Response of Deep Foundations to Seismic Loads in Alabama 
 
By 
 
Kevin Marshall Kane 
 
 
 
 
A thesis submitted to the Graduate Faculty of 
Auburn University 
in partial fulfillment of the 
requirements for the Degree of 
Master of Science 
 
Auburn, Alabama 
December 14, 2013 
 
 
Keywords: pile, buckling, scour, soil-foundation-structure interaction 
 
 
Copyright 2013 by Kevin Marshall Kane 
 
 
Approved by 
 
J. Brian Anderson, Chair, Associate Professor of Civil Engineering 
Justin Marshall, Assistant Professor of Civil Engineering 
Robert Barnes, James J. Mallet Associate Professor of Civil Engineering 
  
ii 
 
ABSTRACT 
 
 
 Deep foundations are commonly used as foundation elements for bridges in 
Alabama.  Due to the implementation of the American Association of State Highway and 
Transportation Officials (AASHTO) Load and Resistance Factor Design (LRFD) Bridge 
Design Specifications, design of critical and essential bridges will be significantly 
impacted for the moderate seismic design category of Alabama.   
 Five bridge case studies were provided by the Alabama Department of 
Transportation (ALDOT) to evaluate the response of typical foundations used for critical 
and essential bridges.  FB-MultiPier, a program that couples nonlinear structural finite 
element analysis with nonlinear static soil models, was used to model both the soil and 
structure (both foundation elements and substructure components) of each case history.  
These models were loaded with a suite of scaled time-history events to simulate an 
earthquake.  Displacement at the top of the pier and ground surface was recorded, as well 
as maximum shear force, bending moment, and demand/capacity (D/C) ratio distribution 
along the length of the driven pile, drilled shaft, or column.  The maximum shear force, 
bending moment, and D/C ratio distributions indicated where the plastic hinge zones 
could be expected to form in the structure.  FB-MultiPier was also used to develop a 
family of foundation response curves that were used in SAP2000 to evaluate the 
performance of the case histories. 
iii 
 
 Pile performance under combined scour and earthquake was reviewed and two 
different scour depth models were developed for one case history.  Buckling criteria for 
foundations in soft clay or liquefiable soil were also reviewed and compared to two case 
histories.   
 It was found that scour depth appears to affect the dynamic response of the bridge 
pier.  The pier modeled with 25% scour depth performed worse (structurally) than the 
same pier modeled with 100% scour depth.  This was due to large displacements at the 
ground surface and large bending moments developing below the ground surface.  The 
pier founded in soft clay over rock performed poorly due to structural failure in the 
foundations.  This was due to flexure failure of the piles.  It was also found that drilled 
shafts embedded in shallow bedrock tend to perform well depending on the natural 
frequency and structural period of the pier.  Recommendations for further research 
address soil susceptibility to scour and liquefaction, full-scale dynamic load testing, and 
correlations between the natural and structural period of a bridge pier and its performance 
during an earthquake event. 
 
 
 
  
iv 
 
ACKNOWLEDGMENTS 
 
 
 First, I would like to thank God for the many blessings He has bestowed upon me 
throughout my life.  It is through Him that all things are possible.  I want to thank Dr. 
Brian Anderson for his guidance throughout this process and giving me the opportunity 
to further my education.  He is not only a mentor but a friend in which I greatly 
appreciate.  I also want to thank Dr. Justin Marshall and Dr. Robert Barnes for their 
guidance and contributions for this project.   
 Thank you to the Alabama Department of Transportation for funding this study.  
Thank you to Kaye Chancellor and Tim Colquett, representatives of ALDOT, for their 
help throughout this project.  Thanks to Jordan Panzer and Jordan Law for their 
collaborative efforts during this project.  I also would like to thank my fellow students 
and professors who have helped me throughout my career, here at Auburn.   
 I want to thank my wonderful girlfriend, Haley Grant.  Her support, compassion, 
and patience throughout this process were unwavering.  Finally, I want to thank my 
parents, Carl and Cathy Kane for their never-ending support, guidance, and love 
throughout my life.  I am extremely blessed to have them as parents. 
 
  
v 
 
TABLE OF CONTENTS 
 
 
ABSTRACT ........................................................................................................................ ii 
ACKNOWLEDGMENTS ................................................................................................. iv 
LIST OF TABLES .............................................................................................................. x 
LIST OF FIGURES .......................................................................................................... xii 
Chapter 1 INTRODUCTION .............................................................................................. 1 
1.1 Objectives ................................................................................................................. 3 
1.2 Scope of Work .......................................................................................................... 4 
Chapter 2 BACKGROUND ................................................................................................ 5 
2.1 Previous Research ..................................................................................................... 5 
2.2 Evaluation of Liquefaction Potential ...................................................................... 10 
2.3 Soil-Foundation-Structure Interaction .................................................................... 16 
2.3.1 Kinematic Interaction ....................................................................................... 17 
2.3.2 Inertial Interaction ............................................................................................ 18 
2.3.3 Seismic and Dynamic Response Analysis Methods ........................................ 19 
2.3.3.1 Substructure Analysis ............................................................................... 20 
2.3.3.2 Direct Analysis.......................................................................................... 22 
2.4 Computer Programs ................................................................................................ 23 
2.4.1 Overview of FB-MultiPier ............................................................................... 23 
2.4.2 Soil Modeling ................................................................................................... 27 
vi 
 
2.4.2.1 Lateral ....................................................................................................... 27 
2.4.2.2 Axial .......................................................................................................... 35 
2.4.2.3 Torsional ................................................................................................... 39 
2.4.2.4 Tip ............................................................................................................. 39 
2.4.2.5 Input Parameters ....................................................................................... 42 
2.4.3 Structural Modeling ......................................................................................... 43 
2.4.4 Foundation Modeling ....................................................................................... 50 
2.4.5 Pile Cap Modeling ........................................................................................... 50 
2.4.6 Pile Group Effects ............................................................................................ 51 
2.4.7 Dynamic Analysis Methods ............................................................................. 54 
2.4.7.1 Time-History Analysis .............................................................................. 54 
2.4.7.2 Modal Response Analysis ......................................................................... 55 
2.4.7.3 Damping .................................................................................................... 57 
2.4.7.4 Dynamic Relaxation.................................................................................. 58 
2.4.8 FB-MultiPier Limitations ................................................................................. 58 
2.5 FHWA LRFD Seismic Analysis and Design of Bridge Foundations ..................... 59 
Chapter 3 LITERATURE REVIEW ................................................................................. 61 
3.1 Pile Failure Modes .................................................................................................. 61 
3.2 Pile Performance in Liquefied Soil and Soft Clay .................................................. 66 
3.2.1 Case Histories .................................................................................................. 66 
3.2.2 Centrifuge Testing ........................................................................................... 71 
3.3 Pile Performance under the combined Effect of Earthquake and Scour ................. 75 
Chapter 4 MODEL GENERATION ................................................................................. 77 
vii 
 
4.1 Time-History Events ............................................................................................... 79 
4.2 Dynamic Analysis Options Used within FB-MultiPier .......................................... 80 
4.2.1 Dynamic Analysis Method Used ..................................................................... 80 
4.2.2 Damping Analysis ............................................................................................ 80 
4.3 Dead Load and Discrete Mass ................................................................................ 85 
4.4 Chambers County ................................................................................................... 86 
4.4.1 Background Information .................................................................................. 86 
4.4.2 Soil Modeling ................................................................................................... 92 
4.5 Etowah County ....................................................................................................... 93 
4.5.1 Background Information .................................................................................. 93 
4.5.2 Soil Modeling ................................................................................................... 99 
4.6 Franklin County .................................................................................................... 101 
4.6.1 Background Information ................................................................................ 101 
4.6.2 Soil Modeling ................................................................................................. 107 
4.7 Lee County ............................................................................................................ 108 
4.7.1 Background Information ................................................................................ 108 
4.7.2 Soil Modeling ................................................................................................. 116 
4.8 Marshall County ................................................................................................... 118 
4.8.1 Background Information ................................................................................ 118 
4.8.2 Soil Modeling ................................................................................................. 126 
Chapter 5 SUBSTRUCTURE ANALYSIS RESULTS AND DISCUSSION ............... 128 
5.1 Chambers County 100% Scour ............................................................................. 130 
5.2 Etowah County ..................................................................................................... 131 
viii 
 
5.3 Franklin County .................................................................................................... 133 
5.4 Lee County ............................................................................................................ 134 
5.5 Marshall County ................................................................................................... 136 
5.6 Discussion ............................................................................................................. 138 
Chapter 6 DIRECT ANALYSIS RESULTS AND DISCUSSION ................................ 139 
6.1 Chambers County 25% Scour Discussion ............................................................ 140 
6.1.1 Longitudinal Results ...................................................................................... 142 
6.1.2 Transverse Results ......................................................................................... 145 
6.2 Chambers County 100% Scour Discussion .......................................................... 148 
6.2.1 Longitudinal Results ...................................................................................... 151 
6.2.2 Transverse Results ......................................................................................... 154 
6.3 Etowah County Discussion ................................................................................... 157 
6.3.1 Longitudinal Results ...................................................................................... 160 
6.3.2 Transverse Results ......................................................................................... 163 
6.4 Franklin County Discussion.................................................................................. 166 
6.4.1 Longitudinal Results ...................................................................................... 167 
6.4.2 Transverse Results ......................................................................................... 170 
6.5 Lee County Discussion ......................................................................................... 173 
6.5.1 Longitudinal Results ...................................................................................... 175 
6.5.2 Transverse Results ......................................................................................... 178 
6.6 Marshall County Discussion ................................................................................. 181 
6.6.1 Longitudinal Results ...................................................................................... 183 
6.6.2 Transverse Results ......................................................................................... 187 
ix 
 
6.7 Direct Analysis Results Summary ........................................................................ 190 
Chapter 7 STATE DOT SURVEY ................................................................................. 193 
7.1 Arkansas Survey Response ................................................................................... 194 
7.2 Kentucky Survey Response .................................................................................. 195 
7.3 South Carolina Survey Response .......................................................................... 197 
7.4 State DOT Survey Summary ................................................................................ 200 
Chapter 8 CONCLUSIONS AND RECOMMENDATIONS......................................... 202 
8.1 Summary of Work ................................................................................................ 202 
8.2 Conclusions ........................................................................................................... 202 
8.3 Recommendations ................................................................................................. 204 
REFERENCES ............................................................................................................... 206 
Appendix A TIME-HISTORY EVENTS ....................................................................... 212 
Appendix B DAMPING ANALYSIS RESULTS .......................................................... 229 
Appendix C CHAMBERS COUNTY BORING LOGS ................................................. 253 
Appendix D ETOWAH COUNTY BORING LOGS ..................................................... 255 
Appendix E FRANKLIN COUNTY BORING LOGS ................................................... 262 
Appendix F LEE COUNTY BORING LOGS ................................................................ 265 
Appendix G MARSHALL COUNTY BORING LOGS ................................................ 271 
Appendix H DIRECT ANALYSIS RESULTS .............................................................. 273 
 
 
  
x 
 
LIST OF TABLES 
 
 
Table 2.1 ? Site class definitions ........................................................................................ 9 
Table 2.2 ? Partitions for seismic design categories A, B, C, and D .................................. 9 
Table 2.3 ? Susceptibility of sedimentary deposits to liquefaction during strong shaking
 ................................................................................................................................... 14 
 
Table 2.4 ? Liquefaction evaluation requirements for each SDC ..................................... 16 
Table 2.5 ? Input parameters needed for FB-MultiPier .................................................... 43 
Table 2.6 ? Rayleigh damping factors used in Brown et al. ............................................. 57 
Table 3.1 ? Summary of pile performances ...................................................................... 68 
Table 3.2 ? Properties of the model and prototype pile .................................................... 72 
Table 3.3 ? Performance of the piles during the centrifuge tests ...................................... 74 
Table 4.1 ? Time steps used for each time-history for each model .................................. 79 
Table 4.2 ? Frequency, structural period, and calculated average damping ratios for each 
bridge ........................................................................................................................ 85 
 
Table 4.3 ? Dead loads and discrete masses used for each case study ............................. 86 
Table 6.1 ? Results overview for Chambers 25% scour longitudinal models ................ 144 
Table 6.2 ? Results overview for Chambers 25% scour transverse models ................... 147 
Table 6.3 ? Results overview for Chambers 100% scour longitudinal models .............. 153 
Table 6.4 ? Results overview for Chambers 100% Scour transverse models ................ 156 
Table 6.5 ? Assumptions used in buckling analysis for Etowah County........................ 157 
Table 6.6 ? Etowah County Pdes/Pcr and Leff/rmin results ................................................. 158 
xi 
 
Table 6.7 ? Results overview for Etowah County longitudinal models ......................... 162 
Table 6.8 ? Results overview for Etowah County transverse models ............................ 165 
Table 6.9 ? Results overview for Franklin County longitudinal models ........................ 169 
Table 6.10 ? Results overview for Franklin County transverse models ......................... 172 
Table 6.11 ? Assumptions used in buckling analysis for Lee County ............................ 173 
Table 6.12 ? Lee County Pdes/Pcr and Leff/rmin results ..................................................... 174 
Table 6.13 ? Results overview for Lee County longitudinal models ............................. 177 
Table 6.14 ? Results overview for Lee County transverse models................................. 180 
Table 6.15 ? Results overview for Marshall County longitudinal models ..................... 186 
Table 6.16 ? Results overview for Marshall County transverse models ........................ 189 
 
  
xii 
 
LIST OF FIGURES 
 
 
Figure 1.1. Standard Specification for PGA (%g) for a 500 year return period ................. 2 
Figure 1.2. LRFD Specification for PGA for 1000-yr return period .................................. 3 
Figure 2.1. Inelastic behavior of bridge elements in design level seismic event ................ 7 
Figure 2.2. Design level seismic hazard curves for select Alabama cities ......................... 8 
Figure 2.3. Flow liquefaction damage to a road in Japan during an offshore earthquake in 
2007 ........................................................................................................................... 11 
 
Figure 2.4. Collapse of the showa bridge in the 1964 Niigata, Japan earthquake ............ 12 
Figure 2.5. Liquefaction susceptibility of Alabama based on Youd and Perkins 1978 .... 15 
Figure 2.6. Inertial interaction model for deep foundations ............................................. 19 
Figure 2.7. Foundation substructure model for kinematic analysis .................................. 21 
Figure 2.8. Example of a foundation stiffness curve ........................................................ 22 
Figure 2.9. Direct (or Total) soil-foundation-structure kinematic interaction model ....... 23 
Figure 2.10. FB-MultiPier editor window ........................................................................ 26 
Figure 2.11. Matlock?s static curve for soft clay .............................................................. 30 
Figure 2.12. Matlock?s cyclic curve for soft clay ............................................................. 30 
Figure 2.13. Reese?s static curve for stiff clay below the water table .............................. 31 
Figure 2.14. Reese?s cyclic curve for stiff clay below the bater table .............................. 31 
Figure 2.15. Reese and Welch?s static curve for stiff clay above water table .................. 32 
Figure 2.16. Reese and Welch?s cyclic curve for stiff clay above water table ................. 32 
Figure 2.17. P-y curves for sand ....................................................................................... 33 
xiii 
 
Figure 2.18. O?Neill?s p-y curve for sand ......................................................................... 33 
Figure 2.19. O?Neil?s static p-y curve for clay ................................................................. 34 
Figure 2.20. O?Neil?s cyclic curve for clay ...................................................................... 34 
Figure 2.21. McVay?s normalized p-y curves corrected for side shear for limestone ...... 35 
Figure 2.22. Axial T-z curve for pile/shaft ....................................................................... 37 
Figure 2.23. Trend lines for drilled shaft side resistance in sand ..................................... 37 
Figure 2.24. Trend lines for drilled shaft aide resistance in clay ...................................... 38 
Figure 2.25. Comparison of normalized T-z curves for limestone ................................... 38 
Figure 2.26. Hyperbolic representation of T-? curve ....................................................... 39 
Figure 2.27. Axial Q-z curve for driven pile .................................................................... 41 
Figure 2.28. Trend Lines for drilled shaft end bearings in sand ....................................... 41 
Figure 2.29. Trend lines for drilled shaft end bearings in clay ......................................... 42 
Figure 2.30. Pier data edit window ................................................................................... 45 
Figure 2.31. Gross properties window .............................................................................. 46 
Figure 2.32. Full cross section properties window ........................................................... 47 
Figure 2.33. Reinforcement specification window ........................................................... 48 
Figure 2.34. Hognestad model for concrete ...................................................................... 49 
Figure 2.35. Default stress-strain curve for 60 ksi steel ................................................... 49 
Figure 2.36. Illustration of p-y multiplier concept for lateral group analysis ................... 53 
Figure 2.37. Modal analysis process for a bridge pier within FB-MultiPier .................... 56 
Figure 3.1. Concept of effective length of pile for different boundary conditions ........... 65 
Figure 3.2. rmin versus Leff for piles studied ...................................................................... 70 
Figure 3.3. Plot of the pile foundations that performed poorly as a function of Pcr ......... 70 
xiv 
 
Figure 3.4. Schematic of forces acting on the model pile ................................................. 71 
Figure 3.5. Schematic representation of the centrifuge test results .................................. 73 
Figure 4.1. Map of Alabama Counties with bridge locations ........................................... 78 
Figure 4.2. Scaled Coalinga North earthquake time-history event ................................... 80 
Figure 4.3. Chambers County 100% scour longitudinal sine wave time-history ............. 83 
Figure 4.4. Chambers County 100% scour longitudinal displacement versus time at the 
top of the pier ............................................................................................................ 83 
 
Figure 4.5. Marshall County longitudinal sine wave time-history ................................... 84 
Figure 4.6. Marshall County longitudinal displacement versus time at the top of the pier
 ................................................................................................................................... 84 
 
Figure 4.7. Chambers County bridge plan and elevation view ......................................... 88 
Figure 4.8. Chambers County typical bridge deck cross section ...................................... 89 
Figure 4.9. Chambers County Bent 3 elevation and end view.......................................... 90 
Figure 4.10. Chambers County cross section of drilled shaft ........................................... 91 
Figure 4.11. Chambers County Bent 3 pier cap cross section .......................................... 91 
Figure 4.12. Chambers County idealized soil profile for Bent 3 ...................................... 93 
Figure 4.13. Etowah County bridge plan and elevation view ........................................... 94 
Figure 4.14. Etowah County typical bridge deck cross section ........................................ 95 
Figure 4.15. Etowah County Bent 2 elevation view ......................................................... 96 
Figure 4.16. Etowah County Bent 2 end view .................................................................. 97 
Figure 4.17. Etowah County Bent 2 pier cap cross section .............................................. 98 
Figure 4.18. Etowah County Bent 2 column cross section ............................................... 98 
Figure 4.19. Etowah County Bent 2 typical pile footing layout ....................................... 99 
Figure 4.20. Etowah County idealized soil profile ......................................................... 101 
xv 
 
Figure 4.21. Franklin County bridge plan and elevation views ...................................... 103 
Figure 4.22. Franklin County typical bridge deck cross section..................................... 104 
Figure 4.23. Franklin County Bent 3 elevation and end view ........................................ 105 
Figure 4.24. Franklin County pier cap cross section ...................................................... 106 
Figure 4.25. Franklin County above ground column cross section ................................ 106 
Figure 4.26. Franklin County below ground drilled shaft cross section ......................... 107 
Figure 4.27. Franklin County idealized soil profile ........................................................ 108 
Figure 4.28. Lee County bridge plan view ..................................................................... 109 
Figure 4.29. Lee County bridge elevation view .............................................................. 110 
Figure 4.30. Lee County typical bridge deck cross section ............................................ 111 
Figure 4.31. Lee County Bent 2 stage one elevation view ............................................. 112 
Figure 4.32. Lee County Bent 2 stage two elevation view ............................................. 113 
Figure 4.33. Lee County Bent 2 stage one and two end view ........................................ 114 
Figure 4.34. Lee County Bent 2 (a) pier cap and (b) column cross section .................... 115 
Figure 4.35. Lee County Bent 2 pile footing layout ....................................................... 116 
Figure 4.36. Lee County idealized soil profile ............................................................... 117 
Figure 4.37. Marshall County bridge plan and elevation view ....................................... 119 
Figure 4.38. Marshall County typical bridge deck cross section .................................... 120 
Figure 4.39. Marshall County Bent 2 shaft elevations.................................................... 121 
Figure 4.40. Marshall County Bent 2 (a) above ground and (b) below ground column and 
shaft cross section ................................................................................................... 121 
 
Figure 4.41. Marshall County Bent 3 elevation and end view........................................ 122 
Figure 4.42. Marshall County Bent 3 pier cap cross section .......................................... 123 
Figure 4.43. Marshall County Bent 3 strut cross section ................................................ 124 
xvi 
 
Figure 4.44. Marshall County Bent 3 (a) above ground and (b) below ground column and 
shaft cross section ................................................................................................... 125 
 
Figure 4.45. Marshall County idealized soil profile ....................................................... 127 
Figure 5.1. Force and moment directions ....................................................................... 128 
Figure 5.2. Chambers County foundation response curves for (a) FX, (b) FY, (c) FZ, (d) 
MX, (e) MY, and (f) MZ ........................................................................................... 130 
 
Figure 5.3. Etowah County foundation response curves for (a) FX, (b) FY, (c) FZ, (d) MX, 
(e) MY, and (f) MZ ................................................................................................... 131 
 
Figure 5.4. Etowah County pile group layout and direction ........................................... 132 
 
Figure 5.5. Franklin County foundation response curves for (a) FX, (b) FY, (c) FZ, (d) MX, 
(e) MY, and (f) MZ ................................................................................................... 133 
 
Figure 5.6. Lee County foundation response curves for (a) FX, (b) FY, (c) FZ, (d) MX, (e) 
MY, and (f) MZ ........................................................................................................ 134 
 
Figure 5.7. Lee County pile group layout and direction ................................................. 135 
 
Figure 5.8. Marshall County Bents 2 and 4 foundation response curves for (a) FX, (b) FY, 
(c) FZ, (d) MX, (e) MY, and (f) MZ .......................................................................... 136 
 
Figure 5.9. Marshall County Bent 3 foundation response curves for (a) FX, (b) FY, (c) FZ, 
(d) MX, (e) MY, and (f) MZ ...................................................................................... 137 
 
Figure 6.1. Chambers County 25% scour longitudinal Kocaeli2 NMCE (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, 
(e) ground surface displacement, and (f) demand capacity ratio ............................ 142 
 
Figure 6.2. Chambers County 25% scour longitudinal San Fernando2 NMCE (a) time-
history event, (b) shear distribution, (c) top of pier displacement, (d) moment 
distribution, (e) ground surface displacement, and (f) demand capacity ratio ........ 143 
 
Figure 6.3. Chambers County 25% scour transverse Kocaeli2 NMCE (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, 
(e) ground surface displacement, and (f) demand capacity ratio ............................ 145 
 
Figure 6.4. Chambers County 25% scour transverse San Fernando2 NMCE (a) time-
history event, (b) shear distribution, (c) top of pier displacement, (d) moment 
distribution, (e) ground surface displacement, and (f) demand capacity ratio ........ 146 
 
xvii 
 
Figure 6.5. Chambers County 25% scour longitudinal Kocaeli2 NMCE (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, 
(e) ground surface displacement, and (f) demand capacity ratio ............................ 149 
 
Figure 6.6. Chambers County 100% Scour Longitudinal Kocaeli2 NMCE (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, 
(e) ground surface displacement, and (f) demand capacity ratio ............................ 150 
 
Figure 6.7. Chambers County 100% scour longitudinal Imperial Valley North (a) time-
history event, (b) shear distribution, (c) top of pier displacement, (d) moment 
distribution, (e) ground surface displacement, and (f) demand capacity ratio ........ 151 
 
Figure 6.8. Chambers County 100% scour longitudinal Kocaeli NMCE (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, 
(e) ground surface displacement, and (f) demand capacity ratio ............................ 152 
 
Figure 6.9. Chambers County 100% scour transverse Coalinga North (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, 
(e) ground surface displacement, and (f) demand capacity ratio ............................ 154 
 
Figure 6.10. Chambers County 100% scour transverse Landers NMCE (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, 
(e) ground surface displacement, and (f) demand capacity ratio ............................ 155 
 
Figure 6.11. Etowah County FB-MultiPier pile number layout ..................................... 159 
 
Figure 6.12. Etowah County longitudinal Coalinga North (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio .............................................. 160 
 
Figure 6.13. Etowah County longitudinal NPS North (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio .............................................. 161 
 
Figure 6.14. Etowah County transverse Kocaeli2 NMCE (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio .............................................. 163 
 
Figure 6.15. Etowah County transverse Landers North (column) (a) time-history event, 
(b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio ................................. 164 
 
Figure 6.16. Franklin County longitudinal LSM North (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio .............................................. 167 
 
xviii 
 
Figure 6.17. Franklin County longitudinal San Fernando2 NMCE (a) time-history event, 
(b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio ................................. 168 
 
Figure 6.18. Franklin County transverse Landers North (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio .............................................. 170 
 
Figure 6.19. Franklin County transverse Landers NMCE (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio .............................................. 171 
Figure 6.20. Lee County longitudinal San Fernando2 NMCE (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio .............................................. 175 
 
Figure 6.21. Lee County longitudinal San Fernando2 North (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio .............................................. 176 
 
Figure 6.22. Lee County transverse Imperial Valley NMCE (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio .............................................. 178 
 
Figure 6.23. Lee County transverse Imperial Valley North (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio .............................................. 179 
 
Figure 6.24. Marshall County longitudinal Imperial Valley NMCE (a) time-history event, 
(b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio ................................. 183 
 
Figure 6.25. Marshall County longitudinal Kocaeli2 NMCE (As if Survived) (a) time-
history event, (b) shear distribution, (c) top of pier displacement, (d) moment 
distribution, (e) ground surface displacement, and (f) demand capacity ratio ........ 184 
 
Figure 6.26. Marshall County longitudinal Kocaeli2 NMCE (failed at time 64.9 sec) (a) 
time-history event, (b) shear distribution, (c) top of pier displacement, (d) moment 
distribution, (e) ground surface displacement, and (f) demand capacity ratio ........ 185 
 
Figure 6.27. Marshall County transverse Imperial Valley NMCE (a) time-history event, 
(b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio ................................. 187 
 
Figure 6.28. Franklin County longitudinal Kocaeli2 NMCE (failed) (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, 
(e) ground surface displacement, and (f) demand capacity ratio ............................ 188 
1 
 
Chapter 1 
INTRODUCTION
 Due to the implementation of the AASHTO LRFD Bridge Design Specifications 
(LRFD Specification) (AASHTO 2013), design of bridges will be significantly impacted 
for the moderate seismic design category1 (SDC) of Alabama.  Since the AASHTO 
Standard Specification for Highway Bridges (Standard Specification) (AASHTO 2002) 
was last updated, there has been a significant amount of geotechnical and seismic hazard 
mapping research.  Under the Standard Specification, Alabama was almost entirely 
classified as SDC A, which requires minimum detailing and no additional analysis for 
bridge design.  The Standard Specification seismic hazard map showing peak ground 
acceleration (PGA) is shown in Figure 1.1. 
                                                 
1 SDC, seismic hazard, and seismic zone all have the same meaning and are used frequently throughout 
literature.  To be consistent, SDC will be used in accordance with the 2009 AASHTO Guide Specifications 
for LRFD Seismic Bridge Design (Guide Specification).   
2 
 
 
Figure 1.1. Standard Specification for PGA (%g) for a 500 year return period (AASHTO 
2002) 
 
 The LRFD Specification seismic hazard maps have been significantly modified 
because of two primary changes: (1) the design level earthquake has increased from a 
500-year return period to a 1000-year return period, and (2) the sources associated with 
Alabama seismicity, the New Madrid Seismic Zone and the East Tennessee Seismic 
Zone, have been further studied, which has consequently increased the PGA values for 
the state (Coulston, 2011).  In addition, the methodology to determine the SDC now 
includes the geotechnical Site Class.  Figure 1.2 shows the seismic hazard map for the 
LRFD Specification.  In comparison to Figure 1.1, Figure 1.2 shows a greater level of 
3 
 
detail.  Subsequently, the PGA has increased significantly in certain areas, especially in 
the northern half of the state. 
 
