Thesis - Hard Binding Copy

8/12/2019 Thesis - Hard Binding Copy

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CERTIFICATE

It is certified that the work contained in this thesis, titled Numerical study of near-

field earthquake effects on concrete gravity dams by Mr. K. Jagan Mohan, has been

carried out under my supervision and is not submitted elsewhere for a degree, to my

knowledge.

__________________________________________________

Advisor: Dr. Ramancharla Pradeep Kumar

Professor

Earthquake Engineering Research Centre

International Institute of Information Technology

December 2012 Hyderabad 500 032


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Dedicated to my mother Rama Devi, father Chinna Subbaiah and dearest friend

Rupak Ashle, whom I miss in this world.


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Acknowledgements

My sincere gratitude goes primarily to my thesis supervisor, Professor Dr. Ramancharla

Pradeep Kumar, firstly because of his vast knowledge shared with us in several fields, be it

technical or non-technical cannot be overstated, and secondly for his personal care,

guidance and supervision over me, for my better career.

I would also like to thank Prof. M Venkateshwarlu for teaching us MathematicalFoundations of Solid Mechanics and Theory of Elasticity and Assistant Prof. Dr. D. Neelima

Satyam for their technical and non-technical support.

I would like to give my sincere thanks to all my colleagues (CASE), EERC members (Admin

Staff, Project Staff, Research Staff and Office boy), M.Tech students and friends who

contributed directly or indirectly in various ways for my research and well being.

I would like to give my true respect to my guardians, brothers, sisters and family members

for their support and special care and love towards me.

I owe to IIIT-H and every single person who attended and took care of me when I was

hospitalised. I would like to thank IIIT-H for releasing medical funds for my recovery.

Finally, I would like to dedicate this thesis to my dearest friend Rupak Ashle, who is no

longer alive. He was been a biggest support to me, which no one else gave in my entire life.

He is the person who always wanted to see me get MS degree deep from his heart and he

always wants to take pride in speaking about my degree. Here this is the thesis for him.

Miss him deep from my heart. Wish his soul would rest in peace.

K Jagan Mohan


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Abstract

Dam is one of the biggest structures built on the Earth. It is known as a life linestructure, as it serves the purpose of irrigation, hydro-electric power generation, flood control,

domestic and industrial water supply etc., which are important for human existence. This makes

dam as a reliable structure. For this reason, dam should always be designed for highest safety,

resisting worst forces of nature. India is a country with over 5,100 large dams. India is also a

seismically active country with over 1,000 active faults. 1988 Bihar earthquake, 1991 Uttarkashi

earthquake, 1993 Killari earthquake, 1997 Jabalpur earthquake, 1999 Chamoli earthquake, 2001

Bhuj earthquake, 2002 Andaman earthquake, 2004 Sumatra earthquake, 2005 Kashmir earthquake,

2011 Sikkim earthquake are some of the earthquakes that has hit India in the recent past. Also

events like 1992 Landers, 1994 Northridge, 1995 Hyogoken-Nambu and few other events that took

place around the world proved how devastating an earthquake could be, particularly if it is near-

field. Near-field ground motions could cause more damaging effects on structures, as they wereobserved to differ dramatically from the characteristics of their far-field counterparts. The

propagation of fault rupture towards a site at very high velocity causes most of the seismic energy

from the rupture to arrive in a single or multiple large long period pulse of motion, which occurs at

the beginning of the record. This characteristic of near-field ground motions could cause damage to

a wide range of structures including dams. Several dams that were built in India, which are in highly

seismic zones are prone to near-field ground motions. In this regard, behavior of a concrete gravity

dam subjected to near-field ground motion should be studied.

In the proposed study, a concrete gravity dam is selected from the National Importance

Dams of India and is numerically modelled along with its foundation and soil strata, using Applied

Element Method (AEM). The dam models are analysed for the components of near-field and far-

field ground motions. The comparisons between these two were drawn to understand the effects of

near-field ground motions on dams. In another study, vertical displacement is given at the bed rock

level to create reverse fault effect, while changing the location of dam alongside fault. Variation of

displacements and stresses at the base, crest, toe, heel, neck, and on upstream and downstream


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when it is modelled on foot wall. This study proved life-line structure like dam has failed to near-

field ground motion. Thus, dams should be designed to resist severe earthquakes.


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Contents

1. Introduction - - - - - - - - - 11.1 Prevalent seismic hazard in India - - - - - - 21.2 Performance of concrete gravity dams subjected to earthquakes - - 51.3 Literature review - - - - - - - - 8

1.3.1 Analytical studies - - - - - - - 81.3.2 Experimental studies - - - - - - 91.3.3 Numerical studies - - - - - - - 9

1.4 Scope of present study - - - - - - - 131.5 Organization of the thesis - - - - - - - 13

2. Numerical Modelling of concrete gravity dam

2.1 Introduction - - - - - - - - 152.2 Selection of concrete gravity dam - - - - - - 15

2.2.1 Dam Geometry - - - - - - - 16

2.2.2 Material properties - - - - - - - 192.3 Ground motions & their characteristics - - - - - 19

2.3.1 Selection of ground motions - - - - - - 202.3.2 Characteristics of ground motions - - - - - 20

2.4 Near-field ground motions - - - - - - - 252.5 Far-field ground motions - - - - - - - 352.6 Numerical method

2.6.1 Introduction - - - - - - - 452.6.2 Mathematical formulation - - - - - - 462.6.3 Element size - - - - - - - - 472.6.4 Material modelling - - - - - - - 472.6.5 Boundary conditions- - - - - - - 482.6.6 Effect of number of connecting springs - - - - 482.6.7 Modelling limitations - - - - - - 49

2.7 Summary - - - - - - - - - 49

3 Linear Earthquake response of concrete gravity dam

3.1 Introduction - - - - - - - - 503.2 Eigen value analysis - - - - - - - 50

f ld h k


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3.4.2 Response of S1 subjected to fault parallel component - - 673.4.3 Response of S2 subjected to fault normal component - - 71

3.4.4 Response of S2 subjected to fault parallel component - - 723.5 Comparison of near-field and far-field response of S1

3.5.1 Fault normal and transverse response of S1 - - - - 763.5.2 Fault parallel and longitudinal response of S1 - - - 76

3.6 Comparison of near-field and far-field response of S23.6.1 Fault normal and transverse response of S2 - - - - 773.6.2 Fault parallel and longitudinal response of S2 - - - 78

3.7 Comparison of Response Spectrum of near-field and far-field ground motions 79

3.8 Summary - - - - - - - - - 82

4 Non-linear Earthquake response of concrete gravity dam

4.1 Introduction - - - - - - - - 834.2 Comparison of near-field and far-field ground motions

4.2.1 S1 and S2 subjected to Tabas ground motion - - - 83

4.2.2 S1 and S2 subjected to Loma Prieta ground motion - - - 854.2.3 S1 and S2 subjected to Landers ground motion - - - 854.2.4 S1 and S2 subjected to Northridge ground motion - - - 864.2.5 S1 and S2 subjected to Kobe ground motion - - - - 89

4.3 Understanding the behaviour of models S1 and S2 with amplified accelerations4.3.1 S1 and S2 subjected to Tabas ground motion - - - 1014.3.2 S1 and S2 subjected to Loma Prieta ground motion - - - 1034.3.3 S1 and S2 subjected to Landers ground motion - - - 105

4.4 Summary - - - - - - - - - 107

5 Non-linear response of concrete gravity dam subjected to fault motion

5.1 Introduction - - - - - - - - 1165.2 Numerical model - - - - - - - - 1175.3 Dynamic soil-structure interaction- - - - - - 121

5.3.1 Direct method - - - - - - - 1215.3.2 Sub-structure method - - - - - - 122

5.4 Non-linear response of concrete gravity dam subjected to fault motion - 1225.4.1 Dam modelled on foot wall - - - - - - 1235.4.2 Dam modelled on hanging wall - - - - - 123


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2.26 Material models for concrete and steel (a) Tension and compression concrete Maekawa model(b) Bi-linear stress strain relation model for steel reinforcement (Kimuro Meguro and Hatem 2001)

- - - - - - - - - - 483.1 Eigen values of first ten mode shapes of S1 - - - - - 51

3.2 Eigen values of first ten mode shapes of S2 - - - - - 52-53

3.3 Linear displacement response of S1 to 5 near-field fault normal ground motions - 59

3.4 Linear displacement response of S1 to 5 near-field fault parallel ground motions - 60

3.5 Linear displacement response of S2 to 5 near-field fault normal ground motions - 64

3.6 Linear displacement response of S2 to 5 near-field fault parallel ground motions - 653.7 Linear displacement response of S1 to 5 far-field transverse ground motions - 69

3.8 Linear displacement response of S1 to 5 far-field longitudinal ground motions - 70

3.9 Linear displacement response of S2 to 5 far-field transverse ground motions - 74

3.10 Linear displacement response of S2 to 5 far-field longitudinal ground motions - 75

3.11 Acceleration Response Spectrum of 5 near-field fault normal ground motions - 80

3.12 Acceleration Response Spectrum of 5 near-field fault parallel ground motions - 81

3.13 Acceleration Response Spectrum of 5 far-field transverse ground motions - 81

3.14 Acceleration Response Spectrum of 5 far-field longitudinal ground motions - 82

4.1 Crack propagation observed in S2 to Tabas near-field fault normal ground motion 85

4.2 Crack propagation observed in S2 to Landers near-field fault normal ground motion 86

4.3 Crack propagation observed in S2 to Landers near-field fault parallel ground motion 86

4.4 Crack propagation observed in s1 to Northridge near-field fault normal ground motion 87

4.5 Crack propagation observed in s1 to Northridge near-field fault parallel ground motion 88

4.6 Crack propagation observed in S2 to Northridge near-field fault normal ground motion 88

4.7 Crack propagation observed in S2 to Northridge near-field fault parallel ground motion 89

4.8 Crack propagation observed in s1 to Kobe near-field fault normal ground motion 91

4.9 Crack propagation observed in s1 to Kobe near-field fault parallel ground motion 914.10 Crack propagation observed in S2 to Kobe near-field fault normal ground motion 92

