of simulated velocities and accelerations in rock sites and basin sites.
The representative transfer function is used to amplify rock motions. The top figure is foreast-west component and the bottom figure is for north-south component. Maximum
values are shown in the top left for each signals. The amplification is much moresignificant for velocities than for accelerations. NS component has larger amplification
than EW component. The transfer function not only amplifies the amplitude of rockmotions but also significantly elongates the duration of strong shakings.

124
Accn EW Highpass at 0.075 Hz Soil
500

665.9 C-Wide-23 Max

0
-500
500

358.2 C-Med-15 Max

0
-500
500

311.3 C-Narrow-13 Max
0
-500
500
418.8 C-Wide-23 Med

Accn cm/s 2

0
-500
500
172.3 C-Med-15 Med

0
-500
500

131.1 C-Narrow-13 Med

0
-500
500

276.3 C-Wide-23 Min
0
-500
500
102.7 C-Med-15 Min

0
-500
500

48.8 C-Narrow-13 Min
0
-500

0

50

100

150

200
Time sec

250

300

350

400

350

400

Accn NS Highpass at 0.075 Hz Soil
500

741.5 C-Wide-23 Max

0
-500
500

356.7 C-Med-15 Max

0
-500
500

263.0 C-Narrow-13 Max

0
-500
500

577.5 C-Wide-23 Med

Accn cm/s 2

0
-500
500

202.8 C-Med-15 Med

0
-500
500

226.3 C-Narrow-13 Med

0
-500
500

300.0 C-Wide-23 Min

0
-500
500

152.4 C-Med-15 Min

0
-500
500

66.4 C-Med-13 Min
0
-500

0

50

100

150

200
Time sec

250

300

Figure 6.12. Simulated accelerations for nine models at the Seattle basin. A highpass filter
at 0.075 Hz is applied. Maximum value for each waveform is shown in front of the model
name. Top figure is for east-west component and bottom figure is for north-south
component.

125
Vel EW Highpass at 0.075 Hz Soil200

224.7 C-Wide-23 Max

0
-200
200

103.7 C-Med-15 Max

0
-200
200

123.8 C-Narrow-13 Max

0
-200
200

120.4 C-Wide-23 Med0

Vel cm/s-200
100
50.4 C-Med-15 Med
0
-100
100
46.9 C-Narrow-13 Med
0
-100
100
92.3 C-Wide-23 Min

0
-100
100

39.7 C-Med-15 Min

0
-100
100

17.1 C-Narrow-13 Min
0
-100

0

200

50

100

150
200
250
300
Time sec
Vel NS Highpass at 0.075 Hz Soil

350

400

350

400

226.2 C-Wide-23 Max

0
-200
200

221.6 C-Med-15 Max

0
-200
200

130.7 C-Narrow-13 Max

0
-200
200

289.1 C-Wide-23 Med0

Vel cm/s-200
100

83.6 C-Med-15 Med

0
-100
100
81.5 C-Narrow-13 Med
0
-100
100
102.3 C-Wide-23 Min

0
-100
100

53.8 C-Med-15 Min

0
-100
100

24.9 C-Narrow-13 Min

0
-100

0

50

100

150

200
Time sec

250

300

Figure 6.13. Simulated velocities for nine models at the Seattle basin. A highpass filter at
0.075 Hz is applied. Maximum value for each trace is shown in the front of the model
name. Top figure is for east-west component and bottom figure is for north-south
component. Notice the different y-axis scales for the top 4 and bottom 5 traces.

126
Disp EW Highpass at 0.075 Hz Soil200

109.4 C-Wide-23 Max

0
-200
200

79.4 C-Med-15 Max

0
-200
200

101.6 C-Narrow-13 Max

0
-200
200

71.6 C-Wide-23 Med0

Disp cm-200
100
30.8 C-Med-15 Med

0
-100
100

31.8 C-Narrow-13 Med

0
-100
100

42.6 C-Wide-23 Min

0
-100
100

30.9 C-Med-15 Min

0
-100
100

17.6 C-Narrow-13 Min

0
-100

0

50

100

150

200
Time sec

250

300

350

400

350

400

Disp NS Highpass at 0.075 Hz Soil200

149.3 C-Wide-29 Max

0
-200
200
173.5 C-Wide-29 Max

0
-200
200

93.4 C-Wide-29 Max

0
-200
200
158.6 C-Wide-29 Max
0

Disp cm-200
100
69.4 C-Wide-29 Max

0
-100
100

74.9 C-Wide-29 Max

0
-100
100

51.0 C-Wide-29 Max
0
-100
100
50.6 C-Wide-29 Max

0
-100
100

25.7 C-Wide-29 Max

0
-100

0

50

100

150

200
Time sec

250

300

Figure 6.14. Simulated displacements for nine models at the Seattle basin. A highpass filter
at 0.075 Hz is applied. Maximum value for each trace is shown in the front of the model
name. Top figure is for east-west component and bottom figure is for north-south
component. Notice the different y-axis scales for the top 4 and bottom 5 traces.

127
3

10

Pesudo Spectral Veloctiy EW Basin 5% damping

C-Wide-23 Max
C-Med-15 Max
C-Narrow-13 Max
C-Wide-23 Med
C-Med-15 Med
C-Narrow-13 Med
C-Wide-23 Min
C-Med-15 Min
C-Narrow-13 Min

2

cm/s

10

1

10

0

10
0.1

3

10

1
Period sec

10

Pseudo Spectral Veloctiy NS Basin 5% damping

C-Wide-23 Max
C-Med-15 Max
C-Narrow-13 Max
C-Wide-23 Med
C-Med-15 Med
C-Narrow-13 Med
C-Wide-23 Min
C-Med-15 Min
C-Narrow-13 Min

2

cm/s

10

1

10

0

10
0.1

1
Period sec

10

Figure 6.15. Pseudo spectral velocities for simulated data at the Settle basin with 5%
damping. The top figure is for east-west component and the bottom figure is for northsouth component. Excluding two extreme cases (C-Wide-23 Max and C-Narrow-13 Min),
Pseudo spectral velocities are mostly concentrated in a belt limited by Med Models (soiledlines). Red lines are for wide models, blue lines are for median models and green lines arefor narrow models.

128

PGA cm/s 2

400
200

300

600
400
200
0

W M N W M N W M N
max
med
min
PGV EW

250

200

200

100
50
0

W M N W M N W M N
max
med
min
PGV NS

300

250

150

PGA NS

800

Rock
Basin

600

0

PGV cm/s

PGA EWPGV cm/s

PGA cm/s 2

800

150
100
50

W M N W M N W M N
max
min
med

0

W M N W M N W M N
max
min
med

Figure 6.16. Comparing simulated PGA and PGV for nine models at rock sites and at the
Seattle basin at station SEA. The left column is for east-west component and the rightcolumn is for north-south component.

