A thesis submitted in partial fulfilment of the requirement for the … · simulate a series of ground motion time histories from earthquakes of varying magnitudes and distances

Seismic risk analysis of Perth metropolitan area

by

Jonathan Zhongyuan Liang

A thesis submitted in partial fulfilment of the requirement for

the Degree of Doctor of Philosophy at The University of

Western Australia

December 2008

i

ACKNOWLEDGEMENT

First of all, I would like to express my deepest gratitude to my supervisor, Professor

Hong Hao, for his patience guidance, invaluable suggestions, and his efforts in

providing me the unique opportunity to pursue my PhD study which is a remarkable

personal achievement in my life.

I would also like to express my sincere gratitude to Mr. Brian A. Gaull for his

constructive suggestions, fruitful discussion and support.

My special thanks to Dr Xinqun Zhu, Dr Boning Li, Dr Hongjie Zhou, Dr En Peng Lina

Ding, Norhisham Bakhary, Ying Wang, Kaiming Bi, and many others for their

friendship, which is the most rewarding achievement.

Great appreciation is dedicated to the School of Civil and Resource Engineering, the

University of Western Australia, for offering a scholarship to me to pursue this study.

I am very thankful to my wife Patrice for her patience and lovely support during the

difficult time of this study. I wish to express my heartfelt appreciation and very special

thanks to my parents Juwen Liang and Weizhen Yu, my brother Luyuan Liang for their

support and inspiration throughout my life.

ii

SUMMARY

Perth is the capital city of Western Australia (WA) and the home of more than three

quarters of the population in the state. It is located in the southwest WA (SWWA), a

low to moderate seismic region but the seismically most active region in Australia. The

1968 ML6.9 Meckering earthquake, which was about 130 km from the Perth

Metropolitan Area (PMA), caused only minor to moderate damage in PMA. With the

rapid increase in population in PMA, compared to 1968, many new structures including

some high-rise buildings have been constructed in PMA. Moreover, increased seismic

activities and a few strong ground motions have been recorded in the SWWA. Therefore

it is necessary to evaluate the seismic risk of PMA under the current conditions. This

thesis presents results from a comprehensive study of seismic risk of PMA. This

includes development of ground motion attenuation relations, ground motion time

history simulation, site characterization and response analysis, and structural response

analysis.

As only a very limited number of earthquake strong ground motion records are available

in SWWA, it is difficult to derive a reliable and unbiased strong ground motion

attenuation model based on these data. To overcome this, in this study a combined

approach is used to simulate ground motions. First, the stochastic approach is used to

simulate ground motion time histories at various epicentral distances from small

earthquake events. Then, the Green’s function method, with the stochastically simulated

time histories as input, is used to generate large event ground motion time histories.

Comparing the Fourier spectra of the simulated motions with the recorded motions of a

ML6.2 event in Cadoux in June 1979 and a ML5.5 event in Meckering in January 1990,

provides good evidence in support of this method. This approach is then used to

simulate a series of ground motion time histories from earthquakes of varying

magnitudes and distances. From the regression analyses of these simulated data, the

attenuation relations of peak ground acceleration (PGA), peak ground velocity (PGV),

and response spectrum of ground motions on rock site in SWWA are derived.

Because seismic source parameters are not exactly known, a statistical study is carried

out to investigate the influence of the random fluctuations of the seismic source

parameters on simulated strong ground motions. The uncertain source parameters, i.e.,

iii

stress drop ratio, rupture velocity and rise time, are assumed to be normally distributed

with the corresponding mean values estimated from the empirical source models and an

assumed coefficient of variation. An ML6.0 and epicentral distance 100 km event is

simulated using Rosenblueth’s point estimate method to estimate the mean and standard

deviation of PGA, PGV and response spectrum. The accuracy of the Rosenblueth’s

approach is proved by Monte Carlo simulations. A sensitivity analysis is performed to

investigate the effect of random fluctuations of each source parameter on strong ground

motion simulation. A coefficient of variation model for ground motion parameters is

developed based on the simulated data as a function of the variations of the three source

parameters and earthquake magnitude. They can be used together with the attenuation

relations to estimate ground motion attenuations with the influence of uncertain source

parameters.

A seismic risk analysis of PMA based on the derived ground motion attenuation model

is performed. The PGA and the design response spectra of ground motions

corresponding to different return periods at rock site are determined. Site

characterization of PMA is performed using the spatial autocorrelation (SPAC) method.

The clonal selection algorithm (CSA) is employed to perform direct inversion of SPAC

curves to determine the soil profiles of representative PMA sites investigated in this

study. Using the simulated bedrock motion as input, the responses of the soil sites are

estimated using numerical method based on the shear-wave velocity vs. depth profiles

determined from the SPAC technique. The response spectrum of the earthquake ground

motion on surface of each site is derived from the numerical results of the site response

analysis, and compared with the respective design spectrum defined in the Australian

Earthquake Loading Code. Discussions on adequacy of the design spectrum are made.

Seismic microzonation for PMA is also defined. The results are summarized in the

microzonation maps in which zones are defined with site response spectrum and PGA

corresponding to different return periods, and fundamental vibration period of the site.

The responses of three typical Perth structures, namely a masonry house, a middle-rise

reinforced concrete frame structure, and a high-rise building of reinforced concrete

frame with core wall on various soil sites subjected to the predicted earthquake ground

motions of different return periods are calculated. Numerical results indicate that the

one-storey unreinforced masonry wall (UMW) building is unlikely to be damaged when

subjected to the 475-year return period earthquake ground motion. However, it will

iv

suffer slight damage during the 2475-return period earthquake ground motion at some

sites. The six-storey RC frame with masonry infill wall is also safe under the 475-year

return period ground motion. However, the infill masonry wall will suffer severe

damage under the 2475-year return period earthquake ground motion at some sites. The

34-storey RC frame with core wall will not experience any damage to the 475-year

return period ground motion. The building will, however, suffer light to moderate

damage during the 2475-year return period ground motion, but it might not be life

threatening.

v

LIST OF PUBLICATIONS

Journal

1. Liang, J., Hao, H., Gaull, B. A. and Sinadinovski, C. [2008]. "Estimation of strong ground

motions in Southwest Western Australia with a combined Green's function and stochastic

approach," Journal of Earthquake Engineering, 12: 382-405.

2. Liang, J., Hao, H. [2008]. " Influence of Uncertain Source Parameters on Strong Ground

Motion Simulation with the Empirical Green’s Function Method," Journal of Earthquake

Engineering, (Accepted).

3. Liang, J., Hao, H., Wang, Y. and B., K. M. [2008]. " Design Earthquake Ground Motion

Prediction for Perth Metropolitan Area with Microtremor Measurements for Site

Characterization," Journal of Earthquake Engineering, (Accepted).

Conference

1. Liang, J., Hao, H. and Gaull, B. A. [2008]. “Seismic Hazard Assessment and Site Response

Evaluation in Perth Metropolitan Area.” The 14th World Conference of Earthquake

Engineering, BeiJing, China, 12-17, Oct, 2008, Paper ID: S03-002.

2. Liang, J., Hao, H. [2008]. “Performance of Power Transmission Tower in PMA under

Simulated Earthquake Ground Motion.” The 14th World Conference of Earthquake

Engineering, BeiJing, China, 12-17, Oct, 2008, Paper ID: 05-05-0043.

3. Liang, J. and Hao, H. [2008]. “Characterization of Representative Site Profiles in PMA

through Ambient Vibration Measurement.” Australian Earthquake Engineering Society

Proceedings of the 2008 Conference, Ballarant, Victoria, Australia.

4. Liang, J., Hao, H. [2008]. “Structural Response to the Updated Design earthquakes in Perth

Metropolitan Area (PMA).” Australian Earthquake Engineering Society Proceedings of the

2008 Conference, Ballarant, Victoria, Australia.

5. Liang, J., Hao, H., Wang, Y. and Bi, K. M. [2008]. " Site Characterization Evaluation in

Perth Metropolitan Area using Microtremor Array Method," The Tenth International

Symposium on Structural Engineering for Young Expert, ChangSha, China, 19-21, Oct,

2008.

vi

6. Liang, J. and Hao, H. [2007]. "Effects of uncertain earthquake source parameters on ground

motion simulation using the empirical Green’s function method," Australian Earthquake

Engineering Society Proceedings of the 2007 Conference, Wollongong, Australia, 23-25,

Nov, 2007.

7. Liang, J. and Hao, H. [2007]. "Seismic site response analysis in Perth Metropolitan Area,"

Australian Earthquake Engineering Society Proceedings of the 2007 Conference,

Wollongong, Australia, 23-25, Nov, 2007.

8. Liang, J., Hao, H., Gaull, B. A. and Sinadinovski, C. [2006]. "Simulation of strong ground

motions with a combined Green's function and Stochastic approach," Australian

Earthquake Engineering Society Proceedings of the 2006 Conference, Canberra, Australia,

24-26, Nov, 2006.

vii

TABLE OF CONTENTS

ACKNOWLEDGEMENT ............................................................................................. i SUMMARY ……………………………………………………………………….ii LIST OF PUBLICATIONS ...........................................................................................v TABLE OF CONTENTS............................................................................................ vii LIST OF TABLES ....................................................................................................... ix LIST OF FIGURES ..................................................................................................... xi LIST OF ABBREVIATIONS.................................................................................... xiv CHAPTER 1 INTRODUCTION ..............................................................................1

1.1 Background ...................................................................................................1 1.2 Research Objective........................................................................................4 1.3 Organization of the Thesis ............................................................................5

CHAPTER 2 LITERATURE REVIEW ...................................................................7 2.1 Introduction...................................................................................................7 2.2 The studies of seismic risk around PMA ......................................................7 2.3 Earthquake sources and the recurrence relationship ...................................11 2.4 Bedrock motion prediction..........................................................................14

2.4.1 Earthquake simulation method............................................................15 2.4.2 Earthquake attenuation models used for SWWA predictions.............23

2.5 Uncertainties in source parameters .............................................................28 2.6 Soil site amplification in PMA....................................................................31

2.6.1 Geology of PMA.................................................................................31 2.6.2 Seismic amplification studies for PMA ..............................................32 2.6.3 Site amplification estimation method .................................................34

2.7 Conclusion ..................................................................................................42 CHAPTER 3 ESTIMATION OF STRONG GROUND MOTIONS IN SWWA

WITH A COMBINED GREEN’S FUNCTION AND STOCHASTIC APPROACH .....................................................................................45

3.1 Introduction.................................................................................................45 3.2 Simulation of strong ground motion ...........................................................46

3.2.1 Case study ...........................................................................................47 3.3 Ground Motion Attenuation Relations........................................................57

3.3.1 Regression model and methodology ...................................................57 3.3.2 Horizontal PGA model........................................................................59 3.3.3 Horizontal PGV model........................................................................63 3.3.4 Response Spectrum model ..................................................................67

3.4 Conclusions.................................................................................................72 CHAPTER 4 INFLUENCE OF UNCERTAIN SOURCE PARAMETERS ON

STRONG GROUND MOTION SIMULATION..............................74 4.1 Introduction.................................................................................................74 4.2 Variations of the Seismic Source Parameters .............................................75 4.3 Ground Motion Simulation with Uncertain Seismic Source Parameters....76

4.3.1 Monte Carlo simulation.......................................................................77 4.3.2 Rosenblueth’s Point estimate method .................................................80 4.3.3 Comparison of the results ...................................................................82

4.4 Sensitivity analysis......................................................................................82 4.4.1 Case Study 1........................................................................................85

viii

4.4.2 Case Study 2........................................................................................89 4.4.3 Case Study 3........................................................................................92

4.5 C.O.V. model ..............................................................................................94 4.5.1 PGA C.O.V. model .............................................................................96 4.5.2 C.O.V. of PGV and response spectrum ..............................................98

4.6 Ground motion attenuation with uncertain source parameters .................102 4.7 Conclusion ................................................................................................103

CHAPTER 5 SEISMIC HAZARD ANALYSIS FOR PMA ................................105 5.1 Introduction...............................................................................................105 5.2 PGA and Response Spectrum of Design Ground Motion on Rock Site ...105

5.2.1 Seismic Source Zones and Recurrence Relationship ........................107 5.2.2 Attenuation Relation for SWWA......................................................108 5.2.3 The Seismic Hazard for PGA............................................................109 5.2.4 Probabilistic Seismic Hazard Spectra ...............................................111

5.3 Time-history simulation............................................................................112 5.4 Summary and Conclusions........................................................................114

CHAPTER 6 SITE RESPONSE EVALUATION AND SEISMIC MICROZONATION FOR PMA ....................................................115

6.1 Introduction...............................................................................................115 6.2 Site Testing and Estimation of Soil Profiles .............................................116

6.2.1 Clonal Selection Algorithm (CSA) ...................................................117 6.2.2 Site Testing and Data Processing......................................................120 6.2.3 Case Study.........................................................................................121 6.2.4 Evaluation of Site Response for PMA ..............................................130 6.2.5 Seismic microzonation maps for PMA .............................................136

6.3 Summary and Conclusions........................................................................141 CHAPTER 7 STRUCTRAL RESPONSE TO PREDICTED EARTHQUAKE

GROUND MOTIONS IN PMA .....................................................142 7.1 Introduction...............................................................................................142 7.2 Buildings in PMA .....................................................................................143 7.3 Structural Response...................................................................................144

7.3.1 Unreinforced masonry building (UMB) ...........................................146 7.3.2 RC structure with masonry infill wall...............................................149 7.3.3 High-rise RC frame with core walls..................................................152

7.4 Conclusion ................................................................................................155 CHAPTER 8 CONCLUSIONS AND RECOMMENDATIONS .........................157

8.1 Summary and Conclusions........................................................................157 8.2 Recommendation for Further Research ....................................................159

REFERENCES …………………………………………………………………….161

ix

LIST OF TABLES

Table 2-1 Perth region bedrock hazard for a 475-year return period of exceedance (Sinadinovski et al., 2006) ..............................................................................10

Table 2-2 Perth region regolith hazard for a 475-year return period of exceedance (Sinadinovski et al. 2006) ...............................................................................10

Table 2-3 Source zone parameters (Gaull and Michael-Leiba, 1987 and Gaull et al., 1990) ...............................................................................................................12

Table 2-4 Summary of seismicity parameters for SWWA (Dhu et al., 2004)........13 Table 2-5 ML Recurrence Parameters for Seismic Source Zones (Hao and Gaull,

2004a)..............................................................................................................14 Table 2-6 Attenuation constants adopted in Gaull and Michael-Leiba (1987), using

the form: cbMLRaeY −= ...................................................................................24 Table 2-7 A summary of site effect information for four zones identified in Gaull

(2003) ..............................................................................................................33 Table 2-8 Regolith thickness, shear wave velocities and natural period for site

classes (from McPherson and Jones, 2006) ....................................................34 Table 3-1 The peak value and the normalized FFT amplitude residual of the

observed and simulated motions .....................................................................55 Table 3-2 Summary of PGA model fit information. .............................................60 Table 3-3 Summary of comparison results of the predictions using the new PGA

model, Gaull (1988) model, Atkinson and Boore (1997) model and Toro et al. (1997) model with the SWWA records...........................................................63

Table 3-4 Summary of PGV model fit information. ..............................................64 Table 3-5 Summary of comparison results of the predictions from the new PGV

model, Gaull (1988) model, and Atkinson and Boore (1997) model with the SWWA records ...............................................................................................67

Table 3-6 Coefficients of horizontal spectral acceleration relations.......................69 Table 4-1: Random variables and their distribution................................................76 Table 4-2 Monte Carlo simulation and K-S test result for PGA, PGV, RMSA and

response spectrum at 0.1sec, 1.0sec, 2.5sec and 5sec .....................................80 Table 4-3 Point estimate and Monte Carlo simulation results for PGA , PGV,

RMSA, response spectrum at 0.1sec, 1.0sec, 2.5sec and 5sec and COAS .....82 Table 4-4 Case study 1 for sensitivity analysis.......................................................84 Table 4-5 Case study 2 for sensitivity analysis.......................................................84 Table 4-6 Case study 3 for sensitivity analysis.......................................................85 Table 4-7 Correlation matrix: PGA C.O.V. with the first order variables..............97 Table 4-8 Correlation matrix: PGA C.O.V. with the second order variables ........97 Table 4-9 Correlation matrix: PGA C.O.V. with the third order variables............97 Table 4-10 Correlation matrix: PGA C.O.V. with the combined variables............97 Table 4-11 Summary of the fitness tests for PGA model ......................................98 Table 4-12 Summary of the fitness test for PGV model.......................................99 Table 4-13 Derived coefficients for estimation of C.O.V. of PGA, PGV and

spectral acceleration with 5% damping.........................................................100 Table 5-1 ML Recurrence Parameters for Seismic Source Zones ........................108 Table 6-1 The site classifications for the study sites ............................................131 Table 7-1 Structural Performance Levels and Damage (FEMA356, 2000)..........145

x

Table 7-2 Dynamic stiffness of shallow or pile foundation (Gazetas, 1990)........146 Table 7-3 The material properties of jarrah and UMW ........................................148 Table 7-4 Vibration periods ..................................................................................149 Table 7-6 Vibration periods ..................................................................................152 Table 7-7 Maximum drift ratio of the RC building model....................................152 Table 7-8 Vibration periods ..................................................................................154 Table 7-9 Maximum drift ratio of the HR building model ...................................155

xi

LIST OF FIGURES

Figure 2-1 Earthquake source zones in SWWA (Gaull and Michael-Leiba, 1987 and Gaull et al., 1990).....................................................................................12

Figure 2-2 Earthquake source zones in SWWA (Dhu et al., 2004)........................13 Figure 2-3 Seismic Source Zones surround PMA (Hao and Gaull, 2004a)..........14 Figure 2-4 Site classes defined for PMA (McPherson and Jones, 2006)................32 Figure 2-5 Simple model assumed by Nakamura (1989) to interpret H/V ratio

technique .........................................................................................................37 Figure 3-1 FFT Comparison of the simulated and recorded ground motions.........51 Figure 3-2 Time histories of the simulated and recorded ground motion...............52 Figure 3-3 FFT Comparison of the simulated and recorded ground motions........53 Figure 3-4 Time histories of the simulated and recorded ground motions. ...........54 Figure 3-5 Time histories and FFT spectra of the Cadoux earthquake in 1979......56 Figure 3-6 The distribution of residuals..................................................................60 Figure 3-7 Comparison of the proposed PGA model with those of Gaull (1988),

Atkinson and Boore (1997) and Toro et al. (1997).........................................61 Figure 3-8 Curves predicted by the proposed PGA model for various magnitudes

plotted with SWWA records. ..........................................................................62 Figure 3-9 Percentage error of predictions from the new PGA model when

compared to SWWA records ..........................................................................62 Figure 3-10 The distribution of residuals................................................................64 Figure 3-11 Comparison of the new PGV model with those of Gaull (1988) and

Atkinson and Boore (1997).............................................................................65 Figure 3-12 Curves predicted by new PGV model for various magnitudes plotted

with SWWA records. ......................................................................................65 Figure 3-13 Percentage error of predictions from the new PGV model when

compared to SWWA records ..........................................................................66 Figure 3-14 Sum of residuals and coefficient of determination of the response

spectrum model ...............................................................................................68 Figure 3-15 Response spectra of ground motions from ML4, ML5, ML6 and ML7

earthquake at epicentral distances of 50km, 100km, 150km and 200km, damping ratio 5%. ...........................................................................................70

Figure 3-16 Predicted response spectra (A is acceleration in mm/s2, D is displacement in mm).......................................................................................71

Figure 4-1 Mean value, standard deviation of PGA, PGV and RMSA of the simulated ground motions ...............................................................................78

Figure 4-2 Mean value and standard deviation of the response spectrum at 0.1sec, 1.0sec, 2.5sec and 5sec....................................................................................78

Figure 4-3 Probability density function of PGA, PGV, RMSA and response spectrum of the simulated ground motion at 0.1sec, 1.0sec, 2.5sec and 5sec and the corresponding lognormal distribution function..................................79

Figure 4-4 Coefficient of variation of PGA, PGV, RMSA and response spectrum of the simulated ground motion with respect to that of the stress drop ratio ..86

Figure 4-5 Coefficient of variation of PGA, PGV, RMSA and response spectrum of the simulated ground motion with respect to that of the phase delay.........87

xii

Figure 4-6 Coefficient of variation of PGA, PGV, RMSA and response spectrum of the simulated ground motion with respect to that of the rise time..............88

Figure 4-7 Comparison of spectral acceleration and C.O.V. spectrum of the simulated ground motion with respect to variation in the stress drop ratio ....89

Figure 4-8 Comparison of spectral acceleration and C.O.V. spectrum of the simulated ground motion with respect to variation in the phase delay ...........89

Figure 4-9 Comparison of spectral acceleration and C.O.V. spectrum of the simulated ground motion with respect to variation in the rise time................89

Figure 4-10 Coefficient of variation of PGA, PGV, RMSA and COAS of simulated ground motions corresponding to earthquakes of ML5.0, ML6.0 and ML7.0 and epicentral distance 100 km when C.O.V. of the stress drop ratio is 50% 91

Figure 4-11 Coefficient of variation of PGA, PGV, RMSA and COAS of simulated ground motions corresponding to earthquakes of ML5.0, ML6.0 and ML7.0 and epicentral distance 100 km when C.O.V. of the phase delay is 50%.......91

Figure 4-12 Coefficient of variation of PGA, PGV, RMSA and COAS of simulated ground motions corresponding to earthquakes of ML5.0, ML6.0 and ML7.0 and epicentral distance 100 km when C.O.V. of the rise time is 50%............92

Figure 4-13 Influence of variation in the stress drop ratio (50% C.O.V) on parameters of ground motions simulated with different epicentral distances.93

Figure 4-14 Influence of variation in the phase delay (50% C.O.V) on parameters of ground motions simulated with different epicental distances.....................93

Figure 4-15 Influence of variation in the rise time (50% C.O.V) on parameters of ground motions simulated with different epicental distances .........................94

Figure 4-16 The distribution of residuals................................................................98 Figure 4-17 Sum of residuals, average residual, standard error of estimate and

coefficient of multiple determination for C.O.V. of the response spectrum model...............................................................................................................99

Figure 4-18 Attenuation model with 50% variation of source parameters (a-c, PGA model, d-f, spectral acceleration model with 5% damping at epicentral distance 100km) ............................................................................................103

Figure 5-1 Seismic Source Zones surround PMA (Hao and Gaull, 2004a)..........108 Figure 5-2 Rock PGA in PMA with a 10% chance of being exceeded in 50 years

(equivalent to the return period of 475 years)...............................................109 Figure 5-3 Rock PGA in PMA with a 2% chance of being exceeded in 50 years

(equivalent to the return period of 2475 years).............................................110 Figure 5-4 Rock PGA seismic hazard curve at longitude 115.85° and latitude

32.00° ............................................................................................................111 Figure 5-5 Calculated response spectrum and their ADRS format.......................112 Figure 5-6 Comparison of the response spectrum of the simulated time history with

the predicted design response spectrum for rock site in PMA......................114 Figure 6-1 Location of sites in PMA investigated in this study............................116 Figure 6-2 Flowchart of CSA................................................................................119 Figure 6-3 Circular array with 7 measurement locations in field measurements .120 Figure 6-4 Site 7: Measured and modelled SPAC function..................................122 Figure 6-5 Identified Shear-wave velocity profile of Site 7 .................................122 Figure 6-6 H/V spectrum of Site 7........................................................................123 Figure 6-7 Response spectrum and amplification spectrum of Site 7...................123 Figure 6-8 Site 4: Measured and modelled SPAC function..................................124 Figure 6-9 Identified Shear-wave velocity profile of site 4 ..................................124 Figure 6-10 H/V spectrum of Site 4......................................................................124 Figure 6-11 Response spectrum and amplification spectrum of Site 4.................124 Figure 6-12 Site 13: Observed and modelled SPAC function ..............................125

xiii

Figure 6-13 Identified shear-wave velocity profile of Site 13 ..............................125 Figure 6-14 H/V spectrum of Site13.....................................................................126 Figure 6-15 Response spectrum and amplification spectrum of Site 13...............126 Figure 6-16 Site 8: Observed and modelled SPAC function ................................127 Figure 6-17 Identified shear-wave velocity profile of Site 8 ................................127 Figure 6-18 H/V spectrum of Site 8......................................................................127 Figure 6-19 Response spectrum and amplification spectrum of Site 8.................127 Figure 6-20 Site 5: Observed and modelled SPAC function ................................128 Figure 6-21 Identified shear-wave velocity profile of Site 5 ................................128 Figure 6-22 H/V spectrum of Site5.......................................................................128 Figure 6-23 Response spectrum and amplification ration spectrum of Site 5 ......128 Figure 6-24 Site 9: Observed and modelled SPAC function ................................129 Figure 6-25 Identified shear-wave velocity profile of Site 9 ................................129 Figure 6-26 H/V spectrum of Site 9......................................................................129 Figure 6-27 Response spectrum and amplification spectrum of Site 9.................129 Figure 6-28 Site 10: Observed and modelled SPAC function ..............................130 Figure 6-29 identified shear-wave velocity profile of Site 10 ..............................130 Figure 6-30 H/V spectrum of Site 10....................................................................130 Figure 6-31 Response spectrum and amplification spectrum of Site 10...............130 Figure 6-32 475-year return period response spectra of S1 to S8.........................132 Figure 6-33 475-year return period response spectra of S9 to S16.......................133 Figure 6-34 2475-year return period response spectra of S1 to S8.......................134 Figure 6-35 2475-year return period response spectra of S9 to S16.....................135 Figure 6-36 Site response spectrum in ADRS format...........................................136 Figure 6-37 Natural period contours .....................................................................138 Figure 6-38 Spectral acceleration (g) contour at 0.2 sec.......................................138 Figure 6-39 Spectral acceleration (g) contour at 0.5 sec.......................................139 Figure 6-40 Spectral acceleration (g) contour at 1.0 sec.......................................139 Figure 6-41 Spectral acceleration (g) contour at 2.0 sec.......................................140 Figure 6-42 Spectral acceleration (g) contour at 3.0 sec.......................................140 Figure 7-1 Building types and percentages in PMA .............................................144 Figure 7-2 3D typical one story residential house model .....................................147 Figure 7-3 UMW building: plan view and right side view ...................................147 Figure 7-4 Six story RC building plan view .........................................................150 Figure 7-5 Six story RC building section view.....................................................151 Figure 7-6 3D six-story RC building model .........................................................151 Figure 7-7 Plane view of the 34 story high-rise building......................................153 Figure 7-8 3D model of the 34 story high-rise building of reinforced concrete

frame with core walls ....................................................................................154

xiv

LIST OF ABBREVIATIONS

CENA: Central or eastern North America

C.O.V.: coefficient of variation

COAS: coefficient of variation of response spectrum

CSA: clonal selection algorithm

DOFS: deviation of Fourier spectra

DSHA: deterministic seismic hazard analysis

ML: local magnitude

H/V: the ratio of the Fourier spectra of the horizontal to vertical component

RMSA: root-mean square acceleration

PGA: peak ground acceleration

PGV: peak ground velocity

PHA: Peak Horizontal Acceleration

PHV : Peak Horizontal Velocity

PMA: Perth Metropolitan Area

PSHA : probabilistic seismic hazard analysis

RC: reinforcement concrete

SCPT: seismic cone penetrometer test

SPAC: spatial autocorrelation

SWWA: the southwest Western Australia

UMW: unreinforced masonry wall

UMB: unreinforced masonry building

WA: Western Australia

School of Civil and Resource Engineering CHAPTER 1 The University of Western Australia

1

CHAPTER 1 INTRODUCTION

1.1 Background

Perth is the largest city in Western Australia and home to three-quarters of the state's

residents. The city is also the fourth most populous urban area in Australia and in recent

years has the fastest growth rate among the major cities in Australia. Unfortunately,

with this growth comes a proportional increase in the vulnerability to natural disasters.

In the past, seismic risk in Western Australia has been considered quite low since it is

located at large distance from any tectonic plate margin and the population is small.

However, in recent decades, there have been a lot of earthquake activities just east of

Perth in an area known as the South-West Seismic Zone. Three large earthquakes have

ruptured the surface and caused considerable destruction in the zone: the 1968

Meckering earthquake, the 1970 Calingiri earthquake and the 1979 Cadoux earthquake.

A sequence of more than 20,000 small earthquakes has also occurred near Burakin since

the beginning of 2001. The 1968 Meckering earthquake occurred only 130km east of

Perth and had a magnitude of 6.9. The earthquake caused almost total destruction in the

small country town and moderate damage in the Perth Metropolitan Area (PMA). It also

caused surface faulting up to 3 metres high and nearly 40km long. Seismic risk in

Western Australia is obviously increasing and it has become important for engineers to

be able to predict the possible intensity of future earthquakes for hazard analysis.

Much effort has been made into investigating the seismic risk of Western Australia and

PMA since 1968. Following the seismicity study of Western Australia by Everingham

(1968), Gaull and Michael-Leiba (1987) defined earthquake source zones in Western

Australia for seismic risk estimation using the Cornell-McGuire method. In a latter

study presented in Hao and Gaull (2004a), some modifications were done to the original

zone boundaries and recurrence relationships to include the most recent activity in the

Burakin area. As only very limited number of earthquake strong ground motion records

are available in southwest Western Australia (SWWA), and most of them were from


2

earthquakes of magnitude less than ML4.5, it is difficult to derive a reliable strong

ground motion attenuation model based on these data. Two peak ground acceleration

(PGA) and peak ground velocity (PGV) attenuation models that were developed using

SWWA data are Gaull and Michael-Leiba (1987) and Gaull (1988). Gaull (1988)

warned that the associated uncertainties should be taken into consideration when the

model was used to predict ground motions, especially those from large events. Since

there was no reliable attenuation model in SWWA, many seismic risk analysis for Perth,

e.g. Dhu et al. (2004) and Jones et al. (2006), and the design response spectrum in

current Australian Earthquake Loading Code (AS1170.4-2007) were based on the

attenuation models developed for Central or eastern North America (CENA). These

attenuation models were used because both CENA and SWWA are located in stable

continental intraplate regions. However, the reliability of these CENA models in

predicting SWWA strong ground motions is still under discussion. Some recent studies

(Hao and Gaull, 2004b; Kennedy et al., 2005) show that none of these models yielded

very satisfactory prediction of the recorded strong ground motions in SWWA. For

example, Hao and Gaull (2004b) compared five CENA ground motion models, and

concluded that these five models derived by different researchers differ significantly in

the lower magnitude range among themselves although they were all derived from the

same recorded CENA data. Hence, using CENA attenuation models to perform seismic

hazard analysis for PMA might transform bias ground motion prediction to the results.

Hao and Gaull (2004b) modified the Atkinson and Boore (1998) model based on the

available strong ground motion records in SWWA, and showed that the modified model

yielded good prediction of the recorded ground motions for moderate magnitude (<

ML5.5) events. However, since the vast majority of strong motion records used to

modify the model was from earthquakes of magnitude ML4.5 or below, its reliability in

representing larger SWWA earthquakes is yet to be known.

As the selection of an appropriate ground motion attenuation relation for use in

probabilistic earthquake hazard evaluation is almost always critical to the results, a

proper ground motion attenuation relation for SWWA should be developed and used in

seismic risk study for PMA site. Because available strong motions in SWWA are biased

towards earthquakes of less than ML4.5, one of the major research works in this study is

to simulate ground motions of earthquakes of magnitudes larger than this and


3

constructing reliable attenuation relations of PGA, PGV and response spectrum of

ground motions on rock site in SWWA based on the simulated data.

The amplitude of earthquake ground motion can be increased or decreased by the

properties and configuration of the near surface material. A defensible seismic risk

analysis should account for these conditions. Amplification of seismic waves in Perth

sedimentary basin has been observed in previous seismic events. For example, panic to

occupants and minor damage in some of the middle-rise buildings in downtown Perth

were caused by the Great Indonesian Earthquake of August 17, 1977, with an epicentral

distance of 2000 km. Gaull et al. (1995) presented an initial analysis of the site

amplification effects of the Perth Basin using microtremor spectral ratios and found that

the Perth Basin might amplify the bedrock motion by 2 to 10 times. Since then, many

efforts have been spent in investigating site response of Perth Basin. Hao and Gaull

(2004a) performed site response analysis for two soft soil sites at PMA based on three

design events corresponding to upper range, lower range and worst scenario event and

indicated that the design spectra in the current Australian code might overestimate

spectra accelerations on soft sites. However, Hao and Gaull (2004a) do not provide the

whole picture for site response in PMA owing to the lack of site information.

McPherson and Jones (2006) investigated regolith thickness and natural period for PMA

by using borehole data, seismic cone penetrometer test (SCPT) data and microtremor

data. They divided PMA into 4 soil classes based on the soil properties. The natural

period of sites in Gaull et al. (1995) and McPherson and Jones (2006) are mainly based

on microtremor data and linear soil properties. Many studies, Jarpe et al. (1989) and

Schnabel (1973), have indicated that soil responses will be nonlinear under strong

shaking. These studies also showed that the amplification factor derived from

microtremor may not give a reliable prediction of strong ground motion response at

some sites. Moreover, soil amplification analysis has not carried out in McPherson and

Jones (2006)’s study. The limitation of previous site response studies for PMA provides

the motivation for this research to perform more detailed studies of site responses across

the PMA.

As discussed above, the design response spectra in current Australian Earthquake

Loading Code were developed primarily from recorded motion in other parts of the

world. However, in some latter studies (e.g. Hao and Gaull, 2004a and Liang and Hao,

2007a), it is demonstrated that the design response spectra in Australian Earthquake


4

Loading Code might underestimate the spectral acceleration on some sites. Hence,

discussion on adequacy of the design spectrum is made. Assessment of the performance

of exiting buildings and infrastructures under the design ground motions derived in this

study is also carried out.

1.2 Research Objective

The study of seismic risk of buildings and infrastructure in PMA is quite limited. No

reliable local earthquake ground motion attenuation model is available yet, and no

systematic site response analysis in PMA has been carried out to provide sufficiently

accurate predictions of strong ground motion time histories for hazard analysis. As there

is an obvious need for a more reliable evaluation of the seismic hazard level for PMA,

this research attempts:

• to review the existing ground motion simulation techniques, site response

evaluation methods and seismic hazard analysis for PMA in the literature.

• to develop a new ground motion attenuation model for rock sites using a

modified ground motion simulation technique.

• to analyse the uncertainty effects of source parameters, i.e., stress drop ratio,

rupture velocity and rise time, on simulated ground motions and to develop a

coefficient of variation model.

• to carry out seismic hazard analysis of PMA based on the new ground motion

attenuation model.

• to estimate site response across the PMA using spatial autocorrelation method

(SPAC) and numerical method with the empirical nonlinear soil properties.

• to obtain the design spectra for the 475-year return period and 2475-year return

period earthquakes based on seismic hazard analysis and site response

evaluation, and compare the proposed design spectra with those specified in the

current Australian Earthquake Loading Code.

