# Modeling of integral abutment bridges considering soil-structure interaction effects

TABLE OF CONTENTS Acknowledgement……...………………………………………………………………...iv Table of Contents……...………………………………………………………….…….....v List of Tables……...…………………………………………………………..………...viii List of Figures……...……………………………………………...……………………...ix Abstract……...……………………………………………………..……….…………...xiii 1. Introduction ................................................................................................................. 1 1.1 General ...................................................................................................................... 1 1.2 Modeling ................................................................................................................... 3 1.3 Finite Element Technology ....................................................................................... 4 1.4 Computational Framework ........................................................................................ 4 1.5 Objectives .................................................................................................................. 5 1.6 Dissertation Layout ................................................................................................... 5 2. Literature Review ........................................................................................................ 6 2.1 Integral Abutment Bridges ........................................................................................ 6 2.2 Current Practices ....................................................................................................... 8 2.3 Skewed IABs ............................................................................................................. 9 2.4 Soil-Structure Interaction ........................................................................................ 11 2.5 Instrumentation Projects .......................................................................................... 12 2.6 Important Loading Cases ........................................................................................ 14 3. Finite Element Technology ....................................................................................... 15 3.1 Soil Element ............................................................................................................ 15 3.1.1 Governing Equations ........................................................................................ 15 3.1.2 Linear Elastic Constitutive Model .................................................................... 20 3.1.3 Bounding Surface Constitutive Model for Clays ............................................. 21 3.1.4 Bounding Surface Constitutive Model for Sands ............................................. 22 3.2 Beam Element ......................................................................................................... 25 3.2.1 Stiffness Matrix ................................................................................................ 26 3.2.2 Mass Matrix ...................................................................................................... 32 3.2.3 Damping Matrix ............................................................................................... 33 3.2.4 Thermal Loading .............................................................................................. 33 3.2.5 Element Transformation ................................................................................... 36 3.2.6 Nonlinear EI ..................................................................................................... 38

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3.3 Plate Element........................................................................................................... 46 3.3.1 Stiffness Matrix ................................................................................................ 47 3.3.2 Numerical Integration ....................................................................................... 53 3.3.3 Mass Matrix ...................................................................................................... 55 3.3.4 Damping Matrix ............................................................................................... 56 3.3.5 Thermal Loading .............................................................................................. 56 3.3.6 Element Transformation ................................................................................... 59 3.3.7 Hourglassing ..................................................................................................... 62 3.4 Numerical Integration ............................................................................................. 67 3.4.1 Time Integration Scheme .................................................................................. 67 3.4.2 Ramped Loading............................................................................................... 70 4. Soil-Structure Interaction .......................................................................................... 76 4.1 Linear Problems ...................................................................................................... 76 4.1.1 Beams on Elastic Foundation ........................................................................... 76 4.1.2 Linear SSI Example Problem ........................................................................... 77 4.2 Soil-Pile Interaction in a Soft Clay ......................................................................... 91 4.2.1 Nonlinear SSI Example Problem ...................................................................... 91 5. Thermal Modeling ................................................................................................... 102 5.1 Linear Temperature Distribution ........................................................................... 102 5.2 Skewed Plates Subjected to Thermal Loading ...................................................... 104 5.3 Assemblies of Elements ........................................................................................ 113 6. TeraGrande Modeling .............................................................................................. 118 6.1 General .................................................................................................................. 118 6.1.1 Explicit Dynamics .......................................................................................... 118 6.1.2 ANATECH Concrete Model .......................................................................... 119 6.1.3 Concrete Cracking .......................................................................................... 120 6.1.4 Reinforcement Modeling ................................................................................ 121 6.1.5 Tied Contact ................................................................................................... 122 6.2 Prestressed Girder Modeling ................................................................................. 123 6.3 Superstructure Model ............................................................................................ 127 6.4 Thermal Analysis .................................................................................................. 130 6.4.1 Temperature Increase ..................................................................................... 130

