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ABSTRACT
POSSIEL, BENJAMIN ALLEN. Point of Fixity Analysis of Laterally Loaded Bridge
Bents. (Under the direction of Dr. Mohammed Gabr and Dr. Mervyn Kowalsky.)
Research work in this thesis deals with the effects of lateral loads in the longitudinal
direction on a substructure’s point of fixity. Full scale tests were performed to model and
test a section of a bridge where the superstructure is connected to the substructure
through elastomeric bearing pads. The connection rotational stiffness between the super
and substructure was measured as an effect of applying a lateral load to the foundation
element and creating a moment at the connection joint. A circular concrete pile, square
concrete pile, and steel H-pile were tested in connection with both type V and type VI
elastomeric bearing pads. The response of these full scale tests were then modeled in FB-
MultiPier as tested and as an equivalent single foundation element. The model response
was then compared to the measured results. Through the use of FB-MultiPier, three
existing North Carolina bridges’ foundation elements were analyzed to determine an
effective range of partial head fixity and its compounding effects on the development of a
foundation element’s depth to fixity.
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Point of Fixity Analysis of Laterally Loaded Bridge Bents
by
Benjamin Allen Possiel
A thesis submitted to the Graduate Faculty of
North Carolina State University
in partial fulfillment of the
requirements for the Degree of
Master of Science
Civil Engineering
Raleigh, NC
2008
APPROVED BY:
_________________________ __________________________
Mohammed A. Gabr, Ph.D. Mervyn J. Kowalsky, Ph.D.
Chair of Advisory Committee Chair of Advisory Committee
_________________________
Roy H. Borden, Ph.D.
Committee Member
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BIOGRAPHY
Benjamin Allen Possiel was born on August 8th
, 1984. He has lived in Raleigh, NC his
whole live and has enjoyed the outdoors and playing sports. He has a strong passion for
service and looks to Jesus Chirst as his savior. Benjamin attended W. G. Enloe High
School in Raleigh, NC and then pursued his B.S. in civil engineering at North Carolina
State University. After developing a strong passion for soil-structure interaction, he
pursued a M.S. at North Carolina State University in the geotechnical department. Upon
graduating, Benjamin plans to start his career with Subsurface Construction Company in
Raleigh, NC. Shortly thereafter on April 5th
, 2008, he will be getting married to an
amazing and wonderful woman who is his best friend and better half, Megan Daniels
Gray.
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TABLE OF CONTENTS
LIST OF TABLES .............................................................................................................. v
LIST OF FIGURES ........................................................................................................... vi
LIST OF EQUATIONS ..................................................................................................... ix
CHAPTER 1: INTRODUCTION ....................................................................................... 1
1.1 Problem Description .............................................................................................................. 1
1.2 Objective ............................................................................................................................... 2
1.3 Approach ............................................................................................................................... 2
1.3.1 Full scale testing ............................................................................................................. 2
1.3.2 Florida-Pier Computer Modeling ................................................................................... 3
1.4 Scope ..................................................................................................................................... 3
1.4.1 Literature Review ........................................................................................................... 3
1.4.2 Experimental Program .................................................................................................... 4
1.4.3 Load Transfer Mechanisms ............................................................................................ 4
1.4.4 Florida-Mulitipier Modeling .......................................................................................... 4
1.4.5 Design Limit States ........................................................................................................ 4
1.4.6 Summary and Conclusions ............................................................................................. 5
CHAPTER 2: LITERATURE REVIEW ............................................................................ 6
2.1 Introduction ........................................................................................................................... 6
2.2 Current Design ...................................................................................................................... 6
2.2.1 Y. Chen (1995) and (Davisson and Robinson, 1965) ..................................................... 7
2.2.2 Pile Bent Design Criteria (Robinson et al, 2006) ......................................................... 13
2.3 Elastomeric Bearing Pad ..................................................................................................... 17
2.4 Summary and Conclusions .................................................................................................. 19
CHAPTER 3: EXPERIMENTAL PROGRAM ................................................................ 21
3.1 Experimental Design ........................................................................................................... 21
3.2 Construction of Test Sample Elements ............................................................................... 26
3.3 Instrumentations and Testing Protocol ................................................................................ 33
CHAPTER 4: TESTING RESULTS ................................................................................ 39
4.1 Bearing Pad Tests ................................................................................................................ 39
4.2 Physical Observations from Testing ................................................................................... 39
4.2.1 Circular Pile .................................................................................................................. 43
4.2.2 Square Pile .................................................................................................................... 47
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....
.
133
4.2.3 H-pile ............................................................................................................................ 49
4.3 Experimental Results ........................................................................................................... 52
4.4 Conclusions ......................................................................................................................... 66
CHAPTER 5: MODELING-FB MULTIPIER ................................................................. 68
5.1 Introduction ......................................................................................................................... 68
5.2 Experimental Modeling ....................................................................................................... 68
5.2.1 Full Scale Modeling ..................................................................................................... 68
5.2.2 Single Pile Modeling .................................................................................................... 78
5.3 North Carolina Bridge Bent Case Study.............................................................................. 83
5.3.1 Halifax County Bridge ................................................................................................. 84
5.3.2 Wake County Bridge .................................................................................................... 93
5.3.3 Robeson County Bridge ............................................................................................. 101
5.4 Conclusions ....................................................................................................................... 110
CHAPTER 6: LIMIT STATES ...................................................................................... 112
6.1 Background ....................................................................................................................... 112
6.2 Analysis ............................................................................................................................. 114
6.3 Summary and Conclusions ................................................................................................ 120
CHAPTER 7: SUMMARY AND CONCLUSIONS ...................................................... 121
7.1 Full Scale Tests ................................................................................................................. 121
7.2 FB-MultiPier Modeling ..................................................................................................... 122
7.3 Limit States ........................................................................................................................ 123
7.4 Conclusions ....................................................................................................................... 123
REFERENCES ............................................................................................................... 129
APPENDIX A: Lateral Force vs. Top Pile Displacement Response .............................. 132
APPENDIX B: Top displacement vs. Contributing Top Displacement Components .... 154
APPENDIX C: Measured vs. Calculated Response ....................................................... 172
APPENDIX D: Percentages of Contributing Top Displacement ................................... 191
APPENDIX E: FB-MultiPier Models ............................................................................. 194
E.1 Full Scale Test Model Results .......................................................................................... 194
E.2 Single Pile Models ............................................................................................................ 200
E.3 Matched Single Pile Results to Actual Test Results ......................................................... 206
APPENDIX A: Lateral Force vs. Top Pile Displacement Response…….…….……....... 133
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LIST OF TABLES
Table 1. Values of nh for sands (from Y. Chen, 1995) ....................................................... 9
Table 2. Comparison of Lf values for fixed head piles (from Y. Chen, 1995) ................. 12
Table 3. Comparison of Lf values for pinned head piles (from Y. Chen, 1995) .............. 12
Table 4. Component properties ......................................................................................... 25
Table 5. Loads for circular pile cases ............................................................................... 36
Table 6. Loads for square pile cases ................................................................................. 36
Table 7. Loads for H-pile cases ........................................................................................ 36
Table 8. Properties of bearing pads under study from Robinson et al (2007) .................. 39
Table 9. Full scale test configurations modeled in FB-MultiPier ..................................... 69
Table 10. Moment of inertia of sections modeled in FB-MultiPier .................................. 73
Table 11. Axial stiffness of full scale foundation elements .............................................. 73
Table 12. Inputted FB-MultiPier data ............................................................................... 74
Table 13. Inputted FB-MultiPier bearing pad stiffness (compression and shear) ............ 74
Table 14. Inputted FB-MultiPier rotational stiffness parameters ..................................... 75
Table 15. FB-MultiPier experimental full scale test results ............................................. 77
Table 16. Equivalent spring stiffness for FB-MultiPier single pile analysis .................... 79
Table 17. Single pile FB-MultiPier results with assumed equivalent stiffness ................ 80
Table 18. FB-MultiPier single pile test results matched to actual test results .................. 81
Table 19. Comparison FB-MultiPier single pile analysis of assumed length effect ......... 83
Table 20. Halifax County FB-MultiPier single pile results of pile cap fixity................... 89
Table 21. Halifax County equivalent length of pile to a depth of fixity ........................... 91
Table 22. Wake County FB-MultiPier single pile results of pile cap fixity ..................... 97
Table 23. Wake County equivalent length of pile to a depth of fixity .............................. 99
Table 24. Robeson County FB-MultiPier single pile results of pile cap fixity ............... 105
Table 25. Robeson County equivalent length of pile to a depth of fixity ....................... 108
Table 26. Input variables for Halifax County bridge section.......................................... 117
Table 27. Results from joint closure investigation for Halifax County Bridge .............. 118
Table 28. Results from simulation assuming essentially free torsion ............................. 118
Table 29. Results from determined required joint thickness for failure due to joint closure
......................................................................................................................................... 119
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LIST OF FIGURES
Figure 1a.) Non-linear soil-pile model b.) Equivalent system model ................................ 7
Figure 2. Equivalent model parameters (from Robinson et al, 2006) ............................... 15
Figure 3. Forces and moments for finite element analysis of bearing pads (from Yazdani
et al, 2000) ........................................................................................................................ 19
Figure 4. Wake County Bridge ......................................................................................... 21
Figure 5. Section of bridge ............................................................................................... 22
Figure 6. Model of test assembly ..................................................................................... 23
Figure 7. Test setup model ............................................................................................... 24
Figure 8. Longitudinal cross section model of connection elements ............................... 25
Figure 9. Flipping of AASHTO girder ............................................................................. 26
Figure 10. Bridge deck casting bed ................................................................................... 27
Figure 11. Reinforcement of diaphragm connection ........................................................ 27
Figure 12. Completed cast of superstructure section ........................................................ 28
Figure 13. Side profile of completed cast of superstructure section ................................. 28
Figure 14. Support block steel reinforcement cage .......................................................... 29
Figure 15. Casting of support blocks ................................................................................ 29
Figure 16. Placement of support blocks ............................................................................ 30
Figure 17. Pinned connection of superstructure ............................................................... 30
Figure 18. Cross sections of piles ..................................................................................... 31
Figure 19. Completion of pile cap pour ............................................................................ 31
Figure 20. Casting of concrete piles ................................................................................. 32
Figure 21. Test setup for circular pile ............................................................................... 33
Figure 22. Illustration of instrumentation positioning ..................................................... 34
Figure 23. Illustration of loading scheme ......................................................................... 35
Figure 24. Elastic cycle lateral loading history ................................................................. 37
Figure 25. Ductility cycle lateral loading history ............................................................. 38
Figure 26. Flexural cracks produced in the square pile .................................................... 41
Figure 27. Visible gap between pile cap and bearing pad ................................................ 42
Figure 28. Shear deformation of the type VI bearing pad ................................................ 43
Figure 29. Pullout of embedded plate in girder ................................................................ 44
Figure 30. Detailed design of embedded plate (from Halifax County Bridge plans) ....... 45
Figure 31a.) and b.) Concrete cracking in the diaphragm under the pile cap ................... 46
Figure 32. Cracks in diaphragm from pullout of embedment plate .................................. 47
Figure 33. Bending of sole plate ....................................................................................... 48
Figure 34. Significant cracking in the pile cap ................................................................. 49
Figure 35. Rotation of the H-pile independent of the pile cap.......................................... 50
Figure 36. Prying of the H-pile in the pile cap ................................................................. 51
Figure 37. Cracks in the pile cap along the adjacent side of loading ................................ 51
Figure 38. Gaps generated between sole plate / cap beam and bearing pad ..................... 52
Figure 39. Components of contributing pile top displacement ......................................... 53
Figure 40. Top displacement components ........................................................................ 54
Figure 41. Measured vs calculated top displacement ....................................................... 55
Figure 42. Pie chart of pile top displacement component percentages ............................. 56
Figure 43. Square pile/BP V: cap moment vs. cap rotation .............................................. 57
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Figure 44. Square pile/BP VI: cap moment vs. cap rotation ............................................ 57
Figure 45. Circular pile/BP V: cap moment vs. cap rotation ............................................ 58
Figure 46. Circular pile/BP VI: cap moment vs. cap rotation .......................................... 58
Figure 47. HP/BP V: cap moment vs. cap rotation ........................................................... 59
Figure 48. HP/BP VI: cap moment vs. cap rotation ......................................................... 59
Figure 49. Secant stiffness of square pile / BP V (pushing direction) .............................. 60
Figure 50. Secant stiffness of square pile /BPV (pulling direction) ................................. 61
Figure 51. Secant stiffness of square pile / BPVI (pushing direction) .............................. 61
Figure 52. Secant stiffness of square pile / BPVI (pulling direction) ............................... 62
Figure 53. Secant stiffness of circular pile / BP V (pushing direction) ............................ 62
Figure 54. Secant stiffness of circular pile/ BP V (pulling direction) .............................. 63
Figure 55. Secant stiffness of circular pile/ BP VI (pushing direction) ............................ 63
Figure 56. Secant stiffness of circular pile / BP VI (pulling direction) ............................ 64
Figure 57. Secant stiffness of H-pile / BP V (pushing direction) ..................................... 64
Figure 58. Secant stiffness of H-pile / BP V (pulling direction) ...................................... 65
Figure 59. Secant stiffness of H-pile/ BP VI (pushing direction) ..................................... 65
Figure 60. Secant stiffness of H-pile/ BP VI (pulling direction) ...................................... 66
Figure 61. FB-MultiPier model of the full scale test on a circular foundation element ... 70
Figure 62. Equivalent cracked moment of inertia for circular columns ........................... 71
Figure 63. Equivalent cracked moment of inertia for square columns ............................. 72
Figure 64. FB-MultiPier experimental full scale test moment results on circular drilled
shaft ................................................................................................................................... 76
Figure 65. FB-MultiPier experimental full scale test displacement results on circular
drilled shaft ....................................................................................................................... 76
Figure 66. FB-MultiPier model of single pile analysis of full scale test of the H-pile ..... 79
Figure 67. Illustration of Halifax County interior bent modeled in FB-MultiPier ........... 85
Figure 68. FB-MultiPier soil profile for the Halifax County interior bent ....................... 86
Figure 69. FB-MultiPier single pile model for Halifax County interior bent pile ............ 88
Figure 70. Halifax FB-MultiPier single pile moment response ........................................ 89
Figure 71. Halifax FB-MultiPier single pile displacement response ................................ 90
Figure 72. Halifax County single pile rotational stiffness effect on equivalent depth to
fixity .................................................................................................................................. 92
Figure 73. Concluding equivalent depth to fixity range for Halifax County pile ............. 93
Figure 74. Illustration of Wake County interior bent modeled in FB-MultiPier .............. 94
Figure 75. FB-MultiPier soil profile for the Wake County interior bent .......................... 95
Figure 76. FB-MultiPier single pile model for Wake County interior bent pile ............... 96
Figure 77. Wake County FB-MultiPier single pile moment response .............................. 97
Figure 78. Wake County FB-MultiPier single pile displacement response ...................... 98
Figure 79. Wake County single pile rotational stiffness effect on equivalent depth to
fixity ................................................................................................................................ 100
Figure 80. Concluding equivalent depth to fixity range for Wake County foundation
element ............................................................................................................................ 101
Figure 81. Illustration of Robeson County interior bent modeled in FB-MultiPier ....... 102
Figure 82. FB-MultiPier soil profile for the Robeson County interior bent ................... 103
Figure 83. FB-MultiPier single pile model for Robeson County interior bent pile ........ 104
Figure 84. Robeson County FB-MultiPier single pile moment response ....................... 105
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Figure 85. Robeson County FB-MultiPier single pile moment response enlarged ........ 106
Figure 86. Robeson County FB-MultiPier single pile displacement response ............... 106
Figure 87. Robeson County FB-MultiPier single pile displacement response enlarged 107
Figure 88. Robeson County single pile rotational stiffness effect on equivalent depth to
fixity ................................................................................................................................ 109
Figure 89. Concluding equivalent depth to fixity range for Robeson County H-pile ..... 110
Figure 90. Joint closure model for 3 spans supported by 2 interior pile bents at the
expansion joints (Robinson et al, 2006) .......................................................................... 112
Figure 91. Halifax County Bridge bent response to lateral load (Robinson 2007) ......... 116
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LIST OF EQUATIONS
Equation 1 (Davisson and Robinson, 1965)
25.
4.1
c
pyp
fE
IEL , clay ............................. 8
Equation 2 (Davisson and Robinson, 1965)
20.
8.1
h
pyp
fn
IEL , sand ........................... 8
Equation 3 Ys = Lc(.5 - .404x + .434x2 - .160x
3) 0 ≤ x < 1.25 ................................. 10
Equation 4 Ys = .36Lc 1.25 ≤ x ≤ 4 ....................................................................... 10
Equation 5 Ym = Lc(.6 - .737x + 1.048x2 - .701x
3 + .174x
4) 0 ≤ x ≤ 1.5 .................... 10
Equation 6 Ym = .37Lc 1.5 < x ≤ 4 .......................................................................... 10
Equation 7 Yb = Lc(1.13 - 1.41x + .856x2 - .17x
3) 0 ≤ x ≤ 2 .................................... 10
Equation 8 Yb = .37Lc 2 < x ≤ 4 .............................................................................. 10
Equation 9 Ys = Lc(.4 - .101x + .057x2) 0 ≤ x ≤ .5 .................................................. 10
Equation 10 Ys = .35Lc .5 < x ≤ 4 ............................................................................. 10
Equation 11 Ym = Lc(.76 - .7x + 1.03x2 - .68x
3 + .16x
4) 0 ≤ x ≤ 1.25 ......................... 10
Equation 12 Ym = .56Lc 1.25 ≤ x ≤ 4 ........................................................................ 10
Equation 13 Yb = Lc(.8 – 1.53x + 2.34x2 – 1.84x
3 + .71x
4 -.106x
5) 0 ≤ x ≤ 1.5 ........... 11
Equation 14 Yb = .35Lc 1.5 < x ≤ 4 ........................................................................... 11
Equation 15
25.
4
e
pyp
ck
IEL ..................................................................................... 11
Equation 16 4
0BLAke ........................................................................................... 11
Equation 17 V
MLe
max .......................................................................................... 15
Equation 18 𝛼 =𝐿𝑒
3𝑉
3𝐸𝑝𝐼𝑝 ∆𝑡 ............................................................................................ 15
Equation 19 V
MLe
max2 ........................................................................................ 16
Equation 20 𝛼 = 𝐿𝑒
3𝑉
12𝐸𝑝𝐼𝑝 ∆𝑡 ......................................................................................... 16
Equation 21 WLh
LWS
ri
2 ...................................................................................... 18
Equation 22 26GSEc .............................................................................................. 18
Equation 23 Ry
yyc
Ry
M
H
IEk
................................................................................... 18
Equation 24 𝑘𝑎 =𝐸𝐴
𝐿 .................................................................................................... 87
Equation 25
Kr
L
EI
Lw
LLTj
P
22
2
2)(
max2
......................................................... 113
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Equation 26 1
maxmax
3
max 23
K
P
Kr
LP
EI
LPtot ................................................. 113
Equation 27 totKPFL *2max ..................................................................... 113
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CHAPTER 1: INTRODUCTION
1.1 Problem Description
Many bridges are currently supported by drilled shafts. Such bents consist of foundation
elements (piles or drilled shafts) connected at the top by a continuous cap beam. Often
the girders from the bridge assembly are connected to the cap of the substructure through
various bearing materials. Lateral loads applied to a bridge create moment that is
transferred from the bridge deck through the bearing connection into the foundation
members and the ground. However, the contribution that these bearing materials,
between the girder and the cap have towards reducing the moment transferred through the
connection assembly is not entirely known.
Current North Carolina Department of Transportation (NC DOT) practice for designing
drilled shafts starts with a computer software program called Georgia Pier (Georgia DOT,
1994). Single piles are analyzed under lateral loading to determine their appropriate
design length and point of fixity. Under buckling analysis, a conservative K-factor of 1.9
to 2.1 is assumed (free head conditions) to model the connection between the super and
substructure. The K-factor is a constant that models the magnitude of rotation at the top
of a pile or drilled shaft which directly affects the assumed location of the point of fixity.
Furthermore, the change in the location of the point of fixity will alter the overall design
pile length. It is therefore important to be able to quantify and incorporate the effects of
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the connection of the super and substructure to more accurately predict and design the
behavior of a bridge’s structural components.
1.2 Objective
The work is focused on the use of elastomeric bearing pads as a bearing material between
the bridge girders and pile cap with its objective being to determine the rotational
stiffness and capacity of bearing pads usually used in a bridge assembly. Once defined,
this information was incorporated into the design of the foundation elements by defining
the degree of rotation at the top of the foundation (instead of the free or fixed
assumptions commonly used). Then, the impact of a specified degree of rotation,
compatible with moment transfer through the bearing pad, on the design length of the
foundation element was developed.
1.3 Approach
1.3.1 Full scale testing
In order to accurately determine the behavior of the elastomeric bearing pads in a bridge
connection full scale testing was performed on bridge elements reconstructed in the
laboratory. The section of a bridge was constructed using current NC DOT design
specifications. The test components allowed for the reproduction and control of lateral
and axial loads transferred through a super to substructure connection. Field loads were
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replicated in the laboratory testing, measurement, and evaluation of the rotational
behavior. Moment transfer through elastomeric bearings was also conducted.
1.3.2 Florida-Pier Computer Modeling
Once the rotational stiffness and limitations of the bearing pad had been measured, a
modeling effort was performed using the laboratory data with the focus being depth to
point of fixity. Using the FB- MultiPier program, current bridge designs were modeled
and compared with the incorporated behavior of the elastomeric bearing pad to determine
its significance in the assessment of point of fixity and the overall foundation length.
1.4 Scope
In order to investigate the significance of the elastomeric bearing pad’s contribution to
the determination of the substructure response of bridges, various tasks were
accomplished. The following is an outline of the project report scope.
1.4.1 Literature Review
A literature review of current design methods for determining the point of fixity of a pile
and the impact of elastomeric bearing pads was conducted. This included current
assumptions made for the design of the super to sub structure connection, and the
properties of the bearing pad that effect the response of the foundation elements.
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1.4.2 Experimental Program
The experimental program covers the full scale testing design and protocol. This
includes the construction and modeling of a section of a bridge for various loading cases
and the different measurements taken from the test.
1.4.3 Load Transfer Mechanisms
The measured results from the full scale tests are presented. The focus is on the
contributing displacement of the rotation of the girder to foundation cap joint. This
section also includes the behavior of the elastomeric bearing pad and the rotational
stiffness of the pile connection.
1.4.4 Florida-Mulitipier Modeling
Measured responses from the full scale tests were replicated through the use of the
Florida-Multipier Program. Accordingly, the contribution of the rotational stiffness of
the elastomeric bearing pad was implemented into the case study analysis and compared
to previous design results.
1.4.5 Design Limit States
Limit states from previous literature will be presented from Robinson et al (2006) and the
level of impact that the rotational stiffness plays within these limit states analyzed.
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1.4.6 Summary and Conclusions
The measured rotational stiffness of the elastomeric bearing pad and the impact of such
stiffness on the pile and drilled shaft foundations are presented and discussed.
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CHAPTER 2: LITERATURE REVIEW
2.1 Introduction
The following literature review begins by analyzing current pile length design and
assumptions. The majority of the analysis of the literature on current design practice
comes from ―Assessment on pile effective length and their effect on design-I.
Assessment‖ by Y. Chen (1995) and ―Pile Length Design Criteria‖ (Robinson et al,
2006). Current literature on the performance of elastomeric bearing pads as a load
transfer mechanism will also be presented.
2.2 Current Design
Current practice of the NC DOT pile design according to (Robinson et al, 2006) can be
summarized by the following procedure.
The initial design begins with the analysis of a given soil profile and known information
about a pile’s capacity, installation techniques and typical displacement limits. From this
set of information the geotechnical group determines preliminary pile lengths and runs
single pile load test in lateral pile analysis software such as LPILE (Ensoft, 2004). For
most cases, a deflection limit of one inch is assigned to the pile top. The software results
of the pile’s moment and deflection along its lengths are investigated where a ―point of
fixity‖ is determined by the depth at which the maximum negative moment is
experienced or where there is a maximum negative deflection. Once informed of the
depth to fixity and pile type information, the structural group can then analyze the
foundation element as a frame.