4.11 Crack propagation observed in S2 to Kobe near-field fault parallel ground motion 92

4.12 Non-linear displacement response of S1 to 5 near-field fault normal ground motions 93


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4.19 Non-linear displacement response of S2 to 5 far-field longitudinal ground motions 100

4.20 Crack propagation observed in S1 to Tabas near-field fault normal ground motion 101

4.21 Crack propagation observed in S1 to Tabas near-field fault parallel ground motion 102

4.22 Crack propagation observed in S2 to Tabas near-field fault parallel ground motion 103

4.23 Crack propagation observed in S1 to Loma Prieta near-field fault normal motion 104

4.24 Crack propagation observed in S2 to Loma Prieta near-field fault normal motion 104

4.25 Crack propagation observed in S2 to Loma Prieta near-field fault parallel motion 104

4.26 Crack propagation observed in S1 to Landers near-field fault normal ground motion 105

4.27 Crack propagation observed in S1 to Landers near-field fault parallel ground motion 106

4.28 Amplified non-linear displacement response of S1, subjected to 5 near-field fault normalground motions - - - - - - - - - 108

4.29 Amplified non-linear displacement response of S1, subjected to 5 near-field fault parallelground motions - - - - - - - - - 109

4.30 Amplified non-linear displacement response of S2, subjected to 5 near-field fault normal

ground motions - - - - - - - - - 1104.31 Amplified non-linear displacement response of S2, subjected to 5 near-field fault parallelground motions - - - - - - - - - 111

4.32 Amplified non-linear displacement response of S1, subjected to 5 far-field transverse groundmotions - - - - - - - - - 112

4.33 Amplified non-linear displacement response of S1, subjected to 5 far-field longitudinal groundmotions - - - - - - - - - 113

4.34 Amplified non-linear displacement response of S2, subjected to 5 far-field transverse groundmotions - - - - - - - - - 114

4.35 Amplified non-linear displacement response of S2, subjected to 5 far-field longitudinal groundmotions - - - - - - - - - 115

5.1 Displacement time history of 2.5m with rise time of 5sec as input - - - 118

5.2 Failure of springs observed in the base when 2.5m displacement is given in 5sec - 118

5.3 (i) model of S2a (ii) displacement of 2.5m as input to S2a - - - - 1195.4 (i) model of S2b (ii) displacement of 2.5m as input to S2b - - - - 119

5.5 (i) model of S2c (ii) displacement of 2.5m as input to S2c - - - - 120

5.6 (i) model of S2d (ii) displacement of 2.5m as input to S2d - - - - 120


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5.12 Failure of dam (at 600m-700m) subjected to 2.5m displacement in the base - 126

5.13 Failure of dam subjected to free-field acceleration recorded at 250m - - 126



5.16 Displacement response at the crest of dam (dam placed at 4 different locations), subjected to2.5m displacement with a rise time of 5 sec - - - - - - 128

5.17 Displacement response at the crest of dam; acceleration recorded at 4 different locationswhen base is subjected to 2.5m displacement with a rise time of 5 sec - - 129

A1.1 Kallanai Dam in India dated 2 nd century AD - - - - - 132A3.1 Fault Normal, Fault Parallel & Vertical Accelerogram of 1994 Northridge earthquake 136

A3.2 1992 Landers earthquake, showing the Forward and Backward Directivity region 137

A3.3 Surface faulting caused major damage to Shii-kang Dam- - - - 138

A4.1 State wise distribution of large dams (existing and ongoing) in India - - 140

A4.2 Distribution of large dams in India - decade wise - - - - 141

A4.3 State wise distribution of large dams (completed) in India - - - 141

A4.4 State wise distribution of large dams (under construction) in India - - 142

A4.5 National Importance Dams of India on Seismic Zonation Map - - - 143

A4.6 National Importance Dams of India placed on Fault & Seismic Zonation map of India 143

A4.7 National Importance Dams of India on Seismic Zonation Map plotted with top 100 active fault - - - - - - - - - - - 144

List of Tables1.1 Important earthquakes in Himalayan Frontal Arc (Kamalesh Kumar (2008),

http://gbpihed.nic.in) - - - - - - - - 3

1.2 Important earthquakes in Peninsular India (Kamalesh Kumar (2008),http://gbpihed.nic.in) - - - - - - - - 3

1.3 Important earthquakes in Northeastern region of India (Kamalesh Kumar (2008),http://gbpihed.nic.in) - - - - - - - - 4

1.4 Concrete dams subjected to significant shaking (PHGA > 0.3g) (Courtesy: USSD Proceedings2012) - - - - - - - - - - 5

2.1 Details of near-field - fault normal ground motions - - - - 23

2.2 Details of near-field - fault parallel ground motions - - - - 23


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3.4 Response of S1 subjected to 5 near-field fault parallel ground motions - - 56

3.5 Comparison of response of S1 subjected to 5 near-field fault normal and fault parallel ground

motions - - - - - - - - - 573.6 Response of S2 subjected to 5 near-field fault normal ground motions - - 61

3.7 Response of S2 subjected to 5 near-field fault parallel ground motions - - 62

3.8 Comparison of response of S2 subjected to 5 near-field fault normal and fault parallel groundmotions - - - - - - - - - 63

3.9 Response of S1 subjected to 5 far-field transverse ground motions - - 66

3.10 Response of S1 subjected to 5 far-field longitudinal ground motions - - 673.11 Response of S1 subjected to 5 far-field transverse and longitudinal ground motions 68

3.12 Response of S2 subjected to 5 far-field transverse ground motions - - 71

3.13 Response of S2 subjected to 5 far-field longitudinal ground motions - - 72

3.14 Response of S2 subjected to 5 far-field transverse and longitudinal ground motions 73

3.15 Fault normal and transverse response of S1 subjected to 5 near-field and far-field ground

motions - - - - - - - - - - 763.16 Fault parallel and longitudinal response of S1 subjected to 5 near-field and far-field groundmotions - - - - - - - - - - 76

3.17 Fault normal-transverse and fault parallel-longitudinal response of S1 subjected to 5 near-fieldand far-field - - - - - - - - - 77

3.18 Fault normal and transverse response of S1 subjected to 5 near-field and far-field groundmotions - - - - - - - - - - 78

3.19 Fault parallel and longitudinal response of S1 subjected to 5 near-field and far-field groundmotions - - - - - - - - - - 78

3.20 Fault normal-transverse and fault parallel-longitudinal response of S2 subjected to 5 near-field and far-field - - - - - - - - - 79

3.21 Linear displacement response at the crest of S1 and S2 subjected to near-field and far-fieldground motions - - - - - - - - - 79

4.1 Comparison of non-linear response of S1 & S2 subjected to near-field & far-field groundmotions - - - - - - - - - - 92

4.2 Comparison of non-linear response of S1 & S2 subjected to amplified near-field & far-fieldground motions - - - - - - - - - 106

5.1 Non-linear displacement response at the crest of dam, between direct method and sub-structure method 122


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Chapter 1

Introduction and Literature Review

1.0 Introduction

Dams are impressive constructions in our world and it is a fascinating chapter of ourhistory to investigate their origin. The history shows, that these constructions are not innovations of nowadays, because the first predecessors have existed even 6000 years beforeour modern times. A dam is a barrier or structure across a stream, river, or a waterway for thepurpose of confining and controlling the flow of water. Depending upon requirements,

construction of a dam can vary in size and material from small earthen embankments tomassive concrete structures. Primary purpose of dams being irrigation, hydro-electric powergeneration, flood control, domestic and industrial water supply etc., makes these structures asone of the life line structures. As such, dams are cornerstones in the water resourcesdevelopment of river basins.

Dams are now built to serve several purposes and are therefore known as multipurpose.With rapid growth of population in India and the consequent demand over water for variouspurposes, it has now become necessary not only to construct new dams with revised designprocedures which can sustain worst forces of nature but also to rehabilitate and maintainexisting ones. Natural disasters like earthquake, landslide, cyclone, flood, drought, etc., are quite

common in different parts of India. These can create catastrophe leading to the loss of life,property damage and socio-economic disturbances. Such losses have grown over the years dueto increase in population and misuse of natural resources.

Among all these natural disasters earthquakes are one of the worst and it is also known


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1.1 Prevalent seismic hazard in India

USGS estimates that around 5 lakh earthquakes hit the Earth every year, 1 lakhof those can be felt, and very few cause damage [http://earthquake.usgs.gov/learn/facts.php].Moreover, in Indian-Subcontinent, particularly the north-eastern and north-western regions arethe most earthquakes-prone regions of the world. 1988 Bihar earthquake, 1991 Uttarkashiearthquake, 1993 Killari earthquake, 1997 Jabalpur earthquake, 1999 Chamoli earthquake,2001 Bhuj earthquake, 2002 Andaman earthquake, 2004 Sumatra earthquake, 2005 Kashmirearthquake, 2011 Sikkim earthquake are some of the worst hit earthquakes, which cumulativelyhave caused over 1 lakh death toll.

