Seismic Hazard Analysis and Seismic Slope Stability Evaluation Using Discrete Faults in Northwestern Pakistan

SEISMIC HAZARD ANALYSIS AND SEISMIC SLOPE STABILITY EVALUATION USING DISCRETE FAULTS IN NORTHWESTERN PAKISTAN

BYUNGMIN KIM

DISSERTATION

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Civil Engineering in the Graduate College of the University of Illinois at Urbana-Champaign, 2012

Urbana, Illinois

Doctoral Committee:

Professor Youssef M.A. Hashash, Chair, Director of Research Associate Professor Scott M. Olson, Co-director of Research Professor Gholamreza Mesri Professor Amr S. Elnashai Associate Professor Junho Song

ABSTRACT

The Mw 7.6 earthquake that occurred on 8 October 2005 in Kashmir, Pakistan, resulted in tremendous number of fatalities and injuries, and also triggered numerous landslides. Although there are no reliable means to predict the timing of the earthquake, it is possible to reduce the loss of life and damages associated with strong ground motions and landslides by designing and mitigating structures based on proper seismic hazard and seismic slope stability analyses. This study presents the methodology and results of seismic hazard and slope stability analyses in northwestern Pakistan. The first part of the thesis describes the methodology used to perform deterministic and probabilistic seismic hazard analyses. The methodology of seismic hazard analysis includes identification of seismic sources from 32 faults in NW Pakistan, characterization of recurrence models for the faults based on both historical and instrumented seismicity in addition to geologic evidence, and selection of four plate boundary attenuation relations from the Next Generation Attenuation of Ground Motions Project. Peak ground accelerations for Kaghan and Muzaffarabad which are surrounded by major faults were predicted to be approximately 3 to 4 times greater than estimates by previous studies using diffuse areal source zones. Seismic hazard maps for PGA and spectral accelerations at periods of 0.2 sec and 1.0 sec corresponding to 475-, 975-, and 2475-year return periods were produced for NW Pakistan. Based on deaggregation results, a discussion of the conditional mean spectra for engineering applications is presented. The second part of the thesis proposes factors that affect distribution of shallow landslides triggered by an earthquake. Landslides are the most common consequence of earthquakes, resulting in significant amount of damages of structures and lives. Significant damage was induced from the landslides triggered by the 2005, Kashmir, Pakistan, earthquake. Therefore, predicting locations and severity of landslide is an essential part of earthquake engineering. However, the currently used seismic slope stability analysis cannot capture the actual trend of landslide distribution, especially high landslide concentration near field. This study proposes the effect of vertical ground acceleration, topographic effects, and bond break effects, in addition to the strong horizontal ground acceleration, as factors that contribute to the landslide distribution near earthquake source. Landslide database from four earthquake cases (1989 Loma-Prieta, U.S.; 1999 Chi-Chi, Taiwan; 2005 Kashmir, Pakistan; and 2008 Wenchuan, China) were selected to verify these factors for slope stability analysis.

To my parents and grandparents

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ACKNOWLEDGEMENT

I would like to express my deep appreciation and respect to my advisor, Professor Youssef M.A. Hashash, and my co-advisor, Professor Scott M. Olson, for their careful attention, patient guidance, enthusiastic advice, and constant support throughout the period of study. Having a chance to study under their supervision was one of the most fortunate things in my life. I would like to extend my sincere appreciation to the members of the committee, Professors Gholamreza Mesri, Amr S. Elnashai, and Junho Song for their insightful advice which significantly enhanced this dissertation. I also appreciate Professors Timothy D. Stark and James H. Long for their skillful and passionate lectures that inspired me greatly. I deeply appreciate Professor Duhee Park at the Hanyang University who led me to Illinois inspiring to aspire to higher education. I would like to thank my gentle officemates, David Groholski, Camilo Phillips, Sungwoo Moon, Michael Musgrove, for making a vibrant research environments with pleasant casual chats as well as helpful discussion. Special thanks are extended to GESO members: Randa Asmar, Fangzhou Dai, Joseph Harmon, Maria Ines Romero, Mark Muszynski, Janson Funk, Andrew Tangsombatvisit, Mohamad Jammoul. I believe we will be all connected as we move forward careers in our own professions, Oscar Moreno-Torres. I am grateful to all members of the Korean Student Association in Civil Engineering, especially to Seung Jae Lee, Junhan Kim, Robin Kim, Hongki Joe, Moochul Shin, Hyungchul Yoon, Seungmin Lim, Junho Chun. I would also like to thank Professors Kyungsoo Park, Sunghan Sim, Taekeun Oh. Most importantly, I would like to thank my parents and younger brother for their love, support, and encouragement. I specially thank my grandparents who passed away during the period of my study. No words can express how grateful I am for their endless love and support on me. The supports from USAID and Higher Education Commission of Pakistan under Award No. AID NAS PGA-7251 are gratefully acknowledged.

TABLE OF CONTENTS

LIST OF SYMBOLS ...... vi LIST OF ABBREVIATIONS ...... viii Chapter 1. INTRODUCTION ...... 1 Chapter 2. PRIOR SEISMIC HAZARD STUDIES IN NW PAKISTAN ...... 3 Chapter 3. DETERMINISTIC SEISMIC HAZARD ANALYSIS ...... 8 Chapter 4. PROBABILISTIC SEISMIC HAZARD ANALYSIS ...... 32 Chapter 5. SEISMIC HAZARD RESULTS ...... 54 Chapter 6. CURRENT SEISMIC SLOPE STABILITY APPROACH ...... 92 Chapter 7. FACTORS THAT AFFECT PSEUDO-STATIC SLOPE STABILITY ...... 111 Chapter 8. PROPOSED NEW APPROACH TO PSEUDO-STATIC SLOPE STABILITY ANALYSIS AND VERIFICATION USING EARTHQUAKE CASES ...... 121 Chapter 9. CONCLUSIONS AND RECOMMENDATION FOR FUTURE RESEARCH ... 154 Appendix A. ESTIMATION OF MOHR-COULOMB STRENGTH PARAMETERS ...... 159 REFERENCES ...... 168

LIST OF SYMBOLS ah horizontal acceleration ah,max maximum horizontal acceleration amax maximum acceleration av vertical acceleration av,max maximum vertical acceleration ay yield acceleration b slope of exponential recurrence model bl slip rate at greater depths bs slip rate at sesimogenic depths c’ cohesion intercept of the failure mass D depth to the bottom of rupture d average displacement over the slip surface

Dt failure mass thickness

Fh horizontal pseudo-static force

Fv vertical pseudo-static force h slope height i slope angle kbond pseudo-static coefficient for bond break effects kh horizontal pseudo-static coefficient kv vertical pseudo-static coefficient M earthquake magnitude mb body wave magnitude mi material constant for intact rock

ML local magnitude

Ms surface wave magnitude mu upper bound magnitude for the exponential recurrence model

Mw moment magnitude

M0 seismic moment 0 m threshold magnitude for the exponential recurrence model Ṅ(mc) Characteristic rate

R source-to-site distance RA rupture area R-factor seismogenic scaling factor S average seismic slip rate Sa Spectral acceleration T spectral period

Ts recurrence interval T* period of interest

Vs,30 shear wave velocity in the upper 30 m W weight of the failure mass

Ztor depth to the top of rupture

Z1.0 depth to shear wave velocity of 1 km/s

Z2.5 depth to shear wave velocity of 2.5 km/s  unit weight of the failure mass ε ground motion uncertainty

λ m annual activity rate of earthquakes of magnitude greater than m μ rigidity of shear modulus which is usually taken to be 3×1011 dyne/cm2 ν activity rate, complementary cumulative earthquake rate for m > m0 ρ correlation coefficient of CMS

ci uniaxial compressive strength of the intact rock

t tensile strength

1 major effective principal stress

 3 minor effective principal stress ’ friction angle of the failure mass

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LIST OF ABBREVIATIONS AFPS French association for earthquake engineering BAAS British association for the advancement of science CMS conditional mean spectra COV coefficient of variation DF disturbance factor DSHA deterministic seismic hazard analysis EC European seismic code provision FS factor of safety GMPE ground-motion prediction equation GSI geological strength index ISC International seismological centre KPSZ Kohat-Potwar-Salt range seismic zone LC landslide concentration LS least square method MBT main boundary thrust MCT main central thrust MKT main karakoram thrust ML maximum likelihood method MMT main mantle thrust NEHRP national earthquake hazards reduction program NGA next generation of ground-motion attenuation models NOAA national oceanic and atmospheric administration PGA peak ground acceleration PGV peak ground velocity PMD Pakistan meteorological department PHSZ Peshawar-Hazara seismic zone PSHA probabilistic seismic hazard analysis SA spectral acceleration SASZ Swat-Astor seismic zone SKSZ Surghar-Kurram seismiczone

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UHS uniform hazard spectra USGS U.S. geological survey V/H ratio vertical-to-horizontal acceleration ratio WGCEP working group on California earthquake probabilities

CHAPTER 1. INTRODUCTION

1.1 Statement of the problem We have been experiencing numerous catastrophic earthquakes all around the world. As there are no reliable means to predict the timing of these earthquakes, engineers focus on preventing significant earthquake loss by designing earthquake-resistant new structures and seismically mitigating existing structures based on proper seismic hazard analysis. However many of current seismic studies employ areal source zones for the region where no sufficient information of faults is available [e.g. Africa (Mavonga and Durrheim 2009); Caribbean Islands (Bozzoni et al. 2011); India (Jaiswal and Sinha 2007); Indonesia and Malaysia (Petersen et al. 2004); Portugal (Vilanova and Fonseca 2007); Spain (Mezcua et al. 2011); United Arab Emirates (Aldama-Bustos et al. 2009)]. The prior seismic hazard studies for NW Pakistan were also conducted based on the diffuse areal source zones, resulting in the distribution of seismic hazard to known faults throughout the entire source area, and thus underestimating ground acceleration. This may cause a serious problem to seismic design for socio-economically important cities located close to major faults like Islamabad and Muzaffarabad. Furthermore, the currently-used seismic slope stability analysis cannot explain the trend of earthquake-induced landslides distribution which is an important aspect that needs to be considered for seismic design. Specifically, the pseudo-static slope stability analysis approach predicts high factor of safety near a fault, which is inconsistent with the observation of high concentration of landslides near a fault. Therefore, it is necessary to investigate the factors that affect the seismic slope stability, in addition to the strong horizontal acceleration.

1.2 Objectives and scope of study The main purpose of this study is to present the methodology and results of seismic hazard analysis using discrete faults and seismic slope stability analysis in NW Pakistan. To achieve this goal, the deterministic and probabilistic seismic hazard analyses are performed for selected major cities using input parameters developed based on available information on seismicity and characteristics of discrete faults. The seismic hazard map corresponding to 475-, 975-, and 2475-year return periods are generated for the entire region of NW Pakistan. Use of the conditional mean spectrum instead of the uniform hazard spectrum is also introduced.

To evaluate the regional performance of earthquake-induce landslide during the 2005 Kahsmir, Pakistan, earthquake, three possible factors are introduced: (1) vertical ground accelerations; (2) topographic effects; and (3) “bond break” effects. The new approach using these three factors is verified by landslide data from three additional earthquakes: 1989 Loma- Prieta, U.S.; 1999 Chi-Chi, Taiwan; and 2008 Wenchuan, China earthquakes.

1.3 Organization of the thesis Chapter 2 introduces prior seismic hazard studies in NW Pakistan, and describes the disadvantage of these studies due to the use of diffuse areal source zone. Chapter 3 describes the methodology of a deterministic seismic hazard analysis for NW Pakistan using discrete faults. This chapter presents source characterization and selection of ground motion prediction models as well as the result of sensitivity analysis and verification of methodology by comparing with measurements from the 2005 Kahsmir, Pakistan, earthquake. Chapter 4 describes characterization of recurrence models for a probabilistic seismic hazard analysis. The results from both deterministic and probabilistic seismic hazard analyses are summarized in Chapter 5, comparing with the results from prior studies using areal source zones. Based on deaggregation results, a discussion of the conditional mean spectra for engineering applications is presented in this chapter. Chapter 6 introduces the characteristics of earthquake-induced landslides and genera approaches to analyze seismic slope stability. This chapter also raises the problem of currently- used pseudo-static slope stability analysis using landslide database from the 2005 Kahsmir, Pakistan, earthquake. Chapter 7 proposes the possible factors that affect the slope stability, resulting in better understanding of regional distribution of earthquake-induced landslides. Chapter 8 verifies the new approach to pseudo-static slope stability analysis using four earthquake cases. Finally, conclusions are reached in Chapter 9, and possible future developments are suggested.

CHAPTER 2. PRIOR SEISMIC HAZARD STUDIES IN NW PAKISTAN

2.1 Introduction Several seismic hazard studies recently have been conducted for regions of Pakistan because of its active tectonic setting, including studies by Monalisa et al. (2007), NORSAR and Pakistan Meteorological Department (PMD) (2006), and PMD and NORSAR (2006). While these studies incorporate historical and instrumented earthquakes, each involves some potentially limiting assumptions regarding seismic source zone characterization and earthquake catalog construction. This chapter summarizes the key features and drawbacks of these prior studies.

2.2 Monalisa et al. (2007) Monalisa et al. (2007) presented a probabilistic seismic hazard analysis (PSHA) for the NW Himalayan belt. Their earthquake catalog includes 1057 instrumentally-recorded earthquakes (Mw ≥ 4) obtained chiefly from the International Seismological Centre (ISC) and U.S. Geological Survey (USGS). Based on this and other geological information, Monalisa et al. (2007) defined four diffuse seismic source zones: the Peshawar-Hazara, Surghar-Kurram, Kohat- Potwar-Salt Range, and Swat-Astor seismic zones (PHSZ, SKSZ, KPSZ, and SASZ, respectively). The corresponding recurrence relations, characterized by b-values, annual activity rates, and upper bound magnitudes (mu), were developed for each seismic source zone. The activity rate and b-value were estimated by earthquake data in each zone, and the upper bound magnitude was estimated by the relationship between magnitude and rupture length (Bonilla et al. 1984; Nowroozi 1985; Slemmons et al. 1989; Wells and Coppersmith 1994). The depth for each seismic zone was defined as the average focal depth of earthquakes in that zone. Monalisa et al. (2007) performed a PSHA using the Ambraseys et al. (1996) and Boore et al. (1997) attenuation relations to predict peak ground accelerations (PGA) for 10 cities, including Islamabad and Muzaffarabad. Careful review of this study called attention to the unexpectedly low ground motions. For example, the PGA with 475-year return period [i.e., 10% probability of exceedance (PE) in 50 years] for Islamabad is only 0.10g and 0.15 g with the attenuation relations of Ambraseys and Simpson (1996) and Boore et al. (1997), respectively, despite Islamabad being located within 4 km of the seismically-active MBT. Similarly, the PGA with 475-year return period is only 0.12g for Muzaffarabad, despite its proximity to the active

Jhelum Fault and Riasi Thrust. PGA values for other cities calculated by Monalisa et al. (2007) are shown in Table 2.1. The seismic hazard is likely underestimated because of the following reasons: 1. Diffuse areal source zones. Areal source zones are useful where faults are not well- characterized. However, the source zones defined by Monalisa et al. (2007) are too diffuse to capture seismicity adjacent to discrete faults. Furthermore, the source zones appear to have neglected the east section of the MBT, which plays an important role in the regional seismic hazard. 2. Incomplete earthquake catalog. The earthquake catalog is missing major events, including the 1555 Kashmir, 1905 Kangra, and 2005 Kashmir earthquakes. In addition, the instrumented earthquake catalog appears incomplete, as illustrated in Figure 2.1. Note that the apparent increase in seismicity in both catalogs in the latter part of the 20th century results from an increase in seismic monitoring, not an increase in actual seismicity. 3. Inconsistency between hazard curves and tabulated PGAs. Values of PGA read from the hazard curves and those tabulated by Monalisa et al. (2007) did not match for many cities. For example, the PGAs reported for Peshawar were 0.14g and 0.15g with 475-year return period using the two attenuation relationships. However, the corresponding PGAs obtained from the hazard curves were approximately 0.32g. Similarly, PGAs reported for Muzaffarabad were 0.10g and 0.13g with 475-year return period, but the hazard curves showed PGAs of about 0.14g and 0.16g.

2.3 PMD and NORSAR (2006) The Pakistan Meteorological Department (PMD) and NORSAR (2006) computed seismic hazard for Azad Kashmir and northern Pakistan using a PSHA based on diffuse areal source zones. The region was divided into 16 diffuse source zones based on tectonic setting and local seismicity. The earthquake catalog used in their study was based chiefly on the NORSAR database which was collected from agencies worldwide (Mw ≥ 4.5) (PMD and NORSAR 2006). Another main source was the PMD database containing historical earthquakes from 1905 and most recent instrumented earthquakes. Recurrence relations and focal depths for each source zone were developed from earthquakes assigned to each zone. The attenuation model proposed by Ambraseys et al. (1996) was used to establish the seismic hazard contour map of PGA values for return periods of 100, 500, and 1000 years.

The PSHA results yielded low PGA values for Islamabad and Muzaffarabad (see Table 2.1). The PGAs for Islamabad for return periods of 500 years and 1000 years are 0.20g and 0.26g, respectively. The PGAs for Muzaffarabad are 0.20g and 0.31g for return periods of 500 and 1000 years, respectively. The likely reason for the low PGAs is that using diffuse areal source zones tends to “smear” local seismicity corresponding to known faults throughout the entire source area, thereby decreasing seismic hazard at locations proximate to active faults.

2.4 NORSAR and PMD (2006) NORSAR and PMD (2006) performed PSHA for the cities of Islamabad and Rawalpindi. The earthquake data obtained from the databases of the ISC, USGS, EHB, NORSAR, and PMD were used. Based on seismo-tectonic setting, 11 shallow area source zones that cover shallow earthquakes, and one deep zone that covers deep earthquakes in Hindu Kush region were defined. However the deep source zone was ignored in their study because it is far from the target cities and does not affect the hazard results. Like other studies (PMD and NORSAR 2006; Monalisa et al. 2007), recurrence relations were developed for each source zone using the earthquakes assigned to each zone. In addition to area source zones, NORSAR and PMD (2006) modeled the Jhelum fault (a strike-slip fault in NW Pakistan) in two segments, and they used the Ambraseys et al. (1996) attenuation relation. PGA values were reported for a grid of 20 points in a single seismic zone, covering Islamabad and Rawalpindi, and values ranged from 0.19g to 0.21g with 500-year return period. These PGAs again are quite low considering that the seismically-active MBT crosses the study area.

2.5 Summary The prior seismic studies for NW Pakistan used diffuse areal source zones, resulting in the PGAs of about 0.1 to 0.2g for 475- or 500-year return period for Muzaffarabad. Considering that Muzaffarabad is the city that was severely affected by the 2005 Kashmir earthquake and located proximate to active faults, this low PGA prediction for Muzaffarabad is unreasonable. PGAs estimated for other cities also rarely exceed 0.2g. Another observation is that PGAs show little variation among cities regardless of their proximity to faults.

Table 2.1 PGAs predicted by Monalisa et al. (2007) for 475-year return period using attenuation relations by Ambraseys et al. (1996) and Boore et al. (1997), and by PMD and NORSAR (2006) for 500-year return period using attenuation relation by Ambraseys et al. (1996).

PGA (g) Site Monalisa et al. (2007) PMD and NORSAR (2006) Ambraseys et al. (1996) Boore et al. (1997) Ambraseys et al. (1996) Astor 0.07 0.082 0.28 Bannu 0.06 0.08 0.08 Islamabad 0.10 0.15 0.20* Kaghan 0.09 0.12 0.20 Kohat 0.20 0.21 0.13 Malakand 0.20 0.21 0.20 Mangla 0.16 0.18 0.10 Muzaffarabad 0.14† 0.16† 0.20 Peshawar 0.32† 0.32† 0.20 Talagang 0.15 0.16 0.12 *NORSAR and PMD (2006) reported PGA values for Islamabad ranging from 0.19g to 0.21g with 500-year return period. †Values from the hazard curves, which are inconsistent with tabulated values in Monalisa et al. (2007).

800 Monalisa et al. (2007) This study

600

f o

400

u N 200

0 1 2 21 31 41 51 61 7 81 91 0 Time 2 9 9 9 9 9 9 9 9 0 02 91 -1 -1 -1 -1 -1 -1 -1 -1 -2 0 (year) 1 2 2 2 2 2 62 2 2 92 2 < 1 2 3 4 5 9 7 8 9 > 19 19 19 19 19 1 19 19 1

Figure 2.1 Instrumented earthquake (Mw ≥ 4.0) from the composite catalog used in this study with time compared with catalog used by Monalisa et al. (2007). The area considered is 69.5 °E – 75.5 °E, 31.5 °N – 36.5 °N.

CHAPTER 3. DETERMINISTIC SEISMIC HAZARD ANALYSIS

3.1 Introduction DSHA has an advantage in that less information is required for fault recurrence rates which is not widely available for NW Pakistan. However, DSHA cannot account for the probability of occurrence of earthquakes. The four steps for a typical deterministic seismic hazard analysis (Reiter 1990) are illustrated in Figure 3.1 and include: 1) Characterization of all possible earthquake zones. This step includes definition of geometry and maximum potential magnitudes of source zones. 2) Selection of source-to-site distance. Generally, the shortest distance to rupture or the shortest horizontal distance from source to site is used as a distance, depending on attenuation relationships also known as ground-motion prediction equations (GMPEs). 3) Selection of the controlling earthquake source in terms of the ground motion parameters. In this step, GMPEs are used the ground motion parameters such as acceleration and velocity at a given magnitude and distance from the source to the site. Comparing all possible source zones, one controlling source zone is selected. 4) Computation of seismic ground motions parameters at the site. Usually, ground acceleration is used.

This chapter describes the methodology of a deterministic seismic hazard analysis (DSHA) (Reiter 1990) for NW Pakistan using information available for individual, discrete faults, rather than diffuse source zones. The tectonic settings and the earthquake catalog compilation were introduced, followed by explanation on fault characterization and selection of GMPEs. This chapter also presents the results of sensitivity analyses for input parameters and validates the developed methodology by comparison with measurements from the 2005 Kashmir, Pakistan, earthquake.

3.2 Tectonic settings Pakistan is located in a highly seismic area and has experienced large and destructive earthquakes historically and in recent times. The most recent severe earthquake occurred on 8 October 2005 in Kashmir, with a moment magnitude of 7.6 and focal depth of 26 km, and was

followed by numerous aftershocks (U.S. Geological Survey (USGS) 2010). This earthquake resulted in at least 86,000 fatalities and more than 69,000 injuries (USGS 2010). The earthquake also triggered over 2,400 landslides, extensive liquefaction in alluvial valleys, and numerous building collapses (Bhat et al. 2005; Jayangondaperumal et al. 2008; Aydan et al. 2009). These consequences in a moderately populated region brought renewed attention to seismic hazards in Pakistan. Pakistan lies on the Indian Plate, which forms the Himalayan mountain ranges and flexures due to collision into the Eurasian Plate at a rate of about 45 mm/year and rotates counterclockwise (Sella et al. 2002) (Figure 3.2). This rotation and translation of the Indian Plate causes left-lateral slip in Baluchistan at 42 mm/year and right-lateral slip in the Indo-Burman ranges at 55 mm/year (Bilham 2004). The two main active fold-and-thrust belts in northwestern Pakistan region are the Sulaiman belt and the northwest (NW) Himalayan belt as shown in Figure 3.2. The Sulaiman mountain belt at the northwestern margin of the Indian subcontinent contains the Chaman fault where the 2008 Balochistan earthquake (Mw 6.4) occurred (Monalisa and Qasim Jan 2010). This focuses on the NW Himalayan belt (area highlighted in Figure 3.2). Faults along the Himalayan belt have produced countless earthquakes, including at least four great (Mw > 8) earthquakes in 1505, 1803, 1934, and 1950. Bilham and Ambraseys (2005) suggested that there is “missing slip” in the Himalayas, reporting that the calculated slip rate of less than 5 mm/yr from the earthquake data over the past 500 years is less than one-third of the observed slip rate (18 mm/yr) in the past decade. This missing slip is equivalent to four about Mw 8.5 earthquakes that could occur in the near future (Bilham and Ambraseys 2005). The NW Himalayan belt includes several major thrusts, such as the MMT (Main Mantle Thrust) and MBT (Main Boundary Thrust), which have produced several great earthquakes. The faults and seismicity in NW Himalayan belt are shown in Figure 3.3.

3.3 Earthquake catalog For this study, a new earthquake catalog has been complied, incorporating historical and instrumented seismicity. Historical earthquakes were obtained from the earthquake database of the National Oceanic and Atmospheric Administration (NOAA) and reviewed based on the literature. Table 3.1 provides details related to the historical earthquakes incorporated in the current catalog.

Figure 2.1 includes instrumented earthquakes in NW Pakistan from catalogs available from the USGS, British Association for the Advancement of Science (BAAS), International Seismological Summary (ISS; 1918~1963), International Seismological Centre (ISC;

1964~present), and PMD. These catalogs use different magnitude scales such as Mw, surface wave magnitude (Ms), body wave magnitude (mb), and local magnitude (ML). These magnitudes were converted to Mw using conversions from Grunthal and Wahlstrom (2003) for ML and Ms, and conversions from Johnston (1996) and Hanks and Kanamori (1979) for mb. Table 3.2 summarized the conversions used in this dissertation. Figure 2.1 compares the catalog used in this dissertation to that used by Monalisa et al. (2007). The discrepancy in these two catalogs results from using different source information. Table 3.3 summarizes the Mw > 6 instrumented earthquakes in NW Pakistan. Duplicate and manmade events among these catalogs were removed while developing a combined historical and instrumented catalog (1505~2006).

3.4 Source characterization Based on the literature and regional tectonic settings, 32 faults in NW Pakistan were identified as shown in Figure 3.3. The earthquakes in northwestern corner of Figure 3.3 were assigned to the Main Karakoram Thrust (MKT) which is not included in this study because this fault is far from the major cities in NW Pakistan, and therefore, will not significantly affect the seismic hazard for these cities. Because the identified faults in NW Pakistan are densely located, the surface projections of these faults cover most of earthquakes illustrated in the figure. Some earthquakes that were difficult to attribute to a specific fault were assigned to the nearest fault, thus a background source model was not considered in addition to the fault models.

3.4.1 Fault geometry Table 3.4 summarizes the geometries for the 32 fault segments considered in this study. Most of characterized faults in NW Pakistan are thrust faults created by compressional stresses due to plate convergence. Other faults, including the Darband, Hissartand, Kund and Nowshera faults, were considered to be normal faults based on the difference of plate motion velocities (52 mm/year and 38 mm/year) measured by Bendick et al. (2007) as shown in Figure 3.3. The USGS divides large faults in California into multiple segments to account for differences in slip rate, maximum magnitude, fault geometry, etc. On this basis, the MBT, one of the chief faults in

the region, was divided into a west segment striking E-W and an east segment striking NW-SE. These segments are subject to different tectonic mechanisms due to their differing orientations. The lengths of faults range from 35 km to 340 km. The other parameters needed to define the fault geometry are dip, depth to top of rupture (Ztor), and depth to bottom of rupture (D), and are illustrated in Figure 3.4. Faults striking from west to east were assumed to dip northward, while faults striking northwest to southeast were assumed to dip northeastward due to the movement of Indian Plate which subducts underneath the Eurasian Plate (McDougall and Khan 1990; Mukhopadhyay and Mishra 2005; Bendick et al. 2007; Raghukanth 2008). It was assumed that thrust faults dip at 30°, while normal and reverse faults dip at 60° due to lack of information on fault dip angle. The Dijabba, Jhelum, and Kalabagh faults are strike-slip (McDougall and Khan 1990; Dasgupta et al. 2000) and were assumed to dip at 90°. Since major cities are located on the footwall side of faults, the influence of dip angles on seismic hazard for these cities is limited, although further study of dip angle may improve the seismic hazard characterization for hanging wall zones. Many of the faults in NW Pakistan lack sufficient characterization to assign other geometric parameters such as top of rupture depth, Ztor, and bottom of rupture depth, D. Therefore, the geometry of well-studied faults in the western U.S. was considered as analogs for some faults in NW Pakistan. Many faults in NW Pakistan and the western U.S. are shallow crustal faults located along plate boundaries and are of similar age (McDougall and Khan 1990; Searle 1996; Dipietro et al. 2000). The northwestern U.S. is located in a collision zone forming the Cascadia subduction zone, resulting in numerous shallow crustal reverse faults. While the San Andreas fault is largely a transform fault, there are several compressional regimes that produce oblique and reverse B-type faults. (B-type faults are major faults with measurable slip rate but inadequate information on segmentation, displacement or date of last earthquake) (WGCEP 2008). While this comparison is limited, it is anticipated that these faults are reasonably analogous to provide missing information on Ztor and D. Based on this assumption, yet limited, analog, identical values of Ztor and logic tree branch weights were assigned to all 32 fault segments. The logic tree branch weights assigned here were used by Petersen (2008) for the

USGS seismic hazard mapping project. Specifically, Ztor = 0, 2 km, and 4 km were assigned based on Mmax for each fault. The logic tree branch weights will be discussed in Section 3.6. A variable depth D was used, with values of 10 km, 15 km, and 20 km, based on the range of D

used by USGS databases for Intermountain West, Pacific Northwest, and California faults (Petersen 2008) and the fault models of Himalayan Frontal Thrust, MBT, and MCT (Main Central Thrust) in the region of India (Seeber and Armbruster 1981).