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6.4.2 Temperature Decrease .................................................................................... 133 6.4.3 Blast Loading .................................................................................................. 136 7. TeraDysac Modeling ............................................................................................... 140 7.1 Problem Description .............................................................................................. 140 7.2 Soil Properties ....................................................................................................... 142 7.3 Structural Properties .............................................................................................. 143 7.3.1 Weighted Average Example ........................................................................... 144 7.3.2 Set-Up for Plane Strain Analysis .................................................................... 145 7.3.3 Set-Up for 3D Analysis .................................................................................. 146 7.4 Applied Thermal Loading ..................................................................................... 148 7.4.1 Validation Technique ..................................................................................... 149 7.5 Linear Elastic Analysis.......................................................................................... 151 7.5.1 Temperature Increase ..................................................................................... 154 7.5.2 Temperature Decrease .................................................................................... 157 7.6 Bounding Surface Analysis ................................................................................... 160 7.6.1 Bounding Surface Properties .......................................................................... 160 7.6.2 Temperature Increase ..................................................................................... 163 7.6.3 Temperature Decrease .................................................................................... 165 7.7 Three-Dimensional Analysis ................................................................................. 166 8. Conclusions ............................................................................................................. 171 8.1 General .................................................................................................................. 171 8.2 Recommendations ................................................................................................. 174 References……...……..…………………………………………..……….…………...182

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LIST OF TABLES Table 3.1: Bounding Surface Model Parameters for Speswhite Kaolin ........................... 22 Table 3.2: Bounding Surface Model Parameters .............................................................. 24 Table 3.3: Integration Points on the Master Element ....................................................... 53 Table 7.1: Young’s Modulus as a Function of N-Value (NAVFAC 1986) .................... 142 Table 7.2: Element Blocks by Color. .............................................................................. 152 Table 7.3: Bounding Surface Properties for Sand Layers ............................................... 162 Table 7.4: Results and Error Estimates for Heating Analysis ........................................ 164 Table 7.5: Results and Error Estimates for Cooling Analysis ........................................ 166

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LIST OF FIGURES Figure 1.1: Schematic Drawing of a Traditional Bridge ..................................................... 2 Figure 1.2: Schematic Drawing of an Integral Abutment Bridge ....................................... 3 Figure 2.1: Skew Angle Depiction.................................................................................... 10 Figure 2.2: Obtuse and Acute Corners in IABs ................................................................ 10 Figure 3.1: Soil-Fluid Mixture .......................................................................................... 15 Figure 3.2: Bounding Surface Representation (Clayey Soils) .......................................... 21 Figure 3.3: Bounding Surface Representation (Sands) ..................................................... 23 Figure 3.4: Beam Element Nodal Variables ..................................................................... 25 Figure 3.5: Beam Element Coordinate Transformation .................................................... 25 Figure 3.6: Temperature Distribution for Beams .............................................................. 34 Figure 3.7: Local Coordinate System for Beam Element ................................................. 36 Figure 3.8: X-Axis Directions for Beam Element ............................................................ 37 Figure 3.9: Typical Moment-Curvature Relationship for a Beam .................................... 39 Figure 3.10: Piece-wise Approximation of the Moment-Curvature Curve for a Beam .... 40 Figure 3.11: Bending Stiffness vs. Bending Moment for a Beam .................................... 40 Figure 3.12: Example Beam Geometry ............................................................................ 41 Figure 3.13: Stress Distribution at Yield .......................................................................... 42 Figure 3.14: Stress Distribution After Yield ..................................................................... 43 Figure 3.15: Stress Distribution at Ultimate Moment ....................................................... 44 Figure 3.16: Moment-Curvature Relationship for the Example Beam ............................. 44 Figure 3.17: Nonlinear EI Example Problem Layout ....................................................... 45 Figure 3.18: EI-Moment Relationship for the Example Beam ......................................... 45 Figure 3.19: Plate Element Nodal Variables ..................................................................... 47 Figure 3.20: Plate Element Layout ................................................................................... 50 Figure 3.21: Plate Element Coordinate Transformation ................................................... 53 Figure 3.22: Temperature Distribution for Plates ............................................................. 56 Figure 3.23: Middle Chords for Plate Element ................................................................. 60 Figure 3.24: Local Coordinate System for Plate Element ................................................ 61 Figure 3.25: w-Hourglassing Mode .................................................................................. 63 Figure 3.26: Problem Set-Up for Hourglassing Example ................................................. 65 Figure 3.27: Deformed Shape for Corner-Supported Plate (No Hourglass Stiffness) ...... 65 Figure 3.28: Deformed Shape for Corner-Supported Plate with Hourglass Stiffness ...... 66 Figure 3.29: Simply-Supported Set-Up for Hourglassing Example ................................. 67 Figure 3.30: Deformed Shape for Simply-Supported Plate (No Hourglass Stiffness) ..... 67 Figure 3.31: Ramped Loading .......................................................................................... 70 Figure 3.32: Cantilever Beam Problem Demonstrating Minor Oscillation ...................... 71 Figure 3.33: Nodal Displacement-Time History for Cantilever Beam Tip ...................... 71 Figure 3.34: Soil-Structure Interaction Problem Demonstrating Oscillation ................... 72 Figure 3.35: Nodal Displacement-Time History (Full Mass) ........................................... 73 Figure 3.36: Nodal Displacement-Time History (Full Mass, Extended Ramp) ............... 73 Figure 3.37: Nodal Displacement-Time History (10% Mass) .......................................... 74 Figure 3.38: Nodal Displacement-Time History (Zero Mass) .......................................... 74 Figure 4.1: Beam on Elastic Foundation........................................................................... 76 Figure 4.2: Problem Set-Up .............................................................................................. 77