Seismic zonation map clearly shows that India is highly vulnerable to earthquakehazard. During last 100 years, India haswitnessed more than 650 earthquakes of magnitude 5.0 [Kamalesh Kumar, 2008].In addition to very active northern andnorth-eastern range, the recent events of 1993 Killari (Maharashtra) and Jabalpur(Madhya Pradesh) in the Peninsular India

have started raising doubts as the disasterscaused by these earthquakes arealarmingly increasing. Earthquake eventsreporting from the Himalayan mountainrange, Andaman and Nicobar Islands, Indo-

Gangetic plain as well as from peninsularregion of India belongs to subductioncategory and a few events had also beenunder intra-plate category. Figure 1.1: Seismic zonation map of India


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important earthquakes that have occurred during the past century in Himalayan Frontal Arc aretabulated below in Table 1.1.

Table 1.1: Important earthquakes in Himalayan Frontal Arc (Kamalesh Kumar (2008), http://gbpihed.nic.in)

Place Year Magnitude Casualty

Kangra Valley April 4, 1905 8.6 >20,000Bihar-Nepal border January 1, 1934 8.4 >10,653

Quetta May 30, 1935 7.6 about 30,000North Bihar 1988 6.5 1000 approximatelyUttarkashi October 20, 1991 6.6 >2,000Chamoli March 29, 1999 6.8 >150Hindukush November 11, 1999 6.2 no death reported

Sikkim September 18, 2011 6.9 about 111The Peninsular India which was once considered as a stable region has started to

experience the earthquakes in increased number because of intra-plate mechanism. Eventhough the magnitudes of these are less and recurrence intervals are larger than those of theHFA, it started to create panic among the inhabitants in this region. Some of the most important

earthquakes that have occurred in Peninsular India in the past are tabulated below in Table 1.2.Table 1.2: Important earthquakes in Peninsular India (Kamalesh Kumar (2008), http://gbpihed.nic.in)

Place Year Magnitude Casualty

Kachchh June 16, 1819 8.5 No recordJabalpur June 2, 1927 6.5 Indore March 14, 1938 6.3 Bhadrachalam April 14, 1969 6.0 Koyna December 10, 1967 6.7 >200Killari (Latur) September 30 1993 6 3 >10 000


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(Burmese arc). Some of the most important earthquakes that have occurred in this region of India in the past are tabulated below in Table 1.3.

Table 1.3: Important earthquakes in Northeastern region of India (Kamalesh Kumar (2008), http://gbpihed.nic.in)

Place Year Magnitude Remark

Cachar March 21, 1869 7.8Numerous earth fissures

and sand craters

Shillong Plateau June 12, 1897 8.7 About 1542 people diedSibsagar August 31, 1906 7.0 Property damageMyanmar December 12, 1908 7.5 Property damage

Srimangal July 8, 1918 7.64500 sq km areasuffered damage

S-W Assam September 9, 1923 7.1 Property damageDhubri July 2, 1930 7.1

Railway lines, culvertsand bridges cracked

Assam January 27, 1931 7.6 Destruction of PropertyN-E Assam October 23, 1943 7.2 Destruction of PropertyUpper Assam July 29, 1949 7.6 Severe damage

Upper Assam August 15, 1950 8.7

About 1520 people died.One of the largest

known earthquake inthe history

Indo-Myanmar

borderAugust 6, 1988 7.5 No casualty reported.

Seismologists seem not to believe that the frequency in the occurrence of earthquakeshas increased. Unfortunately, earthquakes of higher magnitudes which use to occur inuninhabited areas or virtually uninhabited areas have hit some thickly populated areas


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earthquake occurred in these regions, creating more alarming situation and the devastation it would become if such event occurs now. There are several examples, where high number of casualties and deaths occurred when the event occurred during early morning hours and quiteopposite when they occurred during the day time even when the epicenter is too near to theinhabited areas. These examples clearly tell that the time of occurrence of the event and theepicenter also matters, to quantify loss of life and damage to property.

1.2 Performance of concrete gravity dams subjected to earthquakes

Therst failure of a dam due to earthquake reported in the literature was Augusta Dam,Georgia, during the 1886 Charleston, South Carolina earthquake. However, the milestone in theseismic analysis of dams turned after the 1967 Koyna earthquake in India where damage wascaused to the upstream and downstream side of the concrete gravity dam and 1971 San

Fernando earthquake in California where damage was caused to embankment dams (SanFernando dams) and also to an arch-gravity dam (Pacoima dam). Although such ground motionscaused problems to dams, no serious damages were observed. However, during someearthquake events, concrete gravity dams were uprooted when blind faults which were lyingbelow the dam body turned active. These very few events have shown that the earthquakehazard continues to be a serious threat to dams, as the failure of a full reservoir concrete gravitydam could cause catastrophe on the downstream.

In the epicentral area of the earthquake, a number of concrete gravity dams haveexperienced ground shaking. However, only about 20 dams have been subjected to 0.3g PHGAor higher without apparent damage. Some of these concrete dams performance to earthquakesare tabulated below.

Table 1.4: Concrete dams subjected to significant shaking (PHGA > 0.3g) [Courtesy: USSD Proceedings 2012]

DamCountry

Ht. EarthquakeDist. to

fault Mag. PHGA (g) Remarks


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Bear Valley(1912, 1988)

USA 28

Landers

Jun 28, 1992

45.0 7.4 0.18Multiple archmodified to gravity

dam in 1988.

Big BearJun 29, 1992

14.5 6.6 0.57

No damage, except slight displacement of crest bridgegirders.

Gohonmatsu(1900) Japan 33

KobeJan 17, 1995 1.0 7.2 0.83

No damage on thismasonry dam

Shih-Kang(1977)

Taiwan 21.4Chi ChiSep 21, 1999

0.0 7.60.51 h0.53 v

Vertical disp. of 9 m,Rupture of concrete.

Mingtan(1990)

Taiwan 82Chi ChiSep 21, 1999

12.0 7.60.4 to 0.5

(est.)No damage

Kasho (1989) Japan 46.4Western TottoriOct 6, 2000 3.0-8.0 7.3 0.54

Cracks in controlbuilding at crest

Uh (___) Japan 14Western TottoriOct 6, 2000

1.0-3.0 7.3 1.16Small crack at spillway base

Takou (2007) Japan 77TohokuMar 11, 2011

109.0 9.0 0.38Cracking of gate-house walls at crest.

Miyatoko(1993) Japan 48

TohokuMar 11, 2011 135.0 9.0 0.32 No damage

Concrete Arch Dams

Gibraltar(1920, 1990)

USA 52Santa BarbaraJun 29, 1925

? 6.3> 0.3(est.)

No damage. Modifiedin 1990 with RCC.

Pacoima(1929)

USA 113

San FernandoFeb 9, 1971 5.0 6.6

0.6 to0.8

No cracks in arch.

Open joint betweenarch and thrust block.

NorthridgeJan 17, 1994

18.0 6.8 0.53Open joint (2)between arch andthrust block


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Shapai (2003) China 132Wenchuan

May 12, 2008

20.0 8.00.25 to

0.50

(est.)

No Damage

Concrete Buttress Dams

Hsinfengkiang(1959)

China 105ReservoirMar 19, 1962

1.1 6.1 0.54Horizontal cracks intop part of dam

Sefid Rud

(1962)Iran 106

Manjil

Jun 21, 1990

Neardamsite

7.7 0.71 (est.)Horizontal cracksnear crest, minordisp. of blocks

Notes: Legend: Ht.=height, est.=estimated, Dist.=distance, Mag.=magnitude (M L

or M B for less than 6.5 and M S above 6.5), cc=cross canyon, h=horizontal,

v=vertical. PHGA=Peak Horizontal Ground Acceleration, disp.=displacement

Table 1.4 illustrates about the worldwide performance of concrete (Arch, Buttress &

Gravity) dams subjected to ground motions > 0.3g. From the table it can be concluded that concrete dams have performed well when subjected to high intensity accelerations. There might be several reasons why concrete dams have performed well and consistently well than that predicted by design or analysis when shaken by an earthquake. However, the dams present inhighly seismic zones are always under threat as some dams have performed less than what was

expected. Several factors like magnitude, epicentral distance, PHGA, range of frequency cansolely vary the performance of dams subjected to earthquakes. A thorough understanding onthe ground motions should be studied for that respective area before the construction of dam.

For this huge number of strong motion recorders should be placed at or near the damsites, which would increase our knowledge over the performance of severely shaken concrete

dams and that knowledge could be applied in designing future dams. The most significant factors other than magnitude to be considered in determining the response of concrete damsare the epicentral distance to the dam, PHGA and also the spectral acceleration at the naturalfrequency of the dam. PHGAs get amplified from the base of the dam to the crest and peak


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the change in location of geometry. While concrete dams are designed to withstand severeshaking and have performed well in the past, it should not be considered as a positive sign of their performance in the future. Utmost care in design and construction practices should betaken and special attention towards possible faults located near the dam should be given.

1.3 Literature review

Failure of a concrete gravity dam subjected to an earthquake is a very rare case. Even

though there are a very few number of concrete gravity dams which suffered minor damageswhen subjected to earthquakes, the effect that an earthquake can cause even on such a hugeconstruction is already known. One such example is failure of Shih-Kang dam. Since past fewdecades, several researchers have conducted research even by considering site conditions, dam-foundation, and dam-foundation reservoir interactions.