6.5 Nonlinear Performance of Buildings
All of the strong ground motions obtained from rock sites and basin sites in nine models
are used to simulate the nonlinear responses of 20- and 6-story buildings as discussed in
Chapter 2. As before, we list peak interstory drift ration (IDR %) in table 6.3 to get an
insight to the performance of buildings. From these results, we find that many buildings
collapse in basin sites although their performances are acceptable for safety purpose in rocksites. Since there is a large variation in the results, we focus more attention on Med Model.
Figure 6.17 compares the peak IDRs and MRDs for different models. We would discuss inmore detail in the following for different types of buildings.

129
Table 6.3. PGA and PGV of simulated strong ground motions at station SEA andperformance of 20- and 6- story buildings shaken by these motions.
Rock
Basin
C-Wide-23
C-Med-15
C-Narrow-13 C-Wide-23
C-Med-15
C-Narrow-13
Direction
EW
NS
EW
NS
EW
NS
EW
NS
EW
NS
EW
NS
max
428
416
153
134
88
102
666
742
358
357
311
263
PGA
med
267
230
153
161
50
77
419
578 172
203
131
226
2
cm/s
276
300
103
152
49
66
min
208
181
47
51
35
38
max
60
78
39
39
39
38
227
227
103
222
127
131
PGV
med
55
43
21
14
20
18
121
290
52
84
48
82
cm/s
min
32
24
20
16
5
6
92
103
41
54
18
25
3.0
2.3
2.1
2.6
2.0
2.0
CO
CO
CO
CO
CO
CO
U20B max
IDR med
1.6
2.3
0.6
0.4
0.6
0.4
CO
CO
1.5
CO
2.3
CO
(%) min
2.1
CO
2.1
CO
0.5
1.3
0.6
0.7
0.7
0.4
0.1
0.1
1.0
1.2
0.6
1.0
0.8
1.4
CO
CO
3.0
CO
CO
CO
U20P max
IDR med
1.4
1.8
0.4
0.3
0.4
0.3
CO
CO
1.2
2.4
1.2
2.9
(%) min
0.4
0.5
0.4
0.3
0.1
0.1
1.5
1.7
1.0
2.2
0.4
0.6
J20B max
2.8
2.1
1.1
2.2
0.9
2.5
CO
CO
CO
CO
CO
CO
2.3
2.6
0.4
0.3
0.5
0.3
CO
CO
1.9
CO
2.1
4.4
IDR med(%) min
0.9
0.5
0.4
0.2
0.1
0.1
1.6
CO
2.4
4.3
0.7
0.3
1.0
1.1
0.5
0.5
0.5
0.7
CO
CO
CO
6.2
5.0
CO
J20P max
IDR med
1.0
1.2
0.4
0.3
0.4
0.3
4.2
CO
1.1
1.2
1.0
0.9
(%) min
0.5
0.4
0.4
0.2
0.1
0.1
1.9
1.2
1.1
1.0
0.5
0.3
U6B max
1.8
2.0
1.3
1.1
0.9
0.7
CO
CO
CO
CO
CO
CO
IDR med
1.6
1.2
0.3
0.2
0.2
0.4
CO
CO
2.1
3.5
1.7
3.5
(%) min
1.5
1.0
0.2
0.3
0.1
0.1
3.9
4.7
1.3
3.4
0.3
0.6
1.6
2.1
1.0
0.8
0.8
0.5
CO
CO
CO
CO
4.7
CO
U6P max
IDR med
1.0
1.0
0.3
0.2
0.2
0.4
CO
CO
1.3
1.9
1.1
1.8
(%) min
1.1
0.9
0.2
0.3
0.1
0.1
4.6
4.7
1.2
1.8
0.3
0.5
J6B max
1.1
1.5
0.7
0.5
0.4
0.3
CO
CO
CO
CO
5.4
CO
0.8
0.6
0.2
0.2
0.1
0.2
CO
CO
0.8
1.9
0.6
1.9
IDR med(%) min
0.6
0.3
0.1
0.2
0.1
0.1
3.9
3.5
0.7
2.0
0.3
0.4
0.9
1.4
0.6
0.5
0.4
0.3
CO
CO
3.1
3.8
2.3
2.4
J6P max
IDR med
0.6
0.5
0.2
0.2
0.1
0.2
2.4
CO
0.8
0.8
0.7
1.2
(%) min
0.5
0.3
0.1
0.2
0.1
0.1
2.4
2.4
0.7
1.1
0.3
0.4
Red cells with CO represent that buildings collapse in those cases. Organge cells denote large peak IDRs. In these cases,
buildings are severely damaged and close to. Yellow cells denote the cases associated with large deformation and damaged
Results from Med Model are shown in blue and emphasized by grey background. Results from Max Model are shown inblack and results from Min Model are shown in purple.
Model Name

130
20-story Buildings EW

20-story Buildings NS

CollapsePeak IDR %

4
3

5

U20B
U20P
J20B
J20P

4
Peak IDR %

5

2
1
0

3
2
1

WR MR NR WB MB

0NBWR MR NR WB MB

NB

6-story Buildings NS

6-story Buildings EW
CollapsePeak IDR %

4

U6B
U6P
J6B
J6P

5
4
Peak IDR %

5

3
2
1
0

3
2
1

WR MR NR WB MB

0

NB

20-story Buildings EW

150

200

U20B
U20P
J20B
J20P

100
50
0

WR MR NR WB MB

NB

20-story Buildings NS

Max Roof Disp cm

Max Roof Disp cm

Collapse
200

WR MR NR WB MB

150
100
50
0

NB

6-story Buildings EW

WR MR NR WB MB

NB

6-story Buildings NS

Collapse

Max Roof Disp cm

50
40

60

U6B
U6P
J6B
J6P

50
Max Roof Disp cm

60

30
20
10
0

WR MR NR WB MB

NB

40
30
20
10
0

WR MR NR WB MB

NB

Figure 6.17. Peak interstory drift ratio (top) and maximum roof displacements (bottom) of
20- and 6- story buildings at rock and basin sites for Med Models. X-axis lists the model
names. Due to the limited space, we abbreviate wide model as W, median model as M,
narrow model as N, rock model as R, basin model as B. We put all the collapsed cases in
red rectangular boxes.

131

6.5.1 20-Story vs. 6-Story Buildings
6-story buildings perform much better than 20-story buildings. Most of them have smaller
IDRs than 20-story buildings although their strength capacities are much larger than 20story buildings. 6-story buildings located in Seattle basin would collapse for wide model,
while they are strong enough to avoid collapse for all the other models. The performanceof J6P is strikingly better than U6P or J6B. The building is mostly in linear range when
shaken by rock motions and has much smaller IDRs when shaken by basin motions frommedian width and narrow width models.