Figure 1.2. LRFD Specification for PGA for 1000-yr return period (AASHTO 2009) 
1.1 Objectives 
 The primary objective of this research was to evaluate the response of deep 
foundations to seismic loads in Alabama.  The specific objectives of the project included 
the following: 
? Determine if ALDOTs current typical critical and essential bridge design, specifically 
regarding the foundation elements, are suitable for seismic design in Alabama.  
? Determine the effects (if any) that scour and liquefaction have on driven piles and 
drilled shafts during an earthquake event. 
? Review other state DOT?s seismic design practices. 
4 
 
1.2 Scope of Work 
 A comprehensive review of deep foundation literature and design methods for 
seismic design was conducted along with a survey of other state DOTs to review their 
approach to seismic design of bridge foundations. 
 Substructure analysis was completed and static foundation response curves were 
developed.  These curves were used in SAP2000 to represent the foundations for the 
bridges (Panzer 2013).  A direct analysis was conducted in which a bridge bent was 
modeled for each case history and two scour cases for one of the case histories were 
modeled: 25% and 100% of scour depth.  A suite of scaled time-history events developed 
by Panzer (2013) was used to load the bent dynamically.  Displacements at the top of the 
bent and the ground surface were recorded, as well as maximum shear force, bending 
moment and demand/capacity (D/C) ratio distributions. 
 The results of the direct analyses were compared to the literature review findings 
and discussed.  Recommendations for future research were also made. 
 
 
  
5 
 
Chapter 2 
BACKGROUND 
 Chapter 2 provides background information on the relevant topics that this project 
encompassed.  Previous research conducted by Auburn University and methods for 
determining liquefaction potential are presented and discussed.  Soil-foundation-structure 
interaction is discussed in detail as well as different analysis methods for determining the 
foundation response.  An overview of the computer software that was used to conduct the 
analysis methods is provided.  This also includes methods for determining soil 
parameters needed and an overview of the dynamic analysis options available in the 
program.  Finally, a brief overview of FHWA GEC-3 (Kavazanjian et al. 2011) is given, 
which summarizes several key points of emphasis for geotechnical considerations in 
seismic analysis and design. 
2.1 Previous Research 
 A preliminary study (Coulston 2011) funded by the Auburn University Highway 
Research Center at Auburn University (HRC) was conducted to determine whether a set 
of economical bridge design standards, applicable to all hazards in the state, would be 
feasible.  It was decided by ALDOT that its Bridge Bureau will use the Guide 
Specification for LRFD Seismic Bridge Design (Guide Specification), which is a 
displacement-based seismic design guideline, as an alternative to the LRFD Specification 
force-based seismic design provisions.  The HRC study showed the Guide Specification 
to be simpler and more economical.  However, the Guide Specification is only applicable 
6 
 
to Ordinary bridges, not Critical and Essential bridges.  As part of the ongoing research 
by ALDOT, the design of Critical and Essential bridges are to be investigated and 
validated.  Each class has a specific seismic design philosophy that was adopted by 
AASHTO: 
A) Critical Bridge 
A critical bridge is expected to remain open to all traffic, including emergency 
vehicles, and for defense and security purposes after the design earthquake (large rare 
earthquake with a 1000-year return period) (Kavazanjian et al. 2011). 
B) Essential Bridge 
An essential bridge is expected to be usable by emergency vehicles and for security 
and defense purposes after the design earthquake (Kavazanjian et al. 2011). 
C) Ordinary Bridge 
Bridges that don?t fall under the critical or essential class are ordinary bridges.  These 
bridges are designed to allow significant structural damage after the design 
earthquake (Kavazanjian et al. 2011). 
The HRC study also found that a single design standard would not be feasible and further 
investigation was needed, including evaluating the response of deep foundations to 
seismic loads. 
 The primary concern for design of bridges to seismic events is the substructure 
elements, the superstructure-to-substructure connection (including the webwall or 
diaphragm braces), and the foundations (Coulston 2011).  Damage is expected to occur at 
specific ductile elements without causing collapse for design level events (Coulston 
2011).  For the moderate hazard of Alabama, the substructure should be designed to be 
7 
 
the ductile link, whereas the other previously mentioned elements are to remain elastic 
(Coulston 2011).  Figure 2.1 illustrates this behavior.  
 
 
Figure 2.1. Inelastic behavior of bridge elements in design level seismic event (Coulston 
2011) 
 
 As previously mentioned in Chapter 1, the method for determining the SDC has 
significantly changed since the Standard Specification was last updated.  According to 
Coulston (2011), SDC B would likely be the highest design category to occur in 
Alabama.  Figure 2.1 shows the design spectrum for several major cities in Alabama 
based on assuming Site Class D, which is the default soil condition for preliminary 
design.  The different Site Class definitions are displayed in Table 2.1.  Site class is 
determined by averaging the shear wave velocity, shear strength, or N-value throughout 
the top 100 feet of soil and/or rock.  See AASHTO (2009) for further details.  The 
8 
 
criterion for determining the SDC for a given site/area is shown in Table 2.2.  Referring 
to Figure 2.2, the largest spectral acceleration at a period of one second (SA1) is about 
0.18, which is well below the threshold of SDC C, 0.30. 
 
Figure 2.2. Design level seismic hazard curves for select Alabama cities (Coulston 2011) 
  
9 
 
Table 2.1 ? Site class definitions (AASHTO 2009) 
Site 
Class 
Soil Type and Profile 
A Hard Rock with measured shear wave velocity,   ? > 5000 ft/sec 
B Rock with 2500 ft/sec <   ? < 5000 ft/sec 
C Very dense soil and soil rock with 1200 ft/sec <   ? < 2500 ft/sec, or with 
either  ? > 50 blows/ft or   ?  > 2.0 ksf 
D Stiff soil with 600 ft/sec <   ? < 1200 ft/sec, or with either 15 blows/ft <  ? < 
50 blows/ft or 1.0 <   ?  < 2.0 ksf 
E Soil profile with   ? < 600 ft/sec, or with either  ? < 15 blows/ft or   ?  < 
1.0 ksf, or any profile with more than 10 ft of soft clay defined as soil 
with PI > 20, w > 40%, and   ?  < 0.5 ksf 
F Soil requiring  site-specific ground motion response evaluations, such as: 
? Peats of highly organic clays (H > 10 ft of peat or highly organic clay, where 
H = thickness of soil) 
? Very high plasticity clays (H > 25 ft with PI > 75 
? Very thick soft/medium stiff clays (H > 120 ft) 
Exceptions: 
Where the soil properties are not known in sufficient detail to determine the site class, a 
site investigation shall be undertaken sufficient to determine the site class.  Site Class E 
and F could be present at the site or in the event that Site Class E or F is established by 
geotechnical data. 
 
Where: 
  ? = average shear wave velocity for the upper 100 ft of the soil profile as defined in 
Article 3.4.2.2 
 ? = average standard penetration test (SPT) blow count (blows/ft) (ASTM D 1586) for 
the upper 100 ft of the soil profile as defined in Article 3.4.2.2 
  ?  = average undrained shear strength in ksf (ASTM D 2166 or D 2850) for the upper 
100 ft of the soil profile as defined in Article 3.4.2.2 
PI = plasticity index (ASTM D 4318) 
w = moisture content (ASTM D 2216) 
 
Table 2.2 ? Partitions for seismic design categories A, B, C, and D (AASHTO 2009) 
Value of SA1 SDC 
SA1 < 0.15 A 
0.15 < SA1 < 0.30 B 
0.30 < SA1 < 0.50 C 
0.50 < SA1 D 
Where: 
SA1 = Spectral acceleration at a period of 1 second 
 
10 
 
 Currently, the Guide Specification (displacement-based procedure) does not allow 
for design of Critical and Essential bridges.  There are three classes of bridges: (A) 
Critical, (B) Essential, and (C) Other (sometimes called Ordinary) Bridges (in descending 
order of importance) (Kavazanjian et al. 2011).   
2.2 Evaluation of Liquefaction Potential 
 During an earthquake, insitu soils may be susceptible to liquefaction.  
Liquefaction typically occurs when saturated cohesionless soil undergoes undrained 
loading conditions which generate excess pore water pressures (Kramer, 1996).  This 
increase in pore water pressure subsequently decreases soil shear strength and stability; 
the soil then mobilizes until it reaches a state of equilibrium.  There are two general 
modes of liquefaction that can occur: (A) flow liquefaction and (B) cyclic mobility 
(lateral spreading) (Kramer, 1996). 
A) Flow Liquefaction 
Flow liquefaction produces the most dramatic effects of the two, flow failures (or 
landslides), which occur on sloping ground.  Flow liquefaction occurs when the shear 
stress required for static equilibrium is greater than the shear strength of the soil 
(Kramer, 1996).  The soil then ?flows? under the influence of gravity until it reaches 
a stable condition.  These can often be catastrophic, destroying structures and killing 
people in its path.  Figure 2.3 shows an example of damage caused by flow 
liquefaction. 
 
11 
 
 
Figure 2.3. Flow liquefaction damage to a road in Japan during an offshore earthquake in 
2007 (USGS, 2008) 
 
B) Lateral Spreading 
Lateral Spreading, on the other hand, occurs on gently sloping ground or flat ground 
near water when the static shear stress is less than the shear strength of the liquefied 
soil (Kramer 1996).  These deformations can occur well after ground shaking has 
ceased, depending on the length of time required to reach static equilibrium (Kramer 
1996).  This mode can be destructive as well, causing bridges to collapse and 
excessive settlement of structures.  Figure 2.4 shows a collapsed bridge due to lateral 
spreading. 
 
12 
 
 
Figure 2.4. Collapse of the showa bridge in the 1964 Niigata, Japan earthquake (NGDC 
as referenced in Kavazanjian et al. 2011) 
 
 Because both modes of liquefaction can cause significant structural damage to 
existing structures, an evaluation of liquefaction susceptibility is an important aspect of 
seismic design.  Both modes of liquefaction can cause axial and lateral resistance of 
foundations to decrease significantly.   
 In a recent study (Ebersole and Perry 2008), liquefaction potential was mapped 
based on geologic age and origin using the Youd and Perkins (1978) method, which is 
shown in Table 2.3.  This method is based on geologic conditions.  Some geologic 
formations are inherently more susceptible to liquefaction than others.  Figure 2.5 shows 
liquefaction susceptibility for Alabama.  This map clearly indicates the relatively low 
potential for the northern part of the state.  However, almost all of the areas that have a 
high potential for liquefaction are located near stream or river beds where alluvial 
13 
 
cohesionless deposits generally make up the soil stratigraphy and the soils have a high 
degree of saturation.  This is important because many bridges are built to cross 
waterways.   
14 
 
Table 2.3 ? Susceptibility of sedimentary deposits to liquefaction during strong shaking 
(Youd and Perkins 1978) 
 
15 
 
 
Figure 2.5. Liquefaction susceptibility of Alabama based on Youd and Perkins 1978 
(Ebersole and Perry 2008). 
16 
 
 Table 2.4 presents the Guide Specification requirements for liquefaction for each 
SDC.  It should be noted that Kavazanjian et al. (2011) recommended that a liquefaction 
evaluation for SDC B was not necessary.   
Table 2.4 ? Liquefaction evaluation requirements for each SDC (AASHTO 2009) 
Value of SA1 SDC Liquefaction Evaluation Required? 
SA1 < 0.15 A No 
0.15 < SA1 < 0.30 B Should be considered for certain conditions 
0.30 < SA1 < 0.50 C Yes 
0.50 < SA1 D Yes 
Where: 
SA1 = Spectral acceleration at a period of 1 second 
 
 If the site is deemed to have a high potential for liquefaction, a formal 
liquefaction evaluation should be done in most cases.  Referring to Figure 2.4, most of 
the areas that have a high potential for liquefaction are located in the southern part of the 
state, which has a low sesmic hazard (SDC A).  However, the potential for liquefaction 
should always be considered in a SDC B, especially in regard to bridges near waterways 
in the northern part of the state.  The Simplified Procedure, originally developed by Seed 
and Idris (1982) is one of the most common method used to evaluate liquefaction 
potential and is recommended to use should the engineer deem it necessary.  It has been 
revised since its initial development and is presented in Kavazanjian et al. (2011).  It 
should be noted that the Simplified Procedure should be primarily used for sites with 
moderate to strong ground motions (0.2 g < amax < 0.5 g) (Kavazanjian et al. 2011). 
2.3 Soil-Foundation-Structure Interaction 
 Understanding how the global system of any problem works is an important step 
in analysis and design of systems and structures.  In this case, the global system is the 
bridge pier and surrounding elements, which can be broken into two main components:  
17 
 
the soil and structure.  The presence of a constructed facility modifies the free-field 
ground motion at the base of the structure and typically reduces it (Kavazanjian et al. 
2011).  Free-field ground motion is the natural ground motion one would feel standing on 
undisturbed earth during an earthquake event.  The interaction between the soil and the 
structure is commonly referred to as soil-structure interaction (SSI).  The structure can be 
further broken down into two separate components: foundation and above-ground 
structure.  The above-ground structure in the case of the type of bridge under 
consideration is the pier column(s) and cap, and the bridge deck.  The interaction of the 
system is more properly described as soil-foundation-structure interaction (SFSI) which 
will be used throughout this document (Kavazanjian et al. 2011).  There are two sources 
of SFSI:  kinematic interaction and inertial interaction.  Both interactions occur during an 
earthquake event and are complex.  The foundation is loaded kinematically by the 
earthquake, and then the structure begins to move, causing inertial forces to be 
transferred from the structure to the foundation.  
2.3.1 Kinematic Interaction 
 Kinematic interaction directly interplays both the soil and foundation system, 
making this interaction the more complex of the two (Bhattacharya 2003).  Before the 
superstructure begins to oscillate, the piles may be forced, by the soil, to displace 
depending on the flexural stiffness (EI) of the pile (Bhattacharya 2003).  The motion 
difference between the pile and the free-field motion can induce bending moments in the 
pile (Bhattacharya 2003).  Kinematic interaction is often ignored in analysis because it is 
negligible for flexible piles in competent soils and tends to reduce the above-ground 
structural motion for stiff piles (Kavazanjian et al. 2011).  In most applications, kinematic 
18 
 
interaction response analysis is not feasible because it leads to large numerical models 
(Kavazanjian et al. 2011).  However, it can prove to limit conservatism, and could reduce 
costs associated with constructing the bridge.   
2.3.2 Inertial Interaction 
 Inertial interaction takes place as the structure begins to move, and the magnitude 
of the inertial forces depends upon the fundamental period of the structure and the 
frequency content of the ground motions (Kavazanjian et al. 2011).  These inertia forces 
of the structure are transferred to the foundation system as lateral forces, vertical forces 
and bending moments.  To model inertial interaction for deep foundations, an equivalent 
cantilever or spring-dashpot model is used to represent the foundation (Kavazanjian et al. 
2011).  Figure 2.6 shows a generalized form of the inertial interaction model for deep 
foundations.  This is a simple approach and is done often.  However, it cannot account for 
the bending moment distribution in the pile, and, for each of the five relevant degrees of 
freedom (DOF) (2 translational and 3 rotational), the length of the equivalent cantilever 
(or point of fixity) may be different (Kavazanjian et al. 2011).   
 
19 
 
 
Figure 2.6. Inertial interaction model for deep foundations (Kavazanjian et al. 2011) 
2.3.3 Seismic and Dynamic Response Analysis Methods 
 The two most common methods that are used to analyze the seismic response of 
bridge foundations are substructure analysis and direct analysis.  For both methods, 
several factors must be considered: soil stratigraphy and strength parameters, water table 
elevation, foundation types and lengths, pile cap design (if applicable), and different 
geotechnical hazards such as scour and liquefaction.  Each project is different and the 
analysis may or may not need to include consideration for other geotechnical hazards 
besides an earthquake.  Thoughtful consideration must be given to all possibilities before 
implementing an analysis program. 
 Depending on what type of abutment is present, there are different resisting 
mechanisms, including mobilization of the abutment back-wall, that contribute to the 
resistance of a bridge to an earthquake event.  For further detail, see Kavazanjian et al. 
(2011). 
20 
 
2.3.3.1 Substructure Analysis 
Substructure modeling is the simpler and the more common method of the two.  
The most common way to determine the foundation stiffness is by using a computer 
program, such as LPILE or FB-MultiPier, that uses the p-y method to determine soil 
response, then extrapolate the stiffness so that it represents a group stiffness (if 
necessary).  Since the extrapolation method was not used in this project, it is not covered.  
See Kavazanjian et al. (2011), for a more detailed discussion.  While this is widely 
accepted, there is software capable of modeling pile groups more accurately such as 
GROUP and FB-MultiPier (which was used for this research project).  Greater detail 
about FB-MultiPier and the p-y method is covered in section 2.4 of this chapter. 
 There are six DOF for a foundation system and the stiffness of the foundation for 
each degree must be known or estimated.  The DOF are axial and bi-lateral translation (u, 
v, and w) and rotation (?X, ?Y, and ?Z) about each of the three axes.  Sometimes, it may 
be appropriate to assume some DOF are fixed, and therefore, they do not need to be 
evaluated, such as axial translation or torsional rotation.  To determine the response of the 
foundation, a static response analysis is done at the pile head or pile cap head.  See Figure 
2.7 for a representation of substructure modeling.  In this case, it was assumed the pile 
head was fixed within the cap, therefore they were modeled together.  One question that 
is usually asked when determining the response is whether the axial dead load should be 
included in the lateral and rotational push-over analysis.  Lam and Martin (1986) 
concluded the following:  
For convenience in design or analysis, the axial soil support 
characteristics are assumed to be independent of the lateral soil support 
21 
 
characteristics. This is justified because lateral soil reactions are usually 
concentrated along the top 5 or 10 pile diameters whereas almost all of 
the axial soil resistance is developed at greater depths. Therefore, the 
axial and lateral soil support behavior can be studied and analyzed 
separately. 
 The end result of a static foundation response analysis is a family of 
force/moment versus displacement/rotation response curves that represent the pile head 
or the top of a pile group in a structural model.  These curves are almost always 
nonlinear.  The structural and geotechnical engineer must communicate effectively as 
where to properly apply the springs and in what fashion.  Figure 2.8 shows an example of 
a foundation stiffness curve. 
 Figure 2.7. Foundation substructure model for kinematic analysis (Kavazanjian et al. 
2011) 
22 
 
 
 
Figure 2.8. Example of a foundation stiffness curve 
2.3.3.2 Direct Analysis 
 Direct analysis is not done in most applications.  It is simply too time consuming 
and complicated to be used for every project, and most institutions or companies cannot 
afford the type of software that is best suited to run this method of analysis.  Direct 
analysis builds on that of substructure modeling.  However, time-history or response 
spectrum functions, structure configuration, and dead loads must also be input into the 
program.  See section 2.4 for more detail on these topics.  Figure 2.9 shows a detailed 
representation of direct analysis. 
23 
 
 
Figure 2.9. Direct (or Total) soil-foundation-structure kinematic interaction model 
(Kavazanjian et al. 2011) 
 
2.4 Computer Programs 
 While there are several programs that can perform substructure analysis, such as 
LPile (Ensoft 2013(b)) and GROUP (Ensoft 2013(a)), FB-MultiPier (BSI 2013(b)) is 
capable of doing both substructure and direct analysis.  This was an important factor in 
deciding which program to use. 
2.4.1 Overview of FB-MultiPier 
 FB-MultiPier is a hybrid finite element analysis program developed by the Bridge 
Software Institute (BSI), which is headquartered at the University of Florida in 
Gainesville, FL.  It is capable of modeling multiple bridge pier structures that are 
interconnected by single representative bridge spans.  The full structure can be subjected 
24 
 
to a full array of AASHTO load types in a static analysis or time varying load functions 
in a dynamic analysis (BSI 2013(b)). 
The structural elements that it is capable of simulating include foundation 
element(s) (piles and drilled shafts), pile cap(s), column, and pier cap.  All of the 
structural elements can be uniquely modeled by the user.  The program also provides 
standard sections for many common foundation elements (H-pile, drilled shaft, 
prestressed concrete pile, pipe pile, etc.).  For the soil-foundation interaction, FB-
MultiPier uses axial (t-z, Q-z), lateral (p-y), and torsional (T-?) nonlinear spring 
functions (soil springs).  It uses 2-node finite elements below the ground surface to model 
the pile, placing the corresponding axial, lateral, and torsional soil springs at each 
element.  The number of 2-node finite elements can be varied from five to fifty below the 
ground and for the free length of the pile (if any).  FB-MultiPier employs several soil 
spring functions to characterize the soil stiffness as well as the capability to enter a 
customized set of ten curve points if none of the default soil springs are suitable. 
 FB-MultiPier uses an iterative solution method to solve for the structural 
displacements.  This method follows a secant approach where FB-MultiPier finds the 
stiffness of the soil and structure for a computed set of displacements, assembles a 
stiffness matrix, and then solves for a new set of displacements. Convergence is achieved 
when the system is in static equilibrium.  This is determined by comparison of the 
magnitude of the highest out-of-balance nodal force and the tolerance defined by the user 
in the input file.  If the highest out-of-balance force is lower than the tolerance, the 
system is in static equilibrium and the program terminates.  If the program did not 
converge, it is likely due to one of three reasons: (1) structural failure, (2) soil failure, or 
25 
 
(3) numerical instability.  Structural failure occurs when a plastic hinge develops within 
the model and the shaft/column/pile cannot distribute the load any longer and 
subsequently, does not converge to a solution.  Soil failure occurs when the 
displacements of the soil springs are large enough that the soil cannot absorb any more 
load.  This leads to large out-of-balance forces.  Numerical instability can occur from a 
combination of things within the model such as secondary moment effects, time stepping 
issues, corrupt input data, etc.  The output files are a good indication of what causes the 
model to fail (especially the last time-step) and should always be reviewed.  
When first opening FB-MultiPier, the user must open an existing file or select a 
new problem type.  If a new problem type is selected, a default file is automatically 
loaded and displayed (BSI 2013(b)).  Figure 2.10 shows the home screen of FB-
MultiPier.  The top left window is the Model Data window where most of the information 
is entered (BSI 2013(b)).  The top right window is the Pile Edit window and it shows the 
pile group in plan.  The bottom left window is the Soil Edit window where the soil 
stratigraphy is shown.  A 3-D view of the pier structure is shown in the bottom right 
pane.  This graphical user interface allows the user to see the development of the model 
as it is being built, which can help find mistakes and accelerate the process (BSI 
2013(b)). 
 The following sections provide a brief introduction to the system processes and 
various models employed by FB-MultiPier and are taken (in most part) from the FB-
MultiPier User?s Manual (user?s manual) (BSI 2013(b)).  Refer to the user?s manual for 
further details and relevant information.   
26 
 
