Seismic vulnerability and retrofitting of gravity load designed RC buildings

I

ACKNOWLEDGEMENTS
I would like to take this opportunity to express my profound gratitude and sincere
appreciation to my erudite supervisors Professor Tan Kiang Hwee and formerly Professor T.
Balendra, for their kind and systematic guidance and supervision throughout the course of this
study. Their knowledge and experience has been my guiding star throughout this endeavor. I
am forever indebted to my supervisor Prof. Tan Kiang Hwee for the enormous amount of
patience he has shown during my thesis writing.
I would also like to thank the staffs of the Structural Laboratory for their help and advice.
Many thanks to Mr. Sit Beng Chiat, Mr. Edgar Lim, Mr. Ang Beng Onn, Ms Annie Tan, Mr.
Ow Weng Moon, Mr. Kamsan Bin Rasman, Mr. Yip Kwok Keong, Mr. Ong Teng Chew, Mr.
Yong Tat Fah, Mr Wong Kah Wai, Stanley, and Mr. Martin who help in many ways in the
experiment. Special acknowledgement is given to Mr. Choo Peng Kin, Mr. Koh Yian Kheng
and Mr. Ishak Bin A Rahman who had assisted and guided me tremendously in the
experiments.
I would also like to acknowledge NUS for providing all necessary financial and academic
support without which my Ph.D. would not have been possible. I am grateful to my lecturers,
relatives and friends who have supported the study in many ways. Gratitude is extended to my
seniors Dr. Tamali Bhowmik, Dr. Du Hongjian for their kind help with my experiments and
encouragement throughout the study.
I am greatly indebted to my parents and sister who have encouraged me a lot and made
many sacrifices during the study. Thank you for all those sleepless nights you have spent
praying for me. Thank you for understanding and continuing to be an inseparable part of my
life. I am at a loss for words to thank my wife who have suffered a lot and made many
sacrifices, especially during the thesis writing.
Finally I am grateful to Allah for everything that He has granted me.

II

III

DECLARATION

I hereby declare that the thesis is my original work and it has been
written by me in its entirety. I have duly acknowledged all the sources of
information which have been used in the thesis.

This thesis has also not been submitted for any degree in any
university previously.



_________________
Aziz Ahmed
27
th
September 2012



IV



V

TABLE OF CONTENTS

ACKNOWLEDGEMENTS I
DECLARATION III
TABLE OF CONTENTS V
SUMMARY IX
LIST OF FIGURES XI
LIST OF TABLES XVIII
LIST OF SYMBOLS XIX
CHAPTER 1 INTRODUCTION 1
1.1 BACKGROUND 1
1.2 ULTIMATE SEISMIC CAPACITY OF RC GLD STRUCTURES 4
1.3 SEISMIC DEMAND AND ADEQUACY EVALUATION FOR BUILDINGS IN SINGAPORE 9
1.4 SEISMIC RETROFITTING OF RC GLD BUILDINGS IN SINGAPORE 12
1.5 OBJECTIVE AND SCOPE 14
1.6 ORGANIZATION OF THE THESIS 16
CHAPTER 2 LITERATURE REVIEW 25
2.1 GENERAL 25
2.2 SHEAR BEHAVIOR OF LOAD-BEARING ELEMENTS 26
2.3 TOTAL DISPLACEMENT COMPONENTS OF COLUMNS UNDER LATERAL LOAD 34
2.3.1 Flexural deformation 34
2.3.2 Bar slip 37
2.3.3 Shear deformation 38
2.4 SHEAR HINGE MODELS 39
 39
2.4.2  42
2.4.3 Drift capacity model 44
2.4.3.1 Total drift ratio at flexural yielding 44
2.4.3.2 Drift ratio at shear and subsequent axial failure 45
2.5 DEFICIENT BEAM COLUMN JOINTS 47
2.5.1 Experimental study on deficient beam column joints 47
2.5.2 Retrofitting of beam column joints using FRP 48

2.6 FINITE ELEMENT MODELING OF FRP RETROFITTED RC STRUCTURES 49
2.7 DAMAGE INDEX 50
2.8 MACRO MODELING OF BEAM COLUMN JOINT 52
2.9 SUMMARY 54
CHAPTER 3 DUCTILE SHEAR BEHAVIOR OF WIDE COLUMNS AND
SHEAR WALLS 71
3.1 GENERAL 71
3.2 EXPERIMENTAL STUDY ON TYPICAL WIDE COLUMNS 72
3.2.1 Test Program 73
3.2.2 Material properties 74

VI

3.2.2.1 Internal steel reinforcement 74
3.2.2.2 Concrete 75
3.2.3 Fabrication of specimens 75
3.2.4 Test setup 76
3.2.5 Instrumentation 77
3.2.5.1 Strain gauges 77
3.2.5.2 Displacement transducers 77
3.2.6 Test procedure 78
3.3 TEST RESULTS AND DISCUSSION 78
3.4 FINITE ELEMENT ANALYSIS 80
3.4.1 Finite element modeling 80
3.4.2 Material laws 81
3.4.3 Finite element verification study 82
3.4.4 Effect of axial load ratio 84
3.5 DEVELOPMENT OF SHEAR HINGE FOR WIDE COLUMNS 84
3.5.1 Results from experiments and finite element analysis 84
3.5.2 Proposed shear hinge 86

