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Shrey Kumar Shahi January 2013 © 2013 by Shrey Kumar Shahi. All Rights Reserved.

Re-distributed by Stanford University under license with the author.

This work is licensed under a Creative Commons AttributionNoncommercial 3.0 United States License.

http://creativecommons.org/licenses/by-nc/3.0/us/ This dissertation is online at: http://purl.stanford.edu/hb804nv7861

Includes supplemental files:

1. Details about the pulses identified in chapter 4. (Shahi_Thesis_Supplement.zip) ii I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy.

Jack Baker, Primary Adviser I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy.

Gregory Deierlein I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy.

Eduardo Miranda Approved for the Stanford University Committee on Graduate Studies.

Patricia J. Gumport, Vice Provost Graduate Education This signature page was generated electronically upon submission of this dissertation in electronic format. An original signed hard copy of the signature page is on file in University Archives.

iii Abstract Growth of major population centers near seismically active faults has significantly increased the probability of a large earthquake striking close to a big city in the near future. This, coupled with the fact that near-fault ground motions are known to impose larger demands on structures than ground motions far from the fault, makes the quantitative study of near-fault seismic hazard and risk important.

Directivity effects cause pulse-like ground motions that are known to increase the seismic hazard and risk in near-fault region. These effects depend on the source-tosite geometry parameters, which are not included in most ground-motion models used for probabilistic seismic hazard assessment computation. In this study, we develop a comprehensive framework to study near-fault ground motions, and account for their effects in seismic hazard assessment. The proposed framework is designed to be modular, with separate models to predict the probability of observing a pulse at a site, the probability distribution of the period of the observed pulse, and a narrow band amplification of the spectral ordinate conditioned on the period of the pulse. The framework also allows deaggregation of hazard with respect to probability of observing the pulse at the site and the period of the pulse. This deaggregation information can be used to aid in ground-motion selection at near fault sites.

A database of recorded ground motions with each record classified as pulse-like or non-pulse-like is needed for an empirical study of directivity effects. Early studies of directivity effects used manually classified pulses. Manual classification of ground motions as pulse-like is labor intensive, slow, and has the possibility to introduce subjectivity into the classifications. To address these problems we propose an efficient iv algorithm to classify multi-component ground motions as pulse-like and non-pulselike. The proposed algorithm uses the continuous wavelet transform of two orthogonal components of the ground motion to identify pulses in arbitrary orientations. The proposed algorithm was used to classify each record in the NGA-West2 database, which created the largest set of pulse-like motions ever used to study directivity effects.

The framework to include directivity effects in seismic hazard assessment, as proposed in this study, requires a ground-motion model that accounts for directivity effects in its prediction. Most of the current directivity models were developed as a correction for already existing ground-motion models, and were fitted using groundmotion model residuals. Directivity effects are dependent on magnitude, distance, and the spectral acceleration period. This interaction of directivity effects with magnitude and distance makes separation of distance and magnitude scaling from directivity effects challenging. To properly account for directivity effects in a ground-motion model they need to be fitted as a part of the original model and not as a correction. We propose a method to include the effects of directivity in a ground-motion model and also develop models to make unbiased prediction of ground-motion intensity, even when the directivity parameters are not available.

Finally, following the approach used to model directivity effects, we developed a modular framework to characterize ground-motion directionality, which causes the ground-motion intensity to vary with orientation. Using the expanded NGA-West2 database we developed new models to predict the ratio between maximum and median ground-motion intensity over all orientations. Other models to predict distribution of orientations of the maximum intensity relative to the fault and the relationship between this orientation at different periods are also presented. The models developed in this dissertation allow us to compute response spectra that are expected to be observed in a single orientation (e.g., fault normal, orientation of maximum intensity at a period). It is expected that the proposed spectra can be a more realistic representation of single orientation ground motion compared to the median or maximum spectra over all orientations that is currently used.


My foremost thanks goes to my adviser Professor Jack Baker for his guidance and technical advice throughout my PhD. He offered unwavering support, complete freedom to pursue my ideas, and devoted several hours to me in meetings and reviewing my manuscripts. He has played a big role in my development as a researcher and I consider myself extremely fortunate to have been able to work with him.

Thanks to Professor Eduardo Miranda and Professor Greg Deierlein for their invaluable suggestions that improved this thesis significantly. I also wish to thank Professor Anne Kiremidjian for serving on my examination committee, and for several classes which helped me during the course of my research. Thanks to Professor Eric Dunham for chairing my thesis defense committee. I am also grateful to Racquel Hagen, Jill Nomura, Brenda Sampson, Sandra Wetzel and Kim Vonner for their administrative support.

My research at Stanford was supported by funds from the National Science Foundation, Pacific Earthquake Engineering Research Center and the Stanford Graduate Fellowship. Their support is greatly appreciated.

Thanks to all the students, staff and faculty members associated with the John A. Blume Earthquake Engineering Center. The friendly atmosphere at the Blume center made my stay at Stanford enjoyable. I enjoyed technical and philosophical discussions during several interactions with Nirmal Jayaram, Ting Lin, Yoshifumi Yamamoto, Hae Young Noh, Andy Seifried, Krishnan Nair. Thanks to both past and present members of my research group: Nirmal Jayaram, Yoshifumi Yamamoto, Ting Lin, Andy Seifried, Lynne Burks, Mahalia Miller, Christophe Loth, Beliz Ugurhan and Reagan Chandramohan for their friendship and valuable discussions during the vi group meetings.

