Research work in this thesis deals with the effects of lateral loads in the longitudinal

Transcription

1 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.

2 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 28 APPROVED BY: Mohammed A. Gabr, Ph.D. Chair of Advisory Committee Mervyn J. Kowalsky, Ph.D. Chair of Advisory Committee Roy H. Borden, Ph.D. Committee Member

3 BIOGRAPHY Benjamin Allen Possiel was born on August 8 th, 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 5 th, 28, he will be getting married to an amazing and wonderful woman who is his best friend and better half, Megan Daniels Gray. ii

4 TABLE OF CONTENTS LIST OF TABLES... v LIST OF FIGURES... vi LIST OF EQUATIONS... ix CHAPTER 1: INTRODUCTION Problem Description Objective Approach Full scale testing Florida-Pier Computer Modeling Scope Literature Review Experimental Program Load Transfer Mechanisms Florida-Mulitipier Modeling Design Limit States Summary and Conclusions... 5 CHAPTER 2: LITERATURE REVIEW Introduction Current Design Y. Chen (1995) and (Davisson and Robinson, 1965) Pile Bent Design Criteria (Robinson et al, 26) Elastomeric Bearing Pad Summary and Conclusions CHAPTER 3: EXPERIMENTAL PROGRAM Experimental Design Construction of Test Sample Elements Instrumentations and Testing Protocol CHAPTER 4: TESTING RESULTS Bearing Pad Tests Physical Observations from Testing Circular Pile Square Pile iii

5 4.2.3 H-pile Experimental Results Conclusions CHAPTER 5: MODELING-FB MULTIPIER Introduction Experimental Modeling Full Scale Modeling Single Pile Modeling North Carolina Bridge Bent Case Study Halifax County Bridge Wake County Bridge Robeson County Bridge Conclusions CHAPTER 6: LIMIT STATES Background Analysis Summary and Conclusions CHAPTER 7: SUMMARY AND CONCLUSIONS Full Scale Tests FB-MultiPier Modeling Limit States Conclusions REFERENCES APPENDIX A: Lateral Force vs. Top Pile Displacement Response APPENDIX B: Top displacement vs. Contributing Top Displacement Components APPENDIX C: Measured vs. Calculated Response APPENDIX D: Percentages of Contributing Top Displacement APPENDIX E: FB-MultiPier Models E.1 Full Scale Test Model Results E.2 Single Pile Models... 2 E.3 Matched Single Pile Results to Actual Test Results iv

6 LIST OF TABLES Table 1. Values of n h for sands (from Y. Chen, 1995)... 9 Table 2. Comparison of Lf values for fixed head piles (from Y. Chen, 1995) Table 3. Comparison of Lf values for pinned head piles (from Y. Chen, 1995) Table 4. Component properties Table 5. Loads for circular pile cases Table 6. Loads for square pile cases Table 7. Loads for H-pile cases Table 8. Properties of bearing pads under study from Robinson et al (27) Table 9. Full scale test configurations modeled in FB-MultiPier Table 1. Moment of inertia of sections modeled in FB-MultiPier Table 11. Axial stiffness of full scale foundation elements Table 12. Inputted FB-MultiPier data Table 13. Inputted FB-MultiPier bearing pad stiffness (compression and shear) Table 14. Inputted FB-MultiPier rotational stiffness parameters Table 15. FB-MultiPier experimental full scale test results Table 16. Equivalent spring stiffness for FB-MultiPier single pile analysis Table 17. Single pile FB-MultiPier results with assumed equivalent stiffness... 8 Table 18. FB-MultiPier single pile test results matched to actual test results Table 19. Comparison FB-MultiPier single pile analysis of assumed length effect Table 2. Halifax County FB-MultiPier single pile results of pile cap fixity Table 21. Halifax County equivalent length of pile to a depth of fixity Table 22. Wake County FB-MultiPier single pile results of pile cap fixity Table 23. Wake County equivalent length of pile to a depth of fixity Table 24. Robeson County FB-MultiPier single pile results of pile cap fixity Table 25. Robeson County equivalent length of pile to a depth of fixity Table 26. Input variables for Halifax County bridge section Table 27. Results from joint closure investigation for Halifax County Bridge Table 28. Results from simulation assuming essentially free torsion Table 29. Results from determined required joint thickness for failure due to joint closure v