3.6 DEVELOPMENT OF SHEAR HINGE FOR SHEAR WALLS 90
3.7 SUMMARY 91
CHAPTER 4 STUDY ON T-BEAM-WIDE-COLUMN JOINTS 121
4.1 GENERAL 121
4.2 DESCRIPTION OF T-BEAM-WIDE-COLUMN JOINTS 121
4.3 FABRICATION OF SPECIMENS 122
4.3.1 Overview of specimens and reinforcement details 122
4.3.2 Materials 122
4.3.3 Fabrication of joints 123
4.3.3.1 Non-retrofitted joints 123
4.3.3.2 FRP retrofitted joints 125
4.4 TEST SETUP 126
4.5 INSTRUMENTATION 127
4.5.1 Strain gauges 127
4.5.2 Displacement transducers 127
4.6 TEST PROCEDURE 128
4.7 TEST RESULTS AND DISCUSSION 129
4.7.1 General behavior 129
4.7.1.1 Non-retrofitted joints 129
4.7.1.2 FRP retrofitted joints 131
4.7.2 Effectiveness of applied retrofit 134
4.8 FINITE ELEMENT ANALYSIS 136
4.8.1 Finite element modeling 136
4.8.1.1 FRP-retrofitted joints 136
4.8.2 Analysis of results 137
4.8.2.1 Effect of boundary modelling 140
4.8.2.2 Effect of inherent slip 141
4.8.2.3 Effect of difference in cube strength 142
4.9 FURTHER ENHANCEMENT IN JOINT PERFORMANCE 142
4.10 SUMMARY 144

VII

CHAPTER 5 SEISMIC DEMAND AND PERFORMANCE EVALUATION 197
5.1 GENERAL 197
5.2 SELECTED HIGHRISE RC BUILDINGS FOR STUDY 197
5.3 FUNDAMENTAL FREQUENCIES OF BUILDINGS 198
5.4 SEISMIC DEMAND ENVELOPE FOR SINGAPORE SOIL SITES 200
5.4.1 Singapore soil types 200
5.4.2 Generation of response spectra 201
5.4.2.1 Conversion of N
SPT
value to  value 205
5.4.2.2 Calibration of empirical constant 207
5.4.2.3 Effect of new empirical constant 208
5.4.3 Combined response spectrum 209
5.5 MODELING OF THE STRUCTURES 211
5.5.1 25 Story reinforced concrete point block 211
5.5.2 15 Story reinforced concrete point block 212
5.5.3 Basic modeling features 212
5.5.4 Modeling non-linear hinges 213
5.5.4.1 Shear hinge 214
5.5.4.2 Axial hinge 215
5.5.4.3 Flexural hinge 215
5.5.5 Verification of non-linear hinges 215
5.6 EVALUATION OF CAPACITY 217
5.7 POST LOCAL SHEAR FAILURE BEHAVIOR 218
5.8 PROPOSED DAMAGE INDEX 219
5.9 PERFORMANCE OF THE STRUCTURE 223
5.10 PERFORMANCE OF THE RETROFITTED STRUCTURE 225

5.10.1 Macro modelling of T-beam-wide-column joint 225
5.10.2 Macro modeling of retrofitted components 229
5.10.2.1 T-beam-wide-column joint 229
5.10.2.2 Shear wall 230
5.10.2.3 Wide column 231
5.10.3 Capacity evaluation using proposed T-beam-wide-column joint model 232
5.10.3.1 Non-retrofitted structures 232
5.10.3.2 Retrofitted structures 233
5.10.4 Performance of retrofitted structure 235
5.11 SUMMARY 236
CHAPTER 6 CONCLUSIONS AND RECOMMENDATIONS 295
6.1 REVIEW OF WORK 295
6.2 CONCLUSIONS 296
6.3 RECOMMENDATIONS FOR FURTHER RESEARCH 300
REFERENCES 301
APPENDIX 311


