Study of Energy Dissipation Capacity of Rc Bridge

STUDY OF ENERGY DISSIPATION CAPACITY OF

RC BRIDGE COLUMNS UNDER SEISMIC DEMAND

SYED MOHAMMAD ALI

Advisor: Dr. Akhtar Naeem Khan, Professor of Civil Engineering

DISSERTATION Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Civil Engineering

Department of Civil Engineering, N-W.F.P. University of Engineering and Technology, Peshawar, Pakistan, 2009

All rights reserved. No part of this work may be translated, copied, reproduced, stored, in a retrieval system, or transmitted, in any form or by means, electronic, mechanical, photocopying, recording, or otherwise, without the written permission of the copyright owner.

i ABSTRACT

Field studies were carried out to investigate various parameters of bridges found in northern part of Pakistan. After the large Kashmir earthquake of Mw7.6 in 2005, detailed field investigations to study the seismic performance of bridges was also undertaken. A mathematical function to define the functionality of bridges was developed which is helpful for quantifying the seismic resilience of bridges. Criterion for minimum required functionality for different bridges and limit states were defined for extremely large rare earthquake and for moderate occasional earthquakes.

From the field data, typical parameters of reinforced concrete bridges were established. A series of experimental studies were undertaken in the laboratory on four scaled models of a typical bridge that consists of pier having single column. The pier column was of low strength concrete with solid circular cross section. The objective of the study was to experimentally determine the energy dissipation capacity of low strength concrete piers. Two types of tests were done on the four bridge piers: quasi-static cyclic tests and free vibration tests before, during and after the quasi-static tests.

From the experimental results on four scaled low strength bridge piers damping was seen to decrease with increase in damage, natural period of piers doubled near failure, energy degradation was seen to be more in low strength piers. Energy based strength degradation and pinching is predominant in low strength concrete piers along with large permanent deformations. Response modification (R) factors based on natural period of bridge are found to better represent the energy dissipation and are accordingly proposed. The values of R-factor calculated for low strength concrete piers are lower than AASHTO LRFD 2007 thus more conservative. The fragility curves plotted for the bridge columns indicate that for peak ground accelerations (PGA) of seismic Zone 3 and above of the seismic hazard map of Pakistan (for 475-years return period) pushes the bridge in to damage state that is allowed for large earthquakes only (with return period of 2,500 years).

Mathematical function for the quantification of seismic resilience of bridges is proposed for the first time. It is demonstrated that using the general guidelines of AASHTO LRFD 2007 quantification of seismic resilience is possible.

Dedicated to my parents, wife and children for their support and encouragement.

iii ACKNOWLEDGEMENTS

I thank Almighty Allah for giving me the strength and courage to successfully complete this challenging research.

This study was materialized only because of the sincere guidance of my advisor Prof. Dr. Akhtar Naeem Khan who is a very kind person. He has been a consistent support to help in times when I needed it. Because of his untiring hard work and wonderful teaching, I was able to do things which I believe would have not been done otherwise.

I am extremely grateful and obliged to my foreign thesis evaluator Prof. Shamim A. Sheikh of the University of Toronto for his keen interest and guidance. Prof. Sheikh has given me the great privilege in visiting NWFP UET Peshawar in Jan 2008 during the lab testing of my research. I believe that he made history by visiting UET Peshawar to see my research. I am also thankful to Prof. Sheikh for his time and visit to State University of New York at Buffalo in Dec 2008 to see the results of my research and his guidance in the outline of my dissertation. I am especially thankful to him for his encouragement which gave me huge confidence.

I am thankful to Prof. Zia Razzaq of Old Dominion University my foreign thesis evaluator for his kind guidance and especially hosting me to stay for a week in Norfolk, Virginia with him in March 2006 at the stage of preparation of proposal for this study. I especially thank him for taking me to the cemetery where the famous Prof. Hardy Cross is buried in Smithfield, Virginia.

I am thankful to Prof. Andrei M. Reinhorn for his marvelous guidance during my training at UB (SUNY) New York. His wonderful teaching in experimental testing, control systems, guidance in writing a paper related to seismic resilience of bridges and honoring me to be a co-author in this paper are appreciated with sincere thanks.

I thank Prof. George C. Lee of UB (SUNY) for his teaching in class of Bridge Engineering in Spring 2009. His consistent support since 2006 has made possible many things materialize including a MOU that our university signed with MCEER.

iv I am thankful to Prof. Anil K. Chopra of UC Berkeley for his wonderful gift of his famous text book of Earthquake Engineering and his guidance when I visited him in Dec. 2007 in Berkeley.

I am also grateful to Prof. V.V. Bertero of UC Berkeley for giving me his time when I visited his office in Dec. 2007 at Richmond Field Station in Berkeley, California. In this meeting he explained to me the history and background of Response Modification Factor and encouraged to work in the field of earthquake engineering for my country for which I am obliged.

I also thank Prof. G. M. Calvi for providing me the opportunity to attend a course in Pavia, Italy and for accepting to be my Co-Supervisor.

I pay lot of thanks to Prof. Kawashima for his wonderful course in Bridge Engineering in which he exposed me to bridges and seismic issues. His encouragement for working on Indigenous Bridge Design Code for Pakistan is highly appreciated.

I am thankful to Prof. Qaiser Ali, Prof. Zahid Saddiqque, Dr. Tabbsum Zahoor and Prof. Irfan Ullah for their sincere support and kind suggestions as members of my doctoral committee.

I thank Col. (r) Iqbal Haq of MIHA, Islamabad, Prof. Andre Filiatrault, Prof. M. Brneu, Mark Pitman and other faculty and staff of SUNY Buffalo for their hospitality. I also thank Mr. Mian M Ali of Khybers for his kind support to provide data related to bridges.

I am thankful to my uncle Dr. Noor M. Shah, his wife Dr. Tasneem Shah and their children for being our host during our stay at Buffalo. Their generous support and encouragement is appreciated by all of us.

I am grateful to my fantastic colleagues Adeel Arshad, Pervaiz Khan and Yasir Manzoor for their untiring support during the most difficult times and challenges of my research work. They did miracles in terms of experimental work as the testing was demanding. Without the sincere help of my dear colleagues, this research would not have been possible.

v I am thankful to Mr. Shaukat Rasool Pandit and his wife for their unforgettable hospitality during our field visits after the 2005 earthquake. He hosted many of my collogues and foreign guest researchers who visited and made their home a base-camp.

I thank all those for their support, whose names are not mentioned here, especially to the staff of Civil Engineering Department.

I also thank my wife for her patience throughout this study and my parents for their prayers.

vi TABLE OF CONTENTS

ABSTRACT ...... ii ACKNOWLEDGEMENTS ...... iv LIST OF ABBREVIATIONS ...... xii LIST OF SYMBOLS ...... xiv LIST OF FIGURES ...... xvi LIST OF TABLES ...... xxiii

CHAPTER 1 INTRODUCTION ...... 1 1.1 Background ...... 1 1.2 Problem Statement and Research Objectives ...... 3 1.3 Assumptions and Limitations ...... 4 1.4 Outcome of Present Study ...... 5 1.5 Dissertation Organization ...... 6

CHAPTER 2 LITERATURE REVIEW ...... 8 2.1 Introduction ...... 8 2.2 Field Survey and Seismic Resilience ...... 8 2.2.1 History of Seismic Design and Specifications ...... 9 2.2.2 Bridge Engineering and Seismic Hazard in Pakistan ...... 11 2.2.3 Seismic Resilience and Functionality ...... 13 2.3 Seismic Testing Methods ...... 14 2.4 Experimental Testing of Bridges ...... 16 2.5 Numerical Modeling ...... 18 FIGURES ...... 23

CHAPTER 3 . FIELD SURVEY AND DATA COLLECTION ...... 24 3.1 Introduction ...... 24 3.2 Field Survey ...... 24 3.2.1 Survey Route ...... 24 3.2.2 Field Data Collection ...... 25 3.2.3 Data Collection from Design Documents ...... 26 3.2.4 Summary of Parameters of Typical Bridges ...... 27 3.3 Earthquake of October 8, 2005 ...... 27 3.3.1 History of Seismicity ...... 28 3.3.2 History of Bridges ...... 28 3.3.3 Acceleration-Time History Record ...... 29 3.3.4 Defining Limit States ...... 29 3.3.5 Classification of Bridges ...... 29 3.3.6 Damage in Context of Material of Construction...... 30 3.3.7 Details of Damages Observed ...... 31 3.3.7.1 Unseating / Dropdown ...... 31 3.3.7.2 Damage to Abutments and Pounding in Bridges ...... 31 3.3.7.3 Damages to Suspension Bridges ...... 33 3.3.7.4 Access to Bridge and other Failures ...... 34

vii 3.4 Quantifying the Functionality ...... 35 3.4.1 Mathematical Formulation ...... 35 3.4.2 Example: Calculation of Functionality ...... 37 3.4.3 Functionality of 14 Bridges after Earthquake of 2005 ...... 38 3.4.4 History of Bridge Engineering in Pakistan ...... 39 3.5 Recording of Earthquake Time Histories ...... 40 3.6 Summary and Conclusions ...... 41 FIGURES ...... 43 TABLES ...... 58

CHAPTER 4 MODELING AND EXPERIMENTAL WORK ...... 67 4.1 Introduction ...... 67 4.2 Study of Lab Equipment ...... 67 4.2.1 Quasi-Static Cyclic Testing ...... 68 4.2.1.1 Testing Methodology ...... 69 4.2.1.2 Fabrication of Trial Column ...... 69 4.2.1.3 Similitude Requirements ...... 69 4.2.1.4 Boundary Conditions ...... 70 4.2.1.5 Equipment Setup ...... 70 4.2.1.6 Calibration of Equipment ...... 70 4.2.1.7 Test Protocol ...... 71 4.2.1.8 Conclusion on Limitations ...... 73 4.2.2 Dynamic Testing on Shake Table ...... 74 4.2.2.1 Testing Methodology ...... 74 4.2.2.2 Fabrication of Trial Column ...... 74 4.2.2.3 Similitude Requirements ...... 74 4.2.2.4 Test Protocol ...... 75 4.2.2.5 Conclusions on Limitation ...... 75 4.2.3 Specialized Training at SEESL, UB ...... 76 4.3 Formulation of Testing Methodology ...... 76 4.4 Similitude Analysis ...... 77 4.4.1 Scale Factor Related to Geometry ...... 77 4.4.1.1 Scale Factor for Length ...... 77 4.4.1.2 Scale Factor for Area ...... 78 4.4.1.3 Scale Factor for Moment of Inertia ...... 79 4.4.1.4 Scale Factor for Linear Displacements ...... 79 4.4.1.5 Scale Factor for Angular Displacements ...... 79 4.4.2 Scale Factors Related to Material Properties ...... 80 4.4.2.1 Scale Factor for Modulus of Elasticity ...... 80 4.4.2.2 Scale Factor for Stress ...... 81 4.4.2.3 Scale Factor for Specific Weight (column only) ...... 81 4.4.2.4 Scale Factor for Poisson‟s Ratio ...... 82 4.4.2.5 Scale Factor for Strain ...... 82 4.4.3 Scale Factors Related to Loading ...... 82 4.4.3.1 Scale Factor for Concentrated Load ...... 83 4.4.3.2 Scale Factor for Shear Force ...... 83

viii 4.4.3.3 Scale Factor for Moment ...... 83 4.4.4 Scale Factors Related to Dynamic Characteristics ...... 83 4.4.4.1 Scale Factor for Mass (lumped on column top) ...... 83 4.4.4.2 Scale Factor for Acceleration ...... 84 4.4.4.3 Scale Factor for Natural Period ...... 85 4.4.4.4 Scale Factor for Damping Ratio ...... 85 4.4.5 Scale Factor for Energy Dissipated ...... 86 4.4.6 Summary of Discussions...... 86 4.5 Model Geometry ...... 87 4.6 Model Mass ...... 87 4.7 Model Materials ...... 87 4.7.1 Concrete ...... 88 4.7.1.1 Prototype Concrete ...... 88 4.7.1.2 Model Concrete and Fabrication of Models ...... 90 4.7.2 Reinforcing Steel ...... 93 4.7.2.1 Prototype Steel ...... 93 4.7.2.2 Model Steel ...... 94 4.8 Summary of Parameters for Prototype and Model ...... 94 4.9 Experimental Setup ...... 94 4.9.1 Customization of Testing Rig ...... 94 4.9.2 Design of Anchoring System ...... 95 4.9.3 Load Cell ...... 96 4.9.4 Displacement Transducers ...... 96 4.9.5 Force Balanced Accelerometers ...... 96 4.9.6 Data Acquisition Systems ...... 96 4.9.7 Eccentric Mass Vibrator ...... 97 4.10 Test Protocol ...... 97 4.10.1 Quasi-Static Cyclic Tests ...... 97 4.10.2 Free Vibration Testing ...... 98 4.10.3 Forced Vibration Testing ...... 99 FIGURES ...... 100 TABLES ...... 120

CHAPTER 5 EXPERIMENTAL RESULTS ...... 128 5.1 Introduction ...... 128 5.2 Identification of Dynamic Characteristics Before Cyclic Testing ...... 128 5.2.1 Ambient (Free) Vibration Testing ...... 128 5.2.1.1 Discussion ...... 130 5.2.2 Forced Vibration Testing ...... 132 5.3 Quasi-Static Cyclic Testing ...... 133 5.3.1 First Column QSCT-2-003 (2,421 psi) ...... 133 5.3.1.1 Cyclic Testing ...... 133 5.3.1.2 Observations during Testing ...... 133 5.3.1.3 Energy Dissipated ...... 135 5.3.1.4 Stiffness Degradation ...... 136

ix 5.3.1.5 Identification of Dynamic Characteristics during and after Cyclic Testing ...... 137 5.3.2 Second Column QSCT-3-004 (2,307 psi) ...... 137 5.3.2.1 Cyclic Testing ...... 137 5.3.2.2 Observations during Testing ...... 137 5.3.2.3 Energy Dissipated ...... 138 5.3.2.4 Stiffness Degradation ...... 139 5.3.2.5 Identification of Dynamic Characteristics during and after Cyclic Testing ...... 139 5.3.3 Third Column QSCT-4-005 (1,843 psi)...... 140 5.3.3.1 Cyclic Testing ...... 140 5.3.3.2 Observations during Testing ...... 140 5.3.3.3 Energy Dissipated ...... 141 5.3.3.4 Stiffness Degradation ...... 141 5.3.3.5 Identification of Dynamic Characteristics during and after Cyclic Testing ...... 142 5.3.4 Fourth Column QSCT-5-006 (1,781 psi) ...... 143 5.3.4.1 Cyclic Testing ...... 143 5.3.4.2 Observations during Testing ...... 143 5.3.4.3 Energy Dissipated ...... 143 5.3.4.4 Stiffness Degradation ...... 144 5.3.4.5 Identification of Dynamic Characteristics during and after Cyclic Testing ...... 144 5.4 Summary and Conclusions ...... 145 5.4.1 Energy Dissipation ...... 145 5.4.2 Stiffness Degradation ...... 146 5.4.3 Natural Period ...... 147 5.4.4 Damping Ratio ...... 147 FIGURES ...... 148 TABLES ...... 182

CHAPTER 6 NUMERICAL STUDIES ...... 192 6.1 Introduction ...... 192 6.2 Selection of Software for Nonlinear Numerical Modeling ...... 192 6.3 IDARC2D 7.0 Software ...... 193 6.4 Numerical Model and Its Calibration ...... 194 6.4.1 Defining Numerical Model ...... 194 6.4.2 Calibration of Numerical Model ...... 198 6.4.3 Conclusions ...... 199 6.5 Seismic Design of Highway Bridges MCEER/ATC-49 ...... 200 6.5.1 Seismic Performance Objectives ...... 200 6.5.2 Design Earthquakes ...... 202 6.5.3 Acceleration Time Histories ...... 202 6.6 Inelastic Nonlinear Time History Analysis ...... 203 6.6.1 Prototype Bridge Columns ...... 203 6.6.2 Calibration of Damage Indices ...... 204

x 6.6.3 Defining Limiting Values ...... 205 6.6.4 Response Modification Factors...... 205 6.6.5 Maximum Deflections and Residual Deflections ...... 208 6.6.6 Fragility Curves ...... 209 6.7 Summary and Conclusions ...... 210 FIGURES ...... 212 TABLES ...... 223

CHAPTER 7 SUMMARY AND CONCLUSIONS ...... 234 7.1 Summary ...... 234 7.2 Conclusions ...... 236 7.2.1 Conclusions Regarding Functionality of Bridges ...... 236 7.2.2 Conclusions Regarding Experimental Testing...... 237 7.2.3 Conclusions Regarding Hysteretic Energy Dissipation ...... 237 7.2.4 Conclusions Regarding Design Parameters ...... 237 7.2.5 Conclusions Regarding Fragility of Bridges...... 238 7.3 Future Studies ...... 239

REFERENCES ...... 240

VITA...... 249

xi LIST OF ABBREVIATIONS

ASTM America Society of Testing and Materials

ATC Applied Technology Council cm Centimeter.

DI Damage Index.

EMV Eccentric Mass Vibrator. ft feet. g Acceleration due to gravity. gm Grams. in Inch.

ITHA Inelastic Time History Analysis kg Kilogram. kips Kilo pounds. ksi Kilo pounds per square inch. lbs Pounds. m Meter.

MCEER Multidisciplinary Center for Earthquake Engineering Research.

NCEER National Center of Earthquake Engineering Research

MOR Modulus of rupture. mm Millimeter.

MPa Mega Pascal. psi Pounds per square inch.

RC Reinforced Concrete.

SSI Soil Structure Interaction.

xii tf Metric ton force.

TRB Transportation Research Board.

UET University of Engineering & Technology.

xiii LIST OF SYMBOLS

Ap A factor related to area in prototype.

Am A factor related to area in model.

 A Scale factor related to area.

D Scale factor related to linear displacements.

E Scale factor related to modulus of elasticity.

 Scale factor related to specific weight.

I Scale factor related to moment of inertia.

l Scale factor related to linear dimensions.

 Scale factor related to rotational displacements. kcr It is the stiffness of cracked column. ke It is the equivalent stiffness. kuc It is the uncracked stiffness. lm is the length related parameter in model.

l p is the length related parameter in prototype.

 is arithmetic mean.

Pc It is the load at cracking.

Pmax Is the maximum restoring force on hysteresis loop.

Pmin Is the minimum restoring force on the hysteresis loop.

Py0 It is the load at initial yield.

rp is the radial distance in a prototype.

xiv rm is the radial distance in a model.

 is standard deviation. s is the distance traversed in an arc by a prototype. p s is the distance traversed in an arc by a model. m uc It is the displacement at cracking. umax It is the maximum displacements on hysteresis loop. umin It is the minimum displacements on hysteresis loop.

uy0 It is the displacement at initial yield.

xv LIST OF FIGURES

Figure 2.1: Measure of Seismic Resilience (Bruneau, et al., 2003)...... 23 Figure 3.1: Form for field survey of bridges, page 1...... 43 Figure 3.2: Form for field survey of bridges, page 2...... 44 Figure 3.3: Form for field survey of bridges, page 3...... 45 Figure 3.4: Form for field survey of bridges, page 4...... 46 Figure 3.5: Form for field survey of bridges, page 5...... 47 Figure 3.6: Survey area, epicenter & fault of 2005 earthquake & bridges near fault...... 48 Figure 3.7: (a) Drop-down of girder bridge due to failure of stone masonry abutments (b) Unseating of the entire 3-span continuous girder bridge which is 240 m on footwall side of thrust fault...... 48 Figure 3.8: (a) Shear failure of abutment at cold joint of an RC bridge (b) Damage to stone masonry abutment of a truss bridge located 2 km on footwall...... 49 Figure 3.9: (a) Collapse of a suspension bridge over River Neelum due to landslides (b) Slippage of side-sway cable anchor block & failure of approach road to bridge...... 49 Figure 3.10: (a) Severe damage to the stone masonry base of tower in a suspension bridge (b) Collapse of stone masonry retaining wall that resulted in failure of approach road. .. 50 Figure 3.11: Functionality of bridges in generalized form showing different possible scenarios...... 50

Figure 3.12: Functionality of 4 bridges after the Mw7.6 earthquake of 2005...... 51 Figure 3.13: New Seismic Hazard Map for Pakistan based on PGA for 475 yrs return period...... 51 Figure 3.14: Acceleration Time history of vertical component of aftershock recorded at Muzaffarabad, Oct. 28, 2005...... 52 Figure 3.15: Acceleration Time history of North-South component of aftershock recorded at Muzaffarabad, Oct. 28, 2005...... 52 Figure 3.16: Acceleration Time history of East-West component of aftershock recorded at Muzaffarabad, Oct. 28, 2005...... 53 Figure 3.17: Acceleration Time history of Vertical component of aftershock recorded at Abbottabad, Oct. 28, 2005...... 53

xvi Figure 3.18: Acceleration Time history of North-South component of aftershock recorded at Abbottabad, Oct. 28, 2005...... 54 Figure 3.19: Acceleration Time history of East-West component of aftershock recorded at Abbottabad, Oct. 28, 2005...... 54 Figure 3.20: Velocity Time history of vertical component of aftershock recorded at Abbottabad, Oct. 28, 2005...... 55 Figure 3.21: Velocity Time history of North-South component of aftershock recorded at Abbottabad, Oct. 28, 2005...... 55 Figure 3.22: Velocity Time history of East-West component of aftershock recorded at Abbottabad, Oct. 28, 2005...... 56 Figure 3.23: Acceleration Response Spectra for 5% damping due to North-South component of aftershock recorded at Muzaffarabad, Oct. 28, 2005...... 56 Figure 3.24: Acceleration Response Spectra for 5% damping due to East-West component of aftershock recorded at Abbottabad, Oct. 28, 2005...... 57 Figure 4.1: Structural testing frame with adjustable girders and hydraulic jacks...... 100 Figure 4.2: A trial RC column of 1:6 scale to study the equipment and test protocol. ... 100 Figure 4.3: Vertical hydraulic jack with bi-directional rollers on the column top...... 101 Figure 4.4: Two horizontal jacks used for cyclic loading, each jack performed half cycle of lateral loading...... 101 Figure 4.5: Calibration of load cell of hydraulic jack with the help reference load cell. 102 Figure 4.6: Calibration of displacement transducers with the reference transducers. .... 102 Figure 4.7: Testing protocol for cyclic testing of RC column...... 103 Figure 4.8: Hysteresis cycle at 3% drift shows stiffening at peak displacement...... 103 Figure 4.9: Trial RC column of scale 1:10 for dynamic testing on shake table...... 104 Figure 4.10: Accumulated damage to trial RC column in shake table testing...... 104 Figure 4.11: Acceleration time history response of top mass of RC column during 100% run on the shake table...... 105 Figure 4.12: Drawing of the 1:4 model column for quasi-static cyclic testing...... 106 Figure 4.13: ASTM C-136 sieve analysis curve for fine aggregates...... 107 Figure 4.14: ASTM C-136 sieve analysis of coarse aggregates for prototype concrete. 107 Figure 4.15: Modular RC slabs each 4 ft x 4 ft to form the dead mass...... 108

xvii Figure 4.16: An 8 ft x 8 ft RC slab to provide support to modular mass and contributes itself as test mass...... 108 Figure 4.17: Lifting hooks for RC slab flushed inside the slab...... 109 Figure 4.18: RC column base ready for fabrication...... 109 Figure 4.19: RC column rebar and spiral reinforcement ready for concrete pour...... 110 Figure 4.20: ASTM C-136 sieve analysis curve for coarse aggregates used in model concrete...... 110 Figure 4.21: Pedestal on column top used to support the dead mass...... 111 Figure 4.22: Model column in final form with dead mass loaded...... 111 Figure 4.23: Model column rebar and confinement hoops with strain gage installed on rebar...... 112 Figure 4.24: Typical stress-strain curve of concrete...... 112 Figure 4.25: Hydraulic actuators in its original form with fix base suitable for monotonic testing for pushing only...... 113 Figure 4.26: Additional hardware added to make the monotonic testing actuator suitable for cyclic testing...... 113 Figure 4.27: Swivel at frontend of actuator with interfacing plate...... 114 Figure 4.28: Verification test for pulling capacity of hydraulic actuator testing rig...... 115 Figure 4.29: Verification test for pushing capacity of hydraulic actuator testing rig. .... 115 Figure 4.30: Anchor bolts for attaching the base of the column with strong floor...... 116 Figure 4.31: Anchor bolts for anchoring the slab on pedestal column top...... 116 Figure 4.32: Hyper sensitive accelerometer on column top for recording the dynamic response of column...... 117 Figure 4.33: Data acquisition system used for quasi-static testing...... 117 Figure 4.34: Eccentric mass vibrator used for forced vibration testing...... 118 Figure 4.35: Eccentric mass vibrator, accelerometer and data acquisition installed on column top for response measurement...... 118 Figure 4.36: Test protocol for cyclic testing of RC columns...... 119 Figure 4.37: Eccentricity of EMV used in force vibration testing of column...... 119 Figure 5.1: Free vibration response of QSCT-2-003 for identification of dynamic characteristics before cyclic testing in N-S direction...... 148

xviii Figure 5.2: Change in natural period with change in mass for column QSCT-3-004. ... 148 Figure 5.3: Change in damping with change in mass for column QSCT-3-004...... 149 Figure 5.4: Change in natural period with change in mass for column QSCT-4-005. ... 149 Figure 5.5: Change in damping with change in mass for column QSCT-4-005...... 150 Figure 5.6: Change in natural period with change in mass for column QSCT-5-006. ... 150 Figure 5.7: Change in damping with change in mass for column QSCT-5-006...... 151 Figure 5.8: Forced vibration test with EMV installed on column QSCT-2-003...... 151 Figure 5.9: Response time history from forced vibration test of QSCT-2-003 for N-S direction...... 152 Figure 5.10: Cracks started to appear at 1% drift on north side face in QSCT-2-003. ... 152 Figure 5.11: Back bone curve for column QSCT-2-003...... 153 Figure 5.12: Condition of column at 1.5% drift for QSCT-2-003...... 153 Figure 5.13: Condition of column at 2.5% drift for QSCT-2-003...... 154 Figure 5.14: Condition of column at 3.0% drift for QSCT-2-003...... 154 Figure 5.15: Condition of column at 4.0% drift for QSCT-2-003...... 154 Figure 5.16: Hysteresis curves for column QSCT-2-003...... 155 Figure 5.17: Energy dissipated per cycle for column QSCT-2-003...... 156 Figure 5.18: Cumulative energy dissipated for column QSCT-2-003...... 156 Figure 5.19: Equivalent stiffness degradation for column QSCT-2-003...... 157 Figure 5.20: Equivalent damping calculated from hysteresis of column QSCT-2-003. . 157 Figure 5.21: Damage at 1% drift of column QSCT-3-004...... 158 Figure 5.22: Backbone curve from hysteresis data of column QSCT-3-004...... 158 Figure 5.23: Damage of column at 2.0% drift for QSCT-3-004...... 159 Figure 5.24: Damage of column at 3.0% drift for QSCT-3-004...... 159 Figure 5.25: Damage of column at 4.0% drift for QSCT-3-004...... 160 Figure 5.26: Hysteresis curves for column QSCT-3-004...... 161 Figure 5.27: Energy dissipated per cycle for column QSCT-3-004...... 162 Figure 5.28: Cumulative energy dissipated for column QSCT-3-004...... 162 Figure 5.29: Equivalent stiffness degradation for column QSCT-3-004...... 163 Figure 5.30: Equivalent damping calculated from hysteresis of column QSCT-3-004. . 163 Figure 5.31: Change in natural period following drift levels for column QSCT-3-004. 164

xix Figure 5.32: Change in damping following drift levels for column QSCT-3-004...... 164 Figure 5.33: Damage of column at 2% for QSCT-3-004...... 165 Figure 5.34: Backbone curve from hysteresis data of column QSCT-4-005...... 165 Figure 5.35: Damage of column at 3% for QSCT-3-004...... 166 Figure 5.36: Damage of column at 4% for QSCT-3-004...... 166 Figure 5.37: Hysteresis curves for column QSCT-4-005...... 167 Figure 5.38: Energy dissipated per cycle for column QSCT-4-005...... 168 Figure 5.39: Cumulative energy dissipated for column QSCT-4-005...... 168 Figure 5.40: Equivalent stiffness degradation for column QSCT-4-005...... 169 Figure 5.41: Equivalent damping calculated from hysteresis of column QSCT-4-005. . 169 Figure 5.42: Change in natural period following drift levels for column QSCT-4-005. 170 Figure 5.43: Change in damping ratio following drift levels for column QSCT-4-005. 170 Figure 5.44: Backbone curve from hysteresis data of column QSCT-5-006...... 171 Figure 5.45: Damage of column at 1% for QSCT-5-006...... 171 Figure 5.46: Damage of column at 2% for QSCT-5-006...... 172 Figure 5.47: Damage of column at 3% for QSCT-5-006...... 172 Figure 5.48: Damage of column at 4% for QSCT-5-006...... 173 Figure 5.49: Hysteresis curves for column QSCT-5-006...... 174 Figure 5.50: Energy dissipated per cycle for column QSCT-5-006...... 175 Figure 5.51: Cumulative energy dissipated for column QSCT-5-006...... 175 Figure 5.52: Equivalent stiffness degradation for column QSCT-5-006...... 176 Figure 5.53: Equivalent damping calculated from hysteresis of column QSCT-5-006. . 176 Figure 5.54: Change in natural period following drift levels for column QSCT-5-006. 177 Figure 5.55: Change in damping ratio following drift levels for column QSCT-5-006. 177 Figure 5.56: Normalized curve for energy dissipated per cycle for the four columns. .. 178 Figure 5.57: Normalized curve for cumulative energy dissipated for all the columns. .. 178 Figure 5.58: Normalized curve for change in equivalent stiffness for all the columns. . 179 Figure 5.59: Normalized curve for change in natural period in N-S direction for last three columns...... 179 Figure 5.60: Normalized curve for change in natural period in E-W direction for last three columns...... 180

xx Figure 5.61: Normalized curve for change in damping ratio in N-S direction for last three columns...... 180 Figure 5.62: Normalized curve for change in damping ratio in E-W direction for last three columns...... 181 Figure 6.1: Parameters for unconfined concrete including factor ZF for IDARC...... 212 Figure 6.2: Typical range of values for hysteresis parameters...... 212 Figure 6.3: History of displacement control for IDARC quasi-static analysis...... 213 Figure 6.4: Comparison of experimental and numerical results IDARC for hysteresis (a) 1% drift 1st cycle (b) 2% drift 2nd cycle...... 213 Figure 6.5: Comparison of experimental and numerical results IDARC for hysteresis (a) 3% drift 2nd cycle (b) 4% drift 1st cycle...... 214 Figure 6.6: Damage index history in a calibrated numerical model under quasi-static cyclic test for column QSCT-3-004...... 214 Figure 6.7: Response modification factors for damage level “none”...... 215 Figure 6.8: Response modification factors for damage level “minimal”...... 215 Figure 6.9: Response modification factors for damage level “significant”...... 216 Figure 6.10: Proposed R-factors for very important and ordinary bridges for Expected Earthquake (EE)...... 216 Figure 6.11: Proposed R-factors for very important and ordinary bridges for Maximum Credible Earthquake (MCE)...... 217 Figure 6.12: Residual deflections for damage level “none”...... 217 Figure 6.13: Maximum deflections for damage level “none”...... 218 Figure 6.14: Residual deflections for damage level “minimal”...... 218 Figure 6.15: Maximum deflections for damage level “minimal”...... 219 Figure 6.16: Residual deflections for damage level “significant”...... 219 Figure 6.17: Maximum deflections for damage level “significant”...... 220 Figure 6.18: Fragility curves for CAT-1 and CAT-2 concrete strengths for damage level “none”...... 220 Figure 6.19: Fragility curves for CAT-1 and CAT-2 concrete strengths for damage level “minimal”...... 221

xxi Figure 6.20: Fragility curves for CAT-1 and CAT-2 concrete strengths for damage level “significant”...... 221 Figure 6.21: Fragility curves for two concrete strengths for all the three damage levels as per MCEER/ATC-49...... 222

xxii LIST OF TABLES

Table 3.1: Routes, number of bridges surveyed and population served ...... 58 Table 3.2: Route and multi-span RC bridges of survey area ...... 58 Table 3.3: Details of multi-span RC bridges of survey area ...... 59 Table 3.4: Multi-span RC bridges, design year and number of traffic lanes ...... 60 Table 3.5: Details of multi-span RC bridges taken from design documents ...... 61 Table 3.6: Average parameters of concrete bridges from field and documentation ...... 62 Table 3.7: Limit States related to structural damage ...... 63 Table 3.8: Name of the bridges that suffered damage and population they served ...... 63 Table 3.9: Limit State of bridges for classification based on the type of superstructure .. 63 Table 3.10: Limit State of bridges for classification based on the type of substructure ... 64 Table 3.11: Limit State of bridges for classification based on material of construction .. 64 Table 3.12: Key features of bridges that experienced variety of structural damage ...... 64 Table 3.13: Criteria for minimum functionality requirement after a MCE or DE in light of AASHTO ...... 65 Table 3.14: Parameters for 14 bridges to calculate their functionality after the earthquake of 2005 ...... 65 Table 3.15: Summary of ARS, ERS and aftershock time history recorded simultaneously at Muzaffarabad and Abbottabad...... 66 Table 4.1: Specification of hydraulic jacks of structure testing frame ...... 120 Table 4.2: Geometric and material properties of trial bridge column of scale 1:6 for quasi- static cyclic testing ...... 120 Table 4.3: Specifications of Shake Table (Seismic Simulator) R141 ...... 121 Table 4.4: Geometric and material properties of trial bridge column of scale factor 1:10 for shake table testing ...... 121 Table 4.5: Scaling factors for shake table model 1:10...... 121 Table 4.6: Summary of scaling factor used for 1:4 final models ...... 122 Table 4.7: ASTM C-136 sieve analysis of fine aggregates used in experimental work . 123 Table 4.8: Summary of properties of fine aggregates used in experimental work ...... 123 Table 4.9: ASTM C-136 sieve analysis results for coarse aggregates used in prototype concrete...... 123

xxiii Table 4.10: Summary of properties of coarse aggregates used in prototype concrete ... 124 Table 4.11: Summary of properties of hydraulic cement used in experimental work .... 124 Table 4.12: Summary of benchmark characteristic properties of prototype concrete .... 124 Table 4.13: ASTM C-136 sieve analysis of coarse aggregates used in model concrete 125 Table 4.14: Summary of properties of coarse aggregates used in model concrete...... 125 Table 4.15: Summary of characteristic properties of model concrete used in four test columns comprising two groups of concrete strength...... 125 Table 4.16: Mechanical properties of mild steel used in prototype and model...... 126 Table 4.17: Summary of parameters for prototype and model...... 126 Table 4.18: Data for cyclic testing protocol used in first column QSCT-2-003...... 127 Table 4.19: Data for cyclic testing protocol used in last three column columns...... 127 Table 5.1: Dynamic parameters from ambient (free) vibration tests for various stages of loading for fully elastic column QSCT-2-003...... 182 Table 5.2: Dynamic parameters from ambient (free) vibration tests for various stages of loading for fully elastic column QSCT-3-004...... 182 Table 5.3: Dynamic parameters from ambient (free) vibration tests for various stages of loading for fully elastic column QSCT-4-005...... 183 Table 5.4: Dynamic parameters from ambient (free) vibration tests for various stages of loading for fully elastic column QSCT-5-006...... 183 Table 5.5: Values for cracking, initial yield and yield for column QSCT-2-003...... 184 Table 5.6: Values of energy dissipated for column QSCT-2-003...... 185 Table 5.7: Values for cracking, initial yield and yield for column QSCT-3-004...... 186 Table 5.8: Values of energy dissipated for column QSCT-3-004...... 186 Table 5.9: Values of stiffness degradation for column QSCT-3-004...... 187 Table 5.10: Values of natural period and damping ratio for column QSCT-3-004...... 187 Table 5.11: Values for cracking, initial yield and yield for column QSCT-4-005...... 188 Table 5.12: Values of energy dissipated for column QSCT-4-005...... 188 Table 5.13: Values of stiffness degradation for column QSCT-4-005...... 189 Table 5.14: Values of natural period and damping ratio for column QSCT-4-005...... 189 Table 5.15: Values for cracking, initial yield and yield for column QSCT-5-006...... 190 Table 5.16: Values of energy dissipated for column QSCT-5-006...... 190

xxiv Table 5.17: Values of stiffness degradation for column QSCT-5-006...... 191 Table 5.18: Values of natural period and damping ratio for column QSCT-5-006...... 191 Table 6.1: Input text file of QSCT-3-004 for IDARC 2D software...... 223 Table 6.2: Summary of 20 prototype bridge columns used in inelastic nonlinear time history analysis...... 226 Table 6.3: Reinforcement details of prototype columns used in inelastic nonlinear time history analysis...... 227 Table 6.4: Damage Indices correlated to damage levels defined by MCEER/ATC-49. 227 Table 6.5: Limiting values of energy dissipation and ductility for prototype bridge columns...... 227 Table 6.6: Response Modification Factors (R) for 20 prototype bridges for “none” damage level...... 228 Table 6.7: Response Modification Factors (R) for 20 prototype bridges for “minimal” damage level...... 229 Table 6.8: Response Modification Factors (R) for 20 prototype bridges for “significant” damage level...... 230 Table 6.9: Maximum and residual deflections in 20 bridges for the damage level state “none”...... 231 Table 6.10: Maximum and residual deflections in 20 bridges for the damage level state “minimal”...... 232 Table 6.11: Maximum and residual deflections in 20 bridges for the damage level state “significant”...... 233

xxv CHAPTER 1 INTRODUCTION

1.1 Background

Earthquakes can be the deadliest forces of nature that can shake structures to their limits, including bridges due to such factors as large masses lumped on columns of multi-span bridges, sudden loss of support for the super-structure, and failure of other key components. The term used to define the potential of earthquakes is “Seismic Hazard”. Different areas have different seismic hazard based on the studies of past earthquakes by means of geological and seismological studies done by researchers dealing with earth sciences and seismology. Seismic hazard has always been the root cause of concern and controversy among structural engineers and seismologists in relation to the precise definition of the amount and type of shaking expected in the lifetime of a bridge at a particular site. The controversy underlying the seismic hazard among seismologist is due to the reason that the knowledge to understand the mechanics of faults and wave propagation is still not very well-defined. Typically the response spectra plotted are based on uniform hazard which makes the situation complex for a broad range of structural periods of different bridges. However, researchers, government agencies and builders agree on certain values of expected seismic hazard and rely on the field of probabilities and accept the risk that underlies the value chosen for the seismic hazard.