7 LIST OF FIGURES Figure 1a.) Non-linear soil-pile model b.) Equivalent system model... 7 Figure 2. Equivalent model parameters (from Robinson et al, 26) Figure 3. Forces and moments for finite element analysis of bearing pads (from Yazdani et al, 2) Figure 4. Wake County Bridge Figure 5. Section of bridge Figure 6. Model of test assembly Figure 7. Test setup model Figure 8. Longitudinal cross section model of connection elements Figure 9. Flipping of AASHTO girder Figure 1. Bridge deck casting bed Figure 11. Reinforcement of diaphragm connection Figure 12. Completed cast of superstructure section Figure 13. Side profile of completed cast of superstructure section Figure 14. Support block steel reinforcement cage Figure 15. Casting of support blocks Figure 16. Placement of support blocks... 3 Figure 17. Pinned connection of superstructure... 3 Figure 18. Cross sections of piles Figure 19. Completion of pile cap pour Figure 2. Casting of concrete piles Figure 21. Test setup for circular pile Figure 22. Illustration of instrumentation positioning Figure 23. Illustration of loading scheme Figure 24. Elastic cycle lateral loading history Figure 25. Ductility cycle lateral loading history Figure 26. Flexural cracks produced in the square pile Figure 27. Visible gap between pile cap and bearing pad Figure 28. Shear deformation of the type VI bearing pad Figure 29. Pullout of embedded plate in girder Figure 3. Detailed design of embedded plate (from Halifax County Bridge plans) Figure 31a.) and b.) Concrete cracking in the diaphragm under the pile cap Figure 32. Cracks in diaphragm from pullout of embedment plate Figure 33. Bending of sole plate Figure 34. Significant cracking in the pile cap Figure 35. Rotation of the H-pile independent of the pile cap... 5 Figure 36. Prying of the H-pile in the pile cap Figure 37. Cracks in the pile cap along the adjacent side of loading Figure 38. Gaps generated between sole plate / cap beam and bearing pad Figure 39. Components of contributing pile top displacement Figure 4. Top displacement components Figure 41. Measured vs calculated top displacement Figure 42. Pie chart of pile top displacement component percentages Figure 43. Square pile/bp V: cap moment vs. cap rotation vi

8 Figure 44. Square pile/bp VI: cap moment vs. cap rotation Figure 45. Circular pile/bp V: cap moment vs. cap rotation Figure 46. Circular pile/bp VI: cap moment vs. cap rotation Figure 47. HP/BP V: cap moment vs. cap rotation Figure 48. HP/BP VI: cap moment vs. cap rotation Figure 49. Secant stiffness of square pile / BP V (pushing direction)... 6 Figure 5. Secant stiffness of square pile /BPV (pulling direction) Figure 51. Secant stiffness of square pile / BPVI (pushing direction) Figure 52. Secant stiffness of square pile / BPVI (pulling direction) Figure 53. Secant stiffness of circular pile / BP V (pushing direction) Figure 54. Secant stiffness of circular pile/ BP V (pulling direction) Figure 55. Secant stiffness of circular pile/ BP VI (pushing direction) Figure 56. Secant stiffness of circular pile / BP VI (pulling direction) Figure 57. Secant stiffness of H-pile / BP V (pushing direction) Figure 58. Secant stiffness of H-pile / BP V (pulling direction) Figure 59. Secant stiffness of H-pile/ BP VI (pushing direction) Figure 6. Secant stiffness of H-pile/ BP VI (pulling direction) Figure 61. FB-MultiPier model of the full scale test on a circular foundation element... 7 Figure 62. Equivalent cracked moment of inertia for circular columns Figure 63. Equivalent cracked moment of inertia for square columns 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 Figure 66. FB-MultiPier model of single pile analysis of full scale test of the H-pile Figure 67. Illustration of Halifax County interior bent modeled in FB-MultiPier Figure 68. FB-MultiPier soil profile for the Halifax County interior bent Figure 69. FB-MultiPier single pile model for Halifax County interior bent pile Figure 7. Halifax FB-MultiPier single pile moment response Figure 71. Halifax FB-MultiPier single pile displacement response... 9 Figure 72. Halifax County single pile rotational stiffness effect on equivalent depth to fixity Figure 73. Concluding equivalent depth to fixity range for Halifax County pile Figure 74. Illustration of Wake County interior bent modeled in FB-MultiPier Figure 75. FB-MultiPier soil profile for the Wake County interior bent Figure 76. FB-MultiPier single pile model for Wake County interior bent pile Figure 77. Wake County FB-MultiPier single pile moment response Figure 78. Wake County FB-MultiPier single pile displacement response Figure 79. Wake County single pile rotational stiffness effect on equivalent depth to fixity... 1 Figure 8. Concluding equivalent depth to fixity range for Wake County foundation element Figure 81. Illustration of Robeson County interior bent modeled in FB-MultiPier Figure 82. FB-MultiPier soil profile for the Robeson County interior bent Figure 83. FB-MultiPier single pile model for Robeson County interior bent pile Figure 84. Robeson County FB-MultiPier single pile moment response vii

