SEISMIC HAZARD ANALYSIS AND SEISMIC SLOPE STABILITY

EVALUATION USING DISCRETE FAULTS IN NORTHWESTERN

PAKISTAN

BY

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

ii

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.

iii

To my parents and grandparents

iv

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.

v

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

vi

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

m0

threshold magnitude for the exponential recurrence model

Ṅ(mc) Characteristic rate

vii

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

viii

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

ix

UHS uniform hazard spectra

USGS U.S. geological survey

V/H ratio vertical-to-horizontal acceleration ratio

WGCEP working group on California earthquake probabilities

1

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.

2

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.

3

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

4

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.

5

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.

6

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).

Site

PGA (g)

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).

7

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.

Time

(year)

0

200

400

600

800

Num

ber

of

even

ts

<1912

1912

-192

1

1922

-193

1

1932

-194

1

1942

-195

1

1952

-196

1

1962

-197

1

1972

-198

1

1982

-199

1

1992

-200

2

>2002

Monalisa et al. (2007)

This study

8

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

9

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.

10

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

11

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

12

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

Mmax was used directly in the DSHA, and was assigned as the upper bound magnitude, mu, 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:

ls bbfactorR 1 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

13

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

14

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

15

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.

16

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

17

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.

18

Table 3.1 Major historical earthquakes incorporated in the earthquake database for NW Pakistan.

Earthquake Year Estimated

Mw

Estimated

Max.

MMI

Details Source

Paghman,

Afghanistan

(34.60°N,

68.93°E)

1505 7.0 - 7.8 IX - X

60-km rupture of

Chaman fault. Strike-

slip and dip-slip

movement

Quittmeyer and

Jacob (1979)

Kashmir,

Pakistan

(33.50°N,

75.50°E)

1555 7.6 n/a Limited intensity

reports available

Ambraseys and

Douglas (2004)

Alingar Valley,

Afghanistan

(34.83°N,

70.37°E)

1842 n/a VIII - IX

Several hundred

fatalities in Alingar

River valley and

Jalalabad Basin

Quittmeyer and

Jacob (1979)

Kashmir,

Pakistan

(34.60°N,

74.38°E)

1885 6.3 VIII - IX

3,000 fatalities.

Numerous buildings

destroyed; large

fissures observed;

large landslide

triggered south of

Baramula

Lawrence (1967)

Quittmeyer and

Jacob (1979)

Bilham (2004)

Chaman,

Pakistan

(30.85°N,

66.52°E)

1892 6.75 IIV-IX

30-km rupture of

Chaman fault; Left-

lateral strike-slip

movement

Heuckroth and

Karim (1973)

Quittmeyer and

Jacob (1979)

Kangra, India

(33.00°N,

76.00°E)

1905 7.83±0.18 n/a

20,000 fatalities;

100,000 buildings

destroyed; limited

instrumented data

available

Ambraseys and

Bilham (2000)

Kaul (1911)

19

Table 3.2 Magnitude conversions used in this study.

Magnitude conversion relations

Grunthal and Wahlstrom (2003) 2013.0046.008.056.011.067.0 LLw MMM

Grunthal and Wahlstrom (2003) sw MM

Johnston (1996) 2

0 077.0679.028.18log bb mmM

Hanks and Kanamori (1979) 7.10log32 0 MM w

20

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

21

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.

Fault

ID Fault name Type

Dip

(°)

Length

(km)

Max.

magnitude

(Mw)

Slip rate

(mm/yr)

Activity rate

(year-1

)

Characteristic rate

(year-1

)

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

22

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

23

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

24

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.

~ 29 mm/year

Karachi MBT : Main Boundary Thrust

MKT : Main Karakoram Thrust

MMT : Main Mantle Thrust

Baluchistan

Muzaffarabad

Islamabad

500 km

~ 44 mm/year

~ 42 mm/year

Pakistan

India

Afghanistan

25

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.

36 ̊ N

35 ̊ N

34 ̊ N

33 ̊ N

32 ̊ N

70 ̊ E 71 ̊ E 72 ̊ E 73 ̊ E 74 ̊ E 75 ̊ E

Astor

Kaghan

MalakandBalakot

Muzaffarabad

IslamabadKohat

BannuTalagang

Peshawar

GPS measurement by Bendick et al. (2007)

Inferred plate movement based on Larson et al. (1999)

Assumed plate movement

Earthquakes

Mw 4 5 6 7

Zone 1

Zone 2

Zone 3

Mangla 1914

1928

1974

1992

2002

2004

2005

2005

2005

1885

26

Figure 3.4 Definition of fault geometry parameters.

DipDepth to bottom

of rupture (D)

Depth to top

of rupture (Ztor)

27

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.

1 10 100Distance from the fault (km)

0.01

0.1

1

Pea

k G

rou

nd A

ccel

erat

ion (

g)

Foot wall sideAS (2008)

BA (2008)

CB (2008)

CY (2008)

I (2008)

Hanging wall sideAS (2008)

BA (2008)

CB (2008)

CY (2008)

I (2008)

28

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.

Depth to the

top of rupture

(Ztor)

0

2 km

4 km

10 (0.4)

15 (0.4)

20 (0.2)

0.8 (0.2)

0.9 (0.6)

1.0 (0.2)

NWP

Faults

Depth to the

bottom of

rupture (D)

Seismogenic

factor

(R-factor)

Attenuation

relationship

as above

as above

as above

AS (0.25)

BA (0.25)

CB (0.25)

I (0.25)

Magnitude

rangeZtor = 0 Ztor = 2 km Ztor = 4 km

6.5 M 6.75

6.75 M 7.0

7.0 M

0.333 0.333 0.333

0.5 0.5

1.0

Weights for the depth to the top of rupture, Ztor

Maximum

magnitudeFault geometry

29

Figure 3.7 Sensitivity of PGA computed in DSHA to selected GMPEs.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

PG

A (

g)

Islamabad Muzaffarabad

Weighted

AS

BA

CB

I

Median

0

0.2

0.4

0.6

0.8

1

1.2

1.4

PG

A (

g)

Islamabad Muzaffarabad

84th percentile

30

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.

Kaghan

Balakot

Muzaffarabad

Islamabad

Kaghan

Balakot

Muzaffarabad

Islamabad

72.5 E 73 E 73.5 E 74 E

34.5 N

35 N

34 N

33.5 N

72.5 E 73 E 73.5 E 74 E

0.1 0.2 0.3 0.4 0.5 0.6 0.80.7 0.9 1.0 (g)

PGA

31

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.

1 10 100Distance from the fault (km)

0.01

0.1

1P

eak

Gro

und A

ccel

erat

ion (

g)

ComputedAbrahamson-Silva (2008)

Boore-Atkinson (2008)

Campbell-Bozorgnia (2008)

Idriss (2008)

Meanof all median NGAs

Mean of all median NGAs 1

MeasuredAbbottabad

Barotha

Murree

Nilore

Tarbela

1 10 100Distance from the fault (km)

(a) Vs,30 = 560 m/s (b) Vs,30 = 270 m/s

200 200

32

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:

bmam log Eq. (4-1)

33

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:

mm exp 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

00

exp1

expexp

mm

mmmmu

u

m

for umm Eq. (4-3)

where 0exp m , m0 is the threshold magnitude (m

0 = 4 in this study), and m

u is the upper

bound magnitude. Thus m0, m

u, 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, m

u

The value of m0 defines the starting point of the recurrence relationship. If m

0 were set

less than Mw 4.0, recurrence would be underestimated because the composite earthquake catalog

for NW Pakistan compiled for this study lacks data for Mw < 4.0. Therefore, m0 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.

As noted previously, mu

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

34

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 ( sT ) is parallel to the slope of sT1 , 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 sT1 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 sT1 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.

35

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.

36

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

distribution up to magnitude m' with a uniform distribution in the magnitude range of mu

- Δmc to

mu at a rate density cmn . 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, cmN , 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 14

C, 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:

8988.00008016.0 rateSlipratesticCharacteri Eq. (4-4)

37

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.