Apart from seismic hazard which is not in control of the engineers and bridge owners, there are inherent challenges on part of the bridge itself which add to the seismic vulnerability of a bridge. Bridge substructures are mostly made of reinforced concrete which shows highly nonlinear inelastic behavior when loaded beyond the elastic range. A wide range of bridges can be modeled as single-degree-of-freedom (SDOF) systems with a lumped mass on the column top. Small lateral loads in minor earthquakes are usually resisted in the elastic range and damping of the bridge dissipates the energy. However, moderate and large earthquakes are not resisted elastically, that is inelastic action is allowed to develop. A bridge designed to remain elastic under such conditions would be highly uneconomical. In the inelastic range, the energy is dissipated by

1 hysteresis which is an extremely complex phenomenon involving many parameters. The inelastic response is further complicated since the seismic forces acting on the bridge constitute non-proportional loading.

The change of stiffness during the inelastic action changes the response of a structure. The structural strength also degrades due to the large loads cuasing inelastic action in the bridge columns. The response of the bridge column is also affected by repeated cyclic loading excursions of low causing strength degradation. Pinching in the hysteresis is also seen due to cracking of the concrete core. All of these parameters influence the hysteretic energy dissipation. Meanwhile, the objective remains to ensure life safety while the bridge dissipates the energy without losing structural integrity.

Seismic design of bridges has started in most of the developed countries rather recently. In USA, the first seismic provisions were introduced in 1961. In 1971, San Fernando earthquake which devastated many bridges, resulted in spurring seismic research for bridges. Latter Loma Prieta earthquake of 1989 and Northridge earthquake of 1994 again resulted in updating the codes in light of lessons learnt in these earthquakes.

In Japan from Kanto earthquake in 1923 to Kobe earthquake in 1995, various seismic design provisions were given and codes periodically updated. In a period of 70 years until Kobe, hardly few bridges experienced damage or collapse, however, just one earthquake of Kobe devastated 25 bridges. These facts show that the seismic design of bridges is still evolving. A significant problem is that most of the existing bridges were built several decades ago while using older seismic codes.

In Pakistan, only one bridge design code has been published in 1967 based on the US code of 1961. This code has not ever been updated. Also, most of the bridges in Pakistan have been designed using the AASHTO Standard (AASHO, 1961) which has been discontinued in the US since 2007 and replaced by AASHTO-LRFD (AASHTO, 2007). Furthermore, in Pakistan, the use of any specific code has not been mandatory by regulations and the detailing and quality control during construction have also been left to the discretion of the designer, owner or builder.

The present dissertation describes outcome of a study of energy dissipation capacity of low strength reinforced concrete columns under seismic conditions.

2 1.2 Problem Statement and Research Objectives

Most of the studies related to energy dissipation of concrete bridges are conducted for unconfined concrete compressive strength of 3,000 psi (20.7 MPa) and above, as this is generally the strength required for structural concrete. No comprehensive study has been conducted in Pakistan on seismic performance of bridges. Pakistan is one of the most highly seismic areas of the world, such studies are needed. Bridges in Pakistan have their own typical geometry, design and construction practices. Additional aspects of bridge performance which is emerging worldwide are the bridge resilience and the quantification of functionality with regard to seismic resilience.

This dissertation presents a detailed study of a survey of bridges in northern part of Pakistan and the seismic performance of bridges and failures observed during the earthquake of Oct. 8, 2005 that measured Mw7.6. From the field study, a mathematical function is developed to quantify the functionality of bridges which is the measure of bridge resilience. Based on the field observations and data, energy dissipation capacity of reinforced concrete bridge columns having low strength concrete is studied by experimental investigations on solid circular columns. Numerical models are calibrated using the experimental results. Numerical studies based on inelastic dynamic analyses of calibrated models are used in this research to arrive at important results with regard to seismic performance and from which fragility curves are also derived. The following are the main objectives of this study:

1. To undertake field study of bridges in northern part of Pakistan that includes NWFP and Azad Kashmir.

2. To quantify the performance of bridges from the data obtained during the field studies after the large earthquake of 2005.

3. To evaluate through experiments the critical parameters in seismic performance of bridge columns that include:

a. Drift limits which is the basic parameter to calculate other factors.

b. Ductility of a typical bridge column having solid circular cross section and low-strength concrete.

3 c. To investigate the Response Modification Factor called “R-factor” for seismic design of bridges based on experimental results.

d. To evaluate the permanent displacements also called residual displacements, expected in bridges during major seismic events.

e. To develop a numerical model for low-strength concrete and calibrate the hysteresis parameters with the help of experimental results to conduct numerical studies.

4. To develop fragility curves for two groups of low-strength concrete on the basis of experimental results and using the calibrated numerical model.

1.3 Assumptions and Limitations

The following are the assumptions and limitations of the study proposed herein:

1. Bridges are two-lane and have a medium span in the range from 82 feet (25 m) to 89 feet (27 m).

2. Bridge columns have a solid circular cross with a low strength concrete in the range from 1,800 psi (12.4 MPa) to 2,400 psi (16.5 MPa).

3. The longitudinal reinforcement steel ratio is kept constant at 1.47% and the volumetric steel ratio for confining steel is kept at 0.19% for all of the experiments.

4. The experiments are conducted using quasi-static cyclic loading with a constant axial load resulting from a physical mass placed on column top.

5. The numerical model is calibrated for hysteretic modeling parameters using experimental results obtained from the quasi-static cyclic tests.

6. The numerical study conducted is for bridges in far-field, in which the predominant shaking is in only the lateral direction and the earthquake time histories are linearly scaled during various phases of computation.

7. The strain in the steel and concrete was not measured in high lateral drift cycles due to inability of the strain gages to record strains during spalling and local

4 buckling of rebar. The lateral force however was measured at all the stages, with the help of a digital load cell.

1.4 Outcome of Present Study

The outcome of present study is of particular use in Pakistan but also worldwide since it deals with low-strength concrete bridge columns resulting from poor quality of construction or due to an absence or a lack enforcement of quality assurance protocols. Use of mixed standards such as those based on cube strength versus cylinder strength for concrete is yet another problem. Sometimes environmental conditions may also deteriorate the material strength thus making a bridge more vulnerable to earthquakes.

The first contribution of this dissertation is in the emerging field of bridge “resilience”. A mathematical function is proposed which quantifies the functionality of a bridge following an earthquake. Alongside the development of this new mathematical function, “limit states” are defined for various damage levels based on field observations. Furthermore, “threshold criteria” is developed for bridge functionality for „Maximum Credible Earthquake‟ (MCE) and „Design Earthquake‟ (DE) while utilizing the definition of performance criteria outlined in AASHTO LRFD (AASHTO, 2007).

In addition to the main focus of this dissertation in establishing the energy dissipation capacity and finding hysteretic modeling rules for low-strength concrete, there are some new testing approaches adopted which are rarely seen in quasi-static cyclic testing. One is the use of a physical mass of ~44 kips (~20,000 kg) on the column top which helped in obtaining the true conditions of geometric non-linearity due to the so called P effects. Thus, the use of a vertical actuator is avoided thereby eliminating the need for corrections in control and identification of the actual lateral load.

In the present study, the advantage was also taken of the huge physical mass on the column top due to the “inertia” it produced. Forced vibration testing was done using an eccentric mass vibrator while the column was in elastic stage. Free vibration tests which are also called “ambient vibrations tests” were conducted on loaded column during various stages of inelasticity. Inelasticity is produced due to lateral loading in the quasi- static testing. The free vibration tests results provide extremely important data related to

5 the dynamic properties of bridges due to different levels of accumulated damage resulting from low-cycle fatigue. Free vibration tests of the elastic column under increasing mass during the loading stage are also carried out providing a change of the dynamic characteristics due to a change in the mass. The tests on low-strength concrete columns provide useful information in the field of bridge engineering and for those interested in knowing about the variation of dynamic parameters and the seismic performance of such bridges.

1.5 Dissertation Organization

Chapter 2 presents a literature review relevant to this study. This includes a survey of bridges and field studies following earthquakes to observe the seismic performance of bridges, literature related to the concept of seismic resilience, experimental testing and numerical modeling of bridges.

Chapter 3 is related to a field survey of bridges and study of their seismic performance after the earthquake of 2005. The latest concept of seismic resilience and its quantification is also presented in this chapter. A mathematical function for quantifying the functionality of a bridge following an earthquake is presented along with an example for calculating functionality of a bridge which suffered damage in the 2005 earthquake. Limit states and threshold criteria for functionality are also presented.

An important component of this dissertation is the experimental modeling and experimental work, which is presented in Chapter 4. The first part discusses pre- requisites for experimental testing related to equipment operation, calibration, definition of the limits for the testing equipment, followed by a few benchmark tests. In the second part of this chapter, similitude analysis is presented along with modeling of test specimens. The third part deals with experimental work related to the design of concrete mix and various ASTM tests. The forth part presents the customization of test equipment. The last part describes the test protocols for quasi-static cyclic testing, free vibration testing and forced vibration testing.

Chapter 5 describes the experimental results obtained from various tests on total of four columns tested.

6 Chapter 6 describes the numerical studies conducted in this dissertation. The first part of this chapter deals with the selection and description of a software called IDARC (Reinhorn, et al., 2009) used for inelastic studies. The second part deals the procedure for modeling in IDARC with a case study of one of the columns tested. The third part deals with the document MCEER/ATC-49 (ATC and MCEER, 2003) to define various important requirements forming the basis of various limit states and seismic performance criteria. The last part presents a nonlinear inelastic time history analysis including calibration of the numerical model and damage indices with defining limiting values, calculation of the R-factor, maximum residual displacements, and fragility functions for various cases.

7 CHAPTER 2 LITERATURE REVIEW

2.1 Introduction

This chapter briefly reviews the literature related to the research undertaken in this dissertation and includes a field survey of bridges after a large earthquake and resilience of bridges, experimental testing programs, and numerical modeling of inelastic nonlinear structures.

Section 2.2 deals with a review of the literature related to the field survey of bridges for collection of data for use in the experimental study. This section also deals with the “Resilience” of bridges.

Section 2.3 presents literature review regarding testing of structures with a specific emphasis on bridges. Quasi-static testing which is the main testing procedure used in this study is also reviewed.

Section 2.5 reviews the inelastic nonlinear time history analysis. Various hysteretic models are briefly reviewed which form the basis of this study. Hysteretic modeling parameters involving stiffness degradation, strength degradation and pinching are found in various hysteresis models proposed.previously. Response modification factors and fragility curves are also reviewed with specific application to bridges.

2.2 Field Survey and Seismic Resilience

Bridges built in the past may not satisfy the requirement of modern codes which have gone through revolutionary changes (Wang, 2004; Yalcin, 1998). Some bridges had poor quality-control during construction that resulted in low-strength concrete while many bridges are deteriorating (Shkurti, 1998) and thus more vulnerable to seismic activity. Nearly 50% of 575,600 bridges in USA were found to be structurally deficient or functionally obsolete which highlights the fact of ailing infrastructure (Shkurti, 1998). The publication of “AASHTO Standard” (AASHTO, 2002) has been discontinued after its 17th edition. The current applicable standard is the 4th edition of AASHTO-LRFD (AASHTO, 2007). In addition, a more focused document (AASHTO, 2009) for seismic

8 design with improved displacement-based design (AASHTO, 2009) was approved as an alternate to the seismic provisions of the current AASHTO-LRFD Specifications. These significant improvements in the design specifications need to be utilized for a study of the bridges designed with older specifications.

It is also important to conduct a comprehensive survey of bridges to establish various important parameters while employing numerical techniques (Yalcin, 1998). Many valuable lessons were learnt from field studies after the Kobe earthquake which also helped in assessing the vulnerabilities of newly constructed suspension bridges designed for seismic hazard (Wilson, 2008).

Various studies have also been conducted on bridges especially after the major earthquakes (Kawashima & Unjoh, 1996; Kawashima K. , 2000; Kawashima K. , 2006). The studies following an earthquake especially help in understanding the performance of bridges built using design procedures which existed when these were being built.

2.2.1 History of Seismic Design and Specifications

The 1923 Great Kanto earthquake in Japan resulted in destructive damage to structures as a result of which the first set of seismic provisions for highway bridges were introduced in 1926 (Kawashima, 2000). The design specifications for steel highway bridges in Japan were issued in 1939 and were revised in 1956 and 1964. A total of 20% of the bridge self-weight was taken as the lateral load and no other provisions for seismic design were considered (Kawashima, 2000).

In 1971, the first comprehensive seismic design provisions (JRA, 1971) were issued in Japan which used seismic zones and soil conditions. In 1980, a new version of seismic design specification was issued with some changes to the 1971 edition. In 1990, the seismic design specifications of 1980 were revised with major changes. In 1995, forty days after the H-k-n (Kobe) earthquake, specifications were issued for reconstruction and repair. In 1996, a revision of 1990 specification was made which included the 1995 specification. In 2003, another major revision was made to the seismic specification in Japan.

9 In USA, the first edition of the AASHTO Standard then known as AASHO was published in 1931. From the first to the fourth edition of this standard until 1945, seismic loading was not a part of the specification. For the first time in 1949, the fifth edition of AASHTO Standard mentioned the earthquake stresses to be included but no guidelines were given. Also, in the sixth and seventh editions of AASHTO Standard in 1953 and 1957, no guidelines for seismic design were included. The eighth edition in 1961 specified earthquake load for the first time. The next three editions in 1965, 1969 and 1971 which were the ninth, tenth and eleventh editions, respectively, had the same seismic provisions of 1961, without any change. The provisions of 1961 specification were 2% to 6% of the total load to be applied as lateral load depending upon the type of foundation (Wang, 2004).

In the 1971 San Fernando earthquake of California, many bridges suffered extensive damage. California Department of Transportation (CALTRANS) issued new seismic design specifications and these formed the basis of the 1975 AASHTO Interim Specifications after slight modifications. In 1978, the Federal Highway Administration (FHWA) in USA asked the Applied Technology Council (ATC) to review the seismic design procedures and suggest improvements. This resulted in ATC-6 which was adopted by AASHTO in 1983 as Guide Specifications. In 1990, the same were adopted as Seismic Provisions and called Division IA.

After the devastating earthquakes such as the 1989 Loma Preita earthquake in California, and the 1991 earthquakes in Philippines and Costa Rica, AASHTO requested the Transportation Research Board (TRB) to review the current seismic provisions and revise as appropriate. In this regard, National Center of Earthquake Engineering Research (NCEER) prepared the revised and improved seismic provisions. The last version of AASHTO Standard was published in 2002 which was the seventeenth edition. In 2007, AASTHO-LRFD was adopted as the sole Bridge Design Specifications and the older AASHTO Standard was abolished.

In 1994, seismic design provisions were given in AASHTO-LRFD specifications for the first time, revised in 1998 as the second edition, in 2004 as the third edition, and in 2008

10 as the current fourth edition. In 2009 a new alternate set of design specifications are introduced named “AASHTO Guide Specifications for LRFD Seismic Bridge Design”.

In Pakistan, first bridge design specifications were issued in 1967 (CPHB, 1967). These specifications had seismic design requirement adopted from the eleventh edition of AASHTO Standard of 1961. The Government of West Pakistan at that time hired Howard, Needles, Tammen & Bergendoff International, Inc. for preparing the code of practice for highway bridges in Pakistan. Since then, there has been no revision of the 1967 code. Pakistan has mainly been using AASHTO Standard for the design of bridges. But there have been anomalies in that with regard to seismic hazard. In 2007, the Building Code of Pakistan for Seismic Provisions (BCP, 2007) was issued which contained for the first time seismic hazard with a quantifiable value of Peak Ground Acceleration (PGA). The Seismic Hazard Map of 2007 was based on a 475-years return period. Previously, Modified Mercalli Intensity (MMI) scale based earthquake intensity maps have been issued which did not provide specific PGA values. Thus, the bridges designed in the past used arbitrary values of PGA for design.

2.2.2 Bridge Engineering and Seismic Hazard in Pakistan

It is important to note that the Seismic Hazard Map used util 2007 was prepared by the Geological Survey of Pakistan (GSP) and was based on Geophysical Center Quetta‟s instrumental Macro-Earthquake data of 1905 to 1979, and the Seismic Zoning was based on Modified Mercalli Intensity (MMI) Scale (BCP, 1986). Since MMI scale is based on visual observations of damage at a particular location and is related to the type of construction at that site, it does not provide a quantitative measure of the true ground accelerations and may yield only crude estimates of the ground motion intensities. On the other hand, the use of AASHTO Standard Specification without correlating it to the local conditions such as material properties, workmanship and construction practices makes a complex scenario of design and construction, and poses a complex challenge for the engineers. Also, as the database of available earthquake records for the region increases, the seismic hazard map may require revisions, requiring a re-evaluation of already constructed bridges. In Japan, after the 1923 Great Kanto Earthquake of M7.9, the seismic design of bridges was given serious attention and for over a 71-year period

11 util 1995, only 15 bridges collapsed due to earthquakes, indicating a decreasing trend of bridge failures coupled with a maturity of design experience accumulated over the years. However, in 1995, the Hanshin/Awaji Earthquake at Kobe alone destroyed 25 bridges (Kawashima and Unjoh, 1996), after which the Japanese bridge seismic code was revised. After the devastating earthquake of October 8, 2005 in Pakistan, an exhaustive exercise of writing a seismic code for buildings was started which resulted in the publishing of BCP (BCP, 2007). Chapter 2 of this code addresses the Seismic Hazard and has provided the Design Basis Ground Motion with a 10% probability of exceedance in 50 years. Looking into the Seismic Hazard Map of BCP (BCP, 2007), it is evident that almost the entire Pakistan lies in Zone 2A or above, which corresponds to a Peak Ground Acceleration (PGA) in the range of 0.08-0.16 g or higher.

As mentioned earlier, previous seismic zoning for Pakistan was based on a MMI scale devised in 1931. In this MMI-based seismic zoning map, Pakistan is divided into four zones, i.e., Zone 0, Zone 1, Zone 2 and Zone 3 in the order of increasing ground shaking. However, this map does not give a quantifiable measure of ground shaking intensity. The northern part of Pakistan is mainly included in Zone 2, which is categorized as moderate damage area corresponding to an intensity of VII of the MMI scale. On the other hand, the recently published Seismic Hazard Map in BCP (BCP, 2007) has five Seismic Zones, namely, Zone 1, Zone 2A, Zone 2B, Zone 3 and Zone 4, in the order of increasing ground acceleration, according to which some areas such as Balakot, Muzaffarabad, etc. of the northern part of Pakistan are placed in the zone of highest seismic hazard, i.e., Zone 4 with the a PGA ≥ 0.32g. The remaining part of the northern area is placed in Zone 3 that has a PGA in range of 0.24g to 0.32g. The revised seismic zoning map requires that all new structures be designed to withstand higher seismic loading according to the new Seismic Hazard Map, and if necessary be retrofitted to withstand greater seismic loads. Also, according to the 1967 Code of Practice for Highway Bridges(CPHB, 1967), the bridges need to be designed for a lateral force equal to 2% to 6% of the dead load of the structure. The range of 2% to 6% corresponds to various structural forms of foundation resting on different soil profiles. Since CPHB preceded the availability of seismic zoning map, conformance to it does not require taking into account the seismic zoning

12 information. There is a need for making the 1967 code compatible with the recent Seismic Hazard Map and the associated specifications.

As previously mentioned, most of the bridges in Pakistan have been mainly designed using AASHTO Standard Specification which refers to the Seismic Hazard Map of USA. This means that the bridges designed prior to 1979 would have either used 2%-6% of the weight as the lateral force value or would have adopted arbitrary PGA values. The bridges designed after 1979 until 2007 used the Seismic Hazard Map based on the MMI scale without quantifiable PGA values. Consequently, arbitrary PGA values were utilized by the designers. There is a need for the evaluation and retrofitting of existing bridges utilizing the Seismic Hazard Map published in BCP (BCP, 2007) with applicable PGA values based on a 10% probability of exceedence in 50 years. It is important to note that in the older version of the AASHTO Standard of 1980‟s, simplistic elastic design procedures, that is, the Equivalent Static Force Procedure and the Response Spectrum Method were allowed. However, the current AASHTO-LRFD method includes various analysis procedures ranging from linear elastic, to nonlinear inelastic, for example the linear/nonlinear time history analysis. The choice of an analysis procedure is coupled in a rational manner to the importance of a bridge and its location in a particular seismic zone while taking into account the regularity or irregularity of the bridge.

In order to guard against the future earthquakes, it is imperative to evaluate the existing bridges. Work on an indigenous bridge design code needs to be started including a major revision of the 1967 Bridge Code. The Seismic Hazard Map of BCP (BCP, 2007) shows that a huge portion of Pakistan falls into high seismicity areas which are close to such large cities as Karachi, Quetta, Gwadar, Peshawar, Abbottabad, Gujrat, and Islamabad. Since the infrastructure development is moving at a fast pace, the new Seismic Hazard Map must be utilized for both new bridges as well as those that need to be retrofitted.

2.2.3 Seismic Resilience and Functionality

Resilience is defined as “the ability to recover quickly from illness, change, or misfortune” and “the objectives of enhancing seismic resilience are to minimize loss of life, injuries, and other economic losses, in short, to minimize any reduction in quality of life due to earthquakes” (Bruneau et al., 2003).

13 Earthquakes are natural disasters which create great havoc in communities. Earthquake engineering research has been contributing to improve the knowledge and technologies for reducing the seismic risk and improving seismic resilience. However, there is a great need at this time to move beyond a qualitative understanding of disaster resistance and resilience and formulate quantitative measures to both understand and define resilience (Bruneau, et al., 2003).

The Figure 2.1 illustrates the concept of seismic resilience adopted from Bruneau (Bruneau et al., 2003) by means of s relationship between percent quality on infrastructure and time.

Seismic resilience for acute-care facilities has been explored by Bruneau and Reinhorn (Bruneau and Reinhorn, 2007) which attempts to correlate hardcore structural engineering involving floor accelerations and response of structural and nonstructural components to the tools that would quantify resilience for sociopolitical-engineering decisions. An integrated approach for quantifying seismic resilience involves probability functions, fragilities and resilience.

Cimellaro et al. (Cimellaro, Reinhorn, and Bruneau, 200X) present the model for calculating resilience of a hospital network. These state that describing losses as well as the recovery process is challenging but very helpful.

In Kobe earthquake, three major new long-span steel bridges suffered damage which was not anticipated. These bridges were designed using state-of-the-art seismic standards specifically developed for each project (Wilson J. C., 2008). Wilson outlined three characteristics for a resilient system namely, it reduces the chances of a shock; it absorbs a shock if it occurs; and it recovers quickly. He pointed out that these aspects were lacking in these three bridges. He also stated that the time taken to restore the bridges after the Kobe earthquake was three to nine months.

The Federal Highway Administration (FHWA) of USA has initiated a project for enhancing the seismic resilience of highway bridges (Friedland, 2009). Thus, measuring and quantifying seismic resilience is a relatively new area which is still evolving.

2.3 Seismic Testing Methods

14 A variety of testing methods are available and the choice depends on the objective of the study. Tests can be static, quasi-static, pseudo-dynamic and dynamic. The availability of all the tests in one laboratory is possible but the size of testing equipment can significantly vary. Usually choices are always limited in terms of finalizing the size of specimen and/or type of test for a particular size. Cost is generally the main issue that limits the equipment size and capabilities and once a laboratory has made a capital investment, then a researcher may have a limitation of the budget as well. Time is generally another constraint which limits the testing; size of test specimen and number of specimens to be tested are usually governed by time as well. Size of specimen has a relatively indirect relation to time; reducing the size too much may cause excessive time delays compared to a larger test specimen. This can be caused by a lack of the the availability of very small scale components and the difficulty in fabricating tiny pieces with precision. The total testing time is just not the time to test a specimen but it begins from the design of the test specimens to the data processing of the results. In the entire process, the test time may be just a few seconds in dynamic testing, to a few days in static tests but both times may be only a fraction of the overall time taken to conduct the experimental study.

Static tests can be quasi-static monotonic tests and quasi-static cyclic tests. Dynamic tests can be shake table tests and tests utilizing exciters such as eccentric mass vibrators and linear vibrators. There is another class of testing called pseudo-dynamic testing which is sort of quasi-dynamic testing but relatively slow, in which inertial effects from dynamic testing are accounted for by utilizing complex calculations.

There are other classes of very sophisticated testing such as hybrid testing and distributed hybrid testing which involve testing of a part of a structure in computing domain and a part physically in the laboratory and this may be distributed over geographically distant places. Thus, every testing method has its own merits and demerits, however, the choice of a method depends on the test objectives.

Usually quasi-static testing is low-cost and requires relatively less complicated equipment while not requiring very fast control or high volume of hydraulic fluids to provide instantaneous forces and displacements. In these tests, there is enough time to observe

15 and witness changes. Another major advantage is that large specimens can be tested with greater ease. Limitations are that the rate effects are not included in testing (Sullivan, Pinho, and Pavese, 2004).

Dynamic testing such as that of a shake table is very expensive not due to the cost of a specimen but due to the cost involved in operating the shake table. This testing does include the rate effects, and the input to the shake table, usually an earthquake time history, closely matches the real input which a structure would experience (Sullivan, Pinho, and Pavese, 2004; Harris and Sabnis, 1999). There are many difficulties associated with shake table testing. For example, the control is extremely difficult; the chain of events leading to structural failure are difficult to observe due to the very short time domain; and the capability to test large structures is seriously limited. Very few shake tables have the capacity to carry large payloads.

2.4 Experimental Testing of Bridges

Generally, bridges are larger structures in comparison to buildings and thus have a heavy supported mass. A two-lane pre-stressed girder bridge with a span of 25-28 meters (82 ft-92 ft) would impose a load on a pier in the range of 300-400 metric tons (661-882 kips). The huge size of mass and geometric dimensions would require large testing facilities even if scaled models were to be tested in a laboratory.

One of the popular forms for testing bridge columns is quasi-static testing. The advantage of quasi-static testing in addition to advantages mentioned above is that a component can be tested with greater ease.

Sheikh tested fifty-six bar specimens under monotonic loading and used the results of experimental testing (Sheikh, 1978) to present a numerical procedure for predicting the behavior of plastic hinge. The columns tested by Sheikh (Sheikh, 1978) had a concrete strength in the range from 3,540 psi (31.3 MPa) to 5,932 psi (40.9 MPa).

Another series of experiments on concrete columns was done to investigate the strength and ductility, in which concrete strength was in the range from 3,423 psi (23.6 MPa) to 5,250 psi (36.2 MPa) (Zahn, Park, and Priestley, 1989).

16 In a study by Cheok and Stone (Cheok and Stone 1990), six circular concrete bridge columns of scale 1:6 were subjected to quasi-static cyclic loading to study their behavior while varying some of their parameters such as the aspect ratio, axial load, and the type of material. The concrete strength for the columns was 4,000 psi (27.6 MPa).

Some researchers have undertaken full-scale dynamic testing of bridges but mainly limited to ambient vibration testing and/or forced vibration testing using external exciters for the purpose of determining the natural periods, modal shapes and modal damping ratios (Salawu and Williams, 1993).

Sheikh and Toklucu tested twenty-seven reinforced concrete columns under monotonic axial compression with concrete strength in the range from 5,062 psi (34.9 MPa) to 5,207 psi (35.9 MPa) (Sheikh and Toklucu, 1993). In this study, they investigated the effect of various parameters such as the amount and type of lateral steel, spacing of lateral steel and specimen size.

Priestley and Benzoni tested two large-scale circular columns with low longitudinal reinforcement having a concrete strength of 4,360 psi (30.0 MPa) (Priestley and Benzoni, 1996).

Thirty-one concrete column specimens of various shapes, sizes and reinforcements were tested for bridge columns (Hoshikuma, Kawashima, Nagaya, and Taylor, 1997). The strength of concrete in this research was in the range from 2,683 psi (18.5 MPa) to 3,524 psi (24.3 MPa). However, the concrete columns with a strength of 2,683 psi (18.5 MPa) were without any longitudinal reinforcement, had a diameter of 7.9 inches (200 mm), a height of 23.6 inches (600 mm), and confinement steel was provided.

Twelve circular concrete bridge columns of scale 1:4 were tested under cyclic loading. The concrete strengths were in the range from 5,221 psi (36.0 MPa) to 5,802 psi (40.0 MPa) (El-Bahy A. , Kunnath, Stone, and Taylor, 1999). The purpose of this testing was to study the cumulative damage in concrete bridge piers designed with AASHTO specifications. The researchers have also conducted a study of the effect of variable amplitude loading on the column response. (El-Bahy, Kunnath, Stone, and Taylor, 1999).

17 In Japan, Kawashima and others have tested around 50 concrete bridge columns using quasi-static methods. The purpose of testing has been related to various objectives such as the effect of loading hysteresis on ductility, effect of interlocking ties on strength and ductility, verifying plastic hinge lengths, etc. The concrete strength of these columns varied between 2,950 psi (20.3 MPa) to 5,337 psi (36.8 MPa) (Takemura & Kawashima, 1997; Kawashima, Shoji, and Sakakibara, 2000; Fujikura, Kawashima, Shoji, Zhang, and Takemura, 2000).

Plastic hinge analysis in concrete columns was investigated by Bayrak and Sheikh (Bayrak and Sheikh, 2001).

Hollow bridge columns were studied for seismic performance by Mo and Nien (Mo. and Nien, 2002). They tested six concrete bridge columns under quasi-static loading which had concrete strengths in the range from 7,208 psi (49.7 MPa) to 10,153 psi (70.0 MPa).

Another series of bridge column testing was done in which two prototype and four models were subjected to quasi-static testing (Yeh, Mo, and Yang, 2002). The concrete strength for the columns was in the range from 4,221 psi (29.1 MPa) to 4,931 psi (34.0 MPa).

Full-scale testing of five concrete bridge columns was undertaken by Bae (Bae and Bayrak, 2008) to study their seismic performance. Bae and Bayrak performed cyclic testing under constant axial load. The concrete strengths of the columns were between 4,300 psi (29.6 MPa) and 6,300 psi (43.4 MPa).

Two large-scale tests on bridges on shake tables were conducted for verification of bridge condition assessment (Chen, Feng, and Soyoz, 2008). One test was on a two-column reinforced bridge bent and other was on a three-column bent.

2.5 Numerical Modeling

Numerical modeling of bridge columns is most helpful in determining the response of bridges under seismic loading. However, a numerical model has to be representative of the actual bridge behavior. In seismic excitation, the bridges have to dissipate energy in the inelastic range, for which it is necessary to ensure integrity while doing so by having

18 the required ductility, strength, stiffness and reasonable capacity against low-cycle fatigue.

Many researchers in the past have been investigating the performance of brides under seismic loading. Ghobarah and Tso analyzed the bridges and modeled them after the San Franando earthquake of 1971 (Ghobarah and Tso, 1973). Apart from the effect on bridge decks, they found that the outer columns away from the centerline of the bridge deck were more vulnerable due to leverage action.

In 1976, Takizawa and Aoyama (Takizawa and Aoyama, 1976) used tri-linear stiffness degradation model for a bridge and studied the effect of biaxial bending on the bridge columns. The effect of biaxial bending while using a degradation model was found to be significant in comparison to that with a non degradation model. (Takizawa and Aoyama, 1976).

In 1978, Sheikh performed experimental investigations and numerical studies on the effect of confinement on concrete columns (Sheikh, 1978).

In 1986, Wilson formulated a 3-D finite element model to compare the measured and calculated bridge responses. In this study, a few bridges in California were monitored and the actual response of prototype bridges was compared with analytical response (Wilson, 1986).

A two-dimensional model of bridge piers was prepared by Somani (Somani,1987) to account for soil-structure interaction for the pier modeled as a SDOF system. He concluded that the fundamental frequency including the soil-structurewas less than that based on a fixed base model (Somani, 1987).

Response of isolated and non-isolated bridges was compared by Gobarah and Ali (Gobarah and Ali, 1988). For non-isolated bridges they used Clough‟s degradation stiffness model and subjected the bridge to various earthquake time histories for inelastic dynamic analysis. The earthquake records were 1940 El Centro, 1966 Parkfield, 1971 San Fernando, and 1985 Mexico City. They concluded that large inelastic deformations require high ductility.

19 Reinforced concrete members were analyzed by Meyer and others which could be applied to bridges as well (Meyer, Roufaiel, and Arzoumanidis, 1983). They proposed a mathematical model that could suit computer software application and had the nonlinear capabilities. It was pointed out that cyclic behavior in the inelastic range was governed by many variables. Meyer also pointed out that non-linear structural behavior was a result of either geometric non-linearity caused by large deformations or material non- linearity caused by inelastic material behavior (Meyer, 1989).

A non-linear program called “Seismic Analysis of Bridges” (SEISAB-II ) was developed and checked by Liu et al by analyzing a two-span bridge (Liu, Nobari, and Imbsen, 1989). This program was derived from a computer program called “Nonlinear Earthquake Analysis of Bridge Structures” (NEABS) which was developed by Tseng and Penzien.

Sadii and Ghusn (Sadii and Ghusn, 1989).modeled a concrete column using five different springs in the plastic hinge region to model both concrete and steel. A computer program NEABS-86 was used in which the foundation was modeled as a rigid support and structural damping was taken to be 5%.

Saadeghvaziri and Foutch (Saadeghvaziri and Foutch, 1989) studied the effect of vertical accelerations on buildings and bridges. They concluded that always assuming vertical acceleration to be small as compared to the horizontal acceleration is incorrect. They used inelastic properties of concrete and steel and thus simulated the reinforced members under non-proportional lateral and axial loads. The results showed that the scenario of considering combined effect of the vertical and lateral loads results in a critical situation.

Kunnath, Reinhorn and Park (Kunnath, Reinhorn, and Park, 1990) studied various hysteretic models for bridges and found that previously used models were mainly bi- linear elasto-plastic models and well-suited for structural steel only. They concluded that a more elaborate model was required for concrete as energy dissipation in RC structures was dependant on various factors such as the concrete strength, quantity of reinforcing steel, shear, span-to depth ratio, axial stress, etc. They stated that more complex models that account for stiffness degradation such as that proposed by Clough and Johnston in 1966 and by Takeda in 1971 were better. They found that for a better estimation of

20 energy dissipation and to asses the remaining strength of a structure, a model accounting for stiffness degradation, strength degradation and pinching behavior would be required.

In 1990 Spyrakos (Spyrakos, 1990) studied the effect of soil-structure-interaction (SSI) on the bridge piers. He modeled the piers as a SDOF system with linear and rotational springs including damping at the base of the column. He proposed a simple procedure for evaluating the base shear which accounts for SSI.

In order to simulate the non-linear response of bridges, Zelinski and Dubovik (Zelinski & Dubovik, 1991) presented two models called the “tension” and “compression” models. They used a linear elastic program called “STRUDL” to simulate the non-linear response by undertaking iterative analysis in which they kept on changing the boundary conditions.

Zelinski (Zelinski, 1991) studied the use of elastic response spectra (ERS) and showed that the maximum elastic force in structures can be found using linear ERS or modal analysis. He also showed that the seismic retrofit concept of CALTRANS was based on designing the structure elastically for 25% of the maximum elastic force, i.e., using a response modification factor of 4 on the results obtained from linear dynamic analysis. He used many linear analysis programs such as BASP, STRUDL, ABACUS, and SAP90.

It was shown by Harper (Harper, 1991) that the ERS and acceleration response spectra (ARS) of CALTRAN could be used for 0.7 g of bedrock acceleration and alluvial material deeper than 150 feet to perform a dynamic analysis. He showed that linear computer programs can be used to perform the non-linear analysis for capturing the stiffness degradation by iteratively changing the properties of the columns. He changed the properties of a column from a fixed to pin when the ductility demand exceeded the capacity.

Modeling and analysis of bridges was studied by Akkari and Hoffman (Akkari and Hoffman, 1993). They showed the modeling of the bridge superstructure and pointed out that the modeling of the column should be done by assuming it to be fixed to the foundation so that the development of a plastic hinge could be captured.

21 Eberhard et al (Eberhard, Stanton, and Trochalakis, 1996) used DRAIN-2DX developed by Prakash et al and studied the effectiveness of seismic restrainers.

Kunnath and Gross (Kunnath and Gross, 1996) used an inelastic dynamic analysis program called IDARC to study the collapse of Cypress Viaduct which collapsed during the 1989 Loma Prieta earthquake. IDARC has powerful features such as a distributed flexibility model to represent the spread of plasticity especially in reinforced concrete members and the hysteretic model which can account for stiffness degradation, strength degradation, pinching effect and has a shear panel element to model inelastic flexure and shear independently. The analytical results showed that the failure was initiated by shear in the pedestal region which was also the observed failure mechanism.

Malhotra (Malhotra, 2002) studied the effects of cyclic demand since merely the amplitude alone is not sufficient to describe the seismic resistance of a structure. He pointed out that a structure‟s strength, stiffness, and energy-dissipation capacity reduces with an increase in the number of load cycles. He thus presented cyclic-demand spectrum, which in conjunction with the amplitude spectrum, provides a more complete definition of seismic load.

Poljansek et al (Poljansek, Perus, and Fajfar, 2009) did an exhaustive numerical study of concrete columns in which they used database of experimental results from various researchers. The researchers realized that during inelastic cyclic excursions, damage accumulates and the cumulative damage may cause failure of a structure or a member at a smaller deformation level than the ultimate deformation capacity, which resembles the phenomenon of low-cycle fatigue.

An interesting and useful study was undertaken by Kumar et al (Kumar, Gardoni, and Sanchez-Silva, 2009) in which they investigated the life-cycle cost of bridges that have been accumulating damage in seismic-prone regions and also accounting for steel corrosion. The study is helpful in estimating the condition of existing bridges and scheduling inspection. Additionally, deterioration over the bridge life-cycle can be estimated for better design.

22 FIGURES

Figure 2.1: Measure of Seismic Resilience (Bruneau, et al., 2003).