For the current study, a thorough literature review has been conducted to understandthe past research work of earthquake effects on concrete gravity dams. From the conclusionsthrough conducted literature review, the inspiration to take our study in a new angle has beenmarked. The studies presented for literature review are categorized as:

Analytical Studies

Experimental Studies

Numerical Studies

1.3.1 Analytical Studies

Tatsuo Ohmachi (1999) had done fundamental study on near-field effects on earthquakeresponse of arch dams. Effects of directivity of near-field and vertical ground motions on linearresponse of an arch dam were also studied. The strong motion record observed at Pacoima Damstation during the 1994 Northridge earthquake, California was taken as an input motion andconfiguration of Morrow Point dam as a model of an arch dam had been used. Also, while


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1.3.2 Experimental Studies

William P. Donlon (1989) had investigated nonlinear seismic response of concrete gravitydams experimentally using small-scale models. Of primary interest are crack formation, crackopening and closing, and sliding along crack planes. Stability of structure after cracking was alsostudied. Three small-scale models of a single monolith of Pine Flat Dam were tested to determinethe extent of such behaviour and its effect on structural stability. The models were constructed of one polymer-based and two-plaster-based materials developed for these experiments. Theplaster-based materials fulfil the strength, stiffness, and density requirements established by thelaws of similitude, while the polymer-based material fulfils only the stiffness and densityrequirements and are used only in the lower part of the dam where cracking is not expected.Tests were performed with and without water in the reservoir. The results of the experimentsindicate that the neck region of a concrete gravity dam is most susceptible to cracking, although

crack propagation files can differ as a result of variations in excitation, material properties andconstruction techniques. These results also indicate alternate design techniques which couldimprove the seismic stability of a cracked gravity dam.

Jean Proulx (1997) had done experimental and numerical investigation of dam-reservoir-foundation interaction for a large gravity dam. Forced-vibration tests were completed on Outardes

3 gravity dam, located in north-eastern Quebec, Canada. The experimental results weresubsequently used as a basis for a numerical correlation study to evaluate the performance of state-of-the-art finite element programs for earthquake analysis of concrete dams. Theexperimental procedure was presented and involved in the recording of acceleration responseson the 84-m-high dam under harmonic loading. Hydrodynamic pressures were also recorded at

several locations in the reservoir, up to a distance of 90m from the dam face. Extensive studieswere carried out with two- and three-dimensional models. Numerical results were comparedwith complete frequency responses for accelerations and pressures obtained on site. It wasdemonstrated that the two-dimensional approach could only predict the fundamental resonance


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with horizontal bottom. The problem was analysed under the assumption of linear behaviour forthe concrete, foundation rock and water. Based on the analytical procedures developed, acomputer program has been written to evaluate numerically the responses of concrete gravitydams, including various effects of both the impounded water and the foundation rock.

S.S. Bhattacharjee (1993) had studied the seismic fracture analysis of concrete gravitydam using finite element method. He has proposed the smeared crack analysis model based onthe non-linear fracture behaviour of concrete. The features that he had considered in thedevelopment of the model are (i) the strain softening of concrete due to micro cracking; (ii) therotation of the fracture band with the progressive evolution of micro crack damage in finiteelements; (iii) the conservation of fracture energy; (iv) the strain-rate sensitivity of concretefracture parameters; (v) the softening initiation criterion under biaxial loading conditions; and(vi) the closing-reopening of cracks under cyclic loading conditions. A two-dimensional seismic

response analysis of Koyna dam was then performed to demonstrate the application of theproposed non-linear fracture mechanics model. His study had shown that the continuummechanics approach could efficiently predict the localized cracking response of concrete gravitydams if applied with appropriate constitutive models and the seismic fracture response of Koynadam had been satisfactorily reproduced in the analyses using the non-linear smeared fracturemodel.

Abdolrahim Jalali (2000) had studied the aspects of concrete dams response to near-fieldground motions. In this investigation the effects of near-field ground motions on concrete damsare assessed using a collection of some records from actual earthquakes. All of these recordsexhibit main characteristics of near-field ground motions. Another record, the 1940 El-Centro

motion in which near-field effects are absent, is used as a reference. The effects of near-fieldground motions on displacements, and stresses of upstream and downstream faces of Morrow-Point Arch dam, and on stresses, displacements, and base sliding of Pine Flat Concrete gravitydam have been evaluated.


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care of by providing a sumptuous riprap composed of blasted rock from a quarry of competent quartzite, both in u/s and d/s. The top portion of the fill dam was build with the same material towithstand severe accelerations. The designers considered that the dam based on the detaileddynamic analysis carried out for several worst case scenarios and different hazard levels, sufferdeformation to an extent within acceptable limits under postulated MCE. Finally their studyconcluded that the dam design was structurally safe to withstand the MCE.

Tatsuo Ohmachi (2003) had studied near-field effects of hidden seismic faulting on aconcrete dam. The 2000 Western Tottori earthquake (M s 7.3) , Japan, was caused by a hiddenseismic fault underlying the Kasho Dam, a 46 m high concrete gravity dam. Strong-motionaccelerometers registered peak accelerations of 2000 gal at the top and 500 gal in the lowerinspection gallery. Integration of the acceleration records in the gallery showed a permanent displacement of 28 cm to the north, 7 cm to the west, and an uplift of 5 cm. This dam survived

the earthquake without serious damage. However, the reservoir level dropped suddenly by 6 cmfollowed by damped free vibration that continued several hours. Based on numerical simulationand field observations, the water level change is attributed to ground displacement in the near-field and subsequent seiching of the reservoir. The vibration period of the dam in the u/s-d/sdirection changed noticeably during the main shock, probably due to hydrodynamic pressurevariation. The earthquake caused cracking of concrete floor beams in a sub-gate control room,which was repaired by post-tensioning with steel bars, resulting in increased beam rigidity andmicro-tremor instruments were used to evaluate the effectiveness of the repair work. Based onthe experiences at this site, author had strongly recommended that the earthquake response not only of the dam body but of appurtenant structures such as sub-gates control rooms should beconsidered in the structural design of dams.

Vahid Lotfi (2004) had studied dynamic analysis of concrete arch dams based on finiteelement-boundary element (FE-BE) procedure including non-uniform ground motion. In thistechnique, dam body was discretised by finite elements, while foundation rock domain was


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ground motion. While at high frequencies, the opposite behaviour was noticed. This was true forall three types of excitation direction being considered.

Worakanchana Kawin (2005) had studied the failure mechanism of Shih-Kang dam byApplied Element Method (Pradeep Kumar Ramancharla, 2001). Static non-linear analysis andparametric study including dip angle of the fault, fault location were studied. Also, the redesign of Shih-Kang dam was proposed. It was found that concrete dam like the case of Shih-Kang dam canresist very low amount of fault induced ground rupture and deformation. From numerical result,Shih-Kang dam damage mechanism starts from the separation of the dam from its foundation,crack from the top of the dam, shear crack and compression failure. According to the parametricstudy, it was found that the normal fault, if occur under the dam will damage the dam at the lowerdisplacement than the reverse fault. Also, different fault location affects in the different shearspan length. The longer the shear span's length, the more displacement the dam can resist. The

proposal for the rehabilitation of Shih-Kang dam was proposed by placing the slip joint andreinforcement, FRP or expansive concrete to control the crack width of the dam. To place the slipjoint, the accurate knowledge of fault characteristic in the area must be known.

Rajib Sarkar (2007) had studied the response of a dam subjected to dynamic loading in acombined effect of the interaction among dam, reservoir and foundation systems. They adopted

the profile of the Koyna dam for the study. Also, nonlinear concrete properties had been takeninto account through concrete damaged plasticity model to simulate the damage induced in thedam body under a real-time earthquake motion. Tensile damage to the dam structure occurredduring the earthquake motion had been studied and the same had been studied by making fewchanges in parameters like varying the height of the reservoir and the foundation modulus

values, to show the influence of reservoir and foundation materials on the dynamic response of concrete gravity dams. They concluded that with the decrease in the foundation modulus, thedisplacements increased and if reservoir depth considered was less than 0.7 times the full-reservoir depth, the reservoir had no significant impact on the dynamic behaviour of the dam


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dimensional loading conditions. Those characteristics were pre-softening behaviour, softeninginitiation criteria, fracture energy conservation and strain rate effect. After verification of theproposed model by some available numerical tests, dynamic analysis of Morrow Point concretearch dam under the three components of the Taft earthquake scaled to 1.0g was carried out. Inthe analysis, complete fluid-structure interaction was considered accounting for fluidcompressibility and absorptive reservoir boundary condition approximately. The coupledequation resulting from dam-reservoir interaction was solved using staggered method. The

deduced results showed that crack pattern had good agreement with the contour of maximumprincipal stresses and the proposed algorithm also gives reliable solution even in large time steps.

1.4 Scope of present study

Earthquakes and dams both are not new to this world. However, when the effect of strongmotion over different range of structures is known and importance of life line structure like damis also known it should be seen that the dams are constructed to resist earthquakes. India is acountry with over 1,000 active faults and 5,100 large dams constructed and few more underconstruction. Most of these dams are in highly seismic zones under the threat to experiencesevere earthquakes. In an earthquake event, factors like magnitude, peak ground acceleration,velocity pulses, permanent displacement, epicentral distance, directivity, orientation of fault, local

site conditions, soil-structure interaction etc., individually have varying effects on dams. However,in our study we have restricted ourselves with ground motions recorded with epicentral distanceless than 10 km, having forward directivity effects, for different types of faults. For completeanalysis other parameters should have also been considered. However, with limitation of data andcomplexity in solving problem, we had certain limitations.