 
Figure 2.10. FB-MultiPier editor window 
27 
 
2.4.2 Soil Modeling 
 FB-MultiPier is capable of modeling multiple soil sets and layers within a model.  
This is important as site conditions can vary within a few feet.  There are several 
important soil properties that are required as input parameters within the program such 
as: Young?s modulus, Poisson?s ratio, shear modulus, angle of internal friction, undrained 
strength, subgrade modulus, and the water table elevation (BSI 2013(b)).  However, 
depending on what soil model is selected, other properties, such as shear strain, unit skin 
friction and ultimate tip resistance may be required.  The user?s manual provides various 
recommendations for estimating soil properties and for brevity, they are not presented in 
this document.  A brief description of each soil model is given.  More detailed 
information can be found in the user?s manual (BSI 2013(b)). 
 It should be noted that for both lateral and axial (skin and base resistance) 
interaction, American Petroleum Institute?s (API) clay and sand models are also available 
in FB-MultiPier.  For further detail regarding these models, see API (1997). 
2.4.2.1 Lateral 
 For the lateral soil-pile interaction, FB-MultiPier employs six different p-y 
models to choose from as well as a user defined option.  This includes: (A) Matlock?s 
Soft Clay Below Water Table, (B) Reese?s Stiff clay Below Water Table, (C) Reese and 
Welch?s Stiff Clay Above Water Table, (D) Sand of Reese, Cox, and Koop, (E) O?Neill?s 
Sand, (F) O?Neill?s Clay, and (G) Limestone (McVay). 
A) Matlock?s Soft Clay Below Water Table 
Matlock (1970) developed curves for soft clay below the water table for both static 
and cyclic loading conditions.  This representation requires the unit weight, ?; 
28 
 
undrained strength, su; and strain at 50% of the failure load of an unconfined 
compression test, ?50, of the soil to be input for both programs.  Figures 2.11 and 2.12 
are representations of the curves. 
B) Reese?s Stiff Clay Below Water Table 
Figures 2.13 and 2.14 are the p-y curves for stiff clay below the water table developed 
by Reese et al. (1975).  The soil parameters necessary to develop this curve are 
subgrade modulus, k; unit weight, ?; undrained strength, su; and the strain at 50% of 
the failure stress in an unconfined compression test, ?50.  Figure 2.13 is the static case 
and Figure 2.14 is the cyclic case.  
C) Reese and Welch?s Stiff Clay Above Water Table 
Reese and Welch?s (1972) p-y curves are for stiff clay above the water table.  This 
model requires the input of unit Weight, ?; undrained strength, su; and the strain at 50 
% of the failure stress in an unconfined compression test, ?50.  Note that the cyclic 
curve is dependent upon the number of cycles.  Figure 2.15 is the static model and 
Figure 2.16 is the cyclic model. 
D) Sand of Reese, Cox, and Koop 
Reese, Cox, and Koop (1974) developed a model for sands in general.  This model 
requires subgrade modulus, k; effective unit Weight, ??; and the angle of internal 
friction, ?, for the soil.  Figure 2.17 is both the static and cyclic model for sand. 
E) O?Neill?s Sand 
O?Neill and Murchison (1983) developed a model similar to Reese et al. (1974) for 
the lateral soil pile interaction for sand. Similarly, this model requires the input of 
29 
 
subgrade modulus, k; effective unit Weight, ??; and angle of internal friction, ?, for 
the soil.  Figure 2.18 shows O?Neill?s p-y curve for sand. 
F) O?Neill?s Clay 
O?Neill and Gazioglu (1984) developed a model for clay. This model requires the 
input of undrained strength, su; the strain at 50% of the failure stress in an unconfined 
compression test, ?50; and the strain at failure in an unconfined compression test, ?100.  
Figure 2.19 shows the static curve and Figure 2.20 shows the cyclic curve. 
G) Limestone (McVay) 
McVay and Niraula. (2004) developed a model for rock with characteristics of 
Florida limestone.  The model requires the input of unconfined compressive strength, 
qu.  This model was based on twelve lateral load tests conducted in a centrifuge.  It 
should be noted that the report (McVay and Niraula 2004) recommends that full scale 
field tests be conducted to validate the curves.  Figure 2.21 shows the normalized 
curves from the tests conducted. 
30 
 
 Figure 2.11. Matlock?s static curve for soft clay (Matlock 1970) 
 
Figure 2.12. Matlock?s cyclic curve for soft clay (Matlock 1970) 
31 
 
 
Figure 2.13. Reese?s static curve for stiff clay below the water table (after Reese et al. 
1975) 
 
Figure 2.14. Reese?s cyclic curve for stiff clay below the bater table (after Reese et al. 
1975) 
32 
 
 
Figure 2.15. Reese and Welch?s static curve for stiff clay above water table (Reese and 
Welch 1972) 
 
Figure 2.16. Reese and Welch?s cyclic curve for stiff clay above water table (Reese and 
Welch 1972) 
33 
 
 
Figure 2.17. P-y curves for sand (Reese, Cox and Koop 1975) 
 
Figure 2.18. O?Neill?s p-y curve for sand (O?Neil and Murchison 1983) 
34 
 
 
Figure 2.19. O?Neil?s static p-y curve for clay (O?Neill and Gazioglu 1984) 
 
Figure 2.20. O?Neil?s cyclic curve for clay (O?Neill and Gazioglu 1984) 
 
35 
 
 
Figure 2.21. McVay?s normalized p-y curves corrected for side shear for limestone 
(McVay and Niraula 2004) 
 
2.4.2.2 Axial 
 For the axial soil-pile interaction (this section excludes tip resistance), FB-
MultiPier employs three models as well as the user defined option.  These include: (A) 
driven piles, (B) drilled and cast insitu piles/shafts, and (C) axial skin resistance for 
limestone (McVay). 
A) Driven Piles 
This model is for both cohesive and cohesionless soil.  The user must supply the 
initial shear modulus, Gi; Poisson?s ratio, ?? and the maximum shear stress between 
the pile and soil at the depth in question, ?f.  Figure 2.22 shows the axial T-z curve for 
a pile. 
 
36 
 
B) Drilled and Cast Insitu Piles/Shafts 
The T-z curves used are based on the recommendations found in Wang and Reese 
(1993).  They are based on trend lines and computed for each node.  There are three 
models provided for the following soil types: sand, clay and intermediate 
geomaterials (IGM).  For both the sand and clay models, no additional soil properties 
are needed.  Figures 2.23 and 2.24 present the sand and clay trend lines.  The IGM 
model is taken directly from FHWA?s Load Transfer for Drilled Shafts in 
Intermediate Geomaterials (O?Neill 1996).  The user must supply the mass modulus, 
Em; modulus ratio, Em/Ei; surface condition; split tensile strength of the pile concrete; 
unit Weight of the pile concrete ?con; and the slump of the pile concrete.  Refer to the 
FB-MultiPier user manual for more details. 
C) Axial Skin Resistance for Limestone (McVay) 
This model is taken from McVay and Niraula (2004) as previously mentioned.  The 
user must supply the ultimate unit skin friction, fmax.  The curves are based on tests 
performed on 6 feet diameter drilled shaft embedded 18 feet into rock.  Figure 2.25 
shows the comparison of the normalized T-z curves. 
 
 
37 
 
 
Figure 2.22. Axial T-z curve for pile/shaft (McVay et al. 1989) 
 
Figure 2.23. Trend lines for drilled shaft side resistance in sand (BSI 2013(b), and Reese 
and O?Neill 1988) 
 
38 
 
 
Figure 2.24. Trend lines for drilled shaft aide resistance in clay (BSI 2013(b), and Reese 
and O?Neill 1988) 
 
Figure 2.25. Comparison of normalized T-z curves for limestone (BSI 2013(b), Kim 
2001, and McVay and Niraula 2004) 
39 
 
2.4.2.3 Torsional 
 FB-MultiPier uses two models to account for the non-linear torsional (T-?) 
behavior of the soil: a hyperbolic curve and a user defined curve.  The initial slope of the 
hyperbolic curve is a function of the shear modulus, G; and the ultimate value is based 
upon the ultimate shear stress at the soil-pile interface.  Figure 2.26 shows a hyperbolic 
representation of the T-??curve. 
 
 
Figure 2.26. Hyperbolic representation of T-? curve (BSI 2013(b)) 
 
2.4.2.4 Tip 
 FB-MultiPier uses two axial base resistance (or Tip) Q-z models as well as a user 
defined curve.  These models include: (A) driven pile, and (B) drilled and cast insitu 
40 
 
piles/shafts.  For every model in FB-MultiPier, the pile must be embedded in a soil 
element.  The amount of embedment does not matter for axial analysis.  That is not to say 
it does not matter for lateral analysis, however. 
A) Driven Pile 
The nonlinear Q-z model used in FB-MultiPier is a function of the ultimate tip 
resistance, Qf; initial shear modulus, Gi; and Poisson?s ratio, ?.  Figure 2.27 shows the 
Q-z curve for driven pile.  The model used is from McVay (1989). 
B) Drilled and Cast Insitu piles/shafts 
The drilled and cast insitu pile/shafts Q-z curves are based on the recommendation 
given by Reese and Wang, 1993.  They are based on trend lines and computed for 
each node.  Trend lines are provided for sand, clay, and IGM.  For sand and clay, the 
uncorrected SPT blow count and the undrained shear strength, su, is required 
respectively.  For IGM, the mass modulus, Em , is required.  See the user?s manual for 
more information regarding IGM modeling.  Figures 2.28 and 2.29 show the trend 
lines for sand and clay respectively. 
 
41 
 
 
Figure 2.27. Axial Q-z curve for driven pile (BSI 2013(b)) 
 
Figure 2.28. Trend Lines for drilled shaft end bearings in sand (BSI 2013(b), and O?Neill 
and Reese 1999) 
42 
 
 
Figure 2.29. Trend lines for drilled shaft end bearings in clay (BSI 2013(b), and O?Neill 
and Reese 1999) 
 
2.4.2.5 Input Parameters 
 One of the most important aspects of any computer program analysis is the input 
parameters used.  There are many correlations, charts, tables, etc., to determine the soil 
parameters necessary for FB-MultiPier.  The input parameters needed to be determined 
for this project, and sources used to determine parameters are shown in Table 2.5.  The 
shear strength correlations referenced are primarily based on the SPT N-value, which is 
commonly used to determine soil strength and consistency.  
  
43 
 
Table 2.5 ? Input parameters needed for FB-MultiPier 
?? unit Weight 
? (Terzaghi and Peck 1968) 
?? angle of internal friction 
 (Peck et al., 1974); (Barton 1973, and Hoek & Bray 1977, as referenced in Mayne et al. 2001) 
Su and qu undrained shear strength and unconfined compressive strength 
? (Kulhawy and Mayne 1990) 
???? strain at 50% of the failure stress in an unconfined compression test 
? (Reese and Wang 1993) 
????? strain at 100% of the failure stress in an unconfined compression test 
 (In the absence of testing, experience shows that ?100 is somewhere between 7 and 15 % or roughly twice that of ?
50) 
k subgrade modulus  
 (Reese and Wang 1993) 
G initial shear modulus 
? (PL_AID,1989) 
?f? unit skin friction 
 (BSI 2013(a)) 
Qtip axial bearing failure 
? (BSI 2013(a) after Schmertmann (1967)) 
?? Poisson's ratio 
? (BSI 2013(b)) 
N SPT N-value 
 (Value determined based on Standard Penetration Test) 
 
2.4.3 Structural Modeling 
 FB-MultiPier is capable of modeling complex structural components.  The 
structural components are modeled by inputting the pier geometry (pier height, pier cap 
cantilever length, column spacing and offset, number of piers, and pier cap slope), cross-
section parameters, and taper data (if applicable).  Figure 2.30 shows the pier data edit 
window.  The program has default cross sections or the user can model a custom one.  
The cross section can be modeled as one of two types: gross properties and full cross 
section.  The gross properties option requires the specification of the resulting sectional 
44 
 
properties.  This can be cumbersome when modeling complex reinforced concrete cross 
sections.  The full cross section option requires reinforcement details and material 
properties.  The sectional properties are calculated internally.  Figure 2.31 and 2.32 show 
the gross properties and full cross section windows within the program.  Figure 2.33 
shows the reinforcement specification window.  The user has the option of specifying 
reinforcement by custom designation or by percentage of gross area.   
 The program can conduct linear or non-linear analysis for both the pile and pier 
(column and cap).  If linear behavior is selected, it is assumed the behavior is purely 
linear elastic and deflections do not cause secondary moments (BSI 2013(b)).  If non-
linear analysis is selected, the program accounts for second order effects (p-delta) as well 
as stiffness changes within the structure, such as cracking of concrete, and it uses either 
user defined or default stress-strain curves (BSI 2013(b)).  P-delta effects occur when the 
axial force becomes eccentric within the element due to displacements of one end of the 
element relative to the other, causing an out-of-balance moment within the member (BSI 
2013(b)).  The default non-linear stress strain curve of concrete is a function of 
compressive strength and the Young?s modulus of elasticity of the concrete.  The default 
stress-strain curve for mild steel, such as an H-pile, is elastic-perfectly plastic and a 
function of Young?s modulus of elasticity and the yield strength.  These default stress-
strain curves are shown in Figures 2.34 and 2.35.  Concrete modulus is also needed for 
developing the concrete models in FB-MultiPier.  Equation 2.1 presents the concrete 
modulus equation given by ACI (2011) for normal weight concrete:  
         ?    (2.1) 
where: 
Ec = modulus of elasticity of concrete (lb/in2) 
fc? = specified 28-day compressive strength of concrete (lb/in2) 
45 
 
 
Figure 2.30. Pier data edit window 
46 
 
 
Figure 2.31. Gross properties window 
 
47 
 
 
Figure 2.32. Full cross section properties window 
 
48 
 
 
Figure 2.33. Reinforcement specification window 
 
49 
 
 
Figure 2.34. Hognestad model for concrete (Hognestad et al. 1955) 
 
Figure 2.35. Default stress-strain curve for 60 ksi steel (BSI 2013(b)) 
 
50 
 
2.4.4 Foundation Modeling 
 The foundation elements are modeled like that of the structure elements as 
previously mentioned.  There are default options as well as a user defined option 
available.  The option to model multiple pile sets is also available.  For example, if the 
design calls for one drilled shaft tip elevation at 250 feet and the other at 265 feet, FB-
MultiPier can specify 2 (or more) pile sets.  This is an important option, as tip elevations 
or pile types can be different for a large pier structure.   
2.4.5 Pile Cap Modeling 
 The pile cap is modeled based on the concrete?s Young?s modulus of elasticity, 
Poisson?s ratio, thickness, and unit weight of the pile cap material (usually concrete).  To 
avoid stress concentrations at the base column node where it connects to the pile, FB-
MultiPier spreads the load to the four adjacent nodes on the pile cap using rigid 
connectors built in to the program (BSI 2013(b)).  The user has the option to choose 
whether to treat the pile-to-cap connection as pinned or rigid (referred within the program 
as fixed). 
 The pile cap can also be a factor in lateral and axial capacity within the program.  
A simple parametric study was done to compare a pile cap just above the ground surface 
and a fully embedded pile cap.  It was found that the lateral deflections decreased 
significantly when the pile cap was embedded.  Though this is generally correct, the soil 
resistance around the pile cap may change during construction depending on the 
techniques used and depth of embedment.  Therefore, it is up to the engineer to determine 
the ?as built? strength of the soil surrounding the pile cap.  In the analysis edit window, 
the option to include axial bearing effects of the pile cap is available.  It is to the 
51 
 
discretion of the engineer whether to use it or not.  Typically, pile foundations are 
designed with the assumption that the axial forces would be resisted by the piles alone. 
2.4.6 Pile Group Effects 
 Lateral and axial resistance of soil for a group of piles is typically not equal to the 
sum of the individual resistances relative to each pile (BSI 2013(b)).  Generally, the soil 
resistance to a pile within a group is less than the same individual pile (not in a group).  
This difference in resistance of soil to a pile within a group is a function of the pile 
center-to-center (c-c) spacing and location within the group (Brown et al. 1988).  Lateral 
group effects are typically handled by use of p-y multipliers.  P-y multipliers are used to 
degrade the p-y curve to account for the ?shadowing? effect (i.e., loss of soil resistance of 
piles in the trailing rows) (Brown et al. 1988).  When a pile group is loaded, the front row 
(or lead row) carries a larger proportion of the load, whereas the trailing rows carry less 
of a proportion.  Figure 2.36 shows an illustration of a generalized pile group interaction 
when laterally loaded.   
 FB-MultiPier provides the user with three options: (1) use default p-y multipliers, 
(2) user defined p-y multipliers, or (3) do not use p-y multipliers.  The default p-y 
multipliers are based on the recommendation by Brown et al. (1988).  The default 
multipliers used in FB-MultiPier for lateral loading are: 0.8, 0.4, 0.3, 0.2, 0.2, ?.0.3, 
where 0.8 is the lead row and 0.3 is the trail row value (BSI 2013(b)).  These values are 
recommended by Brown et al. (1988) to be used for 3D spacing.  Note that if there are 
four rows, the trail multiplier would be 0.2, whereas if there were ten rows, the trail 
multiplier would be 0.3.  For 5D spacing, Brown et al. (1988) recommends using the 
following p-y multipliers: 1.0, 0.85, 0.7, 0.7, ?, 0.7, where 1.0 is the lead row and 0.7 is 
52 
 
the trail row value.  BSI (2013(b)) also recommended using the same p-y multipliers for 
battered piles.  It is also important to note that FB-MultiPier will apply the p-y multipliers 
to the correct pile rows (lead to trail) based on which direction the piles move (not based 
on which direction the initial load is applied) (BSI 2013(b)).  For dynamic analysis, this 
means that as a pile is moving back and forth, the p-y multipliers will be updated each 
time the piles change the direction of displacement. 
 FB-MultiPier also considers group efficiency for axial loads.  Group efficiency 
for axial loads is the ratio of the amount of axial load the group can resist relative to the 
sum of the single pile resistances that make up the group.  Typically, driven pile group 
efficiencies are greater than one because the soil consolidates during driving, which 
increases the soil axial resistance.  The user has the option to input an efficiency factor 
other than one. Otherwise the default factor is one.  See Hannigan et al. (2006) for 
recommendations for axial group efficiency factors. 
53 
 
 
Figure 2.36. Illustration of p-y multiplier concept for lateral group analysis (Hannigan et 
al. 2006) 
 
 
54 
 
2.4.7 Dynamic Analysis Methods 
 There are two methods that FB-MultiPier employs to predict the dynamic 
response of a system:  transient dynamic (time-history) analysis and modal response 
analysis.  Both dynamic analysis options are briefly discussed herein.  For more detail on 
either analysis type, see Fernandes (1999). 
2.4.7.1 Time-History Analysis 
 FB-MultiPier uses time-history analysis to simulate the structural response under 
an earthquake event.  This is done by loading an earthquake record into the program.  FB-
MultiPier has built in functions and also allows the user to upload their own.  The 
functions can be either applied as load versus time or acceleration versus time.  The ?load 
versus time? functions are generally for impact analysis such as a barge impact. 
 Time-history analysis allows significant inertial and damping effects to be 
considered when determining the structural response.  This done by using implicit time 
integration algorithms to obtain a numerical solution to the equation of motion: 
[ ]{ ?}  [ ]{ ?}  [ ]{ }  { ( )}? (2.2) 
 
where: 
[ ] = mass matrix 
{ ?} = nodal acceleration vector 
[ ] = damping matrix 
{ ?} = nodal velocity vector 
[ ] = stiffness matrix 
{ } = nodal displacement vector 
{ ( )} = external force vector 
 
 FB-MultiPier has the option of using either the Newmark or Wilson-? method to 
determine the numerical solution of Equation 2.2 by using discrete time increments 
55 
 
specified by the user.  Typically, the same time step is used in that of the time function.  
It is possible, however, to use a larger time step to reduce analysis time if the time-history 
event is long.  This skips over some time steps and may miss a few peaks, but generally it 
is not significant in the overall response of the structure.  For more detail regarding time-
history analysis, see Fernandes (1999). 
2.4.7.2 Modal Response Analysis 
 Modal response analysis performs a response spectrum analysis of the structure in 
its equilibrium position (BSI 2013(b)).  The equilibrium position being the response of 
the system after it was statically loaded.  Figure 2.37 shows the cycle for how modal 
analysis is conducted within FB-MultiPier.  To perform modal analysis, FB-MultiPier 
requires the number of modes in which to run and a spectral acceleration function 
(acceleration versus frequency).  Global damping factors can be applied if applicable.  
Fernandes (1999) describes the modal analysis process within FB-MultiPier: 
In the first cycle the earthquake is applied to the structure and the initial 
forces at the base of the piers are computed.  Initially the springs that 
represent the foundation are considered very stiff, to simulate fixed 
supports.  Then for each column a vector of six forces is generated, the 
three forces Fx, Fy, and Fz in the x, y and z directions, and the three 
respective moments.  Then each of these forces is applied to the 
foundation, one at a time, like in a regular static analysis.  This will 
produce three displacements, dX, dY, and dZ, in the x, y, and z directions, 
and three respective rotations, ?X, ?Y, and ?Z, at the base of each 
column.... After all six forces are applied we have the six by six flexibility 
56 
 
matrix for the foundation, one (flexibility matrix) for each column.  
Inverting this matrix we obtain the new stiffness for the foundation, which 
becomes the foundation springs for the base of each pier for the next 
cycle. 
 Note that the force vectors generated represent the foundation response.  
Once two consecutive forces are within the user defined tolerance, the program 
terminates.  Note that in this analysis, the structure is considered linear, but the 
springs generated for each cycle will have characteristics of nonlinear behavior 
(Fernandes 1999). 
 
Figure 2.37. Modal analysis process for a bridge pier within FB-MultiPier 
(Fernandes 1999) 
 
57 
 
2.4.7.3 Damping 
 Damping is a complex and important part of structural response during 
dynamic loading.  It reduces the free motion vibrations in an oscillatory system.  
Damping effects in a real system, such as a bridge, are due to friction, air 
resistance, or other external or internal (within the damped system) physical 
mechanisms.  FB-MultiPier employs Rayleigh mass and stiffness damping factors 
in time-history analysis.  In the initial development of the dynamic analysis option 
in FB-MultiPier (Brown et al. 2001), Rayleigh mass and stiffness damping factors 
for the pier, piles, and soil were determined based on field tests correlated to the 
program results. The Rayleigh damping factors used in Brown et al. (2001) are 
presented in Table 2.6.  From Equation 2.3, we can expand the damping matrix, 
[C], as: 
[ ]   [ ]   [ ]? (2.3) 
 
where: 
  = stiffness proportional damping constant 
[ ] = stiffness matrix 
  = mass proportional damping constant 
[ ] = mass matrix 
 
Table 2.6 ? Rayleigh damping factors used in Brown et al. (2001) 
 Mass????? Stiffness???? 
Pier 0.04 0.01 
Piles 0.001 (steel) 0.001 (steel) 
Soil 0.015 0.015 
 
58 
 
2.4.7.4 Dynamic Relaxation 
 Dynamic relaxation within FB-MultiPier accounts for a static dead load before the 
transient dynamic load is applied.  Static analysis of the structure is conducted before the 
dynamic load is applied and a new stiffness matrix and nodal displacement vector are 
obtained through the static analysis once the system is in equilibrium (BSI 2013(b)).  
This new initial stiffness and nodal displacement vector is then used in the dynamic time-
history analysis.  If this option is not used, it will apply the dead load as an impact load 
simultaneously with the dynamic load (BSI 2013(b)).  This can exaggerate the dynamic 
structural response, and therefore, any assessment made based on that response is 
unreliable (BSI 2013(b)). 
 