47.0

5.0

c

c

mforratesticCharacteri

mforratesticCharacteri

Eq. (4-5 a)

12.2

5.0

c

c

mforratesticCharacteri

mforratesticCharacteri Eq. (4-5 b)

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

38

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.

dRAM 0 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).

1.165.1log 0 wMM Eq. (4-7)

Using the characteristic magnitude (defined earlier) to compute M0, the characteristic rate

can be calculated as:

0M

SRArateisticCharaceter

Eq. (4-8)

39

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

40

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,

41

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

recurrence model are m0, m

u, ν and b-value. If m

0 were set less than Mw 4.0, recurrence would be

underestimated because the composite earthquake catalog for NW Pakistan compiled for this

study lacks data for Mw < 4.0. Therefore, m0 = 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

42

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.

43

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

44

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.

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 sT1 .

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005Time

(year)

0

100

200

300

400

500

600

700

Num

ber

of

even

t

Period 1

Period 2

1 10 100Time interval, Ts (years)

0.01

0.1

1

10

=

T

s

4Mw <5

5Mw <6

Mw

45

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).

0.01 0.1 1 10Activity rate 1 (year-1)

0.01

0.1

1

10

Act

ivit

y r

ate

2 (

yea

r-1)

2

3

5

6

7

8

9

10

11

12

13

1415

16

17

18

20

21

22

23

24 25 26

2829

30

31

32

1

1

46

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.

4 4.5 5 5.5 6 6.5 7 7.5 8Magnitude, Mw

0.01

0.1

1

10

100A

nn

ual

rat

e o

f ev

ents

> M

w (

yea

r-1)

Least Sqare (LS) method

Maximum Likelihood (ML) method

Line with b = 0.8

4 4.5 5 5.5 6 6.5 7 7.5 8Magnitude, Mw

4 4.5 5 5.5 6 6.5 7 7.5 8Magnitude, Mw

0.01

0.1

1

10

100

Ann

ual

rat

e o

f ev

ents

> M

w (

yea

r-1)

(a) (b)

(c)

bML = 0.82

bLS = 0.96

bML = 1.17

bLS = 0.74

bML = 0.92

bLS = 0.85

47

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

48

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.

0.001 0.01 0.1 1 10 100Slip rate (mm/yr)

1E-006

1E-005

0.0001

0.001

0.01

0.1C

har

acte

rist

ic r

ate

(yea

r-1)

California faults (A-Type)

California faults (B-Type)

Intermountain West faults

Pacific Northwest faults

Fit 1

Fit 2

: Characteristic rate = 0.0008016 Slip rate0.8988 (R2 = 0.9038)

: Characteristic rate = 0.001 Slip rate (R2 = 0.6427)

49

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.

4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9Magnitude, Mw

1E-005

0.0001

0.001

0.01

0.1

1

10

100

Annual

rat

e o

f ev

ents

> M

w (

yea

r-1)

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

MBT (west)

MBT (east)

50

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).

Depth to the

top of rupture

(Ztor)

0

2 km

4 km

10

(0.4)

15

(0.4)

20

(0.2)

0.8

0.9

(0.2)

(0.6)

1.0

(0.2)

Mean + 0.5

(0.2)

Mean

(0.6)

Mean - 0.5

(0.2)

Exponential

(0.33)

Charact-

eristic(0.67)

Activity rate 1

(0.5)

Activity rate 2

(0.5)

Charcteristic

rate A

(0.25)

Characteristic

rate B

(0.25)

Characteristic

rate C(0.5)

AS

(0.25)

BA

(0.25)

CB

(0.25)

I

(0.25)

NWP

Faults

Depth to the

bottom of

rupture (D)

Seismogenic

factor

(R-factor)

Magnitude

uncertainty

Recurrence model

Earthquake

rate

Attenuation

relationshipMaximum magnitudeFault geometry

as above

as above

as above

as below

as below

51

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).

0

0.2

0.4

0.6

0.8

1

1.2

1.4

PG

A (

g)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

PG

A (

g)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

PG

A (

g)

Islamabad Muzaffarabad

Weighted average

Char.A

Char.B

Char.C

Act.1

Act.2

(a)

(b)

(c)

52

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).

0

0.2

0.4

0.6

0.8

1

1.2

1.4

PG

A (

g)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

PG

A (

g)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

PG

A (

g)

Islamabad Muzaffarabad

Weighted average

Mean + 0.5

Mean

Mean - 0.5

(a)

(b)

(c)

53

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.

Kaghan

Balakot

Muzaffarabad

Islamabad

Kaghan

Balakot

Muzaffarabad

Islamabad

72.5 E 73 E 73.5 E 74 E

34.5 N

35 N

34 N

33.5 N

72.5 E 73 E 73.5 E 74 E

0.8 0.9

1.0

0.7

0.7

0.6

0.1 0.2 0.3 0.4 0.5 0.6 0.80.7 0.9 1.0 (g)

PGA

54

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

55

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

56

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.

57

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

58

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,

59

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:

T

TRMTSaT

Sa

wSa

ln

ln ,,ln

Eq. (5-1)

where TSaln is the natural logarithm of the spectral acceleration at the period of interest; and

TRM wSa ,,ln and TSaln are the predicted mean and standard deviation, respectively, of

TSaln (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.

60

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:

**,* TTTiTTi

Eq. (5-2)

where *TTi is the mean value of iT , given *T ; and *,TTi is the correlation

coefficient between the ε values at the two periods. Baker (2008) proposed the following relation

to define the correlation coefficient:

min

maxmin189.0maxmin ln

189.0ln163.0359.0

2cos1,

min T

TTITT T

Eq. (5-3)

where minT and maxT are the smaller and larger of the two periods of interest, respectively, and

189.0min TI is a binary function equal to 1 if sec189.0min T and equal to 0 otherwise.

61

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, 2, 21CTT

else if Tmin > 0.109 sec, 1, 21CTT

else 4, 21CTT

Eq. (5-4)

where

109.0,maxln366.0

2cos1

min

max1

T

TC

Eq. (5-5)

otherwise

TifT

TT

eC T

0

sec2.00099.01

11105.01 max

max

minmax

1002

5max Eq. (5-6)

otherwiseC

TifCC

1

max2

3

sec109.0 Eq. (5-7)

109.0cos15.0 max

3314

TCCCC

Eq. (5-8)

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-

62

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.

63

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.

64

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.

Return

period

(years)

Period

(sec)

Islamabad Muzaffarabad

Mean

magnitude

(Mw)

Mean

distance

(km)

Mean

epsilon

Mean

magnitude

(Mw)

Mean

distance

(km)

Mean

epsilon

475

0.05 6.8 11 0.53 6.1 4.8 1.38

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

975

0.05 7.0 8.1 0.72 6.2 4.4 1.64

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

2475

0.05 7.2 6.5 1.09 6.3 4.0 1.96

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

65

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.

0 0.5 1 1.5Peak ground acceleration (g)

0.0001

0.001

0.01

0.1

1A

nnu

al f

requen

cy o

f ex

ceed

ance

Total Hazard

Jhelum Fault

MBT (west)

MMT

Puran Fault

Riwat Thrust

Ret

urn

per

iod (

yea

r)

475

975

2475

0.01 0.1 1 10Period (sec)

0

1

2

3

Spec

tral

acc

eler

atio

n (

g)

PSHA (2475 years)

PSHA (975 years)

PSHA (475 years)

DSHA (84 percentile)

DSHA (Median)

(a) PSHA hazard curve

(b) Spectra

66

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.

67

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.

0 0.5 1 1.5Peak ground acceleration (g)

0.0001

0.001

0.01

0.1

1A

nnu

al f

requen

cy o

f ex

ceed

ance

Total Hazard

Jhelum Fault

Mansehra Thrust

MMT

Puran Fault

Riasi Thrust

Ret

urn

per

iod (

yea

r)

475

975

2475

0.01 0.1 1 10Period (sec)

0

1

2

3

Spec

tral

acc

eler

atio

n (

g)

PSHA (2475 years)

PSHA (975 years)

PSHA (475 years)

DSHA (84 percentile)

DSHA (Median)

(a) PSHA hazard curve

(b) Spectra

68

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.