3.4.2 Maximum Magnitude, Mmax Tocher (1958) first suggested a correlation between measured earthquake magnitude and rupture parameters such as length and displacement. More recently, Wells and Coppersmith (1994) collected source parameters for 421 historical earthquakes and developed empirical relationships between measured magnitude and rupture area (RA), rupture length, and rupture width. These correlations are often used to estimate the maximum magnitude (Mmax) that a fault is capable of producing. Hanks and Bakun (2002; 2008) and the Working Group on California Earthquake Probabilities (WGCEP) (2003) suggested that the Wells and Coppersmith (1994) correlation slightly underestimates Mmax for large RAs and proposed alternate relationships. In this study, Mmax was estimated using both relationships proposed by and Hanks and Bakun (2008) and the Ellsworth B correlation (WGCEP 2003), identical to the approach used by the USGS

(Petersen 2008) and WGCEP (2008). The Mmax values were then averaged, and this averaged u Mmax was used directly in the DSHA, and was assigned as the upper bound magnitude, m , in the PSHA.

3.4.3 R-factor WGCEP (2003) used a seismogenic factor, R, to account for aseismic slip, i.e., fault creep not contributing to seismicity. The R-factor is calculated as:

R factor 1 bs bl Eq. (3-1)

where bs is slip rate at seismogenic depths and bl is slip rate at greater depths. Values of bs can be estimated from geodetic data and bl can be estimated from either geological or geodetic data. An R-factor of unity implies that all fault slip occurs as earthquakes, while R-factor = 0 implies that all fault slip occurs as aseismic creep. Multiplying the computed fault RA by R-factor reduces the effective rupture area, and in turn, decreases the effective Mmax. Singh (2000) suggested that there is an aseismic zone in the region lying between 35°N-40°N and 66°E-76°E which is adjacent to the current study area. Therefore, it is possible for faults in NW Pakistan to

experience aseismic creep. Due to lack of geologic and geodetic information for faults in NW Pakistan, R-factors of 0.8, 0.9, and 1.0 were assigned to the NW Pakistan faults with logic tree branch weights in this study based on the values assigned to California faults (WGCEP 2003; WGCEP 2008).

3.4.4 Comparison with historical earthquake records

Table 3.4 provides Mmax values computed from Mmax-RA relationships (where RA is adjusted by R-factors). These values agree well with historical earthquakes. Most of the faults have Mmax values ranging from 7.1 to 7.9, comparable to the major historical earthquakes in the catalog (Table 3.1; Mw ~ 6.3 to 7.8). Faults with computed Mmax > 8, i.e., MBT (west), MBT

(east), MMT, and MCT, are located along the Himalayan belt, and these Mmax values are consistent with the earthquake magnitudes (Mw ~ 8.5) suggested by Bilham and Ambraseys (2005).

3.5 Attenuation relationships and parameters Since no region-specific ground motion prediction model is available for Pakistan, The five ground-motion prediction equations (GMPEs) developed in the Next Generation of Ground- Motion Attenuation Models (NGA) project (Power et al. 2008) were considered. These GMPEs are the Abrahamson-Silva (2008), Boore-Atkinson (2008), Campbell-Bozorgnia (2008), Chiou- Youngs (2008), and Idriss relations (2008), all of which provide horizontal PGA, peak ground velocity (PGV), and 5% damped elastic pseudo-response spectral accelerations in the period range of 0 to 10 seconds for shallow crustal earthquakes. These GMPEs were developed using significant earthquakes along plate boundaries including the 1995 Kobe, Japan and 1999 Chi- Chi, Taiwan earthquakes as well as numerous earthquakes in the western U.S. As discussed earlier, NW Pakistan is also located in a plate convergence region, and contains many shallow crustal faults including the MBT and MMT. Therefore, applying the NGA GMPEs for NW Pakistan was reasonable. For all of the GMPEs, a Site Class B/C boundary condition in the upper 30m (shear wave velocity in the upper 30m, Vs,30 = 760 m/s) was assumed. The Abrahamson and Silva (2008) and

Chiou and Youngs (2008) GMPEs require a depth where Vs = 1 km/s, termed Z1.0. For Vs,30 =

760 m/, Z1.0 = 32 m and 24 m were computed, respectively, using their recommended

correlations. The Campbell and Bozorgnia (2007) relation requires a depth where Vs = 2.5 km/s,

Z2.5. For Vs,30 = 760 m/s, Z2.5 = 0.63 km was computed using their recommended correlation.

Figure 3.5 compares the PGAs predicted using Vs,30 = 760 m/s. As expected, the predicted PGAs for the hanging wall side of a thrust fault exceed the foot wall values until the source-to-site distance exceeds the distance to the surface of the fault plane. The Chiou and Youngs (2008) relation yields significantly larger PGAs than the other attenuation relations at distances to fault less than 15 km; therefore, their relation was not utilized in this study. In all seismic hazard analyses performed in this study, ground motion parameters computed using the remaining four GMPEs were equally weighted. For this regional study, directivity effects were not incorporated. The NGA-West 2 project is currently underway to incorporate directivity in the NGA GMPEs, with the intent to improve on the directivity formulation proposed by Somerville (1997). Future use of these new GMPEs or the use of region-specific GMPEs will improve the seismic assessment in NW Pakistan.

3.6 DSHA logic tree In a DSHA, a logic tree is used to consider alternative options for input parameters and predictive models used to estimate seismic hazard. Figure 3.6 presents the logic tree and branch weights used for all DSHA performed in this study. Weights of 0.4, 0.4, and 0.2 were assigned to D = 10, 15, and 20 km, respectively based on the data for Quaternary faults in the western U.S (Petersen 2008) and the fault models of Himalayan Frontal Thrust, MBT, and MCT in the region of India (Seeber and Armbruster 1981). Weights of 0.2, 0.6, and 0.2 were assigned to R-factor = 0.8, 0.9, and 1.0, respectively, based on data from California faults (WGCEP 2008). Lastly, the four selected GMPEs were equally weighted.

3.7 Controlling faults at selected sites For locations proximate to multiple individual faults (or fault segments), the DSHA was repeated for each fault segment to define the maximum ground motion parameter predicted at the subject location and to identify the corresponding controlling fault. Table 3.5 lists the controlling faults that yield the highest amplitude spectral accelerations at all periods at selected cities in

NW Pakistan. Because of the similarities of most Mmax values, the controlling fault for most

cities considered here is the most proximate fault. However, for some cities like Astor and

Peshawar, more distant faults with larger Mmax values are the controlling faults.

3.8 DSHA sensitivity analysis Sensitivity analyses were conducted to understand the influence of a number of parameters on the DSHA results. The sensitivity analysis using the depth to the bottom of rupture (D) of 10 km, 15 km, and 20 km revealed that D did not significantly influence the computed hazard for Islamabad and Muzaffarabad. These cities are located on the footwall of the controlling faults, and D does not influence the distance to fault for sites located on the footwall. For sites such as Kaghan, located on a hanging wall, the distance to fault does not change if the site is within the horizontal projection of controlling fault, and therefore, D again has little influence on seismic hazard (e.g., median PGAs of 0.73g and 0.70g for Kaghan were obtained using D=10 km and 20 km, respectively). A sensitivity analysis of thrust fault dip angle was also conducted, considering dip angles of 20° and 40°. This analysis revealed that dip angle (within this range) also has no influence on seismic hazard for most of the major cities located on a footwall. The dip angle has a minor influence on seismic hazard for cities located on a hanging wall. The median PGAs of 0.74g and 0.70g were computed for dip angles of 20° and 40°, respectively for Kaghan. This is primarily because Kaghan is located very close to the fault, and dip angle variation does not significantly affect the closest distance to the fault. On the other hand, Peshawar is located on a hanging wall and approximately 40 km away from the fault. Even though of dip angle variation will affect the closest distance to the fault, the difference in computed PGAs is minor due to the small values of PGA. The median PGAs of 0.23g and 0.33g were computed for dip angles of 20° and 40°, respectively for this city. Similarly, the R-factor has little influence on the seismic hazard, at least for the small range of R values applied in this study. Varying R from 0.8 to 1.0 only increases Mmax by approximately 0.1 magnitude units. For Islamabad, an increase in R from 0.8 to 1.0 increased the median PGA from 0.50g to 0.51g. Figure 3.7 illustrates the DSHA sensitivity to the GMPEs. As illustrated in the figure, the Idriss (2008) GMPE predicts higher PGAs while the other three GMPEs (Abrahamson and Silva 2008; Boore and Atkinson 2008; Campbell and Bozorgnia 2008) predict similar PGAs. As expected, the weighted PGAs are close to the PGAs predicted by these latter three relations.

3.9 Comparison with measurements from the 2005 Kashmir earthquake As an initial validation of the fault model developed here, The measured accelerations during the 2005 Kashmir earthquake predicted by DSHA were compared with those reported by Durrani et al. (2005). In order to predict the ground motion based on the methodology proposed in this study, all parameters and weights proposed in this thesis were considered except for the location of rupture. The 2005 Kashmir earthquake rupture was approximately 60 km long, with a focal depth of about 26 km (USGS 2010). The focal depth was assumed as the depth to the bottom of rupture because most of the aftershocks occurred at shallower depths (Bendick et al. 2007) and other studies also reported similar depths to the bottom of rupture (Durrani et al. 2005; Bendick et al. 2007). Using a dip angle of 30° as assumed for thrust faults in NW Pakistan, maximum magnitudes of 7.60, 7.66, and 7.71 were computed for R-factors of 0.8, 0.9, and 1.0, respectively. These magnitudes are consistent with the reported magnitude (Mw 7.6); therefore, these computed magnitudes in the DSHA were used with branch weights shown in Figure 5. Ztor

= 0 was set because Mw > 7 as described in Figure 3.6. Because site conditions at the recording stations are not known, subsurface conditions at each recording station were assumed to correspond to Site Class C (very dense soil and soft rock) with Vs,30 = 560 m/s and Site Class D

(stiff soil) with Vs,30 = 270 m/s. The DSHA was performed for both Site Classes, and for Vs,30 =

560 m/s and 270 m/s, Z1.0 = 130 m and 500 m were computed, respectively (Abrahamson and

Silva 2008), and Z2.5 = 0.99 km and 2.3 km, respectively (Campbell and Bozorgnia 2008). Figure 3.8 presents contour maps of median and 84th percentile (median plus one standard deviation, ) PGA, respectively, for Site Class B/C boundary conditions corresponding to Vs,30 = 760 m/s. Figure 3.9 shows the predicted PGA attenuation with distance modified to

Site Class C (Vs,30 = 560 m/s) and Site Class D (Vs,30 = 270 m/s) conditions to facilitate comparison to the measured values. The measured values include two PGAs (i.e., two orthogonal directions) at recording stations in Abbottabad, Murree, and Nilore. These data are plotted with a source-to-site distance uncertainty of ±10 km. In addition, horizontal PGAs were recorded on rock at Tarbela Dam and at the base of the Barotha Power Complex. The measurement in Tarbela is suspected to correspond to Site Class B. The mean of all median predictions ± 1σ for

Vs,30 = 560 m/s envelopes the recordings except for the Nilore station. The Nilore measurement was likely affected by the response of the raft foundation where the instrument was placed

(Durrani et al. 2005). Note that for Vs,30 = 270 m/s, the Idriss (2008) GMPE was not used

because it does not apply to Vs,30 < 450 m/s. In this case, the remaining three GMPEs were equally weighted. Overall, it is considered that the comparison is acceptable.

3.10 Summary and discussion In this chapter, the methodology of a deterministic seismic hazard analysis (DSHA) (Reiter 1990) was described for NW Pakistan using information available for individual, discrete faults, rather than diffuse source zones. 32 discrete faults were identified in NW Pakistan based on the literature and regional tectonic settings. Many of these faults lack sufficient characterization to assign geometric parameters such as Ztor, D, dip, R-factor which were assigned based on assumption and analogs with western U.S. faults. Then the maximum magnitudes for faults were estimated using the relationships between rupture area and maximum magnitude, and were compared well with historical earthquakes and earthquake magnitudes suggested by Bilham and Ambraseys (2005). Four GMPEs were selected from NGA project that were developed using earthquakes along plate boundaries. To account for uncertainties, the logic tree was used for input parameters and GMPEs. The sensitivity analyses revealed that the geometric parameters such as Ztor, D, dip, R-factor do not significantly influence the computed seismic hazard. The measured ground accelerations from the 2005 Kahsmir, Pakistan, earthquake were compared with those predicted by DSHA. Because site conditions at the recording stations are not known, the subsurface conditions at each recording station were assumed to correspond to Site Classes C and D. The mean values of all median predictions ± 1σ were in good agreement with the recorded accelerations.

Table 3.1 Major historical earthquakes incorporated in the earthquake database for NW Pakistan. Estimated Estimated Earthquake Year Max. Details Source M w MMI Paghman, 60-km rupture of Afghanistan Chaman fault. Strike- Quittmeyer and 1505 7.0 - 7.8 IX - X (34.60°N, slip and dip-slip Jacob (1979) 68.93°E) movement Kashmir, Pakistan Limited intensity Ambraseys and 1555 7.6 n/a (33.50°N, reports available Douglas (2004) 75.50°E) Alingar Valley, Several hundred Afghanistan fatalities in Alingar Quittmeyer and 1842 n/a VIII - IX (34.83°N, River valley and Jacob (1979) 70.37°E) Jalalabad Basin 3,000 fatalities. Numerous buildings Kashmir, Lawrence (1967) destroyed; large Pakistan Quittmeyer and 1885 6.3 VIII - IX fissures observed; (34.60°N, Jacob (1979) large landslide 74.38°E) Bilham (2004) triggered south of Baramula Chaman, 30-km rupture of Heuckroth and Pakistan Chaman fault; Left- Karim (1973) 1892 6.75 IIV-IX (30.85°N, lateral strike-slip Quittmeyer and 66.52°E) movement Jacob (1979) 20,000 fatalities; Kangra, India 100,000 buildings Ambraseys and (33.00°N, 1905 7.83±0.18 n/a destroyed; limited Bilham (2000) 76.00°E) instrumented data Kaul (1911) available

Table 3.2 Magnitude conversions used in this study. Magnitude conversion relations

2 Grunthal and Wahlstrom (2003) M w  0.67 0.11 0.56 0.08M L  0.046 0.013M L

Grunthal and Wahlstrom (2003) M w  M s

2 Johnston (1996) logM 0  18.28  0.679mb  0.077mb

Hanks and Kanamori (1979) M w  2 3logM 0 10.7

Table 3.3 Major instrumented earthquakes from the composite earthquake catalog used for this study (Mw ≥ 6.0).

Year Latitude Longitude Magnitude (Mw)

1914 32.80 °N 75.30 °E 6.2 1928 35.00 °N 72.50 °E 6.0 1972 36.00 °N 73.33 °E 6.4 1974 35.10 °N 72.90 °E 6.1 1981 35.68 °N 73.60 °E 6.3 1992 33.35 °N 71.32 °E 6.0 2002 35.34 °N 74.59 °E 6.4 2004 33.00 °N 73.10 °E 6.6 2005 34.63 °N 73.63 °E 7.6 2005 34.90 °N 73.15 °E 6.4 2005 34.75 °N 73.20 °E 6.2 2005 34.76 °N 73.16 °E 6.1

Table 3.4 Fault parameters for 32 fault segments considered in this study. Maximum magnitude computed based on Ztor = 0, D = 15 km, and R-factor = 0.9. R, N, and SS denote reverse, normal, and strike-slip, respectively. Max. Activity rate Characteristic rate Fault Dip Length Slip rate Fault name Type magnitude (year-1) (year-1) ID (°) (km) (mm/yr) (Mw) 1 2 A B C 1 Balakot Shear Zone R 60 44 6.9 0.56 0.824 0.000 0.00048 0.00040 0.00049 2 Batal Thrust R 30 65 7.4 0.83 0.745 0.133 0.00068 0.00057 0.00036 3 Bhittani Thrust R 30 39 7.2 0.17 0.118 0.067 0.00017 0.00016 0.00011 4 Darband Fault N 60 51 7.0 1.21 0.157 0.000 0.00095 0.00008 0.00095 5 Dijabba Fault SS 90 83 7.2 0.37 0.549 0.600 0.00033 0.00122 0.00022 6 Himalayan Frontal Thrust R 30 187 8.0 2.39 0.078 0.067 0.00175 0.00014 0.00046 7 Hissartang Fault N 60 129 7.5 3.08 0.157 0.167 0.00221 0.00034 0.00119 8 Jhelum Fault SS 90 138 7.5 3.30 3.960 0.267 0.00234 0.00235 0.00135 9 Kalabagh Fault SS 90 53 7.0 0.24 0.078 0.033 0.00022 0.00009 0.00020 10 Karak Thrust R 60 80 7.3 0.36 0.157 0.067 0.00032 0.00018 0.00020 11 Khair-I-Murat Fault N 60 152 7.6 4.00 0.471 0.500 0.00279 0.00102 0.00137 12 Khairabad Fault R 60 225 7.8 2.00 0.118 0.100 0.00149 0.00022 0.00057 13 Khisor Thrust R 30 96 7.6 0.43 0.196 0.200 0.00038 0.00041 0.00014 14 Kotli Thrust R 30 65 7.4 0.83 0.039 0.033 0.00067 0.00007 0.00036 15 Kund Fault N 60 85 7.3 2.03 0.039 0.033 0.00151 0.00007 0.00108 16 Kurram Thrust R 30 148 7.8 0.66 0.235 0.267 0.00055 0.00054 0.00015 17 MCT R 30 333 8.3 4.25 1.451 0.600 0.00294 0.00166 0.00054 18 Mansehra Thrust R 30 53 7.3 0.68 2.118 0.134 0.00056 0.00125 0.00034 19 Marwat Thrust R 30 35 7.1 0.16 0.235 0.000 0.00015 0.00011 0.00011 20 MBT west R 30 225 8.1 4.00 0.392 0.400 0.00279 0.00083 0.00068 21 MBT east R 30 333 8.3 4.25 1.803 0.23 0.00294 0.00124 0.00054 22 MMT R 30 340 8.3 4.34 7.373 1.833 0.00300 0.00651 0.00054 23 Nathiagali Thrust R 30 59 7.4 0.27 0.196 0.033 0.00024 0.00015 0.00012 24 Nowshera Fault N 60 80 7.3 1.92 0.392 0.467 0.00144 0.00093 0.00106 25 Punjal Thrust R 30 103 7.7 2.46 0.627 0.500 0.00180 0.00110 0.00075 26 Puran Fault R 60 102 7.4 1.31 4.471 0.533 0.00102 0.00303 0.00060 27 Raikot Fault R 60 63 7.1 0.80 0.706 0.000 0.00065 0.00034 0.00053 28 Riasi Thrust R 30 105 7.7 1.34 1.569 0.300 0.00104 0.00124 0.00040 29 Riwat Thrust R 30 38 7.2 0.17 0.275 0.333 0.00016 0.00066 0.00011 30 Salt Range Thrust R 30 193 8.0 0.87 0.196 0.200 0.00070 0.00041 0.00016 31 Stak Fault R 60 62 7.1 0.79 0.824 1.167 0.00065 0.00226 0.00053 32 Surghar Range Thrust R 30 67 7.4 0.30 0.235 0.167 0.00027 0.00038 0.00013

Table 3.5 Controlling faults and closest source-to-site distance for DSHA conducted for major cities in NW Pakistan. Cities Fault number Fault name Closest distance (km) Astor 22 MMT 23.91 Balakot 8 Jhelum Fault 1.94 Bannu 10 Karack Fault 8.57 Islamabad 20 MBT (west) 3.14 Kaghan 17 MCT 3.42 Kohat 20 MBT (west) 1.55 Malakand 22 MMT 21.09 Mangla 5 Dijabba Fault 8.78 Muzaffarabad 28 Riasi Thrust 1.78 Peshawar 20 MBT (west) 20.76 Talagang 30 Salt Range Thrust 23.56

Figure 3.1 Four steps of a deterministic seismic hazard analysis (Kramer 1996).

Afghanistan Muzaffarabad Islamabad

Pakistan ~ 29 mm/year

~ 44 mm/year

Baluchistan India ~ 42 mm/year

Karachi MBT : Main Boundary Thrust MKT : Main Karakoram Thrust 500 km MMT : Main Mantle Thrust

Figure 3.2 General tectonic setting of Pakistan with the velocities of plate movement from Larson et al. (1999) and Bilham (2004). Major faults with two active belts are shown. The dashed rectangle denotes the study area in Northwestern Pakistan.

36 ˚N

1974 Astor 2002 35 ˚N 1928 2005 2005 Kaghan Zone 1 2005 1885 Balakot Malakand Muzaffarabad Peshawar 34 ˚N Zone 2

Zone 3 Kohat Islamabad 1992

2004 33 ˚N Bannu Mangla 1914 Talagang

32 ˚N 70 ˚E 71 ˚E 72 ˚E 73 ˚E 74 ˚E 75 ˚E

GPS measurement by Bendick et al. (2007) Earthquakes Mw 4 5 6 7 Inferred plate movement based on Larson et al. (1999)

Assumed plate movement

Figure 3.3 Faults in NW Pakistan and earthquakes (Mw ≥4.0) from 1505 to 2006 used in this study. Numbers beside faults for identification; see Table 3.4 for fault names and properties. GPS measurements by Bendict et al. (2007) and inferred plate movements from Larson et al. (1999) are shown as arrows. Zones 1, 2, and 3 were used to group faults to estimate individual fault slip rates from available plate movement velocity data.

Depth to top of rupture (Z ) Dip tor Depth to bottom of rupture (D)

Figure 3.4 Definition of fault geometry parameters.

)

(

n 0.1

o r

G Hanging wall side

Foot wall side k

a AS (2008) AS (2008) e P BA (2008) BA (2008) CB (2008) CB (2008) CY (2008) CY (2008) I (2008) I (2008) 0.01 1 10 100 Distance from the fault (km)

Figure 3.5 PGA predictions for the five NGA GMPEs used in this study using Mw = 7.6, Ztor = 0, D = 15 km, and Vs,30 = 760 m/s for foot wall and hanging wall sides.

Fault geometry Maximum Attenuation magnitude relationship

Seismogenic Depth to the factor AS (0.25) (R-factor) bottom of BA (0.25) rupture (D) 0.8 (0.2) Depth to the CB (0.25) top of rupture 10 (0.4) 0.9 (0.6) I (0.25) (Ztor) 1.0 (0.2) 0 15 (0.4) as above

20 (0.2) NWP 2 km as above Faults

4 km as above

Weights for the depth to the top of rupture, Ztor Magnitude Z = 0 Z = 2 km Z = 4 km range tor tor tor 6.5 M 6.75 0.333 0.333 0.333 6.75 M 7.0 0.5 0.5  7.0 M 1.0  

Figure 3.6 Logic tree for faults in NW Pakistan (NWP) for use in the DSHA. The numbers in parentheses represent the weights assigned to each branch. AS, BA, CB, I represent GMPEs proposed by Abrahamson-Silva (2008), Boore-Atkinson (2008), Campbell-Bozorgnia (2008), and Idriss (2008). The weights for the Ztor are shown in the table.

1.4 84th percentile 1.2

) g

( 0.8

G 0.6 P 0.4 0.2 0 Islamabad Muzaffarabad 1.4 Median 1.2 Weighted AS

1 BA )

g CB

( 0.8

A I

G 0.6 P 0.4 0.2 0 Islamabad Muzaffarabad Figure 3.7 Sensitivity of PGA computed in DSHA to selected GMPEs.

35 N

Kaghan Kaghan

Balakot Balakot 34.5 N

Muzaffarabad Muzaffarabad

34 N

Islamabad Islamabad

33.5 N 72.5 E 73 E 73.5 E 74 E 72.5 E 73 E 73.5 E 74 E

PGA 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 (g)

Figure 3.8 Contour maps of median PGA (left) and 84th percentile PGA (right) for the rupture that occurred during the 2005 Kashmir earthquake using the DSHA procedure and Vs,30 = 760 m/s. A grid spacing of 0.1° × 0.1° was used for computations. For comparison to computed PGAs, measurement stations are shown as black squares. The white line denotes the surface rupture trace.

) 1

(

c c

A 0.1

k a

e (a) Vs,30 = 560 m/s (b) Vs,30 = 270 m/s P 0.01 1 10 100 200 1 10 100 200 Distance from the fault (km) Distance from the fault (km)

Computed Measured Abrahamson-Silva (2008) Abbottabad Boore-Atkinson (2008) Barotha Campbell-Bozorgnia (2008) Murree Idriss (2008) Nilore Meanof all median NGAs Tarbela Mean of all median NGAs  1 

Figure 3.9 Comparison of PGA prediction using DSHA for (a) Site Class C (very dense soil and soft rock, Vs,30 = 560 m/s) conditions and (b) Site Class D (stiff soil, Vs,30 = 270 m/s) conditions, with strong ground motions (Durrani et al. 2005) measured during the 2005 Kashmir earthquake. Two measurements for Abbottabad, Murree, and Nilore are two orthogonal recording directions. Idriss (2008) GMPE does not apply for Vs,30 < 450 m/s. The measurement in Tarbela is suspected to correspond to Site Class B.

CHAPTER 4. PROBABILISTIC SEISMIC HAZARD ANALYSIS

4.1 Introduction The probabilistic seismic hazard analysis (PSHA) can incorporate uncertainties in recurrence, Mmax, GMPE, and other parameters. The main benefit of PSHA is that it allows computation of the mean annual rate of exceedance of a ground motion parameter at a particular site based on the aggregate risk from potential earthquake sources. Similar to DSHA, a typical PSHA consists of four main steps (Figure 4.1): 1) Identification and characterization of earthquake source zones. Uniform probability distributions of potential rupture locations are assigned to each source. 2) Characterization of earthquake recurrence. A recurrence relationship, which specifies the average rate at which an earthquake of some size will be exceeded, is developed. 3) Selection of attenuation relationships. The ground motion parameters at the site are determined using the selected attenuation relationships. 4) Computation of ground motion parameters corresponding to a probability of exceedance. The probabilities that the ground motion parameter will be exceeded during a particular time period for all sources are combined.

For the PSHA, the same fault geometries and GMPEs used in the DSHA were considered. However, PSHA also requires earthquake recurrence characteristics for each fault or source. This chapter describes the methodology to characterize two common earthquake recurrence: bounded exponential magnitude distribution and characteristic earthquake distribution.