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2.2.1 Y. Chen (1995) and (Davisson and Robinson, 1965)
In Chen’s 1995 technical paper, ―Assessment on pile effective length and their effect on
design-I. Assessment‖, he presents Davisson and Robinson’s 1965 simplified method for
determining a pile’s point of fixity as well as his own approximate method. Davisson and
Robinson’s method will be presented first, followed by Chen’s approximate method.
Then a comparison between Chen’s approximate method and Davison and Robinson’s
method will be discussed.
Davisson and Robinson proposed a simplified method based on the equivalent beam
model for calculating the point of fixity of a foundation element. Their proposed method
is also known as AASHTO’s LRFD method. This approach assumes that an embedded
foundation element with a non-linear soil reaction can be estimated as a single
homogeneous layer of sand or clay. Figure 1 illustrates this simplification.
Figure 1a.) Non-linear soil-pile model b.) Equivalent system model
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Where,
Le = Total pile equivalent length
Lf = Depth below ground to a ―point of fixity‖
Lu = unbraced pile length
From the equivalent system model in Figure 1 b.), two equations were developed based
on beam-on-elastic-foundation theory to determine the depth to point of fixity for sands
and for clays. The equation for clays is displayed in Equation 1, while the equation for
sands is displayed in Equation 2.
Equation 1 (Davisson and Robinson, 1965)
25.
4.1
c
pyp
fE
IEL , clay
Equation 2 (Davisson and Robinson, 1965)
20.
8.1
h
pyp
fn
IEL , sand
Where,
Ep = Elastic modulus of the pile (tsf)
Ipy = Moment of inertia about weak axis (ft4)
Ec = Elastic modulus of the clay (tsf)
nh = Rate of increase of elastic soil modulus with depth for sand (tsf-ft-1
)
Table 1 presents values of nh found in Chen (1995) to be used in for Davisson and
Robinsons, 1965 method.
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Table 1. Values of nh for sands (from Chen, 1995)
Sand
Type
Saturated
Condition nh (tsf/ft)
Loose Moist / Dry 30
Submerged 15
Medium Moist / Dry 80
Submerged 40
Dense Moist / Dry 200
Submerged 100
Davisson and Robinson’s method for determining the point of fixity of a foundation
element is easy to use, but does not take into account many factors which include the
following.
The effect of horizontal soil stiffness
The degree of fixity of the pile head
A distinction between buckling and bending analyses
In Chen’s paper, he proposed a method that would include the factors that Davission and
Robinson’s method excluded for determining the depth of fixity. Chen’s proposed
method is an approximation of the analytical solution presented in Greimann et al (1987).
In his paper, Chen presents formulas for determining the depth to fixity for both a fixed
top head condition and a pinned head connection. Each pile head connection type
considers a depth to fixity based on the horizontal soil stiffness, bending of the pile, and
buckling of a pile. From these three depths, the largest and most conservative depth is
taken as the depth to fixity.
The following equations are from Chen (1995) for determining the depth to fixity for a
fixed head connection.
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For horizontal soil stiffness:
Equation 3 Ys = Lc(.5 - .404x + .434x2 - .160x
3) 0 ≤ x < 1.25
Equation 4 Ys = .36Lc 1.25 ≤ x ≤ 4
For pile bending:
Equation 5 Ym = Lc(.6 - .737x + 1.048x2 - .701x
3 + .174x
4) 0 ≤ x ≤ 1.5
Equation 6 Ym = .37Lc 1.5 < x ≤ 4
For pile buckling:
Equation 7 Yb = Lc(1.13 - 1.41x + .856x2 - .17x
3) 0 ≤ x ≤ 2
Equation 8 Yb = .37Lc 2 < x ≤ 4
The following equations are from Chen (1995) for determining the depth to fixity for a
pinned head connection.
For horizontal soil stiffness:
Equation 9 Ys = Lc(.4 - .101x + .057x2) 0 ≤ x ≤ .5
Equation 10 Ys = .35Lc .5 < x ≤ 4
For bending moment:
Equation 11 Ym = Lc(.76 - .7x + 1.03x2 - .68x
3 + .16x
4) 0 ≤ x ≤ 1.25
Equation 12 Ym = .56Lc 1.25 ≤ x ≤ 4
For pile buckling:
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11
Equation 13 Yb = Lc(.8 – 1.53x + 2.34x2 – 1.84x
3 + .71x
4 -.106x
5) 0 ≤ x ≤ 1.5
Equation 14 Yb = .35Lc 1.5 < x ≤ 4
Additional important equations include the following.
Equation 15
25.
4
e
pyp
ck
IEL
Equation 16 4
0BLAke
Where,
A and B are constants depending on the soil
ke = effective horizontal soil stiffness
L0 = active pile length in bending (≈ .5 Lc)
Lc = pile length at which the pile behaves flexibly
Lfs = depth to fixity based on horizontal stiffness
Lfm = depth to fixity based on bending moment
Lfb = depth to fixity based on buckling
x = length ratio defined as (Lu/Lc)
Ys = length ratio defined as (Lfs/Lc)
Ym = length ratio defined as (Lfm/Lc)
Yb = length ratio defined as (Lfb/Lc)
Chen compared the LRFD method (Davisson and Robinson, 1965) results with his
proposed method for both the fixed and pinned head connections. Table 2 and Table 3
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12
show the results of the comparison for the fixed and pinned head connections of piles
using the bending moment and buckling methods of Chen.
Table 2. Comparison of Lf values for fixed head piles (from Chen, 1995)
Soil Wetness
(Equations for bending
moment) / LRFD Method
(Equations for buckling) /
LRFD Method
Loose Sand Moist/Dry 1.57-1.70 2.24-2.85
Submerged 1.37-1.48 1.95-2.48
Medium Sand Moist/Dry 1.45-1.56 1.84-2.44
Submerged 1.27-1.36 1.61-2.12
Dense Sand Moist/Dry 1.41-1.49 1.61-2.17
Submerged 1.23-1.30 1.40-1.89
Soft Clay --- 1.04-1.06 1.04-1.26
Medium Clay --- 0.84-0.87 0.84-0.88
Stiff Clay --- 0.84-0.87 0.84-0.87
Very Stiff Clay --- 0.63-0.67 0.63-0.67
Table 3. Comparison of Lf values for pinned head piles (from Chen, 1995)
Soil Wetness
(Equations for
bending
moment) /
LRFD Method
(Equations for
buckling) /
LRFD
Method
Loose Sand Moist/Dry 2.25-2.36 1.61-1.87
Submerged 1.96-2.05 1.40-1.62
Medium Sand Moist/Dry 2.11-2.19 1.45-1.64
Submerged 1.84-1.91 1.26-1.43
Dense Sand Moist/Dry 2.07-2.13 1.38-1.53
Submerged 1.80-1.85 1.20-1.33
Soft Clay --- 1.54-1.58 0.95-1.04
Medium Clay --- 1.27-1.31 0.75-0.82
Stiff Clay --- 1.26-1.31 0.74-0.82
Very Stiff Clay --- 0.95-1.01 0.59-0.63
It can be observed through these comparisons that there is a larger difference between the
LRFD method and Chen’s method for the bending moment method for a pinned head
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pile. However, there is a greater divide between the two methods when comparing
Chen’s buckling method for the fixed head condition.
The two methods do share some results for certain situations such as the bending method
for a fixed head pile in soft clay. Also, for a pinned head pile, almost identical point of
fixities are generated for a pile in very stiff clay when comparing Chen’s bending
moment method to the LRFD method and for a pile in soft clay using Chen’s buckling
method. The largest difference between the LRFD method and Chen’s proposed
buckling method occurs when the two methods are compared for piles in loose sand for a
fixed head pile (2.24-2.85) and for very stiff clay for a pinned head pile (.59-.63).
2.2.2 Pile Bent Design Criteria (Robinson et al, 2006)
In ―Pile Bent Design Criteria‖ by Robinson et al (2006), the LRFD method is presented
along with its own method for determining the point of fixity of a foundation element.
This alternative design method comes from an investigation of current NC DOT design
practice where the method for determining the point of fixity by an equivalent system
does not match the results from a nonlinear soil-pile system (Robinson et al, 2006). The
equivalent system method presented in Robinson et al (2006) provides an equivalent
length for a pile foundation based on the shear and maximum moment for a nonlinear
soil-pile reaction with fixed and free head conditions. Figure 2 shows the equivalent
system model proposed for a nonlinear soil-pile interaction with both a fixed and free
head. The process begins by evaluating a nonlinear soil-pile interaction program through
a computer program such as FB-MultiPier (BSI). From the computer output, the
inflection points of the deflected pile shape as well as the maximum moment and top
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14
deflection are determined. Knowing the applied lateral load and the maximum moment
generated along the pile, an equivalent length is then determined from a model that
assumes either a fixed or free head condition which will produce the same maximum
moment and top pile deflection. The equivalent length is then modeled in a frame
analysis and sent to the structural unit. The suggested equivalent length (Le) developed
by Robinson et al (2006) for a pile fixed at a certain depth is presented in Equation 17
and Equation 19. The coefficient alpha (α) was also introduced by Robinson et al (2006)
for a fixed and free head pile which when multiplied by the moment of inertia of the pile,
produces an equivalent moment of inertia that yields the same displacements as the
nonlinear model at the pile top.
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Figure 2. Equivalent model parameters (from Robinson et al, 2006)
Free head pile:
Equation 17 V
MLe
max
Equation 18 𝜶 = 𝑳𝒆𝟑𝑽
𝟑𝑬𝒑𝑰𝒑∆𝒕
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Fixed head pile:
Equation 19 V
MLe
max2
Equation 20 𝜶 = 𝑳𝒆𝟑𝑽
𝟏𝟐𝑬𝒑𝑰𝒑∆𝒕
Where from Robinson et al (2006),
Lb = Effective length for a stability (buckling) check of the pile. It is taken from the
moment diagram in the nonlinear soil-pile model between the top of the pile and
the
first point of zero moment (inflection point).
Le = The length of a pile fixed at the base that will develop the same maximum
moment,
Mmax, as in the nonlinear soil-pile model under the application of the lateral load V
at the top.
Mmax= Maximum moment developed in both the equivalent model and the nonlinear soil-
pile
model.
V = Lateral force applied at the top of the pile in both the equivalent model and the
nonlinear soil-pile model.
α = Inertia reduction factor that will produce the same lateral stiffness of the non-
linear soil- pile model when multiplied by the moment of inertia of the pile, Ip
Ep = Elastic modulus of the pile
Ip = Moment of inertia of the pile
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17
Δt = deflection at top of pile
The depth to fixity can now be easily determined by subtracting the known length of the
pile extending above ground from the equivalent length calculated. Also presented in
Robinson et al (2006) are case studies for various bridges where the proposed method
was used to determine the equivalent length assuming a free and fixed head condition.
This information and the parameters mentioned will be further analyzed in chapter 5.
2.3 Elastomeric Bearing Pad
Bridge girders are often supported by elastomeric bearing pads. The use of elastomeric
bearing pads as a support mechanism can help distribute loads down to the superstructure
and affect the rotational stiffness connection of the super to sub structure. In ―Validation
of AASHTO Bearing Stiffness for Standard Precast Concrete Bridge Girders‖, Yazdani et
al (2000) presents theoretical properties and the behavior of elastomeric bearing pads.
The goal of their investigation was to gain insight on how the elastomeric bearing pad
stiffness contributed to its performance as a bearing material. ―AASHTO states that the
forces imposed by the end bearing on the substructure are a function of the stiffness of
the bearing and the flexibility of the substructure, and that such forces shall be
incorporated into the design of substructure components (Yazdani et al, 2000).‖
Therefore it is important that the behavior of the elastomeric bearing pad’s stiffness be
further investigated in order to be more accurately incorporated into the design process.
In Yazdani’s work, various equations are presented for determining the compressive,
shear and rotational stiffness of the elastomeric bearing pad based on the shear and elastic
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modulus. The AASHTO standard is to determine a shape factor (S) for a single elastomer
layer and in conjunction with a known shear modulus (G), determine an effective
compressive modulus (Ec). Equation 21 – Equation 23 are from Yazdani et al (2000)
where and illustration of the elastomeric bearing pad under study is in Figure 3.
Equation 21 WLh
LWS
ri
2
Equation 22 26GSEc
Equation 23 Ry
yyc
Ry
M
H
IEk
Where,
S = Shape factor
L = Length of bearing pad (long dimension)
W = Width of bearing pad (short dimension)
hri = Thickness of one elastomer layer
H = Total thickness of the bearing pad
Ec = Elastic Compressive Modulus of the bearing pad
G = Shear Modulus
Iy = Moment of Inertia about the y axis
My = Moment about the y axis
∆Ry = Change in rotation
kRy = Rotational stiffness about the y axis
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Figure 3. Forces and moments for finite element analysis of bearing pads (from
Yazdani et al, 2000)
2.4 Summary and Conclusions
From analyzing previous literature, current design methods include an equivalent model
to represent a nonlinear soil-pile interaction to determine the depth to fixity. These
equivalent models attempt to incorporate multiple soil layers, the effects of the bending
moment and buckling, as well as pile head condition. However, the connection between
a bridge girder and a pile cap with an elastomeric bearing pad is neither a pinned, fixed,
nor a free head condition. Therefore it is important to know the rotational stiffness of the
pile head when it is connected to the superstructure through an elastomeric bearing pad.
This connection rotational stiffness is directly related to the rotational stiffness of the
elastomeric bearing pad and connection components. Yazdani et al (2000) presents a
method for determining the rotational stiffness of the elastomeric bearing pad but the
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rotational stiffness of the entire connection component is not entirely known or
implemented into design practice.
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21
CHAPTER 3: EXPERIMENTAL PROGRAM
3.1 Experimental Design
Full scale laboratory tests were performed to simulate the current North Carolina
Department of Transportation practice for bridge to pile connections. The testing
program was proposed to model a section of a bridge including the load transfer
connection from a bridge deck to the pile foundation. Figure 4 shows the underside of the
Wake County bridge while Figure 5 is a section from the bridge to be modeled in the
testing. The Wake County bridge consisted of 17 AASHTO Type IV girders across the
transverse direction. The girders were connected in the longitudinal direction by a
concrete diaphragm and Type V elastomeric bearing pads were used as bearing surface.
The substructure consisted of a continuous cap beam with interior bents consisting of
seven drilled shafts. The drilled shafts were 4.5 feet (1.372 meters) in diameter and were
spaced at 21.3 feet (6.5 meters) on center.
Figure 4. Wake County Bridge
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Figure 5. Section of bridge
The tested section was modeled after the configuration shown in Figure 5 where one
girder assembly is supported by a pile cap with the loads of interest in the axial and
longitudinal directions. Figure 6 is an inverted model of the bridge section as tested in
the laboratory. Such inversion was necessary in order to test the bridge section in a
laboratory setting.
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Figure 6. Model of test assembly
A profile view and dimensions of the test set up are shown in Figure 7. In this case, the
steel frame support and bracing (part 1) to support the 220 kip actuator (part 2) which
provides lateral loading are visible. The actuator was bolted to the top of the pile while a
hydraulic 60 ton jack (part 3) was designed to tension a steel dywidag bar that ran
through the middle of the pile providing simulated axial pile loading. Also, four
hydraulic 60 ton jacks (part 4) were positioned over a steel HHS beam to provide
independent loading to the pile cap connection to the superstructure. The supports of the
test setup as indicated in Figure 7 (part 6) were constructed as concrete blocks which
were stressed to the floor and supported the structure by 7 foot long, 5 inch diameter steel
pins.
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Figure 7. Test setup model
1: Steel Frame
2: Actuator to apply horizontal load
3: 60 ton hydraulic jack applying axial pile load
4: 60 ton hydraulic jacks applying axial bearing pad load
5: HSS steel beam to distribute bearing pad axial load
6: Support blocks
The superstructure testing sample was constructed of two AASHTO girders joined by a
diaphragm assembly with a continuous bridge deck slab. A side view of the different
connection elements in the orientation that would be seen in the field is presented in
Figure 8.
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Figure 8. Longitudinal cross section model of connection elements
Table 4. Component properties
E I
Components ksi kN/cm^2 in^4 cm^4
Girder/Slab 3824 2637 147015 6119226
Steel Anchor bolts 29000 20003 3.14 131
Steel Sole Plates 29000 20003 4.23 176
For this test the girder/deck slab was constructed separately as described below with two
steel embedded plates at the end where the diaphragm joins the two girders. At the
location of the two embedded plates, the sole plates were welded with 16 inch (40.64cm)
welds on either side to secure them to the embedded plates. Four anchor bolts were cast
12 inches (30.48cm) in to the pile cap with 8 inches (20.32cm) exposed. Two bearing
pads were placed on the inverted girder/deck slab assembly directly over the center of
each sole plate. The inverted pile and pile cap were then placed over the bearing pads
allowing the exposed anchor bolts to pass through the holes in the sole plates,
sandwiching the bearing pads. To secure the section, nuts were attached and tightened.
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26
This test setup was chosen in order to model the load transferred from the bridge deck to
foundation elements.
3.2 Construction of Test Sample Elements
Construction and testing was performed at the Constructed Facilities Laboratory (CFL) at
North Carolina State University. The assembly of the test setup began with the
construction of the superstructure section of the sample. Two, 30 foot (9.14m) AASHTO
type II girders were delivered by the NC DOT to the CFL as shown in Figure 9. The
girders were then inverted and placed over the casting bed for the steel reinforced bridge
deck section.
Figure 9. Flipping of AASHTO girder
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Figure 10. Bridge deck casting bed
After the girders were inserted over the bridge deck casting bed, the steel reinforcement
for the diaphragm connection and the diaphragm and bridge deck were cast in place as
shown in Figure 9 and Figure 12.
Figure 11. Reinforcement of diaphragm connection
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Figure 12. Completed cast of superstructure section
Figure 13. Side profile of completed cast of superstructure section
Two concrete support blocks were used to provide the pinned connection of the
superstructure system. The support blocks were placed on either side of the bridge section
at each end and were designed in an L shape to reduce cost. Figure 14 shows the steel
reinforcement and foam inserts (which would later be chipped out to allow the support
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blocks to be tied to the floor of the CFL). Figure 14 shows the casting of the concrete
blocks. The two blocks were tied down to the strong floor at the CFL using 60 ton
hydraulic jacks.
Figure 14. Support block steel reinforcement cage
Figure 15. Casting of support blocks
Figure 16 and Figure 16 show the blocks in place providing support, through pin
connection, to the bridge girders.
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Figure 16. Placement of support blocks
Figure 17. Pinned connection of superstructure
After completion of the superstructure components assembly, the substructure elements
were constructed. The substructure elements included a steel reinforced circular concrete
pile (18 inch diameter), steel reinforced square concrete pile (20 x 20 inch), and a steel H-
Pile (12 x 63). Figure 18 shows the cross sections of the different piles.
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Figure 18. Cross sections of piles
The test piles and pile caps were cast together through two vertical concrete pour
segments. Anchor bolt studs were placed in the pile cap per NC DOT specifications. The
piles were cast vertically where the first concrete pour was for the pile caps and the
second for the two concrete piles. Figure 19 and Figure 19 show the casting operation for
the concrete test piles.
Figure 19. Completion of pile cap pour
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Figure 20. Casting of concrete piles
Once the test sample members had been constructed, sole plates were welded onto the
girders’ embedded plates using ¾ inch thick, 16 inch long welds. The bearing pads were
then placed over the sole plates and a test pile was bolted to the sole plate. Before lateral
load was applied using a computer controlled hydraulic actuator, the reaction frame was
erected with appropriate bracing and was bolted to the top of the pile. A 2.5 foot by 2.5
foot by 2.5 foot box was additionally cast on the top of the circular pile in order to
provide the necessary connection between the pile and the loading actuator. The final
assembly of the test sample with the circular pile is shown in Figure 21.
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Figure 21. Test setup for circular pile
3.3 Instrumentations and Testing Protocol
A total of 53 sensors were used in the test setup to measure different parameters. Figure
22 illustrates the positioning of the different instrumentation. Load cells which were
placed under the hydraulic jacks provided measurements of axial load to the pile, and to
the bearing pads (LC1 through LC3). Clinometers were used to measure the rotation of
the top of the pile, the pile cap, and the girder (Clin-1 through Clin-3). Strain gages were
placed on either side of each pile, on the longitudinal steel reinforcement for the concrete
pile and directly on the H-Pile flanges (SG1 through SG12). Linear displacement pots
were positioned along the length of the pile to determine the curvature with loading (P9
through P12) while various linear pots measured the compression, shear and translation
deformation of the two bearing pads under loading (see bearing pad detail). String pots
were also located at the top of the pile to measure the displacement of the pile and
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possible translation (SP1, SP12, SP8) as well as the lateral movement of the pile cap (SP9
and SP11) and the potential deflection of the girder (SP2, SP4, SP5, SP7, SP13, SP15).
Figure 22. Illustration of instrumentation positioning
The testing included combinations of varying axial load and lateral load to the three piles
with two different elastomeric bearing pads used during testing. Each pile was tested in
configuration with the type V and type VI elastomeric bearing pads which were
previously tested individually in shear and compression modes. The circular and square
piles were tested under three axial load ratios (ALR). For each ALR, three different
―bearing pad‖ axial loads (P) were applied (axial loads were applied independently to
pads). For the steel H-Pile, axial loads were only applied on each set of bearing pads
(and not on the pile). Figure 23 illustrates the different tests for each pile. For each of
these tests, lateral loading cycles were applied until yielding of the steel occurred (elastic
cycles). In addition, one set of lateral loading cycles was applied past yield until system
SP 15 SP 5 SP 7
SP 13
CLIN-1
CLIN-2
LC 1 CLIN-3
SP 9 (TOP CAP BEAM ,CENTER) SP 11 (BOTTOM CAP BEAM, CENTER)
SP 1 (COLUMN TOP, CENTER) SP 12 (COLUMN, CENTER) PARALLEL TO EACH OTHER
SP 8 (COLUMN TOP, CENTER) (TRANSVERSE DIRECTION, CENTER)
SP 4 SP 2
P 14 P 10 P 11 P 12
P 9 P 13 P 15 P 16
SG7 SG8 SG9 SG10 SG11 SG12
SG1 SG2 SG3 SG4 SG5 SG6
LC2 LC3
TOTAL NUMBER OF INSTRUMENTS:
MTS load
P 21
P 20P 22
P 23
LPOT
4"
3"3"
4"
P 4 P19
P 7P 6
8 3
1 17
1 5
22 2
Bearing Pads
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failure occurred (ductility cycles). The ductility cycles, performed on each pile setup, are
indicated by the stars in Figure 23.
Figure 23. Illustration of loading scheme
The different axial loading combinations applied to each pile (ALR 1, 2, 3) as well as to
each bearing pad combination can be seen in Table 4 through Table 7. The ALR applied
to each pile is a percentage of the estimated piles ultimate load under compression. The
different ALR used for the concrete piles were based on the yielding load in the
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longitudinal reinforcement steel in the circular and square piles. The H-Pile tested was
not subjected to axial load, but it was assumed that the pile experienced 109 kips (485kN)
which was 30% of its ultimate capacity.
Table 5. Loads for circular pile cases
Case ALR (%) Pile Load
P
kips (kN)
Load on one Bearing Pad
P1
kips (kN)
P2
kips (kN)
P3
kips (kN)
1 4 46 (205) 11 (51) 17 (76) 23 (102)
2 6 69 (307) 17 (76) 26 (116) 34 (151)
3 8 92 (409) 23 (102) 34 (151) 46 (205)
Table 6. Loads for square pile cases
Case ALR (%) Pile Load
P
kips (kN)
Load on one Bearing Pad
P1
kips (kN)
P2
kips (kN)
P3
kips (kN)
1 3 54 (240) 13.5 (60) 20 (89) 27 (120)
2 4 72 (320) 18 (80) 27 (120) 36 (160)
3 5 90 (400) 23 (151) 34 (151) 45 (200)
Table 7. Loads for H-pile cases
Case Pile Load
P
kips (kN)
Load on one Bearing Pad
P1
kips (kN)
P2
kips (kN)
P3
kips (kN)
1 109 (485) 27 (120) 41 (182) 55 (245)
For the elastic-range loading cycles, the piles were loaded in increments of 3/4 inch top
displacement to a total displacement of 3 inches (in both directions, pushing/pulling). At
a top pile displacement of 3 inches, the lateral load applied was near the yielding load of
the steel in the circular pile (which was the first pile tested and the basis for the loading
protocol).