• to evaluate the response of typical buildings and infrastructure to the simulated

design ground motion time histories derived from seismic hazard analysis in this

study, and hence to evaluate the possible damage scenarios in PMA in

earthquakes of different return periods.


5

1.3 Organization of the Thesis

The thesis is structured as follows:

Chapter 2 reviews the existing ground motion simulation techniques, attenuation models

currently used in PMA and site characterization and site response analysis methods. The

advantages and disadvantages of these techniques and models are discussed.

In Chapter 3, a modified ground motion simulation technique is presented and the

accuracy of this method is tested in two case studies. This approach is then applied to

simulate ground motions for SWWA. New attenuation relations of PGA, PGV and

response spectrum of ground motions on rock site in SWWA are derived based on these

simulated data. The proposed attenuation model is compared with the model by Gaull

(1988), Atkinson and Boore (1997), and Toro et al. (1997). The predictions of these

models are also compared with the available SWWA records. Discussions on the

applicability and accuracy of each model are made with respect to the recorded data in

SWWA.

In Chapter 4, a statistical study of the effects of random fluctuations of the seismic

source parameters on simulated strong ground motions is performed using the Monte

Carlo simulation method and the Rosenblueth’s point estimate method. The accuracy of

the Rosenblueth’s point esimtate method in modelling the effect of random fluctuations

of seismic source parameters on simulated ground motions is verified. A sensitivity

analysis is also preformed to investigate the effect of random fluctuation of each source

parameters on simulated strong ground motions. A coefficient of variation model is

developed based on the simulated data using the Rosenblueth’s point estimate method.

In Chapter 5, seismic hazard analysis for PMA is carried out using the proposed

attenuation model. The design response spectra of rock site ground motions

corresponding to the 475-year return period earthquake and the 2475-year return period

earthquake in SWWA are derived.

Chapter 6 investigates the soil profiles and properties of a number of selected sites

around PMA and performs site response analysis to calculate the ground motions on


6

surface of soil sites in PMA. Site investigation is performed using the SPAC method.

The clonal selection algorithm (CSA) is adopted to perform direct inversion of SPAC

curves to determine the soil profiles of the sites. Using the derived shear-wave velocity

profiles, detailed site response analyses are carried out to estimate motions on ground

surface. Response spectra of the study sites are calculated and compared to that

specified by the current Australian code (AS1170.4-2007). Discussions on adequacy of

the code specified design response spectrum are made. Seismic microzonation for PMA

is defined based on the site investigation and ground motion simulation results. The

microzonation maps are given in terms of the site response spectrum and the

fundamental vibration period of the ground in the area.

In Chapter 7, the responses of three typical Perth structures, namely a masonry house, a

middle-rise reinforced concrete frame structure, and a high-rise building of reinforced

concrete frame with core wall, on various soil sites subjected to the predicted

earthquake ground motions of different return periods are calculated. Numerical results

are used to assess the seismic damage scenario of these buildings. The seismic safety of

building structures in PMA is evaluated according to the various design and safety

criteria for nonductile building frames.

Chapter 8 summaries the major results and findings in this research project, and

concludes the thesis. Recommendations for further research works are also given in this

chapter.


7

CHAPTER 2 LITERATURE REVIEW

2.1 Introduction

The definition of earthquake sources and their seismic recurrence characteristics,

ground motion estimation and local site effects are key issues for seismic hazard

analysis and seismic risk evaluation. Although many researches related to seismic

hazard analysis for PMA have been carried out since early 70’s, the accuracy of their

findings are in doubt due to the limited resources, such as the lack of recorded data and

geological description. This study will concentrate on seeking a way to reduce the

uncertainty that surrounds strong ground shaking and provides a more reliable and

confident estimation of seismic hazard in PMA. With these objectives, the following

subjects in the literature are extensively reviewed.

• The previous studies of seismic risk around PMA.

• Earthquake sources and their seismic recurrence relationship in SWWA;

• Bedrock motion simulation; including earthquake attenuation models and

earthquake simulation method;

• Uncertainties in earthquake source parameters.

• Soil site amplification; including geology and site effect in PMA, and site

amplification estimation method.

2.2 The studies of seismic risk around PMA

Many efforts have been spent in investigating the seismic risk level for PMA after the

1968 Meckering earthquake. Everingham (1968) carried out pioneering earthquake

hazard studies which attempted to determine earthquake frequency in SWWA. The

initial study was followed by the estimation of ground intensity return periods for ten

major centres in Western Australia (WA) by Everingham and Gregson (1970). McCue

(McCue, 1973) carried out an earthquake hazard assessment of SWWA. Subsequently,

McEwin et al. (1976) made the first attempt to zone the whole of Australia and get an


8

overestimated risk prediction since it is based on the attenuation model derived from

Californian data. Denham (1976) published a preliminary Australian earthquake hazard

zoning map based on a series of studies, i.e. McCue (1973) and McEwin et al. (1976).

In 1987, Gaull and Michael-Leiba (1987) studied the seismic risk of SWWA using

Cornell-McGuire method and formed earthquake risk maps from their analysis. Because

of a lack of recorded data in WA, PGA and PGV attenuation relationship adopted in

their study was developed based on a two-stage process, i.e., a) estimation of mean

isoseismal radii from local isoseismal maps; and b) conversion to PGA and PGV using

existing intensity-SGM models. Their work estimates that the maximum earthquake for

the seismic zone 1 (the minimum distance from the edge of zone 1 to Perth is 50km) is

ML7.5 and the ground motion intensity with a 10% probability of exceedance at Perth

during a 50 year interval is a PGV or PGA of 48 mm/s or 0.44 m/s2 respectively. Gaull

and Michael-Leiba (1987) strongly recommended that the possibility of seismic

amplification in the Perth Basin should be investigated.

In 2003, Wilson and Lam (2003) presented a normalised design response spectrum

(NDRS) for rock sites in Australia based on a response spectral velocity of 1.8 times the

peak ground velocity, and corner periods of T1=0.35secs and T2=1.5secs.

Recommended response spectra for soil sites have also been presented in acceleration-

displacement response spectra (ADRS) format. The recommended NDRS was based on

the stochastic simulations of seismological model known as the Component Attenuation

Model (CAM) presented by Lam et al.(2000a, 2000b). They concluded that the

recommended rock response spectra for 500 year return period is generally consistent

with the AS1170.4-1993 spectrum in the low period range, however, more accurately

represents the displacement demand expected in the higher period range.

In 2004, Dhu et al. (2004) modified the original zone boundaries and recurrence

relationships presented in Gaull et al. (1990) to include a variety of regional structural

trends and tectonic issues and the most recent seismicity in the area. Since there is no

available spectral attenuation model derived for Australian Earthquakes and crustal

conditions at that moment, three different attenuation models from CENA, i.e. Atkinson

and Boore (1997), Toro et al. (1997) and Somerville et al. (1995), has been

incorporated in their study to estimate earthquake hazard for PMA. Their study showed

that Atkinson and Boore (1997) model leads to notably higher estimates of hazard


9

ranging from PGAs of 0.22g in the north-east through to 0.16g in the south-west.

Estimation of earthquake hazard predicted using Toro et al. (1997) model are only

marginally higher than the previous Australian standard (AS1170.4-1993), i.e. the

estimated PGA ranges from 0.12g in the north-east down to 0.09g in the south-west.

Using Somerville et al. (1995) results in marginally lower estimates than the previous

Australian standard (AS1170.4-1993) with values ranging from 0.09g in the north-east

to 0.07g in the south-west. As there is no quantitative evidence to support the

preferential use of any of the three CENA models, the estimates for the three CENA

models were averaged with equal weighting in order to provide a combined estimation

of hazard for PMA. The averaged PGA on rock is estimated ranging from 0.14g in the

north-east to 0.1g in the south-west for a return period of 475 years. The study

concluded that the earthquake hazard on rock in Perth is moderately higher than that

predicted in the previous Australian standard (AS1170.4-1993). The earthquake hazard

for the built environment will be higher when local geological effects are taken into

account.

In 2006, a report presented by Sinadinovski et al., , which was compiled as a Chapter

for a study of natural hazard risk in Perth presented by Jones et al. (2006), performed a

detail seismic risk analysis in PMA. For the first time, spectral acceleration study for

PMA was carried out. Two CENA spectral acceleration attenuation models were

adopted in their study, i.e. Atkinson and Boore (1997) model and Toro et al. (1997)

model. The seismic zones closest to Perth and their boundaries used in their study was

consistent with that employed in Dhu et al. (2004). The PGAs predicted by Atkinson

and Boore (1997) model and Toro et al. (1997) model in Sinadinovski et al. (2006)’s

study were more than 1.5 times and nearly 2 times than those in Dhu et al. (2004)’s

study, respectively. The spectral accelerations at three periods were also estimated for

bedrock and regolith hazard analysis. The comparison of PGA and spectral acceleration

prediction presented in Sinadinovski et al. (2006) with those defined in the previous

Australian Code (AS1170.4-1993) and current Australian Code (AS1170.4-2007) were

summarised in Table 2-1 and Table 2-2 below. As can be seen, Sinadinovski et al.

(2006)’s study predicted the PGA in PMA greatly exceeds that in AS1170.4-1993 and

AS1170.4-2007.


10

Table 2-1 Perth region bedrock hazard for a 475-year return period of exceedance

(Sinadinovski et al., 2006)

Both standards1 AS1170.4-1993 AS1170.4-2007 Perth

Metropolitan location PGA(g) SA at

0.3s(g) SA at

1.0s(g) SA at

0.3s(g) SA at

1.0s(g)

Midland 0.0932 [0.261]3

0.233 [0.226]

0.116 [0.070]

0.273 [0.226]

0.082 [0.070]

Perth CBD 0.089 [0.232]

0.223 [0.205]

0.111 [0.065]

0.262 [0.205]

0.078 [0.065]

Fremantle 0.088 [0.229]

0.220 [0.202]

0.110 [0.064]

0.259 [0.202]

0.077 [0.064]

Table 2-2 Perth region regolith hazard for a 475-year return period of exceedance

(Sinadinovski et al. 2006)

Both standards1 AS1170.4-1993 AS1170.4-2007 Perth

Metropolitan location PGA(g) SA at

0.3s(g) SA at

1.0s(g) SA at

0.3s(g) SA at

1.0s(g)

Midland 0.0932 [0.159]3

0.233 [0.277]

0.145 [0.047]

0.342 [0.277]

0.116 [0.047]

Perth CBD 0.089 [0.139]

0.223 [0.248]

0.139 [0.043]

0.328 [0.248]

0.111 [0.043]

Fremantle 0.088 [0.132]

0.220 [0.243]

0.138 [0.042]

0.324 [0.243]

0.110 [0.042]

Note for Table 2-1 and Table 2-2: 1Bedrock PGA are the same in both AS1170.4-1993 and AS1170.4-2007 . 2Hazard values have been interpolated from hazard maps in standards to capture

variations across the study region. 3Values derived from Sinadinovski et al. (2006)’s study are shown in squared brackets.

In 2004, Hao and Gaull (2004a) performed a probabilistic seismic hazard analysis

(PSHA) for PMA using the modified CENA model for SWWA. In their study, different

b-value and A-value of recurrence relationship from Gaull and Michael-Leiba (1987)

and Dhu et al. (2004) were adopted since different regression method was used. It was

found that the 475-year return period design event for rock sites in Perth were estimated

to be about 0.09g, consistent with the corresponding results from the current Australian

Earthquake Loading Code (AS1170.4-2007). The soil site amplifications for PMA were

also investigated based on available geology information and showed that the current


11

Australian Earthquake Loading Code (AS1170.4-2007) generally overestimates ground

motion spectral accelerations in the period range of engineering interests.

2.3 Earthquake sources and the recurrence

relationship

The definition of earthquake sources and their seismic recurrence relationship is one of

the key issues in PSHA. As discussed above, different zonations and seismic recurrence

relationship models have been used for PSHA in literature. Seismic zonation are based

on information from regional geology and neotectonics, seismicity, stress field, damage

analysis of historic strong earthquakes, geophysics and others. These subjects are

weighted differently in the combined statistics and thus different conclusions could be

resulted even from the same information. Seismic zonation and seismic recurrence

relationship in SWWA have been improved many times after the first seismic hazard

study presented by Everingham in 1968 with the further in depth understanding of local

geology and great quantity of seismic record available.

Gaull and Michael-Leiba (1987) reviewed previous studies and carried out the seismic

risk analysis of SWWA using Cornell-McGuire method and formed earthquake risk

maps from their analysis. The earthquake risk maps presented in Gaull and Michael-

Leiba (1987) were subsequently incorporated into the probabilistic earthquake hazard

maps of Australia (Gaull et al., 1990). It was from these maps that the earthquake

hazard maps in the previous earthquake loadings standard (AS1170.4-1993) were

derived. The seismic zonation and seismic recurrence relationships presented in Gaull

and Michael-Leiba (1987) are shown in Figure 2-1 and listed in Table 2-3, respectively.


12

Figure 2-1 Earthquake source zones in SWWA (Gaull and Michael-Leiba, 1987 and

Gaull et al., 1990)

Table 2-3 Source zone parameters (Gaull and Michael-Leiba, 1987 and Gaull et al.,

1990)

Source zone A b Min Max Area(km2) 1 73.0 0.90 2.0 7.5 17000 2 16.95 1.00 2.0 7.5 92300 3 2.00 1.00 4.0 7.5 311250 4 1.00 0.67 4.0 8.0 545000 5 1.66 0.83 4.0 7.0 238000 6 0.14 0.83 4.0 6.0 18200 7 0.46 0.63 3.0 4.5 3900 8 3.60 0.94 4.0 7.7 135700 9 2.80 0.91 4.0 6.0 84200 10 7.50 1.01 4.0 7.5 24400

Background 0.60 1.00 2.0 5.0 10000 Min = Minimum Richter magnitude earthquake in zone

Max = Maximum Richter magnitude earthquake in zone

A = Number of earthquakes per annum above Min

b = Richter (1958) constant called b value

Some modifications presented in Dhu et al. (2004) were done to the original zone

boundaries and recurrence relationships to include the most recent researches related to

seismicity in the region ranging from historical seismicity through to a variety of

structural and tectonic issues. This updated seismic source zone map shown in Figure


13

2-2 and recurrence relationship model listed in Table 2-4 were adopted in the seismic

risk analysis presented by Sinadinovski et al. (2006).

Figure 2-2 Earthquake source zones in SWWA (Dhu et al., 2004)

Table 2-4 Summary of seismicity parameters for SWWA (Dhu et al., 2004)

Source zone Area(km2) Mmin Mmax b Amin Zone1 25365 3.9 7.5 1 1.29 Zone2 134344 3.9 7.5 1 0.02 Zone3 330916 3.9 7.5 1 0.11

Background 373291 3.9 7.5 1 0.05 Yilgarn 460465 3.9 7.5 1 0.04

Notes: Mmin = the minimum moment magnitude

Mmax = the maximum moment magnitude

Amin = the number of earthquakes per year with M≥Mmin normalized to 100000

km2

Different b-value and A-value of recurrence relationship from Gaull and Michael-Leiba

(1987) and Dhu et al. (2004) were adopted in Hao and Gaull (2004a) since different

regression method was used. The maximum likelihood method was used in Gaull and

Michael-Leiba (1987) and Dhu et al. (2004), and the least squares method was

employed in Hao and Gaull (2004a) to determine the b-value and A-value of recurrence

relationship. The seismic zonation and recurrence relationship presented in Hao and

Gaull (2004a) were shown in Figure 2-3 and listed in Table 2-5, respectively.


14

Figure 2-3 Seismic Source Zones surround PMA (Hao and Gaull, 2004a)

Table 2-5 ML Recurrence Parameters for Seismic Source Zones (Hao and Gaull, 2004a)

SZ A B 1 2.88 0.75 2 4.22 1.27 3 3.1 0.85

Background 1.78 1 Note: A value corresponds to 10,000 square kilometres.

2.4 Bedrock motion prediction

Predicting seismic ground shaking is an important step in anticipating earthquake

effects on people and structure. There are three methods of obtaining accelerograms on

bedrock: (i) Database of accelerograms (recorded on rock outcrops or in downholes); (ii)

Stochastic simulations of the seismological model and (iii) Green’s Function Method

which is sub-divided into the Empirical Green’s Function Method and the Stochastic

Green’s Function Method. Ideally, the empirical attenuation relations developed from

the recorded data at the site under consideration should be used. However, in most

engineering applications, this is not possible because of the lack of recorded data. The

common approaches are then to use the empirical relations developed at other sites with

similar tectonic and geophysical conditions, or to adopt ground motion simulation

techniques, i.e. Stochastic simulation techniques or Green’s Function Method. Both of

these approaches have been considered in previous seismic hazard study for PMA.


15

2.4.1 Earthquake simulation method

Strong ground motion simulation is an alternative approach to estimate ground motion

at sites where few strong ground motion records are available. There are two popular

approaches of simulating strong ground motions, namely stochastic approach and

Green’s Function method.

2.4.1.1 Stochastic approach

Stochastic approach (Hanks and McGuire, 1981; Boore, 1983 and 2003; Boore and

Atkinson, 1987; Hao and Gaull, 2004b) is based on a set of assumptions regarding the

earthquake source spectrum, propagation path and site conditions. The accelerations are

modelled as band limited finite-duration white Gaussian process passed through a

number of filters. The basic equation proposed by Boore (2003) is given as:

( ) ( ) ( ) ( ) ( )fIfGfRPfMEfRMY hypo ,,,, 00 = , (2-1)

where Mo is the seismic moment, f is the frequency. The first filter E(Mo,f) in Equation

2-1 represents the source spectrum. The most commonly used model of the earthquake

source spectrum is the ω-squared model, proposed by Aki (1967). The dependence of

the corner frequency f0 on seismic moment determines the scaling of the spectrum from

one magnitude to another. Besides the ω-squared model, a variety of other models have

also been used with the stochastic method. Equations 2-2 and 2-3 have been used to

predict ground motions in CENA.

( ) ( )fMSCMfME ,, 000 = , (2-2)

( ) ( ) ( )fMSfMSfMS ba ,,, 000 ×= , (2-3)

where C=<RΘФ>VF/(4πρβ3R0), in which <RΘФ> is the radiation pattern, V represents

the partition of total shear-wave energy into horizontal component, F is the effect of the

free surface, ρ and β respectively are the density and shear-wave velocity in the vicinity


16

of the source, and R0 is a reference distance. For WA condition ρ=2750 kg/m3, and

β=3910 m/s (Dentith et al., 2000). Many spectral shape of Sa(f) and Sb(f) have been

suggested by different authors. For example, Atkinson and Boore (1995) proposed the

following equation:

( )( ) ( )

( ) 0.1,/1/1

122 =

++

+−

= fSffff

fS bba

aεε

(2-4)

where ε is a relative weighting parameter, fa and fb are two corner frequencies. Since the

geophysical conditions of SWWA and CENA are quite similar, Hao and Gaull (2004b)

used a few CENA models to simulate ground motion time histories in SWWA. After

comparing the ground motion spectra estimated from CENA models with the actual

recorded motions, Hao and Gaull (2004b) indicated that the model by Atkinson and

Boore (1995) gives relatively better prediction at both near source and large epicentral

distance.

In Equation 2-1, P(R,f) describes the spectral amplitude attenuation with the closest

distance from the rupture surface. The simplified path effect P(R,f) is given by the

multiplication of the geometrical spreading and the anelastic attenuation:

( ) ( ) ( )fRAnRGafRP ,, = , (2-5)

where Ga(R) is the geometrical attenuation,

( )( )( )⎪⎩

⎪⎨

⎧

>≤<≤

=DRRDDDRDDDRR

RGa5.2/5.25.1/15.25.15.1/15.1/1

2/1

,

(2-6)

in which D is the earth’s crust thickness, and An(R,f) is the anelastic attenuation:

( ) βπ QfRefRAn /, −= . (2-7)

The Q function is given by Q=680f 0.36 in most ENA models.


17

In Equation 2-1, the filter G(f) represents the effect of site condition and I(f) is related to

the type of ground motion. Site condition function can be expressed as:

( ) ( ) ( )fDfAfG = (2-8)

in which A(f) is the amplification function, depending on the shear-wave velocity and

depth. A(f) can be simply given by the squre root if the impedance ratio between the

source and the surface. The diminution function D(f) is used to model the path-

independent loss of high-frequency in the ground motions. Two D(f) filters commonly

used are:

1) the fmax filter proposed by Hanks (1982) and Boore (1983)

( ) ( )[ ] 2/18max/1

−+= fffD ; (2-9)

and 2) the К0 filter by Anderson and Hough (1984)

( ) ( )ffD 0exp πκ−= . (2-10)

Since all the CENA models overestimate SWWA ground motion spectral value at

frequencies higher than about 20 Hz, Hao and Gaull (2004b) modified the fmax filter to:

( )( )

( )⎪⎪

⎩

⎪⎪

⎨

⎧

>+

≤+

=

kmRff

fR

kmRff

fD10,

/10.70001

10,/1

5.0

6max

8max

,

(2-11)

and fmax=35Hz, and Q=700f 0.25. It should be noted that the above Equation 2-11 is not

continuous at R=10km. This is because the number of available recorded strong motion

data is very limited to derive a continuous D(f) function. It was demonstrated that

Atkinson and Boore (1995) model with the modified fmax filter and Q value gives

reasonable prediction of the strong ground motions recorded on rock site in SWWA.

However, because only very few ground motion records are available and most of them

are from earthquakes of magnitude less than ML5.0, this modified model may be biased


18

towards lower magnitude earthquake ground motions. In other words, its validity in

predicting ground motions in SWWA from minor-moderate magnitude earthquakes was

proven, but its reliability in predicting ground motions from large earthquakes is yet to

be known.

2.4.1.2 Green’s Function method

Green’s Function method is the other method that is based on the representation

theorem for a kinematic dislocation model. The equation for the method is given by Aki

and Richards (1980), which gives the elastic displacement u caused by a displacement

discontinuity [u(ξ,τ)] across an internal surface Σ as

( ) ( )[ ] ( ) ( )ξτξτξτ Σ= ∫ ∫∫∞

∞−Σ

dvtxGcudtxu kqipjkpqji ,;,,, ,

,(2-12)

where cjkpq are the elastic constants, Gip,q(x,t,ξ,τ) is the Green’s source function, ν is unit

normal to the fault surface, ξ and x represent a point on the fault plane and the

observation point respectively. Somerville et al. (1991) rewrites the above equation in

the far-field as

( ) ( ) ( ) ηξηξηξ ddtxGtDtxuL W

,,,,,,0 0

∗= ∫ ∫ &, (2-13)

where (ξ,η) defines a point on the fault plane, L is the fault length, W is the fault width,

D is the slip time history, G is the impulse response of the medium and * represents a

convolution.

Since the earth’s real structure is more complicated than assumed, accurate and

complete modelling of a Green’s function representation of the displacements of the

medium would be extremely difficult. To overcome this difficulty, Hartzell (1978)

proposed an empirical Green’s function method to model strong ground motions from a

large earthquake by using the aftershock records as an empirical earth response. The

equation can be written as


19

( ) ( ) ( )[ ] ( )i

n

iii tHtQtUtU τ−∗= ∑

=1 , (2-14)

( ) ( ) ( ) ( )tRtMtStU iiii ∗∗= , (2-15)

in which Qi is a generalised scaling factor, H is the Heaviside unit step function, τi is a

phase delay term, Si is the source function, Mi is the earth response and Ri is the receiver

function. The effects of Si, Mi and Ri are all included in the aftershock. Theoretically,

aftershock recordings are required to be well distributed over the fault plane and be of a

sufficient number so that there are no “blank” areas. In reality, the recorded aftershocks

are usually not well distributed over the fault plane.

Following the idea of Hartzell (1978), Beresnev and Atkinson (1997) simulated ground

motions from large earthquake event using stochastic finite-fault simulation technique

in which the fault plane is discretized into equal rectangular elements, each of which is

treated as a point source. Ground motion contributions from the subsources are

calculated using a stochastic model. The results showed that a simple summation of

stochastic point sources distributed over a large fault plane is capable of simulating high

frequency ground motions from finite faults.

In the empirical Green’s function technique of Irikura (1986), the large event has been

modelled from the aftershocks that may not be well distributed within the rupture plane.

Irikura (1986) divided the mainshock fault plane into subfault plane to satisfy the

scaling law of the source spectral. The size of the main-fault and sub-fault corresponds

to the rupture area of main event and small event respectively. Because the frequency

contents of a small event are usually not the same as those of a large event, direct

application of Equation 2-14 may not be able to generate representative ground motions

from large event with proper frequency contents. To overcome this, Irikura et al. (1997)

modified an exponential slip function to boost the low-frequency energy in the

simulation. The equation of Irikura et al. (1997) is given as

∑∑==

⋅∗⋅=N

jij

N

i

tuCtFrrtU11

))(()()/()(,

(2-16)

Where


20

{ ( )( ) } ( ) ( ) }{ ( ) }{[ ]∑′−

=

′−−−−×′−−−−−′

+−=−nN

kij

ijij

nNTkttnNkn

ttttF)1(

1

)1/(11/1exp1exp1)/1(

)()(

δ

δ

(2-17)

and

( ) rijsijij VrrVrrt // 00 −+−= , (2-18)

with * as a symbol for convolution and :

U(t): the ground motion of large event;

r: the distance between the hypocenter of small event and the receiver;

rij: the distance between the subfault (i,j) and the receiver;

r0: the distance between the subfault (i,j) and the hypocenter of large event;

F(t) : the slip-time filtering function;

C: the stress drop ratio;

Vs: the shear wave velocity;

Vr: the rupture velocity;

u(t): the contribution of the jth sub event;

δ(t-tij): Dirac delta function;

tij: phase delay term;

n’: an appropriately selected integer to eliminate spurious periodicity.

N is the scaling law between large and small event. There are two scaling relations

between large and small event. One of them is given by Kanamori and Anderson (1975)

as

NmMdDTWWLL OOee ===== 3/1)/(//// τ , (2-19)

where L and Le are the length of the rupture plane of the large and small events,

respectively; W and We are the width of the rupture plane of the large and small events,

T and τ are the slip duration of the large and small events, respectively; D and d are the

slip of the large and small events, respectively; and Mo and mo are the seismic moment

of large and small event, respectively. This scaling law is based on the assumption of

size-independent stress drop that is proportional to Mo/(LW)3/2 or mo(LeWe)3/2, i.e. the


21

stress drop is a constant between the large event and the small event, Mo/(LW)3/2 is equal

to mo(LeWe)3/2 and Equation 2-19 is established.

Another scaling law is based on the ω-square model of Aki (1967) and Brune (1970).

The shape of the ω-squared source spectra is given as

( ) ( )[ ]20 /1/~~

cffUfU += , (2-20)

where Ũ(f) is the amplitude of displacement spectrum, Ũ0 is the flat level of

displacement spectrum at low frequencies and fc is the corner frequency. The scaling of

the spectrum from one magnitude to another is then determined by specifying the

dependence of the corner frequency fc on seismic moment. The assumption of similarity

in the earthquake source proposed by Aki (1967) implies that Mofc3 is constant and is

related to the stress drop. Hence, the spectral relationship between large and small

events can be written as

( ) NmMaANmMuU ==== 3/10000

30000 /~/~,/~/~

(2-21)

where ũ0 is the flat level of the displacement spectrum of small event, Ã0 and ã0 are that

of the acceleration spectra, for large and small events, respectively.

Follow the basic theory of the scaling law described above, Irikura (1986) introduced

following Equation 2-22 that can be used in different stress drop between small and

large event.

CNdDNCmMTWWLL OOee ===== /,)/(/// 3/1τ , (2-22)

where C is the stress drop ratio.

Many previous studies, e.g. Hadley and Helmberger (1980), Irikuro (1983), Somerville

et al. (1991), modelled the large event by delaying and summing small events along the

fault rupture or fault area directly. The problem is that this will underestimate low-


22

frequency components in the synthetic record (Frankel, 1995 and Joshi and Midorikawa,

2004). Boatwright (1988) demonstrated that the subevents which are comprised in large

earthquakes exhibit the characteristics of asperity failures and most small and moderate

earthquakes whose recordings might be used as Green’s functions exhibit crack-like

scaling characteristics which are deficient in their low-frequency radiation or require the

multiple rupture of the same fault area. Since asperities are the appropriate models for

subevent which is used as Green’s function, a simple filtering operation is proposed by

Boatwright (1988) to transform the crack model to the asperity model. Following the

idea of Boatwright (1988), Frankel (1995) and Irikura et al. (1997) modified their

simulation method to overcome the problem. In the Frankel (1995) method, the

aftershock sum is convolution with the slip velocity function for simulating the large

event. The spectra of the relative slip velocity function is given as

( ) ( )( )2

2

1 /1/1

cmain

csmall

ffff

CfS+

+=

, (2-23)

∑= Δ

Δ= n

ismall

small

i

main

M

MC

10

01

σσ

, (2-24)

in which, the subscript ‘main’ and ‘small’ represent main event and small event

respectively, Δσi/Δσsmall is the ratio of the stress drop of cell i to that of the small event.

The spectrum of the relative slip velocity function is derived from dividing the main

event source spectrum model by small source spectrum model. Frankel et al. (1996)’s

source spectrum model has the form:

( )( )2/1

196cff

fFea+

= . (2-25)

The comparison studies of Frankel et al. (1996)’s source spectrum model and other

CENA model have been carried out by Hao and Gaull (2004b). Frankel (1995)’s

method has good agreement between simulated and observed spectra between 0.5 Hz

and 20 Hz. However, Frankel’s model is based on the concept that the incoherent

summation process does not change the shape of the spectrum significantly, only its

absolute amplitude. In fact, incoherent summation process will change the shape of the

spectrum significantly in the low frequency range, which is determined by interval of

incoherent summations. Irikura et al. (1997) introduced a modified filter F(t) (Equation


23

2-23) to get the synthetic record having a basic spectral shape of ω-squared source

model in a broad frequency range. Irikura et al. (1997)’s method makes synthetic record

match not only the moment at low frequencies but also spectral contents at high-

frequencies to keep the stress-drop constant independent of the source size. The method

can be easily extended to cases having different stress parameters between small and

large events.

Since the assumption of empirical Green’s function method is that the effect of focal

mechanic, earth response and propagation path have been included in aftershocks and

small events, the large event ground motion can be simulated accurately and completely

at locations where the small event data is recorded. When the epicentral distance or the

location where the large event ground motion is going to be simulated is different from

that of the small event ground motion that will be used in the simulation is recorded,

reliable ground motion simulation may not be achieved because of the path and site

effects.

2.4.2 Earthquake attenuation models used for SWWA

predictions

Two PGA and PGV attenuation models that were developed using limited SWWA data

are Gaull and Michael-Leiba (1987) and Gaull (1988). The model developed from the

first reference was based on intensity information as obtained from isoseismal maps in

Western Australia. Gaull (1988) model was derived from twenty-one filtered

accelerograms which were recorded in SWWA. Other popular models used in

predicting ground motion attenuations in SWWA are mainly those from central and

eastern North America (CENA), such as the model derived by Atkinson and Boore

(1997) and Toro et al. (1997). These models are commonly used because both CENA

and SWWA are located in stable continental intraplate region. The models derived by

Atkinson and Boore (1997) and Toro et al. (1997) were based on stochastically

simulated accelerograrms.


24

2.4.2.1 Gaull and Michael-Leiba (1987) model

As there are only few recordings of ground acceleration from large earthquakes

(ML>5.5) on the shield in Western Australia, Gaull and Michael-Leiba (1987)

developed a ground motion attenuation model from isoseismal maps. The model based

on a two-stage process, i.e., a) estimation of mean isoseismal radii from local isoseismal

maps; and b) conversion to PGA and PGV using existing intensity-SGM models. The

adopted values for the attenuation constants are presented in Table 2-6.

Table 2-6 Attenuation constants adopted in Gaull and Michael-Leiba (1987), using the

form: cbMLRaeY −=

Ground motion parameter, Y A b c

Intensity (MM)=InY 9.03 1.50 1.39

Peak ground velocity (mms-1) 3.30 1.04 0.96

Peak ground acceleration (ms-1) 0.025 1.10 1.03

2.4.2.2 Gaull (1988) model

The attenuation relationship developed by Gaull (1988) is one of the few models

developed for WA using local records. The model gives attenuation relations for Peak

Horizontal Acceleration (PHA) and Peak Horizontal Velocity (PHV) derived from

twenty-one filtered accelerograms which were recorded in SWWA. It is important to be

aware that PHA and PHV in this model refer to ground periods of 0.1 s or more.

Removal of the lower periods through the filter was carried out on the assumption that

such vibrations do not impact on most engineering structures. Also, because the

available data recorded in SWWA are very limited and most of them are associated with

earthquakes of magnitude less than or equal to ML4.5, Gaull (1988) warned that the

associated uncertainties should be taken into consideration when the model was used to

predict ground motions, especially those from large events. It is stated in the paper that

alluvial and hard rock sites respectively amplified and attenuated the mean peak ground

acceleration estimates by up to a factor of three. Therefore, to use these models,

amplification factors should be known for the site.


25

The peak ground acceleration attenuation relationship is given in Equation 2-26 below.

The equation is recommended for use with magnitudes of 4.5 to 7 and distances of 5km

to 200km.

2.10045.0log77.0)6(20

3log5log +−−−⎥⎦

⎤⎢⎣⎡ +

= slantslantslant RRML

RPHA (2-26)

Where: PHA is the peak horizontal ground acceleration in m/s2;

Rslant is the slant distance in km;

ML is Richter scale magnitude.

The peak horizontal ground velocity is estimated by Equation 2-27 below. This model is

recommended for earthquakes of magnitude 2 to 6.3.

33.0005.0log14.16.0log −−−= slantslant RRMLPHV (2-27)

in which PHV is in mm/s.

As these models have been derived from mainly small magnitude events, there is

uncertainty in the model being able to accurately describe the attenuation of strong

motions from large events. The models are recommended for use for earthquakes of

magnitude 4.5 to 7 for peak ground acceleration and magnitudes 2 to 6.3 for peak

ground velocity. From the table of events used in the development of the models, there

are only five listed that have a magnitude over 4.5. There may be cause for concern that

magnitudes over this range are not properly represented. In a paper by Sinadinovski and

Robinson (2003), it indicated that the uncertainty in the Gaull formula has been

underestimated. Hence, some CENA attenuation models have been adopted in PSHA

for PMA.

2.4.2.3 Atkinson and Boore (1997) model

Atkinson and Boore (1997) presented equations for peak ground acceleration and peak

ground velocity for the attenuation of ground motions on hard rock sites in CENA. The


26

attenuation equations were obtained by regression of a subset of simulated ground

motion data. The ground motion data was simulated using a stochastic earthquake

spectrum model. Peak ground acceleration and peak ground velocity were simulated for

moment magnitudes of 4 to 7.25 in 0.25 magnitude-unit increments for hypocentral

distances of 10km to 500km in increments of 0.1 log units. Fifty trials were used for

each magnitude-distance combination.