9 Figure 85. Robeson County FB-MultiPier single pile moment response enlarged Figure 86. Robeson County FB-MultiPier single pile displacement response Figure 87. Robeson County FB-MultiPier single pile displacement response enlarged 17 Figure 88. Robeson County single pile rotational stiffness effect on equivalent depth to fixity Figure 89. Concluding equivalent depth to fixity range for Robeson County H-pile Figure 9. Joint closure model for 3 spans supported by 2 interior pile bents at the expansion joints (Robinson et al, 26) Figure 91. Halifax County Bridge bent response to lateral load (Robinson 27) viii

10 LIST OF EQUATIONS Equation 1 (Davisson and Robinson, 1965).25 E pi py L f 1.4, clay... 8 Ec E pi py Equation 2 (Davisson and Robinson, 1965) L f 1.8, sand... 8 nh Equation 3 Y s = L c ( x +.434x x 3 ) x < Equation 4 Y s =.36L c 1.25 x Equation 5 Y m = L c ( x x x x 4 ) x Equation 6 Y m =.37L c 1.5 < x Equation 7 Y b = L c ( x +.856x x 3 ) x Equation 8 Y b =.37L c 2 < x Equation 9 Y s = L c ( x +.57x 2 ) x Equation 1 Y s =.35L c.5 < x Equation 11 Y m = L c ( x + 1.3x x x 4 ) x Equation 12 Y m =.56L c 1.25 x Equation 13 Y b = L c ( x x x x x 5 ) x Equation 14 Y b =.35L c 1.5 < x Equation 15 E pi py L c 4 ke BL Equation 16 k A e Equation 17 M L e max V Equation 18 α = L3 ev EpIp t Equation 19 2M L max e V Equation 2 α = Equation 21 Equation 22 Equation 23 L e 3 V 12EpIp t LW S h L W ri 2 E c 6GS k Ry EcI y M y H Ry Equation 24 k a = EA L Equation 25 L2 j ( T ) L 2 P max w L L 2 2EI Kr.2 ix

11 Equation P max L P max L P max tot EI Kr K1 FL Pmax K2* tot Equation 27 x

12 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 1

13 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 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 2

14 replicated in the laboratory testing, measurement, and evaluation of the rotational behavior. Moment transfer through elastomeric bearings was also conducted 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 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. 3

15 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 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 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 Design Limit States Limit states from previous literature will be presented from Robinson et al (26) and the level of impact that the rotational stiffness plays within these limit states analyzed. 4

16 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. 5

17 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, 26). 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, 26) 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, 24). 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. 6

18 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 7

19 Where, Le = Total pile equivalent length L f = Depth below ground to a point of fixity L u = 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) L f E pi py 1.4 Ec.25, clay Equation 2 (Davisson and Robinson, 1965) Where, E p = Elastic modulus of the pile (tsf) I py = Moment of inertia about weak axis (ft 4 ) Ec = Elastic modulus of the clay (tsf) L f E pi py 1.8 nh.2, sand n h = Rate of increase of elastic soil modulus with depth for sand (tsf-ft -1 ) Table 1 presents values of n h found in Chen (1995) to be used in for Davisson and Robinsons, 1965 method. 8