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Figure 4.3: Point Load Applied to Axial Bar .................................................................... 79 Figure 4.4: Finite Element Set-Up for Point Load Analysis ............................................. 79 Figure 4.5: Beam Displacement (Winkler vs. Vesic) ....................................................... 81 Figure 4.6: Beam Rotation (Winkler vs. Vesic) ............................................................... 81 Figure 4.7: Beam Shear Force (Winkler vs. Vesic) .......................................................... 82 Figure 4.8: Beam Bending Moment (Winkler vs. Vesic) ................................................. 82 Figure 4.9: Elastic Beam Analysis Set-Up ....................................................................... 83 Figure 4.10: Euler-Bernoulli Beam Displacement Comparison ....................................... 84 Figure 4.11: Euler-Bernoulli Beam Rotation Comparison ............................................... 84 Figure 4.12: Finite Element Model Set-Up for Linear Soil-Structure Analysis ............... 85 Figure 4.13: Beam Displacement (Vesic vs. TeraDysac) ................................................. 86 Figure 4.14: Beam Rotation (Vesic vs. TeraDysac) ......................................................... 86 Figure 4.15: Beam Shear Force (Vesic vs. TeraDysac) .................................................... 87 Figure 4.16: Beam Bending Moment (Vesic vs. TeraDysac) ........................................... 87 Figure 4.17: TeraDysac Linear SSI Analysis Deformed Shape ....................................... 88 Figure 4.18: Beam Displacement (Vesic vs. TeraDysac – 3D) ........................................ 89 Figure 4.19: Beam Rotation (Vesic vs. TeraDysac – 3D) ................................................ 89 Figure 4.20: Beam Shear Force (Vesic vs. TeraDysac – 3D) ........................................... 90 Figure 4.21: Beam Bending Moment (Vesic vs. TeraDysac – 3D) .................................. 90 Figure 4.22: Nonlinear SSI Example Set-Up .................................................................... 91 Figure 4.23: Problem Set-Up for Nonlinear SSI TeraDysac Analysis ............................. 92 Figure 4.24: Loading and Node Sets for Nonlinear SSI TeraDysac Analysis .................. 92 Figure 4.25: Initial Vertical Stress State Contours (kPa) .................................................. 93 Figure 4.26: Deviator Stress-Strain Curve at 20 m Depth ................................................ 94 Figure 4.27: Stress Paths at 20 m Depth ........................................................................... 94 Figure 4.28: p-y Curves Obtained from LPILE ................................................................ 95 Figure 4.29: Soil Contribution to Nodal Force ................................................................. 96 Figure 4.30: Free Body Diagram of the Center Node ....................................................... 96 Figure 4.31: p-y Curves Obtained from TeraDysac.......................................................... 97 Figure 4.32: p-y Curve Comparison ................................................................................. 97 Figure 4.33: Pile Deflection Comparison for Nonlinear SSI Analysis ............................. 98 Figure 4.34: Pile Rotation Comparison for Nonlinear SSI Analysis ................................ 99 Figure 4.35: Pile Shear Force Comparison for Nonlinear SSI Analysis........................... 99 Figure 4.36: Pile Bending Moment Comparison for Nonlinear SSI Analysis .................. 99 Figure 4.37: Pore Water Pressure Contours (kPa) .......................................................... 101 Figure 4.38: Pore Water Pressure-Time History (kPa, s) ............................................... 101 Figure 5.1: Deformed Shape (No Gradient) ................................................................... 102 Figure 5.2: Curvature Depiction (Positive Gradient) ...................................................... 102 Figure 5.3: Curvature Depiction (Negative Gradient) .................................................... 103 Figure 5.4: Finite Element Mesh for Gradient Analysis ................................................. 103 Figure 5.5: Deformed Shape for Gradient Analysis ....................................................... 104 Figure 5.6: Square Test Plate Set-Up .............................................................................. 105 Figure 5.7: Square Plate Corner Forces .......................................................................... 105 Figure 5.8: Rhombus Plate Set-Up ................................................................................. 106 Figure 5.9: Rhombus Plate Corner Forces ...................................................................... 106 Figure 5.10. Rectangular Plate Set-Up .......................................................................... 107