4.2 Bounded exponential distribution recurrence model The exponential recurrence distribution was first introduced by Gutenberg and Richter (1954), which can be expressed as:

log m  a  bm Eq. (4-1)

where λm is the complementary cumulative earthquake rate for magnitudes > m (i.e., λm is the annual rate of exceedance of magnitude m), and a and b are constants. Eq. (4-1) can also be expressed in exponential form as:

m  exp  m Eq. (4-2) where α = 2.303a and β= 2.303b. To limit the maximum earthquake magnitude, Cornell and Vanmarcke (1969) proposed the bounded exponential recurrence, which can be expressed as:

0 u 0 exp m  m  exp m  m  u   for m  m Eq. (4-3) m 1 exp mu  m0  where  exp  m0 , m0 is the threshold magnitude (m0 = 4 in this study), and mu is the upper bound magnitude. Thus m0, mu, β, and ν are the important parameters that characterize the recurrence relation for each fault.

4.2.1 Threshold magnitude, m0, and upper bound magnitude, mu The value of m0 defines the starting point of the recurrence relationship. If m0 were set less than Mw 4.0, recurrence would be underestimated because the composite earthquake catalog 0 for NW Pakistan compiled for this study lacks data for Mw < 4.0. Therefore, m was set to be 4.0. For the same reason, previous studies (NORSAR and PMD 2006; PMD and NORSAR 2006; Monalisa et al. 2007) also used m0 values of 4.0 to 4.5. u As noted previously, m was set to be same as Mmax. The USGS (Petersen 2008) assigns uncertainties in mu of 0.2 magnitude unit for epistemic uncertainty, and 0.24 magnitude unit for aleatory uncertainty. Epistemic and aleatory uncertainties were combined in the analyses and a total uncertainty of 0.5 magnitude units was applied to the mean upper bound magnitude.

4.2.2 Activity rate Activity rate, ν in Eq. (4-3), is the complementary cumulative earthquake rate for m > m0. The activity rate for each fault is calculated by dividing the cumulative number of earthquakes occurring along each fault with Mw > 4.0 (starting from large magnitude and working toward

smaller magnitude) by the corresponding time interval (Ts). Earthquakes with large focal depth were excluded from the analysis unless the magnitude was sufficiently large to influence the seismic hazard. Specifically, earthquakes with focal depths > 35 km and Mw < 5, as well as those with focal depth > 45 km and Mw < 6, were excluded. Two estimates of activity rate (as explained below) were computed for each fault as shown in Table 3.4. Figure 4.2 presents the instrumented earthquake distribution in NW Pakistan from 1960 to 2006. As discussed earlier, it is clear that the catalog is incomplete, at least for times prior to about 1972. Therefore, using the sample from entire time interval severely underestimates the mean rate of occurrence. On the other hand, a reduced time interval may not be suitable to define return periods of large earthquakes. Therefore, it is important to determine the time interval where the mean complementary cumulative earthquake rate (λ) remains unchanged over time. The completeness analysis proposed by Stepp (1972) was used for three magnitude groups

(4≤Mw<5, 5≤Mw<6, and Mw≥6). Stepp (1972) suggested that if the slope of the standard deviation of λ (    Ts ) is parallel to the slope of 1 Ts , λ can be considered as stable for that Ts. Figure 4.3 shows the result of completeness analysis for time intervals that increase in 5- year steps, measured from 2006 (i.e., 2002-2006, 1997-2006, 1992-2006, etc.). The events for 4

≤ Mw < 6 are complete during the 5- to 30-year interval. The departure of σλ from after

30-year interval can be explained by incomplete reporting of earthquakes. The events for Mw ≥ 6 are complete during the 55- to 100-year interval. The large earthquakes (Mw≥6) are much fewer than small and intermediate earthquakes (4≤Mw<6) and do not significantly influence the estimate of activity rate. In addition, the σλ for these large earthquakes is slightly higher than, and parallel to the line of during the 25- to 30-year interval. Therefore, “Activity rate 1” was computed for each fault using a 25-year time interval in the earthquake catalog from 1981 to

2006 (Period 1) where λ for 4≤Mw<6 seems reasonably stable. Figure 4.2 clearly shows a spike in the instrumented catalog in 2005, associated with the large number of foreshocks and aftershocks (Mw ≥ 4) accompanying the 2005 Kashmir earthquake. Therefore, it is suspected that the foreshocks and aftershocks associated with this large event could bias the hazard calculation. Thus, “Activity rate 2” was computed for each fault using a 30-year period in the catalog from 1975 to 2004 (Period 2), excluding earthquakes associated with the 2005 Kashmir event. Figure 4.4 compares activity rates 1 and 2 for the faults.

Then, the earthquakes from 1981 to 2006 were declustered using the method by Gardner and Knopoff (1974). The total activity rate using these declustered earthquakes was estimated to be approximately 15.2 per year which is between two values of activity rate using Period 1 (30.7 per year) and Period 2 (9.4 per year). Therefore, it can be concluded that the approach using two activity rates is reasonable.

4.2.3 b-value The b-value establishes the slope of the exponential recurrence model. Figure 4.5 shows the regression lines using Least Square (LS) method and Maximum Likelihood (ML) method (Weichert 1980) for the complementary cumulative rate of observed earthquakes from Period 1

(1981-2006) and Period 2 (1975-2004) for 4≤Mw<6. Figure 4.5 also shows b = 0.8 lines, which is the b-value used by most faults in the USGS seismic hazard mapping project (Petersen 2008). These comparisons illustrate that the regression lines using LS and ML methods poorly fit the data through all magnitude ranges. For earthquakes occurring during Period 1 (1981-2006) in Figure 4.5 (a), the LS line captures the overall trend of earthquake rate, but it significantly underestimates the complementary cumulative earthquake rate for the largest magnitude. On the other hand, the ML line captures the data at small magnitude range and the largest magnitude. The b = 0.8 line is similar to the ML line. For earthquakes for Period 2 (1975-2004) in Figure 4.5 (b), the ML line fails to capture the data above Mw = 4.5, while the LS line fits most of data. The b = 0.8 line is similar to the LS trend line. For declustered earthquakes (1981-2006) in Figure 4.5 (c), the ML and LS lines are similar and fit most of data except for the largest magnitude. The b = 0.8 line is similar to ML and LS lines, but closer to the point for the largest magnitude, maintaining the best fit for small magnitude range. Considering these comparisons, it was concluded that the b = 0.8 line provides a reasonable fit to the earthquake data (especially for small and large magnitudes), and this b- value was used for all faults in NW Pakistan. Varying the b-value from 0.80 to 0.85 does not significantly affect the PGA. For example, the PGAs with 475-year return period for Muazaffarabad using b = 0.80 and 0.85 were estimated to be 0.64g and 0.62g, respectively.

4.3 Characteristic distribution recurrence model Youngs and Coppersmith (1985) observed that large magnitude earthquakes commonly occur at a higher rate than predicted by the exponential distribution model (Figure 4.6). These large earthquake are called the characteristic earthquake. They proposed an alternate recurrence model, termed the characteristic distribution model, that combines an exponential magnitude u distribution up to magnitude m' with a uniform distribution in the magnitude range of m - Δmc to u m at a rate density nmc . The present study used the characteristic model with characteristic magnitude range, Δmc, of 0.5 as suggested by Youngs and Coppersmith (1985). The  characteristic earthquake, Nmc , was estimated by various methods as explained subsequently. The upper bound magnitude was used as the characteristic magnitude for each fault. A total uncertainty of ± 0.5 magnitude units was applied to the mean characteristic magnitude. Characteristic rate is the rate at which the characteristic earthquake occurs and is usually determined using the slip rate estimated by geodetic and geologic evidence, cosmogenic dating methods using 14C, 3He, or 10Be, and paleoseismic data for the region. However, as discussed above, faults in NW Pakistan are not thoroughly investigated and the slip rate of each fault is not accurately known. In addition, the historical seismicity record is not long enough to include the characteristic events. Therefore, it is difficult to estimate the characteristic rate for faults in NW Pakistan. As a result, Kim et al. (2010) only employed exponential recurrence models to evaluate seismic hazard in Islamabad and Muzaffarabad. This study proposes three alternative methods to estimate characteristic rates. These three alternative characteristic rates for mean characteristic magnitude are listed for each fault in Table 3.4.

4.3.1 Characteristic rate A (relation between slip rate and characteristic rate) The slip rates and characteristic rates for 250 faults in the U.S. Intermountain West, 60 faults in the U.S. Pacific Northwest, and 151 A-type and B-type faults in California are compared in Figure 4.7. The two regression fits were tested as shown in Figure 4.7. Although Fit 2 is simpler than Fit 1, the coefficient of determination (R2) for Fit 2 is smaller than that for Fit 1, suggesting that Fit 1 fits data better than Fit 2. Therefore, Fit 1 was selected in this study, which is expressed as:

Characteristic rate  0.0008016Slip rate0.8988 Eq. (4-4)

Bendick et al. (2007) reported that velocities inferred from GPS measurements from 2001 to 2003 for observation sites near Balakot and Islamabad are approximately 52 mm/yr and 38 mm/yr, respectively. It was assumed that the velocity of the Indian Plate in the southern part of the study area and that of the Eurasian Plate in the northern part of the study area are the same as the values observed by Larson et al. (1999) (44 mm/year and 29 mm/year, respectively). The difference in velocities (52 mm/year – 29 mm/year) yields a total compression rate for Zone 1 of approximately 23 mm/year. Similarly, a total extension rate for Zone 2 of about 14 mm/yr can be computed from the difference in velocities of 52 mm/year and 38 mm/year. For Zone 3, the shape of the Khair-I-Murat fault suggested that it is a normal fault formed by differential slip on its northern and southern segments. The MBT west segment is a thrust fault where considerable amount of compression stress occurs. The Khairabad fault, next to the MBT west segment, is also considered as reverse fault. Based on these considerations, the velocity of 44 mm/year was assumed on the southern part of MBT, which results in compressional slip rates of 4 mm/year for the MBT west segment and 2 mm/year to Khairabad fault. Another velocity of 40 mm/year was assumed on the southern parts of the Khair-I-Murat fault. This assumed velocity results in an extentional slip rate of 4 mm/year for the Khair-I-Murat fault . The total slip rate for the remaining faults in Zone 3 is then 4 mm/year based on the difference in the measured velocity (44 mm/year) and the assumed velocity (40 mm/year). The total slip rate for each zone was distributed to individual faults by assuming that slip rate is proportion to fault length. The assigned slip rate was used with Eq. (4-4) to compute the characteristic rate for the mean characteristic magnitude for each fault. The characteristic rates for mc ± 0.5 magnitude units was computed using the relationship between return period and magnitude proposed by Slemmons (1982) as shown below.

Characteristic rate for m 0.5 Eq. (4-5 a) c  0.47 Characteristic rate for mc

Characteristic rate for m 0.5 c  2.12 Eq. (4-5 b) Characteristic rate for mc

4.3.2 Characteristic rate B (relation between activity rate and characteristic rate)

The second method is to assume that the characteristic rate is proportional to the activity rate of each fault. To estimate the overall characteristic rate, earthquakes with Mw > 6.5 over a 100-year period (1907-2006) for NW Pakistan were considered. The completeness analysis (Figure 4.3) indicated that the earthquake catalog compiled in this study provides a reasonably complete representation of moderate to large earthquakes (Mw ≥ 6.0) over this 100-year time frame. The measured earthquake rate for Mw > 6.5 was estimate to be approximately 0.03 (per year) as shown in Figure 4.8. This earthquake rate then was distributed to each fault proportional to its activity rate. Because two different activity rate sets (Activity rate 1 and Activity rate 2) were used, there are also two characteristic rate B sets. The average of the two sets was used in the analysis.

4.3.3 Characteristic rate C (seismic moment balance method) Many researchers (WGCEP 2003; Petersen 2008; WGCEP 2008) use the seismic moment balance method to estimate the characteristic rate of faults. Aki (1966) proposed a relationship between seismic moment, M0, and average fault rupture displacement per event over the slip surface, d.

M 0  RAd Eq. (4-6) where μ is fault rigidity (usually taken to be 3×1011 dyne/cm2).

The average displacement per event can be also expressed as S × Ts where S is the average slip rate and Ts is the recurrence interval (Wallace 1970). Seismic moment can be estimated as a function of earthquake magnitude using the equation below proposed by Hanks and Kanamori (1979).

log M0 1.5M w 16.1 Eq. (4-7)

Using the characteristic magnitude (defined earlier) to compute M0, the characteristic rate can be calculated as: RAS Characeteristic rate  Eq. (4-8) M 0

4.4 Total recurrence Using all the parameters mentioned above, recurrence models for each fault were established. Figure 4.8 presents the total recurrence models (exponential and characteristic models), i.e., the sum of all recurrence models for individual faults in NW Pakistan. The weighted average of activity rates, characteristic rates, and R-factors were used to construct this total recurrence. The complementary cumulative rate of earthquake events for various time intervals and regions were compared with the total recurrence as shown in Figure 4.8. In the small magnitude range, the total complementary cumulative rates of the exponential models are comparable to the observed earthquake rates. They slightly overestimate the middle magnitude range, but fit well the data for magnitude around 6.5 Mw. This phenomenon can be also observed in the fault recurrence model for Northern California (WGCEP 2008). The total complementary cumulative rates for large magnitude range (Mw > 6.5) computed based on 25- to 30-year interval are also consistent with observed earthquake rate using 100-year interval. Therefore, exponential rates appear to be reasonable averages between data in the short interval and data in the long interval. The measured earthquake rates for large earthquakes for all of Pakistan and for only NW Pakistan with two different time intervals (1907-2006 and 1505-2006) are included in Figure 4.8. The maximum earthquake magnitudes in NW Pakistan in both time periods of 1907-2006 and 1505-2006 match with the mean upper bound magnitude – 0.5 magnitude unit. The maximum earthquake magnitude throughout all of Pakistan matches with the mean upper bound magnitude + 0.5 magnitude unit. The predicted earthquake rates from both exponential and characteristic models are comparable to the measured earthquake rates in NW Pakistan in time period of 1907- 2006 and throughout all of Pakistan in time period of 1505-2006. Overall, the total recurrence model is in good agreement with the seismicity data in Pakistan.

4.5 Logic trees for PSHA Figure 4.9 shows the logic tree used for the PSHA. The PSHA logic tree contains the same branches for fault geometry, R-factor, and attenuation relationships as that used in the DSHA. A weight of 0.6 was assigned to the mean upper bound magnitude and 0.2 to the mean upper bound magnitude ± 0.5 units. For the recurrence models, the characteristic model was

weighted at 2/3 and bounded exponential model was weighted at 1/3. These weights were selected because there is evidence that the characteristic recurrence relationship captures the earthquake rate of individual faults better than the bounded exponential recurrence relationship (Youngs and Coppersmith 1985). The two sets of activity rates for the bounded exponential recurrence model were equally weighted. Weights of 0.25 were assigned to the proposed Characteristic rates A and B, and a weight of 0.5 was assigned to Characteristic rate C, the commonly-used moment balance method.

4.6 PSHA sensitivity analysis Sensitivity analyses for two parameters in the PSHA logic tree, earthquake rate and upper bound magnitude, were performed to evaluate the influence of these parameters on the computed seismic hazard. The sensitivity analysis for earthquake rate is shown Figure 4.10. The results are shown for Islamabad and Muzaffarabad for a 2475-, 975-, and 475-year return periods. For Islamabad, the PSHA yielded the highest PGA using characteristic rate A. The PGA estimated using activity rate 1 is significantly high for Muzaffarabad, while the PGA estimated using activity rate 1 is almost the same as that estimated using activity rate 2 for Islamabad. Activity rate 1 includes the numerous aftershocks of 2005 Kashmir earthquake. Therefore, activity rate 1 for the faults near Muzaffarabad (located near the 2005 fault rupture) is greater than activity rate 2. In contrast, there is no significant difference between activity rate 1 and activity rate 2 for faults near Islamabad. The sensitivity of PGA to the mean upper bound magnitude is shown in Figure 4.11. It is notable that the greater magnitudes yield lower PGAs because the characteristic rates were adjusted according to the magnitude. That is, smaller characteristic rates were assigned to larger magnitudes because larger magnitude earthquakes tend to occur less frequently. The weighted average PGA is close to that computed using the mean magnitude value.

4.7 Evaluation of the proposed PSHA procedure Figure 4.12 shows contour maps of PGA for 475- and 2475-year return periods over the same area evaluated using DSHA. The proposed PSHA procedure was used to generate this contour map, and PGAs are reported for Vs,30 = 760 m/s. For Muzaffarabad, the PGAs corresponding to the 475- and 2475-year return periods are approximately 0.6g and 1.0g, respectively, which are consistent with median PGA and 84th percentile PGA, respectively,

obtained from the DSHA of 2005 Kashmir earthquake (Section 3.9). The PSHA and DSHA results compare similarly for Balakot.

4.8 Summary and discussion This chapter describes the methodology to characterize the earthquake recurrence models for faults in NW Pakistan. The important parameters that characterize the bounded exponential 0 u 0 recurrence model are m , m , ν and b-value. If m were set less than Mw 4.0, recurrence would be underestimated because the composite earthquake catalog for NW Pakistan compiled for this 0 study lacks data for Mw < 4.0. Therefore, m = 4.0 was used. The Mmax computed based on the rupture area were used as mu. The completeness analysis revealed that earthquake catalog for 25- to 30-year time interval from 2006 is reasonably complete. Therefore, the “Activity rate 1” for each fault was computed using a 25-year time interval in the earthquake catalog from 1981 to 2006 (Period 1). However, large number of foreshocks and aftershocks accompanying the 2005 Kashmir earthquake were suspected to bias the seismic hazard calculation. Thus, “Activity rate 2” for each fault was computed using a 30-year period in the catalog from 1975 to 2004 (Period 2), excluding earthquakes associated with the 2005 Kashmir event. These activity rates were compared well with the one computed by using declustered earthquakes. It was found that the regression lines using least square and maximum likelihood methods could not fit the overall trend of complementary cumulative earthquake rate. Therefore, b = 0.8, used or most faults in the USGS seismic hazard mapping project (Petersen 2008), was chosen because it provide more reasonable fit to the earthquake data. For characteristic recurrence model, the upper bound magnitude was used as the characteristic magnitude for each fault. Three methods to estimate characteristic rates are described in this chapter. The first method assumes that the characteristic rate is related with the slip rate of faults. The second method employs the assumption that the characteristic rate is proportional to the activity rate. The third method is using the seismic moment balance method proposed by Aki (1966). All these parameters and models were implemented in the logic tree and reasonable weight for each branch of the logic tree was assigned. Sensitivity analyses for earthquake rate and upper bound magnitude were performed to evaluate the influence of these parameters on the computed seismic hazard. The PGA estimated using Activity rate 1 is significantly high for Muzaffarabad due to inclusion events from the 2005 Kashmir earthquake, while the PGA estimated using Activity rate 1 is almost the same as that estimated using Activity

rate 2 for Islamabad. Using the methodology developed in this chapter, the PGAs corresponding to the 475- and 2475-year return periods are approximately 0.6g and 1.0g, respectively, which are consistent with median PGA and 84th percentile PGA, respectively, obtained from the DSHA of 2005 Kashmir earthquake.

Figure 4.1 Four steps of a probabilistic seismic hazard analysis (Kramer 1996).

700 Period 1

600 t

n Period 2

e 500

f 400

r e

b 300 m

u 200 N 100 0 Time 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 (year)

Figure 4.2 Earthquake distribution (31.5°N-36°N, 69.5°E-75.5°E) as a function of time. Two different periods were considered to estimate earthquake recurrence for the faults considered in this study. Period 1 is from 1981 to 2006 and the Period 2 is from 1975 to 2004.







 

0.1 4Mw <5

5Mw <6

Mw  0.01 1 10 100 Time interval, Ts (years)

Figure 4.3 Completeness analysis for NW Pakistan for different magnitudes using Stepp (1972) method. σλ = standard deviation, λ = rate of earthquake occurrence, and Ts = time interval. The solid lines are parallel to 1 Ts .

1 22 1 31

)

1 -

r 5 17 a 26

e 2411 25

y (

20 2

e 28

t 16 8 a

r 21

y 1330 t

i 7 32

v i

t 2 18 c

A 12 0.1 6 3 10

1415 9 23

0.01 0.01 0.1 1 10 Activity rate 1 (year-1) Figure 4.4 Comparison of fault activity rates (Activity rate 1:1982 to 2006; and Activity rate 2: 1975 to 2004). Numbers represent the fault number used in this study (see Table 3.4).

)

1 -

r 100 a

e (a) (b) y

( bML = 0.82 b = 1.17

ML w bLS = 0.96 b = 0.74

M 10 LS

t n

e 1

t 0.1

u n

n 0.01

A 4 4.5 5 5.5 6 6.5 7 7.5 8 4 4.5 5 5.5 6 6.5 7 7.5 8 Magnitude, M Magnitude, M

) w w

1 -

r 100 a

e (c) y

( b = 0.92

ML Least Sqare (LS) method w b = 0.85

M 10 LS

Maximum Likelihood (ML) method

s Line with b = 0.8

t n

e 1

t 0.1

u n

n 0.01

A 4 4.5 5 5.5 6 6.5 7 7.5 8 Magnitude, Mw Figure 4.5 Regression lines using Least Square (LS) method and Maximum Likelihood method (Weichert 1980) for the complementary cumulative rate of observed earthquakes for (a) Period 1 (1981-2006), (b) Period 2 (1975-2004), and (c) declustered catalog (1981-2006). The b = 0.8 line starting from an annual earthquake rate at Mw=4 for each case is also shown.

Figure 4.6 Hypothetical recurrence relationship (Youngs and Coppersmith 1985).

0.1

California faults (A-Type) California faults (B-Type) Intermountain West faults

0.01 Pacific Northwest faults

)

r a

e 0.001

(

a r

a 0.0001

h C

1E-005

Fit 1: Characteristic rate = 0.0008016 Slip rate0.8988 (R2 = 0.9038) Fit 2: Characteristic rate = 0.001 Slip rate (R2 = 0.6427) 1E-006 0.001 0.01 0.1 1 10 100 Slip rate (mm/yr) Figure 4.7 Relationship between slip rates and characteristic rates of western U.S faults. A-type faults in California are divided into several segments, each with a unique slip rate. The characteristic rates for these faults were calculated using three methods [a-priori, Ellsworth of WGCEP (2003), and Hanks and Bakun (2008)] used by WGCEP (2008). Error bars are used to illustrate uncertainties in slip rates and characteristic rates for these faults.

100

) 1

- 10

(

w 1

M M BT > (e ast

s )

t 0.1 M

n BT e (we

v st)

f 0.01

a r

0.001

u n

n 0.0001 A

1E-005 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9

Magnitude, Mw

Earthquakes in NW Pakistan during Period 1 (1981-2006) Earthquakes in NW Pakistan during Period 2 (1975-2004) Declustered earthquakes in NW Pakistan (1981-2006)

Large earthquakes (Mw>6.5) in all of Pakistan (1907-2006)

Large earthquakes (Mw>6.5) in all of Pakistan (1505-2006)

Large earthquakes (Mw>6.5) in NW Pakistan (1907-2006)

Large earthquakes (Mw>6.5) in NW Pakistan (1505-2006)

Total exponential model with mean Mmax and mean Mmax 0.5

Total characteristic model with mean Mmaxand mean Mmax 0.5

MBT exponential model with mean Mmax

MBT characteristic model with mean Mmax

Figure 4.8 Complementary cumulative rate of observed earthquakes and recurrence models from the composite catalog used in this paper. The total recurrence models represent the sum of the recurrence models of all of the individual faults. The recurrence models for the east and west MBT segments are shown as examples.

Attenuation Fault geometry Maximum magnitude Recurrence model relationship

Earthquake rate

Activity rate 1 as below (0.5) Exponential (0.33) Magnitude Activity rate 2 as below uncertainty (0.5) Seismogenic factor Mean + 0.5 (R-factor) AS (0.2) Charcteristic Depth to the (0.25) bottom of rate A 0.8 Mean (0.25) rupture (D) BA (0.2) (0.6) Charact- Characteristic (0.25) eristic rate B Depth to the 10 0.9 Mean - 0.5 (0.67) (0.25) top of rupture CB (0.4) (0.6) (0.2) Characteristic (Z ) (0.25) tor rate C 0 15 1.0 as above (0.5) (0.4) (0.2) I (0.25) NWP 2 km 20 as above Faults (0.2)

4 km as above

Figure 4.9 Logic tree for faults in NW Pakistan used in the PSHA. Numbers in parentheses represent weights assigned to each branch. The weights for Ztor are the same as used for the DSHA (Figure 3.6).

1.4 (a) 1.2

) g

( 0.8

G 0.6 P 0.4 0.2 0 1.4 (b) 1.2

) g

( 0.8

G 0.6 P 0.4 0.2 0 1.4 (c) 1.2 Weighted average 1 Char.A

) Act.1 g

( 0.8 Char.B

A Act.2

G 0.6 Char.C P 0.4 0.2 0 Islamabad Muzaffarabad Figure 4.10 Sensitivity of PGA computed at Islamabad and Muzaffarabad in the PSHA to the characteristic rates and activity rates for return periods of (a) 2475 years (b) 975 years, and (c) 475 years. All other parameters are used with weights shown in the logic tree (Figure 4.9).

1.4 (a) 1.2

) g

( 0.8

G 0.6 P 0.4 0.2 0 1.4 (b) 1.2

) g

( 0.8

G 0.6 P 0.4 0.2 0 1.4 (c) 1.2 Weighted average

1 Mean + 0.5

) g

( 0.8 Mean

A Mean - 0.5

G 0.6 P 0.4 0.2 0 Islamabad Muzaffarabad

Figure 4.11 Sensitivity of PGA computed at Islamabad and Muzaffarabad in the PSHA to the upper bound magnitudes for return periods of (a) 2475 years (b) 975 years, and (c) 475 years. All other parameters are used with weights shown in the logic tree (Figure 4.9).

35 N 0.8 0.9 0.6 Kaghan Kaghan

0.7 Balakot Balakot 34.5 N

Muzaffarabad Muzaffarabad

0.7 34 N

Islamabad Islamabad 1.0

33.5 N 72.5 E 73 E 73.5 E 74 E 72.5 E 73 E 73.5 E 74 E

PGA 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 (g)

Figure 4.12 Contour maps of PGA for 475- (left) and 2475-year (right) return periods using the PSHA procedure and Vs,30 = 760 m/s. A grid spacing of 0.1° × 0.1° was used for computations.

CHAPTER 5. SEISMIC HAZARD RESULTS This chapter summarizes the results of both probabilistic and deterministic seismic hazard analyses performed for the 11 cities for an assumed bedrock with Vs,30 of 760 m/s. (Site effects can be considered separately by performing site response analysis or by applying site coefficients.), using the procedures described in Chapter 3 and Chapter 4. This chapter presents PSHA hazard curves for PGA, PSHA uniform hazard spectra (UHS), and DSHA hazard spectra for the 11 cities and seismic hazard maps of PGA and SAs (T=0.2 and 1.0 sec) for 475-, 975-, and 2475-year return periods. Based on deaggregation results, a discussion of the conditional mean spectra for engineering applications is also presented.