The attenuation relationships derived by Atkinson and Boore (1997) are shown below

(Equation 2-28 and Equation 2-29).

hypohypo RRMwMwPGA 00311.0ln)6(123.0)6(686.0841.1ln 2 −−−−−+= (2-28)

hypoRMwMwPGV ln)6(0859.0)6(972.0697.4ln 2 −−−−+= (2-29)

Where: PGA is peak ground acceleration in g;

PGV is peak ground velocity in cm/s;

Rhypo is hypocentral distance in km;

Mw is moment magnitude.

Atkinson and Boore (1997) recommend that these attenuation models can be used for

hazard analysis. The models were found to be most accurate for cases where the

expected ground motions are relatively large (over 0.25g). For moderate to small

ground motions the equations are quite conservative and the user is cautioned to keep

this in mind when using them. To avoid overestimation in low-seismicity regions,

Atkinson and Boore recommend that the simulation results be referred to instead of

using the equations.

2.4.2.4 Toro et al. (1997) model

Ground motion attenuation equations for peak ground acceleration have also been

developed by Toro et al. (1997) for rock sites in the mid-continent of CENA and the

Gulf of CENA. The peak ground acceleration models have been based on the

predictions of a stochastic model for source excitation and a model of path effects that


27

considers multiple rays in a horizontally layered model of the crust. These models were

derived from analysis of CENA ground motion data and other relevant data.

The peak ground acceleration equation for the mid-continent and the gulf of CENA are

shown below (Equation 2-30 and Equation 2-31):

PGA model for the mid-continent of CENA:

22 3.9

0021.00,100

lnmax)27.116.1(ln27.1)6(81.02.2ln

+=

−⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛−−−−+=

RR

RRRMPGA

M

MM

MW

(2-30)

PGA model for the gulf of CENA:

22 9.10

0014.00,100

lnmax)49.161.1(ln49.1)6(92.091.2ln

+=

−⎥⎦⎤

⎢⎣⎡−−−−+=

RR

RR

RMPGA

M

MM

Mw

(2-31)

in which, PGA is peak ground acceleration in g and R is the closest horizontal distance

to the earthquake rupture in km.

These equations are recommended for horizontal components of peak ground

acceleration with earthquake moment magnitudes of 4 or above and for distances less

than 200km on rock site conditions. The equations were compared to CENA records

that met these criteria. The comparisons illustrate that the peak ground acceleration

predicted by the equation are generally consistent with observations.


28

2.5 Uncertainties in source parameters

In the empirical Green’s function model of Irikura (1986), the earthquake source is

characterized by a set of source parameters, i.e., stress drop ratio, fault dimensions,

rupture velocity and rise time. These parameters are usually derived from empirical

source models. Statistical studies of these parameters have been carried out by several

researchers (Tocher, 1958; Iida, 1965; Ambraseys and Zatopek, 1968; Matsuda, 1975;

Geller, 1976; Wells and Coppersmith, 1994; Dowrick and Rhoades, 2004, etc.) with the

aim of establishing empirical formulae for source parameters as a function of the

earthquake magnitude. However, because different data set have been used and because

of uncertainties in local condition of various seismic sources which all affect the source

parameters, little agreement can be found in these studies.

One important parameter for the Green’s function method is the stress-drop ratio, which

is proportional to M0fc3 (Aki, 1967; Brune, 1970). To estimate the stress drop from

seismic data, it is necessary to know the fault dimensions and the average displacement.

The stress drops are generally considered to be uncertain to various extents because of

the poor accuracy of source dimension estimations. It is still under debate on how the

stress drop is related to earthquake magnitude. Street et al. (1975) and Street and

Turcotte (1977) suggested that stress drop increases with seismic moment for CENA. In

contrast, Somerville et al. (1987) and Boore and Atkinson (1987) indicated that the

constant stress-drop assumption appears to be supported by CENA data. Purcaru and

Berckhemer (1982) based on the analysis of a dataset of 240 observed records

concluded that stress drop in large to very large earthquakes varies from a few bar to

some 100-150 bar. For smaller events, stress drop may vary over an even larger range.

Furthermore, average stress drop for interplate earthquake is about 30 bars compared to

about 100 bar for intraplate events (Lay and Wallace, 1995), which implies that

intraplate faults have higher levels of stress release than interplate faults although the

intraplate events have smaller fault dimensions for the same moment release.

Earthquakes in SWWA are intraplate events and the stress drop does not seem to be

constant in small magnitude event as observed in the data of Burakin earthquake (Allen

et al., 2006). However, for earthquakes of magnitude ML5 and above, compared with

the recorded data, Liang et al. (2006) found that the constant-stress scaling law is

suitable as most simulated motions based on a constant stress drop assumption well fit


29

with the record motions. However it is difficult to further verify this argument because

of the lack of data from large magnitude events.

For the fault dimension, it usually can only be estimated approximately from the rupture

duration with an assumed rupture velocity. Since no seismic source parameters for the

SWWA earthquake are available, empirical relations between earthquake magnitude

and fault length, fault area and rupture velocity derived in other regions are reviewed

here.

There are many empirical relations between the earthquake magnitude and fault length

in the literature, e.g.:

99.732.1log −= ML (for worldwide earthquake, Iida, 1965) (2-32)

76.502.1log −= ML (for USA, Tocher, 1958) (2-33)

5.3log6.1 −= LM (for Parkfield and Imperial earthquakes, Press, 1967)

(2-34)

7.6log9.1 −= LM (for Parkfield region, Wyss and Brune, 1968) (2-35)

38.614.1log −= ML (for Anatolia, Ambraseys and Zatopek, 1968) (2-36)

9.26.0log −= ML (for Japan, Matsuda, 1975) (2-37)

Similarly, many empirical relations of earthquake magnitude and fault area are available:

76.6,28.232log <−= SS MMFA (Geller, 1976) (2-38)

)05.025.22(log5.1log 0 ±+= FAM (for dip-slip earthquake, Purcaru and

Berckhemer, 1982) (2-39)

49.17log45.2log 0 += FAM (for strike-slip earthquake, Purcaru and

Berckhemer, 1982) (2-40)

3/20

151023.2 MFA −×= (Somerville et al., 1999) (2-41)


30

A worldwide data base for 421 historical earthquakes was used in Wells and

Coppersmith’s (1994) study. The updated and revised empirical relationships among

magnitude, rupture length, rupture width, rupture area and the surface displacement

were developed. These models were associated with different slip types of earthquakes.

A number of values for rupture velocity have been suggested and used in the literature.

Geller (1976) concluded that averaging the reported rupture velocities yields the relation

Vr=0.72β, where β is the shear wave velocity ranging from 3.5 km/sec for shallow

crustal events to 4.5 km/sec for events breaking the entire lithosphere. Purcaru and

Berckhemer (1982) studied earthquake parameters based on a dataset of 240

earthquakes and indicated that rupture velocity can be from 1km/sec to 4.8km/sec. A

rupture velocity of 3.0km/sec for New Zealand data is derived by Dowrick and Rhoades

(2004).

The rise time is given as Equation 2-42 in Purcaru and Berckhemer (1982).

uuT &/= (2-42)

where u is the average seismic slip and u& is the slip velocity. Many studies showed

that the rise time can be related to the rupture velocity (Boore, 1978), the effective

dynamic stress (Brune, 1970; Kanamori, 1972), the static stress drop (Noguchi and Abe,

1977) or fault dimensions (Purcaru and Berckhemer, 1982). Purcaru and Berckhemer

(1982) also indicated that rise time varies from less than one second to several hundreds

of seconds.

As shown, since many unknown and/or uncertain factors influence these parameters,

they inevitably vary from site to site and from event to event at same sites. In most

previous studies of ground motion simulation, these parameters are assumed as

deterministic. The effects of their variations on earthquake ground motions are not

properly studied yet. In this thesis, the influences of the statistical variations of the

uncertain source parameters on simulated ground motions will be studied.


31

2.6 Soil site amplification in PMA

Site response deserves a great deal attention and consideration since very large

amplification of ground motion which caused loss of life and structural damages can be

generated by seismic resonance in very soft clay layers. This phenomenon has been

proved in many previous earthquakes, such as the 1985 Mexico, 1989 Loma Prieta,

1994 Northridge and 1995 Kobe earthquakes, which caused significant damage due to

soft clay deposits underneath the downtown area of these cities. Amplification of

seismic waves in Perth sedimentary basin was also observed. For example, panic to

occupants and minor damage in some of the middle-rise buildings in downtown Perth

were caused by the Great Indonesian Earthquake of August 17, 1977, with an epicentral

distance of 2000 km (McGuire, 1995). Many efforts have been spent in investigating the

site response of Perth Basin and some publications can be found in the literature， e.g.

Gaull et al. (1995), Gaull (2003), Hao and Gaull (2004b) and McPherson and Jones

(2006).

2.6.1 Geology of PMA

Perth has two distinct geological areas that are separated by the Darling Fault. East of

the Darling Fault is the Darling Plateau, an area of granitic rocks about 2.6 billion years

old. The Swan Coastal Plain, which lies to the west of the Darling Fault, developed over

a deep trough filled with sedimentary rocks about 12km thick. The Plain is mainly

covered by sand left by the retreating sea. The type of minerals and rocks extracted in

the Perth region include sand, limestone, clay and shales, bauxite, and hard rock. A

recent study of geology for PMA was carried out by McPherson and Jones in 2006.

McPherson and Jones (2006) conducted a detailed analysis of site classes for PMA

based on many previous studies, e.g. Playford et al., (1976) and Davidson (1995), and a

statistical analysis of borehole data, seismic cone penetrometer test (SCPT) data and

microtremor data. Based on their analyses, they divided PMA into four site classes as

shown in Figure 2-4.


32

Figure 2-4 Site classes defined for PMA (McPherson and Jones, 2006)

2.6.2 Seismic amplification studies for PMA

Only limited researches were carried out to investigate the site amplification effects of

the Perth Basin before 1995. Gaull et al. (1995) presented an initial analysis of the site


33

amplification effects of the Perth Basin using microtremor spectral ratios. Simultaneous

measurements of microtremors were carried out on sites with a 3km grid over most

metropolitan area of Perth. They constructed microzonation maps of Perth from

microtremor spectral ratios and found that spectral ratios correlated well with geological

subsurface layers. In that study, they also provided a tentative assessment of Perth’s

ground motion and site amplification, and local confirmation of the relationship

between site amplification and local geology. It was shown that the Perth Basin might

amplify the bedrock motion by 2 to 10 times.

Based on microtremor spectral ratios survey for PMA, more detailed study of site effect

was performed in Gaull (2003). The resonance periods throughout the regolith of the

PMA were identified using H/V method. The shear wave velocity in the upper layer was

estimated using the quarter wavelength theory. An empirical relation between the

average horizontal spectral amplification and shear wave velocity by Borcherdt (1991),

and the Imai and Tonouchi (1982) relation between standard penetration test (SPT) and

the shear wave velocity were used to assess the shear wave velocity. Four zones in the

PMA that have different periodic response during earthquake excitation were identified

and are summarised in Table 2-7.

Table 2-7 A summary of site effect information for four zones identified in Gaull (2003)

Soil Type Depth (m) Resonance Periods (sec)

Vs (m/s)

Zone 1 Shallow sand 10 0.1-0.3 285-450

Zone 2 Calcareous sand and Aeolian sand

20-40 0.3-0.7 180-265

Zone 3 Unconsolidated sediments(sand and silt)

>40 0.9-1.7 220

Zone 4 Pebbly silt and alluvial sandy clay

- 0.1-2.0 190-235

Note: Vs -shear wave velocity.

McPherson and Jones (2006) presented detail studies of site classes for PMA based on

available boreholes data, SCPT data and microtremor data. The estimated mean value

and standard deviation of regolith thickness, shear wave velocities and natural period of

each site class in McPherson and Jones (2006)’s study are listed in Table 2-8.


34

Table 2-8 Regolith thickness, shear wave velocities and natural period for site classes

(from McPherson and Jones, 2006)

Site Class Mean

thickness (m)

STD thickness

(m)

Mean Vs (m/s)

STD Vs (m/s)

Mean Period (sec)

STD Period (sec)

Shallow sand 20 13 294 43 0.65 0.46

Deep sand 42 14 300 82 0.5 0.5 Mud-

dominated 18 13 330 179 0.5 0.35

Limestone-dominated 40 18 900 - 0.22 0.38

Note: STD-standard deviation.

By comparing the shear wave velocity estimated in Gaull (2003) with that presented in

their study, McPherson and Jones (2006) indicated that overall the shear wave velocity

estimates presented by Gaull (2003) do not compare favourably with the measured shear

wave velocities and should be used with caution in relation to earthquake studies.

Because McPherson and Jones (2006) only approximately divided the PMA into four

zones, although mean and standard deviation for each zone is given, further study and

specific site investigations are deemed necessary to more accurately quantify the site

properties and site effects on seismic wave propagations in PMA.

Furthermore, many studies, e.g., Jarpe et al. (1989) and Schnabel (1973), have indicated

that soil responses will be nonlinear under strong shaking. These studies also showed

that the amplification factor derived from microtremor may not give a reliable

prediction of strong ground motion response at some sites. Soil amplification analysis

was not carried out in the previous studies by Gaull (2003) and McPherson and Jones

(2006).

2.6.3 Site amplification estimation method

Seismic wave propagation in a medium bounded by a free surface can be categorized

into two types: body waves and surface waves. Body waves propagate through the

interior of the medium and along the free surface and are of two types: P- and S-waves.

P-waves propagate with a compressive disturbance while S-waves induce a shearing

deformation. The particle motion associated with P-waves is parallel to the direction of


35

propagation, while the particle motion associated with S-waves is perpendicular to the

direction of wave propagation. According to the plane of the particle motion, S-waves

can be subdivided into two types: vertically polarized shear (SV) and horizontally

polarized shear (SH) waves.

The amplitude of earthquake ground motion can be increased or decreased by both the

properties and configuration of the near surface material through which seismic waves

propagate. Those properties which most affect the level of ground motion are

impedance and absorption. As Aki and Richards (1980) point out, impedance is the

resistance to particle (rock or soil) motion. For horizontally polarized shear waves (SH)

it can be defined as the product of the density (p), the shear wave velocity (P) and the

cosine of the angle of incidence. The angle of incidence, the angle between the vertical

and the direction of seismic wave propagation, is usually small near the earth's surface

and its cosine can be assumed to be equal to one. Particle velocity is inversely

proportional to the square root of the impedance. As a seismic wave passes through a

region of increasing impedance, the resistance to motion increases and, to preserve

energy, the particle velocity and therefore the amplitude of the seismic wave decreases.

Other factors aside, seismic waves of the same distance from an earthquake would be

higher on low density, low velocity soil than on high density, high velocity rock.

Many experimental, empirical and numerical methods have been developed to evaluate

site effect. These methods own its advantages and limitations. Numerical methods are

founded on the wave propagation theory and are suitable to the urban areas with weak

seismicity. Many approaches and computer programs have been developed to study site

effect as early as 70’s, e.g. Schnabel et al. (1972), Wolf (1985), Idriss and Sun (1992),

Hao (1993), Bardet et al. (2000) and etc. A computer program named SHAKE

(Schnabel et al., 1972) was developed to calculate the site amplification with an input

SH wave. This program, which used an equivalent linearization method in the

frequency-domain, assuming steady-state excitation, solves the fundamental dynamic

equations of motion in the frequency domain. The basic equations used in the program

are to calculate the responses associated with vertically propagating SH wave through

the linear viscoelastic system. SHAKE was subsequently updated by Idriss and Sun

(1992). Usually, the nonlinearity of the site response is estimated with the equivalent

linearization method and the empirical nonlinear soil properties. To do this the site

conditions with detailed soil profiles need be determined first.


36

Empirical approaches are based on analysing a very large number of observations of the

effects of soft sediments on seismic wave propagation to develop empirical relations

between surface geology and various measurements of earthquake motion. Empirical

methods have been very popular in regions where both multiple earthquake

observations and abundant information on surface geology are available.

For experimental methods, macroseismic observations, microtremor measurements,

weak seimicity survey or strong-motion accelerograms are used to estimate both site

periods and amplification. In regions of high seismicity, it is possible to obtain

simultaneous records on the soft soil stations and on the hard rock reference stations.

The records can be used to determine the differences in the response of soft soil sites

relative to a firm rock site. In regions where seismicity is low or moderate, microtremor

measurements are a proposed alternative used to characterize site response.

Microtremor measurements have been adopted in some studies for PMA, e.g. Gaull et

al. (1995), Gaull (2003) and Asten et al. (2003).

H/V ratio technique and array methods that are two kinds of microtremor measurements

have been widely applied in recent years. The H/V ratio technique, which is based on

analysing the ratio between the Fourier spectra of the horizontal and vertical

components, was firstly proposed by Nogoshi and Igarashi (1971), and refined and used

by Shiono et al. (1979) and Kobayashi (1980). They concluded that the ratio can be

applied to identify the fundamental frequency of soft soil sites. Nakamura (1989; 1996;

2000) suggested that the ratio provides information not only about resonant frequencies

but also about the corresponding amplification. The underlying assumption of this

approach is that microtremors consist of vertically propagating S wave. As proposed by

Nakamura (1989), in the Fourier domain there are four amplitude spectra, namely

horizontal and vertical components of motion at the surface and at the base of the soft

soil layer (Figure 2-5).


37

Figure 2-5 Simple model assumed by Nakamura (1989) to interpret H/V ratio technique

The assumption proposed by Nakamura is that microtremor motion is due to very local

sources, such as traffic in close proximity to the seismometer, therefore neglecting any

contribution from deep sources. It can then be understood that the vertical component of

motion is not amplified by the soft soil layer. Assuming that very local sources will not

affect microtremor motion at the base of the soil layer, it is possible to estimate the

spectral shape of the source of microtremor motion (AS) as a function of frequency (ω):

)()(

)(ωω

ωBedrock

SurfaceS V

VA = (2-43)

It is assumed that the transfer functions of surface layers can be given by the following

equation:

)()(

)(ωω

ωBedrock

SurfaceE H

HS = (2-44)

The fundamental reason for the division of horizontal by vertical Fourier spectra is to

compensate SE by the source spectrum. A modified site effect spectral ratio (SM) can be

given as:

)()(

)()(

)()()(

ωωωω

ωωω

Bedrock

Bedrock

Surface

Surface

S

EM

VHVH

ASS == (2-45)

The final assumption for all frequencies of interest is:

VSurface

HSurface

HBedrock

VBedrock


38

1)()(=

ωω

Bedrock

Bedrock

VH (2-46)

Thus, site effect spectral ratio (SM) can be given by the spectral ratio between the

horizontal and the vertical components of the motion at the surface.

)()(

)(ωω

ωSurface

SurfaceM V

HS = (2-47)

In Equation 2-43 to 2-47, AS is spectral shape of the source of microtremor motion; SE is

the site effect; SM is the modified site effect compensated by source spectrum; subscript

Surface is motion at surface; subscript Bedrock is motion at the base of the sedimentary

layer; V is the vertical component and H is the horizontal component.

H/V ratio method is very popularly used in estimating site periods because of its

inexpensive and convenience in application. However, the reliability of using H/V

method is still being debated. Some researchers, such as Lermo and Chavez-Garcia

(1994), commented that the H/V method allows adequate compensation of source and

Rayleigh wave effects producing an accurate estimate of both soil period and

amplification. Others, such as Lachet and Bard (1994) and Field and Jacob (1993),

however, argued that the amplitude of spectral ratio peak of the H/V method does not

correlate well with the S-wave amplification at the site resonant frequency. McPherson

and Jones (2006) also pointed out that the estimated shear-wave velocity of PMA based

on borehole data in their study is not consistent with that in Gaull (2003) using H/V

method. Furthermore, theoretical basis of the H/V method is still unclear as the peak of

the spectral ratio may be associated with the Rayleigh wave’s vertical component,

instead of the amplification of S-wave on horizontal components. Hence, more work

still needs to be done to assess the effectiveness and reliability of the H/V method.

Array methods are based on inverse analysis of the dispersion curve of wave

propagation along the site to estimate the site properties. Tokimatsu (1997) categorised

array methods as active methods and passive methods. The active methods measure

Rayleigh waves in vertical pound vibrations induced either by an impulsive source or an

exciter oscillating with a vertical harmonic motion. The active methods only can

explore surface soils to a depth smaller than 10 to 20 meters since it is difficult to


39

generate long wavelengths by using artificial impulsive loadings and the frequency

range of the signals are limited.

Two popular passive methods, namely spatial autocorrelation (SPAC) method and

frequency-wavenumber method (f-k method), have been developed to extract the

Rayleigh wave from measured microtremors. Tokimatsu (1997) concluded that for

wavelengths up to 40m both methods give consistent results relating to dispersion

curves obtained. However, Okada (2003) demonstrated that the f-k method lacks

fundamental logical theory in its identification of surface waves and analysis of

dispersion characteristics. The SPAC method, as described by Okada (2003) with basic

theory developed by Aki (1957), shows clearer logical theory, requires fewer stations, a

smaller array than the f-k method and achieves comparable results in separating surface

waves from microtremors. A large array is unfavourable due to the fact it increases the

field effort and decreases field efficiency, and also alters the assumption that layers are

sub-parallel under the array. The basic principles of the SPAC method are (Okada 2003):

1. Assume the complex wave motion of microtremors to be a stochastic process in time

and space.

2. A spatial autocorrelation coefficient for microtremor data, as observed with a circular

array, can be defined when the waves composing the microtremors are dispersive like

surface waves; and hence,

3. The spatial autocorrelation coefficient is a function of phase velocity and frequency.

The methodology of the SPAC technique as given by Okada (2003) is outlined in the

following formulae.

Spectral representation of microtremors in a polar coordinate system is written as:

( )θθξ sin,cosr= and ( )φφ sin,coskK =

( ) ( ){ } ( )∫ ∫ ∫∞

∞−

∞−+=

0

2

0,,cosexp,,

πφωζφθωθ KdirktirtX (2-48)

in which, ξ is a position vector, K is the wavenumber vector, ξ(ω,K,ø) is a complex-

value stochastic process satisfying the following relationships:


40

(i) ( ) 0],,[ =φωζ KdE (for all ω,K,ø), (2-49)

(ii) ( )φωφωζ ,,]),,([ 2 KdHKdE = (for all ω,K, ø), (2-50)

where H(ω,K, ø) is the integrated spectrum of X(t,r,θ).

(iii) for any two distinct ω, and ω’ (where ω≠ω’), and two distinct sets (K, ø) and (K’,

ø’) (where K≠K’ and ø≠ø’),

( ) ( ) 0],,,,[ * =′′′ φωζφωζ KdKdE (2-51)

where * denotes the complex conjugate.

Since only the Rayleigh wave (the vertical component of the microtremors) is extracted

form microtremors, Equation 2-48 becomes:

( ) ( ) ( ){ } ( )∫ ∫∞

∞−−+=

πφωζφθωωθ

2

0,cosexp,, dirktirtX (2-52)

( )( ) φωφω

φωφωζddh

dHdE,

,]),([ 2

=

= (2-53)

where h(ω, ø) is called “frequency-direction spectral density”.

Suppose there are two microtremor observation stations A and B, the distance between

which is r. Let A be the origin of the coordinate system (0,0), then the coordinates of

station B are (r,θ).

The microtremor record at station A is given as:

( ) ( ) ( )∫ ∫∞

∞−=

πφωζω

2

0,exp0,0, dtitX (2-54)

The microtremor record at station B is given as:

( ) ( ) ( ){ } ( )∫ ∫∞

∞−−+=

πφωζφθωωθ

2

0,cosexp,, dirktirtX (2-55)

The spatial autocorrelation function (SPAC function) between A and B is


41

( ) ( ) ( )

( ) ( )

( ) ( ){ } ( ) ( )],,[cosexp

,,0,0,21lim

],,0,0,[,

*2

0

2

0

*

*

φωζφωζφθωω

θ

θθ

π π′′′−′+−′=

=

=

∫ ∫ ∫ ∫

∫∞

∞−

∞

∞−

−∞→

ddEkirti

dtrtXtXT

rtXtXErST

TT (2-56)

Combining Equations 2-50, 2-51, 2-52 and 2-53, Equation 2-56 becomes:

( ) ( ) ( ){ }

( )∫

∫ ∫∞

∞−

∞

∞−

=

⎥⎦⎤

⎢⎣⎡ −=

ωθω

ωφφωφθθπ

drg

ddhirkrS

,,

,cosexp,2

0 (2-57)

where ( ) ( ){ } ( )∫ −=π

φφωφθθω2

0,cosexp,, dhirkrg is called the spatial covariance

function of the microtremors at the angular frequency ω.

Hence, the spatial covariance function and the spatial autocorrelation function at station

A can be represented in Equation 2-58 and Equation 2-59 respectively.

( ) ( ) ( )ωφφωωπ

0

2

0,0,0, hdhg == ∫ (2-58)

( ) ( )[ ] ( )∫∞

∞−== ωω dhtXES 0

20,0,0,0 (2-59)

The directional average of the spatial covariance function by averaging g(ω,r,θ) over all

directions can be given as:

( ) ( )

( ){ } ( )

( ) ( )

( ) ( )( ) ( )( ) ( )rkJg

hrkJ

dhrkJ

dhrkJ

ddhirk

drgrg

0

00

2

00

2

0 0

2

0

2

0

2

0

0,0,

,

,

,cosexp21

,,21,

ωω

φφω

φφω

θφφωφθπ

θθωπ

ω

π

π

π π

π

==

=

=

−=

=

∫∫

∫ ∫

∫

(2-60)

in which,


42

( ){ } ( )rkJdirk 0

2

0cosexp

21

=−∫π

θφθπ

(2-61)

where J0(rk) is the Bessel function of the first kind of zero order with the variable rk. The directional average of the spatial autocorrelation function also can be reduced to

( ) ( ) ( )∫∞

∞−= ωω drkJhrS 00 (2-62)

The spatial autocorrelation coefficient can be represented as:

( ) ( ) ( )( )

( )( )ωω

ωωωρ

crJrkJ

hrgr

/

/,,

0

0

0

===

(2-63)

or ( ) ( )( )fcfrJrf /2, 0 πρ = (2-64)

where c(ω) is the phase velocity and k=ω/ c(ω).

Hence, the phase velocity c(ω) can be derived from the spatial autocorrelation

coefficient via the first kind of zero order Bessel function. The subsurface parameters

are estimated by fitting the phase velocities to a model dispersion curve computed for a

layered site, namely numerical inversion.

2.7 Conclusion

(i) As only very limited number of earthquake strong ground motion records are

available in southwest Western Australia (SWWA), and most of them were from

earthquakes of magnitude less than ML4.5, it is difficult to derive a reliable

strong ground motion attenuation model based on these data.

(ii) Using CENA attenuation models to perform seismic hazard analysis for PMA

might bias the ground motion estimates because of possible biases associated

with attenuation relationships developed from the database recorded in different

regions.

(iii) Stochastic method is only a mathematical realization of a time history to match a power

or a response spectrum. It can be used with confidence only if a reliable target power or

design spectrum is available. A study by Hao and Gaull (2004) revealed that none of the


43

existing ground motion models give very satisfactory prediction of the recorded strong

ground motions in WA. Therefore a modified ground motion model from an ENA

model was proposed for WA motions. However, as the available strong ground motion

records in SWWA are very limited and are all from moderate magnitude (< ML5.5)

events, the modified model may be biased towards small earthquake ground motions

and is not reliable in representing larger SWWA earthquakes. In such a case the

stochastic simulation will not yield reliable ground motion time history from large

earthquakes.

(iv) Proper use of Green’s function approach can give good simulation of ground

motions of large earthquakes from the recorded small event data if the seismic

source and wave propagation path are similar.

(v) Many uncertainties exist in the seismic source and path parameters which may

greatly affect the simulated ground motions using Green’s function approach.

Their influence on simulated earthquake ground motions are not properly

studied yet in the literature.

(vi) The limitations of previous site response studies for PMA have been discussed.

More detailed studies of PMA site response to ground motion are necessary.

(vii) The site amplification estimation methods have been reviewed. The advantages

and limitations of these methods are also examined.

The limitation of ground motion prediction and seismic hazard analysis for PMA in

previous studies has been discussed. There has been a growing awareness for the need

of performing more detailed studies of ground motion prediction of SWWA and site

responses in PMA In this thesis, a combined stochastic and Green’s function simulation

method is developed and used to simulate ground motions for constructing more

reliable attenuation models of PGA, PGV and ground motion spectral accelerations for

SWWA. The probabilistic seismic hazard analysis (PSHA) based on the developed

ground motion attenuation model is performed first to determine the 475-year return

period and 2475- year return period design events. As the available geology information

and site response studies in PMA is very limited, in order to perform site amplification

analysis, a site survey is performed around Perth using two microtremor methods,

namely the spatial autocorrelation (SPAC) method and the H/V method. The clonal


44

selection algorithm (CSA) is adopted to perform direct inversion of SPAC curves to

determine the soil profiles of the study sites. Using the derived shear-wave velocity

profiles, detailed site response analyses are carried out to estimate motions on ground

surface.


45

CHAPTER 3 ESTIMATION OF STRONG GROUND MOTIONS IN SWWA WITH A COMBINED GREEN’S FUNCTION AND

STOCHASTIC APPROACH

3.1 Introduction

As only very limited number of earthquake strong ground motion records are available

in southwest Western Australia (SWWA), it is difficult to derive a reliable and unbiased

strong ground motion attenuation model based on these data. Several popular models

for CENA have been employed to perform PSHA of PMA in some previous studies as

reviewed in Chapter 2. Hao and Gaull (2004a) demonstrated that none of these CENA

models give very satisfactory predictions of the recorded ground motions in SWWA;

and among them the model by Atkinson and Boore (1995) yields relatively better

predictions. Subsequently Hao and Gaull (2004b) modified the Atkinson and Boore

(1995) model based on the available strong ground motion records in SWWA, and

showed that the modified model together with the SWWA seismological parameters

improved the accuracy of prediction of the recorded strong ground motions in SWWA.

Although the modified model by Hao and Gaull (2004b) yielded good prediction of the

recorded ground motions for moderate magnitude (< ML5.5) events, its reliability in

representing larger SWWA earthquakes is yet to be known. This is because the vast

majority of strong motion records used to modify the model was from earthquakes of

magnitude ML4.5 or below. This means the model could be biased to the ground

motion characteristics associated with such events and consequently giving rise to a

narrower frequency band biased towards the high frequency region. Unfortunately this

cannot be verified because of the lack of SGM data from larger earthquakes.

Hence, it is necessary to carry out further studies of SWWA strong ground motion

prediction, concentrating on those associated with larger earthquakes. Because available

strong motions in SWWA are biased towards earthquakes of less than ML4.5, our aim


46

is to generate ground motions of earthquakes of magnitudes larger than this and

constructing PGA, PGV and response spectrum model based on the simulated data.

3.2 Simulation of strong ground motion

Two popular approaches of simulating strong ground motions have been reviewed in

previous Chapter. As the assumption of empirical Green’s function method is that the

effect of focal mechanic, earth response and propagation path have been included in

aftershocks and small events, ground motions from a large event can be simulated

accurately and completely at a distance which is the same as that of the recorded small

event data, but it is more difficult to get accurate simulations of ground motions at

different distances. Since the stochastic model by Hao and Gaull (2004b) has been

proven yielded reliable simulations of ground motions from small earthquakes, using

the combination of Green’s function and stochastic method, this problem can be

overcome. In this Chapter, ground motion time histories at various distances for minor

to moderate earthquake events (≤ML5.0) will be simulated using the stochastic model

of Hao and Gaull (2004b), these time histories will then be used to simulate time

histories of large to major magnitude events using empirical Green’s Function method

by Irikura et al. (1997). The reason to use the combined stochastic and Green’s function

simulation is because 1) the stochastic model was proven yielded satisfactory prediction

of recorded ground motions from small events in SWWA, but may not be appropriate

for motions from large earthquakes as discussed above; 2) proper usage of Green’s

function approach can give good simulation of ground motions of large earthquakes

from those of small events; 3) ground motion time histories at varying distances can be

simulated using stochastic approach and used as input for Green’s function simulation,

thus allow for a development of attenuation relations. To test the accuracy of this

method Fourier spectra derived from the simulated motions will be compared with the

equivalent derived from the only two largest recorded motions available in SWWA

(ML6.2 event centred in Cadoux in June 1979 and a ML5.5 event centred in Meckering

in January 1990).


47

3.2.1 Case study

3.2.1.1 Parameters for simulation

Many parameters, including strong ground motion duration, fault length of an event,

rupture area, moment and rise time need be defined for ground motion simulation.

Many definitions of strong ground motion duration have been given for different

purposes (Bolt, 1973, Trifunac and Brady, 1975, Vanmarcke and Lai, 1980, Atkinson,

1993, and Atkinson and Somerville, 1994). Among them, two simple measures of

duration have been used widely. One defines duration as the elapsed time between the

first and last acceleration excursions greater than a given level, usually 0.05g (Page et

al., 1975). Bolt (1973) called this interval the “bracketed duration”. Gaull (1988)

applied this duration definition and quantified the level as 0.0005g to get a magnitude-

dependence duration in SWWA. The other is measured by integrating squared

acceleration and adopting 95 percentile time interval (Husid et al., 1969), or 90

percentile time interval (Trifunac and Brady, 1975). The first definition is more suitable

to the duration of strong ground motion but is difficult to be consistent since the

different level was used. Since only very limited number of earthquake strong ground

motion records are available in SWWA and most of the recorded data are associated

with earthquakes of magnitude less than or equal to ML4.5, the second definition will

be used in this study to derive the duration of ground motion. It will be applied to

estimate ground motion duration for stochastic simulation.

The ground motion duration is sum of the source duration and the path-dependent

duration. Source duration is related to the inverse of the corner frequency, such as

af/5.0 in Atkinson and Boore (1995), or af/1 in Frankel et al. (1996). The path-

dependent duration is defined as a function of epicentral distance. In this study, a new

SWWA ground motion duration is proposed, which is derived by using the regression

method from the limited SWWA database that included 119 Burakin earthquake records

from 2001/02 sequence, and 6 historical records with magnitudes from 3.1 to 5.5. Since

the data is not well distributed along distance and magnitudes, and especially it lacks

data in higher magnitudes and at medium to large distances, the new SWWA duration


48

model may include some bias. The proposed equation to estimate SWWA ground

motion duration is

26.029.4/5.0 RfT ad += , (3-1)

in which Td is ground motion duration in sec and R is the epicentral distance in km. This

relation is used in the present study to estimate ground motion duration in stochastic

simulation.

To estimate the length of fault in accordance with surface-wave magnitude, a relation

that was used by Gaull and Michael-Leiba (1987) will be used in this study. It is given

below

sML 5.02.3log += , (3-2)

where L is the length of the fault measured in cm and Ms is the surface-wave magnitude.