I am highly indebted to my friends outside the Blume center specially Kuldeep Lonkar, Amrita Lonkar, Supreet Bahga, Mayank Agarwal, Bhupesh Chandra, Krishnamurthy Iyer, Manu Bansal, Uzma Hussain Barlaskar, and Nikhil Ghare for their help and support throughout my stay at Stanford.

I will always be grateful to Manisha for her unwavering love and support in the roles of friend and wife, that she played during the long course of my PhD. Her support even from 3000 miles away was critical in helping me finish the PhD.

Finally, I dedicate this thesis to my parents who have supported me in all my decisions. I wish to express my gratitude to them for their unconditional support and love that they have always showered on me.

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5.1 Coefficients for the CBR ground-motion model............. 110

5.2 Coefficients for the CBSB ground-motion model............. 116

5.3 Period independent coefficients of the directivity terms......... 116

5.4 Coefficients for the average directivity amplification model....... 132

5.5 Standard deviation of total error (σ) for different models considered in the study.................................. 139

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7.1 Fitted values of ln(SaRotD100 /SaRotD50 ) with the within-event standard deviation (φ), between-event standard deviation (τ ) and total standard deviation (σ), estimated by mixed effects regression. Note that the estimates are for mean of ln(SaRotD100 /SaRotD50 ) and geometric mean of SaRotD100 /SaRotD50 and the reported standard deviations are for ln(SaRotD100 /SaRotD50 ) estimates................... 164

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1.1 Map of Imperial Valley earthquake rupture with the location of sites where ground motion was recorded. Site (c) close to the epicenter is the Bonds Corner station (NGA # 160) and directivity pulse was not observed here. While, directivity pulse is observed at site (b) El Centro Array # 4 station (NGA # 179), which is located down the rupture at a similar distance as site (c) from the fault. Fault normal component of the two ground motions is shown in this figure............ 4

1.2 Some examples of ground-motion recordings with directivity pulse. a) Brawley Airport station from Imperial Valley, 1979 earthquake (NGA # 161), b) Lucerne station from Landers, 1992 earthquake (NGA #

879) and c) Rinaldi station from Northridge, 1994 earthquake (NGA # 1063)................................... 7

2.1 Illustration of the procedure used by Baker (2007) algorithm to extract the largest pulse from a velocity time history (1979 Imperial Valley, EC Meloland Overpass recording). In this case the pulse is large and the ground motion is classified as pulse-like................. 21

2.2 Pulse Indicator values as a function of orientation for the 1979 Imperial Valley, EC County Center recording. Shaded orientations indicate orientations in which a strong pulse is apparent. For more information on how pulse indicator is calculated, see Baker (2007)......... 22 xv

2.3 Response spectra (5% damped) of 1979 Imperial Valley, El Centro Array # 5 ground motion in fault normal orientation. The Boore and Atkinson (2007) median prediction and the response spectra from residual ground motion are also shown.................. 28

2.4 Plot explaining the parameters needed to fit the logistic regression for (a) strike-slip, (b) non-strike-slip faults. The parameter α, the angle between orientation of interest and the strike of the fault, is also shown.

(after Somerville et al., 1997)...................... 29

2.5 Map of 1979, Imperial valley earthquake (M = 6.53) showing (a) contours of probability of pulse occurrence for the given rupture, (b) sites where pulse-like ground motion was observed. The site within the shaded circle is the one for which example hazard analysis is done... 30

2.6 Map of 1994, Northridge earthquake (M = 6.69) showing (a) contours of probability of pulse occurrence for the given rupture, (b) sites where pulse-like ground motion was observed.................. 31

2.7 Plot of probability of pulse at α given pulse at site for both strike-slip (SS) and non-strike-slip (NSS) faults................... 33

2.8 Pulse period versus earthquake magnitude for observed pulse-like ground motions................................... 35

2.9 Observed values of residual ground motions.............. 37

2.10 Amplification factor for Sa due to the presence of pulse-like features in ground motions. (a) Plot of predictive equation along with the observed data. (b) Mean amplification due to pulses oriented in different directions.................................. 38

2.11 Ratio of standard deviation of residuals from predictions of pulse-like spectra (σlnSa,pulse ) to the BA2008 ground-motion model standard deviation (σlnSa,gmm )............................. 40

2.12 Median Sa (2 sec) prediction from Boore-Atkinson 2008 model with and without the de-amplification along with the actual observations from Northridge earthquake. The Boore-Atkinson model prediction includes the inter-event residual of the Northridge earthquake.......... 43

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4.1 Different types of ground motions a) Clear pulse (El Centro Array # 4 recording, from the 1979 Imperial Valley earthquake), b) Clear nonpulse (Pasadena-CIT recording, from the 1971 San Fernando earthquake) and c) An ambiguous pulse (Salton Sea Wildlife Refuge recording, from the 1987 Superstition Hills earthquake)............ 79

4.2 The Pasadena - CIT Athenaeum recording from San Fernando (1971) earthquake (original ground motion) is broken down into 50 wavelets using the continuous wavelet transform. The wavelets are summed together to get the reconstructed ground motion, which is an approximation of the original ground motion. The quality of approximation improves as the number of wavelets used is increased.......... 82

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