5.1 Islamabad Figure 5.1 presents the seismic hazard curves for PGA at 5% damping and select uniform hazard response spectra for the city of Islamabad. Hazard curves from the top five contributing faults are included in the figure. The PGAs corresponding to 475-, 975-, and 2475-year return periods are approximately 0.35g, 0.48g, and 0.69g, respectively. The individual fault hazard curves illustrate that the MBT west segment contributes the most to the hazard at most commonly-employed return periods. This fault is located closer to the city than any other fault, exhibits a high activity rate, and has a large maximum moment magnitude, Mmax. Response spectra (Figure 5.1b) can be used to evaluate structural response at different natural periods. The SA is highest at T = 0.2 sec (1.73g for a 2475-year return period), while at T = 1.0 sec, SA is estimated to be 0.67g for 2475-year return period, which is similar to the PGA value. Deaggregation of seismic hazard for Islamabad was conducted for three SAs (at T = 0.05 sec, 0.2 sec, and 1.0 sec) for a 475-year return period as shown in Figure 5.2. Deaggregation provides the relative contribution to seismic hazard from each fault (i.e., seismic source) in terms of Mw, source-to-site distance, R, and ground motion uncertainty, ε. The magnitude bin width is

0.2 Mw units, and the distance bin width is 5 km units. The mean and modal values of Mw, R, and ε that correspond to a given maximum amplitude can be calculated from the deaggregation analysis. Mean values of Mw and R are commonly used to represent the controlling earthquake size and location for developing site-specific time histories (Bernreuter 1992; U.S. Department of Energy (U.S. DOE) 1996; U.S. Nuclear Regulatory Commission (U.S. NRC) 1997).

The mean values of Mw, R, and ε for Islamabad are shown in Table 5.1. These mean values of Mw and R can be used to develop conditional mean spectra (discussed in a later

section), perform liquefaction analyses, or analyze seismic slope stability, etc. Modal values are used to select the controlling earthquake when a site is proximate to two equally hazardous faults (Bazzurro and Cornell 1999). For Islamabad, large earthquakes on the nearby MBT west segment dominate the hazard. There is a small contribution from more distant faults for T = 1.0 sec. Deaggregation analyses for 975-and 2475-year return periods show similar trends. A DSHA spectrum (Figure 5.1b) was constructed for the controlling fault (MBT west segment) determined by deaggregation. The median DSHA spectrum is comparable to the UHS for a 975-year return period, while the 84th percentile DSHA spectrum is higher than the UHS for a 2475-year return period.

5.2 Muzaffarabad The seismic hazard results for the city of Muzaffarabad are shown in Figure 5.3. As shown in the PSHA hazard curve, PGAs corresponding to 475-, 975-, and 2475-year return periods are 0.64g, 0.80g, and 1.02g, respectively. These PGAs are greater than those for Islamabad because Muzaffarabad is proximate to more faults with higher activity rates and larger

Mmax. It can be noted that the Jhelum fault contributes most to the hazard. The highest spectral acceleration is 2.70g at a period of 0.2 sec for a 2475-year return period. The deaggregation results for the three SAs (at T = 0.05 sec, 0.2 sec, and 1.0 sec) for a 475-year return period for Muzaffarabad are shown in Figure 5.4. Similar to Islamabad, large earthquakes on the nearby faults dominate the hazard at all return periods and spectral periods.

There is a small contribution from more distant faults for T = 1.0 sec. Mean values of Mw, R, and ε for Muzaffarabad are shown in Table 5.1. DSHA spectra were also constructed for Muzaffarabad using the controlling Riasi fault. Overall, the median DSHA spectrum is similar to the 475-year return period UHS for T > 0.5 sec, but lower than the 475-year return period UHS for T < 0.5 sec, while the 84th percentile DSHA spectrum ranges from the 975-year return period at short periods to the 2475-year return period UHS at long periods.

5.3 Kaghan The seismic hazard results for the city of Kaghan are shown in Figure 5.5. The PGAs for 475-, 975-, and 2475-year return periods are estimated to be 0.58g, 0.75g, and 1.00g, respectively. These values are comparable with those for Muzaffarabad. The MCT fault

contributes significantly to the hazard at PGAs greater than 0.4g. For smaller PGAs, the MMT and the Balakot Shear Zone contribute most to the hazard. The UHS for the 2475-year return period yields SAs of 2.67g and 1.06g at T = 0.2 sec and 1.0 sec, respectively. The 84th percentile DSHA spectrum is in good agreement with UHS for a 2475-year return period, while the median DSHA spectrum falls between the UHS for 475- and 975-year return periods.

5.4 Peshawar The PGAs for 475-, 975-, and 2475-year return periods for the city of Peshawar were estimated to be 0.21g, 0.28g, and 0.38g, respectively, from the hazard curve in Figure 5.6. These PGAs are considerably smaller than those for Islamabad, Muzaffarabad, and Kaghan mainly because of the larger source-to-site distances for Peshawar. The MBT west segment and Hissartang fault are the two primary contributing faults (Figure 5.6a). The MBT west segment contributes slightly more to hazard despite a larger source-to-site distance because it exhibits a larger Mmax and higher activity rate than the Hissartan fault. The SAs at T = 0.2 sec and 1.0 sec for a 2475-year return period are 1.01g and 0.42g, respectively. The median and 84th percentile DSHA spectra are comparable to the UHS for 475- and 2475-year return periods, respectively.

5.5 Summary of seismic hazard analyses for eleven NW Pakistan cities Figure 5.7 compares SAs at T = 0.01 sec (PGA), 0.2 sec, and 1.0 sec computed using both DSHA and PSHA for the 11 cities in NW Pakistan shown in Figure 1 for an assumed bedrock outcrop with Vs,30 = 760 m/s. The highest PGAs are estimated to occur in Kaghan and Muzaffarabad, with PGAs for a 2475-year return period exceeding 1.0g as a result of their proximity to major active faults. Although Islamabad and Kohat are both approximately 5 km away from the MBT west segment, the PGAs for these cities are not as high as Kaghan and Muzaffarabad because they are located on the foot-wall side of the fault. The cities of Astor, Bannu, Malakand, Mangla, Peshawar, and Talagang are located much farther from significant faults; therefore, PGAs for these cities are considerably lower. Accelerations estimated by DSHA are comparable to those from PSHA. In general, median accelerations agree well with those corresponding to 475- or 975-year return periods, while the 84th percentile accelerations are comparable to those corresponding to the 2475-year return period. The PSHA hazard curves, PSHA uniform hazard spectra, and DSHA hazard spectra for the rest of cities are shown in Figure 5.8 through Figure 5.14.

5.6 Comparison with previous studies Figure 5.15 compares PGAs corresponding to a 475-year return period from PSHA and median PGAs from DSHA with those computed in previous studies (PMD and NORSAR 2006; Monalisa et al. 2007). This comparison clearly illustrates the differences between computed seismic hazard using individual faults and that using area sources or diffuse seismicity for cities close to active faults (e.g., Islamabad, Kaghan, Kohat, and Muzaffarabad). However, the differences are smaller for cities located far from active faults. For example at Astor, Monalisa et al. (2007) and PMD and NORSAR (2006) computed PGAs of 0.08g for a 475-year return period and 0.28g for a 500-year return period, respectively. This study yielded similar PGAs: 0.21g for a 475-year return period from PSHA, and median PGA of 0.21g from DSHA because only a few faults exist near this city and the distance between controlling fault (the MMT) and the city is approximately 24 km. Monalisa et al. (2007) and PMD and NORSAR (2006) both predicted the smallest PGA for Bannu (0.07g and 0.08g, respectively). Although the faults near this city have lower activity rates compared to other faults in NW Pakistan, these PGA values appear too small because the city is located less than 10 km from an active fault. In contrast, a PGA of 0.16g was computed for a 475-year return period from the PSHA and a median PGA of 0.30g from the DSHA. Similarly, Islamabad is located less than 5 km from the MBT west segment, one of the most hazardous faults in NW Pakistan. Previous studies predicted very small PGAs for this city: 0.13g by Monalisa et al. (2007) and 0.20g by PMD and NORSAR (2006). In contrast, for Islamabad a PGA = 0.35g was computed for a 475-year return period using PSHA and a median PGA = 0.51g using DSHA. As additional examples, Monalisa et al. (2007) and PMD and NORSAR (2006) computed PGAs of 0.11g and 0.20g for Kaghan, respectively, despite the city being surrounded by several active faults with high activity rates. In contrast, the highest PGAs were computed for this city, with a PGA = 0.58g for 475-year return period (PSHA) and a median PGA = 0.72g (DSHA). Similarly, Monalisa et al. (2007) and PMD and NORSAR (2006) computed PGAs of 0.21g and 0.13g, respectively, for Kohat. However, this city, like Islamabad, is located adjacent to the MBT west segment. As a result, this study computed much larger PGAs, similar to those for Islamabad. Lastly, Muzaffarabad is located close to the epicenter of the 2005 Kashmir earthquake, and experienced severe damage during that earthquake. Moreover, this city is proximate to

several active faults including the MBT(east), MCT, and Jhelum fault. Despite this, Monalisa et al. (2007) and PMD and NORSAR (2006) computed PGAs of 0.15g and 0.20g, respectively, for Muzaffarabad. In contrast, this study computed much larger PGAs: 0.64g with 475-year return period by PSHA and median PGA of 0.54g by DSHA that compare reasonably with those measured in 2005. These values are also comparable with the deterministic prediction (PGA = 0.66g) by Durrani et al. (2005), using the GMPE by Ambraseys et al. (2005a). Only in cities located farther from mapped faults (e.g., Malakand, Mangla, Peshawar, and Talagang) do the PGAs computed in this study compare reasonably with those computed by Monalisa et al. (2007) and PMD and NORSAR (2006). In summary, PGAs estimated in this study using individual faults show distinct differences at cities located at variable source-to-site distances, in contrast to previous studies that used areal source zones, and computed PGAs that rarely exceeded 0.2g and showed little variation among cities. As anticipated, PGAs computed for cities located far from faults (e.g., Astor, Malakand, Mangla, Peshawar, and Talagang) are similar to or slightly higher than those computed using areal source zones. In contrast, PGAs computed for cities located close to faults (e.g., Islamabad, Kaghan, Kohat, and Muzaffarabad) are 2 to 4 times greater than those predicted by previous studies using areal source zones.

5.7 Hazard maps Seismic hazard maps for NW Pakistan were produced using PSHA for an assumed bedrock condition with Vs,30 = 760 m/s (NEHRP B/C boundary) on a 0.1° × 0.1° grid spacing. Figure 5.16 through Figure 5.18 provide seismic hazard maps of PGA for 475-, 975-, and 2475- year return periods, respectively. As higher ground accelerations are expected along the active faults, the hazard map contours generally envelope known faults. As anticipated, the contours are wider on the hanging wall side of reverse and normal faults because higher ground accelerations are predicted on the hanging-wall side than on the footwall side. The largest PGAs (> 0.8g for a 475-year return period) are predicted along the MMT. The next highest PGAs are along the MBT east segment (> 0.6 g) and the MBT west segment (> 0.4g), both for a 475-year return period. The PGAs are computed to be relatively low near the southern faults, including the Kurram Thrust and Salt Range Thrust because of their low activity rates. Figure 5.19 through Figure 5.24 provide seismic hazard maps for SAs (T = 0.2 sec and 1.0 sec) for return periods of 475, 975, and 2475 years. These maps show trends similar to PGA,

with the largest SAs occurring along the MMT. Maximum SAs exceed 2.0g, 2.8g, and 4.0g at T = 0.2 sec for 475-, 975-, and 2475-year return periods, respectively. Again, the hazard maps for SA at T = 1.0 sec are similar to those for PGA, with the largest SAs values occurring along the MMT.

5.8 Conditional mean spectra (CMS)

5.8.1 The CMS framework The uniform hazard spectrum from a PSHA is often used to develop spectrum-compatible ground motions for engineering analysis. This UHS is constructed by enveloping the spectral amplitudes predicted by PSHA at all periods. The amplitude has a corresponding “standard” normal random variable, or ε, computed as:

ln SaT   M ,R,T  T   ln Sa w Eq. (5-1)  ln SaT  where ln SaT  is the natural logarithm of the spectral acceleration at the period of interest; and

ln SaM w , R,T  and  lnSaT  are the predicted mean and standard deviation, respectively, of

(McGuire 1995). No single earthquake will produce a response spectrum as high as the UHS throughout the frequency range considered (Baker and Cornell 2006). For example, the high- and low- frequency portions of a UHS often correspond to different events (i.e., the high-frequency portion of the UHS is often dominated by small nearby earthquakes, while the low-frequency portion of the UHS is often dominated by larger, more distant earthquakes), Therefore, using a UHS as a target or design spectrum, can be conservative if the structures at a site have a narrow range of natural frequencies. A conditional mean spectrum (CMS) accounts for the variation of SA amplitudes and ε for periods of interest, while maintaining the rigor of PSHA. The CMS yields a spectrum that is smaller than the UHS, allowing a more efficient seismic design. The procedure for computing CMS is summarized as follows (Baker 2008).

1) Determine the target SA and the associated Mw, R, and ε at the period of interest (T*).

2) Compute the median and standard deviation of the response spectrum, given Mw and R.

3) Compute ε at other periods, given ε(T*). 4) Compute the CMS.

5.8.2 Application of CMS to two cities in NW Pakistan

Step 1: Determine the target SA and the associated Mw, R, and ε at T*. The UHS for the cities of Islamabad and Muzaffarabad were developed using PSHA (Figure 5.1b and Figure 5.3b). For this example, periods of interest were selected as T* = 0.05 sec, 0.2 sec, and 1.0 sec.

Since the target SA(T*) was obtained from PSHA, the associated Mw, R, and  values can be taken as the mean values from deaggregation. These values are provided in Table 5.1 for return periods of 475, 975, and 2475 years.

Step 2: Compute the median and standard deviation of the response spectrum, given Mw and R. The Next Generation Attenuation (NGA) GMPEs used for the seismic hazard analysis were employed in this step. These GMPEs are: Abrahamson-Silva (2008), Boore-Atkinson (2008), Campbell-Bozorgnia (2008), and Idriss (2008). The CMS were developed separately using each GMPE and later combined using equal weights. Step 3: Compute ε at other periods, given ε(T*). Baker (2008) indicated that conditional mean ε at other periods can be computed as:

* *  *  Ti ,T T  Eq. (5-2)  Ti   T 

* * where  * is the mean value of  Ti  , given  T  ; and T ,T  is the correlation  Ti   T  i coefficient between the ε values at the two periods. Baker (2008) proposed the following relation to define the correlation coefficient:

  T  T  T ,T  1 cos  0.359  0.163I ln min ln max  Eq. (5-3) min max  Tmin 0.189   2  0.189  Tmin 

where Tmin and Tmax are the smaller and larger of the two periods of interest, respectively, and

I is a binary function equal to 1 if T  0.189sec and equal to 0 otherwise. Tmin 0.189 min

Equation (3) is valid only for the 0.05 < T (sec) < 5. Baker and Jayaram (2008) proposed a refined correlation model that is valid over a wider period range of 0.01 to 10 seconds as:

if Tmax < 0.109 sec,   C  T1 , T2  2

else if Tmin > 0.109 sec,   C  T1 , T2  1 Eq. (5-4)

else   C  T1 , T2  4 where

  T  C 1 cos  0.366ln max  1    Eq. (5-5)  2  maxTmin ,0.109

  1  Tmax Tmin  1 0.1051 5   if Tmax  0.2sec C  100Tmax   Eq. (5-6) 2   1 e Tmax  0.0099   0 otherwise

C2 if Tmax  0.109sec C3   Eq. (5-7) C1 otherwise

  Tmax  C4  C1  0.5 C3  C3 1 cos  Eq. (5-8)   0.109 

where Tmin = min(T1,T2), and Tmax = max(T1,T2). Figure 5.25 compares these two correlation coefficients. Step 4: Compute CMS. Using the correlation coefficient proposed by Baker and Jayaram (2008), the CMS at three target periods (T* = 0.05 sec, 0.2 sec, and 1.0 sec) corresponding to the UHS for 2475-, 975-, and 475-year return periods for Islamabad and Muzaffarabad were constructed as shown in Figure 5.26 and Figure 5.27, respectively. For Islamabad, when the SA at T* = 0.05 sec with 475-year return period is selected, the computed CMS is similar to the UHS. The SA for the CMS is only slightly smaller (approximately 0.1 g) than the UHS SA at longer periods. When SA at T* = 0.2 sec with 475-

year return period is considered, the CMS becomes slightly smaller than the UHS at periods of 0.05 sec and 1.0 sec. However the CMS becomes similar to the UHS for PGA and SA at periods > 3.0 sec. The CMS becomes significantly smaller than the UHS at T < 1.0 sec when the SA at T* = 1.0 sec is targeted. The SA at T = 0.2 sec and the PGA are reduced by approximately 0.35g and 0.13 g, respectively. A similar trend can be observed when the UHS for 975-year return period is targeted at periods of 0.05 sec, 0.2 sec, and 1.0 sec, but the difference between the CMS and the UHS becomes larger. When the CMS is generated for SA at T* = 1.0 sec, the SA at T = 0.2 sec and the PGA are reduced by approximately 0.46g and 0.27g, respectively. For the UHS with 2475-year return period, the difference between the UHS and the CMS is substantial. Especially when the SA at T* = 1.0 sec is targeted, the SA at T* = 0.2 sec and the PGA are reduced to approximately 0.86g and 0.33g, respectively. The CMS for Muzaffarabad show greater differences than that for Islamabad (Figure 5.27). When the SA at T* = 1.0 sec for 2475-year return period is targeted, the SA at T* = 0.2 sec and the PGA are reduced by a factor of approximately 2. When the SAs at T* = 0.05 sec and 0.2 sec were targeted, the SA at longer period is significantly reduced.

5.9 Summary and conclusion Using the procedures described in Chapter 3 and Chapter 4, both probabilistic and deterministic seismic hazard analyses performed for the 11 cities. The highest PGAs are estimated to occur in Kaghan and Muzaffarabad, with PGAs for a 2475-year return period exceeding 1.0g as a result of their proximity to major active faults. The cities of Astor, Bannu, Malakand, Mangla, Peshawar, and Talagang are located much farther from significant faults; therefore, PGAs for these cities are considerably lower. In general, median accelerations agree well with those corresponding to 475- or 975-year return periods, while the 84th percentile accelerations are comparable to those corresponding to the 2475-year return period. PGAs estimated in this study using individual faults show distinct differences at cities located at various source-to-site distances, in contrast to previous studies that used areal source zones and computed PGAs that rarely exceeded 0.2 g and showed little variation among cities. PGAs computed for cities located far from faults are similar to or slightly higher than those computed using areal source zones, whereas PGAs computed for cities located close to faults are 2 to 4 times greater than those predicted by previous studies using areal source zones.

This chapter also presents the hazard maps. As higher ground accelerations are expected along the active faults, the hazard map contours generally envelope known faults. The largest PGAs (> 0.8g for a 475-year return period) are predicted along the MMT. The next highest PGAs are observed along the MBT east segment (> 0.6 g) and the MBT west segment (> 0.4g), both for a 475-year return period. It should be noted that the hazard maps are generated based on the identified faults in NW Pakistan, and it is possible that the hazard is underestimated if there are missing faults in the region. The concept of CMS proposed by Baker (2008) was applied to the UHS for cities of Islmabad and Muzaffarabad. The CMS at T* = 0.05 sec and 0.2 sec are not significantly different from the UHS. However, it the difference between the UHS and the CMS is substantial when SA at T* = 1.0 sec is targeted.

Table 5.1 Mean moment magnitude and distance from deaggregation analysis for cities of Islamabad and Muzaffarabad. For Islamabad, all earthquakes correspond to the MBT fault, and for Muzaffarabad, all earthquakes correspond to the Riasi fault. Islamabad Muzaffarabad Return Period Mean Mean Mean Mean period Mean Mean (sec) magnitude distance magnitude distance (years) epsilon epsilon (Mw) (km) (Mw) (km) 0.05 6.8 11 0.53 6.1 4.8 1.38 475 0.2 6.9 11 0.53 6.4 5.1 1.25 1.0 7.3 22 0.51 7.1 9.4 0.95 0.05 7.0 8.1 0.72 6.2 4.4 1.64 975 0.2 7.1 8.7 0.71 6.5 4.4 1.54 1.0 7.4 14 0.67 7.1 7.6 1.22 0.05 7.2 6.5 1.09 6.3 4.0 1.96 2475 0.2 7.2 6.7 1.07 6.5 3.9 1.86 1.0 7.5 8.8 0.98 7.1 6.1 1.55

(a) PSHA hazard curve Total Hazard e

c Jhelum Fault

n a

d 0.1 MBT (west)

e e

c MMT

f Puran Fault

y Riwat Thrust

c 0.01

)

r y

f 475

(

d u

0.001 975 o

p A

2475

t e

0.0001 R 0 0.5 1 1.5 Peak ground acceleration (g) 3 PSHA (2475 years) (b) Spectra PSHA (975 years)

PSHA (475 years) )

g DSHA (84 percentile)

(

n 2

o DSHA (Median)

t c

e 1

p S

0 0.01 0.1 1 10 Period (sec)

Figure 5.1 Seismic hazard analysis results for Islamabad for an assumed bedrock with Vs,30 of 760 m/s. (a) PSHA hazard curves for PGA at 5% damping. The hazards from the top five contributing faults are shown; (b) PSHA uniform hazard spectra (UHS) at various return periods and DSHA hazard spectra.

Figure 5.2 Deaggregation of seismic hazard for Islamabad for 475-year return period at three spectral periods: (a) 0.05 sec, (b) 0.2 sec, and (c) 1.0 sec.

(a) PSHA hazard curve Total Hazard e

c Jhelum Fault

n a

d 0.1 Mansehra Thrust

e e

c MMT

f Puran Fault

y Riasi Thrust

c 0.01

)

475 (

d u

0.001 975 o

p A

2475

t e

0.0001 R 0 0.5 1 1.5 Peak ground acceleration (g) 3 PSHA (2475 years) (b) Spectra PSHA (975 years)

PSHA (475 years) )

g DSHA (84 percentile)

(

n 2

o DSHA (Median)

t c

e 1

p S

0 0.01 0.1 1 10 Period (sec)

Figure 5.3 Seismic hazard analysis results for Muzaffarabad for an assumed bedrock with Vs,30 of 760 m/s. (a) PSHA hazard curves for PGA at 5% damping. The hazards from the top five contributing faults are shown; (b) PSHA uniform hazard spectra (UHS) at various return periods and DSHA hazard spectra.

Figure 5.4 Deaggregation of seismic hazard for Muzaffarabad for 475-year return period at three spectral periods: (a) 0.05 sec, (b) 0.2 sec, and (c) 1.0 sec.

(a) PSHA hazard curve Total Hazard e

c Balakot Shear Zone

n a

d 0.1 Mansehra Thrust

e e

c MMT

x e

MCT

y Puran Fault

c 0.01

)

f y

475

(

d u

0.001 975 o

p A

2475

t e

0.0001 R 0 0.5 1 1.5 Peak ground acceleration (g) 3 PSHA (2475 years) (b) Spectra PSHA (975 years)

PSHA (475 years) )

g DSHA (84 percentile)

(

n 2 DSHA (Median)

t c

e 1

p S

0 0.01 0.1 1 10 Period (sec)

Figure 5.5 Seismic hazard analysis results for Kaghan for an assumed bedrock with Vs,30 of 760 m/s. (a) PSHA hazard curves for PGA at 5% damping. The hazards from the top five contributing faults are shown; (b) PSHA uniform hazard spectra (UHS) at various return periods and DSHA hazard spectra.

(a) PSHA hazard curve Total Hazard e

c Hissartang Fault n a MBT (west)

d 0.1

e e

c MMT

x e

Nowshera Fault

y Puran Fault

c 0.01

)

f y

475

(

d u

0.001 975 o

p A

2475

t e

0.0001 R 0 0.5 1 1.5 Peak ground acceleration (g) 3 PSHA (2475 years) (b) Spectra PSHA (975 years)

PSHA (475 years) )

g DSHA (84 percentile)

(

n 2

o DSHA (Median)

t c

e 1

p S

0 0.01 0.1 1 10 Period (sec)

Figure 5.6 Seismic hazard result for Peshawar for an assumed bedrock with Vs,30 of 760 m/s. (a) PSHA hazard curves for PGA at 5% damping. The hazards from the top five contributing faults are shown; (b) PSHA uniform hazard spectra (UHS) at various return periods and DSHA hazard spectra.

)

g (

1.5

o i

t (a) PGA

a r

e 1

c a

0.5

c e

p 0 S 3 (b) SA (T=0.2 sec)

) 2.5

(

o i

t 2

l e

c 1.5

a r

t 1

e p S 0.5

) 0

g (

1.5

n o

i (c) SA (T=1.0 sec)

a r

e 1

c a

0.5

c e

p 0 S ad t d d b r g r o u a n t n la a a n o k n ab ha a a g ar w a st la n g h ak n f a g a a m a o l a af sh la A B B la K K a M z e a Is M u P T M PSHA DSHA 475-yr return period 84 percentile 975-yr return period Median 2475-yr return period

Figure 5.7 Comparisons of spectral accelerations computed by PSHA at 475-, 975-, and 2475- year return periods with median and 84th percentile spectral accelerations computed by DSHA for 11 cities in NW Pakistan for an assumed bedrock with Vs,30 of 760 m/s. (a) PGA; (b) SA (T = 0.2 sec); and (c) SA (T = 1.0 sec)

(a) PSHA hazard curve Total Hazard e

c Jhelum fault

n a

d 0.1 MCT

e e

c MMT

f Raikot fault

y Stak fault

c 0.01

)

r f

475 y

(

d u

0.001 975 o

p A

2475

t e

0.0001 R 0 0.5 1 1.5 Peak ground acceleration (g) 3 PSHA (2475 years) (b) Spectra PSHA (975 years)

PSHA (475 years) )

g DSHA (84 percentile)

(

n 2

o DSHA (Median)

t c

e 1

p S

0 0.01 0.1 1 10 Period (sec)

Figure 5.8 Seismic hazard result for Astor for an assumed bedrock with Vs,30 of 760 m/s. (a) PSHA hazard curves for PGA at 5% damping. The hazards from the top five contributing faults are shown; (b) PSHA uniform hazard spectra (UHS) at various return periods and DSHA hazard spectra.

(a) PSHA hazard curve Total Hazard e

c Balakot shear zone

n a

d 0.1 Jhelum fault

e e

c MMT

f Mansehra fault

y Puran fault

c 0.01

)

r f

475 y

(

d u

0.001 975 o

p A

2475

t e

0.0001 R 0 0.5 1 1.5 Peak ground acceleration (g) 3 PSHA (2475 years) (b) Spectra PSHA (975 years)

PSHA (475 years) )

g DSHA (84 percentile)

(

n 2

o DSHA (Median)

t c

e 1

p S

0 0.01 0.1 1 10 Period (sec)

Figure 5.9 Seismic hazard result for Balakot for an assumed bedrock with Vs,30 of 760 m/s. (a) PSHA hazard curves for PGA at 5% damping. The hazards from the top five contributing faults are shown; (b) PSHA uniform hazard spectra (UHS) at various return periods and DSHA hazard spectra.

(a) PSHA hazard curve Total Hazard e

c Karack fault

n a

d 0.1 Khair-I-Murat fault

e e

c Kurram thrust

f MMT

y Surghar range thrust

c 0.01

)

r f

475 y

(

d u

0.001 975 o

p A

2475

t e

0.0001 R 0 0.5 1 1.5 Peak ground acceleration (g) 3 PSHA (2475 years) (b) Spectra PSHA (975 years)

PSHA (475 years) )

g DSHA (84 percentile)

(

n 2

o DSHA (Median)

t c

e 1

p S

0 0.01 0.1 1 10 Period (sec)

Figure 5.10 Seismic hazard result for Bannu for an assumed bedrock with Vs,30 of 760 m/s. (a) PSHA hazard curves for PGA at 5% damping. The hazards from the top five contributing faults are shown; (b) PSHA uniform hazard spectra (UHS) at various return periods and DSHA hazard spectra.

(a) PSHA hazard curve Total Hazard e

c Hissartang fault

n a

d 0.1 Khair-I-Murat fault

e e

c Khairrabad fault

f MBT (west)

y MMT

c 0.01

)

r f

475 y

(

d u

0.001 975 o

p A

2475

t e

0.0001 R 0 0.5 1 1.5 Peak ground acceleration (g) 3 PSHA (2475 years) (b) Spectra PSHA (975 years)

PSHA (475 years) )

g DSHA (84 percentile)

(

n 2

o DSHA (Median)

t c

e 1

p S

0 0.01 0.1 1 10 Period (sec)

Figure 5.11 Seismic hazard result for Kohat for an assumed bedrock with Vs,30 of 760 m/s. (a) PSHA hazard curves for PGA at 5% damping. The hazards from the top five contributing faults are shown; (b) PSHA uniform hazard spectra (UHS) at various return periods and DSHA hazard spectra.