Because the earthquake source parameters in SWWA are not well studied and the

geophysical conditions of CENA are relatively similar to that of SWWA, many CENA

parameters are adopted here. A relation derived by Somerville et al. (2001) will be used

to estimate the rupture area in this study. It is given as

3/20

16109.8 MA ××= − , (3-3)

where A is the rupture area in km2 and M0 is the seismic moment in dyne-cm.

Boore and Atkinson (1987) pointed out that constant-stress model appears to be

supported by CENA data. Following this idea, the constant-stress model is also used in

this study. The shear wave velocity β in SWWA is about 3.91km/s (Dentith et al., 2000),

which is used in this study. Because no magnitude conversion relation that is

specifically for SWWA earthquakes is available, a popularly used conversion relation

for CENA earthquakes (Hanks and kanamori, (1979) is used. It has the form

05.165.1010 += wMMLog (3-4)


49

where Mw is the moment magnitude and M0 is in dyne-cm. This conversion relation was

also used in Hao and Gaull (2004b). There is no reliable relation between ML and Mw

for SWWA either. A popularly used conversion relation between Ms and ML for

Australian earthquakes is used first to convert ML to Ms (Everingham, 1987). It has the

form

Ms = 1.3ML -2.0 (3-5)

and from the relation given by Doyle (1995), Mw = Ms for range in this study, viz

5.0<MS<7.6. Based on these relations, for ML=7.0, an estimation gives Mw =7.1. It

should be noted that these relations are the best available for SWWA. It is desirable to

derive the conversion relations for SWWA earthquakes. However, it can be done only

after more data are available.

The rise time was computed according to Somerville et al. (1993).

( ) 3/10

91072.1 MT −×= , (3-6)

where T is the rise time in seconds and M0 is in dyne-cm.

3.2.1.2 Simulation and Comparison

The Green’s function method has been cited many times in its application to simulation

of large earthquakes from smaller ones, such as Sinadinovski et al. (1996); Frankel

(1995); Joyner and Boore (1986), Sinadinovski et al. (2006). In SWWA there are only

two recordings which are of sufficient magnitude that can be used for comparison

purposes with the simulated events using this procedure. One is the large Cadoux

earthquake in 1979 of magnitude ML6.2 which was recorded about 96 km away to the

south at Meckering. The other one is the ML5.5 Meckering earthquake which occurred

in 1990 and was recorded near Dowerin, some 78 km away.

Hence, the hybrid method used to simulate events that matched these magnitude and

distance parameters, required two steps: Firstly, Hao and Gaull (2004b)’s stochastic


50

model was used to simulate events of ML4.5 with the same epicentral distances as those

events used. Secondly, the empirical Green’s Function method by Irikura et al. (1997)

was then used to increase the magnitude of the simulated ML4.5 event to ML5.5 and

ML6.2 respectively.

Figure 3-1 to Figure 3.4 show the comparisons of the FFT spectrum and time histories

of the simulated and recorded ground motion. The two horizontal components of the

recorded motions as shown in the figures are given as either EW (East-West) and NS

(North-South), or as indicated in Figure 3-3 and Figure 3-4 as r (Radial) and t

(Transverse) directions. As shown, the FFT spectra of the simulated and recorded

motions match reasonably well.


51

100

101

102

10-4

10-3

10-2

10-1

100

101

Frequency (Hz)

Am

plitu

de (m

m/s

)

FFT Comparison---6.2ML,96km

Observed event(EW):PGA=207.09,PGV=19.40 Observed event(NS):PGA=175.40,PGV=12.71Simulated event:PGA=223.92PGV=9.81

Figure 3-1 FFT Comparison of the simulated and recorded ground motions.


52

0 5 10 15 20

-200

-150

-100

-50

0

50

100

150

200

Acc

eler

atio

n (m

m/s

2)

Duration (sec)

1979 Cadoux event(EW)---6.2ML,96km

0 5 10 15 20

-20

-15

-10

-5

0

5

10

15

20

Vel

ocity

(mm

/s)

Duration (sec)

1979 Cadoux event(EW)---6.2ML,96km

0 5 10 15 20

-200

-150

-100

-50

0

50

100

150

200

Acc

eler

atio

n (m

m/s

2)

Duration (sec)

1979 Cadoux event(NS)---6.2ML,96km

0 5 10 15 20

-20

-15

-10

-5

0

5

10

15

20

Vel

ocity

(mm

/s)

Duration (sec)

1979 Cadoux event(NS)---6.2ML,96km

0 5 10 15 20

-200

-150

-100

-50

0

50

100

150

200

Acc

eler

atio

n (m

m/s

2)

Duration (sec)

Simulated event---6.2ML,96km

0 5 10 15 20-20

-15

-10

-5

0

5

10

15

20

Vel

ocity

(mm

/s)

Duration (sec)


Figure 3-2 Time histories of the simulated and recorded ground motion.


53

100

101

102

10-3

10-2

10-1

100

Frequency (Hz)

Am

plitu

de (m

m/s

)

FFT Comparison---5.5ML,78km

Observed event(r):PGA=98.19,PGV=1.37 Observed event(t):PGA=26.15,PGV=0.64Simulated event:PGA=64.23,PGV=1.04

Figure 3-3 FFT Comparison of the simulated and recorded ground motions.


54

0 5 10 15-100

-80

-60

-40

-20

0

20

40

60

80

100

Acc

eler

atio

n (m

m/s

2)

Duration (sec)

1990 Meckering event(r)---5.5ML,78km

0 5 10 15

-1

-0.5

0

0.5

1

Vel

ocity

(mm

/s)

Duration (sec)

1990 Meckering event(r)---5.5ML,78km

0 5 10 15-100

-80

-60

-40

-20

0

20

40

60

80

100

Acc

eler

atio

n (m

m/s

2)

Duration (sec)

1990 Meckering event(t)---5.5ML,78km

0 5 10 15

-1

-0.5

0

0.5

1

Vel

ocity

(mm

/s)

Duration (sec)

1990 Meckering event(t)---5.5ML,78km

0 5 10 15-100

-80

-60

-40

-20

0

20

40

60

80

100

Acc

eler

atio

n (m

m/s

2)

Duration (sec)


0 5 10 15

-1

-0.5

0

0.5

1

Vel

ocity

(mm

/s)

Duration (sec)


Figure 3-4 Time histories of the simulated and recorded ground motions.

It should be noted that, as shown in the above figures, the quality of the recorded time

histories is not very good. Unfortunately, these are the only available strong ground

motion time histories recorded in SWWA from earthquakes of magnitude larger than

ML5.5. To further check the reliability of using the simulated ground motion time

histories in structural response analysis, the ground motion parameters that affect

structural responses, i.e., the PGA and PGV value of the observed and simulated motion

and the deviation of the Fourier spectra are compared and the values are listed in Table

3-1. The deviation of Fourier spectra is the normalized residual, defined as:


55

∫∫ −

= b

a r

b

a sr

dfA

dfAADOFS

)( (3-7)

in which Ar and As are FFT amplitude of the recorded and simulated time history

respectively, a and b define the frequency bandwidth. In this study, a is 0.5Hz, b is

50Hz, and f is frequency in Hz.

Table 3-1 The peak value and the normalized FFT amplitude residual of the observed

and simulated motions

1979 Cadoux event, ML6.2, 96km 1990 Meckering event, ML5.5, 78kmRecorded Record

EW NS Simulated r t Simulated

PGA (mm/s2) 207.09 175.40 223.92 98.19 26.15 64.23

PGV (mm/s) 19.40 12.71 9.81 1.37 0.64 1.04

DOFS 0.235 0.237 -0.152 -0.909 As shown in Table 3-1, the DOFS is 0.235 and 0.237 for EW and NS direction of the

1979 Cadoux event. For the 1990 Meckering event, the DOFS value for the main wave

energy direction (radial) is -0.152. It means that the Fourier spectra of simulated ground

motion are very similar to those of the recorded motion. The largest DOFS between the

simulated and recorded motion occurs in the transverse direction of the 1990 Meckering

earthquake. It is -0.909, indicating the FFT amplitude of the simulated motion is almost

double of the recorded motion. Many factors could cause these discrepancies, such as the

difference in source, path and local site conditions used in the Green’s function simulation and

the actual earthquake scenario. Moreover, the records from the 1990 Meckering earthquake used

for comparison are not of high quality. They were digitized from the original analog records.

This could also introduce some errors, especially in the low frequency range. In view of many

uncertainties involved in an earthquake ground motion time history, the FFT spectrum of the

simulated and recorded motion are considered match reasonably well.

As shown, the PGA and PGV of the simulated motion are also comparable to those of

the recorded motion. The relatively larger PGV value of the recorded ML6.2 event is

thought to be caused by the site effect. This is discussed below.


56

Duration (sec)

Acce

lera

tion

(mm

/s^2

)

Cadoux earthquake in 1979 (ML 6.2)EW Component

Epicentral distance: 96km

0 4 8 12 16 20 24 28 32 36 40-240-180-120

-600

60120180240

Frequency, Hertz

AMP

(mm

/s)

FFT

0 15 30 45 60 75 90 1050

15

30

45

60

75

90

Duration (sec)

Acc

eler

atio

n (m

m/s

^2)

Cadoux earthquake in 1979 (ML 6.2)NS Component

Epicentral distance: 96km

0 4 8 12 16 20 24 28 32 36 40-200-150-100

-500

50100150200

Frequency, Hertz

AMP

(mm

/s)

FFT

0 15 30 45 60 75 90 1050

10

20

30

40

50

60

Figure 3-5 Time histories and FFT spectra of the Cadoux earthquake in 1979.

Figure 3-5 shows the recorded acceleration time histories and the corresponding FFT

spectra. As shown, two unusual low-frequency peaks exist in the FFT spectra of the

recorded motions. These two low-frequency peaks are interpreted to be caused by site

effects, as these dominant low frequency peaks are not observed in all the other

recorded motions on rock site in SWWA. This was ascertained by filtering out the

frequencies greater than those of the second peak (i.e. f > 1.2 Hz). This proved that the

energy at the said frequency had contributions from all 3 main wave-forms (P, S and

surface waves in different time windows), thereby dismissing the surface-wave and or

digitising error alternatives. Other supporting evidence that it was site effect-induced

was provided by another (albeit shortened) nearby recording of the same event. This

was founded on hard granite and although a similar peak occurred in the FFT spectra it

was not as dominant.

Besides this site effect, another obvious parameter that may affect the comparison is the

duration. As shown in the above figures, the available time histories are incomplete

strong motion records, especially those recorded during the 1979 Cadoux earthquake, in

which the records starts and ends abruptly. These may also introduce further


57

uncertainties to the recorded motion and affect the comparison. Unfortunately, they are

the only available local records in SWWA, as discussed above.

As observed above, the simulated ground motions have comparable FFT spectra and

peak values as compared with the recorded motions in SWWA. Since FFT spectrum,

PGA and PGV are the primary ground motion parameters that affect structural response,

the above procedure is used to simulate a set of ground motion time histories and derive

ground motion attenuation models for SWWA. It is believed that, as compared to the

currently used models from elsewhere to predict ground motions in SWWA for

engineering use, the attenuation model for response spectrum developed in this study

based on the motions obtained from simulations is the only one that considered the local

ground motion characteristics, and is therefore more representative of local ground

motions than the CENA models in structural response analysis.

3.3 Ground Motion Attenuation Relations

As discussed above, a set of ground motions from earthquakes of magnitudes varying

from ML4.0 to ML7.0 with an increment of ML0.5, and epicentral distances from 10km

to 200km with an increment of 20 km are generated and used as supplement to the

SWWA earthquake database. Earthquakes of magnitude less than ML5.0 have been

simulated by Hao and Gaull (2004b) stochastic model. Those larger than ML5.0 are

simulated by Green’s function. These simulated motions, together with the recorded

motions are then used to derive attenuation models for PGA, PGV and response

spectrum. There are a total of 903 time histories, including 881 simulated and 22

recorded from earthquakes of magnitude larger than ML4.0 available after simulations.

These time histories are used to derive ground motion attenuation relations.

3.3.1 Regression model and methodology

Commencing from the commonly used regression model of the form below (Reiter,

1991):


58

( ) ( ) ( ) ( ) εlnln,lnlnlnlnˆln 43211 +++++= iPfRMfRfMfbY , (3-8)

where Ŷ is the strong motion parameter to be estimated (PGA, PGV and SA), b1 is a

constant scaling factor, f1(M) is a function of the independent variable M (magnitude or

earthquake source size), lnf2(R) is a function of the independent variable R (source to

site distance), f3(M,R) is a possible joint function of M and R, f4(Pi) is a function or

functions representing possible source or site effects and ε is an error term representing

the uncertainty in Ŷ. Since simulated data and recorded data are derived from bedrock

site, site effect factor will not be considered in this model. DataFit software is used to fit

a regression model to the new set of data that is generated in the simulations and

nonlinear regression is chosen to model the data. Many models are reviewed to choose

one that would best represent the data and the SWWA records. Part of the process for

choosing a model is to examine the coefficients chosen in the model and to assess if the

model is scientifically meaningful. For this case, the model has to be able to realistically

describe the attenuation of the strong ground motion. The model coefficient matrix is

made up and each coefficient that is chosen in a model is tested whether it would be

able to realistically describe the attenuation. Several criteria are examined to determine

the goodness of fit of the model. Sum of residuals is calculated using Equation 3-9. The

average residual is the average value of the residuals and the absolute residual sum of

squares is the sum of the squares of the differences between the actual data points and

the predicted values. If the curve passed through each data point, the sum of residuals,

the average residual and the absolute residual sum of squares would be zero. Error

variance and standard error of estimate are also calculated for each model by Equation

3-10 and Equation 3-11 respectively.

Sum of residual=∑=

−n

iii YY

1

)ˆ( . (3-9)

( )pn

YYn

iii

−

−=∑=

2

12

ˆ

σ̂ , (3-10)

2ˆˆ σσ = , (3-11)

where 2σ̂ is the error variance and σ̂ is the standard error of estimate. Yi and Ŷi are the

ith recorded value and the ith predicted value respectively. n is the number of predicted

values and p is the number of variables in the model. They give an idea about how


59

scattered the residuals are around the average. As the error variance and the standard

error approaches zero, it is more certain that the regression model accurately describes

the data. The coefficient of multiple determination measures the proportion of variation

in the data points that is explained by the attenuation model. The coefficient of multiple

determination value of R2 should be in the range from 0 to 1. A value of 1 will mean

that the curve passes through every data point. A value of 0 means that the regression

model does not describe the data any better than a horizontal line passing through the

average of the recorded data points. It should be noted that sometimes R2 value could be

larger than 1. This indicates the regression model does not reflect the data at all, and a

different model should be used. The coefficient of multiple determinations is calculated

for each model using the formula below:

∑

∑

=

=

−

−= n

ii

n

ii

YY

YYR

1

2

1

2

2

)(

)ˆ( , (3-12)

where Y is the average of the recorded values. The percentage error is the percentage of

error in the predicted value as compared to the actual recorded value. An error

percentage of zero means that the estimated value is equal to the actual value. The

percentage error is calculated using the formula below:

i

ii

YYY

Errorˆ

%−

= , (3-13)

3.3.2 Horizontal PGA model

The model is derived according to the regression analysis described above and the

results are given below:

εlnln147.0ln374.1016.0832.0688.3ln ++−−+= RMLRRMLPGA , (3-14)

where PGA is the peak ground acceleration (mm/s2), R is the epicentral distance (km)

and ML is the Richter magnitude. Table 3-2 gives a summary of the results of tests


60

carried out to assess the goodness of fit of Equation 3-14 for the simulated and recorded

data. The variance of lnε equals the square of the standard error of estimate which is

given in Table 3-2. The distribution of the error term can be seen in Figure 3-6. It

indicates that the distribution of residuals is close to the normal distribution. The

computed value of the t test is measured and shows the 95% confidence interval on the

residuals with a zero mean normal distribution.

Table 3-2 Summary of PGA model fit information.

New PGA model Sum of Residuals -1.411E-09 Average Residual -1.563E-12

Residual Sum of Squares (Absolute) 1220.796 Error Variance 1.360

Standard Error of the Estimate 1.166 Coefficient of Multiple Determination(R^2) 0.65

-3 -2 -1 0 1 2 30

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Data

Den

sity

The distribution of the error term

ResidualsNormal ditribution

-3 -2 -1 0 1 2 30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Data

Cum

ulat

ive

prob

abilit

y

ResidualsNormal distribution

Figure 3-6 The distribution of residuals

Figure 3-7 shows the comparison of the suggested PGA model (Equation 3-14) and

PGA model including σ± (σ is the standard deviation of lnε) with those predicted

using the PGA model of Gaull (1988), Atkinson and Boore (1997) and Toro et al.

(1997). It shows that most of models locate in the interval between new PGA model

with σ± . That means the PGA values predicted by those models are within the 84.1%

confidence interval of the new PGA model. Furthermore, the new model predicts lower

values than the other models when magnitude is less than 6, but the difference is

diminishing at ML7. The attenuation ratio of the new PGA model is quite similar to

Gaull (1988) model for moderate magnitude events and is larger than that of CENA


61

models. The factors of difference between Gaull (1988) model, which was also derived

from SWWA data, and the new model are probably due to three reasons:

i) Gaull (1988) included both soft and hard sites in his data, whereas the new PGA

model is based on “rock-sites” only;

ii) The set of records used by Gaull (1988) is dominated by small magnitude

earthquakes which control the equation and

iii) As discussed in the Introduction Gaull filtered the accelerograms to remove

frequencies of little engineering experience (i.e. T < 0.1 s).

It can also be seen that most CENA PGA models give rise to greater PGA estimates

than corresponding estimates derived from the new PGA model. Figure 3-8 and Figure

3-9 show the new model plotted with the available SWWA records with distance larger

than 10km and ML>4.

101

102

10-1

100

101

102

103

Epicentral Distance (km)

PG

A (m

m/s

2 )

PGA model comparison---4ML

PGA plus STDPGA minus STDPGA modelGaull(1988) modelAtkinson and Boore (1997) modelToro et al. gulf modelToro et al. mc model

10

110

210

0

101

102

103

104


PG

A (m

m/s

2 )



(a) (b)

101

102

100

101

102

103

104


PG

A (m

m/s

2 )



10

110

210

1

102

103

104

105


PG

A (m

m/s

2 )



(c) (d)

Figure 3-7 Comparison of the proposed PGA model with those of Gaull (1988),

Atkinson and Boore (1997) and Toro et al. (1997)


62

4.394.6

4.6

4.65.5

4.5

4.1

4.07

4.22

4.2

4.394.6

4.074.22

6.26.2

6.24.1

4.1 5.15.2

5.2

0.1

1

10

100

1000

10000

10 100 1000

Epicentral distance (km)

PGA (mm/s^2)

ML4

ML5

ML6

ML7

Figure 3-8 Curves predicted by the proposed PGA model for various magnitudes plotted

with SWWA records.

New PGA model

-250-200-150-100-50

050

100150200250

10 60 110 160 210


resi

dual

(%)

Figure 3-9 Percentage error of predictions from the new PGA model when compared to

SWWA records

To study the reliability of commonly used attenuation models in predicting the Western

Australian recorded data, Table 3-3 gives the error and residuals of the predicted PGA

by various models against the recorded data. It indicates that the present PGA model

gives better results for average residual, smaller residual sum of squares and lower

percentage error than all of the existing models. The model also shows that it delivers a

better explanation of the variation in the peak ground acceleration of the records with a


63

coefficient of determination of close to one. The standard error of the estimate of this

model is smaller than any other model, which means it most accurately describes the

data.

Table 3-3 Summary of comparison results of the predictions using the new PGA model,

Gaull (1988) model, Atkinson and Boore (1997) model and Toro et al. (1997) model

with the SWWA records

New PGA model

Gaull (1988)

Atkinson and Boore (1997)

Toro et al. (1997) (gulf)

Toro et al. (1997) (mid)

Sum of Residuals 66.94 -433.12 -3523.21 -762.94 -1443.72 Average Residual 3.04 -19.69 -160.15 -34.68 -65.62 Residual Sum of Squares (Absolute) 29616.95 46464.10 943484.51 84748.84 179006.39

Error Variance 1480.85 2323.20 47174.23 4237.44 8950.32 Standard Error of the Estimate 38.48 48.20 217.20 65.10 94.61

Coefficient of Multiple Determination(R^2) 0.75 1.34 10.78 1.36 2.44

Sum of Percentage Error -7.39 -58.75 -607.55 -163.64 -308.54

3.3.3 Horizontal PGV model

The model derived to represent peak ground velocity of strong ground motion on rock sites is given below:

εlnln03.0ln62.0015.0519.1305.3ln ++−−+−= RMLRRMLPGV (3-15)

where PGV is the peak ground velocity (mm/s). A summary of the results of tests

carried out to assess the goodness of fit of Equation 3-15 for the simulated and recorded

data is given in Table 3-4. The distribution of the error term can be seen in Figure 3-10.

It indicates that the distribution of residuals is similar to the normal distribution. The

computed value of the t test is measured and shows the 95% confidence interval on the

residuals with a zero mean normal distribution. The Standard Error of the Estimate of

PGV model is larger than that of PGA model, which is because PGV is significantly


64

influenced by the wave energy at low to medium frequency, which includes more

uncertainties than PGA. Usually larger variations in PGV predictions are expected.

Table 3-4 Summary of PGV model fit information.

New PGV model Sum of Residuals 4.811E-10 Average Residual 5.328E-13

Residual Sum of Squares (Absolute) 1516.987 Error Variance 1.69

Standard Error of the Estimate 1.3 Coefficient of Multiple Determination(R^2) 0.61

-3 -2 -1 0 1 2 30

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Data

Den

sity

The distribution of residuals


-3 -2 -1 0 1 2 30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Data

Cum

ulat

ive

prob

abilit

y



Figure 3-11 shows the comparison of the predicted PGV (Equation 3-15) and PGV

model including σ± with those predicted using the PGV model of Gaull (1988) and

Atkinson and Boore (1997). It shows that most of the predictions by the Gaull and

Atkinson and Boore models locate in the interval between the new PGV model with

σ± , which means the PGV values predicted by those models are within the 84.1%

confidence interval of the new PGV model. Comparing with the Gaull (1988) model, it

is seen that the new model predicted higher PGV for the case with magnitude larger

than 4, which could be due to Gaull (1988) filtered the accelerograms to include only

the ground motion signal at periods of engineering interest (i.e. 0.1 secs and above).

Comparing the new PGV model with Atkinson and Boore (1997) model indicates that

the PGV values predicted by Atkinson and Boore (1997) model resemble those

predicted by the new model with the magnitude less than 6 and epicentral distance less

than 100km. The difference increases when magnitude is larger than 6. Figure 3-12 and

Figure 3-13 show the new model plotted with the SWWA records.


65

101

102

10-2

10-1

100

101

102


PG

V (m

m/s

)

PGV model comparison---4ML

PGV plus STDPGV minus STDPGV modelGaull(1988) modelAtkinson and Boore (1997) model

10

110

210

-2

10-1

100

101

102


PG

V (m

m/s

)



(a) (b)

101

102

10-1

100

101

102

103


PG

V (m

m/s

)



10

110

210

0

101

102

103

104


PG

V (m

m/s

)



(c) (d)

Figure 3-11 Comparison of the new PGV model with those of Gaull (1988) and

Atkinson and Boore (1997)

4.22

4.6

4.07

4.6

6.2

5.5

4.1

4.14.074.2

4.39

4.39

4.6

4.224.6

6.26.2

4.5

4.1

5.1

5.2

5.2

0.01

0.1

1

10

100

1000

10 100 1000


PGV

(mm

/s^2

) ML4ML5ML6ML7

Figure 3-12 Curves predicted by new PGV model for various magnitudes plotted with

SWWA records.


66

New PGV model

-1400-1200-1000-800-600-400-200

0200

10 60 110 160 210

Epicentral distance

resi

dual

(%)

Figure 3-13 Percentage error of predictions from the new PGV model when compared

to SWWA records

Table 3-5 gives the previously defined error and residuals of the PGV from the

proposed model against the recorded data. It shows that although the percentage error of

the new PGV model is larger than Gaull (1988) model, the present PGV model gives

better results for average residual, smaller residual sum of squares than that of Gaull

(1988) model and Atkinson and Boore (1997) model. The model also shows that it

delivers a better explanation of the variation in the peak ground velocity with a

coefficient of determination close to one. The standard error of the estimate of this

model is smaller than any other model, which means it most accurately describes the

data.


67

Table 3-5 Summary of comparison results of the predictions from the new PGV model,

Gaull (1988) model, and Atkinson and Boore (1997) model with the SWWA records

New PGV model Gaull (1988) Atkinson and

Boore (1997 Sum of Residuals -21.32 22.12 -31.01 Average Residual -0.97 1.01 -1.41

Residual Sum of Squares (Absolute) 247.97 481.98 291.48

Error Variance 12.40 24.10 14.57 Standard Error of the Estimate 3.52 4.91 3.82

Coefficient of Multiple Determination(R^2) 0.89 0.13 0.64

Sum of Percentage Error 174.27 99.90 382.81

3.3.4 Response Spectrum model

Using the simulated ground motion time histories, the spectral accelerations with 5%

damping are calculated. The best-fitted spectral acceleration equation is defined as

ReMRdcRbMLaY L lnlnln ++++= , (3-16)

where Y is the value of spectral acceleration (mm/s2). Figure 3-14 shows the sum of

residuals and coefficient of determination of response spectrum models. The mean of

sum of residuals and the mean of coefficient of determination are 1.74E-10 and 0.682

respectively, which means that the response spectrum model can accurately describe the

data.


68

Period (sec)

Sum of residuals

0 3 6 9 12 15 18 21 24 27 30-8E-9-4E-9

04E-98E-9

1.2E-81.6E-8

2E-82.4E-8

Period (sec)

Coefficient of Multiple Determination(R^2)

0.05 0.1 0.5 1 5 10 500.2

0.5

1

Figure 3-14 Sum of residuals and coefficient of determination of the response spectrum

model

Table 3-6 lists the coefficients of the horizontal spectral acceleration relations. Figure

3-15 and Figure 3-16 show the estimated response spectra for events of magnitudes

ML4 to ML7 at epicentral distances between 50 and 200 km. It can be seen in these

figures that the attenuation of the spectral acceleration at high frequency is faster than at

low frequency. Likewise, it is observed that ground motions from larger magnitude

events have more prominent low frequency energy.


69

Table 3-6 Coefficients of horizontal spectral acceleration relations.

Period a b c d e 0.05 1.776 1.253 -0.016 -0.294 -0.028 0.10 1.598 1.312 -0.010 -0.507 -0.028 0.15 1.939 1.279 -0.005 -0.706 -0.018 0.20 1.570 1.243 -0.008 -0.571 -0.014 0.25 1.102 1.322 -0.008 -0.502 -0.024 0.30 1.310 1.321 -0.006 -0.623 -0.024 0.35 1.361 1.335 -0.006 -0.688 -0.021 0.40 1.147 1.322 -0.010 -0.611 -0.012 0.45 1.021 1.289 -0.013 -0.579 0.004 0.50 0.476 1.330 -0.016 -0.419 -0.002 0.55 -0.323 1.430 -0.018 -0.175 -0.033 0.60 -0.857 1.487 -0.019 -0.050 -0.045 0.65 -1.371 1.554 -0.019 0.029 -0.054 0.70 -1.716 1.602 -0.019 0.017 -0.053 0.75 -2.124 1.663 -0.019 0.019 -0.055 0.80 -2.515 1.715 -0.019 0.047 -0.059 0.85 -3.000 1.786 -0.019 0.116 -0.070 0.90 -3.475 1.850 -0.019 0.188 -0.081 0.95 -3.780 1.885 -0.019 0.196 -0.081 1.00 -3.901 1.892 -0.019 0.134 -0.070 2.00 -6.193 2.126 -0.017 -0.199 -0.022 3.00 -7.234 2.208 -0.016 -0.333 0.000 4.00 -8.124 2.287 -0.018 -0.311 0.004 5.00 -8.704 2.322 -0.018 -0.298 0.009 6.00 -9.127 2.330 -0.019 -0.332 0.020 7.00 -9.455 2.326 -0.019 -0.376 0.033 8.00 -9.867 2.346 -0.019 -0.373 0.036 9.00 -10.260 2.364 -0.019 -0.376 0.040 10.00 -10.565 2.380 -0.019 -0.395 0.044 20.00 -12.462 2.477 -0.018 -0.334 0.031 30.00 -13.499 2.527 -0.018 -0.195 0.009


70

10-2 10-1 100 101 10210-3

10-2

10-1

100

101

102

103

104

Period (sec)

Spe

ctra

l Acc

eler

atio

n (m

m/s2 )

Response Spectrum---Epicentral distance:50km

ML4ML5ML6ML7

10-2 10-1 100 101 102

10-3

10-2

10-1

100

101

102

103

104

Period (sec)

Spe

ctra

l Acc

eler

atio

n (m

m/s2 )


ML4ML5ML6ML7

(a) (b)

10-2 10-1 100 101 102

10-4

10-3

10-2

10-1

100

101

102

103

Period (sec)

Spe

ctra

l Acc

eler

atio

n (m

m/s2 )


ML4ML5ML6ML7

10-2 10-1 100 101 102

10-4

10-3

10-2

10-1

100

101

102

103

Period (sec)

Spe

ctra

l Acc

eler

atio

n (m

m/s2 )


ML4ML5ML6ML7

(c) (d)

Figure 3-15 Response spectra of ground motions from ML4, ML5, ML6 and ML7

earthquake at epicentral distances of 50km, 100km, 150km and 200km, damping ratio

5%.


71

Period (sec)

Pseu

do- v

eloc

ity (m

m/s

)

Response SpectrumEpicentral distance: 100km

Damping ratio: 5%

0.01 0.1 1 10 1000.01

0.1

1

10

100

1000 A

100 A

10 A

1 A

0.1 A

0.01 A

0.001 A

100 D

10 D

1 D

0.1 D

0.01 D0.001 D

0.0001 D

ML4ML5ML6ML7

Figure 3-16 Predicted response spectra (A is acceleration in mm/s2, D is displacement in mm)


72

3.4 Conclusions

The method which combines empirical Green’s function and stochastic simulation has

been presented and tested in this work. CENA data were used for some source

parameters in absence of data in SWWA. This approach is used to simulate a series of

ground motions from earthquakes of varying magnitude and distance and the simulated

events are added to the SWWA earthquake database. PGA, PGV and response spectrum

relations were derived by the updated database. The main conclusions of the study are

that:

(i) By comparing the model with the recorded data of the two earthquake events in

SWWA, the method which combines empirical Green’s function method and stochastic

method was shown to be suitable as most of the simulated time histories fit reasonably

well against those of records.

(ii) Although some parameters from CENA model are used due to the limited

availability of the parameters of the earthquake source in SWWA, the simulation results

are satisfactory as compared to the recorded data.

(iii) Four previous PGA models, three developed for CENA and one for SWWA, and

the proposed PGA model in this study are tested against the SWWA records. The results

show that the suggested model yields most reliable predictions amongst all the PGA

attenuation models. Most of CENA models produce greater PGA’s and this difference

diminishes at higher magnitudes (ML7).

(iv) The PGV models are also analysed for their accuracy in predicting the SWWA

records. It is found that the model provided by Gaull (1988) gives a lower percentage

error when compared to the records; however the new PGV model generates a more

accurate description of the variation in the records. The PGV model by Atkinson and

Boore (1997) resembles those predicted by the new model with the magnitude less than

6 and epicentral distance less than 100km. The difference is increasing when magnitude

is larger than 6.


73

(v) An attenuation model for ground motion spectral accelerations is proposed in this

study.

(vi) The new attenuation models suggested in this study are derived from a large

simulated database covering a large distance range, an appropriate magnitude range and

provide a more reliable prediction of the available SWWA records than other models

considered. Therefore, it is expected that the new equations are likely to provide the

more reliable seismic hazard analysis in SWWA. However, the new model should be

continually tested as new results come to hand.


74

CHAPTER 4 INFLUENCE OF UNCERTAIN SOURCE PARAMETERS

ON STRONG GROUND MOTION SIMULATION

4.1 Introduction

Because studies of the earthquake source and path parameters in SWWA are limited,

many of the CENA parameters are adopted to simulate ground motions as shown in the

previous Chapter. The reliability of using these parameters was proven only with four

strong ground motion records in two earthquake events. In reality, many uncertainties

exist in the seismic source and path parameters. In Chapter 2, many source parameter

models have been reviewed and showed that source parameters vary from site to site

and from event to event. It is very unlikely that these CENA source parameters will be

the same as those of SWWA. Variations of these parameters may greatly affect the

simulated ground motions using Green’s function approach. However, there is no study

on how the variation in source parameters will affect the simulated ground motion in the

literature. This Chapter focuses on investigating the effects of variations of uncertain

earthquake source parameters on the ground motions simulated using the empirical

Green’s function approach. Statistical variations of the various source parameters are

considered in the simulation and their effects on the simulated ground motions are

examined. An ML6.0 and epicentral distance 100 km event is simulated as an example.

Each source parameter is assumed statistically varying with a normal distribution. The

source parameter value from the CENA model is taken as the mean value with an

assumed standard deviation in this study. Rosenblueth’s point estimate method

(Rosenblueth, 1981) is used in the statistical simulations to estimate the mean and

standard deviation of peak ground acceleration (PGA), peak ground velocity (PGV),

root-mean square acceleration (RMSA) and response spectrum of the simulated ground

motions. The accuracy of the Rosenblueth’s point estimate method is verified by Monte

Carlo simulations. The Monte Carlo simulation results are also used to derive the

distribution types of the parameters of the simulated ground motion time histories. To


75

evaluate the influence of the statistical variations of the uncertain seismic source

parameters on the simulated ground motions, a sensitivity analysis for each source

parameter is preformed by varying the level of uncertainty, i.e., the assumed standard

deviation. A model for coefficient of variation of the simulated ground motion is also

developed based on simulated data using Rosenblueth’s point estimate method.

4.2 Variations of the Seismic Source Parameters

In the empirical Green’s function method shown in Equations 2-22 to 2-24, the

earthquake source is characterized by a set of source parameters, i.e., stress drop, fault

dimensions, rupture velocity and rise time. These parameters affect the simulated

ground motions. In this study, the source parameters, i.e., the stress drop ratio, rupture

velocity or phase delay and rise time are assumed to vary randomly. The fault size is

closely related to the seismic magnitude. It is assumed to be deterministic in this study.

As can be seen in Equations 2-22 to 2-25, the stress drop ratio affects the N value which

causes the change of the number of superposition. The rise time of large event

determines the corner frequency of spectrum. Phase delay term has an effect on phase

spectrum. It should be noted that the variations of the path parameters are not explicitly

considered in this study. However they are implicitly included in stochastic simulations

of ground motions because the simulations are carried out according to the target

ground motion spectrum, which usually are the mean spectrum of the expected ground

motions.