6.5.2 Buildings with Brittle Welds vs. Perfect Welds
Table 6.3 and figure 6.17 provide response comparison between buildings with brittle
welds and with perfect welds. Perfect welds in buildings could largely reduce the peak IDRand, prevent buildings collapse in certain cases. Figure 6.18 directly compare theperformances of U20 with two type welds in Med Model. Due to the small deformations ineast-west direction, there is no large difference for the performance of buildings with brittle
and perfect weld. However, in north-south direction, all U20B collapse in basin sites
whereas U20P do not collapse in med and narrow models. Comparing with strengthening
and stiffening high-rise buildings, fixing brittle welds is a more efficient way to increase
the capacity of buildings especially for high-rise buildings.

132
Roof Displacements EW U20B

100

62.8 C-Wide-23 Rock

0
-100
100
41.4 C-Med-15 Rock

0
-100
100

36.9 C-Narrow-13 RockRoof Disp cm

0
-100
200

Collapse C-Wide-23 Basin
0
-200
100
50.0 C-Med-15 Basin
0
-100
100

79.3 C-Narrow-13 Basin

0
-100

0

50

100

150

200

250
300
Time sec

350

400

450

500

Roof Displacements EW U20P

100

82.7 C-Wide-23 Rock

0
-100
100
41.9 C-Med-15 Rock

0
-100
100

37.1 C-Narrow-13 RockRoof Disp cm

0
-100
200
Collapse C-Wide-23 Basin

0
-200
100

74.7 C-Med-15 Basin

0
-100
100
84.6 C-Narrow-13 Basin
0
-100

0

50

100

150

200

250
300
Time sec

350

400

450

500

Figure 6.18. Compare roof displacement time histories for U20B and U20P to six Med
Models in east-west component. The maximum value is shown on the top right of eachtrace. In this direction, there is not much difference for buildings with brittle welds andperfect welds because of the small deformations.

133
Roof Displacements NS U20B

100

69.1 C-Wide-23 Rock
0
-100
100
30.4 C-Med-15 Rock
0
-100
100
26.7 C-Narrow-15 RockRoof Disp cm

0
-100
200

Collapse C-Wide-23 Basin

0
-200
200

Collapse C-Med-15 Basin

0
-200
200

Collapse C-Narrow-13 Basin

0
-200

0

50

100

100

150

200

250
300
350
Time sec
Roof Displacements NS U20P

400

450

500

88.5 C-Wide-23 Rock
0
-100
100
31.4 C-Med-15 Rock

0
-100
100

27.0 C-Narrow-13 RockRoof Disp cm

0
-100
200

Collapse C-Wide-23 Basin

0
-200
100
100.7 C-Med-15 Basin
0
-100
100

126.8 C-Narrow-13 Basin

0
-100
0

50

100

150

200

250
300
Time sec

350

400

450

500

Figure 6.19. Compare roof displacement time histories for U20B and U20P to six Med
Models in north-south component. The maximum value is shown on the top right of eachtrace. In this direction, motions in basin sites cause all U20B collapse whereas did notcause U20P collapse in med and narrow models.

134

6.5.3 Stiffer vs. More Flexible Buildings
From table 6.3 and figure 6.17, we find that the performance of stiffer stronger Japanese
high-rise buildings especially with perfect welds have smaller IDRs than corresponding
more flexible U.S. Buildings. This statement seems conflict with the results we obtained
from the Sumatra event where there is no evidence of advantage of J20 over U20. To
explain this conflict, we need to refer the frequency contents of the ground motions. Recall
that the natural period of U20 is about 3.5 sec and natural period of J20 is about 3.15 sec.
Pseudo spectral velocity for Sumatra event (figure 5.12) has a peak around 2 sec for Soil-L
model. So PSV3.5 is smaller than PSV3.15 especially in the north-south direction. This
explains the better performance of flexible buildings to stiffer buildings. In the Cascadia
event, pseudo spectral velocity (figures 6.8 and 6.15) has several local peaks and it causes
PSV3.5 larger than PSV3.15 for many cases. This explains the worse performance of flexible
buildings than stiffer buildings.
Olsen (2008) used thousand of synthetics from several scenario earthquakes in Los Angeles
and San Francisco to simulate the response of J20 and U20. Based on her simulation, it was
found that U20 have 1-4 times larger collapse possibility than J20. However, most of thesesynthetics have a frequency upper limit of 0.5 Hz. The signal information from 0 to 2 sec
is missing. So the response spectrum with peak around 2 sec shown in records from
IBUH03 would not be reflected in these synthetics. Therefore, in general, a stiffer highstrength Japanese building performs better than a more flexible lower-strength U.S.
building. However, in some cases, it is not true. Overall, it is really hard to determine
whether stiffer or flexible high-rise buildings are better. The real performance of buildings
depends largely on the frequency content of the strong ground motions.
The frequency content in the ground motions also explains why J6P has the best
performance in our simulation. Recall the natural period of U6 is about 1.5 sec and J6 isabout 1.17 sec. In the pseudo spectral velocity of all our models, PSV1.17 is always smaller
than PSV1.5. According to the nearly linear relationship between PSV and peak IDR for135
buildings with perfect welds (figure 3.18), it is not surprise to find that J6P has smaller

deformation that U6P.

6.5.4 Responses of Buildings for Different Site Conditions
Table 6.3 and figure 6.17 also show that the Seattle basin amplification is significant. It not
only amplifies the amplitude of ground motion by 2.5 to 5 times but also elongate theshaking duration by 150 to 200 sec. At rock sites, high-rise buildings were shaken for about
2 minutes while at basin sites, the shaking would last more than 5 minutes.
At basin sites, simulated collapse occurs for all types of buildings when ground motions are
estimated from wide model. Large yielding occurs for 20-story buildings when motions
are estimated from median and narrow model. The long duration would make the local
bucking critical after plastic hinges developed which is the case in many of our simulations.
This would make the real performance of high-rise buildings in Seattle even worse than our
simulation as we have discussed in section 5.5.5.

6.5.5 Response of Buildings to Motions from Different Fault Width Models
If the rupture extended beyond the Olympic Mountain, our simulation shows that 20- and6-story buildings in the Seattle basin area would mostly collapse. If the rupture extended tothe coastline, our simulation shows that the buildings with brittle welds would collapse andthe buildings with perfect welds would be heavily yielded. However if hysterics and local
bucking considered, these more than 4 minutes strong shaking could probably collapse
these buildings.

136

CHAPTER 7

Determining Broadband Displacements by Combining
Inertial Seismic Records and High-Sample Rate GPS
Records
In this chapter, we develop a new data processing methodology based on the data recorded
from colocated inertial seismic and high-frequency GPS stations, and apply this method torecordings from the 2003 Tokachi-Oki earthquake (Mw 8.1) to recover accurate strong
ground motion displacements. This method saves significant time and reduces sensitivity to
the choice of processing parameters.