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Figure 5.11: Rectangular Plate Corner Forces ................................................................ 108 Figure 5.12: Rectangular Plate (Deformed Shape) ......................................................... 109 Figure 5.13: Parallelogram Plate Set-Up ........................................................................ 110 Figure 5.14: Parallelogram Plate Corner Forces ............................................................. 110 Figure 5.15: Skewed IAB Deck Idealization Highlighting Corner Forces ..................... 111 Figure 5.16: Skewed Plate with Corner Connections ..................................................... 112 Figure 5.17: Corner-Connecting Beams ......................................................................... 112 Figure 5.18: 100 Element Plate for Mesh Assembly ...................................................... 113 Figure 5.19: 10 Element Beam for Mesh Assembly ....................................................... 114 Figure 5.20: Beam and Plate Mesh Assembly ................................................................ 115 Figure 5.21: Deformed Shape (Both Element Blocks Heated) ....................................... 116 Figure 5.22: Deformed Shape (Plate Element Block Heated Only) ............................... 116 Figure 5.23: Deformed Shape (Beam Element Block Heated Only) .............................. 117 Figure 6.1: Compressive Stress-Strain Curve (Pa) ......................................................... 120 Figure 6.2: Tensile Stress-Strain Curve (Pa) .................................................................. 120 Figure 6.3: Concrete Stress-Strain Diagram ................................................................... 121 Figure 6.4: Bridge Girder Mesh ...................................................................................... 122 Figure 6.5: Tied Contact Between Mesh Instances ........................................................ 123 Figure 6.6: Prestressed Tendons in Bridge Girder .......................................................... 123 Figure 6.7: Girder End Caps ........................................................................................... 124 Figure 6.8: Loading Amplitudes for Girder Analysis ..................................................... 124 Figure 6.9: Important Node Sets for Girder Analysis ..................................................... 125 Figure 6.10: Crack Pattern at 0.15 s ................................................................................ 125 Figure 6.11: Crack Pattern at 0.6 s .................................................................................. 125 Figure 6.12: Midspan Displacement-Time History from Girder Analysis ..................... 126 Figure 6.13: Minnesota IAB Model (Piers and Pier Piles Included) .............................. 127 Figure 6.14: Pier Piles (Above Grade) Mesh .................................................................. 128 Figure 6.15: Minnesota IAB Superstructure Model (Rebar Shown) .............................. 128 Figure 6.16: Superstructure Interior Nodes .................................................................... 129 Figure 6.17: Superstructure End Node Set ..................................................................... 129 Figure 6.18: Superstructure Crack Pattern for Temperature Increase ............................ 130 Figure 6.19: Girder Crack Pattern for Temperature Increase ......................................... 131 Figure 6.20: Strain Contours for Temperature Increase ................................................. 132 Figure 6.21: Strain Contours for Temperature Increase (Close-Up) .............................. 132 Figure 6.22: Deck Schematic at Pier Locations .............................................................. 133 Figure 6.23: Bridge Deck Stress (Pa) Contours for Temperature Decrease ................... 134 Figure 6.24: Stress (Pa) Contours Viewed from Beneath Bridge ................................... 134 Figure 6.25: Deck Crack Pattern for Temperature Decrease .......................................... 135 Figure 6.26: Deck Compressive Stress-Strain Curve (Pa) .............................................. 135 Figure 6.27: Blast Pressure (Pa) vs. Time (s) ................................................................. 137 Figure 6.28: Blast Pressure (Pa) vs. Distance (m) .......................................................... 137 Figure 6.29: Superstructure Pressure (Pa) 6 ms After Blast Initiation ........................... 137 Figure 6.30: Superstructure Deformed Shape at 0.15 s (Magnified by 15) .................... 138 Figure 6.31: Bridge Deck Crack Pattern ......................................................................... 138 Figure 6.32: Bridge Girders Crack Pattern ..................................................................... 139 Figure 7.1: Concrete IAB (Photo Courtesy of Huang et al. 2004) ................................. 140