VIII



IX

SUMMARY
Buildings in Singapore were designed according to the British Standard without
any seismic provision. However, due to the far-field effects of earthquakes in
Sumatra, these buildings are occasionally subjected to tremors. Previous studies
showed that some buildings may suffer damage due to the worst possible earthquake.
Continuing from past studies, two different types of residential buildings have been

selected for further analysis because of unique components they comprise, such as
wide columns and T-beam-wide-column joints. Moreover, past researches on such
buildings have been primarily focused on estimation of the maximum lateral load
capacity rather than the displacement capacity. On the other hand, this study aims to
estimate the ultimate seismic capacity of these buildings based on displacement
capacity. For this purpose shear hinges are proposed based on existing literature and
new experiments to model the ductile shear behavior of typical columns and shear
walls found in Singapore.
Shear behavior becomes more significant for wide columns because of low shear
span/depth ratio and high length/width ratio. Tests on wide columns provided evidence
of ductile shear behavior. Test results were used to verify the micro FEA models of the
columns which were also used to study the effect of axial load ratio which were used
together with the test results to propose the shear hinge for these columns.
Experiments were carried out on 2/5-scale T-beam-wide-column joints. Tests
were performed to investigate the behavior of exterior and interior joints. A practical
FRP retrofit model was applied on two other specimens to determine the effectiveness
of FRP retrofit on such joints. All these specimens were used to verify micro FEA
models. Using the verified retrofit modelling approach an enhanced FRP retrofit
scheme was proposed.

X

Using the joint test data, constitutive relationship for flexure was proposed for
both non-retrofitted and retrofitted T-beam-wide-column-joints which can be used in
macro finite element analysis. Using previous experimental studies, constitutive
relationships for retrofitted wide columns and shear walls were proposed. With these
proposed constitutive relationships FE models of the selected two buildings were
generated and non-linear pushover analysis was performed using the macro finite
element analysis software SAP2000.
To develop a demand envelope, formulae to calculate shear wave velocity of soil

layers was calibrated for Singapore soils. Based on response spectra developed for 10
soil sites, a demand curve was proposed for Kallang soil formation for the expected
worst case scenario of earthquake of moment magnitude 

 at 600 km from
Singapore.
Furthermore, a comprehensive procedure to determine a new damage index for the
analysed structures was proposed in this study which accounts for ductile shear
behavior and the role of frame and wall in a structure in providing the overall stability
of the structure. The performance state of the analysed structure was thus derived
based on the damage index at the performance point. The improved performance due
to the application of FRP retrofit was also derived using the same approach. The
approach developed in this study can be adapted to accurately estimate the ultimate
seismic capacity and the effectiveness of similar retrofit techniques on similar non-
seismically designed buildings.


XI

LIST OF FIGURES
CHAPTER 1 INTRODUCTION
Figure 1.1: Global seismic hazard map (GSHAP, 1999) 18
Figure 1.2: Regional seismic hazard map: South East Asia (GSHAP, 1999) 18
Figure 1.3: Sumatra fault and subduction of the Indian-Australian Plate into Eurasian
Plate (Balendra et al. 2001) 19
Figure 1.4: Typical slab block in Singapore 20
Figure 1.5: Typical point block in Singapore 21
Figure 1.6: Unique features found in the buildings 22
Figure 1.7: Details of the tested beam-column joints (Dhakal et al. 2005) 23

CHAPTER 2 LITERATURE REVIEW
Figure 2.1: Traditional understanding of shear failure of RC columns based on flexural
and shear strength (Setzler 2005) 57
Figure 2.2: Shear displacement response curve (Krolicki 2011) 57
Figure 2.3: Load-deformation curve for non-linear static analysis (Gerin and Adebar
2004), comparison with membrane element test SE8, (Stevens et al. 1991) 58
Figure 2.4: Specimen dimensions (mm) and application of stresses (Stevens et al.
1991) 58
Figure 2.5: FEMA-356 generalized load-deformation function for shear walls
compared to results from a membrane element test (Stevens at al. (1991) (Gerin and
Adebar 2004) 59
Figure 2.6: Specimen dimensions and test set up (dimensions in mm) (Sezen 2002) 60
Figure 2.7: Lateral load-shear displacement model by Sezen (2002) 61
Figure 2.8: Correlation between yield shear strain and various parameters for columns
failing in pure shear (Patwardhan 2005) 61
Figure 2.9: Load-shear deformation model proposed by Patwardhan (2005) 62
Figure 2.10: Behavior of (a) flexure and slip hinge and (b) shear hinge for different
column categories (Setzler 2005) 63
Figure 2.11: Idealized backbone plotted with column test data (Elwood and Moehle
2004) (Column data from Sezen (2002) 64
Figure 2.12: Components of lateral deformation in a reinforced concrete column
(Elwood and Moehle 2004) 65
Figure 2.13: Flexural deformation of a column (Elwood and Moehle 2004) 65
Figure 2.14: Bilinear approximation of moment-curvature curve (Elwood and Moehle
2004) 65
Figure 2.15: Bar slip in a column (Flores 2007) 66
Figure 2.16: Fixed-fixed column subjected to lateral loads 66
Figure 2.17: Shear deformation in a column (Flores 2007) 66
Figure 2.18: Wide column joint tested by Li et al. (2009a) 67
Figure 2.19: Test setup by Li et al. (2009a) 67

Figure 2.20: FRP retrofit scheme applied by Li et al. (2009b) 68

XII

Figure 2.21: Basic concept of a damage index (Kappos 1997) 69
Figure 2.22: Schematic of the joint model 69