23 CHAPTER 3 . FIELD SURVEY AND DATA COLLECTION

3.1 Introduction

This chapter describes the field survey carried out in the northern part of Pakistan and Kashmir to gather data of the bridges constructed in this high seismicity area. Besides the field visits, data was also gathered from design reports, specifications and construction drawings of the bridges from the study area as well as outside it. As a part of the field study in which various parameters of the bridges were recorded, special attention was paid to collecting data related to bridge damages that occurred as a result of the large earthquake of October 8, 2005 measuring Mw7.6. From the extensive field visits over a period of 2 years in which data was gathered with regard to performance of the bridges, a mathematical function is proposed that encompasses the overall functionality of a bridge. Using AASHTO bridge design specifications, the minimum functionality requirement is spelled out for maximum credible earthquake (MCE) and design earthquake (DE). The functionality of damaged bridges is plotted to contrast it from their required performance. From the field data, typical parameters of bridge systems are identified which are then used to undertake an experimental investigation on scaled models in a seismic laboratory (Akhtar Naeem Earthquake Engineering Center, UET Peshawar) to study the energy dissipation capacity of bridges which typically exhibit low concrete strength.

3.2 Field Survey

Field surveys undertaken at various times had three main objectives: to know the typical bridge systems, to study the damage as a result of the Oct. 8, 2005 earthquake, and finding the typical material strengths. During the process of the field survey, various documents such as the specifications, design documents and drawings were also studied. The details of the field survey are presented below.

3.2.1 Survey Route

24 The survey route was such that it covered major road network of northern part of Pakistan and Kashmir. The survey started from Havalian on national highway N-35 which goes to China, historically known as the Silk Route and also called Kara Kurrum Highway (KKH). Another important segment of the road network that branches off from KKH at Manshera towards Kashmir had many bridges and was important since it is closer to the epicenter of the Oct. 8, 2005 earthquake. The road network surveyed is identified in Table 3.1 which also summarizes the survey route/location, the number of bridges, and approximate population served by the route. The bridges in this table are sub-divided as single-span and multi-span. The total number of major bridges on the route is 90.

3.2.2 Field Data Collection

For collection of the field data of bridges, a form was designed. The main objective of the form was to capture the maximum possible detail of a bridge. The GPS coordinates for each bridge surveyed were recorded on the form. The form can be seen in Figure 3.1 to Figure 3.5 that was used during the field surveys. The last page of this form was used to record the rebound hammer values using a Schmidt Hammer on concrete bridges.

Various visits were organized to the study area at different times also including visits after the Mw 7.6 Oct. 8, 2005 earthquake that killed more than 80,000 people and resulted in loss to infrastructure (Rao, Kumar, Kalpna, Tsukuda, & Ramesh, 2006). In the field visit, data was collected for the geometric details of the bridges such as the span and the width of the bridge, the height of the piers, number and type of columns, etc. A rebound hammer was used to collect the data to assess the in-situ strength and consistency of the quality of concrete present in the bridge. Sketches of the bridges were also made for easy description for defining the various components. Since the focus of this study was reinforced concrete bridges with piers, the relevant data for multi-span bridges collected is summarized in Table 3.2 and Table 3.3. Table 3.2 presents the name of the bridge, its route, year built (in some cases approximate year), and the number of traffic lanes. Table 3.3 presents the number of spans for each bridge, the total bridge length, the type of pier and its dimensions. In some cases, approximate dimensions are given due to inaccessibility. From the data, the average diameters of circular columns is calculated to

25 be 51 inches (1.3 m), the average height of the piers for all the bridges is calculated to be 26 ft-2 in (7.98 m), and the average span lengths are calculated to be 103 ft (31.4 m). The data with regard to the reinforcements could not be obtained due to unavailability of construction drawings.

During the survey, Schmidt Hammer was also used on the substructure of multi-span RC bridges to assess the consistency of the quality of concrete used. In some bridges, very low rebound values (in the range of 10) were observed. A majority of the bridges had a rebound value in range of 25-35, however, a few bridges had a rebound number of around, 60. In bridges with low rebound values, a significant variation was seen throughout the substructure which indicated poor quality control during construction, however, in bridges with high values of the rebound number, the quality of concrete seemed to be uniform throughout the substructure. In older bridges constructed in the early 1990‟s or before, cube strength was used for quality assurance which thus results in lower values of the cylinder strength. Typically a 3,000 psi concrete cube corresponds to around 2,400 psi cylinder strength, which is a ratio of 0.80 (Day, 1999). From the field observations of the rebound hammer values, the expected mean strength of concrete would be around 2,400 psi cylinder strength whereas field observations suggested even lower values around 75% less than 2,400 psi would make around mean plus one standard deviation ( 1 ).

3.2.3 Data Collection from Design Documents

Data related to bridges from different parts of NWFP and Punjab was also collected from various design documents. Table 3.4 lists the bridges, the year of design, and the number of traffic lanes. Table 3.5 presents the corresponding number of spans, the total span length, type of pier, height of pier, and the pier dimensions. From this data, the average height of the columns is calculated to be 20 ft-6 in (6.3 m), the average diameter is calculated to be 4 ft-3 in (1.3 m), and the average span length is calculated to be 91 ft (27.6 m). From the reinforcement data, the average size of the rebar used is 1-inch (25 mm), the average number of rebar is 35, the average diameter of confinement reinforcement is around 0.43 inch (11 mm) and the average pitch of the spiral used is 5.7 inch (145 mm) and typically 60 grade mild steel deformed bars are used. Typical cube or

26 cylinder design strengths specified for bridge substructures was 3,000 psi. In modern bridges, usually 3,000 psi cylinder strength (ASTM C873-04, 2004) is specified, however, it was observed that in the field, 3,000 psi cube strength was used in construction, especially in older bridges.

3.2.4 Summary of Parameters of Typical Bridges

From the field study and collection of data from documents, average parameters are outlined for typical concrete bridges. These parameters then formed the basis for experimental investigations undertaken in this study. The average values calculated from the field data and documents were found to be 97 ft (29.5 m) for the span, 23 ft (7.1 m) for the pier height and 51 inches (1.3 m) for the column diameter. The summary of various parameters for the concrete bridges collected from the field and from documentation is presented in Table 3.6. From the data for single solid circular concrete columns, it is seen that the average span is around 85 ft (26 m) for which the load on the columns is around 683 kips (310 tf).

3.3 Earthquake of October 8, 2005

On October 8, 2005, the Balakot-Bagh thrust fault ruptured along a length of ~100 km (Rao, Kumar, Kalpna, Tsukuda, and Ramesh, 2006). An another source report estimated it at ~70 km (Kaneda et al, 2008). The focal depth of the earthquake was shallow and reported to be 26 km (USGS, 2005; Rao, Kumar, Kalpna, Tsukuda, and Ramesh, 2006) caused severe damage in areas close to the fault. Figure 3.6 shows the location of the epicenter of Oct. 8, 2005 earthquake on the map. According to estimates more than 80,000 people lost their lives and around 4 million people were left homeless (Rao, Kumar, Kalpna, Tsukuda, & Ramesh, 2006). The fault ruptured very close to populated areas and in some cases directly beneath the cities of Balakot, Muzaffarabad and Bagh which caused extensive damage to infrastructure.

A total of 90 bridges were surveyed in the northern part of Pakistan and Kashmir, out of which ~82 bridges are located within 50 km radius and ~25 bridges within 25 km radius of the epicenter. The map in Figure 3.6 shows some of the bridges that were surveyed in this region; the electronic version of this map is accessible on the Internet via Google

27 Maps (Syed, 2008) The same map can also be opened in Google Earth and the GPS coordinates of the plotted bridges can be read. The fault rupture is also plotted on this map using the GPS coordinates taken from Kaneda et al (Kaneda et al, 2008).

3.3.1 History of Seismicity

Pakistan and its adjoining regions have a history of large seismic events, such as, the

1905 Kangra earthquake measuring a surface wave magnitude (Ms) 8.0, the 1974 Pattan earthquake of moment magnitude (Mw) 6.0 (Pakistan Metrological Department and

NORSAR Norway, 2006), and 1935 Quetta earthquake of Mw 8.1. The recent catalogue prepared by PMD (Pakistan Metrological Department and NORSAR Norway, 2006) suggests that more than 40 earthquakes of magnitude Ms ≥ 7 have occurred between the period of 1900 to 2005 in the Himalayan region that influences northern part of Pakistan and Kashmir. These facts highlight the potential of future earthquakes in this region and it is estimated that earthquakes of Mw 8.0 or larger are likely to occur in this region (Bilham and Wallace, 2006)..

Many large cities in the world are located close to active thrust faults and are exposed to serious seismic hazard. The surface ruptures of thrust faults are much less common than other fault types, and more information of such faults is needed for better understanding (Kaneda et al, 2008). This aspect and others discussed earlier indicate a serious challenge to the engineering community of Pakistan in particular and engineers across the world in general to understand the performance of bridges during seismic events like the 2005 in Pakistan and prepare for large expected earthquakes expected in the future.

3.3.2 History of Bridges

Some of the in-service bridges of the survey region in particular date back to the early twentieth century. Modern bridges constructed by various departments are gradually replacing the old typically single-lane bridges. Information collected during discussions with officials of various departments suggests that currently there are ~6,000 bridges on the national highways of Pakistan, out of which ~67% bridges were constructed until the 1980‟s. Majority of the bridges were reportedly designed using the AASHTO Standard Specifications.

28 3.3.3 Acceleration-Time History Record

This study presents the findings of the survey carried out to assess the damage to the bridges following the October 8, 2005 earthquake over a road network of ~400 km. During the survey, structural details along with GPS coordinates of various important bridges were recorded. It is worth mentioning that very few acceleration records of the October 8 earthquake are available, which makes difficult to estimate the level of ground shaking at different bridge sites. Only one time history record of October 8 earthquake is available for the survey area which was recorded at Abbottabad (Durrani, Elnashai, Hashash, Kim, and Masud, 2005). At Abbottabad, the PGA was 0.231 g (E-W) with the highest amplification ratio of about 4 for the 5% damped Elastic Response Spectrum in the range of 0.4-2.0 seconds. It also gave predictions of PGA for stiff and soft soils that are calculated using various models. The predicted ground shaking from the epicenter at 25 km is found to be in the range of 0.25-0.4 g and the PGA at 50 km is ~0.15-0.23 g. This closely agrees with the recorded PGA in Abbottabad which is ~54 km from the epicenter.

3.3.4 Defining Limit States

The structural damage recorded in the field is classified according to five Limit States as defined in Table 3.7. Each limit state is given a value so that a bridge with no damage has a value of 1 and a bridge that collapsed has a value of 0. These limit states are assessed from the field experience.

3.3.5 Classification of Bridges

The survey of bridges over ~400 km of main roads and the route are shown in Figure 3.6. The details of the route, the number of bridges on each route, and the approximate population served is provided in Table 3.1.

Fourteen bridges out of 90 were found to have experienced some form of damage following the earthquake. These 14 bridges are listed in Table 3.8, which summarizes the importance according to AASHTO (2007) , the limit state and the approximate. number of population served. The bridges surveyed are assessed for their limit states according to Table 3.7 and the results are presented in Table 3.9 while categorizing the bridges with

29 respect to the superstructure. The limit state of the bridges on the basis of substructure is presented in Table 3.10. The limit state of bridges on the basis of material of construction is provided in Table 3.11.

The 14 bridges that experienced some form of damage are summarized in Table 3.12. In this table the serial number corresponds to the bridges with same number as listed in Table 3.8. The table also lists the material of construction and the limit state of the bridge after the earthquake. Since 13 of the bridges were close to the fault (near-field), therefore the distance from the fault is also presented. It is also worth mentioning here that the use of only the epicenter distance may give a misleading assessment of the level of shaking that a bridge may experience.

3.3.6 Damage in Context of Material of Construction

Table 3.11 shows that 15 bridges that make around 17% of the total bridges surveyed contained stone masonry which is at odds with the normal practice in Pakistan. The data of the bridges collected outside the study area indicate that the current practice in Pakistan favors a reinforced concrete substructure, and post tensioned I-girders with a RC slab. A high incidence of significant damage was observed in the stone masonry bridges, irrespective of the structural form of the bridge. Damage to RC bridges was observed to be relatively less. Reinforced concrete bridges with partial use of stone masonry in some parts of the bridge experienced damage due to failure of stone masonry components. Within stone masonry bridges, those with dressed stones and uniform thickness of mortar performed relatively well. During the survey, Schmidt Hammer was also used on substructure of multi-span RC bridges to assess the consistency of the quality of concrete used. In some bridges very low rebound values (in range of 10) were observed, majority of bridges had rebound value in range of 25-35, however few bridges had rebound number around 60‟s. In bridges with low rebound values significant variation was seen throughout the substructure which indicated poor quality control during construction, however in bridges with high values of rebound number the quality of concrete seemed to be uniform throughout the substructure.

Thrust fault caused the 2005 earthquake and the level of damage was greatly influenced by the location of the bridges. On the hanging wall side, the stone masonary bridges

30 experienced, significantly more damage compared to the damage on the footwall side. However, a fair performance of the stone masonry bridges on the footwall side should not be taken as an indicator of acceptable performance.

3.3.7 Details of Damages Observed

In this section, various types of damage related to the limit states observed in the bridges and summarized in Table 3.12 are described in detail along with pictures.

3.3.7.1 Unseating / Dropdown

Figure 3.7 (a) shows the collapse of a RC bridge under construction (sr.No 10, Table 3.12) located ~8 km from Muzaffarabad City on road from Muzaffarabad to Garhi Dupata. Latter this bridge was replaced with a pre-stressed girder bridge. This was a 2- lane single span bridge ~15 m long and ~8.5 m wide and classified as critical in light of AASHTO (AASHTO, 2007). The superstructure comprised of 5 RC girders that were monolithic with the concrete deck. The substructure comprised of stone masonry abutments that were 4 to 5 m in height.The dropdown of the bridge was attributed to the failure of stone masonry abutment. The bridge site was 1.4 km from the fault on the footwall side and 21.6 km from the epicenter.

A bridge in Balakot City experienced unseating of its exterior girder along the entire length of the bridge (sr.No.3, Table 3.12), as shown in Figure 3.7 (b). It is a 3-span 2- lane continuous bridge with a total length of ~100 m and with a width of~8 m. The height of the wall piers is ~3 m. The bridge is classified as Critical. The superstructure has four variable-depth RC girders and moved ~1 m in the transverse direction and ~0.5 m in the longitudinal direction resulting in an unseating of all the girders which reduced the bridge capacity from 2-lane to 1-lane. This bridge is located 240 m on the hanging wall side of the fault and probably experienced a vertical acceleration of around 1.0 g (Durrani, Elnashai, Hashash, Kim, and Masud, 2005). The dropdown was prevented because of the girder continuity. The restoration of the bridge took ~4 months which commenced shortly after the earthquake. The restoration improved the structural capacity of the bridge by at least 25% relative to its original capacity.

3.3.7.2 Damage to Abutments and Pounding in Bridges

31 Pounding caused severe damage to Garhi Dupata RC bridge (sr.#4 Table 3.12) which is 21 km from Muzaffarabad City. This bridge is located 560 m on footwall side has 2- lanes and has ~120 m long 1-span whereas the width of the bridge is ~8 m and height of abutments is ~7 m. Abutments of this bridge have cantilever arms towards river side which span ~1/4th and the center portion comprises of an RC twin-box girder that rests on the cantilever arms of the abutment thus making it a contiguous span. Out of phase movement between the cantilevered parts of the superstructure and center box-section resulted in pounding and crushing of concrete at the expansion joint. The forces developed in the superstructure caused shear failure of a cold joint in one abutment shown in Figure 3.8 (a). It was seen that public lost its confidence to use the full 2-lanes of the bridge due to the failure that they saw at base and self-regulated the bridge to be used as 1-lane, however after few months they re-started to use the full 2-lanes without any repair. This confidence of public was noted and is denoted by  which can have a value between 0 to 1.

Pounding associated slight damage was observed in a 2-lane ~8.5 m wide bridge within the city of Muzaffarabad (sr.#12 Table 3.12). The height of pier is ~15 m. The center span is simply supported and rests on cantilever arms of the piers. Pounding at the expansion joint in the superstructure occurred probably due to asynchronous motion between the two piers.

A 2-lane slab bridge with a span ~6 m in Balakot City with stone masonry abutments also suffered moderate damage (sr.#1 Table 3.12). This bridge is classified as critical and was the closest to fault located 70 m on footwall side with height of abutments ~1.5-2.0 m.

A steel truss bridge built in 1900‟s during the British rule spans on Neelum River within the city of Muzaffarabad (sr.#13 Table 3.12) and only used for pedestrians. This 1-lane bridge rests on dressed stone masonry abutments, shown in Figure 3.8 (b). The light damage does not seem to have occurred due to the October 8 earthquake; however, it may have increased the pre-existing damage. The relatively better performance can be attributed to massive abutments that have better stability; the quality of construction was very good with finely dressed stones and uniform thickness of mortar in the bedding planes.

32 RC bridge near Besham called Kund Bridge (sr.#14 Table 3.12) on River Indus is classified as Critical. This bridge is ~140 km from the Abbottabad City on Silk Route. It is a 1-lane pre-stressed girder bridge. The bridge has one pier in river which has cantilevers on either side on which simple girders rest. On the left bank of the river an abutment has a cantilever to only one side which provides an unbalanced mass towards river. Cracks were observed in the abutment on left bank. The site inspection suggests that some minor cracks may be present earlier that most likely grew further during the October 8 earthquake.

3.3.7.3 Damages to Suspension Bridges

The hilly parts of northern Pakistan and Azad Kashmir have rivers and deep ravines. Typically 1-lane jeepable suspension bridges are provided due to their suitability. These us high strength steel suspension cables with a wooden deck, however new bridges or the ones being rehabilitated are employing steel sheet on top of the wooden deck to provide better quality of ride and avoid damage to it. RC or stone masonry towers are used in some cases RC towers are provided with stone masonry abutments and in some cases the entire tower and base are made of stone masonry. Many suspension bridges suffered damage in contrary to what was reported by (Durrani, Elnashai, Hashash, Kim, & Masud, 2005), due to use of masonry.

Figure 3.9 (a) shows a collapsed suspension bridge on Kamsar Road Muzaffarabad classified as Essential (sr.#8 Table 3.12). The bridge was located 1 km on hanging wall side and landslides caused the anchor blocks of the cables to move away which resulted in collapse of the bridge. Another failure that was observed on this site was the complete wash out of the approach roads due to landslides.

A suspension bridge in Balakot City is 150 m from fault on hanging wall side (sr.#2 Table 3.12) suffered severe damage due to sliding of the anchor blocks of the side-sway stabilizing cables. Figure 3.9 (b) shows the damaged bridge and the anchor block that slipped. The stone masonry base of the RC tower also suffered damage and the bridge was displaced in the transverse direction due to pulling force of the fallen anchor block. The approach road also failed. It is worth noting that direction of sliding of the anchor block and sliding of the 3 span RC bridge (sr.#3, Table 3.12) is also downstream. This

33 suggests that the direction of seismic forces generated in these two bridges were predominately in the downstream direction, both bridges are within 240 m on hanging wall side from the fault.

The stone masonry base of a suspension bridge at Thota (sr.#9 Table 3.12) classified as Essential suffered severe damage, see Figure 3.10 (a). The stone masonry foundation below the RC tower is ~13 m and the tower height is ~10 m. The tower lost ~1/3rd of its base as the stones gave way. The base shear caused failure of the bond between stones in the foundation. The access to bridge for vehicles was lost due to failure of the approach road.

Another suspension bridge on Garhi Dupata Road collapsed due to failure of its stone masonry tower that had height of ~7 m (sr.#5 Table 3.12). After the collapse, two main suspension cables were intact and deck was used by pedestrians. Latter an incident of fire in a small shop melted the downstream cable and caused the collapse of the deck. The failure highlights the importance of keeping flammable substances away from bridges.

3.3.7.4 Access to Bridge and other Failures

Many bridges were left unfit for service due to failure of their approach roads. A 1-lane steel truss bridge on Garhi Dupata Road (sr.#13 Table 3.12) having a span of ~50 m shown in Figure 3.10 (b) is another example in which access to bridge was lost and the bridge was rendered completely unfit for service. The main cause of failure of approach roads in most bridges was the collapse of stone masonry retaining walls provided for the approach.

A stone arch bridge on Garhi-Dupata Road was constructed using rounded dry stones filled below the bridge deck. This bridge had moderate damage (sr.#7 Table 3.12) due to failure of stone masonry that supported the dry fill rocks and the bridge was left unserviceable for all kind of vehicles. The bridge was located 980 m on footwall side.

An RC bridge in Muzaffarabad City (sr.#6 Table 3.12) has 2-lanes with height of piers ~12 m. No significant damage could be attributed to earthquake except for a horizontal crack in the pier base which may be a result of poor cold joint preparation at the time of

34 construction. Considering the fact that Muzaffarabad is now placed in Zone 4 (PGA >0.32 g) by BCP (BCP, 2007), the performance of this bridge to future earthquakes needs investigation.

3.4 Quantifying the Functionality

From the field observations of bridge performance a mathematical function is defined which is used to quantify the functionality of a bridge before and after an earthquake. This function quantifies the performance of a bridge with a dimensionless number for which section 3.10.3 of AASTHO (AASHTO, 2007) is used to spell out the performance requirement for design earthquake (DE) having 475 yrs return period and maximum credible earthquake (MCE) with 2,500 yrs return period. It is concluded that depending on the importance of a bridge, number of lanes and whether it is a DE or MCE, functionality of the bridges can be calculated and compared with threshold criteria for functionality established in light of AASHTO (AASHTO, 2007). From the performance of bridges observed after the 2005 Mw7.6 earthquake and restoration process of the damaged bridges it is realized that there are some parameters that need to be defined by the bridge owner (government) for timely restoration. The functionality function which is defined here is just not limited to structural damage but also accounts for volume of vehicular traffic and pedestrians using it. Finally recommendations are made for improving the design and construction features of bridges with the aim of minimizing such damages in future.

3.4.1 Mathematical Formulation

From field data and studies collected during visits to affected areas following the Oct. 2005 earthquake, spanning over a period of 2 yrs, some reported visits are (Naeem, et al., 2005), (EERI, 2006), (Dellow, Ali, Syed, Hussain, Khazai, & Nisar, 2006), (Syed & Shakal, 2007), functionality of the bridges is defined with the help of a mathematical function. The concept of resilience presented by (Bruneau & Reinhorn, 2007) and (Bruneau, et al., 2003) is also used to arrive at this linear form of functionality function as described in Eq.(3.1). Figure 3.11 defines various terms used and shows generalized cases of restorability or no restorability with D as delay in response time to start the

35 restorability. Functionality encompasses the overall performance of the bridge after an earthquake and AASHTO (AASHTO, 2007) is referred to spell out the minimum acceptable threshold functionality. In mathematical form functionality is:

* F()() t Fo F  R t  T (3.1)

Where,

* FFf  Rt() * (3.2) ttf 

* t t t f , Ft() is the functionality of the bridge at any time, Fo is the functionality of the bridge prior to earthquake and usually it is unity but can be less than 1, F * is the functionality of the bridge after the earthquake, Rt() is the restorability for the bridge, T is the time required for restorability, Ff is the final restored functionality of the bridge,

* t is the start time for restoration, and t f is the end of restoration time. When restoration

* of a bridge starts immediately after the earthquake without any delay, then tt o (Figure 3.11).

The functionality of the bridge before the earthquake is provided as:

LVSN F  o  o po  o  (3.3) oo LVNSD D pD D

Where   1, and these are weighing factor that spell out whether the bridge is mainly intended for pedestrians or vehicles. Here it is proposed that  and  are to be defined by the owner of the bridge, whereas 0  or 1. Lo and LD are number of lanes before the earthquake and number of lanes required by design respectively, Vo and `VD are velocities of vehicular traffic before the earthquake and design respectively and directly relate to volume of vehicular traffic the bridge can carry, N po and N pD are the capacities of the bridge to serve the number of pedestrians before the earthquake and design respectively, So and SD are the limit states of the bridge before the earthquake

36 and as per design respectively (refers to Table 3.7), o is a confidence factor related to public to use the bridge before the occurrence of earthquake and 01 o  .

After the occurrence of earthquake the functionality of the bridge F * is defined as under:

****** **LVSSSN p  FPPP      (3.4) LVSNSS o o o po o o

The conditional probability defines the functionality of the bridge in the case when some structural damage occurs. The numerator terms are values after the earthquake and denominator terms are before the earthquake. Refer Table 3.7 for the limit states.

After the restorability of the bridge the final functionality is calculated using Eq.(3.5). In some cases the value of Ff can even exceed 1.00; it would be the case when capacity of the bridge is increased beyond its original capacity. The numerator values in following equation are after restoration of the bridge is done.

LVNSf f pf f Fff      (3.5) LVNSo o o o

3.4.2 Example: Calculation of Functionality

In light of importance categories of AASHTO (AASHTO, 2007) and field observations the minimum functionality requirement is established for MCE and DE separately. The 3-span RC bridge with 2-traffic lanes in Balakot City (sr.#3 Table 3.8 and Table 3.12) is presented here in detail to calculate the functionality of this bridge and its restorability and whether it qualified the criteria. Refer to Eq.(3.1) for defining the functionality. Fo is taken unity here which holds in most of the bridges except two (sr.#10 and sr.#13 Table 3.12) as bridge at sr.#10 was under construction and bridge at sr.#13 was closed for vehicular traffic prior to earthquake. The functionality of the bridge F * is calculated

* from Eq.(3.4) for which various parameters are now discussed. SSo is the limit state of the bridge determined from Table 3.7 and for this bridge the structural damage was classified as moderate (MD) for which Table 3.7 provides a value 0.50. Due to the structural damage that resulted in reduction of traffic lanes from two to one thus gave

37 * LLo  0.50 , however the number pedestrian using the bridge was not reduced which provided NNpf o 1. The value of weighing factors  and  were taken 0.5 giving equal importance to pedestrian and vehicles, however it is suggested that these factors should be defined by the owner, changing their values would result in different functionality for the same damage state. The confidence of public represented by * was unity as public was using the bridge without any hesitation. Therefore from this data the value of F * was calculated to be 0.38. From the field data it was seen that after a delay ~D=3 months the restoration of bridge started and it took ~4 months to restore and restoration resulted in higher capacity as lateral restrainers and elastomeric bearing pads were provided. It is believed that this intervention caused a ~25% increase in structural capacity over the original i.e. SSfo1.25 thus resulted in Ff 1.13. The criterion for threshold functionality after a MCE or DE is presented in Table 3.13 for up to 3-lane bridges, which is developed in light of AASHTO (AASHTO, 2007). It should be noted

* that for calculating the functionality as given in Table 3.13 the values of LLo are established from section 3.10.3 of AASHTO (AASHTO, 2007), however the

* corresponding values of SSo are proposed based on field observations and judgment.

3.4.3 Functionality of 14 Bridges after Earthquake of 2005

The 14 bridges that suffered loss of functionality after the earthquake are assessed in light of functionality function described above, the parameters for calculating the functionality are presented in Table 3.14 in which it is assumed that     0.50,

* * VVVVVVo D o  f o 1 and   of   1.0 except bridge at sr.#4 which has

* 0.75. The parameters for Fo in Table 3.14 for all the bridges are unity except bridges at sr.#10 and sr.#13 have LLoD 0 .

From the data of Table 3.14 the functionality curves are plotted in Figure 3.12 for 4 bridges only. The functionality curves can be used to calculate a single indicator i.e. resilience factor (Bruneau & Reinhorn, 2007) for the global evaluation.

38 Based on criteria defined in Table 3.13 two minimum performance lines are shown one for DE and other for MCE. If Oct. 8, 2005 is classified as DE (475 yrs return period) then it is seen that 9 bridges out of 14 bridges that experienced damage fail the functionality criteria as defined in Table 3.13. However still 5 bridges out of 14 fail even if this earthquake is categorized as MCE. Only 5 bridges that suffered damage are qualified as fulfilling the functionality criteria both for MCE and DE.

3.4.4 History of Bridge Engineering in Pakistan

It is important to note that Seismic Hazard Map used till 2007 was based on Modified Mercalli Intensity (MMI) Scale (BCP, 1986) prepared by Geological Survey of Pakistan based on Quetta‟s instrumental Macro-Earthquake data of 1905-1979. According to this map Pakistan was divided into four zones and the survey area belonged to moderate damage area corresponding to MMI intensity of VII. On the other hand the recently published Seismic Hazard Map in BCP (BCP, 2007) is based on DE with 10% probability of exceedance in 50 yrs (475 yrs return period), and provides 5 hazard zones as shown in Figure 3.13. Many areas such as Balakot, Muzaffarabad etc. of survey area are now placed in zone of highest Seismic Hazard i.e. Zone 4 (PGA ≥ 0.32 g). It is worth noting that majority of Pakistan is now placed in Zone 2A (0.08-0.16 g) or above. Here it is important to note that according to Bridge Design Code (CPHB, 1967) the bridges need to be designed for a lateral force that is 2%-6% of the dead load of the structure since CPHB (CPHB, 1967) preceded the availability of seismic zoning maps.

As most of the bridges in Pakistan to date are mainly designed using AASHTO Standard Specification and it refers to Seismic Hazard Map of USA. This means that bridges that were designed prior to 1979 would have either used 2%-6% of weight as lateral force value or would have adopted arbitrary PGA values; and bridges designed after the publication of Seismic Hazard Map 1979-2007, which is based on MMI scale, does not give PGA values for a return period, for the design using AASHTO. This requires immediate attention to undertake exercise of evaluation and retrofitting of existing bridges in light of new Seismic Hazard Map published in BCP (BCP, 2007). Damage of 14 bridges (16% of 90 bridges surveyed) as a result of October 8, 2005 earthquake is a quite a high number. 15 bridges were damaged in Japan in 71 years, whereas only in

39 1995 Kobe earthquake 25 bridges were damaged (Kawashima & Unjoh, 1996). Since the potential of large earthquakes Mw8 or above is high for Pakistan (Bilham & Wallace, 2006) therefore damage to 16% earthquake in 2005 earthquake is alarming, as in Japan merely one earthquake after 71 years brought unexpectedly huge damage to bridges.

In order to guard against the future earthquakes it is imperative to evaluate the existing bridges in scientific manner such as current research underway. Work on bridge design specification specific to Pakistan need to start which may be the revision of 1967 Bridge Code in light of latest AASHTO (AASHTO, 2007) specifications. From the Seismic Hazard Map Figure 3.13, it is evident that huge portion of Pakistan falls in high seismicity which includes big cities like Karachi, Quetta, Gwadar, Peshawar, Abbottabad, Gujrat, Islamabad etc. Future infrastructure development and retrofitting of existing bridges requires immediate attention to define specifications, in light of new Hazard Map.

3.5 Recording of Earthquake Time Histories

During the course of this research, earthquake time histories were recorded from time to time with the help of specialized tri-axial sensors comprising of strong motion accelerometers and broadband seismometers. Although this activity was not directly part of this research but it was extremely important exercise with regard to understanding the fundamentals of sensors, data acquisition equipment and data processing which included the process of data calibration, baseline correction, filtering and applying various data processing techniques. It will be discussed in latter parts of experimental testing related to free vibration testing and forced vibration testing that the understanding and experience gained in this process was fully utilized for these tests on the bridge columns.

An important recording here is discussed which was an aftershock after Oct. 8, 2005 earthquake. The aftershock happened on Oct. 28, 2005 and was measured to be Mw5.3 and reported by USGS as well. The depth of hypocenter was 10 km thus making it shallow. This aftershock was simultaneously recorded at Muzaffarabad and Abbottabad. The distance of epicenter was 43 km from Muzaffarabad and 57 km from Abbottabad. The recorded and processed acceleration time histories for Muzaffarabad had maximum vertical component of 1.47% g and is shown in Figure 3.14, the maximum for North-

40 South component was 2.80% g and is shown in Figure 3.15 and the maximum for East- West component was 1.43% and is shown in Figure 3.16. The same aftershock recorded at Abbottabad had vertical component of 0.44% g and is shown in Figure 3.17, the North- South component was 0.69% g and is shown in Figure 3.18 and the East-West component was 0.92% and is shown in Figure 3.19 (Syed, et al., 2006).

For the same aftershock broadband seismometers were also used, the seismometer in Muzaffarabad clipped however the seismometer of Abbottabad did recorded the event. The corrected and processed velocity time history for the vertical component had maximum of 0.11 in/sec (2.8 mm/sec) and is shown in Figure 3.20, the maximum velocity for North-South component was 0.22 in/sec (5.6 mm/sec) shown in Figure 3.21 and for East-West the maximum velocity was 0.28 in/sec (7.1 mm/sec) and is shown in Figure 3.22. (Syed, et al., 2006)

From these records the 5% damped Acceleration Response Spectra (ARS) is plotted for North-South component of Muzaffarabad record and is shown in Figure 3.23, the ARS for East-West component for Abbottabad is shown in Figure 3.24. The maximum amplification for Muzaffarabad record is seen to be 6.4 times the ground acceleration whereas for Abbottabad the maximum amplification of 3.3 is seen. The results are tabulated in Table 3.15.

3.6 Summary and Conclusions

Based on the survey of bridges carried out after the Mw7.6 earthquake of October 8, 2005, following recommendations are made:

1. Stone masonry structures should be avoided in regions Zone 2A and above. Existing bridges in this zone and above should be evaluated for seismic performance and retrofitted if necessary. Bridges should be provided with ductile lateral restraints.

2. An inspection program needs to be put in place with inspection at suitable intervals and inventory of bridges should be prepared. Initially, those bridges that are considered important may be inventoried. For long term monitoring of important bridges, non-destructive tests and study of dynamic characteristics of these bridges should be carried out through field tests for comparison with results after a seismic event.

41 3. Commercial activities requiring use of flammable products should be prohibited in the vicinity of bridges and quality of construction works should be improved.

4. Bridges close to the fault if repaired should be designed to avoid loss of functionality in future earthquakes. New bridges that are critical should be located sufficiently away from the fault so that fault displacement does not affect the bridge.

5. The threshold criteria for functionality as described in Table 8 need to be redefined in case owner of the bridge fixes new weighing factors for vehicular and pedestrian traffic. Bridge owner needs to define acceptable delay and restorability time for MCE and DE.

42 FIGURES

Figure 3.1: Form for field survey of bridges, page 1.

Figure 3.2: Form for field survey of bridges, page 2.

Figure 3.3: Form for field survey of bridges, page 3.

Figure 3.4: Form for field survey of bridges, page 4.

Figure 3.5: Form for field survey of bridges, page 5.

Figure 3.6: Survey area, epicenter & fault of 2005 earthquake & bridges near fault.

Figure 3.7: (a) Drop-down of girder bridge due to failure of stone masonry abutments (b) Unseating of the entire 3-span continuous girder bridge which is 240 m on footwall side of thrust fault.

Figure 3.8: (a) Shear failure of abutment at cold joint of an RC bridge (b) Damage to stone masonry abutment of a truss bridge located 2 km on footwall.

Figure 3.9: (a) Collapse of a suspension bridge over River Neelum due to landslides (b) Slippage of side-sway cable anchor block & failure of approach road to bridge.

Figure 3.10: (a) Severe damage to the stone masonry base of tower in a suspension bridge (b) Collapse of stone masonry retaining wall that resulted in failure of approach road.

F(t) Improving functional capacity Permanent loss of beyond original state functional capacity

to Fo

(Ff ,tf ) AASHTO DE Threshold R(t ) AASHTO MCE (F*,t*)

(F*,t*) Threshold Functionalityof bridge

D t Time (days) Figure 3.11: Functionality of bridges in generalized form showing different possible scenarios.

50 #11 : Truss Bridge on Garhi-Dupata Rd. #3 : 3-span RC Bridge Balakot City 1.50 1.50 1.25 1.25 1.00 1.00 0.75 0.75

0.50 0.50 Funtionality Funtionality 0.25 0.25 0.00 0.00 -200 0 200 400 600 800 1000 1200 -200 0 200 400 600 800 1000 1200 MCE & DE = Pass Time (days) MCE = Pass; DE = Fail Time (days)

Bridge Perform. Baseline Perform. Bridge Perform. Baseline Perform.

AASHTO DE AASHTO MCE AASHTO DE AASHTO MCE

#7 : Stone arch bridge Garhi-Dupata Rd. #9 : Sus. Bridge Thota 1.50 1.50 1.25 1.25 1.00 1.00 0.75 0.75

0.50 0.50 Funtionality Funtionality 0.25 0.25 0.00 0.00 -200 0 200 400 600 800 1000 1200 -200 0 200 400 600 800 1000 1200 MCE & DE = Fail Time (days) Time (days) MCE = Pass; DE = Fail Bridge Perform. Baseline Perform. Bridge Perform. Baseline Perform. AASHTO DE AASHTO MCE AASHTO DE AASHTO MCE

Figure 3.12: Functionality of 4 bridges after the Mw7.6 earthquake of 2005.

Figure 3.13: New Seismic Hazard Map for Pakistan based on PGA for 475 yrs return period.

Figure 3.14: Acceleration Time history of vertical component of aftershock recorded at Muzaffarabad, Oct. 28, 2005.

Figure 3.15: Acceleration Time history of North-South component of aftershock recorded at Muzaffarabad, Oct. 28, 2005.

Figure 3.16: Acceleration Time history of East-West component of aftershock recorded at Muzaffarabad, Oct. 28, 2005.

Figure 3.17: Acceleration Time history of Vertical component of aftershock recorded at Abbottabad, Oct. 28, 2005.

Figure 3.18: Acceleration Time history of North-South component of aftershock recorded at Abbottabad, Oct. 28, 2005.

Figure 3.19: Acceleration Time history of East-West component of aftershock recorded at Abbottabad, Oct. 28, 2005.

Figure 3.20: Velocity Time history of vertical component of aftershock recorded at Abbottabad, Oct. 28, 2005.

Figure 3.21: Velocity Time history of North-South component of aftershock recorded at Abbottabad, Oct. 28, 2005.

Figure 3.22: Velocity Time history of East-West component of aftershock recorded at Abbottabad, Oct. 28, 2005.

Figure 3.23: Acceleration Response Spectra for 5% damping due to North-South component of aftershock recorded at Muzaffarabad, Oct. 28, 2005.

Figure 3.24: Acceleration Response Spectra for 5% damping due to East-West component of aftershock recorded at Abbottabad, Oct. 28, 2005.

57 TABLES

Table 3.1: Routes, number of bridges surveyed and population served

Number of Bridges* Population ID Route/Location Name Single MultiSpan Served Span (thousand) 1 Havalian-Abbottabad- 13 2 >200 Mansehra 2 Mansehra-Battagram- 26 11 >150 Bisham 3 Mansehra-Attar Shisha- 1 2 >50 Garhi Habibullah- Muzaffarabad 4 Attar Shisha-Balakot 3 1 >50 5 Muzaffarabad-Kohala 13 4 >150 6 Muzaffarabad-Garhi 7 1 >200 Dupata 7 Muzaffarabad City 3 3 >150 Sub-total 66 24 Total 90 *Actual number of bridges on the routes listed may be more than the number presented; minor bridges were not surveyed.