2.4.8 FB-MultiPier Limitations 
 While FB-MultiPier is a very powerful program, there are several 
limitations that the user should be aware of.  These limitations can affect the 
quality of the output.  Therefore, it is important to understand them to properly 
interpret the output generated.  Most of these limitations directly affect the 
dynamic analysis.   
? FB-MultiPier can only apply 100 percent of the ground motion in the X, Y 
or Z direction (or a combination of the three).  It cannot apply, for 
example, 30 percent in the X direction and 70 percent in the Y direction.   
? There is an apparent limitation in the number of decimal places the time 
and acceleration values can be in the ?.acc? input files.  If the time step 
was originally 0.005 seconds, duplicating numbers would be read by the 
59 
 
program due to rounding by the program.  Also, if the time step was 0.01 
seconds and the time history function is over 100 seconds long, the 
program would only recognize numbers to the accuracy of 0.1.  For 
example, the program would read 100 until 100.05, and then read 100.05 
as 100.1 and so forth until it reached 101.05.  This can cause numerical 
error within the program. 
? FB-MultiPier has a memory restriction of 4GB.  This is too low for a 
dynamic model with many piles and structural members, and causes the 
program to crash due to insufficient memory capacity.  Increasing the time 
step was an option to lower the amount of memory needed for analysis.  
BSI is currently in the process of correcting this memory restriction.   
? Batch mode cannot be used when using the dynamic relaxation option.  
The program will not start the dynamic analysis after the static analysis is 
completed to use the new stiffness matrix and displacements.  BSI is 
currently in the process of correcting this issue. 
2.5 FHWA LRFD Seismic Analysis and Design of Bridge Foundations 
 Recently, the FHWA sponsored the revision of GEC-3 (Kavazanjian et al. 
2011), to include the LRFD guidelines developed by AASHTO.  Along with 
Kavazanjian et al. (2011), a course was developed (Kavazanjian et al. 2012) that 
aims to illustrate the principles and methodologies for LRFD seismic analysis and 
design of geotechnical features and structural foundations for bridges 
(Kavazanjian et al. 2012).  Three design examples were presented to show the 
procedures that need to be addressed in the seismic design process in accordance 
60 
 
with AASHTO specifications for LRFD seismic design (Kavazanjian et al. 2012).  
There are several points of emphasis pertaining to geotechnical considerations 
that were addressed in Kavazanjian et al. (2012) document: 
1. Development of the acceleration response spectrum for use in structural design, 
including adjustment for local site conditions. 
2. Deaggregation of the seismic hazard to get the earthquake magnitude for seismic 
stability analysis. 
3. Evaluation of lateral pile stiffness (p-y behavior) for the piles for both the 
abutments and the central piers (substructure analysis) 
4. Evaluation of vertical pile capacity (including uplift) and spring stiffness for both 
abutment and central pier piles (substructure analysis). 
5. Evaluation of the seismic stability of the abutment slope. 
6. Evaluate the seismic passive resistance and spring stiffness of the abutment wall. 
7. Evaluate liquefaction and lateral spreading potential of slopes at the abutments. 
8. Evaluation of the bearing capacity, sliding resistance and spring stiffness of the 
pier and abutment footings (if applicable). 
All of these points of emphasis are discussed in detail in Kavazanjian et al. 
(2011).  
61 
 
Chapter 3 
LITERATURE REVIEW 
 Chapter 3 is a summary of literature to explain deep foundation (referred to as pile 
in this chapter) behavior during an earthquake event.  Pile failure modes that are possible 
during an earthquake event are presented and discussed, as well as case histories of past 
pile performance during earthquake events.  Finally, pile performance and 
recommendations are reviewed and discussed for the combined effect of earthquake and 
scour.   
3.1 Pile Failure Modes 
 During an earthquake, deep foundations have the capacity to perform well and 
maintain overall stability.  However, it is important to understand the different failure 
modes a pile can undergo during an earthquake.  This allows the engineer to design the 
proper foundation while accounting for the different failure modes that could occur.  Pile 
failure can occur in several different ways.  The mechanisms of pile failure are shear 
force and flexure failure, and excessive settlement, all of which can be induced by several 
different modes.  There are two primary categories of pile failure during an earthquake: 
(a) pile failure without liquefaction-induced phenomena and (b) pile failure with 
liquefaction-induced phenomena (Wei et al. 2008).  A brief description of each category 
is presented: 
 
 
62 
 
A) Pile failure with no liquefaction-induced phenomena 
1) Failure due to the inertial force of the superstructure  
Ishihara (1997) described this as the ?top down effect? because the inertial force 
exerted by the superstructure is transferred down to the upper portion of the pile, 
inducing large bending moments at the pile cap and pile head(s).  Therefore, most 
of the damage and pile failure is located at joints between the pile cap and pile 
head or at the top of the pile (Wei et al. 2008). 
2) Failure at the interface of soft and hard soil layers (Wei et al. 2008) 
Excessive bending moment and shear force can also develop at the interface of 
two distinct soil layers of differing strength (i.e. a large deposit of soft clay over 
very dense sand).  Wei et al. (2008) also states that the p-y curve method, which is 
commonly used to determine the response of deep foundations, cannot reflect the 
actual situation that occurs between the two soil layers; therefore, careful 
consideration and proper engineering judgment should be used to determine the 
most representative response of a deep foundation system in this situation. 
3) Pile settlement due to thixotropy 
Thixotropy is a unique phenomenon that generally occurs in flocculated clayey 
soil.  Thixotropy is a time-dependent process that occurs when the soil is softened 
due to remolding of the soil skeleton that is induced by a dynamic loading; it then 
returns to its original, harder state after the loading is over and the particles 
realign (McCarthy 2007).  Thixotropy of soft soil can occur during an earthquake, 
therefore, the axial resistance of the soil can be greatly reduced which could cause 
excessive settlement. 
63 
 
4) Retaining wall or embankment near pile foundations (Wei et al. 2008) 
Earthquakes can cause retaining wall or embankment failures without the soil 
liquefying (i.e. tension cracks, etc.) during and after the event.  The soil could 
induce large passive pressures on the pile foundation should the soil mobilize, 
which could lead to excessive bending moment and ultimately structural failure of 
the pile.  
B) Pile failure with liquefaction-induced phenomena (Wei et al. 2008) 
1) Failure without lateral spreading 
If the soil liquefies, but does not undergo lateral spreading, it can create non-
uniform distributions in liquefied strength and thickness of the soil (Wei et al. 
2008).  The load distribution of the structure can become eccentric which could 
lead to differential settlement.  However, if the distribution of soil strength and 
thickness are uniform, the pile could still fail at the liquefied and non-liquefied 
soil interface due to the inertial loading of the structure (Wei et al. 2008).   
2) Failure with lateral spreading 
Bridges often span rivers.  The soil profile of these areas often includes 
liquefiable sand and silt layers sloping towards the river (Wei et al. 2008).  If the 
liquefied soil is present below the ground surface, the non-liquefiable soil (crust) 
above the liquefied layer can place a significant amount of passive pressure on the 
pile foundations as the liquefied soil displaces the top layer during liquefaction 
(Berrill et al. 2001).  This results in increased shear and bending at the pile head 
and cap.  The lateral and axial resistance of the soil also drastically decreases, and 
the pile can become unstable.  The main cause for pile failure during an 
64 
 
earthquake is thought to be due to lateral spreading around the pile according to a 
report published by National Research Council (NRC) Committee on Earthquake 
Engineering (1985).  They go on to claim that lateral spreading is responsible for 
more damage during an earthquake than any other mode of ground failure due to 
liquefaction.  This failure mechanism is widely accepted and has been used as the 
explanation for pile failure in many earthquakes (Bhattacharya 2003). 
 Another failure mechanism that can develop during an earthquake that does not 
necessarily lie within the two categories previously described is pile buckling.  Typically, 
buckling is accounted for in design by considering: (a) piles in very soft clay, (b) during 
installation by driving, and (c) partially exposed piles such as offshore platforms or jetties 
(Fleming et al., 1992)  Recently there has been research (Bhattacharya et al. (2004), 
Knappett and Madabhushi (2005), Kimura and Tokimatsu (2005), and Shanker et al. 
(2007)) suggesting that this is an important aspect of pile foundation design for 
earthquake loading and should be accounted for (Bhattacharya et al. 2008).  Buckling is 
only a problem if there is not sufficient lateral restraint to keep the pile from displacing 
laterally.  This can happen when soil liquefies and the effective stress is zero.  The easiest 
concept to describe buckling is that the axial design load Pdes must be less than the critical 
buckling load Pcr.  Euler?s formula for calculating Pcr is shown as equation 3.1: 
     
 
        (3.1) 
 
  
65 
 
where: 
Pcr = critical buckling load (kips) 
Leff = effective length of the pile in the liquefiable or soft clay region.  See 
Figure 3.1 for an explanation of the different boundary conditions.  Some 
designers may prefer to increase the effective length by a few diameters 
to account for imperfect fixity in the non-liquefying layer (Bhattacharya 
2003) (in) 
E = modulus of elasticity (ksi) 
I = cross-sectional area moment of inertia (in4)  
 
 
Figure 3.1. Concept of effective length of pile for different boundary conditions 
(Bhattacharya 2003). 
 
 The engineer must estimate the height of the liquefiable layer (or resulting free 
length of the pile) and the pile head and tip condition.  Leff is also different for each 
direction of buckling (longitudinal and transverse).  Typically, a drilled shaft embedded 
into rock will have an estimated Leff of 2 times the free length (Figure 3.1(a)) (length 
66 
 
from rock line to pile cap) in the longitudinal direction; whereas, in the transverse 
direction, Leff is most likely the same as the free length (assumed that the pier cap and 
column connection is rigid [fixed]).  For driven piles, a pinned connection is typically 
assumed for piles driven to bedrock (small embedment) and a fixed connection at the pile 
head embedded into the footing (Figure 3.1(c)).  Therefore, Leff is 2 times the length of 
the pile.  However, if stiff soil is in the upper or lower portion of the soil profile, partial 
fixity should be considered which would change Leff. 
3.2 Pile Performance in Liquefied Soil and Soft Clay 
 The Bhattacharya (2003) document was a primary source for pile buckling (see 
previous section), past pile performance (case histories) during an earthquake, and 
centrifuge testing and should be referred to for further detail. 
3.2.1 Case Histories 
 Pile foundations have been known to have both good and bad performance during 
an earthquake event.  Bhattacharya (2003) presents a summary of fourteen case histories 
of pile performance.  The pile types included in the case studies are reinforced concrete 
(drilled shafts), prestressed concrete piles, and steel pipe piles.  It was not conclusive that 
one pile type out-performed another.  They are presented in Table 3.1.  There are two 
important ratios that Bhattacharya discusses that are helpful in the design and selection of 
pile types and sizes:  Pdes/Pcr (Pdes is the design axial load for the pile) and Leff/rmin (also 
known as effective slenderness ratio).  Equation 3.2 shows how to calculate rmin: 
     ?   (3.2) 
 
 
 
67 
 
where: 
rmin = minimum radius of gyration of the pile section about any axis of bending (in) 
I = minimum cross-sectional area moment of inertia (in4)  
A = area of the pile section (in2) 
 
   Bhattacharya (2003) noted that the piles that failed had a Pdes/Pcr ratio between 
0.5 and 1.0; he then hypothesized that a pile having a Pdes/Pcr ratio of 0.5 or less would 
most likely perform well during an earthquake event.  Bhattacharya also hypothesized 
that if the effective slenderness ratio is 50 or less, the pile is likely to perform well.  
These hypotheses were based on fourteen case studies presented in Table 3.1.  Figure 3.2 
shows the slenderness ratio threshold of 50 and the case history values are shown for 
comparison.  Figure 3.3 shows the Pdes/Pcr thresholds of 0.5 and 1.0 with the case 
histories plotted for comparison.  It should also be noted that the piles that performed 
well in the case histories reviewed had a Pdes/Pcr ratio less than 0.1. 
68 
 
Table 3.1 ? Summary of pile performances (after Bhattacharya 2003) 
Case History and 
Reference 
L* 
(m) 
L0** 
(m) 
Pile 
Section/Type 
Framing 
Action/?*** 
Value 
Leff 
(m) 
rmin 
(m) Leff/rmin 
Pdes 
(MN) 
Pcr 
(MN) Pdes/Pcr 
Lateral 
Spreading 
Observed? Performance 
10 storey-Hokuriku 
building, 1964 
Niigata earthquake, 
Hamada (1992) 
12 5 
0.4m dia 
reinforced 
concrete 
(RCC) 
Large piled raft 
with basement, 1 5 0.1 50 0.77 12.4 0.062 Yes Good 
Landing bridge, 
1987 Edgecumbe 
earthquake, Berrill 
et al (2001) 
9 4 
0.4m square 
prestressed 
concrete 
(PSC) 
Raked piles, no 
sway frame, 0.5 2 0.12 17 0.62 139 0.004 Yes Good 
14 storey building in 
American park, 
1995 Kobe 
earthquake, 
Tokimatsu et al 
(1996) 
33 11 2.5m dia RCC 
Large pile group 
and large pile dia, 
1.0 
11 0.63 19 18 3915 0.005 Yes Good 
Kobe Shimim 
hospital, 1995 Kobe 
earthquake, Soga 
(1997) 
30 6.2 
0.66m 
dia Steel 
tube 
Large piled raft 
with basement, 
1.0 
6.2 0.23 27 3 91 0.033 No Good 
Hanshin expressway 
pier, 1995 Kobe 
earthquake, Ishihara 
(1997) 
41 15.9 1.5m dia RCC Small group (22 piles), 1.0 15.9 0.38 42 14 305 0.046 Yes Good 
LPG tank 101, Kobe 
earthquake, Ishihara 
(1997) 
27 15 1.1m dia RCC Large piled raft, 1.0 15 0.28 53 4.1 79 0.052 Yes Good 
N.H.K building, 
1964 Niigata 
earthquake, Hamada 
(1992) 
12 9.3 0.35m dia RCC  
Groups tied by 
flexible beam, 
Less embedment 
at pile tip, 2.0 
18.6 0.09 207 0.43 0.52 0.827 Yes Poor 
 
69 
 
Table 3.1 ? Summary of pile performances (continued) (after Bhattacharya 2003) 
Case History and 
Reference 
L* 
(m) 
L0** 
(m) 
Pile 
Section/Type 
Framing 
Action/?*** 
Value 
Leff 
(m) 
rmin 
(m) Leff/rmin 
Pdes 
(MN) 
Pcr 
(MN) Pdes/Pcr 
Lateral 
Spreading 
Observed? Performance 
NFCH building, 
1964 Niigata 
earthquake, 
Hamada (1992) 
9 7 0.35m dia RCC hollow 
Groups tied by 
flexible beam, 
Less embedment 
at pile tip, 2.0 
14 0.10 140 0.29 0.82 0.354 Yes Poor 
Showa bridge, 1964 
Niigata earthquake, 
Hamada (1992) 
25 19 0.6m dia Steel tube A single row of piles, 2.0 38 0.21 181 0.96 1.1 0.873 Yes Poor 
Yachiyo Bridge, 
1964 Niigata 
earthquake, 
Hamada (1992) 
11 8 0.3m dia RCC  Isolated footing, 2.0  16 0.08 200 0.34 0.39 0.872 Yes Poor 
Gaiko Ware House, 
1983 Chubu 
earthquake, 
Hamada (1992) 
18 14 0.6m dia PSC hollow Isolated footing, 2.0 28 0.16 175 1.47 1.61 0.913 Yes Poor 
4 storey fire house, 
1995 Kobe 
earthquake, 
Tokimatsu et al 
(1996) 
30 16.4 0.4m dia PSC Groups tied by beam, 1.0 16.4 0.10 161 0.89 1.15 0.774 Yes Poor 
3 storied building at 
Fukae, 1995 Kobe 
earthquake, 
Tokimatsu et al 
(1998) 
20 16 0.4m dia PSC hollow Groups tied by beam, 1.0 16 0.12 133 0.72 1.02 0.706 Yes Poor 
LPG tank 106,107 ?
1995 Kobe 
earthquake, Ishihara 
(1997) 
20 15 0.3m dia RCC hollow Groups tied by beam, 1.0 15 0.08 187 0.46 0.38 1.211 No Poor 
*L = Length of the pile;    **L0 = Length of pile in liquefiable region/bucking zone;    ***? = Factor for estimating Leff, where Leff = ?L0 
70 
 
 
Figure 3.2. rmin versus Leff for piles studied (Bhattacharya 2003) 
 
 Figure 3.3. Plot of the pile foundations that performed poorly as a function of P
cr versus 
Pdes (Bhattacharya 2003) 
 
71 
 
3.2.2 Centrifuge Testing 
 To verify that a Pdes/Pcr ratio of 0.5 or less and a slenderness ratio of 50 or less 
would indicate good pile performance during an earthquake, Bhattacharya (2003) 
conducted a series of centrifuge tests with different control parameters and soil 
conditions.  Figure 3.4 shows the set-up for the centrifuge test.  Table 3.2 shows the 
properties of the model (one used in the centrifuge tests) and prototype piles.  The model 
pile was 7 times stronger than an equivalent concrete pile and 1.5 times stronger than an 
equivalent steel pile in terms of plastic moment (Mp) 
 
Figure 3.4. Schematic of forces acting on the model pile (Bhattacharya 2003) 
  
72 
 
Table 3.2 ? Properties of the model and prototype pile (Bhattacharya 2003) 
Properties Model Prototype Section (50-g) 
Material Aluminium Alloy (Dural) Aluminium Alloy (Dural) 
E (Young's Modulus) 70 GPa 70 GPa 
Outside Diameter 9.3 mm 465 mm 
Inside Diameter 8.5 mm 425 mm 
rmin of the section 3.1 mm 155 mm 
Yield Stress 250 MPa 250 MPa 
Plastic Moment 
Capacity (Mp) 8175 Nmm 8175 x 50
3 = 1021.8kNm 
EI of the Section 7.77 x 106 Nmm2 7.77 x 10
6 x 504 = 48.6 x 103 
kNm2 
 
 The centrifuge test results verified the hypothesis Bhattacharya (2003) proposed 
for pile performance criteria based on the Pdes/Pcr ratio, which was based on the case 
histories presented in section 3.2.1.  Figure 3.5 presents the results of the centrifuge 
testing.  Table 3.3 also shows the results of each pile performance during the tests.  Test 
SB-05 was not included because the results were identical to test SB-04.  It was not 
conclusive that the slenderness ratio has a direct effect on the pile performance.  This is 
clear when comparing Pile 3 to Piles 4, 5, and 6, as the slenderness ratio of Pile 3 is less 
than that of Piles 4, 5, and 6, but still failed during the centrifuge test.  However, Pile 9 
had a slenderness ratio less than 50 (29) and did not fail.  Note that Pcr also takes into 
account the axial load applied to the column and Leff, whereas the slenderness ratio is 
based solely on geometry of the column.  However, the slenderness ratio could still be 
used as a guide to determine shaft, column, or pile section. 
73 
 
 
Figure 3.5. Schematic representation of the centrifuge test results (Bhattacharya 2003) 
  
74 
 
Table 3.3 ? Performance of the piles during the centrifuge tests (Bhattacharya 2003) 
Test ID Pile ID 
Head 
Mass 
(kg) 
Max 
Load P 
(N) 
P/A 
(MPa) 
Leff 
(Leff/rmin) P/Pcr Remarks 
SB-02 
Pile length 
= 160mm 
rmin =3.1mm 
A=9.7 mm2 
1 1.96 768 79 Leff = 355mm (114) 0.97 
Failed at 40-
g during 
swing up 
2 1.56 642 65 Leff = 350mm (113) 1.01 
Failed at 42-
g during 
swing up 
3 1.26 617 63 Leff = 345mm (111) 0.97 Failed during earthquake 
SB-03 
Pile length 
= 180mm 
rmin =3.1mm 
A = 11.2 
mm2 
4 0.60 294 26.3 Leff = 372mm (120) 0.50 Did not collapse 
5 0.45 220 19.7 Leff = 370mm (119) 0.35 Did not collapse 
6 0.23 113 10.1 Leff = 370mm (119) 0.22 Did not collapse 
SB-04 
Pile length 
= 180mm 
rmin = 
3.1mm 
A = 11.2 
mm2 
7 1.25 610 54.5 Leff = 420mm (135) 1.04 Failed during earthquake 
8 1.78 872 78 Leff = 445mm (144) 1.48 Failed during earthquake 
9 4.68 2249 201 Leff = 90mm (29) 0.25 Did not collapse 
SB-06 
Pile length 
= 180mm 
rmin = 
3.1mm 
A = 11.2 
mm2 
10 1.50 735 65.6 Leff = 445mm (144) 1.25 Failed during earthquake 
11 0.55 269 24 Leff = 370mm (119) 0.46 Did not collapse 
12 0.90 441 39.4 Leff = 378mm (122) 0.75 Failed during earthquake 
 
  
75 
 
3.3 Pile Performance under the combined Effect of Earthquake and Scour 
 The combined effect of flood-induced scour and earthquake hazards is a complex 
problem.  There are three components of scour that should be considered: (a) long-term 
aggradation and degradation, (b) contraction scour, and (c) local scour (Ghosn et al. 
2003).  Aggradation and degradation is long-term elevation change due to deposition or 
erosion of the streambed of the waterway.  Contraction scour is often due to the bridge 
embankments constricting the main channel (causes water to accelerate).  Local scour 
occurs when the water around the bridge piers accelerates in concurrence with rising 
water levels (Ghosn et al. 2003). 
 Because of the uncertainty of when an earthquake will occur, it is possible that the 
soil could scour around a bridge before or even during an earthquake.  One of the major 
questions is how much scour to account for during the design process.  If the insitu soil is 
susceptible to scour, the lateral stiffness of the foundation can be significantly reduced by 
the lack of soil resistance.  However, scour can possibly reduce the applied inertial 
forces, which could also reduce the demand for lateral capacity (Ghosn et al. 2003).  This 
means that scour has the potential to be both harmful and beneficial to bridge response 
during an earthquake; therefore, it is important to check different scenarios.   
 In Ghosn et al. (2003), the authors suggest using a scour factor of 0.25 (25% of 
the maximum anticipated scour depth be used in design) when combining scour and 
earthquake events.  This was based on the fact that the inertial forces are partially offset 
by the reduction in soil resistance capacity due to scour.  They presented the following 
load combination: 
Extreme Event VI: 1.25 DC  +  1.00 EQ; 
0.25 SC 
76 
 
where: 
DC = Dead Load 
EQ = Earthquake Load 
SC = Design Scour Depth 
 
 The second recommendation they provide is to design the foundations so that they 
are twice the length of the scour depth.  This recommendation attempts to ensure that the 
resistance capacity needed to resist an earthquake event will not be reduced below the 
demand.  However, some instances may necessitate longer foundation lengths, and this 
recommendation should be a minimum controlling factor when considering scour in 
design.  It should be noted that the design scour depth used in the Ghosn et al. (2003) is 
based on Richardson and Davis (1995).   
 
  
77 
 
Chapter 4 
MODEL GENERATION 
 Five bridge piers2 were modeled in FB-MultiPier to evaluate the response to 
seismic loading.  Each pier was modeled using a bridge design provided by ALDOT.  All 
of these bridges have been built and are in use in the state of Alabama.  Each bridge is 
located in a different county; therefore, each bridge will be referred to by the county 
name.  Figure 4.1 shows the locations of the bridges throughout the state.  For each 
bridge, the middle bridge pier was used for the response analysis.  A representative soil 
profile was developed using the lower bound of the boring log data (SPT N-values).  In 
some instances, multiple boring logs were taken at the same bent location, but to the right 
and left of the centerline of the bridge.  In this case, both boring logs were used to 
develop the profile by taking the lower bound of each layer (if layer matching between 
boring logs was relatively good).  Before the bridge piers were modeled in FB-MultiPier, 
the soil profiles were developed.  Soil layer type and elevation, water table elevation, and 
soil properties were all recorded in a spreadsheet, along with the type of lateral, axial, 
torsional, and tip models used in FB-MultiPier. 
 It was determined that the abutments cannot be used to resist longitudinal 
displacements because the gap between the girders and the abutment walls are 4 inches or 
greater for each bridge.  This gap prevents the use of the passive earth pressure behind 
the abutment wall from mobilizing in a seismic event, which would provide longitudinal 
                                                 
2 Pier and bent have the same meaning in this document and are used interchangeably throughout.  
78 
 
resistance.  If integral abutments are used, the passive pressure could be relied on to resist 
longitudinal displacements.   
 
Figure 4.1. Map of Alabama Counties with bridge locations (modified after Yellow Maps 
2010) 
 
79 
 
4.1 Time-History Events 
 Ten time-history events were used in the analysis and can be found in Appendix 
A.  These original time-history events are records of free-field ground acceleration versus 
time of an actual earthquake event.  The original time-history events were modified using 
scale factors to represent an earthquake that would be typical in Alabama.  There were 
two different scale factors used for each time-history, North and North Maximum 
Considered Earthquake (NMCE).  For further detail regarding the modification factors 
and development of the time history events used, see Panzer (2013).  Each one was 
applied longitudinally and transversely separately for each bridge case.  Figure 4.2 shows 
the scaled Coalinga North time-history event used in dynamic analysis.  See Appendix A 
for all of the scaled time-history events.  All time-history events included 20-30 seconds 
of time when acceleration is equal to zero after the strong shaking.  This is to show the 
bridge response after the event.  Table 4.1 shows the time steps used for every time-
history for each model.  The Lee County time step had to be increased due to the file size 
limitations for the output files.  
Table 4.1 ? Time steps used for each time-history for each model 
 
80 
 
 
Figure 4.2. Scaled Coalinga North earthquake time-history event 
4.2 Dynamic Analysis Options Used within FB-MultiPier 
4.2.1 Dynamic Analysis Method Used 
 Time-history analysis was used to evaluate the dynamic structural response of the 
bridge piers modeled.  There are three time stepping options available: average 
acceleration (Newmark), linear acceleration (Newmark), and Wilson-?.  The average 
acceleration option was used because it is typically more stable from a computational 
standpoint, and is one of the most effective and popular implicit techniques used for 
structural dynamic problems (Hughes and Belytschko 1983).   
4.2.2 Damping Analysis 
 For each model, Eigenvector analysis was conducted using FB-MultiPier?s modal 
analysis option to determine the natural period and the circular frequency of the pier.  
81 
 
Then, a classic sine wave time-history curve was developed for each model and run using 
the Rayleigh damping factor values for the pier previously shown in Table 2.17.  Mass 
and stiffness damping factors for the piles and soil were ignored in this analysis for 
simplicity (and consistency) and due to lack of information regarding cyclic response of 
the soil for each case history.  This approach was accepted as reasonable because it is 
conservative to ignore the damping effects of the soil and piles.  However, it was noticed 
that if zero is entered into any one of the six input boxes of the mass and stiffness 
damping factors, Rayleigh damping would not be considered at all within the program 
analysis.  Therefore, a low mass and stiffness factor of 0.000001 was applied to both the 
piles and soil. 
 The displacement at the top of the pier versus time was plotted and the damping 
was calculated using the peak displacements that occurred once the amplitude of the sine 
wave time-history curve was zero.  The sine wave curves were plotted so that the bridge 
would go through three cycles (time [in seconds] of three times the structural period) of 
the sine wave, then a circular frequency of zero was introduced for roughly 10 seconds.  
The equations used to develop the sine wave time-history curve and damping factors are 
shown as equations 4.1 and 4.2.   
           (4.1) 
?          
   