20 Table 1. Values of n h for sands (from Chen, 1995) Sand Type Loose Medium Dense Saturated Condition nh (tsf/ft) Moist / Dry 3 Submerged 15 Moist / Dry 8 Submerged 4 Moist / Dry 2 Submerged 1 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. 9

21 For horizontal soil stiffness: Equation 3 Y s = L c ( x +.434x x 3 ) x < 1.25 Equation 4 Y s =.36L c 1.25 x 4 For pile bending: Equation 5 Y m = L c ( x x x x 4 ) x 1.5 Equation 6 Y m =.37L c 1.5 < x 4 For pile buckling: Equation 7 Y b = L c ( x +.856x x 3 ) x 2 Equation 8 Y b =.37L c 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 Y s = L c ( x +.57x 2 ) x.5 Equation 1 Y s =.35L c.5 < x 4 For bending moment: Equation 11 Y m = L c ( x + 1.3x x x 4 ) x 1.25 Equation 12 Y m =.56L c 1.25 x 4 For pile buckling: 1

22 Equation 13 Y b = L c ( x x x x x 5 ) x 1.5 Equation 14 Y b =.35L c 1.5 < x 4 Additional important equations include the following. Equation 15 L c E pi py 4 ke.25 Equation 16 k e A BL 4 Where, A and B are constants depending on the soil k e = effective horizontal soil stiffness L = active pile length in bending (.5 L c ) L c = pile length at which the pile behaves flexibly L fs = depth to fixity based on horizontal stiffness L fm = depth to fixity based on bending moment L fb = depth to fixity based on buckling x = length ratio defined as (L u /L c ) Y s = length ratio defined as (L fs /L c ) Y m = length ratio defined as (L fm /L c ) Y b = length ratio defined as (L fb /L c ) 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 11

23 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 Submerged Medium Sand Moist/Dry Submerged Dense Sand Moist/Dry Submerged Soft Clay Medium Clay Stiff Clay Very Stiff Clay 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 Submerged Medium Sand Moist/Dry Submerged Dense Sand Moist/Dry Submerged Soft Clay Medium Clay Stiff Clay Very Stiff Clay 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 12

24 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 ( ) and for very stiff clay for a pinned head pile ( ) Pile Bent Design Criteria (Robinson et al, 26) In Pile Bent Design Criteria by Robinson et al (26), 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, 26). The equivalent system method presented in Robinson et al (26) 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 13

25 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 (L e ) developed by Robinson et al (26) 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 (26) 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. 14

26 Figure 2. Equivalent model parameters (from Robinson et al, 26) Free head pile: Equation 17 L e M max V Equation 18 α = L e 3 V 3E p I p t 15

27 Fixed head pile: Equation 19 L e 2M max V Equation 2 α = L e 3 V 12E p I p t Where from Robinson et al (26), L b = 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). L e = 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. M max = Maximum moment developed in both the equivalent model and the nonlinear soilpile 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 nonlinear soil- pile model when multiplied by the moment of inertia of the pile, I p Ep Ip = Elastic modulus of the pile = Moment of inertia of the pile 16

28 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 (26) 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 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 (2) 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, 2). 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 17

29 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 (E c ). Equation 21 Equation 23 are from Yazdani et al (2) where and illustration of the elastomeric bearing pad under study is in Figure 3. Equation 21 LW S 2 h L W ri 2 Equation 22 E c 6GS Equation 23 k Ry E c I H y M y Ry Where, S = Shape factor L = Length of bearing pad (long dimension) W = Width of bearing pad (short dimension) h ri = Thickness of one elastomer layer H = Total thickness of the bearing pad E c = Elastic Compressive Modulus of the bearing pad G = Shear Modulus I y = Moment of Inertia about the y axis M y = Moment about the y axis Ry = Change in rotation k Ry = Rotational stiffness about the y axis 18