(a) PSHA hazard curve Total Hazard e

c MBT (west)

n a

d 0.1 MMT

e e

c Nowshera fault

f Mansehra thrust

y Puran fault

c 0.01

)

r f

475 y

(

d u

0.001 975 o

p A

2475

t e

0.0001 R 0 0.5 1 1.5 Peak ground acceleration (g) 3 PSHA (2475 years) (b) Spectra PSHA (975 years)

PSHA (475 years) )

g DSHA (84 percentile)

(

n 2

o DSHA (Median)

t c

e 1

p S

0 0.01 0.1 1 10 Period (sec)

Figure 5.12 Seismic hazard result for Malakand for an assumed bedrock with Vs,30 of 760 m/s. (a) PSHA hazard curves for PGA at 5% damping. The hazards from the top five contributing faults are shown; (b) PSHA uniform hazard spectra (UHS) at various return periods and DSHA hazard spectra.

(a) PSHA hazard curve Total Hazard e

c Dijabba fault

n a

d 0.1 Jhelum fault

e e

c MBT (east)

f Riasi thrust

y Riwat thrust

c 0.01

)

r f

475 y

(

d u

0.001 975 o

p A

2475

t e

0.0001 R 0 0.5 1 1.5 Peak ground acceleration (g) 3 PSHA (2475 years) (b) Spectra PSHA (975 years)

PSHA (475 years) )

g DSHA (84 percentile)

(

n 2

o DSHA (Median)

t c

e 1

p S

0 0.01 0.1 1 10 Period (sec)

Figure 5.13 Seismic hazard result for Mangla for an assumed bedrock with Vs,30 of 760 m/s. (a) PSHA hazard curves for PGA at 5% damping. The hazards from the top five contributing faults are shown; (b) PSHA uniform hazard spectra (UHS) at various return periods and DSHA hazard spectra.

(a) PSHA hazard curve Total Hazard e

c Dijabba fault

n a

d 0.1 Jhelum fault

e e

c Khair-I-Murat fault

f MBT (west)

y Salt range thrust

c 0.01

)

r f

475 y

(

d u

0.001 975 o

p A

2475

t e

0.0001 R 0 0.5 1 1.5 Peak ground acceleration (g) 3 PSHA (2475 years) (b) Spectra PSHA (975 years)

PSHA (475 years) )

g DSHA (84 percentile)

(

n 2

o DSHA (Median)

t c

e 1

p S

0 0.01 0.1 1 10 Period (sec)

Figure 5.14 Seismic hazard result for Talagang for an assumed bedrock with Vs,30 of 760 m/s. (a) PSHA hazard curves for PGA at 5% damping. The hazards from the top five contributing faults are shown; (b) PSHA uniform hazard spectra (UHS) at various return periods and DSHA hazard spectra.

0.8

)

g (

0.6

c c

a 0.4

a 0.2

e P

0 d d d ba r g r u a n t n la a a n o n ab a a a g ar w a st n gh h ak n f a g a m a o l a af sh la A B la K a M z e a Is K M u P T M

Monalisa et al. (2007) (475-yr return period) PMD and NORSAR (2006) (500-yr return period) This study-PSHA (475-yr return period) This study-DSHA (median)

Figure 5.15 PGAs computed by PSHA and DSHA for an assumed bedrock with Vs,30 of 760 m/s, compared to those computed by others (PMD and NORSAR 2006; Monalisa et al. 2007). PGAs estimated by Monalisa et al. (2007) correspond to a 475-year return period, while PMD and NORSAR (2006) values correspond to a 500-year return period.

PGA (g) Reverse fault 36 ˚N Normal fault 1.2 Strike-slip fault 1.0 0.8 Astor 0.8 0.6 35 ˚N 0.4 Kaghan 0.2 Balakot Malakand Muzaffarabad

Peshawar 0.4 34 ˚N

Kohat Islamabad 0.4

Mangla 33 ˚N Bannu Talagang

32 ˚N

70 ˚E 71 ˚E 72 ˚E 73 ˚E 74 ˚E 75 ˚E

Figure 5.16 Seismic hazard map of NW Pakistan for PGA for a 475-year return period. A 0.1° × 0.1° grid spacing was analyzed using PSHA for an assumed bedrock with Vs,30 of 760 m/s. The contour interval is 0.2g.

PGA (g) Reverse fault 36 ˚N Normal fault 1.2 Strike-slip fault 1.0 0.8 Astor 0.6 1.0 35 ˚N 0.4 Kaghan 0.2 Balakot Malakand Muzaffarabad

Peshawar

34 ˚N 0.6

Islamabad Kohat 0.4

Mangla 33 ˚N Bannu Talagang

32 ˚N

70 ˚E 71 ˚E 72 ˚E 73 ˚E 74 ˚E 75 ˚E

Figure 5.17 Seismic hazard map of NW Pakistan for PGA for a 975-year return period. A 0.1° × 0.1° grid spacing was analyzed using PSHA for an assumed bedrock with Vs,30 of 760 m/s. The contour interval is 0.2g.

PGA (g) Reverse fault 36 ˚N Normal fault 1.2 Strike-slip fault 1.0 0.8 Astor 0.6 35 ˚N 0.4 Kaghan 0.2 Balakot Malakand Muzaffarabad

Peshawar 34 ˚N

Kohat Islamabad

Mangla 33 ˚N Bannu Talagang

32 ˚N

70 ˚E 71 ˚E 72 ˚E 73 ˚E 74 ˚E 75 ˚E

Figure 5.18 Seismic hazard map of NW Pakistan for PGA for a 2475-year return period. A 0.1° ×

0.1° grid spacing was analyzed using PSHA for an assumed bedrock with Vs,30 of 760 m/s. The contour interval is 0.2g.

SA (g) Reverse fault 36 ˚N 4.0 Normal fault 3.6 Strike-slip fault 3.2 2.8 Astor 2.4 35 ˚N 2.0 1.6 Kaghan 1.2 Balakot 0.8 0.4 Malakand Muzaffarabad Peshawar 34 ˚N

Kohat Islamabad

Mangla 33 ˚N Bannu Talagang

32 ˚N

70 ˚E 71 ˚E 72 ˚E 73 ˚E 74 ˚E 75 ˚E

Figure 5.19 Seismic hazard map of NW Pakistan for SA (T=0.2 sec) for a 475-year return period. A 0.1° × 0.1° grid spacing was analyzed using PSHA for an assumed bedrock with Vs,30 of 760 m/s. The contour interval is 0.4g.

SA (g) Reverse fault 36 ˚N 4.0 Normal fault 3.6 Strike-slip fault 3.2 2.8 Astor 2.4 35 ˚N 2.0 1.6 Kaghan 1.2 Balakot 0.8 0.4 Malakand Muzaffarabad Peshawar

34 ˚N 1.2 Kohat Islamabad

Mangla 33 ˚N Bannu Talagang 0.8

32 ˚N

70 ˚E 71 ˚E 72 ˚E 73 ˚E 74 ˚E 75 ˚E

Figure 5.20 Seismic hazard map of NW Pakistan for SA (T=0.2 sec) for a 975-year return period. A 0.1° × 0.1° grid spacing was analyzed using PSHA for an assumed bedrock with Vs,30 of 760 m/s. The contour interval is 0.4g.

SA (g) Reverse fault 36 ˚N 4.0 Normal fault 3.6 Strike-slip fault 3.2 2.8 Astor 2.4 35 ˚N 2.0 1.6 Kaghan 1.2 Balakot 0.8 0.4 Malakand Muzaffarabad Peshawar

34 ˚N 1.6 Kohat Islamabad

Mangla 33 ˚N Bannu 0.8 Talagang

32 ˚N

70 ˚E 71 ˚E 72 ˚E 73 ˚E 74 ˚E 75 ˚E

Figure 5.21 Seismic hazard map of NW Pakistan for SA (T=0.2 sec) for a 2475-year return period. A 0.1° × 0.1° grid spacing was analyzed using PSHA for an assumed bedrock with Vs,30 of 760 m/s. The contour interval is 0.4g.

PGA (g) Reverse fault 36 ˚N Normal fault 1.2 Strike-slip fault 1.0 0.8 Astor 0.6 35 ˚N 0.4 Kaghan 0.2 Balakot Malakand Muzaffarabad

Peshawar 0.4 34 ˚N

Kohat Islamabad

Mangla 33 ˚N Bannu Talagang

32 ˚N

70 ˚E 71 ˚E 72 ˚E 73 ˚E 74 ˚E 75 ˚E

Figure 5.22 Seismic hazard map of NW Pakistan for SA (T=1.0 sec) for a 475-year return period. A 0.1° × 0.1° grid spacing was analyzed using PSHA for an assumed bedrock with Vs,30 of 760 m/s. The contour interval is 0.2g.

PGA (g) Reverse fault 36 ˚N Normal fault 1.2 Strike-slip fault 1.0 0.8 Astor 0.6 35 ˚N 0.4 Kaghan 0.2 Balakot Malakand Muzaffarabad 0.4 Peshawar 34 ˚N 0.6 0.6

Islamabad Kohat 0.4

Mangla 33 ˚N Bannu Talagang

32 ˚N

70 ˚E 71 ˚E 72 ˚E 73 ˚E 74 ˚E 75 ˚E

Figure 5.23 Seismic hazard map of NW Pakistan for SA (T=1.0 sec) for a 975-year return period. A 0.1° × 0.1° grid spacing was analyzed using PSHA for an assumed bedrock with Vs,30 of 760 m/s. The contour interval is 0.2g.

PGA (g) Reverse fault 36 ˚N Normal fault 1.2 Strike-slip fault 1.0 0.8 Astor 0.6 35 ˚N 0.4 Kaghan 0.2 Balakot Malakand Muzaffarabad

Peshawar 0.8 34 ˚N

Kohat Islamabad 0.6

Mangla 33 ˚N Bannu Talagang

32 ˚N

70 ˚E 71 ˚E 72 ˚E 73 ˚E 74 ˚E 75 ˚E

Figure 5.24 Seismic hazard map of NW Pakistan for SA (T=1.0 sec) for a 2475-year return period. A 0.1° × 0.1° grid spacing was analyzed using PSHA for an assumed bedrock with Vs,30 of 760 m/s. The contour interval is 0.2g.

1 Baker and Jayaram 0.9 (2008) T*=0.05 sec 0.8 T*=0.1 sec

T*=0.2 sec 

0.7 ,

t T*=0.5 sec

n e i T*=2.0 sec

c 0.6

i f

f T*=10 sec

o c

0.5

t a

l 0.4

r o

C 0.3 Baker (2008) T*=0.1 sec 0.2 T*=0.2 sec T*=0.5 sec 0.1 T*=2.0 sec 0 0.01 0.1 1 10 Period (sec) Figure 5.25 Comparison of correlation coefficient proposed by Baker (2008) and Baker and Jayaram (2008).

UHS (475 years) )

g 1.6 CMS

(

t a

r 1.2

l 0.8

e p

S 0.4

0 2

UHS (975 years) )

g 1.6 CMS

(

t a

r 1.2

l 0.8

e p

S 0.4

0 2

UHS (2475 years) )

g 1.6 CMS

(

t a

r 1.2

l 0.8

e p

S 0.4

0 0.01 0.1 1 10 Period (sec)

Figure 5.26 CMS at T* = 0.05, 0.2, and 1 second for 475-, 975-, and 2475-year return periods in Islamabad.

2.8 UHS (475 years)

2.4 )

g CMS

(

n 2

a r

e 1.6

c a

1.2

r t

c 0.8

p S 0.4

0 2.8 UHS (975 years)

2.4 )

g CMS

(

n 2

a r

e 1.6

c a

1.2

r t

c 0.8

p S 0.4

0 2.8 UHS (2475 years)

2.4 )

g CMS

(

n 2

a r

e 1.6

c a

1.2

r t

c 0.8

p S 0.4

0 0.01 0.1 1 10 Period (sec)

Figure 5.27 CMS at T* = 0.05, 0.2, and 1 second for 475-, 975-, and 2475-year return periods in Muzaffarabad.

CHAPTER 6. CURRENT SEISMIC SLOPE STABILITY APPROACH

6.1 Introduction This chapter introduces the characteristics of earthquake-induced landslides and general approaches to analyze seismic slope stability (pseudo-static analysis, the Newmark (1965) sliding block method, modified Newmark method, simplified displacement charts, and energy- based methods). This study focuses on whether slopes fail during earthquakes rather than estimating displacements. Therefore, the pseudo-static slope stability analysis is selected to evaluate the regional performance of slopes during an earthquake, and discussed in detail. Although sophisticated analyses (i.e., 2D and 3D limit equilibrium, 2D and 3D finite element, and 2D and 3D discrete element analyses) are available to analyze the stability of individual slopes, these are not practical to assess the regional performance of slopes. Therefore, this study presents a simplified seismic slope stability analysis using estimated rock properties and slope geometries in the affected areas. To better understand landslide distributions and help explain the high concentration of landslides in the near-field, this study proposes several factors that are not commonly incorporated in current slope stability practice.

6.2 Earthquake-induced landslides Earthquake-induced landslides can cause numerous fatalities and can create massive disruption following an earthquake as a result of blocking critical transportation routes in mountainous terrain, damming waterways, and triggering seiches or tsunamis. For example, the

2008 Wenchuan earthquake (moment magnitude, Mw 7.9) in China triggered more than 15,000 landslides, rockfalls, and debris flows, resulting in approximately 20,000 deaths (Yin et al. 2009).

The 2005 Kashmir, Pakistan, earthquake (Mw 7.6) triggered more than 2,400 landslides (Sato et al. 2007), including the 68×106 m3 Hattian Bala rock avalanche which destroyed an entire village and caused about 1,000 fatalities (Dunning et al. 2007). The 1999 Chi-chi, Taiwan, earthquake 2 (Mw 7.6) triggered more than 9,200 landslides throughout a region of approximately 128 km (Liao 2000). The largest of these was the Tsaoling landslide which involved 125×106 m3 of rock and caused 39 fatalities (Tang et al. 2009). The 1989 Loma Prieta, California, earthquake (Mw 6.9) triggered thousands of landslides over an area of about 15,000 km2, damaging more than 200 residences, numerous roads, and other structures, with damage estimates exceeding US$30 million (Keefer and Manson 1998).

Material type (soil or rock) and the character of movement are used to classify seismically-induced landslides as shown in Table 6.1 and Table 6.2 (Keefer 2002). For example, “disrupted” landslides involve broken, sheared, and disturbed material, while “coherent” landslides involve a few relatively intact blocks that rotate and/or translate on a failure surface, and generally exhibit lower velocities than disrupted slides (Keefer 1984). Numerous factors influence the seismic stability of slopes and the landslide characteristics, including the geologic and hydrologic conditions (e.g., weathering); topography: climate; and the strength of shaking (i.e., ground motion amplitude and frequency content; earthquake magnitude). Factors such as topsoil thickness and vegetation have no significant impact on the earthquake induced landslides, although they become more important for rainfall triggered landslides (Khazai and Sitar 2004). Because earthquake-induced landslides cause significant damage, the distribution of landslide has been of interest for many scientists and engineers. One of the pioneering researches was conducted by Keefer (1984). He proposed the relation between earthquake magnitude and area affected by landslides based on historical earthquake data. According to his relation, the area of approximately 100,000 km2 can be possibly affected by landslides induced by the earthquake of Mw = 8.0 (Figure 6.1). He also proposed the relation between maximum distance of landslides from fault and earthquake magnitude as shown in Figure 6.2. Keefer (1984) illustrated the minimum earthquake magnitudes required to trigger different types of landslides as shown in Table 6.3. Rock falls, rock slides, soil falls, and disrupted soil slides can be triggered by small magnitude earthquake (Mw = 3.6), whereas rock avalanches and soil avalanches require large magnitude (Mw = 5.7 and 6.3, respectively). Similar correlations have related landslide concentration to distance from fault (Keefer 2000; Khazai and Sitar 2004; Sato et al. 2007; Dai et al. 2011). These studies suggest that landslides are highly concentrated near the fault (near-field).

6.3 General approaches to analyze seismic slope stability Several simplified methods are available to estimate the factor of safety (FS) against sliding and displacements during earthquake-induced landslides. These methods include pseudo- static analysis, the Newmark (1965) sliding block method, modified Newmark methods, simplified displacement charts, and energy-based methods. Terzaghi (1950) first applied a pseudo-static approach to analyze seismic slope stability. This approach is based on conventional limit equilibrium slope stability analysis with horizontal

and vertical pseudo-static forces that act on the critical failure mass. This approach predicts the

FS against sliding, and can be also used to determine a yield acceleration (ay) for use in a Newmark sliding block analysis to estimate displacements. Newmark (1965) developed a sliding block analysis to estimate permanent displacements of a sliding mass. In this method, the sliding mass is represented as a rigid block on an inclined plane and displacements are integrated from base acceleration pulses that exceed the block’s yield acceleration. If the acceleration does not exceed the yield acceleration, there is no computed sliding block displacement. Makdisi and Seed (1978) proposed a simple method for the seismic design of embankments, that uses the concept originally proposed by Newmark (1965). They used a finite element analysis to compute the variation of permanent displacement with ay/amax (where amax is the peak ground acceleration) and earthquake magnitude. The analyses employed several real and hypothetical dams with heights ranging from 30 to 60 m and constructed of compacted fine- grained soils or very dense coarse-grained soils that were subjected to several recorded and synthetic ground motions scaled to represent different earthquake magnitudes. The displacement was normalized by the peak base acceleration and fundamental period of the embankment. Yegian et al. (1991) and Bray et al. (1998) proposed variations of this method to estimate seismic slope displacement. When seismic waves propagate through a slope, different parts of the slope will move by different amounts and with different phases (Kramer and Smith 1997). This phenomenon is most significant for thick, soft materials and short wavelengths. To accommodate these factors, many researchers have modified the Newmark method to accommodate compliant slope materials (e.g., Lin and Whitman 1983; Kramer and Smith 1997; Rathje and Bray 2000). In addition, Matasovic et al. (1997) incorporated a degrading yield acceleration into the Newmark method to accommodate potential cyclic degradation of soil shear strength. Kokusho and Kabasawa (2003) proposed an energy-based approach, and Kokusho and Ishizawa (2007) further developed it. Specifically, their model accounts for potential energy of the sliding mass, earthquake energy contributing to slope failure, dissipated energy due to sliding mass deformation, and kinetic energy of the sliding mass. They correlated these energies with residual horizontal displacement, material properties (mass of soil block and friction angle), and

average slope angle. Consequently, they found that the residual horizontal displacement can be estimated from the earthquake energy. This study focuses on whether slopes fail during earthquakes rather than estimating displacements. Therefore, the factor of safety against sliding using a pseudo-static slope stability analysis approach is considered. Furthermore, this approach is applied regionally to evaluate landslide concentration, and the analyses described below were not derived from any particular slope.

6.4 Pseudo-static slope stability analysis As noted above, Terzaghi (1950) first applied a pseudo-static approach to analyze seismic slope stability. This approach uses a single, monotonically-applied horizontal and/or vertical acceleration to represent earthquake loading. (Although the vertical acceleration can be included in a pseudo-static analysis, it is rarely used in practice, as explained below.) The horizontal and vertical pseudo-static forces, Fh and Fv, respectively, act through the sliding mass centroid and are defined as:

ahW avW Fh   khW and Fv   kvW Eq. (6-1) g g

where ah and av = horizontal and vertical accelerations, respectively; kh and kv = dimensionless horizontal and vertical pseudo-static coefficients, respectively; and W = weight of the failure mass. Using an infinite slope analysis with this approach has the benefits of being simple and able to reasonably approximate shallow slope failures, including earthquake-induced shallow, disrupted landslides which constitute most of the landslides in the study areas. Due to the small thickness of landslide mass, it was assumed that the water table was below the sliding plane. For an infinite slope where horizontal and vertical pseudo-static seismic loads act through the sliding mass centroid, FS is calculated as:

c 1 kv cosi  kh sin itan  D Eq. (6-2) FS  t 1k v sin i  kh cosi

where c’ and ’ are Mohr-Coulomb strength parameters that describe the shear strength on the failure plane;  = unit weight of failure mass; i = slope and failure plane angles; and D = failure mass thickness. The horizontal pseudo-static force has a larger influence on the FS than the vertical pseudo-static force, as Fh reduces the resisting force and increases the driving force. Thus, selecting appropriate values for kh is important for estimating meaningful values of FS. Many investigators have suggested values of pseudo-static coefficients. For example, Terzaghi (1950) proposed kh = 0.1 for “severe” earthquakes (Rossi-Forel intensity IX); kh = 0.2 for “violent, destructive” earthquakes (Rossi-Forel X); and kh = 0.5 for “catastrophic” earthquakes. Seed

(1979) suggested kh = 0.10 (M = 6.5) to 0.15 (M = 8.25) for earth dams constructed of ductile soils with crest accelerations less than 0.75g. Later, Pyke (1991) proposed a relation between pseudo-static coefficient and Mw, where kh approaches 0.5 for Mw > 8.0. Other researchers have proposed pseudo-static coefficients that vary with anticipated maximum horizontal acceleration, ah,max at the base of sliding mass. For example, Marcuson and

Curro (1981) suggested kh = (1/3 to 1/2)×(ah,max/g). Hynes-Griffin and Franklin (1984) suggested 1/3 kh = 0.5×(ah,max/g). Nozu et al. (1997) proposed a slightly different form [kh=1/3 (ah,max/g) ], which gives higher pseudo-static coefficient than the former two approaches for ah,max ≤ 0.5g, and falls between the other two approaches for ah,max > 0.5g. Anderson et al. (2008) pointed out that the pseudo-static coefficient is typically assumed to be less than 50 percent of ah,max, but is a function of the slope height and frequency content of the ground motion. Two conventionally- used horizontal pseudo-static coefficients, kh = 0.5(ah,max/g) and kh = 0.33(ah,max/g) were employed. In addition, kh = 0.9(ah,max/g) was considered to account for shallow slides where wave incoherency and scattering effects may be less prevalent than in large landslides. Equal weights were assigned to these three values of kh for statistical analysis. Many researchers have discounted vertical acceleration in computing FS because, as noted by Kramer (1996), the vertical pseudo-static force reduces both driving and resisting forces. The effect of discounting the vertical pseudo-static force is examined subsequently.

6.5 Evaluating the pseudo-static approach using landslides triggered by the 2005 Kashmir, Pakistan, earthquake

The 2005 Kashmir earthquake (Mw=7.6) occurred in the northern Pakistan where thrust movements dominant due to the Indian plate colliding with the Eurasian plate. The Balakot- Garhi fault which ruptured during the earthquake is a 50-km-long thrust fault with a dip of 30°NE and rupture depth of 26 km. Sato et al. (2007) reported that 2,424 landslides occurred in their 55 km x 51 km study area. As shown in Figure 6.3, the landslides are highly concentrated along the fault. Sato et al. (2007) performed a statistical analysis of the distribution of landslides triggered by the earthquake. Based on these data, the landslide distribution was expressed as a landslide concentration (LC), which is defined as the number of landslides per square kilometer of surface area (Keefer 2000). The rock slopes in the area affected by the earthquake are mainly sedimentary, igneous, and metamorphic rocks of Precambrian to Quaternary ages (Sato et al. 2007). Landslides occurred most frequently in the Tertiary-age Murree Formation (Tmm) which consists of hard sandstone and siltstone with thin intraformational conglomerate lenses (Sato et al. 2007). Kamp et al. (2008) described the failed sedimentary rocks as undeformed to tightly- folded, highly-cleaved and fractured. To perform a pseudo-static slope stability analysis, a number of rock properties are needed, as well as geometric properties of the slope. For individual slopes, these values are evaluated as part of a site characterization program. However, for this study, the regional performance of rock slopes is of interest; therefore, this study characterizes these parameters in terms of typical mechanical and geometric properties that apply to the affected region as a whole. The rock properties needed for the analysis are total unit weight, , and Mohr-Coulomb shear strength parameters, ' and c'. The geometric parameters needed are Dt and i (defined above). Because Mohr-Coulomb strength properties for rock specimens are seldom measured directly (other than for joints), the Hoek-Brown strength criterion (Hoek et al. 2002) was used to estimate appropriate Mohr-Coulomb strength parameters. The Hoek-Brown criterion requires the following parameters (Hoek et al. 2002): rock uniaxial unconfined compressive strength, c; material constant for intact rock, mi; Geological Strength Index, GSI; and disturbance factor, DF, that accounts for the degree of disturbance to the rock mass from blasting and/or stress relief. These parameters were estimated from reported geologic and geotechnical conditions in the affected region. The Hoek-Brown strength parameters were then converted to equivalent Mohr- 97

Coulomb shear strength parameters over the appropriate effective confining stress range for use in the pseudo-static slope stability analysis. As discussed by Hoek et al. (2002), the degree of weathering plays an important role in estimating rock strength parameters. Sato et al. (2007) reported that 79% of the landslides were shallow, disrupted rockslides, and Owen et al. (2008) observed that these shallow landslides typically involved the top few meters of weathered bedrock, regolith, and soil. Figure 6.4 shows the picture of shallow landslides triggered by 2005 Kashmir earthquake. For the Mohr-Coulomb strength parameters, it was assumed that the values computed using the Hoek-Brown criterion were mean values, and standard deviations were estimated using coefficients of variation (COV) of 5%, 30%, and 15% for , c', and ', respectively, as suggested by Lee et al. (1983). Using the Hoek-Brown parameters in Table 6.4 for the Kashmir earthquake case yield ' = 40 ± 6° and c' = 27 ± 8 kPa. Detailed explanation is presented in Appendix A.

Based on the observation by Owen et al. (2008), Dt = 1 to 5 m were considered. Figure 6.5 (a) shows the distribution of slope angles for slope that failed during the 2005 Kashmir earthquake (Kamp et al. 2008). Dai and Wang (1992) suggested that 99.73% of all values of a normally distributed parameter fall within three standard deviations of the mean. Assuming a mean value of 3 m and minimum and maximum values of 1 and 5 m, respectively, the “three- sigma rule” was applied to estimate a standard deviation of 0.67 m. Figure 6.5(a) shows the distribution of slope angles for slopes that failed during the 2005 Kashmir earthquake (Kamp et al. 2008). This study considered a normal distribution with a mean slope angle of 28° and a standard deviation of 9° to represent the failed slope data. The actual cumulative distribution of documented slope angles is similar to the theoretical cumulative normal distribution as shown in Figure 6.5(a). Table 6.4 summarizes the geometric parameters for this case. Figure 6.6 shows the horizontal ground accelerations predicted using four GMPEs released by Next Generation Attenuation (NGA) projects (Abrahamson and Silva 2008; Boore and Atkinson 2008; Campbell and Bozorgnia 2008; Idriss 2008). Figure 6.7 compares the static and pseudo-static FS against sliding, using mean material properties and slope geometries, horizontal ground accelerations predicted for the 2005 Kashmir earthquake by the four GMPEs, and kh = 0.5, with the LC data from Sato et al. (2007). The static FS was calculated to be approximately 2.6. When the horizontal acceleration was incorporated, the FS becomes 1.3 at distances close to the fault. The mean FS did not become smaller than unity even when the 98

horizontal acceleration was at its maximum. Although some combinations of material properties and slope geometries cause the FS to become smaller than unity, this mean FS distribution cannot explain the high LC near the fault. Similar disparity between the LC data and pseudo- static FS was observed when using mean strength and geometry parameters for the 1989 Loma- Prieta, U.S.; 1999 Chi-Chi, Taiwan; and 2008 Wenchuan, China, earthquakes.