Earthquakes in SWWA are intraplate events and the stress drop does not seem to be

constant in small magnitude event, as observed in the data of Burakin earthquake (Allen

et al., 2006). However, for earthquakes of magnitude above 5, compared with the

recorded data, Liang et al. (2006) found that the constant-stress scaling law seems

suitable because simulated motions based on a constant stress drop assumption well fit

with the recorded motions. To study the effect of stress drop variation on ground

motions in this study, the constant stress-drop ratio is assumed with a normal

distribution.


76

Another parameter that significantly affects the ground motion is the phase delay which

is also assumed to vary randomly. Rupture velocity is a main factor that affects phase

delay. In this study, the mean rupture velocity is taken as 0.8 times of the shear wave

velocity of 3.91 km/sec of the seismic source in SWWA (Dentith et al., 2000). The

normal distribution is also assumed.

The mean value of rise time was computed using Equation 4-1 (Somerville et al., 1993).

It is also assumed to vary randomly. It should be noted that the stress-drop ratio, rupture

velocity and rise time may be inter related. In this study, however, they are assumed to

be statistically independent of each other owing to the lack of information on their cross

correlation.

( ) 3/10

91072.1 MT −×= (4-1)

4.3 Ground Motion Simulation with Uncertain Seismic

Source Parameters

As an example, ground motion time history from an ML6.0 and epicentral distance 100

km event is simulated from a small event of ML4.5 and the same epicentral distance

with statically varying source parameters. The mean value, coefficient of variation and

distribution type of the three random source parameters are defined in Table 4-1. Monte

Carlo simulation and Rosenblueth’s point estimate method are applied in the simulation

to estimate the mean values and standard deviations of the PGA, PGV, RMSA and

response spectra of the simulated ground motion time histories. The Monte Carlos

simulation results are also used to determine the distribution types of these parameters

of the simulated time history.

Table 4-1: Random variables and their distribution

Parameters Mean Coefficient of variation,% Distribution

Stress drop ratio 1 10 normal Phase delay term (rupture

velocity) 3.1 (km/sec) 10 normal

rise time 0.39(sec) 10 normal


77

4.3.1 Monte Carlo simulation

Monte Carlo simulation is a widely used computational method for generating

probability distributions of variables that depend on other variables or parameters

represented as probability distributions (Ergonul, 2005). Monte Carlo simulation would

involve many calculations of the intake rate rather than a single calculation. For each

calculation, the computation would use the values for input parameters randomly

selected from the probability density function for the variable. Over multiple

calculations, the simulation uses a range of values for the input parameters that reflect

the probability density function of each input parameter. Thus, the repetitive simulations

use many randomly selected combinations of the stress-drop ratio, phase delay and rise

time. For each combination of the randomly selected variables, a ground motion time

history is simulated, and the PGA, PGV, RMSA and response spectrum determined. A

probability density function or cumulative density function of PGA, PGV, RMSA and

response spectrum can then be determined from a large number of simulations. The

mean value and standard deviation of PGA, PGV, RMSA and response spectrum can

also be derived.

Convergence test needs be conducted to check the number of Monte Carlo simulations

required to obtain converged simulation results. In this study, the PGA, PGV, RMSA

and response spectrum values of the simulated ground motion at 0.1sec, 1.0sec, 2.5sec

and 5sec are used as the quantity for convergence test. The time interval between 5 and

95 percent of total Arias Intensity is used to compute the RMSA. It is found that the

mean value and Standard deviation of PGA, PGV, RMSA and the response spectrum

amplitudes at 0.1sec, 1.0sec, 2.5sec and 5sec remained virtually unchanged after 600

simulations as shown in Figure 4-1 and Figure 4-2. Therefore, in the subsequent

calculations 600 simulations are performed for each case. The 600 simulated data for

PGA, PGV, RMSA and response spectrum values at the selected periods all display a

lognormal distribution. To verify these observations, a Kolmorogov–Smirnov goodness-

of-fit test (K–S test) is applied to check the lognormal distribution assumptions for PGA,

PGV, RMSA and response spectrum. The significance level alpha for the test is chosen

to be 0.01 in this study.


78

0 200 400 600 800 1000190

200

210

220

230

240

250

260

Monte Carlo runs

Mea

n PG

A (m

m/s

2 )

0 200 400 600 800 1000

0

10

20

30

40

50

60

Monte Carlo runs

Stan

dard

dev

iatio

n of

PG

A

0 200 400 600 800 10003.4

3.6

3.8

4

4.2

4.4

4.6

4.8

5

Monte Carlo runs

Mea

n P

GV

(mm

/s)

0 200 400 600 800 1000

0

0.2

0.4

0.6

0.8

1

Monte Carlo runs

Stan

dard

dev

iatio

n of

PG

V

0 200 400 600 800 100056

58

60

62

64

66

Mea

n RM

SA

Monte Carlo runs0 200 400 600 800 1000

0

1

2

3

4

5

6

7

8

Sta

ndar

d de

viat

ion

of R

MSA

Monte Carlo runs

Figure 4-1 Mean value, standard deviation of PGA, PGV and RMSA of the simulated

ground motions

0 500 1000400

450

500

550

Monte Carlo runs

Mea

n

0 500 100035

40

45

50

Monte Carlo runs

Mea

n

0 500 10003

3.5

4

4.5

Monte Carlo runs

Mea

n

0 500 10000.9

1

1.1

1.2

1.3

Monte Carlo runs

Mea

n

5.0sec2.5sec

1.0sec0.1sec

0 500 10000

50

100

150

Monte Carlo runs

Sta

ndar

d de

viat

ion

0 500 10000

5

10

15

Monte Carlo runs

Sta

ndar

d de

viat

ion

0 500 10000

1

2

Monte Carlo runs

Sta

ndar

d de

viat

ion

0 500 10000

0.2

0.4

Monte Carlo runs

Sta

ndar

d de

viat

ion

0.1sec 1.0sec

2.5sec 5.0sec

Figure 4-2 Mean value and standard deviation of the response spectrum at 0.1sec,

1.0sec, 2.5sec and 5sec


79

Figure 4-3 illustrates the density histograms of the PGA, PGV, RMSA and response

spectrum at 0.1sec, 1.0sec, 2.5sec and 5sec, and the corresponding lognormal

distribution function. As shown, lognormal distribution function fits the simulated data

well. All parameters pass the K-S test with a 1% significance level, indicating a very

good fit of lognormal distribution to the PGA, PGV, RMSA and response spectrum.

Table 4-2 gives the results of Monte Carlo simulation and K-S test.

140 160 180 200 220 240 260 280 3000

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

PGA Data

Den

sity

pga dataLognormal fit

2.5 3 3.5 4 4.5 5 5.5 60

0.1

0.2

0.3

0.4

0.5

0.6

0.7

PGV Data

Dens

ity

pgv dataLognormal fit

50 55 60 65 700

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

RMSA Data

Den

sity

RMSA dataLognormal fit

300 350 400 450 500 550 600 6500

1

2

3

4

5

6

7

x 10-3

Response Spectrum 0.1sec Data

Dens

ity

RSP0.1sec dataLognormal fit

20 30 40 50 60 70

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045


Dens

ity


2.5 3 3.5 4 4.5 5 5.5 60

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5


Dens

ity


0.8 1 1.2 1.4 1.6 1.8

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5


Dens

ity


Figure 4-3 Probability density function of PGA, PGV, RMSA and response spectrum of

the simulated ground motion at 0.1sec, 1.0sec, 2.5sec and 5sec and the corresponding

lognormal distribution function


80

Table 4-2 Monte Carlo simulation and K-S test result for PGA, PGV, RMSA and

response spectrum at 0.1sec, 1.0sec, 2.5sec and 5sec

Mean Standard deviation

The test statistic

The critical value

PGA (mm/s2) 203.481 26.00 0.0362 0.0661 PGV(mm/s) 3.79 0.68 0.0392 0.0661 RMSA(mm/s2) 59.3 4.09 0.0297 0.0661 RSP0.1sec(mm/s2) 414.99 59.64 0.0183 0.0661 RSP1.0sec(mm/s2) 42.83 9.53 0.0542 0.0661 RSP2.5sec(mm/s2) 4.09 0.81 0.0402 0.0661 RSP5.0sec(mm/s2) 0.98 0.12 0.0657 0.0661

4.3.2 Rosenblueth’s Point estimate method

Monte Carlo simulation is straightforward to use and can give reliable estimations of

statistical parameters of the simulated ground motion time histories. It is often used

because the response statistics of a nonlinear dynamic system are usually difficult to be

derived. However, Monte Carlo simulation is extremely time consuming and needs a

large number of simulations, e.g., 600 simulations in this case, to get the converged

estimations. Rosenblueth derived an approximate method, Rosenblueth’s point estimate

method, to estimate the response statistics (Rosenblueth, 1981). The method allows a

direct estimation of the response moments (mean and standard deviation). It gives exact

estimation if the distributions of the random variables are normal, and very good

approximation if the distributions of the variables are close to normal. Because it is

computationally more efficient than the Monte Carlo simulation method, in this study,

the Rosenblueth’s point estimate method is used in the calculations. Its reliability is

verified by using the Monte Carlos simulation results.

To use the Rosenblueth’s point estimate method, 8 simulations are needed for three

random variables in this study. Use PGA as an example to demonstrate the method, as

indicated in Equation 4-2, PGA+++ is the PGA value of the ground motion time history

simulated with mean value plus one standard deviation of the three random source

parameters, i.e, stress-drop ratio μ1 and s1; rupture velocity μ2 and s2; and rise time μ3

and s3. Similarly, PGA--- is the PGA value of the time history simulated using mean

value minus one standard deviation of the three random source parameters.


81

( ) ( ) ( )[ ]332211 ,, sssfPGA +++=+++ μμμ

( ) ( ) ( )[ ]332211 ,, sssfPGA −−−=−−− μμμ

( ) ( ) ( )[ ]332211 ,, sssfPGA −−+=−−+ μμμ

( ) ( ) ( )[ ]332211 ,, sssfPGA −++=−++ μμμ

( ) ( ) ( )[ ]332211 ,, sssfPGA ++−=++− μμμ

( ) ( ) ( )[ ]332211 ,, sssfPGA +−−=+−− μμμ

( ) ( ) ( )[ ]332211 ,, sssfPGA +−+=+−+ μμμ

( ) ( ) ( )[ ]332211 ,, sssfPGA −+−=−+− μμμ .

(4-2)

The point-mass weights also need be determined. In this work, it is assumed that these

three variables are not dependent on each other. Thus, the correlation coefficient is zero

and the point-mass weights are given as:

125.081

=⎟⎠⎞

⎜⎝⎛======== −+−+−++−−++−−++−−+−−−+++ PPPPPPPP (4-3)

The mean and standard deviation of PGA can then be calculated by

−+−−+−+−++−++−−+−−++−++−

−++−++−−+−−+−−−−−−++++++

+++++++=

PGAPPGAPPGAPPGAPPGAPPGAPPGAPPGAPPGAμ

(4-4)

222

2222222

PGAPGAPPGAP

PGAPPGAPPGAPPGAPPGAPPGAPPGA

μ

σ

−++

+++++≈

−+−+−+

+−−++−−++−−+−−−+++

−+−+−+

+−−++−−++−−+−−−+++

(4-5)

Following the same procedure, the mean and standard deviation of PGV, RMSA and

response spectrum can also be calculated. Using the point estimate method, the

statistical parameters of PGA, PGV, RMSA and response spectrum are derived and

listed in Table 4-3. The coefficient of variation of response spectrum (COAS) shown in

Table 4-3 is defined as:

∫∫= b

a m

b

a s

dTSa

dTSaCOAS (4-6)


82

in which sSa and mSa are standard deviation and mean value of the response spectrum,

respectively. a and b define the period bandwidth. In this study, a is 0.01sec and b is

5sec. T is period in sec. COAS is used to estimate the coefficient of variation of

response spectrum in defined period range.

Table 4-3 Point estimate and Monte Carlo simulation results for PGA , PGV, RMSA,

response spectrum at 0.1sec, 1.0sec, 2.5sec and 5sec and COAS

Point estimation method Monte Carlo simulation Mean C.O.V (%) Mean C.O.V (%) PGA (mm/s2) 209.95 13.8 203.48 12.8 PGV (mm/s) 3.41 13.2 3.79 17.4

RMSA(mm/s2) 60.3 7.3 59.3 6.9 RSP0.1sec(mm/s2) 401.35 11.3 414.99 14.4 RSP1.0sec(mm/s2) 45.48 19.6 42.83 22.3 RSP2.5sec(mm/s2) 4.43 16.9 4.09 19.8 RSP5.0sec(mm/s2) 0.97 6.2 0.98 12.2

COAS 17.5 18.6

4.3.3 Comparison of the results

Table 4-3 compares the results obtained by Monte Carlo simulation and point estimate

method. It can be seen that the Rosenblueth’s point estimate method gives similar

results as the Monte Carlo simulations. Rosenblueth’s point estimate method is a lot

more efficient in calculating response statistics as it only requires 8 simulations as

compared to 600 simulations with Monte Carlo simulation. Numerical results also

indicate that variations of the earthquake source parameters significantly affect the

simulated ground motions. With 10% variations in the source parameters, the variation

of PGA, PGV and response spectrum of the simulated ground motion are all more than

10%, indicating the importance of reliably determining the earthquake source

parameters in ground motion simulations.

4.4 Sensitivity analysis


83

To gain a better insight on the impact of the variations of source parameters on the

strong ground motion, a sensitivity analysis is performed. Three Case studies are

considered in sensitivity analysis to investigate which parameter has more significant

influence on the simulated ground motion. Case 1 studies the influence of variation of

each of the three source parameters on the simulated ground motion. In which, the

coefficient of variation of each source parameter is assumed to be 10%, 50%, 70% and

90%, respectively while the other two parameters are assumed as deterministic as

indicated in Table 4-4. The ground motions are simulated for all the assumed scenarios

and the variations of the simulated ground motion parameters are determined. The same

example of an ML6.0 and epicentral distance 100 km event is considered. PGA, PGV,

RMSA and spectral accelerations are calculated using the Rosenblueth’s point estimate

method. Coefficients of variation of PGA, PGV, RMSA and response spectrum with

respect to those listed in Table 4-4 are estimated. The sensitivity of the simulated

ground motions to the change in the source parameter values is examined from the

numerical results.

Case 2 investigates the influence of the variations of source parameters on the simulated

ground motions with different magnitudes. In this case, each source parameter is

assumed to have a 50% coefficient of variation in the simulation. Ground motions

corresponding to earthquakes of magnitudes ML5.0, ML6.0 ML7.0 and epicentral

distance 100km are simulated from the same small event of ML4.5 and epicentral

distance 100km. Descriptions of the simulations in this case are listed in Table 4-5.

Coefficients of variation of PGA, PGV, RMSA and response spectrum corresponding to

those listed in Table 4-5 are calculated using Rosenblueth’s point estimate method.

Case 3, as described in Table 4-6, is performed to study the effects of random

fluctuations of the seismic source parameters on simulated ground motions with

different epicentral distances. 50% coefficient of variation is again assumed for each

source parameter. The epicentral distance of 50km, 100km, 150km and 200km and

ML6.0 earthquake are considered. The simulation is carried out from a small event of

ML4.5 at the same distance as that of the simulated event. Coefficients of variation of

PGA, PGV, RMSA and response spectrum of the simulated ground motions are

calculated and used to examine the influence of the source parameters.


84

Table 4-4 Case study 1 for sensitivity analysis

Coefficient of Variation (C.O.V.) Sub-case No. Stress drop Phase delay Rise time Case 1-1 10% 0% 0% Case 1-2 30% 0% 0% Case 1-3 50% 0% 0% Case 1-4 70% 0% 0% Case 1-5 90% 0% 0% Case 1-6 0% 10% 0% Case 1-7 0% 30% 0% Case 1-8 0% 50% 0% Case 1-9 0% 70% 0% Case 1-10 0% 90% 0% Case 1-11 0% 0% 10% Case 1-12 0% 0% 30% Case 1-13 0% 0% 50% Case 1-14 0% 0% 70% Case 1-15 0% 0% 90%


Coefficient of Variation (C.O.V.) Sub-case No. Magnitude Stress drop Phase delay Rise time Case2-1 ML5 50% 0% 0% Case 2-2 ML5 0% 50% 0% Case 2-3 ML5 0% 0% 50% Case 2-4 ML6 50% 0% 0% Case 2-5 ML6 0% 50% 0% Case 2-6 ML6 0% 0% 50% Case 2-7 ML7 50% 0% 0% Case 2-8 ML7 0% 50% 0% Case 2-9 ML7 0% 0% 50%


85


Coefficient of Variation (C.O.V.) Sub-case No. Epicentral Distance Stress drop Phase delay Rise time

Case 3-1 50km 50% 0% 0% Case 3-2 50km 0% 50% 0% Case 3-3 50km 0% 0% 50% Case 3-4 100km 50% 0% 0% Case 3-5 100km 0% 50% 0% Case 3-6 100km 0% 0% 50% Case 3-7 150km 50% 0% 0% Case 3-8 150km 0% 50% 0% Case 3-9 150km 0% 0% 50% Case 3-10 200km 50% 0% 0% Case 3-11 200km 0% 50% 0% Case 3-12 200km 0% 0% 50%

4.4.1 Case Study 1

As shown in Figure 4-4, when only stress drop ratio has random fluctuation among the

three source parameters with a 10%-90% coefficient of variation, the coefficient of

variation of PGA and RMSA is more than that of the stress drop ratio. Those

corresponding to PGV and COAS are, however, slightly less than that of the stress drop

ratio, indicating a reduction in uncertainties. These observations indicate that variation

in the stress drop ratio has a more significant effect on ground motion PGA and RMSA

than PGV and COAS. This is probably because the stress drop ratio has a more

pronounced influence on ground motion in the high frequency range, which in turn

affects ground motion accelerations. Its influence on ground motion velocity is less

significant because ground velocity is relatively less sensitive to high frequency

contents as compared to acceleration.


86

10 20 30 40 50 60 70 80 900

20

40

60

80

100

120

Stress Drop Ratio C.O.V.

C.O

.V.

C.O.V.of PGA, PGV, RMSAand response spectrum

PGAPGVRMSACOAS

Figure 4-4 Coefficient of variation of PGA, PGV, RMSA and response spectrum of the

simulated ground motion with respect to that of the stress drop ratio

Figure 4-5 shows the coefficient of variation of each ground motion parameter against

that of the phase delay. It shows that variation in the phase delay has insignificant effect

on PGA and RMSA. The coefficient of variation of PGA and RMSA are all less than

about 20% when that of the phase delay varies from 10% to 90%. Its influence on PGV

and COAS are also insignificant when the variation in the phase delay is less than 70%.

However, when the coefficient of variation of the phase delay is more than 70%, it

significantly affects PGV and COAS of the simulated ground motion. This is because

the phase delay acts as a “low-pass” filter in the summation process of ground motion

simulation. Variation in phase delay will result in variation in the low cut-off frequency

of the “low-pass” filter. Hence, uncertain phase delay has less influence on PGA and

response spectrum in the high frequency range, but affects noticeably in the low

frequency range of the response spectrum. Uncertain phase delay also affects PGV

especially when the cut-off frequency of the “low-pass” filter is high.


87

10 20 30 40 50 60 70 80 900

20

40

60

80

100

Phase Delay C.O.V.

C.O

.V.


PGAPGVRMSACOAS


simulated ground motion with respect to that of the phase delay

The influence of changing the rise time on various ground motion parameters is shown

in Figure 4-6. As shown, the coefficients of variation of all the simulated ground

motion parameters are less than that of the rise time, indicating a reduction in

uncertainties. Nevertheless, the simulated ground motion is also sensitive to rise time.

The coefficients of variations of all the simulated ground motion parameters increase

with that of the rise time. Random fluctuations in rise time affect ground motion PGV

and COAS more than PGA and RMSA.


88

10 20 30 40 50 60 70 80 900

20

40

60

80

100

Rise Time C.O.V.

C.O

.V.


PGAPGVRMSACOAS


simulated ground motion with respect to that of the rise time

Mean, mean plus one standard deviation and mean minus one standard deviation of the

spectral acceleration and the corresponding coefficient of variation with respect to the

variation of each source parameter are presented in Figure 4-7 to Figure 4-9. They show

that the stress drop ratio affects the response spectrum in the high frequency range more

significantly, as observed above. Variation in the rise time produces a noticeable change

in the spectral acceleration in the middle frequency band. Figure 4-8 shows that the

variation in the phase delay affects more significantly the spectral acceleration in the

low frequency range. Changing the coefficient of variation of the phase delay from 10%

to 70% only slightly increases the coefficient of variation of the spectral acceleration of

the simulated ground motion. Whereas changing the coefficient of variation of the stress

drop ratio and rise time from 10% to 70% significantly increases the coefficient of

variation of the spectral acceleration of the simulated ground motion.


89

10-2 100 10210-1

100

101

102

103

Spe

ctra

l Acc

eler

atio

n(m

m/s2 )

Period (sec)

Stress drop ratiowith 10% C.O.V.

MeanMean+STDMean-STD

10-2 100 10210-1

100

101

102

103

104

Spe

ctra

l Acc

eler

atio

n(m

m/s2 )

Period (sec)

Stress drop ratiowith 70% C.O.V.


10-2 10-1 100 10110-1

100

101

102

Coe

ffici

ent o

f var

iatio

n(%

)

Period (sec)

Stress drop ratioCoefficient of variation Spectrum

10%70%

Figure 4-7 Comparison of spectral acceleration and C.O.V. spectrum of the simulated

ground motion with respect to variation in the stress drop ratio

10-2 100 10210-1

100

101

102

103

Spe

ctra

l Acc

eler

atio

n(m

m/s2 )

Period (sec)

Phase delaywith 10% C.O.V.


10-2 100 10210-1

100

101

102

103

Spe

ctra

l Acc

eler

atio

n(m

m/s2 )

Period (sec)

Phase delaywith 70% C.O.V.


10-2 10-1 100 101

10-2

10-1

100

101

102

Coe

ffici

ent o

f var

iatio

n(%

)

Period (sec)

Phase delayCoefficient of variation Spectrum

10%70%


ground motion with respect to variation in the phase delay

10-2 100 10210-1

100

101

102

103

Spe

ctra

l Acc

eler

atio

n(m

m/s2 )

Period (sec)

Rise timewith 10% C.O.V.


10-2 100 10210-1

100

101

102

103

Spe

ctra

l Acc

eler

atio

n(m

m/s2 )

Period (sec)

Rise timewith 70% C.O.V.


10-2 10-1 100 101

10-2

10-1

100

101

102

Coe

ffici

ent o

f var

iatio

n(%

)

Period (sec)

Rise timeCoefficient of variation Spectrum

10%70%


ground motion with respect to variation in the rise time

4.4.2 Case Study 2


90

Assuming a 50% coefficient of variation in each source parameter, ground motions

corresponding to different earthquake magnitudes are simulated. Coefficient of variation

of PGA, PGV, RMSA and response spectrum of the simulated ground motions of

different magnitudes are presented in Figure 4-10 to Figure 4-12. As can be seen in

Figure 4-10, the influences of variation in the stress drop ratio on PGA, RMSA and

COAS remain almost unchanged with earthquake magnitude. However, variation in the

stress drop ratio affects the coefficient of variation of PGV of small magnitude

earthquakes more than that of large magnitude earthquakes, implying a reduction of the

influence level of the stress drop ratio on ground motions of large magnitude

earthquakes.

Figure 4-11 shows the coefficients of variation of the simulated ground motion

parameters corresponding to different earthquake magnitudes and a 50% variation in the

phase delay. As shown, the coefficient of variation of PGA changes from about 8% at

ML5 to 35% at ML7 and the coefficient of variation of RMSA varies from about 8% at

ML5 to 32% at ML7, indicating an increase in the influence of the phase delay

fluctuation with the earthquake magnitude on PGA and RMSA of the simulated ground

motions. The influences on PGV and COAS, however, reduce from about 23% and 33%

at ML5.0 to about 9% and 27% at ML7.0, respectively. Figure 4-12 shows variations of

the simulated ground motion parameters when the variation in rise time is 50%. As

shown, the effect of the rise time fluctuation remains almost the same to PGA and PGV.

Whereas, COAS changes from about 15% at ML5 to 45% at ML7 and the coefficient of

variation of RMSA varies from about 8% at ML5 to 18% at ML7, indicating an increase

in the influence level of the rise time on the simulated motions with earthquake

magnitude.

The above observations indicate that the variation in the stress drop ratio more

significantly affects ground motions from small magnitude earthquakes, whereas the

variation in the rise time has more pronounced effects on ground motions of large

magnitude earthquakes. The effects of variation in the phase delay on PGA and RMSA

of the simulate ground motions increase slightly with earthquake magnitude, but on

PGV and COAS decrease with earthquake magnitude. These observations show that the

influences of the variation in source parameters on simulated ground motions are

dependent on earthquake magnitude.


91

5 5.5 6 6.5 70

20

40

60

80

100

120

140

Magnitude

C.O

.V.

PGAPGVRMSACOAS

Figure 4-10 Coefficient of variation of PGA, PGV, RMSA and COAS of simulated

ground motions corresponding to earthquakes of ML5.0, ML6.0 and ML7.0 and

epicentral distance 100 km when C.O.V. of the stress drop ratio is 50%

5 5.5 6 6.5 70

10

20

30

40

50

Magnitude

C.O

.V.

PGAPGVRMSACOAS



epicentral distance 100 km when C.O.V. of the phase delay is 50%


92

5 5.5 6 6.5 70

10

20

30

40

50

60

70

Magnitude

C.O

.V.

PGAPGVRMSACOAS



epicentral distance 100 km when C.O.V. of the rise time is 50%

4.4.3 Case Study 3

Coefficients of variation of PGA, PGV, RMSA and COAS of the simulated ground

motions with respect to different cases in Table 4-6 are calculated using the

Rosenblueth’s point estimate method and are shown in Figure 4-13 to Figure 4-15. As

can be seen in these Figures, the influence of variation in the source parameters on PGA,

PGV and COAS is relatively independent of the epicentral distance. When the

epicentral distance increases from 50km to 200km, the C.O.V. of these ground motion

parameters only experience insignificant changes. However, the influence of variation

in the rise time on RMSA is dependent on the epicentral distance. Variation in RMSA

increases from about 10% at epicentral distance 50km to about 23% at epicentral

distance 200km.


93

50 100 150 2000

10

20

30

40

50

60

70

80


C.O

.V.

PGAPGVRMSACOAS

Figure 4-13 Influence of variation in the stress drop ratio (50% C.O.V) on parameters of

ground motions simulated with different epicentral distances

50 100 150 2000

10

20

30

40

50


C.O

.V.

PGAPGVRMSACOAS

Figure 4-14 Influence of variation in the phase delay (50% C.O.V) on parameters of

ground motions simulated with different epicental distances


94

50 100 150 2000

10

20

30

40

50


C.O

.V.

PGAPGVRMSACOAS

Figure 4-15 Influence of variation in the rise time (50% C.O.V) on parameters of

ground motions simulated with different epicental distances

The above analyses demonstrate the influences of variations in earthquake source

parameters on simulated ground motions. Ideally, reliable source parameters should be

used in strong ground motion predictions. In reality, unfortunately, reliable seismic

source parameters are usually not available. This is the case for SWWA earthquakes.

Hence, the best achievable ground motion prediction is to include the effects of the

possible uncertainties in source parameters and carry these uncertainties through to the

predictions. The above sensitivity studies demonstrated that the influences of the

variations in source parameters on simulated ground motions are dependent on

earthquake magnitude, but are relatively insensitive to epicentral distance. Hence, a

model which determines the coefficient of variation of the various parameters of the

simulated strong ground motions is developed in this study as a function of the

variations of the source parameters and earthquake magnitude, but independent of the

epicentral distance.

4.5 C.O.V. model

To develop the coefficient of variation models for various ground motion parameters

with respect to the variations in source parameters and earthquake magnitude, a set of


95

ground motions with magnitudes varying from ML5.0 to ML7.0 with an increment of

ML1.0, epicentral distances from 50km to 200km with an increment of 50 km and

coefficient of variation of each source parameter from 10% to 90% with an increment of

20% are generated. Coefficients of variation of PGA, PGV and response spectrum are

calculated for each increment. There are a total of 180 coefficients of variation of PGA,

PGV and response spectrum available after simulation. Since the simulated data are for

ground motions on bedrock site, the derived C.O.V. model is only applicable to rock

site condition.

Variable selection process is carried out based on the sensitivity analysis presented

above and the correlation matrix analysis to select independent variables from a pool of

possible candidates that should be included in the regression model. The correlation

matrix is an array of the correlation coefficients that are calculated from all the possible

pairings of the independent variables. The correlation matrix for each ground motion

parameter is given in Table 4-7 to Table 4-10. Each "cell" of the matrix contains a

correlation coefficient between the variables represented by the particular row and

column that the cell occupies. The correlation coefficient of two variables X1 and X2 is

defined as:

( )21

21

21 ,

XXXX

XXCOVσσ

ρ = (4-7)

in which COV(X1,X2) is the covariance of the two variables X1 and X2, σ X1 and σ X2 are

standard deviation of variable X1 and X2, respectively. A perfect correlation of 1.0

indicates a perfect linear relationship, and a correlation of 0.0 indicates no linear

relationship exits. Inspection of the correlation matrix can provide information about the

linear relationships that exist among variables. It also can identify which variables

correlate with each of the other variables, or those that may be relatively independent of

one another. Several criteria, e.g., sum of residuals, average residual, absolute residual

sum of squares, standard error of estimate and coefficient of multiple determination, are

examined to determine the goodness of fit of the regression model. If the curve passed

through each data point, the sum of residuals, the average residual and the absolute

residual sum of squares would be zero. As the standard error approaches zero and the


96

coefficient of multiple determination approaches 1, it is more certain that the regression

model accurately describes the data.

4.5.1 PGA C.O.V. model

The correlation matrix, which is based on 180 C.O.V. of PGA, is shown in Table 4-7 to

Table 4-10. It is evident that the intercorrelation between PGA (y) and stress drop ratio

(x1) is more significant than that between other parameters. On the contrary, there is

low correlation between coefficients of variation of PGA and epicentral distance,

indicating that including the epicentral distance term in the model does not improve the

statistical goodness of fit. Table 4-7 to Table 4-9 show that the explained variance

cannot be improved significantly as the order of x2, x4 and x5 increases. Table 4-10

indicates that the correlation between y and x1*x4, x2*x4 and x3*x4 are evident. Based

on correlation matrix and the comparison of the results of residuals and the coefficient

of multiple determinations, the proposed model is constructed as

10987652

4322

1... aTMaDMaSMaMaTaTaDaSaSaPGA VOC +++++++++= (4-8)

where ... VOCPGA is coefficient of variation of PGA. S, D, and T are coefficient of

variation of the stress drop ratio, phase delay and rise time, respectively. M is local

magnitude. The coefficients a1-a10 are listed in Table 4-13. A summary of the results of

tests carried out to assess the goodness of fit of Equation 4-8 for the regression data is

given in Table 4-11. As can be seen in Table 4-11, the sum of residuals and the

coefficient of determination are -2.282E-10 and 0.93 respectively, which means that the

regression model can accurately describe the data. The distribution of the error term can

be seen in Figure 4-16. It is evident that the distribution of residuals is similar to the

normal distribution. The computed value of the t test is measured and shows the 95%

confidence interval on the residuals with a zero mean normal distribution.


97

Table 4-7 Correlation matrix: PGA C.O.V. with the first order variables

Stress

drop ratio (x1)

Phase delay (x2)

Rise time (x3)

Magnitude (x4)

Epicentral distance

(x5) Stress drop ratio (x1) 1.000 0.338 0.338 0.000 0.000

Phase delay (x2) 0.338 1.000 0.338 0.000 0.000 Rise time (x3) 0.338 0.338 1.000 0.000 0.000

Magnitude (x4) 0.000 0.000 0.000 1.000 0.000 Epicentral distance

(x5) 0.000 0.000 0.000 0.000 1.000

PGA (y) 0.735 0.100 0.062 0.106 0.017

Table 4-8 Correlation matrix: PGA C.O.V. with the second order variables

x1^2 x2^2 x3^2 x4^2 x5^2 x1^2 1.000 0.231 0.231 0.000 0.000 x2^2 0.231 1.000 0.231 0.000 0.000 x3^2 0.231 0.231 1.000 0.000 0.000 x4^2 0.000 0.000 0.000 1.000 0.000 x5^2 0.000 0.000 0.000 0.000 1.000

y 0.774 0.026 0.172 0.107 0.014

Table 4-9 Correlation matrix: PGA C.O.V. with the third order variables

x1^3 x2^3 x3^3 x4^3 x5^3 x1^3 1.000 0.177 0.177 0.000 0.000 x2^3 0.177 1.000 0.177 0.000 0.000 x3^3 0.177 0.177 1.000 0.000 0.000 x4^3 0.000 0.000 0.000 1.000 0.000 x5^3 0.000 0.000 0.000 0.000 1.000

y 0.766 0.009 0.222 0.108 0.011

Table 4-10 Correlation matrix: PGA C.O.V. with the combined variables

x1*x4 x2*x4 x3*x4x1*x4 1.000 0.330 0.330 x2*x4 0.330 1.000 0.330 x3*x4 0.330 0.330 1.000

y 0.708 0.067 0.090


98

Table 4-11 Summary of the fitness tests for PGA model

Sum of Residuals -2.282E-10 Average Residual -1.268E-12

Residual Sum of Squares (Absolute) 11299.50 Standard Error of the Estimate 8.15

Coefficient of Multiple Determination(R^2) 0.93

-20 -15 -10 -5 0 5 10 15 200

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Residual Data

Den

sity


-20 -15 -10 -5 0 5 10 15 20

0

0.2

0.4

0.6

0.8

1

Residual Data

Cum

ulat

ive

prob

abili

ty



4.5.2 C.O.V. of PGV and response spectrum

Relations for coefficient of variation of PGV and response spectrum at various periods

with variations in source parameters and earthquake magnitude are also developed.

Similar models as that given in Equation 4-8 for PGA are used. The coefficients a1-a10

are listed in Table 4-13. Table 4-12 gives a summary of the results of tests carried out to

assess the goodness of fit of the C.O.V. model for PGV. For response spectrum at

various periods, the sum of residuals, average residual, standard error of estimate and

coefficient of multiple determinations are shown in Figure 4-17. The mean of sum of

residuals and the mean of coefficient of determination for response spectrum are

2.631E-012 and 0.84 respectively, implying the response spectrum model can

accurately describe the data.