Table 3.2: Route and multi-span RC bridges of survey area

Year No of Route S.No Bridge Built Traffic ID Lanes 1 Ayub Bridge 1 1978 2 2 Qaid-e-Azam Bridge 7 ~1970‟s 2 3 Allama Iqbal Bridge 7 ~2000 2 4 Chehla Bandi 7 1979 2 Bridge 5 Kohala Bridge 5 ~1990‟s 2 6 UN* 5 - 2 7 UN 5 - 2 8 UN 5 - 2 9 UN 3 2004 2 10 Hassari Bridge 3 ~1995 2 11 Ghandian Bridge 2 - 2 12 Acharian Bridge 2 1974 2 13 Kund Bridge 2 1982 1 14 Balakot City Bridge 4 ~1970‟s 2 * UN= Unknown Name

58 Table 3.3: Details of multi-span RC bridges of survey area

# of Total Pier Height Dimensions S.#α Spans Length TypeΨ 1 8 908 ft Solid 16 ft 3.51 ft (277 m) Circular (4.9 m) (1.07 m) 2 4 404 ft Solid ~26 ft - (123 m) ~Square (8.0 m) 3 3 328 ft Hollow 499 ft 28 x 7 ft (100 m) Rectangular (15.2 m) (8.5 x 2.0 m) 4 3 407 m Solid Wall 39 ft 26 x 5 ft (124 m) (12.0 m) (8.0 x 1.5 m) 5 3 ~316 ft Hollow ~31 ft ~26 x 8 ft (110 m) Rectangular (9.5 m) (8.0 x 2.5 m) 6 2 262 ft Solid 36 ft 5 ft (80 m) Circular (11.0 m) (1.5 m) 7 2 131 ft Solid 18 ft 5 ft (40 m) Circular (5.5 m) (1.6 m) 8 2 144 ft Solid 29 ft 5 ft (44 m) Circular (8.9 m) (1.5 m) 9 3 325 ft Solid 21 ft 3 ft (99 m) Circular (6.3 m) (1.0 m) 10 2 246 ft Solid 21 - (75 m) Circular (6.4 m) 11 3 394 Solid 31 ft 4 ft (120 m) Circular (9.5 m) (1.2 m) 12 3 305 ft Solid ~11 ft 4 ft (93 m) Circular (3.5 m) (1.2 m) 13 4 502 Hollow ~21 ft ~13 x 8 ft (156 m) Rectangular (6.5 m) (4.0 m x 2.5 m) 14 3 ~328 ft Wall ~10 ft ~26 x 7 ft (100 m) (3.0 m) (8.0 x 2.0 m) α These sr.# correspond to bridges in Table 3.2. Ψ Based on observations and judgment.

59 Table 3.4: Multi-span RC bridges, design year and number of traffic lanes

Year # of Traffic S.# Bridge Designed Lanes 1 Khaki Bridge Manshera 2004 2 2 Kanair Kass Bridge Abbottabad 1999 2 3 Bridge over Kurrum River 1999 1 4 Bridge over Koremung Alpuri Nullah 1999 1 5 Lora-Rai Road Bridge 1999 2 6 Bridge on Ara Bagulani Gandi Umar Khan Road 2000 2 7 Bridge on Swabi-Topi-Darband Road 1999 2 8 Bridge on Kabul River at Misribanda 2002 1 9 Bridge on Kabul River at Pirsabak 2002 1 10 Bridge on Kohat Khushalgarh Road 2002 2 11 Subhan Bridge at Barikab 1999 1 12 Bridge on Haro River on Lora Nagri Tutial Road 1998 2 13 Bridge on Haro River on Lora Swargali Road - 2 14 Bridge on Rustam-Pirsai Road 1998 1 15 Bridge on Rustam-Baroch Road (km 0+573) 1998 2 16 Bridge on Rustam-Baroch Road (km 0+650) 1998 2 17 Bridge on Hamzakot-Parmulai 1998 1 18 Bridge on Sunderwal-Shahi Road 1998 2 19 Bridge on Thandiani-Pattan Khurd Road 1999 2 20 Gumrakhas Bridge 2006 2 21 Kund Mor Bridge 2006 2 22 Chitral bridge LRTP 2006 2 23 FWO-CDA (Gumrah Kas) 2004 2 24 Jerma Bridge (N-55) 2003 2 25 Bridge on N-50 2003 2 26 Korang Bridge 2005 2 27 Bridge on N Sutlej 2002 2 28 Pusha Bridge (N-55) 2003 2 29 Rainee Canal 2004 2 30 Vedora Bridge (N-70) 2004 2

60 Table 3.5: Details of multi-span RC bridges taken from design documents

# of Total Pier Height Dimensions S.#γ Spans Length Type 1 2 197 ft Solid 15 ft 5 ft (60 m) Circular (4.6 m) (1.5 m) 2 2 197 ft Solid 15 ft 5 ft (60 m) Circular (4.7 m) (1.5 m) 3 2 194 ft Solid 8.9 ft 4 ft (59 m) Circular (2.7 m) (1.2 m) 4 2 236 Hollow 51 ft 13 x 10 ft (72 m) Rectangular (15.5 m) (4.0 x 3.0 m) 5 4 289 ft Solid 14 ft 5 ft (88 m) Circular (4.2 m) (1.5 m) 6 2 158 Solid 15.4 ft 5 ft (48 m) Circular (4.7 m) (1.5 m) 7 17 2,812 ft Hollow 126 ft 29 x 29 ft (857 m) Rectangular (38.5 m) (8.8 x 8.8 m) 8 9 873 ft Solid 13 ft 5 ft (266 m) Circular (4.0 m) (1.5 m) 9 9 873 ft Solid 13 ft 5 ft (266 m) Circular (4.0 m) (1.5 m) 10 2 118 ft Solid 5 ft 4 ft (36 m) Circular (1.4 m) (1.2 m) 11 2 135 ft Solid 14 ft 5 ft (41 m) Circular (4.4 m) (1.5 m) 12 5 361 ft Solid 9 ft 5 ft (110 m) Circular (2.7 m) (1.5 m) 13 3 233 ft Solid 16 ft 3 ft (71 m) Circular (4.8 m) (1.0 m) 14 2 194 ft Solid 7 ft 4 ft (59 m) Circular (2.0 m) (1.2 m) 15 2 98 Solid 12 ft 3 ft (30 m) Circular (3.7 m) (0.8 m) 16 4 308 ft Solid 6 ft 5 ft (94 m) Circular (1.9 m) (1.5 m) 17 2 194 ft Solid 12 ft 4 ft (59 m) Circular (3.5 m) (1.2 m) 18 3 203 ft Solid 12 ft 5 ft (62 m) Circular (3.5 m) (1.5 m) 19 2 154 ft Solid 31 ft 3 ft (47 m) Circular (9.4 m) (1.0 m) 20 2 151 ft Solid 20 ft 4 ft (46 m) Circular (6.0 m) (1.2 m) 21 2 151 ft Hollow 26 ft 5 ft (46 m) Circular (7.8 m) (1.4 m)

61 22 2 223 ft Hollow 41 ft 5 ft (68 m) Circular (12.5 m) (1.5 m) 23 4 394 ft Solid 23 ft 4 ft (120 m) Circular (7.1 m) (1.2 m) 24 4 459 ft Solid 21 ft 4 ft (140 m) Circular (6.5 m) (1.2 m) 25 4 272 ft Solid 7 ft 3 ft (83 m) Circular (2.0 m) (0.8 m) 26 5 472 ft Solid 20 ft 4 ft (144 m) Circular (6.0 m) (1.2 m) 27 12 1,919 ft Solid 16 ft 7 ft (585) Circular (5.0 m) (2.0 m) 28 2 177 ft Solid 26 ft 4 ft (54 m) Circular (8.0 m) (1.2 m) 29 3 276 ft Solid 16 ft 3 ft (84 m) Circular (5.0 m) (1.0 m) 30 5 394 ft Solid 7 ft 3 ft (120 m) Circular (2.0 m) (1.0 m) γ These sr.# correspond to bridges in Table 3.4.

Table 3.6: Average parameters of concrete bridges from field and documentation

Parameter Data from Average S.# Field Data Documents 1 Span 103 ft (31.4 m) 91 ft (27.6 m) 97 ft (29.5 m) 2 Number of lanes 1.9  2 1.8 2 2 3 Column height 26.2 ft (7.98 m) 20.5 ft (6.3 m) 23 ft (7.1 m) 4 Column diameter 51 in (1.3 m) 51 in (1.3 m) 51 in (1.3 m) 5 Rebar size - 1 in (25 mm) 1 in (25 mm) 6 Rebar ratio - 1.37% 1.37% 7 Spiral bar size for - 0.43 in (11 mm) 0.43 in (11 mm) confinement 8 Pitch of spiral - 5.7 in (145 mm) 5.7 in (145 mm) 9 Grade - 60 ksi (414 MPa) 60 ksi (414 MPa) 10 Concrete cylinder 2,400 psi ( ) 3,000 psi 2,400 psi strength 1,800 psi ( 1 ) (cylinder-modern) 1,800 psi (cube-old) 11 Load on column (363 tf) (327 tf) 760 kips (345 tf)

62 Table 3.7: Limit States related to structural damage

Code Damage Reusability Reparability Restorability Value ND No damage Yes No need No need 1.0 LD Slightly damaged Yes Yes Completely 0.75 MD Moderately Yes Difficult Yes completely 0.50 damaged to original state SD Severely damaged Partial Difficult Not to original 0.25 state CO Collapse No No No 0.0

Table 3.8: Name of the bridges that suffered damage and population they served

ASSHTO Limit Population served S.# Bridge Name Classification State (000’s) 1 Slab bridge Balakot City Critical MD >200 2 Suspension bridge Balakot City Other SD Mainly pedestrians 3 3-span bridge Balakot City Critical MD >300 4 Garhi Dupata City Bridge Critical SD >250 5 Suspension bridge Maghoi Essential CO >5 6 Chela Bandi Bridge Essential LD >50 7 Arch Bridge Garhi-Dupta Road Critical MD >300 8 Suspension bridge Kamsar Essential CO >5 Road 9 Suspension bridge Thota Essential SD >5 10 Bridge on Garhi Dupata Road Critical CO >300 11 Truss Bridge Garhi Dupata Essential LD >5 Road 12 Allama Iqbal Bridge Essential LD >75 13 Truss bridge in Muzaffarabad Other LD Pedestrians only City 14 Kund Bridge Besham Critical LD >10

Table 3.9: Limit State of bridges for classification based on the type of superstructure

Limit I Girder (PSa) / T Box Truss Suspension Arch Total State (RCb) Girder / Slab Girder ND 60 3 2 8 3 76 LD 1 2 2 - - 5 MD 1 1 - 0 1 3 SD - 1 - 2 - 3 CO 1 - - 2 - 3 Total 63 7 4 12 4 90

63 Table 3.10: Limit State of bridges for classification based on the type of substructure

Limit Single Multi Abutments (single span) / Wall Total State Column Column tower base ND 1 - - 75 76 LD 3 - - 2 5 MD - - 2 1 3 SD - - - 3 3 CO - - - 3 3 Total 4 - 2 84 90

Table 3.11: Limit State of bridges for classification based on material of construction

Limit Reinforced Concrete Stone Masonry & mix of Stone Others Total State (RC) Masonry & RC (SM&RC) ND 13 7 56 76 LD 4 1 - 5 MD 1 2 - 3 SD 1 2 - 3 CO - 3 - 3 Total 19 15 56 90

Table 3.12: Key features of bridges that experienced variety of structural damage

Distance from # of Limit ASSHTO S.# Materialα Locationβ Fault Epicenter Traffic State Classification Lanes 1 SM MD FW 70 m 26.2 km 2 Critical 2 SM SD HW 150 m 25.9 km 1 Other 3 RC MD HW 240 m 25.8 km 2 Critical 4 RC SD FW 560 m 28.9 km 2 Critical 5 SM CO FW 760 m 27.3 km 1 Essential 6 RC LD FW 870 m 19.5 km 2 Essential 7 SM MD FW 980 m 23.3 km 2 Critical 8 SM CO HW 1.0 km 17.5 km 1 Essential 9 SM SD FW 1.0 km 25.8 km 1 Essential 10 SM CO FW 1.4 km 21.6 km 2 Critical 11 SM LD FW 1.9 km 21.0 km 1 Essential 12 RC LD FW 2.0 km 20.6 km 2 Essential 13 SM LD FW 2.0 km 20.6 km 1 Other 14 RC LD Far field NA 83.5 km 1 Critical α SM = Stone masonry and RC = Reinforced concrete; β FW=footwall and HW=Hanging wall

64 Table 3.13: Criteria for minimum functionality requirement after a MCE or DE in light of AASHTO

AASHTO DE MCE Bridge Lanes F * LL* SS* o o DE MCE 1 1.00 0.75 1.00 0.50 0.75 0.50 Critical 2 1.00 0.75 0.50 0.50 0.75 0.38 3 1.00 0.75 0.33 0.50 0.75 0.33 1 1.00 0.50 0 0.25 0.50 0.13 Essential 2 0.50 0.50 0 0.25 0.38 0.13 3 0.33 0.50 0 0.25 0.33 0.13 1 1.00 0.25 0 0.25 0.25 0.13 Others 2 0.50 0.25 0 0.25 0.19 0.13 3 0.33 0.25 0 0.25 0.17 0.13

Table 3.14: Parameters for 14 bridges to calculate their functionality after the earthquake of 2005

* Fo parameters F parameters Ff parameters L N S * * * S.# o po o L N p S L f N pf S f L S D N pD D L N S L N S o po o o o o 1 1.00 1.00 1.00 0.50 1.00 1.00 1.00 1.00 1.00 2 1.00 1.00 1.00 0 1.00 0.50 1.00 1.00 0.50 3 1.00 1.00 1.00 0.50 1.00 0.50 1.00 1.00 1.25 4 1.00 1.00 1.00 1.00 1.00 0.25 1.00 1.00 0.25 5 1.00 1.00 1.00 0 0 0 0 0 0 6 1.00 1.00 1.00 1.00 1.00 0.75 1.00 1.00 0.75 7 1.00 1.00 1.00 0 1.00 0.50 1.00 1.00 1.00 8 1.00 1.00 1.00 0 0 0 0 0 0 9 1.00 1.00 1.00 0 1.00 0.25 1.00 1.00 0.75 10 0 1.00 1.00 0 0 0 0 0 0 11 1.00 1.00 1.00 0 1.00 1.00 1.00 1.00 1.00 12 1.00 1.00 1.00 1.00 1.00 0.75 1.00 1.00 0.75 13 0 1.00 1.00 0 1.00 0.75 1.00 1.00 0.75 14 1.00 1.00 1.00 1.00 1.00 0.75 1.00 1.00 0.75

65 Table 3.15: Summary of ARS, ERS and aftershock time history recorded simultaneously at Muzaffarabad and Abbottabad.

66 CHAPTER 4 MODELING AND EXPERIMENTAL WORK

4.1 Introduction

The RC bridge pier selected for this study was a single column solid circular section. A comprehensive field survey and gathering of bridge drawings and specifications was conducted. Data gathered from the survey formed the basis for this research. The details of the survey are described in the previous chapter. It is evident from the field data that material of construction are generally poor and design practice is not uniform due to the absence of an indigenous bridge design code. The poor strength of aging infrastructure remains an issue in developed world.

In this chapter various issues relating to experimental testing are described. The first part of this chapter deals with the study of lab equipment. The study of equipment involves determining correct procedures of use, fixing threshold parameters in regard to maximum capabilities of equipment and calibration. This exercise was done by testing two columns.

The second part of this chapter describes the formulation of testing strategy that was worked out on the basis of experience gained in testing two columns.

Third part of the chapter deals with similitude analysis to work out scale factors for finalizing various parameters in scaled models. On the basis of similitude analysis the scale factors are finalized while considering limitation of lab and equipment, this is presented in the fourth part of this chapter.

Fifth and sixth part of this chapter describes the mass and materials respectively. Mass requirements are described in detail to account for special needs of the free vibration testing. Materials are the most important constituent of the test columns therefore various tests that are performed in lab are described here in context of ASTM standards.

The final test setup for quasi-static testing in light of finalized scale factors and test protocol is described in last part of this chapter.

4.2 Study of Lab Equipment

67 The laboratories of Civil Engineering Department have equipment that can be used for Quasi-Static Monotonic Testing, Quasi-Static Cyclic Testing and Shake Table Dynamic Testing. It was felt necessary to first develop understanding of the equipment that will be used along with the objective to calibrate various gadgets. This study involved testing the trial bridge columns by using various state-of-the-art equipments that were housed in various laboratories of the NWFP UET including the Earthquake Engineering Center. The study also helped in understanding the limitation of various testing equipment and their influence on the boundary conditions. Byproduct of this exercise was thorough understanding of the instrumentation process and data processing of the experimental outcome.

Two main facilities that were available and were studied included “Structural Testing Frame” housed in Structural Laboratory and Shake Table R-141 (Seismic Simulator) installed in the Earthquake Engineering Center. In order to effectively study the equipment it was decided to prepare two approximately scaled models of bridge columns and test one on each of the equipment. The aim of this methodology was to have two prong benefits, one to understand the use of equipment and second was to firm up for the fabrication of test models for actual study. Both the equipments and fabrication of the two trial specimens is discussed in detail in the following paragraphs.

4.2.1 Quasi-Static Cyclic Testing

The Structural Testing Frame, shown in Figure 4.1 consists of space frame that has adjustable girders that can be used to adjust the position of the loading jacks or the position of test object within the frame. The frame has four linear hydraulic jacks for vertical and horizontal loading. Two hydraulic jacks are of 25 metric ton capacity and the other two are of 50 metric tons capacity. All the four jacks have loading head that can be used for pushing only, which in its original form provides only the monotonic testing capability. The specifications of the hydraulic jacks are presented in Table 4.1. This facility has a manually operated Hydraulic Power Supply that can independently control the four jacks through a manifold.

It was decided to fabricate a 1:6 scale model of RC bridge column that can be used to study the working of the quasi-static cyclic testing system. The geometric and material

68 properties of this test column are presented in Table 4.2. The process of testing the column also gave an opportunity to carry out instrumentation that was helpful for in- depth understanding of the intricacies behind installation of various transducers, gages, and load cells etc. along with providing opportunity to process the voluminous data obtained from the cyclic testing.

4.2.1.1 Testing Methodology

In order to carry out the quasi-static cyclic testing on the 1:6 scale model column, first step was to plan a strategy for testing. Major issues related to testing were simulation of dead mass on column top and application of lateral force for cyclic testing. It was decided that the effect of dead mass on column top will be simulated by using a vertical jack, while lateral loading was applied using two horizontal jacks installed on either side of the column in the direction of cyclic loading.

4.2.1.2 Fabrication of Trial Column

RC column of scale factor l = 6 was fabricated, shown in Figure 4.2. The scaled trial column did not strictly meet the requirements of similitude, as the primary purpose of this column was not to obtain scientific data but to familiarize with the process of testing and to study the equipment. A top beam was fabricated on the column top that was used to apply the load from the vertical jack and also to help in application of lateral load from the horizontal jacks. The size of this beam was fixed considering the limitations of the jacks and anticipated lateral drift.

4.2.1.3 Similitude Requirements

The trial bridge column was reinforced concrete which was geometrically scaled to 16th of the prototype column. For fulfilling the requirements of a complete model (also called true model) it is necessary to correspondingly scale various material properties (Harris & Sabnis, 1999). For this trial column it was decided to keep the model and prototype material properties same, which made it a simple model, because steel reinforcement is the main element and scaling of its mechanical properties was not possible. Also, it is recommended to use the same material properties when the model is to be tested in its inelastic range (Reinhorn A. M., 2008; Bracci, 1992).

69 4.2.1.4 Boundary Conditions

It was decided to use hydraulic jack installed in vertical direction to apply the required dead load on the column top. The arrangement allowed using a vertical jack that was fixed at the base. To avoid the restraint due to friction at the column top between the head of jack and top surface of column, six bi-directional rollers were used, each having 2 inch diameter, three in the longitudinal direction and the other three in transverse direction, as shown in Figure 4.3.

4.2.1.5 Equipment Setup

In order to carry out the quasi-static cyclic testing on the 1:6 scale model column, first step was to re-arrange various girders that included precisely positioning one vertical and two horizontal jacks. As the heads of the jacks did not had an arrangement for cyclic testing, so two jacks were used to push from each side. The arranged horizontal jacks are shown in Figure 4.4.

Displacement transducers were used to record the displacement of column in the plane of application of load. The lateral load was recorded from the load cells of the jacks. The control of vertical load jack was kept constant throughout the test in an attempt to keep the load constant. Electronic data logger unit was used for recording the test data.

4.2.1.6 Calibration of Equipment

Before the start of test, a process of calibration was carried out. This included calibration of load cells of hydraulic jacks, displacement transducers and speed of the hydraulic jack. The load cells were calibrated using reference load cell used for calibration only, shown in Figure 4.5. Displacement transducers were calibrated in a process which involved simultaneous data recording from all transducers that included reference displacement transducers, shown in Figure 4.6.

The hydraulic jack has control valves that allow the adjustment of pressure which in turn sets the maximum force that can be applied at particular pressure. However, the speed of jack is also dependant on the pressure that is set by the pressure valves. Since the quasi- static testing is to be applied at certain predefined speed (frequency) and yet the column under test would need to be subjected to the lateral force, therefore careful study of the

70 jack and its hydraulic power supply was required. The speed of the hydraulic jacks was calibrated by recording the displacement of the jack along with time at a particular pressure of the hydraulic oil. The pressure of oil was varied and the process was repeated until sufficient data sets were obtained. From this data settings of the hydraulic power supply were derived that gave the required force and speed of the jack.

4.2.1.7 Test Protocol

The column was tested under cyclic load. The time period of cycle was taken to be 150 seconds i.e. 0.0067 Hz. The number of cycles per drift was kept three and the scheme of cyclic loading is shown in Figure 4.7. It was decided to keep the vertical load as 8.1 metric tons corresponding to a typical two-lane I-girder bridge system having a span of 25 meters. A hysteresis curve of 3% drift is shown in Figure 4.8. This figure shows that at 3% drift level stiffening is occurring at the peak load which is the stiffening due to boundary conditions that are not reflecting the actual case in which P  results in reducing the stiffness at the peak load in high drift cycles. The total number of cycles experienced by the column at failure was 37 on 4.0% drift.

The shape of hysteresis such as shown in Figure 4.8 was unusual as it shows an in-cycle stiffness increase at the end of quarter and three-quarter cycles, and made the end of curve kink-upward and kink-downward respectively. This unusual stiffening occurred due to fixed jack at base that causes P moment in opposite direction to the direction of applied lateral load. Thus with increase in drift the moment also increases which is acting opposite to moment cased by lateral load thereby causing stiffening effect.

 MFHPnet     (4.1)

 Where: M net is the resultant moment acting on column base when moment caused by lateral and vertical load is counter-acting each other;

F is the lateral load applied by the hydraulic jack;

H is height of column from its base to point of application of lateral load;

P is the vertical load supported by the column;

71  is the lateral deflection of column measured in horizontal plane at point of application of lateral load.

The moment given by Eq.(4.1) is an unusual case that was caused by fix base jack and is contrary to case of usual bridge columns in which moment due to lateral load and moment due to P  act in same direction as provided in Eq. (4.2).

MFHPnet     (4.2)

Where: Mnet is the resultant moment acting on column base when moment caused by lateral and vertical load is acting in the same direction.

Quasi-static cyclic testing is relatively a slow test in which participation of mass to produce inertial effects is negligible. Also the velocity is relatively slow and effect of damping becomes negligible. The equation of motion is provided below:

mu cu  ku  F() t (4.3)

Where: m is the mass supported on column;

u is the acceleration experienced by the mass;

c is the damping offered by the column system;

u is the velocity of the mass;

k is the stiffness of the RC column under test;

u is the lateral displacement of the column measure in horizontal direction at line of application of lateral force;

is the damping offered by the column system;

Ft() is the lateral force applied to column mass.

mu0; cu  0;  ku  F ( t ) (4.4)

Therefore the resistive force offered by the column under test at any time is provided by the equation given below:

72 F() t ku (4.5)

Since the testing is carried out beyond the elastic limits therefore the above Equation (4.5) becomes:

F() t ki u (4.6)

Where: ki is the stiffness of the inelastic RC column under test.

Since in the quasi-static testing the force applied to the test column is measured using the load cell and corresponding displacement is measured with a displacement transducer therefore the only unknown term in Eq.(4.6) is the stiffness which can be calculated at any position.

4.2.1.8 Conclusion on Limitations

The process of equipment study through testing a trial column gave invaluable experience. During the process various important facts were realized that are summarized below:

1. It is not possible to keep the vertical load constant in a manual hydraulic power supply system of jacks. The load decreased with application of lateral drift as the beam on column top rotated, thereby resulting in reduction of vertical load.

2. Since the vertical jack was fixed at the base that resulted in P  moment which is contrary to usual bridge column condition, therefore this produced a stiffening effect shown in the hysteresis curves of the column, which was considered unsatisfactory. This problem could be overcome if the jack moves along with column top which means that actuator base should not have been fixed. It was concluded that the boundary conditions in this case were not satisfactory due to use of jack with fixed base. Therefore this methodology of testing was rejected and it was decided to cast dead mass on top of test columns to simulate true boundary conditions.

3. Absence of overhead crane made the movement of objects very difficult, slowed the pace of work and posed severe constraints in terms of fabricating a large test column. It was decided to do the actual quasi-static cyclic testing of columns in

73 Earthquake Engineering Center as over head crane and strong wall is available. It would be possible to prepare bigger models due to larger space.

4. It was decided that the quasi-static monotonic testing facility would be upgraded to quasi-static cyclic testing facility after necessary additions to hydraulic actuators so that only one jack is needed to carry out the cyclic testing.

4.2.2 Dynamic Testing on Shake Table

The Seismic Simulator R141 (also called Shake Table) a state-of-the-art facility housed in Earthquake Engineering Center, is a single degree of freedom system, with specifications provided in Table 4.3. It was decided to study this equipment by testing a trial bridge column on the table. The testing of another column on the table helped in familiarization with the table that helped in ascertaining the limitation of the table.

4.2.2.1 Testing Methodology

For the shake table testing it was decided to fabricate a trial column with scale factor for length, l 10 . The column had a dead mass on top fabricated along with the column. The trial column was to be anchored down with the table top and subjected to a scaled time history of a seismic event. It was decided to install accelerometers at the top of the column to record the response amplification, an accelerometer at column base to record the actual input motion imparted to column base. The transfer function thus can be calculated between drive motion of table and response at column top.

4.2.2.2 Fabrication of Trial Column

The 1:10 RC column was fabricated, shown in Figure 4.9 the dynamic testing of which helped in understating the use of equipment, instrumentation, data acquisition, and data processing. In this trial column the similitude requirements were not implemented in strict manner, as the primary purpose of this trial column was not to obtain scientific data but was to familiarize with the process of testing and to study the equipment. Geometric and material properties of the trial column are presented in Table 4.4. The dead mass on trial column top represents a typical single lane Pakistani bridge of 18 meter span.

4.2.2.3 Similitude Requirements

74 Since the trial column was simple model therefore various similitude requirements that were considered are discussed here. The scale factor in this case was taken to be 10.0. Various approximate similitude requirements for the simple model are shown in Table 4.5.

4.2.2.4 Test Protocol

It was decided to use the acceleration time history of October 8, 2005 Kashmir earthquake measuring 7.6Mw recorded at Abbottabad. The time history was scaled before it was run on the shake table. The time of the acceleration history was scaled down by a factor of l and the acceleration was scaled up by a factor of l , whereas the scale factor in this case was l 10 . Various similitude requirements for the simple model are shown in Table 4.5.

The trial column was mounted on the table top and Abbottabad time history was run. Three piezoelectric accelerometers were installed, one at column base, one on column top in direction of shake table motion and one on column top in transverse direction to shake table motion. It was decided to run various percentages of acceleration time history of Abbottabad in ascending order. The sequence was 5%, 10%, 25%, 50%, 75% and 100%. It is important to note that this methodology of testing provided input energy in various steps of ascending order and the damage experienced by the trial column was accumulated damage from various runs. The damage after the last run is shown in Figure 4.10. The column base was accelerated to around 2.3 g in 100% run and the top mass experienced an acceleration of 3.0 g. The acceleration time history response of top mass of the column is shown in Figure 4.11.

4.2.2.5 Conclusions on Limitation

The trial testing on Shake Table R141 provided invaluable conclusions that are summarized below:

1. The maximum load carrying capacity of Shake Table R141 is 8,000 kg which is a limited payload for testing bridge columns due to extremely heavy loads in bridges.

75 2. If very small scale models are to be tested on this shake table with an approximate scale factor of 20 or more, the similitude requirements suggest making very small models weighing around few hundred kilograms only. Experience showed that with such scale factors it becomes practically impossible to obtain very small size rebar having deformations that would reasonably simulate the bond. This issue requires a balance to choose a scale factor to be large enough to capture all construction details and small enough to ensure availability of deformed bars(Mander, Waheed, Chaudhary, & Chen, 1993). For very small scale it does not remain feasible to ensure tolerances of sizes, covers, bar spacing, instrumentation etc. Size effects become aggravated and may result in misleading conclusions.

4.2.3 Specialized Training at SEESL, UB

A six months long specialized training was under taken (Syed, 2008). Although this training was undertaken after the completion experimental testing but it was extremely helpful in strengthening the learning of dynamic testing facilities that include 6DOF shake tables, large hydraulic actuators, sensors and design of experimental testing projects. The training was extremely helpful the data processing obtained from experiments conducted in Peshawar.

4.3 Formulation of Testing Methodology

In light of the results obtained from the study of limitation of lab equipment and from carrying out the testing on trial columns, it was decided to carryout Quasi-Static Cyclic testing on RC bridge columns for the study on energy dissipation capacity on test columns that would be fabricated for collection of scientific data. It was decided that scale factor for geometric scaling would be taken as 1:4 as this would result in a reasonable and manageable size test columns. Here it is worth mentioning that selection of scale for the model is dependent on many factors which include the laboratory facilities and limitation of test equipment(Mander, Waheed, Chaudhary, & Chen, 1993). An important decision was made with regard to dead mass simulation, and it was decided to physically fabricate the actual required mass for the scaled models. The purpose was

76 to avoid boundary condition problem that was experienced in trial test column. Secondly it was decided to carryout Hybrid Quasi-Static Cyclic Testing that involved not only conventional way of performing the quasi-static cyclic testing but also involved Ambient Vibration Testing of the RC model column to study the dynamic behavior of the model test column under test load. It was believed that the dynamic data obtained from the ambient vibrations of the test column would provide data that would be used in determining the actual dynamic characteristics of the test columns. It was decided that modular dead mass would be fabricated so that gradually increasing mass can be applied to test columns and correspondingly dynamic behavior of fully elastic test columns could be studied under varying mass. Similarly dynamic behavior of test columns would be studied at various levels of inelasticity which would result from quasi-static cyclic testing of columns under various levels of lateral drift demand. It was believed that such dynamic data would be extremely helpful in establishing actual behavior of RC columns at various states that would include knowing the actual parameters such as natural period of vibration, damping of the system, and actual effective stiffness, at various stages.

4.4 Similitude Analysis

After careful study of the requirements of dynamic and quasi-static testing, study of operational requirements of the laboratory equipment, physical limitations of the laboratory space, precision and limitations of sensors to be used, limitations of the data acquisition system and financial constraints, various important decisions were made that are described in detail in following paragraphs.

4.4.1 Scale Factor Related to Geometry

Various factors related to Dimension of “Length” are discussed here.

4.4.1.1 Scale Factor for Length

Size of a specimen is one of the most important parameter from various prospects, therefore the scale factor for length l was of significance and needed due care in selection. The scale factor for length can make the model very large if a smaller value of scale factor is selected which can result in cost implications, limitation of lifting devices

77 and limitation of loading devices available in the lab, as well as space limitation. And if a very large value of this scale factor is selected, it can result in difficulties associated with fabrication, tolerances, difficulty in getting small diameter rebar having deformations etc. (Mander, Waheed, Chaudhary, & Chen, 1993).

The choice of scale factor also depends on type of testing, if elastic studies are to be done then significantly small models can be prepared but for inelastic studies the strength models would require making relatively larger models. In bridge studies the range for 1 1 strength models can vary between to (Harris & Sabnis, 1999). 20 4

The length is one of the basic independent dimensions used in dimensional analysis and it is related to various parameters in fulfilling the similitude requirements, and the effect of length goes beyond the physical and administrative limitations. This factor affects other characteristics of materials and structural parameters such as specific weight, concentrated loads, moments, shear force and acceleration requirements.

In this study, after conducting the trial shake table tests on scale factor 10 and trial quasi- static test with scale factor 6, provided a reasonable insight into limitations associated with various testing parameters as discussed above. The scale factor for length

(geometry) was then pre-selected to be l 4.0 . This factor was considered to be the most suitable to result in a reasonable size specimen that could optimally cater for issues discussed in preceding sections.

Thus from above discussion we have:

lp l   4.0 (4.7) lm

Where: l is the scale factor related to linear geometric terms;

l p is the length related parameter in prototype;

lm is the length related parameter in model.

4.4.1.2 Scale Factor for Area

78 In light of above, as the area is derived as a result of multiplication of two lengths, therefore the scale factor for area of the bridge column is described below:

2 Alpp 2 A  A2  A l A 16.0 (4.8) Am lm

Where: Ap and Am are factor related to area terms in prototype and model respectively;

 A is the scale factor for area.

4.4.1.3 Scale Factor for Moment of Inertia

The scale factor for moment of inertia is calculated from dimensional analysis to fulfill the similitude requirements, is give below:

4 lp 4 I 4   I   l   I  64.0 (4.9) lm

Where: I is the scale factor related to moment of inertia.

4.4.1.4 Scale Factor for Linear Displacements

The scale factor for linear displacements in prototype and model will have the same basic scale factor as that of length determined from dimensional analysis, to meet the requirement of similitude and is described below:

lp D    D   l   D  4.0 (4.10) lm

Where: D is the scale factor related to linear displacements.

4.4.1.5 Scale Factor for Angular Displacements

From dimensional analysis it is calculated that the scale factor for angular displacement will be unity. Thus the rotational value of a quantity in a model does not require modification as the scale factor is unity and angular quantities in model are equal to that in prototype. This is described below:

79 slpp

rlpp          1.0 (4.11) slmm

rlmm

Where:  is the scale factor related to rotational displacements;

sp is the distance traversed in an arc by a prototype;

sm is the distance traversed in an arc by a model;

rp is the radial distance in a prototype;

rm is the radial distance in a model.

4.4.2 Scale Factors Related to Material Properties

It was decided to conduct quasi-static cyclic testing on RC columns which would push the columns into inelastic range in the region of plastic hinge. To avoid scaling of mechanical properties of concrete and reinforcing steel, it was decided to use same material characteristic in model as that of prototype, as modeling mechanical properties of rebar is rather difficult especially when dealing with inelastic material response. Using the same material properties eliminates many complications. Further the similitude rules do not satisfy inelastic behavior and are very complex, therefore (Reinhorn A. M., 2008) suggests using same prototype material in model and hold the same stress-strain rates. This is because of the fact that in testing inelastic response of structures made of materials not having same materials characteristics as that of prototype would undergo states that are not consistent with the response of prototype. And it would rather get very difficult to correlate the behavior of model and prototype.

4.4.2.1 Scale Factor for Modulus of Elasticity

In light of preceding section, it was established that same materials would be used thus the modulus of elasticity of reinforcing steel and concrete would also be same. Therefore scale factor for modulus of elasticity would be as under:

80 Ep E  1.0 (4.12) Em

Where: E is the scale factor related to modulus of elasticity.

4.4.2.2 Scale Factor for Stress

Since it was pre-decided that same materials were to be used in model, as that of prototype therefore this leads to conclusion that the scale factor for stress would be unity and is described below:

load F  p Stress 2  E  area L m

 1.0 (4.13)

Where:  is the scale factor related to modulus of elasticity.

4.4.2.3 Scale Factor for Specific Weight (column only)

The RC column under test was made of two main components, one was column itself and second part was the dead mass supported on column top. Here in this section only the RC column is discussed. To fulfill the requirements of similitude on the basis of dimensional analysis carried out for specific weight of the material, result is presented below:

 1 E ;  1.0;  4.0   (4.14)  El   required l 4

Where:  is the scale factor related to specific weight of material.

The Eq.(4.14) is the scale factor for specific weight in the case when no dynamic excitation is involved which implies to quasi-static testing only.

However, for the case of dynamic excitation the requirement for scale factor related to specific weight would be as follows:

 1  E   1.0;   4.0;    (4.15) El  required l  a4  a

81 Where: a is the scale factor related to acceleration.

Here the value of a needs to be preselected, a natural choice would be to take its value as unity. This would result in:

1   (4.16) required 4

However, as described in preceding sections it was pointed out that similar materials are used thus the provided specific weight for the model is:

1.0 (4.17)    provided

This study involved predominately quasi-static cyclic testing which does not involve the excitation of mass and the required specific weight is described in Eq.(4.14). Whereas provided specific weight is described in Eq.(4.17). The specific weight requirement here in quasi-static test is only related to produce correct stresses in column due to self 0weight. It would be shown latter that this deviation from requirement of similitude is harmless as column mass is hardly 1.8% of the total mass.

4.4.2.4 Scale Factor for Poisson’s Ratio

Since Poisson‟s ratio is a dimensionless number therefore the scale factor for it is always unity.

 1.0 (4.18)

4.4.2.5 Scale Factor for Strain

Strains are also dimensionless and therefore the scaling factor for strain is also always unity.

 1.0 (4.19)

4.4.3 Scale Factors Related to Loading

Various forms of loading exists which need to be scaled appropriately, these are discussed here.

82 4.4.3.1 Scale Factor for Concentrated Load

The concentrated load when scaled need to fulfill the requirements of similitude. From the dimensional analysis, the scale factor for concentrated load is calculated as under.

2 Q E l;  E 1.0;  l 4.0  Q 16.0 (4.20)

Where: Q is the scale factor related to concentrated force.