7.1 Introduction
Accurate measurement of coseismic near-source ground displacement time histories is ofgreat importance. These displacement time histories are often very diagnostic in the
inversion of seismic data to derive source rupture models. Furthermore, they can also be
important to understand the deformations of flexible buildings that experience large
nonlinear deformations. Unfortunately, derivation of ground displacement from theanalysis of inertial seismograms always results in ground motions that diverge with time.
The dashed lines shown in figure 7.1 are the horizontal displacements derived from double
integration of accelerograms (corrected for preevent means) recorded at K-Net station
HKD084 during the 2003 Tokachi-Oki earthquake. These integrated accelerograms

137
compare poorly with 1 Hz GPS observations of ground motion recorded at nearby stations.

Unfortunately the divergent displacement records are typical.

The problem is that arecorded accelerogram a s (t ) , actually consists of⎛ ∂u (t ) ⎞as (t ) = u (t ) + g sin ⎜ z ⎟ + ε s (t ) ,(7.1)⎝ ∂x ⎠⎛ ∂u (t ) ⎞where u(t) is the true displacement, g sin ⎜ z ⎟ is the gravitational acceleration caused⎝ ∂x ⎠
by tilting of the seismometer (this term drops out for vertical components), and ε s (t ) iserror introduced by the seismometer and digitizer. Even though significant progress has
been made in reducing ε s (t ) , the tilting term is an independent degree of freedom thatcannot be removed from this problem unless there is an independent data stream, such as
inertial rotation or GPS displacement data (Clinton, 2004).
In the mean time, researchers have also proposed numerous data processing techniques toeliminate the displacement drifts caused by the tilting and instrumental errors as we
mentioned in section 3.2 (USGS data; Caltech EERL report 1974-1976; Iwan, Moser et al.,
1985; Boore, 2001; Zhu, 2003; Shakal, Huang et al., 2004). Unfortunately, all of these
correction approaches require the specification of processing parameters that strongly affectthe derived ground displacements.

While approximate knowledge of the static

displacement (typically from geodetic data) can help to constrain these processing
techniques, it can be time consuming to employ trial and error to discover the processing
parameters that produce the desired ground displacements from processing the seismic data.
In this chapter, we develop a new data processing methodology based on colocated inertial
seismic and high-frequency GPS stations, and apply this method to recordings from the2003 Tokachi-Oki earthquake (Mw 8.1) to recover accurate strong ground motion
displacements. This method saves significant time and reduces sensitivity to the choice ofprocessing parameters.

138
80

Displacement from GPS station:124 and Seismic station:HKD084
seismic at HKD084
GPS at 0124

60
EW

40
20

Displacement cm

0
-20
0

50

100

40
20

150
seismic at HKD084
GPS at 0124

NS

0
-20
-40
0

50

100

150

Time sec

Figure 7.1. Horizontal displacements from GPS station 124 (solid line) and doubleintegrated seismic station HKD084 (dashed line) during the 2003 Tokachi-Oki earthquake.
These two stations are very close to each other (about 1 km apart). The recording
frequency is 100 Hz for seismic data and 1 Hz for GPS data.

7.2 Correction Scheme

7.2.1 Seismic Data
If we doubly integrate equation (7.1) and assume that the tilt is small, we obtaint t⎡ ⎛ ∂u (t ) ⎞⎤u (t ) = ∫∫ a (τ )dτ − ∫ ∫ ⎢ g ⎜ z ⎟ + ε s (t )⎥dτ .
∂x ⎠⎦t
0 0⎣ ⎝(7.2)

In most existing correction schemes, it is assumed that there are discrete steps in thebaseline of recorded acceleration. That is, it is assumed thatn⎛ ∂u (t ) ⎞g ⎜ z ⎟ + ε s (t ) ≈ ∑ bi H (t − ti )⎝ ∂x ⎠
i =1
,

(7.3)

where H(t) is a Heaviside step function, bi is the amplitude of the ith step, and ti is the timeat which it occurs.

In practice, usually only one step and sometimes two steps are

139
considered. Unfortunately, it is extremely difficult to determine the starting time of steps,

not to mention that real baseline offsets could be far more complex than the sum of several
Heaviside functions. If we substitute equation (7.3) into equation (7.2), we find thatnu (t ) = ∫∫ a(τ )dτ − ∑ bi (t − ti ) 2 H (t − ti ) .
t

(7.4)

i =1

Or in other words, current correction schemes are equivalent to adding one or two
parabolas to the displacement time series. Since each parabolic correction has a Fourier
amplitude spectrum that scales as f -3, these baseline corrections have very little effect at
high frequencies. That is, these shifts predominantly contaminate the long-period parts ofwaveforms; short-period waveforms are relatively immune from these baseline issues.

7.2.2 GPS Data
Traditionally, GPS receivers have been used to record slow movements of the Earth thatdevelop over days and years (Segall and Davis, 1997). In these studies, one position isestimated for each site over a 24-hour period. Time series of these positions can then be
used to study plate tectonics and plate boundary processes. The primary usage of GPS inearthquake studies has been the calculation of “static” offsets. By comparing the 24-hour
average position of a receiver before and after an earthquake, permanent grounddeformation can be inferred. In previous baseline correction approaches, the permanent
displacement measured by GPS has been used as a valuable constraint to find the inversion
parameters (Boore, 2001).
Recently, it has been shown that GPS receivers operating at high sample rates (1 Hz) canbe used to measure seismic waves associated with large earthquakes (Ji, Larson et al., 2003;
Larson, Bodin et al., 2003; Larson, Bilich et al., 2006). These GPS positions are
intrinsically different from data collected with traditional seismic instruments. Noise levels
on a seismic observable are related to the type of seismometer and its local environment.

140
In contrast, the GPS observable is not position; it is the measurement of distance between a

GPS satellite transmitter and a ground antenna. The GPS position estimates ordisplacements of interest to seismologists are computed in a least-squares analysis of GPS
distance observations from four or more satellites and two or more receivers1. The major
error sources that must be addressed in GPS least squares analysis are satellite and receiver
positions, satellite and receiver clocks, and atmospheric delays. Because the range
observations are biased by an unknown number of integer cycles, phase ambiguity terms
are also estimated for each satellite-receiver pair. While the orbits are very precisely
determined, they are not without error, and this impacts how well receiver positions can be
determined. Another critical issue for high-rate GPS studies is the geometry of the GPS
constellation. While the precision of a 24-hour average position has only a slightdependence on geometry, initial high-rate GPS studies in Alaska showed that the east
component of displacement was much better determined than the north component (Larson,
Bodin et al., 2003). Both horizontal components are more precisely determined than thevertical component, by a factor of 2 to 3.
Evaluating the noise levels in high-rate GPS time series is an area of active research(Langbein and Bock, 2004; Genrich and Bock, 2006; Larson, Bilich et al., 2006). Most
studies find the short periods (0.1-10 sec) are characterized by white noise; longer period
noise falls off as 1/f. Bilich (2006) has shown that the white part of the error spectrum
depends critically on the receiver manufacturer. For the Tokachi-Oki dataset, these values
are 0.4 and 1.7 mm for east and north components; for San Simeon (Ji, Larson et al., 2003),
a different receiver was used and the high-frequency precisions (0.2 and 0.4 mm) weremuch better.
Some of the long period errors can be removed by modified sidereal filtering (Choi, Bilich
et al., 2004). Because the GPS constellation repeats its orientation in space approximately

1

It is possible to compute the position of a single GPS receiver if one has access to very accurate
high-rate estimates of each satellite’s clock behavior (Zumberge et al. 1997). In practice, these are
not available and thus measurements from two or more receivers are needed to remove the effectof the satellite clocks.