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Figure 7.2: Elevation View of Minnesota IAB ............................................................... 141 Figure 7.3: Transverse Section (Through Deck) ............................................................. 141 Figure 7.4: Soil Stratigraphy with Used E/N Ratios ....................................................... 143 Figure 7.5: Cross-Section Pier Piles Above Grade ......................................................... 144 Figure 7.6: Bridge Details at Pier Locations ................................................................... 147 Figure 7.7: 3D TeraDysac Superstructure Model ........................................................... 147 Figure 7.8: Temperature Gradient (Sunny Summer Day, After Huang et al. 2004) ....... 148 Figure 7.9: Temperature Gradient (Cloudy Winter Day, After Huang et al. 2004) ....... 149 Figure 7.10: Superstructure Temperature Input (Heating) ............................................. 150 Figure 7.11: 2D IAB Finite Element Model ................................................................... 151 Figure 7.12: Element Block View .................................................................................. 152 Figure 7.13: Structure Assembly at Abutment ............................................................... 153 Figure 7.14: Junction Undeformed and Deformed Shapes ............................................. 153 Figure 7.15: Boundary Nodes for 2D Analysis .............................................................. 154 Figure 7.16: IAB Deformed Shape for Temperature Increase ........................................ 154 Figure 7.17: Abutment and Abutment Pile Displacement for Temperature Increase ..... 155 Figure 7.18: Developed Pore Water Pressure (kPa) During Temperature Increase ....... 157 Figure 7.19: IAB Deformed Shape for Temperature Decrease ...................................... 158 Figure 7.20: Abutment and Abutment Pile Displacement for Temperature Decrease ... 158 Figure 7.21: Developed Pore Water Pressure (kPa) During Temperature Decrease ...... 159 Figure 7.22: Soil Profile Composition (Nevada Sand and Speswhite Kaolin) ............... 161 Figure 7.23: Initial Stress State (kPa) for Bounding Surface Analysis........................... 163 Figure 7.24: Abutment and Abutment Pile Deformation Comparison ........................... 164 Figure 7.25: Bounding Surface Pore Pressure Development (kPa) ................................ 165 Figure 7.26: Abutment and Abutment Pile Deformation Comparison ........................... 166 Figure 7.27: 3D Superstructure Model (Non-Skewed) ................................................... 167 Figure 7.28: Plan View of 3D Superstructure Models .................................................... 168 Figure 7.29: Abutment Deformations from 3D Analyses ............................................... 169 Figure 7.30: 3D Superstructure Corner Forces ............................................................... 170 Figure 8.1: Full 3D Minnesota IAB Model .................................................................... 176 Figure 8.2: Full 3D Minnesota Bridge Model (Skewed) ................................................ 176 Figure 8.3: 3D Reduced Model (Skewed IAB) .............................................................. 177 Figure 8.4: Elevation View of 3D Reduced Model (Skewed IAB) ................................ 177 Figure 8.5: Element Block Composition for Nonlinear Pile Analysis............................ 179