? (4.2) 
 
  
82 
 
where: 
     = calculated acceleration used in the time-history function 
  = circular frequency 
  = time in seconds 
? = calculated damping ratio 
  = number of peak after the first initial peak when acceleration is equal to 
zero 
   = displacement recorded at the first initial peak when acceleration is equal 
to zero 
     = displacement recorded at the jth peak when acceleration is equal to zero 
 
 The calculated damping ratios for four of the six bridge piers were all within 1-
4%; therefore, for simplicity, the initial damping factors were used for the dynamic 
analysis.  The Marshall county bridge was not included because the damping ratios were 
extremely high.  This is believed to be because of the large strut that is used to connect 
the columns of the bent.  Figure 4.3 and 4.4 show Chambers County 100% scour sine 
wave and displacement versus time at the top of the pier respectively in the longitudinal 
direction.  Figure 4.5 and 4.6 show the Marshall County sine wave and displacement 
versus time at the top of the pier respectively in the longitudinal direction to show 
contrast between the two.  Refer to Appendix B for the results of each bridge for damping 
analysis.  Table 4.2 shows the average calculated damping factors for both the 
longitudinal and transverse directions respectively for each bridge.   
83 
 
 
Figure 4.3. Chambers County 100% scour longitudinal sine wave time-history 
 Figure 4.4. Chambers County 100% scour longitudinal displacement versus time at the 
top of the pier 
 
84 
 
 Figure 4.5. Marshall County longitudinal sine wave time-history 
 Figure 4.6. Marshall County longitudinal displacement versus time at the top of the pier 
 
85 
 
Table 4.2 ? Frequency, structural period, and calculated average damping ratios for each 
bridge  
Bridge 
Longitudinal Transverse 
Frequency 
(rad/sec) 
Period 
(sec) 
Percent 
Damping 
Frequency 
(rad/sec) 
Period 
(sec) 
Percent 
Damping 
Chambers 25% 6.454 0.974 0.25% 11.455 0.549 0.2% 
Chambers 100% 5.935 1.059 3.96% 10.724 0.586 3.18% 
Etowah 4.307 1.459 2.14% 7.551 0.832 1.70% 
Franklin 7.566 0.83 2.1% 12.725 0.494 1.2% 
Lee 5.492 1.144 1.92% 8.958 0.701 2.82% 
Marshall 2.483 2.531 N/A 0.707 0.889 N/A 
 
4.3 Dead Load and Discrete Mass 
 Dead loads and discrete masses were applied to each direct analysis model.  This 
was done to account for the weight of the bridge deck and girders.  Factored live load was 
not taken into account for this analysis.  Dead loads were calculated based on typical 
cross sections given and the standard unit weight of normalweight, reinforced concrete 
(150 pcf).  The discrete masses were calculated using the dead weight divided by the 
acceleration of gravity (386.2 in/sec2).  The dead load was applied in the z (vertical) 
direction and the discrete masses were applied in the x and y (horizontal) direction 
because vertical acceleration was not used for the case studies.  The dead weight was 
applied to each bearing pad location, whereas the discrete masses were applied in 
between the bearing pad locations.  The bearing pad locations were taken from the center 
line of each girder in the typical cross section provided in the subsequent sections for 
each case study.  Therefore, the dead load used to calculate each discrete mass was the 
combination of the loads on each bearing pad.  The reason for applying dead loads at 
each bearing pad is because in some cases, the spans supported by the bent were different 
86 
 
lengths and therefore the dead load applied to the pads would be different on each side of 
the bent.  Table 4.3 presents the dead loads and discrete masses used for each case study.   
Table 4.3 ? Dead loads and discrete masses used for each case study 
Bearing Pad 
Location  
Left Bearing 
Pad (kips) 
Discrete Mass 
(kip-sec2/in) 
Right Bearing 
Pad (kips) 
Chambers County 
Exterior 65 0.34 65 
Interior (for all) 60 0.31 60 
Exterior 65 0.34 65 
Etowah County 
Exterior 130 0.67 116 
Interior (for all) 105 0.54 82 
Exterior 130 0.67 116 
Franklin County 
Exterior 125 0.65 125 
Interior (for all) 100 0.52 100 
Exterior 125 0.65 125 
Lee County 
Exterior 120 0.62 120 
Interior (for all) 100 0.52 100 
Exterior 120 0.62 120 
Marshall County 
Exterior 120 0.62 120 
Interior (for all) 110 0.57 110 
Exterior 120 0.62 120 
 
4.4 Chambers County 
4.4.1 Background Information 
 The Chambers County Bridge is a bridge replacement project over Oseligee 
Creek.  The total bridge span is 240 ft and rests on two abutments and two central piers.  
It is not skewed and has a total roadway width of 32 ft and 9 in.  See Figure 4.7 and 4.8 
for the plan and elevation views and the bridge deck cross section.  The foundations used 
for both the abutments and piers are drilled shafts.  Because the abutments were not 
modeled, they are not discussed.  Bent 3 was modeled in FB-MultiPier.  Bent 2 and 3 are 
built the same but with slightly different tip elevations.  Both have similar soil conditions.  
87 
 
Bent 3 consists of a pier cap and two shafts.  The shafts are 3.5 ft in diameter with twelve 
No. 11 longitudinal reinforcing bars.  Figure 4.9, 4.10, and 4.11 show Bent 3 elevation 
view, the shaft cross-section, and the pier cap cross section respectively. 
88 
 
 
Figure 4.7. Chambers County bridge plan and elevation view (ALDOT 2008) 
89 
 
 
Figure 4.8. Chambers County typical bridge deck cross section (ALDOT 2008) 
90 
 
 
 
Figure 4.9. Chambers County Bent 3 elevation and end view (ALDOT 2008) 
91 
 
 
Figure 4.10. Chambers County cross section of drilled shaft (ALDOT 2008) 
 
 
Figure 4.11. Chambers County Bent 3 pier cap cross section (ALDOT 2008) 
92 
 
4.4.2 Soil Modeling 
 A formal site investigation, using the standard penetration test (SPT) and rock 
coring, was conducted by the Bureau of Materials and Tests within ALDOT.  According 
to the geotechnical report, the site is located in the Southern Piedmont Upland district and 
underlain by Ropes Creek Amphibolite and the Agricola Schist of Precambrian to 
Paleozoic age (ALDOT 2008).  The ground water table (GWT) elevation at Bent 3 was 
found to be that of the water elevation of Osiligee Creek at 72 ft (ALDOT 2008).  There 
is roughly 16 feet of top soil that was assumed to scour to bedrock at an elevation of 63 
ft.  Static analysis of the lateral capacity of the drilled shafts was done using LPile and the 
input parameters were included in the geotechnical report.  The same input parameters 
were used in FB-MultiPier.  However, some parameters that were needed for FB-
MultiPier were not provided and had to be determined based on the boring logs.  Figure 
4.12 shows the idealized soil profile that was developed and used in FB-MultiPier.  For 
the 25% scour case, the top 25% of the soil (above the bedrock) was simply removed 
from the existing conditions.  The insitu soils were determined to be a site class E.  
However, if 100% scour is assumed, the site class would be C.  Refer to Appendix C for 
the original boring logs and other relative information.   
93 
 
 
Figure 4.12. Chambers County idealized soil profile for Bent 3 
4.5 Etowah County 
4.5.1 Background Information 
 The Etowah County Bridge is a bridge replacement on I-59 south bound lanes 
over US-11 and Norfolk Southern Railroad.  The total bridge span is 265 feet and rests on 
two abutments and one central pier (bent 2).  It is skewed approximately 30? and has a 
total roadway width of 46 feet and 9 in.  See Figure 4.13 and 4.14 for the plan and 
elevation views and the bridge deck cross section.  The foundations used for both the 
abutments and piers are 12x53 H-piles.  Because the abutments were not modeled, they 
are not discussed.  Bent 2 was modeled in FB-MultiPier and consists of a pier cap and 
three columns that are each supported by pile footings.    Figures 4.15, 4.16, and 4.17 
show the Bent 2 elevation view, end view, and pier cap cross section.  Figure 4.18 and 
4.19 show the column cross section and pile footing layout respectively.  
94 
 
 
Figure 4.13. Etowah County bridge plan and elevation view (ALDOT 2011) 
 
95 
 
 
Figure 4.14. Etowah County typical bridge deck cross section (ALDOT 2011) 
96 
 
 
Figure 4.15. Etowah County Bent 2 elevation view (ALDOT 2011)
97 
 
 
Figure 4.16. Etowah County Bent 2 end view (ALDOT 2011) 
98 
 
 
Figure 4.17. Etowah County Bent 2 pier cap cross section (ALDOT 2011) 
 
Figure 4.18. Etowah County Bent 2 column cross section (ALDOT 2011) 
99 
 
 
Figure 4.19. Etowah County Bent 2 typical pile footing layout (ALDOT 2011) 
4.5.2 Soil Modeling 
 A formal site investigation, using the SPT and rock coring, was conducted by 
Terracon (formerly Gallet and Associates).  According to the geotechnical report, the site 
is at or very near the contact between Bangor Limestone and Monteagle Limestone 
deposits.  Bangor Limestone consists of medium-gray bioclastic and oolitic limestone 
containing interbeds of dusky red and olive green mudstone (Gallet 2008).  The 
Monteagle Limestone deposit consists of light-gray oolitic limestone containing 
100 
 
interbedded argillaceous, bioclastic, or dolomitic limestone, dolomite, and medium gray 
shale (Gallet 2008). 
 The GWT elevation at Bent 2 was recorded as 620 feet during the initial site 
investigation (Gallet 2008).  The boring logs taken near bent 2 indicated that insitu soils 
consist of approximately 50 feet of soft clay from the ground surface.  A void was then 
encountered for roughly 15 feet until limestone bedrock was reached at an approximate 
depth of 65 feet (578.5 feet elevation).  All input parameters needed for FB-MultiPier 
were determined based on the boring logs and rock core testing.  The mobilized end 
bearing resistance (referred to as axial bearing failure in FB-MultiPier) was determined 
using FB-Deep.  All relative information regarding input parameters for Etowah County 
used in FB-Deep are in Appendix C.  Figure 4.20 shows the idealized soil profile that was 
developed and used in FB-MultiPier.  The insitu soils were determined to be a site class 
E.  Refer to Appendix D for the original boring logs as well.   
 Default p-y multipliers were used for lateral analysis in Etowah models.  A pile 
group efficiency of 1.0 was used for the axial analysis based on recommendations made 
by Hannigan et al. (2006).  The pile cap, in this case, was buried several feet below the 
ground surface. 
101 
 
 Figure 4.20. Etowah County idealized soil profile 
4.6 Franklin County 
4.6.1 Background Information 
 The Franklin County Bridge is a bridge over Little Bear Creek on the east bound 
lane of S.R 24 (Corridor V).  The total bridge span is 300 ft and rests on two abutments 
and two central piers.  It is not skewed and has a total roadway width of 42 ft and 9 in.  
See Figure 4.21 and 4.22 for the plan and elevation views and the bridge deck cross 
section.  The foundations used for both the abutments and piers are drilled shafts.  
Because the abutments were not modeled, they are not discussed.  Bent 3 was modeled in 
FB-MultiPier.  Bent 2 and 3 are built the same but with slightly different tip elevations 
102 
 
and soil conditions.  Bent 3 consists of a pier cap and two shafts.  The shafts are 4.5 ft in 
diameter with twelve No. 11 longitudinal reinforcing bars above the ground surface, and 
5 ft in diameter with the same reinforcement alignment below the ground surface.  Figure 
4.23 and 4.24 shows the Bent 3 elevation view and pier cap cross section.  The pier cap 
was modeled as flat on top due to program capabilities.  Figure 4.25 and 4.26 show the 
shaft cross section. 
103 
 
 
Figure 4.21. Franklin County bridge plan and elevation views (ALDOT 2005) 
104 
 
 
Figure 4.22. Franklin County typical bridge deck cross section (ALDOT 2005) 
105 
 
 
Figure 4.23. Franklin County Bent 3 elevation and end view (ALDOT 2005)
106 
 
 
Figure 4.24. Franklin County pier cap cross section (ALDOT 2005) 
 
Figure 4.25. Franklin County above ground column cross section (ALDOT 2005) 
107 
 
 
Figure 4.26. Franklin County below ground drilled shaft cross section (ALDOT 2005) 
4.6.2 Soil Modeling 
 A formal site investigation, using the SPT and rock coring, was conducted by the 
Bureau of Materials and Tests within ALDOT.  According to the geotechnical report, the 
site is located in the Moulton Valley district of the Highland Rim physiographic section 
and underlain by Bangor Limestone of Mississippian age (ALDOT 2005).  The GWT 
elevation at Bent 3 was recorded as 528 ft at a 24 hour reading after the initial site 
investigation (ALDOT 2005).  There is roughly 3 ft of top soil that was assumed to scour 
to bedrock at an elevation of 525.6 ft.  Static analysis of the lateral capacity of the drilled 
shafts was done using LPile and the input parameters were included in the geotechnical 
report.  The same input parameters were used in FB-MultiPier.  However, some 
parameters that were needed for FB-MultiPier were not provided and had to be 
determined based on the boring logs.  Figure 4.27 shows the idealized soil profile that 
was developed and used in FB-MultiPier.  The soft clay layer was not included in the 
analysis, but shown here for reference.  Due to the bedrock being very close to the 
108 
 
surface, the soil is a site class C.  Refer to Appendix E for the original boring logs and 
input parameters.   
 
Figure 4.27. Franklin County idealized soil profile 
4.7 Lee County 
4.7.1 Background Information 
 The Lee County Bridge is a bridge replacement for Bent Creek Road over I-85.  
The total bridge span is 270 feet and rests on two abutments and one central pier (bent 2).  
It is not skewed and has a total roadway width of 80 feet and 9 in.  See Figure 4.28 and 
4.29 for the plan and elevation views and Figure 4.30 for the bridge deck cross section.  
The foundations used for both the abutments and piers are 12x53 H-piles.  Because the 
abutments were not modeled, they are not discussed.  Bent 2 was modeled in FB-
MultiPier and consists of a pier cap and three columns that are each supported by pile 
footings.  The bridge was built in two stages to avoid closing the existing road.  The 
bridge was modeled in FB-MultiPier as one bent, however, due to program limitations.  
Figure 4.30 and 4.31 show the Bent 2 stage one and two elevation view.  Figure 4.32 
shows the bent 2 stage one and two end view, and Figure 4.33 and 4.34 show the column 
and pier cap cross sections and the pile footing layout respectively.  
109 
 
 Figure 4.28. Lee County bridge plan view (ALDOT 2006) 
110 
 
 Figure 4.29. Lee County bridge elevation view (ALDOT 2006) 
 
 
 
 
 
 
 
111 
 
 
Figure 4.30. Lee County typical bridge deck cross section (ALDOT 2006) 
 
112 
 
 
Figure 4.31. Lee County Bent 2 stage one elevation view (ALDOT 2006)
113 
 
 
Figure 4.32. Lee County Bent 2 stage two elevation view (ALDOT 2006)
114 
 
 
Figure 4.33. Lee County Bent 2 stage one and two end view (ALDOT 2006)
115 
 
 
(a) (b) 
 
Figure 4.34. Lee County Bent 2 (a) pier cap and (b) column cross section (ALDOT 2006)
116 
 
 Figure 4.35. Lee County Bent 2 pile footing layout (ALDOT 2006) 
4.7.2 Soil Modeling 
 A formal site investigation, using the SPT and rock coring, was conducted by the 
Bureau of Materials and Tests within ALDOT.  According to the geotechnical report, the 
site is in the Southern Piedmont Upland district of the Piedmont Upland physigraphic 
section.  The project is located in the Towaliga fault zone and is underlain by 
blastomylonite which is schist and gneiss that has been pulverized by the lateral 
movement of the fault (ALDOT 2006). 
117 
 
 The GWT elevation at Bent 2 at 24 hours after drilling was estimated to be 655 
feet elevation during the initial site investigation (ALDOT 2006).  The boring logs taken 
near bent 2 indicated that insitu soils consist of approximately 30 feet of stiff sandy silt 
from the ground surface underlain by hard weathered gneiss.  All input parameters 
needed for FB-MultiPier were determined based on the boring logs and rock core testing.  
The axial bearing failure (or mobilized end bearing) was determined using FB-Deep.  All 
relative information regarding input parameters for Lee County used in FB-Deep are in 
Appendix F.  Figure 4.36 shows the idealized soil profile that was developed and used in 
FB-MultiPier.  The insitu soils were determined to be a site class D.  Refer to Appendix F 
for the original boring logs.   
 Default p-y multipliers were used for lateral analysis in the Lee County models.  
It was determined that these were adequate for use.  A pile group efficiency of 1 was used 
for the axial analysis.  For driven piles, axial group efficiency can be greater than 1 in 
some cases, due to densification of the surrounding soil during pile driving. 
 Figure 4.36. Lee County idealized soil profile 
 
118 
 
4.8 Marshall County 
4.8.1 Background Information 
 The Marshall County Bridge provided by ALDOT is a bridge over Scarham 
Creek on State Route 75 (south bound lane).  The total bridge span is 520 ft and rests on 
two abutments and three central piers.  It is not skewed and has a total roadway width of 
40 ft.  See Figure 4.37 and 4.38 for the plan and elevation views and the bridge deck 
cross section.  The foundations used for both the abutments and piers are drilled shafts.  
Because the abutments were not modeled, they are not discussed.  The foundations for 
Bents 2, 3, and 4 were modeled in FB-MultiPier to develop static stiffness response 
curves for the SAP model.  All of the bents were modeled using the same soil profile, 
which was the lower bound.  Bent 2 and 4 have the same section properties; therefore, 
one model was developed to represent both bents.  Bent 3 has a larger shaft diameter than 
that of Bents 2 and 3 was the bent modeled for direct analysis. 
 The shafts for Bent 2 and 4 are 5 ft in diameter with 24 No. 11 longitudinal 
reinforcing bars above the ground surface, and 5.5 ft in diameter with the same 
reinforcement alignment below the ground surface.  Figure 4.39 shows the Bent 2 shaft 
elevations only and Figure 4.40 shows the shaft cross sections.  The shafts for Bent 3 are 
6 ft in diameter with 32 No. 11 longitudinal reinforcing bars above the ground surface, 
and 6.5 ft in diameter with the same reinforcement alignment below the ground surface.  
Figures 4.41, 4.42, and 4.43 show the Bent 3 elevation view, pier cap cross section, and 
strut cross section.  Figure 4.44 shows the shaft cross sections. 
 
119 
 
 
Figure 4.37. Marshall County bridge plan and elevation view (ALDOT 2003) 
120 
 
 
Figure 4.38. Marshall County typical bridge deck cross section (ALDOT 2003) 
121 
 
 
Figure 4.39. Marshall County Bent 2 shaft elevations (ALDOT 2003) 
 
(a) (b) 
 
Figure 4.40. Marshall County Bent 2 (a) above ground and (b) below ground column and shaft cross section (ALDOT 2003) 
122 
 
 
Figure 4.41. Marshall County Bent 3 elevation and end view (ALDOT 2003)
123 
 
 
Figure 4.42. Marshall County Bent 3 pier cap cross section (ALDOT 2003) 
124 
 
 
Figure 4.43. Marshall County Bent 3 strut cross section (ALDOT 2003)
125 
 
 (a) (b) 
 
Figure 4.44. Marshall County Bent 3 (a) above ground and (b) below ground column and shaft cross section (ALDOT 2003)
126 
 
4.8.2 Soil Modeling 
 A formal site investigation, using the SPT and rock coring, was conducted by the 
Bureau of Materials and Tests within ALDOT.  According to the geotechnical report, the 
site is located in the Sand Mountain district of the Cumberland Plateau physiographic 
section and underlain by Pottsville Formation of Pennsylvanian age (ALDOT 2003).  The 
Pottsville Formation consists of over 400 feet of brown gray thin- to thick-bedded 
sandstone, gray shale, siltstone, conglomerate, and coal beds (ALDOT 2003).  The GWT 
elevation at Bent 3 was recorded as 860 feet at a 24 hour reading after the initial site 
investigation (ALDOT 2003).  There was not a GWT elevation recorded for Bents 2 and 
4.  There is roughly 3-4 ft of top soil that was assumed to scour to bedrock at all of the 
bents.  The elevations for Bent 2 and 4 can be seen on Figure 4.38.  However, it should 
be noted that only the shaft length and free length is critical for Bents 2 and 4.  Uniaxial 
compression testing was done at different stations and depths.  The lowest value was used 
as a representative unconfined compressive strength.  All other input parameters needed 
for FB-MultiPier were determined based on the boring logs.  Figure 4.45 shows the 
idealized soil profile that was developed and used in FB-MultiPier (elevations shown are 
for Bent 3).  The same soil parameters were used for all the bents.  The soft clay layer 
was not included in the analysis, but shown here for reference.  Due to the bedrock being 
very close to the surface, the soil is a site class C.  Refer to Appendix G for the original 
boring logs and input parameters.  Note that the multiple elevations in Figure 4.45 refer 
to the elevations of the soil profile at each drilled shaft for Bent 3.  Refer to Figure 4.41 
for elevation difference at each shaft. 
127 
 
 
Figure 4.45. Marshall County idealized soil profile 
 
  
128 
 
Chapter 5 
SUBSTRUCTURE ANALYSIS RESULTS AND DISCUSSION 
 Static foundation response curves for each bridge were developed to represent the 
foundations for the SAP2000 models (Panzer 2013).  Each foundation was represented 
with a family of six non-linear curves.  The curves were developed using FB-MultiPier.  
The six curves include the response curves for the forces in the FX, FY, and FZ directions, 
as well as the moments in the MX, MY, and MZ directions (see Figure 5.1).  Referring to 
Chapter 2, section 2.5, the points of emphasis covered in substructure analysis are 3 and 4 
which include evaluating the lateral and vertical stiffness of the shafts or pile groups, 
excluding uplift and abutment response. 
 Figure 5.1. Force and moment directions 
 
129 
 
 One representative set of curves was developed for each bridge case except for 
the Marshall County Bridge.  Bents 2 and 4 of this bridge had smaller drilled shaft sizes; 
therefore, a separate response curve family for both bents was developed to adequately 
represent the foundations.  The abutments were modeled as fixed in the FZ direction for 
the SAP2000 models.  Refer to Panzer (2013) for further detail regarding abutment 
foundation modeling. 
 The loading of each foundation was applied at the center-most point.  For the Lee 
and Etowah County Bridges (H-Pile foundations), the center of the pile cap was the point 
of loading.  The point of loading for the drilled shaft bridge foundations was always in 
the center of the shaft, but the elevation differed.  The Chambers County Bridge bent 
does not change in diameter; therefore, the loads were applied to the shaft at the rock line.  
The 100% scour case was the only model used for SAP2000 analysis, and is the only one 
presented here.  The Franklin and Marshall County Bridges had an increased diameter of 
6 inches at the elevation of the soil.  The point of loading was applied at the elevation 
where the increase in shaft size occurs.  The case with dead load applied was also 
evaluated for comparison to the recommendation given by Lam and Martin (1986).  Dead 
load was not included to develop the response curve, FZ, however.  Figures 5.2, 5.3, 5.5, 
5.6, and 5.8 present the static foundation response curves developed for each case history.  
Also, pile group layouts are shown for the Etowah and Lee County models (see figure 5.4 
and 5.7).   
  
130 
 
5.1 Chambers County 100% Scour 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 
(e) 
 
(f) 
Figure 5.2. Chambers County foundation response curves for (a) FX, (b) FY, (c) FZ, (d) 
MX, (e) MY, and (f) MZ 
 
 
 
131 
 
5.2 Etowah County 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 
(e) 
 
(f) 
 
Figure 5.3. Etowah County foundation response curves for (a) FX, (b) FY, (c) FZ, (d) MX, 
(e) MY, and (f) MZ 
 
 
132 
 
 
Figure 5.4. Etowah County pile group layout and direction 
 
  
133 
 
5.3 Franklin County 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 
(e) 
 
(f) 
 
Figure 5.5. Franklin County foundation response curves for (a) FX, (b) FY, (c) FZ, (d) MX, 
(e) MY, and (f) MZ 
 
 
134 
 
5.4 Lee County 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 
(e) 
 
(f) 
 
Figure 5.6. Lee County foundation response curves for (a) FX, (b) FY, (c) FZ, (d) MX, (e) 
MY, and (f) MZ 
 
 
135 
 
 
Figure 5.7. Lee County pile group layout and direction 
 
  
136 
 
5.5 Marshall County 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 
(e) 
 
(f) 
 
Figure 5.8. Marshall County Bents 2 and 4 foundation response curves for (a) FX, (b) FY, 
(c) FZ, (d) MX, (e) MY, and (f) MZ 
 
137 
 
 
(a) 
 
(b) 
 (c)  (d) 
 
(e) 
 
(f) 
 
Figure 5.9. Marshall County Bent 3 foundation response curves for (a) FX, (b) FY, (c) FZ, 
(d) MX, (e) MY, and (f) MZ 
 
 
 
138 
 
5.6 Discussion 
 As mentioned in chapter 2, the most common way to develop the spring stiffness 
is without taking into account the dead load.  Generally, the dead load increased the 
stiffness or made no difference at all, making the recommendation by Lam and Martin 
(1986) conservative.  However, the rotational stiffness about the X-axis decreased in the 
Etowah County model when the dead load was applied.  It is difficult to discern exactly 
why this occurred.  However, one possibility is that the added weight caused the battered 
piles to be more susceptible to bending.  This is because the axial load distributed to the 
piles increased.  For this research, the response curves with dead load applied were 
applied to the SAP2000 models (Panzer 2013) to more accurately represent foundation 
behavior. 
 
 
  
139 
 
Chapter 6 
DIRECT ANALYSIS RESULTS AND DISCUSSION
 The results from the direct analysis of the five bridge case studies are presented. 
For each bridge, the earthquake time-history used and the displacement at the top of the 
pier and the head of the shaft or pile footing was recorded.  The largest shear force, 
bending moment, and D/C ratio distribution for a shaft or pile is also presented for one 
time step.  This time step is indicated by a black vertical line on the time-history plots.  
Note that the D/C ratio is based on the axial-force D/C (which is a function of bending 
moment).  For the failed models, the time step in which these distributions are taken at 
are not necessarily the last time step before the program terminated.  Typically, the last 
time step before failure is numerically flawed and inconclusive; therefore, the time-step 
with the next largest shear force and bending moment are shown.  This is to give an 
indication of where the shear forces and bending moments are developing relative to the 
ground surface or rock line.   
 There were 17 scaled time-history events used for each bridge case in each 
direction (longitudinal and transverse): Coalinga North, Imperial Valley NMCE and 
North, Kobe NMCE and North, Kocaeli NMCE and North, Kocaeli2 NMCE and North, 
Landers NMCE and North, LSM North, NPS North, San Fernando NMCE and North, 
and San Fernando2 NMCE and North.  All results are presented in Appendix H.  The 
following presents a discussion of each case history and its overall performance, as well 
as a selection of detailed results and tabular summary for each case history.  The case 
140 
 
histories provided did not have liquefaction potential; therefore, a liquefaction case was 
not explicitly done.  However, parallels from the Etowah County case history can be 
drawn due to the weak insitu soil that the foundations are embedded.   
 The results overview table indicates how the structure performed based on 
whether the program converged or not.  If the model did not converge, the performance 
was described as ?failed,? and a probable cause of failure (structural, soil, or numerical 
instability) was provided (refer back to section 2.4.1).  The time of occurrence that the 
maximum forces were generated is provided for each model, as well as the location of the 
maximum values along the shaft, pile, or column to compare to the elevation of the 
ground surface or pier cap.   
6.1 Chambers County 25% Scour Discussion 
 The Chambers County 25% scour Bridge performed poorly, overall.  Most of the 
failed models were suspected to have failed because of either structural failure or soil 
failure.  Soil failure is likely due to large displacements that the soil spring undergoes.  
These displacements can become so large that the soil can no longer resist the lateral 
forces and the out-of-balance forces become extremely large.  Referring back to the soil 
profile for Chambers County (Figure 4.12), the soil layers over rock are relatively weak, 
which suggests that large displacements at the ground surface are not unlikely to occur.  
Also, there is an interface of soft and hard soils (as discussed in section 3.1).  The 
maximum bending moments appeared to develop above the rock line, but below the 
ground surface line.  This is important because typically, bridges are detailed to develop a 
plastic hinge at the ground surface and at the pier cap/column connection because that is 
inherently the most likely place it will occur.  This is to allow enough ductility so the 
141 
 
structure does not collapse (see section 2.1).  If damage occurs at those hinge zones, it 
also allows the damage to be identified and repaired without excavating to the damaged 
areas.  The models that were loaded in the transverse direction generally showed that the 
largest moment and D/C ratio were at the top of the bent where the column connects to 
the pier cap.  This is a desired plastic hinge zone location.  However, large moments and 
D/C ratios were still developing well below the ground surface, which could possibly 
develop into plastic hinge zones as well.   
 It is difficult to discern whether scour, the soft/hard soil interface, or a 
combination of the two had the most impact of the bridge bent performance.  
Liquefaction was not taken into account for this model.  However, there are two 
cohesionless layers that could have the potential to liquefy; however, the scouring effect 
is a similar loss in soil resitance and is compared for the Chambers County 100% scour 
case, which is in section 6.2.  Tables 6.1 and 6.2 show an overview of the results; this 
includes the location of the maximum shear force, bending moment and D/C ratio along 
the drilled shaft.  The highlighted rows correspond to the selected results shown in 
Figures 6.1 ? 6.4.  The ground surface indicates the ground surface after 25% scour.  
Note that the rock line is approximately at an elevation of 63 feet.  The kink that typically 
occurs around elevation 63 seen in the shear force, bending moment, and D/C 
distributions indicates this drastic change in soil resistance.   
  