CHAPTER 3 DUCTILE SHEAR BEHAVIOR OF WIDE COLUMNS AND SHEAR
WALLS
Figure 3.1: Wide column reinforcement details 97
Figure 3.2: Average stress-strain characteristics of steel reinforcement 97
Figure 3.3: Reinforcement details and strain gauge locations 98
Figure 3.4: Front view of test set-up 99
Figure 3.5: Side view of test set-up 100
Figure 3.6: Top view of test set-up 100
Figure 3.7: Location of displacement transducers 101
Figure 3.8: Failure pattern of the columns 102
Figure 3.9: Load displacement curves of the columns 103
Figure 3.10: 3D Meshing of the columns 104
Figure 3.11: Support condition and loading on the columns 105
Figure 3.12: Stress-strain curve for steel used in ABAQUS (Hibbit et al. 2010) 106
Figure 3.13: Stress-strain curve of concrete damaged plasticity model used in
ABAQUS (Hibbit et al. 2010) 107
Figure 3.14: Compressive stress-inelastic strain relationship used in ABAQUS (Hibbit
et al. 2010) for ALR0.3-1 108
Figure 3.15: Comparison between test and finite element results 109
Figure 3.16: Effect of bar slip component in total displacement 110
Figure 3.17: Cracking pattern of the specimen ALR0.3-1 111
Figure 3.18: Effect of axial load ratio 112
Figure 3.19: Shear stress vs shear strain relationship from experiments and finite

element analyses 113
Figure 3.20: Idealized shear stress-shear strain behavior of the wide columns 114
Figure 3.21: Schematic diagram of the proposed shear hinge for wide columns 114
Figure 3.22: Proposed correlation between ultimate shear strain and axial load ratio 115
 116
Figure 3.24: Comparison with Load-displacement curve recommended by Elwood &
Moehle (2004) 117
Figure 3.25: Comparison of load-displacement curve recommended by Elwood &

proposed shear hinges 118
Figure 3.26: Proposed idealized shear stress-shear strain behavior for the shear wall119
Figure 3.27: Comparison with Load-displacement curve recommended 120
by Gerin and Adebar (2004) 120

CHAPTER 4 STUDY ON T-BEAM-WIDE-COLUMN JOINTS
Figure 4.1: Plan view of the 15 storey point block 150
Figure 4.2: Prototype frame and selected joints from the 15 storey point block (in mm)

XIII

Error! Bookmark not defined.
Figure 4.3: Dimensions of the scaled models (in mm) 152
Figure 4.4: Reinforcement details of the scaled exterior joints (in mm) 153
Figure 4.5: Reinforcement details of the tested specimens (in mm) 154
Figure 4.6: Rebar cages of the tested specimens 155
Figure 4.7: Inserted bolts and PVC pipe to prepare connecting holes 156
Figure 4.8: Joint strengthened against local bearing failure 156
Figure 4.9: Practical retrofit scheme applied on the exterior joint 157
Figure 4.10: Practical retrofit scheme applied on the interior joint 159
Figure 4.11: Front view of the test set up (in mm) 160

Figure 4.12: Side view of the test set up 161
Figure 4.13: Application of axial load through post tension 162
Figure 4.14: Location of strain gauges on rebar 163
Figure 4.15: Location of strain and omega gauges on concrete for non-retrofitted joints
163
Figure 4.16: Location of strain gauges and omega gauges on concrete and FRP for
retrofitted joints 164
Figure 4.17: Location of displacement transducers on exterior joints 165
Figure 4.18: Location of displacement transducers on interior joints 166
Figure 4.19: Cyclic loading history for retrofitted specimens 167
Figure 4.20: Non-retrofitted exterior joint being tested 168
Figure 4.21: Overall view of the failed non-retrofitted exterior joint 168
Figure 4.22: Shear compression failure Error! Bookmark not defined.
Figure 4.23: Complete cracking of the slab 169
Figure 4.24: Top lateral load vs lateral deflection for the non-retrofitted exterior Joint
170
Figure 4.25: Non-retrofitted interior joint being tested 170
Figure 4.26: Overall view of the failed non-retrofitted exterior joint 171
Figure 4.27: Shear compression failure 171
Figure 4.28: Flexural failure under tension 172
Figure 4.29: Top lateral load vs lateral deflection for the non-retrofitted Interior Joint
172
Figure 4.30: Retrofitted exterior joint being tested 173
Figure 4.31: Overall view of the failed retrofitted exterior joint 173
Figure 4.32: FRP debonding is shown by the yellow lines 174
Figure 4.33: Complete FRP rupture 174
Figure 4.34: Lateral load vs. top lateral deflection for the retrofitted exterior joint 175
Figure 4.35: Retrofitted interior joint being tested 176
Figure 4.36: Overall view of the failed retrofitted interior joint 176
Figure 4.37: Complete FRP rupture 177

Figure 4.38: FRP debonding and rupture 177
Figure 4.39: Complete cracking of slab under tension 178
Figure 4.40: Complete cracking of slab under tension in opposite direction 178

