EFFECTS OF DESIGN PARAMETERS ON DECK CRACKING FROM RESTRAINED
CONCRETE SHRINKAGE IN JOINTLESS BRIDGES
By
David Jonathan Stringer

A THESIS
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
MASTER OF SCIENCE
Civil Engineering
2012

ABSTRACT
EFFECTS OF DESIGN PARAMETERS ON DECK CRACKING FROM RESTRAINED
CONCRETE SHRINKAGE IN JOINTLESS BRIDGES
By
David Jonathan Stringer
Bridges have traditionally relied on a system of expansion joints, roller supports, and other
structural releases to accommodate expansion and contraction movements due to temperature,
creep, and shrinkage loading. Joints and elements in their vicinity experience a high amount of
damage and degradation; thus modern design approaches are advocating their removal, with
movement accommodated through flexible piles and abutment walls. While jointless bridges
have been performing well, many of them suffer from widespread early-age transverse deck
cracking. A literature review and field investigation was conducted to identify the primary
causes for early-age deck cracking in jointless bridges. The most dominant source of early-age
transverse deck cracking is due to restrained concrete shrinkage. Experimentally-calibrated
finite-element models were used to predict cracking behavior in various full bridge systems with
different bridge design parameters undergoing shrinkage loading. Simulation results confirmed
that the more restraint present in the system the more cracking that will occur. Models showed
that steel and concrete beam bridges are equally susceptible to restrained shrinkage cracking.
The lowest amount of cracking was predicted for bridges with non-integral abutments, higher
shear connector spacing, and a low-shrinkage concrete mix. Changing the deck reinforcement
configuration had little effect on bridge performance. Of the parameters considered, a lowshrinkage mix had the greatest impact on minimizing deck cracking. Overall, the simulations
indicated that restrained shrinkage cracking in jointless bridge decks is unavoidable, but that
modifying design details and improving concrete mixture designs can help reduce its extent.

ACKNOWLEDGEMENTS
Throughout my research, there are several people who have provided me support,
guidance, and encouragement. I would like to thank my advisor, Dr. Rigoberto Burgueño, for
his significant guidance, insight, and support during my time at Michigan State University.
The Michigan Department of Transportation (MDOT), Office of Research and Best
Practices provided funding and financial support for this project. I greatly appreciate these
contributions.
I would also like to thank my committee members, Dr. Venkatesh Kodur and Dr. Parviz
Soroushian, for being a part of my committee.
I would like to extend my gratitude to the MSU Civil Infrastructure Laboratory staff
members, Mr. Sia Ravanbakhsh and Mr. Charles Meddaugh. I greatly appreciate their assistance
and guidance with the construction and testing of my laboratory models.
I also would like to thank my fellow graduate students, Ms. Lauren Fedak, Mr. Ata
Babazedehnaseri, Mr. Yi Sun, Ms. Caroline Williams, Ms. Annelise Herringa, Mr. Nan Hu, and
Mr. Erik Ohlsson, for their help with the laboratory investigation and field inspection.
I also thank my family members and friends, for providing me strength, motivation, and
support through my graduate studies.
Finally, I would like to thank my God and my Lord and Savior Jesus Christ, for His grace
and provision at all times, and for giving me the knowledge and strength to complete this
research.

iii

TABLE OF CONTENTS
List of Tables…………… ............................................................................................................ vii
List of Figures ................................................................................................................................ ix
1

INTRODUCTION ................................................................................................................... 1
1.1
Background ...................................................................................................................... 1
1.2
Motivation ........................................................................................................................ 4
1.3
Research Objectives ......................................................................................................... 6
1.4
Report Organization ......................................................................................................... 7

2

LITERATURE REVIEW ........................................................................................................ 8
2.1
Sources Contributing to Deck Cracking .......................................................................... 8
2.1.1
Material Properties and Mix Design ........................................................................ 8
2.1.2
Soil-Structure Interaction and Abutment Movement ................................................ 9
2.1.3
Temperature, Creep, and Shrinkage effects ............................................................ 11
2.1.4
Bridge Design Features .......................................................................................... 16
2.2
Concrete Shrinkage Standard Tests................................................................................ 22
2.3
Questions and Outstanding Issues Remaining ............................................................... 23
2.4
Conclusions, Recommendations, and Suggestions for Prototype Bridge System ......... 24