4.4.3.2 Scale Factor for Shear Force

From the dimensional analysis the scale factor for shear force is calculated as follows:

2 V E l;  E 1.0;  l 4.0  V 16.0 (4.21)

Where: V is the scale factor related to shear force.

4.4.3.3 Scale Factor for Moment

The scale factor for moment is calculated from dimensional analysis as follows:

3 M E l; E 1.0;  l 4.0  M 64.0 (4.22)

Where: M is the scale factor related to bending moment.

4.4.4 Scale Factors Related to Dynamic Characteristics

This study on RC bridge piers was carried out using quasi-static testing. However a hybrid approach was used during the cyclic testing as suggested by Prof. S. A. Sheikh (Sheikh S. A., 2008) which employed the concept of Ambient Vibration Testing also called free vibration testing (Chopra, 2001) at various stages of quasi-static cyclic testing to study the dynamic characteristics of RC model columns as a mean to identify their behavior especially in nonlinear material range. Related scale factors are discussed below.

4.4.4.1 Scale Factor for Mass (lumped on column top)

In this study the test column was analogous to an inverted pendulum with mass lumped on top of the RC column. The lumped mass represented the mass of the super-structure

83 in a bridge system. From dimensional analysis carried out for the lumped mass, the scale factor is provided below:

3 1 m l;   ; l 4.0  m   16.0 (4.23) required 4 required

Where: m is the scale factor related to mass;

 is the scale factor related to mass density, the scale factor is same as that for specific weight calculated in Eq.(4.14).

From Eq.(4.23) the mass required for the model is calculated below:

MMV  16 p  16 MM  p   p p (4.24)  mrequired m m Mm 16 16

Where: M p is the mass of prototype structure;

M m is the mass in model;

 p is the specific weight of prototype material.

It is important to note that the provided scale factor for the mass is 16.0 Thus the mass similitude requirements for the lumped mass on column top is fulfilled and the column top mass is 98.2% of the total mass of the system.

4.4.4.2 Scale Factor for Acceleration

It is important to consider the scale factor for the acceleration as this would later be used in calculating the scale factor for natural period of the RC column system. From dimensional analysis the scale factor for the acceleration is described in Eq.(4.15). It was pointed out there that this factor was preselected as unity.

a 1.0 (4.25)

It is important to mention here that this formed the basis to calculate the scale factor for 1 specific mass which then came out to be   for the case of column only as required 4

84 stated in Eq.(4.16). However, for the top mass the scale factor for the net mass was calculated to be 16 in Eq.(4.23).

The acceleration due to gravity is constant and was taken unity in model and prototype; however it is possible to have tests in which similitude would require to scale acceleration due to gravity which would require use of equipment called centrifuge. For this study the scale factor for acceleration due to gravity is given below:

g 1.0 (4.26)

Where: g is the scale factor related to acceleration due to gravity.

4.4.4.3 Scale Factor for Natural Period

From the dimensional analysis for natural period of the column system, results are presented as under:

l t ;  l  4;  a  1   t  2.0 (4.27) a

Where: t is the scale factor related to time period.

Here it is very important to recall that Eq.(4.27) is based on the premise that specific 1 mass of the system is   . However, this assumption holds only for the top required 4 mass and not for the column itself, but this deviation did not cause any harm to the modeling and its associated results because of the fact that predominant mass contribution from the column top mass amounted more than 98.2%. This issue is discussed in detail in the forthcoming section 4.4.6.

4.4.4.4 Scale Factor for Damping Ratio

The damping ratio is a dimensionless quantity the scale factor is thus unity and described below:

 1.0 (4.28)

Where:  is the scale factor related to damping ratio.

85 4.4.5 Scale Factor for Energy Dissipated

The scale factor for energy dissipated by the RC column in inelastic range would be estimated by following equation:

e f  d  e () EL23  L  e  E  L

3 e   E  l (4.29)

Where: e is the scale related to energy dissipated;

e is the energy dissipated;

f is the force acting;

d is the displacement due to application of force;

E is the modulus of elasticity;

L is the dimension of length.

4.4.6 Summary of Discussions

Scale factors are presented in tabular form in Table 4.6 in similar fashion as that provided in a PhD dissertation (Bracci, 1992) for comparing the required scale factors verses the provided scale factors.

In this study the preselected scaling factors were related to length, material and acceleration as described in preceding sections. From Eq.(4.7), l 4.0 ; is preselected scale factor for length, from Eq.(4.12), E 1.0 is preselected scale factor for modulus of elasticity which refers to same material and from Eq.(4.26) it is evident that same acceleration is used and scale factor is unity. All the other scale factors are then accordingly calculated by dimensional analysis to fulfill the similitude requirements.

It is pointed out here that all the similitude requirements are met, except a minor deviation to fulfill the requirement of specific mass for RC column only. The total mass of the whole test specimen was 42.4 kips (19.6 tf), which comprised of the top mass and mass of column itself. Similitude requirement was met for top mass that amounts to 42.4 kips (19.2 tf) which makes 98.3% of the total mass. However, since the required scale

86 factor for the specific mass was 0.25 and provided scale factor was 1 for the RC column case only; this deviation resulted in an error of 1.3% in total mass of the test object. It is important to realize that the mass of column was a distributed mass over the entire height which makes the share of column mass even less, thus further reducing the deviation from 1.3% in dynamic response measurements such as for finding the time period of the system. However the contribution of this 1.3% deviation in static response that is related to stresses is also negligible since this offset would just introduce an estimated error of  4.9 psi only, which causes an approximate error of 0.25% in stress measurements.

From the above discussion it is concluded that it would be fair to state that similitude requirements for this study were met. A negligible deviation of mass requirement for column only has no effect in the study as the deviation is so small that it is rounded off in actual measurement of physical qualities due to resolution of equipments being used.

4.5 Model Geometry

The geometry of the model was established in light of the similitude analysis undertaken in previous section. The scale factor for length l selected in this study was 4. From the survey of bridges and data gathered, a representative bridge pier and its loads were established and the geometry of the model was derived from the geometry of prototype. The diameter of the model column was 12 inches; clear height of column was 5 ft-9 in. The distance from column base to point of application of lateral load was 6 ft-3 in. Figure 4.12 shows the drawings of the model pier that was tested in the laboratory.

4.6 Model Mass

The mass in typical prototype bridges is around 310 tons. From the similitude analysis undertaken the mass for model is calculated from scale factor of 16 as presented in Eq.(4.23). This leads to a model mass requirement of 19.38 tons. The mass requirement of model is fulfilled by using modular concrete slabs that are described in detail in forthcoming paragraphs.

4.7 Model Materials

87 The model material was same as that of prototype and their scale factors were calculated in previous sections and are summarized in Table 4.6. In this section the model materials are discussed with regard to their properties and in case of concrete the mix design properties are also presented.

4.7.1 Concrete

The model concrete was prepared from the results obtained from testing prototype concrete. A series of experimental investigations in the laboratories were carried out in which concrete cylinders and beams were made and tested according to ASTM standards for determining the mechanical properties of prototype concrete. The size of coarse aggregates for prototype concrete was chosen to be same as that used in field. Based on data gathered from various sources that included field exploration it was decided to achieve two mix designs:

1. 2,400 psi (16.5 MPa); and

2. 1,800 psi (12.4 MPa).

One major reason for testing 2,400 psi concrete is the finding that existing bridges built in 70‟s and 80‟s had concrete strength of 3,000 psi which corresponded to cube strength. In this study testing of concrete was done using ASTM standard that uses cylinders (ASTM C873-04, 2004). The ratio between cube and cylinder strength is around 1.25(Day, 1999) which means that a 3,000 psi cube would be around 2,400 psi cylinder. Since many bridges had poorer strength, therefore it was decided to also test columns with strength 25% less than 2,400 psi which come around 1,800 psi.

Mechanical characteristics of prototype concrete were studied that included finding the crushing strength (ASTM C873-04, 2004), modulus of rupture (ASTM C78-02, 2004) and modulus of elasticity (ACI 318-02, 2001), which served as bench mark for the mix design of model concrete. In model concrete, size of coarse aggregates was reduced with an attempt to achieve similarity of bond behavior between concrete and reinforcement. In forthcoming sections first the prototype concrete is discussed after which model concrete is presented which is used in preparation of test columns.

4.7.1.1 Prototype Concrete

88 Mix design was done for the desired concrete strengths. For prototype concrete the size of aggregate was chosen to be same as that used in practice. The purpose of preparing prototype cylinders was to determine mechanical properties of unconfined concrete which would serve as the benchmark for model concrete. Constituents of concrete are described below:

Fine Aggregates:

Sieve analysis of the fine aggregates used in preparing the prototype concrete was done according to ASTM (ASTM C136-04, 2004). The results of the sieve analysis are presented in Table 4.7 and curve of the same is presented in Figure 4.13 from which the fineness modulus of the sand was calculated to be 2.3. The specific gravity of the fine aggregates was also determined according to ASTM (ASTM C128-04, 2004), which was 2.56 and water absorption was 3.41%. Void ratio of sand was found to be 0.018 and bulk density was 151 lb/ft3. These properties are summarized in Table 4.8 and same fine aggregates were used in model concrete.

Coarse Aggregates:

Sieve analysis of the coarse aggregates was done in light of ASTM(ASTM C136-04, 2004) the results are presented in Table 4.9 and curve is plotted in Figure 4.14. The specific gravity was found to be 2.63 and water absorption of 0.64%. The bulk density was found to be 88.2 lb/ft3, void ratio was 0.46 and water content was 0.115%. The results are summarized in Table 4.10.

Cement:

Type-I hydraulic cement (ASTM C150-04, 2004) was used in all experimental work including prototype and model. Various tests were performed to characterize the cement. The setting time of the cement was determined in light of ASTM standard (ASTM C191- 04a, 2004), from which initial setting time was calculated to be 105 minutes and final setting time was 216 minutes. The density of the hydraulic cement was calculated to be 189 lb/ft3 in light ASTM standard (ASTM C188-95(2003), 2004). Fineness of cement was found to be 90.2% using ASTM standard (ASTM C117-04, 2004). Tensile strength of cement was found to be 380 psi. The compressive strength of cement was found to be

89 2,590 psi as per ASTM standard (ASTM C109/C109M-02, 2004). The summary of results is presented in Table 4.11.

The mix design for the two strength groups was worked out to be as under using the aforementioned constituents of concrete and characteristic properties are also provided:

1. For 2,400 psi prototype concrete: 1 : 1.5 : 2 by weight with water to cement ratio of 0.55. The cylinders prepared with this mix design were then tested as per ASTM standard (ASTM C873-04, 2004) and the average strength obtained was 2,406 psi (16.6 MPa). The MOR was determined for this mix design as per ASTM standard (ASTM C78-02, 2004) and was 684 psi (4.7 MPa). The modulus of elasticity calculated as per ACI (ACI 318-02, 2001) was established to be 2,796 ksi (19,277 MPa).

2. For 1,800 psi prototype concrete: 1 : 1.5 : 3 by weight with water to cement ratio of 0.55. The cylinders prepared with this mix design were then tested as per ASTM standard (ASTM C873-04, 2004) and the average strength obtained was 1,846 psi (12.7 MPa). The MOR was determined for this mix design as per ASTM standard (ASTM C78-02, 2004) and was 496 psi (3.4 MPa). The modulus of elasticity calculated as per ACI (ACI 318-02, 2001) was established to be 2,443 ksi (16,844 MPa).

These properties of prototype concrete groups are summarized in Table 4.12.

4.7.1.2 Model Concrete and Fabrication of Models

It is important to mention that aggregates were scaled in model concrete to make sure that realistic similitude of bond between rebar and model concrete was achieved. The entire model consisted of four parts that were constructed in four phases:

Phase-I: Construction of RC modular slabs for dead mass

Phase-II: Construction of RC base

Phase-III: Construction of RC column

Phase-IV: Construction of RC column top pedestal

90 Here it worth mentioning that four columns were fabricated in once piece comprising of column base, column itself and pedestal on column top. The modular dead mass was mounted on each column once at a time during the testing. The scheme resulted in time saving, economizing the cost and reusability of dead mass for future testing.

Phase-I: Construction of RC modular slabs for dead mass

The first phase was to construct the modular dead mass. Commonly available aggregates were used to achieve a concrete that is good enough to provide mass. Two main types of RC slabs were used: a. 4ft. x 4ft. RC slabs: These were twelve in number non-structural slabs each having thickness of 12 inches. These were designed as non-structural slabs strong enough to support their self weight only. The mix used for these slabs was 1:2:4 (cement : fine aggregates : coarse aggregates) by volume with water to cement ratio of around 0.6. The cement, fine and coarse aggregates used had same properties as that of the prototype concrete as defined in previous sections. Three 0.5 inch diameter grade 60 reinforcement was used in both directions in the form of a ring. These 12 slabs weighed 39.91 kips in total which was 71.7% of the total mass. These slabs are shown in Figure 4.15. b. 8ft. x 8ft. RC slab: This was a structural slab having a thickness of 12 inches. This was designed to support all the twelve 4ft square slabs. The mix design was 1:1.5:3 by volume with water cement ratio of around 0.58. The cement, fine and coarse aggregates used had same properties as that of the prototype concrete as defined in previous sections. The reinforcement comprised of 0.5 inch diameter 60 grade steel bars spaced 5 inches on centers in both directions in the form of a ring to provide reinforcement on top and bottom. This slab shown in Figure 4.16 weighed 10.6 kips which is 24.5% of the total mass.

The slabs were provided with hooks near the four corners for lifting shown in Figure 4.17. The hooks were provided in depression, in such a manner that they were flushed with the top surface of slabs.

Phase-II: Construction of RC base

91 The base at the column was to provide strong support to the column that was subjected to lateral load and also the dead mass on column top. The size of the base was 7 ft in length, 3 ft in width and 20 inches in height. The cement, fine and coarse aggregates used had same properties as that of the prototype concrete as defined in previous sections. The reinforcement comprised of 0.5 inch diameter 60 grade steel placed 6.5 inch on centers in the form of a ring in both directions. The concrete mix is 1:1.7:3.4 by volume with water cement ratio of 0.58. The slab was anchored down to strong floor with the help of studs that passed the through holes in base and strong floor. The column base is shown in Figure 4.18 which is ready for concrete pour. The base was provided with four hooks near the corners to lift the base along with the column and pedestal at column top, the combined weight of these three parts was around 6.72 kips (3 tons).

Phase-III: Construction of RC column

Four columns were fabricated each at different time. Two columns had target strength of 2,400 psi and remaining two had target of 1,800 psi concrete strength. Properties of all the ingredients of concrete used in model column were similar to those described in prototype concrete except the coarse aggregates, whose properties are described below:

Coarse aggregates used in model concrete:

Sieve analysis of the coarse aggregates for model concrete was done in light of ASTM(ASTM C136-04, 2004) the results are presented in Table 4.13 and curve is plotted in Figure 4.20. The specific gravity was found to be 2.54 and water absorption of 2.53%. The bulk density was found to be 88.3 lb/ft3, void ratio was 0.44 and water content was 0.64%. The results are summarized in Table 4.14.

Mix Design for 2,400 psi strength model concrete:

The proportions of ingredients by weight were, 1:1.5:3 with water to cement ratio of 0.62 for first column QSCT-2-003 and it was 1:1.5:3 with water to cement ratio of 0.58 for column QSCT-3-004. The average strength of cylinders tested as per ASTM (ASTM C873-04, 2004) at the time of quasi-static testing for first column QSCT-2-003 was 2,421 psi and for second column QSCT-3-004 it was 2,307 psi. Slight variation in strength for latter column is probably due to mixing and placement of concrete, preparation of test

92 cylinders etc., but it is acceptable as the error is less than 4% in both the columns from the target strength. The modulus of elasticity calculated from ACI (ACI 318-02, 2001) is 2, 798 ksi and 2,737 ksi for columns QSCT-2-003 and QSCT-3-004 respectively. And MOR determined experimentally as per ASTM (ASTM C78-02, 2004) for QSCT-2-003 was 674 psi and for QSCT-3-004 was 597 psi. The results are summarized in Table 4.15.

Mix Design for 1,800 psi strength model concrete:

The proportions of ingredients by weight were, 1:2.15:4.3 with water to cement ratio of 0.58 for both columns QSCT-4-005 and QSCT-5-006. The average strength of cylinders tested as per ASTM (ASTM C873-04, 2004) at the time of quasi-static testing for first column QSCT-4-005 was 1,843 psi and for second column it was 1,781 psi. The modulus of elasticity calculated from ACI (ACI 318-02, 2001) is 2, 439 ksi and 2,397 ksi for columns QSCT-4-005 and QSCT-5-006 respectively. And MOR determined experimentally as per ASTM (ASTM C78-02, 2004) for both the columns was 515 psi. The results are summarized in Table 4.15.

Phase-IV: Construction of RC column top pedestal

Since modular dead mass was to be reused in each column, therefore each column needed an interfacing element to attach the mass to it. For this a pedestal of size 30 in x 30 in in plan with depth of 12 in was cast-in-place on each column top. This pedestal needed to be strong enough to support approximately 20 metric tons of mass. Figure 4.21 shows the pedestal top with four through holes that would hold down the mass above it. Another important function of this pedestal was to provide attachment for actuator to apply lateral load for cyclic testing. The mix design of this pedestal was 1:1.5:3 with water to cement ratio of 0.58. Steel reinforcement used was 0.5 inch diameter 60 grade space at 4.5 inch on centers.

The RC test column is shown in Figure 4.22 in its final form with mass loaded on column and anchored to pedestal on top of column. The column base also anchored to strong floor.

4.7.2 Reinforcing Steel

4.7.2.1 Prototype Steel

93 From the data obtained from field survey indicates that deformed bars are in practice, however in past plain bars were also used. Commonly used steel should conform to ASTM standard for mild steel (ASTM A615/A615M-03a, 2004). In this study deformed bars having diameter of 1 inch and grade 60 are defined for prototype structures and is 3 thus taken as benchmark. For confinement steel usually inch diameter bars of grade 60 8 are used.

4.7.2.2 Model Steel

The reinforcement used in model was from commonly available steel in the market. Deformed bars of diameter size 0.291 inch (7.4 mm) were used for rebar having yield strength of 53 ksi. Due to unavailability of smaller bar size for confinement; plain mild steel wire having diameter of 0.0394 inch (1 mm) was used. Figure 4.23 shows the rebar and confinement hoops in the model column. A summary of the properties of steel for prototype and model are described in Table 4.16.

4.8 Summary of Parameters for Prototype and Model

Based on similitude analysis undertaken for the model bridge column various parameters were finalized. It is important now to know the comparison of selected key features between prototype and model bridge columns. The summary of comparison for key features is presented in Table 4.17, for further in-depth details and other features please refer to previous sections and their tables. A typical stress-strain curve for the concrete used is provided in Figure 4.24. Due to limitation of extensor meter working with UTM the stress-strain data for steel rebar was not taken.

4.9 Experimental Setup

In order to undertake the experimental program for quasi-static cyclic testing the experimental setup is presented in this section to describe the key elements.

4.9.1 Customization of Testing Rig

The quasi-static cyclic testing was done using one linear hydraulic actuator which has 50 tons of loading capability. This actuator being part of structural testing frame as

94 described in Section 4.2.1 and its features presented in Table 4.1 was brought into Earthquake Engineering Center along with its hydraulic power supply to conduct this quasi-static cyclic testing. The reason to use Earthquake Center for this final study was due to the availability of bigger space for fabrication of large specimens, availability of crane for movement of heavy masses which was not possible in Structural Testing Laboratory. Beside this, using two actuators for cyclic testing had associated problems such as controlling two actuators for one test, need of two reaction frames on either side of test specimen which was not available in Earthquake Center and inability to hold the specimen in an event of structural collapse of test specimen at higher drift levels during the testing.

Since originally the actuator had fix base with front end of actuator only suitable for monotonic testing involving pushing only is shown in Figure 4.25. One actuator was added with additional hardware to make it suitable for cyclic testing to enable pulling capability also in addition to pushing, is shown in Figure 4.26. This was achieved by providing two swivels one at the frontend and the other at backend of the actuator with interfacing plate that could be connected to test specimen as shown in Figure 4.27. Before the start of cyclic testing the whole system was tested for verification of push and pull capacity in two separate tests. The pull test is shown in Figure 4.28 and the push test is shown in Figure 4.29. The verification test suggests a safe working capacity of 33 kips (15 tons) for both push and pull in a cyclic testing.

4.9.2 Design of Anchoring System

Two locations in test specimen needed the anchors. The first was the base of the column that was anchored down with the 12 inch thick strong floor and second was the 8 feet square slab that was anchored at the column top pedestal of 12 inch thickness. In both cases the forces were estimated and accordingly the diameter of the anchors was selected. The length of anchors was defined by the geometric requirements.

The four anchoring bolts for column base were 44 in long and had diameter of 1.75 in, these are shown in Figure 4.30. The four anchor bolts for 8 ft square slab were 27 in length and had diameter of 1 inch are shown in Figure 4.31. Both the anchor bolts were of mild steel with yield strength of 40 ksi.

95 4.9.3 Load Cell

The load cell is attached to the actuator shaft and measures the load in ton-force. The least count for the load cell is 0.28 kips (125 kg). The load cell was calibrated before the test with the help of reference load cell also shown in Figure 4.5. The calibration of load cell is mentioned in section 4.2.1.6.

4.9.4 Displacement Transducers

The displacement at the column top at the point line of application of lateral load was measured with the help of linear variable differential transformer (LVDT) and string- potentiometer. The resolution of these transducers was around 0.05 mm. Their calibration is explained in section 4.2.1.6.

4.9.5 Force Balanced Accelerometers

The quasi-static testing was supplemented by ambient and force vibration testing. Only ambient vibration testing was done after various drift levels have been applied. In both types of testing the dynamic response of the structure was measured with the help of a hyper sensitive tri-axial forced balanced accelerometers. These accelerometers were installed on column top mass to record the time history of motion. The sensitivity of the accelerometer used was 0.4 g . Figure 4.32 shows the accelerometer on column top for recording the response.

4.9.6 Data Acquisition Systems

The data was recorded during the quasi-static cyclic testing using UCAM-70 data acquisition system. This system is suitable for quasi-static testing and comprises of 30 channels. In this study the data was sampled at frequency of around 1.5 Hz. It is important to recall here that the frequency of cyclic testing was around 0.0067 Hz, which shows that the sampling frequency was well above the Nyquist-Shannon sampling frequency. Theoretical required minimum frequency of sampling was 0.0134 Hz and preferred minimum required sampling frequency was 0.067 (Dally, Riley, & McConnell, 2004) whereas actual sampling was done more than 22 times the minimum required frequency of 0.067. The data acquisition system is shown in Figure 4.33.

96 The dynamic response of the column due to ambient and forced vibration was measured with the data acquisition system DR-4000. The data was sampled at 100 Hz for the ambient and forced vibration testing whereas the response of the system under measurement was below 1.5 Hz, thus it also satisfied the Nyquist rule.

4.9.7 Eccentric Mass Vibrator

Forced vibration testing was only done in one column QSCT-2-003 to cross check the data obtained from the free vibration response. Forced vibration testing was done using the MK-138 (ANCO Engineers Inc., 2005) Eccentric Mass Vibrator (EMV) shown in Figure 4.34. The EMV was installed on column top and hypersensitive accelerometer and data acquisition system were also placed, this arrangement is shown in Figure 4.35. Since various loading schemes related to eccentricity of the EMV are available, the configuration generating the least force was used to avoid damage to the column and was limited to 290 lbs-inch. The speed of the EMV was controlled by the variable speed controller. It was ensured that EMV is securely attached to the column top mass.

4.10 Test Protocol

The RC model columns were subjected to three types of testing that were quasi-static cyclic, ambient vibration and forced vibration testing. Forced vibration test was only done on one column to compare the results with ambient vibration tests. The major part of this study was quasi-static cyclic testing of the four RC columns with geometric scale factor of 4. The test protocol for this study for each column is explained below.

4.10.1 Quasi-Static Cyclic Tests

The first column was named QSCT-2-003 and was subjected to scheme in which 3 cycles per drift level were used and total of 37 cycles were applied till failure at 4% drift. This was the first column of the series with average strength of 2,421 psi. The details of this column are explained in Table 4.15. The testing frequency was fixed at 150 seconds for one cycle of drift which corresponds to 0.0067 Hz for a cycle. The loading scheme for cyclic testing is shown in Figure 4.7 and the data for it is shown in Table 4.18.

97 The remaining three columns were QSCT-3-004, QSCT-4-005 and QSCT-5-006 with average strengths of 2,307 psi, 1,843 psi and 1,781 psi respectively. The loading protocol was modified to 2 cycles per drift and total of 13 cycles till failure at 4% drift were used. The loading frequency was kept same as 0.0067 Hz. This scheme is shown in Figure 4.36 and its data is shown in Table 4.19. The change in scheme was suggested by Prof. Shamim A. Sheikh (Sheikh S. A., 2008) who was the external member of the research committee. After completion of drift cycle at various levels pictures were taken and cracks appearing on the column were marked. For all the cases the testing was to be continued at least till 20% reduction in strength was observed, which means that during the test the maximum force was monitored for each cycle until a cycle experiences a maximum force that is 80% of the maximum force in the preceding cycles (Kawashima K. , 2006; Poljansek, Perus, & Fajfar, 2009). This point corresponds to a failure state or the state beyond which performance is not acceptable.

4.10.2 Free Vibration Testing

An important feature of this study was the determination of dynamic characteristics of columns with the help of ambient vibration tests undertaken at various stages of column testing. Ambient vibration test was done before the start of quasi-static test and also after various levels of drifts were applied. However the first column QSCT-2-003 was only tested before the quasi-static testing started. The ambient vibration testing involved using high sensitivity force balanced accelerometer and data acquisition system for dynamic measurement explained in section 4.9.5 and section 4.9.6 respectively. The last three columns QSCT-3-004, QSCT-4-005 and QSCT-5-006 were also tested during the loading of modular slabs to see the change of dynamic properties of column due to increase in mass.

This testing required moving the whole mass with application of sudden initial force and then allowing the column to vibrate freely and recording the response. The force to the column was provided by a person who would stand on the column top and would suddenly jump on column and would then stand still during the entire period of recording the vibration response. It is important to note that ambient vibration testing was always done after detaching the actuator from the column to allow the column to freely vibrate

98 without any constraints. The ambient vibration testing of columns at drift level of 3% and 4% with more than 19 tons of mass at column top was very challenging task due to the possibility of collapse.

4.10.3 Forced Vibration Testing

Only the first column QSCT-2-003 was tested with Eccentric Mass Vibrator (EMV) MK- 138 with the sole purpose to verify the results of ambient vibration testing for the identification of dynamic properties of the RC column. This test was done prior to start of quasi-static cyclic testing when the column was fully elastic. The configuration of EMV shown in Figure 4.37 was used for this test (ANCO Engineers Inc., 2005). The EMV was securely anchored at the column top and the sensitive accelerometer along with data acquisition was place on the column top. The EMV was powered and frequency of the eccentric mass was slowly and incrementally increased. For every incremental increase in the frequency of the EMV about 10-15 seconds were allowed for the column to respond to the applied eccentric force. It is important to note that below the natural frequency of the column it did not showed any noticeable vibrations but as soon as the frequency of loading of the EMV reached close to natural frequency of column significant vibrations could be observed and at that point the EMV was stopped to avoid damage to the column.

99 FIGURES

Figure 4.1: Structural testing frame with adjustable girders and hydraulic jacks.

Figure 4.2: A trial RC column of 1:6 scale to study the equipment and test protocol.

100

Figure 4.3: Vertical hydraulic jack with bi-directional rollers on the column top.

Figure 4.4: Two horizontal jacks used for cyclic loading, each jack performed half cycle of lateral loading.

101

Figure 4.5: Calibration of load cell of hydraulic jack with the help reference load cell.

Figure 4.6: Calibration of displacement transducers with the reference transducers.

102

Figure 4.7: Testing protocol for cyclic testing of RC column.

LatLoad (k) -1

-2

-3

-4 -4% -3% -2% -1% 0% 1% 2% 3% 4% Drift (%) Figure 4.8: Hysteresis cycle at 3% drift shows stiffening at peak displacement.

103

Figure 4.9: Trial RC column of scale 1:10 for dynamic testing on shake table.

Figure 4.10: Accumulated damage to trial RC column in shake table testing.

104 4.0

3.0

2.0

1.0

0 Real,EU

-1.0

-2.0

-3.0

-4.0 0 5.0 10.0 15.0 20.0 25.0

Figure 4.11: Acceleration time history response of top mass of RC column during 100% run on the shake table.

105 1219mm square blocks 37.5mm spiral pitch 305mm Each block 305mm in height 5-12mm Ø 26-7.37mm rebar with Ø rebar 15mm clr cvr

305 50 ton 762 N Hydraulic 11-1" Ø 1283 Actuator 2 508 bars 305mm

1067 2134

2438 26-7.37mm Ø rebar

2133

5-1mmØ spiral @ 37.5mm pitch 914 2438

305mm Ø Column base 762mm square top pedestal Ø=305mm

Figure 4.12: Drawing of the 1:4 model column for quasi-static cyclic testing.

106

Figure 4.13: ASTM C-136 sieve analysis curve for fine aggregates.

Figure 4.14: ASTM C-136 sieve analysis of coarse aggregates for prototype concrete.

107

Figure 4.15: Modular RC slabs each 4 ft x 4 ft to form the dead mass.

Figure 4.16: An 8 ft x 8 ft RC slab to provide support to modular mass and contributes itself as test mass.

108

Figure 4.17: Lifting hooks for RC slab flushed inside the slab.

Figure 4.18: RC column base ready for fabrication.

109

Figure 4.19: RC column rebar and spiral reinforcement ready for concrete pour.

Figure 4.20: ASTM C-136 sieve analysis curve for coarse aggregates used in model concrete.

110

Figure 4.21: Pedestal on column top used to support the dead mass.

Figure 4.22: Model column in final form with dead mass loaded.

111

Figure 4.23: Model column rebar and confinement hoops with strain gage installed on QSCT-2-003rebar. Cyclinders Test for Compressive Strength

3,000

2,500

2,000

1,500

1,000 ConcreteStress (psi) fc y = -3E-18x6 + 5E-14x5 - 4E-10x4 + 2E-06x3 - 0.0044x2 + 5.524x - 54.383 R2 = 0.998 500

0 0 1,000 2,000 3,000 4,000 5,000 6,000

Strain (με) Figure 4.24: Typical stress-strain curve of concrete.

112

Figure 4.25: Hydraulic actuators in its original form with fix base suitable for monotonic testing for pushing only.

Figure 4.26: Additional hardware added to make the monotonic testing actuator suitable for cyclic testing.

113

Figure 4.27: Swivel at frontend of actuator with interfacing plate.

114

Figure 4.28: Verification test for pulling capacity of hydraulic actuator testing rig.

Figure 4.29: Verification test for pushing capacity of hydraulic actuator testing rig.

115

Figure 4.30: Anchor bolts for attaching the base of the column with strong floor.

Figure 4.31: Anchor bolts for anchoring the slab on pedestal column top.

116

Figure 4.32: Hyper sensitive accelerometer on column top for recording the dynamic response of column.

Figure 4.33: Data acquisition system used for quasi-static testing.

117

Figure 4.34: Eccentric mass vibrator used for forced vibration testing.

Figure 4.35: Eccentric mass vibrator, accelerometer and data acquisition installed on column top for response measurement.

118

Figure 4.36: Test protocol for cyclic testing of RC columns.

Figure 4.37: Eccentricity of EMV used in force vibration testing of column.

119 TABLES

Table 4.1: Specification of hydraulic jacks of structure testing frame

S. No. Item Description Remarks 1 Hydraulic Jack 50 ton Quantity = 2 Capacity 110.2 kips (50 tf) Stroke 12 in (300 mm) Type Linear single ended Maximum speed 0.256 in/sec (6.5 mm/sec) Total length 2,062 mm (81.2 in) In retracted position 2 Hydraulic Jack 25 ton Quantity = 2 Capacity 55.1 kips (25 tf) Stroke 12 in (304.8 mm) Type Linear single ended Maximum speed 0.256 in/sec (6.5 mm/sec) Total length 2,062 mm (81.2 in) 3 Hydraulic Power Supply Operating pressure 3,000 psi (~210 kg/cm2) Manifold capacity Four valves Motor 3 phase Speed Control Adjustable Pressure Control Adjustable Control Manual

Table 4.2: Geometric and material properties of trial bridge column of scale 1:6 for quasi- static cyclic testing

Parameter Prototype Trial Column (Model) Scale Factor 1 6 Column clear height 33 ft (10.158 m) 5 ft-6 in (1.676 m) Column diameter 3 ft (914.4 mm) 6 in (152.4 mm) Dead mass on column top 643.7 kips (292 tf) 17.9 kips (8.1 tf) Rebar percentage 1.60% 1.60% Rebar diameter 1 in (25.4 mm) 0.25 in (6.4 mm) Confinement bar diameter 3/8 in (9.5 mm) 0.096 in (2.4 mm) Confinement percentage 0.20 % 0.20 % Concrete strength 1,900 psi (13.10 MPa) 1,736 psi (11.97 MPa) Rebar yield strength 60 ksi (413.69 Mpa) 47.4 ksi (326.81 Mpa)

120 Table 4.3: Specifications of Shake Table (Seismic Simulator) R141

S. No. Item Description Remarks 1 Axis of motion 1, linear 2 Nominal payload 8.8 kips (4.0 tf) Rated capacity 3 Maximum payload 16.6 kips (8.0 kg) 4 Maximum acceleration ±1.1 g At nominal payload 5 Maximum velocity ±3.6 ft/sec (±1.1 m/sec) At nominal payload 6 Displacement ± 5 in (±127 mm) 7 Table top size 5 ft x 5 ft (1.5 m x 1.5 m) Aluminum top

Table 4.4: Geometric and material properties of trial bridge column of scale factor 1:10 for shake table testing

Parameter Prototype Column Model Column Scale Factor 1 10 Column Clear Height 25 ft () 2 ft-6 in () Column Diameter 3ft-4in () 4 in () Dead mass on column top 220.4 kips (100 tf) 2.204 kips (1 tf) Rebar percentage 6.0% 6.0% Rebar diameter 1 in (25.4 mm) 3/8 in (9.5 mm) Confinement bar diameter 3/8 in (9.5 mm) ¼ in (6.4 mm) Confinement percentage 6.52% 2.48% Concrete strength 3,000 psi (20.7 MPa) 3,000 psi (20.7 MPa) Rebar yield strength 60 ksi (414 MPa) 60 ksi (414 MPa)

Table 4.5: Scaling factors for shake table model 1:10.

Category Item Dimensions Scale Factors Loading Force F 2 l -2 Acceleration FL l Time T 1 l Geometry Linear dimension L Displacement L Material Properties Modulus FL-2 1 Stress FL-2 1 Strain - 1 Poison Ratio - 1 Mass density ML-3 or FL-4T2 1 Energy FL 3 l

121 Table 4.6: Summary of scaling factor used for 1:4 final models

Scale Factor Item General Case Required Provided

Length, l l ? 4.0 4.0 2 Area, A Al   16.0 16.0 4 Moment of inertia, I Il   64.0 64.0

Linear displacement, D Dl   4.0 4.0

Angular displacement,   1.0 1.0 1.0

Modulus of elasticity, E E ? 1.0 1.0

Stress,    E 1.0 1.0 Specific mass for column       0.25 1.0 only-static case,  El Specific mass for column        0.25 1.0 only-dynamic case, E l a 

Poisson‟s Ratio,   1.0 1.0 1.0

Strain,   1.0 1.0 1.0 2 Concentrated load, Q Q   E  l 16.0 16.0 2 Shear force, V V   E  l 16.0 16.0 3 Moment, M M   E  l 64.0 64.0 3 Mass on column top, m ml    16.0 16.0

Acceleration, a a ? 1.0 1.0 Gravitational 1.0 acceleration, g g 1.0 1.0

l Time period, t t 2.0 2.0 a

Damping ratio,   1.0 1.0 1.0 3 Energy, e e   E  l 64.0 64.0

122 Table 4.7: ASTM C-136 sieve analysis of fine aggregates used in experimental work

ASTM Weight Retained % Weight Cumulative % Cumulative % Sieve # (gm) Retained Retained Passed 4 0.4 0.08 0.08 99.20 8 1.6 0.32 0.4 99.6 16 35.8 7.16 7.56 92.44 30 157.8 31.56 39.12 60.88 50 221.5 44.3 83.42 16.58 100 69.8 13.96 97.38 2.62 Pan 13.1 2.62 100 0 Total weight of specimen = 500 gm; Sum of cumulative % retained = 227.96.

Table 4.8: Summary of properties of fine aggregates used in experimental work

Item Value Moisture content 4.5% Void ratio 0.018 Fineness modulus 2.3 Bulk density 151 lb/ft3 (2,420 kg/m3) Water absorption 3.41% Specific gravity 2.56

Table 4.9: ASTM C-136 sieve analysis results for coarse aggregates used in prototype concrete.

ASTM Weight Retained % Weight Cumulative % Sieve # (gm) Retained Passed 1.5” 0 0 100 1” 49 0.98 99.02 0.75” 460.7 9.21 89.81 0.5” 1,846 36.92 52.89 0.375” 1,159 23.18 29.71 0.25” 1,222 24.44 5.27 Pan 263.3 5.26 0 Total weight of specimen = 5,000 gm.

123 Table 4.10: Summary of properties of coarse aggregates used in prototype concrete

Item Value Moisture content 0.12% Void ratio 0.46 Bulk density 88.2 lb/ft3 (1,412kg/m3) Water absorption 0.64% Specific gravity 2.63

Table 4.11: Summary of properties of hydraulic cement used in experimental work

Item Value Type Type-I hydraulic Initial setting time 105 minutes Final setting time 216 minutes Fineness 90.2% Density 189 lb/ft3 (3,028 kg/m3) Tensile strength 380 psi Compressive strength 2,590 psi (17.9 MPa)

Table 4.12: Summary of benchmark characteristic properties of prototype concrete

Group Item Value Proportion by weight* 1:1.5:2 Water/Cement ratio 0.55 2,400 psi Average cylinder strength 2,406 psi (16.6 MPa) MOR 684 psi (4.7 MPa) Modulus of elasticity 2,796 ksi (19,277 MPa) Proportion by weight 1:1.5:3 Water/Cement ratio 0.55 1,800 psi Average cylinder strength 1,846 psi (12.7 MPa) MOR 496 psi (3.4 MPa) Modulus of elasticity 2,443 ksi (16,844 MPa) * The proportions are ratios of the quantities; Cement : Fine Aggregates : Coarse Aggregates.