XIV

Figure 4.41: Top lateral load vs. lateral deflection for the non-retrofitted interior Joint
179
Figure 4.42: Comparison between non-retrofitted and retrofitted exterior joint 180
Figure 4.43: Comparison between non-retrofitted and retrofitted interior joint 180
Figure 4.44 Meshing of the interior joint 181
Figure 4.45: Boundary conditions of the interior joint 181
Figure 4.46: Comparison of lateral load displacement relationship obtained from test
and ABAQUS for non-retrofitted exterior joint 182
Figure 4.47: Comparison of lateral load displacement relationship obtained from test
and ABAQUS for non-retrofitted interior joint 182
Figure 4.48: Comparison of lateral load displacement relationship obtained from test
and ABAQUS for retrofitted exterior joint 183
Figure 4.49: Comparison of lateral load displacement relationship obtained from test
and ABAQUS for retrofitted interior joint 183
Figure 4.50: Comparison of non-retrofitted and retrofitted exterior joint in ABAQUS
184
Figure 4.51: Comparison of non-retrofitted and retrofitted interior joint in ABAQUS
184
Figure 4.52: Equivalent Plastic strain at the ultimate capacity of non-retrofitted exterior
joint (simulating the test specimen) 185
Figure 4.53: Equivalent Plastic strain at the ultimate capacity of non-retrofitted interior
joint (simulating the test specimen) 186
Figure 4.54: Equivalent Plastic strain distribution at the ultimate capacity of FRP
retrofitted exterior joint (simulating the test specimen) 187

Figure 4.55: Equivalent Plastic strain at the ultimate capacity of non-retrofitted interior
joint (simulating the test specimen) 188
Figure 4.56: Envelope of measured FRP strain gauge readings up to rupture 189
Figure 4.57: Effect of axial load ratio on lateral load displacement relationship of non-
retrofitted exterior joint 190
Figure 4.58: Effect of axial load ratio on lateral load displacement relationship of non-
retrofitted interior joint 190
Figure 4.59: Elastic end roller support for exterior joint 191
Figure 4.60: Comparison of lateral load displacement relationship obtained from test
and ABAQUS (both types of boundary model) for non-retrofitted exterior joint 192
Figure 4.61: Comparison of lateral load displacement relationship obtained from test
and ABAQUS (both types of boundary model) for non-retrofitted interior joint 192
Figure 4.62: Comparison of lateral load displacement relationship obtained from test
and ABAQUS (both types of boundary model) for retrofitted exterior joint 193
Figure 4.63: Comparison of lateral load displacement relationship obtained from test
and ABAQUS (both types of boundary model) for retrofitted interior joint 193
Figure 4.64: Comparison of moment curvature relationship obtained from both types
of boundary model in ABAQUS for non-retrofitted interior joint 194
Figure 4.65: Effect of difference in concrete cube strength on lateral load displacement
relationships for retrofitted exterior joint 194

XV

Figure 4.66: Enhanced retrofit technique 195
Figure 4.67: Comparison of proposed and actual retrofitted exterior joint in ABAQUS
196
Figure 4.68: Comparison of proposed and actual retrofitted interior joint in ABAQUS
196

CHAPTER 5 SEISMIC DEMAND AND PERFORMANCE EVALUATION

Figure 5.1: Typical 15 story point block in Singapore 248
Figure 5.2: Sensor locations on the 25 storey building 249
Figure 5.3: Power spectral density curves in X and Y directions for a typical building
250
Figure 5.4: Correlation between building height and translational time period in weak
direction 251
Figure 5.5: Correlation between building height and translational time period in strong
direction 251
Figure 5.6: Correlation between building height and torsional time period 251
Figure 5.7: 52
Figure 5.8: Present understanding of the age of Kallang formation (Pitts, 1992) 253
Figure 5.9: Soil damping ratio vs. shear strain (%) for clay and sand 253
Figure 5.10: Shear modulus/ shear modulus at low strain 0.001% (G/G
max
) vs. shear
strain (%) for clay and sand 253
Figure 5.11: Shear wave velocity profile at the soft soil site (Pan et al. 2003) 254
Figure 5.12: Calibration of the proposed constant 254
Figure 5.13: Base shear demand for site C1, C2 and C3 255
Figure 5.14: Demand envelope S
a
vs T 256
Figure 5.15: Construction of a 5 percent-damped elastic response spectrum (ATC-40
1996) 256
Figure 5.16: Demand envelop S
a
vs S
d
257
Figure 5.17: (a) Plan view of the 25 storey building (b) SAP2000 model 257