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Figure 24. Elastic cycle lateral loading history
The ―ductility cycles‖ were performed where the load was applied to the test sample in
both directions at the top displacement associated with the yield load (1μ) for three
cycles. Additional cycles were also performed in sets of three where the load was then
increased to 1.5μ and 2μ. The circular pile ductility cycle was performed on the type VI
bearing pad where the yielding top displacement was 3.24 inches (8.23cm), and testing
was terminated at the completion of the 1.5 μ loading cycles. The square pile ductility
cycle was performed on the type V bearing pad where the yielding top displacement was
3.26 inches (8.28cm), and testing was terminated after the first cycle of 2μ. The H-Pile
ductility cycle was performed on the type VI bearing pad where the yielding top
displacement was 6.23 inches (15.82cm), and testing was terminated at the completion of
the 1.5μ cycles.
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Figure 25. Ductility cycle lateral loading history
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CHAPTER 4: TESTING RESULTS
4.1 Bearing Pad Tests
In Robeson et al (2007), tests were performed on the type V and type VI elastomeric
bearing pads where the shear modulus and compressive modulus were determined. For
the shear tests, normal loads of 50 kips, 100 kips, 150 kips were applied to the bearing
pads and then a horizontal load was applied while deformation was measured at the same
time. For the compression tests, each bearing pad was compressed up to a 200 kip load
while deformation was measured. From these tests the shear modulus (G) and the
compressive elastic modulus (E) were determined which will later be used in the FB-
MultiPier modeling. Table 8 shows the properties of the bearing pads and the results for
shear under a 50 kip normal load and compression from Robinson et al (2007).
Table 8. Properties of bearing pads under study from Robinson et al (2007)
Property BP V BP VI
W (in) 13 11
L (in) 25 23
t (in) 3.5625 1.5
G (psi) 101 134
E (psi) 25000 30000
4.2 Physical Observations from Testing
The first case tested was for the circular pile under 4% axial load ratio on Type V bearing
pads with bearing pad load of P1. The testing continued with increased bearing pad loads
for a given axial load ratio on the pile. Once testing was complete on the Type V bearing
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pad, the Type VI bearing pad was tested in the system. The same testing sequence was
performed on the Type VI bearing pad except that after completion of the first loading
protocol (elastic cycles), the second loading protocol was applied until a ductility of 1.5
on the column was reached along with an ALR of 6% and a bearing pad load of P3 (Refer
back to Loading Scheme for notation in Chapter 3).
The second phase of testing continued with the square pile. This phase began with
testing the Type VI bearing pad by increasing bearing pad load and then increasing the
axial load ratio. For testing on the Type V bearing pad, the axial load ratio (ALR)
sequence followed 3%, 5%, and 4%. The ductility cycles were performed on the bearing
pad load of P3 with the 4% axial load ratio on the Type V bearing pad.
The last phase concluded with the H-Pile tests. Axial load was not applied to the HP pile.
Testing began with the Type V bearing pad followed by the second loading protocol
which was applied after the last elastic cycle on the P3 load and Type VI bearing pad.
It should be noted that the first yielding of the longitudinal steel bars in the square and
circular piles occurred at around 3 inch (76 mm) top deflection of the pile. The computed
first yield displacement and force occur at around 1 inch (25.4 mm) for a fixed base
column, which contrast with the columns under study. The connection under study
provides an additional flexibility to the system. Therefore, under the same lateral force,
the first yield displacement occurs at a higher value than the one expected for a fixed base
column. This initial testing observation led to the testing sequence design of intervals of
0.75 inches and ending the elastic cycle tests approximately at a 3 inch top deflection.
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Throughout the elastic cycles (first loading protocol) on the concrete pile, the cracks that
developed in the pile and pile cap were monitored as well as the behavior of the bearing
pad and connections. As testing progressed on the circular piles, flexural cracks initially
developed near the base of the connection between the cap beam and pile. These cracks
started developing at 7 inches above the pile cap and continued further up the pile in
intervals of 7-8 inches as the bearing pad load and pile axial load increased for a total of
eight cracks on each side (pushing/pulling). This same behavior occurred during the
testing of the square pile except that the cracks developed on spacing intervals of
approximately ~12 inches starting from the pile to pile cap connection.
Figure 26. Flexural cracks produced in the square pile
It was noticed that during the circular pile ―8% axial loading case‖ and P3 on the Type V
bearing pad, that the pile cap rotation produced a visible gap ~1/8in between the bearing
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pad and pile cap. As testing continued more visible gaps were noticed near the peak of
each elastic cycle for the different circular pile cases. In some cases the edge of the
bearing pad was not touching the pile cap or the sole plate. Figure 27 shows the gaps
between the pile cap and bearing pad, as well as similar gaps between bearing pad and
sole plate, which developed as the pile was being pushed.
Figure 27. Visible gap between pile cap and bearing pad
During the procession of the testing sequence, the deformation in the bearing pad became
more notable as the axial load and bearing pad load were increased. Figure 28 shows the
deformation of the Type VI bearing pad positioned the furthest away from the actuator
during pushing of the pile (for the circular pile under the ductility cycle).
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Figure 28. Shear deformation of the type VI bearing pad
As testing progressed into the ductility cycles for each pile, more observations were
made.
4.2.1 Circular Pile
As loading increased it was observed that a deflection of 3.26 inches at the top of the
pile produced yielding of the longitudinal steel rebar. When the pile was loaded to
ductility 1.5 (4.89 inches of displacement) the testing was terminated because
bending was noted around the weak axis of the sole plate. The weakest link for this
connection was the sole plate that is located at the top of the bearing pad (reverse side
of Figure 8). The force produced by the bending of the sole plates caused a gap
between the embedded plate and the girder due to the pulling action. However, the
force experienced during this test was not enough to pull out the embedded plate from
the girder. Figure 29 shows the gap produced between the embedded plate and the
girder as well as the gap between the bearing pads and sole plate.
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Figure 30 shows the design configuration of the four anchor studs embedded seven
inches into the girder, which prevents the embedded plate from pulling out when the
bond force is not exceeded. The bending of sole plates caused crushing of the concrete
around the diaphragm area (Figure 31a and b).
Figure 29. Pullout of embedded plate in girder
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Figure 30. Detailed design of embedded plate (from Halifax County Bridge plans)
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a.)
b.)
Figure 31a.) and b.) Concrete cracking in the diaphragm under the pile cap
During the ductility phase loading, the sole plate bent approximately to 0.5 inches (12.7
mm) as the force was increased. This behavior as well as the pullout of the embedded
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plate in the girders occurred in the square pile as well as in the H-Pile with elastic testing
cycles progressing into inelastic cycles (second loading protocol).
4.2.2 Square Pile
The observed data indicated that the square pile experienced the same top deflection in
the pile at first yield of the longitudinal reinforcing steel as did the circular pile (3.26‖).
Testing in the ductility cycles continued where embedment plate pullout and sole plate
bending was more noticeable and more significant due to the weakening of the
connection (from the circular pile testing) and higher applied lateral forces. The square
pile is stiffer than the circular column; thus higher forces were expected to displace it the
same amount as the circular column. Figure 32 shows the increase in cracks in the
diaphragm due to bending of the sole plates and pulling out of the embedment plate.
Also, Figure 33 captures the bending of the sole plate during the second loading protocol
(ductility cycles) of the square pile.
Figure 32. Cracks in diaphragm from pullout of embedment plate
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Figure 33. Bending of sole plate
Figure 32 and Figure 33 show the cracks at the diaphragm and bending of the sole plate
at a ductility of 2 (6.52 inches). Testing of the square pile was ended after one cycle of
ductility 2 (push only) because significant cracking of the concrete cap was observed
above the anchor bolt on the back side of the pile cap. Figure 34 reveals the cracking of
the concrete at this location as well as bending of the soil plate and pull out of the
embedded plate.
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Figure 34. Significant cracking in the pile cap
4.2.3 H-pile
During the first protocol of testing for the H-pile, similar behavior was noticed as in the
previous tests on the circular and square piles. More significant shear deformation of the
bearing pad, sole plate bending, and embedment plate pull out action with increasing
lateral load were observed as compared to the square and circular piles. After completion
of the elastic cycles, the most noteworthy difference in the behavior of the pile was that at
the final peaks of the loading elastic cycles, cracks developed between the H-pile and the
pile cap. These cracks became more significant as the second protocol of testing began
because a top deflection of 6.23 inches at a horizontal load of ~18 kips was needed to
reach the first yielding of the H-pile. Testing continued until the completion of a ductility
of 1.5 where the top deflection of the pile reached 9.34 inches. When this point in the
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second protocol of testing was reached, measurements of top deflection became
inaccurate due to the configuration of the test setup. In addition the pile was rotating
significantly independent of the pile cap, as displayed in Figure 35. Figure 36 and Figure
38 show the damage at different points in the specimen at a top deflection of 9.34 inches.
Figure 35. Rotation of the H-pile independent of the pile cap
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Figure 36. Prying of the H-pile in the pile cap
Figure 37. Cracks in the pile cap along the adjacent side of loading
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Figure 38. Gaps generated between sole plate / cap beam and bearing pad
4.3 Experimental Results
After completion of testing, the measured results were analyzed to determine the
contribution of the various test components to the total top displacement of the pile. A
string pot was attached at the top of the pile which measured the total top deflection of
the piles throughout the testing sequence. The results of the test revealed that the total
top deflection of the pile was a sum of the following components: pile bending, bearing
pad shear deformation, girder rotation, and pile cap rotation.
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Figure 39. Components of contributing pile top displacement
Measurements of the contributing displacements were determined at the peaks of each
testing protocol for both pushing and pulling of the test piles during the elastic and
ductility cycles. The rotation of the girder was determined from the clinometer data
indicated by the CLIN-1 on Figure 22. The rotation of the pile cap was also determined
from two string pots (SPOT 9 and SPOT 11) located at the top and bottom of the pile cap.
The contributing top displacement from pile bending was determined from estimating the
curvature of the pile from the compressive displacement measurements at four points
along either side of the pile (LPOT 9 through 16). The last component of contributing
pile top displacement was the shear deformation of the pile measured by linear pots, two
pots per bearing pad as indicated in Figure 22 by LLOT 2, LLPOT1, LPOT 20, and
LPOT 21. Figure 40 shows the calculated contributing top displacement of each
component with respect to the overall top displacement measured at the peaks of each
cycle.
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Figure 40. Top displacement components
From Figure 40 it is evident that the sum of the contributing components, indicated by the
circles, is close to the measured top displacement of the pile. Figure 41 shows the
measured top displacement versus the calculated top displacement throughout the history
of one elastic loading cycle on the square pile.
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Figure 41. Measured vs calculated top displacement
Figure 40 and Figure 41 show that the measured top displacement associated with each
contributing displacement component is valid. Also, the test results revealed that the pile
cap rotation had the most significant contribution to the top displacement of the pile,
followed by the bending of the pile, and then the bearing pad shear with the girder
rotation contributing the least. Figure 42 shows the percentages of the contributing
components of the total top deflection of 0.75 inches for the square pile under an ALR of
3% and a bearing pad load of P1 on the Type V bearing pad.
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Experim
enta
l D
ispla
cem
ent
[m]
1 2 3 4 5 6 7 8
-3
-2
-1
0
1
2
3
cycle
Experim
enta
l D
ispla
cem
ent
(in)
3% ALR Square / BP V / BP Load 1
Measured Top Displacement
Calculated Displacement
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Figure 42. Pie chart of pile top displacement component percentages
From these results it is evident that the rotation of the pile cap is very significant in the
overall response of the pile. Therefore, it is important that the degree of fixity of the pile
cap be modeled correctly in design analyses. In order to determine the pile cap fixity
effects, the results and measurements of the cap rotation and moment at the pile cap need
to be analyzed to estimate the rotational stiffness. Figure 43 through Figure 48 show
plots of the moment in the pile cap versus its measured rotation for the different elastic
loading cases for each pile and BP type.
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Figure 43. Square pile/BP V: cap moment vs. cap rotation
Figure 44. Square pile/BP VI: cap moment vs. cap rotation
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Figure 45. Circular pile/BP V: cap moment vs. cap rotation
Figure 46. Circular pile/BP VI: cap moment vs. cap rotation
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Figure 47. HP/BP V: cap moment vs. cap rotation
Figure 48. HP/BP VI: cap moment vs. cap rotation
The moment verses rotation results show that overall for each loading case, the behavior
of the bearing pad is somewhat consistent. Increasing the loads in the bearing pad and in
the pile cause an increase in cap moment to generate the same cap rotation. In general
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the maximum moment in the pile cap for all of the piles and loading cases was
approximately between 150 and 225 k-ft. Also, the maximum cap rotation was around
0.5 degrees for all the loading cases except for the H-pile tests on the Type V bearing pad
where the maximum pile cap rotation was more than double the value experienced in the
other cases.
Based on the moment and rotation at the pile cap for each loading case, the secant
stiffness at the peak of each loading cycle can be found. This secant stiffness at the 0.75,
-.075, 1.5, -1.5, 2.25, -2.25, 3, and -3 inch top displacements was generated by dividing
the measured cap moment by the cap rotation. Figure 49 through Figure 60 plot the
secant stiffness determined at each top displacement peak where the stiffness from the
actuator pulling and pushing for each pile case is designated.
Figure 49. Secant stiffness of square pile / BP V (pushing direction)
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Figure 50. Secant stiffness of square pile /BPV (pulling direction)
Figure 51. Secant stiffness of square pile / BPVI (pushing direction)
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Figure 52. Secant stiffness of square pile / BPVI (pulling direction)
Figure 53. Secant stiffness of circular pile / BP V (pushing direction)
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Figure 54. Secant stiffness of circular pile/ BP V (pulling direction)
Figure 55. Secant stiffness of circular pile/ BP VI (pushing direction)
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Figure 56. Secant stiffness of circular pile / BP VI (pulling direction)
Figure 57. Secant stiffness of H-pile / BP V (pushing direction)
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Figure 58. Secant stiffness of H-pile / BP V (pulling direction)
Figure 59. Secant stiffness of H-pile/ BP VI (pushing direction)
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Figure 60. Secant stiffness of H-pile/ BP VI (pulling direction)
The rotational secant stiffness from the different piles shows some trends. When the
actuator was pulling the piles, there was a more significant decrease in the rotational
secant stiffness in the pile cap as opposed to the pushing direction. Between the different
loading cases for the circular and square piles, the difference in the rotational stiffness
decreased as the pile was pushed/pulled further away. However, for the H-pile results the
stiffness remained somewhat uniform overall throughout lateral pile.
4.4 Conclusions
From the full scale testing, the rotational stiffness of the connection between the super to
sub structure was measured. These results showed that the rotational stiffness contributed
significantly to the pile displacement. Knowing that the connection has an important
effect on the pile behavior, the measured rotational stiffness determined from full scale
testing should be applied to current bridge structures’ point of fixity analysis. The depth
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to fixities of current bridge structures’ are determined by the traditional method of
assuming either a fixed or free head connection. Analyzing the depth to fixity of
traditional methods and then comparing them to the results from inputting the measured
rotational stiffness of the connection can prove to be very significant.
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CHAPTER 5: MODELING-FB MULTIPIER
5.1 Introduction
The full scale test configurations were modeled in the computer program FB-MultiPier
developed by the Bridge Software Institute (2000). This computer program was used to
model the full scale experimental results for facilitating a comparative analysis. FB-
MultiPier was also utilized to model three existing bridge bents in North Carolina and to
compare the results to an equivalent single pile analysis (Robinson et al 2006). For these
three case studies, the effect of the rotational stiffness between the super to substructure
on the depth to a ―point of fixity‖ is analyzed.
5.2 Experimental Modeling
The full scale tests performed in the laboratory were first modeled in FB-MultiPier as a
bridge section. An additional analysis was then performed to model the full scale tests as
an ―equivalent single pile‖ which allowed for the direct input and modeling of the
measured rotational stiffness. The single pile analysis results were used to investigate the
justification of modeling existing bridge piers as single piles which is the current practice
of several Departments of Transportation including the NCDOT.
5.2.1 Full Scale Modeling
The modeling of the circular, square, and H-pile foundation elements was first performed
to determine if the measured experimental displacements could be matched by the model.
For each foundation element and bearing pad configuration, a model was generated to
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match the response at 1.5 inch top deflection. This displacement level was chosen
because it was near the displacement limit for which many piles are designed including
NC DOT piles. Table 9 shows the full scale tests modeled in FB-MultiPier.
Table 9. Full scale test configurations modeled in FB-MultiPier
Pile BP Type
ALR % :
Load Case
Number
Axial
Load on
Pile
(kips)
Axial Load on
One Bearing
Pad (kips)
Target Top
Displacement
(in)
Circular V 8 : 3 92 46 1.5
Circular VI 8 : 3 92 46 1.5
Square V 5 : 3 90 45 1.5
Square VI 5 : 3 90 45 1.5
H-Pile V --- : 3 ---- 55 1.5
H-Pile VI --- : 3 ---- 55 1.5
FB-MultiPier, allows the user to input bearing pad configurations and properties. From
these properties and details, the program determines the deformations and forces
generated from certain applied loads. In Robinson et al (2007) the properties of the Type
V and Type VI bearing pads were measured. However, the shear stiffness measured in
those tests were subjected to specific applied normal stresses. The shear stiffness
properties of the bearing pads under a normal force of 50 kips, found in Robinson et al
(2007), was used because this force was the closest to the normal forces in the bearing
pads for the modeled full scale tests cases presented in Table 9.
The full scale test cases were modeled in FB-Multipier by representing the ―support
blocks‖ as piles that were fixed from any movement. These support piles were placed in a
soil profile that consisted of rock. The properties and dimensions of the two AASHTO
Type II girders were input into the program with a diaphragm connection in the center
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and pinned connections to the outside support piles. Figure 61 illustrates the FB-
MultiPier model of the full scale test setup for the circular drilled shaft case.
Figure 61. FB-MultiPier model of the full scale test on a circular foundation element
For the six cases that were analyzed (two for each foundation element), the measured
force from each loading case at the 1.5 inch target top displacement of the pile was
recorded and then applied as the lateral force in the FB-MultiPier analyses. This lateral
force was placed at a location equivalent to the location used during testing, which was
roughly 12-15 inches from the pile tip. The measured displacements were recorded at
these points (Recall that the sample tested in the lab was configured upside down). FB-
MultiPier requires that some part of the foundation element be bearing in a soil profile
but, the full scale tests were performed with no soil. As a result, the foundation elements
were placed in a soil profile that consisted of a uniform sand layer that had an associated
P-y curve that allowed free movement of the pile within the soil profile. Furthermore,
during full scale testing, the concrete piles were subjected to cracking under the bending
associated with the 1.5 inch displacements. As a result the cracked moment of inertia
was used for the model piles. This cracked moment of inertia for the concrete sections
were determined by a function of their axial load ratio as defined in Priestley et al (2007).
For the H-pile, the measurements from the full scale testing indicated that the pile was
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not subjected to strains close to its yield values. Accordingly, the full properties of the
steel H-pile were used.
Figure 62 and Figure 63 show the applied reduction factor used to determine the cracked
moment of inertia for the foundation elements.
Where:
EI = equivalent cracked stiffness
EIg = gross stiffness
ρ1 = Area of reinforcing steel / Area of concrete
Nu = Applied compressive load
f’c = compressive strength of concrete
Ag = gross cross-sectional area
Figure 62. Equivalent cracked moment of inertia for circular columns
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Figure 63. Equivalent cracked moment of inertia for square columns
It should be noted that for the circular pile, the square cross section connection at the top
of the full scale tests was considered during the estimation of the moment of inertia to be
used in FB-MultiPier. The associated reduction factor of the square cross section of the
top of the circular foundation element is indicated in Figure 63 by an asterisk (*). The
overall input moment of inertia was then determined by taking the weighted average of
the two cross sections. Table 9 shows the foundation element moment of inertia used in
the FB-MultiPier analysis and Table 11 displays the foundation element axial stiffness.
The concrete was assumed to have a compressive strength, f’c of 4.5 ksi which was
measured from cylinders. A 29000 ksi elastic modulus was used for the steel H-pile.
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Table 10. Moment of inertia of sections modeled in FB-MultiPier
Foundation
Element
Moment of Inertia
(in^4) Section
Behavior Ixx Iyy
18" Circular 2757 2757 Cracked
20" Square 3333 3333 Cracked
12x63 H-Pile 472 153 Elastic
Pile Cap 67500 67500 Uncracked
Table 11. Axial stiffness of full scale foundation Elements
Foundation
Element
EA/L
Stiffness
(k/in)
Circular 11158
Square 11246
H-Pile 3924
For a bridge configuration model in FB-MultiPier, the user must input a plot of the
compression, shear, and rotation stiffness of the bearing pads. The bearing pad
compressive stiffness and shear stiffness were estimated by using Young’s Modulus and
the Shear Modulus measured from tests reported in Robinson et al (2007). It was
assumed that the bearing pad shear stiffness was equivalent in both the transverse and
longitudinal direction as well as fixed from rotation about the vertical axis. The rotational
stiffness measured from the full scale tests was a representation of the entire connection
assembly including the anchor bolts and the two bearing pads. However, this overall
rotational stiffness cannot directly be imputed into FB-MultiPier. The user must input a
relationship for the rotational stiffness of the bearing pad for a bridge configuration. As a
result, a few assumptions were made to facilitate the analysis. First, the analysis was
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performed assuming that the rotational stiffness relationship was linear. Also, the
inputted rotational stiffness of the bearing pad was assumed to be half of the rotational
stiffness measured from the full scale test as a basis for the initial analysis. Table 12
through Table 14 show the inputted rotational stiffness measurements for each loading
case.
Table 12. Inputted FB-MultiPier data
Pile BP
Type
ALR % / P
Load Case
Number
Axial
Load on
Pile (kips)
Axial
Load on
One
Bearing
Pad
(kips)
Horzontal
Load
Applied
by
Actuator
(kips)
Actual
Measured
Displacement
(in)
Circular V 8 / 3 92 46 5.67 1.13
Circular VI 8/ 3 92 46 6.88 1.10
Square V 5 / 3 90 45 9.25 1.50
Square VI 5 / 3 90 45 10.87 1.49
H-Pile V ---- / 3 ---- 55 7.55 1.53
H-Pile VI ---- / 3 ---- 55 7.49 1.54
Table 13. Inputted FB-MultiPier Bearing Pad Stiffness (Compression and Shear)
Pile BP
Type
Shear Stiffness Compressive Stiffness
Load
(kips)
Displacement
(in)
Stiffness
(kip/in)
Load
(kips)
Displacement
(in)
Stiffness
(kip/in)
Circular V 5.67 0.616 9.21 46 0.020 2281
Circular VI 6.88 0.304 22.60 46 0.009 5060
Square V 9.25 1.004 9.21 45 0.020 2281
Square VI 10.87 0.481 22.60 45 0.009 5060
H-Pile V 7.55 0.819 9.21 55 0.024 2281
H-Pile VI 7.49 0.331 22.60 55 0.011 5060
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Table 14. Inputted FB-MultiPier rotational stiffness parameters
Pile BP
Type
Rotational Stiffness (Measured) 1/2*Rotational Stiffness
(Full Scale: FB-MultiPier Model)
Moment
(kip-in)
Rotation
(rad)
Stiffness
(kip-
ft/rad)
Moment
(kip-in)
Rotation
(rad)
Stiffness
(kip-ft/rad)
Circular V 891 0.0040 18429 445 0.0040 9214
Circular VI 1080 0.0035 25774 540 0.0035 12887
Square V 1453 0.0045 27116 726 0.0045 13558
Square VI 1707 0.0042 33467 853 0.0042 16733
H-Pile V 1185 0.0112 8802 593 0.0112 4401
H-Pile VI 1176 0.0025 39708 588 0.0025 19854
The full scale tests modeled in FB-MultiPier were conducted assuming a linear pile
behavior due to the nature of inputting the gross section properties of the foundation
elements. The input length required for FB-Multipier is the length of the pile tip to the
center of the pile cap which was equivalent to 154 inches (12.83 feet). However, since
the point of cap rotation was not determined from the full scale tests, it was assumed to
lie between the pile cap and elastomeric bearing pads. The maximum moments presented
in the FB-MulitiPier are a result of an equivalent moment arm length from the pile tip up
to the middle of the pile cap. Figure 64 illustrates the linear moment response of the pile
and Figure 65 shows the displacement response of the circular pile from the FB-MultiPier
results with the type V elastomeric bearing pad. The measured displacements were
recorded at the point of applied lateral load which was located at a depth of 11.8 feet.