124 Table 4.13: ASTM C-136 sieve analysis of coarse aggregates used in model concrete

ASTM Weight Retained % Weight Cumulative % Sieve # (gm) Retained Passed 1.5” 0 0 100 1” 0 0 100 0.75” 0 0 100 0.5” 7 0.35 99.65 0.375” 4.9 0.245 99.40 0.25” 1,599.5 79.97 19.43 Pan 388.6 19.43 0 Total weight of specimen = 2,000 gm; fineness modulus was calculated to be 5.8.

Table 4.14: Summary of properties of coarse aggregates used in model concrete.

Item Value Moisture content 0.64% Void ratio 0.44 Bulk density 88.3 lb/ft3 (1,414 kg/m3) Water absorption 2.53% Specific gravity 2.54

Table 4.15: Summary of characteristic properties of model concrete used in four test columns comprising two groups of concrete strength.

Value Group Item QSCT-2-003 QSCT-3-004 Proportion by weight 1:1.5:3 1:1.5:3 Water/Cement ratio 0.62 0.58 Average cylinder 2,421 psi (16.7 MPa) 2,307 psi (15.9 MPa) 2,400 psi strength MOR 674 psi (4.6 MPa) 597 psi (4.1 MPa) Modulus of elasticity 2,798 ksi (19,291 MPa) 2,737 ksi (18,871 MPa) QSCT-4-005 QSCT-5-006 Proportion by weight 1:2.15:4.3 1:2.15:4.3 Water/Cement ratio 0.58 0.58 Average cylinder 1,843 psi (12.7 MPa) 1,781 psi (12.3 MPa) 1,800 psi strength MOR 515 psi (3.6 MPa) 515 psi (3.6 MPa) Modulus of elasticity 2,439 psi (16,816 MPa) 2,397 psi (16,527 MPa)

125 Table 4.16: Mechanical properties of mild steel used in prototype and model.

Group Parameter Prototype Steel Model Steel Type Deformed Deformed Diameter 1 in (25 mm) 0.291 in (7.4 mm) Number 36 26 Rebar Yield strength ~ 60 ksi (414 MPa) 53 ksi (365 MPa) Ultimate strength ~ 75 ksi (517 MPa) 70.4 ksi (485 MPa) % elongation ~8% 20.1% Type Deformed Plain Diameter 0.375 in (10 mm) 0.03937 in (1 mm) Confinement Pitch 6 in (150 mm) 1.5 in (37.5 mm) steel Yield strength ~60 ksi (414 MPa) - Ultimate strength ~ 75 ksi (517 MPa) 89 ksi (614 MPa) % elongation 10-12% -

Table 4.17: Summary of parameters for prototype and model.

Parameter Prototype Model Column diameter 48 in (1,219 mm) 12 in (304.8 mm) Column height 25 ft (7.62 m) 6 ft-3 in (1,905 mm) Supported mass 678.3 kips (308 tf) 42.4 kips (19.24 tf) Dead load stresses 375 psi (2.6 MPa) 381 psi (2.6 MPa) Rebar diameter 1 in (25 mm) 0.291 in (7.4 mm) Number of rebar 36 26 Diameter of confinement 0.375 in (10 mm) 0.03937 in x 5 Nos. reinforcement (1 mm x 5 Nos.) Pitch of confinement 6 in (150 mm) 1.5 in (37.5 mm) reinforcement Coarse aggregate size 0.75 in (20 mm) 0.25 in (6.4 mm) down down Ratio of rebar diameter to 1.25 1.16 coarse aggregate diameter

126 Table 4.18: Data for cyclic testing protocol used in first column QSCT-2-003.

Drift # of Cycles 0.10% 1 0.20% 3 0.30% 3 0.40% 3 0.50% 3 0.75% 3 1.00% 3 1.50% 3 2.00% 3 2.50% 3 3.00% 3 3.50% 3 4.00% 3 Total 37

Table 4.19: Data for cyclic testing protocol used in last three column columns.

Drift # of Cycles 0.10% 1 0.25% 2 0.50% 2 1.00% 2 2.00% 2 3.00% 2 4.00% 2 Total 13

127 CHAPTER 5 EXPERIMENTAL RESULTS

5.1 Introduction

This chapter presents the experimental results of quasi-static cyclic testing performed on four model RC bridge columns of geometric scale factor 4. Two columns had concrete strength of around 2,400 psi whereas other two had strength of around 1,800 psi. Additionally the columns were also tested using ambient vibration testing and one column was subjected to force vibration testing. The purpose of these additional tests was to undertake the identification of dynamic characteristics of these columns at various levels of elastic and inelastic states. Complete description of the models and testing protocol is described in previous chapter.

5.2 Identification of Dynamic Characteristics Before Cyclic Testing

Each of the four columns were tested for identification of dynamic characteristics before the start of quasi-static cyclic testing. This helped in identification of natural period and damping of the system. For this purpose ambient and force vibration tests were conducted.

It is important to note the directions and sign conventions as:

1. North-South (N-S) direction is the longitudinal direction in which the cyclic lateral load is applied. The test always started in this direction for all the four columns. Force and displacements are positive in this direction.

2. East-West (E-W) direction is the transverse direction to the lateral load application. Force and displacements are negative in this direction

5.2.1 Ambient (Free) Vibration Testing

The first column QSCT-2-003 was installed with sensitive tri-axial accelerometer on column top after the installation of full mass. The column was shaken by sudden application of force by a person standing on the column top. The free vibration response was recorded for around 10-20 seconds and is shown in Figure 5.1 for North-South

128 direction which is the longitudinal direction in which the lateral load was applied latter in cyclic testing. Damping of the system can only be determined by experiment; and from the acceleration response time history it was determined (Chopra, 2001) as follows.

1 a  ln i (5.1) 2j aij

Where:  is the damping ratio;

th ai is the acceleration response at i peak;

aij is the acceleration response at latter peak.

From the free vibration response for 100% mass of 19.24 tons on column top, the period of vibration is determined to be 0.78 seconds that is 1.28 Hz whereas the damping ratio was found to be 4.08% using Eq.(5.1) for the N-S direction of column. Here it is important to note that the peak acceleration to which the column was excited was 2.9% g and natural frequency was calculated using Fast Fourier Transform (FFT) which transforms the series of discrete data set from time domain to frequency domain (Chopra, Fast Fourier Transform, 2001). Manual procedure was also used to find the period from the time history data using the data processing software to find the time lengths between two consecutive peaks and it was found to be very close to the value determined from FFT. Similarly the frequency for orthogonal direction E-W is found to be 1.28 Hz which is 0.78 seconds and damping ratio of 4.29%. These dynamic characteristics are listed in Table 5.1.

The second column QSCT-3-004 was also subjected to free vibration response study. In this case and remaining columns the ambient vibration free response was recorded for various stages of loading the mass on column top. For 8 ft square slab and column pedestal had a mass of 5.21 tons and is 27.1% of the total mass on column top, the natural frequency was found to be 3.4 Hz (0.29 seconds) with damping of 8.66%. The natural frequency for transverse direction (E-W) was found to be 3.57 Hz (0.28 second) with damping ratio of 11.79%. When further one layer was added having mass of 4.65 tons (24.2%) thus making a total mass of 9.86 tons (51.3%) on column top, the natural frequency was found to be 2.2 Hz (0.45 sec) and damping ratio of 3.75% for longitudinal

129 (N-S) direction; whereas for transverse direction the natural frequency was 2.25 Hz (0.44 sec) with damping ratio of 9.07%. After loading the final layer of slabs which made the total mass on column top of 19.24 tons (100%), the natural frequency in longitudinal (N- S) direction was 1.27 Hz (0.79 sec) with damping ratio of 3.14%; whereas for transverse direction the natural frequency was found to be 1.4 Hz (0.71 sec) and damping ratio of 2.09%. The free vibration response data at around 75% of the loading was not taken due to technical difficulties with data acquisition system at that time. The dynamic characteristics obtained from free vibration tests for column QSCT-3-004 are presented in Table 5.2.

In similar way the free vibration data for QSCT-4-005 and QSCT-5-006 was also measured and the dynamic characteristics are presented in Table 5.3 and Table 5.4 for the two columns respectively. These tables present the data for elastic columns prior to quasi-static testing.

5.2.1.1 Discussion

In previous section results of free vibration response of RC column prior to quasi-static cyclic testing is presented. The main features of these tests were that mass was gradually added in approximate steps of around 25%. In all the cases it is seen that the natural frequency is decreasing with the increase in mass and the damping ratio also has a similar decreasing trend.

For the first column which has average strength of 2,421 psi, only one free vibration test at 100% mass was conducted and the natural frequency for this column at 100% mass was 1.28 Hz (0.78 sec) with damping ratio 4.08% in N-S longitudinal direction.

We know that the natural period and natural frequency of the system is given by following equation.

m 21 Tfnn2     (5.2) kTnn

Where: Tn is the natural period of the system;

m is the mass of the system;

130 k is the stiffness of the system;

n is the circular frequency of the system;

fn is the cyclic frequency of the system.

However it is important to note that the periods that are found from the free vibration tests are for the damped system and the relation between damped and un-damped system are given by the following equation:

2 TTnD1   (5.3)

Where: TD is the damped natural period of the system;

 is the damping ratio of the system.

For the second QSCT-3-004 column which had average strength of 2,307 psi, the free vibration test were done for 27.1%, 51.3% and 100% of mass and the natural period and damping for this column for longitudinal (N-S) and transverse (E-W) direction were found. For change in natural period please refer to Figure 5.2 and refer to Figure 5.3 for change in damping ratios due to increase in mass.

It is important to note that the time period is increasing (frequency is decreasing) due to increase in mass which is consistent with Eq.(5.2). A decreasing trend is seen in damping ratio which is decreasing with increase in mass, which is consistent with Eq.(5.4).

c  (5.4) 2mn

Where: c is the damping constant of the system;

m is the mass of the system.

For the third column QSCT-4-005 which had average strength of 1,843 psi, the free vibration test were done for 27.1%, 51.3%, 75.6% and 100% of mass and the natural period and damping for this column for longitudinal (N-S) and transverse (E-W) direction were found. For change in natural period please refer to Figure 5.4 and refer to Figure 5.5 for change in damping ratios due to increase in mass. The trend of change in natural

131 period and damping ratio in this column is also consistent with the Eq.(5.2) and Eq.(5.4) respectively.

For the third column QSCT-5-006 which had average strength of 1,781 psi, the free vibration test were done for 27.1%, 51.3%, 75.6% and 100% of mass and the natural period and damping for this column for longitudinal (N-S) and transverse (E-W) direction were found. For change in natural period please refer to Figure 5.6 and refer to Figure 5.7 for change in damping ratios due to increase in mass. The trend of change in natural period and damping ratio in this column is also consistent with the Eq.(5.2) and Eq.(5.4) respectively.

For all the columns the natural period is in range of 0.28-0.35 seconds for 27.1% mass and increases to 0.69-0.88 seconds for 100% mass. The damping ratio varies from 7.21%-11.08% for 27.1% mass to 2.38%-4.88% for 100%.

5.2.2 Forced Vibration Testing

Forced vibration test was performed on only one column QSCT-2-003 with the help of Eccentric Mass Vibrator (EMV) which applies sinusoidal input force and creates a resonance when frequency of forcing function becomes equal to that of structure. The sole purpose of this test was to cross check the response calculated from free vibration test. The EMV installed on column top is shown in Figure 5.8. After installation of EMV and accelerometers on column top the frequency of EMV was varied as per test protocol mentioned in section 4.10.3. The response time history of the column is shown in Figure 5.9. From the EMV results it is observed that the resonance of column response occurs at a frequency of 1.25 Hz (0.8 sec). The free vibration response of this column has provided the natural frequency of 1.28 Hz (0.78 sec) for longitudinal (N-S) direction. Thus it is clear that the two results are in close agreement to each other, the difference being within 2.5%. The frequency for lateral (E-W) direction was found to be 1.24 Hz (0.81 sec) from EMV test, whereas from free vibration test it was found to be 1.28 Hz (0.78 sec) which shows close agreement between force vibration and free vibration response as the difference being 3.8%. Thus the agreement between force vibration and free vibration tests provided confidence that results of free vibration results are reliable. Force vibration test was not undertaken for other columns and after different levels of

132 drifts to avoid any damage to columns as forced vibration test is dynamic test which may cause collapse or severe damage to the column if the control is lost or mismanaged.

5.3 Quasi-Static Cyclic Testing

The main part of this study is related to quasi-static cyclic testing of four columns which had geometric scale factor of 4. First two columns had target strength of 2,400 psi whereas other two columns had target strength of 1,800 psi. This section presents the results of quasi-static cyclic testing for each column separately. It is important to mention that 3 inch squares where marked and numbered on each column for mapping the cracks on column for drift levels.

5.3.1 First Column QSCT-2-003 (2,421 psi)

The first column QSCT-2-003 had material properties as described in section 4.7 and dynamic characteristics of this column are discussed in section 5.2.

5.3.1.1 Cyclic Testing

The quasi-static testing of this column was done following the protocol described in section 4.10.1. The main features of the testing were 3 cycles per drift and total number of 37 cycles till failure at 4% drift. The loading pattern is shown in Figure 4.7. A positive force is used to describe push of actuator which is acting in north direction on the column whereas negative force is used for pull acting in south direction. In similar way positive displacement is used for movement of column in north direction and negative displacement is used to describe displacement in south direction.

5.3.1.2 Observations during Testing

The testing began with one cycle of 0.1% drift which was followed by three cycles each of 0.2%, 0.4%, 0.5% and 0.75% drift. Minor hair line cracks were seen around 0.5% drift level, which were so narrow that they were hardly visible. At 1.0% drift visible cracks appeared that are shown in Figure 5.10 for the north and south face of the column. The maximum restoring force at this stage was (+) 4.96 kips in north direction and (-) 6.76 kips in south direction. From the analysis of hysteresis curves it is clear that this point is the initial yield point, which means that at 1% drift (1.91 mm) the steel started to yield.

133 Further from the analysis of data plotted for the displacement hysteresis curves it is observed that initial cracking of concrete occurred at around 0.48% drift, initial yield at 1.0% and yield at 1.13% for the force applied in north direction and for the force applied in south direction the cracking occurred at 0.50%, initial yield at 0.98% and yield at 1.10%, which is evident from the plot of backbone curve shown in Figure 5.11. The values for cracking, initial yield and yield are provided in Table 5.5.

From the above observations and data the uncracked stiffness, cracked stiffness and equivalent stiffness are calculated as under. The uncracked stiffness is defined as:

Pc kuc  (5.5) uc

Where: kuc is the uncracked stiffness;

Pc is the load at cracking;

uc is the corresponding displacement at cracking.

From the above equation two values of uncracked stiffness are determined one for the pushing force when applied in north direction and other for pulling force in south direction, the uncracked stiffness for north direction was 10.28 k/in and for south direction it was 11.87 k/in. These values are presented in Table 5.5. Also the cracked stiffness is defined as:

Py0 kcr  (5.6) uy0

Where: kcr is the cracked stiffness;

Py0 is the load at initial yield;

uy0 is the corresponding displacement at initial yield.

The value of cracked stiffness for north direction was calculated to be 6.67 kips/in and for south direction it was 9.25 kips/in and both are provided in Table 5.5.

134 However the equivalent stiffness (Kawashima K. , 2006) was calculated from the following formulation:

PPmax min ke  (5.7) uumax min

Where: ke is the equivalent stiffness;

Pmax and Pmin are the maximum and minimum restoring forces on respectively on hysteresis loop;

umax and umin are the maximum and minimum displacements respectively on hysteresis loop.

From Eq.(5.7) the equivalent uncracked stiffness was determined as 11.09 kips/in, the crack equivalent cracked stiffness was found to be 7.96 kips/in, these values are tabulated in Table 5.5.

After applying further three cycles per drift the cracks at 1.5% drift are shown in Figure 5.12 for north and south face of the column that further grew.

Figure 5.13 shows the north and south face of column at 2.5% drift. At this stage significant spalling was seen, it is believed that at this stage buckling of bars did occurred especially at south face.

The column faces at 3% drift are shown in Figure 5.14. At this stage significant spalling of concrete appears on both faces and buckling of bars is also visible. The concrete cover on both faces did spall to a height of around 6 inches. The data for first cycle of 3.0% drift was not recorded due to some technical problem.

At final drift level of 4% the concrete cover further spall off as shown in Figure 5.15. It is important to note that at 4% drift only one cycle could be applied as the strength of the column deteriorated significantly, therefore further testing was stopped.

5.3.1.3 Energy Dissipated

135 From the load-deformation data the hysteresis curves were plotted and energy dissipated in each cycle was calculated. Hysteresis curves for various stages of cyclic testing corresponding to 0.50%, 1.0%, 2.0%, 3.0%, 3.50% and 4.0% are shown in Figure 5.16.

It is noticed that energy dissipated per cycle increased with the increase in drift. The maximum energy dissipated was in first cycle of 4.0% drift. It is further noticed that energy dissipation per cycle is more in first cycle than second or third cycle and difference is less among the second and third cycle.

The values of energy dissipated per cycle and cumulative energy dissipated are provided in Table 5.6. The energy dissipated per cycle is plotted in Figure 5.17,.from this figure it is clear that energy dissipation starts at around 1.0% drift which is in order with previous discussions of section 5.3.1.2 in which yield point was established. Here it is worth mention that energy dissipation happens when the system yields, prior to that for elastic system there is no hysteretic energy dissipation.

The cumulative energy graph is shown in Figure 5.18 with polynomial equation defining the curve shown on the figure. Here in this column it is important to note that the numbers of cycles are 34 before failure at around 4.0% is reached.

5.3.1.4 Stiffness Degradation

From the hysteresis data obtained from the cyclic testing the equivalent stiffness (Kawashima K. , 2006) can be obtained from Eq.(5.7) for each loop of hysteresis. The stiffness degradation curve for this column is shown in Figure 5.19, for which a polynomial equation is also presented on the figure. In this case it important to note that the ratio between initial to final stiffness is 11.1 which shows significant stiffness degradation of the column at 4.0% drift.

From the values of equivalent stiffness, energy dissipated and from input energy to the system the equivalent damping (Kawashima K. , 2006) can be calculated as follows which is an indicator of the energy dissipated in straining the system.

W  (5.8) e 2W

Whereas W can be calculated from the following equation:

136 k We u22 u (5.9) 2  max min 

Where: W is the strain energy input to the system;

e is the equivalent damping ratio of the system;

W is the energy dissipated in a hysteresis loop;

k is the equivalent stiffness; e

umax and umin are the maximum and minimum displacements respectively on the hysteresis loop.

5.3.1.5 Identification of Dynamic Characteristics during and after Cyclic Testing

In this column only once the dynamic parameters were studied before the start of cyclic test when the column was loaded with full (100%) mass on column top and there were no free vibration tests during the cyclic testing and after the completion of this testing.

5.3.2 Second Column QSCT-3-004 (2,307 psi)

The quasi-static testing of this column was done following the protocol described in section 4.10.1 and Table 4.19.

5.3.2.1 Cyclic Testing

The main features of the testing were 2 cycles per drift and total number of 13 cycles till failure at 4% drift. The loading pattern is shown in Figure 4.36. A positive force is used to describe push of actuator which is acting in north direction on the column whereas negative force is used for pull acting in south direction. In similar way positive displacement is used for movement of column in north direction and negative displacement is used to describe displacement in south direction.

5.3.2.2 Observations during Testing

The testing began with one cycle of 0.1% drift which was followed by two cycles each of 0.25%, 0.50%, 1.0%, 2.0, 3.0% and 4.0% drift. Equivalent damping is shown in Figure 5.20 that should not be confused with damping ratio determined from free vibration tests, such as shown in Figure 5.32. Equivalent damping provides an estimate that how much

137 energy is dissipated while the column develops inelastic action. This figure shows a general trend of equivalent damping that is calculated to be 25%. Very thin hair line cracks appeared before 0.5% drift, which were so fine that they were not clearly visible. However at 1.0% drift, visible cracks appeared that are shown in Figure 5.21 for the north and south face of the column. From the analysis of hysteresis curves it is clear that 1% drift was the point is the initial yield, which means that at 1% drift (1.91 mm) the rebar just started to yield. Further from the analysis of data plotted for the displacement hysteresis curves it is observed that for north direction force initial cracking of concrete occurred at around 0.35%% drift, initial yield at 1.0% and yield at 1.10% and for the force applied in south direction the cracking occurred at 0.50%, initial yield at 1.0% and yield at 1.10%, which is evident from the plot of backbone curve shown in Figure 5.22. The values for cracking, initial yield and yield are provided in Table 5.7.

From the above data the uncracked stiffness, cracked stiffness and equivalent stiffness are calculated from Eq.(5.5), Eq. (5.6) and Eq.(5.7) respectively. The uncracked stiffness is found to be 13.71 kips/in for north direction and 13.33 kips/in for south direction; the cracked stiffness for north direction is found to be 6.47 kips/in and for south direction it is found to be 9.33 kips/in; whereas the equivalent stiffness is found to be 13.52 kips/in for uncracked stiffness case and 7.90 kips/in for cracked stiffness case. These values are summarized in Table 5.7.

After applying further two cycles per drift the cracks at 2.0% drift are shown in Figure 5.23 for north and south face of the column that further increased. However it is important to note that the cracks in QSCT-2-003 were more at this stage than this column as this column is subjected to less number of cycles.

Figure 5.24 shows the north and south face of column at 3.0% drift. At this stage significant spalling was seen, it is believed that at this stage buckling of bars did occurred especially at south face.

The column faces at 4% drift are shown in Figure 5.25. At this stage significant spalling of concrete appears on both faces and buckling of bars is also visible. The concrete cover on both faces did spall to a height of around 6 inches.

5.3.2.3 Energy Dissipated

138 From the load-deformation data the hysteresis curves were plotted and energy dissipated in each cycle was calculated. Hysteresis curves for various stages of cyclic testing corresponding to 0.25%, 0.50%, 1.0%, 2.0%, 3.0%, and 4.0% are shown in Figure 5.26.

The values of energy dissipated per cycle and cumulative energy dissipated are provided in Table 5.8. The energy dissipated per cycle is plotted in Figure 5.27, from this figure it is clear that energy dissipation starts at around 1.0% drift. The cumulative energy graph is shown in Figure 5.28 with polynomial equation defining the curve shown on the figure. Here in this column it is important to note that the numbers of cycles are 13 before failure at around 4.0%.

5.3.2.4 Stiffness Degradation

From the hysteresis data obtained from the cyclic testing the equivalent stiffness (Kawashima K. , 2006) can be obtained from Eq.(5.7) for each loop of hysteresis. The stiffness degradation curve for this column is shown in Figure 5.29 for which a polynomial equation is also presented on the figure and the values of stiffness degradation are provided in Table 5.9. In this case it important to note that the ratio between initial to final stiffness is 10.9 which shows significant stiffness degradation of the column at 4.0% drift.

From the values of equivalent stiffness, energy dissipated and from input energy to the system, the equivalent damping (Kawashima K. , 2006) is calculated to be 0.24 at 4% drift using Eq.(5.8) which is an indicator of the energy dissipated in straining the system and is shown in Figure 5.30.

5.3.2.5 Identification of Dynamic Characteristics during and after Cyclic Testing

In this second column QSCT-3-004 free vibration testing was conducted after the completion of 1%, 2%, 3% and 4% drifts. This free vibration testing thus gave very important information with regard to natural period and damping of the system after

139 various levels of inelasticity, and this scheme was suggested by Prof. S. Sheikh (Sheikh S. A., 2008).

The change in natural period of the system after the cyclic testing of various drift levels of two cycles each is presented in Figure 5.31 for both N-S and E-W directions. Here it worth mentioning that at 0% drift there are various values of time period plotted, these are before the start of cyclic test and the period change was due to increase in mass only.

It is worth noting that the time period of the column changes from 0.76 sec to 1.50 sec which is almost double for the N-S direction, whereas for E-W direction the period changes from 0.69 sec to 1.01 sec which around 1.5 times the original. This is consistent with the fact the north and south faces got more damaged than east and west faces of the column so the overall reduction in stiffness is more predominant in N-S direction than E- W direction.

From the free vibration results the change in damping is also determined and plotted in Figure 5.32, it seen that at the start of testing the damping ratio for N-S direction is 3.14% which reduced to 2.62% after 4% drift thus the final damping reduced by 17% whereas for E-W direction the damping increased by 2.39 times the original damping ratio. All the numerical values discussed in this section are presented in

Table 5.10.

5.3.3 Third Column QSCT-4-005 (1,843 psi)

The quasi-static testing of this column was done following the same protocol as for previous column and described in section 4.10.1 and Table 4.19.

5.3.3.1 Cyclic Testing

The testing protocol was similar to previous column QSCT-3-004 and comprised of 2 cycles per drift and total of 13 cycles till failure at 4% drift.

5.3.3.2 Observations during Testing

Hair line cracks appeared around 0.25% drift and were so fine that they were not visible. Cracks at 2.0% drift are shown in Figure 5.33 for the south face of the column. From the analysis of hysteresis curves it is clear that around 0.75% drift was the point of initial

140 yield. Further from the analysis of data plotted for the displacement hysteresis curves it is observed that for north direction initial cracking of concrete occurred at around 0.25%% drift, initial yield at 0.71% and yield at 0.82% and for the force applied in south direction the cracking occurred at 0.22%, initial yield at 0.78% and yield at 0.87%, which is evident from the plot of backbone curve shown in Figure 5.34. The values for cracking, initial yield and yield are provided in Table 5.11.

After applying further two cycles per drift the cracks at 3.0% drift are shown in Figure 5.35 for north and south face of the column that further increased.

The column faces at 4% drift are shown in Figure 5.36. At this stage significant spalling of concrete appears on both faces and buckling of bars is also visible. The concrete cover on both faces did spall to a height of around 5.5 inches.

5.3.3.3 Energy Dissipated

From the load-deformation data the hysteresis curves were plotted and energy dissipated in each cycle was calculated. Hysteresis curves for various stages of cyclic testing corresponding to 0.25%, 0.50%, 1.0%, 2.0%, 3.0%, and 4.0% are shown in Figure 5.37.

Similarly like previous columns it is noticed that energy dissipated per cycle increased with the increase in drift. The maximum energy dissipated was in first cycle of 3% drift. It is further noticed that energy dissipation per cycle is more in first cycle than second cycle.

The values of energy dissipated per cycle and cumulative energy dissipated are provided in Table 5.12. The energy dissipated per cycle is plotted in Figure 5.38, from this figure it is clear that energy dissipation starts at around 1.0% drift. The cumulative energy graph is shown in Figure 5.39 with polynomial equation defining the curve shown on the figure. Here in this column it is important to note that the numbers of cycles are 12 before failure at 4%, the second cycle of 4% drift which was the last cycle was stopped due to significant damage that occurred in the plastic hinge region.

5.3.3.4 Stiffness Degradation

From the hysteresis data obtained from the cyclic testing the equivalent stiffness can be obtained from Eq.(5.7) for each loop of hysteresis. The stiffness degradation curve for

141 this column is shown in Figure 5.40 for which a polynomial equation is also presented on the figure and the values of stiffness degradation are provided in Table 5.13. In this case it is important to note that the ratio between initial to final stiffness is 14.6 which shows significant stiffness degradation of the column occurs till 4.0% drift.

From the values of equivalent stiffness, energy dissipated and from input energy to the system, the equivalent damping (Kawashima K. , 2006) is calculated to be 0.23 at 4% drift using Eq.(5.8) which was an indicator of the energy dissipated in straining the system and is shown in Figure 5.41.

5.3.3.5 Identification of Dynamic Characteristics during and after Cyclic Testing

In this third column QSCT-4-005 free vibration testing was also conducted after the completion of 1%, 2%, 3% and 4% drifts. This free vibration testing provided very important information with regard to natural period and damping of the system after various levels of inelasticity, and this scheme was suggested by Prof. S. Sheikh (Sheikh S. A., 2008).

The change in natural period of the system after the cyclic testing of various drift levels of two cycles each is presented in Figure 5.42 for both N-S and E-W directions. Here it worth mentioning that at 0% drift there are various values of time period plotted, these are before the start of cyclic test and the period change was due to increase in mass only.

It is worth noting that the time period of the column changes from 0.80 sec to 1.98 sec which is 2.5 times of the initial period for the N-S direction, whereas for E-W direction the period changes from 0.79 sec to 1.01 sec which around 1.3 times the original. This is consistent with the fact the north and south faces got more damaged than east and west faces of the column so the overall reduction in stiffness is more predominant in N-S direction than E-W direction.

From the free vibration results the change in damping is also determined and plotted in Figure 5.43, it seen that at the start of testing the damping ratio for N-S direction is 2.38% which slightly reduced to 2.33% after 4% drift, whereas in E-W direction the damping increased by 1.44 times the original damping ratio. All the numerical values discussed in this section are presented in Table 5.14.

142 5.3.4 Fourth Column QSCT-5-006 (1,781 psi)

The quasi-static testing of this column was done following the same protocol as for previous column and described in section 4.10.1 and Table 4.19.

5.3.4.1 Cyclic Testing

The testing protocol was similar to previous column QSCT-4-005 and comprised of 2 cycles per drift and total of 13 cycles till failure at 4% drift.

5.3.4.2 Observations during Testing

Hair line cracks appeared around 0.25% drift and were so fine that they were hardly visible. From the analysis of hysteresis curves it is clear that around 1.0% drift was the point of initial yield for both the columns. Further from the analysis of data plotted for the displacement hysteresis curves it is observed that for north direction initial cracking of concrete occurred at around 0.25%% drift, initial yield at 1.0% and yield at 1.05% and for the force applied in south direction the cracking occurred at 0.25%, initial yield at 1.0% and yield at 1.05%, which is evident from the plot of backbone curve shown in Figure 5.44. The values for cracking, initial yield and yield are provided in Table 5.15.

The column at 1.0% drift is shown in Figure 5.45 for north face of the column. After applying further two cycles per drift the cracks at 2.0% drift are shown in Figure 5.46 for north and south face of the column that further increased.

The column faces at 3% drift are shown in Figure 5.47. At this stage significant spalling of concrete appears on both faces and buckling of bars is also visible, the damage at north face is around 7 inch and around 6 inches on south face.

The damage to column at 4% drift is shown in Figure 5.48. At this level significant damage to column occurs especially to north face and the height of damage was around 7 inches or more and width of damage was also significant.

5.3.4.3 Energy Dissipated

143 Similarly like previous columns it is noticed that energy dissipated per cycle increased with the increase in drift. The maximum energy dissipated was in first cycle of 4% drift. It is further noticed that energy dissipation per cycle is more in first cycle than second cycle which is typical in all columns and at all drift levels.

The values of energy dissipated per cycle and cumulative energy dissipated are provided in Table 5.16. The energy dissipated per cycle is plotted in Figure 5.50, from this figure it is clear that energy dissipation starts at around 1.0% drift. The cumulative energy graph is shown in Figure 5.51 with polynomial equation defining the curve shown on the figure. Here in this column it is important to note that the numbers of cycles are 12 before failure at 4%, the second cycle of 4% drift which was the last cycle was not started due to significant damage that occurred in the plastic hinge region during the first cycle of 4% drift.

5.3.4.4 Stiffness Degradation

From the hysteresis data obtained from the cyclic testing the equivalent stiffness can be obtained from Eq.(5.7) for each loop of hysteresis. The stiffness degradation curve for this column is shown in Figure 5.52 for which a polynomial equation is also presented on the figure and the values of stiffness degradation are provided in Table 5.17. In this case it is important to note that the ratio between initial to final stiffness is 27.9 which shows extraordinary stiffness degradation of the column that occurs till 4.0% drift.

From the values of equivalent stiffness, energy dissipated and from input energy to the system, the equivalent damping (Kawashima K. , 2006) is calculated to be 0.37 at 4% drift using Eq.(5.8) which was an indicator of the energy dissipated in straining the system and is shown in Figure 5.53.

5.3.4.5 Identification of Dynamic Characteristics during and after Cyclic Testing

In this fourth and last column QSCT-5-006 free vibration testing was also conducted after the completion of 1%, 2%, and 3% drifts. The free vibration testing was not done after 4% drift due to severe damage that occurred in the plastic hinge zone. This free vibration testing provided very important information with regard to natural period and damping of

144 the system after various levels of inelasticity, and this scheme was suggested by Prof. S. Sheikh (Sheikh S. A., 2008).

The change in natural period of the system after the cyclic testing of various drift levels of two cycles each is presented in Figure 5.54 for both N-S and E-W directions. Here it worth mentioning that at 0% drift there are various values of time period plotted, these are before the start of cyclic test and the period change were due to increase in mass only.

It is worth noting that the time period of the column changes from 0.88 sec to 1.64 sec which is 1.9 times of the initial period for the N-S direction, whereas for E-W direction the period changes from 0.85 sec to 1.10 sec which around 1.3 times the original. This is consistent with the fact the north and south faces got more damaged than east and west faces of the column so the overall reduction in stiffness is more predominant in N-S direction than E-W direction.

From the free vibration results the change in damping is also determined and plotted in Figure 5.55, it seen that at the start of testing the damping ratio for N-S direction is 4.74% which reduced to 2.35% after 3% drift, whereas in E-W direction the damping reduced by 39% the original damping ratio. All the numerical values discussed in this section are presented in Table 5.18.

5.4 Summary and Conclusions

This section summarizes results of all the four columns tested in this study. The discussion presented here would mainly compare the results with the help of figures.

5.4.1 Energy Dissipation

Normalized curve for the energy dissipated for all the four columns are plotted in Figure 5.56. The first column here is used as reference for plotting the energy dissipation per cycle for rest of three columns. From the analysis of the curves it is observed that huge variation of around 3.4 at low drift cycles of 0.5% is seen which has no significance as the energy dissipation really starts around 1% drift for all the columns as yielding start around 1%. Therefore comparison at 1% and above drift level is important which shows that average deviation for column QSCT-3-004 is around 1.29, 1.35 for column QSCT-4-

145 005 and 1.29 for last column QSCT-5-006. Thus it would be reasonable to say that these three columns are dissipating energy per cycle very close to each other and all the three are approximately 1.31 times more that first column QSCT-2-003. The reason for this difference is that first column QSCT-2-003 was tested using total of 37 cycles till failure at 4% drift with 3 cycles per drift whereas the remaining three columns were tested using total 13 cycles till failure with 2 cycles per drift. Since the first column is experiencing more cycles which causes to reduce its energy dissipation capacity per cycle, however the cumulative energy dissipation in first column would be more due to more yield events being experienced till failure.

This Figure 5.56 thus shows that strength difference among the column has no effect on energy dissipation per cycle of columns whereas this capacity to dissipate energy per cycle is sensitive to number of cycles per drift.

Now the comparison for cumulative energy dissipation is presented. In similar fashion first column QSCT-2-003 is used as reference column and normalized curves for remaining three columns is presented in Figure 5.57. Since energy dissipation starts around 1% drift therefore the high deviation at lower drifts levels are ignored. At 1% drift the deviation of three columns is around 0.77 and this difference increases with drift and becomes maximum at 4% drift to around 0.50. This shows that energy dissipation in three columns is about half at 4% when it is close to failure and these columns were tested with less number of cycles. However it is important to note that cumulative energy dissipation of the three columns is very close to each other which again speaks of an important feature that strength of concrete columns is not effecting the energy dissipation capacity.

5.4.2 Stiffness Degradation

The equivalent stiffness is normalized to the first column and plotted in Figure 5.58. The analysis of this figure shows that at 0.25% drift the three columns have stiffness 1.08 times more than first column. At 1% drift which is around the yield, the stiffness of all the columns is approximately same. The average deviation of stiffness of second column QSCT-3-004 is 1.18, of third column QSCT-4-005 is 1.03 and for last column QSCT-5- 006 is 0.94. This shows that strength does have influence on stiffness degradation as

146 third and forth a column that has strength around 1,800 psi and have normalized values of 1.03 and 0.94 whereas second column has strength of 2,381 psi and its normalized value is 1.18. The first column had normalized value of 1 close to weaker strength columns due to the fact it was subjected to 37 cycles of total with 3 cycles per drift which resulted in normalized value close to weaker strength columns.

5.4.3 Natural Period

The first column QSCT-2-003 was only subjected to free vibration test at 100% of mass load at its top prior to start of quasi-static cyclic test. The natural periods normalized for N-S direction for all columns are shown in Figure 5.59. From the curves it is noticed that change in period for all the three columns is in close range to each other till 2% drift. However after 2% drift there is significant change in the values of last two columns and their period increase more than a factor of 2 which shows that significant degradation occurred in low strength columns that have strength around 1,800 psi which is also in agreement with the stiffness degradation response discussed in previous section.

For the transverse direction the last column has higher values of deviation that the other two columns. The data for E-W direction is shown in Figure 5.60.

5.4.4 Damping Ratio

The normalized values of damping ratio are plotted while considering first column as reference. Here it is mentioned again that first column QSCT-2-003 was tested for free vibration only once before the start of quasi-static testing when it was loaded with full 100% mass on its column top. The normalized curves for N-S direction are plotted in Figure 5.61 and for E-W direction they are plotted in Figure 5.62.

It is seen that the general trend for both directions is that damping ratio ultimately near failure at 4% reduces and it is seen that there is slight increase at around 3% drift in all the three columns. However there is no specific relation observed for different strengths or with drift levels.

147 FIGURES

Figure 5.1: Free vibration response of QSCT-2-003 for identification of dynamic characteristics before cyclic testing in N-S direction.

Figure 5.2: Change in natural period with change in mass for column QSCT-3-004.

148

Figure 5.3: Change in damping with change in mass for column QSCT-3-004.

Figure 5.4: Change in natural period with change in mass for column QSCT-4-005.

149

Figure 5.5: Change in damping with change in mass for column QSCT-4-005.

Figure 5.6: Change in natural period with change in mass for column QSCT-5-006.

150

Figure 5.7: Change in damping with change in mass for column QSCT-5-006.

Figure 5.8: Forced vibration test with EMV installed on column QSCT-2-003.

151

Figure 5.9: Response time history from forced vibration test of QSCT-2-003 for N-S direction.

Figure 5.10: Cracks started to appear at 1% drift on north side face in QSCT-2-003.

152

Figure 5.11: Back bone curve for column QSCT-2-003.

Figure 5.12: Condition of column at 1.5% drift for QSCT-2-003.