142 
 
6.1.1 Longitudinal Results 
 (a)  (b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure 6.1. Chambers County 25% scour longitudinal Kocaeli2 NMCE (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio 
 
143 
 
 
(a) 
 
(b) 
 (c)  (d) 
 
(e) 
 
(f) 
 
Figure 6.2. Chambers County 25% scour longitudinal San Fernando2 NMCE (a) time-
history event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, 
(e) ground surface displacement, and (f) demand capacity ratio 
 
 
144 
 
Table 6.1 ? Results overview for Chambers 25% scour longitudinal models (highlighted ones are shown in Figures 6.1 and 6.2) 
 
 
 
145 
 
6.1.2 Transverse Results 
 (a)  (b) 
 
(c) 
 (d) 
 (e)  (f) 
 
Figure 6.3. Chambers County 25% scour transverse Kocaeli2 NMCE (a) time-
history event, (b) shear distribution, (c) top of pier displacement, (d) moment 
distribution, (e) ground surface displacement, and (f) demand capacity ratio 
 
 
146 
 
 
(a) 
 
(b) 
 (c)  (d) 
 
(e) 
 
(f) 
 
Figure 6.4. Chambers County 25% scour transverse San Fernando2 NMCE (a) 
time-history event, (b) shear distribution, (c) top of pier displacement, (d) moment 
distribution, (e) ground surface displacement, and (f) demand capacity ratio 
 
147 
 
Table 6.2 ? Results overview for Chambers 25% scour transverse models (highlighted ones are shown in Figures 6.3 and 6.4) 
 
 
 
148 
 
6.2 Chambers County 100% Scour Discussion 
 The Chambers 100% scour model performed well, overall.  The three models that 
failed all used NMCE scaled time-history events, which are of larger magnitude and, 
typically, more harmful than the North scaled time-histories.  The North scaled events are 
more representative of what the state of Alabama would generally experience. 
 The 100% scour model performed much better than the 25% scour model (based 
on structural performance of the bent).  This shows the importance of checking both 
scenarios because it is difficult to determine which case could be worse.  Figures 6.5 and 
6.6 show the longitudinal Kocaeli2 results for the Chambers 25% and 100% scour cases, 
respectively.  These figures compare the location of the maximum shear forces and 
bending moments that are developing within the model.  It is clear that there is a 
possibility of plastic hinges developing beneath the ground surface in the 25% scour case; 
whereas, the plastic hinges would most likely develop at the rock line or slightly above 
for the 100% scour case.   
 Table 6.3 presents the results overview of all the longitudinal models, and figures 
6.7 and 6.8 show a selection of longitudinal detailed results.  The transverse models 
showed that the hinge zones would most likely develop at the column/pier cap interface 
or at the rock line.  This is important because it shows that the plastic hinge zones are 
developing at the desired locations.  See Table 6.4 for the results overview and figures 
6.9 and 6.10 for a selection of transverse detailed results.   
  
149 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure 6.5. Chambers County 25% scour longitudinal Kocaeli2 NMCE (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio 
 
 
 
 
 
150 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure 6.6. Chambers County 100% Scour Longitudinal Kocaeli2 NMCE (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio 
 
151 
 
6.2.1 Longitudinal Results 
 (a)  (b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure 6.7. Chambers County 100% scour longitudinal Imperial Valley North (a) time-
history event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, 
(e) ground surface displacement, and (f) demand capacity ratio 
 
152 
 
 
(a) 
 
(b) 
 (c)  (d) 
 
(e) 
 
(f) 
 
Figure 6.8. Chambers County 100% scour longitudinal Kocaeli NMCE (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio 
 
153 
 
Table 6.3 ? Results overview for Chambers 100% scour longitudinal models (highlighted ones are shown in Figures 6.5 and 6.6) 
 
 
154 
 
6.2.2 Transverse Results 
 (a)  
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure 6.9. Chambers County 100% scour transverse Coalinga North (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio 
 
 
155 
 
 
(a)  (b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure 6.10. Chambers County 100% scour transverse Landers NMCE (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio 
 
156 
 
Table 6.4 ? Results overview for Chambers 100% Scour transverse models (highlighted ones are shown in Figures 6.7 and 6.8) 
 
 
157 
 
6.3 Etowah County Discussion 
 The Etowah County bridge models performed poorly.  Moreover, the piles were 
the main cause of failure.  See Table 6.7 and 6.8 for an overview of the longitudinal and 
transverse results, respectively.  The models suggested that the piles were failing in 
bending.  This is thought to be a buckling problem due to several factors.  The length of 
the piles was approximately 60 feet (including embedment into the pile cap) and the 
width of the pile is only 12.045 inches.  Referring back to Figure 4.20 in Chapter 4, the 
soil profile of Etowah County, it is apparent that the insitu soils are relatively weak (shear 
strength is 700 psf or less in lower layers).  There is also a void layer that is almost 15 
feet in depth, which does not provide any lateral resistance. 
 To determine if the problem is, in fact, most likely buckling, equation 3.1, 
presented in Chapter 3, was used to check Bhattacharya?s (2003) recommendation that a 
Pdes/Pcr ratio of greater than 0.5 indicated that buckling may be an issue.  Table 6.5 shows 
the assumptions made to calculate the ratios. 
Table 6.5 ? Assumptions used in buckling analysis for Etowah County 
Leff 100 ft 
E  29000 ksi 
I  393 in4 
Section Area of H-pile 15.5 in2 
Pcr 78 kips 
rmin  5.04 in 
Pcolumn 680 kips/column 
No. of piles/column 7  
FS(assumed) 2  
Pdes/pile 194 kips 
 
 Leff was determined based on the assumption that the pile is pinned at the rock 
line and fixed at the pile cap.  Therefore, the depth of the soft soil region, which was 
158 
 
estimated as roughly 50 feet, was multiplied by a factor of 2 to estimate the effective 
length.  The largest moment of inertia was used because the bending was about the axis it 
was calculated.  This also was a conservative assumption.  The load per column was 
based on the dead loads from the bridge deck.  The load of the pier cap, column, and pile 
cap were not included as it only increased the Pdes/Pcr ratio.  A pile efficiency of one was 
assumed for each pile.  Table 6.6 summarizes the calculations made.   
Table 6.6 ? Etowah County Pdes/Pcr and Leff/rmin results 
Pdes/Pcr 2.49 
Leff/rmin 238 
 
 Based from these calculations, buckling is most likely the main cause for pile 
failure for the Etowah County bridge models.  It is also important to note that the 
transverse models were failing about the same axis as the longitudinal models.  This 
suggests that it was failing regardless of which direction the load function was applied.  
Figure 6.11 shows the pile number layout for the model.  Figures 6.12 ? 6.14 show the 
displacements at the top of the pier and pile cap, along with the shear force, bending 
moment and D/C ratio distributions for the length of the pile.  Note that these 
distributions are all below the ground surface.  Figure 6.15 shows the displacement at the 
top of the pier and pile cap, as well as the shear force, bending moment, and D/C ratio 
distribution along the length of the column.   
159 
 
 Figure 6.11. Etowah County FB-MultiPier pile number layout 
 
160 
 
6.3.1 Longitudinal Results 
 (a)  
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure 6.12. Etowah County longitudinal Coalinga North (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
161 
 
 
(a)  (b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure 6.13. Etowah County longitudinal NPS North (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
162 
 
Table 6.7 ? Results overview for Etowah County longitudinal models (highlighted ones are shown in Figures 6.9 and 6.10) 
 
 
163 
 
 
6.3.2 Transverse Results 
 (a)  (b) 
 
(c) 
 
(d) 
 
(e) 
 
(f) 
 
Figure 6.14. Etowah County transverse Kocaeli2 NMCE (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
164 
 
 
 (a)  (b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure 6.15. Etowah County transverse Landers North (column) (a) time-history event, 
(b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
165 
 
Table 6.8 ? Results overview for Etowah County transverse models (highlighted ones are shown in Figures 6.12 and 6.13) 
 
 
166 
 
6.4 Franklin County Discussion 
 The Franklin county bridge models performed fair, overall.  Most of the models 
that failed were NMCE earthquake events, which are the higher magnitude events.  See 
Table 6.9 and 6.10 for the longitudinal and transverse results, repsectively.  Figures 6.16 
? 6.19 present a selection of detailed results.  Only one model (San Fernando2 NMCE 
Longitudinal) showed a plastic hinge developing due to structural failure (see Figure 
6.17).  Note that the change in D/C ratio distribution at elevation 530 feet is due to the 
change in shaft size, which is consistent with what is to be expected (lower capacity for a 
smaller shaft size).  When the model does not show a plastic hinge zone developing in the 
last time step before it fails, it is difficult to discern whether the failure was structural, or 
numerical.  Soil failure is unlikely because the drilled shafts are embedded into bedrock.  
If the last time step shows large bending moments and shear forces, and D/C ratios are 
approaching one, then structural failure may be a likely cause that the model failed.  
Otherwise, it could be due to numerical instability within the model.  However, the 
bending moment and D/C ratio distributions for Franklin County show that if the 
structure does fail, it is likely the failure will occur in the desired plastic hinge zones and 
not in the foundations.  Liquefaction was not taken into account for this model because of 
the thin layer of soil over bedrock.  
 
  
167 
 
6.4.1 Longitudinal Results 
 (a)  (b) 
 (c)  
(d) 
 (e)  (f) 
 
Figure 6.16. Franklin County longitudinal LSM North (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
168 
 
 
(a) 
 
(b) 
 (c)  
(d) 
 (e)  (f) 
 
Figure 6.17. Franklin County longitudinal San Fernando2 NMCE (a) time-history event, 
(b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
169 
 
Table 6.9 ? Results overview for Franklin County longitudinal models (highlighted ones are shown in Figures 6.14 and 6.15) 
 
 
170 
 
6.4.2 Transverse Results 
 (a)  (b) 
 (c)  
(d) 
 (e)  (f) 
 
Figure 6.18. Franklin County transverse Landers North (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
 
171 
 
 
(a)  (b) 
 (c)  
(d) 
 (e)  (f) 
 
Figure 6.19. Franklin County transverse Landers NMCE (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
172 
 
Table 6.10 ? Results overview for Franklin County transverse models (highlighted ones are shown in Figures 6.16 and 6.17) 
 
 
173 
 
6.5 Lee County Discussion 
 The Lee county bridge models performed well.  None of the models failed in the 
longitudinal or transverse direction.  See Table 6.13 and 6.14 for an overview of the 
longitudinal and transverse results, respectively.  Like the Etowah County bridge, the Lee 
County bridge foundations are H-piles.  Referring to Figure 4.36 in chapter 4, the soil 
profile for Lee County was saturated cohesionless soil over bedrock.  Based on Figure 
2.5, the potential for liquefaction is low in this part of the state, and therefore, was not 
considered for this analysis.  The depth to rock was about half of that of Etowah County, 
and the soil had moderate strength.  For comparison, buckling analysis was done for the 
Lee County model as well.  Table 6.11 shows the assumptions made. 
Table 6.11 ? Assumptions used in buckling analysis for Lee County 
Leff 50 ft 
E  29000 ksi 
I  393 in4 
Section Area of H-pile 15.5 in2 
Pcr 312 kips 
rmin  5.04 in 
Pcolumn 725 kips/pile footing 
No. of piles/column 9  
FS(assumed) 2  
Pdes/pile 161 kips 
 
 The free length of the pile was estimated as 25 feet.  Leff was determined by 
multiplying the free length by 2.  This is because the pile is assumed to be pinned at the 
rock layer and fixed at the pile cap.  Instead of using just the bridge deck dead load, the 
column and pile footing load was also taken into account.  The section properties 
remained the same as Etowah.  Pile efficiency of 1 was assumed and the number of piles 
for each footing is nine.  Table 6.12 summarizes the calculations made. 
174 
 
Table 6.12 ? Lee County Pdes/Pcr and Leff/rmin results 
Pdes/Pcr 0.52 
Leff/rmin 119 
 
 Based from these calculations, buckling could be an issue for the Lee County 
model.  It is important to note that when evaluating the buckling stability of a pile 
embedded in cohesionless soils, it is assumed that the soil liquefied and lateral resistance 
is basically zero.  However, it should be noted that even in a liquefied state, soil still 
possesses residual strength (which is typically low) that can be relied on. However, it is 
more conservative to assume the lateral resistance is zero.  It should also be noted that for 
the Lee County models, the time steps were larger than the other models.  This was due 
to FB-MultiPier?s restriction of memory that could be used for analysis at the time these 
models were run.  The file sizes were simply too big for the program to access during 
analysis and the program would crash.  Therefore, the time steps were increased to 
decrease the size of the output files being created.  The increase in time steps is not 
thought to have a significant impact on the analysis, as the time steps were still relatively 
small (greatest one being 0.05 seconds).  Figures 6.20 ? 6.23 show the displacements at 
the top of the pier and pile cap, along with the shear force, bending moment and D/C 
ratio distributions for the length of the pile.  Note that these distributions are all below the 
ground surface.  See Table 6.15 and 6.16 for an overview of the longitudinal and 
transverse results, respectively.   
  
175 
 
6.5.1 Longitudinal Results 
 (a)  
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure 6.20. Lee County longitudinal San Fernando2 NMCE (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
176 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure 6.21. Lee County longitudinal San Fernando2 North (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
177 
 
Table 6.13 ? Results overview for Lee County longitudinal models (highlighted ones are shown in Figures 6.18 and 6.19) 
 
 
178 
 
6.5.2 Transverse Results 
 (a)  (b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure 6.22. Lee County transverse Imperial Valley NMCE (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
179 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure 6.23. Lee County transverse Imperial Valley North (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
180 
 
Table 6.14 ? Results overview for Lee County transverse models (highlighted ones are shown in Figures 6.20 and 6.21) 
 
 
181 
 
6.6 Marshall County Discussion 
 The Marshall County bridge model performed well, overall.  The longitudinal 
model seemed to have instability problems for some time-history events.  This is most 
likely due to the large displacements that were generated.  These displacements can cause 
secondary moments which can cause large out-of-balance forces to occur.  See Table 
6.15 and 6.16 for an overview of the longitudinal and transverse results, respectively.  
Figures 6.24 ? 6.28 show the displacements at the top of the pier and ground surface, 
along with the shear force, bending moment and D/C ratio distributions for the length of 
the shaft. 
 Referring to Figure 6.25, the displacement when the acceleration is zero is nearly 
zero as well.  However, the failed models showed that the bending moment and shear 
force were very high at the last time step, which then caused the model to fail.  The Kobe 
NMCE and the Kocaeli2 NMCE models are thought to have failed due to numerical 
instability because the displacements were nearly zero for the last 35 seconds.  The 
transverse models performed well.  The strut provided extra stiffness in the transverse 
direction.  For the longitudinal models, there is an indication that the strut?s mass created 
some inertial effects within the model.  The bending moment and D/C distributions show 
slight changes at the strut elevation, which indicates that the strut affected the response of 
the pier slightly in the longitudinal direction.  This can be seen on the shear force 
distribution figures (more drastically in the transverse direction).  The models also 
showed that the largest moment was developing at the rock line, which is a desired plastic 
hinge zone location.  It should also be noted that the bent is very tall. The free length of 
the columns is approximately 60 feet, which can lead to large displacements at the top of 
182 
 
the pier, especially in the longitudinal direction.  Liquefaction was not considered 
because the rock layer is very shallow on site and the thin soil layer is assumed to scour.  
Buckling was not checked for this model even though the pier was very tall 
(approximately 60 feet from the ground surface).  This is because of the extra transverse 
resistance the strut provided and its overall performance when seismically loaded. 
  
183 
 
6.6.1 Longitudinal Results 
 (a)  (b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure 6.24. Marshall County longitudinal Imperial Valley NMCE (a) time-history event, 
(b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
184 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure 6.25. Marshall County longitudinal Kocaeli2 NMCE (As if Survived) (a) time-
history event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, 
(e) ground surface displacement, and (f) demand capacity ratio 
 
 
 
 
 
185 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure 6.26. Marshall County longitudinal Kocaeli2 NMCE (failed at time 64.9 sec) (a) 
time-history event, (b) shear distribution, (c) top of pier displacement, (d) moment 
distribution, (e) ground surface displacement, and (f) demand capacity ratio 
 
186 
 
Table 6.15 ? Results overview for Marshall County longitudinal models (highlighted ones are shown in Figures 6.22, 6.23 and 6.24) 
 
 
187 
 
6.6.2 Transverse Results 
 (a)  (b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure 6.27. Marshall County transverse Imperial Valley NMCE (a) time-history event, 
(b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
188 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure 6.28. Franklin County longitudinal Kocaeli2 NMCE (failed) (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio 
 
189 
 
Table 6.16 ? Results overview for Marshall County transverse models (highlighted ones are shown in Figures 6.25 and 6.26) 
 
 
190 
 
6.7 Direct Analysis Results Summary 
 Five bridge pier case histories were modeled in FB-MultiPier: Chambers County 
25% and 100% scour, Etowah County, Franklin County, Lee County, and Marshall 
County.  Dynamic analysis was run for each model using a suite of scaled earthquake 
time-history events. 
 The Chambers County case history was modeled for two cases: 25% scour and 
100% scour.  The Chambers County bridge bent for the 25% scour case performed 
poorly, overall.  Most of the failed models were suspected to have failed because of either 
structural failure or soil failure.  Soil failure is likely due to large displacements that the 
soil spring undergoes.  The insitu soil above the rock line for the Chambers County case 
history was very weak and provided little lateral resistance.  Bending moment and D/C 
ratio was typically largest below the ground surface and above the rock line in the 
longitudinal direction.  In the transverse direction, it was largest at the column/pier cap 
connection.  However, large bending moments were still developing below the ground 
surface.  This suggests that plastic hinges may develop in these locations.  If a plastic 
hinge developed under the ground surface, it would be difficult to identify and repair. 
 In comparison, the Chambers County bridge bent for the 100% scour case 
performed well, overall.  The three models that failed all used NMCE scaled earthquake 
time-history events, which are of larger magnitude and, typically, more harmful than the 
North scaled time-histories.  The North scale factor events are more representative of 
what the state of Alabama would generally experience.  Bending moment and D/C ratio 
was typically largest at the rock line and column/pier cap connection when seismically 
191 
 
loaded in the longitudinal and transverse directions, respectively.  This suggests that 
plastic hinges may develop in these locations, which would be ideal.   
 The Etowah County bridge pier models performed poorly due to pile failure.  
Every model failed due to structural failure within the H-pile foundations (specifically the 
battered piles).  It appeared that the soft clay provided very little lateral resistance, 
causing the piles to buckle. 
 The Franklin County bridge bent models performed fair, overall.  Most of the 
models that failed were subjected NMCE earthquake events, which are the higher 
magnitude events.  Bending moment and D/C ratio was typically largest at the rock line 
and column/pier cap connection when seismically loaded in the longitudinal and 
transverse directions, respectively.  This suggests that plastic hinges may develop in these 
locations, which would be ideal.   
 The Lee County bridge pier models performed well, overall.  All of the models 
survived the earthquake event they were subjected to.  The moderate strength 
cohesionless soil seemed to provide adequate lateral resistance.  The highest D/C ratio for 
any pile was 0.6.  The bending moment and D/C ratio in the columns were largest at the 
column base and the column/pier cap connection in the longitudinal and transverse 
directions, respectively.  This suggests that plastic hinges are most likely to form at these 
locations.   
 The Marshall County bridge bent models performed well, overall.  Bending 
moment and D/C ratio was typically largest at the rock line and column/pier cap 
connection when seismically loaded in the longitudinal and transverse directions, 
respectively.  This suggests that plastic hinges may develop in these locations, which 
192 
 
would be ideal.  Some displacements at the top of the pier were very large.  This is 
expected because of the free length of the bent.  Typically, structures with longer period 
tend to displace more that structures with shorter periods.    
 The major limitation to these models is that only one bridge pier was modeled.  In 
the complete system for a bridge, interaction between the bridge deck, abutments, and 
other bridge piers (if applicable) is very important.  The interaction between these 
components can possibly provide additional stiffness, which could reduce the inertial 
forces generated within the bridge piers.  Without the interaction of the bridge deck, the 
displacements at the top of the pier are not completely accurate.  However, these models 
provided an indication of where maximum shear forces and bending moments would 
develop within the bridge pier, specifically in the foundations.  This subsequently 
suggests probable locations of plastic hinge zones that would develop, which is a key 
component of seismic design of bridges. 
 
  
193 
 
Chapter 7 
STATE DOT SURVEY
 As part of the research scope, several southeastern state DOTs were surveyed to 
compare their seismic design process, specifically to deep foundations, to ALDOT?s 
current practice.  The survey was sent to eleven states: Arkansas, Florida, Georgia, 
Kentucky, Louisiana, Mississippi, North Carolina (NC), South Carolina (SC), Tennessee, 
Virginia, and West Virginia.  At the time of writing this document, three had replied: 
Arkansas, Kentucky, and South Carolina.  Below is the survey submitted to the state 
DOTs: 
1. Do you use/prefer driven piles, drilled shafts, spread footings, or a combination of 
the three for foundation design in a seismic area? 
2. If driven piles are used for foundation design in a seismic area, what type(s) and 
configuration(s) is/are most often used?  If it is a group configuration, please 
provide typical spacing, batter (if applicable), and driving criteria. 
3. Is there a specific standard you use to determine if insitu soils on site are 
potentially susceptible to liquefaction (i.e. geologic age and origin, water table 
levels, fines content, etc.)? 
4. Have you ever taken remedial measures to meet seismic standards (current 
foundations not adequate or weak soil layer is a concern), specifically in regards 
to the foundations? If so, what was done and why? 
194 
 
5. Have your foundation designs been validated through computer program 
modeling or some other method?  If so, what program(s) did you use and how 
(combination of programs, run dynamic analysis or push-over analysis, etc.)? 
7.1 Arkansas Survey Response 
1. Since our bridge foundations in seismic zones are predominantly in soils with 
very deep overburden, we typically use driven trestle pile bents or pile footings.   
Drilled shafts may also be used, however, we have experienced difficulties in the 
past with construction procedures used in the placement of slurry-displaced 
drilled shafts; so. the majority of our seismic bridges are designed using piling. 
2. Pile Types:   Steel H-piles where significant depth of sand or clay exists over 
rock, Concrete piles in Seismic Zone 2 (assumed to also mean SDC B) or less, 
and Concrete-filled steel shell piles in all seismic zones. 
Pile Spacing:   As required by design, but not less than LRFD Specification 
minimum requirements. 
Pile Batter:   Typically use vertical piles unless other present or more frequently 
occurring design concerns such as earth pressure (end bents), bridge curvature, 
water velocity, etc. out weigh concerns from the extreme seismic event.  When 
battered piling is used in seismic zones, the batter is minimized from our standard 
4H:12V to 1.5H:12V. 
Driving Criteria:  Ultimate bearing capacity is typically determined using a Wave 
Equation Analysis (WEAP) where hammer approval and bearing graph 
relationships are determined and provided for the Contractor?s use. 
195 
 
3. Liquefaction susceptibility is determined by using the water table, soil type, and 
SPT blow counts from field sampling to calculate a factor of safety using a 
procedure developed by Youd and Idriss (2001). 
4. No remedial measures have been taken on in-situ soil to date.  Geosynthetic 
internal reinforcement is used in bridge embankments when required by design 
and minimum pile tip elevations may be specified to ensure pile tips are not 
established in a liquefiable layer.  Pile buckling due to a longer unsupported 
length in liquefiable layers is not typically considered.  Our liquefactions 
calculations often result in a combination of liquefiable and non-liquefiable 
layers.  Some soil resistance is considered to be available during liquefaction and 
steel shell piles are concrete-filled to help resist buckling. 
5. We model our bridges using the SEISAB program in conjunction with a response 
spectrum analysis and this provides us with the seismic forces to use in our 
foundation design for the extreme event case. 
7.2 Kentucky Survey Response 
1.  We typically use driven piles in areas where seismic design is a consideration. 
However, the selection of foundation type is typically not governed by seismic 
design considerations. Due to considerations other than seismic design driven 
piles are typically the appropriate foundation type in the New Madrid Seismic 
Zone (NMSZ) where there are significant seismic design considerations. 
However, we would potentially use another foundation type such as drilled shafts 
or spread footings on bedrock if warranted by the site conditions. 
196 
 
2. We typically use steel piles (H or pipe) with a group configuration when we use 
driven piles. The spacings are typically 3 ft to 10 ft depending on loads, and 
whether pile is point bearing or friction. We typically avoid battered piles in 
seismic zones. Driving criteria would typically be determined using dynamic 
testing and in some cases only dynamic formulas. We are currently working on a 
bridge over Kentucky Lake (in the NMSZ) where we will be performing static 
and pseudo-static (i.e. Statnamic) testing in conjunction with dynamic testing to 
determine pile driving criteria. 
3. Preliminary liquefaction assessments may be based on SPT blow counts, CPT 
testing, water table, and fines content. On our Lake Bridges Project (the 
previously-mentioned bridge over Kentucky Lake and a nearby bridge over Lake 
Barkley) rigorous liquefaction analyses were performed using site-specific ground 
motions, equivalent linear site response analyses using shear modulus values 
determined from in-situ and laboratory resonant column testing, and both CPT 
and SPT data. These analyses are generally based on the NCEER workshop 
recommendations as published in the American Society of Civil Engineers 
(ASCE) Journal (2001) (Youd and Idriss 2001). 
4. On our Lake Bridges project we specified deep soil mixing (DSM) to mitigate 
against liquefaction due to the liquefaction predicted for a 2500 year seismic 
event. We had a single bidder that was significantly higher than the Engineer?s 
estimate and the bid was rejected. Subsequently, the seismic design criteria were 
changed to design for the 1000 year event and DSM was no longer required. We 
re-let the project and construction is currently ongoing. 
197 
 
5. Foundations are sometimes modeled with GT STRUDL to estimate seismic 
response.  On our Lake Bridge Projects, dynamic modeling using time histories 
are being performed using SAP and MIDAS. Push over analyses was also 
performed. 
7.3 South Carolina Survey Response 
1. South Carolina Department of Transportation (SCDOT) exclusively uses either 
driven piles or drilled shafts to support our bridges.  Spread footings are not 
allowed at any location that will undergo soil Shear Strength Loss (SSL) (i.e. 
liquefaction).  Deep foundations are designed to incorporate downdrag should 
settlement caused by SSL be present at the location. 
2. SCDOT uses precast, prestressed concrete piles, H-piles and combination piles to 
support our bridges depending on the load (axial and lateral) and the soil that the 
foundations will be driven into.  Our typical pile sizes are indicated in Table 7.1. 
  