30 Figure 3. Forces and moments for finite element analysis of bearing pads (from Yazdani et al, 2) 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 (2) presents a method for determining the rotational stiffness of the elastomeric bearing pad but the 19

31 rotational stiffness of the entire connection component is not entirely known or implemented into design practice. 2

32 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 21

33 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. 22

34 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 22 kip actuator (part 2) which provides lateral loading are visible. The actuator was bolted to the top of the pile while a hydraulic 6 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 6 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. 23

35 Figure 7. Test setup model 1: Steel Frame 2: Actuator to apply horizontal load 3: 6 ton hydraulic jack applying axial pile load 4: 6 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. 24

36 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 Steel Anchor bolts Steel Sole Plates 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 (4.64cm) welds on either side to secure them to the embedded plates. Four anchor bolts were cast 12 inches (3.48cm) in to the pile cap with 8 inches (2.32cm) 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. 25

37 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, 3 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 26

38 Figure 1. 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 27

39 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 28

40 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 6 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. 29

41 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 (2 x 2 inch), and a steel H- Pile (12 x 63). Figure 18 shows the cross sections of the different piles. 3

42 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 31

43 Figure 2. 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

44 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 33

45 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). SP 1 (COLUMN TOP, CENTER) SP 12 (COLUMN, CENTER) PARALLEL TO EACH OTHER LC 1 CLIN-3 SP 8 (COLUMN TOP, CENTER) (TRANSVERSE DIRECTION, CENTER) P 21 P 2 4" P 4 3" P 6 Bearing Pads P 7 3" P " P 22 P 23 LPOT SG1 SG2 SG3 SG4 SG5 SG6 P 9 P 13 P 15 P 16 LC2 CLIN-2 P 14 P 1 P 11 P 12 LC3 SG7 SG8 SG9 SG1 SG11 SG12 SP 9 (TOP CAP BEAM,CENTER) SP 11 (BOTTOM CAP BEAM, CENTER) CLIN-1 SP 15 SP 4 SP 5 SP 2 SP 7 SP 13 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 34

46 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 35

47 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 19 kips (485kN) which was 3% of its ultimate capacity. Table 5. Loads for circular pile cases Case ALR (%) Pile Load Load on one Bearing Pad P P1 P2 P3 kips (kn) kips (kn) kips (kn) kips (kn) (25) 11 (51) 17 (76) 23 (12) (37) 17 (76) 26 (116) 34 (151) (49) 23 (12) 34 (151) 46 (25) Table 6. Loads for square pile cases Pile Load Load on one Bearing Pad Case ALR (%) P P1 P2 P3 kips (kn) kips (kn) kips (kn) kips (kn) (24) 13.5 (6) 2 (89) 27 (12) (32) 18 (8) 27 (12) 36 (16) (4) 23 (151) 34 (151) 45 (2) Table 7. Loads for H-pile cases Pile Load Load on one Bearing Pad Case P P1 P2 P3 kips (kn) kips (kn) kips (kn) kips (kn) 1 19 (485) 27 (12) 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). 36

48 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. 37

49 Figure 25. Ductility cycle lateral loading history 38

50 CHAPTER 4: TESTING RESULTS 4.1 Bearing Pad Tests In Robeson et al (27), 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 5 kips, 1 kips, 15 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 2 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 5 kip normal load and compression from Robinson et al (27). Table 8. Properties of bearing pads under study from Robinson et al (27) Property BP V BP VI W (in) L (in) t (in) G (psi) E (psi) 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 39

51 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.75 inches and ending the elastic cycle tests approximately at a 3 inch top deflection. 4

52 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 41

53 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). 42

54 Figure 28. Shear deformation of the type VI bearing pad As testing progressed into the ductility cycles for each pile, more observations were made 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. 43

55 Figure 3 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 44

56 Figure 3. Detailed design of embedded plate (from Halifax County Bridge plans) 45

57 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.5 inches (12.7 mm) as the force was increased. This behavior as well as the pullout of the embedded 46

58 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) 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 47

59 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. 48

60 Figure 34. Significant cracking in the pile cap 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 49

61 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 5

62 Figure 36. Prying of the H-pile in the pile cap Figure 37. Cracks in the pile cap along the adjacent side of loading 51