Current study would give a scope for proper understanding of how the effects would varybetween near-field and far-field earthquakes. Even though very few concrete dams haveundergone minor failures when subjected to earthquakes, near-field earthquakes have capacityto destabilize the dams. This current study would give an understanding of how near-field


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Chapter (2) describes the selection of dam and its geometrical details. It also explains about theground motions considered and their characteristics. Finally Applied Element Method (AEM)(Hatem, 1998) the numerical modelling used is described with its formulation and limitations.

Chapter (3) describes the comparison of linear earthquake response between components of near-field and far-field on non-over flow section of dam with foundation system and on non-overflow section of dam with foundation and base.

Chapter (4) describes the comparison of non-linear earthquake response between componentsof near-field and far-field on non-over flow section of dam with foundation system and on non-over flow section of dam with foundation and base. Initiation of cracks and its propagation is alsodescribed.

Chapter (5) describes the non-linear response of concrete gravity dam subjected to fault motion.

Parametric study is done, by modeling the dam on hanging wall and foot wall. The behaviour of dam, initiation of cracks and its propagation is also described.

Conclusions and future scope of work are given in Chapter (6).

Appendix (A1) gives the information on history and necessity of dams.

Appendix (A2) gives different causes of dam failures.

Appendix (A3) gives a special focus on near-field earthquake effects.

Appendix (A4) gives the information on large dams in India.


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Chapter 2

Numerical Modelling of Concrete Gravity Dam

2.1 Introduction

This chapter mainly focuses in describing the selection process of a concrete gravitydam in India, for the analysis based on its importance. Geometrical details of dam, its materialproperties, and ground motions considered for the analysis and their characteristics aredescribed. Later a numerical method called Applied Element Method [Hatem et.al. 1998, 2000],its mathematical formulation, modeling limitations and its application in analysis of concrete

gravity dam subjected to near-field and far-field ground motions are described.

2.2 Selection of concrete gravity dam

By the time India got independence in 1947, there were less than 300 large dams inIndia. At present this number has grown to about 5,100 [National Register of Large Dams 2009], with 181 dams of national importance. India is a seismically active country, with historyof major earthquakes having occurred in the past. North-eastern and north-western parts of India are seismically very active as the Indo-Australian plate is sub-ducting under Eurasianplate at this region. Along with intra-plate earthquakes, India has witnessed several severeearthquakes.

These earthquakes resulted in the failures of different range of structures from smallbuildings to major dams. The 1967 Koyna earthquake is one example, which caused minordamage to the upstream and downstream side of Koyna dam without causing flooding. As it is aconcrete gravity dam, it has withstood the event. However, there are several other examples in


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In this concern, a large dam has been selected from India, by taking few parameters intoconsideration. Depending upon services utilized from dams for multi-purposes, NRLD hasclassified a list of 181 dams among 5,100 dams as National Importance Dams. Due tounavailability of complete data of 181 dams from 2009 report, data from previous report available has been considered. By the time report of National Importance Dams was made in2002, there were 4,525 dams and 70 National Importance Dams [Appendix-A2]. These dams areplaced on India map with the information of their latitude-longitude. Later the map is

overlapped with seismic zonation map of India along with 1040 active faults and lineaments[Geological Survey of India, 2000]. Top 100 active faults are identified based on the cumulativeenergy generated from those faults in the previous earthquakes. Finally a map is prepared byover lapping National Importance Dams of India, Seismic Zonation map of India and top 100active faults of India. For the study, among 70 national importance dams, dams >100m (23dams) are listed and dams in seismiczones IV and V (11 dams) are furthershort listed. In those final 11 short listeddams, the seismic safety of 103m highconcrete gravity Koyna dam located inseismic zone IV had been widely debated

and because of that probably this dam hasbeen studied very extensively. Failure of such a large dam would evidently createcatastrophe. So, for our study we thushave considered Koyna dam for theanalysis as it has undergone M

W6.3

magnitude earthquake on 11th December1967. It has also experienced 17earthquakes of MW5.0 and also over 150


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one of the oldest continental blocks on the earths surface. Prior to the year 1962, this shieldwas referred to as a stable rock. However, the December 11th, 1967 earthquake of MW6.3 in the

Koyna region contradicted all these beliefs. However, the dam in the region withstood thissignificant seismic activity without much damage. For the study we have considered two modelsfirst one is a non-overflow section of the dam along with foundation and the second model is anon-overflow section of dam with foundation and base. These two models are considered andstudied individually.

2.2.1.1 Non-overflow section of dam with foundation (Structure S1)

The structure is 103m high and 70m wide at the base and 15m wide at the crest. Thedam on the downstream is planned and designed out of conventional style by providing largeneck portion in an inclined position. The change of cross section of dam at the neck happens at 67m height from the base. Width at this height of 67m, where the cross section gets changed is20 m. Also the dam is provided with a concrete foundation of 100m x 5m (fig. 2.3). The wholedam is divided into many blocks; with separation joints being provided between two adjacent blocks, each being 15m wide. Even though the numerical modeling is in 2D it considers theeffect of thickness therefore, thickness of 15m is considered for modeling. The bottom of thedam is considered as fixed for this model and analysis is done individually on it.

2.2.1.2 Non-overflow section of dam with foundation and base (Structure S2)

Foundation conditions depend upon the geological character and thickness of the stratawhich should carry the weight of dam, their inclination, permeability, and relation of underlyingstrata, existing faults and fissures. The foundation will limit the choice of type to a certain

extent, although such limitations can frequently be modified, considering the height of theproposed dam. For the foundation base, homogeneous strata of granite rock of length 800m andheight 50m is modeled. The dam with concrete foundation is placed at the centre of the base forthe study. The dimensions and material properties of the dam remains the same as S1.


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2.2.2 Material Properties

For the dam, properties like density, Poisson's ratio, compression resistance and tensionresistance values are taken from a reference paper [Rajib Sarkar et al., 2005]. In which, theyhave studied the non-linear behavior of Koyna dam by considering that the properties of Koynadam taken are actual from its design.

Properties of Dam

Youngs Modulus (Ec): 3.1027x107 kN/m2

Poissons Ratio (): 0.2

Density of Concrete (): 2.643 t/m3

Tension Resistance (t ): 2.58x103 kN/m2

Compression Resistance (c): 2. 41x104 kN/m2Even though the site is one of the oldest continental blocks of earth's surface, the dam is

assumed to be built on hard strata and analyzed. Therefore, homogeneous granite rock isconsidered as base.

Properties of base

Youngs Modulus (E): 6.0x107 kN/m2

Poissons Ratio (): 0.2

Density of Granite rock (): 2.7 t/m3

Tension Resistance (t ): 1.6x104 kN/m2

Compression Resistance (c): 1.6x105 kN/m2

2.3 Ground motions and their characteristics

Seismic inputs are the earthquake data that are necessary to perform different types of


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frequency etc. Selection of ground motions used in the study and their characteristics aredescribed in coming sections.

2.3.1 Selection of ground motions

For the study, we have considered 10 near-field ground motions (fault normal and fault parallel components) and for the same near field events 10 far-field ground motions (transverseand longitudinal components) are considered and among these 10 only 5 ground motionsdepending on their characteristics have been selected for the study.

The PGA's of 10 near-field fault normal ground motions ranges between 0.432 - 1.088,PGA's of 10 near-field fault parallel ground motions ranges between 0.37 - 0.978 are considered.For the same events, PGA's of 10 far-field transverse ground motions ranges between 0.027 -0.496 and PGA's of 10 far-field longitudinal ground motions ranges between 0.0262 - 0.515 areselected. The PGA's and duration of ground motions ranges from low to high and the frequencycontent ranges from resonating to non-resonating frequencies. The details of the groundmotions are listed from Table 2.1 to Table 2.4 and the ground motion records and their Fourieramplitude spectrums are shown from fig. 2.4 to fig. 2.23

2.3.2 Characteristics of ground motions

It is necessary to describe the characteristics of the ground motion that are of engineering significance and to identify a number of ground motion parameters that reflect those characteristics. For engineering purposes, three characteristics of earthquake motions (1)amplitude, (2) frequency content, and (3) duration of the motion are important to be studied.Plenty of different ground motion parameters have been proposed, each of which provides

information about one or more of these characteristics. In practice, it is usually necessary to usemore than one of these parameters to characterize a particular ground motion adequately(Kramer, 1996). These (amplitude, frequency, duration) characteristics differ dramaticallybetween near-field and far-field ground motions.


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longer than about 0.5 seconds [Paul Somerville, 2005]. However, near fault recordings fromrecent earthquakes indicate that the pulse is a narrow band pulse whose period increases with

magnitude, causing the response spectrum to have a peak whose period increases withmagnitude, such that the near-fault ground motions from moderate magnitude earthquakesmay exceed those of larger earthquakes at intermediate period. Parameters like rupturedirectivity, recordings close to the epicenters, faulting mechanism and duration can causechanges in the characteristics of near-field ground motions.