198 
 
Table 7.1 ? South Carolina?s Typical Pile Types and Sizes 
Pile Type Size 
Steel H-piles 
HP 12x53 
HP 14x73 
HP 14x89 
HP 14x1171 
Steel Pipe Piles 
16-inch2 
18-inch2 
20-inch2 
24-inch2 
Prestressed Concrete Piles3 
18-inch 
20-inch 
24-inch 
30-inch4 
36-inch4 
Combination Piles 
18-inch3 with W 8x58 stinger 
20-inch3 with HP 10x57 stinger 
24-inch3 with HP 12x53 stinger 
1used where penetration is minimal and nominal capacity is large 
2wall thickness is ? inch for all pipe pile sizes 
3prestressed concrete piles are square in section 
4these sizes are only allowed with the written approval of SCDOT 
 
 Please note that the pipe piles are typically filled with concrete to improve 
seismic performance.  Typically SCDOT uses pile bents for driven piles, with pile 
footings being used on a relatively limited basis.  The piles are installed typically 
no closer than 3 diameters apart in the transverse direction.  Driving criteria is 
based either on reaching a specified tip elevation or is based on achieving a 
specified nominal capacity.  SCDOT also tries to indicate which loading condition 
controlled the design i.e. axial or lateral and static (strength) or seismic (extreme 
event).  For drilled shafts, SCDOT typically uses a single drilled shaft supporting 
a single column with multiple columns supporting the bent (typically 3 to 5 
columns) depending on the width of the bridge.  We also have used hammer-head 
199 
 
type foundations before as well as drilled shaft footings [e.g.  The Cooper River 
Bridge (Arthur Ravenel, Jr. Bridge) in Charleston, SC]. 
3. SCDOT has adopted the use of the Idriss and Boulanger (2008) procedure.  We 
both screen the site for potential SSL as well as conduct a full SSL analysis.  
These procedures are contained in Chapter 13 of the SCDOT Geotechnical 
Design Manual (GDM) v. 1.1 (SCDOT 2010).  A copy of this Chapter, as well as 
the entire GDM, is available at the SCDOT website.   Please note that we are in 
the process of revising our GDM and would be willing to provide ALDOT a draft 
copy of our GDM for reference. 
4. First, SCDOT does not retrofit bridges to meet seismic performance.  Second, if 
SCDOT reviews the project, we do not allow deep foundations to be founded in 
liquefiable or soft clays that may undergo SSL during seismic shaking.  Finally, 
we account for the movement of the end slope into the bridge either through 
acceptable movements and the necessary loads being applied to the bridge or 
through ground improvement.  If slope stability is not an issue we would typically 
design the bridge to accommodate the downdrag on the piles by checking the pile 
capacity.  If slope instability is an issue, we start using the cheapest and easiest 
ground improvement method we can (i.e. geogrid) and then proceed toward the 
most expensive ground improvement method e.g. DSM or some other in-situ 
modification.  Our number one rule is no collapse of the bridge. 
5. The designers use L-pile, CSiBridge (CSI 2013), Leap Bridge (RC-Pier). 
Dynamic analysis is run using CSiBridge; this program allows performing the 
response spectral analysis and the push-over analysis.  The designer shall meet the 
200 
 
requirements of the Seismic Design Specifications.  (Please note that this last 
answer was prepared by our Seismic Design Support Section). 
7.4 State DOT Survey Summary 
1. All states use driven piles for seismic design, but seismic hazard may not 
necessarily be the controlling factor in foundation selection and design.  Arkansas 
primarily uses driven piles for seismic bridges.  Kentucky generally uses driven 
piles as well; however, it is usually due to other considerations other than seismic 
hazard, and considers other foundation types is the it is warranted by the site 
conditions.  SC exclusively uses driven piles and/or drilled shafts to support 
bridges in seismic hazard.   
2. Each state uses a variety of driven piles.  Most of the time, the selection of 
foundation type is dependent upon site conditions.  Arkansas uses steel H-piles 
when significant depth of sand or clay to bedrock is present; concrete piles are 
used for seismic zone 2 (SDC B) or less, and steel pipe piles filled with concrete 
can be used for all seismic zones.  Kentucky typically uses steel (H or pipe) piles 
when using driven piles.  SC uses steel, concrete, or combination piles depending 
on local site conditions and are typically pile bents (not pile footings).  Group 
spacing is typically what is recommended by design standards for all DOTs.  SC 
did state that in the transverse direction, pile spacing is no less than three 
diameters.  Arkansas decreased their typical batter slope (1.5H:12V) when in a 
seismic zone and Kentucky usually avoids battered piles all together in seismic 
areas.  SC did not comment.  Driving criteria is determined by WEAP analysis for 
Arkansas; Kentucky uses statnamic or dynamic (most likely Pile Driving 
201 
 
Analyzer [PDA]); and SC uses a specified tip elevation that must be reached or 
achieving a specified nominal capacity.   
3. Liquefaction assessments are handled differently by all three states.  Arkansas 
uses the Youd and Idriss (2001) procedure; whereas Kentucky generally conducts 
a preliminary assessment based on SPT and CPT testing, water table elevation 
and fines content.  If further evaluation is needed, they perform analysis based on 
the NCEER workshop published in the ASCE Journal (2001) (Youd and Idriss 
2001).  SC adopted the Idriss and Boulanger (2008) procedure.  They have also 
documented in the SCDOT GDM, a standardized procedure for the department to 
use (SCDOT 2010).  
4. Remedial measures are generally not taken by any of the DOTs.  Kentucky did 
order DSM to be done based on a 2500 year seismic event, but was eventually not 
economically feasible because the seismic event was lowered to 1000 year.  SC 
makes an interesting point in that it does not allow deep foundations to be 
founded in soft clay or liquefiable sands if it was reviewed by the SCDOT.  They 
did not expound on how they determine a suitable foundation selection and design 
for a site given those characteristics. 
5. All three DOTs use computer programs to determine seismic response.  SC?s 
approach is very similar to part of this research project?s scope.  It uses LPILE to 
determine the foundation response, and then inputs the foundation springs into 
CSiBridge to perform a response spectral analysis as well as a static pushover 
analysis 
.
202 
 
Chapter 8 
CONCLUSIONS AND RECOMMENDATIONS
 The research is summarized including the literature review, substructure and 
direct analysis done in FB-MultiPier, and the state DOT survey.  Conclusions were made 
based on those results and recommendations are provided to improve future research of 
deep foundation response to seismic and dynamic loads. 
8.1 Summary of Work 
 ALDOT provided five case histories of bridges to determine the response of the 
foundations to seismic loads relative to Alabama.  Substructure analysis was done and the 
response curves developed were used in SAP2000 to represent the foundations for the 
bridges.  A bridge bent was then modeled for each case history and direct analysis was 
conducted.  The Chambers County case history was modeled for two scour cases: 25% 
and 100% scour.  A suite of scaled earthquake time-history events developed by Panzer 
(2013) was used to load the bent dynamically.  Displacements at the top of the bent and 
the ground surface were recorded, as well as maximum shear force, bending moment and 
D/C ratio distributions.  The results of the direct analysis were compared to the literature 
review and discussed.  Finally, a survey was sent out to multiple state DOTs to review 
their approach to seismic design of bridge foundations. 
8.2 Conclusions  
 Based on the research, the following conclusions were made on the response of 
deep foundations to seismic and dynamic loads. 
203 
 
? The drilled shaft case histories with drilled shafts embedded in shallow bedrock 
performed well, overall.  If structural failure occurred (plastic hinge zones 
developed), they typically developed at the rock line (longitudinal direction) or 
column/pier cap connection (transverse). 
? It appeared, based on the Chambers County case histories, that the 25% scour 
case was more detrimental to the performance of the drilled shaft foundations than 
the 100% scour case.  Plastic hinge zones seemed to be developing below the 
ground surface in the 25% scour case due to the low lateral resistance provided by 
the soil layers above the bedrock. 
? The driven pile case histories performed well when founded in competent soil 
(Lee County case history).  However, the Etowah case history suggested that pile 
performance is poor when thick layers of soft clay are present, even in a moderate 
seismic hazard.  Buckling, due to the lack of lateral resistance by the soil is most 
likely the cause of failure. 
? Plastic hinge zones typically formed at the rock line in the longitudinal direction 
and at the pier cap in the transverse direction when the bed rock was shallow. 
? If soft soils are present over rock, plastic hinges may form below the ground 
surface, but above the rock line. 
? If driven piles are founded through soil that provides adequate lateral resistance, 
plastic hinges would most likely form at the base of the column or at the top of 
the pier cap for longitudinal and transverse directions, respectively. 
? Deep foundations should be evaluated for buckling using the recommendation 
(Pdes/Pcr < 50) made by Bhattacharya (2003). 
204 
 
? An alternative (or adaptive) foundation design should be considered for sites that 
have liquefiable or soft clay soils present. 
? If seismic design is required, a detailed site investigation as well as laboratory 
tests should be conducted to more accurately estimate the soil parameters.  This 
could potentially lead to a more efficient foundation design and reduce 
construction costs. 
? In high seismic areas (relative to Alabama), shear wave velocity testing should be 
done.  This could possibly lead to higher site classifications (A being the highest) 
which could lessen the seismic design requirements for critical and essential 
bridges in Alabama. 
? Remedial measures are typically not taken by any of the states that responded to 
the survey. 
? Though the likelihood of liquefaction occurring in Alabama is very low for most 
parts of the state, the potential for liquefaction should always be considered 
especially in regard to bridges near waterways in the northern part of the state.   
? Soil data compiling of recent, past sites and future sites or bridge projects should 
be done to map site class and the SDC throughout the state.  This can possibly 
expedite the design phase of future projects.   
? It appeared that the models with a lower frequency and higher structural period 
performed better than those with a higher frequency and lower period.   
8.3 Recommendations 
 There are several recommendations for foundation design considerations and 
future research on the response of deep foundations to seismic loading. 
205 
 
1. If scour is a possibility, deep foundations should be designed so that they are (at 
minimum) twice the length than the design scour depth (Ghosn et al. 2003). 
2. Increase the drilled shaft diameter at the ground surface.  If plastic hinges develop 
due to insufficient capacity, this will increase the likelihood of them developing at 
the ground surface. 
3. Further scour analysis should be done for both drilled shaft and driven pile 
foundations.  Multiple scour depths and soil types should be considered. 
4. Soil susceptibility to scour within the state of Alabama should be further 
researched in order to better predict scour depths and behavior. 
5. Further research regarding the structural period and frequency of a structure 
should be done to determine if there is a correlation to dynamic performance; and 
to determine if certain thresholds should be met for design standards.   
6. Foundation response, using computer modeling, should be evaluated for 
liquefaction using residual soil strength to define the soil.   
7. A full scale dynamic testing program coupled with direct analysis using a 
computer program (such as FB-MultiPier) should be conducted to better 
understand foundation response and to compare with FB-MultiPier?s output 
results.   
  
206 
 
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207 
 
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Mechanism of Pile Failure in Liquefiable Deposits During Earthquakes.? 
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Berril, J.B., Christensen, S. A., Keenan, R. P., Okada, W. and Pettinga, J.R. (2001). 
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Brown, D. A., O?Neill, M. W., Hoit, M., McVay, M., Naggar, M. H. El, Chakraborty, S., 
(2001). Static and Dynamic Lateral Loading of Pile Groups. Report 461, National 
Cooperative Highway Research Program, Washington D.C.  
 
Brown, D. A., Morrison, C., and Reese, L. C. (1988). ?Lateral Load Behavior of Pile 
Group in Sand.? Journal of Geotechnical Engineering, 114(11), 1261 - 1276. 
 
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Coulston, P. (2011). ?Influence of the LRFD Bridge Design Specifications on Seismic 
Design in Alabama.? Master?s Thesis, Auburn University, Auburn, Alabama. 
 
CSI (Computers and Structures, Inc.) (2013). CSiBridge, Walnut Creek, CA. 
 
Ebersole, Sandy M. and Perry, Shinisha L. (2008). ?Seismic Amplification and 
Liquefaction Susceptibility Mapping in Alabama.? Geological Survey of Alabama 
Open-File Report 0807, pp 21, 4 plates. 
 
Ensoft, Inc. (2013)a. GROUP v8.0 for windows, Austin, Texas 
 
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University of Florida, Gainesville, Florida. 
 
Gallet & Associates (2008). ?Bridge Replacement on I-59 SBL over Norfolk Southern 
Railroad and US 11, Etowah County ? Project No. STMAAF-I059 (342),? 
Foundation Report, Terracon (formerly Gallet & Associates), Huntsville, AL. 
 
Ghosn, M., Moses, F., and Wang, J. (2003). Design of Highway Bridges of Extreme 
Events. Report No. 489, National Cooperative Highway Research Program, 
Washington D.C. 
 
208 
 
Hannigan, P. J., Goble, G.G., Likins, G.E., and Rausche, F. (2006). Design and 
Construction of Driven Pile Foundations, Reference Manual ? Volume 1. Report 
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Hognestad, E., Hanson, N. W. and McHenry, D. (1955) ?Concrete stress distribution in 
ultimate strength design.?. Journal of the American Concrete Institute. Part 1. 
27(4), 455-479. 
 
Hughes, T. J. R. and Belytschko, T. (1983). ?A Precis of Developments in Computational 
Methods for Transient Analysis.? Journal of Applied Mechanics, 50(12), 1033-
1041. 
 
Idriss, I. M. and Boulanger, R. W. (2008) Soil Liquefaction During Earthquake. 
Earthquake Engineering Research Institute, Oakland, California. 
 
Ishihara, K. (1997). Terzaghi oration: ?Geotechnical Aspects of the 1995 Kobe 
Earthquake.? Proceedings of ICSMFE, Hamburg, 2047-2073. 
 
Kavazanjian, E. Jr., Marsh, M. L., and Banks, G. (2012). LRFD Seismic Analysis and 
Design of Transportation Geotechnical Features and Structural Foundations, 
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No. 132094, Federal highway Administration Washington D.C. 
 
Kavazanjian, E. Jr., Wang, J. J., Martin, G. R., Shamsabadi, Anoosh, Lam, Ignatius, 
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Kim, M. (2001). ?Analysis of Osterberg and Statnamic Axial Load Testing and 
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Kimura, Y. and Tokimatsu, K. (2005). ?Buckling Stress of Steel Pile with Vertical Load 
in Liquefied Soil.? Journal of Structural and Construction Engineering, (595) 73-
78. 
 
Knappett, J. and Madabhushi, S. (2005) Modeling of Liquefaction-Induced Instability in 
Pile Groups. Seismic Performance and Simulation of Pile Foundations in 
Liquefied and Laterally Spreading Ground, 255-267. 
 
Kramer, S. L. (1996). Geotechnical Earthquake Engineering. Prentice Hall, Inc., Upper 
Saddle River, NJ. 
 
209 
 
Kulhawy, F.H. and Mayne, P.W. (1990) Manual on Estimating Soil Properties for 
Foundation Design. Report No. EPRI EL-6800, Electric Power Research 
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Lam, I., and Martin, G. (1986), Seismic Design of Highway Bridge Foundations Vol. II ? 
Design Procedures and Guidelines. Report No. FHWA/RD-86/102, Federal 
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Matlock, H. (1970). ?Correlations for Design of Laterally Loaded Piles in Soft Clay.? 
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FL. 
 
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210 
 
 
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Austin, Texas. 
 
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212 
 
Appendix A 
TIME-HISTORY EVENTS
 The time-history events used for direct analysis are presented.  For graphical 
purposes, the 30-40 seconds when the acceleration is zero is not shown on the plots. 
 
 
Figure A.1. Coalinga North time-history event 
213 
 
 
Figure A.2. Imperial Valley NMCE time-history event 
214 
 
 
Figure A.3. Imperial Valley North time-history event 
215 
 
 
Figure A.4. Kobe NMCE time-history event 
216 
 
 
Figure A.5. Kobe North time-history event 
217 
 
 
Figure A.6. Kocaeli NMCE time-history event 
218 
 
 
Figure A.7. Kocaeli North time-history event 
219 
 
 
Figure A.8. Kocaeli2 NMCE time-history event 
220 
 
 
Figure A.9. Kocaeli2 North time-history event 
221 
 
 
Figure A.10. Landers NMCE time-history event 
222 
 
 
Figure A.11. Landers North time-history event 
223 
 
 
Figure A.12. LSM North time-history event 
224 
 
 
Figure A.13. NPS North time-history event 
225 
 
 
Figure A.14. San Fernando NMCE time-history event 
226 
 
 
Figure A.15. San Fernando North time-history event 
227 
 
 
Figure A.16. San Fernando2 NMCE time-history event 
228 
 
 
Figure A.17. San Fernando2 North time-history event 
  
229 
 
Appendix B 
DAMPING ANALYSIS RESULTS
The damping analysis results are presented.  The sine wave was used in FB-MultiPier to 
determine the response of the structure.  Displacement versus time was then used to 
determine the percent damping of the system. 
 
Figure B.1. Chambers County 25% Scour longitudinal sine wave time-history 
230 
 
 
Figure B.2. Chambers County 25% scour longitudinal displacement versus time at the top 
of the pier 
 
231 
 
 
Figure B.3. Chambers County 100% Scour longitudinal sine wave time-history 
 
232 
 
 
Figure B.4. Chambers County 100% scour longitudinal displacement versus time at the 
top of the pier 
233 
 
 
Figure B.5. Etowah County longitudinal sine wave time-history 
234 
 
 
Figure B.6. Etowah County longitudinal displacement versus time at the top of the pier 
235 
 
 
Figure B.7. Franklin County longitudinal sine wave time-history 
236 
 
 
Figure B.8. Franklin County longitudinal displacement versus time at the top of the pier 
237 
 
 
Figure B.9. Lee County longitudinal sine wave time-history 
238 
 
 
Figure B.10. Lee County longitudinal displacement versus time at the top of the pier 
239 
 
 
Figure B.11. Marshall County longitudinal sine wave time-history 
240 
 
 
Figure B.12. Marshall County longitudinal displacement versus time at the top of the pier 
241 
 
 
Figure B.13. Chambers County 25% scour transverse sine wave time-history 
242 
 
 
Figure B.14. Chambers County 25% scour transverse displacement versus time at the top 
of the pier 
 
243 
 
 
Figure B.15. Chambers County 100% scour transverse sine wave time-history 
 
244 
 
 
Figure B.16. Chambers County 100% scour transverse displacement versus time at the 
top of the pier 
245 
 
 
Figure B.17. Etowah County transverse sine wave time-history 
246 
 
 
Figure B.18. Etowah County transverse displacement versus time at the top of the pier 
247 
 
 
Figure B.19. Franklin County transverse sine wave time-history 
248 
 
 
Figure B.20. Franklin County transverse displacement versus time at the top of the pier 
249 
 
 
Figure B.21. Lee County transverse sine wave time-history 
250 
 
 
Figure B.22. Lee County transverse displacement versus time at the top of the pier 
251 
 
 
Figure B.23. Marshall County transverse sine wave time-history 
252 
 
 
Figure B.24. Marshall County transverse displacement versus time at the top of the pier 
 
  
253 
 
Appendix C 
CHAMBERS COUNTY BORING LOGS
 Appendix C contains all relevant soil information regarding Chambers County 
that was used in developing the soil profile for FB-MultiPier. 
 
Figure C.1. Chambers County Bent 3 boring log (ALDOT 2008) 
 
254 
 
Table C.1 ? Chambers County L-Pile Soils Input Data for the bents 
 
255 
 
Appendix D 
ETOWAH COUNTY BORING LOGS 
 Appendix D contains all relevant soil information regarding Etowah County that 
was used in developing the soil profile for FB-MultiPier. 
 
256 
 
 
Figure D.1. Etowah County Bent 2 boring log (Gallet 2008) 
257 
 
 
Figure D.2. Etowah County Bent 2 boring log (cont?d) (Gallet 2008) 
258 
 
 
Figure D.3. Etowah County Bent 2 boring log (Gallet 2008) 
259 
 
 
Figure D.4. Etowah County Bent 2 boring log (cont?d) (Gallet 2008) 
 
Table D.1 ? Etowah County soil input parameters for FB-Deep 
 
  
260 
 
FB-Deep Output: 
 
PILE INFORMATION (Pile Length = 60.00 (ft))  
   ===========================================  
     Section Type: H-Section, Flange width = 12.05(in) 
     Section Depth = 12.05(in), True cross-sectional area = 15.50(in^2) 
     Length = 60.00(ft), Tip Elevation = 577.50(ft) 
     Unit Weight of Pile = 290.00(pcf), Weight of pile = 0.94(tons) 
 
     Skin friction capacity  
     ----------------------  
      Soil    Bottom    Average       Ult. Skin  
     Layer   Elev.     SPT Blows     Friction    Thick.          Soil Type  
      Num.    (ft)       (Blows/ft)       (Tons)      (ft)  
       ----- -------- ------------- ------------ ------- ------------------------------  
           1   578.75         10.08          41.38     58.75  1- Plastic Clay                
           2   570.25         50.00           0.00        8.50  4- Lime Stone/Very shelly sand 
       (* IN LAYERS ABOVE BEARING LAYER)  
 
       Ultimate skin friction in layers above bearing layer  =   41.38(tons) 
       Average SPT in Bearing layer above tip              =   50.00(blow/ft) 
       Ultimate skin friction in bearing layer                =    1.89(tons) 
       Corrected Ultimate skin friction in bearing layer     =    1.81(tons) 
       Total Skin Friction                                     =   43.19(tons) 
 
     End bearing capacity  
     -------------------- 
        ELEVATION    SPT Blows    UNIT E. B. 
          (ft)       (Blows/ft)   (tsf)    
       ---------- -------------- ---------- 
           585.53      24.89      29.87  <-- 8B above pile tip 
           578.75      50.00      60.00 
           577.50      50.00      60.00  <-- Pile tip elevation 
           573.99      50.00      60.00  <-- 3.5B below pile tip 
 
       Average unit end bearing above pile tip           =   47.28(tsf) 
       Average unit end bearing below pile tip           =   60.00(tsf) 
       Average unit end bearing in vicinity of pile tip  =   53.64(tsf) 
 
       Critical depth of embedment in bearing layer  =    6.02(ft) 
       Actual depth of embedment                     =    1.25(ft) 
 
       Maximum mobilized end bearing capacity    =   52.85(tons) 
       Corrected mobilized end bearing capacity  =   50.85(tons) 
 
 
261 
 
     Pile Capacity  
     ------------- 
       Estimated Davisson capacity  =   94.04(tons) 
       Allowable pile capacity      =   47.02(tons) 
       Ultimate pile capacity       =  144.89(tons) 
 
  
262 
 
Appendix E 
FRANKLIN COUNTY BORING LOGS
 Appendix E contains all relevant soil information regarding Franklin County that 
was used in developing the soil profile for FB-MultiPier. 
 
Figure E.1. Franklin County Bent 3 boring log (ALDOT 2005) 
 
263 
 
 
Figure E.2. Franklin County Bent 3 boring log (ALDOT 2005)
264 
 
Table E.1?Franklin County L-Pile soil input data for Bent 3 
 
265 
 
Appendix F 
LEE COUNTY BORING LOGS
 Appendix F contains all relevant soil information regarding Lee County that was 
used in developing the soil profile for FB-MultiPier. 
 