63 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. 52

64 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 2, and LPOT 21. Figure 4 shows the calculated contributing top displacement of each component with respect to the overall top displacement measured at the peaks of each cycle. 53

65 Figure 4. Top displacement components From Figure 4 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. 54

66 Experimental Displacement (in) Experimental Displacement [m] 3% ALR Square / BP V / BP Load Measured Top Displacement Calculated Displacement cycle Figure 41. Measured vs calculated top displacement Figure 4 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.75 inches for the square pile under an ALR of 3% and a bearing pad load of P1 on the Type V bearing pad. 55

67 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. 56

68 Figure 43. Square pile/bp V: cap moment vs. cap rotation Figure 44. Square pile/bp VI: cap moment vs. cap rotation 57

69 Figure 45. Circular pile/bp V: cap moment vs. cap rotation Figure 46. Circular pile/bp VI: cap moment vs. cap rotation 58

70 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 59

71 the maximum moment in the pile cap for all of the piles and loading cases was approximately between 15 and 225 k-ft. Also, the maximum cap rotation was around.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.75, -.75, 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 6 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) 6

72 Figure 5. Secant stiffness of square pile /BPV (pulling direction) Figure 51. Secant stiffness of square pile / BPVI (pushing direction) 61

73 Figure 52. Secant stiffness of square pile / BPVI (pulling direction) Figure 53. Secant stiffness of circular pile / BP V (pushing direction) 62

74 Figure 54. Secant stiffness of circular pile/ BP V (pulling direction) Figure 55. Secant stiffness of circular pile/ BP VI (pushing direction) 63

75 Figure 56. Secant stiffness of circular pile / BP VI (pulling direction) Figure 57. Secant stiffness of H-pile / BP V (pushing direction) 64

76 Figure 58. Secant stiffness of H-pile / BP V (pulling direction) Figure 59. Secant stiffness of H-pile/ BP VI (pushing direction) 65

77 Figure 6. 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 66

78 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. 67

79 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 (2). 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 26). 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 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 68

80 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 : Circular VI 8 : Square V 5 : Square VI 5 : H-Pile V --- : H-Pile VI --- : 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 (27) 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 5 kips, found in Robinson et al (27), 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 69

81 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 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 (27). For the H-pile, the measurements from the full scale testing indicated that the pile was 7

82 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 EI g = gross stiffness ρ 1 = Area of reinforcing steel / Area of concrete N u = Applied compressive load f c = compressive strength of concrete A g = gross cross-sectional area Figure 62. Equivalent cracked moment of inertia for circular columns 71

83 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 29 ksi elastic modulus was used for the steel H-pile. 72

84 Table 1. Moment of inertia of sections modeled in FB-MultiPier Foundation Element Moment of Inertia (in^4) Ixx Iyy Section Behavior 18" Circular Cracked 2" Square Cracked 12x63 H-Pile Elastic Pile Cap Uncracked Table 11. Axial stiffness of full scale foundation Elements Foundation Element EA/L Stiffness (k/in) Circular Square 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 (27). 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 73

85 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 / Circular VI 8/ Square V 5 / Square VI 5 / H-Pile V ---- / H-Pile VI ---- / Table 13. Inputted FB-MultiPier Bearing Pad Stiffness (Compression and Shear) Pile BP Type Load (kips) Shear Stiffness Displacement (in) Stiffness (kip/in) Load (kips) Compressive Stiffness Displacement (in) Stiffness (kip/in) Circular V Circular VI Square V Square VI H-Pile V H-Pile VI

86 Table 14. Inputted FB-MultiPier rotational stiffness parameters Pile BP Type Rotational Stiffness (Measured) Moment (kip-in) Rotation (rad) Stiffness (kipft/rad) 1/2*Rotational Stiffness (Full Scale: FB-MultiPier Model) Moment (kip-in) Rotation (rad) Stiffness (kip-ft/rad) Circular V Circular VI Square V Square VI H-Pile V H-Pile VI 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. 75

87 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 76

88 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 Circular VI Square V Square VI H-Pile V H-Pile VI 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 1%. 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 77