99

Table 4-12 Summary of the fitness test for PGV model

Sum of Residuals -8.138E-10 Average Residual -4.521E-12

Residual Sum of Squares (Absolute) 89742.59 Standard Error of the Estimate 22.98

Coefficient of Multiple Determination(R^2) 0.52

0 1 2 3 4 5-4

-2

0

2

4

6

8

10x 10

-12

Period (sec)

Sum

of r

esid

uals

Sum of Residuals

0 1 2 3 4 5-2

-1

0

1

2

3

4

5x 10

-14

Period (sec)

Ave

rage

resi

dual

s

Average Residuals

0 1 2 3 4 50.65

0.7

0.75

0.8

0.85

0.9

0.95

1

Period (sec)

Coe

ffici

ent o

fm

ultip

le d

eter

min

atio

n

Coefficient of Multiple Determination

0 1 2 3 4 5

8

10

12

14

16

18

20

Period (sec)

Stan

dard

err

orof

the

estim

ate

Standard Error of the Estimate

Figure 4-17 Sum of residuals, average residual, standard error of estimate and

coefficient of multiple determination for C.O.V. of the response spectrum model


100

Table 4-13 Derived coefficients for estimation of C.O.V. of PGA, PGV and spectral acceleration with 5% damping

Period a1 a2 a3 a4 a5 a6 a7 a8 a9 a10 PGA 0.0059 0.8017 -1.4268 0.0102 -1.9787 -5.0402 -0.0457 0.2939 0.2801 34.0646 PGV 0.0011 2.9807 0.2177 0.0093 -1.1584 14.5174 -0.4082 0.0134 0.1632 -73.7255 0.05 0.0121 -0.0783 -0.0142 0.0119 -1.5839 -1.4041 0.0016 0.0466 0.1508 19.1187 0.10 0.0096 0.4377 -0.1386 0.0144 -2.1306 -2.9611 -0.0347 0.0683 0.2546 26.885 0.15 0.0055 0.2329 -0.7465 0.0137 -2.7096 -7.5746 0.0152 0.1461 0.3567 59.0004 0.20 0.0114 -0.4704 0.2152 0.0106 -2.5448 -5.3213 0.0668 -0.0141 0.386 47.6415 0.25 0.0026 1.6169 0.78 0.0101 -2.2434 -3.045 -0.1558 -0.0862 0.3559 30.1745 0.30 0.0015 1.3617 0.4462 0.007 -2.2543 -2.7141 -0.0887 0.0016 0.414 26.4653 0.35 -0.0015 2.1188 -0.399 0.0064 -2.0543 -2.3611 -0.1709 0.1276 0.3932 21.5071 0.40 0.0014 0.7474 -0.4787 0.0059 -3.1279 -12.4334 0.0052 0.1344 0.5721 84.4605 0.45 0.0007 1.6032 -0.1466 0.003 -3.1343 -13.6079 -0.1376 0.086 0.6165 88.508 0.50 -0.0005 2.9591 0.0442 0.0036 -3.0204 -9.231 -0.3647 0.0556 0.5807 66.0848 0.55 0.0034 2.6791 -0.241 0.0048 -3.1028 -6.1566 -0.3962 0.0815 0.5539 57.4671 0.60 0.0035 3.2704 0.0756 0.0039 -2.5026 -0.0389 -0.4835 0.0329 0.4797 14.6218 0.65 0.0005 2.5514 -0.263 -0.0003 -2.4366 -3.6126 -0.2964 0.1227 0.5506 25.6039 0.70 -0.0024 2.5369 -0.6539 -0.0025 -2.0868 -4.2583 -0.2535 0.1943 0.5341 23.3933 0.75 0.0017 2.0802 -0.7336 -0.0005 -2.6951 -3.4187 -0.2453 0.1992 0.5899 22.5661 0.80 0.0043 1.4183 -0.4681 0.0022 -2.8716 -3.8794 -0.192 0.158 0.5798 28.4949 0.85 0.0035 1.1964 0.1714 0.0007 -2.5866 -3.9116 -0.1512 0.0738 0.5597 26.4479 0.90 -0.0001 1.4471 0.7736 -0.0014 -2.1661 -2.3889 -0.1541 -0.008 0.5261 12.5933


101

Period a1 a2 a3 a4 a5 a6 a7 a8 a9 a10 0.95 -0.0025 1.6188 1.223 -0.0008 -2.5222 -1.8874 -0.1674 -0.0784 0.5664 9.6962 1.00 -0.0041 1.5551 1.6252 -0.0009 -2.3214 1.5665 -0.1404 -0.1406 0.5302 -12.1091 1.50 -0.0007 -0.2975 0.3484 0.0006 -3.2679 -7.0657 0.1182 0.0869 0.6386 46.7464 2.00 -0.0013 0.0686 0.8419 -0.0023 -2.5719 -0.1178 0.0465 0.0175 0.5594 1.514 2.50 -0.009 1.0548 0.1417 -0.003 -2.3849 1.1786 -0.0231 0.1467 0.5383 -9.5914 3.00 -0.0051 1.2485 -0.8579 -0.001 -2.7081 -1.9652 -0.1021 0.3117 0.5653 10.4071 3.50 -0.0016 1.0062 -1.8978 0.0038 -2.4146 -3.6458 -0.1133 0.4774 0.4265 26.9609 4.00 -0.0006 1.2414 -1.9128 0.0057 -2.2777 -0.8093 -0.1794 0.472 0.3663 13.8185 4.50 0.0016 0.9809 -2.1313 0.0075 -2.1869 -2.9088 -0.1659 0.5042 0.3158 28.2011 5.00 0.0024 1.0643 -2.0725 0.0073 -1.6241 -1.5197 -0.1936 0.4925 0.2089 21.6303


102

4.6 Ground motion attenuation with uncertain source

parameters

The previous chapter presented the attenuation relations of PGA, PGV and response

spectrum of ground motions on rock site in SWWA derived from the simulated ground

motion data with a combined Green’s function and stochastic method. The source

parameters used in the simulations are those for CENA model, or the mean values in the

above calculations. Therefore, these attenuation relations can be extended to include the

effects of the source parameter uncertainties by using the C.O.V model presented above.

Some examples of ground motion prediction associated with uncertainty in each source

parameter are calculated and shown in Figure 4-18. Using the attenuation relations

developed in Chapter 3 and the C.O.V model developed in this study, the ground

motion attenuations with the effect of uncertain source parameters can be obtained.


103

101

10210

0

101

102

103

104


PGA

(mm

/s2 )

PGA with 50% C.O.V.in Stress drop ratio

ML5 Mean PGAML6 Mean PGAML7 Mean PGAPGA plus STDPGA minus STD

101

10210

0

101

102

103

104


PGA

(mm

/s2 )

PGA with 50% C.O.V.in Phase delay


(a) (b)

101

10210

0

101

102

103

104


PGA

(mm

/s2 )

PGA with 50% C.O.V.in Rise time


10-1

100

10110

-1

100

101

102

103

Period (sec)

Spec

tral

Acc

eler

atio

n (m

m/s

2 )

Response Spectrum50% C.O.V. of Stress drop ratio

ML5ML6ML7Mean plus STDMean minus STD

(c) (d)

10-1

100

101

100

101

102

103

Period (sec)

Spec

tral

Acc

eler

atio

n (m

m/s

2 )

Response Spectrum50% C.O.V. of Phase delay


10-1

100

101

100

101

102

103

Period (sec)

Spec

tral

Acc

eler

atio

n (m

m/s

2 )

Response Spectrum50% C.O.V. of Rise time


(e) (f)

Figure 4-18 Attenuation model with 50% variation of source parameters (a-c, PGA

model, d-f, spectral acceleration model with 5% damping at epicentral distance 100km)

4.7 Conclusion


104

This Chapter studies the effects of variations in seismic source parameters on ground

motions simulated with a combined stochastic and Green’s function method. The

Rosenblueth’s point estimate method, which is proven yielding reliable estimation of

the simulated ground motion statistics, is used to estimate mean, standard deviation and

coefficient of variation of PGA, PGV, RMSA and COAS of the simulated ground

motions corresponding to various levels of variations in the stress drop ratio, the phase

delay and the rise time of the seismic source. A sensitivity analysis is carried out to

study the influences of variations of each seismic source parameter on simulated ground

motions with different earthquake magnitudes and different epicentral distances. The

effects of seismic source parameter variations on ground motion simulation are

demonstrated. It is found that variations in the stress drop ratio have the most significant

effects on PGA, PGV and response spectrum of the simulated ground motions, followed

by the rise time. Variations in the phase delay have the least effect, among the three

source parameters considered in the study, on PGA and PGV, but significantly

influence the ground motion frequency contents.

It is found that the influences of the source parameter variations on the coefficient of

variation of PGA, PGV and response spectrum of the simulated ground motions are

dependent on the earthquake magnitudes but are insensitive to the epicentral distance.

The relations of coefficients of variation of PGA, PGV and response spectrum of the

simulated ground motions as a function of variations of the seismic source parameters

and earthquake magnitude are also derived. They can be used together with the

attenuation relations developed in Chapter 3 to estimate ground motion attenuations

with the influence of uncertain source parameters.


105

CHAPTER 5 SEISMIC HAZARD ANALYSIS FOR PMA

5.1 Introduction

A combined stochastic and Green’s function simulation method was developed in

Chapter 3 to construct attenuation models of PGA, PGV and ground motion spectral

accelerations for SWWA. The influence of uncertain source parameters on strong

ground motion simulation and attenuation models was investigated in Chapter 4. The

new attenuation models were derived from a large simulated database covering a large

distance range and an appropriate magnitude range, and were proven to provide more

reliable predictions of the available SWWA records than other models considered.

Therefore, it is expected the new equations are likely to provide the more reliable

seismic hazard results in SWWA.

As the selection of an appropriate ground motion attenuation relation for use in

probabilistic earthquake hazard evaluation is almost always critical to the results, in this

study, the new attenuation model presented in Chapter 3 is employed to derive PGA and

design response spectra of rock site ground motions corresponding to the 475-year

return period earthquake and the 2475-year return period earthquake in SWWA. The

calculated PGA and response spectra on rock site are compared to that specified in the

current Australian Earthquake Loading Code (AS1170.4-2007). Discussion on

adequacy of the design spectrum against that of the seismic analysis results in this study

is made.

5.2 PGA and Response Spectrum of Design Ground

Motion on Rock Site

Two basic methodologies used for the purpose of seismic hazard analysis are the

“deterministic” (DSHA) and the “probabilistic” (PSHA) approaches. In the


106

deterministic approach, the strong-motion parameters are estimated for the maximum

credible earthquake, assumed to occur at the closest possible distance from the site of

interest, without considering the likelihood of its occurrence during a specified period.

On the other hand, the probabilistic approach integrates the effects of all the earthquakes

expected to occur at different locations during a specified life period, with the

associated uncertainties and randomness taken into account.

The basic inputs required for both approaches are the same, which include data on past

seismicity, knowledge of the tectonic features, information on site soil condition and the

underlying geology of the surrounding area, and the attenuation characteristics of the

strong-motion parameter to be used for quantifying the hazard. The first step of analysis

is also the same in both approaches, wherein all possible seismic source zones are

identified on the basis of available data on tectonic features and the spatial distribution

of the epicenters of past earthquakes.

In the deterministic seismic hazard analysis (DSHA), the maximum possible earthquake

is estimated for each of the seismic sources. This earthquake, commonly termed as the

maximum credible earthquake (MCE), is assumed to occur at a location in the particular

seismic source zone, which minimizes its distance from the site of interest. For each of

these MCEs, the value of the associated strong-motion parameter at the selected site is

most commonly estimated by using an appropriate empirical attenuation relation. The

MCE that produces the largest value of the strong-motion parameter is considered for

practical applications, with the assumption that it will never be exceeded.

However, the database used and each step of analysis are generally associated with large

uncertainties, and thus, selecting the worst scenario is neither likely to represent reality

nor is a good engineering decision. Further, the DSHA does not provide a means to

quantify the amount of risk for particular earthquake scenarios. In the PSHA approach,

the maximum possible earthquake in each seismic source is assigned a finite probability

of occurrence during a specified time interval, to account for the fact that the recurrence

interval of such an event is normally much longer than the time periods of interest in

practical applications.

Though it may be difficult to establish an approach to seismic hazard assessment that

will be the ideal tool for all situations, in view of the above discussion, it may be


107

concluded that the PSHA approach should be a preferred choice. Acknowledging the

fact that the basic purpose of both the DSHA and PSHA approaches is to facilitate

engineering designs and decisions, and not to predict the actual earthquakes and ground

motions, it is concluded that the PSHA approach provides a scientifically more sound

method for seismic hazard analysis.

The computer program SEISRISK III (Bender and Perkins, 1987) is used in this study

to perform the probabilistic seismic hazard analysis (PSHA). SEISRISK III is one of a

series of computer programs developed by the US Geological Survey to calculate the

maximum ground motion levels that have a specified probability of not being exceeded

during a fixed time period at a set of sites uniformly spaced on a two-dimensional grid.

The earthquake sources are modelled as either points located randomly within

seismically homogeneous source zones or as finite length ruptures that occur randomly

along linear fault segments. A detailed discussion of the computational methodology is

outside the scope of this study. Those wishing for more detailed information about the

program should refer to the original documentation. However, a brief description of

some key assumptions and input parameters relating to the calculation of earthquake

hazard in this study is included below.

5.2.1 Seismic Source Zones and Recurrence Relationship

The definition of seismic source zones and their recurrence relationships in SWWA

have been carried out by Gaull and Michael-Leiba in 1987. Some modifications

presented in Hao and Gaull (2004a) were applied to the original zone boundaries and

recurrence relationships to include the most recent activities in the Burakin area in

SWWA. This updated seismic source zone map shown in Figure 5-1 and the recurrence

relationship model listed in Table 5-1 is adopted in this study. It should be noted that

the recurrence relationship for Zone 4 is calculated from Background zone in Table 5-1

of Gaull and Michael-Leiba (1987). Because the SEISRISK programme does not have

the facility for “Background Seismicity” as in the Cornell McGuire Programme, it was

decided to introduce a fourth zone between Zone 3 and Zone 2 and use the normalised

recurrence rates of seismicity as defined in Table 5-1 and call it “Background Zone”.

Because this zone falls under and is adjacent to the PMA, it is thought the relatively low

seismicity level in this zone may well be significant.


108

Figure 5-1 Seismic Source Zones surround PMA (Hao and Gaull, 2004a)

Table 5-1 ML Recurrence Parameters for Seismic Source Zones

SZ A B 1 2.88 0.75 2 4.22 1.27 3 3.1 0.85 4 1.78 1

Note: Zone 4 A-value is per 10,000 square kilometres.

5.2.2 Attenuation Relation for SWWA

As discussed above, an appropriate attenuation relation should be used in this study for

the PMA site because of possible biases associated with attenuation relationships

developed from the database recorded in different regions. For example, Douglas (2004)

has shown that there seems to be a significant difference in ground motions between

California and Europe. Therefore, the attenuation model, developed in Chapter 3 based

on local ground motion records and simulated ground motions for local conditions, is

adopted in this study.

Zone 4


109

5.2.3 The Seismic Hazard for PGA

PGA on rock in PMA with a 10% and a 2% probability of being exceeded in 50 years

are calculated using the attenuation model presented in Chapter 3 and are shown in

Figure 5-2 and Figure 5-3, respectively. As can be seen in Figure 5-2, PGA on rock is

estimated ranging from 0.14g in the north-east through to 0.09g in the south-west for

return period of 475 years. Comparing to the PGA of 0.09g with the same probability

given in the current Australian earthquake loading code, the code underestimates PGA

in the north-east part of PMA. The PGA for return period of 2475 years is estimated in

the range of 0.24g to 0.36g. To investigate the effect of each zone on PGA of PMA,

rock PGA seismic hazard curve at longitude 115.85° and latitude 32.00° in PMA is

plotted in Figure 5-4. It is shown that the effect of zone1 is the most significant whereas

zone2 contributes the least in terms of PGA at PMA.

115.7 115.8 115.9 116-32.2

-32.15

-32.1

-32.05

-32

-31.95

-31.9

-31.85

-31.8

-31.75

0.09

0.095

0.1

0.105

0.11

0.115

0.12

0.125

0.13

0.135

0.14

Figure 5-2 Rock PGA in PMA with a 10% chance of being exceeded in 50 years

(equivalent to the return period of 475 years)

Lat

itude

Longitude

g


110

115.7 115.8 115.9 116-32.2

-32.15

-32.1

-32.05

-32

-31.95

-31.9

-31.85

-31.8

-31.75

0.24

0.26

0.28

0.3

0.32

0.34

0.36

Figure 5-3 Rock PGA in PMA with a 2% chance of being exceeded in 50 years

(equivalent to the return period of 2475 years)

It is interesting to compare these estimated PGA‘s from Figure 5-2 for downtown Perth

with those of Hao and Gaull (2004a). Interpolating from Figure 5-2 above, the PGA

which has a 10% chance of exceedance in 50 years on rock-sites is about 0.105 g. This

is slightly greater than what was achieved by Hao and Gaull (2004a) where an

equivalent estimate of about 0.09g was obtained. The difference in the two results could

be easily explained with the higher standard deviation of 1.17 in this study compared

with 0.7 in Hao and Gaull (2004a) paper.

Lat

itude

Longitude

g


111

0 0.1 0.2 0.3 0.4 0.5 0.6 0.710-4

10-3

10-2

10-1

PGA (g)

Year

ly E

xcee

danc

e

Seismic Hazard Curves for Site PGAPGA from total ZonesPGA from Zone1PGA from Zone2PGA from Zone3PGA from Zone4

Figure 5-4 Rock PGA seismic hazard curve at longitude 115.85° and latitude 32.00°

5.2.4 Probabilistic Seismic Hazard Spectra

The 5% damped spectral accelerations corresponding to the probabilistic seismic hazard

levels for return period of 475 years and 2475 years are estimated at periods of 0.02,

0.05, 0.2, 0.3, 0.4, 0.5, 0.75, 1.0, 1.5, 2.0, 3.0, 4.5 second by using the above attenuation

model. The spectral accelerations observed at the central business district (CBD) of

Perth (longitude 115.85° and latitude 32.00°) are used in this study. The comparisons of

the calculated spectral accelerations and those of the code spectrum are given in Figure

5-5. The comparisons show that the spectral accelerations on rock site corresponding to

the 475-year return period in general lie between the code spectrum of strong rock and

rock site within the range of 0sec to 0.5sec. However, the code spectrum might

underestimate spectral acceleration at the period range of 0.5sec to 2sec. This might be

because the attenuation model appears to predict higher spectral acceleration at low

frequency than that of CENA models. This characteristic has been observed in many

individual dataset recorded surround SWWA, such as Burakin events. Allen et al. (2006)

also indicated that the WA model predicts higher Fourier amplitudes at low frequencies

than Atkinson (2004). Nevertheless, further investigations are needed as new data come

to hand. Since the natural period for most of buildings lies within the range of 0.5sec to

2sec, inadequacy of the design spectrum will deeply affect the seismic design of

buildings. Further studies are deemed necessary to investigate the behaviour of


112

buildings under the calculated spectral acceleration. For the 2475-year return period

scenario, as shown in Figure 5-5, the current code underestimates predicted spectral

acceleration across the entire period range, especially for the range of low frequency.

This is probably due to two reasons:

(i) The attenuation model derived from Chapter 3 has higher standard deviation than

that adopted in previous studies.

(ii) In general, the ground motion corresponding to long return period contains more

low frequency component than that of short return period as the larger magnitude event

is expected in longer return period. However, the code spectrum corresponding to 2475-

year return period is obtained from the 475-year return period spectrum multiplying the

probability factor for the annual probability of exceedance, which might misjudge the

low frequency component in the 2475-year return period.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

0.05

0.1

0.15

0.2

0.25

Period (sec)

Spec

tral

Acc

eler

atio

n (g

)

475-year Return Period

475-year return periodCode:RockCode:Strong Rock

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

0

0.1

0.2

0.3

0.4

0.5

0.6

Period (sec)

Spec

tral

Acc

eler

atio

n (g

)2475-year Return Period

2475-year return periodCode:RockCode:Strong Rock

0 0.01 0.02 0.03 0.04 0.05 0.06 0.070

0.05

0.1

0.15

0.2

0.25ADRS Format - 475-year Return Period

Spec

tral A

ccel

erat

ion

(g)

Spectral Displacement (m) 0 0.05 0.1 0.15 0.2 0.25

0

0.1

0.2

0.3

0.4

0.5

ADRS Format - 475-year Return Period

Spec

tral

Acc

eler

atio

n (g

)

Spectral Displacement (m)

Figure 5-5 Calculated response spectrum and their ADRS format

5.3 Time-history simulation

Sometimes time history analysis is needed. Usually numerically simulated ground

motion time histories are used as input in such analyses because it is very unlikely to

find a strong ground motion record at a site under consideration, which satisfies the

design ground motion level, i.e., has the compatible PGA and response spectrum. The


113

ground motions can be obtained by scale up the recorded motions at the site from small

earthquake events if such recorded motions are available. However, it should be noted

that this approach is usually not recommended because ground motion from a larger

earthquake may have very different characteristics, besides larger amplitude, longer

duration and different frequency content. Scaling only the amplitude of a recorded time

history from a small event may not lead to a reliable prediction of ground motion time

histories at the same site from a large earthquake. Hence, stochastic simulations are

used to generate time histories that are compatible to the respective spectrum defined

above.

The magnitudes of the design ground motion are chosen based on recurrence

relationship of seismic Zones. The magnitude of design event for 475-year return period

is ML6 and that for 2475-year return period is ML7.5. The epicentral distances to

produce predicted PGA value of about 0.1g and 0.25g for 475-year return period and

2475-year return period on rock site using the proposed attenuation model are

approximately 25km and 70km, respectively. The time history duration value of 12sec

for 475-year return period event and 30sec for 2475-year return period event are

estimated based on the duration model of SWWA proposed in Chapter 3. The duration

of the design ground motion is measured by integrating squared acceleration and

adopting 97.5 percentile time intervals. The simulated acceleration time histories and

the comparison of the spectrum of the simulated motion and the target spectrum are

shown in Figure 5-6. The simulated acceleration time histories will be used for

evaluating site response and structural response in PMA.

0 10 20 30 40 50

-0.2

0

0.2

Acc

eler

atio

n (g

)

Duration (sec)

2475-Year Return Period


114

Figure 5-6 Comparison of the response spectrum of the simulated time history with the

predicted design response spectrum for rock site in PMA

5.4 Summary and Conclusions

A probabilistic seismic hazard assessment has been carried out for PMA. The results of

the seismic hazard assessment are presented in terms of the horizontal peak ground

acceleration and uniform hazard response spectra for structural periods up to 4.5

seconds for rock site ground conditions. The following conclusions are made:

(i) It is found that PGA on rock is estimated ranging from 0.14g in the north-east

through to 0.09g in the south-west for return period 475 years. The current code value

underestimates PGA in most of the PMA especially to the north-east. The PGA for

return period 2475 years is estimated in the range of 0.24g to 0.36g.

(ii) From the results of this study it is suggested that the code spectrum corresponding to

475-year return period underestimates the spectral accelerations at the CBD of Perth in

the period range of 0.5sec to 2sec.

(iii) For the 2475-year return period, the current code underestimates the predicted

spectral acceleration across the entire period range, especially in the low frequency

range.

(iv) The proposed design ground motions on rock site corresponding to the 475-year

return period and 2475-year return period are simulated, which will be used as input in

the site response and structural response analyses in the following chapters.


115

CHAPTER 6 SITE RESPONSE EVALUATION AND SEISMIC MICROZONATION FOR PMA

6.1 Introduction

The attenuation models and ground motion predictions presented in previous chapters

are for seismic motions on rock sites. Amplification of seismic waves in Perth

sedimentary basin has been observed in previous seismic events. The limitations of the

previous site response studies for PMA have been discussed in Chapter 2. The potential

amplification of ground motion in Perth Basin and the limitation of the previous site

response studies for PMA provide the motivation to perform more detailed studies of

site responses across the PMA. As the available geology information in PMA is very

limited, in order to perform site amplification analysis, a site survey is performed

around Perth using SPAC methods. The clonal selection algorithm (CSA) is adopted to

perform direct inversion of SPAC curves to determine the soil profiles of the study sites.

The shear-wave velocity profiles vs. depth for the top hundred metres of the 16 sites are

determined using the SPAC method. These shear-wave velocity profiles are compared

to available soil profile information obtained in previous studies, i.e. Asten et al. (2003)

and McPherson and Jones (2006). The site vibration frequencies are also estimated

using the derived soil profiles and compared with the H/V measurements. Favourable

comparisons are obtained. Using the derived shear-wave velocity profiles, detailed site

response analyses with consideration of soil nonlinear behaviour are carried out using

SHAKE2000 with the simulated rock motion as input. Owing to the lack of nonlinear

soil properties in PMA, those derived by Seed and Idriss (1970), Sun et al. (1988) and

Schnabel (1973) are used in this study to model the nonlinear soil modulus value and

damping ratio for sand, clay and rock, respectively. The response spectra of ground

motions on soil sites are derived from the calculated ground motion time histories, and

are compared with the respective design spectrum defined in the Current Australian

Earthquake Loading Code (AS 1170.4-2007). Discussions on adequacy of the design

spectrum are made. Seismic microzonation for PMA is defined. The results are


116

summarized in the microzonation maps in which the zones are characterized with site

response spectrum and fundamental vibration period of ground.

6.2 Site Testing and Estimation of Soil Profiles

During December 2007 and May 2008, site survey was performed in 16 selected sites

around PMA as shown in Figure 6-1.

Figure 6-1 Location of sites in PMA investigated in this study

The soil profiles of these sites are estimated using SPAC method and inversion

technique of CSA. The SPAC method has been reviewed in Chapter 2. The classical

SPAC method is to undertake a two-stage process where the SPAC spectrum is first

inverted to velocities by numerical solution to Equation 6-1.


117

( ) ( )( )fcfrJrfSPAC /2, 0 π= (6-1)

where SPAC(f,r) is the spatial autocorrelation coefficient, f is frequency in Hz, c(f) is the

phase velocity, r is the radius of array of measurement stations and J0 is the Bessel

function of the first kind of zero order. These velocities form a phase-velocity

dispersion curve, usually considered to be the dispersion curve for fundamental-mode of

Rayleigh waves.

The second stage of the process is to fit the phase velocities to a model dispersion curve

computed for a layered site, namely numerical inversion. A modified approach,

introduced by Asten et al. (2002, 2003, 2004), Asten (2005) and Wathelet et al. (2005)

is to fit the observed SPAC coherency spectrum directly with a modelled SPAC

spectrum. This approach has two key advantages; firstly it reduces bias associated with

phase-velocity estimates made in the presence of incoherent noise, and secondly it

eliminates the uncertainties associated with multi-valued solutions of the inverse of the

Bessel function.

The modified SPAC method is employed in this study. The numerical modeling of

SPAC spectrum is calculated according to Lai and Rix (1998) as solution of the

eigenvalue problem of Rayleigh waves in elastic vertically-heterogeneous media.

6.2.1 Clonal Selection Algorithm (CSA)

As an inverse problem, many methods can be used to obtain the soil profile parameters

for a given SPAC spectrum. Asten et al. (2002, 2003, 2004) used trial-and-error

approach to determine the site properties to match the theoretical SPAC spectrum with

the measured data. Others used some traditional inversion techniques, e.g. Monte Carlo

method (Keilis-Borok and Yanovskaya, 1967), Genetic algorithms (Moro et al., 2007),

Neighbourhood algorithm (Sambridge, 1999; Wathelet et al., 2005). In this study, a new

genetic-based method, namely the Clonal Selection Algorithm (CSA) is used to find the

soil parameters from the SPAC spectrum. The CSA is presented by Castro and Zuben

(2000) in 2000. It is one of the three information processing methods based on

organisms. The other two are neural network method and genetic algorithm. By


118

comparing the CSA and the standard genetic algorithm, Castro and Zuben (2000)

indicated that the CSA can reach a diverse set of local optima solutions, while the GA

tends to polarize the whole population of individuals towards the best candidate solution.

Furthermore, the CSA has the ability of getting out local minima, operates on a

population of points in search space simultaneously, and employs probabilistic

transition rules instead of deterministic ones. Because of these good features, the CSA

has been used in the literature for solving various inverse problems, e.g. Ou and Wang

(2007), Guney et al. (2008).

The CSA is developed on the basis of the clonal selection principle of the immune

system (IS). When an antigen is detected, some subpopulation of its bone marrow

derived cells (B lymphocytes) can recognize the antigen with a certain affinity (degree

of match). The B lymphocytes will be cloned to proliferate (divide) and eventually

mature into terminal (non-dividing) antibody secreting cells, called plasma cells.

Proliferation of the B lymphocytes is a mitotic process which produces exact copies of

the parent cells, creating a set of clones identical to the parent cell. The proliferation rate

is directly proportional to the affinity level, i.e. the higher the affinity levels of B

lymphocytes, the more of them will be readily selected for cloning and cloned in larger

numbers. The B lymphocytes with high antigenic affinities are selected to become

memory cells. The B lymphocytes that are not simulated to proliferate as they do not

match any antigens will eventually die. This process enables the new cells to match the

antigen more closely. The cloning and maturation processes are called the clonal

selection principle.

A flowchart of the CSA is shown in Figure 6-2. The CSA starts by parameter setting, i.e.

determining the population size, updation limit and termination criteria. The initial

population of antibodies (candidate solutions) are randomly generated. The antibodies

are evaluated over an affinity (fitness) function and sorted in decreasing order of affinity.

The antibodies with high affinity are selected and cloned proportionally to their

affinities. The antibody population is updated by replacing the antibodies having lower

affinities with other improved members of maturated antibody population. With this

replacement, the diversity of antibody population is maintained so that the new areas of

the search space can be potentially explored. These processes are repeated until a

termination criterion is achieved.


119

Figure 6-2 Flowchart of CSA

When inversion of SPAC curves is performed, the key element of optimization is the

model evaluation, which is performed by means of an objective function that allows the

quantitative estimation of the model convergence. It is assumed that the spatial

autocorrelation coefficient SPAC(f, r), as shown in Equation 6-1, is expressed as a

function of the subsurface parameters using Equation 6-2 and Equation 6-3.

),,,,( ρhvvfcc sp= (6-2)

),,,,(),( ρhvvfSPACrfSPAC s= (6-3)

in which v and vs are Poisson’s ratio and shear wave velocity, h and ρare layer

thickness and density, respectively. The objective function (Equation 6-4) is expressed

as the difference between the observed SPAC spectrum and that calculated in theory

and is optimized by the CSA.

2)( cali

obsi

N

ii SPACSPACSPAC −=Δ ∑

(6-4)

where obsiSPAC and cal

iSPAC are the observed and the theoretical SPAC spectrum at the ith

frequency. As shear-wave velocity and layer thickness have more significant effect on

Rayleigh wave propagation than other parameters (Xia et al., 1999) and with the aim of


120

reducing the computational effort by limiting the number of variables, only the

Poisson’s ratio, shear wave velocity of each layer are updated. The density is assumed

as a constant in this study. The initial layer thickness is assumed to be 10 m. If any two

adjacent layers have similar Poisson’s ratio and shear wave velocity, they are combined

as one layer.

6.2.2 Site Testing and Data Processing

Site survey was performed in 16 sites around PMA as shown in Figure 6-1. The

deployment consisted of two circular arrays with respective radii of 48 and 59 m. As

can be seen in Figure 6-3, each circular array consisted of three accelerometers, with an

additional accelerometer at the center station. Vertical ground accelerations were

recorded at 500 samples /sec. Two sets of data were recorded with approximately 15

minutes in each set. After recording the vertical accelerations, the three accelerometers

on the outer ring were taken and placed at the same locations of the accelerometers on

the inner ring to record horizontal and vertical ground accelerations. An additional

accelerometer was also placed at the center station in the horizontal direction.

Simultaneous horizontal and vertical ground accelerations were recorded at the center

and the three inner ring stations for estimating the H/V spectrum. Similarly, two sets of

data with duration of 15 minutes each were recorded.

Figure 6-3 Circular array with 7 measurement locations in field measurements

In processing the data, each 15-minutes recording is divided into five windows.

Synchronized records of 3 minutes long were taken out and baseline corrected and


121

transformed to the frequency domain. A matrix of coherencies between the recorded

vertical ground vibrations at the center station and one of the stations on the inner or

outer ring is constructed. The coherencies calculated from ground vibrations in five 3-

minutes time windows in both sets of the recorded data are averaged to get the

assembled mean of the calculated coherencies. A total of 10 coherency functions are

averaged to reduce the effect of random noises.

Similarly the simultaneously measured horizontal and vertical ground vibrations at four

locations in each measurement are divided into 3-minute windows. After baseline

corrections, the ratios of the Fourier spectra of the horizontal and vertical motions are

averaged. The spectral ratios are then used to identify the vibration frequencies of the

site.

6.2.3 Case Study

Using the SPAC method and the CSA technique, the subsurface parameters of the study

sites are estimated. The following 7 examples with detailed site survey processing are

reported. The observations and discussions for the other sites are similar to these 7 sites.

Therefore they are not presented in detail. Only the final results are presented.

6.2.3.1 S7 (Crimea Ten Park)

The observed SPAC function for the arrays of radius 59m and 48m and the

corresponding fitted curves are shown in Figure 6-4. The field observed and modelled

SPAC functions for the 59m radius array agree with each other over the range of 1.0 to

10.0Hz. Those for the 48m radius array also match with each other at frequencies above

1.0Hz. At frequencies below 1.0 Hz, however, the modelled SPAC function does not

converge to the observed SPAC function. This is because it is difficult to reliably

measure low-frequency ambient ground vibrations as they are very sensitive to noises

that inevitably exist in field measurements. Since low-frequency wave penetrates deeper

into the ground, the lower the ground motion frequency accurately measured, the deeper

the soil profile can be reliably determined. A previous study (Tokimatsu et al., 1997)

demonstrated that the use of short-period microtremors (more than 1.0 Hz) can

reasonably determine the shear wave velocity profile of the site up to 100m. In this

study, the shear-wave velocities up to only 100 m are determined because of the


122

unsatisfactory match between the measured and modelled SPAC functions at

frequencies below 1.0 Hz. The identified shear wave velocity profile for this site is

given in Figure 6-5. It should be noted that Asten, et al. (2003) also derived the shear

wave velocity of this site using the SPAC method. As shown, the shear-wave velocities

derived in this study agree reasonably well with those obtained by Asten et al. (2003).

The results however predict lower shear-wave velocity than that of SCPT data. Asten et

al. (2003) indicated that the SCPT penetrated only to a depth of 18.8m and presumably

halted by coarse sands. As a soil profile with a shear wave velocity greater than 360m/s

is referred to as rock (AS 1170.4-2007), the calculated shear-wave velocity profile

suggests a shallow bedrock interface at approximately 30m in this site. According to the

shear-wave velocity obtained, this site can be classified as a shallow soil site with a soil

layer depth of about 30m according to the classifications suggested by the current

Australian Earthquake Loading Code (AS 1170.4-2007).