6.6 Summary This chapter summarizes the general approaches to analyze seismic slope stability. Terzaghi (1950) first applied a pseudo-static approach to analyze seismic slope stability that results in prediction of factor of safety against sliding. The Newmark (1965) sliding block analysis is to estimate permanent displacements of a sliding mass. Makdisi and Seed (1978) proposed a simple method for the seismic design of small embankments that uses the concept originally proposed by Newmark (1965). Many researchers later modified the Newmark method to deal with compliant slope materials (e.g., Lin and Whitman 1983; Kramer and Smith 1997; Rathje and Bray 2000). In order to evaluate slope failure including flow failures from their initiation to termination, Kokusho and Kabasawa (2003) proposed an energy approach. The pseudo-static slope stability analysis is selected in this study to evaluate the regional performance of slopes during earthquake. A pseudo-static slope stability analysis was conducted for the 2005 Kahsmir, Pakistan, earthquake. The rock strength parameters and slope geometry parameters were obtained from the literature (Sato et al. 2007; Kamp et al. 2008; Owen et al. 2008). Using horizontal ground accelerations predicted using four GMPEs released by Next Generation Attenuation (NGA) projects (Abrahamson and Silva 2008; Boore and Atkinson 2008; Campbell and Bozorgnia 2008; Idriss 2008), mean factor of safety against sliding was computed. However, this FS could not capture the trend of LC data. The static FS was calculated to be approximately 2.6. When the horizontal acceleration was incorporated, the FS becomes 1.3 at distances close to the fault, but is still greater than unity.

Table 6.1 Characteristics of earthquake-induced landslides (disrupted type) (Keefer 2002). Internal Water content Typical Min. Typical Name Type of movement Typical volumes Typical displacements disruption D U PS S depths slope (°) velocities May fall to base of steep Most less than 1 × 104 m3; source slope and move as far Bouncing, rolling, High or Extremely Rock falls × × × × Shallow 40 maximum reported 2 × as several tens or hundreds of free fall very high rapid 107 m3 meters farther, on relatively gentle slopes May slide to base of steep Most less than 1 × 104 m3; Disrupted Rapid to source slope and several tens Translational sliding High × × × × Shallow 35 maximum reported 2 × rock slide very rapid or hundreds of meters farther, 109 m3 on relatively gentle slopes Complex, involving Very rapid Rock sliding, to 5 × 105–2 × 108 m3 or Very high × × × × Deep 25 Several kilometers avalanches flow, and extremely more occasionally free fall rapid Most less than 1,000 m3; Bouncing, rolling, High or Extremely Most come to rest at or near Soil falls × × × × Shallow 40 maximum volumes not free fall very high rapid bases of steep source slopes well documented May slide to base of steep Most less than 1 × 104 m3; Disrupted Moderate source slope and several tens Translational sliding High × × × × Shallow 15 maximum reported 4.8 × soil slides to rapid or hundreds of meters farther, 107 m3 on relatively gentle slopes Complex, involving Very rapid Volumes not well Several tens of meters to Soil sliding, to Very high × × × × Shallow 25 documented; maximum several kilometers beyond avalanches flow, and extremely reported 1.5 × 108 m3 steep source slopes occasionally free fall rapid Notes: Names: “rock” signifies bedrock that is relatively firm and intact prior to landslide initiation, and “soil” signifies loose, unconsolidated or poorly cemented aggregates of particles that may or may not contain organic materials. Internal disruption: “slight” signifies landslide consists of one or a few coherent blocks; “moderate” signifies several coherent blocks; “high” signifies numerous small blocks and individual soil grains and rock fragments; “very high” signifies nearly complete disaggregation into individual soil grains or small rock fragments. Depth: shallow signifies generally < 3 m deep; deep signifies generally > 3 m deep. Water content: D = dry; U = moist but unsaturated; PS = partly saturated; S = saturated. Velocity: very slow = 1 × 10−6–3 × 10−6 m/min; slow = 3 × 10−6–3 × 10−5 m/min; moderate = 3 × 10−5–0.001 m/min; rapid = 0.001–0.3 m/min; very rapid = 0.3–180 m/min; extremely rapid = >180 m/min.

100

Table 6.2 Characteristics of earthquake-induced landslides (coherent type) (Keefer 2002). Water Min. Type of Internal Typical Typical Name content slope Typical volumes Typical displacements movement disruption depths velocities D U PS S (°) Most between 100 and a Typically less than 10 Rock Rotational Slight or few million m3; maximum ? × × × Deep 15 Slow to rapid m; occasionally 100 m slumps sliding moderate at least tens of millions of or more m3 Most between 100 and a Typically less than 100 Rock block Translational Slight or few million m3; maximum m; maximum ? × × × Deep 15 Slow to rapid slides sliding moderate at least tens of millions of displacements not well m3 documented Most between 100 and 1 × Typically less than 10 Rotational Slight or Soil slumps ? × × × Deep 7 Slow to rapid 105 m3; occasionally 1 × m; occasionally 100 m sliding moderate 105 to several million m3 or more Typically less than 100 Most between 100 and 1 × Soil block Translational Slight or m; maximum ? ? × × Deep 5 Slow to rapid 105 m3; maximum reported slides sliding moderate displacements not well 1.12 × 108 m3 documented Very slow to Generally Most between 100 and 1 × Typically less than 100 Translational moderate; Slow earth shallow; 106 m3; maximum reported m; maximum sliding and Slight × × 10 occasionally, flows occasionally between 3 × 107 and 6 × displacements not well internal flow with very rapid deep 107 m3 documented surges Lateral Generally spreads and Most between 100 and 1 × Typically less than Translation on moderate; flows × × Variable 0.3 Very rapid 105 m3; largest reported 9.6 10m; maximum fluid basal zone occasionally Soil lateral × 106 m3 reported 600 m slight or high spreads Volumes not well Rapid soil Very rapid to Flow Very high ? ? ? × Variable 2.3 documented; largest are at A few m to several km flows extremely rapid least several million m3 Generally lateral Generally high Generally rapid spreading or or very high; to extremely Volumes not well Not well documented, Subaqueous flow; occasionally × × Variable 0.5 rapid; documented; largest are at but some move more landslides occasionally moderate or occasionally least tens of millions of m3 than 1 km sliding slight slow to moderate Note: See Table 6.1.

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Table 6.3 Minimum ML required to trigger landslides (Keefer 1984). The numbers in parentheses are Mw converted using conversion from Grunthal and Wahlstrom (2003).

ML (Mw) Description 4.0 (3.6) Rock falls, rock slides, soil falls, disrupted soil slides 4.5 (4.1) Soil slumps, soil block slides Rock slumps, rock block slides, slow earth flows, soil 5.0 (4.6) lateral spreads, rapid soil flows, and subaqueous landslides 6.0 (5.7) Rock avalanches 6.5 (6.3) Soil avalanches

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Table 6.4 Hoek-Brown parameters and geometry parameters for four cases. Selected values 1989 2008 Parameter 2005 1999 Notes References Loma- Wench- Kashmir Chi-Chi Prieta uan Estimated from rock  Hoek and Bray 21 ± 1 21 ± 1 24 ± 1 24 ± 1 type and degree of kN/m3) (1981) weathering Estimated from rock ci (MPa) 2 0.8 2 2 type and degree of Hoek et al. (1998) weathering Estimated from rock m 14 14 14 14 Hoek et al. (1998) i type Estimated from rock type, rock mass Marinos et al. GSI 30 30 30 30 structure, and joint (2005) surface conditions No evidence of DF 0 0 0 0 Hoek et al. (1998) blasting or stress relief

' Estimated using Hoek- 40 ± 6 33 ± 5 51 ± 8 40 ± 6 Hoek et al. (2002) (°) Brown criterion

c' Estimated using Hoek- 27 ± 8 20 ± 6 11 ± 3 27 ± 8 Hoek et al. (2002) (kPa) Brown criterion

 0.73 ± 0.29 ± 0.73 ± 0.73 ± Estimated using Hoek- t Hoek et al. (2002) (kPa) 0.15 0.07 0.15 0.15 Brown criterion Keefer (1984) Based on generalized Khazai and Sitar D description of typical t 3 ± 0.67 3 ± 0.67 0.7 ± 0.2 3 ± 0.67 (2004) (m) depths of disrupted Owen et al. (2008) slides in rock slopes Yin et al. (2010) Khazai and Sitar i (2004) 28 ± 9 27± 9 65 ± 15 33 ± 10 See Figure 6.5 (°) Kamp et al. (2008) Yin et al. (2010)

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Figure 6.1 Relations between area affected by landslides and earthquake magnitude (Keefer 2002). Circles are data from Keefer (1984) and Keefer and Wilson (1989). Dashed line is approximate upper bound from Keefer (1984). Solid line is least-squares linear regression mean from Keefer and Wilson (1989). Most magnitudes smaller than 7.5 are surface-wave (Ms), and most magnitude of 7.5 or larger are moment magnitude (Mw).

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Figure 6.2 Maximum distance from fault rupture zone to landslides with respect to earthquake magnitudes. Dashed line represents disrupted slides and falls, dash-double-dot line represents coherent slides, and dotted line represents lateral spreads and earth flows (Keefer 1984).

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Figure 6.3 Distribution of landslides triggered by the 2005 Kashmir earthquake, shown as red dots. Epicenter (star mark), Balokot-Garhi fault (light line), Jhelum fault (dark line), and cities of Muzaffarabad (M) and Balakot (B) are also shown. (Sato et al. 2007).

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Figure 6.4 Photograph of shallow landslides triggered by 2005 Kahsmir, Pakistan, earthquake (by Prof. Hashash).

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Figure 6.5 Distribution of slope angles for (a) 2005 Kashmir, Pakistan, earthquake (Kamp et al. 2008), (b) 1989 Loma Prieta earthquake (Khazai and Sitar 2004), (c) 1999 Chi-Chi, Taiwan, earthquake (Khazai and Sitar 2004), and (d) 2008 Wenchuan, China, earthquake (Yin et al. 2010).

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1.2

) g

( Abrahamson-Silva (2008)

n o

i Boore-Atkinson (2008)

t a

r Campbell-Bozorgnia (2008) e

l 0.8 e

c Idriss (2008)

n 0.6

a 0.4

i r

o 0.2 H

0 0 10 20 30 40 50 Distance from surface projection of updip edge of fault plane (km)

Figure 6.6 Horizontal accelerations with respect to source-to-site distance predicted using the NGA GMPEs for the Mw 7.6 Kashmir, Pakistan, earthquake.

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22 2 3

2.8

2.6

1.6 2.4

) 2

m 2.2

i n

l 2

a t

l 1.2 1.8

(

L g

1.6

e f

a 1.4

o c

0.8 1.2

e 1

l s

d Mean parameters

n 0.8

a Tensile strength = 0.73 kPa L 0.4 Unit weigth = 21 kN/m3 0.6 Cohesion intercept = 27 kPa Friction angle = 40o 0.4 Slope thickness = 3 m Slope angle = 28o 0.2

0 0 0 10 20 30 40 50 Distance from surface projection of updip edge of fault plane (km)

LC for 2005 Kashmir, Pakistan earthquake

FS with kh Static FS

Figure 6.7 Landslide concentration data for the 2005 Kashmir, Pakistan, earthquake by Sato et al. (2007) and the mean factor of safety calculated by using existing pseudo-static method.

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CHAPTER 7. FACTORS THAT AFFECT PSEUDO-STATIC SLOPE STABILITY

7.1 Introduction To address the disparity between LC data and the FS predicted by existing pseudo-static slope stability approach, this study proposes three factors that potentially would affect LC near earthquake source zones in addition to the horizontal acceleration: vertical ground acceleration, topographic effects, and “bond break” effect. This chapter introduces the vertical GMPE proposed by Campbell and Bozorgnia (2003) and Ambraseys et al. (2005b) and vertical-to- horizontal ratios proposed Ambraseys and Simpson (1996) and Elnashai and Papazouglou (1997). The field and numerical studies evaluating topographic effects are also presented. Finally, the bond break effect associated with vertical acceleration is proposed.

7.2 Incorporating vertical acceleration into pseudo-static analysis Vertical accelerations traditionally have been ignored in pseudo-static slope stability analyses because it is believed to have little influence on slope stability because it reduces both the driving and resisting forces. For a typical set of strength and geometric properties, Figure 7.1 shows that the vertical pseudo-static coefficient (kv) actually increases the FS when kh is smaller than 0.2. However, when kh exceeds 0.2, kv decreases the FS. In addition, kv tends to increase the

FS when the sliding mass is thinner and the slope is steeper, regardless of kh, while kv decreases the FS when the sliding mass is thicker and the slope is gentler (assuming constant strength parameters with depth).

In addition to the direct effect of kv, many researchers have reported that the maximum vertical acceleration can equal or exceed the horizontal acceleration close to the causative fault, particularly for large magnitude earthquakes. To evaluate vertical accelerations, some researchers, e.g, Campbell and Bozorgnia (2003) and Ambraseys et al. (2005b), have proposed vertical acceleration attenuation relationships; however, these methods are limited by a lack of recorded ground motions. Despite this limitation, they used available strong-motion data for shallow crustal earthquakes recorded throughout the world (Campbell and Bozorgnia 2003) and in Europe and the Middle East (Ambraseys et al. 2005b). Other researchers have proposed relationships between horizontal and vertical accelerations. For example, Figure 7.2 presents vertical-to-horizontal acceleration ratios (V/H) proposed by Ambraseys and Simpson (1996) and Elnashai and Papazouglou (1997). The Ambraseys and Simpson (1996) relation is based on 110 111

near-field recordings (R < 15 km) relatively large (surface wave magnitude, Ms > 6), shallow (focal depth < 20 km), interplate earthquakes. They suggested that V/H slightly exceeds 1 for source-to-site distances less than about 5 km for large thrust fault ruptures and for moderate-to- strong strike-slip events. Their relations for reverse fault were linearly extrapolated to a distance of 50 km. Elnashai and Papazouglou (1997) proposed relations that adopted Ambraseys and Simpson (1995) for distances to the fault less than 15 km, Abrahamson and Litehiser (1989) for distances larger than 30 km, and a linear interpolation for distances between 15 km and 30 km. (see Figure 7.2). These V/H relations represent free-field conditions, as most records were obtained from free-field stations, with some from basements or ground floors of buildings. Both relations suggest that the V/H ratio slightly exceeded 1.0 for Ms ≥ 7.5 earthquakes in the near- field. Due to a lack of studies on the vertical pseudo-static coefficient kv, this study used the same scaling factor as the horizontal coefficient. i.e., kv = 0.33, 0.5, 0.9(av,max/g).

7.3 Topographic effects It is well-known that seismic waves can be amplified or deamplified when propagated through a soil column, depending on soil properties. These effects are termed one-dimensional (1D) site effects. Seismic waves also can be amplified or deamplified due to constructive or destructive interference when the waves encounter surface topographic irregularities such as valleys, peaks, and plateaus. These phenomena are termed topographic effects or two- dimensional (2D) site effects. In many settings, waves constructively interfere near the crest of a slope. For example, during the 1971 San Fernando, California, earthquake (Mw 6.6), severe ground cracking was observed in a very restricted area at the top of a ridge while no significant slope failures occurred (Nason 1971) (Figure 7.3 a). Similarly, Castellani et al. (1982) observed that during the Irpinia,

Italy, earthquake (Mw 6.9), building damage was concentrated around the top of a hill, while the village at the foot of the hill was only slightly damaged (Figure 7.3 b). These observations led to several full-scale field studies evaluating topographic effects where aftershocks were monitored along hills or ridges (e.g., Celebi 1987; Hartzell et al. 1994; Graizer 2009). Recently Hough et al. (2010) investigated topographic effects using aftershocks of the 2010 Mw 7.0 Haiti earthquake. However, in many of these cases 1D site effects cannot be conclusively distinguished from topographic effects. Therefore, some laboratory shaking table

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and centrifuge studies have been performed to evaluate topographic effects (e.g., Kovacs et al. 1971; Stamatopoulos et al. 2007). Many numerical studies have been conducted to investigate topographic effects, including studies by Idriss and Seed (1967), Boore (1972), Smith (1975), Sanchezsesma et al. (1982), Sitar and Clough (1983), Ashford et al. (1997), Ashford and Sitar (1997), and Bouckovalas and Papadimitrious (2005). Many recent studies have addressed specific observations or recordings. For example, Gazetas et al. (2002), Assimaki and Gazetas (2004), and Assimaki et al. (2005) evaluated topographic effects observed during the 1999 Athens,

Greece earthquake (Mw 5.9). Lungarini et al. (2005) used a finite element method to simulate topographic effects observed at Mt. Etna, Italy and observed that the maximum computed displacement occurred at or near the peak of the mountain. The topographic horizontal amplification factors observed in these field and numerical studies are summarized in Figure 7.4. Results reported in terms of velocity and displacement were not included in Figure 7.4. Some studies defined the amplification factor as the ratio of ah,max at crest to ah,max at free field beyond the crest. Others used the ratio of ah,max at the crest to ah,max at the toe. No distinction was made between these two definitions of amplification factors assuming that ah,max at free filed beyond the crest and ah,max at toe are the same for a rigid homogeneous rock. Figure 7.4 also includes the topographic amplification factors recommended by the European Seismic Code provision (EC8 2000) and French Seismic Code provision (French Association for Earthquake Engineering (AFPS) 1995). Some of the studies mentioned above also examined topographic amplification factors for vertical accelerations (e.g., Idriss and Seed 1967; Smith 1975; Sitar and Clough 1983; Ashford and Sitar 1997; Ashford et al. 1997; Assimaki et al. 2005; Bouckovalas and Papadimitriou 2005). However, all of these studies considered the response of vertical acceleration that was transformed from a horizontal input motion (i.e., no vertical input acceleration was included). Celebi (1991) reported vertical topographic amplification factors from 0.91 to 1.86 during aftershocks of the 1983 Coalinga, California, earthquake (Mw=6.5). Based on numerical simulations, Zhao and Valliappan (1993) reported topographic amplification factors of 1.5 to 1.8 for the response of various topographies to vertically-incident P-waves, These values are reasonably consistent with the horizontal topographic amplification factors reported in Figure 7.4;

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therefore, vertical topographic amplification factors were assumed to be same as horizontal topographic amplification factors. Most of the shallow, disrupted landslides examined in this study were initiated near slope crests, topographic amplification factors only near the crest were considered. As illustrated in Figure 7.4, horizontal topographic amplification factors range from about 1.0 to 1.9 at the crest. To account for variability, the “three-sigma rule” was applied, and a mean of 1.45 and a standard deviation of 0.15 were estimated. Assuming that vertical topographic amplification is same as the horizontal amplification, horizontal and vertical topographic factors of 1.3, 1.45, and 1.6 were used in the statistical analyses (described subsequently) with weights of 0.2, 0.6, and 0.2, respectively. The range also is supported by Ashford and Sitar (2002) who suggested that amplification due to topography is on the order of 50% regardless of slope geometries and soil profiles.

7.4 Potential bond break effect associated with vertical acceleration Figure 7.5 (a) schematically illustrates the forces involved in a static infinite slope (side forces were assumed to be equal and opposite, and therefore were not included). When an earthquake occurs, the P-waves result in vertical surface accelerations and potentially can “break” weak bonds (i.e., cementation or cohesion) if a pseudo-static vertical acceleration exceeds the slice weight plus tensile force along the base of a slice (Figure 7.5 b). When a distance from the fault is less than 5 km, horizontal and vertical peak ground accelerations can be coincident (Collier and Elnashai 2001). In this case, it was considered that the vertical accelerations still contribute to bond breakage at the same time the horizontal and vertical accelerations shake the sliding mass. Furthermore, high amplitude accelerations oriented perpendicular to the sliding mass, due to the vector resultant of horizontal and vertical accelerations, can increase the possibility of bond break. However, this effect was not considered in the analysis. Using force equilibrium (Figure 7.5 b), bond break occurs when:

Fv  t l cosi W Eq. (7-1 a)

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 t  cos i av,max g  1 Eq. (7-1 b)   Dt

where Fv is the vertical pseudo-static force, equal to kbond×av,max×W. The term kbond, is taken as 1.0 based on the assumption that the maximum acceleration will progressively occur at a slope and potentially break any bond forces along the entire base of the sliding mass. As discussed earlier, topographic amplification factors only near the crest were considered because most of the shallow, disrupted landslides examined in this study were initiated near slope crests. If the bond forces within the rock mass are broken, rock cohesion is considered to be zero for pseudo-static stability calculations.

7.5 Summary Vertical accelerations traditionally have been ignored in pseudo-static slope stability analyses because it is believed to have little influence on slope stability because it reduces both the driving and resisting forces. However, this study revealed that the vertical accelerations play a role in decreasing the FS with large horizontal accelerations. In addition, Ambraseys and Simpson (1996) and Elnashai and Papazouglou (1997) proposed vertical-to-horizontal acceleration ratios that predict the vertical acceleration equal to or greater than horizontal acceleration close to the fault, particularly for large magnitude earthquakes. Furthermore, the vertical acceleration contributes to break the bond force within the rock mass, especially when it is amplified by topographic effect. Based on numerous field and numerical studies, the topographic amplification factors of 1.3, 1.45, and 1.65 were proposed with weights of 0.2, 0.6, and 0.2, respectively.

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2.6 k = 0.5 2.4 v Unit weight = 23 kN/m3 k = 0.4 v Friction angle = 40o 2.2 g kv = 0.3

n Cohesion intercept= 22 kPa i

d k = 0.2 o i v Slope angle = 30

l 2

t kv = 0.1 Slope thickness = 3 m

s n

i 1.8 kv = 0

y 1.6

a s

1.4

r o

t 1.2

c a F 1

0.8

0.6 0 0.1 0.2 0.3 0.4 0.5 Horizontal pseudo-static coefficient, kh

Figure 7.1 Pseudo-static FS computed using various combinations of horizontal and vertical pseudo-static coefficient, kh and kv. Strength and geometric properties represent typical values listed in Table 6.4.

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1.2

Elnashai and Papazouglou (1997) Ambraseys and Simpson (1996)

r a

e 0.8



a l t Ms=

a 7.5

o t

z Ms= r 7.0

i 0.6

e r

o M V s=6.5 H Ms=6.0 Ms=5.5 0.4 M M M M M s s s s s= =5 =6 =6 =7 7 .5 .0 .5 .0 .5

0.2 0 10 20 30 40 50 Distance from the fault (km)

Figure 7.2 Vertical-to-horizontal acceleration ratio for thrust faults by Elnashai and Papazouglou (1997) and Ambraseys and Simpson (1996). Extrapolated portion from Ambraseys and Simpson (1996) is shown in thinner lines.

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(a)

(b)

Figure 7.3 (a) Ground cracking (indicated by XXXs) during the 1971 San Fernando, California, earthquake (Nason 1971); (b) Destruction of a village during the Irpinia, Italy, earthquake (Castellani et al. 1982).

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Figure 7.4 Topographic factors proposed by various researchers.

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Fv=av,max/gW l D

W W

T N i tlcosi (a) (b)

Figure 7.5 Illustration showing procedure of slope stability analysis taking account bond break effect. (a) Dimensions and forces involved in static stability, where W = slice weight; N = normal force; and T = shear force. Side forces are assumed to be equal and opposite, and therefore were not included. (b) Evaluation of “bond break” where av,max = maximum vertical acceleration; t = tensile strength.

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CHAPTER 8. PROPOSED NEW APPROACH TO PSEUDO-STATIC SLOPE STABILITY ANALYSIS AND VERIFICATION USING EARTHQUAKE CASES

8.1 Introduction The proposed procedure for pseudo-static slope stability analysis is presented in Figure 8.1. This procedure accounts for potential vertical accelerations, topographic effects, and bond break effects which were discussed in Chapter 7. This chapter compares factors of safety predicted using the proposed pseudo-static slope stability analysis to landslide concentration data from four earthquakes (2005 Kahsmir, Pakistan, earthquake; 1989 Loma-Prieta, U.S., earthquake; 1999 Chi-Chi, Taiwan, earthquake; and 2008 Wenchuan, China, earthquake). A logic tree approach was employed to perform all the calculations incorporating the uncertainties in each of the parameters.

8.2 2005 Kashmir, Pakistan earthquake As mentioned earlier, vertical accelerations were predicted using two attenuation relationships (Campbell and Bozorgnia 2003; Ambraseys et al. 2005b) and two vertical-to- horizontal acceleration ratios (Ambraseys and Simpson 1996; Elnashai and Papazoglou 1997). These predicted vertical accelerations for the 2005 Kashmir earthquake are shown in Figure 8.2. Table 6.4 summarizes the geometries and rock properties used in the analysis. Figure 8.3 shows the logic tree employed for the 2005 Kashmir earthquake case. The logic tree incorporates mean

(μ) values and mean values ± 1 standard deviation (σ) for material properties (, c', ', and t), and slope geometry parameters (i and Dt). For subsequent statistical analysis, it was assumed that these parameters followed normal distributions, and the weights of 0.6 and 0.2 were assigned to μ and  ± σ values, respectively as shown in Figure 8.3. The logic tree incorporates the four horizontal and four vertical acceleration attenuation relations described above, three topographic factor values, and three values of horizontal and vertical pseudo-static coefficients. This results in 314,928 branches in the logic tree. The logic tree allows us to calculate FS for each branch individually and estimate the mean FS using the weights assigned to each branch. Figure 8.4 compares the mean FS to the LC data collected by Sato et al. (2007). The mean static FS was calculated to be about 2.6, and the mean FS decreased to 1.3 near the fault when horizontal acceleration was included. Clearly these FS values cannot explain the observed LC data. Horizontal accelerations with topographic effects also did not decrease the FS below

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unity. However, when topographic amplification factors were applied to both horizontal and vertical accelerations, the FS became less than unity within about 10 km from the fault. When bond break effects were applied, the FS became smaller than unity at R ~ 13 km. Both of these effects are consistent with the increase in LC that occurs around R ~ 15 km. Figure 8.4 also includes the FS ± 1 standard deviation. Given the large number of variables in the logic tree, the considerable uncertainty in FS was unavoidable. To illustrate the effects of individual variable uncertainty, Figure 8.5 presents mean FS and mean FS ± 1 for several variables involved in the FS calculation. The standard deviation for the static FS is about 0.89. However, when vertical acceleration, topographic effect, and bond break effect were included in the analysis, the standard deviation decreased to 0.63. Thus, the uncertainties in the pseudo-static FS calculation do not appear to overshadow the observed trends in mean FS. Similarly, Figure 8.6 shows the results of a sensitivity analysis for the following rock and geometric parameters: , ', c', i, and Dt. Since the failed rock slopes in this study are consistently highly weathered, the tensile strengths are estimated to be very small. Therefore, the uncertainty in tensile strength did not have much effect on FS in this study, thus the result for tensile strength is not shown here. It is notable that the variation in slope angle results in the largest standard deviation, whereas the variation of unit weight produces minor standard deviation. Another observation is that variation in FS resulting from rock and geometric parameter uncertainties decreases as R decreases. This occurs because ground accelerations have more influence on the FS as ground accelerations become larger. Figure 8.7 shows the results of a sensitivity analysis considering horizontal and vertical pseudo-static coefficients, horizontal and vertical ground accelerations, and the topographic factor. Monte-Carlo simulations were conducted to validate the logic tree approach. Truncated normal distributions (truncated at ±3) were selected for the rock parameters and slope thickness. For slope angles, the same distributions that are reported as shown in Figure 6.5 were used for all earthquake cases. The simulations involved 10,000 runs. Figure 8.8(a) shows the mean FS and mean FS ± 1σ estimated using the Monte-Carlo simulations for the 2005 Kashmir earthquake. The standard deviation for FS was estimated to be slightly larger than that generated by the logic tree approach. This occurs because the Monte-Carlo simulations considered wider ranges for each parameters (up to three standard deviations of each mean parameter), whereas the logic tree approach constrains the parameters to within the mean ± one standard deviation. However, the 122

overall results are similar to those by the logic tree approach. When all factors (horizontal and vertical accelerations, topographic effects, and bond break effects) were considered, the factor of safety became less than unity at approximately 14 km from the updip edge of the fault plane, close to the distance where the LC data start to increase abruptly.