Moment and deflection model results from FB-MultiPier are located in Appendix E.
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Figure 64. FB-MultiPier experimental full scale test moment results on circular
drilled shaft
Figure 65. FB-MultiPier experimental full scale test displacement results on circular
drilled shaft
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The results from FB-MultiPier were computed assuming that the input bearing pad
stiffness is equivalent to ½ of the overall connection stiffness. The actual versus
computed displacements are shown in Table 15.
Table 15. FB-MultiPier experimental full scale test results
Pile BP Type
Actual
Measured
Displacement
(in)
FB-Multipier
Displacement
(in)
% Difference
from Actual
Measurements
Circular V 1.13 1.12 -0.7
Circular VI 1.10 1.01 -8.0
Square V 1.50 1.59 6.3
Square VI 1.49 1.38 -7.3
H-Pile V 1.53 1.44 -6.0
H-Pile VI 1.54 0.98 -36.3
From these results it can be seen that with the assumptions made, FB-MultiPier modeled
the actual full scale tests fairly well with the exception of the H-Pile case with bearing
pad type VI. For the H-pile case with the type VI bearing pad, the difference between the
FB-MultiPier results and the actual test results could not be achieved under 10%. During
full scale testing, it was observed that as the displacement of the H-pile increased above
1.5 inches, cracking occurred between the embedded pile and concrete cap. As
displacements increased to 3 inches for each test, significant rotation and failure occurred
between the steel pile and concrete cap. As a result, the tests performed on the H-pile
under the type VI bearing pad were already subjected to failure loads which caused
independent rotation between the H-pile and cap connection. This independent rotation
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was not accounted for in FB-MultiPier and it is believed that this is the reason for
significant difference in results.
5.2.2 Single Pile Modeling
The full scale tests performed in the laboratory were also modeled in FB-MultiPier using
single pile configurations with a rotational, compression, and shear spring at its top. This
type of analysis is common in current bridge design where a single pile is modeled, and
based on the response, the point of fixity is determined. For this analysis in FB-
MultiPier, the user may input stiffness at the center of the pile cap to restrain the pile. To
model the overall stiffness of the bearing pad it was assumed that the input rotational
stiffness would be equivalent to the measured rotational stiffness from the full scale test.
For the single pile analysis, it was assumed that the compressive stiffness used in the
analysis would be equivalent to the compressive stiffness of one bearing pad. It was also,
assumed that the shear stiffness of the entire joint was to be modeled in the single pile
analysis as two times the measured shear stiffness of one bearing pad. These assumptions
were necessary because the effect of modeling equivalent bearing pad orientations was
unknown to the author. Figure 66 shows an illustration of a single pile analysis in FB-
MultiPier.
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Figure 66. FB-MultiPier model of single pile analysis of full scale test of the H-pile
It should be noted that the soil for the single pile analysis was assumed as a uniform sand
layer. The equivalent spring stiffness assumed for the different single pile models can be
seen in Table 16.
Table 16. Equivalent spring stiffness for FB-MultiPier single pile analysis
Pile BP Type
Equivalent
Shear
Stiffness
(k/in)
Equivalent
Compressive
Stiffness (k/in)
Rotational
Stiffness
Measured
(k-ft/rad)
Circular V 18.4 2281 18429
Circular VI 45.2 5060 25774
Square V 18.4 2281 27116
Square VI 45.2 5060 33467
H-Pile V 18.4 2281 8802
H-Pile VI 45.2 5060 39708
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The results from the single pile analyses for the three foundation elements with the
assumed equivalent spring stiffness are presented in Table 17.
Table 17. Single Pile FB-MultiPier results with assumed equivalent stiffness
Pile BP Type
Actual
Measured
Displacement
(in)
FB-Multipier
Displacement
Single Pile (in)
% Difference
from Actual
Measurements
Circular V 1.13 1.33 17.7
Circular VI 1.10 1.23 11.6
Square V 1.50 1.77 18.2
Square VI 1.49 1.61 7.7
H-Pile V 1.53 2.38 55.8
H-Pile VI 1.54 1.01 -34.6
It can be seen that these analyses produced displacements that were greater than the
actual test results except for the H-pile case with the type VI bearing pad (the computed
value was smaller than the measured value). The average percent difference for the
concrete pile cases was close to 14%. The single pile analysis over-predicted the actual
tests results whereas the full scale model results under-predicted the actual pile
displacements. This may be due to the fact that for the single pile analysis there is no
connection assigned to the top of the pile, leaving only the springs connections. Despite
that being the case, conservative results are still generated. The H-Pile cases had very
high percent differences as can be seen in Table 17.
Assuming the same stiffness parameters under compression and shear, the required
rotational stiffness for the single pile analysis in FB-MultiPier can be determined,
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producing the same displacements as the full scale tests. The single pile analyses were
set up to match the measured test displacements with a minimal percent difference by
changing the joint rotational stiffness. The results of these tests are presented in Table
18.
Table 18. FB-MultiPier single pile test results matched to actual test results
Pile BP
Type
Actual
Measured
Displacement
(in)
FB-MultiPier
Displacement
Single Pile:
Modified (in)
% Difference
from Actual
Measurements
Required
Rotational
Stiffness of
Joint (kip-
ft/rad)
Proportion
of Original
Rotational
Stiffness
Circular V 1.13 1.13 0 31000 1.7
Circular VI 1.10 1.10 0 36000 1.4
Square V 1.50 1.50 0 51000 1.9
Square VI 1.49 1.49 0 42000 1.3
H-Pile V 1.53 1.53 0 17500 2.0
H-Pile VI 1.54 1.54 0 14800 0.4
These single pile FB-MultiPier results show that the required rotational stiffness is
greater than the actual measured rotational stiffness except for the H-pile case on the type
VI bearing pad. For the different foundation elements under type V bearing pads, the
required rotational stiffness was on average 1.86 times greater than the measure rotational
stiffness. For the foundation elements under type VI bearing pads (excluding the H-pile
case) the average required rotational stiffness was 1.35 times greater than the measured
rotational stiffness. It appears from these tests that the FB-MultiPier models, under the
current assumptions, can predict the actual results under specific cases. These included
cases where rotational stiffness is 1.9 times the actual rotational stiffness of the connect
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joint for a type V bearing pad and is 1.35 times the actual rotational stiffness of the
connection joint for a type VI bearing pad. These results are pertinent to the full scale
tests performed under specific horizontal load, axial load and the assumption about the
shear and compressive stiffness. It seems acceptable to assume that the H-pile results
from the single pile analysis were poor due to the rotation of the pile at the connection of
the pile cap as was mentioned previously.
The rotational moment from the full scale tests was computed based on the moment arm
equal to the distance between the point of load application and the pile cap. This
rotational stiffness (computed as moment/angle of rotation) was then inputted into the
single pile analysis at the center of the pile cap. As a result, it may be beneficial to check
the length from the pile tip to the pile cap if it is set equal to the total length of the pile
plus the pile cap since the measured rotation was assumed to occur at that location. This
analysis will provide information on the differences between the two rotational stiffness
levels that achieved the measured pile displacement at the two different input lengths and
will comment on how they compare to the measured rotational stiffness.
The analysis was then performed by inputting the total length of the pile tip to the pile
cap so that the springs would attach to the model pile at the point where the rotation was
assumed to occur for the connection joint. Table 19 shows the results for a single pile
model for the square pile with the type V bearing pad.
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Table 19. Comparison FB-MultiPier single pile analysis of assumed length effect
Pile BP
Type
FB-
MultiPier
Input
Length:
Pile Tip
to Center
of Pile
Cap (ft)
Actual
Measured
Displ. (in)
FB-
MultiPier
Displ.
Single
Pile:
Modified
(in)
% Difference
from Actual
Measurements
Required
Rotational
Stiffness of
Joint (kip-
ft/rad)
Proportion
of Original
Rotational
Stiffness
Square V 12.83 1.50 1.50 0 51000 1.9
Square V 14.33 1.50 1.50 0 480000 18
By changing the input length in FB-MultiPier, the required rotational stiffness to match
the actual test displacement for the extended pile becomes 18 times the original measured
rotational stiffness. It seems therefore, that the original assumptions with inputting the
actual length of the center of the pile cap to the tip of the pile produced the most
comparable results since only 1.9 times, versus 18 times, the actual rotation was needed
to match measured displacement.
5.3 North Carolina Bridge Bent Case Study
Three North Carolina bridges were further investigated by applying rotational stiffness
parameters to the pile head connection joint. The three bridges selected were ones from
Halifax County, Robeson County, and Wake County in which each had interior bent
foundation elements consisting of square pre-stressed concrete piles, steel H-piles and
drilled shafts, respectfully. These bridges’ interior bents were modeled in FB-MultiPier
in Robinson et al (2006), and Robinson et al (2007) and the interior bridge bent models
were obtained with the author’s permission. From these modeled interior bents, a single
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pile analysis was performed to determine the effect of the rotational stiffness of the
connection joint on the pile head fixity condition. Also analyzed was the joint’s rotational
stiffness effect on the depth to fixity based on the procedures for and equivalent fixed pile
based analysis as presented in Robinson et al (2006). The single pile analysis for each
foundation element was modeled by applying an equivalent lateral load at the center of
the pile cap. This equivalent lateral load was determined by taking the maximum LFD
factored longitudinal load that would be applied to the bridge at a bent bearing location
and then multiplying that by the number of bearing locations divided by the number of
foundation elements supporting the bent.
5.3.1 Halifax County Bridge
The Halifax County Bridge information was obtained from Robinson et al (2006). This
bridge consists of 8 interior bents and 2 end bends that span over Beech Swamp on US
301/ NC 481. The super structure consists of 15 concrete cored slabs with two, 1 inch
thick type I and type II elastomeric bearing pads at the 15 support locations along the pile
cap. The interior bent modeled consisted of a pile cap that had a cross section 39 inches
wide and 30 inches deep. The cap beam supported eight, 18 inch square pre-stressed
concrete piles that were on average a distance of 45 feet from the center of the pile cap to
the pile tip. The unsupported free lengths of the piles were on average 14.8 feet from the
center of the pile cap to the ground surface.
The soil profile modeled consisted of the water table existing at the ground elevation.
The upper 3.3 feet of soil consisted of a layer of loose sand with a friction angle of 30
degrees. This sand layer was underlain by 14.7 feet of clayey material with an undrained
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shear strength of 400 pounds per square foot. Under this clayey material there existed a 5
foot thick layer of coarse sand with a friction angle of 29 degrees. Below the coarse sand
there was another stiff clay layer that was modeled with an undrained shear strength of
3750 pounds per square foot. The pile was driven to have end bearing in this stiff layer.
Figure 61 is an illustration of the interior bent while Figure 68 illustrates the soil profile
which was modeled for the Halifax County Bridge in Robinson et al (2006).
Figure 67. Illustration of Halifax County interior bent modeled in FB-MultiPier
Page 97
86
Figure 68. FB-MultiPier soil profile for the Halifax County interior bent
5.3.1 Single Pile Analysis
A single pile model was generated from the Halifax County interior bent model from
Robinson et al (2006). The single pile was loaded laterally in the longitudinal direction
by 1.7 kips. This was initially run on the free head assumption where the pile was
allowed to translate in the horizontal direction and was free to rotate. The rotational
stiffness was then increased by a Rotational Stiffness Ratio (RSR); the rotational stiffness
applied divided by the axial stiffness of the pile where the rotational stiffness applied was
Page 98
87
in units of k-ft/rad or KN-m/rad and the axial pile stiffness was in units of kips/in or
kN/m. The axial stiffness was determined by the following equation:
Equation 24 𝒌𝒂 =𝑬𝑨
𝑳
Where,
𝑘𝑎 = the axial stiffness of the foundation element (k/in or kN/m)
E = young’s modulus of the foundation element: concrete or steel (ksi or kPa)
A = cross-sectional area of the foundation element (in2 or m
2)
L = length of pile from center of pile cap to pile tip (ft or m)
This RSR ratio was increased until a rotational stiffness applied to the pile head caused it
to behave as if it were fixed at the top but also free to translate. This procedure for
analysis was followed for the other bridges investigated as well. Figure 69 presents and
illustration of the Halifax County single pile model.
Page 99
88
Figure 69. FB-MultiPier single pile model for Halifax County interior bent pile
The axial stiffness of the 18‖ pre-stressed square concrete pile investigated was 2649
k/in. The RSR’s were then increased until a rotational stiffness at the top of the pile
caused the pile head to behave as if it were fixed from rotation. Table 20 shows the
RSRs and the associated rotational stiffness used for this model as well as the results.
Figure 70 and Figure 71 show the pile moment and displacement response as the RSR
was increased.
Page 100
89
Table 20. Halifax County FB-MultiPier Single Pile results of pile cap fixity
RSR
Rotational
Stiffness
(kip-
ft/rad)
Mmax (k-ft) Pile Top
Deflection
(in)
Depth to Mmax
from Center of
Pile Cap (ft)
0.001 2.6 28.09 0.375 18.2
0.01 26.5 28.04 0.375 18.2
0.1 265 27.63 0.369 18.2
1 2649 24.27 0.321 17.6
2 5298 21.69 0.284 17.6
5 13246 17.35 0.222 17.6
10 26491 14.34 0.178 0
20 52982 16.82 0.144 0
50 132456 18.77 0.118 0
100 264912 19.53 0.107 0
1000 2649121 20.27 0.098 0
10000 26491206 20.34 0.097 0
Figure 70. Halifax FB-MultiPier single pile moment response
-45
-40
-35
-30
-25
-20
-15
-10
-5
0
-30 -20 -10 0 10 20 30
Dep
th f
rom
Cen
ter
of
Pil
e C
ap
(ft
)
Moment in Pile (k-ft)
RSR=.1
RSR = 1
RSR = 2
RSR = 5
RSR = 10
RSR = 20
RSR = 50
RSR= 100
RSR = 1000
Page 101
90
Figure 71. Halifax FB-MultiPier single pile displacement response
RSRs of 0.001 and 0.01 are not shown in Figure 70 and Figure 71 because they generated
the same moment and deflection response as when the RSR equaled 0.1. Therefore, with
a rotational stiffness equal to 265 k-ft/rad or less, the Halifax County single pile model
would behave as a free head condition. The RSR data set at 10000 is also not shown in
Figure 70 and Figure 71 because it produced the same moment and deflection as when
the RSR equaled 1000. As a result, a rotational stiffness of at least 2649121 k-ft/rad
produces a behavior in the pile equivalent to assuming a fixed head condition. From this
analysis, the difference in pile head deflection between the free head pile behavior at an
RSR of 0.1 and the fixed head pile behavior at an RSR of 1000 was 0.278 inches.
Another aspect that was analyzed was the ―depth to a point of fixity‖ based on the head
fixity condition. The free and fixed head equivalent models from Robinson et al (2006)
-45
-40
-35
-30
-25
-20
-15
-10
-5
0
-0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
Dep
th f
rom
Cen
ter
of
Pil
e C
ap
(ft
)Pile Displacement (in)
RSR=.1
RSR = 1
RSR = 2
RSR = 5
RSR = 10
RSR = 20
RSR = 50
RSR = 100
RSR = 1000
Page 102
91
for determining an equivalent length, Le for depth to fixity will be applied based on to the
range of rotational stiffness analyzed (Refer to Chapter 2). For this investigation the
equivalent free head depth to fixity length will be applied to the RSR cases where the
maximum moment occurs at some depth below the top of the pile. The equivalent fixed
head depth to fixity length will be applied to the RSR cases where the maximum moment
occurs at the pile head (indicated in Table 20). Table 21 and Figure 72 show the
associated RSR along with the results of the maximum moment and equivalent length of
depth to fixity analysis.
Table 21. Halifax County equivalent length of pile to a depth of fixity
RSR
Mmax (k-ft)
Equivalent
Depth to
Point of
Fixity Le
(ft)
Assumed Head
Condition Model
from Robinson et al
(2006)
0.001 28.09 16.6 Free
0.01 28.04 16.6 Free
0.1 27.63 16.4 Free
1 24.27 14.4 Free
2 21.69 12.9 Free
5 17.35 10.3 Free
10 14.34 17.0 Fixed
20 16.82 19.9 Fixed
50 18.77 22.2 Fixed
100 19.53 23.1 Fixed
1000 20.27 24.0 Fixed
10000 20.34 24.1 Fixed
Page 103
92
Figure 72. Halifax County single pile rotational stiffness effect on equivalent depth
to fixity
Upon observation of Figure 72, it should be noted that for the single pile model of the
Halifax County Bridge that from a RSR up to 0.1, an equivalent depth to fixity can be
modeled by the free head assumption presented in Robinson et al (2006). This modeling
yielded an equivalent depth to fixity of 16.6 feet and an α value of .309 (Refer to α
description in Chapter 2). After an RSR of 0.1, the rotational stiffness has an effect on
the pile head. However, as this rotational stiffness in the pile head is increased, the free
head behavior modeled by Robinson et al (2006) was not effective for the Halifax County
model. Also, from a RSR of 100 or more, the equivalent pile depth to fixity seems to be
accurately modeled by the fixed head assumptions of Robinson et al (2006) at an
equivalent depth of 24.1 feet and a corresponding α value of .915. With an RSR of less
than 100, the fixed pile head assumptions from Robinson et al (2006) cannot accurately
be applied because there is only partial fixity of the pile head. From this analysis it is
evident that for the Halifax County model, the range of partial head fixity can account for
5
10
15
20
25
30
0.001 0.01 0.1 1 10 100 1000
Eq
uiv
ale
nt
Len
gth
, L
e (f
t)
RSR (k-ft/rad / k/in)
Le Based on
Fixed Head
Assumption
Le Based on
Free Head
Assumption
Page 104
93
7.5 feet of the equivalent depth to fixity between the free head and fixed head behavior
which falls in a RSR range of 0.1 to 100. Figure 73 presents the concluding results for
the Halifax County single pile model equivalent depth to fixity.
Figure 73. Concluding equivalent depth to fixity range for Halifax County pile
5.3.2 Wake County Bridge
Robinson et al (2007) provided the Wake County Bridge information. This bridge
consisted of 3 interior bents and 2 end bends that span Richland Creek on NC 98. The
super structure consists of seventeen, 4.5 foot (1.372m) pre-stressed concrete girders,
cast-in-place concrete slabs, and a continuous diaphragm connection at interior bent
locations. For this bridge, there were two rows of type V elastomeric bearing pads located
at the 17 support locations along the pile cap. The interior bent modeled consisted of a
pile cap that had a cross section of 49 inches (1.25m) wide, 30 inches (.76m) thick, and
10
12
14
16
18
20
22
24
26
0.001 0.01 0.1 1 10 100 1000
Eq
uiv
ale
nt
Len
gth
, L
e (f
t)
RSR (k-ft/rad / k/in)
Partial Head Fixity Effective Range
Acceptable
Fixed Head
Assumption
Acceptable
Free Head
Assumption
Page 105
94
160 feet (48.7 m) long. The supporting foundation elements consisted of seven, 4.5 foot
(1.372m) diameter drilled with an average length of 42.7 feet (13m) from the height of
the water table to the pile tip. The foundation elements had an average free length of 38.1
feet (11.6 m) from the center of the pile cap to the water table. The foundation elements
consisted of 4 foot (1.22 m) diameter columns.
The water table in the soil profile was located at 38.1 feet (11.6 m) below the center of
the pile cap. Below the water table at 23 feet (7 m) existed a 10.5 foot (3.2 m) layer of
weathered rock was found that was modeled as stiff clay with an unconfined shear
strength of 8000 lbs per square foot (383 kPa) strength. Under this stiff clayey material
was the base material which consisted of weathered limestone. The shafts were drilled to
provide end bearing in this weathered limestone layer. Figure 61 is an illustration of the
interior bent and Figure 68 illustrates the soil profile which was modeled for the Wake
County Bridge in Robinson et al (2007).
Figure 74. Illustration of Wake County interior bent modeled in FB-MultiPier
Page 106
95
Figure 75. FB-MultiPier soil profile for the Wake County interior bent
5.3.2.1 Single Pile Analysis
A single pile model was generated based on the interior bent model from Robinson et al
(2007). The single pile model was analyzed under a lateral load in the longitudinal
direction by 3.2 kips (14.2 kN). Figure 69 shows the Wake County single foundation
element analyzed.
Page 107
96
Figure 76. FB-MultiPier single pile model for Wake County interior bent pile
The axial stiffness of the foundation element was determined to be 141 k/in (24658
kN/m). From the axial stiffness, the input parameters were generated and can be viewed
along with the results in Table 20.
Figure 77 and Figure 78 show the pile moment and displacement response as the RSR
was increased for the Wake County single pile model.
Page 108
97
Table 22. Wake County FB-MultiPier single pile results of pile cap fixity
RSR Rot. Stiffness
(k-ft/rad) Mmax (k-ft)
Pile Top
Deflection
(in)
Depth to Mmax
from Center of
Pile Cap (ft)
0.001 0.14 198.8 0.484 62.3
0.01 1.4 198.7 0.484 62.3
0.1 14 197.3 0.480 63.6
1 141 184.9 0.437 63.6
2 281 174.1 0.402 63.6
5 704 153.0 0.331 63.6
10 1407 135.0 0.270 64.9
20 2815 118.7 0.217 63.5
50 7037 105.5 0.169 64.9
100 14074 100.4 0.150 0
1000 140743 106.5 0.130 0
10000 1407430 107.1 0.128 0
Figure 77. Wake County FB-MultiPier single pile moment response
-80
-70
-60
-50
-40
-30
-20
-10
0
-125 -75 -25 25 75 125 175 225
Dep
th f
rom
Cen
ter
of
Pil
e C
ap
(ft
)
Moment in Pile (k-ft)
RSR =.1
RSR = 1
RSR = 2
RSR = 5
RSR = 10
RSR = 20
RSR = 50
RSR = 100
RSR = 1000
Page 109
98
Figure 78. Wake County FB-MultiPier single pile displacement response
The RSR values at 0.001 and 0.01 are not shown in Figure 70 and Figure 71 because they
had the same moment and deflection response as an RSR value of 0.1. From these results
of the Wake County single pile model, a rotational stiffness equal to 14 k-ft/rad or less
would behave under free head conditions. In this analysis, the RSR data set at 10000 was
not shown in Figure 70 and Figure 71 because it produced the same moment and
deflection as at the RSR of 1000. As it can be seen by the deflected shape and moment
diagram, a rotational stiffness of at least 140743 k-ft/rad can be evaluated under a fixed
head condition. With these results, the difference in pile head deflection between the free
head pile behavior at an RSR of 0.1 and the fixed head pile behavior at an RSR of 1000
was found to be 0.35 inches.
As in the investigation of the Halifax County modeled pile, the Wake County foundation
element depth to a point of fixity was analyzed. Table 23 and Figure 79 show the
-80
-70
-60
-50
-40
-30
-20
-10
0
-0.10 0.00 0.10 0.20 0.30 0.40 0.50D
epth
fro
m C
ente
r of
Pil
e C
ap
(ft
)Pile Displacement (in)
RSR=.1
RSR = 1
RSR = 2
RSR = 5
RSR = 10
RSR = 20
RSR = 50
RSR = 100
RSR = 1000
Page 110
99
associated RSRs along with the results of the maximum moments and equivalent point of
fixity lengths based on the Robinson et al (2006) models.