Figure 5.18: P, M2, M3, V2 and V3 orientations used in SAP2000 (2009) 258
Figure 5.19: Locations of non-linear hinges on beams, columns and braces 258
Figure 5.20: Location of various performance states on the plastic hinge (SAP2000,
2009) 259
Figure 5.21: Constitutive relationship for non-linear hinges 260
Figure 5.22: Plan view and dimensions of the tested sub-frame (Li, 2006) 261
Figure 5.23: Comparison of SAP2000 model with experiment by Li (2006) 261
Figure 5.24: Plan view and dimensions of the tested shear wall (Li 2006) 262
Figure 5.25: Comparison of SAP2000 model with experiment by Kong (2004) 262
Figure 5.26: Comparison of SAP2000 model with test results of wide column ALR0.3-
1 (Chapter 3) 263
Figure 5.27: Analysis of 25 storey building with infill walls loaded in Y direction 264
Figure 5.28: Capacity of the 25 storey building with infill loaded along Y direction 265
Figure 5.29: Capacity of the 25 storey structure 266

XVI

Figure 5.30: Capacity of the 15 storey structure 266
Figure 5.31: Storey-wise damage ratios at collapse of the 25 structure with infill loaded
along Y direction 267
Figure 5.32: Performance of the 25 structure with infill loaded along Y direction 268
Figure 5.33: Storey-wise damage ratios of the 25 structure with infill loaded along Y
direction at performance point for the earthquake (b)  (c)
percentage of damage index at  269
Figure 5.34: Schematic of the joint model 270
Figure 5.35: Reinforcement details of the beam section 270
Figure 5.36: Moment curvature relationship of non-retrofitted Exterior joint 271
Figure 5.37: Moment curvature relationship of non-retrofitted Interior joint 271
Figure 5.38: Plastic rotation of the columns section 272
Figure 5.39: Proposed flexural hinge for T-Beam-wide-column joint 273

Figure 5.40: Verification of the proposed joint model against the tested exterior joint
274
Figure 5.41: Verification of the proposed joint model against the tested interior joint
274
Figure 5.42: Comparison of moment curvature relationships of non-retrofitted and
enhanced retrofitted exterior joint 275
Figure 5.43: Comparison of moment curvature relationships of non-retrofitted and
enhanced retrofitted interior joint 275
Figure 5.44: Proposed flexural hinge for retrofitted T-Beam-wide-column joint 276
Figure 5.45: Verification of the proposed retrofitted joint model against the ABAQUS
models for exterior joints 277
Figure 5.46: Verification of the proposed retrofitted joint model against the ABAQUS
models for interior joints 277
Figure 5.47: Moment curvature relationship of shear wall tested by Li (2006) 278
Figure 5.48: The stress-strain curve of the confined concrete (Teng 2001) 279
Figure 5.49 Wall divided into regions (Li 2006) 279
Figure 5.50: The stress-strain curves for the confined concrete at different regions (Li
2006) 280
Figure 5.51: Proposed shear hinge for the shear wall 280
Figure 5.52: Verification of proposed shear hinge for the shear wall 281
Figure 5.53: Lateral load-deflection relationship of wide columns with and without
FRP wrap 282
Figure 5.54: Verification of proposed force controlled shear hinge for wide column 282
Figure 5.55: Comparison of Capacity of the 25 storey infilled structure modelled using
FEMA-356 or proposed joint 283
Figure 5.56: Comparison of Capacity of the 25 storey without infill structure modelled
using FEMA-356 or proposed joint model 283
Figure 5.57: Comparison of Capacity of the 15 storey infilled structure modelled using
FEMA-356 or proposed joint model 284
Figure 5.58: Comparison of Capacity of the 15 storey structure without infill modelled

using FEMA-356 or proposed joint model 284

XVII

Figure 5.59: Proposed retrofit scheme for shear wall in 25 storey building 285
Figure 5.60: Proposed retrofit scheme for wide column and beam-column-joint in 25
storey building 286
Figure 5.61: Proposed retrofit scheme for wide column and beam-column-joint in 15
storey building 287
Figure 5.62: Lateral load displacement relationships for full scale interior joint 288
Figure 5.63: Lateral load displacement relationships for 2/5
th
scaled interior joint 288
Figure 5.64: Locations of non-linear hinges on retrofitted beams, columns in a frame
289
Figure 5.65: Effect of retrofit on the capacity curves for 25 storey infilled block loaded
along X axis 290
Figure 5.66: Effect of retrofit on the capacity curves for 25 storey infilled block loaded
along Y axis 290
Figure 5.67: Effect of retrofit on the capacity curves for 25 storey non-infilled block
loaded along X axis 291
Figure 5.68: Effect of retrofit on the capacity curves for 25 storey non- infilled block
loaded along Y axis 291
Figure 5.69: Effect of retrofit on the capacity curves for 15 storey infilled block loaded
along X axis 292
Figure 5.70: Effect of retrofit on the capacity curves for 15 storey infilled block loaded
along Y axis 292
Figure 5.71: Effect of retrofit on the capacity curves for 15 storey non-infilled block
loaded along X axis 293
Figure 5.72: Effect of retrofit on the capacity curves for 15 storey non-infilled block

loaded along Y axis 293
Figure 5.73: Comparison of performance of the retrofitted and non-retrofitted 25 storey
infilled structure loaded along Y direction 294