In near-field ground motions, the directivity effects play their role with variedcharacteristics. Forward rupture directivity effects occur when two conditions are met: therupture front propagates towards the site, and the direction of slip on the fault is aligned withthe site [Paul Somerville, 2005]. The conditions for generating forward rupture directivityeffects are readily met in strike slip faulting, where the rupture propagates horizontally along

strike either unilaterally or bilaterally, and the fault slip direction is oriented horizontally in thedirection along the strike of the fault. However, not all near-fault locations experience forwardrupture directivity effects in a given event. Backward directivity effects, which occur when therupture propagates away from the site, give rise to the opposite effect: long duration motionshaving low amplitudes at long periods. The conditions required for forward directivity are alsomet in dip-slip faulting. The alignment of both the rupture direction and the slip direction updipon the fault plane produces rupture directivity effects at sites located around the surfaceexposure of the fault (or its updip projection if it does not break the surface) [Paul Somerville,2005].

Amplitude: Horizontal accelerations have commonly been used to describe the groundmotions. The peak horizontal acceleration for a given component of motion is simply the largest (absolute) value of horizontal acceleration obtained from the accelerogram of that component.The largest dynamic forces induced in certain types of structures (very stiff) areclosely relatedto the peak horizontal accelerations [Kramer, 1996].


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The Fourier transform of an accelerogram t x is given by,

dt et x X t i

)(21)( (2.1)

Where, t x is the acceleration record and is frequency.

Duration: The duration of strong ground motion can have a strong inuence onearthquake

damage. It is related to the time required for accumulation of strain energy by rupture along thefault. There are different procedures for calculating the duration of ground motion, out of whichwe have considered Trifunac and Brady (1975) method for calculating the duration of groundmotion.

Trifunac and Brady Duration (1975) is based on the time interval between the points at which

5% and 95% of the total energy has been recorded.

Details of the ground motions with magnitude, epicentral distance, PGA, duration andfrequency range are given below from table 2.1 to table 2.4. Further the Ground motions andtheir Fourier Amplitude Spectrums are given from fig. 2.4 to fig. 2.23.


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Table 2.1: Details of near-field - fault normal ground motions

Sl.No

Near-Field - Fault Normal ground motions

EarthquakeDate of

occurrenceStation MW

EpicentralDistance

(Km)

PGA(g)

Duration(sec)

Frequency(Hz)

1 Tabas 16-09-1978 Tabas 7.4 1.2 0.9 18.52 0.012-5.4442 Loma Prieta 18-10-1989 Los Gatos 7.0 3.5 0.718 6.240.024-1.099

3 Loma Prieta 18-10-1989 Lex. Dam 7.0 6.3 0.686 3.27 0.024-0.834

Erzincan 13-03-1992MeteorogicalStation

6.7 2.0 0.432 7.14 0.024-1.489

5 Cape Mendocino 25-04-1992 Petrolia 7.1 8.5 0.638 15.84 0.073-2.6376

Landers 28-06-1992Lucernevalley

7.3 1.1 0.713 13.38 0.015-17.71

7 Northridge 17-01-1994 Rinaldi 6.7 7.5 0.89 7.01 0.049-1.7098 Northridge 17-01-1994 Olive View 6.7 6.4 0.732 5.820.012-3.2849 Kobe 17-01-1995 Kobe 6.9 3.4 1.088 7.5 0.269-2.62510 Kobe 17-01-1995 Takatori 6.9 4.3 0.786 10.69 0.024-0.952

Table 2.2: Details of near-field - fault parallel ground motions

Sl.No

Near-Field - Fault Parallel ground motions

EarthquakeDate of


EpicentralDistance

(Km)

PGA(g)

Duration(sec)

Frequency(Hz)

1 Tabas 16-09-1978 Tabas 7.4 1.2 0.978 17.64 0.012-6.5192 Loma Prieta 18-10-1989 Los Gatos 7.0 3.5 0.458 10.67 0.024-1.1723 Loma Prieta 18-10-1989 Lex. Dam 7.0 6.3 0.37 5.08 0.024-2.0754

E iMeteorogical

6 7 2 0 10 085


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Table 2.3: Details of far-field - transverse ground motions

Sl.No

Far-Field - Transverse ground motions

EarthquakeDate of


EpicentralDistance

(Km)

PGA(g)

Duration(sec)

Frequency(Hz)

1 Tabas 16-09-1978 Sedeh 7.35 177.9 0.027 29.48 0.024-1.1472 Loma Prieta 18-10-1989 HCL 6.93 47.9 0.215 13.62 0.024-1.4643 Loma Prieta 18-10-1989 Sunnyvale 6.93 42.13 0.209 25.29 0.024-1.8064 Erzincan 13-03-1992 Erzincan 6.69 8.97 0.496 7.35 0.024-1.4655 Cape Mendocino 25-04-1992 Petrolia 7.01 53.34 0.178 19.84 0.292-3.6256 Landers 28-06-1992 Anaheim 7.28 146.11 0.0353 25.62 0.012-2.00

7 Northridge 17-01-1994AnacapaIsland 6.69 77.39 0.0367 13.90 2.294-6.933

8 Northridge 17-01-1994 Anaheim 6.69 70.45 0.0659 18.40 0.073-4.9569 Kobe 17-01-1995 99999HIK 6.9 135.63 0.148 11.08 0.50-2.79510 Kobe 17-01-1995 99999FUK 6.9 196.18 0.0422 32.62 0.280-2.783

Table 2.4: Details of far-field - longitudinal ground motions

Sl.No

Far-Field - Longitudinal ground motions

EarthquakeDate of


EpicentralDistance

(Km)

PGA(g)

Duration(sec)

Frequency(Hz)

1 Tabas 16-09-1978 Sedeh 7.35 177.9 0.0262 29.66 0.024-4.7852 Loma Prieta 18-10-1989 HCL 6.93 47.9 0.247 17.40 0.024-1.363 Loma Prieta 18-10-1989 Sunnyvale 6.93 42.13 0.207 21.175 0.024-1.8314 Erzincan 13 03 1992 Erzincan 6.69 8.97 0 515 7.46 0 024 1 806


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2.4 Near-Field ground motions and their Fourier amplitude spectrums

Figure 2.4: Tabas near-field (a) Fault normal ground motion (b) Fault normal Fourier amplitude spectrum (c) Fault parallel ground motion (d) Fault parallel Fourier amplitude spectrum

Tabas is a city in and capital of Tabas County, Yazd Province, IRAN. The city hasexperienced a severe earthquake on September 16th, 1978. Tectonics of east-central Iran as part of the Alpine-Himalayan orogenic belt has been the subject of numerous discussions as the

Tabas - Tabas Station


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Figure 2.5: Loma Prieta - Los Gatos near-field (a) Fault Normal ground motion (b) Fault normal Fourier amplitudespectrum (c) Fault Parallel ground motion (d) Fault parallel Fourier amplitude spectrum

Loma Prieta is a Northern California mountain in the Santa Cruz Mountains, CA, USA. OnOctober 18th, 1989 a right-lateral strike-slip along the San Andreas fault which lasted for about

15 seconds resulted in a severe earthquake. This major earthquake struck the San Francisco BayArea. Fault normal and fault parallel ground motion records of near-field considered for thestudy are produced in fig. 2.5. Los Gatos station which is 3.5 km from epicenter recorded themagnitude of the near-field ground motion as MW 7.0. PGA's of fault normal and fault parallel

Loma Prieta Los Gatos Station


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Figure 2.6: Loma Prieta - Lexington Dam near-field (a) Fault Normal ground motion (b) Fault normal Fourieramplitude spectrum (c) Fault Parallel ground motion (d) Fault parallel Fourier amplitude spectrum

Another near-field record at Lexington Dam station which is at 6.3 km from epicenterrecorded 7.0 MW. Fault normal and fault parallel ground motion records of near-field consideredfor the study are produced in fig. 2.6. PGA's of fault normal and fault parallel are 0.686g and0.37g respectively. Predominant frequency ranges between 0.024-0.83 for fault normal and0.024-2.075 for fault parallel.

Loma Prieta Lexington Dam Station


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Figure 2.7: Erzincan near-field (a) Fault Normal ground motion (b) Fault normal Fourier amplitude spectrum (c)Fault Parallel ground motion (d) Fault parallel Fourier amplitude spectrum

Erzincan is the capital of Erzincan Province in the eastern Anatolian region of Turkey.On March 13th, 1992 a severe earthquake has struck Erzincan. Slip along the North AnatolianFault, which is a major active right-lateral moving strike-slip fault in northern Anatolia whichruns along the transform boundary between the Eurasian Plate and the Anatolian Plate is thereason. The Erzincan basin lies on the intersection of this fault on its northern side. Fault normaland fault parallel records of near-field considered for the study are produced in fig. 2.7. Erzincan

Erzincan - Erzincan Station


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Figure 2.8: Cape Mendocino near-field (a) Fault Normal ground motion (b) Fault normal Fourier amplitude spectrum(c) Fault Parallel ground motion (d) Fault parallel Fourier amplitude spectrum

Cape Mendocino located on the Lost Coast entirely within Humboldt County, California,USA, is the westernmost point on the coast of California. Three earthquakes with epicenters

nearby at Petrolia and offshore west of Cape Mendocino, on 25, 26 April 1992 showed that theCascadia subduction zone is both capable of producing large earthquakes and generatetsunamis. Fault normal and fault parallel records of near-field considered for the study areproduced in fig. 2.8. Petrolia station which is 8.5 km from epicenter recorded the magnitude of

Landers - Petrolia Station


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Figure 2.9: Lander's near-field (a) Fault Normal ground motion (b) Fault normal Fourier amplitude spectrum (c)Fault Parallel ground motion (d) Fault parallel Fourier amplitude spectrum