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ABSTRACT Soil-structure interaction problems are both highly interesting and highly complex. To model soil-structure interaction problems accurately, the constitutive parts (i.e. foundations, soils, and superstructures) must be considered. Implementing the finite element technology necessary to analyze soil-structure interactions problems is a significant task. In this work, structural elements were added to the soil analysis computer program TeraDysac (Muraleetharan et al. 2003, Ravichandran 2005) and the soil-structure interaction in integral abutment bridges (IABs) was studied. IABs are a form of bridge where the superstructure ends are cast integrally with the abutments. The abutments, which are supported on piles in weak-axis bending move into and away from the backfill soils when the bridge deck undergoes thermal loading. These bridges provide numerous advantages to traditional bridges including reduced maintenance, simpler bridge hardware, and better water-tightness. However, because the superstructure movement is not accommodated with rollers or bearing pads like in traditional bridges, a complex soil-structure interaction problem emerges. Three-dimensional (3D) Timoshenko beam elements and Reissner-Mindlin plate elements were developed. The merging of soil and structural elements allows bridge models to be developed that consider all of the components of an actual bridge in a realistic manner. In addition to the structural elements, a thermal loading scheme and a nonlinear beam bending stiffness () scheme were also developed. In IABs, the abutment piles sometimes yield and hence enter a nonlinear range, so a nonlinear application may be important. Both linear elastic and bounding surface soil models were considered in this work to model the stress-strain behavior of soils.

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Several soil-structure interaction problems were analyzed in this work. Beams on elastic foundations were studied and comparisons were made between analytical results and the solutions obtained from a TeraDysac finite element analysis. A nonlinear soil- structure interaction analysis using TeraDysac with a bounding surface clay model is compared with results obtained from LPILE (ENSOFT 2007), which uses a approach. To test and validate the developed finite element technology, results from the field instrumentation of an IAB in Minnesota were used (see Huang et al. 2004). Two thermal events were studied in this work, a heating event during the summer and a temperature drop during the winter. The IAB used for the validation has a zero skew angle. A series of two-dimensional (2D) analyses were used to study the bridge behavior. A method for obtaining the approximate 2D structural properties is discussed. A 3D analysis comparing the Minnesota IAB superstructure (no skew) and a skewed version of the same superstructure is presented. A non-uniform abutment movement and stress distribution in the backfill soils in the skewed example show the importance of a 3D analysis when IABs are skewed. The reinforced concrete behavior at the bridge site was studied in detail using the finite element program TeraGrande (ANATECH 2005). TeraGrande models the rebar accurately and uses a smeared crack concrete model. Significant nonlinear behavior (e.g. cracking) was not seen for the thermally-induced abutment movements. Therefore, the developed linear structural elements were deemed acceptable for the IAB analyses performed in this work.

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1. Introduction 1.1 General Bridges present a challenge for both structural and geotechnical engineers. The desirable characteristics of a bridge include simple construction, minimal maintenance, smooth riding for users (including transition areas over abutments and bents), water-tightness, and long service lives. Bridges are interesting soil-structure interaction problems because cyclic loading due to heating and cooling causes the superstructure to move relative to foundation soils. Generally speaking, these movements are small, but can be quite important from an engineering standpoint. Traditional bridges (see Figure 1.1) accommodate cyclic loading with the following components: simply-supported girders, roller supports at intermediate bents, and expansion joints at approach slabs. These components allow for expansion and contraction of the roadway during thermal loading cycles without developing significant loads in the superstructure. The major pitfalls of traditional bridges include: rough riding for users (specifically over the bridge abutments), poor water-tightness, leakage through joints, corrosion of bearings and girders, freezing of trapped water in joints, and high levels of required maintenance.

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Figure 1.1: Schematic Drawing of a Traditional Bridge In an integral abutment bridge (IAB), there is continuity in the bridge system (see Figure 1.2). These systems have numerous advantages over traditional bridges. Namely, the girder-supporting hardware is simpler, less maintenance is required, and construction is easier. Today, IAB systems can be found in almost every state. These systems are superior to traditional bridges in several areas, but are not fully pursued because there are still uncertainties with respect to their behavior and design (see Chapter 2). A typical IAB system consists of the following components: a bridge superstructure (consisting of the roadway deck, abutments, piers, girders, parapet walls), drilled shafts and pile foundations, and select fill and native soils. The bridge superstructure is generally a reinforced concrete deck sitting on pre-stressed concrete girders or heavy duty steel sections. The piers are typically resting on drilled shaft foundations, while the abutments are located on driven steel H-piles in weak-axis bending. The abutments move due to thermal effects in IABs as opposed to traditional bridges where rollers and expansion joints allow the bridge deck to move, but the abutments remain stationary.