141
every sidereal day (one day minus 246 sec), some of the geometry related systematic errors

such as multipath, which generally have periods of 100-500 seconds, can be modeled using
empirical corrections (Larson, Bilich et al., 2006). Amplitude spectra of the east-westcomponent of 100 seconds preevent noise from GPS receiver 0124 is shown in figure 7.2.
For the high-rate GPS data recorded during the Tokachi-Oki earthquake, a standard
deviation calculated from the 500 seconds before the earthquake yielded precisions of 4.5,
8.4, and 15.3 mm in the east, north, and vertical components (Miyazaki, Larson et al.,2004).

Amplitude Spectra

Fourier Spectra of pre-event Noise
10

-1

10

-2

10

-3

10

-4

GPS noise
Seismic noise

-2

-1

10

10

10

0

1

10

Frequency Hz

Amplitude Spectra

Figure 7.2. Amplitude spectra of east-west preevent noise at GPS station 0124 and K-Net
station HKD084 recordings. 100 and 10 seconds preevent signals are chosen for 0124 andHKD084 respectively.
10

2

10

1

10

0

10

-1

10

-2

10

-3

Fourier Spectra of displacement at HKD084 and 0124
GPS at 0124
Seismic at HKD084

10

-2

-1

10
Frequencu Hz

10

0

10

1

Figure 7.3. Amplitude spectra of displacements. Dashed line is for 200 seconds east-west
data recorded at GPS receiver 0124. Solid grey line is for 200 seconds double integrationof east-west accelerograms at K-Net HKD084. All the displacements time series aretapered by Chebyshev window at 80 sec to 200 sec to make sure that the signals are
periodic function for Fourier transformation.

142
Figure 7.2 also shows the 10 seconds preevent noise spectrum from the K-Net seismic

station HKD084. In this earthquake, the preevent signal recorded by event-triggered
accelerometers is less than 15 seconds, so we can not find the seismic noise larger than 0.1
Hz. However, we clearly discover that noise is much lower for the inertial seismometersthan for GPS receivers at high-frequency band. Although, this view of the seismometer
noise is somewhat deceptive in that it does not include any baseline shifts that are
introduced in large amplitude shaking from several sources, including tilting from soil
compaction and unknown instrumental effects, the f -3 scales for their spectra will notlargely increase the seismic noise at high frequency band.

7.2.3 Correction Scheme
From the above discussion, we know that seismic data has high-quality at high frequency
band whereas high-sample rate GPS data has high-quality at long period up to static
frequency. Fourier amplitude spectra for displacement obtained from GPS receiver 0124
and accelerometer at HKD084 is shown at figure 7.3. It clearly shows the complementaryadvantages of high-sample rate GPS data and seismic data. These motivated us to develop a
procedure for processing data in a manner that can make the best use of their individual
advantages.
The purpose of this method is to extract the displacement trend from the double-integrated
accelerogram recordings. The procedure can be summarized by the following equation:⎡⎤u B (t ) = f LP (t ) ∗ ⎢ ∫∫ a s (τ )d τ − DG (t )⎥ ,
⎣t
⎦

(7.5)

where, u B (t ) is the displacement trend produced by accelerogram baseline offset. DG (t ) is
the GPS displacement time series, and f LP (t ) is low-pass filter. In this study, we use zerophase 4th-order Butterworth filters. After we find u B (t ) , the final strong groundaccelerations, velocities and displacements can be calculated as:

143
u processed (t ) = ∫∫ as (τ )dτ − u B (t )

(7.6)

t

u processed (t ) = ∫∫ as (τ )dτ −tu processed (t ) = as (t ) −d(uB (t ))
dt

(7.7)

d2
(uB (t )) .
dt 2

(7.8)

All the above steps are processed at time domain and u B (t ) is the final output for each site.
It is extremely difficult to recover the displacements from frequency domain constituting
by that of GPS data at low-frequency band and that of seismic data at high-frequency band.
The reason is that Fourier transformation is only valid for periodic functions, so thedisplacement time series obtained by frequency domain analysis are distorted from the real
ground displacement with permanent deformation. In other words, Fourier domain analysis
does not have the capacity to recover the static residual displacements.
In this method, the only parameter that needs to be determined by user is the cornerfrequency of the low-pass filter. In our Matlab package CIT_GFD, we provided a way todefine this corner frequency: the frequency where accelerogram began to diverge fromGPS recordings in low-frequency band. In other words, when exceeding this frequency,
accelerogram can no longer provide high-quality data. To elaborate the reason underlying
this setting, we can express equation (7.5) in another way:⎡⎤u B (t ) = f LP (t ) ∗ ⎢ ∫∫ as (τ )dτ − DG (t )⎥⎣t⎦= [1 − f HP (t )] ∗ ∫∫ as (τ )dτ − f LP (t ) ∗ DG (t )where, f LP (t ) = 1 − f HP (t )t⎡⎤= ∫∫ as (τ )dτ − ⎢ f HP (t ) ∗ ∫∫ as (τ )dτ + f LP (t ) ∗ DG (t )⎥ .
t
t
⎦
⎣

(7.9)

144
Equation (7.9) shows that the displacement trend is identical to the residual when processeddata is subtracted from the seismic displacement. And the processed data is high-frequency
part of seismic data plus low-frequency part of GPS recordings. The corner frequency is theplace to separate high-frequency part from low-frequency part, where seismic data is usedin the former and GPS data is used in the latter. For example, in figure 7.3, seismic datafrom HKD084 is poor at frequency smaller than 0.02 Hz, whereas GPS data from 0124 ispoor at frequency larger than 0.2 Hz. Since in high-frequency region, data quality fromseismic instruments is much higher than that from GPS receiver, it is better to exhaust use
seismic data. So we set 0.02 Hz as the corner frequency for this site. In fact, the final
processed displacements are not sensitive to the corner frequency (see figure 7.4). Although
the shapes of derived baseline offsets of accelerogram change, the noise/signal ratios are
too small to be important for building design.