89 was not accounted for in FB-MultiPier and it is believed that this is the reason for significant difference in results 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. 78

90 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 Circular VI Square V Square VI H-Pile V H-Pile VI

91 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 Circular VI Square V Square VI H-Pile V H-Pile VI 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, 8

92 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 (kipft/rad) Proportion of Original Rotational Stiffness Circular V Circular VI Square V Square VI H-Pile V H-Pile VI 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 81

93 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. 82

94 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 (kipft/rad) Proportion of Original Rotational Stiffness Square V Square V 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 (26), and Robinson et al (27) and the interior bridge bent models were obtained with the author s permission. From these modeled interior bents, a single 83

95 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 (26). 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 Halifax County Bridge The Halifax County Bridge information was obtained from Robinson et al (26). This bridge consists of 8 interior bents and 2 end bends that span over Beech Swamp on US 31/ 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 3 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 3 degrees. This sand layer was underlain by 14.7 feet of clayey material with an undrained 84

96 shear strength of 4 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 375 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 (26). Figure 67. Illustration of Halifax County interior bent modeled in FB-MultiPier 85

97 Figure 68. FB-MultiPier soil profile for the Halifax County interior bent Single Pile Analysis A single pile model was generated from the Halifax County interior bent model from Robinson et al (26). 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 86

98 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 k a = EA L Where, k a = 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 (in 2 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. 87

99 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 2 shows the RSRs and the associated rotational stiffness used for this model as well as the results. Figure 7 and Figure 71 show the pile moment and displacement response as the RSR was increased. 88

100 Depth from Center of Pile Cap (ft) Table 2. Halifax County FB-MultiPier Single Pile results of pile cap fixity Rotational Stiffness (kipft/rad) M max (k-ft) Pile Top Deflection (in) Depth to M max from Center of Pile Cap (ft) RSR Moment in Pile (k-ft) RSR=.1 RSR = 1 RSR = 2 RSR = 5 RSR = 1 RSR = 2 RSR = 5 RSR= 1 RSR = 1 Figure 7. Halifax FB-MultiPier single pile moment response 89

101 Depth from Center of Pile Cap (ft) Pile Displacement (in) RSR= RSR = 1 RSR = 2 RSR = 5 RSR = 1 RSR = 2 RSR = 5 RSR = 1 RSR = 1 Figure 71. Halifax FB-MultiPier single pile displacement response RSRs of.1 and.1 are not shown in Figure 7 and Figure 71 because they generated the same moment and deflection response as when the RSR equaled.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 1 is also not shown in Figure 7 and Figure 71 because it produced the same moment and deflection as when the RSR equaled 1. As a result, a rotational stiffness of at least 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.1 and the fixed head pile behavior at an RSR of 1 was.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 (26) 9

102 for determining an equivalent length, L e 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 2). 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 M max (k-ft) Equivalent Depth to Point of Fixity L e (ft) Assumed Head Condition Model from Robinson et al (26) RSR Free Free Free Free Free Free Fixed Fixed Fixed Fixed Fixed Fixed 91

103 Equivalent Length, Le (ft) Le Based on Fixed Head Assumption Le Based on Free Head Assumption RSR (k-ft/rad / k/in) 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.1, an equivalent depth to fixity can be modeled by the free head assumption presented in Robinson et al (26). This modeling yielded an equivalent depth to fixity of 16.6 feet and an α value of.39 (Refer to α description in Chapter 2). After an RSR of.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 (26) was not effective for the Halifax County model. Also, from a RSR of 1 or more, the equivalent pile depth to fixity seems to be accurately modeled by the fixed head assumptions of Robinson et al (26) at an equivalent depth of 24.1 feet and a corresponding α value of.915. With an RSR of less than 1, the fixed pile head assumptions from Robinson et al (26) 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 92

104 Equivalent Length, Le (ft) 7.5 feet of the equivalent depth to fixity between the free head and fixed head behavior which falls in a RSR range of.1 to 1. Figure 73 presents the concluding results for the Halifax County single pile model equivalent depth to fixity Partial Head Fixity Effective Range Acceptable Fixed Head Assumption Acceptable Free Head Assumption RSR (k-ft/rad / k/in) Figure 73. Concluding equivalent depth to fixity range for Halifax County pile Wake County Bridge Robinson et al (27) 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, 3 inches (.76m) thick, and 93