Batter pile Pier Girder Bearing Expansion joint Deck joints

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Figure 1.2: Schematic Drawing of an Integral Abutment Bridge 1.2 Modeling To study the behavior of IAB systems, modeling that considers soil, structure, and their interaction needs to be done. Underlying and backfill soils in IAB systems need to be modeled accurately. A soil model accounting for the complexities inherent to soils, namely solid, liquid, and gas constituents, hysteresis, plastic deformation, pore water pressure development, anisotropy, and load- and time-dependence is desirable. A structural model which can account for the relevant behavior of the superstructure (i.e. the girders and deck) and the foundation (i.e. the piles and drilled shafts) is also needed. Coupling soil and structural models provides a basis for modeling IAB behavior accurately. Once the finite element technology is in place and validated against instrumented results, then many different bridge geometries, foundation designs, and loading scenarios can be simulated to gain insight into IAB performance during various events.

Pier

Flexible pile Integral abutment Bearing

Pavement Girder Deck

Approach slab

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1.3 Finite Element Technology Analytical solutions for real world problems are often impossible to obtain. So mathematical models are formed and numerical techniques are used to find approximate solutions. For example, the finite element and finite difference methods can be used to solve governing differential equations and find numerical approximations. TeraDysac (Muraleetharan et al. 2003, Ravichandran 2005) is a fully-coupled soil analysis code with considerations for pore water and pore air pressure and soil nonlinearity. Bounding surface plasticity soil models (Dafalias and Herrmann 1982, Yogachandran 1991) are available in addition to a linear elastic constitutive model. This work consists of adding a Timoshenko beam element and a Reissner-Mindlin plate element to the TeraDysac computer code. Also, the capability to model thermal events is developed. Coupling beams, plates, and soil elements in a finite element model allow for a user to simulate real-world systems. Though this work focuses on IABs, the technology developed can be extended to other systems (e.g. buildings and their foundations, port facilities, and offshore oil rigs). 1.4 Computational Framework Models of complex systems such as an IAB require a high number of finite elements, sometimes on the order of hundreds of thousands to obtain accurate results. This means that big problems can not be analyzed on single processor personal computers. Even medium sized problems may take days or even weeks to analyze on a single processor machine. In practice, this is unacceptable, so parallel computing must be used. Dividing a large problem up into smaller parts and then using a different processor to analyze each part allows for a significant decrease in computational time. In this work, the parallel

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processing capabilities available within the TeraScale framework (ANATECH 2001) were utilized. 1.5 Objectives The objectives of this work include the following: 1. Develop and implement structural elements (beams and plates) in TeraDysac. 2. Knowing that foundation elements (i.e. driven piles) can go beyond yielding in some IAB systems, implement an algorithm to account for this behavior. 3. Develop thermal loading capabilities in the finite element code. 4. Analyze IAB systems (soil and superstructure) for various thermal load cases and validate the results against instrumented field studies. 5. Use an external nonlinear finite element application, TeraGrande (ANATECH 2005) to verify that linear assumptions for superstructure elements are acceptable for this work. 6. Gain insight into IAB performance and design. 1.6 Dissertation Layout This dissertation is organized into 8 chapters. Chapter 2 provides a literature review considering previous and relevant work to the field of IAB modeling. Chapter 3 discusses all of the relevant finite element technology. Chapter 4 deals with soil-structure interaction. Modeling thermal events is discussed in Chapter 5. Chapter 6 contains the TeraGrande finite element analyses which substantiate the use of linear structural elements in TeraDysac. Chapter 7 provides all of the TeraDysac results and comparisons with monitored field studies. Chapter 8 contains concluding remarks and suggestions for future work.

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2. Literature Review 2.1 Integral Abutment Bridges In traditional bridges, structural releases are provided in bridges to permit thermal expansion and contraction. These joints lead to water-tightness problems. Water runoff into newly opened deck joints can cause extensive damage. Water corrodes the underlying steel elements (girders, supports, connection hardware, etc). Water can also damage the concrete and expose reinforcing steel and subsequently corrode that. This problem is magnified in states subject to heavy snow storms, where sodium chloride and calcium chloride are commonly used in de-icing applications. The emergence of joint problems came in the 1960s as traffic loads increased in speed, volume, and weight. The cost of maintenance or replacement of expansion joints is a considerable portion of the total money spent by state Departments of Transportation (DOTs) every year. Joints and bearings in traditional bridges have emerged as major sources of bridge maintenance problems (Wolde-Tinsae and Greimann 1988). In an IAB, there are no rollers or simple supports at the abutments. Instead, the girder ends are cast integrally with the abutment, hence the terminology integral abutment bridge. These bridges have been commissioned for some time. States like Ohio, Oregon, and South Dakota have been employing IABs since the 1930s (Hassiotis and Roman 2005). IABs have shown to be better from a fiscal standpoint than traditional bridges. They generally have a lower construction cost and much lower life cycle costs because of