Figure 6-4 Site 7: Measured and

modelled SPAC function

0 200 400 600 800 1000 12000

20

40

60

80

100

120

DEP

TH (m

)SHEAR WAVE VELOCITY (m/s)

Predicted ASTEN,et.al.(2003)SCPT Only

Figure 6-5 Identified Shear-wave velocity

profile of Site 7

Figure 6-6 presents the averaged H/V spectrum and Figure 6-7 shows the response

spectrum and amplification spectrum of Site 7. The response spectrum and

amplification spectrum are calculated using SHAKE2000 with the built-in nonlinear

soil properties proposed by Seed and Idriss (1970). The simulated rock motion time

history is used as input. The shear wave velocity of the bedrock is assumed to be

900m/s in the study. As shown, the H/V technique predicts the 1st modal frequency as

1.45Hz and the 2nd modal frequency as 3.7Hz. The amplification spectrum gives the 1st

modal frequency as 1.62Hz and the 2nd modal frequency as 3.3Hz. Although the

frequencies obtained using the H/V and SPAC methods are not exactly the same, they

are within a reasonable margin of each other. Comparing with the previous study by


123

McPherson and Jones (2006), as summarized in Table 2-8, in which they concluded that

for a shallow sand site in PMA with a mean thickness of 20m and standard variation of

13m, the mean natural period is 0.65 and standard variation 0.46sec. This is in good

agreement with the predicted site condition of Site 7 in this study.

The comparison of the calculated spectral acceleration and the current code spectral

acceleration (AS 1170.4-2007) for shallow soil sites is given in Figure 6-7. As shown,

the current design spectrum underestimates the response spectrum in the period range of

0.5 sec to 1.0 sec, but is conservative at period below 0.5 sec.

Figure 6-6 H/V spectrum of Site 7

Figure 6-7 Response spectrum and

amplification spectrum of Site 7

6.2.3.2 S4 (Warwick)

Figure 6-8 shows the observed and modelled SPAC function for the two arrays. As

shown, the theoretical function fits the observed SPAC function well in the range of

0.3Hz to 5.0Hz and is a close match above 5.0Hz. Figure 6-9 compares the shear-wave

velocity profile obtained in this study with that in Asten et al. (2003) and that from

SCPT data. As shown, the three shear wave velocity profiles match reasonably well

with each other except in the first layer with a depth of 10m, where this study predicts a

significantly lower shear wave velocity than that derived from Asten et al. (2003) and

SCPT data. The lower shear wave velocity prediction for the first layer might be

because of the fluctuation of ground water table. Based on the identified shear wave

velocity, we suggest the bedrock interface locates at approximately 50m. As the site

vibration period is greater than 0.6s and the depths of soil exceed 40m, according to the


124

suggested site classifications in current Australian code (AS 1170.4-2007), this site is

identified as a deep soil site with a soil layer depth of about 50m.

Figure 6-8 Site 4: Measured and


0 200 400 600 800 10000

20

40

60

80

100

120

140

DEP

TH (m

)

SHEAR WAVE VELOCITY (m/s)

Predicted ASTEN,et.al.(2003)SCPT Only

Figure 6-9 Identified Shear-wave velocity

profile of site 4

The averaged H/V spectrum, response spectrum and amplification spectrum of Site 4

are shown in Figure 6-10 and Figure 6-11. As shown, the first two peaks of H/V

spectrum occur at 0.97Hz and 2.2Hz, respectively, which correspond to the 1st and 2nd

mode of the site. The two modes in the amplification spectrum occur at frequencies of

0.9Hz and 1.89Hz, respectively. According to McPherson and Jones (2006), for a deep

sand site in PMA, the mean fundamental period is 0.5 sec with a standard deviation also

0.5 sec. Examining the spectral accelerations presented in Figure 6-11 reveals that the

current code spectral values are conservative for this site.





125

6.2.3.3 S13 (Guildford)

The observed and modelled SPAC functions are shown in Figure 6-12. Reasonable

agreements are observed again. The identified shear wave velocity profile, as shown in

Figure 6-13, suggests a shallow bedrock interface at approximately 10m with an

underlying low shear wave velocity soil layer at 60m, which has a thickness of about

10m. Because no other data for this site can be found for comparison, and this site falls

in the mud-dominated site category, the prediction of mean and mean plus and mean

minus one standard deviation shear wave velocity by McPherson and Jones (2006) for

this site category is depicted in Figure 6-13. If the low velocity soil layer located at 60m

depth is ignored, the estimated averaged shear wave velocity in the top 20 m is within

the mean minus standard deviation range. The H/V spectrum of the site (Figure 6-14)

shows that the first peak is located at 0.64Hz and the second peak at about 1.05 Hz. The

calculated transfer function (Figure 6-15) suggests a 1st mode frequency of 0.61Hz and

2nd modal frequency of 1.08Hz, indicating the H/V method gives consistent estimation

of the vibration frequencies of this site. However, McPherson and Jones (2006)

predicted higher fundamental vibration frequency for this site category with the mean

and the standard deviation of natural period 0.5sec (2.0Hz) and 0.35 sec, respectively.

The observed lower natural frequency for Site 13 is because of the irregular soil profiles

where a soft layer is trapped between two stiffer layers. Comparing the calculated

spectral accelerations with that of the current code design spectrum, as presented in

Figure 6-15, it shows that the current code spectral values are conservative for the

period below 2sec.

Figure 6-12 Site 13: Observed and


0 200 400 600 8000

20

40

60

80

100

120

DEP

TH (m

)


PredictedMeanMean plus one STDMean minus one STD

Figure 6-13 Identified shear-wave

velocity profile of Site 13


126

Figure 6-14 H/V spectrum of Site13



6.2.3.4 S8 (Mt Lawley)

Figure 6-16 shows a close match between the observed and modelled SPAC function.

The identified shear wave velocity profile (Figure 6-17) suggests that Site 8 is a shallow

soil site with a soil depth of about 10m. The identified shear wave velocity profile is

also comparable to the prediction by McPherson and Jones (2006) for this site class as

shown in Figure 6-17. As shown in Figure 6-19, the 1st modal frequency of 0.94Hz and

2nd modal frequency of 3.17Hz are obtained from the site amplification spectrum. They

are reasonably consistent with the peaks at 0.81Hz and 3.50Hz in H/V ratio spectrum

(Figure 6-18). However, the H/V spectrum displays a few more peaks, with the second

dominant peak at about 1.1Hz. The exact reason for this is not known, possibly because

of noises or unknown vibration sources in the proximity of the site. The estimated

natural period for this site is longer than that predicted by McPherson and Jones (2006),

in which the mean and the standard deviation of natural period are estimated to be

0.65sec (1.54Hz) and 0.46sec, but it falls within the range of the mean plus one standard

deviation. The comparisons of the calculated spectral accelerations and the code spectral

accelerations are also given in Figure 6-19. The calculated spectral accelerations lie well

below the code spectrum for periods below 0.7sec, but goes over the code spectrum in

the range of 0.7sec to 2sec.


127



0 200 400 600 8000

20

40

60

80

100

120

DEP

TH (m

)








6.2.3.5 S5 (Wembley)

The comparison of the observed and the fitted SPAC function illustrated in Figure 6-20

shows that the modelled SPAC function successfully captures the trend of the observed

SPAC function. Figure 6-21 shows that a regular soil profile where the stiffness of layer

increases with increasing depth is observed in Site 5. The base rock is located

approximately 70m below the ground surface. This site locates in the deep sand site area

as suggested by McPherson and Jones (2006). The calculated base rock location

however is deeper than the mean (40 m) plus one standard deviation (18 m) of the soil

thickness proposed by McPherson and Jones (2006). The calculated transfer function

(Figure 6-23) suggests the 1st modal frequency of 0.61Hz and 2nd modal frequency of

1.42Hz. As shown in Figure 6-22, the peak in H/V spectrum is not obvious, indicating

the failure of the H/V method for reliably identifying the vibration frequencies of this

site. As compared with the result from McPherson and Jones (2006), in which the mean

natural period of deep sand site is 0.5sec (2Hz) and the variation is 0.5sec, this study


128

predicts a longer natural period. This is because the current study predicts a deeper soil

profile. The calculated spectral accelerations are well below the code spectrum across

the entire frequency range as shown in Figure 6-23.



0 200 400 600 800 10000

20

40

60

80

100

120

DEP

TH (m

)





Figure 6-22 H/V spectrum of Site5


amplification ration spectrum of Site 5

6.2.3.6 S9 (Langley Park) and S10 (Raphael Park)

Site 9 (Langley Park) and Site 10 (Raphael Park) are located in the central business

district (CBD) of Perth and on each side of Swan river. The comparison of the observed

SPAC function and the fitted function for the two sites are shown in Figure 6-24 and

Figure 6-28, respectively. The identified shear-wave velocity profiles of the two sites

are shown in Figure 6-25 and Figure 6-29. Both sites fall in the deep soil site category.

The bedrock location of Site 9 is about 70m and that of Site 10 is below 100m. The

bedrock depth of Site 9 is verified by borehole data available at a location less than


129

200m from Site 9 (Stewart, 2001), in which it indicates that the rock layer (sandstone)

located at approximately 73m below the ground surface. However, no shear wave

velocity for each layer is presented in Stewart (2001). The predicted soil profiles of Site

9 and Site 10 conflict with the site description, i.e., shallow sand site, proposed by

McPherson and Jones (2006). Unfortunately, no borehole data around Site 10 is

available to clarify this confliction. As shown in Figure 6-27 and Figure 6-31, although

Site 9 and Site 10 have different shear-wave velocity profiles, they have same 1st and 2nd

modal vibration frequencies (0.27Hz and 1.01Hz). As shown in Figure 6-26 and Figure

6-30, the H/V spectrum displays more peaks, with peaks occurring near these two

frequencies. The comparison of the calculated response spectrum and code spectra, as

shown in Figure 6-27 and Figure 6-31, indicates that the code spectrum is conservative

at two sites for period below 2sec, but slightly underestimates the response spectrum for

period above 3sec.



0 200 400 600 8000

20

40

60

80

100

120

DEP

TH (m

)









130



0 200 400 600 8000

20

40

60

80

100

120

DEP

TH (m

)



Figure 6-29 identified shear-wave





6.2.4 Evaluation of Site Response for PMA

The response spectra of the study sites corresponding to the 475-year return period and

2475-year return period events are depicted in Figure 6-32 to Figure 6-35, respectively.

To evaluate the adequacy of the design spectrum, the code spectrum and the spectrum

of the outcrop motion are also shown in Figure 6-32 to Figure 6-35. According to the

shear-wave velocity profiles vs. depth for the top hundred metres of the study sites

obtained by SPAC method and the site classifications suggested by the current

Australian Earthquake Loading Code (AS 1170.4-2007), the study sites are classified as

shallow soil site, deep soil site and very soft soil site, respectively, as shown in Table

6-1.


131

Table 6-1 The site classifications for the study sites

Study Sites Classifications Study Sites Classifications S1 Very soft soil site S9 Deep\soft soil site S2 Shallow soil site S10 Deep\soft soil site S3 Shallow soil site S11 Very soft soil site S4 Deep\soft soil site S12 Shallow soil site S5 Deep\soft soil site S13 Deep\soft soil site S6 Very soft soil site S14 Very soft soil site S7 Shallow soil site S15 Shallow soil site S8 Shallow soil site S16 Very soft soil site

As shown in Figure 6-32 and Figure 6-33, for the 475-year return period, significant

deamplification of outcrop motion at periods below 1 sec is observed in most of the

study sites which are classified as very soft soil site and deep soil site, which result in

the code spectra being conservative at these sites for periods below 1sec. The spectral

accelerations corresponding to the deep soil sites and very soft soil sites lie well below

the design spectra specified in the current Australian code. However, for shallow soil

sites, the current code underestimates the spectral values of S3 and S4 at periods

between 0.5sec and 1sec; respectively; and undervalues the spectral values of S2, S8,

S12 and S15 at periods between 1sec and 3sec. This implies that the shallow soil site

spectrum in the current code should be used with caution in structure design. For the

case of 2475-year return period, as shown in Figure 6-34 and Figure 6-35, the code

overestimates the spectral values of the very soft soil site and deep soil site at period

below 1sec, whereas the code undervalues the spectral values at period above 1.5sec.

The spectral acceleration corresponding to the shallow soil sites goes over the current

code spectrum at period above 0.5sec. The code underestimates the design spectrum

from most of the study sites at long period range, which might be because the ground

motion corresponding to the 2475-year return period contains more low frequency

component than that of the short return period as the larger magnitude event is expected

in longer return period. However, the code spectrum corresponding to the 2475-year

return period is obtained from the 475-year return period spectrum by multiplying a

probability factor for the annual probability of exceedance, as discussed above. This

might misjudge the low frequency component in the 2475-year return period.


132

Figure 6-32 475-year return period response spectra of S1 to S8


133



134



135



136

475-year return period

S4 S7 S14

0 0.01 0.02 0.03 0.04 0.05 0.06 0.070

0.05

0.1

0.15

0.2

0.25

Spec

tral

Acc

eler

atio

n (g

)


ADRS

0 0.01 0.02 0.03 0.04 0.05 0.06 0.070

0.1

0.2

0.3

0.4

Spec

tral

Acc

eler

atio

n (g

)


ADRS

0 0.02 0.04 0.06 0.08 0.1 0.12 0.140

0.05

0.1

0.15

0.2

0.25

Spec

tral

Acc

eler

atio

n (g

)


ADRS

2475-year return period

S4 S7 S14

0 0.05 0.1 0.15 0.2 0.25 0.3 0.350

0.1

0.2

0.3

0.4

Spec

tral

Acc

eler

atio

n (g

)


ADRS

0 0.05 0.1 0.15 0.2 0.250

0.2

0.4

0.6

0.8

Spec

tral

Acc

eler

atio

n (g

)


ADRS

0 0.2 0.4 0.6 0.80

0.1

0.2

0.3

0.4

Spec

tral

Acc

eler

atio

n (g

)


ADRS

Figure 6-36 Site response spectrum in ADRS format

6.2.5 Seismic microzonation maps for PMA

As shown from Figure 6-37 to Figure 6-42, the natural period and the response

spectrum corresponding to the 475-year return period at frequencies of 0.2, 0.5, 1.0, 2.0

and 3.0sec for the study sites are interpolated and plotted onto maps of PMA. Natural

period contour map and spectral acceleration contour maps are obtained in two major

steps. Firstly, the control points are generated based on the co-ordinates of 16 testing

sites. Secondly, PMA is meshed into 50m by 50m grid. The co-ordinates of each grid

points are estimated. Control points are irregularly-spaced field measurements. The data

are generally represented as xyz triplets, where x and y are spatial coordinates and z is

the nature period or spectral acceleration. The z values of the grid points are computed

by a weighted mean. The z values at the control points are weighted by the inverse

distance di from the grid points.

Commenting on each of these contour maps in order, there appear to be two regions in

the central and northwest of the mapped area which have long natural periods. This is

because a soft soil layer with soil depth of more than 80m is observed at S5 (Monger

Lake Reserve), S9 (Langley Park) and S10 (Raphael Park). These long period features

have been known to follow some deep geological feature and provide a predicted

boundary of Perth Basin. This observation is consistent with Gaull (1995) in which this


137

region has greatest amplification at long period and is identified as the central basin. It

should be pointed out that most of the central business district (CBD) of Perth

(longitude 115.85° and latitude 32.00°) is located at long natural period sites. The

natural period of around 1sec is observed in the remaining regions of PMA.

It can be seen that the greatest spectral accelerations for the 0.2sec map in Figure 6-38

are located at central north and southwest corners of the mapped area, which is due to

the short natural period at S7 and S3. The lower value contours of the spectral

acceleration run throughout the Perth Basin region, indicating significant

deamplification of outcrop motion at short periods. The 0.5sec contours, as seen in

Figure 6-39, have a similar shape to those in Figure 6-38 except that the lower value

contours of the spectral acceleration run throughout not only the Perth Basin region, but

also the east regions. The 1sec contours is shown in Figure 6-40. Again, the general

features of the contours on this map are similar to those in Figure 6-38 and Figure 6-39.

The regions with relatively high value contours of the spectral acceleration located at

central north and southwest corners of the mapped area are expanded.

The high value contours of spectral acceleration associated with long period, starting

from the 2sec map (Figure 6-41), are observed in east of PMA and south of the Perth

city. It is possible that the natural periods of around 2sec are recorded in these regions

(S13, S14, S15 and S16). The 3sec contour map in Figure 6-42 shows that the high

value contours appear in east of the area and a small region around the centre of PMA.

According to the above analysis, very soft soil layers or deep soil lays run throughout

most of PMA. This might be the reason that amplification of seismic waves at low

frequencies in Perth sedimentary basin has been observed in previous seismic events.

For example, panic to occupants and minor damage in some of the middle-rise buildings

in downtown Perth were caused by the Great Indonesian Earthquake of August 17, 1977,

with an epicentral distance of 2000 km. However, this observation should be further

verified as more geology information comes to hand.


138

Longitude

Latit

ude

115.7 115.8 115.9 116-32.2

-32.15

-32.1

-32.05

-32

-31.95

-31.9

-31.85

-31.8

-31.75

1

2

3

4

5

6

Figure 6-37 Natural period contours

Longitude

Latit

ude

115.7 115.8 115.9 116-32.2

-32.15

-32.1

-32.05

-32

-31.95

-31.9

-31.85

-31.8

-31.75

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Figure 6-38 Spectral acceleration (g) contour at 0.2 sec

sec

Spec

tral

acc

eler

atio

n (g

)


139

Longitude

Latit

ude

115.7 115.8 115.9 116-32.2

-32.15

-32.1

-32.05

-32

-31.95

-31.9

-31.85

-31.8

-31.75

0.05

0.1

0.15

0.2

0.25

0.3


Longitude

Latit

ude

115.7 115.8 115.9 116-32.2

-32.15

-32.1

-32.05

-32

-31.95

-31.9

-31.85

-31.8

-31.75

0.05

0.06

0.07

0.08

0.09

0.1

0.11

0.12

0.13

0.14


Spec

tral

acc

eler

atio

n (g

) Sp

ectr

al a

ccel

erat

ion

(g)


140

Longitude

Latit

ude

115.7 115.8 115.9 116-32.2

-32.15

-32.1

-32.05

-32

-31.95

-31.9

-31.85

-31.8

-31.75

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

0.055

0.06

0.065


Longitude

Latit

ude

115.7 115.8 115.9 116-32.2

-32.15

-32.1

-32.05

-32

-31.95

-31.9

-31.85

-31.8

-31.75

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045


Spec

tral

acc

eler

atio

n (g

) Sp

ectr

al a

ccel

erat

ion

(g)


141


In this chapter, results from site characterization studies performed in PMA are

presented. The shear-wave velocities vs. depth profiles for the top hundred metres of 16

sites are obtained using the SPAC method and the CSA technique. The response spectra

corresponding to the 475-year return period and 2475-year return period earthquake

ground motions at the study sites are calculated based on the seismic hazard study for

PMA and compared to the design spectra defined in the current Australian code. The

natural period for the study sites is derived from the calculated amplification spectrum.

Using the calculated natural period and response spectrum of these sites, seismic

microzonation maps for PMA is constructed. The study revealed that

(i) Both the SPAC method and H/V method give similar identifications of vibration

frequencies in most sites. However, H/V method is a lot more sensitive to measurement

noises and fails to reliably identify the vibration frequencies of the deep soil sites. Most

identified site vibration frequencies in this study are in general lower than those

obtained by McPherson and Jones (2006). The identified shear-wave velocity profiles

with SPAC method are comparable to the available site properties obtained by other

researchers.

(ii) Comparing the predicted response spectra corresponding to the 475-year return

period earthquake ground motions to that specified in the current code indicates that the

current code underestimates the spectral acceleration of the shallow soil site at period

range of 0.5 to 3.0 sec, indicating that the design response spectrum of shallow soil site

in the current code should be used with caution in structure design.

(iii) Comparing the predicted response spectra corresponding to the 2475-year return

period earthquake ground motions to that defined in the current code reveals that the

current code underestimates the spectral acceleration of most sites in long period range.

(iv) Seismic microzonation maps show that long period sites (more than 1sec) run

throughout most of PMA, which results in significant deamplification of bedrock

motion at high frequency range. Most of CBD of Perth is located at long natural period

sites.


142

CHAPTER 7 STRUCTRAL RESPONSE

TO PREDICTED EARTHQUAKE

GROUND MOTIONS IN PMA

7.1 Introduction

The results presented in the previous chapters revealed possible underestimation of

earthquake ground motions in the Australian Earthquake Loading code in certain period

ranges and some site conditions. This indicates the need for seismic evaluation of the

performance of existing structures to earthquake ground motions predicted in this study

in order to better meet the requirement that life safety and business interruption due to

earthquakes can be controlled to acceptable levels. In practice, different codes have

different design philosophies. The corresponding definitions of design earthquakes in

different codes also depend on the specific design procedures and the requirements of

earthquake performance of the structures. For example, Eurocode8 (2005) and US

Uniform Building Code (UBC, 1995) adopt a one-level design procedure to satisfy a

‘life-safety’ objective. Elastic response spectrum corresponds to the 475-year return

period earthquake ground motion (for the no-collapse requirement) for structures of

ordinary importance are defined in Eurocode8 (2005). In contrast, the seismic design

codes in Japan, New Zealand and China employ a two-level design procedure in which

both the life-safety objective under a rare earthquake and the damage-limitation

objective under a more frequent earthquake need be satisfied. In Australian Code, one

level design procedure is adopted for structures with an importance level less than 4. A

special study is required for importance level 4 structures to make sure they remain

serviceable for immediate use after an earthquake. In Chapter 6, design response spectra

of ground motions corresponding to the 475-year return period earthquake and the

2475-year return period earthquake in PMA are defined according to the probabilistic

seismic hazard analysis (PSHA) and site response evaluation. In this chapter, the

responses of three typical Perth structures, namely a masonry house, a middle-rise


143

reinforced concrete frame structure, and a high-rise building of reinforced concrete

frame with core wall on typical soil sites, i.e., shallow soil (S7), deep/soft soil (S4) and

very soft soil (S14) subjected to the predicted earthquake ground motions of different

return periods are calculated. Numerical results are used to assess the seismic damage of

these buildings. The seismic safety of building structures in PMA is evaluated according

to the various design and safety criteria for nonductile building frames.

7.2 Buildings in PMA

Only minor structural damage was reported in PMA during the 1968 ML6.9 Meckering

earthquake occurred 130km east of Perth. At that time most of buildings were one-

storey masonry houses. Since 1968, the population of the Perth has considerably

increased and the types of structures in and around Perth have changed significantly

from low-rise masonry buildings in 1968 to the many high-rise reinforced concrete (RC)

frame structures present now. A study presented by ABS (2001) showed that there are

more than 350000 buildings in PMA. Over 95% of the total building stock of PMA is

residential buildings. Industrial and commercial building stock represents less than 5%

of the total building stock. The building stock is classified into four categories in Jones

et al. (2006) by construction types. As shown in Figure 7-1, unreinforced masonry

buildings (UMB) make up over 88% of the total building stock. Steel framed, timber

framed buildings, reinforced and pre-cast concrete buildings represent less than 12% of

the total building stock. Although reinforced buildings make up only 0.25% of the total

building stock, more and more reinforced middle-rise and high-rise buildings are

expected around the central business district (CBD) of Perth as a result of the rapid

economic and population growth. In this study, three typical Perth structures, namely a

masonry house, a middle-rise reinforced concrete frame structure, and a high-rise

building of reinforced concrete frame with core wall are selected and their performance

under the predicted ground motions are evaluated.


144

2.538.39

0.25

88.83

Steel framed buildings

Timber framed buildings

Reinforced and pre-cast concrete buildings

Unreinforced masonry buildings

Figure 7-1 Building types and percentages in PMA

7.3 Structural Response

Three-component ground acceleration time-histories corresponding to the 475-year

return period and 2475-year return period are simulated. These simulated surface

ground motions are applied along the three principal axes of the structure to estimate

nodal displacement and element force of the structure. The amplitude of the vertical

component is assumed to be 2/3 of the horizontal component. Linear elastic dynamic

analyses are carried out using SAP2000 to determine the response of the selected

buildings. If significant damage was predicted, non-linear analyses were conducted. The

damage level of the RC building and high-rise building structure is determined by

comparing the inter-storey drift against the seismic performance levels of structures

defined by FEMA356 (2000), as given in Table 7-1. Strength check was carried out to

unreinforced masonry building to estimate the damage level.


145

Table 7-1 Structural Performance Levels and Damage (FEMA356, 2000)

Element Collapse

Prevention

Life Safety Immediate

Occupancy

Infill unreinforced

masonry wall

(UMW)

0.6% transient or

permanent

0.5% transient;

0.3% permanent

0.1% transient;

negligible

permanent

Concrete Frames 4% transient or

permanent

2% transient;

1% permanent

1% transient;

negligible

permanent

Concrete Wall 2% transient or

permanent

1% transient;

0.5% permanent

0.5% transient;

negligible

permanent

The soil-structure interaction effect is approximately included in the analysis of

structures located on soil sites by adding static soil springs and dashpots (frequency

independent) to each support. The masonry house and six-story RC building are

supported by shallow foundations. The foundation of masonry house is strip footing

with a width of 1m. Square shallow foundation with a width of 2m is used in the six-

story RC building. The high-rise building is supported by piles. The diameter of pile is

1.2m. The stiffness coefficients of the foundations are calculated by the formulas given

in (Gazetas, 1990) and are listed in Table 7-2, where B and L are the width and length

of the shallow foundation; υ is Poisson’s ratio of soil; G is the effective shear modulus

of soil; Ab is area of foundation; d is diameter of pile; Ep and Es are the elastic modulus

of pile and soil, respectively; Lp is the length of pile. It should be noted that equivalent

foundation spring and dashpot are frequency dependent. However, in this calculation,

only the static frequency independent spring stiffness and dashpot are used because the

calculations are carried out in the time domain. This simplification is very commonly

adopted by many researchers and in practice. It is also used here for its straightforward

implementation. The soil-structure interaction effects modelled are therefore only

approximate.


146

Table 7-2 Dynamic stiffness of shallow or pile foundation (Gazetas, 1990)

Masonry House (Shallow)

3-Storey Building

(Shallow )

34-Storey Building (Pile)

Kh ( )85.050.22

22 χ

υ+

−=

GLK y

⎟⎠⎞

⎜⎝⎛ −

−−=

LBGLKK yx 1

75.02.0υ

υ−29GB 21.0)(

s

ps E

EdE

Kv ( )75.054.173.0

12 χ

υ+

−GL

with 24LAb=χ υ−1

54.4 GB

( )⎟⎟⎠

⎞⎜⎜⎝

⎛−

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ s

pp

EE

dL

s

pps E

EdL

dE3/2

9.1

Kθ ⎠⎞

⎜⎝⎛ +⎟

⎠⎞

⎜⎝⎛

−=

LB

BLIGK bxrx 5.04.2

1

25.075.0

υ

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛

−=

15.075.0 3

1 BLIGK byry υ

υ−1

6.3 3GB 75.0

315.0 ⎟⎟⎠

⎞⎜⎜⎝

⎛

s

ps E

EEd

7.3.1 Unreinforced masonry building (UMB)

A wide range of buildings, including residential houses, shops, schools, churches and

hospitals, are constructed of unreiforced masonry in PMA and is the most common

construction form for new residential structures. A typical one story residential house is

chosen to be modelled as shown in Figure 7-2. Figure 7-3 shows the plan view and side

view of the building. It should be noted that this kind of structure is not required for

earthquake resistant design in the current Australian Code (AS 1170.4-2007) since the

structure height is less than 8.5m and the hazard factor (kpZ) for PMA is less than 0.11.

However, lives will be placed at risk if the buildings fail to resist predicted earthquake

forces as this type of structure occupies the highest proportion of existing buildings in

PMA (up to 88%). Hence, the building performance during the predicted ground

shakings is investigated in this study.

The model house considered here uses jarrah trusses for the roof framing and

unreinforced masonry for the wall. The thickness of the unreinforced masonry wall

(UMW) is 100 mm. Frame elements are used to model all jarrah truss members. UMW

is assumed to be uniform elements representing the combination of brick and mortar

and is modelled as shell element with 4 nodes and 6 degrees of freedom in each node.


147

The material properties of jarrah and UMW used in the analysis are summarised in

Table 7-3. The material properties of jarrah are derived from HB 2.2 (2003). The

material properties of UMW are obtained from a study of homogenized dynamic

masonry properties proposed by Wei and Hao (2008). Dead load is the self-weight of

the structural component. No imposed load is considered in the analysis.

Figure 7-2 3D typical one story residential house model

Figure 7-3 UMW building: plan view and right side view


148

Table 7-3 The material properties of jarrah and UMW

Material Type Description Value

Density (kg/m3) 800

Tension 50 Characteristic

strength (MPa) Compression 60 Jarrah

Young’s modulus (GPa) 1.1

Density (kg/m3) 1800

Ex 3.67

Ey 3.92

Ez 3.47

Gxy 1.86

Gyz 1.58

Modulus of elasticity

(GPa)

Gxz 1.50

Compressive strength（MPa） 10

UMW

Tensile strength (MPa) 1

The structure responses of the residential house on 3 site conditions subjected to the

predicted earthquake ground motions of 475-year and 2475-year return periods

presented in the previous chapter are analysed using SAP2000’s linear elastic dynamic

analysis option. The natural period of the first three modes are calculated and listed in

Table 7-4. The maximum compression and tension stress developed in unreinforced

masonry wall during the design earthquake have been investigated. Except for the case

of unreinforced masonry wall located at S7 subjected to the 2475 years return period

motion, the maximum compression and tension stress developed in unreinforced

masonry wall are well below the tensile strength and compression strength of

unreinforced masonry wall defined in Wei and Hao (2008). The maximum tension

stress of 1.08MPa estimated in the case of unreinforced masonry wall located at S7

subjected to the 2475 years return period ground motion slightly exceeds the defined

tension strength of 1MPa, indicating the unreinforced masonry building will suffer

slight damage during the 2475-year return period earthquake. These results were

obtained based on the masonry material properties listed in Table 7-3, It should be noted

that the masonry material properties used in this study are the homogenized properties

derived by Wei and Hao (2008) for study of masonry wall failure to blast loading.

Earthquake loading rate is substantially slower than the blast loading rate. In that case


149

the damage induced by earthquake loading is likely governed by the weak mortar

strength, which is about 0.2 MPa under tensile force. The induced tensile stress is 5

times larger than the mortar tensile strength, indicating the masonry wall may suffer

significant damage under such earthquake loads. It is recommended that further analysis

with detailed distinctive modelling of mortar and brick should be carried out to

investigate the performance of unreinforced masonry structures to the predicted

earthquake ground motions.

Table 7-4 Vibration periods

Period (sec)Site First mode Second mode Third mode

Shallow soil (S7) 0.158 0.119 0.09Deep/soft soil (S4) 0.159 0.120 0.09Very soft soil (S14) 0.160 0.122 0.09

7.3.2 RC structure with masonry infill wall

The plan view and the elevation of the selected model RC building with infill wall are

presented in Figure 7-4 and Figure 7-5. The column dimension is designed as 0.4×

0.4m whereas 0.2×0.6m for bean elements. The concrete material is C30 with the

modulus of elasticity of 28GPa. The specified yield strength of steel is taken as 250MPa.

Significant effect of the masonry infill wall on the stiffness and strength of frame

buildings has been reported in the literature (i.e. Lee and Woo, 2002 and Lu, 2002).

Mehrabi et al. (1996) also indicated that the ratio of stiffness of infilled frame and bare

frame can be 50 and the ratio of lateral resistance strength of infilled frame and bare

frame is more than 2 under the condition of weak frame and strong panel. This study

therefore includes the contribution of infill masonry walls in the model. The masonry

infill walls are modelled as the equivalent diagonal compression-only struts as shown in

Figure 7-6. The width of the equivalent strut is estimated using Equation 7-1 and 7-2

proposed by FEMA356 (2000) guidelines.

224.01 )(175.0 LHhW col += −λ (7-1)


150

41

inf

inf1 4

2sin

⎥⎥⎦

⎤

⎢⎢⎣

⎡=

hIEtE

colfe

me θλ (7-2)

in which W is the width of the equivalent diagonal compression strut in inches, H and L

are the height and length of the frame in inches, Eme and Efe are the elastic moduli of the

column and of the infill panel in ksi, tinf is the thickness of the infill panel in inches, θ

is the angle whose tangent is the infill height-to-length aspect ratio in radians, Icol is the

moment of inertia of column in in4 and hinf is the height of the infill panel in inches. hcol

is the column height between centrelines of beams.

Static load applied to the structure consists of dead and imposed load. Dead load is the

self-weight of the structural components. Imposed load on the floor area is 3kN/m2.

Loading on beams is 4.4kN/m, which is applied to the beams that support hollow brick

walls with a height of 2.4m.

Figure 7-4 Six story RC building plan view


151

Figure 7-5 Six story RC building section view

Figure 7-6 3D six-story RC building model

The nature frequencies and periods of the first three modes are calculated and listed in

Table 7-5. The investigation focuses on calculating the inter-storey drifts of the

reinforced concrete frame and masonry infill wall. The inter-storey drift is then used as

a criterion to assess the structure performance. The maximum inter-story drift of the 6-

storey building to the surface ground motions at different site conditions are

summarized in Table 7-6. Under the 475-year return period ground motion, the storey

drifts of the 6-storey building are 0.199% and 0.114%, which are observed in the X and

Y direction at site S7, followed by 0.124% at S4 and 0.104% at S14.The storey drifts is

more than 0.1%, indicating that the concrete frame of the 6-storey building will suffer

light damage in infill masonry wall when subjected to the 475-year return period event.

The damage to the masonry wall is beyond the range for immediate occupancy.

However, the damage level is small and imposes no life safety threat to occupants. For

the 2475-year return period, the 6-storey building will suffer light damage in infill


152

masonry wall at S4 and S14. When the building is located on S7 site, the largest storey

drift is 0.359%, which is closed to the boundary of life safety criteria of infill masonry

wall (0.5%). To investigate the inelastic seismic response of the RC building, nonlinear

dynamic time history analysis was also carried out for the building located at S7 site

subjected to the 2475-year return period earthquake ground motion. The nonlinear

structural model comprised PMM hinges (P: axial force, MM: biaxial moment) for

columns and M3 hinges (uniaxial moment) are used to simulate the plastic hinges for

the beam elements. The build-in default hinge properties for concrete members in

SAP2000 are based on Table 9.6, 9.7 and 9.12 in ATC-40, which are adopted in the

analysis. The numerical results show that the largest storey drift of the building is about

0.52%. It is larger than 0.5%, indicating that the infill UMW will suffer severe damage

to the ground excitations.