8.3 1989 Loma-Prieta, U.S. earthquake

In 1989, a Mw 6.9 earthquake occurred in the San Francisco Bay-Monterey Bay region of California. The rupture occurred on the San Andreas Fault system with a rupture depth of 3 km to 18 km. The faulting mechanism was oblique reverse with a dip of 60° SW. The region affected by the earthquake includes a variety of sedimentary, igneous, and metamorphic rocks and unconsolidated sedimentary deposits from Jurassic through Holocene-aged (Keefer and Manson 1998). Keefer (2000) performed a statistical analysis of the distribution of 1046 landslides in the southern Santa Cruz Mountains, triggered by the 1989 Loma-Prieta earthquake over an area of 192.41 km2. The fault and landslide locations are shown in Figure 8.11. Based on these data, Keefer (2000) expressed the landslide distribution as a landslide concentration (LC), which is defined as the number of landslides per square kilometer of surface area. Approximately 74% of the 1046 landslides studied by Keefer (2000) were disrupted slides and falls, and the majority of the 1046 landslides occurred in the Purisima Formation, a weakly-cemented sandstone and siltstone. Keefer (2000) reported that the Purisima Formation in which most of landslides occurred consists of weakly cemented sandstones and siltstones, and the rocks are poorly to moderately indurated, and structurally deformed by pervasive folding and local faulting. Keefer and Manson (1989) also reported that disrupted landslides in all units occurred in materials that typically were weakly cemented, closely fractured, intensely weathered, and broken by joints. Based on these descriptions, Table 6.4 summarizes the Hoek-Brown parameters assigned for this case. Mohr- Coulomb strength parameters were computed as: ' = 33° and c' = 20 kPa for the appropriate range of stresses (corresponding to Dt). These calculated values are consistent with the mean ' = 33.1° and median c' = 25.2 kPa measured by McCrink and Real (1996) in the Purisima Formation at a depth of 3 m. As discussed by Keefer (1984), disrupted slides and falls typically involve only the upper few meters of overburden. Therefore, Dt = 1 to 5 m were considered. Figure 6.5 (b) shows the

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distribution of slope angles for slope that failed during the 1989 Loma Prieta earthquake (Khazai and Sitar 2004). A normal distribution was assumed with a mean slope angle of 27° and a standard deviation of 9° to represent the failed slope data. Table 6.4 summarizes the geometric parameters for this case. Figure 8.11 shows the results of the pseudo-static infinite slope stability analyses using the proposed procedure and logic tree approach. The horizontal acceleration (which increases for shorter source-to-site distances, R) clearly reduces the FS, but is not sufficient to drop the mean FS below unity. As anticipated, the vertical acceleration alone does not have much effect on FS because Mw < 7.0. Incorporating topographic effects on the horizontal acceleration significantly reduces the FS; however, the mean FS does not drop below unity R ≤ 6 km. This is inconsistent with the LC data, which shows a significant change in landslide concentration at R ~ 9 km. Incorporating topographic effects with the vertical acceleration also decreases the FS at near- fault distances, with the mean FS = 1.0 at R ~ 10 km, consistent with the significant change in LC. When the bond break effect is incorporated, a further slight decrease in FS occurs at R ≤ 3 km. Similar to the case of Kashmir earthquake, Monte-Carlo simulations yielded results similar to the logic tree approach, as shown in Figure 8.8(b). Figure 8.12 presents mean FS and mean FS ± 1 for several variables involved in the FS calculation. Similarly with the case for the 2005 Kahsmir, Pakistan, earthquake, the standard deviation decreases as more factors are included. The standard deviation for the static FS is about 0.73. However, when all other factors were considered, the standard deviation decreased to 0.44 near fault. Figure 8.13 and Figure 8.14 show the results of a sensitivity analysis for the rock and geometric parameters. The sensitivity analyses again show the similar trend with the case or the 2005 Kahsmir, Pakistan, earthquake.

8.4 1999 Chi-Chi, Taiwan earthquake

The 1999 Chi-Chi earthquake (Mw 7.6) occurred in the mountainous terrain of central Taiwan, and triggered more than 10,000 landslides throughout an area of approximately 11,000 km2 (Hung 2000). The Cher-Long-Pu Fault that ruptured during this event is a thrust fault (dip = 38°, depth to the bottom of rupture = 20 km) trending from south to north (Meunier et al. 2007) as shown in Figure 8.15. The horizontal and vertical accelerations predicted for this earthquake are shown in Figure 8.16.

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Figure 8.15 also shows the landslide locations along the fault and the geologic setting of the affected area. Most of the landslides were shallow, disrupted slides and falls in Tertiary sedimentary and submetamorphic rocks (Khazai and Sitar 2004). The landslide masses commonly were dry, highly disaggregated, weakly cemented, closely fractured, intensely weathered, and broken by conspicuous, highly persistent joints (Khazai and Sitar 2004). Estimated rock properties are presented in Table 6.4. Khazai and Sitar (2004) reported that depth of sliding typically ranged from several decimeters to a meter, and Figure 6.5(c) presents the range of slope angles where the landslides occurred. Although there is slight difference between the distribution of documented slopes and the theoretical normal distribution, it is considered that this difference is acceptable. The resulting geometric parameters are also summarized in Table 6.4. Using the geometric and rock properties in Table 6.4, the computed Mohr-Coulomb strength paremeters are: ' = 51° and c' = 11 kPa for the appropriate range of stresses (corresponding to D). Unlike other cases, the 1999 Chi-Chi, Taiwan earthquake triggered the landslides mostly on steep slopes. In shallow slides, wave incoherency is more likely on steep slopes than on gentle slopes because the vertical travel path of the ground motions increases as the slopes become steeper. It was also found that the FS becomes unreasonable when both kv and i are large in Eq. 6-2. Therefore, to account for potential wave incoherency, yet avoid unreasonable estimates of

FS, kh and kv were limited to values of 0.7(ah,max/g) and 0.7(av,max/g), respectively, for i ≥ 50°. Figure 8.17 shows the mean FS compared to LC data collected by Khazai and Sitar (2004). As a result of the fairly steep slopes, the static FS was computed as 1.4. The FS with the horizontal acceleration became smaller than unity at R ~ 27 km, which is consistent with an increase in LC. However, the FS increases when the vertical accelerations are included because the sliding mass is thin and the slope is steep. When topographic effects were considered, the FS decreases to unity for R ~ 30 km, which approximately matches the distance where LC begins to increase. Bond break effects occur at R ~ 13 km, and the mean FS decreases significantly near the fault. However, it is anticipated that the LC data does not show a significant increase near the fault (even with the small FS at R < 10 km) because the slopes become gentler and more sparsely located near the fault than at some distance from the fault (Meunier et al. 2007). Similar to the case of Kashmir earthquake, Monte-Carlo simulations yielded results similar to the logic tree approach, as shown in Figure 8.8(c).

125

Figure 8.18 presents mean FS and mean FS ± 1 for several variables involved in the FS calculation. Figure 8.19 and Figure 8.20 show the results of a sensitivity analysis for the rock and geometric parameters.

8.5 2008 Wenchuan, China earthquake

On 12 May 2008, the Wenchuan earthquake (Mw 7.9) occurred in the Sichuan Province of China. The earthquake occurred in the compression zone between the Indian and Eurasian plates along the Longmenshan-Beichuan-Yinxiu fault zone (rupture length = 300 km, rupture depth = 14 to 19 km, dip = 60°) (Cui et al. 2009). The isoseismic map along the fault is shown in Figure 8.21. The horizontal and vertical accelerations predicted for this earthquake are shown in Figure 8.22. Figure 8.21 shows the distribution of over 56,000 earthquake-triggered landslides, distributed over an area of 811 km2. These were identified by Dai et al. (2011) using aerial photos and high-resolution satellite images. Yin et al. (2009) and Dai et al. (2011) reported that most of the landslides occurred in weathered or heavily fractured sandstone, siltstone, slate, and phyllite. Based on these descriptions, Table 6.4 summarizes the estimated rock properties. The majority of landslides were shallow, disrupted landslides and rock falls from steep slopes, typically involving the top few meters of weathered bedrock, regolith, and colluvium (Dai et al. 2011). Similarly, Yin et al. (2009) reported typical sliding depths of about 1 to 5 m and slope angles as shown in Figure 6.5. From these descriptions, Table 6.4 includes the estimated geometric parameters for these landslides. The equivalent Mohr-Coulomb strength parameters were calculated as ' = 40° and c' = 27 kPa for the appropriate range of stresses. Figure 8.23 compares the mean FS to the LC data collected by Dai et al. (2011). The static FS was calculated to be 2.1, and the FS decreased to about 1.1 near the fault when horizontal accelerations were included. This mean FS is not consistent with the LC data, particularly at short source-to-site distances. When topographic effects were applied to horizontal accelerations, the mean FS becomes smaller than unity at R ~ 10 km. However, a slight decrease in FS within 10 km from the fault cannot explain the large LC in the near field. Topographic effects on both horizontal and vertical accelerations, as well as bond break effects, decrease the FS below unity within about 13 km of the fault, consistent with the abrupt change in LC at R ~

126

12 km. The Monte-Carlo simulations yielded similar results to the logic tree approach, as shown in Figure 8.8(d). Figure 8.24 presents mean FS and mean FS ± 1 for several variables involved in the FS calculation. Figure 8.25 and Figure 8.26 show the results of a sensitivity analysis for the rock and geometric parameters.

8.6 Summary and conclusion This chapter predicts FS using the proposed pseudo-static slope stability analysis for four earthquakes (2005 Kahsmir, Pakistan, earthquake; 1989 Loma-Prieta, U.S., earthquake; 1999 Chi-Chi, Taiwan, earthquake; and 2008 Wenchuan, China, earthquake). In order to account for uncertainties, the proposed logic tree incorporates mean (μ) values and mean values ± 1 standard deviation (σ) for material properties (, c', ', and t), slope geometry parameters (i and Dt), and the four horizontal and four vertical acceleration attenuation relations. When the proposed factors were considered (vertical ground accelerations, topographic effects, and bond break effects in addition to horizontal accelerations), the mean FS could capture the key features of LC data (abrupt change and high concentration near fault). A series of sensitivity analyses are also presented in this chapter. As the propose factors were included, the standard deviations of FS were computed. For all of cases, standard deviation decreases when horizontal acceleration was considered. Standard deviation also decreases as R decreases. This is because of that ground accelerations have more influence on the FS as ground accelerations become larger. In general, variation in slope angle results in the largest standard deviation, whereas the variation of unit weight produces minor standard deviation.

127

Step 1. Predict horizontal ground acceleration using four attenuation relationships from NGA project (AS08, BA08, CB08, and I08).

Step 2. Predict vertical ground acceleration, using the attenuation relationships by A 05 and CB03 and V/H ratios proposed by EP97 and AS96.

Step 3. Apply topographic factor to both horizontal and vertical accelerations.

Step 4. Check if soil bond breaks when the vertical ground motion arrives.

Step 5. Calculate factor of safety for infinite slope using pseudo-static slope stability analysis including horizontal and vertical accelerations.

Figure 8.1 Flow chart of new approach for the pseudo-static slope stability analysis. AS08, BA08, CB08, and I 08 represent Abrahamson and Silva (2008), Boore and Atkinson (2008), and Campbell and Bozorgnia (2008), and Idriss (2008), respectively. A 05, CB03, EP97, and AS96 represent Ambraseys et al. (2005), Campbell and Bozorgnia (2003), Elnashai and Papazouglou (1997), and Ambraseys and Simpson (1996), respectively.

128

1.2

) Ambraseys et al. (2005)

g 1

(

n Campbell-Bozorgnia (2003)

i t

a Elnashai-Papazouglou (1997)

r 0.8 e

l Ambraseys-Simpson (1996)

d 0.6

l 0.4

r e

V 0.2

0 0 10 20 30 40 50 Distance from surface projection of updip edge of fault plane (km)

Figure 8.2 Vertical acceleration along the distance from the fault predicted for the Mw 7.6 Kashmir, Pakistan, earthquake.

129

Material property Slope geometry Seismic parameter

 c' ' t D i ah av T.F kh kv (kN/m3) (kPa) () (kPa) (m) () A 05 0.9 as below (0.25) (1/3) 0.58 18 CB03 0.9 0.5 as below as below as below (0.2) (0.2) AS08 (0.25) (1/3) (1/3) 34 0.73 2.33 28 (0.25) EP97 1.3 0.5 0.33 (0.2) (0.6) (0.2) (0.6) BA08 (0.25) (0.2) (1/3) (1/3) 19 40 0.88 3 38 (0.25) AS96 1.45 0.33 as above (0.2) (0.6) (0.2) (0.6) (0.2) CB08 (0.25) (0.6) (1/3) as above 20 27 46 3.67 (0.25) 1.6 as above as above as above (0.2) (0.6) (0.2) (0.2) I 08 (0.2) as above 21 35 (0.25) Slope model as above (0.6) (0.2) 22 as above (0.2)

Figure 8.3 Logic tree of slope model for the case of 2005 Kashmir, Pakistan, earthquake.

130

22 2 3 2.8 2.6

) 1.6 2.4

k /

s 2.2

l i

s 2

l s

( 1.2 1.8

, 1.6

e f

a 1.4

e o

c 0.8 1.2

c c

d i

l Mean parameters s 0.8

d Tensile strength = 0.73 kPa n

a 3 L 0.4 Unit weight = 21 kN/m 0.6 Cohesion intercept= 27 kPa Friction angle = 40o 0.4 Slope thickness = 3 m Slope angle = 28o 0.2 0 0 0 10 20 30 40 50 Distance from surface projection of updip edge of fault plane (km)

LC for 2005 Kashmir, Pakistan earthquake

FS with kh+kv+Topographic effect + Bond break effect

FS with kh+kv+Topographic effect

FS with kh + Topographic effect

FS with kh+kv

FS with kh Static FS

Figure 8.4 Landslide concentration data for the 2005 Kashmir, Pakistan, earthquake (Sato et al. 2007) and factor of safety calculated by using various effects. The mean FS ± 1 standard deviation are shown in a shaded area.

131

2 3 g 2 3

)

l )

2.5 s

1.6 1.6

m s

k n

/ i i / 2

2 s

e g

1.2 g 1.2

y s

s 1.5 1.5

f n

n 0.8 0.8

( 1

r L

L 0.4 0.4 o

0.5 o 0.5

t c

(a) c (b)

a F

0 0 F 0 0 g

2 3 g 2 3

)

) s

2.5 s 2.5

1.6 1.6

m s

k n

/ i i

/ 2 2

e g

1.2 g 1.2

y s

s 1.5 1.5

f n

n 0.8 0.8

( 1

r L

L 0.4 0.4 o

0.5 o 0.5

t c

a F

0 0 F 0 0 g

2 3 g 2 3

n n

i i

d d

i i

l l

) ) s

2.5 s 2.5

2 2

1.6 1.6

t t

m s m s

k n k n

i / i

/ 2 2

s s

a a

e e g

1.2 g 1.2

d d

a a

i i

l l

y y s

s 1.5 1.5

t t

d d

e e

f f n

n 0.8 0.8

a a

l l

s s

(

( 1 1

f f

o o

C C

r r L

L 0.4 0.4 o

0.5 o 0.5

t t c

(e) c (f)

a a F 0 0 F 0 0 0 10 20 30 40 50 0 10 20 30 40 50 Distance from surface projection Distance from surface projection of updip edge of fault plane (km) of updip edge of fault plane (km)

Figure 8.5 Mean factor of safety and mean ± 1 standard deviation predicted for the 2005 Kahsmir, Pakistan, earthquake for adding each factor: (a) static condition, (b) with horizontal acceleration (ah), (c) with ah and vertical acceleration (av), (d) with ah and topographic effect, (e) with ah, av, and topographic effect, and (f) ah, av, topographic effect, and bond break effect.

132

2 2.4 2 2.4 g

i d

(b) d i

(a) i

)

) s

2 2 s

1.6 1.6

m s

k n

/ i i

1.6 / 1.6

e g

1.2 1.2 g

y s

1.2 s 1.2

f n

0.8 n 0.8

( 0.8

r L

0.4 L 0.4 o

0.4 0.4 o

a F

0 0 0 0 F g

2 2.4 2 2.4 g

i d

(d) d i

)

l )

2 s

1.6 1.6

m s

k n

/ i i

1.6 / 1.6

e g

1.2 1.2 g

y s

1.2 s 1.2

f n

0.8 n 0.8

( 0.8

r L

0.4 L 0.4 o

0.4 0.4 o

a F 0 0 0 0 F

2 2.4 g 0 10 20 30 40 50 n

i Distance from surface projection d

(e) i

l )

2 s of updip edge of fault plane (km) 2

1.6

m s

k n i

/ 1.6

a e

1.2 g

l y

s 1.2

t d

e FS with mean parameter f

n 0.8

( 0.8

FS with mean parameter + 1 

r L 0.4 FS with mean parameter - 1 

0.4 o

c a

0 0 F 0 10 20 30 40 50 Distance from surface projection of updip edge of fault plane (km) Figure 8.6 Results of sensitivity analysis for material properties and slope geometry parameters for the 2005 Kahsmir, Pakistan, earthquake: (a) unit weight, (b) cohesion intercept, (c) friction angle, (d) slope thickness, and (e) slope angle. Mean FS and mean FS ± 1 standard deviation (σ) are shown for each parameter.

133

2 2.4 2 2.4 g

d i

(a) (b) i

l )

kh=0.33(ah,max/g) ) s

2 2 s

1.6 1.6

m s

k n n

k k =0.33(a /g) i

/ v h,max i

1.6 / 1.6

e g

1.2 1.2 g

0.5 l

y s

1.2 s 1.2

d e

0.7 e

f n

0.8 n 0.8

l s

0.7 s

( 0.8

0.5 f

r L

0.4 L 0.4 o

0.4 0.4 o

a F

0 0 0 0 F g

2 2.4 2 2.4 g

i d

)

l )

2 s

1.6 1.6

m s s

T.F. =1.3 m

k n

/ i i

1.6 / 1.6

e g

1.2 1.2 g

y s

1.6 1.2 s 1.2

f n

0.8 1.45 n 0.8 a

AS a

( 0.8

BA f

r L

0.4 L 0.4 o

0.4 0.4 o t

CB t

a a

F I 0 0 0 0 F

2 2.4 g 0 10 20 30 40 50 n i Distance from surface projection

(e) d

l )

2 s of updip edge of fault plane (km) 2

1.6

m s

k n i

/ 1.6

a e

1.2 g AS: Abrahamson-Silva 2008

y BA: Boore-Atkinson 2008

s 1.2

A t

e f

n 0.8 CB: Campbell-Bozorgnia 2008 a

a CB

( 0.8 I: Idriss 2008

f o

C EP

L 0.4

0.4 o

AS t A: Ambraseys et al. 2005

c a

0 0 F CB: Campbell-Bozorgnia 2003 0 10 20 30 40 50 EP: Elnashai-Papazouglou 1997 Distance from surface projection AS: Ambraseys-Simpson 1996 of updip edge of fault plane (km)

Figure 8.7 Results of sensitivity analysis for (a) kh, (b) kv, (c) topographic factor, (d) horizontal acceleration, and (e) vertical acceleration for the 2005 Kahsmir, Pakistan, earthquake.

134

Figure 8.8 Mean factor of safety and mean ± 1 standard deviation by using the Monte-Carlo simulation for (a) 2005 Kashmir, Pakistan earthquake, (b) 1989 Loma-Prieta earthquake, (d) 1999 Chi-Chi, Taiwan earthquake, and (d) 2008 Wenchuan, China earthquake.

135

Figure 8.9 Limits of southern Santa Cruz Mountains landslide area (left) and locations of earthquake-induced landslides with the surface projection of fault rupture (right) (Keefer 2000)

136

0.8

)

(

n o

i 0.6

n 0.4

r G

0.2

0 0 10 20 30 40 50 Distance from surface projection of updip edge of fault plane (km)

Horizontal accelerations Vertical accelerations Abrahamson and Silva (2008) Ambraseys et al. (2005) Boore and Atkinson (2008) Campbell and Bozorgnia (2003) Campbell and Bozorgnia (2008) Elnashai and Papazouglou (1997) Idriss (2008) Ambraseys and Simpson (1996)

Figure 8.10 Horizontal and vertical accelerations with respect to source-to-site distance predicted for the Mw 6.9 1989 Loma-Prieta earthquake.

137

2 3 2.8 2.6

) 1.6 2.4

k /

s 2.2

l i

s 2

l s

( 1.2 1.8

, 1.6

e f

a 1.4

e o

c 0.8 1.2

c c

F d

i Mean parameters l s 0.8

d Tensile strength = 0.29 kPa n a Unit weight = 21 kN/m3 L 0.4 0.6 Cohesion intercept = 20 kPa Friction angle = 33o 0.4 Slope thickness = 3 m Slope angle = 27o 0.2 0 0 0 10 20 30 40 50 Distance from surface projection of updip edge of fault plane (km)

LC for 1989 Loma Prieta, CA earthquake

FS with kh+kv+Topographic effect + Bond break effect

FS with kh+kv+Topographic effect

FS with kh + Topographic effect

FS with kh+kv

FS with kh Static FS

Figure 8.11 Landslide concentration data for the 1989 Loma-Prieta earthquake by Keefer (2000) and factor of safety calculated by using various effects. The mean FS ± 1 standard deviation are shown in a shaded area.

138

2 3 g 2 3

)

l )

2.5 s

1.6 1.6

m s

k n

/ i i

/ 2 2

e g

1.2 g 1.2

y s

s 1.5 1.5

f n

n 0.8 0.8

( 1

r L

L 0.4 0.4 o

0.5 o 0.5

t c

(a) c (b)

a F

0 0 F 0 0 g

2 3 g 2 3

)

) s

2.5 s 2.5

1.6 1.6

m s

k n

/ i i

/ 2 2

e g

1.2 g 1.2

y s

s 1.5 1.5

f n

n 0.8 0.8

( 1

r L

L 0.4 0.4 o

0.5 o 0.5

t c

a F

0 0 F 0 0 g

2 3 g 2 3

n n

i i

d d

i i

l l

) ) s

2.5 s 2.5

2 2

1.6 1.6

t t

m s m s

k n k n

i / i

/ 2 2

s s

a a

e e g

1.2 g 1.2

d d

a a

i i

l l

y y s

s 1.5 1.5

t t

d d

e e

f f n

n 0.8 0.8

a a

l l

s s

(

( 1 1

f f

o o

C C

r r L

L 0.4 0.4 o

0.5 o 0.5

t t c

(e) c (f)

a a F 0 0 F 0 0 0 10 20 30 40 50 0 10 20 30 40 50 Distance from surface projection Distance from surface projection of updip edge of fault plane (km) of updip edge of fault plane (km)

Figure 8.12 Mean factor of safety and mean ± 1 standard deviation predicted for the 1989 Loma- Prieta, U.S., earthquake for adding each factor: (a) static condition, (b) with horizontal acceleration (ah), (c) with ah and vertical acceleration (av), (d) with ah and topographic effect, (e) with ah, av, and topographic effect, and (f) ah, av, topographic effect, and bond break effect.

139

2 2.4 2 2.4 g

)

) s

2 2 s

1.6 1.6

m s

k n

/ i i

1.6 / 1.6

e g

1.2 1.2 g

y s

1.2 s 1.2

f n

0.8 n 0.8

( 0.8

r L

0.4 L 0.4 o

0.4 0.4 o

t c

(a) (b) c

a F

0 0 0 0 F g

2 2.4 2 2.4 g

)

l )

2 s

1.6 1.6

m s

k n

/ i i

1.6 / 1.6

e g

1.2 1.2 g

y s

1.2 s 1.2

f n

0.8 n 0.8

( 0.8

r L

0.4 L 0.4 o

0.4 0.4 o

t c

a F 0 0 0 0 F

2 2.4 g 0 10 20 30 40 50 n

i Distance from surface projection

l )

2 s of updip edge of fault plane (km) 2

1.6

m s

k n i

/ 1.6

a e

1.2 g

l y

s 1.2

t d

e FS with mean parameter f

n 0.8

( 0.8 FS with mean parameter + 1 

r L 0.4 FS with mean parameter - 1 

0.4 o t

(e) c a

0 0 F 0 10 20 30 40 50 Distance from surface projection of updip edge of fault plane (km)

Figure 8.13 Results of sensitivity analysis for material properties and slope geometry parameters for the 1989 Loma-Prieta, U.S., earthquake: (a) unit weight, (b) cohesion intercept, (c) friction angle, (d) slope thickness, and (e) slope angle. Mean FS and mean FS ± 1 standard deviation (σ) are shown for each parameter.

140

2 2.4 2 2.4 g

d i

k =0.33(a /g) i

l )

h h,max ) s

2 2 s

1.6 1.6 k =0.33(a /g) t

v v,max t

m s

k n

/ i i

1.6 / 1.6

e g

1.2 1.2 g

y s

1.2 s 1.2

t t

d 0.5(a /g)

d e

h,max e

f n

0.8 n 0.8 0.5(a /g) a

v,max a

( 0.8

0.9(ah,max/g) 0.9(av,max/g) f

r L

0.4 L 0.4 o

0.4 0.4 o

t c

(a) (b) c

a F

0 0 0 0 F g

2 2.4 2 2.4 g

)

l )

2 s

1.6 1.6

m s s

TF =1.30 m

k n

/ i i 1.6 /

s 1.6

e g

1.2 1.2 g

a i

y s

1.2 s 1.2

d e

BA e

f n

0.8 1.45 n 0.8

( 0.8

( CB 0.8

1.60 f

r r

L I

0.4 L 0.4 o

0.4 0.4 o

t c

a F 0 0 0 0 F

2 2.4 g 0 10 20 30 40 50 n

i Distance from surface projection

l )

2 s of updip edge of fault plane (km) 2

1.6

m s

k n i

/ 1.6

a e

1.2 g AS: Abrahamson-Silva 2008 d

A a

y BA: Boore-Atkinson 2008

s 1.2

t d

CB e f

n 0.8 CB: Campbell-Bozorgnia 2008

l s

( 0.8 I: Idriss 2008

AS r

L 0.4

0.4 o t A: Ambraseys et al. 2005

(e) c a

0 0 F CB: Campbell-Bozorgnia 2003 0 10 20 30 40 50 EP: Elnashai-Papazouglou 1997 Distance from surface projection AS: Ambraseys-Simpson 1996 of updip edge of fault plane (km)

Figure 8.14 Results of sensitivity analysis for (a) kh, (b) kv, (c) topographic factor, (d) horizontal acceleration, and (e) vertical acceleration for the 1989 Loma-Prieta, U.S., earthquake.

141

Figure 8.15 Locations of landslides induced by 1999 Chi-Chi, Taiwan, earthquake along the Cher-Long-Pu fault and geological setting of affected area (Khazai and Sitar 2004)

142

0.8

)

(

o i

t 0.6

n 0.4

r G

0.2

0 0 10 20 30 40 50 Distance from surface projection of updip edge of fault plane (km)

Figure 8.16 Horizontal and vertical accelerations with respect to source-to-site distance predicted for the Mw 7.6 1999 Chi-Chi, Taiwan, earthquake.

143

1 3 2.8 Mean parameters Tensile strength = 0.73 kPa 2.6 Unit weight = 24 kN/m3

) 0.8 2.4 2 Cohesion intercept = 11 kPa

m o

k Friction angle = 51 /

s 2.2

e Slope thickness = 0.7 m

d i

o n l Slope angle = 65 i

s 2

l s

( 0.6 1.8

, 1.6

e f

a 1.4

e o

c 0.4 1.2

c c

i l

s 0.8

n a

L 0.2 0.6 0.4 0.2 0 0 0 10 20 30 40 50 Distance from surface projection of updip edge of fault plane (km)

LC for 1999 Chi-Chi, Taiwan earthquake

FS with kh+kv+Topographic effect + Bond break effect

FS with kh+kv+Topographic effect

FS with kh + Topographic effect

FS with kh+kv

FS with kh Static FS

Figure 8.17 Landslide concentration data for the 1999 Chi-chi, Taiwan, earthquake (Khazai and Sitar 2004) and factor of safety calculated by using various effects. The mean FS ± 1 standard deviation are shown in a shaded area.