Fc = 0.02 Hz

Acceleration Baseline Offset
50

100

50

100

100

Acceleration Baseline Offset
-5
0

150

40
20
0
-20
50

100
Time sec(a)150

Velocity cm/s
50

100

100

50

100

150

40
20
0
-20
50

100

150

0

-50
0

150
combinedseismic
GPS

60

0

50

50

0

-50
0

150
combinedseismic
GPS

60

0

50

Displacement cm

Displacement cm

Velocity cm/s

00

Acceleration Baseline Offset

50

Displacement cm

Velocity cm/s

50

-50
0

0

-0.5
0

150

Fc = 0.2 Hz

5
cm/s2

0

-0.5
0

Fc = 0.05 Hz

0.5
cm/s2

cm/s2

0.5

150
combinedseismic
GPS

60
40
20
0
-20
0

50

100

Time sec

Time sec

(b)

(c)

150

Figure 7.4. Derived acceleration baseline offsets and the final velocities and displacements
results processed by different corner frequencies. Corner frequency is 0.02 Hz at case (a),0.05 at case (b) and 0.2 Hz at case (c). The blue lines at the last two rows represent final
results. Notice that corner frequencies do not affect the final processed velocities anddisplacements. Although the shapes of baseline offsets differ, if you choose reasonable
smaller corner frequency (smaller than 0.1 Hz), we can capture the approximate shape ofthe baseline offsets.

145
To qualify this method, as (t ) and DG (t ) should be collected from colocated seismic andGPS station pair. For the Tokachi-Oki earthquake 2003, there are no exactly colocatedstation pairs, so the requirement has been relaxed to station pairs very close to each other.
In general, the long-period ground deformations are not sensitive to the small distancechanges; therefore the difference of two long-period ground displacements recorded atstations very closed to each other is very small. This can be seen from figure 7.1. In thisexample, the displacements collected from the seismic station HKD084 (43.1116N,
144.1269E) and GPS station 124 (43.1206N, 144.1265E) are compared. These two
instruments are approximately 1 km apart; the difference between the two displacements inthe first 40 seconds is so small that we can regard these two stations as a colocated stationpair.

7.3 Error Analysis
In this section, we use a known displacement history to demonstrate whether this method
has the ability to recover an accurate measure of ground displacement. By doing this, we
arbitrarily choose a stable ground displacement and assume that it is accurate (the firstcolumn in figure 7.5). First, we perturb it with acceleration baseline offsets (the second
column in figure 7.5) to generate a typical-looking seismic recording (solid lines in thethird column in figure 7.5). Secondly we resample the original ground displacement to 1
Hz (the first column in figure 7.6) and perturb it with randomly recorded GPS noise (thesecond column in figure 7.6) to generate a typical-looking GPS recording (solid lines in thethird column in figure 7.6). Finally, we processed these artificial recordings by CIT_GFD
program. The corner frequency chosen by the program is 0.02 Hz. Figure 7.7 (a) compare
the program derived acceleration baseline offset with the real added acceleration baseline
offset. The corresponding velocities are show in figure 7.7 (b). The displacement error
caused by this method is shown in solid line in figure 7.7 (c). As expected, in long-period
region, the processing error is mainly caused by the filter applying to the GPS noise, while
it is caused by the filter applying to the jumps in the added acceleration baseline offset.

146
Baseline Offset

Accn cm/s2

0.4
0.2
0
0

50

100

150

200

Accn
50

+

-50
0

50

100

150

-50
0

200

80
Original Disp

+

20
0

Disp cm

Disp cm

60
40

Vel
0

=

50

100

150

Vel cm/s

0

Vel cm/s

Vel cm/s

Original Vel

0
Vel
-50
0

200

80

80

60

60

40

=

20
0

0

50

100
150
Time sec

200

0

50

100

150

200

100
150
Time sec

200

40
20
0
-20

-20

-20

After adding baseline offset

50

Disp cm

50

50

100
150
Time sec

0

200

50

Figure 7.5. Baseline offset (dot-dash lines in the second columns,) is added to the original
data (the first column, with reasonable displacement) to generate typical seismic recordings(solid lines in the third column). The first row is acceleration. Since the baseline offset isextremely small, it is not necessary to plot the original and disturbed acceleration. The
second row shows velocity and the third row shows displacement. In this example, we use
a two-step Heaviside function. One step occurs at 40 sec and the other occurs at 65 sec.
50

1

GPS recording noise

Disp cm

60

50

-50
0

200

+

0

=

0
-1

-20
200

-2
0

50

100

150

200

60

1

20

100
150
Time sec

150

0

2

Original Disp

50

100

Vel cm/s

0
-0.5
0

100
150
200
Resample disp anddifferentiate to get vel

40

0

=

Disp
50

100
150
Time sec

200

Disp cm/s

80

Vel cm/s

+

Vel

0.5

Disp cm

Vel cm/s

050After adding GPS noise

Vel

Resampled Vel

-50
0

50

40

Disp

20
0
-20
0

50

100
150
Time sec

200

Figure 7.6. GPS noise (the dash lines in the second column,) is added to the original
displacement data (the first column) to make typical GPS recordings (the solid lines in thethird column). The first row gives velocity and the second row shows the displacement.

The errors also depend on the corner frequency. Figure 7.8 shows the processing errors
using corner frequency at 0.05 Hz and 0.2 Hz. Obviously, when corner frequency equals
0.2 Hz, the derived acceleration baseline offset can not capture the pulse shape of the addedbaseline shift at all. Although the displacement error is not large, the acceleration error is

147
increased dramatically which is critical for structural design. When corner frequency equals

0.05 Hz, the derived acceleration baseline shift can almost capture the shape of the addedbaseline offset, and displacement error is relatively smaller. This is because the timedifference of the two consecutive step functions is 30 sec, which is close to this corner
period. However, in real recordings, since we do not know time interval or even thenumbers of time intervals, it is better to choose a longer corner period.

Accn cm/s 2

Fc = 0.02 Hz
0.3

(a)

0.2
0.1
0

-0.1
0

50

100

150

200

Added seismic baseline offset
Derived baseline offset by CIT-GFD
Vel cm/s

20 (b)
10
0
0
4

50

(c)

100
150
200
High-passed seismic baseline offset
Low-passed GPS noise
Processed displacement error

Disp cm

2
0
-2
-4
0

50

100
Time sec

150

200

Figure 7.7. Processing error using corner frequency equals 0.02 Hz. (a) Comparing theacceleration baseline offset derived by CIT-GFD (solid line) and the added acceleration
baseline offset. (b) The derived and added velocity caused by acceleration baseline offset.
(c) The difference between the processed displacement and the original displacement (solidline). This error is caused by the high-passed filter to baseline offset (dot-dash line) and the
low-passed filter to the GPS noise (grey dash line).