Shallow soil (S7) 0.526 0.492 0.372Deep/soft soil (S4) 0.527 0.496 0.375Very soft soil (S14) 0.537 0.536 0.405

Table 7-6 Maximum drift ratio of the RC building model

Drift Ratio (%)Analysis Method

Site Condition

Return Period (years) UX UY

475 0.199 0.114 S7 2475 0.359 0.236 475 0.124 0.076 S4 2475 0.141 0.081 475 0.104 0.059

Linear Dynamic analysis

S14 2475 0.107 0.066

Non-linear Dynamic analysis

S7 2475 0.521 0.237

7.3.3 High-rise RC frame with core walls

The high-rise building shown in Figure 7-7 and Figure 7-8 is a 34-storey RC frame with

core walls. It mainly serves as business office. As shown, the building is irregular in

shape and the plan dimension is 40.05×20m with a total height of 136.26m from the


153

base. The lateral force resisting structural system consists of RC moment resisting

frames attached to the concrete core walls at the centre. Typical section dimension of

the column is 900×900mm and the depth of the beams is 700mm. The typical thickness

of walls is 300mm. The specific strength of concrete fcu for beam is 30MPa and for

column and core wall are 60MPa. The elastic modulus of C30 and C60 concrete are

28GPa and 40GPa, respectively. Static load applied to the structure consists of dead and

imposed load. Dead load is the self-weight of the structural components. Imposed load

on the floor area is 3kN/m2. The self-weight of all brick walls, both internal and external,

are calculated and are applied to the beams.

Figure 7-7 Plane view of the 34 story high-rise building

Y

X


154

Figure 7-8 3D model of the 34 story high-rise building of reinforced concrete frame

with core walls

The natural periods of the first three modes are calculated and listed in Table 7-7. The

response of the 34-storey building to the 475-year return period ground motions and

2475-year return period ground motions on various sites are summarized in Table 7-9.

Numerical results show that the maximum inter-storey drift during the 475-year return

period ground motions is 0.213% when the building is located on S14, indicating the

building is safe since the largest storey drift is less than the critical value of immediate

occupancy of concrete wall (0.5%) and concrete frame (1%). However, when the

building is built on S14, the largest storey drift of the building to the 2475-year return

period ground motions is between 0.5% and 1%. These results indicate that the building

will experience light to moderate damages at concrete walls, but the building will

satisfy a life-safety objective since the largest storey drift is less than 1%.



S7 3.750 2.594 2.019S4 3.751 2.595 2.023S14 3.758 2.603 2.054


155

Table 7-8 Maximum drift ratio of the HR building model

Drift Ratio (%) Site Condition Return Period (years) UX UY

475 0.102 0.166S7 2475 0.329 0.386475 0.089 0.160S4 2475 0.304 0.385475 0.172 0.213S14 2475 0.259 0.749

7.4 Conclusion

In this chapter, the performance of three typical Perth structures, namely a masonry

house, a middle-rise reinforced concrete frame structure, and a high-rise building of RC

frame with core wall on various soil sites subjected to the predicted earthquake ground

motions of different return periods are investigated. The study revealed that:

(i) Based on the analysis using the homogenized masonry material properties, one-

storey UMW building is unlikely to be damaged when subjected to the 475-year return

period ground motion. However, it will suffer slight damage during the 2475-return

period earthquake ground motion at some sites. Because earthquake loading rate is

relatively slow as compared to the blast loading, masonry wall damage to earthquake

loadings is governed by weak mortar strength. Using homogenized masonry material

properties may lead to overestimation of the masonry wall strength to resist earthquake

loadings. It is recommended to perform detailed modelling of masonry wall with

distinctive brick and mortar properties to further investigate the masonry wall

performance under predicted earthquake ground excitations.

(ii) The six-storey RC frame with masonry infill will suffer light damage under the 475-

year return period ground motion. The infill masonry wall will suffer severe damage

under the 2475-year return period earthquake ground motion at some sites.

(iii) The 34-storey RC frame building with core wall will not suffer any damage to the

475-year return period ground motion. The building will experience light to moderate


156

damage during the 2475-year return period ground motion, but the building will still

satisfy the life-safety objective.


157

CHAPTER 8 CONCLUSIONS AND

RECOMMENDATIONS


As only a very limited number of earthquake strong ground motion records are available

in southwest Western Australia (SWWA), it is difficult to derive a reliable and unbiased

strong ground motion attenuation model based on these data. To overcome this, in this

study a method which combines empirical Green’s function and stochastic simulation

was proposed to simulate ground motions. By comparing the simulated ground motion

time histories with the recorded time histories of the two earthquake events in SWWA,

it was found that the proposed method gave reliable simulations of earthquake ground

motion time histories in SWWA.

A set of ground motion time histories corresponding to earthquakes of magnitudes

varying from ML4.0 to ML7.0 with an increment of ML0.5, and epicentral distances

varying from 10km to 200km with an increment of 20 km, were then generated using

the proposed method. These simulated ground motion time histories were used as

supplements to the SWWA earthquake database and were used to derive attenuation

models for PGA, PGV and response spectrum. The derived attenuation model was

compared with three CENA models and one model developed for SWWA. It was found

that the proposed model in this study yielded most reliable predictions of the available

ground motions records in SWWA amongst all the attenuation models.

Since the new attenuation model suggested in this study was derived from a large

simulated database covering a large distance range, an appropriate magnitude range and

provide a more reliable prediction of available SWWA records than other models

considered, it is expected the new equations are likely to provide the more reliable

seismic hazard results in SWWA.


158

A statistical study of the effects of random fluctuations of the seismic source parameters

on simulated strong ground motions was performed using Rosenbluth’s point estimate

method. Random fluctuations of three source parameters, namely the stress drop ratio,

rupture velocity and rise time, were considered. Because the study of the SWWA

seismic source parameters was quite limited, the corresponding values derived from

CENA were adopted and assumed to be mean values in simulating ground motions in

SWWA. A sensitivity analysis was carried out to study the influences of variations of

each of these three seismic source parameters on simulated ground motions with

different earthquake magnitudes and different epicentral distances. It was found that

variations in stress drop ratio have the most significant effects on PGA, PGV and

response spectrum of the simulated ground motions, followed by rise time. Variations in

phase delay have the least effect, among the three source parameters considered in the

study, on PGA and PGV, but significantly influence the ground motion frequency

contents. The influences of the source parameter variations on the simulated ground

motions are dependent on the earthquake magnitudes but are insensitive to the

epicentral distance. The relations of coefficients of variation of PGA, PGV and response

spectrum of the simulated ground motions as a function of variations of the seismic

source parameters and earthquake magnitude were also derived. They can be used

together with the attenuation relations developed in this study to estimate ground

motion attenuations with the influence of uncertain source parameters.

Using the attenuation model proposed in this study, a probabilistic seismic hazard

assessment was carried out for PMA. The results show that PGA on rock is estimated

ranging from 0.14g in the north-east through to 0.09g in the south-west for return period

of 475 years. The current code value underestimates PGA in most of the PMA

especially to the north-east. The PGA for return period of 2475 years is estimated in the

range of 0.24g to 0.36g. The code spectrum corresponding to the 475-year return period

underestimates the spectral accelerations at the CBD of Perth in the period range of

0.5sec to 2sec. The code spectrum corresponding to the 2475-year return period

underestimates predicted spectral acceleration across the entire period range, especially

in the range of low frequency.

The microtremor survey method (SPAC), a genetic-based method (CSA technique), and

the wave propagation theory are combined together to characterize the site conditions in

PMA. Comparing the calculated surface ground motion response spectra corresponding


159

to the 475-year return period to that specified in the current code, the current code

underestimates the spectral acceleration of the sites which are classified as shallow soil

site at periods range of 0.5 to 3sec, indicating that the design response spectrum of

shallow soil site in the current code should be used with caution in structure design. The

current code spectrum corresponding to the 2475-year return period underestimates the

spectral acceleration of most of sites investigated in this study in the long period range.

Using the calculated natural period and response spectrum of the study sites, seismic

microzonation maps for PMA was constructed. Seismic microzonation maps show that

long period (more than 1sec) runs throughout most of PMA, which results in significant

deamplification of bedrock motion at high frequency range. Most of CBD of Perth is

located at long natural period sites.

The performance of three typical Perth structures, namely a masonry house, a middle-

rise reinforced concrete frame structure, and a high-rise building of RC frame with core

wall on various soil sites subjected to the predicted earthquake ground motions of

different return periods are investigated. The results show that one-storey UMW

building is unlikely to be damaged when subjected to the 475-year return period ground

motion. It will suffer slight damage during the 2475-return period earthquake ground

motion at some sites. These results were obtained by using homogenized masonry

material properties. Further study with detailed modelling of masonry wall is recommended to

investigate the masonry wall response to predicted earthquake ground motions. The six-storey

RC frame building with masonry infill wall will suffer light damage under the 475-year

return period ground motion. The infill masonry wall will suffer severe damage during

the 2475-year return period ground motion on some sites. The 34-storey RC frame with

core wall will not suffer any damage to the 475-year return period ground motion. The

building will experience light to moderate damages at core wall during the 2475-year

return period ground motion, but the building will still satisfy the life-safety objective.

8.2 Recommendation for Further Research

The study of seismic risk of PMA has been carried out in this research. It can be further

improved in the future study in the following aspects:


160

(i) The definition of earthquake sources and their seismic recurrence characteristics,

ground motion estimation and local site effects are key issues for seismic hazard

analysis and seismic risk evaluation.. Seismic zonation and their seismic recurrence

characteristics are based on information from regional geology and neotectonics,

seismicity, stress field, damage analysis of historic strong earthquakes, geophysics and

others. These subjects are weighted differently in the combined statistics and thus

different conclusions could be resulted even from the same information. Further

research should be conducted to reduce the uncertainties of the estimation.

(ii) It was proved that the new attenuation models proposed in this study provide more

reliable predictions of the limited available earthquake ground motions than other

models commonly used in SWWA. However, the proposed model is obtained from a

database in which most strong ground motions corresponding to ML>5 events are

numerically simulated. The new model should be continually tested as new records

come to hand.

(iii) It was found that variations in the seismic source parameters have the significant

effects on PGA, PGV and response spectrum of the simulated ground motions. Hence,

more detailed study in seismic source parameters of SWWA need to be carried out.

(iv) It was found that the code spectrum corresponding to the 2475-year return period

motion underestimates the predicted spectral acceleration across the entire period range,

especially in the low frequency range. Site response studies also indicated that the code

spectrum might underestimate predicted spectral acceleration in some frequency range

at some site.

(v) The structural response analysis presented in the thesis is based on limited structural

information and intended to give a reasonably indication of seismic safety of building

structures in PMA. More detailed analysis, e.g. the out-of-plane failure of infill

unreinforced masonry wall, connection of structural elements, should be carried out

during the final evaluation of the proposed design of a new building or during the

detailed evaluation of existing buildings.

School of Civil and Resource Engineering REFERENCES The University of Western Australia

161

REFERENCES ABS (2001). Building Approvals, Australia. ABS Cat. No 8731.0. Canberra, Australian Bureau of Statistics, . Aki, K. (1957). "Space and time spectra of stationary stochastic waves, with special reference to microtremors." Bulletin, Eurthq. Res. Inst. 35: 415-456. Aki, K. (1967). "Scaling laws of seismic spectrum." J. Geophys. Res. 72: 1217-1231. Aki, K. and P. G. Richards (1980). Quantitative Seismology: Theory and Methods. San Francisco, W. H. Freeman. Allen, T. I., T. Dhu, P. R. Cummins and J. F. Schneider (2006). "Empirical Attenuation of Ground-Motion Spectral Amplitudes in Southwestern Western Australia." Bull. Seism. Soc. Am. 96: 572-585. Ambraseys, N. N. and A. Zatopek (1968). "The Varto Ustukran (Anatolia) earthquake of 19 August, 1966." Bull. Seism. Soc. Am. 58: 47-102. Anderson, J. G. and S. E. Hough (1984). "A model for the shape of the Fourier amplitude spectrum of acceleration at high frequencies." Bull. Seis. Soc. Am. 74: 1969-1993. AS1170.4-1993 (1993). ":Structural design actions - Earthquake actions in Australia." Australia Standards. AS1170.4-2007 (2007). ":Structural design actions - Earthquake actions in Australia." Australia Standards. Asten, M. W. (2005). An assessment of information on the shear-velocity profile at Coyote Creek, San Jose, from SPAC processing of microtremor array data. Blind comparisons of shear-wave velocities at closely spaced sites in San Jose, California. M. W. Asten, and Boore, D.M., U.S. Geological Survey. Asten, M. W., T. Dhu, A. Jones and T. Jones (2003). Comparison of shear-velocities measured from microtremor array studies and SCPT data acquired for earthquake site hazard classification in the northern suburbs of Perth W.A. Proceedings of a Conference of the Australian Earthquake Engineering Soc., Melbourne. Asten, M. W., T. Dhu and N. Lam (2004). Optimised array design for microtremor array studies applied to site classification; observations, results and future use. Conference Proceedings of the 13th World Conference of Earthquake Engineering, Vancouver. Asten, M. W., N. Lam, G. Gibson and J. Wilson (2002). Microtremor survey design optimised for application to site amplification and resonance modelling, in Total Risk Management in the Privatised Era. Proceedings of Conference, Australian Earthquake Engineering Soc., Adelaide.


162

Atkinson, G. M. (1993). "Notes on ground motion parameters for eastern North America: duration and H/V ratio." Bull. Seism. Soc. Am. 83: 587-596. Atkinson, G. M. (2004). "Empirical attenuation of ground-motion spectral amplitudes in southeastern Canada and the northeastern United States." Bull. Seism. Soc. Am. 94: 1079-1095. Atkinson, G. M. and D. M. Boore (1995). "Ground motion relations for eastern North America." Bull. Seism. Soc. Am. 85: 1995. Atkinson, G. M. and D. M. Boore (1997). "Some Comparisons Between Recent Ground Motion Relations." Seismological Research Letters 68: 24-40. Atkinson, G. M. and D. M. Boore (1998). "Evaluation of models for earthquake source spectra in eastern North America." Bull. Seism. Soc. Am. 88(4): 917-934. Atkinson, G. M. and P. G. Somerville (1994). "Calibration of Time History Simulation Method." Bull. Seism. Soc. Am. 84: 400-414. Bardet, J. P., K. Ichii and C. H. Lin (2000). EERA, a computer program for equivalent linear earthquake site response analysis of layered soil deposits, University of Southern California. Bender, B. and D. M. Perkins (1987). "SEISRISK III: A Computer Program for Seismic Hazard Estimation." U.S. Geological Survey Bulletin 1772, U.S. Department of the Interior. Beresnev IA, Atkinson GM. (1997) Modelling "nite-fault radiation from the ωn spectrum. Bulletin of the Seismological Society of America 1997; 87(1):67}84. Boatwright, J. (1988). "The seismic radiation from composite models of faulting." Bull. Seism. Soc. Am. 78: 489-508. Bolt, B. A. (1973). Duration of strong ground motion. World Conference on Earthquake Engineering, 5th, Rome. Boore, D. M. (1978). Modeling of near-fault motions. San Diego, Strong ground motion, N.S.F. Seminar Workshop: 30-35. Boore, D. M. (1983). "Stochastic simulation of high frequency ground motion based on Seismological Models of Radiated Spectra." Bull. Seismol. Soc. Am. 73: 1865-1894. Boore, D. M. (2003). "Simulation of ground motion using the stochastic method." Pure and Applied Geophys. 160: 635-676. Boore, D. M. and G. M. Atkinson (1987). "Stochastic prediction of ground motion and spectral response parameters at hard-rock sites in Eastern North America." Bull. Seismol. Soc. Am. 77: 440-467. Borcherdt, R. D. (1991). On the observation, characterisation and predictive GIS mapping of strong ground shaking for seismic zonation. (A case study in the San


163

Francisco Bay region, California). Pacific Conference on Earthquake Engineering, New Zealand. Brune, J. N. (1970). "Tectonic stress and spectra of seismic shear waves from earthquakes." J. Geophys. Res. 75: 4997-5009. Castro, L. N. d. and F. J. V. Zuben (2000). The clonal selection algorithm with engineering applications. In Workshop Proceedings of GECCO, Workshop on Artificial Immune Systems and Their Applications, Las Vegas, USA. Davidson, W. A. (1995). Hydrogeology and groundwater resources of the Perth region, Western Australia. Denham, D. (1976). "Earthquake hazard in Australia." Australian Academy of Science 7: 94-118. Dentith, M., V. Dent and B. Drummond (2000). "Deep crustal structure in the southwestern Yilgarn Craton, Western Australia." Tectonophysics 324: 227-255. Dhu, T., C. Sinadinovski, M. Edwards, D. Robinson, T. Jones and A. Jones (2004). Earthquake risk assessment for Perth, Western Australia. Proceedings of the 13th World Conference on Earthquake Engineering, Vancouver. Douglas, J. (2004). Use of analysis of variance for the investigation of regional dependence of strong ground motions. Proceedings of Thirteenth World Conference on Earthquake Engineering. Dowrick, D. J. and D. A. Rhoades (2004). "Relations Between Earthquake Magnitude and Fault Rupture Dimensions: How Regionally Variable Are They?" Bull. Seism. Soc. Am. 94(3): 776-788. Doyle, H. (1995). Seismology, John Wiley and Sons. Ergonul, S. (2005). "A probabilistic approach for earthquake loss estimation." Structural Safety 27: 309-321. Eurocode8 (2005). Design of structures for earthquake resistance, British Standards Institution. Everingham, I. B. (1968). Seismicity of Western Australia, Bureau of Mineral Resources, Australia: Report 132. Everingham, I. B., D. Denham and S. A. Greenhalgh (1987). "Surface-wave magnitudes of some early Australian earthquakes." BMR Journal of Australian Geology and Geophysics 10: 253-259. Everingham, I. B. and P. J. Gregson (1970). "Meckering earthquake intensities and notes on earthquake risk for Western Australia." BMR Record 1970/97, Bureau of Mineral Resources, Australia. FEMA356 (2000). Prestandard and Commentary for the Seismic Rehabilitation of Buildings. Washington DC, Federal Emergency Management Agency.


164

Field, E. H. and K. Jacob (1993). "The theoretical response of sedimentary layers to ambient seismic noise." Geophysical Res. Lett. 20-24: 2925-2928. Frankel, A. (1995). "Simulation strong motions of large earthquakes using recordings of small eathquakes: the Loma Prieta mainshock as a test case." Bull. Seism. Soc. Am. 85: 1144-1160. Frankel, A., C. Mueller, T. Barnhard, D. Perkins, E. Leyendecker, N. Dickman, S. Hanson and M. Hopper (1996). National Seismic Hazard Maps: Documentation June 1996., U.S. Geol. Surv. Open-File Rpet.: 96-532,69. Gaull, B. (2003). "Seismic parameters for the upper sediments of the Perth Basin." AGS Symposium. Gaull, B., H. Kagami and H. Taniguchi (1995). "The Microzonation of Perth, Western Australia, Using Microtremor Spectral Ratios." Earthquake Spectra 11: 173-191. Gaull, B. and M. Michael-Leiba (1987). "Probabilistic earthquake risk maps of southwest Western Australia." BMR Journal of Australian Geology and Geophysics 10: 145-151. Gaull, B. A. (1988). Attenuation of strong ground motion in space and time in southwest Western Australia,. Ninth WCEE, Tokyo-Kyoto, Japan. Gaull, B. A. and M. Michael-Leiba (1987). "Probabilistic earthquake risk maps of southwest Western Australia." BMR Journal of Australian Geology and Geophysics 10: 145-151. Gaull, B. A., M. O. Michael-Leiba and J. M. W. Rynn (1990). "Probabilistic earthquake risk maps of Australia." Australian Journal of Earth Sciences 37: 169–187 Gazetas, G. (1990). "Foundation vibration", In Foundation engineering handbook, 2nd edition, New York, Van Nostrand Reinhold. Geller, R. J. (1976). "Scaling relations for earthquake source parameters and magnitudes." Bull. Seism. Soc. Am. 66(5): 1501-1523. Guney, K., B. Babayigit and A. Akdagli (2008). "Interference suppression of linear antenna arrays by phase-only control using a clonal selection algorithm." Journal of the Franklin Institute(345): 254-266. Hadley, D. M. and D. V. Helmberger (1980). "Simulations of strong ground motion." Bull. Seism. Soc. Am. 70: 617-630. Hanks, T. C. (1982). "fmax." Bull. Seis. Soc. Am. 72: 1867-1879. Hanks, T. C. and H. kanamori (1979). "A moment magnitude scale." Journal of Geophysical Research 84(B5): 2348-2350. Hanks, T. C. and R. K. McGuire (1981). "The character of high-frequency strong ground motions." Bull. Seis. Soc. Am. 71 (6): 2071-2095.


165

Hao, H. (1993). Input seismic motions for use in the structural response analysis. The Sixth International Conference on Soil Dynamics and Earthquake Engineering. Hao, H. and B. Gaull (2004a). Design earthquake ground motion prediction and simulation for PMA based on a modified ENA seismic ground motion model for SWWA. Mt Gambia, Australia, Proceedings of the Annual Australian Earthquake Engineering Society Conference. Hao, H. and B. Gaull (2004b). Prediction of seismic ground motion in Perth Western Australia for engineering application. Proceedings of the 13th World Conference on Earthquake Engineering, Vancouver, Canada. Hartzell, S. H. (1978). "Earthquake aftershocks as Green functions." Geophy. Res. Lett. 5: 1-4. HB2.2 (2003). Australian Standards for civil engineering students – Structural engineering, Standards, Australia. Husid, R., H. Median and J. Rios (1969). "Analysis de Terremotos Morteamericanos y Japonsesses." Pevista del IDIEM 8, Chile. Idriss, I. M. and J. I. Sun (1992). User's Manual for SHAKE91, Department of Civil & Environmental Engineering, University of California at Davis. Iida, K. (1965). "Earthquake magnitude, earthquake fault, and source dimensions." J.Earth Sci.,Nagoya Univ. 13: 115-32. Imai, T. and K. Tonouchi (1982). Correlation of N-value with S-Wave velocity and Shear Modulus. Proc. 2nd Conf on Penetration testing, Amsterdam. Irikura, K. (1986). Prediction of strong acceleration motion using empirical Green's function. Proc. 7th Japan Earthquake Engineering Symposium. Irikura, K., T. Kagawa and H. Sekiguchi (1997). "Revision of the empirical Green's function method by Irikura (1986), Programme and Abstracts." Seismol. Soc. Jpn. B25.: 2. Irikuro, K. (1983). "Semi-empirical estimation of strong ground motions during large earthquakes." Bull.Disaster Prev.Res.Inst.,Kyoto Univ. 33: 63-104. Jarpe, S., L. Hutchings, T. Hauk and A. Shakal (1989). "Selected strong- and weak-motion data from the Loma Prieta earthquake sequence." Seismological Research Letters 60: 167-176. Jones, T., M. Middelmann and N. Corby (2006). Natural hazard risk in Perth, Western Australia. Canberra, Geoscience Australia: Chapter 5. Joshi, A. and S. Midorikawa (2004). "A simplified method for simulation of strong ground motion using finite rupture model of the earthquake source." Journal of Seismology 8: 467-484.


166

Joyner, W. B. and D. M. Boore (1986). "On simulating large earthquakes by Green's-function; Addition of smaller earthquakes." 37 Geophysical Monograph of American geophysical union, WashingtonD.C., USA. Kanamori, H. (1972). "Determination of effective tectonic stress associated with earthquake faulting." The Tottori earthquake of 1943. Phys. Earth Planet. Inter. 5: 426-434. Kanamori, H. and D. L. Anderson (1975). "Theoretical basis of some empirical relations in seismology." Bull. Seismol. Soc. Am. 65: 1073-1095. Keilis-Borok, V. I. and T. B. Yanovskaya (1967). "Inverse problems of seismology " Geophys. J.(13): 223-234. Kennedy, J., H. Hao and B. Gaull (2005). Earthquake Ground Motion Attenuation Relations for SWWA. Australian Earthquake Engineering Society Proceedings of the 2005 Conference, Albury. Kobayashi, K. (1980). A method for presuming deep ground soil structures by means of longer period microtremors. Processings of the Seventh World Conf. Earthq. Engn., Istanbul, Turkey. Lachet, C. and P. Y. Bard (1994). "Numerical and theoretical investigations on the possibilities and limitations of the "Nakamura's" technique." J. Phys. Earth. 42: 377-397. Lai, C. G. and G. J. Rix (1998). Simultaneous inversion of Rayleigh phase velocity and attenuation for near-surface site characterization., Georgia Institute of Technology, School of Civil and Environmental Engineering: 258 pp. Lam, N.T.K., Wilson, J.L., Chandler, A.M. and Hutchinson, G.L. (2000). “Response Spectral Relationships for Rock Sites Derived from the Component Attenuation Model”, Earthquake Engineering and Structural Dynamics, 29(10), 1457-1490. Lam, N.T.K., Wilson, J.L., Chandler, A.M., and Hutchinson, G.L. (2000). “Response Spectrum Modelling for Rock Sites in Low and Moderate Seismicity Regions Combining Velocity, Displacement and Acceleration Predictions”, Earthquake Engineering and Structural Dynamics, 29,1491-1525. Lay, T. and T. C. Wallace (1995). Modern Global Seismology. San Diego, Academic Press. Lee, H. and S. Woo (2002). "Effect of masonry infills on seismic performance of a 3-storey R/C frame with non-seismic detailing." Earthquake Engineering and Structural Dynamics 31(2): 353-378. Lermo, J. and F. J. Chavez-Garcia (1994). "Are microtremors useful in site response evaluation?" Bull. Seism. Soc. Am. 84: 1350-1364. Liang, J. Z. and H. Hao (2007a). Seismic site response analysis in Perth Metropolitan Area. Australian Earthquake Engineering Society Proceedings of the 2007 Conference, Wollongong, Australia.


167

Liang, J. Z., H. Hao, B. A. Gaull and C. Sinadinovski (2006). Simulation of strong ground motions with a combined Green's function and Stochastic approach. Australian Earthquake Engineering Society Proceedings of the 2006 Conference, Canberra. Liang, J. Z., H. Hao, B. A. Gaull and C. Sinadinovski (2008a). "Estimation of strong ground motions in Southwest Western Australia with a combined Green's function and stochastic approach." Journal of Earthquake Engineering 12: 382-405. Lu, Y. (2002). "Comparative study of seismic behavior of multistory reinforced concrete framed structures." Journal of Structural Engineering, ASCE 128(2): 169-178. Matsuda, T. (1975). "Magnitude and recurrence interval of earthquakes from fault." Zisin, J. Seismol. Soc. Japan 28: 269-83. McCue, K. F. (1973). On the seismicity of Western Australia, . Report to the Western Australia Public Works Department and the Commonwealth Department of Works, Parts I and II. Perth. McEwin, A. J., R. Underwood and D. Denham (1976). "Earthquake risk in Australia " BMR Journal of Australian Geology and Geophysics 1: 15-21. McPherson, A. and A. Jones (2006). Appendix D: PERTH BASIN GEOLOGY REVIEW and SITE CLASS ASSESSMENT. Perth Basin Geology. Mehrabi, A., P. Shing, M. Shuller and J. Noland (1996). "Experimental evaluation of masonry-infilled RC frames." Journal of Structural Engineering, ASCE 122(3): 228-237. Moro, G. D., M. Pipan and P. Gabrielli (2007). "Rayleigh wave dispersion curve inversion via genetic algorithms and Marginal Posterior Probability Density estimation." Journal of Applied Geophysics 61: 39-55. Nakamura, Y. (1989). "A method for dynamic characteristics estimation of subsurface using microtremor on the ground surface." Quarterly Report Railway Tech. Res. Inst. 30(1): 25-30. Nogoshi, M. and T. Igarashi (1971). "On the amplitude characteristics of microtremor." Tour. Seism. Soc. Japan 24: 26-40 (in Japanese). Noguchi, S. and K. Abe (1977). "Earthquake source mechanism ans Ms-Mb relation." J. Seismol. Soc. Japan 30: 487-507. Okada, H. (2003). "The microtremor survey method." Geophysical Monograph Series, Society of Exploration Geophysicists 12. Ou, J. and Y. Wang (2007). Finite element model updating using clonal selection algorithm. The second international conference on structural condition assessment, monitoring and improvement, ChangSha, China. Page, R. A., D. M. Broore and J. H. Dietrich (1975). "Estimation of bedrock motion at the ground surface." Profess.Paper 941-A.


168

Playford, P. E., A. E. Cockbain and G. H. Low (1976). "Geology of the Perth Basin Western Australia " Geological Society of Western Australia, Bulletin: 124. Press, F. (1967). Dimensions of the source region for small shallow earthquakes. Proceedings of the VESIAC Conference on the Source Mechanism of Shallow Seismic Events, VESIAC. Purcaru, G. and H. Berckhemer (1982). "Quantitative relations of seismic source parameters and a classification of earthquakes." Tectonophysics 84: 57-128. Reiter, L. (1991). Earthquake hazard analysis. New York, Columbia University Press. Richer, C. F. (1958). Elementary seismology. San Francisco, Freeman and Company. Rosenblueth, E. (1981). "Two-point estimates in probabilities." Appl. Math. Modelling 5: 329-335. Sambridge, M. (1999). "Geophysical inversion with a neighbourhood algorithm—I. Searching a parameter space." Geophys. J. Int.(138): 479-494. Schnabel, P. B. (1973). Effects of Local Geology and Distance from Source on Earthquake Ground Motions, University of California, Berkeley, California. Schnabel, P. B., J. Lysmer and H. B. Seed (1972). SHAKE-A computer program for earthquake response analysis of horizontally layered sites Earthquake Engineering Research Center, University of California at Berkeley. Seed, H. B. and I. M. Idriss (1970). Soil Moduli and Damping Factors for Dynamic Response Analysis. Report No. EERC 75-29, Earthquake Engineering Research Center. Berkeley, California, University of California. Shiono, K., Y. Ohta and K. Kudo (1979). "Observation of 1 to 5 sec microtremors and their applications to earthquake engineering, Part VI: existence of Rayleigh wave components." Jour. Seism. Soc. Japan 32: 115-124 (in Japanese). Sinadinovski, C., M. Edwards, N. Corby, M. Milne, K. Dale, T. Dhu, A. Jones, A. McPherson, T. Jones, D. Gray, D. Robinson and J. White (2006). Natural Hazard Risk in Perth, Western Australia. Chapter 5: Earthquake risk, Geoscience Australia. Sinadinovski, C., K. F. McCue, M. Somerville, T. Muirhead and K. Muirhead (1996). "Simulation of intra-plate earthquakes in Australia using Green's function Method: Sensitivity Study for Newcastle event." The Australian Earthquake Loading Standard; Proceedings of the Australian Earthquake Engineering Society; Adelaide: Paper No. 11. Sinadinovski, C. and D. Robinson (2003). Seismicity in the southwest of Western Australia. Proceedings of Australian Earthquake Engineering Society Conference, 2003, Melbourne. Somerville, P., N. Collins, N. Abrahamson, R. Graves and C. Saikia (1995). "Ground motion attenuation relations for central and eastern United States." Bull. Seism. Soc. Am. 85(1): 17-30.


169

Somerville, P., N. Collins, N. Abrahamson, R. Graves and C. Saikia (2001). Ground motion attenuation relations for the central and eastern United States. Final report, the U.S. Geological Survey. Somerville, P., K. Irikura, S.Sawada, Y. Iwasaki, M. Tai and M. Fishimi (1993). Spatial Distribution of Slip on Earthquake Fault. Proc. 22 JSCA Earthquake Engin. Symp. Somerville, P., K., R. Irikura, S. Graves, D. Sawada, N. Wald, Y. Abrahamson, T. Iwasaki, N. S. Kagawa and A. Kowada (1999). "Characterizing crustal earthquake slip models for the prediction of strong ground motion." Seis. Res. Lett. 70(1): 59-80. Somerville, P., Mrinal.Sen and B. Cohee (1991). "Simulation of strong ground motions recorded during the 1985 Michoacan, Mexico and Valparaiso, Chile earthquakes." Bull. Seismol. Soc. Am. 81: 1-27. Somerville, P. G., J. P. Mclaren, L. V. Lefever, R. W. Burger and D. V. Helmberger (1987). "Comparison of source scaling relations of eastern and western North American earthquakes." Bull. Seism. Soc. Am. 77: 322-346. Stewart, D. (2001). Geotechnical Borehole Database, Perth Central Business District, Western Australia (Perliminary-issued for comments). Perth, Australian Geomechanics Society. Street, R. L., R. B. Herrmann and O. W. Nuttli (1975). "Spectral characteristics of the Lg wave generated by central United States earthquakes." Geophys. J. R. Astr. Soc. 41(51-63). Street, R. L. and F. T. Turcotte (1977). "A study of northeastern North American spectral moments magnitudes and intensities." Bull. Seism. Soc. Am. 67: 599-614. Tocher, D. (1958). "Earthquake energy and ground breakage." Bull. Seism. Soc. Am. 48: 147-153. Tokimatsu, K. (1997). Geotechnical site characterization using surface waves. Proceedings of the First International Conference on Earthquake Geotechnical Engineering. Toro, G. R., N. A. Abrahamson and J. F. Schneider (1997). "Model of Strong Ground Motions from Earthquakes in central and Eastern North America: Best estimates and Uncertainties." Seismological Research Letters 68: 41-57. Trifunac, M. D. and A. D. Brady (1975). "A study on the duration of strong earthquake ground motion." Bull. Seism. Soc. Am. 65: 581-626. UBC (1995). Uniform Building Code. Volume 2 Structural Engineering Design Provisions, Proceedings of International Conference of Building Official, California. Vanmarcke, E. H. and S.-s. P. Lai (1980). "Strong-motion duration and RMS amplitude of earthquake records." Bull. Seism. Soc. Am. 70: 1293-1307.


170

Wathelet, M., D. Jongmans and M. Ohrnberger (2005). "Direct Inversion of Spatial Autocorrelation Curves with the Neighborhood Algorithm." Bull. Seism. Soc. Am. 95: 1787-1800. Wei, X., Y. and H. Hao (2008). "Numerical derivation of homogenized dynamic masonry material properties with strain rate effects " Accepted, Int J Impact Engng. Wells, D. L. and K. J. Coppersmith (1994). "New Empirical Relationships among Magnitude, Rupture Length, Rupture Width, Rupture Area, and Surface Displacement." Bull. Seism. Soc. Am. 84: 974-1002. Wilson JL, Lam NTK, (2003), A recommended earthquake response model for Australia, Australian Journal of Structural Engineering, Vol.5 No.1 pp 17-27. Wolf, J. P. (1985). Soil-structure Interaction, Prentice Hall. Wyss, M. and J. N. Brune (1968). "Seismic moment, stress and source dimensions for earthquakes in the California-Nevada region." J. Geophys. Res. 73: 4681-4694. Xia, J., R. D. Miller and C. B. Park (1999). "Estimation of near-surface shear-wave velocity by inversion of Rayleigh waves " Geophysics(64): 691-700.

Documents

A thesis submitted in partial fulfilment of the requirement for the … · simulate a series of ground motion time histories from earthquakes of varying magnitudes and distances