XVIII

LIST OF TABLES
Table 2.1: Virtual test matrix used by Patwardhan (2005) 56

Table 3.1: Comparison of model and prototype column 93
Table 3.2: Properties of steel reinforcement 94
Table 3.3: Concrete properties of specimen tested 94
Table 3.4: Pushover test results 94
Table 3.5: The compression and tension damage behavior ( Jankowiak and Odygowski
2005) 94
Table 3.6 Comparison between experiment and finite element study 95
Table 3.7: Data points for proposed shear hinges 96
Table 3.8: Data points for the proposed shear hinge for shear wall 96

Table 4.1: Comparison of model and prototype joint 145
Table 4.2: Concrete properties of specimen tested 146
Table 4.3: Properties of steel reinforcement 146
Table 4.4: Properties of CFRP sheets 146
Table 4.5: Mix proportion of resin 146
Table 4.6 Summary of test results 147
Table 4.7 Comparison with FE study (Exterior joint) 148
Table 4.8 Comparison with FE study (Interior joint) 149

Table 5.1: Summary of ambient vibration study 238
Table 5.2: Soil factor  239
Table 5.3: Correction factors for calculating  (Sherif and Radding, 2001) 239
Table 5.4: Layer wise measured shear wave velocity () at two sites in Singapore
(Leong et al. 2003) 239
Table 5.5:  value for different soil layers on Kallang marine clay formation 240
Table 5.6: Modeling parameters and numerical acceptance criteria for non-linear
procedures  reinforced concrete beams (Table 6-7 from FEMA-356 (2000)) 241
Table 5.7: Modeling parameters and numerical acceptance criteria for non-linear
procedures  reinforced concrete columns (Table 6-8 from FEMA-356 (2000)) 242
Table 5.8: Summary of capacity evaluation study 243
Table 5.9: Weightage factors for various performance levels for flexure and shear
hinge 244
Table 5.10: Correlation between structural damage and performance state 243
Table 5.11: Criteria for Performance Level Detection at each storey 244
Table 5.12: Component performance state details at collapse and performance points
245
Table 5.13: Comparison of the effect of the proposed joint 247
Table 5.14: Performance state comparison 247



XIX

LIST OF SYMBOLS
a
Shear span
ALR
Axial load ratio
A

G

Gross sectional area
A
st

Area of transverse steel in the direction of loading
A
v

Shear area of column cross section
b
Width of the cross-section
C
Performance state Collapse
CAM
Component Attenuation Model
CP
Performance state Collapse prevention



Empirical constant by Ohta and Goto (1978)



Empirical constant by Jamiolkowski et al. (1988)
C
A

0.4 time the spectral response acceleration
C
B

Borehole diameter correction
C
E

Correction factor for hammer efficiency
C
S

Sample barrel correction
C
R

Rod length correction
C
N

Over burden pressure correction
C
V

Spectral response acceleration



Height of neutral axis
CFRP

Carbon fibre reinforced polymer
d
Distance from the extreme compression fibre to the centroid of the tension steel
Effective depth of the component
d
b

Diameter of flexural reinforcement
d
C

Depth of the column core measured parallel to the applied shear, or
Damage variable under compression
d
cal

Value of damage variable at calculated from analysis
d
o

Value of damage variable at zero damage



Structural damage index

XX




Non-structural damage index



Damage ratios of beams



Damage ratios of columns



Damage ratios of frame



Non-structural damage ratio



Structural damage ratio



Damage ratios of walls



Damage ratios of masonry infills

D
t

Damage variable under tension
d
u

Value of damage variable at maximum damage
E

E
c


E
f


Es

EPA
Effective peak acceleration of the ground
f
cu

Concrete compressive cube strength
F
1

Age factor

F
2
Soil factor
f
c
'
Concrete compressive cylinder strength
f
s

Stress in tensile reinforcing bars
f
y

Yield strength of longitudinal steel reinforcements
Yield strength of steel
f
YL

Yield strength of longitudinal steel
f
ys

Yield strength of transverse steel
f
u

Ultimate strength of steel bars
FEA
Finite element analysis

FRP
Fibre reinforced polymer
g
Acceleration of gravity
G
Shear modulus

GFRP
Glass fibre reinforced polymer

XXI

G
max

initial shear modulus
GLD
Gravity load designed
h
Height of the storey
Height of the retrofitted section
H
Height of a building
IO
Performance state Immediate occupancy
I
g

Uncracked moment of inertia of cross section of the column
I

yy

Moment of inertia of a section in y-y direction
I
zz

Moment of inertia of a section in z-z direction
J
xx

Torsional moment of inertia of a section in x-x direction
k
factor related to the displacement ductility
L
Height of cantilever column
Length of the column