Figure F.1. Lee County Bent 2 boring log (ALDOT 2006) 
266 
 
 
Figure F.1. Lee County Bent 2 boring log (ALDOT 2006) 
267 
 
 
Figure F.3. Lee County Bent 2 boring log (ALDOT 2006)
268 
 
Table F.1 ? Lee County uniaxial compression testing results (boxed value is one used for FB-MultiPier) (ALDOT 2006) 
 
 
269 
 
Table F.2. Lee County FB-Deep soil input parameters 
 
 
FB-Deep Output: 
PILE INFORMATION (Pile Length = 30.00 (ft))  
   ===========================================  
     Section Type: H-Section, Flange width = 12.05(in) 
     Section Depth = 12.05(in), True cross-sectional area = 15.50(in^2) 
     Length = 30.00(ft), Tip Elevation = 627.25(ft) 
     Unit Weight of Pile = 200.00(pcf), Weight of pile = 0.32(tons) 
 
     Skin friction capacity  
     ----------------------  
      Soil     Bottom      Average       Ult. Skin  
    Layer      Elev.      SPT Blows      Friction    Thick.          Soil Type  
     Num.     (ft)          (Blows/ft)        (Tons)       (ft)  
       ----- -------- ------------- ------------ ------- ------------------------------  
           1     627.75         17.03            27.47       29.50      2- Clay and silty sand         
           2     616.25         30.00              0.00       11.50      4- Lime Stone/Very shelly sand 
       (* IN LAYERS ABOVE BEARING LAYER)  
 
       Ultimate skin friction in layers above bearing layer  =   27.47(tons) 
       Average SPT in Bearing layer above tip                =   30.00(blow/ft) 
       Ultimate skin friction in bearing layer                =    0.45(tons) 
       Corrected Ultimate skin friction in bearing layer     =    0.45(tons) 
       Total Skin Friction                                     =   27.92(tons) 
  
270 
 
     End bearing capacity  
     -------------------- 
        ELEVATION    SPT Blows    UNIT E. B. 
          (ft)       (Blows/ft)   (tsf)    
       ---------- -------------- ---------- 
           635.28      23.31      25.74  <-- 8B above pile tip 
           627.75      30.00      36.00 
           627.25      30.00      36.00  <-- Pile tip elevation 
           623.74      30.00      36.00  <-- 3.5B below pile tip 
 
       Average unit end bearing above pile tip           =   31.19(tsf) 
       Average unit end bearing below pile tip           =   36.00(tsf) 
       Average unit end bearing in vicinity of pile tip  =   33.59(tsf) 
 
       Critical depth of embedment in bearing layer  =    6.02(ft) 
       Actual depth of embedment                      =    0.50(ft) 
 
       Maximum mobilized end bearing capacity    =   33.10(tons) 
       Corrected mobilized end bearing capacity  =   32.80(tons) 
 
     Pile Capacity  
     ------------- 
       Estimated Davisson capacity  =   60.72(tons) 
       Allowable pile capacity      =   30.36(tons) 
       Ultimate pile capacity       =   93.53(tons) 
 
 
  
271 
 
Appendix G 
MARSHALL COUNTY BORING LOGS
 Appendix G contains all relevant soil information regarding Marshall County that 
was used in developing the soil profile for FB-MultiPier. 
 
Figure G.1. Marshall County Bent 3 boring log (ALDOT 2003)
272 
 
Table G.1 ? Marshall County uniaxial compression test results (boxed value was used for FB-MultiPier) (ALDOT 2003) 
 
 
273 
 
Appendix H 
DIRECT ANALYSIS RESULTS 
 The results from the direct analysis are presented.  This includes the time-history, 
top-of-pier and ground surface displacement, and shear, moment, and demand/capacity 
ratio distribution for the length of the pile, shaft, or column.  
 
 
  
274 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.1. Chambers County 25% Scour Longitudinal Coalinga North (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio 
 
275 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.2. Chambers County 25% Scour Longitudinal Imperial Valley NMCE (a) time-
history event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, 
(e) ground surface displacement, and (f) demand capacity ratio 
  
276 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.3. Chambers County 25% Scour Longitudinal Imperial Valley North (a) time-
history event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, 
(e) ground surface displacement, and (f) demand capacity ratio 
  
277 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.4. Chambers County 25% Scour Longitudinal Kobe NMCE (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio 
 
 
 
278 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.5. Chambers County 25% Scour Longitudinal Kobe North (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio 
 
 
 
279 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.6. Chambers County 25% Scour Longitudinal Kocaeli NMCE (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio 
 
 
 
280 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.7. Chambers County 25% Scour Longitudinal Kocaeli North (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio 
 
 
 
281 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.8. Chambers County 25% Scour Longitudinal Kocaeli2 NMCE (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio 
 
 
 
282 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.9. Chambers County 25% Scour Longitudinal Kocaeli2 North (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio 
 
. 
 
283 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.10. Chambers County 25% Scour Longitudinal Landers NMCE (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio 
 
 
 
284 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.11. Chambers County 25% Scour Longitudinal Landers North (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio 
 
 
 
285 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.12. Chambers County 25% Scour Longitudinal LSM North (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio 
 
 
 
286 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.13. Chambers County 25% Scour Longitudinal NPS North (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio 
 
 
 
287 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.14. Chambers County 25% Scour Longitudinal San Fernando NMCE (a) time-
history event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, 
(e) ground surface displacement, and (f) demand capacity ratio 
 
 
 
288 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.15. Chambers County 25% Scour Longitudinal San Fernando North (a) time-
history event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, 
(e) ground surface displacement, and (f) demand capacity ratio 
 
 
 
289 
 
 
(a) 
 
(b) 
 (c)  (d) 
 
(e) 
 
(f) 
 
Figure B.16. Chambers County 25% Scour Longitudinal San Fernando2 NMCE (a) time-
history event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, 
(e) ground surface displacement, and (f) demand capacity ratio 
 
 
290 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.17 Chambers County 25% Scour Longitudinal San Fernando2 North (a) time-
history event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, 
(e) ground surface displacement, and (f) demand capacity ratio 
 
 
 
291 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.18. Chambers County 25% Scour Transverse Coalinga North (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio 
 
292 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.19. Chambers County 25% Scour Transverse Imperial Valley NMCE (a) time-
history event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, 
(e) ground surface displacement, and (f) demand capacity ratio 
  
293 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.20. Chambers County 25% Scour Transverse Imperial Valley North (a) time-
history event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, 
(e) ground surface displacement, and (f) demand capacity ratio 
 
 
 
294 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.21. Chambers County 25% Scour Transverse Kobe NMCE (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio 
 
 
 
295 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.22. Chambers County 25% Scour Transverse Kobe North (a) time-history event, 
(b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
296 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.23. Chambers County 25% Scour Transverse Kocaeli NMCE (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio 
 
 
 
297 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.24. Chambers County 25% Scour Transverse Kocaeli North (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio 
 
 
 
298 
 
 
(a) 
 
(b) 
 (c)  
(d) 
 (e)  
(f) 
 
Figure B.25. Chambers County 25% Scour Transverse Kocaeli2 NMCE (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio 
 
 
 
299 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.26. Chambers County 25% Scour Transverse Kocaeli2 North (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio 
 
. 
 
300 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.27. Chambers County 25% Scour Transverse Landers NMCE (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio 
 
 
 
301 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.28. Chambers County 25% Scour Transverse Landers North (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio 
 
 
 
302 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.29. Chambers County 25% Scour Transverse LSM North (a) time-history event, 
(b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
303 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.30. Chambers County 25% Scour Transverse NPS North (a) time-history event, 
(b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
304 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.31. Chambers County 25% Scour Transverse San Fernando NMCE (a) time-
history event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, 
(e) ground surface displacement, and (f) demand capacity ratio 
 
 
 
305 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.32. Chambers County 25% Scour Transverse San Fernando North (a) time-
history event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, 
(e) ground surface displacement, and (f) demand capacity ratio 
 
 
 
306 
 
 
(a) 
 
(b) 
 (c)  (d) 
 
(e) 
 
(f) 
 
Figure B.33. Chambers County 25% Scour Transverse San Fernando2 NMCE (a) time-
history event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, 
(e) ground surface displacement, and (f) demand capacity ratio 
 
 
307 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.34. Chambers County 25% Scour Transverse San Fernando2 North (a) time-
history event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, 
(e) ground surface displacement, and (f) demand capacity ratio 
 
 
 
308 
 
 
(a) (b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.35. Chambers County 100% Scour Longitudinal Coalinga North (a) time-
history event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, 
(e) ground surface displacement, and (f) demand capacity ratio 
 
309 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.36. Chambers County 100% Scour Longitudinal Imperial Valley NMCE (a) 
time-history event, (b) shear distribution, (c) top of pier displacement, (d) moment 
distribution, (e) ground surface displacement, and (f) demand capacity ratio 
  
310 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.37. Chambers County 100% Scour Longitudinal Imperial Valley North (a) time-
history event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, 
(e) ground surface displacement, and (f) demand capacity ratio 
 
 
 
311 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.38. Chambers County 100% Scour Longitudinal Kobe NMCE (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio 
 
 
 
312 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.39. Chambers County 100% Scour Longitudinal Kobe North (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio 
 
 
 
313 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.40. Chambers County 100% Scour Longitudinal Kocaeli NMCE (a) time-
history event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, 
(e) ground surface displacement, and (f) demand capacity ratio 
 
 
 
314 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.41. Chambers County 100% Scour Longitudinal Kocaeli North (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio 
 
 
 
315 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.42. Chambers County 100% Scour Longitudinal Kocaeli2 NMCE (a) time-
history event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, 
(e) ground surface displacement, and (f) demand capacity ratio 
 
 
 
316 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.43. Chambers County 100% Scour Longitudinal Kocaeli2 North (a) time-
history event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, 
(e) ground surface displacement, and (f) demand capacity ratio 
 
. 
 
317 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.44. Chambers County 100% Scour Longitudinal Landers NMCE (a) time-
history event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, 
(e) ground surface displacement, and (f) demand capacity ratio 
 
 
 
318 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.45. Chambers County 100% Scour Longitudinal Landers North (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio 
 
 
 
319 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.46. Chambers County 100% Scour Longitudinal LSM North (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio 
 
 
 
320 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.47. Chambers County 100% Scour Longitudinal NPS North (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio 
 
 
 
321 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.48. Chambers County 100% Scour Longitudinal San Fernando NMCE (a) time-
history event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, 
(e) ground surface displacement, and (f) demand capacity ratio 
 
 
 
322 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.49. Chambers County 100% Scour Longitudinal San Fernando North (a) time-
history event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, 
(e) ground surface displacement, and (f) demand capacity ratio 
 
 
 
323 
 
 
(a)  (b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.50. Chambers County 100% Scour Longitudinal San Fernando2 NMCE (a) 
time-history event, (b) shear distribution, (c) top of pier displacement, (d) moment 
distribution, (e) ground surface displacement, and (f) demand capacity ratio 
 
 
324 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.51 Chambers County 100% Scour Longitudinal San Fernando2 North (a) time-
history event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, 
(e) ground surface displacement, and (f) demand capacity ratio 
 
 
 
325 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.52. Chambers County 100% Scour Transverse Coalinga North (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio 
 
326 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.53. Chambers County 100% Scour Transverse Imperial Valley NMCE (a) time-
history event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, 
(e) ground surface displacement, and (f) demand capacity ratio 
  
327 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.54. Chambers County 100% Scour Transverse Imperial Valley North (a) time-
history event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, 
(e) ground surface displacement, and (f) demand capacity ratio 
 
 
 
328 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.55. Chambers County 100% Scour Transverse Kobe NMCE (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio 
 
 
 
329 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.56. Chambers County 100% Scour Transverse Kobe North (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio 
 
 
 
330 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.57. Chambers County 100% Scour Transverse Kocaeli NMCE (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio 
 
 
 
331 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.58. Chambers County 100% Scour Transverse Kocaeli North (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio 
 
 
 
332 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.59. Chambers County 100% Scour Transverse Kocaeli2 NMCE (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio 
 
 
 
333 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.60. Chambers County 100% Scour Transverse Kocaeli2 North (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio 
 
. 
 
334 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.61. Chambers County 100% Scour Transverse Landers NMCE (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio 
 
 
 
335 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.62. Chambers County 100% Scour Transverse Landers North (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio 
 
 
 
336 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.63. Chambers County 100% Scour Transverse LSM North (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio 
 
 
 
337 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.64. Chambers County 100% Scour Transverse NPS North (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio 
 
 
 
338 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.65. Chambers County 100% Scour Transverse San Fernando NMCE (a) time-
history event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, 
(e) ground surface displacement, and (f) demand capacity ratio 
 
 
 
339 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.66. Chambers County 100% Scour Transverse San Fernando North (a) time-
history event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, 
(e) ground surface displacement, and (f) demand capacity ratio 
 
 
 
340 
 
 
(a)  (b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.67. Chambers County 100% Scour Transverse San Fernando2 NMCE (a) time-
history event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, 
(e) ground surface displacement, and (f) demand capacity ratio 
 
 
341 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.68. Chambers County 100% Scour Transverse San Fernando2 North (a) time-
history event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, 
(e) ground surface displacement, and (f) demand capacity ratio 
 
 
 
342 
 
 
(a) (b) 
 
(c) 
 
(d) 
 
(e) 
 
(f) 
 
Figure B.69. Etowah County Longitudinal Coalinga North (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
343 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.70. Etowah County Longitudinal Imperial Valley NMCE (a) time-history event, 
(b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
  
344 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.71. Etowah County Longitudinal Imperial Valley North (a) time-history event, 
(b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
345 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.72. Etowah County Longitudinal Kobe NMCE (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
 
 
346 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.73. Etowah County Longitudinal Kobe North (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
 
 
347 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.74. Etowah County Longitudinal Kocaeli NMCE (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
348 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.75. Etowah County Longitudinal Kocaeli North (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
 
 
349 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.76. Etowah County Longitudinal Kocaeli2 NMCE (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
350 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.77. Etowah County Longitudinal Kocaeli2 North (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
. 
 
351 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.78. Etowah County Longitudinal Landers NMCE (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
352 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.79. Etowah County Longitudinal Landers North (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
 
 
353 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.80. Etowah County Longitudinal LSM North (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
 
 
354 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.81. Etowah County Longitudinal NPS North (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
 
 
355 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.82. Etowah County Longitudinal San Fernando NMCE (a) time-history event, 
(b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
356 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.83. Etowah County Longitudinal San Fernando North (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
357 
 
 
(a)  (b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.84. Etowah County Longitudinal San Fernando2 NMCE (a) time-history event, 
(b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
358 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.85. Etowah County Longitudinal San Fernando2 North (a) time-history event, 
(b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
359 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.86. Etowah County Transverse Coalinga North (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
360 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.87. Etowah County Transverse Imperial Valley NMCE (a) time-history event, 
(b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
  
361 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.88. Etowah County Transverse Imperial Valley North (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
362 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.89. Etowah County Transverse Kobe NMCE (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
 
 
363 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.90. Etowah County Transverse Kobe North (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
 
 
364 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.91. Etowah County Transverse Kocaeli NMCE (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
 
 
365 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.92. Etowah County Transverse Kocaeli North (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
 
 
366 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.93. Etowah County Transverse Kocaeli2 NMCE (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
367 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.94. Etowah County Transverse Kocaeli2 North (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
. 
 
368 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.95. Etowah County Transverse Landers NMCE (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
 
 
369 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.96. Etowah County Transverse Landers North (column) (a) time-history event, 
(b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
370 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.97. Etowah County Transverse LSM North (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
 
 
371 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.98. Etowah County Transverse NPS North (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
 
 
372 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.99. Etowah County Transverse San Fernando NMCE (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
373 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.100. Etowah County Transverse San Fernando North (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
374 
 
 
(a)  (b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.101. Etowah County Transverse San Fernando2 NMCE (a) time-history event, 
(b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
375 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.102. Etowah County Transverse San Fernando2 North (a) time-history event, 
(b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
376 
 
 
(a) (b) 
 
(c) 
 
(d) 
 
(e) 
 
(f) 
 
Figure B.103. Franklin County Longitudinal Coalinga North (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
377 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.104. Franklin County Longitudinal Imperial Valley NMCE (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio 
  
378 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.105. Franklin County Longitudinal Imperial Valley North (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio 
 
 
 
379 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.106. Franklin County Longitudinal Kobe NMCE (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
380 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.107. Franklin County Longitudinal Kobe North (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
 
 
381 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.108. Franklin County Longitudinal Kocaeli NMCE (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
382 
 
 
(a) 
 
(b) 
 (c)  
(d) 
 (e)  (f) 
 
Figure B.109. Franklin County Longitudinal Kocaeli North (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
383 
 
 
(a) 
 
(b) 
 (c)  
(d) 
 (e)  (f) 
 
Figure B.110. Franklin County Longitudinal Kocaeli2 NMCE (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
384 
 
 
(a) 
 
(b) 
 (c)  
(d) 
 (e)  (f) 
 
Figure B.111. Franklin County Longitudinal Kocaeli2 North (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
. 
 
385 
 
 
(a) 
 
(b) 
 (c)  
(d) 
 (e)  (f) 
 
Figure B.112. Franklin County Longitudinal Landers NMCE (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
386 
 
 
(a) 
 
(b) 
 (c)  
(d) 
 (e)  (f) 
 
Figure B.113. Franklin County Longitudinal Landers North (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
387 
 
 
(a) 
 
(b) 
 (c)  
(d) 
 (e)  (f) 
 
Figure B.114. Franklin County Longitudinal LSM North (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
 
 
388 
 
 
(a) 
 
(b) 
 (c)  
(d) 
 (e)  (f) 
 
Figure B.115. Franklin County Longitudinal NPS North (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
 
 
389 
 
 
(a) 
 
(b) 
 (c)  
(d) 
 (e)  (f) 
 
Figure B.116. Franklin County Longitudinal San Fernando NMCE (a) time-history event, 
(b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
390 
 
 
(a) 
 
(b) 
 (c)  
(d) 
 (e)  (f) 
 
Figure B.117 Franklin County Longitudinal San Fernando North (a) time-history event, 
(b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
391 
 
 
(a)  (b) 
 (c)  
(d) 
 (e)  (f) 
 
Figure B.118. Franklin County Longitudinal San Fernando2 NMCE (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio 
 
 
392 
 
 
(a) 
 
(b) 
 (c)  
(d) 
 (e)  (f) 
 
Figure B.119. Franklin County Longitudinal San Fernando2 North (a) time-history event, 
(b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
393 
 
 
(a) 
 
(b) 
 (c)  
(d) 
 (e)  (f) 
 
Figure B.120. Franklin County Transverse Coalinga North (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
394 
 
 
(a) 
 
(b) 
 (c)  
(d) 
 (e)  (f) 
 
Figure B.121. Franklin County Transverse Imperial Valley NMCE (a) time-history event, 
(b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
  
395 
 
 
(a) 
 
(b) 
 (c)  
(d) 
 (e)  (f) 
 
Figure B.122. Franklin County Transverse Imperial Valley North (a) time-history event, 
(b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
396 
 
 
(a) 
 
(b) 
 (c)  
(d) 
 (e)  (f) 
 
Figure B.123. Franklin County Transverse Kobe NMCE (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
 
 
397 
 
 
(a) 
 
(b) 
 (c)  
(d) 
 (e)  (f) 
 
Figure B.124. Franklin County Transverse Kobe North (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
 
 
398 
 
 
(a) 
 
(b) 
 (c)  
(d) 
 (e)  (f) 
 
Figure B.125. Franklin County Transverse Kocaeli NMCE (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
399 
 
 
(a) 
 
(b) 
 (c)  
(d) 
 (e)  (f) 
 
Figure B.126. Franklin County Transverse Kocaeli North (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
 
 
400 
 
 
(a) 
 
(b) 
 (c)  
(d) 
 (e)  (f) 
 
Figure B.127. Franklin County Transverse Kocaeli2 NMCE (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
401 
 
 
(a) 
 
(b) 
 (c)  
(d) 
 (e)  (f) 
 
Figure B.128. Franklin County Transverse Kocaeli2 North (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
. 
 
402 
 
 
(a) 
 
(b) 
 (c)  
(d) 
 (e)  (f) 
 
Figure B.129. Franklin County Transverse Landers NMCE (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
403 
 
 
(a) 
 
(b) 
 (c)  
(d) 
 (e)  (f) 
 
Figure B.130. Franklin County Transverse Landers North (column) (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio 
 
 
 
404 
 
 
(a) 
 
(b) 
 (c)  
(d) 
 (e)  (f) 
 
Figure B.131. Franklin County Transverse LSM North (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
 
 
405 
 
 
(a) 
 
(b) 
 (c)  
(d) 
 (e)  (f) 
 
Figure B.132. Franklin County Transverse NPS North (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
 
 
406 
 
 
(a) 
 
(b) 
 (c)  
(d) 
 (e)  (f) 
 
Figure B.133. Franklin County Transverse San Fernando NMCE (a) time-history event, 
(b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
407 
 
 
(a) 
 
(b) 
 (c)  
(d) 
 (e)  (f) 
 
Figure B.134. Franklin County Transverse San Fernando North (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
408 
 
 
(a)  (b) 
 (c)  
(d) 
 (e)  (f) 
 
Figure B.135. Franklin County Transverse San Fernando2 NMCE (a) time-history event, 
(b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
409 
 
 
(a) 
 
(b) 
 (c)  
(d) 
 (e)  (f) 
 
Figure B.136. Franklin County Transverse San Fernando2 North (a) time-history event, 
(b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
410 
 
 
(a) (b) 
 
(c) 
 
(d) 
 
(e) 
 
(f) 
 
Figure B.137. Lee County Longitudinal Coalinga North (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
411 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.138. Lee County Longitudinal Imperial Valley NMCE (a) time-history event, 
(b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
  
412 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.139. Lee County Longitudinal Imperial Valley North (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
413 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.140. Lee County Longitudinal Kobe NMCE (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
 
 
414 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  
(f) 
 
Figure B.141. Lee County Longitudinal Kobe North (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
 
 
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0 10 20 30 40 50 60 70
Displacemen
t 
(in)
Ti me (sec)
415 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.142. Lee County Longitudinal Kocaeli NMCE (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
 
 
416 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.143. Lee County Longitudinal Kocaeli North (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
 
 
417 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.144. Lee County Longitudinal Kocaeli2 NMCE (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
 
 
418 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.145. Lee County Longitudinal Kocaeli2 North (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
. 
 
419 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.146. Lee County Longitudinal Landers NMCE (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
 
 
420 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.147. Lee County Longitudinal Landers North (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
 
 
421 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.148. Lee County Longitudinal LSM North (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
 
 
422 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.149. Lee County Longitudinal NPS North (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
 
 
423 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.150. Lee County Longitudinal San Fernando NMCE (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
424 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.151 Lee County Longitudinal San Fernando North (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
425 
 
 
(a)  (b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.152. Lee County Longitudinal San Fernando2 NMCE (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
426 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.153. Lee County Longitudinal San Fernando2 North (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
427 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.154. Lee County Transverse Coalinga North (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
428 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.155. Lee County Transverse Imperial Valley NMCE (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
  
429 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.156. Lee County Transverse Imperial Valley North (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
430 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.157. Lee County Transverse Kobe NMCE (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
 
 
431 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.158. Lee County Transverse Kobe North (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
 
 
432 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.159. Lee County Transverse Kocaeli NMCE (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
 
 
433 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.160. Lee County Transverse Kocaeli North (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
 
 
434 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.161. Lee County Transverse Kocaeli2 NMCE (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
 
 
435 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.162. Lee County Transverse Kocaeli2 North (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
. 
 
436 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.163. Lee County Transverse Landers NMCE (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
 
 
437 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.164. Lee County Transverse Landers North (column) (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
438 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.165. Lee County Transverse LSM North (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
 
 
439 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.166. Lee County Transverse NPS North (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
 
 
440 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.167. Lee County Transverse San Fernando NMCE (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
441 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.168. Lee County Transverse San Fernando North (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
442 
 
 
(a)  (b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.169. Lee County Transverse San Fernando2 NMCE (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
443 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.170. Lee County Transverse San Fernando2 North (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
444 
 
 
(a) (b) 
 
(c) 
 
(d) 
 
(e) 
 
(f) 
 
Figure B.171. Marshall County Longitudinal Coalinga North (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
445 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.172. Marshall County Longitudinal Imperial Valley NMCE (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio 
  
446 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.173. Marshall County Longitudinal Imperial Valley North (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio 
 
 
 
447 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 
(e) 
 
(f) 
 
Figure B.174. Marshall County Longitudinal Kobe NMCE (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
448 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.175. Marshall County Longitudinal Kobe North (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
 
 
449 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.176. Marshall County Longitudinal Kocaeli NMCE (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
450 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.177. Marshall County Longitudinal Kocaeli North (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
451 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.178. Marshall County Longitudinal Kocaeli2 NMCE (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
452 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.179. Marshall County Longitudinal Kocaeli2 North (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
. 
 
453 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.180. Marshall County Longitudinal Landers NMCE (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
454 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.181. Marshall County Longitudinal Landers North (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
455 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.182. Marshall County Longitudinal LSM North (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
 
 
456 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.183. Marshall County Longitudinal NPS North (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
 
 
457 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.184. Marshall County Longitudinal San Fernando NMCE (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio 
 
 
 
458 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.185. Marshall County Longitudinal San Fernando North (a) time-history event, 
(b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
459 
 
 
(a)  (b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.186. Marshall County Longitudinal San Fernando2 NMCE (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio 
 
 
460 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.187 Marshall County Longitudinal San Fernando2 North (a) time-history event, 
(b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
461 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.188. Marshall County Transverse Coalinga North (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
462 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.189. Marshall County Transverse Imperial Valley NMCE (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio 
  
463 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.190. Marshall County Transverse Imperial Valley North (a) time-history event, 
(b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
464 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.191. Marshall County Transverse Kobe NMCE (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
 
 
465 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.192. Marshall County Transverse Kobe North (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
 
 
466 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.193. Marshall County Transverse Kocaeli NMCE (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
467 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.194. Marshall County Transverse Kocaeli North (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
468 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.195. Marshall County Transverse Kocaeli2 NMCE (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
469 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.196. Marshall County Transverse Kocaeli2 North (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
. 
 
470 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.197. Marshall County Transverse Landers NMCE (a) time-history event, (b) 
shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
471 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.198. Marshall County Transverse Landers North (column) (a) time-history 
event, (b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) 
ground surface displacement, and (f) demand capacity ratio 
 
 
 
472 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.199. Marshall County Transverse LSM North (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
 
 
473 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.200. Marshall County Transverse NPS North (a) time-history event, (b) shear 
distribution, (c) top of pier displacement, (d) moment distribution, (e) ground surface 
displacement, and (f) demand capacity ratio 
 
 
 
474 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.201. Marshall County Transverse San Fernando NMCE (a) time-history event, 
(b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
 
 
 
475 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.202. Marshall County Transverse San Fernando North (a) time-history event, 
(b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
476 
 
 
(a)  (b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.203. Marshall County Transverse San Fernando2 NMCE (a) time-history event, 
(b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio 
477 
 
 
(a) 
 
(b) 
 
(c) 
 
(d) 
 (e)  (f) 
 
Figure B.204. Marshall County Transverse San Fernando2 North (a) time-history event, 
(b) shear distribution, (c) top of pier displacement, (d) moment distribution, (e) ground 
surface displacement, and (f) demand capacity ratio