Landers is a small town in California, USA. On 28 June 1992 five separate fault segmentsin sequence: Johnson Valley, Landers, Homestead Valley, Emerson, and Camp Rock experienced

main shock rupture generating magnitude MW 7.3 earthquake. The Landers quake is alsosometimes referred to as "the Landers sequence." The mechanism by which Landers ruptured iscalled "cascading rupture" whereby the rupture of one fault triggers the rupture of aneighboring fault Fault-normal and fault parallel records of near-field considered for the study

Landers - Petrolia Station


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Figure 2.10: Northridge - Rinaldi near-field (a) Fault Normal ground motion (b) Fault normal Fourier amplitudespectrum (c) Fault Parallel ground motion (d) Fault parallel Fourier amplitude spectrum

Northridge is a community located in the San Fernando Valley region of the city of LosAngeles, California, USA. On 17 January 1994 an earthquake of magnitude MW6.7 has struck thisplace. Despite the area's proximity to the San Andreas Fault, the Northridge earthquake did not occur along this fault, however, on the previously undiscovered Northridge blind thrust fault (also known as Pico thrust fault). The 6.7 MW ground motion recorded at Rinaldi station is 7.5km from epicenter. Fault normal and fault parallel records of near-field considered for the study

Northridge Rinaldi Station


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Figure 2.11: Northridge - Olive View near-field (a) Fault Normal ground motion (b) Fault normal Fourier amplitudespectrum (c) Fault Parallel ground motion (d) Fault parallel Fourier amplitude spectrum

Another near-field record of the 6.7 MW Northridge ground motion recorded at OliveView station is 6.4 km from epicenter. Fault normal and fault parallel records of near-fieldconsidered for the study are produced in fig. 2.11. PGA's of fault normal and fault parallel are0.732g and 0.595g respectively. Predominant frequency ranges between 0.012-3.284 for fault normal and 0.732-3.271 for fault parallel.

Northridge Olive View Station


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Figure 2.12: Kobe near-field (a) Fault Normal ground motion (b) Fault normal Fourier amplitude spectrum (c) Fault Parallel ground motion (d) Fault parallel Fourier amplitude spectrum

Kobe is the 5th largest city in Japan and is the capital city of Hyogo Prefecture on thesouthern side of the mainland of Honshu. On 17 January 1995 an earthquake of magnitude MW6.9 has struck this city. The great Hanshin earthquake (also Kobe earthquake) began north of the island of Awaji, which lies just south of Kobe. It spread toward the southwest along theNojima fault on Awaji and toward the northeast along the Suma and Suwayama faults, whichrun through the center of Kobe. Observations of deformations in these faults suggest that the

Kobe Kobe Station


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Figure 2.13: Kobe - Takatori near-field (a) Fault Normal ground motion (b) Fault normal Fourier amplitudespectrum (c) Fault Parallel ground motion (d) Fault parallel Fourier amplitude spectrum

Another near-field record of the 6.9 MW Kobe ground motion recorded at Takatoristation is 4.3 km from epicenter. Fault normal and fault parallel records of near-field consideredfor the study are produced in fig. 2.13. PGA's of fault normal and fault parallel are 0.786g and0.424g respectively. Predominant frequency ranges between 0.024-0.952 for fault normal and0.024-1.953 for fault parallel.

Kobe Takatori Station


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2.5 Far-Field ground motions and their Fourier amplitude spectrums

Figure 2.14: Tabas-Sedeh far-field (a) Transverse ground motion (b) Transverse Fourier amplitude spectrum (c)Longitudinal ground motion (d) Longitudinal Fourier amplitude spectrum

Tabas event recorded far-field at Sedeh station at an epicentral distance of 177.9 km had

a magnitude of MW 7.35, with transverse and longitudinal PGA's as 0.027g and 0.0262grespectively. Predominant frequency ranges between 0.024-1.147 for transverse and 0.024-4.785 for longitudinal. The amplitude of acceleration varied with high rate between fault normalof near-field & transverse of far-field and between fault parallel of near-field and longitudinal of

Tabas Sedeh Station


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Figure 2.15: Loma Prieta - Hollister City Hall far-field (a) Transverse ground motion (b) Transverse Fourieramplitude spectrum (c) Longitudinal ground motion (d) Longitudinal Fourier amplitude spectrum

Loma Prieta event recorded far-field at Hollister City Hall station at an epicentraldistance of 47.9 km had a magnitude of MW 6.93, with transverse and longitudinal PGA's as0.215g and 0.247g respectively. Predominant frequency ranges between 0.024-1.464 fortransverse and 0.024-1.36 for longitudinal. Transverse and longitudinal records of far-fieldconsidered for the study are produced in fig.2.15.

Loma Prieta Hollister City Hall Station


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Figure 2.16: Loma Prieta - Sunnyvale far-field (a) Transverse ground motion (b) Transverse Fourier amplitudespectrum (c) Longitudinal ground motion (d) Longitudinal Fourier amplitude spectrum

Another Loma Prieta event considered for the study recorded far-field at Sunnyvalestation at an epicentral distance of 42.13 km had a magnitude of MW6.93, with transverse andlongitudinal PGA's as 0.209g and 0.207g respectively. Predominant frequency ranges between0.024-1.806 for transverse and 0.024-1.831 for longitudinal. Transverse and longitudinalrecords of far-field considered for the study are produced in fig. 2.16.

Loma Prieta Sunnyvale Station


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Figure 2.17: Erzincan far-field (a) Transverse ground motion (b) Transverse Fourier amplitude spectrum (c)Longitudinal ground motion (d) Longitudinal Fourier amplitude spectrum

Erzincan event considered for the study recorded far-field at Erzincan station at anepicentral distance of 8.97 km had a magnitude of MW 6.69, with transverse and longitudinalPGA's as 0.178g and 0.154g respectively. Predominant frequency ranges between 0.024-1.465for transverse and 0.024-1.806 for longitudinal. Transverse and longitudinal records of far-fieldconsidered for the study are produced in fig.2.17.

Erzincan - Erzincan Station


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Figure 2.18: Cape Mendocino far-field (a) Transverse ground motion (b) Transverse Fourier amplitude spectrum (c)Longitudinal ground motion (d) Longitudinal Fourier amplitude spectrum

Cape Mendocino event considered for the study recorded far-field at Petrolia station at an epicentral distance of 53.34 km had a magnitude of MW7.01, with transverse and longitudinalPGA's as 0.496g and 0.515g respectively. Predominant frequency ranges between 0.292-3.625for transverse and 0.012-2.722 for longitudinal. Transverse and longitudinal records of far-fieldconsidered for the study are produced in fig. 2.18.

Cape Mendocino - Petrolia Station


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Figure 2.19: Landers far-field (a) Transverse ground motion (b) Transverse Fourier amplitude spectrum (c)Longitudinal ground motion (d) Longitudinal Fourier amplitude spectrum

Landers event considered for the study recorded far-field at Anaheim station at anepicentral distance of 146.11 km had a magnitude of MW7.28, with transverse and longitudinalPGA's as 0.035g and 0.047g respectively. Predominant frequency ranges between 0.012-2.00fortransverse and 0.012-2.197 for longitudinal. Transverse and longitudinal records of far-fieldconsidered for the study are produced in fig. 2.19.

Landers Anaheim Station


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Figure 2.20: Northridge-Anacapa Island far-field (a) Transverse ground motion (b) Transverse Fourier amplitudespectrum (c) Longitudinal ground motion (d) Longitudinal Fourier amplitude spectrum

Northridge event considered for the study recorded far-field at Anacapa Island station at an epicentral distance of 77.39 km had a magnitude of MW6.69, with transverse and longitudinalPGA's as 0.036g and 0.067g respectively. Predominant frequency ranges between 2.294-6.933for transverse and 1.635-6.665 for longitudinal. Transverse and longitudinal records of far-fieldconsidered for the study are produced in fig. 2.20.

Northridge Anacapa Station

h d h


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Figure 2.21: Northridge-Anaheim far-field (a) Transverse ground motion (b) Transverse Fourier amplitudespectrum (c) Longitudinal ground motion (d) Longitudinal Fourier amplitude spectrum

Northridge event considered for the study recorded far-field at Anaheim station at anepicentral distance of 70.45 km had a magnitude of MW6.69, with transverse and longitudinalPGA's as 0.066g and 0.072g respectively. Predominant frequency ranges between 0.073-4.956for transverse and 0.024-4.468 for longitudinal. Transverse and longitudinal records of far-fieldconsidered for the study are produced in fig. 2.21.

Northridge - Anaheim Station

K b 99999HIK S i


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Figure 2.22: Kobe-99999HIK far-field (a) Transverse ground motion (b) Transverse Fourier amplitude spectrum (c)Longitudinal ground motion (d) Longitudinal Fourier amplitude spectrum

Kobe event considered for the study recorded far-field at 99999HIK station at anepicentral distance of 135.63 km had a magnitude of MW 6.9, with transverse and longitudinalPGA's as 0.148g and 0.147g respectively. Predominant frequency ranges between 0.50-2.795 fortransverse and 0.732-3.027 for longitudinal. Transverse and longitudinal records of far-fieldconsidered for the study are produced in fig. 2.22.

Kobe 99999HIK Station

Kobe 99999FUKStation


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Figure 2.23: Kobe-99999FUK far-field (a) Transverse ground motion (b) Transverse Fourier amplitude spectrum (c)Longitudinal ground motion (d) Longitudinal Fourier amplitude spectrum

Kobe event considered for the study recorded far-field at 99999FUK station at anepicentral distance of 196.18 km had a magnitude of MW 6.9, with transverse and longitudinalPGA's as 0.042g and 0.034g respectively. Predominant frequency ranges between 0.280-2.783for transverse and 0.402-2.868 for longitudinal. Transverse and longitudinal records of far-fieldconsidered for the study are produced in fig. 2.23.