144

0.8 3 g 0.8 3

)

l )

2.5 s

m s s

m 0.6 0.6

k n

/ i i / 2

2 s

y s

s 0.4 1.5 0.4 1.5

( 1

o C

C 0.2

0.2

L o

0.5 o 0.5

t c

(a) c (b)

a F

0 0 F 0 0 g

0.8 3 g 0.8 3

)

) s

2.5 s 2.5

m s s

m 0.6 0.6

k n

/ i i

/ 2 2

y s

s 0.4 1.5 0.4 1.5

( 1

o C

C 0.2 0.2

L o

0.5 o 0.5

t c

a F

0 0 F 0 0 g

0.8 3 g 0.8 3

n n

i i

d d

i i

l l

) ) s

2.5 s 2.5

2 2

t t

s m s

m 0.6 0.6

k n k n

i / i

/ 2 2

s s

a a

e e

g g

d d

a a

i i

l l

y y s

s 0.4 1.5 0.4 1.5

t t

d d

e e

f f

n n

a a

l l

s s

(

( 1 1

f f

o o C

C 0.2 0.2

r r

L L o

0.5 o 0.5

t t c

(e) c (f)

a a F 0 0 F 0 0 0 10 20 30 40 50 0 10 20 30 40 50 Distance from surface projection Distance from surface projection of updip edge of fault plane (km) of updip edge of fault plane (km) Figure 8.18 Mean factor of safety and mean ± 1 standard deviation predicted for the 1999 Chi- Chi, Taiwan, earthquake for adding each factor: (a) static condition, (b) with horizontal acceleration (ah), (c) with ah and vertical acceleration (av), (d) with ah and topographic effect, (e) with ah, av, and topographic effect, and (f) ah, av, topographic effect, and bond break effect.

145

0.8 2 0.8 2 g

i d

(b) d i

(a) i

)

1.6 1.6

m s s

0.6 m 0.6

k n

/ i

e g

1.2 1.2 g

y s

0.4 s 0.4

f n

0.8 n 0.8

(

o C

0.2 C 0.2

r L

0.4 L 0.4

a F

0 0 0 0 F g

0.8 2 0.8 2 g

i d

(d) d i

)

1.6 1.6

m s s

0.6 m 0.6

k n

/ i

e g

1.2 1.2 g

y s

0.4 s 0.4

f n

0.8 n 0.8

(

o C 0.2 C

0.2

r L

0.4 L 0.4

a F 0 0 0 0 F

0.8 2 g 0 10 20 30 40 50 n

i Distance from surface projection d

(e) i

l )

s of updip edge of fault plane (km) 2

1.6

t s

m 0.6

k n

/ i

a e

1.2 g

l y

s 0.4

t d

e FS with mean parameter f

n 0.8

(

FS with mean parameter + 1 

f o

C 0.2

L 0.4 FS with mean parameter - 1 

c a

0 0 F 0 10 20 30 40 50 Distance from surface projection of updip edge of fault plane (km) Figure 8.19 Results of sensitivity analysis for material properties and slope geometry parameters for the 1999 Chi-Chi, Taiwan, earthquake: (a) unit weight, (b) cohesion intercept, (c) friction angle, (d) slope thickness, and (e) slope angle. Mean FS and mean FS ± 1 standard deviation (σ) are shown for each parameter.

146

0.8 2 0.8 2 g

d i

(a) (b) i

)

1.6 k =0.33(a /g) 1.6 t

k =0.33(a /g) v v,max t s

m h h,max s

0.6 m 0.6

k n

/ i

e g

1.2 1.2 g

y s

0.4 s 0.4

e f

0.5 f n

0.8 n 0.8

a a

a 0.9

(

f 0.5

0.9 f

o C

0.2 C 0.2

r L

0.4 L 0.4

a F

0 0 0 0 F g

0.8 2 0.8 2 g

i d

)

1.6 1.6

m s s

0.6 m 0.6

k n n

T.F. =1.3 k

/ i

e g

1.2 1.2 g

y s

0.4 s 0.4

f n 1.6 0.8 n 0.8

a AS

(

1.45 (

BA f

o C 0.2 C

0.2

r L

0.4 L 0.4

o o

t CB

c a

I a F 0 0 0 0 F

0.8 2 g 0 10 20 30 40 50 n i Distance from surface projection

(e) d

l )

s of updip edge of fault plane (km) 2

1.6

t s

m 0.6

k n

/ i

a e

1.2 g AS: Abrahamson-Silva 2008

y BA: Boore-Atkinson 2008

s 0.4

t d

A e f

n 0.8 CB: Campbell-Bozorgnia 2008

( CB I: Idriss 2008

f o

C 0.2

L EP 0.4 o t A: Ambraseys et al. 2005

AS c a

0 0 F CB: Campbell-Bozorgnia 2003 0 10 20 30 40 50 EP: Elnashai-Papazouglou 1997 Distance from surface projection AS: Ambraseys-Simpson 1996 of updip edge of fault plane (km)

Figure 8.20 Results of sensitivity analysis for (a) kh, (b) kv, (c) topographic factor, (d) horizontal acceleration, and (e) vertical acceleration for the 1999 Chi-Chi, Taiwan, earthquake.

147

Figure 8.21 Distribution of earthquake-triggered landslides (black polygons) on the isoseismic map (Dai et al. 2011)

148

0.8

)

(

o i

t 0.6

n 0.4

r G

0.2

0 0 10 20 30 40 50 Distance from surface projection of updip edge of fault plane (km)

Figure 8.22 Horizontal and vertical accelerations with respect to source-to-site distance predicted for the Mw 7.9 2008 Wenchuan, China, earthquake.

149

8 3

Mean parameters 2.8 Tensile strength = 0.73 kPa 7 Unit weight = 24 kN/m3 2.6 Cohesion intercept = 27 kPa ) 2.4 2 o

m Friction angle = 40

k 6 /

s Slope thickness = 3 m 2.2 e

o g

d Slope angle = 33

l i

s 2

n s

l s

( 1.8

, 1.6

n y

o 4

e f

a 1.4

e o

c 1.2

n 3

c c

i l s 0.8

d 2

n a

L 0.6

1 0.4 0.2 0 0 0 10 20 30 40 50 Distance from surface projection of updip edge of fault plane (km)

LC for 2008 Wenchuan, China earthquake

FS with kh+kv + Topographic effect + Bond break effect

FS with kh+kv + Topographic effect

FS with kh + Topographic effect

FS with kh+kv

FS with kh Static FS

Figure 8.23 Landslide concentration data for the 2008 Wenchuan, China, earthquake (Dai et al. 2010) and factor of safety calculated by using various effects. The mean FS ± 1 standard deviation are shown in a shaded area.

150

8 3 g 8 3

)

l )

2.5 s

m s s

m 6 6

k n

/ i i / 2

2 s

y s

s 4 1.5 4 1.5

( 1

o C

C 2

L o 0.5 o (b) 0.5

(a) t

a F

0 0 F 0 0 g

8 3 g 8 3

)

) s

2.5 s 2.5

m s s

m 6 6

k n

/ i i

/ 2 2

y s

s 4 1.5 4 1.5

( 1

o C

C 2 2

L o

a F

0 0 F 0 0 g

8 3 g 8 3

n n

i i

d d

i i

l l

) ) s

2.5 s 2.5

2 2

t t

s m s

m 6 6

k n k n

i / i

/ 2 2

s s

a a

e e

g g

d d

a a

i i

l l

y y s

s 4 1.5 4 1.5

t t

d d

e e

f f

n n

a a

l l

s s

(

( 1 1

f f

o o C

C 2 2

r r

L L o

(e) 0.5 o (f) 0.5

t t

c c

a a F 0 0 F 0 0 0 10 20 30 40 50 0 10 20 30 40 50 Distance from surface projection Distance from surface projection of updip edge of fault plane (km) of updip edge of fault plane (km)

Figure 8.24 Mean factor of safety and mean ± 1 standard deviation predicted for the 2008 Wenchuan, China, earthquake for adding each factor: (a) static condition, (b) with horizontal acceleration (ah), (c) with ah and vertical acceleration (av), (d) with ah and topographic effect, (e) with ah, av, and topographic effect, and (f) ah, av, topographic effect, and bond break effect.

151

8 2.4 8 2.4 g

i d

(b) d i

(a) i

)

) s

2 2 s

m s s

6 m 6

k n

/ i i

1.6 / 1.6

y s

4 1.2 s 4 1.2

( 0.8

o C

2 C 2

L o

0.4 0.4 o

a F

0 0 0 0 F g

8 2.4 8 2.4 g

i d

(d) d i

)

l )

2 s

m s s

6 m 6

k n

/ i i 1.6 /

s 1.6

y s

4 1.2 s 4 1.2

( 0.8

o C 2 C

L o

0.4 0.4 o

a F 0 0 0 0 F

8 2.4 g 0 10 20 30 40 50 n

i Distance from surface projection d

(e) i

l )

2 s of updip edge of fault plane (km)

t s

m 6

k n i

/ 1.6

l y

s 4 1.2

t d

e FS with mean parameter

( 0.8

FS with mean parameter + 1 

f o

C 2

r L FS with mean parameter - 1 

0.4 o

c a

0 0 F 0 10 20 30 40 50 Distance from surface projection of updip edge of fault plane (km)

Figure 8.25 Results of sensitivity analysis for material properties and slope geometry parameters for the 2008 Wenchuan, China, earthquake: (a) unit weight, (b) cohesion intercept, (c) friction angle, (d) slope thickness, and (e) slope angle. Mean FS and mean FS ± 1 standard deviation (σ) are shown for each parameter.

152

8 2.4 8 2.4 g

d i

(a) (b) i

l )

kh=0.33(ah,max/g) ) s

2 2 s

m s s

6 m 6 n

k k =0.33(a /g) n

k v v,max

/ i i

1.6 / 1.6

y s

4 1.2 s 4 1.2 t

0.5 t

l s

0.9 s

( 0.8

o C

2 C 2

L o

0.4 0.4 o t

0.5 t

c a

0.9 a F

0 0 0 0 F g

8 2.4 8 2.4 g

i d

)

l )

2 s

m s s

6 m 6

k n n

T.F. =1.3 k

/ i i 1.6 /

s 1.6

y s

4 1.2 s 4 1.2

d e

BA e

f n

1.45 n

( 0.8 1.6 ( 0.8

o C 2 C

r L

L I o

0.4 0.4 o

a F 0 0 0 0 F

8 2.4 g 0 10 20 30 40 50 n i Distance from surface projection

(e) d

l )

2 s of updip edge of fault plane (km)

t s

m 6

k n i

/ 1.6

a e

g AS: Abrahamson-Silva 2008 d

A a

y BA: Boore-Atkinson 2008

s 4 1.2 t

d CB

e f

n CB: Campbell-Bozorgnia 2008

a l

EP s

( 0.8 I: Idriss 2008

f o

C 2

r L

0.4 o

t A: Ambraseys et al. 2005

c a

0 0 F CB: Campbell-Bozorgnia 2003 0 10 20 30 40 50 EP: Elnashai-Papazouglou 1997 Distance from surface projection AS: Ambraseys-Simpson 1996 of updip edge of fault plane (km)

Figure 8.26 Results of sensitivity analysis for (a) kh, (b) kv, (c) topographic factor, (d) horizontal acceleration, and (e) vertical acceleration for the 2008 Wenchuan, China, earthquake.

153

CHAPTER 9. CONCLUSIONS AND RECOMMENDATION FOR FUTURE RESEARCH

9.1 Summary and conclusions Several seismic hazard studies have been recently conducted for regions of Pakistan because of its active tectonic setting. However, the prior seismic studies used the diffuse areal source zones, resulting in underestimation of seismic hazard near faults. The earthquake-induced landslide is one of the most common secondary effects of earthquake as extensive landslides occurred in NW Pakistan during the 2005 Kashmir earthquake. However, the currently used approach of seismic slope stability analysis cannot capture the regional distribution of landslides. The goal of this research is to assess the seismic hazard in NW Pakistan using discrete faults rather than areal sources, and to propose the factors that affect the seismic slope stability and explain the regional distribution of earthquake-induced landslides.

9.1.1 Seismic hazard analyses The methodology of seismic hazard analysis in NW Pakistan was proposed in this dissertation. In lieu of using the area source zones proposed by other studies (NORSAR and PMD 2006; PMD and NORSAR 2006; Monalisa et al. 2007), 32 discrete faults were employed with their surface traces, geometries, and faulting mechanisms. Then the earthquake catalog was used to construct the exponential recurrence models. For activity rate of the exponential recurrence model, two different period of earthquake catalogs were used; including and excluding the earthquake event in 2005. This was because of that extremely high amount of foreshocks and aftershocks of 2005 Kashmir earthquake could bias the result. The earthquake data from the recent 30-year interval were used to estimate the activity rate and b-value because earthquakes for 4≤Mw<6 are considered to be incomplete prior to 1975. The large magnitude range of computed recurrence model matches with the earthquake data for 100-year interval. In order to estimate characteristic rate of the characteristic recurrence model, three methods were proposed. The first method assumes that the characteristic rate is related with the slip rate of faults. The second method employs the assumption that the characteristic rate is proportional to the activity rate. The third method is using the seismic moment balance method proposed by Aki (1966). All these parameters and models were implemented in the logic tree and reasonable weight for each branch of the logic tree was assigned. Finally four NGAs were selected based on

154

the fact that they can capture the measured ground acceleration during the 2005 Kashmir, Pakistan, earthquake, and were used according to the fault models developed in this study. Seismic hazard curves and seismic hazard spectra were generated for selected cities. Seismic hazard maps corresponding to 475-, 975-, and 2475-year return periods were also generated for the region of NW Pakistan. The results show that cities with the highest hazards are Kaghan and Muzaffarabad, with PGA ~ 0.6g for a 475-year return period. Islamabad, the capital city of Pakistan, also has a significant seismic hazard, much higher than predicted by previous studies. On the other hand, much lower ground motions were predicted for the cities located farther from active faults, including Astor, Bannu, Malakand, Mangla, Peshawar, and Talagang. However, the PGAs computed for these cities are still similar to or slightly higher than those by previous studies. Despite the uncertainties and assumptions associated with both the deterministic and probabilistic seismic hazard analyses, the results from both methodologies were comparable, thus providing a measure of confidence in the results. The computed hazards also correspond well to the known seismic history of the region, including the recent 2005 Kashmir earthquake. In addition, use of the conditional mean spectrum instead of the uniform hazard spectrum could provide significant efficiency in seismic design in many cities in NW Pakistan.

9.1.2 Seismic slope stability analyses When earthquakes occur in mountainous regions, earthquake-induced landslides and rockfalls commonly cause significant damage. However, current practice of using pseudo-static slope stability analysis to evaluate landslides only accounts for the horizontal ground acceleration, and does not predict factors of safety that are consistent with available landslide concentration data. This study proposed three other factors that can influence rock slope stability: (1) vertical ground accelerations; (2) topographic effects; and (3) “bond break” effects. The vertical ground acceleration, when estimated using available attenuation relations and vertical-to-horizontal acceleration ratios, can equal the horizontal acceleration in the near- fault region for large magnitude earthquakes. For gentle to moderate slopes (i.e., less than ~ 60°) and sliding depths exceeding about 1 m, incorporating large vertical accelerations in a pseudo- static stability analysis tends to decrease the FS. While the effect of vertical acceleration on the computed FS is not significant, this study suggests that it should not be ignored. Furthermore,

155

both the horizontal and vertical accelerations may be amplified near slope crests as a result of constructive geometric wave interference, i.e., topographic effects. When the vertical acceleration was amplified by a topographic factor, the effect of vertical accelerations on FS became more important. Lastly, the occurrence of high amplitude vertical accelerations on slopes may damage or “break” interparticle bonding (i.e., cementation, cohesion, etc.) along rock bedding planes, particularly near the ground surface where weathering and jointing is commonly more severe, effectively eliminating the equivalent cohesion of the rock. If bonding is destroyed, the FS can decrease considerably. In fact, observations in many earthquakes suggest that most earthquake-induced landslides are shallow, disrupted slides and falls that occur near slope crests or peaks, where topographic amplification and bond break effects are most likely to occur. In this dissertation, a new approach to evaluate regional pseudo-static slope stability that accounts for vertical accelerations, potential topographic amplification, and potential bond breakage was proposed. The procedure was incorporated into a logic tree approach to account for variability in both rock and geometric properties of the slope. To examine the applicability of the newly proposed method, factors of safety computed with this procedure was compared to landslide concentration data collected during four recent earthquakes (1989 Loma-Prieta, 1999 Chi-Chi, 2005 Kashmir, and 2008 Wenchuan). Observations from these events all show abrupt changes in landslide concentration in the near-fault region. When the computed FS incorporates vertical accelerations, topographic effects, and bond breakage, the FS trends are consistent with the observed trends in landslide concentration, and qualitatively explain the abrupt increase in landslide concentration in the near-fault region of these earthquakes.

9.2 Recommendations for future work 1) Although this study estimated some of the input parameters based on best estimates due to lack of information on fault properties in NW Pakistan, it is necessary to obtain these parameters as appropriately as possible in the future to yield the most reliable results. Obtaining the precise fault width and dip is very important task in seismic hazard analysis not only because the fault geometry determines the distance between source and site, but also because it affects the determination of upper bound magnitude. Slip rate of individual fault is another important fault property that needs

156

to be well investigated because it plays a significant role in estimating the proper characteristic rate. 2) Unfortunately, no region-specific ground motion prediction model is available for Pakistan although this region is seismically highly active. Developing the GMPE that is suitable for local conditions in Pakistan is the essential task that will improve the seismic hazard assessment of this region. 3) There are seismic hazard studies conducted based on the area source zone for various regions because the faults are not well-characterized, resulting in underestimation of seismic hazard. It is necessary to assess the seismic hazard using available information on discrete faults for these regions. 4) The proposed factors that affect the slope stability need to be applied to other methods including Newmark’s sliding method and energy-based method. The new approach proposed in this thesis can also be extended to evaluate the stability of individual slopes.

157

APPENDICES

158

APPENDIX A. ESTIMATION OF MOHR-COULOMB STRENGTH PARAMETERS A1. DETERMINATION OF PARAMETERS FOR HOEK-BROWN CRITERION

1) Uniaxial compressive strength of the intact rock, σci

No information is available for the uniaxial compressive strength of intack rock for the failure mass of four earthquake cases in this study. Therefore, ci = 2 MPa was considered based on the typical value for highly weathered rock (Table A. 1) suggested by Hoek et al. (1998) for the case of 1999 Chi-Chi, 2005 Kahsmir, and 2008 Wenchuan earthquakes. Measured values of friction angle and cohesion intercept are available for the case of 1989 Loma-Prieta earthquake by McCrink and Real (1996). The ci of 0.8 MPa was then estimated to yield the equivalent Mohr-Coulomb parameters consistent with the measured mean friction angle and median cohesion intercept of 33.1° and 25.2 kPa, respectively.

2) Material constant for intact rock, mi

mi can be obtained from Table A. 2. Majority of landslides occurred in sedimentary rocks which consist of sandstone and siltstone for all cases of earthquake. Therefore the average of mi for sandstone (19) and siltstone (9) was used in the analysis.

3) Geological strength index, GSI

GSI classification is based on an assessment of the lithology, structure and condition of discontinuity surfaces in the rock mass (Marinos et al. 2005). Based on the description of failure mass, it can be concluded for all earthquake cases that the surface conditions of failure masses are highly weathered, and the structures are blocky/disturbed and folded. Therefore, the GSI of 30 was obtained from Figure A. 1.

The descriptions for surface condition and structure of failure mass for four earthquake cases are as below:

159

2005 Kashmir, Pakistan, earthquake: Kamp et al. (2008) described the failed sedimentary rocks as undeformed to tightly-folded, highly-cleaved and fractured. Owen et al. (2008) observed that these shallow landslides typically involved the top few meters of weathered bedrock, regolith, and soil.

1989 Loma-Prieta, U.S., earthquake: Keefer (2000) reported that the Purisima Formation in which most of landslides occurred consists of weakly cemented sandstones and siltstones, and the rocks are poorly to moderately indurated, and structurally deformed by pervasive folding and local faulting. Keefer and Manson (1989) also reported that disrupted landslides in all units occurred in materials that typically were weakly cemented, closely fractured, intensely weathered, and broken by joints.

1999 Chi-Chi, Taiwan, earthquake: The landslide masses commonly were dry, highly disaggregated, weakly cemented, closely fractured, intensely weathered, and broken by conspicuous, highly persistent joints (Khazai and Sitar 2004).

2008 Wenchuan, China, eartqhauke: Yin et al. (2009) and Dai et al. (2011) reported that most of the landslides occurred in weathered or heavily fractured sandstone, siltstone, slate, and phyllite.

4) Disturbance factor (DF)

Hoek et al. (2002) proposed the use of disturbance factor (DF) to account for the effects of heavy blast damage and stress relief due to removal of the overburden. As shown in Table A. 3, DF = 0 is suggested when there is no damage from blasting or excavation, whereas DF= 1 is suggested for the rocks affected by heavy blast damage or stress relief. The DF was considered to be 0 in this study because there was no evidence for disturbance due to heavy blasting and stress relief for all earthquake cases.

160

A2. ESTIMATION OF TENSILE STRENGTH AND MOHR-COULOMB STRENGTH PARAMETERS Hoek and Brown (Hoek and Brown 1980) proposed the failure criterion for heavily jointed rock masses which can be expressed as:

0.5        3  1   3  ci m  s Eq. (A-1)   ci 

where 1 and  3 are the major and minor effective principal stresses

 ci is the uniaxial compressive strength of the intact rock m and s are material constants, where s =1 for intact rock.

The generalized Hoek-Brown criterion takes into account the GSI, and can be expressed as (Hoek et al. 2002):

a        3  Eq. (A-2) 1   3  ci mb  s   ci 

where mb is a reduced value of the material constant mi, and is given by

 GSI 100  mb  mi exp  Eq. (A-3)  28 14DF 

 GSI 100  s  exp  Eq. (A-4)  9  3DF 

1 1 a   eGSI 15  e20 3  Eq. (A-5) 2 6

The tensile strength can be computes as: 161

s ci  t   Eq. (A-6) mb

Since most of slope stability analysis requires the Mohr-Coulomb strength parameters that are not directly measured for rock, it is necessary to determine equivalent friction angle and cohesion intercept parameters for failure mass. This can be done by fitting an average linear relationship to the Hoek-Brown criterion for an appropriate stress range.

Using the fitting process that involves balancing the areas above and below the Mohr- Coulomb plot, Hoek et al. (2002) proposed the following equations for ' and c':

 6am s  m   a1    sin 1  b b 3n  Eq. (A-7)   a1  21 a2  a 1 6amb s  mb 3n  

 1 2as  1 am   s  m   a1 c  ci b 3n b 3n 1 6am s  m   a1 1 a2  a b b 3n 1 a2  a Eq. (A-8)

 3max where  3n   ci

Figure A. 2 shows Hoek-Brown criteria and Mohr-Coulomb fits corresponding to appropriate stress ranges based on thickness and unit weight of failure mass (i.e. approximately 0.06-0.08 MPa for 2005 Kahsmir, 1989 Loma-Prieta, and 2008 Wenchuan earthquakes, and approximately 0.02 MPa for 1999 Chi-Chi earthquake).

162

Table A. 1 Field estimates of the uniaxial compressive strength of intact pieces (Hoek et al. 1998). Uniaxial Point load Term compressive index Field estimate of strength Examples strength (MPa) (MPa) Extremely Specimen can only be chipped with a Fresh basalt, chert, diabase, gneiss, >250 >10 strong geological hammer granite, quartzite Amphibolite, sandstone, basalt, gabbro, Very Specimen requires many blows of a 100-250 4-10 gneiss, granodiorite, limestone, marble, strong geological hammer to fracture it rhyolite, tuff Specimen requires more than one blow of a Limestone, marble, phyllite, sandstone, Strong 50-100 2-4 geological hammer to fracture it schist, shale Cannot be scraped or peeled with a pocket Medium Claystone, coal, concrete, schist, shale, 25-50 1-2 knife, specimen can be fractured with a strong siltstone single blow from a geological hammer Can be peeled with a pocket knife with Weak 5-25 * difficulty, shallow indentation made by firm Chalk, rocksalt, potash blow with point of a geological hammer Crumbles under firm blows with point of a Very weak 1-5 * geological hammer, can be peeled by a Highly weathered or altered rock pocket knife Extremely 0.25-1 * Indented by thumbnail Stiff fault gouge weak * Point load tests on rocks with a uniaxial compressive strength below 25 MPa are likely to yield ambiguous results

163

Table A. 2 Values of constant mi for intact rock. Values in parenthesis are estimates (Hoek et al. 1998). Texture Rock type Class Group Coarse Medium Fine Very fine Conglomerate Sandstone Siltstone Claystone Sedimentary Clastic (22) 19 9 4 Greywacke

(18) Chalk Non-clastic Organic 7 Coal

(8-21) Sparitic Micritic Breccia Carbonate limestone limestone (20) (10) 8 Gypstone Anhydrite Chemical 16 13 Marble Hornfels Quartzite Metamorphic Non-foliated 9 19 24 Migmatite Amphilbolite Mylonites Slightly foliated (30) 25-31 (6) Gneiss Schists Phyllites Slate Foliated 33 4-8 (10) 9 Granite Rhyolite Obsidian Igneous Light 33 (16) (19) Granodiorite Dacite

(30) (17) Diorite Andesite

(28) 19 Gabbro Dolerite Basalt Dark 27 (19) (17) Norite

22 Extrusive Agglomerate Breccia Tuff

pyroclastic type (20) (19) (15)

164

Table A. 3 Guidelines for estimating disturbance factor, DF (Hoek et al. 2002). Suggested appearance of rock mass Description of rock mass value of DF Excellent quality controlled blasting or excavation by Tunnel Boring Machine results in minimal disturbance to the confined rock mass surrounding a tunnel. DF = 0

Mechanical or hand excavation in poor quality rock masses (no blasting) results in minimal DF = 0 disturbance to the surrounding rock mass. Where squeezing problems result in significant floor heave, disturbance can be severe unless a DF = 0.5 temporary invert, as shown in the photograph, is No invert placed. Very poor quality blasting in a hard rock tunnel results in severe local damage, extending 2 or 3 m, in the surrounding rock mass. DF = 0.8

Small scale blasting in civil engineering slopes results in modest rock mass damage, particularly DF = 0.7 if controlled blasting is used as shown on the left Good blasting hand side of the photograph. However, stress relief results in some disturbance. DF = 1.0 Poor blasting

Very large open pit mine slopes suffer significant DF = 1.0 disturbance due to heavy production blasting and Production also due to stress relief from overburden blasting removal. In some softer rocks excavation can be carried DF = 0.7 out by ripping and dozing and the degree of Mechanical damage to the slopes is less. excavation

165

Figure A. 1 Geological strength index for jointed rocks (Hoek and Marinos 2000).

166

0.2 (a) (b)

0.16

)

M (

0.12

r 0.08

e h S Hoek-Brown Criterion 0.04 Mohr-Coulomb Fit

0 0.2 (c) (d)

0.16

)

M (

0.12

r 0.08

h S 0.04

0 0 0.05 0.1 0.15 0.2 0.25 0 0.05 0.1 0.15 0.2 0.25 Effective normal stress (MPa) Effective normal stress (MPa) Figure A. 2 Hoek-Brown criteria and corresponding Mohr-Coulomb fits for (a) 2005 Kahsmir, Pakistan, earthquake, (b) 1989 Loma-Prieta, U.S. earthquake, (c) 1999 Chi-Chi, Taiwan, earthquake, and (d) 2008 Wenchuan, China, earthquake.

167

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