148
0.3
0.2
0.1
0
-0.1
0

50

100

150

Vel cm/s

Vel cm/s

10

50

100

150

200

50

100

150

200

50

100
Time sec

150

200

10
0

0
0

50

100

150

4

High-passed seismic baseline offset
Low-passed GPS noise
Processed displacement error

0

200

4
2
Disp cm

Disp cm

0
-0.5

20

20

0
-2
-4
0

1
0.5

-1
0

200

Added seismic baseline offset
Derived baseline offset by CIT-GFD

2

Fc = 0.2 Hz

1.5
Accn cm/s2

Accn cm/s2

Fc = 0.05 Hz

50100
Time sec

150

200

0
-2
-4
0

(a)
Figure 7.8. The acceleration baseline offsets and displacement error derived by different
corner frequencies. Corner frequency equals 0.05 Hz at column (a) and equals 0.02 Hz atcolumn (b).

7.4 Results
To demonstrate the implementation of this method we use data from the 2003 Tokachi-Oki
earthquake Mw 8.1. This earthquake is far and away the largest event recorded by anextensive strong motion network. It also recorded continuous high-frequency GPS data at
many receivers (Miyazaki, Larson et al., 2004). Indeed, it is the most suitable database to
exhibit the benefits of this methodology.
All the colocated seismic and GPS (without power failure) station pairs are shown in figure
7.9. Figure 7.11 lists the derived baseline offsets and corrected ground velocities anddisplacements for seismic station HKD095 and GPS station 521. East-west, south-northand vertical components are given individually. Corner frequencies chosen by the program
are listed in figures. Figure 7.12 and 7.13 give another example for station HKD129 andGPS station 136. Notice the seismic recording at east-west direction provided a relatively
stable displacement, so the corner frequency used in this direction is extremely small which

149
means a majority of seismic data contributes to the corrected result. More results for othercolocated

pairs

can

be

found

at

the

followinglink:

http://www.ecf.caltech.edu/~jingy/HULDresults.htm.
These figures illustrate that the final velocities are almost the same as velocities integrated
from strong motion accelerations whereas they are not quite similar with velocities
differentiated from geodetic displacements. This is reasonable because velocities include
much more frequency components higher than 1 Hz which can not be captured by recent
GPS receivers. These figures also indicate that the final displacements are similar withgeodetic displacements in envelops; meanwhile they follow the short periodic waveforms
in seismic displacements. The overall indicates that we successfully recovered the realcoseismic ground motions.

Figure 7.9. Distribution of colocated seismic and GPS station pairs on Hokkaido. The solid
red dots represent high-frequency GPS stations which suffered telemetry power failure
during the 2003 Tokachi-Oki earthquake. The solid pink dots recovered the entire event.
The triangles and squares represent seismic network K-Net and KiK-Net respectively.
Open red ellipses are used to group the colocated seismic and GPS station pairs.

150
0.2

30

EW

0.1

Fc =0.02 Hz

0
-0.1
0

50

100

0
-10
0

150

-0.05
50

5

Vel cm/s

Accn cm/s2

Fc =0.015 Hz

-0.1
0

100

150

100

50

100

150

100

150

NS

0
-5
-10
0

150

0.1

10
UD
Fc =0.025 Hz

0
-0.05
-0.1
0

50

5

Vel cm/s

Accn cm/s2

50

10
NS

0

0.05

EW
EW

10

0.1
0.05

Velocity caused by accn baseline offset

20

Vel cm/s

Accn cm/s2

0.3

Derived acceleration baseline offset

100

UD

0
-5
-10
0

150

50

Time sec

Time sec

Figure 7.10. Derived baseline offsets from GPS station 521 and K-Net station HKD095.
These two stations are about 4 km away from each other. They are about 150 km from theepicenter.
GPS 0521 Seismic HKD095
80
EW

20
0

40
20
0

-20
0

50

100

EW

60

Displacement cm

Velocity cm/s

40

-20
0

150

50

100

150

20
NS

20
0
-20
0

0

Displacement cm

Velocity cm/s

40

NS

-20
-40
-60
-80
-100

50

100

150

0

50

100

150

40
UD

Displacement cm

Velocity cm/s

40
20
0

20

combinedseismic
GPS

UD

0
-20

-20
0

50

100
Time sec

150

-40
0

50

100

150

Time sec

Figure 7.11. Original and corrected velocities (left panel) and displacements (right panel)from GPS station 521 and K-Net station HKD095. The red dashed lines represent seismic
time series, the green dash dotted lines represent GPS time series and the solid blue lines
are the results processed by our correction scheme.

151
0.02

EW
Vel cm/s

Accn cm/s

2

Derived acceleration baseline offset

0
Fc = 0.005 Hz

Velocity caused by accn baseline offset
2
EW
1

-0.02
0

50

100

0
-1
-2
0

150

50

100

150

50

100

150

50
100
Time sec

150

NS
Vel cm/s

Accn cm/s

2

2
0.02

Fc = 0.015Hz

0
-0.02
0

50

100

NS

1
0
-1
-2
0

150

UD
Vel cm/s

Accn cm/s

2

2
0.02
0
Fc = 0.02Hz
-0.02
0

50
100
Time sec

UD

1
0
-1
-2
0

150

Figure 7.12. Derived baseline offsets from GPS station 136 and K-Net station HKD129.
These two stations are about 2.7 km away from each other. They are about 225 km fromthe epicenter.
GPS 0136 Seismic HKD0129
60
EW
Displacement cm

Velocity cm/s

40
20
0
-20
0

50

100

EW

40
20
0
-20
-40
0

150

50

100

150

60
NS
Displacement cm

Velocity cm/s

40
20
0
-20
0

50

100
UD

20
0
-20
0

50

100
Time sec

150

20
0
-20
-40
0
60

150

Displacement cm

Velocity cm/s

40

NS

40

40

50

100

150
combinedseismic
GPS

UD

20
0
-20
-40
0

50

100

150

Time sec

Figure 7.13: Original and corrected velocities (left panel) and displacements (right panel)from GPS station 136 and K-Net station HKD129.

152

7.5 Conclusions
By introducing high-frequency GPS data, our study provides a new way to recover strong
ground displacements. It is essentially a combination of seismic and geodetic data recordedat the same place, fully employed the advantages of each type of data. This method is easy
to implement and is consistent and robust for all stations. As long as colocated data are
available, results can be generated within seconds. Choice of corner frequencies of thefilters is the only thing that needs to be determined. Fortunately, the final results are notsensitive to this parameter. The Matlab package CIT-GFD provided a way to find thecorner frequency which is the place where seismic data begins to diverge from GPS data infrequency domain. No other human judgments are needed. In addition, this method ismore general in that it can deal with the case where acceleration baseline offsets cannot be
simplified as one- or two-step Heaviside functions. Given the promise of this new method,
we recommend that high-frequency GPS receivers be collocated at seismic stations in the
future.