153

Figure 5.13: Condition of column at 2.5% drift for QSCT-2-003.

Figure 5.14: Condition of column at 3.0% drift for QSCT-2-003.

Figure 5.15: Condition of column at 4.0% drift for QSCT-2-003.

154

Figure 5.16: Hysteresis curves for column QSCT-2-003.

155

Figure 5.17: Energy dissipated per cycle for column QSCT-2-003.

Figure 5.18: Cumulative energy dissipated for column QSCT-2-003.

156

Figure 5.19: Equivalent stiffness degradation for column QSCT-2-003.

Figure 5.20: Equivalent damping calculated from hysteresis of column QSCT-2-003.

157

Figure 5.21: Damage at 1% drift of column QSCT-3-004.

Figure 5.22: Backbone curve from hysteresis data of column QSCT-3-004.

158

Figure 5.23: Damage of column at 2.0% drift for QSCT-3-004.

Figure 5.24: Damage of column at 3.0% drift for QSCT-3-004.

159

Figure 5.25: Damage of column at 4.0% drift for QSCT-3-004.

160

Figure 5.26: Hysteresis curves for column QSCT-3-004.

161

Figure 5.27: Energy dissipated per cycle for column QSCT-3-004.

Figure 5.28: Cumulative energy dissipated for column QSCT-3-004.

162

Figure 5.29: Equivalent stiffness degradation for column QSCT-3-004.

Figure 5.30: Equivalent damping calculated from hysteresis of column QSCT-3-004.

163

Figure 5.31: Change in natural period following drift levels for column QSCT-3-004.

Figure 5.32: Change in damping following drift levels for column QSCT-3-004.

164

Figure 5.33: Damage of column at 2% for QSCT-3-004.

Figure 5.34: Backbone curve from hysteresis data of column QSCT-4-005.

165

Figure 5.35: Damage of column at 3% for QSCT-3-004.

Figure 5.36: Damage of column at 4% for QSCT-3-004.

166

Figure 5.37: Hysteresis curves for column QSCT-4-005.

167

Figure 5.38: Energy dissipated per cycle for column QSCT-4-005.

Figure 5.39: Cumulative energy dissipated for column QSCT-4-005.

168

Figure 5.40: Equivalent stiffness degradation for column QSCT-4-005.

Figure 5.41: Equivalent damping calculated from hysteresis of column QSCT-4-005.

169

Figure 5.42: Change in natural period following drift levels for column QSCT-4-005.

Figure 5.43: Change in damping ratio following drift levels for column QSCT-4-005.

170

Figure 5.44: Backbone curve from hysteresis data of column QSCT-5-006.

Figure 5.45: Damage of column at 1% for QSCT-5-006.

171

Figure 5.46: Damage of column at 2% for QSCT-5-006.

Figure 5.47: Damage of column at 3% for QSCT-5-006.

172

Figure 5.48: Damage of column at 4% for QSCT-5-006.

173

Figure 5.49: Hysteresis curves for column QSCT-5-006.

174

Figure 5.50: Energy dissipated per cycle for column QSCT-5-006.

Figure 5.51: Cumulative energy dissipated for column QSCT-5-006.

175

Figure 5.52: Equivalent stiffness degradation for column QSCT-5-006.

Figure 5.53: Equivalent damping calculated from hysteresis of column QSCT-5-006.

176

Figure 5.54: Change in natural period following drift levels for column QSCT-5-006.

Figure 5.55: Change in damping ratio following drift levels for column QSCT-5-006.

177

Figure 5.56: Normalized curve for energy dissipated per cycle for the four columns.

Figure 5.57: Normalized curve for cumulative energy dissipated for all the columns.

178

Figure 5.58: Normalized curve for change in equivalent stiffness for all the columns.

Figure 5.59: Normalized curve for change in natural period in N-S direction for last three columns.

179

Figure 5.60: Normalized curve for change in natural period in E-W direction for last three columns.

Figure 5.61: Normalized curve for change in damping ratio in N-S direction for last three columns.

180

Figure 5.62: Normalized curve for change in damping ratio in E-W direction for last three columns.

181 TABLES

Table 5.1: Dynamic parameters from ambient (free) vibration tests for various stages of loading for fully elastic column QSCT-2-003.

Mass on Item Long. Direction Tran. Direction column top (N-S) (E-W)

4.80 tf fn (tn ) - - (25.0%)  - - 9.45 tf ( ) - - (49.1%) - - 14.13 tf ( ) - - (73.4%) - - 19.24 tf ( ) 1.28 Hz (0.78 sec) 1.28 Hz (0.78 sec) (100%) 4.08% 4.29%

Table 5.2: Dynamic parameters from ambient (free) vibration tests for various stages of loading for fully elastic column QSCT-3-004.

Mass on Item Long. Direction Tran. Direction column top (N-S) (E-W) 4.80 tf ( ) 3.40 Hz (0.29 sec) 3.57 Hz (0.28 sec) (25.0%) 8.66% 11.79% 9.45 tf ( ) 2.2 Hz (0.45 sec) 2.25 Hz (0.44 sec) (49.1%) 3.75% 9.07% 14.13 tf ( ) - - (73.4%) - - 19.24 tf ( ) 1.27 Hz (0.79 sec) 1.45 Hz (0.69 sec) (100%) 3.14% 2.09%

182 Table 5.3: Dynamic parameters from ambient (free) vibration tests for various stages of loading for fully elastic column QSCT-4-005.

Mass on Item Long. Direction Tran. Direction column top (N-S) (E-W)

4.80 tf fn (tn ) 3.45 Hz (0.29 sec) 3.23 Hz (0.31 sec) (25.0%)  11.02% 5.43% 9.45 tf ( ) 2.00 Hz (0.50 sec) 1.96 Hz (0.51 sec) (49.1%) 4.21% 5.33% 14.13 tf ( ) 1.54 Hz (0.65 sec) 1.56 Hz (0.64 sec) (73.4%) 2.86% 2.96% 19.24 tf ( ) 1.25 Hz (0.80 sec) 1.45 Hz (0.79 sec) (100%) 2.38% 2.45%

Table 5.4: Dynamic parameters from ambient (free) vibration tests for various stages of loading for fully elastic column QSCT-5-006.

Mass on Item Long. Direction Tran. Direction column top (N-S) (E-W) 4.80 tf ( ) 2.86 Hz (0.35 sec) 2.86 Hz (0.35 sec) (25.0%) 9.69% 7.21% 9.45 tf ( ) 1.85 Hz (0.54 sec) 1.89 Hz (0.53 sec) (49.1%) 8.11% 7.02% 14.13 tf ( ) 1.41 Hz (0.71 sec) 1.43 Hz (0.70 sec) (73.4%) 4.84% 6.18% 19.24 tf ( ) 1.14 Hz (0.88 sec) 1.18 Hz (0.85 sec) (100%) 4.74% 4.88%

183 Table 5.5: Values for cracking, initial yield and yield for column QSCT-2-003.

Item Value for North Direction Value for South Direction

Pc 4.54 kips -3.61 kips

uc 0.48% (9.1 mm) -0.50% (-9.5 mm) k 12.61 kips/in 9.63 k/in uc k 11.12 kips/in Equivalent uc

Py0 5.85 kips -5.96 kips

uy0 1.0% (19.1 mm) -0.98% (-18.7 mm) k 7.8 kips/in 8.11 kips/in cr 7.96 kips/in Equivalent

Py 6.55 kips -6.6 kips

uy 1.13% (21.5 mm) -1.10% (-21.0 mm) u 3.20% max  2.75 d

184 Table 5.6: Values of energy dissipated for column QSCT-2-003.

Energy Dissipated Cumulative Energy Drift Cycle per Cycle Dissipated (%) (k-in) (k-in) 0.10% 1 0.0074 0.0074 1 0.0572 0.0646 0.20% 2 0.0301 0.0947 3 0.0220 0.1167 1 0.0655 0.1822 0.30% 2 0.0307 0.2129 3 0.0194 0.2323 1 0.1489 0.3812 0.40% 2 0.1442 0.5254 3 0.1019 0.6273 1 0.2264 0.8537 0.50% 2 0.1812 1.0349 3 0.1610 1.1959 1 0.7108 1.9067 0.75% 2 0.4360 2.3427 3 0.3773 2.7200 1 1.7301 4.4501 1.00% 2 0.9495 5.3996 3 0.7476 6.1472 1 5.0466 11.1938 1.50% 2 3.1634 14.3572 3 2.9736 17.3308 1 7.6513 24.9821 2.00% 2 6.8228 31.8049 3 7.1726 38.9775 1 12.6079 51.5854 2.50% 2 12.1823 63.7677 3 11.5594 75.3271 1 16.4000 91.7721 3.00% 2 15.8111 91.1382 3 14.7018 105.8400 1 17.1472 122.9872 3.50% 2 16.9812 139.9684 3 14.4004 154.3688 4.00% 1 19.7943 174.1631 Test stopped due to strength degradation

185 Table 5.7: Values for cracking, initial yield and yield for column QSCT-3-004.

Item Value for North Direction Value for South Direction

Pc 4.64 kips -4.0 kips

uc 0.35% (6.7 mm) -0.50% (-9.5 mm) k 17.68 kips/in 10.67 k/in uc k 14.18 kips/in Equivalent uc

Py0 5.89 kips -5.96 kips

uy0 1.0% (19.1 mm) -1.0% (-19.1 mm) k 7.85 kips/in 7.95 kips/in cr 7.90 kips/in Equivalent

Py 6.34 kips -6.61 kips

uy 1.10% (21.0 mm) -1.10% (-21.0 mm) u 4.00% max  3.64 d

Table 5.8: Values of energy dissipated for column QSCT-3-004.

Energy Dissipated Cumulative Energy Drift Cycle per Cycle Dissipated (k-in) (k-in) 0.1% 1 0.02 0.02 1 0.15 0.16 0.25% 2 0.10 0.26 1 0.58 0.84 0.50% 2 0.33 1.16 1 2.41 3.57 1.0% 2 1.35 4.92 1 10.39 15.32 2.0% 2 8.04 23.35 1 20.37 43.73 3.0% 2 17.60 61.33 1 28.25 89.58 4.0% 2 20.82 110.39 Test stopped due to strength degradation

186 Table 5.9: Values of stiffness degradation for column QSCT-3-004.

Stiffness Drift (kips/in) 0.10% 16.62 0.25% 14.25 0.25% 13.81 0.50% 12.34 0.50% 11.48 1.00% 7.91 1.00% 7.55 2.00% 4.45 2.00% 4.12 3.00% 3.50 3.00% 2.74 4.00% 2.25 4.00% 1.52

Table 5.10: Values of natural period and damping ratio for column QSCT-3-004.

N-S Direction E-W Direction Drift Time Damping Time Damping Period Ratio Period Ratio 0.0% 0.29 8.66% 0.28 11.79% 0.0% 0.45 3.75% 0.44 9.07% 0.0% 0.76 3.14% 0.69 2.09% 1.0% 1.10 3.96% 0.80 3.80% 2.0% 1.26 3.88% 0.94 3.33% 3.0% 1.39 3.95% 1.01 5.59% 4.0% 1.50 2.62% 1.01 4.99%

187 Table 5.11: Values for cracking, initial yield and yield for column QSCT-4-005.

Item Value for North Direction Value for South Direction

Pc 3.57 kips -3.13 kips

uc 0.25% (4.8 mm) -0.22% (-4.2 mm) k 19.04 kips/in 18.97 kips/in uc k 19.07 kips/in Equivalent uc

Py0 5.27 kips -5.43 kips

uy0 0.73% (13.5 mm) -0.78% (-14.8 mm) k 9.63 kips/in 9.28 kips/in cr 9.46 kips/in Equivalent

Py 5.97 kips -6.15 kips

uy 0.82% (15.6 mm) -0.87% (-16.6 mm) u 3.00% max  3.45 d

Table 5.12: Values of energy dissipated for column QSCT-4-005.

Energy Dissipated Cumulative Energy Drift Cycle per Cycle Dissipated (k-in) (k-in) 0.1% 1 0.13 0.13 1 0.10 0.23 0.25% 2 0.10 0.33 1 0.63 0.96 0.50% 2 0.38 1.34 1 2.34 3.68 1.0% 2 1.54 5.23 1 11.66 16.89 2.0% 2 9.82 26.71 1 22.26 48.97 3.0% 2 14.29 63.26 4.0% 1 22.19 85.44 Test stopped due to strength degradation

188 Table 5.13: Values of stiffness degradation for column QSCT-4-005.

Drift Stiffness (kips/in) 0.10% 22.48 0.25% 18.07 0.25% 16.79 0.50% 12.04 0.50% 11.76 1.00% 7.88 1.00% 7.69 2.00% 4.21 2.00% 3.87 3.00% 2.57 3.00% 2.10 4.00% 1.72 4.00% 1.54

Table 5.14: Values of natural period and damping ratio for column QSCT-4-005.

N-S Direction E-W Direction Drift Time Damping Time Damping Period Ratio Period Ratio 0.0% 0.29 11.02% 0.31 5.43% 0.0% 0.50 4.21% 0.51 5.33% 0.0% 0.65 2.86% 0.64 2.96% 0.0% 0.80 2.38% 0.79 2.45% 1.0% 0.97 4.17% 0.83 3.07% 2.0% 1.19 4.97% 0.94 3.26% 3.0% 1.67 2.75% 0.99 3.35% 4.0% 1.98 2.33% 1.01 3.54%

189 Table 5.15: Values for cracking, initial yield and yield for column QSCT-5-006.

Item Value for North Direction Value for South Direction

Pc 4.24 kips -3.76 kips

uc 0.50% (4.8 mm) -0.50% (-4.8 mm) k 11.31 kips/in 10.03 kips/in uc k 10.67 kips/in Equivalent uc

Py0 5.34 kips -5.51 kips

uy0 1.0% (19.1 mm) -1.0% (-19.1 mm) k 7.12 kips/in 7.35 kips/in cr 7.24 kips/in Equivalent

Py 6.00 kips -6.00 kips

uy 1.05% (-16.6 mm) -1.05% (-16.6 mm) u 3.00% max  2.86 d

Table 5.16: Values of energy dissipated for column QSCT-5-006.

Energy Dissipated Cumulative Energy Drift Cycle per Cycle Dissipated (k-in) (k-in) 0.1% 1 0.01 0.01 1 0.07 0.09 0.25% 2 0.07 0.16 1 0.48 0.64 0.50% 2 0.31 0.95 1 2.04 2.99 1.0% 2 1.41 4.39 1 10.07 14.46 2.0% 2 8.60 23.06 1 21.62 44.68 3.0% 2 16.51 61.19 4.0% 1 25.83 87.02 Test stopped due to strength degradation

190 Table 5.17: Values of stiffness degradation for column QSCT-5-006.

Drift Stiffness (kips/in) 0.10% 16.65 0.25% 14.30 0.25% 13.17 0.50% 10.60 0.50% 10.31 1.00% 7.17 1.00% 6.99 2.00% 3.90 2.00% 3.77 3.00% 2.59 3.00% 2.09 4.00% 1.22 4.00% 0.60

Table 5.18: Values of natural period and damping ratio for column QSCT-5-006.

N-S Direction E-W Direction Drift Time Damping Time Damping Period Ratio Period Ratio 0.0% 0.35 9.69% 0.35 7.21% 0.0% 0.54 8.11% 0.53 7.02% 0.0% 0.71 4.84% 0.70 6.18% 0.0% 0.88 4.74% 0.85 4.88% 1.0% 1.10 4.62% 0.87 2.89% 2.0% 1.21 4.18% 0.99 3.31% 3.0% 1.64 2.35% 1.10 2.98%

191 CHAPTER 6 NUMERICAL STUDIES

6.1 Introduction

The quasi-static testing of bridge columns in laboratory was done on two groups of low strength concrete comprising of two columns in each group. The experimental study provided the response of typical concrete bridges that exist in Pakistan. Numerical models of the columns were prepared and calibrated using experimental results. The nonlinear material response was the main cause of energy dissipation in hysteretic cycles. From the nonlinear material response a damage index for each column was calculated to quantify the state of column after repeated load reversal of low cycle fatigue. The numerical models were prepared in open source program IDARC 2D versions 7.0 (Reinhron, et al., 2009). The Smooth Hysteretic Model (SHM) (Sivaselvan & Reinhorn, 2000) was used for modeling the nonlinear material response under cyclic loading. After calibration of numerical model nonlinear time history analysis was done using earthquake time histories. The calibrated numerical model thus served the purpose of providing control parameters that were related to stiffness degradation, ductility based strength degradation and energy based strength degradation and slip occurring at plastic hinge. The control parameters thus established were then used for nonlinear time history analysis of prototype bridge column. The results of nonlinear time history analysis thus provided calculation of response modification factor, damage indices residual displacements and the data also provided the basis for developing fragility curves for two groups of concrete strength.

6.2 Selection of Software for Nonlinear Numerical Modeling

In order to model the experimental response of bridge columns those were tested in laboratory and to use the calibrated model for nonlinear time history analysis, robust and powerful software was needed that would be powerful enough to capture the constitutive relationship of concrete and steel. Since the lab tests were done using quasi-static loading in displacement control domain using relatively low concrete strengths it was observed during the tests that stiffness degradation and strength degradation occurred

192 followed by pinching of concrete in plastic hinge zone. Thus it was necessary to use software that would be able to model the lab tests and provided reasonable results as the calibrated model would then be used for nonlinear time history analysis.

During the visit to SUNY Buffalo (Syed, 2008) the Prof. Reinhorn suggested using IDARC2D version 7.0 (Reinhron, et al., 2009) and provided the source of IDARC software.

6.3 IDARC2D 7.0 Software

IDARC2D is developed for modeling of inelastic structures for analysis, design and support of experimental studies and to link experimental research and analytical developments (Valles, Reinhorn, Kunnath, Li, & Madan, 1996). It is an open source software built in FORTRAN (Reinhron, et al., 2009) and capable of taking care of material and geometric nonlinearities. Properties of members are calculated by fiber models or by mechanics based formulations and solutions are obtained using step-by-step integration of equations of motions using Newmark Beta method (Valles, Reinhorn, Kunnath, Li, & Madan, 1996). The software uses distributed flexibility model that has replaced the commonly used hinge model developed for steel frames as the hinge model is not suitable for reinforced concrete elements since the inelastic deformation is distributed along the member rather than being concentrated at critical sections (Park, Ang, & Wen, 1986) thus the revised formulation can now handle flexural or shear failures with the possibilities of numerical overflow eliminated.

Original versions of IDARC used the three-parameter model to capture the hysteretic response and was piece-wise linear to account for stiffness degradation, strength degradation and slip also referred as polygonal hysteretic model (PHM). The newer versions now offer the option to opt for smooth hysteretic model (SHM) (Sivaselvan & Reinhorn, 1999). The SHM model adopted in IDARC2D is a variation of the original model proposed by Bouc (Bouc, 1967) and modified by several others (Sivaselvan & Reinhorn, 1999).

The earlier versions of IDARC contained damage model developed by Park (Park, Ang, & Wen, 1984) to provide a measure of the accumulated damage sustained by the

193 structure, a new model was added in the latter versions of software that was referred to as fatigue based damage model developed by Reinhorn (Reinhorn & Valles, 1995).

6.4 Numerical Model and Its Calibration

IDARC software has the capability to be used for cyclic loading in force control or displacement control mode. Since the quasi-static cyclic testing of the four columns was done in displacement control therefore this feature of the IDARC was extremely helpful in calibration of numerical model with the results obtained from lab testing.

In first step the model columns that were tested in lab were defined in the input text file of IDARC, the input file has free format to read all input data (Reinhorn, et al., 2009).

6.4.1 Defining Numerical Model

An input text file of IDARC for column QSCT-3-004 is presented in Table 6.1. First line of the input file contained the title of the column being modeled.

3rd line contained the control data which included information such as number of stories, number of concrete types used, number of steel reinforcement types used, whether to include P  or not, spread of plasticity or concentrated plasticity, linear flexibility distribution or uniform distribution of flexibility in plastic hinge region and operating system being used. In this modeling of column QSCT-3-004 only one concrete type was used, one type of steel reinforcement was used, was included, spread plasticity was used as concrete elements show spalling of concrete and formation of plastic hinge over relatively large length in contrast to steel elements which usually relatively have small plastic hinge length, the distribution of flexibility in plastic hinge was taken to be linear than uniform as this closely relates to actual case and Windows was selected as operating system.

5th line defines the number of types of elements used in the numerical model. Here in thus study only one type of “column” element was used.

7th line in the input text file of IDARC defined the number of elements for each element type. Here in this study only one number of columns in element type “column” was used.

194 9th line defines the system of units and for this study “kips” and “inches” unit were selected thus all the inputs and outputs are in this system of units.

Line # 11 defined the elevation of floor levels, here in this study only one floor at 75 inches was used.

Line # 13 defined the number if identical frames and in this it was one.

Line # 15 defined the number of column lines that was one in this study.

Line # 17 defined the nodal weights, the stories and frame on which they were placed. In this study 42.4 kips of nodal weight was placed on story # 1 at floor level 1.

Line # 19 provided the option to define the material properties which IDARC uses to generate envelopes or user chooses to provide the complete moment-curvature data. In this study first option was used in which geometric and material properties were defined which IDARC used to generate envelopes.

Line # 21 was used to define the properties of concrete that included unconfined compressive strength, Young‟s modulus, strain at maximum concrete strength, modulus of rupture, ultimate strain in compression and parameter defining slope of falling branch. All these properties were defined from the experimental results except last two which were taken as default values that were calculated by the IDARC program using equations Eq.(6.1) to Eq.(6.3). In these equations the factor ZF defines the shape of the descending branch as shown in Figure 6.1, taken from IDARC report (Valles, Reinhorn, Kunnath, Li, & Madan, 1996) and the expression developed by Kent and Park (Kent & Park, 1971) is used as:

0.5 ZF  (6.1) 50uh   50   0

Where:

' 30 fc 50u ' (6.2) fc 1000

 b 50hs 0.75  (6.3) sh

195 Whereas:

 b is the width of the confined core,

s is the volumetric ratio of confinement steel to core concrete,

sh is the spacing of hoops,

' fc is the unconfined concrete compression strength,

0 is the strain at centroidal axis of concrete in compression block.

Line # 23 defined the steel reinforcement properties which included yield strength, ultimate strength, modulus of elasticity, modulus of strain hardening and strain at start of hardening. Last two values in this line were used as defaults that were calculated from IDARC. Default values were used due to non-availability stress-strain data due to nonfunctioning of extensometer to record data in digital format. The modulus of strain hardening was calculated by IDARC in Eq.(6.4), and strain at start of hardening was calculated by Eq.(6.5).

ES ESH  (6.4) 60 and

EPSH  3.0% (6.5)

Whereas:

ESH is the modulus of strain hardening in units of ksi,

ES is modulus of elasticity in units of ksi,

EPSH is the strain at start of hardening.

Line # 25 defined the number sets i.e. types of hysteretic rules that can be different for different elements. In this study it was one.

Line # 26 defined the parameters used in hysteretic modeling. Since the second value in this line was “2” this is a fix value that forces the IDARC program to use Smooth

196 Hysteretic Model (SHM). Thus for the entire study SHM was used in quasi-static and nonlinear time history analysis. The first value in this line was “1” that described the hysteretic rule set number which was only one throughout this numerical model. Third item on this line defined the stiffness degradation parameter  , 4th term defined the

th ductility-based strength decay parameter 1 , 5 term defined the hysteretic energy-based

th strength decay parameter 2 , 6 term defined the smoothness parameter for elastic to yield transformation N , 7th term defined the shape of unloading parameter , 8th term

th defined the slip length parameter Rs , 9 term defined the slip sharpness parameter  , 10th term in this line defined the mean moment level of slip  , and remaining three terms were related to gap opening and closing and were not used. A guide to various parameters is provided in Figure 6.2 which is adopted from user‟s guide of IDARC (Reinhorn, et al., 2009). Here it is worth mentioning that these parameters were altered during the process of calibration and are discussed in detail in next section. The parameter  is used to capture the stiffness degradation. The factor  is used to capture the strength degradation. However, strength degradation is sub-divided into two parts that are independent of each other; one is due to ductility whereas the other is strength degradation due to energy dissipation that might occur at the same ductility demand.

Line # 28 was related to moment curvature relationship but was not used in this study.

Line # 30 defines the shape of column and in this study it was circular.

Line # 31 defines the section details of the circular column. 1st item defines the column set number, 2nd item defines the concrete type number, 3rd item defines the steel type set, 4th item defines the hysteretic rule number, 5th item defines the column height, 6th and 7th items define the rigid arms on bottom and top respectively which were not used in this study, 8th item defined the axial load on the column, 9th item defined the outer diameter of the column, 10th item defined the center to center of hoop reinforcement, 11th item defined the distance between the centers of longitudinal bars that are opposite to each other along the diameter, 12th item defined the number of longitudinal bars, 13th item defined the diameter of longitudinal bars, 14th item defined the diameter of hoop bars and last item defined the spacing of hoop bars.

197 Line # 33 defined the connectivity of column.

Line # 35 defined the type of analysis to be done such as quasi-static cyclic, inelastic dynamic, monotonic pushover analysis, inelastic incremental static analysis and incremental dynamic analysis. In Table 6.1 the case shown is for quasi-static cyclic analysis for calibration of numerical model, latter cases involved inelastic dynamic analysis.

Line # 37 defined the static loading cases which included uniformly distributed loads on beams, laterally load joints, nodal moments, concentrated vertical loads. In this study we had only one vertical concentrated load.

Line # 38 provided the number of incremental steps in which static loads were applied.

Line # 40 provided details of nodal loads in which load number, frame number, story number, column number and magnitude of external nodal load was specified respectively.

Line # 42 was the option to choose either force control or displacement control. In this study displacement control was chosen since all lab tests were done in displacement control.

Line # 43 defined the number of story levels on which displacement was to be applied.

Line # 44 defined the list of story level on which displacement was applied.

Line # 45 defined the number of points in the displacement history.

Line # 46-57 defined the values of displacement for control and are shown in Figure 6.3.

Remaining lines were used to define the output control.

6.4.2 Calibration of Numerical Model

Next step after defining the numerical model and its debugging was to calibrate the numerical model with the experimental results. Since hysteresis data of the experimental results was available from lab tests, following conditions were met for calibration of numerical model by changing the values of parameters for hysteresis modeling rules till:

198  the cumulative energy dissipated in all cycles in numerical model was close to experimental results,

 the energy dissipated per cycle was close enough in numerical model and experimental results, and

 shape of hysteresis from numerical model was reasonably similar to that of experimental results.

For column QSCT-3-004 the comparison numerical results of hysteresis to that of experimental results is shown in Figure 6.4 and Figure 6.5 which shows reasonable match. This process of calibration was repeated for all the four columns in order to calibrate them for onward usage in nonlinear time history analysis.

6.4.3 Conclusions

The parameters for hysteretic rules of first two columns i.e. QSCT-2-003 and QSCT-3- 004 that represented Group-I with 2,400 psi target strength were very close to each other whereas hysteresis parameters for Group-II columns that represented 1,800 psi strength comprising of columns QSCT-4-005 and QSCT-5-006 matched each other within same group.

The difference between the results of two groups of column was that the value of 2 the parameters responsible for defining hysteretic energy-based strength decay had lower value in Group-II (1,800 psi) than Group-I (2,400 psi). The value of for Group-I was 0.55 and its value for Group-II was 0.68. This shows that Group-II will show more strength degradation for the case in which more cycles of energy is dissipated under same ductility demand. However here it is important to compare these relative results with globally defined values of (HBE) reported by Reinhorn (Reinhorn, et al., 2009) and reproduced in Figure 6.2; according to this figure a value of 0.6 for represents severe deterioration. Group-I had value of as 0.55 which represents high deterioration whereas Group-II had very high value of which was 0.68 and represents extremely high strength deterioration.

199 The values of parameter for stiffness degradation  and ductility-based strength degrading parameter 1 were same for both groups, however their value of 2.0 and

1 0.55 were severe as mentioned in Figure 6.2, which indicates that low strength concrete such as that of Group-I and Group-II do have severe stiffness degradation and strength degradation based on ductility, however there is no difference between the two groups.

Pinching of concrete was found to be different in two groups. The values related to pinching for Group-I were Rs  0.28, 0.30 and 0.30, and for Group-II were

Rs  0.30 , 0.35 and 0.40. This showed that pinching was more predominant in Group-II which has lower strength than Group-I and thus the energy dissipation due to pinching was also less and this was also seen in experimental results.

6.5 Seismic Design of Highway Bridges MCEER/ATC-49

The numerical model developed in IDARC for low strength concrete bridges was calibrated with experimental results, and was used to undertake nonlinear dynamic analysis for estimation of various parameters that included response modification factors, residual displacements and development of fragility curves. Before an exhaustive study is described to find these factors, a guideline document ATC-49 is briefly reviewed which was used as reference for establishing various parameters.

A comprehensive document MCEER/ATC-49 was prepared as a result of joint venture between Applied Technology Council (ATC) and Multidisciplinary Center for Earthquake Engineering Research (MCEER) of State University of New York at Buffalo with regard to LRFD guidelines for the seismic design of highway bridges (ATC and MCEER, 2003)(ATC and MCEER, 2003). This document latter served the basis for AASHTO LRFD Bridge Design Specifications as well.

6.5.1 Seismic Performance Objectives

As first step, seismic performance objectives of bridges need to be established along with classification bridges themselves. Not all the bridges have same importance and thus their performance objectives can vary from each other.

200 MCEER/ATC-49 (ATC and MCEER, 2003)(ATC and MCEER, 2003) is used to spell out these basic question and following two main categories of bridges are deduced:

 CAT-I: Very important bridges

 CAT-II: Ordinary bridges

The performance objective as per MCEER/ATC-49 for Cat-I bridges is to always keep them “operational”. In a Maximum Credible Earthquake (MCE) these bridges should have immediate service and minimal damage, whereas for Expected Earthquake (EE) the performance objective for this category are to have immediate service and damage be limited to minimal to none.

For Cat-II bridges the performance objectives in light of MCEER/ATC-49 is always to ensure “life safety”. In a MCE service level may suffer significant disruption and damage can be significant, however in an EE the performance requirement for service is immediate and damage to be minimal.

Various terms used in performance objectives related to “Service Levels” are defined by MCEER/ATC-49 as under:

“Immediate” service level: Full access to normal traffic shall be available following an inspection of the bridge.

“Significant Disruption” service level: Limited access (reduced lanes, light emergency traffic) may be possible after shoring. However bridge may need to be replaced.

Also terms used in performance objectives related to “Damage Levels” are defined by MCEER/ATC-49 as under:

“None” damage level: Evidence of movement may be present but no notable damage.

“Minimal” damage level: Some visible signs of damage. Minor inelastic response may occur, but post-earthquake damage is limited to narrow flexural cracking in concrete and the onset of yielding in steel. Permanent deformations are not apparent, and any repairs could be made under non-emergency conditions with the exception of superstructure joints.

201 “Significant” damage level: Although there is no collapse, permanent offsets may occur and damage consisting of cracking, reinforcement yield, and major spalling of concrete and extensive yielding and local buckling of steel columns, global and local buckling of steel braces, and cracking in the bridge deck slab at shear studs on the seismic load path is possible. These conditions may require closure to repair the damage. Partial or complete replacement of columns may be required in some cases. For sites with lateral flow due to liquefaction, significant inelastic deformation is permitted in the piles, whereas for all other sites the foundations are capacity-protected and no damage is anticipated. Partial or complete replacement of the columns and piles may be necessary if significant lateral flow occurs. If replacement of columns or other components is to be avoided, the design approaches producing minimal or moderate damage such as seismic isolation or the control and reparability design concept should be assessed.

6.5.2 Design Earthquakes

In MCEER/ATC-49 the higher level earthquake considered is the Maximum Considered Earthquake (MCE) which has a probability of exceedance of approximately 3% in 75- year which corresponds to a return period of 2,462 years.

On the other hand Expected Earthquake (EE) has 50% probability of exceedance in 75- year which corresponds to a return period of 100 years.

6.5.3 Acceleration Time Histories

In order to undertake the nonlinear inelastic time history analysis (ITHA) for establishing various parameters, earthquake time histories were required. According to MCEER/ATC-49 at least three time histories shall be used for ITHA. The three time histories can be recorded, simulated-recorded, or spectrum-matched motions for either MCE or EE.

MCEER/ATC-49 states that design actions shall be taken as the maximum response calculated for the three ground motions and if seven time histories are used the design actions may be taken as the mean response.

For this study three ground motions were chosen to use them for inelastic nonlinear time history analysis. The three time histories were from:

202 1. October 8, 2005 Kashmir earthquake of Mw7.6 with PGA of 0.23 g recorded at Abbottabad.

2. May 18, 1940 Imperial Valley earthquake with PGA of 0.35 g recorded at El Centro.

3. January 17, 1994, Northridge earthquake with PGA of 0.34 g recorded at Nordhoff fire station.

6.6 Inelastic Nonlinear Time History Analysis

Inelastic nonlinear time history analysis was performed on the calibrated numerical model to establish response modification factor, maximum and residual displacements and to draw fragility curves. Three selected time histories as described in above section were used for this purpose. The calibrated numerical model was used in which prototype bridge columns were defined and were subjected to increasing levels of ground motions by scaling the time histories. Three levels of damage index were defined each corresponding to seismic performance objectives defined in MCEER/ATC-49 (ATC and MCEER, 2003)(ATC and MCEER, 2003). The damage indices (Valles, Reinhorn, Kunnath, Li, & Madan, 1996) were also calibrated with the help of results from experimental work and were consistent with values indicated by Park (Park, Ang, & Wen, 1986). For each level of seismic performance objectives the PGA was noted along with corresponding values of energy dissipated by the bridge column, maximum and residual displacements and force in the inelastic system and elastic force in corresponding system that remained elastic. This provided data for calculating the response modification factor and to plot fragility curves for the two categories of numerical model i.e. one representing 2,400 psi concrete and other representing 1,800 psi concrete strength.

6.6.1 Prototype Bridge Columns

The experimental work performed in the lab on scaled models was helpful to study response of concrete bridge columns that have low strength (2,400 psi and 1,800 psi) and the results were used to calibrate a numerical model in IDARC 2D. The calibrated

203 numerical model provided parameters for hysteretic rules that were then used to analyze the prototype bridge columns.

Since two categories of bridge columns were tested in the lab in which CAT-I represented 2,400 psi concrete strength and CAT-II represented 1,800 psi, therefore two calibrated numerical models were used for inelastic nonlinear time history analysis. Within each category two groups of bridge columns were analyzed, in which one group had column diameter of 48 inches (1,220 mm) and second group had diameter of 59 inches (1,500 mm). All the other parameters were kept same except for the height which was varied for each case. Thus total of 20 bridge columns were analyzed. These columns are summarized in Table 6.2. The confinement steel for all the columns was same. Here it is worth mentioning that the height of the column mentioned is from the bottom of the column to center of mass of superstructure which is above the pier cap i.e. transom. Reinforcement details of the columns are provided in Table 6.3. The highest period of the bridge is 1.63 seconds and the lowest period is 0.23 seconds.

The damping ratio from free vibration results suggested values ranging from average value of 3.59% for an elastic system to an average value of 1.83% for an inelastic system are calculated. Usually 5% is taken as the damping ratio for most of the concrete structures (Priestley, Seible, & Calvi, 1996) but based on the experimental results a value of 4% damping was adopted for nonlinear time history analysis, which will slightly affect the response in the elastic range. Since inelastic nonlinear time history analysis is performed which takes care of hysteretic energy dissipation therefore equivalent viscous damping is not required for numerical analysis (Priestley, Seible, & Calvi, 1996).

6.6.2 Calibration of Damage Indices

The damage index calculated by IDARC 2D was an important parameter to define the state of structure. IDARC uses modified Park & Ang model (Park, Ang, & Wen, 1984) and also uses fatigue based damage model (Reinhorn & Valles, 1995). The seismic performance objectives defined in MCEER/ATC-49 (ATC and MCEER, 2003)(ATC and MCEER, 2003) defines damage which was correlated to damage index calculated by program IDARC. The quasi-static tests on columns were also used to calibrate the damage indices.

204 In first step the calibrated numerical model for quasi-static tests was used to correlate various levels of damages as stated by MCEER/ATC-49. As sample damage index history during the quasi-static test can be seen in Figure 6.6. The damage indices correlated to damage levels described in MCEER/ATC-49 are stated below:

1. Damage level “None”: Damage Index is  0.05.

2. Damage level “Minimal”: Damage Index is 0.05-0.15.

3. Damage level “Significant”: Damage Index is 0.15-0.50.

The same correlation damage index data is presented in Table 6.4.

6.6.3 Defining Limiting Values

From the damage indices fixed for seismic performance objectives various limiting values were also established that include energy dissipation and ductility for the prototype bridge columns. Here it is important to note that energy dissipation capacity for any level of damage was calculated from prototype column and its value was close to 64 times the model column which is in close agreement with scale factor established for similitude laws. The limiting values for prototype columns are provided in Table 6.5.

From MCEER/ATC-49 the limit on maximum deflections is imposed from geometric constraints on service level as under:

“Immediate” service level: Horizontal alignment offset or longitudinal joint opening shall be ≤ 3.96 inches (100 mm).

“Significant Disruption” service level: Horizontal alignment offset or longitudinal joint opening shall be ≤ 39.36 inches (1,000 mm).

Criterion for residual displacement is not explicitly specified; however it should be less than the seat width requirement.

6.6.4 Response Modification Factors

It is uneconomical to design a bridge to resist rare and large earthquake elastically (ATC and MCEER, 2003)(ATC and MCEER, 2003). Since strong earthquakes impart huge amount of energy into the bridge which needs to be dissipated. For elastic systems

205 damping is the main source of energy dissipation and this usually is in the range 5% for elastic systems (Priestley, Seible, & Calvi, 1996), which is very less in comparison to the energy delivered to the system. Thus dissipation of energy while bridge remains elastic would be highly uneconomical. Thus bridges are designed in such a way that they will go inelastic as they would be designed for lower value of lateral load. This would results in development of inelastic actions in the concrete columns and is a major source of energy dissipation. In this process it necessary to ensure that bridge would have life safety for extremely large events. Bridges are classified for their importance and accordingly the degree of inelastic action to be allowed is fixed for particular bridge system. The factor by which the response of a hypothetical elastic bridge is reduced is called the Response Modification Factor “R” or “q”. This factor can be calculated by flowing equation for an idealized single-degree-of-freedom (SDOF) oscillator having a nonlinear hysteretic behavior (Kawashima K. , 2006):

EL FTR(,) EL RT (,,,) EL  NL  (6.6) T FTNL (,,) YT NL

Where:

R is the response modification factor based on ductility,

T is the natural period of the bridge,

EL NL FR and FY are the maximum restoring forces with a linear and nonlinear hysteresis in bridge column.

 is target i.e. a predefined ductility factor, T

EL and NL are damping ratios assumed in the linear and nonlinear responses,

However it is worth noting that inelastic nonlinear time history analysis conducted in this study uses elastic damping and energy dissipation in inelastic excursions by hysteresis rules that were calibrated from the experimental results.