69

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.

0 0.5 1 1.5Peak ground acceleration (g)

0.0001

0.001

0.01

0.1

1A

nnu

al f

requen

cy o

f ex

ceed

ance

Total Hazard

Balakot Shear Zone

Mansehra Thrust

MMT

MCT

Puran Fault

Ret

urn

per

iod (

yea

r)

475

975

2475

0.01 0.1 1 10Period (sec)

0

1

2

3

Spec

tral

acc

eler

atio

n (

g)

PSHA (2475 years)

PSHA (975 years)

PSHA (475 years)

DSHA (84 percentile)

DSHA (Median)

(a) PSHA hazard curve

(b) Spectra

70

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.

0 0.5 1 1.5Peak ground acceleration (g)

0.0001

0.001

0.01

0.1

1A

nnu

al f

requen

cy o

f ex

ceed

ance

Total Hazard

Hissartang Fault

MBT (west)

MMT

Nowshera Fault

Puran Fault

Ret

urn

per

iod (

yea

r)

475

975

2475

0.01 0.1 1 10Period (sec)

0

1

2

3

Spec

tral

acc

eler

atio

n (

g)

PSHA (2475 years)

PSHA (975 years)

PSHA (475 years)

DSHA (84 percentile)

DSHA (Median)

(a) PSHA hazard curve

(b) Spectra

71

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)

0

0.5

1

1.5S

pec

tral

acc

eler

atio

n (

g)

0

0.5

1

1.5

2

2.5

3

Spec

tral

acc

eler

atio

n (

g)

0

0.5

1

1.5

Spec

tral

acc

eler

atio

n (

g)

Astor

Bal

akot

Ban

nu

Isla

mab

ad

Kag

han

Koh

at

Mal

akan

d

Man

gla

Muz

affa

raba

d

Pesha

war

Talag

ang

PSHA475-yr return period

975-yr return period

2475-yr return period

DSHA84 percentile

Median

(a) PGA

(b) SA (T=0.2 sec)

(c) SA (T=1.0 sec)

72

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.

0 0.5 1 1.5Peak ground acceleration (g)

0.0001

0.001

0.01

0.1

1A

nnu

al f

requen

cy o

f ex

ceed

ance

Total Hazard

Jhelum fault

MCT

MMT

Raikot fault

Stak fault

Ret

urn

per

iod (

yea

r)

475

975

2475

0.01 0.1 1 10Period (sec)

0

1

2

3

Spec

tral

acc

eler

atio

n (

g)

PSHA (2475 years)

PSHA (975 years)

PSHA (475 years)

DSHA (84 percentile)

DSHA (Median)

(a) PSHA hazard curve

(b) Spectra

73

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.

0 0.5 1 1.5Peak ground acceleration (g)

0.0001

0.001

0.01

0.1

1A

nnu

al f

requen

cy o

f ex

ceed

ance

Total Hazard

Balakot shear zone

Jhelum fault

MMT

Mansehra fault

Puran fault

Ret

urn

per

iod (

yea

r)

475

975

2475

0.01 0.1 1 10Period (sec)

0

1

2

3

Spec

tral

acc

eler

atio

n (

g)

PSHA (2475 years)

PSHA (975 years)

PSHA (475 years)

DSHA (84 percentile)

DSHA (Median)

(a) PSHA hazard curve

(b) Spectra

74

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.

0 0.5 1 1.5Peak ground acceleration (g)

0.0001

0.001

0.01

0.1

1A

nnu

al f

requen

cy o

f ex

ceed

ance

Total Hazard

Karack fault

Khair-I-Murat fault

Kurram thrust

MMT

Surghar range thrust

Ret

urn

per

iod (

yea

r)

475

975

2475

0.01 0.1 1 10Period (sec)

0

1

2

3

Spec

tral

acc

eler

atio

n (

g)

PSHA (2475 years)

PSHA (975 years)

PSHA (475 years)

DSHA (84 percentile)

DSHA (Median)

(a) PSHA hazard curve

(b) Spectra

75

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.

0 0.5 1 1.5Peak ground acceleration (g)

0.0001

0.001

0.01

0.1

1A

nnu

al f

requen

cy o

f ex

ceed

ance

Total Hazard

Hissartang fault

Khair-I-Murat fault

Khairrabad fault

MBT (west)

MMT

Ret

urn

per

iod (

yea

r)

475

975

2475

0.01 0.1 1 10Period (sec)

0

1

2

3

Spec

tral

acc

eler

atio

n (

g)

PSHA (2475 years)

PSHA (975 years)

PSHA (475 years)

DSHA (84 percentile)

DSHA (Median)

(a) PSHA hazard curve

(b) Spectra

76

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.

0 0.5 1 1.5Peak ground acceleration (g)

0.0001

0.001

0.01

0.1

1A

nnu

al f

requen

cy o

f ex

ceed

ance

Total Hazard

MBT (west)

MMT

Nowshera fault

Mansehra thrust

Puran fault

Ret

urn

per

iod (

yea

r)

475

975

2475

0.01 0.1 1 10Period (sec)

0

1

2

3

Spec

tral

acc

eler

atio

n (

g)

PSHA (2475 years)

PSHA (975 years)

PSHA (475 years)

DSHA (84 percentile)

DSHA (Median)

(a) PSHA hazard curve

(b) Spectra

77

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.

0 0.5 1 1.5Peak ground acceleration (g)

0.0001

0.001

0.01

0.1

1A

nnu

al f

requen

cy o

f ex

ceed

ance

Total Hazard

Dijabba fault

Jhelum fault

MBT (east)

Riasi thrust

Riwat thrust

Ret

urn

per

iod (

yea

r)

475

975

2475

0.01 0.1 1 10Period (sec)

0

1

2

3

Spec

tral

acc

eler

atio

n (

g)

PSHA (2475 years)

PSHA (975 years)

PSHA (475 years)

DSHA (84 percentile)

DSHA (Median)

(a) PSHA hazard curve

(b) Spectra

78

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 0.5 1 1.5Peak ground acceleration (g)

0.0001

0.001

0.01

0.1

1A

nnu

al f

requen

cy o

f ex

ceed

ance

Total Hazard

Dijabba fault

Jhelum fault

Khair-I-Murat fault

MBT (west)

Salt range thrust

Ret

urn

per

iod (

yea

r)

475

975

2475

0.01 0.1 1 10Period (sec)

0

1

2

3

Spec

tral

acc

eler

atio

n (

g)

PSHA (2475 years)

PSHA (975 years)

PSHA (475 years)

DSHA (84 percentile)

DSHA (Median)

(a) PSHA hazard curve

(b) Spectra

79

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.

0

0.2

0.4

0.6

0.8P

eak g

roun

d a

ccel

erat

ion

(g)

Astor

Ban

nu

Isla

mab

ad

Kag

han

Koh

at

Mal

akan

d

Man

gla

Muz

affa

raba

d

Pesha

war

Talag

ang

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)

80

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.

Astor

Kaghan

Malakand

Balakot

Muzaffarabad

IslamabadKohat

BannuTalagang

Peshawar

Mangla

36 ̊ N

35 ̊ N

34 ̊ N

33 ̊ N

32 ̊ N

70 ̊ E 71 ̊ E 72 ̊ E 73 ̊ E 74 ̊ E 75 ̊ E

0.4

0.4

0.8

Reverse fault

Normal fault

Strike-slip fault

PGA (g)

1.2

1.0

0.8

0.6

0.4

0.2

81

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.

Astor

Kaghan

Malakand

Balakot

Muzaffarabad

IslamabadKohat

BannuTalagang

Peshawar

Mangla

36 ̊ N

35 ̊ N

34 ̊ N

33 ̊ N

32 ̊ N

70 ̊ E 71 ̊ E 72 ̊ E 73 ̊ E 74 ̊ E 75 ̊ E

0.4

0.6

1.0

Reverse fault

Normal fault

Strike-slip fault

PGA (g)

1.2

1.0

0.8

0.6

0.4

0.2

82

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.