Table 23. Wake County equivalent length of pile to a depth of fixity
RSR
Mmax (k-ft)
Equivalent
Depth to
Point of
Fixity Le
(ft)
Assumed Head
Condition Model
from Robinson et al
(2006)
0.001 198.8 62.4 Free
0.01 198.7 62.3 Free
0.1 197.3 61.9 Free
1 184.9 58.0 Free
2 174.1 54.6 Free
5 153.0 48.0 Free
10 135.0 42.4 Free
20 118.7 37.2 Free
50 105.5 33.1 Free
100 100.4 63.0 Fixed
1000 106.5 66.8 Fixed
10000 107.1 67.2 Fixed
Page 111
100
Figure 79. Wake County single pile rotational stiffness effect on equivalent depth to
fixity
Figure 79 shows that up to an RSR of 0.1, the equivalent depth to fixity can be modeled
by the free head assumption, presented in Robinson et al (2006). This assumption yielded
both an equivalent depth to fixity of 62.4 feet (19 m) and a corresponding α value of
0.791. As the rotational stiffness in the pile head is increased past an RSR of 0.1, the free
head behavior modeled by Robinson et al (2006) should not be used. For an RSR of
1000 and greater, the equivalent depth to fixity is accurately modeled by the fixed head
model in Robinson et al (2006). For these conditions, the equivalent depth to fixity was
67.2 feet (20.5 m) with a corresponding α value of 2.95. For the Wake County single pile
model, the range of partial head fixity can account for 5 feet (4.1 m) of the equivalent
depth to fixity between the free head and fixed head Robinson et al (2006) models. This
corresponds to a RSR range of 0.1 to 1000.
Figure 80 presents the concluding results for the equivalent depth to fixity for the Wake
County Bridge foundation element modeled.
Page 112
101
Figure 80. Concluding equivalent depth to fixity range for Wake County foundation
element
5.3.3 Robeson County Bridge
The Robeson County Bridge information was obtained from Robinson et al (2006). This
bridge consisted of 1 interior bent and 2 end bends that span over Lumber River on NC
Route 1303. The super structure consisted of fifteen, 3 foot by 1.75 foot pre-stressed
concrete cored slabs. For this bridge, two rows of type II elastomeric bearing pads were
located at the 15 support locations along the pile cap. The interior bent modeled
consisted of a pile cap that was 33 inches wide and 30 inches thick. The supporting
foundation elements consisted of eight, 14 x 73 H-piles that were 55 feet long from the
center of the pile cap to pile tip. The piles had a free length of 8 feet from the center of
55
57
59
61
63
65
67
69
0.001 0.01 0.1 1 10 100 1000
Eq
uiv
ale
nt
Le
ng
th, L
e (
ft)
RSR (k-ft/rad / k/in)
Partial Head Fixity Effective Range
Le Based on Fixed Head Assumption
Le Based on Free Head Assumption
Page 113
102
the pile cap to the ground level and the two end piles in the interior bent were battered at
1:8.
The soil profile modeled consisted of the water table located at a depth 5 feet below the
center of the pile cap. A sandy silt layer existed 8 feet below the water table which was
modeled as a non-cohesive sand with a friction angle of 28 degrees. This sandy silt layer
extended to a depth of 49.2 feet below the center. Below this sandy material was a stiff
clay layer with an undrained shear strength of 6480 lbs per square foot, in which the pile
was driven to produce satisfactory end bearing. Under this stiff clay layer was another
sandy material that was very dense with a friction angle of 35 degrees. Figure 61 and
Figure 82 illustrate the interior bent and soil profile model for the Robeson County bridge
in Robinson et al (2006).
Figure 81. Illustration of Robeson County interior bent modeled in FB-MultiPier
Page 114
103
Figure 82. FB-MultiPier soil profile for the Robeson County interior bent
5.3.3.1 Single Pile Analysis
From the Robeson County interior bent model in Robinson et al (2006), a single pile
model was generated in same manner as the Halifax and Wake County bridges. The
single pile was analyzed under a lateral load of 1.3 kips. Figure 69 presents and
illustration of the Robeson County single pile model.
Page 115
104
Figure 83. FB-MultiPier single pile model for Robeson County interior bent pile
The axial stiffness of the 55 foot long 14 x 73 H-piles was 940 k/in. Table 20 shows the
single pile input parameters and results. Figure 70 through Figure 87 show the pile
moment and displacement response as the RSR was increased.
Page 116
105
Table 24. Robeson County FB-MultiPier single pile results of pile cap fixity
RSR
Rot.
Stiffness
(kip-ft/rad)
Mmax (k-ft)
Pile Top
Deflection
(in)
Depth to Mmax
from Center
of Pile Cap
(ft)
0.001 0.9 12.97 0.3068 11.18
0.01 9 12.95 0.3062 11.18
0.1 94 12.75 0.3005 11.18
1 940 11.00 0.251 12.23
2 1881 9.84 0.2204 12.23
5 4700 7.95 0.1707 11.18
10 9403 6.65 0.1365 0
20 18806 7.72 0.1113 0
50 47000 8.54 0.0919 0
100 94030 8.86 0.0845 0
1000 940303 9.16 0.0774 0
10000 9403030 9.20 0.0767 0
Figure 84. Robeson County FB-MultiPier single pile moment response
-60
-55
-50
-45
-40
-35
-30
-25
-20
-15
-10
-5
0
-10 -5 0 5 10 15
Dep
th B
elow
Cen
ter
of
Pil
e C
ap
(ft)
Moment in Pile (k-ft)
RSR =.1
RSR = 1
RSR = 2
RSR = 5
RSR = 10
RSR = 20
RSR = 50
RSR = 100
RSR = 1000
Page 117
106
Figure 85. Robeson County FB-MultiPier single pile moment response enlarged
Figure 86. Robeson County FB-MultiPier single pile displacement response
-35
-30
-25
-20
-15
-10
-5
0
-10 -5 0 5 10 15D
epth
Bel
ow
Cen
ter
of
Pil
e C
ap
(ft
)
Moment in Pile (k-ft)
RSR =.1
RSR = 1
RSR = 2
RSR = 5
RSR = 10
RSR = 20
RSR = 50
RSR = 100
RSR = 1000
-55
-50
-45
-40
-35
-30
-25
-20
-15
-10
-5
0
-0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
Dep
th B
elow
Cen
ter
of
Pil
e C
ap
(ft
)
Pile Displacement (in)
RSR=.1
RSR = 1
RSR = 2
RSR = 5
RSR = 10
RSR = 20
RSR = 50
RSR = 100
RSR = 1000
Page 118
107
Figure 87. Robeson County FB-MultiPier single pile displacement response enlarged
As was the case for the Halifax and Wake County single pile models, an RSR value equal
to 0.001 or 0.01 is not shown in Figure 70 through Figure 71 because they contained the
same moment and deflection response as an RSR of 0.1 for the Robeson County model.
As a result, a rotational stiffness less than or equal to 94 k-ft/rad could be modeled as a
free head condition. Also, in this analysis the RSR data set at 10000 is not shown in
Figure 70 through Figure 71 because it produced the same moment and deflection as that
at an RSR of 1000. This infers that a rotational stiffness of 940303 k-ft/rad or greater can
be modeled under a fixed head condition for the Robeson County single pile model.
With these results, the difference in pile head deflection from the free head pile behavior
at an RSR of 0.1 and the fixed head pile behavior at an RSR of 1000 is 0.23 inches.
As was analyzed for the Halifax and Wake County modeled piles, the Robeson County
H-pile depth to a point of fixity was also studied. Table 25 shows the associated RSR
-30
-25
-20
-15
-10
-5
0
-0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35D
epth
Bel
ow
Cen
ter
of
Pil
e C
ap
(ft
)
Pile Displacement (in)
RSR=.1
RSR = 1
RSR = 2
RSR = 5
RSR = 10
RSR = 20
RSR = 50
RSR = 100
RSR = 1000
Page 119
108
along with the results of the maximum moment and equivalent length of depth to fixity
analysis. These results were also plotted in Figure 72.
Table 25. Robeson County equivalent length of pile to a depth of fixity
RSR
Mmax (k-ft)
Equivalent
Depth to
Point of
Fixity Le
(ft)
Assumed Head
Condition Model
from Robinson et al
(2006)
0.001 12.97 10.2 Free
0.01 12.95 10.2 Free
0.1 12.75 10.0 Free
1 11.00 8.7 Free
2 9.84 7.7 Free
5 7.95 6.3 Free
10 6.65 10.5 Fixed
20 7.72 12.2 Fixed
50 8.54 13.5 Fixed
100 8.86 14.0 Fixed
1000 9.16 14.4 Fixed
10000 9.20 14.5 Fixed
Page 120
109
Figure 88. Robeson County single pile rotational stiffness effect on equivalent depth
to fixity
Figure 72 shows that for the Robeson County single pile model for a RSR up to 0.1; an
equivalent depth to fixity can be modeled by the free head assumption presented in
Robinson et al (2006). This free head model yielded an equivalent depth to fixity of 10-
10.2 feet and a corresponding α value of 0.342. As the rotational stiffness in the pile
head is increased past an RSR equal to 0.1, the free head behavior modeled by Robinson
et al (2006) becomes ineffective. Also, at a RSR of 100 and greater, the equivalent pile
depth to fixity seems to be accurately modeled by the fixed head assumptions of
Robinson et al (2006). This fixed head model produces an equivalent depth to fixity of
14 to 14.5 feet with an α value of 0.982. From this analysis it is evident that for the
Robeson County single pile model, the range of partial head fixity can account for 4.3
5
6
7
8
9
10
11
12
13
14
15
0.001 0.01 0.1 1 10 100 1000
Eq
uiv
ale
nt
Len
gth
, L
e (f
t)
RSR (k-ft/rad / k/in)
Le Based on
Fixed Head
Assumption
Le Based on
Free Head
Assumption
Page 121
110
feet of the equivalent depth to fixity between the free head and fixed head behavior which
falls in a RSR range of 0.1 to 100.
Figure 89 presents the concluding results for the equivalent depth to fixity for the
Robeson County Bridge H-pile modeled.
Figure 89. Concluding equivalent depth to fixity range for Robeson County H-pile
5.4 Conclusions
From the full scale test models, it was shown that the maximum displacement generated
in laboratory could be modeled through the FB-MultiPier program. Also, an equivalent
single pile analysis predicted the behavior of the laboratory data by assuming equivalent
5
6
7
8
9
10
11
12
13
14
15
0.001 0.01 0.1 1 10 100 1000
Eq
uiv
ale
nt
Len
gth
, L
e (f
t)
RSR (k-ft/rad / k/in)
Partial Head Fixity Effective Range
Le Based
on Fixed
Head Assumption
Le Based
on Free
Head Assumption
Page 122
111
parameters for the elastomeric bearing pads with joint rotational stiffness. The equivalent
parameters were chosen such that when multiplied by a certain factor they would be
equivalent to the rotational stiffness measured during full scale testing. The results from
the H-pile models with the type VI bearing pad were found to be inaccurate because
independent rotation occurred between the steel H-pile and cap beam during laboratory
testing and could not be accurately accounted for when modeled in FB-MultiPier.
The North Carolinian Bridge case study showed the effects of the rotational stiffness of
the pile head condition in accordance with the equivalent depth to fixity model proposed
by Robeson et al (2006). This analysis provided equivalent parameters that would
produce the same maximum moment and pile top lateral deflection if the foundation
elements were to be analyzed as column fixed at the base for both free and fixed head
condition. These results showed that for each type of pile in its respective soil profile
there was a range between the free and fixed head condition which could account for
partial fixity of the pile head. Depending on the pile length and soil profile, the partial
fixity of the pile head accounted for differences between the equivalent depth to fixity
between the free and fixed head cases. The pile head partial fixity accounted for 4.3 feet,
4.8 feet, and 7.5 feet of the depth to a point of fixity for the Robeson, Wake and Halifax
models, respectively. Also, the effect of the rotational stiffness of the pile head
accounted for 25% of the embedded length into the soil for the Halifax County
foundation element, 15% of the embedded length for the Wake County foundation
element, and 8% of the embedded length for the Robeson County foundation element.
Page 123
112
CHAPTER 6: LIMIT STATES
6.1 Background
One of the serviceability limit states, due to lateral loading in the transverse direction
mentioned in the Robinson et al (2006) report, was due to joint closure. For this type of
limit state, different equations were presented which indicated the distance that a joint
gap would close if an applied horizontal load in the transverse direction along a
horizontal load were transferred.
Figure 90 shows a conceptual model for determining the different components associated
with the joint closure serviceability limit state presented in the Robinson et al (2006)
report. The model is based on representing the bridge as a beam with supports replaced
by springs.
Figure 90. Joint closure model for 3 spans supported by 2 interior pile bents at the
expansion joints (Robinson et al, 2006)
Page 124
113
The following equations are used for estimating the force required to close the joints and
the lateral displacement.
Equation 25
Kr
L
EI
Lw
LLTj
P
22
2
2)(
max2
Equation 26 1
maxmax
3
max 23
K
P
Kr
LP
EI
LPtot
Equation 27 totKPFL *2max
Where,
Pmax = Force required to close the expansion joint (force units)
FL = Total lateral force that will close the expansion joint and move the pile bent laterally
(force units)
tot = Lateral displacement limit (length)
j = Joint width (length)
K1 = Abutment stiffness (trans-rot) (force/length)
K2 = Pile group stiffness (trans-rot)(force/length)
Kr = rotational stiffness of the bearing pad in the transverse direction (force-length/rad)
L = exterior span lengths (length)
L2 = interior span length (length)
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w = width of span (length)
EI = flexural stiffness of the superstructure (trans-rot)(force-lenght2)
= coefficient of thermal expansion (1/Temperature)
T = Temperature
The parameter which was not fully defined in the Robinson et al (2006) report was the
rotational stiffness. From the full scale testing, super to sub structure rotational stiffness
values in the longitudinal direction were measured for three different pile cross sections
under various loads. For this analysis, the assumptions included that the rotational and
torsional stiffness are related with the value of the torsional stiffness varying. By
applying different magnitudes of the rotational stiffness into the joint closure limit state
problem the limiting failure modes may be determined. This analysis will be beneficial
in determining the effect that the rotational stiffness in the transverse direction has in
causing different parts of the bridge assembly to govern failure.
6.2 Analysis
An existing bridge is analyzed in which Model 3 from Robinson et al (2006) shown in
Figure 90 can be implemented to determine if the joint closure serviceability limit state is
a governing failure mode for the bridge system. The bridge being analyzed is the Halifax
County Bridge which consists of 9 spans. The interior girder spans are supported by a
continuous cap beam with 8 piles. The supporting square piles are 18 inches (45.7cm) in
width and are between 40 feet (12.2m) and 50 feet (15.2m) long. The interior bents’
connection with the superstructure for 2 spans is through 15 Type I elastomeric bearing
pads. For this bridge configuration, parameters will be changed slightly so that similar
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parameters from full scale testing on a 20 inch (50.8cm) square pile under a Type V and
Type VI bearing pad may be used. The rotational stiffness determined from full scale
testing on the square pile will be multiplied by a factor of 15 to simulate the torsional
stiffness of the entire bent connection of the Halifax County Bridge. Additional
simulations are also run assuming 1/10, 0.5, 2, and 10 times the original torsional
stiffness to study what effect the rotational stiffness has on the failure component of the
bridge. The simulation is run assuming that the original joint gap between the spans is 0.5
inches (1.27cm). If it is determined that there will be a component of the bridge that will
fail before the joint closes, the required original joint gap will be calculated that ensures
that the joint closure is the limiting failure mode.
Individual simulations were performed on similar interior pile bents and the results
showed that the pile bent could not tolerate a horizontal load (transverse direction)
greater than 44 kips(195kN) and would fail with a maximum displacement of 0.6
inches(1.5cm). Figure 91 shows the tolerable response curve of the lateral load verse
transverse displacement of the pile bent.
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Figure 91. Halifax County Bridge bent response to lateral load (Robinson, 2007)
From Figure 91 the K2 term is defined for Equation 25 and a known limit of the pile
bents capacity is determined for system. Knowing the pile group’s capacity at a
horizontal applied load of 44kips (195kN), it can be determined if this capacity will be
the governing failure parameter compared to the joint closure serviceability limit.
The abutment stiffness variable (K1), was applied to this bridge from tests on another
bridge from Maroney (1995) and the response of the abutment stiffness was used in the
analysis. Table 26 shows the input variables based on details of the Halifax County
Bridge, as well as information presented in Figure 91. It should be noted that it was
assumed for this analysis that the thermal expansion component was not significant.
Halifax County--1 row 8 PSC piles, with Dead Load
0
5
10
15
20
25
30
35
40
45
50
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Transverse Displacement (in)
To
tal
Ap
pli
ed
Tra
nsvers
e L
oad
(kip
s)
Halifax County--1 row 8 PSC
piles, with Dead Load
Note: Dead load was approximately
400 kN on each pile
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Table 26. Input variables for Halifax County Bridge section
E (Young’s
Modulus of
concrete) 550609 Ksf 26314593 kN/m2
I (moment of
inertia of
superstructure) 6253 ft4 53.97 m
4
L (length of
outer spans) 40 Ft 12.2 m
L2 (length of
interior span) 35 Ft 10.7 m
W (width of
span) 35 Ft 10.7 m
t (thickness of
deck) 1.75 Ft 0.5 m
K1 2579 k/ft 123269 kN/m2
K2 884 k/ft 42267 kN/m2
α∆T (joint
thermal
expansion
component) 0
The rotational stiffness values were taken from the results of the square pile; 3% ALR
loading case of P1 on bearing pad type V at 0.75 inch (1.91cm) top displacement, the
closest to the maximum capacity of 0.6 inch (1.52cm) of the pile group presented in
Figure 91. This particular loading case from the full scale test was deemed important
because this loading sequence produced the maximum measured rotational stiffness for
the square pile configuration. Also, the rotational stiffness used from full scale testing
was used as only a representation of the torsional stiffness required. The results from the
application of the limit state problem presented in
Figure 90 for the Halifax County Bridge is displayed in Table 27.
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Table 27. Results from joint closure investigation for Halifax County Bridge
Factors
of
Torsional
Stiffness
Assumed
Torsional Stiffness
(Kr)
Thickness of
expansion
joint (δj)
Force Required
to Close Gap
(Pmax)
Total
Transverse
Lateral
Displacement
from Pmax
(δt)
Total lateral
force that will
close the exp.
Joint and move
the pile laterally
(FL)
k-ft/rad kN-m/rad in cm kips kN in cm kips kN
original 184349 249481 0.50 1.27 11.0 48.7 1.19 3.03 1066 4735
1/10 18435 24948 0.50 1.27 1.1 4.87 1.15 2.92 1016 4512
1/5 36870 49896 0.50 1.27 2.2 9.7 1.15 2.93 1022 4537
1/2 92174 124741 0.50 1.27 5.5 24.4 1.17 2.97 1039 4611
2 368697 498962 0.50 1.27 21.9 97.2 1.24 3.16 1122 4982
5 921743 1247406 0.50 1.27 54.5 242.3 1.39 3.54 1288 5719
10 1843487 2494812 0.50 1.27 108.5 482.0 1.64 4.18 1562 6937
As shown in Table 27, the force required to close a 0.5 inch (1.27cm) expansion joint
(FL) does not vary significantly as a function of the range of torsional stiffness inputted
into the model. These results also show that the force required to close the expansion
joint is larger than the lateral load capacity of the interior pile bents (44kips/195kN). If
the torsional stiffness is reduced to essentially zero, allowing free torsion, its effects are
minimal on the overall system. Table 28 shows the results of the simulation for
essentially free torsion of the connection. The pile bent’s lateral capacity still governs as
the failure mode.
Table 28. Results from simulation assuming essentially free torsion
Factors of
Torsional
Stiffness
Assumed
Torsional Stiffness
Thickness of
expansion
joint (δj)
Force Required
to Close Gap
(Pmax)
Total
Transverse
Lateral
Displaceme
nt from
Pmax (δt)
Total lateral
force that will
close the exp.
Joint and move
the pile laterally
(FL)
k-
ft/rad
kN-
m/rad In cm kips kN in cm kips kN
original 0.00 0.00 0.50 1.27 0.00 0.00 1.14 2.90 1011 4488
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The Table 28 data also shows that allowing the interior pile bents to twist freely still does
not lead the joints to close. For this particular bridge case, it would take 1011 kips
(4488kN) to close the expansion joint where the pile would have already experienced its
lateral displacement limit of 0.6 inches (1.52cm) at 44 kips(195kN).
The most significant contributing factor upon the force required to close the expansion
joint is the abutment rotational stiffness, as evident by the nature of Equation 27. Even
though the results in Table 27 showed that the joint closure would not be the governing
failure mode for a 0.5 inch (1.27cm) expansion joint, the required expansion joint
thickness to cause the joint failure to be the governing failure mode can be determined.
By limiting the required lateral force to close the expansion gap to 44 kips (195kN), the
joint thicknesses that correspond to failure by joint closure are presented in Table 29 as a
function of rotational stiffness.
Table 29. Results from determined required joint thickness for failure due to joint
closure
Factors
of
Torsional
Stiffness
Assumed
Torsional Stiffness
Thickness of
expansion joint
required for joint
closure failure
mode (δj)
Force Required
to Close Gap
(Pmax)
Total
Transverse
Lateral
Displaceme
nt from
Pmax (δt)
Total lateral
force that
will close
the exp.
Joint and
move the
pile laterally
(FL)
k-ft/rad
kN-
m/rad in cm kips kN in cm kips kN
original 0.00 0.00 0.0218 0.0553 0.00 0.00 0.05 0.13 44 195
1/10 18435 24948 0.0216 0.055 0.05 0.21 0.05 0.13 44 195
1/5 36870 49896 0.0215 0.0547 0.09 0.42 0.05 0.13 44 195
1/2 92174 124741 0.0212 0.0538 0.23 1.03 0.05 0.13 44 195
2 368697 498962 0.0196 0.0498 0.86 3.81 0.05 0.12 44 195
5 921743 1247406 0.0171 0.0434 1.86 8.28 0.05 0.12 44 195
10 1843487 2494812 0.0141 0.0358 3.06 13.57 0.05 0.12 44 195
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The results in Table 29 show that the largest expansion joint for which the failure mode is
―joint closure‖ is 0.0218 inches (0.0553cm). Hence, based on the stiffness and results
presented, the pile bents lateral capacity will be the governing limit state.
6.3 Summary and Conclusions
It was determined that the abutment rotational stiffness of the foundation element has the
most significant impact on the joint failure model. Also, the analysis showed that the
foundation element would fail before joint closure would occur. It should be noted that
this conclusion is only for the particular details for the Halifax County Bridge and the
previously assumed model parameters. However, it does show that the effects of the
torsional stiffness on the limit state of the bridge configuration due to lateral load are
minimal when the limit state is governed by the magnitude of lateral pile deformation.
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CHAPTER 7: SUMMARY AND CONCLUSIONS
The main focus of the full scale testing investigation was to determine the connection
rotational stiffness between the super and substructure through elastomeric bearing pad
connections. The other aspects of this study were to model the full scale testing in a
computer program and analyze how the rotational stiffness at the connection head of a
foundation element affected the equivalent depth to fixity model by Robinson et al
(2006). In addition, limit states in terms of deck gap closure and lateral deformation of
pile foundations were studied.
7.1 Full Scale Tests
The full scale tests simulated a section of the connection elements according to NC DOT
design specifications. These tests, with an elastomeric bearing pad and anchor bolt joint
connection allowed for the connection stiffness to be measured. Test results showed that
the rotational stiffness of the connection accounted for roughly 60 % of the overall
displacement measured at the point of lateral load application. As the loads were
increased past yielding of the longitudinal steel in the concrete foundation elements, it
was observed that the pile cap began to lift off of the bearing pad, the sole plates
experienced flexural bending, and the embedded plate in the girder experienced signs of
pull out. For the H-pile test, as loads were increased to cause top deflections greater than
1.5 inches, cracking increased between the connection of the steel H-pile and the concrete
pile cap. From testing of the H-pile, it was shown there may be a concern with the 12
inch requirement for embedment length of the H-pile in the pile cap since pull out action
occurred before yielding of the steel H-pile. From these tests it was observed that the
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maximum moment at the bottom of pile cap was in the range of 150 k-ft to 225 k-ft with
a pile cap rotation of 0.5 degrees.
7.2 FB-MultiPier Modeling
The full scale tests were modeled in FB-MultiPier and the rotational stiffness of the
bearing pad assumed half that measured in the laboratory. Equivalent single pile analyses
were then performed in FB-MultiPier. From these single pile models it was determined
that the same deflections as the measured full scale tests could be made by assigning
equivalent shear and compression stiffness for the elastomeric bearing pads.