In this study three damage index (DI) levels were fixed i.e. DI ≤ 0.05, DI = 0.05-0.15 and DI = 0.15-0.50 as described in detail in Section 6.6.2 in light of MCEER/ATC-49 that

206 were representing three damage levels (ATC and MCEER, 2003)(ATC and MCEER, 2003). Three earthquake time histories were used that were defined in Section 6.5.3. From the results of inelastic nonlinear time history analysis in IDARC 2D for the calibrated numerical model used for two categories of bridges each having two groups of bridge within each category on the basis of column diameter, already detailed in Section 6.6.1.

The Response Modification Factors are calculated and are tabulated in Table 6.6 for damage level “none”. The graphs of same are presented in Figure 6.7. The R values for damage level “minimal” are provided in Table 6.7 and their graphs are provided in Figure 6.8. For the damage level “significant” the values of R are provided in Table 6.8 and their graphs are provided in Figure 6.9.

It is seen in the figures that R-value varies with period of the structure. The value of R is close or even below 1.0 at short periods where as it increases with increase in period. For damage level none and minimal the value of R almost remains constant over mid and long period range but for significant earthquakes the value for long period range again reduces.

From the inelastic nonlinear time history analysis results for structures on stiff soils, R- factor for a MCE event is proposed for very important bridges in Eq.(6.7) and for ordinary bridges Eq.(6.8):

1.25 2.78  (TTnn  0.25);0.25   0.70 R   (6.7) 2.50;0.70Tn 1.70

1.25 6.11  (TTnn  0.25);0.25   0.70  RT4.0;0.70 n  1.10 (6.8)  4.0 2.5  (TTnn  1.10);1.10   1.70

Whereas:

Tn is the natural period of the elastic structure in seconds,

R is the response modification factor.

207 Also R-factors are proposed for expected earthquake for structures on stiff soils; Eq. (6.9) is proposed for very important bridges and Eq. (6.10) is proposed for ordinary bridges.

0.90 0.78  (TTnn  0.25);0.25   0.70 R   (6.9) 1.25;0.70Tn 1.70

0.90 1.89  (TTnn  0.25);0.25   0.70  RT1.75;0.70 n  1.10 (6.10)  1.75 0.83  (TTnn  1.10);1.10   1.70

6.6.5 Maximum Deflections and Residual Deflections

Deflections were measured and reported for each inelastic time history analysis (ITHA). In addition to maximum deflections, residual displacements were also recorded and were compared against the geometric criteria set in Section 6.6.3. ITHA was performed for 20 bridges and corresponding to 3 damage levels defined by damage indices.

The results of ITHA for damage level “none” are tabulated in Table 6.9 and the residual displacements are presented in Figure 6.12 whereas maximum displacements are shown in Figure 6.13. Table 6.10 contains the deflection data for damage level “nominal” and this data for residual displacements is shown in graphical form in Figure 6.14 and maximum deflections are shown in Figure 6.15. For damage level “significant” the results of deflections from ITHA is presented in Table 6.11 and residual deflections are presented in Figure 6.16 whereas maximum displacements are shown in Figure 6.17.

It is seen from these figures that for the damage level case “none” the deflection limits are not exceeded, in this case permanent deflections are extremely small. And for this case no pattern is seen for small or large diameter columns, nor does strength seem to play any role in this case.

It is seen that for the case of damage level “minimal”, which represents EE, that the diameter plays important role in controlling the maximum deflections than the role of concrete strength. The graphs show that larger diameter has more deflection than smaller diameter. Both CAT-I and CAT-II strength columns for 1.5 m closely resemble in performance and have more deflection than smaller diameter columns, as shown in Figure 6.15. This behavior becomes predominant from period range 0.6 seconds and

208 above. The larger diameter columns exceed the deflection limits at around 0.8 seconds whereas smaller diameter columns reach the deflection limits around 1.0 second period. There was no clear trend in residual displacement except that for this damage state 1.5 m column of CAT-I had least residual displacements.

From the last case of MCE corresponding to damage level “significant”, it is seen that larger diameter of CAT-II still shows maximum deflection like in previous case of EE. The two groups i.e. CAT-I and CAT-II columns both having 1.2 m diameter were still close to each other in the MCE. The only exception in performance was seen for 1.5 m column of CAT-I which exhibited small deflection than rest of the three groups. This exception in trend may be attributed to larger diameter with relatively better strength in extremely large ductility range would have performed better. This behavior is seen to start from above 0.8 second period range which means that essentially all the groups of columns are same below 0.8 second period. The extremely large earthquake put huge deflection demand and bridges with period around 0.4 second and below were within the deflection limits and the deflection increased with period increase. The residual displacements were less only in 1.5 m column with concrete strength of 2,400 psi, whereas 2.5 m column of 1,800 psi strength exceeded the deflection limits around 0.5 second period and remaining two groups of bridges i.e. 1.2 m for 2,400 psi and 1,800 psi exceeded deflection limits around 0.7 seconds.

6.6.6 Fragility Curves

Fragility curves or fragility functions are probability distributions to indicate the probability of a particular damage state to occur in a structure as a function of a single predictive demand parameter such as acceleration (Porter, Hamburger, & Kennedy, 2007).

Fragility curves were plotted for the reinforced bridge columns having two categories of concrete strengths i.e. CAT1 having 2,400 psi and CAT2 having 1,800 psi. From MCEER/ATC-49 (ATC and MCEER, 2003)(ATC and MCEER, 2003) three levels of damage were outlined in previous sections, for each damage level a damage index was established. Therefore six fragility curves were plotted, i.e. two fragility curves for each damage level and within each damage level two types of concrete strengths were used.

209 The fragility curves plotted were based log-normal distribution as the choice of lognormal distribution being standard for most of the scientific data (Limpert, Sthahel, & Abbt) and fits well for variety of data related structural failures (Porter, Hamburger, & Kennedy, 2007).

Fragility curve for damage level “none” is plotted in Figure 6.18, which shows that for both categories of concrete i.e. 2,400 psi and 1,800 psi the fragility curves are similar. This means that probability of occurrence of damage “none” as defined in MCEER/ATC- 49 is same for both categories of concrete bridges. This is due to the fact that both the system for this damage level are to remain elastic therefore within elastic range both would essentially behave in same way thus have same probability distribution.

For damage level “minimal” the fragility curve is shown in Figure 6.19. This figure shows that the probability of occurrence of damage level “nominal” is slightly more in 1,800 psi CAT2 concrete than CAT1 of 2,400 psi. This is due to the fact that this level corresponds to start of yielding in rebar and minor cracking and since CAT2 is low strength than CAT1 therefore there is more probability that CAT2 would enter into inelastic state earlier than CAT1, however it is important to note that there is small difference between the two.

Figure 6.20 shows the fragility curve for damage level “significant”. Here it is remarkable to see that there is huge difference between the two categories of concrete. Lower strength concrete has much more probability to undergo significant damage level than relatively higher strength concrete. This is related to the fact that low strength concrete would deteriorate much more quickly in inelastic range due to loss of strength related to ductility and low-cycle fatigue.

All the six fragility curves discussed above are combined and shown in Figure 6.21. This figure shows the relative difference between the six curves on same scale. It is seen that CAT1 bridge columns are performing relatively well than the rest.

6.7 Summary and Conclusions

This chapter comprised of numerical analysis from which important results were drawn. The numerical model developed was calibrated using the experimental results. In order

210 to carryout numerical analysis an appropriate software was selected which could provide direct means of calibration of numerical model with experimental results. A powerful software IDARC 2D version 7.0 was selected for numerical studies. IDARC was used for quasi-static cyclic analysis and thus provided the basis for calibration. Hysteretic modeling parameters were determined and the calibrated numerical mode was then used to run inelastic-time-history-analysis (ITHA) for prototype bridge columns. MCEER/ATC-49 document was then used as base document for defining various limits and defining seismic performance objectives. A suit of three time histories was selected for the ITHA. Parameters such as energy dissipated, maximum deflection, residual deflection, and force in an equivalent elastic system was determined. From the data thus obtained response modification factor “R” was calculated. Log-normal distribution was used to calculate the fragility curves.

Response modification factors for various time periods were determined corresponding to various damage state levels for two concrete strengths. Equations are proposed for low strength concrete bridges typically found in Pakistan and found elsewhere in the world due to degrading concrete or due to poor quality of construction.

Displacement results show that for MCE the deflection for bridges having time period more than 0.4 seconds would experience significant displacements. Permanent deflections can also be an issue in structures having natural period above 0.7 seconds.

Fragility curves plotted for the bridges show that in EE the difference between the two types of concrete strengths i.e. 2,400 psi and 1,800 psi is marginal, however for MCE the difference of performance between these bridges with these two concrete strengths becomes substantial which shows that low strength concrete shows early deterioration than relatively higher strength concrete.

211 FIGURES

Figure 6.1: Parameters for unconfined concrete including factor ZF for IDARC.

Figure 6.2: Typical range of values for hysteresis parameters.

212 5

3 2.2499 2 1.5011

1 0.752 0.3758 0.1863 0 -0.1878 -0.3747 -1

-2 -1.4979 -2.2487 -3 -1.5018

-4

-5 0 20 40 60 80 100 120 Figure 6.3: History of displacement control for IDARC quasi-static analysis.

(a) (b) 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 1 0 0

-1 -1

Force (kips) Force (kips) Force -2 -2 -3 -3 -4 -4 -5 -5 -6 IDARC -6 IDARC -7 Experimental -7 Experimental -8 -8 -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 Drift (in) Drift (in) Figure 6.4: Comparison of experimental and numerical results IDARC for hysteresis (a) 1% drift 1st cycle (b) 2% drift 2nd cycle.

213 (a) (b) 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 1 0 0

-1 -1

Force (kips) Force (kips) Force -2 -2 -3 -3 -4 -4 -5 -5 -6 IDARC -6 IDARC -7 Experimental -7 Experimental -8 -8 -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 Drift (in) Drift (in) Figure 6.5: Comparison of experimental and numerical results IDARC for hysteresis (a) 3% drift 2nd cycle (b) 4% drift 1st cycle.

1.0 0.9 0.8 0.7 0.6 0.5 0.4 DamageIndex 0.3 0.2 0.1 0.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Drift (inches) Figure 6.6: Damage index history in a calibrated numerical model under quasi-static cyclic test for column QSCT-3-004.

214 1.4

1.2

1.0

0.8 R 0.6 CAT1-1.5m Pier

0.4 CAT1-1.2m Pier CAT2-1.2m Pier 0.2 CAT2-1.5m Pier 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 Period (Tn) Seconds Figure 6.7: Response modification factors for damage level “none”.

3.0

2.5

2.0

R 1.5 CAT1-1.5m Pier 1.0 CAT1-1.2m Pier CAT2-1.2m Pier 0.5 CAT2-1.5m Pier 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 Period (Tn) Seconds Figure 6.8: Response modification factors for damage level “minimal”.

215 8.0 CAT1-1.5m Pier 7.0 CAT1-1.2m Pier 6.0 CAT2-1.2m Pier 5.0 CAT2-1.5m Pier

R 4.0 3.0 2.0 1.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 Period (sec) Figure 6.9: Response modification factors for damage level “significant”.

3.00

2.75

2.50

2.25

2.00

1.75

R 1.50

1.25

1.00 CAT1-1.2m CAT1-1.5m 0.75 CAT2-1.2m 0.50 CAT2-1.5m V. Imp. Bridges 0.25 Ordinary Bridges 0.00 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 Period (Tn) Seconds Figure 6.10: Proposed R-factors for very important and ordinary bridges for Expected Earthquake (EE).

216 8.0 7.5 CAT1-1.2m 7.0 CAT1-1.5m 6.5 CAT2-1.2m 6.0 CAT2-1.5m 5.5 V. Imp. Bridges 5.0 Ordinary Bridges 4.5

R 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 Period (Tn) Seconds Figure 6.11: Proposed R-factors for very important and ordinary bridges for Maximum Credible Earthquake (MCE).

0.6

0.5

CAT1-1.5m 0.4 CAT1-1.2m 0.3 CAT2-1.2m 0.2 CAT2-1.5m

0.1 Residual Displacement (inches) Displacement Residual

0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 Tn (sec) Figure 6.12: Residual deflections for damage level “none”.

217 4.5 CAT1-1.5m 4.0 CAT1-1.2m 3.5 CAT2-1.2m 3.0 CAT2-1.5m 2.5

2.0 Deflection Limits

1.5

1.0

0.5 Maximum Displacement (inches) Displacement Maximum 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 Tn (sec) Figure 6.13: Maximum deflections for damage level “none”.

10.0 9.0 CAT1-1.5m 8.0 CAT1-1.2m 7.0 CAT2-1.2m 6.0 5.0 CAT2-1.5m 4.0 3.0 2.0

Residual Displacement (inches) Displacement Residual 1.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 Tn (sec) Figure 6.14: Residual deflections for damage level “minimal”.

218 10.0 CAT1-1.5m 9.0 8.0 CAT1-1.2m 7.0 CAT2-1.2m 6.0 CAT2-1.5m 5.0 Deflection Limits 4.0 3.0 2.0

1.0 Maximum Displacement (inches) Displacement Maximum 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 Tn (sec) Figure 6.15: Maximum deflections for damage level “minimal”.

45.0

40.0

35.0 CAT1-1.5m 30.0 CAT1-1.2m 25.0 CAT2-1.2m 20.0 CAT2-1.5m

15.0

10.0

Residual Displacement (inches) Displacement Residual 5.0

0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 Tn (sec) Figure 6.16: Residual deflections for damage level “significant”.

219 45.0 CAT1-1.5m 40.0 CAT1-1.2m 35.0 CAT2-1.2m 30.0 CAT2-1.5m 25.0

20.0 Deflection Limits

15.0

10.0

5.0 Maximum Displacement (inches) Displacement Maximum 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 Tn (sec) Figure 6.17: Maximum deflections for damage level “significant”.

1.0 0.9 0.8 0.7 0.6 0.5

0.4 Probability 0.3 CAT1 0.2 0.1 CAT2 0.0 0.00 0.05 0.10 0.15 0.20 0.25 0.30

PGA Figure 6.18: Fragility curves for CAT-1 and CAT-2 concrete strengths for damage level “none”.

220 1.0 0.9 0.8 0.7 0.6 0.5

0.4 Probability 0.3 CAT1 0.2 0.1 CAT2 0.0 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

PGA Figure 6.19: Fragility curves for CAT-1 and CAT-2 concrete strengths for damage level “minimal”.

1.0 0.9 0.8 0.7 0.6 0.5

0.4 Probability 0.3 CAT1 0.2 0.1 CAT2 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1

PGA Figure 6.20: Fragility curves for CAT-1 and CAT-2 concrete strengths for damage level “significant”.

221 1.0 0.9 0.8 0.7 0.6 0.5 0.4

Probability CAT1 CAT2 0.3 0.2 CAT1 CAT2 0.1 CAT1 CAT2 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

PGA Figure 6.21: Fragility curves for two concrete strengths for all the three damage levels as per MCEER/ATC-49.

222 TABLES

Table 6.1: Input text file of QSCT-3-004 for IDARC 2D software.

Lines # Input Text File for IDARC 2D

Line # 1 Model Col. QSCT-3-004 SHM – Quasi-static Cyclic Displacement Controlled Test

Line # 2 CONTROL DATA

Line # 3 1, 1, 1, 1, 0, 1, 0, 0, 1

Line # 4 ELEMENT TYPES

Line # 5 1, 0, 0, 0, 0, 0, 0, 0, 0, 0

Line # 6 ELEMENT DATA

Line # 7 1, 0, 0, 0, 0, 0, 0, 0, 0

Line # 8 UNIT SYSTEM (KIPS/INCH)

Line # 9 1

Line # 10 FLOOR ELEVATIONS

Line # 11 75.0

Line # 12 DESCRIPTION OF IDENTICAL FRAMES

Line # 13 1

Line # 14 PLAN CONFIGURATION (SINGLE COLUMN LINE)

Line # 15 1

Line # 16 NODAL WEIGHTS

Line # 17 1, 1, 42.4

Line # 18 CODE FOR SPECIFICATION OF USER PROPERTIES

Line # 19 0

Line # 20 CONCRETE PROPERTIES

Line # 21 1, 2.307, 2737.0, 0.18, 0.597, 0.0, 0.0

Line # 22 REINFORCEMENT PROPERTIES

Line # 23 1, 53.0, 70.4, 29000.0, 0.0, 0.0

Line # 24 HYSTERETIC MODELING RULES

Line # 25 1

Line # 26 1, 2, 2.0, 0.55, 0.62, 3.0, 1.0, 0.28, 0.35, 0.35, 2.0, 1000.0, 2.0

Line # 27 MOMENT CURVATURE ENVELOPE GENERATION

Line # 28 0

223 Line # 29 COLUMN DIMENSIONS

Line # 30 3

Line # 31 1,1,1,1, 75.0,0.0,0.0, 42.4, 12.0, 0.591, 10.431, 26, 0.291, 0.0964, 1.5

Line # 32 COLUMN CONNECTIVITY

Line # 33 1,1,1,1,0,1

Line # 34 ANALYSIS TYPE

Line # 35 4

Line # 36 STATIC ANALYSIS OPTION (Axial Force Only)

Line # 37 0,0,0,1

Line # 38 4,1

Line # 39 Nodal Loads

Line # 40 1, 1, 1, 1, 42.4

Line # 41 Quasistatic Analysis

Line # 42 1

Line # 43 1

Line # 44 1

Line # 45 115

Line # 46 0 0.0746 0 -0.0762 0 0.1863 0 -0.1878 0 0.1865

Line # 47 0 -0.1881 0 0.3758 0 -0.3747 0 0.3782 0 -0.3749

Line # 48 0 0.3705 0.752 0.3697 0 -0.3699 -0.7507 -0.37 0 0.3705

Line # 49 0.752 0.3697 0 -0.3699 -0.7507 -0.37 0 0.3706 0.7516 1.1274

Line # 50 1.5011 0.7516 0.3706 0 -0.3749 -0.7509 -1.4979 -0.7507 -0.3712 0

Line # 51 0.3706 0.7516 1.1274 1.5011 0.7516 0.3706 0 -0.3749 -0.7509 -1.4979

Line # 52 -0.7507 -0.3712 0 0.5612 1.125 2.2499 1.1269 0.5595 0 -0.5595

Line # 53 -1.1269 -2.2487 -1.1204 -0.5575 0 0.5612 1.125 2.2499 1.1269 0.5595

Line # 54 0 -0.5595 -1.1269 -2.2487 -1.1204 -0.5575 0 0.7509 1.5018 2.2526

Line # 55 2.9983 2.2513 0.752 0 -0.7509 -1.5018 -2.2526 -2.9983 -2.2513 -0.752

Line # 56 0 0.7509 1.5018 2.2526 2.9983 2.2513 0.752 0 -0.7509 -1.5018

Line # 57 -2.2526 -2.9983 -2.2513 -0.752 0

Line # 58 0.005

Line # 59 SNAPSHOT OUTPUT

Line # 60 0,

224 Line # 61 0,0,0,0,0

Line # 62 OUTPUT CONTROL

Line # 63 1,1,1

Line # 64 CYC1.OUT

Line # 65 MISCELLANEOUS OUTPUT INFORMATION

Line # 66 1,0,0,0,0,0

Line # 67 COLUMN OUTPUT

Line # 68 1

225 Table 6.2: Summary of 20 prototype bridge columns used in inelastic nonlinear time history analysis.

Bridge Strength Diameter Height Period Reinforcement ' Code f c (Seconds) Ratio B1.1 34 ft-8 in 1.52 (10.566 m) B1.2 26 ft-3 in 1.00 (8.0 m) B1.3 48 inches 25 ft-0 in 0.93 1.53% (1,220 mm) (7.620 m) B1.4 19 ft-8 in 0.65 (6.0 m) B1.5 13 ft-1 in 0.35 2,400 psi (4.0 m) B1.6 (16.55 MPa) 39 ft-4 in 1.21 (12.0 m) B1.7 32 ft-10 in 0.92 (10.0 m) B1.8 59 inches 26 ft-3 in 0.66 1.40% (1,500 mm) (8.0 m) B1.9 19 ft-8 in 0.43 (6.0 m) B1.10 13 ft-1 in 0.23 (4.0 m) B2.1 34 ft-8 in 1.63 (10.566 m) B2.2 26 ft-3 in 1.07 (8.0 m) B2.3 48 inches 25 ft-0 in 1.00 1.53% (1,220 mm) (7.620 m) B2.4 19 ft-8 in 0.70 (6.0 m) B2.5 13 ft-1 in 0.38 1,800 psi (4.0 m) B2.6 (12.41 MPa) 39 ft-4 in 1.30 (12.0 m) B2.7 32 ft-10 in 0.99 (10.0 m) B2.8 59 inches 26 ft-3 in 0.71 1.40% (1,500 mm) (0.71 m) B2.9 19 ft-8 in 0.46 (6.0 m) B2.10 13 ft-1 in 0.25 (4.0 m)

226 Table 6.3: Reinforcement details of prototype columns used in inelastic nonlinear time history analysis.

Bridge Code Rebar Diameter # of rebar Diameter of Spiral pitch confinement B1.1-B1.5 26 B1.6-B1.10 1.164 in 36 0.386 in 6 in B2.1-B2.5 (30 mm) 26 (10 mm) (150 mm) B2.6-B2.10 36

Table 6.4: Damage Indices correlated to damage levels defined by MCEER/ATC-49.

MCEER/ATC-49 defined Value of Damage Index Damage Level None ≤ 0.05 Minimal 0.05-0.15 Significant 0.15-0.50

Table 6.5: Limiting values of energy dissipation and ductility for prototype bridge columns.

MCEER/ATC-49 defined Damage Energy Ductility Damage Level Index (k-in) µ None ≤ 0.05 190 ≤ 1.0 Minimal 0.05-0.15 1,440 ≤ 1.14 Significant 0.15-0.50 5,760 ≤ 3.0

227 Table 6.6: Response Modification Factors (R) for 20 prototype bridges for “none” damage level.

EL NL Energy F FY S.# Code R R Dissipated (kips) (kips) (k-in) 1 B1.1 58 56 1.04 77 2 B1.2 110 89 1.24 85 3 B1.3 98 83 1.18 71 4 B1.4 94 88 1.07 58 5 B1.5 130 130 1.00 76 6 B1.6 82 79 1.04 96 7 B1.7 118 94 1.18 79 8 B1.8 107 106 1.01 74 9 B1.9 140 138 1.01 74 10 B1.10 207 221 0.94 164 11 B2.1 55 50 1.10 56 12 B2.2 90 78 1.15 165 13 B2.3 85 68 1.25 43 14 B2.4 74 97 0.76 45 15 B2.5 146 131 1.11 75 16 B2.6 84 78 1.08 148 17 B2.7 95 87 1.09 66 18 B2.8 135 125 1.08 79 19 B2.9 171 156 1.10 70 20 B2.10 230 207 1.11 92

228 Table 6.7: Response Modification Factors (R) for 20 prototype bridges for “minimal” damage level.

EL NL Energy F FY S.# Code R R Dissipated (kips) (kips) (k-in) 1 B1.1 155 78 1.99 634 2 B1.2 217 103 2.11 1,028 3 B1.3 208 107 1.94 875 4 B1.4 188 137 1.37 735 5 B1.5 243 192 1.27 645 6 B1.6 299 113 2.65 1,186 7 B1.7 245 135 1.81 1,326 8 B1.8 233 169 1.38 1,312 9 B1.9 280 222 1.26 1,117 10 B1.10 259 276 0.94 862 11 B2.1 154 72 1.88 740 12 B2.2 108 97 1.11 898 13 B2.3 191 101 1.89 867 14 B2.4 234 126 1.86 770 15 B2.5 292 195 1.50 582 16 B2.6 108 108 1.85 1,264 17 B2.7 143 132 1.08 1,440 18 B2.8 352 160 2.20 1,309 19 B2.9 445 221 2.01 905 20 B2.10 319 291 1.10 1,142

229 Table 6.8: Response Modification Factors (R) for 20 prototype bridges for “significant” damage level.

EL NL Energy F FY S.# Code R R Dissipated (kips) (kips) (k-in) 1 B1.1 202 78 2.59 1,922 2 B1.2 671 105 6.39 2,863 3 B1.3 810 111 7.30 3,177 4 B1.4 451 143 3.15 3,425 5 B1.5 373 207 1.80 2,682 6 B1.6 838 121 6.93 5,736 7 B1.7 1,069 147 7.27 5,661 8 B1.8 501 187 2.68 5,181 9 B1.9 456 241 1.89 4,449 10 B1.10 383 349 1.10 3,631 11 B2.1 190 72 2.64 1,807 12 B2.2 454 98 4.63 1,774 13 B2.3 572 101 5.66 2,677 14 B2.4 489 130 3.76 3,130 15 B2.5 442 190 2.33 3,043 16 B2.6 265 108 2.45 3140 17 B2.7 648 131 4.95 4,418 18 B2.8 730 164 4.45 5,582 19 B2.9 680 213 3.19 4,503 20 B2.10 473 316 1.50 4,343

230 Table 6.9: Maximum and residual deflections in 20 bridges for the damage level state “none”.

 residual S.# Code max (inches) (inches) 1 B1.1 2.30 0.14 2 B1.2 1.24 0.49 3 B1.3 1.18 0.30 4 B1.4 0.62 0.08 5 B1.5 0.28 0.03 6 B1.6 2.08 0.31 7 B1.7 1.80 0.27 8 B1.8 0.73 0.09 9 B1.9 0.40 0.04 10 B1.10 0.27 0.04 11 B2.1 2.36 0.10 12 B2.2 2.02 0.02 13 B2.3 1.41 0.13 14 B2.4 1.06 0.16 15 B2.5 0.34 0.06 16 B2.6 2.69 0.03 17 B2.7 1.83 0.16 18 B2.8 1.39 0.02 19 B2.9 0.68 0.11 20 B2.10 0.25 0.02

231 Table 6.10: Maximum and residual deflections in 20 bridges for the damage level state “minimal”.

 residual S.# Code max (inches) (inches) 1 B1.1 7.60 5.86 2 B1.2 4.23 2.82 3 B1.3 3.70 1.21 4 B1.4 2.12 0.05 5 B1.5 0.72 0.02 6 B1.6 2.65 0.37 7 B1.7 4.70 1.04 8 B1.8 3.25 0.20 9 B1.9 1.42 0.02 10 B1.10 0.47 0.00 11 B2.1 8.89 8.87 12 B2.2 4.44 0.39 13 B2.3 3.89 2.40 14 B2.4 2.62 0.21 15 B2.5 1.20 0.05 16 B2.6 9.02 5.56 17 B2.7 5.89 0.43 18 B2.8 3.47 0.26 19 B2.9 2.17 0.09 20 B2.10 0.59 0.06

232 Table 6.11: Maximum and residual deflections in 20 bridges for the damage level state “significant”.

 residual S.# Code max (inches) (inches) 1 B1.1 34.24 33.97 2 B1.2 14.75 14.55 3 B1.3 14.99 14.85 4 B1.4 7.85 1.38 5 B1.5 2.42 0.26 6 B1.6 18.58 3.23 7 B1.7 15.48 0.96 8 B1.8 9.17 0.84 9 B1.9 4.33 0.04 10 B1.10 1.37 0.07 11 B2.1 34.34 33.90 12 B2.2 16.63 16.10 13 B2.3 22.20 22.06 14 B2.4 7.80 3.74 15 B2.5 3.03 0.01 16 B2.6 39.79 39.79 17 B2.7 23.79 23.78 18 B2.8 9.09 6.27 19 B2.9 5.78 4.28 20 B2.10 1.72 0.01

233 CHAPTER 7 SUMMARY AND CONCLUSIONS

7.1 Summary

Bridges are specialized structures that carry heavy mass on the column top. During a seismic excitation huge inertial forces are generated whose energy needs to be dissipated. For small earthquakes the energy is dissipated elastically due to damping but the energy imparted by large earthquakes is dissipated by inelastic action developed in the bridge columns. Since seismic design of bridges started in early 60‟s and large infrastructure has been built in last few decades and the seismic design codes are still in the process of becoming mature. The energy dissipation in concrete by hysteresis is a complex phenomenon and depends on many factors. Investigations to understand this phenomenon was undertaken by many researchers and yet there are factors that need further investigation.

Present study has been carried out to investigate and understand the energy dissipation through hysteresis in low strength concrete bridge columns which is an unaddressed area at this moment. Important contributions of this study are estimation of a response modification factor “R” used in design of bridges and associated parameters such as ductility, permanent displacements and plotting fragility curves. In addition to this, quantification of resilience of bridges with the help of functionality function is established.

Before presenting the conclusions and recommendations of this study, a brief summary of the work carried out is presented. First of all field study of bridges was undertaken along with data collection of design documents. A comprehensive study of seismic performance of bridges following the Oct. 8, 2005 earthquake was done. From the seismic performance field survey of about 90 bridges (of which 14 suffered some form of damage), a mathematical function for functionality of bridges was developed that is helpful in quantification of seismic resilience of bridges. From the field survey of bridge parameters it was found that the average span for all bridge types was 97 feet (29.5 m) whereas bridges of single column with solid circular section have an average span of 85 feet (26.0 m). The average pier height was found to be 23 feet (7.1 m). Majority of the

234 bridges were two-lane and average weight on column top was found to be 683 kips (310 tons). The most important parameter that was strength of concrete was found to vary throughout and mean was around 2,400 psi with some bridges with as low as 1,800 psi.

Four bridge columns scaled to geometric scale factor of 1:4 were fabricated in lab of which two had concrete cylinder strength of 2,400 psi and two were of 1,800 psi. Quasi- static cyclic testing was done on all columns along with series of free vibration tests, while forced vibration test was done on one column. The results of these experiments provided understanding of seismic performance of low strength concrete. Inelastic nonlinear time history analysis of prototype bridge columns was done using calibrated numerical models in IDARC 2D program. MCEER/ATC-49 was used as reference document to define various limiting values and for calibrating the damage index. The hysteretic modeling rules accounted for stiffness degradation, strength degradation due to ductility demand and due to low cycle fatigue, and effect of pinching.

Limit states with regard to seismic performance objectives that are defined in MCEER/ATC-49 were used for two classes of bridges, i.e., very important and ordinary bridges for MCE and DE. Since this study addresses two concrete strengths namely 2,400 psi and 1,800 psi therefore analysis was done for both the classes of concrete strengths. Damage Index (DI) which accounts for all the hysteretic modeling parameters defined above was calibrated from the experimental results. Non-linear inelastic time history analysis was performed with increasing order of scaling of the time history till limit state was reached. For each case results were recorded and values of different parameters were calculated. IDARC 2D calculates the DI which accounts for low-cycle fatigue as well, thus ID was used as one of the main parameter for limit state but a energy dissipation was also watched for its limiting value during the inelastic dynamic analysis

Since purpose of this study was to study the seismic energy dissipation capacity of bridge columns, therefore broad range of bridges having single solid circular cross-section were studied which was depicted from natural period of the bridge columns.

For two concrete strength groups i.e. 2,400 psi and 1,800 psi, two diameters of bridge columns were fixed for each strength case. Height was varied to account for change in

235 time period of the bridge. In total of 20 bridges in total of 4 groups were studied that had elastic natural period ranging 0.25 seconds to 1.68 seconds.

In design of structures for extreme events such as MCE and DE, seismic codes allow the use of force-base design procedures that involves the elastic analysis response divided by Response Modification Factor “R”. One of the main objectives of this study was to estimate and propose R-factor for bridges that have low concrete strength. These results would be helpful in development indigenous bridge design code for Pakistan. The conclusions drawn are presented in following section.

7.2 Conclusions

From the numerical analysis important conclusions are drawn and accordingly recommendations are for made for five distinct areas as following:

7.2.1 Conclusions Regarding Functionality of Bridges

1. The resilience of bridges can be quantified with the help of mathematical function developed for functionality. The functionality of the bridge is expressed with a dimensionless number which can range generally between 0 to 1. However, the value of functionality can increase beyond one for a bridge strengthened or improved beyond its original functionality. For calculating the functionality various parameters are used that include vehicular design speed, number of traffic lanes, volume of pedestrians, weighing factors with regard to use of bridge, limit states and confidence factor for public‟s willingness to use the bridge. These factors can alter the functionality of bridge. Mathematically the functionality of a bridge is given by Eq.(3.1) and subsequent related equations.

2. A functionality criterion is also suggested with the help of design specifications of AASHTO LRFD and experience from field investigations. Two classes of functionality criterion are suggested, one for MCE and other for DE. Within each class, values of minimum required functionality are suggested for a single-lane, two-lane and multi-lane bridge while taking into account the importance classification of a bridge.

236 7.2.2 Conclusions Regarding Experimental Testing

It is shown that conducting free vibration and forced vibration testing during various phases of quasi-static cyclic testing is extremely helpful in estimation of dynamic characteristics of test structures at different stages of inelasticity. It is recommended to conduct free vibration testing to improve the understanding of structures that are passing through various phases of inelasticity.

7.2.3 Conclusions Regarding Hysteretic Energy Dissipation

1. Experimental results indicate that energy dissipation capacity 2,400 psi and 1,800 psi columns are almost same. Thus strength of concrete in this range does not affect the total energy absorption capacity.

2. Stiffness degradation and ductility-based strength degradation is seen to be relatively independent of concrete strength. However, hysteretic energy-based strength degradation which is low-cycle fatigue is seen to be more in low strength concrete of 1,800 psi than 2,400 psi concrete.

3. Pinching is slightly more in low strength concrete which leads to less energy dissipation in a seismic event during large ductility demands.

4. The level of damage as indicated by damage index is more for same level of ductility demand and energy dissipation in 1,800 psi concrete than 2,400 psi concrete.

5. Permanent deformations are seen to be more in 1,800 psi concrete than 2,400 psi concrete.

7.2.4 Conclusions Regarding Design Parameters

1. It was observed that Response Modification Factor “R-factor” is dependant on the period of structure, which is in agreement with MCEER/ATC-49. General trend was a small value of R-factor for bridges having small natural period, higher value of R for mid-range period structures and slightly less value of R-factor for long period structures. Thus as a result of this study R-factor is suggested by mathematical equations which are function of natural period of elastic structure.

237 2. MCEER/ATC-49 recognizes two seismic performance levels and in this study two types of bridges i.e. very important and ordinary were defined, and also we have MCE and DE. Therefore two sets of equations for types of bridges are proposed for MCE and also two sets for DE. Thus total of four equations for R- factor are proposed in this study that are function of natural period of bridge. The mathematical equations for R-factor are Eq.(6.7) to Eq.(6.10).

3. For MCE it was seen that value of R-factor was high for 2,400 psi concrete and slightly less for 1,800 psi concrete in mid-period range, whereas the difference tends to diminish in low and high period ranges. For DE value of R-factor has shown to be relatively independent of material strength.

4. Deflections are one major factor in seismic design. It was seen that maximum deflection criteria during the MCE was satisfied for all the bridges. However in case of permanent displacements it was seen that the column having concrete strength of 2,400 psi and diameter of 59 inches (1.5 m) performed the best and the residual displacements remained the lowest as compared to rest of the three groups (i.e. 2,400 psi with 1.2 m diameter, 1,800 psi with 1.5 m diameter and 1,800 psi with 1.2 m diameter). It is concluded that special attention should be paid to structures that have period above 0.70 seconds. For DE it was seen that maximum deflections were within limits for around period of 0.90 seconds and exceeded the limit state value above this period, whereas residual deflections were large for period range above 1.0 seconds.

7.2.5 Conclusions Regarding Fragility of Bridges

1. Scaling of time histories over a broad range of PGA should be avoided as much as possible, as large magnitude earthquakes usually predominately contain low frequencies content and scaling of a small earthquake to high values of PGA may not be realistic.

2. This study shows that fragility curves plotted for two concrete strengths i.e. 1,800 and 2,400 psi for three levels of damage index (DI), and are such that for damage level “none” and “minimal” the fragility curves for two material strengths are

238 practically same i.e. bridges having both types of strength will perform equally same during an EE. However for the case of damage level “significant” which represent a MCE the bridges with 2,400 psi would outperform the bridges having 1,800 psi concrete. This suggests that resilience of 2,400 psi concrete bridge column would be better than lower value of concrete. The current seismic hazard published in Building Code of Pakistan in 2007 is for a return period of 475- years, whereas bridges need to be designed for MCE that has a return period of 2,500-years and poses a serious challenge to existing bridge stock and for those to be designed in future.

7.3 Future Studies

Following research studies are proposed for future work.

1. To study the effect of seismic demand on hollow bridge columns having relatively low concrete strength.

2. It is suggested to study different methods of retrofitting the current stock of bridges which do not satisfy the requirements of seismic provisions. This retrofitting study should also consider the MCE with a return period of ~ 2,500 years, which is not yet given in Seismic Hazard Map of Pakistan 2007.

3. To develop fragility curves incorporating boundary conditions that incorporate presence of bearing pads along with girders while considering vertical ground accelerations to account for non-proportional loading.

4. To incorporate soil-structure interaction with piles attached to the bridge pier.

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248 VITA Dr. Syed Mohammad Ali was born in Abbottabad (Feb. 14, 1974), NWFP Pakistan. He did his high school (10th grade) from F. G. Boys Public High School Abbottabad in 1990. He completed his higher secondary education (12th grade) from P.A.F College Chaklala, Rawalpindi in 1992. From 1993-1997 he did his B.Sc. in Civil Engineering from NWFP University of Engineering & Technology Peshawar. He joined Khyber Consulting Engineers Peshawar in Feb. 1998 and remained there as Structural Engineer till Aug. 2002. He joined NWFP UET as Lecturer in Aug. 2002. He did his M.Sc. in Structural Engineering from NWFP UET Peshawar in Sep. 2004. He became Assistant Professor in Aug. 2005. He started his PhD studies in Aug 2004 and finished in 2009.

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