Astor

Kaghan

Malakand

Balakot

Muzaffarabad

IslamabadKohat

BannuTalagang

Peshawar

Mangla

36 ̊ N

35 ̊ N

34 ̊ N

33 ̊ N

32 ̊ N

70 ̊ E 71 ̊ E 72 ̊ E 73 ̊ E 74 ̊ E 75 ̊ E

Reverse fault

Normal fault

Strike-slip fault

PGA (g)

1.2

1.0

0.8

0.6

0.4

0.2

83

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.

Astor

Kaghan

Malakand

Balakot

Muzaffarabad

IslamabadKohat

BannuTalagang

Peshawar

Mangla

36 ̊ N

35 ̊ N

34 ̊ N

33 ̊ N

32 ̊ N

70 ̊ E 71 ̊ E 72 ̊ E 73 ̊ E 74 ̊ E 75 ̊ E

SA (g)

4.0

2.0

1.6

1.2

0.8

0.4

3.6

3.2

2.8

2.4

Reverse fault

Normal fault

Strike-slip fault

84

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.

Astor

Kaghan

Malakand

Balakot

Muzaffarabad

IslamabadKohat

BannuTalagang

Peshawar

Mangla

36 ̊ N

35 ̊ N

34 ̊ N

33 ̊ N

32 ̊ N

70 ̊ E 71 ̊ E 72 ̊ E 73 ̊ E 74 ̊ E 75 ̊ E

0.8

1.2

SA (g)

4.0

2.0

1.6

1.2

0.8

0.4

3.6

3.2

2.8

2.4

Reverse fault

Normal fault

Strike-slip fault

85

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.

Astor

Kaghan

Malakand

Balakot

Muzaffarabad

IslamabadKohat

BannuTalagang

Peshawar

Mangla

36 ̊ N

35 ̊ N

34 ̊ N

33 ̊ N

32 ̊ N

70 ̊ E 71 ̊ E 72 ̊ E 73 ̊ E 74 ̊ E 75 ̊ E

0.8

1.6

SA (g)

4.0

2.0

1.6

1.2

0.8

0.4

3.6

3.2

2.8

2.4

Reverse fault

Normal fault

Strike-slip fault

86

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.

Astor

Kaghan

Malakand

Balakot

Muzaffarabad

IslamabadKohat

BannuTalagang

Peshawar

Mangla

36 ̊ N

35 ̊ N

34 ̊ N

33 ̊ N

32 ̊ N

70 ̊ E 71 ̊ E 72 ̊ E 73 ̊ E 74 ̊ E 75 ̊ E

0.4

Reverse fault

Normal fault

Strike-slip fault

PGA (g)

1.2

1.0

0.8

0.6

0.4

0.2

87

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.

Astor

Kaghan

Malakand

Balakot

Muzaffarabad

IslamabadKohat

BannuTalagang

Peshawar

Mangla

36 ̊ N

35 ̊ N

34 ̊ N

33 ̊ N

32 ̊ N

70 ̊ E 71 ̊ E 72 ̊ E 73 ̊ E 74 ̊ E 75 ̊ E

0.4

0.4

0.60.6

Reverse fault

Normal fault

Strike-slip fault

PGA (g)

1.2

1.0

0.8

0.6

0.4

0.2

88

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.

Astor

Kaghan

Malakand

Balakot

Muzaffarabad

IslamabadKohat

BannuTalagang

Peshawar

Mangla

36 ̊ N

35 ̊ N

34 ̊ N

33 ̊ N

32 ̊ N

70 ̊ E 71 ̊ E 72 ̊ E 73 ̊ E 74 ̊ E 75 ̊ E

0.6

0.8

Reverse fault

Normal fault

Strike-slip fault

PGA (g)

1.2

1.0

0.8

0.6

0.4

0.2

89

Figure 5.25 Comparison of correlation coefficient proposed by Baker (2008) and Baker and

Jayaram (2008).

0.01 0.1 1 10Period (sec)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1C

orr

elat

ion c

oef

fici

ent,

Baker and Jayaram

(2008)T*=0.05 sec

T*=0.1 sec

T*=0.2 sec

T*=0.5 sec

T*=2.0 sec

T*=10 sec

Baker (2008)T*=0.1 sec

T*=0.2 sec

T*=0.5 sec

T*=2.0 sec

90

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

Islamabad.

0

0.4

0.8

1.2

1.6

2

Spec

tral

acc

eler

atio

n (

g)

UHS (475 years)

CMS

0

0.4

0.8

1.2

1.6

2

Spec

tral

acc

eler

atio

n (

g)

UHS (975 years)

CMS

0.01 0.1 1 10Period (sec)

0

0.4

0.8

1.2

1.6

2

Spec

tral

acc

eler

atio

n (

g)

UHS (2475 years)

CMS

91

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

Muzaffarabad.

0

0.4

0.8

1.2

1.6

2

2.4

2.8

Spec

tral

acc

eler

atio

n (

g)

UHS (475 years)

CMS

0

0.4

0.8

1.2

1.6

2

2.4

2.8

Spec

tral

acc

eler

atio

n (

g)

UHS (975 years)

CMS

0.01 0.1 1 10Period (sec)

0

0.4

0.8

1.2

1.6

2

2.4

2.8

Spec

tral

acc

eler

atio

n (

g)

UHS (2475 years)

CMS

92

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 m

3 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

(Mw 7.6) triggered more than 9,200 landslides throughout a region of approximately 128 km2

(Liao 2000). The largest of these was the Tsaoling landslide which involved 125×106 m

3 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).

93

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

94

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

95

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:

Wkg

WaFandWk

g

WaF v

vvh

hh

Eq. (6-1)

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:

ikik

D

cikik

FShv

t

hv

cossin1

tansincos1

Eq. (6-2)

96

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

kh = 0.5×(ah,max/g). Nozu et al. (1997) proposed a slightly different form [kh=1/3 (ah,max/g)1/3

],

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.

97

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-

98

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

99

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.

100

Table 6.1 Characteristics of earthquake-induced landslides (disrupted type) (Keefer 2002).

Name Type of movement Internal

disruption

Water content

D U PS S

Typical

depths

Min.

slope (°)

Typical

velocities Typical volumes Typical displacements

Rock falls Bouncing, rolling,

free fall

High or

very high × × × × Shallow 40

Extremely

rapid

Most less than 1 × 104 m

3;

maximum reported 2 ×

107 m

3

May fall to base of steep

source slope and move as far

as several tens or hundreds of

meters farther, on relatively

gentle slopes

Disrupted

rock slide Translational sliding High × × × × Shallow 35

Rapid to

very rapid

Most less than 1 × 104 m

3;

maximum reported 2 ×

109 m

3

May slide to base of steep

source slope and several tens

or hundreds of meters farther,

on relatively gentle slopes

Rock

avalanches

Complex, involving

sliding,

flow, and

occasionally free fall

Very high × × × × Deep 25

Very rapid

to

extremely

rapid

5 × 105–2 × 10

8 m

3 or

more Several kilometers

Soil falls Bouncing, rolling,

free fall

High or

very high × × × × Shallow 40

Extremely

rapid

Most less than 1,000 m3;

maximum volumes not

well documented

Most come to rest at or near

bases of steep source slopes

Disrupted

soil slides Translational sliding High × × × × Shallow 15

Moderate

to rapid

Most less than 1 × 104 m

3;

maximum reported 4.8 ×

107 m

3

May slide to base of steep

source slope and several tens

or hundreds of meters farther,

on relatively gentle slopes

Soil

avalanches

Complex, involving

sliding,

flow, and

occasionally free fall

Very high × × × × Shallow 25

Very rapid

to

extremely

rapid

Volumes not well

documented; maximum

reported 1.5 × 108 m

3

Several tens of meters to

several kilometers beyond

steep source slopes

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.