Kobe 99999FUKStation

2.6 Numerical Method


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2.6.1 Introduction

Numerical methods for the analysis of structures can be broadly classified in to two. Thefirst one is based on continuum mechanism. Finite Element Method (FEM) [Jr. William Weaver,James M. Gere, 1966] is one such example. However, it cannot perform the analysis up tocollapse because of limitations that exist in representation of cracks and separation distancebetween elements. FEM can answer only one question will the structure fail or not? it cant tellhow the structure collapse

On the other hand, second category of numerical methods is based on discrete element methods, like Extended Discrete Element Method [Williams J.R, Hocking G, and Mustoe G.G.W,1985; A.A. Balkema, Rotterdam, 1985] for nonlinear analysis of structures. This method cantrack the behavior from zero loading to total collapse of structure. However, this method is lessaccurate than FEM in small deformation range. So this can answer only the second questionhow does the structure collapse?

To follow total structural behavior from small deformation range to complete collapse, aunique, efficient and accurate technique is required. Tagel Din Hatem (1988) gave a new

method of analyzing the structural behavior from zero loading, crack initiation & propagation,separation of structural members till the total collapse with reliable accuracy, and withrelatively simple material models. The method is now known as Applied Element Method(AEM) and is widely in usage.

Applied element method is a discrete method in which the elements are connected by

pair of normal and shear springs which are distributed around the element edges is shown infig. 2.24. Stresses and deformations of each and every element are represented by these shearand normal springs. The motion of element is rigid body motion and the internal deformationsof the element are taken by springs only Elements can be connected by any number of springs

2.6.2 Mathematical formulation


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The governing dynamic equation for a structure is given in equation 2.2

g u M t f KuuC u M )( (2.2)

Where [M] is mass matrix; [C] is damping matrix; [K] is nonlinear stiffness matrix; f(t) isincremental applied load vector U and its derivatives are the incremental displacement,velocity and acceleration vectors respectively. The above equation is used in AEM and is solvednumerically using Newmark's beta method.

Figure 2.24: Element components for formulating stiffness matrix [Kimuro Meguro and Hatem 2001]

Figure 2.25: Quarter portion of stiffness matrix

moment of inertia about centroid of the element. The mass matrix is a diagonal matrix. If


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element size is small response of the structure is very near to the continuous/distributed mass

system. If damping is present, response of the structure will get reduced. Damping matrix iscalculated from therst mode asfollows:

n M C 2 (2.4)

Where is damping ratio and n is rst natural frequency of the structure. The general equationfor free vibration without damping is:

0 Kuu M

(2.5)For a non-trivial solution, determinant of the above matrix must be equal to zero and solution of determinant of the matrix gives natural frequencies of the structure.

2.6.3 Element size

Element size in a structure is one important parameter to be considered in any

numerical modeling. Large element size decreases structures displacement and leads toincreasing stiffness and failure load of the structure. For any numerical analysis three important requirements (convergence, stability and accuracy) are necessary.

1. Convergence - As element size decreases, numerical solution should close to theexact/theoretical solution.

2. Stability - The numerical solution should be stable in the presence of numerical roundoff errors.

3. Accuracy - The numerical procedure should provide results that are close to the exact solution.

For the study, the element size of the models is fixed as 1m x 1m after few parametricstudies. With the limitations in the AEM, this element size has been fixed. Limitations in AEM aredescribed in section 2.6.6.

2 6 4 Material modeling

redistributed by applying the redistributed force values in the reverse direction. For concrete


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springs subjected to tension, spring stiffness is assumed as the initial stiffness till it reaches the

crack point. After cracking, stiffness of springs subjected to tension are assumed zero. Forreinforcement, bi-linear stress strain relation is assumed. After yield of reinforcement, steelspring stiffness is assumed as 0.01 of the initial stiffness. For cracking criteria [Tagel-din-Hatem,1998], principal stress based on failure criteria is adopted. The models for concrete, both incompression and tension and the reinforcement bi-linear model are shown in fig. 2.26 (a) & (b).

Figure 2.26: Material models for concrete and steel (a) Tension and compression concrete Maekawa model (b) Bi-

linear stress strain relation model for steel reinforcement (Kimuro Meguro and Hatem 2001)

2.6.5 Boundary conditions

In actual field condition, soil does not have boundary. As, modeling of whole earth is not possible, we have considered a portion of it for our study. For this small portion, appropriateboundary conditions should be applied. Wave generated from source in field can travel infinite

distance, until its strength becomes negligible. To restrict the generated waves from source, aboundary condition should be used where, the waves will be absorbed and radiation of waves isminimized. Bottom of the models (S1 and S2) are modeled as fixed, and sides of the base inmodel S2 is modeled as absorbing boundaries The non reflecting boundaries approximate the

that 2n springs are connecting two elements together. Each spring represent a distance of


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(D/2n). In horizontal and vertical degrees of freedom case, the number of connecting springs

has no effect on the element stiffness as decreasing the number of connecting springs leads toincreasing of area represented by each spring. Finally, the total area becomes the same as that represented by one whole element. Rotation of an element if mainly resisted by shear springstogether with normal springs.

In case of two connecting springs, the numerically obtained rotational stiffness is

smaller than the theoretical value by 25% which is quite large. However, this error reduces toless than 1% if the number of connecting springs is 10 or more [Tagel-din-Hatem, 1998]. Thiseffect is dominant if the element size is small because the relative rotation between adjacent elements becomes small.

2.6.7 Modeling limitations

AEM is a discrete element method and it has got some limitations. Only two models(steel and concrete) and two materials (soil and concrete) are considered. Any other materialcan be used by giving its properties. However, material models are only concrete and steel. Forthe current study, reservoir condition is not considered as water has not been modeled in AEM.Therefore hydrostatic and hydrodynamic pressures are not considered. Also two loads cannot be given simultaneously on a structure. Therefore, when ground motions are given as input, thestructure is subjected to only ground motion, which will not happen in real time. Several forceslike hydrostatic, hydrodynamic, silt load, wave pressure, uplift etc. cannot be givensimultaneously and have to be studied individually. Work is being done to incorporate theselimitations.

2.8 Summary

In this chapter, a concrete gravity dam based on its importance is selected. Later twomodels, concrete gravity dam with foundation and concrete gravity dam with foundation andbase are modeled using applied element method. Material properties considered for modeling

Chapter 3


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p

Linear Earthquake Response of Concrete Gravity Dam

3.1 Introduction

The main focus of this chapter is to study the linear earthquake response of (i) aconcrete gravity dam with foundation (Structure 1 - S1) as one model and (ii) a concrete gravitydam with foundation and base (Structure 2 - S2) as another model. The above two models aresubjected to fault normal and fault parallel components of near-field ground motions,transverse and longitudinal components of far-field ground motions. Comparison among thesecomponents are drawn for understanding the linear behavior of concrete gravity dam.

3.2 Eigen value analysis

Dynamic characteristics of any structure could be evaluated by its natural frequenciesand vibration mode shapes. This could be achieved through eigen value analysis. The analysisdeals with undamped free vibration of the structure and does not represent response due to any

loading, but yields the natural frequencies (eigen values) and corresponding vibration modeshapes (eigen vectors) of the structure when there is no dissipation of energy due to damping.The amplitude of the free vibration will depend on the initial conditions and in the absence of damping, the vibration will continue without any decay. The solution of equation (3.1) for anystructure give the eigenvalues and their corresponding eigen vectors.

0 Kuu M (3.1)

in which [M] and [K] are the global mass matrix and stiffness matrix of the dam and are obtainedby assembling the mass matrices and stiffness matrices of relevant elements of dam model and

of the structure matches with the freqeuncy of the ground motion, the phenomenon of ll f l h h h d d d


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resonance will occur causing failure to the structure. In the next section this study is discussed.

Mode 1F 2 82 H


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Frequency: 2.82 HzTime Period: 0.355 Sec

Mode 2Frequency: 6.97 HzTime Period: 0.143 Sec



Mode 5Frequency: 26.05 Hz

Mode 6Frequency: 32 62 Hz


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Frequency: 32.62 HzTime Period: 0.030 Sec




Mode 10Frequency: 55.41 HzTime Period: 0 018 Sec

Table 3.1: Eigen values of first ten mode shapes of S1


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Modes Frequency (Hz) Time Period (sec)

Mode 1 2.98 0.335Mode 2 7.78 0.128Mode 3 15.26 0.065Mode 4 23.54 0.042Mode 5 32.03 0.031


Table 3.2: Eigen values of first ten mode shapes of S2

Modes Frequency (Hz) Time Period (sec)Mode 1 2.82 0.355Mode 2 6.97 0.143


Mode 8 44.13 0.022Mode 9 49.76 0.020Mode 10 55.41 0.018

3.3 Near field earthquakes


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3.3.1 Response of S1 subjected to fault normal component

The first ten natural frequencies and mode shapes of S1 are given in table 3.1 andrepresented in fig. 3.1. PGA's, predominant frequency ranges and displacements of S1 at different cross sections for 5 near-field fault normal ground motions are given in table 3.3.Arbitrary element numbers (535, 2285, 3496, and 4130) are considered at different crosssections to study the var

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