105 16 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 1.5 foot (3.2 m) layer of weathered rock was found that was modeled as stiff clay with an unconfined shear strength of 8 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 (27). Figure 74. Illustration of Wake County interior bent modeled in FB-MultiPier 94

106 Figure 75. FB-MultiPier soil profile for the Wake County interior bent Single Pile Analysis A single pile model was generated based on the interior bent model from Robinson et al (27). 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. 95

107 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 2. Figure 77 and Figure 78 show the pile moment and displacement response as the RSR was increased for the Wake County single pile model. 96

108 Depth from Center of Pile Cap (ft) Table 22. Wake County FB-MultiPier single pile results of pile cap fixity RSR Rot. Stiffness (k-ft/rad) M max (k-ft) Pile Top Deflection (in) Depth to M max from Center of Pile Cap (ft) Moment in Pile (k-ft) RSR =.1 RSR = 1 RSR = 2 RSR = 5 RSR = 1 RSR = 2 RSR = 5 RSR = 1 RSR = 1 Figure 77. Wake County FB-MultiPier single pile moment response 97

109 Depth from Center of Pile Cap (ft) Pile Displacement (in) RSR=.1 RSR = 1 RSR = 2 RSR = 5 RSR = 1 RSR = 2 RSR = 5 RSR = 1 RSR = 1 Figure 78. Wake County FB-MultiPier single pile displacement response The RSR values at.1 and.1 are not shown in Figure 7 and Figure 71 because they had the same moment and deflection response as an RSR value of.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 1 was not shown in Figure 7 and Figure 71 because it produced the same moment and deflection as at the RSR of 1. As it can be seen by the deflected shape and moment diagram, a rotational stiffness of at least 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.1 and the fixed head pile behavior at an RSR of 1 was found to be.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 98

110 associated RSRs along with the results of the maximum moments and equivalent point of fixity lengths based on the Robinson et al (26) models. Table 23. Wake County equivalent length of pile to a depth of fixity M max (k-ft) Equivalent Depth to Point of Fixity L e (ft) Assumed Head Condition Model from Robinson et al (26) RSR Free Free Free Free Free Free Free Free Free Fixed Fixed Fixed 99

111 Figure 79. Wake County single pile rotational stiffness effect on equivalent depth to fixity Figure 79 shows that up to an RSR of.1, the equivalent depth to fixity can be modeled by the free head assumption, presented in Robinson et al (26). This assumption yielded both an equivalent depth to fixity of 62.4 feet (19 m) and a corresponding α value of.791. As the rotational stiffness in the pile head is increased past an RSR of.1, the free head behavior modeled by Robinson et al (26) should not be used. For an RSR of 1 and greater, the equivalent depth to fixity is accurately modeled by the fixed head model in Robinson et al (26). For these conditions, the equivalent depth to fixity was 67.2 feet (2.5 m) with a corresponding α value of 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 (26) models. This corresponds to a RSR range of.1 to 1. Figure 8 presents the concluding results for the equivalent depth to fixity for the Wake County Bridge foundation element modeled. 1

112 Equivalent Length, Le (ft) Partial Head Fixity Effective Range Le Based on Fixed Head Assumption Le Based on Free Head Assumption RSR (k-ft/rad / k/in) Figure 8. Concluding equivalent depth to fixity range for Wake County foundation element Robeson County Bridge The Robeson County Bridge information was obtained from Robinson et al (26). This bridge consisted of 1 interior bent and 2 end bends that span over Lumber River on NC Route 133. 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 3 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 11

113 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 648 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 (26). Figure 81. Illustration of Robeson County interior bent modeled in FB-MultiPier 12

114 Figure 82. FB-MultiPier soil profile for the Robeson County interior bent Single Pile Analysis From the Robeson County interior bent model in Robinson et al (26), 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. 13

115 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 94 k/in. Table 2 shows the single pile input parameters and results. Figure 7 through Figure 87 show the pile moment and displacement response as the RSR was increased. 14