101

Table 6.2 Characteristics of earthquake-induced landslides (coherent type) (Keefer 2002).

Name Type of

movement

Internal

disruption

Water

content

D U PS S

Typical

depths

Min.

slope

(°)

Typical

velocities Typical volumes Typical displacements

Rock

slumps

Rotational

sliding

Slight or

moderate ? × × × Deep 15 Slow to rapid

Most between 100 and a

few million m3; maximum

at least tens of millions of

m3

Typically less than 10

m; occasionally 100 m

or more

Rock block

slides

Translational

sliding

Slight or

moderate ? × × × Deep 15 Slow to rapid

Most between 100 and a

few million m3; maximum

at least tens of millions of

m3

Typically less than 100

m; maximum

displacements not well

documented

Soil slumps Rotational

sliding

Slight or

moderate ? × × × Deep 7 Slow to rapid

Most between 100 and 1 ×

105 m

3; occasionally 1 ×

105 to several million m

3

Typically less than 10

m; occasionally 100 m

or more

Soil block

slides

Translational

sliding

Slight or

moderate ? ? × × Deep 5 Slow to rapid

Most between 100 and 1 ×

105 m

3; maximum reported

1.12 × 108 m

3

Typically less than 100

m; maximum

displacements not well

documented

Slow earth

flows

Translational

sliding and

internal flow

Slight × ×

Generally

shallow;

occasionally

deep

10

Very slow to

moderate;

occasionally,

with very rapid

surges

Most between 100 and 1 ×

106 m

3; maximum reported

between 3 × 107 and 6 ×

107 m

3

Typically less than 100

m; maximum

displacements not well

documented

Lateral

spreads and

flows

Soil lateral

spreads

Translation on

fluid basal zone

Generally

moderate;

occasionally

slight or high

× × Variable 0.3 Very rapid

Most between 100 and 1 ×

105 m

3; largest reported 9.6

× 106 m

3

Typically less than

10m; maximum

reported 600 m

Rapid soil

flows Flow Very high ? ? ? × Variable 2.3

Very rapid to

extremely rapid

Volumes not well

documented; largest are at

least several million m3

A few m to several km

Subaqueous

landslides

Generally lateral

spreading or

flow;

occasionally

sliding

Generally high

or very high;

occasionally

moderate or

slight

× × Variable 0.5

Generally rapid

to extremely

rapid;

occasionally

slow to moderate

Volumes not well

documented; largest are at

least tens of millions of m3

Not well documented,

but some move more

than 1 km

Note: See Table 6.1.

102

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

5.0 (4.6) Rock slumps, rock block slides, slow earth flows, soil

lateral spreads, rapid soil flows, and subaqueous landslides

6.0 (5.7) Rock avalanches

6.5 (6.3) Soil avalanches

103

Table 6.4 Hoek-Brown parameters and geometry parameters for four cases.

Parameter

Selected values

Notes References 2005

Kashmir

1989

Loma-

Prieta

1999

Chi-Chi

2008

Wench-

uan

kN/m

3)

21 ± 1 21 ± 1 24 ± 1 24 ± 1

Estimated from rock

type and degree of

weathering

Hoek and Bray

(1981)

ci (MPa) 2 0.8 2 2

Estimated from rock

type and degree of

weathering

Hoek et al. (1998)

mi 14 14 14 14 Estimated from rock

type Hoek et al. (1998)

GSI 30 30 30 30

Estimated from rock

type, rock mass

structure, and joint

surface conditions

Marinos et al.

(2005)

DF 0 0 0 0 No evidence of

blasting or stress relief Hoek et al. (1998)

'

(°) 40 ± 6 33 ± 5 51 ± 8 40 ± 6

Estimated using Hoek-

Brown criterion Hoek et al. (2002)

c'

(kPa) 27 ± 8 20 ± 6 11 ± 3 27 ± 8

Estimated using Hoek-

Brown criterion Hoek et al. (2002)

t

(kPa)

0.73 ±

0.15

0.29 ±

0.07

0.73 ±

0.15

0.73 ±

0.15

Estimated using Hoek-

Brown criterion Hoek et al. (2002)

Dt

(m) 3 ± 0.67 3 ± 0.67 0.7 ± 0.2 3 ± 0.67

Based on generalized

description of typical

depths of disrupted

slides in rock slopes

Keefer (1984)

Khazai and Sitar

(2004)

Owen et al. (2008)

Yin et al. (2010)

i

(°) 28 ± 9 27± 9 65 ± 15 33 ± 10 See Figure 6.5

Khazai and Sitar

(2004)

Kamp et al. (2008)

Yin et al. (2010)

104

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).

105

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).

106

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).

107

Figure 6.4 Photograph of shallow landslides triggered by 2005 Kahsmir, Pakistan, earthquake

(by Prof. Hashash).

108

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).

109

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.

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

0

0.2

0.4

0.6

0.8

1

1.2H

ori

zonta

l g

rou

nd a

ccel

erat

ion (

g)

Abrahamson-Silva (2008)

Boore-Atkinson (2008)

Campbell-Bozorgnia (2008)

Idriss (2008)

110

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.

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

0

0.4

0.8

1.2

1.6

2L

andsl

ide

conce

ntr

atio

n,

LC

(la

nd

slid

es/k

m2)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

3

Fac

tor

of

safe

ty a

gai

nst

sli

din

gLC for 2005 Kashmir, Pakistan earthquake

FS with kh

Static FS

Mean parameters

Tensile strength = 0.73 kPa

Unit weigth = 21 kN/m3

Cohesion intercept = 27 kPa

Friction angle = 40o

Slope thickness = 3 m

Slope angle = 28o

22

111

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

112

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

113

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;

114

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:

WilF tv cos Eq. (7-1 a)

115

1cos

max,

t

t

vD

iga

Eq. (7-1 b)

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.

116

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.

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

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

kv = 0.5

kv = 0.4

kv = 0.3

kv = 0.2

kv = 0.1

kv = 0

Unit weight = 23 kN/m3

Friction angle = 40o

Cohesion intercept= 22 kPa

Slope angle = 30o

Slope thickness = 3 m

117

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.

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

0.2

0.4

0.6

0.8

1

1.2

V

ertica

l ac

cele

rati

on

Hori

zonta

l ac

cele

ration

Elnashai and Papazouglou (1997)

Ambraseys and Simpson (1996)

Ms=7.5Ms=7.0

Ms=6.5Ms=6.0

Ms=5.5

Ms=7.5

Ms=7.0

Ms=6.5

Ms=6.0

Ms=5.5

118

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).

(a)

(b)

119

Figure 7.4 Topographic factors proposed by various researchers.

120

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.

lD

W

T N

W

tlcosii

Fv=av,max/gW

(a) (b)

121

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

122

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

123

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

124

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.

125

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).

126

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 ~

127

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.

128

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.

Step 1. Predict horizontal ground acceleration

using four attenuation relationships from NGA

project (AS08, BA08, CB08, and I08).

Step 5. Calculate factor of safety for infinite slope

using pseudo-static slope stability analysis including

horizontal and vertical accelerations.

Step 4. Check if soil bond breaks when the vertical

ground motion arrives.

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.

129

Figure 8.2 Vertical acceleration along the distance from the fault predicted for the Mw 7.6

Kashmir, Pakistan, earthquake.