Case study analyses were performed on three North Carolina bridges in Halifax, Wake
and Robeson County. From these analyses it was determined that the pile head should be
modeled as a partially fixed head between a RSR of 0.1 to 100 for the Halifax and
Robeson County foundation elements and between an RSR of 0.1 to 1000 for the Wake
County foundation element. The equivalent depth to fixity of the pile was affected by the
head fixity condition. These results showed that the pile head rotational stiffness could
account for a range in length which was 25% of the equivalent depth to fixity for the
Halifax County foundation element, 15% of the Wake County foundation element
equivalent depth to fixity, and 8% of the equivalent depth to fixity of the Robeson County
bridge foundation element.
These results performed for the three bridge foundation elements are limited to the type
of foundation element and the soil profile. All of these components could affect the
results of how the foundation element head fixity condition impacts the equivalent depth
to fixity. It is recommended that further investigations and modeling be performed to
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determine how the soil profile, foundation element type, and element free length in
combination with the head rotational stiffness affect the equivalent depth to fixity.
7.3 Limit States
An additional study was performed on the proposed limit state of joint closure in the
transverse direction in Robeson et al (2006). From this study it was determined that the
abutment rotational stiffness in the transverse had the most significant impact on the
response of the joint closure. However, for the analyzed Halifax County Bridge, it was
determined that the foundation element would fail before joint closure would occur.
7.4 Conclusions
i. Observations from the performance testing indicated the first yielding of the
longitudinal steel bars in the square and circular piles occurred at
approximately 3 in (76 mm) top deflection (at the point of load application).
ii. In the case of the circular pile it was observed that a deflection of 3.26 inches
(83 mm) at the point of load application produced yielding of the longitudinal
steel. When the pile was loaded to ductility 1.5 (4.89 inches displacement) the
testing was terminated because bending was noted around the weak axis of the
sole plate. It was observed that the weakest link for this connection was the
sole plate that is located at the top of the bearing pad. The force produced by
the bending of the sole plates caused a gap between the embedded plate and
the girder because of the pulling action. However, the force experienced
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during this test was not enough to pull out the embedded plate from the girder.
The bending of sole plates caused crushing of the concrete around the
diaphragm area.
iii. Results from performance testing also indicated an increase in the rotational
stiffness of the connection corresponding to an increase in the test pile and
bearing pad stiffness (as induced by applying higher axial loads.) For the
conditions simulated in this testing program, the largest contributors to the
total displacement response of the tested system were cap beam rotation
(approximately 59%), followed by the pile lateral deformation (approximately
30%).
iv. The results from the full scale testing show the capacity of sole plate-anchor
bolt and bearing pads system for transferring the applied moments. Given the
test component strength and stiffness parameters, the maximum moment in
the pile cap for all piles tested was between 150 (218.5) and 225(327.8) k-ft
(kN/cm). The maximum cap rotation was approximately 0.5 degrees for all
loading cases except for the H-pile tests on the Type V bearing pad. In this
case, the maximum pile cap rotation was more than double that experienced in
the other cases.
v. Observations of the system components during testing indicated that the steel
sole plates located at the top of the bearing pads were bent during load
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application, which led to crushing of the concrete at the diaphragm area.
Under the applied lateral loads, the bending action of the sole plates led to pull
out of the embedded plate on the girder. The embedded plate had four studs of
178 mm (7 in) in length, which provided enough strength against the pulling
force produced by the bending of the sole plates.
vi. In the case of the H-pile testing (which was tested after the square and circular
cross sections) a top deflection of 6.23 inches (158 mm) at a horizontal load of
~18 kips was needed to reach the first yielding. After completion of the elastic
cycles, significant cracks developed between the H-Pile and the pile cap.
These cracks became more pronounced as the second loading protocol began.
Testing continued to the completion of a ductility of 1.5 where the top
deflection at the point of load application reached 9.34 inches (237 mm). The
prying action of the embedded part of the HP pile caused large damage in the
cap beam.
vii. The general trend observed during testing was an increase in the rotational
stiffness with increased confining stress (as induced by axial load on the pads)
for the square concrete pile. The secant rotational stiffness for the square pile
under the P3 load level of approximately 45 kips was 550 k-ft/deg for type V
bearing pad and 660 k-ft/deg for type VI at 1 inch lateral displacement (at the
point of load application.) At the same displacement level with the use of the
circular pile, the secant rotational stiffness was approximately 325 k-ft/deg for
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the system with both type V and VI bearing pads. By comparison the secant
rotational stiffness for the H-pile was approximately 150 k-ft/deg for the
system with both type V and VI bearing pads. The square pile was stiffer than
both the circular and HP piles which contributed to the increased ductility of
the connection.
viii. The magnitude of rotational stiffness may be affected by several factors.
These include the elastic modulus for the bearing pads, the load applied to the
bearing pad, the bending of the sole plate, and cracking and failure of the bent
cap around the anchor bolt.
ix. The full scale test can be modeled in FB- MultiPier while assuming that the
rotational stiffness of the bearing pad is equivalent to half the rotational
stiffness measured for the connection joint. This model produced results
within 10% error of the measured results for the desired 1.5 inch pile
deflection for both types of bearing pad configurations. The H-pile model with
the type VI bearing pad did not produce comparable results per observed
results noted above (see conclusions, part vi).
x. The equivalent single pile model assumed that the joint shear stiffness was
equal to twice the shear stiffness of one bearing pad. The model also assumed
that the joint compressive stiffness was equal to the compressive stiffness of
one bearing pad, and that the rotational stiffness implemented was equal to
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that which was measured. These models generated results which were within
20% error of the measured results for the concrete piles modeled, all of which
were predictions greater than that of the measured displacements.
xi. The case study analyses showed the effects of a partial head fixity condition
on the equivalent depth to fixity length model proposed in Robinson et al
(2006). The results illustrated that the partial head fixity condition for the
Halifax County model could account for a range of 7.5 feet of length while,
for the Wake County model it could account for a range of 4.8 feet in length.
In the Robeson County model the partial head fixity condition could account
for 4.3 feet in length between the fixed and free head, depth to fixity models
generated by Robinson et al (2006).
xii. Currently, NCDOT routinely utilizes a performance level of one inch lateral
displacement at the bent cap to assess shaft length. Robinson et al (2006)
suggested a serviceability limit state of the superstructure characterized by
expansion joint closure due to lateral loading in the transverse direction.
Analyses on interior bents showed that shaft bents analyzed in this study could
not tolerate a horizontal load (transverse direction) greater than those required
to close the expansion joint. For example, if the torsional stiffness is assumed
essentially to equal zero, the total lateral force to close the expansion joint is
equal to 1,011 kips (4488 kN). At the same time, the shaft bent experienced a
lateral displacement limit of 0.6 inches (1.52cm) at 44 kips (195kN).
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Accordingly, the lateral deformation of the shaft bents represents the critical
juncture in the serviceability limit state.
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REFERENCES
American Association of State Highway and Transportation Officials (AASHTO).
(2004). AASHTO LRFD Bridge Design Specifications, Customary U.S. Units, Third
Edition, Washington, D.C.
American Institute of Steel Construction. (2001). ―Manual of Steel Construction: Load
and Resistance Factor Design.‖ 3rd
ed.
Bridge Software Institute (BSI). (2000). FB-MultiPier Manual, Version 4. University of
Florida, USA. http://bsi-web.ce.ufl.edu/
Chen, Y. (1997). ―Assessment of Pile Effective Lengths and Their Effects on Design—I.
Assessment,‖ Computers and Structures, Vol. 62, No. 2. 265-286.
Davisson, M.T., and Robinson, K.E. (1965). ―Bending and Buckling of Partially
Embedded Piles.‖ Proc. Sixth International Conference Soil Mechanics and Foundation
Engineering. University of Toronto Press, Montreal, Canada. 243-246.
Ensoft, Inc. (2004). LPILE Manual. Austin, Texas, USA
Georgia Department of Transportation (revised, 1994). ―Analysis and Design of Multiple
Column Piers for Bridges E75700,‖ Georgia Pier Program Manual Version 4.2. Revised
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by the North Carolina Department of Transportation. 132 pages.
MacGregor, J., and Wight, J., (2005) ―Reinforced Concrete: Mechanics and Design.‖ 4th
ed. Prentice Hall, Upper Saddle River, New Jersey
Maroney, B. (1995). "Large scale bridge abutment test to determine stiffness
and ultimate strength under seismic loading," PhD dissertation, Univ. of
California, Davis, Calif.
North Carolina Department of Transportation. (2003). Highway Design Branch—Design
Manual: Structure Design, State of North Carolina, Raleigh, North Carolina
Priestley, M., Calvi, G., and Kowalsky, M., (2007). ―Displacement-based seismic design
of structures.‖ IUSS Press, Pavia, Italy
Robinson, B. (2007). Personal Communication
Robinson, B., Suarez, V., Robalino, P., Kowalsky, M. and Gabr, M., ―Pile Bent Design
Criteria.‖ NCDOT Research Project 2005-19. Report no. FHWA/NC/2006-14. June,
2006.
Robinson, B., Vidot, A., Park, Y.J., Possiel, B., Suarez, V., Kowalsky, M., and Gabr, M.,
(2007) "Design Criteria for Post and Beam Bents with Drilled Shafts." FHWA/NC/2006-
48
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Yazdani, N., Scott, E., and Chun, C.,(2000) ―Validation of AASHTO Bearing Stiffness
for Standard Precast Concrete Bridge Girders‖, ACI Structural Journal, V. 97, No.3,
May-June, pp. 436-443.
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APPENDIX A: LATERAL FORCE VS. TOP PILE DISPLACEMENT RESPONSE
Figure 92
Figure 93
-100
-80
-60
-40
-20
0
20
40
60
80
100
Forc
e[k
N]
-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20
3% ALR Square/BPV/Load 1
-8 -6 -4 -2 0 2 4 6 8-25
-20
-15
-10
-5
0
5
10
15
20
25
Displacement [in]-(bottom scale) / [m]-(top scale)
Forc
e [
kip
s]
-100
-80
-60
-40
-20
0
20
40
60
80
100
Forc
e[k
N]
-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20
3% ALR Square/BPV/Load 2
-8 -6 -4 -2 0 2 4 6 8-25
-20
-15
-10
-5
0
5
10
15
20
25
Displacement [in]-(bottom scale) / [m]-(top scale)
Forc
e [
kip
s]
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Figure 94
Figure 95
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-60
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-20
0
20
40
60
80
100
Forc
e[k
N]
-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20
3% ALR Square/BPV/Load 3
-8 -6 -4 -2 0 2 4 6 8-25
-20
-15
-10
-5
0
5
10
15
20
25
Displacement [in]-(bottom scale) / [m]-(top scale)
Forc
e [
kip
s]
-100
-80
-60
-40
-20
0
20
40
60
80
100
Forc
e[k
N]
-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20
4% ALR Square/BPV/Load 1
-8 -6 -4 -2 0 2 4 6 8-25
-20
-15
-10
-5
0
5
10
15
20
25
Displacement [in]-(bottom scale) / [m]-(top scale)
Forc
e [
kip
s]
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Figure 96
Figure 97
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-20
0
20
40
60
80
100
Forc
e[k
N]
-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20
4% ALR Square/BPV/Load 2
-8 -6 -4 -2 0 2 4 6 8-25
-20
-15
-10
-5
0
5
10
15
20
25
Displacement [in]-(bottom scale) / [m]-(top scale)
Forc
e [
kip
s]
-100
-80
-60
-40
-20
0
20
40
60
80
100
Forc
e[k
N]
-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20
4% ALR Square/BPV/Load 3
-8 -6 -4 -2 0 2 4 6 8-25
-20
-15
-10
-5
0
5
10
15
20
25
Displacement [in]-(bottom scale) / [m]-(top scale)
Forc
e [
kip
s]
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Figure 98
Figure 99
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0
20
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60
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100
Forc
e[k
N]
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5% ALR Square/BPV/Load 1
-8 -6 -4 -2 0 2 4 6 8-25
-20
-15
-10
-5
0
5
10
15
20
25
Displacement [in]-(bottom scale) / [m]-(top scale)
Forc
e [
kip
s]
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0
20
40
60
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100
Forc
e[k
N]
-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20
5% ALR Square/BPV/Load 2
-8 -6 -4 -2 0 2 4 6 8-25
-20
-15
-10
-5
0
5
10
15
20
25
Displacement [in]-(bottom scale) / [m]-(top scale)
Forc
e [
kip
s]
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Figure 100
Figure 101
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0
20
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60
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100
Forc
e[k
N]
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5% ALR Square/BPV/Load 3
-8 -6 -4 -2 0 2 4 6 8-25
-20
-15
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0
5
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Displacement [in]-(bottom scale) / [m]-(top scale)
Forc
e [
kip
s]
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40
60
80
100
Forc
e[k
N]
-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20
3% ALR Square/BPVI/Load 1
-8 -6 -4 -2 0 2 4 6 8-25
-20
-15
-10
-5
0
5
10
15
20
25
Displacement [in]-(bottom scale) / [m]-(top scale)
Forc
e [
kip
s]
Page 149
138
Figure 102
Figure 103
-100
-80
-60
-40
-20
0
20
40
60
80
100
Forc
e[k
N]
-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20
3% ALR Square/BPVI/Load 2
-8 -6 -4 -2 0 2 4 6 8-25
-20
-15
-10
-5
0
5
10
15
20
25
Displacement [in]-(bottom scale) / [m]-(top scale)
Forc
e [
kip
s]
-100
-80
-60
-40
-20
0
20
40
60
80
100
Forc
e[k
N]
-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20
3% ALR Square/BPVI/Load 3
-8 -6 -4 -2 0 2 4 6 8-25
-20
-15
-10
-5
0
5
10
15
20
25
Displacement [in]-(bottom scale) / [m]-(top scale)
Forc
e [
kip
s]
Page 150
139
Figure 104
Figure 105
-100
-80
-60
-40
-20
0
20
40
60
80
100
Forc
e[k
N]
-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20
4% ALR Square/BPVI/Load 1
-8 -6 -4 -2 0 2 4 6 8-25
-20
-15
-10
-5
0
5
10
15
20
25
Displacement [in]-(bottom scale) / [m]-(top scale)
Forc
e [
kip
s]
-100
-80
-60
-40
-20
0
20
40
60
80
100
Forc
e[k
N]
-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20
4% ALR Square/BPVI/Load 2
-8 -6 -4 -2 0 2 4 6 8-25
-20
-15
-10
-5
0
5
10
15
20
25
Displacement [in]-(bottom scale) / [m]-(top scale)
Forc
e [
kip
s]
Page 151
140
Figure 106
Figure 107
-100
-80
-60
-40
-20
0
20
40
60
80
100
Forc
e[k
N]
-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20
4% ALR Square/BPVI/Load 3
-8 -6 -4 -2 0 2 4 6 8-25
-20
-15
-10
-5
0
5
10
15
20
25
Displacement [in]-(bottom scale) / [m]-(top scale)
Forc
e [
kip
s]
-100
-80
-60
-40
-20
0
20
40
60
80
100
Forc
e[k
N]
-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20
5% ALR Square/BPVI/Load 1
-8 -6 -4 -2 0 2 4 6 8-25
-20
-15
-10
-5
0
5
10
15
20
25
Displacement [in]-(bottom scale) / [m]-(top scale)
Forc
e [
kip
s]
Page 152
141
Figure 108
Figure 109
-100
-80
-60
-40
-20
0
20
40
60
80
100
Forc
e[k
N]
-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20
5% ALR Square/BPVI/Load 2
-8 -6 -4 -2 0 2 4 6 8-25
-20
-15
-10
-5
0
5
10
15
20
25
Displacement [in]-(bottom scale) / [m]-(top scale)
Forc
e [
kip
s]
-100
-80
-60
-40
-20
0
20
40
60
80
100
Forc
e[k
N]
-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20
5% ALR Square/BPVI/Load 3
-8 -6 -4 -2 0 2 4 6 8-25
-20
-15
-10
-5
0
5
10
15
20
25
Displacement [in]-(bottom scale) / [m]-(top scale)
Forc
e [
kip
s]
Page 153
142
Figure 110
Figure 111
-100
-80
-60
-40
-20
0
20
40
60
80
100
Forc
e[k
N]
-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20
4% ALR Circular/BPV/Load 1
-8 -6 -4 -2 0 2 4 6 8-25
-20
-15
-10
-5
0
5
10
15
20
25
Displacement [in]-(bottom scale) / [m]-(top scale)
Forc
e [
kip
s]
-100
-80
-60
-40
-20
0
20
40
60
80
100
Forc
e[k
N]
-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20
4% ALR Circular/BPV/Load 2
-8 -6 -4 -2 0 2 4 6 8-25
-20
-15
-10
-5
0
5
10
15
20
25
Displacement [in]-(bottom scale) / [m]-(top scale)
Forc
e [
kip
s]
Page 154
143
Figure 112
Figure 113
-100
-80
-60
-40
-20
0
20
40
60
80
100
Forc
e[k
N]
-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20
4% ALR Circular/BPV/Load 3
-8 -6 -4 -2 0 2 4 6 8-25
-20
-15
-10
-5
0
5
10
15
20
25
Displacement [in]-(bottom scale) / [m]-(top scale)
Forc
e [
kip
s]
-100
-80
-60
-40
-20
0
20
40
60
80
100
Forc
e[k
N]
-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20
6% ALR Circular/BPV/Load 1
-8 -6 -4 -2 0 2 4 6 8-25
-20
-15
-10
-5
0
5
10
15
20
25
Displacement [in]-(bottom scale) / [m]-(top scale)
Forc
e [
kip
s]
Page 155
144
Figure 114
Figure 115
-100
-80
-60
-40
-20
0
20
40
60
80
100
Forc
e[k
N]
-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20
6% ALR Circular/BPV/Load 2
-8 -6 -4 -2 0 2 4 6 8-25
-20
-15
-10
-5
0
5
10
15
20
25
Displacement [in]-(bottom scale) / [m]-(top scale)
Forc
e [
kip
s]
-100
-80
-60
-40
-20
0
20
40
60
80
100
Forc
e[k
N]
-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20
6% ALR Circular/BPV/Load 3
-8 -6 -4 -2 0 2 4 6 8-25
-20
-15
-10
-5
0
5
10
15
20
25
Displacement [in]-(bottom scale) / [m]-(top scale)
Forc
e [
kip
s]
Page 156
145
Figure 116
Figure 117
-100
-80
-60
-40
-20
0
20
40
60
80
100
Forc
e[k
N]
-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20
8% ALR Circular/BPV/Load 1
-8 -6 -4 -2 0 2 4 6 8-25
-20
-15
-10
-5
0
5
10
15
20
25
Displacement [in]-(bottom scale) / [m]-(top scale)
Forc
e [
kip
s]
-100
-80
-60
-40
-20
0
20
40
60
80
100
Forc
e[k
N]
-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20
8% ALR Circular/BPV/Load 2
-8 -6 -4 -2 0 2 4 6 8-25
-20
-15
-10
-5
0
5
10
15
20
25
Displacement [in]-(bottom scale) / [m]-(top scale)
Forc
e [
kip
s]
Page 157
146
Figure 118
Figure 119
-100
-80
-60
-40
-20
0
20
40
60
80
100
Forc
e[k
N]
-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20