153

CHAPTER 8

Concluding Remarks

8.1 Summary of ResearchThis study is essentially in two parts. One part is simulating strong ground motions fromgiant subduction earthquakes and the other is simulating the nonlinear performance of steel
moment-resisting frame buildings subjected to these synthetics. It combines theconventional work done by seismologists and earthquake engineers.
The strong motions recordings from the 2003 Tokachi-Oki earthquake were first studied.
They show significant spatial variation of shaking on Hokkaido Island. The contour mapsof peak interstory drift ratios demonstrate that the 20- and 6-story flexible steel momentresisting frame buildings designed according to both 1994 Uniform Building Code and1987 Japanese building code would have been strongly excited throughout the coastal
region, with the potential for collapses at some locations. Among all the ground motion
intensity measures, the response spectrum best predicts the performance of buildings.
However, it fails when large deformations occur in the buildings. A collapse factor was
introduced to describe the collapse safety margin of buildings. It reveals that although
Japanese buildings are 20% to 30% stronger than U.S. buildings, their capacity to resist
collapse does not proportionally increase.

154
After this comprehensively study of Tokachi-Oki event, their records constitute thedatabase of empirical Green’s functions to simulate the strong motions for the 2004
Sumatra-Andaman earthquake and a scenario Cascadia earthquake. The Cascadia
earthquake is assumed to have the same source model as the Sumatra event. Synthetics
from rupture models with different width and from observation stations with different site
conditions were estimated. The empirical Green’s function method is able to simulate thebroadband waves and does not have any limits for the frequency range. The basin site
amplification is represented by a transfer function obtained through deconvolving rockrecords from basin records. Although there is a large variation in the results, all thesynthetics have very long shaking duration. The nonlinear performance of 20- and 6-story
SMRF buildings excited by these synthetics is estimated. The simulations show that the 20story buildings in Banda Aceh would have yielded in the Sumatra event while the 20-story
buildings in Seattle basin would collapse in the Cascadia event.

8.2 Conclusionsz

The first numerical simulation of the response of flexible steel buildings in Seattle due
to a giant Cascadia subduction earthquake. Although there is a large uncertainty for thestrong motions synthetics caused by the site amplification, rupture models and choiceof empirical Green’s functions, the simulated waveforms are consistent with available
data and current knowledge. Uncertainty also exits in the finite-element methodbuilding models. It can be caused by unmodeled local buckling during long duration
shaking and caused by unknown weaknesses that have not been discovered yet inbuildings. Since the effects from some uncertainties may cancel with each other tosome degree, we can conclude based on our simulations that the high-rise buildings in
the Seattle basin designed according to California building code may not survive in the
expected giant Cascadia subduction earthquakez

The site condition is of particular importance to the simulated ground motions in
Seattle. Site amplification from the Seattle basin is significant. The PGV (peak ground155
velocity) of Seattle basin synthetics can be 6 times larger than the PGV of rocksynthetics in the scenario Cascadia event although the amplification for PGA is not so
obvious. The importance of basin amplification is also demonstrated in the TokachiOki event. The Yufutsu basin which is located more than 200 km away from theepicenter amplifies the long period motions large enough so that we could expect
irreparable damage for 20-story buildings.
z

All the synthetics from giant subduction earthquakes, especially at the basin sites,
exhibit very long duration strong shaking. The duration can be as long as 5 minutes in
the Seattle basin. These motions are strong enough to cause large lateral deformationand to develop plastic hinges; the long duration would lead to an accumulation of suchdamages. With so many cycles after yielding, the stress and stiffness degradation
would be extremely significant. Since Frame-2D used a degradation model which did
not include effects from local flange buckling, our building simulations should beconsidered to give a low estimate. It would be valuable to include local flange bucklingand web distortion into Frame-2D in the future.

z

The down-dip limit of rupture significantly affects the resulting synthetics. Althoughsimulated teleseismic P-waves are similar for models with wide, median and narrowrupture width, the strong ground motions simulated from a wide model can be 2.5 to 4
times larger than those simulated from a narrow model. However, based on our current
knowledge, there is no unique solution of the rupture models. More scenarios should
be considered to include this large uncertainty.

z

Any high-rise buildings in the coastal regions would have been strongly shaken in the2003 Tokachi-Oki earthquake. Although none of the buildings collapsed in our
simulations, some of the 20-story buildings were very close to collapsing (at somestations, increasing the ground motion amplitude by 6% would cause simulated
collapse for 20-story U.S. building with brittle welds, and increasing 12.5% would
cause 20-story U.S buildings with perfect welds collapse.).

z

156
The fracture of welds in the connections of beams and columns dramatically reduces

the strength and ductility of buildings. Brittle welds induce the concentrated
deformation at some stories in the buildings. The increased nonlinearity effects makeprediction of structural performance much more difficult by using just ground motion
intensities. Existing weak stories also give rise to high collapse potential for high-risebuildings under P-Delta effects. Therefore fixing brittle welds is an efficient way toenhance the lateral force resisting capacity of existing steel buildings.
zStrengthening buildings has much less impact on the seismic design than fixing thewelds in the connections. In general, a stiffer high-strength Japanese building performs
better than a more flexible lower-strength U.S. building. However, in some cases, theopposite occurs. In the Tokachi-Oki earthquake, we found that 20-story Japanesebuildings with perfect welds perform worse than 20-story U.S. buildings with perfectwelds in areas suffering very strong shaking. This also happened in our Sumatra
simulation. These different behaviors are caused by the different frequency content of
the input ground motions. For example, when excited by a record from station
IBUH03 which has a response spectrum peak around 2 sec, flexible high-rise buildings
perform better than stiffer buildings. Overall, it is really hard to determine whether
stiffer or flexible high-rise buildings are better. But we do know that strengthen highrise buildings is less efficient for seismic design than fixing brittle welds.

8.3 Future Directionsz

The long duration scenario shows a great demand of including stiffness and strength
degradation into the hysteretic behavior of our FEM model. It can be included bymodeling buckling or by establishing a failure criterion that is related to energy(personal communication with Professor Chia-Ming Uang).

z

In this study, our focus area is Seattle. However, there are several other big cities along
the Cascadia subduction zone, such as Portland and Vancouver, which have many

157
flexible structures. In the future, strong ground motions and the nonlinear performanceof high-rise buildings in these cities are worthwhile simulating if we have more
information about their site conditions.
zMore realizations with different sets of empirical Green’s functions, basin transfer
functions, location of hypocenter and rupture directions should be considered in the
future. A reasonable result could be found through a statistical model based on manydifferent cases.

158

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