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

0

0.2

0.4

0.6

0.8

1

1.2V

erti

cal

gro

und a

ccel

erat

ion (

g) Ambraseys et al. (2005)

Campbell-Bozorgnia (2003)

Elnashai-Papazouglou (1997)

Ambraseys-Simpson (1996)

130

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

20

(0.2)

(0.6)

(0.2)

21

22

AS08

(kN/m3)

c'

(kPa)

'

()

i

()

D

(m)

t

(kPa)

ahav T.F kvkh

(0.2)

(0.6)

(0.2)

(0.2)

(0.6)

(0.2)

(0.2)

(0.6)

(0.2)

(0.2)

(0.6)

(0.2)

(0.2)

(0.6)

(0.2)

BA08

CB08

I 08

19

27

35

34

40

46

0.58

0.73

0.88

2.33

3

3.67

18

28

38

(0.25)

(0.25)

(0.25)

(0.25)

(0.25)

(0.25)

(0.25)

(0.25)

(0.2)

(0.6)

(0.2)

(1/3)

(1/3)

1.3

1.45

1.6

0.9

0.33

Slope model

Material property Slope geometry Seismic parameter

A 05

CB03

EP97

AS96

as above

as above

as above as above

as above

as above

as above

as above

as below

as belowas belowas below

(1/3)

0.5

(1/3)

(1/3)

0.9

0.33

(1/3)

0.5

131

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.

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

0

0.4

0.8

1.2

1.6

2L

andsl

ide

conce

ntr

atio

n,

LC

(la

nd

slid

es/k

m2)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

3

Fac

tor

of

safe

ty a

gai

nst

sli

din

gLC 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

Mean parameters

Tensile strength = 0.73 kPa

Unit weight = 21 kN/m3

Cohesion intercept= 27 kPa

Friction angle = 40o

Slope thickness = 3 m

Slope angle = 28o

22

132

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.

0

0.4

0.8

1.2

1.6

2L

C (

landsl

ides

/km

2)

0

0.5

1

1.5

2

2.5

3

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

0

0.4

0.8

1.2

1.6

2

LC

(la

ndsl

ides

/km

2)

0

0.5

1

1.5

2

2.5

3

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

0

0.4

0.8

1.2

1.6

2

LC

(la

ndsl

ides

/km

2)

0

0.5

1

1.5

2

2.5

3

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

0

0.4

0.8

1.2

1.6

2

LC

(la

ndsl

ides

/km

2)

0

0.5

1

1.5

2

2.5

3

Fac

tor

of

safe

ty a

gai

nst

sli

din

g0 10 20 30 40 50

Distance from surface projection

of updip edge of fault plane (km)

0

0.4

0.8

1.2

1.6

2

LC

(la

ndsl

ides

/km

2)

0

0.5

1

1.5

2

2.5

3

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

0 10 20 30 40 50Distance from surface projection

of updip edge of fault plane (km)

0

0.4

0.8

1.2

1.6

2

LC

(la

ndsl

ides

/km

2)

0

0.5

1

1.5

2

2.5

3

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

(a) (b)

(c) (d)

(e) (f)

133

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.

0

0.4

0.8

1.2

1.6

2L

C (

landsl

ides

/km

2)

0

0.4

0.8

1.2

1.6

2

2.4

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

0

0.4

0.8

1.2

1.6

2

LC

(la

ndsl

ides

/km

2)

0

0.4

0.8

1.2

1.6

2

2.4

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

0

0.4

0.8

1.2

1.6

2

LC

(la

ndsl

ides

/km

2)

0

0.4

0.8

1.2

1.6

2

2.4

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

0 10 20 30 40 50Distance from surface projection

of updip edge of fault plane (km)

0

0.4

0.8

1.2

1.6

2

LC

(la

ndsl

ides

/km

2)

0

0.4

0.8

1.2

1.6

2

2.4

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

FS with mean parameter

FS with mean parameter + 1

FS with mean parameter - 1

0 10 20 30 40 50Distance from surface projection

of updip edge of fault plane (km)

0

0.4

0.8

1.2

1.6

2

LC

(la

ndsl

ides

/km

2)

0

0.4

0.8

1.2

1.6

2

2.4

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

(a) (b)

(c) (d)

(e)

134

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.

0

0.4

0.8

1.2

1.6

2L

C (

landsl

ides

/km

2)

0

0.4

0.8

1.2

1.6

2

2.4

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

0

0.4

0.8

1.2

1.6

2

LC

(la

ndsl

ides

/km

2)

0

0.4

0.8

1.2

1.6

2

2.4

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

0

0.4

0.8

1.2

1.6

2

LC

(la

ndsl

ides

/km

2)

0

0.4

0.8

1.2

1.6

2

2.4

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

0 10 20 30 40 50Distance from surface projection

of updip edge of fault plane (km)

0

0.4

0.8

1.2

1.6

2

LC

(la

ndsl

ides

/km

2)

0

0.4

0.8

1.2

1.6

2

2.4

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

AS

BA

CB

I

0 10 20 30 40 50Distance from surface projection

of updip edge of fault plane (km)

0

0.4

0.8

1.2

1.6

2

LC

(la

ndsl

ides

/km

2)

0

0.4

0.8

1.2

1.6

2

2.4

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

A

CB

EP

AS

(a) (b)

(c) (d)

(e)

kh=0.33(ah,max/g)

0.5

0.5

T.F. =1.3

1.451.6

AS: Abrahamson-Silva 2008

BA: Boore-Atkinson 2008

CB: Campbell-Bozorgnia 2008

I: Idriss 2008

A: Ambraseys et al. 2005

CB: Campbell-Bozorgnia 2003

EP: Elnashai-Papazouglou 1997

AS: Ambraseys-Simpson 1996

0.7

kv=0.33(ah,max/g)

0.7

135

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.

136

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)

137

Figure 8.10 Horizontal and vertical accelerations with respect to source-to-site distance predicted

for the Mw 6.9 1989 Loma-Prieta earthquake.

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

0

0.2

0.4

0.6

0.8

1G

round

acc

eler

atio

n (

g)

Horizontal accelerationsAbrahamson and Silva (2008)

Boore and Atkinson (2008)

Campbell and Bozorgnia (2008)

Idriss (2008)

Vertical accelerationsAmbraseys et al. (2005)

Campbell and Bozorgnia (2003)

Elnashai and Papazouglou (1997)

Ambraseys and Simpson (1996)

138

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.

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

0

0.4

0.8

1.2

1.6

2L

andsl

ide

conce

ntr

atio

n,

LC

(la

nd

slid

es/k

m2)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

3

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

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

Mean parameters

Tensile strength = 0.29 kPa

Unit weight = 21 kN/m3

Cohesion intercept = 20 kPa

Friction angle = 33o

Slope thickness = 3 m

Slope angle = 27o

139

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.

0

0.4

0.8

1.2

1.6

2L

C (

landsl

ides

/km

2)

0

0.5

1

1.5

2

2.5

3

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

0

0.4

0.8

1.2

1.6

2

LC

(la

ndsl

ides

/km

2)

0

0.5

1

1.5

2

2.5

3

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

0

0.4

0.8

1.2

1.6

2

LC

(la

ndsl

ides

/km

2)

0

0.5

1

1.5

2

2.5

3

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

0

0.4

0.8

1.2

1.6

2

LC

(la

ndsl

ides

/km

2)

0

0.5

1

1.5

2

2.5

3

Fac

tor

of

safe

ty a

gai

nst

sli

din

g0 10 20 30 40 50

Distance from surface projection

of updip edge of fault plane (km)

0

0.4

0.8

1.2

1.6

2

LC

(la

ndsl

ides

/km

2)

0

0.5

1

1.5

2

2.5

3

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

0 10 20 30 40 50Distance from surface projection

of updip edge of fault plane (km)

0

0.4

0.8

1.2

1.6

2

LC

(la

ndsl

ides

/km

2)

0

0.5

1

1.5

2

2.5

3

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

(a) (b)

(c) (d)

(e) (f)

140

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.

0

0.4

0.8

1.2

1.6

2L

C (

landsl

ides

/km

2)

0

0.4

0.8

1.2

1.6

2

2.4

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

0

0.4

0.8

1.2

1.6

2

LC

(la

ndsl

ides

/km

2)

0

0.4

0.8

1.2

1.6

2

2.4

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

0

0.4

0.8

1.2

1.6

2

LC

(la

ndsl

ides

/km

2)

0

0.4

0.8

1.2

1.6

2

2.4

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

0 10 20 30 40 50Distance from surface projection

of updip edge of fault plane (km)

0

0.4

0.8

1.2

1.6

2

LC

(la

ndsl

ides

/km

2)

0

0.4

0.8

1.2

1.6

2

2.4

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

FS with mean parameter

FS with mean parameter + 1

FS with mean parameter - 1

0 10 20 30 40 50Distance from surface projection

of updip edge of fault plane (km)

0

0.4

0.8

1.2

1.6

2

LC

(la

ndsl

ides

/km

2)

0

0.4

0.8

1.2

1.6

2

2.4

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

(a) (b)

(c) (d)

(e)

141

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.