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minimal maintenance. Retrofitting traditional bridges with IAB features has also been shown to be cost effective (Nickerson 1996). In IABs, the thermal loading causes bending in the piles supporting the abutments. Flexibility at the abutment is provided by the use of a stub abutment supported by a single row of piles in weak-axis bending. In some cases, piles are placed in predrilled holes and then filled with sandy material. Approach slabs are usually poured behind integral abutments in order to prevent compaction of backfill soils by traffic loading and offer a smooth transition to the bridge (Arockiasamy et al. 2004). A numerical study conducted by Yang et al. (1985) investigated the effect predrilled oversized holes have on abutment pile response. A finite element model of beam-column elements and nonlinear soil springs was used for the study. The work revealed that oversized holes, especially holes drilled to significant depths did much to alleviate overstressing the steel H-piles used under the abutment. Piles without oversized holes in harder materials such as stiff clay or compacted fill were shown to develop plastic hinges much quicker for prescribed transverse tip displacement than their counterparts with predrilled holes. IABs have proven to be economical and effective in eliminating joint maintenance issues, but they are not without problems. When the bridge expands and contracts during thermal loading, soil at the interface is disturbed. Ground subsidence adjacent to abutments (under approach slabs) has been observed. Subsidence behind the abutment wall can cause structural problems in the approach slab if bending loads are significant as vehicles pass over the slab. In the long term, these bridges can cause a buildup of lateral

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earth pressures on the abutments due to the soil-mechanics phenomenon known as ratcheting (Horvath 2004). In some cases, special additions are made to IAB systems to alleviate high pressures behind the abutments and high stresses in the abutment piles. A field experiment was conducted in North Dakota which addressed this matter (Jorgenson 1983). A 137 m IAB with concrete box girders was instrumented and monitored for a period of one year. 10 cm thick strips of compressible pressure relief material were placed in a slot between the abutments and the granular backfill. 5 cm layers of the material were placed on both sides of the abutment pile webs. These piles were in oversized holes filled with sand. These methods were shown to be effective in this case, as little yielding of the abutment piles was observed and plastic hinges did not form. 2.2 Current Practices IABs have been in use for many years, but there still is no comprehensive design procedure. Each state highway department manages its own integral abutment program and establishes guidelines with regard to design and construction. Not having an organized design and construction procedure leads to variation in the analysis, design, and construction practices of IABs between states (Arockiasamy et al. 2004). An excellent survey on current practices in the United States and Canada was conducted by Kunin and Alampalli (2000). The responses from 39 states and Canadian provinces provided insight into the differences in IAB design and construction practices. With the exception of one state, the opinion of the bridges was positive. Due to some expensive repair operations on bridge approaches, Arizona did not recommend IAB use. Most agencies were found to use AASHTO recommendations for temperature variation

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according to their region and the following formula to calculate the estimated bridge thermal movement: (2.1) where is the coefficient of linear thermal expansion of the superstructure, is the temperature change, and is the bridge length. Passive soil pressure was commonly used behind the abutments, but some states use an active and passive combination. Three agencies reported not considering earth pressure in their designs. A majority of the responses revealed that skew effects are not considered with respect to soil pressure. A significant number of agencies (almost half) design piles solely for axial loads. The program LPILE (ENSOFT 2007) was used by some of the agencies for their pile design. In addition to soil nonlinearity, LPILE can consider structural nonlinearity (e.g. loss of bending stiffness in the piles). 2.3 Skewed IABs A skewed IAB is one in which the abutments are not perpendicular to the roadway centerline (see Figure 2.1). A comprehensive survey of highway departments in all 50 states was conducted to determine design practices and performance of skewed IABs (Greimann et al. 1983). This survey revealed 26 states were using skewed IABs, but designing them primarily based on local experience. No theoretical or computational methods were used in most of the designs. There was noticeable variation in the practices from state to state, including abutment pile orientation and the use of batter piles for certain skew angles.