LS
Performance state Life safety



plastic hinge length of column
M
p
Maximum moment capacity of the section
M
cr

Cracking moment

MDOF
Multi-degree-of-freedom
M
Y

Column moment at yielding of the longitudinal reinforcement
M
w

Moment magnitude of earthquakes
M
y

Column moment at yielding of the longitudinal reinforcement
Yield moment
M
W

Moment magnitude of earthquake



Damage vale of beam



Damage vale of column



Damage vale of shear wall



Damage vale of masonry infills



Number of beams in a storey



Number of columns in a storey



Number of walls in a storey

XXII




Number of masonry infills in a storey
N
spt

N value of the standard penetration test for soil (blow/30cm)





corrected for field procedures and apparatus
P
r
Axial load ratio
P
y

Lateral load capacity at yield

P
y

Ultimate lateral load capacity
PI
Plasticity index for the soil
RC
Reinforced concrete
s
Spacing between transverse reinforcement
S
a

Spectra acceleration
S
d

Spectra displacement

SDOF
Single-degree-of-freedom
t
Thickness of a section
T
Time period
t
f

Thickness of FRP sheet
T
X
Translational time period about weak axis
T
Y
Translational time period about strong axis
T
T
Torsional time period
u
Bond stress between the longitudinal reinforcement and column footing
v
Shear capacity of a section expressed in terms of stress
v
c

Shear capacity provided by concrete in terms of stress
v
s

Shear capacity provided by transverse reinforcement in terms of stress
v
f

Shear capacity of FRP wrap in terms of stress



shear carried by shear wall at i
th
storey
V
Shear force
V
c

Shear force carried by concrete
V
cr

Shear capacity at cracking
V
s

Shear force carried by the transverse steel
V
f

Shear capacity of FRP wrap in terms of force
V

s

Shear wave velocity

XXIII

V
y

Column shear at initial yielding of the longitudinal reinforcement
V
u

Ultimate shear strength capacity



Weightage factor for beams



Stiffness recovery factors after compression failure
Weightage factor for columns



Weightage factor for frame



Stiffness recovery factors after tensile failure



Weightage factor for shear wall
Z
Depth of soil where blow count 

is taken



Total displacement capacity of the column at loss of axial capacity

Lateral displacement



Displacement at initial cracking



Final flexural displacement



Final slip displacement









Shear displacement at initial cracking

Shear displacement at maximum strength

Yield displacement



Ultimate displacement

Tangent of the crack angle
An exponent in the damage index formula
Stiffness reduction factor


Enhancement factor of Moment capacity due to retrofitting



Shear strain at initial yielding



Reference shear strain




ultimate shear strain



Total drift ratio at yield



Drift ratio due to flexure



Drift ratio due to slip



Drift ratio due to shear

c

Strain of concrete

XXIV


cu

Ultimate strain of concrete

f

Effective FRP strain at failure

s

Strain of reinforcing bars

y

Yield strain of reinforcing bars

Damping ratio of soil



Instantaneous damping

Damping ratio



Plastic rotational capacity



Displacement ductility




Maximum shear strength

Density of soil at the layer

l

Reinforcement ratio of the longitudinal bars

f

FRP shear reinforcement ratio

v
Transverse reinforcement ratio

co

Concrete stress at initial yield

cu
Ultimate stress

t

Concrete stress at tensile failure

Poisson ratio




Curvature corresponding to first yielding of reinforcement at column base



Ultimate curvature




Chapter 1 Introduction

1

CHAPTER 1
INTRODUCTION
1.1 Background
Figure 1.1 presents the global seismic hazard map and Figure 1.2 presents the
regional seismic hazard map for South East Asia (GSHAP 1999). It can be observed
that Singapore clearly falls in a low seismic hazard zone. This is because Singapore is
located on a stable part of the Eurasian Plate, with the nearest earthquake fault about
400 km away in Sumatra (Figure 1.3). It is noteworthy that more than 70% of the land
area of the world has similar low seismic hazard classification.
Taking advantage of this, buildings in Singapore are gravity-load designed (GLD)
structures, according to BS8110 (1985), which does not have any seismic provision.
However, due to the far-field effects of earthquakes in Sumatra (Balendra et al. 2002,
2003), buildings in Singapore, of which most are reinforced concrete (RC) shear wall
and frame structures, are occasionally subjected to tremors that occur at the Sumatra
fault and the subduction of the Indian-Australian plate into the Eurasian Plate.

Therefore, the need to evaluate the seismic vulnerability of buildings in Singapore
in case a larger or nearer earthquake occurs; has been studied to some extent (Balendra
et al., 2007). The seismic vulnerability was evaluated by combining the seismic
demand and the capacity of the structure in A-D format (acceleration- displacement
format), as proposed by Freeman et al. (1975) and Freeman (1978). The research on
seismic performance including strength capacity of GLD reinforced concrete structures
has been carried out in Singapore context by various researchers (Kong et al. 2003;
Koh 2003; Balendra et al. 2001; Balendra et al. 1999). A microscopic model
calibrated for shear walls was used to determine the capacity of the full scale shear