0

0.4

0.8

1.2

1.6

2L

C (

landsl

ides

/km

2)

0

0.4

0.8

1.2

1.6

2

2.4

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

0

0.4

0.8

1.2

1.6

2

LC

(la

ndsl

ides

/km

2)

0

0.4

0.8

1.2

1.6

2

2.4

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

0

0.4

0.8

1.2

1.6

2

LC

(la

ndsl

ides

/km

2)

0

0.4

0.8

1.2

1.6

2

2.4

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

0 10 20 30 40 50Distance from surface projection

of updip edge of fault plane (km)

0

0.4

0.8

1.2

1.6

2

LC

(la

ndsl

ides

/km

2)

0

0.4

0.8

1.2

1.6

2

2.4

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

AS

BA

CB

I

0 10 20 30 40 50Distance from surface projection

of updip edge of fault plane (km)

0

0.4

0.8

1.2

1.6

2

LC

(la

ndsl

ides

/km

2)

0

0.4

0.8

1.2

1.6

2

2.4

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

A

CB

EP

AS

(a) (b)

(c) (d)

(e)

kh=0.33(ah,max/g)

0.5(ah,max/g)

kv=0.33(av,max/g)

0.5(av,max/g)

TF =1.30

1.451.60

AS: Abrahamson-Silva 2008

BA: Boore-Atkinson 2008

CB: Campbell-Bozorgnia 2008

I: Idriss 2008

A: Ambraseys et al. 2005

CB: Campbell-Bozorgnia 2003

EP: Elnashai-Papazouglou 1997

AS: Ambraseys-Simpson 1996

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

142

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)

143

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.

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

0

0.2

0.4

0.6

0.8

1G

round

acc

eler

atio

n (

g)

Horizontal accelerationsAbrahamson and Silva (2008)

Boore and Atkinson (2008)

Campbell and Bozorgnia (2008)

Idriss (2008)

Vertical accelerationsAmbraseys et al. (2005)

Campbell and Bozorgnia (2003)

Elnashai and Papazouglou (1997)

Ambraseys and Simpson (1996)

144

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.

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

0

0.2

0.4

0.6

0.8

1L

andsl

ide

conce

ntr

atio

n,

LC

(la

nd

slid

es/k

m2)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

3

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

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

Mean parameters

Tensile strength = 0.73 kPa

Unit weight = 24 kN/m3

Cohesion intercept = 11 kPa

Friction angle = 51o

Slope thickness = 0.7 m

Slope angle = 65o

145

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.

0

0.2

0.4

0.6

0.8L

C (

landsl

ides

/km

2)

0

0.5

1

1.5

2

2.5

3

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

0

0.2

0.4

0.6

0.8

LC

(la

ndsl

ides

/km

2)

0

0.5

1

1.5

2

2.5

3

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

0

0.2

0.4

0.6

0.8

LC

(la

ndsl

ides

/km

2)

0

0.5

1

1.5

2

2.5

3

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

0

0.2

0.4

0.6

0.8

LC

(la

ndsl

ides

/km

2)

0

0.5

1

1.5

2

2.5

3

Fac

tor

of

safe

ty a

gai

nst

sli

din

g0 10 20 30 40 50

Distance from surface projection

of updip edge of fault plane (km)

0

0.2

0.4

0.6

0.8

LC

(la

ndsl

ides

/km

2)

0

0.5

1

1.5

2

2.5

3

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

0 10 20 30 40 50Distance from surface projection

of updip edge of fault plane (km)

0

0.2

0.4

0.6

0.8

LC

(la

ndsl

ides

/km

2)

0

0.5

1

1.5

2

2.5

3

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

(a) (b)

(c) (d)

(e) (f)

146

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.

0

0.2

0.4

0.6

0.8L

C (

landsl

ides

/km

2)

0

0.4

0.8

1.2

1.6

2

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

0

0.2

0.4

0.6

0.8

LC

(la

ndsl

ides

/km

2)

0

0.4

0.8

1.2

1.6

2

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

0

0.2

0.4

0.6

0.8

LC

(la

ndsl

ides

/km

2)

0

0.4

0.8

1.2

1.6

2

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

0 10 20 30 40 50Distance from surface projection

of updip edge of fault plane (km)

0

0.2

0.4

0.6

0.8

LC

(la

ndsl

ides

/km

2)

0

0.4

0.8

1.2

1.6

2

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

FS with mean parameter

FS with mean parameter + 1

FS with mean parameter - 1

0 10 20 30 40 50Distance from surface projection

of updip edge of fault plane (km)

0

0.2

0.4

0.6

0.8

LC

(la

ndsl

ides

/km

2)

0

0.4

0.8

1.2

1.6

2

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

(a) (b)

(c) (d)

(e)

147

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.

0

0.2

0.4

0.6

0.8L

C (

landsl

ides

/km

2)

0

0.4

0.8

1.2

1.6

2

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

0

0.2

0.4

0.6

0.8

LC

(la

ndsl

ides

/km

2)

0

0.4

0.8

1.2

1.6

2

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

0

0.2

0.4

0.6

0.8

LC

(la

ndsl

ides

/km

2)

0

0.4

0.8

1.2

1.6

2

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

0 10 20 30 40 50Distance from surface projection

of updip edge of fault plane (km)

0

0.2

0.4

0.6

0.8

LC

(la

ndsl

ides

/km

2)

0

0.4

0.8

1.2

1.6

2

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

AS

BA

CB

I

0 10 20 30 40 50Distance from surface projection

of updip edge of fault plane (km)

0

0.2

0.4

0.6

0.8

LC

(la

ndsl

ides

/km

2)

0

0.4

0.8

1.2

1.6

2

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

A

CB

EP

AS

(a) (b)

(c) (d)

(e)

kh=0.33(ah,max/g)

0.5

T.F. =1.3

1.451.6

AS: Abrahamson-Silva 2008

BA: Boore-Atkinson 2008

CB: Campbell-Bozorgnia 2008

I: Idriss 2008

A: Ambraseys et al. 2005

CB: Campbell-Bozorgnia 2003

EP: Elnashai-Papazouglou 1997

AS: Ambraseys-Simpson 1996

0.9

kv=0.33(av,max/g)

0.50.9

148

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

149

Figure 8.22 Horizontal and vertical accelerations with respect to source-to-site distance predicted

for the Mw 7.9 2008 Wenchuan, China, earthquake.

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

0

0.2

0.4

0.6

0.8

1G

round

acc

eler

atio

n (

g)

Horizontal accelerationsAbrahamson and Silva (2008)

Boore and Atkinson (2008)

Campbell and Bozorgnia (2008)

Idriss (2008)

Vertical accelerationsAmbraseys et al. (2005)

Campbell and Bozorgnia (2003)

Elnashai and Papazouglou (1997)

Ambraseys and Simpson (1996)

150

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.

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

0

1

2

3

4

5

6

7

8L

andsl

ide

conce

ntr

atio

n,

LC

(la

nd

slid

es/k

m2)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

3

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

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

Mean parameters

Tensile strength = 0.73 kPa

Unit weight = 24 kN/m3

Cohesion intercept = 27 kPa

Friction angle = 40o

Slope thickness = 3 m

Slope angle = 33o

151

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.