8% ALR Circular/BPV/Load 3
-8 -6 -4 -2 0 2 4 6 8-25
-20
-15
-10
-5
0
5
10
15
20
25
Displacement [in]-(bottom scale) / [m]-(top scale)
Forc
e [
kip
s]
-100
-80
-60
-40
-20
0
20
40
60
80
100
Forc
e[k
N]
-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20
4% ALR Circular/BPVI/Load 1
-8 -6 -4 -2 0 2 4 6 8-25
-20
-15
-10
-5
0
5
10
15
20
25
Displacement [in]-(bottom scale) / [m]-(top scale)
Forc
e [
kip
s]
Page 158
147
Figure 120
Figure 121
-100
-80
-60
-40
-20
0
20
40
60
80
100
Forc
e[k
N]
-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20
4% ALR Circular/BPVI/Load 2
-8 -6 -4 -2 0 2 4 6 8-25
-20
-15
-10
-5
0
5
10
15
20
25
Displacement [in]-(bottom scale) / [m]-(top scale)
Forc
e [
kip
s]
-100
-80
-60
-40
-20
0
20
40
60
80
100
Forc
e[k
N]
-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20
4% ALR Circular/BPVI/Load 3
-8 -6 -4 -2 0 2 4 6 8-25
-20
-15
-10
-5
0
5
10
15
20
25
Displacement [in]-(bottom scale) / [m]-(top scale)
Forc
e [
kip
s]
Page 159
148
Figure 122
Figure 123
-100
-80
-60
-40
-20
0
20
40
60
80
100
Forc
e[k
N]
-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20
6% ALR Circular/BPVI/Load 1
-8 -6 -4 -2 0 2 4 6 8-25
-20
-15
-10
-5
0
5
10
15
20
25
Displacement [in]-(bottom scale) / [m]-(top scale)
Forc
e [
kip
s]
-100
-80
-60
-40
-20
0
20
40
60
80
100
Forc
e[k
N]
-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20
6% ALR Circular/BPVI/Load 2
-8 -6 -4 -2 0 2 4 6 8-25
-20
-15
-10
-5
0
5
10
15
20
25
Displacement [in]-(bottom scale) / [m]-(top scale)
Forc
e [
kip
s]
Page 160
149
Figure 124
Figure 125
-100
-80
-60
-40
-20
0
20
40
60
80
100
Forc
e[k
N]
-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20
6% ALR Circular/BPVI/Load 3
-8 -6 -4 -2 0 2 4 6 8-25
-20
-15
-10
-5
0
5
10
15
20
25
Displacement [in]-(bottom scale) / [m]-(top scale)
Forc
e [
kip
s]
-100
-80
-60
-40
-20
0
20
40
60
80
100
Forc
e[k
N]
-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20
8% ALR Circular/BPVI/Load 1
-8 -6 -4 -2 0 2 4 6 8-25
-20
-15
-10
-5
0
5
10
15
20
25
Displacement [in]-(bottom scale) / [m]-(top scale)
Forc
e [
kip
s]
Page 161
150
Figure 126
Figure 127
-100
-80
-60
-40
-20
0
20
40
60
80
100
Forc
e[k
N]
-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20
8% ALR Circular/BPVI/Load 2
-8 -6 -4 -2 0 2 4 6 8-25
-20
-15
-10
-5
0
5
10
15
20
25
Displacement [in]-(bottom scale) / [m]-(top scale)
Forc
e [
kip
s]
-100
-80
-60
-40
-20
0
20
40
60
80
100
Forc
e[k
N]
-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20
8% ALR Circular/BPVI/Load 3
-8 -6 -4 -2 0 2 4 6 8-25
-20
-15
-10
-5
0
5
10
15
20
25
Displacement [in]-(bottom scale) / [m]-(top scale)
Forc
e [
kip
s]
Page 162
151
Figure 128
Figure 129
-100
-80
-60
-40
-20
0
20
40
60
80
100
Forc
e[k
N]
-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20
H-Pile/BPV/Load 1
-8 -6 -4 -2 0 2 4 6 8-25
-20
-15
-10
-5
0
5
10
15
20
25
Displacement [in]-(bottom scale) / [m]-(top scale)
Forc
e [
kip
s]
-100
-80
-60
-40
-20
0
20
40
60
80
100
Forc
e[k
N]
-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20
H-Pile/BPV/Load 2
-8 -6 -4 -2 0 2 4 6 8-25
-20
-15
-10
-5
0
5
10
15
20
25
Displacement [in]-(bottom scale) / [m]-(top scale)
Forc
e [
kip
s]
Page 163
152
Figure 130
Figure 131
-100
-80
-60
-40
-20
0
20
40
60
80
100
Forc
e[k
N]
-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20
H-Pile/BPV/Load 3
-8 -6 -4 -2 0 2 4 6 8-25
-20
-15
-10
-5
0
5
10
15
20
25
Displacement [in]-(bottom scale) / [m]-(top scale)
Forc
e [
kip
s]
-100
-80
-60
-40
-20
0
20
40
60
80
100
Forc
e[k
N]
-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20
H-Pile/BPVI/Load 1
-8 -6 -4 -2 0 2 4 6 8-25
-20
-15
-10
-5
0
5
10
15
20
25
Displacement [in]-(bottom scale) / [m]-(top scale)
Forc
e [
kip
s]
Page 164
153
Figure 132
Figure 133
-100
-80
-60
-40
-20
0
20
40
60
80
100
Forc
e[k
N]
-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20
H-Pile/BPVI/Load 2
-8 -6 -4 -2 0 2 4 6 8-25
-20
-15
-10
-5
0
5
10
15
20
25
Displacement [in]-(bottom scale) / [m]-(top scale)
Forc
e [
kip
s]
-100
-80
-60
-40
-20
0
20
40
60
80
100
Forc
e[k
N]
-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20
H-Pile/BPVI/Load 3
-8 -6 -4 -2 0 2 4 6 8-25
-20
-15
-10
-5
0
5
10
15
20
25
Displacement [in]-(bottom scale) / [m]-(top scale)
Forc
e [
kip
s]
Page 165
154
APPENDIX B: TOP DISPLACEMENT VS. CONTRIBUTING TOP
DISPLACEMENT COMPONENTS
Figure 134
Figure 135
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Calc
ula
ted D
ispla
cem
ent
[m]
-0.08 -0.05 -0.03 0.00 0.03 0.05 0.08
3%ALR Square/ BPV / BP Load 1
-3 -2 -1 0 1 2 3
-3
-2
-1
0
1
2
3
Measured Displacement: Bottom Scale (in) / Top Scale [m]
Calc
ula
ted D
ispla
cem
ent
(in)
Measured Top Displacement
Cap rotation Displ
Pile Bending Displ
BP Lateral Displ
Girder Rotation Displ
Total Calculated Top Displ
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Calc
ula
ted D
ispla
cem
ent
[m]
-0.08 -0.05 -0.03 0.00 0.03 0.05 0.08
3%ALR Square/ BPV / BP Load 2
-3 -2 -1 0 1 2 3
-3
-2
-1
0
1
2
3
Measured Displacement: Bottom Scale (in) / Top Scale [m]
Calc
ula
ted D
ispla
cem
ent
(in)
Measured Top Displacement
Cap rotation Displ
Pile Bending Displ
BP Lateral Displ
Girder Rotation Displ
Total Calculated Top Displ
Page 166
155
Figure 136
Figure 137
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Calc
ula
ted D
ispla
cem
ent
[m]
-0.08 -0.05 -0.03 0.00 0.03 0.05 0.08
3%ALR Square/ BPV / BP Load 3
-3 -2 -1 0 1 2 3
-3
-2
-1
0
1
2
3
Measured Displacement: Bottom Scale (in) / Top Scale [m]
Calc
ula
ted D
ispla
cem
ent
(in)
Measured Top Displacement
Cap rotation Displ
Pile Bending Displ
BP Lateral Displ
Girder Rotation Displ
Total Calculated Top Displ
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Calc
ula
ted D
ispla
cem
ent
[m]
-0.08 -0.05 -0.03 0.00 0.03 0.05 0.08
4%ALR Square/ BPV / BP Load 1
-3 -2 -1 0 1 2 3
-3
-2
-1
0
1
2
3
Measured Displacement: Bottom Scale (in) / Top Scale [m]
Calc
ula
ted D
ispla
cem
ent
(in)
Measured Top Displacement
Cap rotation Displ
Pile Bending Displ
BP Lateral Displ
Girder Rotation Displ
Total Calculated Top Displ
Page 167
156
Figure 138
Figure 139
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Calc
ula
ted D
ispla
cem
ent
[m]
-0.08 -0.05 -0.03 0.00 0.03 0.05 0.08
4%ALR Square/ BPV / BP Load 2
-3 -2 -1 0 1 2 3
-3
-2
-1
0
1
2
3
Measured Displacement: Bottom Scale (in) / Top Scale [m]
Calc
ula
ted D
ispla
cem
ent
(in)
Measured Top Displacement
Cap rotation Displ
Pile Bending Displ
BP Lateral Displ
Girder Rotation Displ
Total Calculated Top Displ
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Calc
ula
ted D
ispla
cem
ent
[m]
-0.08 -0.05 -0.03 0.00 0.03 0.05 0.08
5%ALR Square/ BPV / BP Load 1
-3 -2 -1 0 1 2 3
-3
-2
-1
0
1
2
3
Measured Displacement: Bottom Scale (in) / Top Scale [m]
Calc
ula
ted D
ispla
cem
ent
(in)
Measured Top Displacement
Cap rotation Displ
Pile Bending Displ
BP Lateral Displ
Girder Rotation Displ
Total Calculated Top Displ
Page 168
157
Figure 140
Figure 141
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Calc
ula
ted D
ispla
cem
ent
[m]
-0.08 -0.05 -0.03 0.00 0.03 0.05 0.08
5%ALR Square/ BPV / BP Load 2
-3 -2 -1 0 1 2 3
-3
-2
-1
0
1
2
3
Measured Displacement: Bottom Scale (in) / Top Scale [m]
Calc
ula
ted D
ispla
cem
ent
(in)
Measured Top Displacement
Cap rotation Displ
Pile Bending Displ
BP Lateral Displ
Girder Rotation Displ
Total Calculated Top Displ
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Calc
ula
ted D
ispla
cem
ent
[m]
-0.08 -0.05 -0.03 0.00 0.03 0.05 0.08
5%ALR Square/ BPV / BP Load 3
-3 -2 -1 0 1 2 3
-3
-2
-1
0
1
2
3
Measured Displacement: Bottom Scale (in) / Top Scale [m]
Calc
ula
ted D
ispla
cem
ent
(in)
Measured Top Displacement
Cap rotation Displ
Pile Bending Displ
BP Lateral Displ
Girder Rotation Displ
Total Calculated Top Displ
Page 169
158
Figure 142
Figure 143
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Calc
ula
ted D
ispla
cem
ent
[m]
-0.08 -0.05 -0.03 0.00 0.03 0.05 0.08
4%ALR Square/ BPVI / BP Load 1
-3 -2 -1 0 1 2 3
-3
-2
-1
0
1
2
3
Measured Displacement: Bottom Scale (in) / Top Scale [m]
Calc
ula
ted D
ispla
cem
ent
(in)
Measured Top Displacement
Cap rotation Displ
Pile Bending Displ
BP Lateral Displ
Girder Rotation Displ
Total Calculated Top Displ
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Calc
ula
ted D
ispla
cem
ent
[m]
-0.08 -0.05 -0.03 0.00 0.03 0.05 0.08
4%ALR Square/ BPVI / BP Load 2
-3 -2 -1 0 1 2 3
-3
-2
-1
0
1
2
3
Measured Displacement: Bottom Scale (in) / Top Scale [m]
Calc
ula
ted D
ispla
cem
ent
(in)
Measured Top Displacement
Cap rotation Displ
Pile Bending Displ
BP Lateral Displ
Girder Rotation Displ
Total Calculated Top Displ
Page 170
159
Figure 144
Figure 145
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Calc
ula
ted D
ispla
cem
ent
[m]
-0.08 -0.05 -0.03 0.00 0.03 0.05 0.08
4%ALR Square/ BPVI / BP Load 3
-3 -2 -1 0 1 2 3
-3
-2
-1
0
1
2
3
Measured Displacement: Bottom Scale (in) / Top Scale [m]
Calc
ula
ted D
ispla
cem
ent
(in)
Measured Top Displacement
Cap rotation Displ
Pile Bending Displ
BP Lateral Displ
Girder Rotation Displ
Total Calculated Top Displ
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Calc
ula
ted D
ispla
cem
ent
[m]
-0.08 -0.05 -0.03 0.00 0.03 0.05 0.08
5%ALR Square/ BPVI / BP Load 1
-3 -2 -1 0 1 2 3
-3
-2
-1
0
1
2
3
Measured Displacement: Bottom Scale (in) / Top Scale [m]
Calc
ula
ted D
ispla
cem
ent
(in)
Measured Top Displacement
Cap rotation Displ
Pile Bending Displ
BP Lateral Displ
Girder Rotation Displ
Total Calculated Top Displ
Page 171
160
Figure 146
Figure 147
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Calc
ula
ted D
ispla
cem
ent
[m]
-0.08 -0.05 -0.03 0.00 0.03 0.05 0.08
5%ALR Square/ BPVI / BP Load 2
-3 -2 -1 0 1 2 3
-3
-2
-1
0
1
2
3
Measured Displacement: Bottom Scale (in) / Top Scale [m]
Calc
ula
ted D
ispla
cem
ent
(in)
Measured Top Displacement
Cap rotation Displ
Pile Bending Displ
BP Lateral Displ
Girder Rotation Displ
Total Calculated Top Displ
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Calc
ula
ted D
ispla
cem
ent
[m]
-0.08 -0.05 -0.03 0.00 0.03 0.05 0.08
5%ALR Square/ BPVI / BP Load 3
-3 -2 -1 0 1 2 3
-3
-2
-1
0
1
2
3
Measured Displacement: Bottom Scale (in) / Top Scale [m]
Calc
ula
ted D
ispla
cem
ent
(in)
Measured Top Displacement
Cap rotation Displ
Pile Bending Displ
BP Lateral Displ
Girder Rotation Displ
Total Calculated Top Displ
Page 172
161
Figure 148
Figure 149
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Calc
ula
ted D
ispla
cem
ent
[m]
-0.08 -0.05 -0.03 0.00 0.03 0.05 0.08
4%ALR Circular/ BPV / BP Load 1
-3 -2 -1 0 1 2 3
-3
-2
-1
0
1
2
3
Measured Displacement (in)
Calc
ula
ted D
ispla
cem
ent
(in)
Measured Top Displacement
Cap rotation Displ
Pile Bending Displ
BP Lateral Displ
Girder Rotation Displ
Total Calculated Top Displ
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Calc
ula
ted D
ispla
cem
ent
[m]
-0.08 -0.05 -0.03 0.00 0.03 0.05 0.08
4%ALR Circular/ BPV / BP Load 2
-3 -2 -1 0 1 2 3
-3
-2
-1
0
1
2
3
Measured Displacement (in)
Calc
ula
ted D
ispla
cem
ent
(in)
Measured Top Displacement
Cap rotation Displ
Pile Bending Displ
BP Lateral Displ
Girder Rotation Displ
Total Calculated Top Displ
Page 173
162
Figure 150
Figure 151
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Calc
ula
ted D
ispla
cem
ent
[m]
-0.08 -0.05 -0.03 0.00 0.03 0.05 0.08
4%ALR Circular/ BPV / BP Load 3
-3 -2 -1 0 1 2 3
-3
-2
-1
0
1
2
3
Measured Displacement (in)
Calc
ula
ted D
ispla
cem
ent
(in)
Measured Top Displacement
Cap rotation Displ
Pile Bending Displ
BP Lateral Displ
Girder Rotation Displ
Total Calculated Top Displ
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Calc
ula
ted D
ispla
cem
ent
[m]
-0.08 -0.05 -0.03 0.00 0.03 0.05 0.08
6%ALR Circular/ BPV / BP Load 1
-3 -2 -1 0 1 2 3
-3
-2
-1
0
1
2
3
Measured Displacement (in)
Calc
ula
ted D
ispla
cem
ent
(in)
Measured Top Displacement
Cap rotation Displ
Pile Bending Displ
BP Lateral Displ
Girder Rotation Displ
Total Calculated Top Displ
Page 174
163
Figure 152
Figure 153
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Calc
ula
ted D
ispla
cem
ent
[m]
-0.08 -0.05 -0.03 0.00 0.03 0.05 0.08
6%ALR Circular/ BPV / BP Load 3
-3 -2 -1 0 1 2 3
-3
-2
-1
0
1
2
3
Measured Displacement (in)
Calc
ula
ted D
ispla
cem
ent
(in)
Measured Top Displacement
Cap rotation Displ
Pile Bending Displ
BP Lateral Displ
Girder Rotation Displ
Total Calculated Top Displ
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Calc
ula
ted D
ispla
cem
ent
[m]
-0.08 -0.05 -0.03 0.00 0.03 0.05 0.08
8%ALR Circular/ BPV / BP Load 1
-3 -2 -1 0 1 2 3
-3
-2
-1
0
1
2
3
Measured Displacement (in)
Calc
ula
ted D
ispla
cem
ent
(in)
Measured Top Displacement
Cap rotation Displ
Pile Bending Displ
BP Lateral Displ
Girder Rotation Displ
Total Calculated Top Displ
Page 175
164
Figure 154
Figure 155
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Calc
ula
ted D
ispla
cem
ent
[m]
-0.08 -0.05 -0.03 0.00 0.03 0.05 0.08
8%ALR Circular/ BPV / BP Load 2
-3 -2 -1 0 1 2 3
-3
-2
-1
0
1
2
3
Measured Displacement (in)
Calc
ula
ted D
ispla
cem
ent
(in)
Measured Top Displacement
Cap rotation Displ
Pile Bending Displ
BP Lateral Displ
Girder Rotation Displ
Total Calculated Top Displ
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Calc
ula
ted D
ispla
cem
ent
[m]
-0.08 -0.05 -0.03 0.00 0.03 0.05 0.08
8%ALR Circular/ BPV / BP Load 3
-3 -2 -1 0 1 2 3
-3
-2
-1
0
1
2
3
Measured Displacement (in)
Calc
ula
ted D
ispla
cem
ent
(in)
Measured Top Displacement
Cap rotation Displ
Pile Bending Displ
BP Lateral Displ
Girder Rotation Displ
Total Calculated Top Displ
Page 176
165
Figure 156
Figure 157
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Calc
ula
ted D
ispla
cem
ent
[m]
-0.08 -0.05 -0.03 0.00 0.03 0.05 0.08
4%ALR Circular/ BPVI / BP Load 1
-3 -2 -1 0 1 2 3
-3
-2
-1
0
1
2
3
Measured Displacement (in)
Calc
ula
ted D
ispla
cem
ent
(in)
Measured Top Displacement
Cap rotation Displ
Pile Bending Displ
BP Lateral Displ
Girder Rotation Displ
Total Calculated Top Displ
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Calc
ula
ted D
ispla
cem
ent
[m]
-0.08 -0.05 -0.03 0.00 0.03 0.05 0.08
4%ALR Circular/ BPVI / BP Load 2
-3 -2 -1 0 1 2 3
-3
-2
-1
0
1
2
3
Measured Displacement (in)
Calc
ula
ted D
ispla
cem
ent
(in)
Measured Top Displacement
Cap rotation Displ
Pile Bending Displ
BP Lateral Displ
Girder Rotation Displ
Total Calculated Top Displ
Page 177
166
Figure 158
Figure 159
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Calc
ula
ted D
ispla
cem
ent
[m]
-0.08 -0.05 -0.03 0.00 0.03 0.05 0.08
4%ALR Circular/ BPVI / BP Load 3
-3 -2 -1 0 1 2 3
-3
-2
-1
0
1
2
3
Measured Displacement (in)
Calc
ula
ted D
ispla
cem
ent
(in)
Measured Top Displacement
Cap rotation Displ
Pile Bending Displ
BP Lateral Displ
Girder Rotation Displ
Total Calculated Top Displ
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Calc
ula
ted D
ispla
cem
ent
[m]
-0.08 -0.05 -0.03 0.00 0.03 0.05 0.08
6%ALR Circular/ BPVI / BP Load 1
-3 -2 -1 0 1 2 3
-3
-2
-1
0
1
2
3
Measured Displacement (in)
Calc
ula
ted D
ispla
cem
ent
(in)
Measured Top Displacement
Cap rotation Displ
Pile Bending Displ
BP Lateral Displ
Girder Rotation Displ
Total Calculated Top Displ
Page 178
167
Figure 160
Figure 161
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Calc
ula
ted D
ispla
cem
ent
[m]
-0.08 -0.05 -0.03 0.00 0.03 0.05 0.08
6%ALR Circular/ BPVI / BP Load 2
-3 -2 -1 0 1 2 3
-3
-2
-1
0
1
2
3
Measured Displacement (in)
Calc
ula
ted D
ispla
cem
ent
(in)
Measured Top Displacement
Cap rotation Displ
Pile Bending Displ
BP Lateral Displ
Girder Rotation Displ
Total Calculated Top Displ
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Calc
ula
ted D
ispla
cem
ent
[m]
-0.08 -0.05 -0.03 0.00 0.03 0.05 0.08
6%ALR Circular/ BPVI / BP Load 3
-3 -2 -1 0 1 2 3
-3
-2
-1
0
1
2
3
Measured Displacement (in)
Calc
ula
ted D
ispla
cem
ent
(in)
Measured Top Displacement
Cap rotation Displ
Pile Bending Displ
BP Lateral Displ
Girder Rotation Displ
Total Calculated Top Displ
Page 179
168
Figure 162
Figure 163
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Calc
ula
ted D
ispla
cem
ent
[m]
-0.08 -0.05 -0.03 0.00 0.03 0.05 0.08
8%ALR Circular/ BPVI / BP Load 1
-3 -2 -1 0 1 2 3
-3
-2
-1
0
1
2
3
Measured Displacement (in)
Calc
ula
ted D
ispla
cem
ent
(in)
Measured Top Displacement
Cap rotation Displ
Pile Bending Displ
BP Lateral Displ
Girder Rotation Displ
Total Calculated Top Displ
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Calc
ula
ted D
ispla
cem
ent
[m]
-0.08 -0.05 -0.03 0.00 0.03 0.05 0.08
8%ALR Circular/ BPVI / BP Load 2
-3 -2 -1 0 1 2 3
-3
-2
-1
0
1
2
3
Measured Displacement (in)
Calc
ula
ted D
ispla
cem
ent
(in)
Measured Top Displacement
Cap rotation Displ
Pile Bending Displ
BP Lateral Displ
Girder Rotation Displ
Total Calculated Top Displ
Page 180
169
Figure 164
Figure 165
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Calc
ula
ted D
ispla
cem
ent
[m]
-0.08 -0.05 -0.03 0.00 0.03 0.05 0.08
HPile/ BPV / BP Load 1
-3 -2 -1 0 1 2 3
-3
-2
-1
0
1
2
3
Measured Displacement: Bottom Scale (in) / Top Scale [m]
Calc
ula
ted D
ispla
cem
ent
(in)
Measured Top Displacement
Cap rotation Displ
Pile Bending Displ
BP Lateral Displ
Girder Rotation Displ
Total Calculated Top Displ
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Calc
ula
ted D
ispla
cem
ent
[m]
-0.08 -0.05 -0.03 0.00 0.03 0.05 0.08
HPile/ BPV / BP Load 2
-3 -2 -1 0 1 2 3
-3
-2
-1
0
1
2
3
Measured Displacement: Bottom Scale (in) / Top Scale [m]
Calc
ula
ted D
ispla
cem
ent
(in)
Measured Top Displacement
Cap rotation Displ
Pile Bending Displ
BP Lateral Displ
Girder Rotation Displ
Total Calculated Top Displ
Page 181
170
Figure 166
Figure 167
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Calc
ula
ted D
ispla
cem
ent
[m]
-0.08 -0.05 -0.03 0.00 0.03 0.05 0.08
HPile/ BPV / BP Load 3
-3 -2 -1 0 1 2 3
-3
-2
-1
0
1
2
3
Measured Displacement: Bottom Scale (in) / Top Scale [m]
Calc
ula
ted D
ispla
cem
ent
(in)
Measured Top Displacement
Cap rotation Displ
Pile Bending Displ
BP Lateral Displ
Girder Rotation Displ
Total Calculated Top Displ
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Calc
ula
ted D
ispla
cem
ent
[m]
-0.08 -0.05 -0.03 0.00 0.03 0.05 0.08
HPile/ BPVI / BP Load 1
-3 -2 -1 0 1 2 3
-3
-2
-1
0
1
2
3
Measured Displacement: Bottom Scale (in) / Top Scale [m]
Calc
ula
ted D
ispla
cem
ent
(in)
Measured Top Displacement
Cap rotation Displ
Pile Bending Displ
BP Lateral Displ
Girder Rotation Displ
Total Calculated Top Displ
Page 182
171
Figure 168
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Calc
ula
ted D
ispla
cem
ent
[m]
-0.08 -0.05 -0.03 0.00 0.03 0.05 0.08
HPile/ BPVI / BP Load 2
-3 -2 -1 0 1 2 3
-3
-2
-1
0
1
2
3
Measured Displacement: Bottom Scale (in) / Top Scale [m]
Calc
ula
ted D
ispla
cem
ent
(in)
Measured Top Displacement
Cap rotation Displ
Pile Bending Displ
BP Lateral Displ
Girder Rotation Displ
Total Calculated Top Displ
Page 183
172
APPENDIX C: MEASURED VS. CALCULATED RESPONSE
Figure 169
Figure 170
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Experim
enta
l D
ispla
cem
ent
[m]
1 2 3 4 5 6 7 8
-3
-2
-1
0
1
2
3
cycle
Experim
enta
l D
ispla
cem
ent
(in)
3% ALR Square / BP V / BP Load 1
Measured Top Displacement
Calculated Displacement
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Experim
enta
l D
ispla
cem
ent
[m]
1 2 3 4 5 6 7 8
-3
-2
-1
0
1
2
3
cycle
Experim
enta
l D
ispla
cem
ent
(in)
3% ALR Square / BP V / BP Load 2
Measured Top Displacement
Calculated Displacement
Page 184
173
Figure 171
Figure 172
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Experim
enta
l D
ispla
cem
ent
[m]
1 2 3 4 5 6 7 8
-3
-2
-1
0
1
2
3
cycle
Experim
enta
l D
ispla
cem
ent