0

2

4

6

8L

C (

landsl

ides

/km

2)

0

0.5

1

1.5

2

2.5

3

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

0

2

4

6

8

LC

(la

ndsl

ides

/km

2)

0

0.5

1

1.5

2

2.5

3

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

0

2

4

6

8

LC

(la

ndsl

ides

/km

2)

0

0.5

1

1.5

2

2.5

3

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

0

2

4

6

8

LC

(la

ndsl

ides

/km

2)

0

0.5

1

1.5

2

2.5

3

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

0 10 20 30 40 50Distance from surface projection

of updip edge of fault plane (km)

0

2

4

6

8

LC

(la

ndsl

ides

/km

2)

0

0.5

1

1.5

2

2.5

3

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

0 10 20 30 40 50Distance from surface projection

of updip edge of fault plane (km)

0

2

4

6

8

LC

(la

ndsl

ides

/km

2)

0

0.5

1

1.5

2

2.5

3

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

(a) (b)

(c) (d)

(e) (f)

152

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.

0

2

4

6

8L

C (

landsl

ides

/km

2)

0

0.4

0.8

1.2

1.6

2

2.4

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

0

2

4

6

8

LC

(la

ndsl

ides

/km

2)

0

0.4

0.8

1.2

1.6

2

2.4

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

0

2

4

6

8

LC

(la

ndsl

ides

/km

2)

0

0.4

0.8

1.2

1.6

2

2.4

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

0 10 20 30 40 50Distance from surface projection

of updip edge of fault plane (km)

0

2

4

6

8

LC

(la

ndsl

ides

/km

2)

0

0.4

0.8

1.2

1.6

2

2.4

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

FS with mean parameter

FS with mean parameter + 1

FS with mean parameter - 1

0 10 20 30 40 50Distance from surface projection

of updip edge of fault plane (km)

0

2

4

6

8

LC

(la

ndsl

ides

/km

2)

0

0.4

0.8

1.2

1.6

2

2.4

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

(a) (b)

(c) (d)

(e)

153

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.

0

2

4

6

8L

C (

landsl

ides

/km

2)

0

0.4

0.8

1.2

1.6

2

2.4

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

0

2

4

6

8

LC

(la

ndsl

ides

/km

2)

0

0.4

0.8

1.2

1.6

2

2.4

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

0

2

4

6

8

LC

(la

ndsl

ides

/km

2)

0

0.4

0.8

1.2

1.6

2

2.4

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

0 10 20 30 40 50Distance from surface projection

of updip edge of fault plane (km)

0

2

4

6

8

LC

(la

ndsl

ides

/km

2)

0

0.4

0.8

1.2

1.6

2

2.4

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

AS

BA

CB

I

0 10 20 30 40 50Distance from surface projection

of updip edge of fault plane (km)

0

2

4

6

8

LC

(la

ndsl

ides

/km

2)

0

0.4

0.8

1.2

1.6

2

2.4

Fac

tor

of

safe

ty a

gai

nst

sli

din

g

A

CB

EP

AS

(a) (b)

(c) (d)

(e)

kh=0.33(ah,max/g)

0.5

T.F. =1.3

1.61.45

AS: Abrahamson-Silva 2008

BA: Boore-Atkinson 2008

CB: Campbell-Bozorgnia 2008

I: Idriss 2008

A: Ambraseys et al. 2005

CB: Campbell-Bozorgnia 2003

EP: Elnashai-Papazouglou 1997

AS: Ambraseys-Simpson 1996

0.9

kv=0.33(av,max/g)

0.50.9

154

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

155

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,

156

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

157

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.

158

APPENDICES

159

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:

160

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.

161

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:

5.0

331

sm

ci

ci

Eq. (A-1)

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

ci

bci sm

3

31 Eq. (A-2)

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

DF

GSImm ib

1428

100exp Eq. (A-3)

DF

GSIs

39

100exp Eq. (A-4)

32015

6

1

2

1 eea GSI Eq. (A-5)

The tensile strength can be computes as:

162

b

cit

m

s Eq. (A-6)

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':

1

3

1

31

61212

6sin

a

nbb

a

nbb

msamaa

msam

Eq. (A-7)

aa

msamaa

msmasac

a

nbb

a

nbnbci

21

6121

121

1

3

1

33

where ci

n

max3

3

Eq. (A-8)

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).

163

Table A. 1 Field estimates of the uniaxial compressive strength of intact pieces (Hoek et al. 1998).

Term

Uniaxial

compressive

strength (MPa)

Point load

index

(MPa)

Field estimate of strength Examples

Extremely

strong >250 >10

Specimen can only be chipped with a

geological hammer

Fresh basalt, chert, diabase, gneiss,

granite, quartzite

Very

strong 100-250 4-10

Specimen requires many blows of a

geological hammer to fracture it

Amphibolite, sandstone, basalt, gabbro,

gneiss, granodiorite, limestone, marble,

rhyolite, tuff

Strong 50-100 2-4 Specimen requires more than one blow of a

geological hammer to fracture it

Limestone, marble, phyllite, sandstone,

schist, shale

Medium

strong 25-50 1-2

Cannot be scraped or peeled with a pocket

knife, specimen can be fractured with a

single blow from a geological hammer

Claystone, coal, concrete, schist, shale,

siltstone

Weak 5-25 *

Can be peeled with a pocket knife with

difficulty, shallow indentation made by firm

blow with point of a geological hammer

Chalk, rocksalt, potash

Very weak 1-5 *

Crumbles under firm blows with point of a

geological hammer, can be peeled by a

pocket knife

Highly weathered or altered rock

Extremely

weak 0.25-1 * Indented by thumbnail Stiff fault gouge

* Point load tests on rocks with a uniaxial compressive strength below 25 MPa are likely to yield ambiguous results

164

Table A. 2 Values of constant mi for intact rock. Values in parenthesis are estimates (Hoek et al. 1998).

Rock type Class Group Texture

Coarse Medium Fine Very fine

Sedimentary Clastic Conglomerate

(22)

Sandstone

19

Siltstone

9

Claystone

4

Greywacke

(18)

Non-clastic Organic Chalk

7

Coal

(8-21)

Carbonate Breccia

(20)

Sparitic

limestone

(10)

Micritic

limestone

8

Chemical Gypstone

16

Anhydrite

13

Metamorphic Non-foliated Marble

9

Hornfels

19

Quartzite

24

Slightly foliated Migmatite

(30)

Amphilbolite

25-31

Mylonites

(6)

Foliated Gneiss

33

Schists

4-8

Phyllites

(10)

Slate

9

Igneous Light Granite

33

Rhyolite

(16)

Obsidian

(19)

Granodiorite

(30)

Dacite

(17)

Diorite

(28)

Andesite

19

Dark Gabbro

27

Dolerite

(19)

Basalt

(17)

Norite

22

Extrusive

pyroclastic type

Agglomerate

(20)

Breccia

(19)

Tuff

(15)

165

Table A. 3 Guidelines for estimating disturbance factor, DF (Hoek et al. 2002).

appearance of rock mass Description of rock mass Suggested

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

disturbance to the surrounding rock mass. DF = 0

Where squeezing problems result in significant

floor heave, disturbance can be severe unless a

temporary invert, as shown in the photograph, is

placed.

DF = 0.5 No invert

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

if controlled blasting is used as shown on the left

hand side of the photograph. However, stress

relief results in some disturbance.

DF = 0.7

Good blasting

DF = 1.0

Poor blasting

Very large open pit mine slopes suffer significant

disturbance due to heavy production blasting and

also due to stress relief from overburden

removal.

In some softer rocks excavation can be carried

out by ripping and dozing and the degree of

damage to the slopes is less.

DF = 1.0

Production

blasting

DF = 0.7

Mechanical

excavation

166

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

167

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.

0

0.04

0.08

0.12

0.16

0.2S

hea

r st

ress

(M

Pa)

Hoek-Brown Criterion

Mohr-Coulomb Fit

0 0.05 0.1 0.15 0.2 0.25Effective normal stress (MPa)

0

0.04

0.08

0.12

0.16

0.2

Shea

r st

ress

(M

Pa)

0 0.05 0.1 0.15 0.2 0.25Effective normal stress (MPa)

(a) (b)

(c) (d)

168

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