(in)
3% ALR Square / BP V / BP Load 3
Measured Top Displacement
Calculated Displacement
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Experim
enta
l D
ispla
cem
ent
[m]
1 2 3 4 5 6 7 8
-3
-2
-1
0
1
2
3
cycle
Experim
enta
l D
ispla
cem
ent
(in)
4% ALR Square / BP V / BP Load 1
Measured Top Displacement
Calculated Displacement
Page 185
174
Figure 173
Figure 174
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Experim
enta
l D
ispla
cem
ent
[m]
1 2 3 4 5 6 7 8
-3
-2
-1
0
1
2
3
cycle
Experim
enta
l D
ispla
cem
ent
(in)
4% ALR Square / BP V / BP Load 2
Measured Top Displacement
Calculated Displacement
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Experim
enta
l D
ispla
cem
ent
[m]
1 2 3 4 5 6 7 8
-3
-2
-1
0
1
2
3
cycle
Experim
enta
l D
ispla
cem
ent
(in)
5% ALR Square / BP V / BP Load 1
Measured Top Displacement
Calculated Displacement
Page 186
175
Figure 175
Figure 176
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Experim
enta
l D
ispla
cem
ent
[m]
1 2 3 4 5 6 7 8
-3
-2
-1
0
1
2
3
cycle
Experim
enta
l D
ispla
cem
ent
(in)
5% ALR Square / BP V / BP Load 2
Measured Top Displacement
Calculated Displacement
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Experim
enta
l D
ispla
cem
ent
[m]
1 2 3 4 5 6 7 8
-3
-2
-1
0
1
2
3
cycle
Experim
enta
l D
ispla
cem
ent
(in)
5% ALR Square / BP V / BP Load 3
Measured Top Displacement
Calculated Displacement
Page 187
176
Figure 177
Figure 178
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Experim
enta
l D
ispla
cem
ent
[m]
1 2 3 4 5 6 7 8
-3
-2
-1
0
1
2
3
cycle
Experim
enta
l D
ispla
cem
ent
(in)
3% ALR Square / BP VI / BP Load 1
Measured Top Displacement
Calculated Displacement
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Experim
enta
l D
ispla
cem
ent
[m]
1 2 3 4 5 6 7 8
-3
-2
-1
0
1
2
3
cycle
Experim
enta
l D
ispla
cem
ent
(in)
4% ALR Square / BP VI / BP Load 1
Measured Top Displacement
Calculated Displacement
Page 188
177
Figure 179
Figure 180
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Experim
enta
l D
ispla
cem
ent
[m]
1 2 3 4 5 6 7 8
-3
-2
-1
0
1
2
3
cycle
Experim
enta
l D
ispla
cem
ent
(in)
4% ALR Square / BP VI / BP Load 2
Measured Top Displacement
Calculated Displacement
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Experim
enta
l D
ispla
cem
ent
[m]
1 2 3 4 5 6 7 8
-3
-2
-1
0
1
2
3
cycle
Experim
enta
l D
ispla
cem
ent
(in)
4% ALR Square / BP VI / BP Load 3
Measured Top Displacement
Calculated Displacement
Page 189
178
Figure 181
Figure 182
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Experim
enta
l D
ispla
cem
ent
[m]
1 2 3 4 5 6 7 8
-3
-2
-1
0
1
2
3
cycle
Experim
enta
l D
ispla
cem
ent
(in)
5% ALR Square / BP VI / BP Load 1
Measured Top Displacement
Calculated Displacement
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Experim
enta
l D
ispla
cem
ent
[m]
1 2 3 4 5 6 7 8
-3
-2
-1
0
1
2
3
cycle
Experim
enta
l D
ispla
cem
ent
(in)
5% ALR Square / BP VI / BP Load 2
Measured Top Displacement
Calculated Displacement
Page 190
179
Figure 183
Figure 184
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Experim
enta
l D
ispla
cem
ent
[m]
1 2 3 4 5 6 7 8
-3
-2
-1
0
1
2
3
cycle
Experim
enta
l D
ispla
cem
ent
(in)
5% ALR Square / BP VI / BP Load 3
Measured Top Displacement
Calculated Displacement
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Experim
enta
l D
ispla
cem
ent
[m]
1 2 3 4 5 6 7 8
-3
-2
-1
0
1
2
3
cycle
Experim
enta
l D
ispla
cem
ent
(in)
4% ALR Circular / BP V / BP Load 1
Measured Top Displacement
Calculated Displacement
Page 191
180
Figure 185
Figure 186
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Experim
enta
l D
ispla
cem
ent
[m]
1 2 3 4 5 6 7 8
-3
-2
-1
0
1
2
3
cycle
Experim
enta
l D
ispla
cem
ent
(in)
4% ALR Circular / BP V / BP Load 2
Measured Top Displacement
Calculated Displacement
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Experim
enta
l D
ispla
cem
ent
[m]
1 2 3 4 5 6 7 8
-3
-2
-1
0
1
2
3
cycle
Experim
enta
l D
ispla
cem
ent
(in)
4% ALR Circular / BP V / BP Load 2
Measured Top Displacement
Calculated Displacement
Page 192
181
Figure 187
Figure 188
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Experim
enta
l D
ispla
cem
ent
[m]
1 2 3 4 5 6 7 8
-3
-2
-1
0
1
2
3
cycle
Experim
enta
l D
ispla
cem
ent
(in)
4% ALR Circular / BP V / BP Load 3
Measured Top Displacement
Calculated Displacement
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Experim
enta
l D
ispla
cem
ent
[m]
1 2 3 4 5 6 7 8
-3
-2
-1
0
1
2
3
cycle
Experim
enta
l D
ispla
cem
ent
(in)
6% ALR Circular / BP V / BP Load 1
Measured Top Displacement
Calculated Displacement
Page 193
182
Figure 189
Figure 190
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Experim
enta
l D
ispla
cem
ent
[m]
1 2 3 4 5 6 7 8
-3
-2
-1
0
1
2
3
cycle
Experim
enta
l D
ispla
cem
ent
(in)
6% ALR Circular / BP V / BP Load 3
Measured Top Displacement
Calculated Displacement
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Experim
enta
l D
ispla
cem
ent
[m]
1 2 3 4 5 6 7 8
-3
-2
-1
0
1
2
3
cycle
Experim
enta
l D
ispla
cem
ent
(in)
8% ALR Circular / BP V / BP Load 1
Measured Top Displacement
Calculated Displacement
Page 194
183
Figure 191
Figure 192
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Experim
enta
l D
ispla
cem
ent
[m]
1 2 3 4 5 6 7 8
-3
-2
-1
0
1
2
3
cycle
Experim
enta
l D
ispla
cem
ent
(in)
8% ALR Circular / BP V / BP Load 2
Measured Top Displacement
Calculated Displacement
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Experim
enta
l D
ispla
cem
ent
[m]
1 2 3 4 5 6 7 8
-3
-2
-1
0
1
2
3
cycle
Experim
enta
l D
ispla
cem
ent
(in)
8% ALR Circular / BP V / BP Load 3
Measured Top Displacement
Calculated Displacement
Page 195
184
Figure 193
Figure 194
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Experim
enta
l D
ispla
cem
ent
[m]
1 2 3 4 5 6 7 8
-3
-2
-1
0
1
2
3
cycle
Experim
enta
l D
ispla
cem
ent
(in)
4% ALR Circular / BP VI / BP Load 1
Measured Top Displacement
Calculated Displacement
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Experim
enta
l D
ispla
cem
ent
[m]
1 2 3 4 5 6 7 8
-3
-2
-1
0
1
2
3
cycle
Experim
enta
l D
ispla
cem
ent
(in)
4% ALR Circular / BP VI / BP Load 2
Measured Top Displacement
Calculated Displacement
Page 196
185
Figure 195
Figure 196
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Experim
enta
l D
ispla
cem
ent
[m]
1 2 3 4 5 6 7 8
-3
-2
-1
0
1
2
3
cycle
Experim
enta
l D
ispla
cem
ent
(in)
4% ALR Circular / BP VI / BP Load 3
Measured Top Displacement
Calculated Displacement
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Experim
enta
l D
ispla
cem
ent
[m]
1 2 3 4 5 6 7 8
-3
-2
-1
0
1
2
3
cycle
Experim
enta
l D
ispla
cem
ent
(in)
6% ALR Circular / BP VI / BP Load 1
Measured Top Displacement
Calculated Displacement
Page 197
186
Figure 197
Figure 198
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Experim
enta
l D
ispla
cem
ent
[m]
1 2 3 4 5 6 7 8
-3
-2
-1
0
1
2
3
cycle
Experim
enta
l D
ispla
cem
ent
(in)
6% ALR Circular / BP VI / BP Load 2
Measured Top Displacement
Calculated Displacement
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Experim
enta
l D
ispla
cem
ent
[m]
1 2 3 4 5 6 7 8
-3
-2
-1
0
1
2
3
cycle
Experim
enta
l D
ispla
cem
ent
(in)
6% ALR Circular / BP VI / BP Load 3
Measured Top Displacement
Calculated Displacement
Page 198
187
Figure 199
Figure 200
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Experim
enta
l D
ispla
cem
ent
[m]
1 2 3 4 5 6 7 8
-3
-2
-1
0
1
2
3
cycle
Experim
enta
l D
ispla
cem
ent
(in)
8% ALR Circular / BP VI / BP Load 1
Measured Top Displacement
Calculated Displacement
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
Experim
enta
l D
ispla
cem
ent
[m]
1 2 3 4 5 6 7 8
-3
-2
-1
0
1
2
3
cycle
Experim
enta
l D
ispla
cem
ent
(in)
8% ALR Circular / BP VI / BP Load 2
Measured Top Displacement
Calculated Displacement
Page 199
188
Figure 201
Figure 202
-0.1
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
0.1
Experim
enta
l D
ispla
cem
ent
[m]
1 2 3 4 5 6 7 8-4
-3
-2
-1
0
1
2
3
4
cycle
Experim
enta
l D
ispla
cem
ent
(in)
HPile / BP V / BP Load 1
Measured Top Displacement
Calculated Displacement
-0.1
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
0.1
Experim
enta
l D
ispla
cem
ent
[m]
1 2 3 4 5 6 7 8-4
-3
-2
-1
0
1
2
3
4
cycle
Experim
enta
l D
ispla
cem
ent
(in)
HPile / BP V / BP Load 2
Measured Top Displacement
Calculated Displacement
Page 200
189
Figure 203
Figure 204
-0.1
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
0.1
Experim
enta
l D
ispla
cem
ent
[m]
1 2 3 4 5 6 7 8-4
-3
-2
-1
0
1
2
3
4
cycle
Experim
enta
l D
ispla
cem
ent
(in)
HPile / BP V / BP Load 3
Measured Top Displacement
Calculated Displacement
-0.1
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
0.1
Experim
enta
l D
ispla
cem
ent
[m]
1 2 3 4 5 6 7 8-4
-3
-2
-1
0
1
2
3
4
cycle
Experim
enta
l D
ispla
cem
ent
(in)
HPile / BP VI / BP Load 1
Measured Top Displacement
Calculated Displacement
Page 201
190
Figure 205
-0.1
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
0.1
Experim
enta
l D
ispla
cem
ent
[m]
1 2 3 4 5 6 7 8-4
-3
-2
-1
0
1
2
3
4
cycle
Experim
enta
l D
ispla
cem
ent
(in)
HPile / BP VI / BP Load 2
Measured Top Displacement
Calculated Displacement
Page 202
191
APPENDIX D: PERCENTAGES OF CONTRIBUTING TOP DISPLACEMENT
Table 30. Square pile with the type V BP: percentages of contributing top
displacement
ALR
P load number
on Bearing
Pad: (see
Figure 23)
Percentage
Contribution
Due to Pile
Bending (%)
Percentage
Contribution
Due to BP
Shear (%)
Percentage
Contribution
Due to Cap
Rotation (%)
Percentage
Contribution
Due to Girder
Rotation (%)
3 1 26.27 4.65 64.54 4.54
3 2 28.67 5.08 61.47 4.78
3 3 31.91 5.95 57.52 4.62
4 1 25.7 5.57 61.59 7.13
4 2 29.65 6.23 58.48 5.63
4 3 33.93 4.35 59.96 1.75
5 1 24.77 6.02 61.02 8.19
5 2 30.38 6.66 57.74 5.23
5 3 33.56 6.99 53.75 5.70
Table 31. Square pile with the type VI BP: percentages of contributing top
displacement
ALR
P load number
on Bearing
Pad (see
Figure 23)
Percentage
Contribution
Due to Pile
Bending (%)
Percentage
Contribution
Due to BP
Shear (%)
Percentage
Contribution
Due to Cap
Rotation (%)
Percentage
Contribution
Due to Girder
Rotation (%)
3 1 16.81 5.56 77.63 0
3 2 24.79 5.36 65.13 4.72
3 3 30.24 6.06 59.13 4.58
4 1 29.97 4.88 60.75 4.41
4 2 32.78 5.34 58.38 3.51
4 3 36.18 5.54 52.34 5.94
5 1 25.33 11.11 57.20 6.35
5 2 32.13 4.03 56.30 7.54
5 3 36.87 6.05 51.76 5.32
Page 203
192
Table 32. Circular pile with the type V BP: percentages of contributing top
displacement
ALR
P load number
on Bearing
Pad (see
Figure 23)
Percentage
Contribution
Due to Pile
Bending (%)
Percentage
Contribution
Due to BP
Shear (%)
Percentage
Contribution
Due to Cap
Rotation (%)
Percentage
Contribution
Due to Girder
Rotation (%)
4 1 27.41 2.36 66.86 3.38
4 2 30.25 2.86 63.12 3.77
4 3 32.70 3.35 60.82 3.12
6 1 30.12 2.62 55.52 11.74
6 2
Error in
Measurements
Error in
Measurements
Error in
Measurements
Error in
Measurements
6 3 35.46 3.78 50.20 10.60
8 1 32.47 3.25 59.39 4.89
8 2 37.39 3.82 55.55 3.23
8 3 42.91 4.55 50.91 1.64
Table 33. Circular pile with the type VI BP: percentages of contributing top
displacement
ALR
P load number
on Bearing
Pad (see
Figure 23)
Percentage
Contribution
Due to Pile
Bending (%)
Percentage
Contribution
Due to BP
Shear (%)
Percentage
Contribution
Due to Cap
Rotation (%)
Percentage
Contribution
Due to Girder
Rotation (%)
4 1 28.33 2.21 62.86 6.59
4 2 32.62 2.63 59.71 5.04
4 3 38.87 2.95 54.77 3.41
6 1 33.53 2.89 60.00 3.57
6 2 39.33 3.02 53.25 4.41
6 3 45.13 2.71 44.15 8.00
8 1 38.12 2.49 52.62 6.77
8 2 37.25 2.51 42.60 17.64
8 3 48.75 3.27 42.67 5.32
Page 204
193
Table 34. H-pile with the type V BP: percentages of contributing top displacement
ALR
P load number
on Bearing
Pad (see
Figure 23)
Percentage
Contribution
Due to Pile
Bending (%)
Percentage
Contribution
Due to BP
Shear (%)
Percentage
Contribution
Due to Cap
Rotation (%)
Percentage
Contribution
Due to Girder
Rotation (%)
--- 1 10.57 3.65 83.59 2.20
--- 2 10.38 4.51 83.45 1.66
--- 3 11.81 4.88 82.11 1.21
Table 35. H-pile with the type VI BP: percentages of contributing top displacement
ALR
P load number
on Bearing
Pad (see
Figure 23)
Percentage
Contribution
Due to Pile
Bending (%)
Percentage
Contribution
Due to BP
Shear (%)
Percentage
Contribution
Due to Cap
Rotation (%)
Percentage
Contribution
Due to Girder
Rotation (%)
--- 1 20.60 6.88 60.22 12.30
--- 2 37.25 2.51 42.60 17.64
--- 3
Error in
Measurements
Error in
Measurements
Error in
Measurements
Error in
Measurements
Page 205
194
APPENDIX E: FB-MULTIPIER MODELS
E.1 Full Scale Test Model Results
Figure 206
Figure 207
-14
-12
-10
-8
-6
-4
-2
0
-80-70-60-50-40-30-20-100
Dep
th f
rom
Cen
ter o
f P
ile
Ca
p (
ft)
Moment in Pile (k/ft)
Circular Pile with Type V Bearing Pad:
Moment Response
-14
-12
-10
-8
-6
-4
-2
0
0 0.25 0.5 0.75 1 1.25 1.5
Dep
th f
rom
Cen
ter o
f P
ile
Ca
p (
ft)
Pile Lateral Deflection (in)
Circular Pile with Type V Bearing Pad:
Displacement Response
Page 206
195
Figure 208
Figure 209
-14
-12
-10
-8
-6
-4
-2
0
-90-80-70-60-50-40-30-20-100
Dep
th f
rom
Cen
ter o
f P
ile
Ca
p (
ft)
Moment in Pile (k/ft)
Circular Pile with Type VI Bearing Pad:
Moment Response
-14
-12
-10
-8
-6
-4
-2
0
0 0.25 0.5 0.75 1 1.25 1.5
Dep
th f
rom
Cen
ter o
f P
ile
Ca
p (
ft)
Pile Lateral Deflection (in)
Circular Pile with Type VI Bearing Pad:
Displacement Response
Page 207
196
Figure 210
Figure 211
-14
-12
-10
-8
-6
-4
-2
0
-120-100-80-60-40-200
Dep
th f
rom
Cen
ter o
f P
ile
Ca
p (
ft)
Moment in Pile (k/ft)
Square Pile with Type V Bearing Pad: Moment
Response
-14
-12
-10
-8
-6
-4
-2
0
0 0.25 0.5 0.75 1 1.25 1.5 1.75 2
Dep
th f
rom
Cen
ter o
f P
ile
Ca
p (
ft)
Pile Lateral Deflection (in)
Square Pile with Type V Bearing Pad:
Displacement Response
Page 208
197
Figure 212
Figure 213
-14
-12
-10
-8
-6
-4
-2
0
-140-120-100-80-60-40-200
Dep
th f
rom
Cen
ter o
f P
ile
Ca
p (
ft)
Moment in Pile (k/ft)
Square Pile with Type VI Bearing Pad:
Moment Response
-14
-12
-10
-8
-6
-4
-2
0
0 0.25 0.5 0.75 1 1.25 1.5 1.75 2
Dep
th f
rom
Cen
ter o
f P
ile
Ca
p (
ft)
Pile Lateral Deflection (in)
Square Pile with Type VI Bearing Pad:
Displacement Response
Page 209
198
Figure 214
Figure 215
-14
-12
-10
-8
-6
-4
-2
0
-100-80-60-40-200
Dep
th f
rom
Cen
ter o
f P
ile
Ca
p (
ft)
Moment in Pile (k/ft)
H-Pile with Type V Bearing Pad: Moment
Response
-14
-12
-10
-8
-6
-4
-2
0
0 0.25 0.5 0.75 1 1.25 1.5 1.75
Dep
th f
rom
Cen
ter o
f P
ile
Ca
p (
ft)
Pile Lateral Deflection (in)
H-Pile with Type V Bearing Pad: Displacement
Response
Page 210
199
Figure 216
Figure 217
-14
-12
-10
-8
-6
-4
-2
0
-100-80-60-40-200
Dep
th f
rom
Cen
ter o
f P
ile
Ca
p (
ft)
Moment in Pile (k/ft)
H-Pile with Type VI Bearing Pad: Moment
Response
-14
-12
-10
-8
-6
-4
-2
0
0 0.25 0.5 0.75 1 1.25
Dep
th f
rom
Cen
ter o
f P
ile
Ca
p (
ft)
Pile Lateral Deflection (in)
H-Pile with Type VI Bearing Pad:
Displacement Response
Page 211
200
E.2 Single Pile Models
Figure 218
Figure 219
-14
-12
-10
-8
-6
-4
-2
0
-80-70-60-50-40-30-20-100
Dep
th f
rom
Cen
ter o
f P
ile
Ca
p (
ft)
Moment in Pile (k/ft)
Circular Single Pile Model with Type V
Bearing Pad: Moment Response
-14
-12
-10
-8
-6
-4
-2
0
0 0.25 0.5 0.75 1 1.25 1.5 1.75
Dep
th f
ro
m C
en
ter o
f P
ile C
ap
(ft
)
Pile Lateral Deflection (in)
Circular Single Pile Model with Type V
Bearing Pad: Displacement Response
Page 212
201
Figure 220
Figure 221
-14
-12
-10
-8
-6
-4
-2
0
-90-80-70-60-50-40-30-20-100
Dep
th f
rom
Cen
ter o
f P
ile
Ca
p (
ft)
Moment in Pile (k/ft)
Circular Single Pile Model with Type VI
Bearing Pad: Moment Response
-14
-12
-10
-8
-6
-4
-2
0
0 0.25 0.5 0.75 1 1.25 1.5
Dep
th f
rom
Cen
ter o
f P
ile
Ca
p (
ft)
Pile Lateral Deflection (in)
Circular Single Pile Model with Type VI
Bearing Pad: Displacement Response
Page 213
202
Figure 222
Figure 223
-14
-12
-10
-8
-6
-4
-2
0
-120-100-80-60-40-200
Dep
th f
rom
Cen
ter o
f P
ile
Ca
p (
ft)
Moment in Pile (k/ft)
Square Single Pile Model with Type V Bearing
Pad: Moment Response
-14
-12
-10
-8
-6
-4
-2
0
0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25
Dep
th f
rom
Cen
ter o
f P
ile
Ca
p (
ft)
Pile Lateral Deflection (in)
Square Single Pile Model with Type V Bearing
Pad: Displacement Response
Page 214
203
Figure 224
Figure 225
-14
-12
-10
-8
-6
-4
-2
0
-140-120-100-80-60-40-200
Dep
th f
rom
Cen
ter o
f P
ile
Ca
p (
ft)
Moment in Pile (k/ft)
Square Single Pile Model with Type VI
Bearing Pad: Moment Response
-14
-12
-10
-8
-6
-4
-2
0
0 0.25 0.5 0.75 1 1.25 1.5 1.75 2
Dep
th f
rom
Cen
ter o
f P
ile
Ca
p (
ft)
Pile Lateral Deflection (in)
Square Single Pile Model with Type VI
Bearing Pad: Displacement Response
Page 215
204
Figure 226
Figure 227
-14
-12
-10
-8
-6
-4
-2
0
-100-80-60-40-200
Dep
th f
rom
Cen
ter o
f P
ile
Ca
p (
ft)
Moment in Pile (k/ft)
H-Pile Single Model with Type V Bearing Pad:
Moment Response
-14
-12
-10
-8
-6
-4
-2
0
0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75
Dep
th f
rom
Cen
ter o
f P
ile
Ca
p (
ft)
Pile Lateral Deflection (in)
H-Pile Single Model with Type V Bearing Pad:
Displacement Response
Page 216
205
Figure 228
Figure 229
-14
-12
-10
-8
-6
-4
-2
0
-100-80-60-40-200
Dep
th f
rom
Cen
ter o
f P
ile
Ca
p (
ft)
Moment in Pile (k/ft)
H-Pile Single Model with Type VI Bearing
Pad: Moment Response
-14
-12
-10
-8
-6
-4
-2
0
0 0.25 0.5 0.75 1 1.25
Dep
th f
rom
Cen
ter o
f P
ile
Ca
p (
ft)
Pile Lateral Deflection (in)
H-Pile Single Model with Type VI Bearing
Pad: Displacement Response
Page 217
206
E.3 Matched Single Pile Results to Actual Test Results
Figure 230
Figure 231
-14
-12
-10
-8
-6
-4
-2
0
-80-70-60-50-40-30-20-100
Dep
th f
rom
Cen
ter o
f P
ile
Ca
p (
ft)
Moment in Pile (k/ft)
Matched Circular Single Pile Model with Type
V Bearing Pad: Moment Response
-14
-12
-10
-8
-6
-4
-2
0
0 0.25 0.5 0.75 1 1.25 1.5
Dep
th f
ro
m C
en
ter o
f P
ile C
ap
(ft
)
Pile Lateral Deflection (in)
Matched Circular Single Pile Model with Type
V Bearing Pad: Displacement Response
Page 218
207
Figure 232
Figure 233
-14
-12
-10
-8
-6
-4
-2
0
-90-80-70-60-50-40-30-20-100
Dep
th f
rom
Cen
ter o
f P
ile
Ca
p (
ft)
Moment in Pile (k/ft)
Matched Circular Single Pile Model with Type
VI Bearing Pad: Moment Response
-14
-12
-10
-8
-6
-4
-2
0
0 0.25 0.5 0.75 1 1.25 1.5
Dep
th f
rom
Cen
ter o
f P
ile
Ca
p (
ft)
Pile Lateral Deflection (in)
Matched Circular Single Pile Model with Type
VI Bearing Pad: Displacement Response
Page 219
208
Figure 234
Figure 235
-14
-12
-10
-8
-6
-4
-2
0
-120-100-80-60-40-200
Dep
th f
rom
Cen
ter o
f P
ile
Ca
p (
ft)
Moment in Pile (k/ft)
Matched Square Single Pile Model with Type
V Bearing Pad: Moment Response
-14
-12
-10
-8
-6
-4
-2
0
0 0.25 0.5 0.75 1 1.25 1.5 1.75
Dep
th f
rom
Cen
ter o
f P
ile
Ca
p (
ft)
Pile Lateral Deflection (in)
Matched Square Single Pile Model with Type
V Bearing Pad: Moment Response
Page 220
209
Figure 236
Figure 237
-14
-12
-10
-8
-6
-4
-2
0
-140-120-100-80-60-40-200
Dep
th f
rom
Cen
ter o
f P
ile
Ca
p (
ft)
Moment in Pile (k/ft)
Matched Square Single Pile Model with Type
VI Bearing Pad: Moment Response
-14
-12
-10
-8
-6
-4
-2
0
0 0.25 0.5 0.75 1 1.25 1.5 1.75
Dep
th f
rom
Cen
ter o
f P
ile
Ca
p (
ft)
Pile Lateral Deflection (in)
Matched Square Single Pile Model with Type
VI Bearing Pad: Moment Response
Page 221
210
Figure 238
Figure 239
-14
-12
-10
-8
-6
-4
-2
0
-100-80-60-40-200
Dep
th f
rom
Cen
ter o
f P
ile
Ca
p (
ft)
Moment in Pile (k/ft)
Matched H-Pile Model with Type V Bearing
Pad: Moment Response
-14
-12
-10
-8
-6
-4
-2
0
0 0.25 0.5 0.75 1 1.25 1.5 1.75 2
Dep
th f
rom
Cen
ter o
f P
ile
Ca
p (
ft)
Pile Lateral Deflection (in)
Matched H-Pile Model with Type V Bearing
Pad: Displacement Response