3

FIELD INSPECTION ........................................................................................................... 25
3.1
Past Field Investigation Studies that have been Performed ........................................... 25
3.2
Bridge Information Provided by MDOT........................................................................ 27
3.3
Parameters Considered and Bridges Visited .................................................................. 27
3.4
Field Inspection Results ................................................................................................. 30
3.4.1
Transverse Cracking ............................................................................................... 35
3.4.2
Longitudinal Cracking ............................................................................................ 35
3.5
Summary and Conclusions ............................................................................................. 36

4

EXPERIMENTAL EVALUATION ..................................................................................... 38
4.1
Approach ........................................................................................................................ 38
4.2
Test Unit Design Parameters .......................................................................................... 40
4.2.1
Steel Beam Size Determination ............................................................................... 40
4.2.2
Diaphragm Section Determination ......................................................................... 41
4.2.3
Shear Connector Layout Determination ................................................................. 45
4.2.4
Deck Reinforcing Steel Determination ................................................................... 47
4.2.5
Weld Design ............................................................................................................ 49
4.2.6
Pin Support Design ................................................................................................. 51
4.2.7
Ring Test ................................................................................................................. 52
4.3
Instrumentation Layout .................................................................................................. 54
4.3.1
Strain Gages............................................................................................................ 54
4.3.2
LVDTs ..................................................................................................................... 57
4.3.3
Thermocouples ........................................................................................................ 58
4.3.4
Instrumentation Naming Scheme ............................................................................ 58
4.4
Test Unit Construction and Casting ............................................................................... 60
4.4.1
Formwork................................................................................................................ 61
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4.4.2
Reinforcing Steel ..................................................................................................... 65
4.4.3
Instrumentation Installation.................................................................................... 67
4.4.4
Test unit Casting ..................................................................................................... 70
4.4.4.1
Concrete Mix Design ....................................................................................... 70
4.4.4.2
Concrete casting .............................................................................................. 70
4.4.5
Completed test units ................................................................................................ 74
4.4.6
Concrete Shrinkage Ring Tests ............................................................................... 76
4.5
Results ............................................................................................................................ 77
4.5.1
Data Acquisition ..................................................................................................... 77
4.5.2
Concrete Material Testing ...................................................................................... 78
4.5.3
Ambient temperature and relative humidity ........................................................... 83
4.5.4
Thermocouples ........................................................................................................ 88
4.5.5
LVDT’s .................................................................................................................... 93
4.5.6
Strain Gages............................................................................................................ 95
4.5.7
Ring Test Crack Growth ....................................................................................... 103
4.6
Data Analysis ............................................................................................................... 105
4.6.1
Temperature .......................................................................................................... 105
4.6.2
Vertical Displacements ......................................................................................... 105
4.6.3
Strains ................................................................................................................... 106
5

COMPUTATIONAL EVALUATION ................................................................................ 107
5.1
Modeling Approach...................................................................................................... 107
5.1.1
Free shrinkage model ........................................................................................... 110
5.2
Computer Modeling Features ....................................................................................... 111
5.3
Material Properties ....................................................................................................... 113
5.4
Laboratory Models ....................................................................................................... 116
5.4.1
Concrete Shrinkage Ring Test .............................................................................. 116
5.4.2
Lab Test Unit Test unit Models ............................................................................. 122
5.4.3
Discussion ............................................................................................................. 137
5.4.3.1
Validation of Computer Modeling Approach ................................................ 137
5.4.3.2
Effects of Design Parameters at the Sub-assembly level ............................... 138

6

PARAMETRIC STUDY ON FULL BRIDGE MODELS .................................................. 140
6.1
Parameters Considered ................................................................................................. 143
6.2
Loading method............................................................................................................ 144
6.2.1
Shrinkage loading ................................................................................................. 144
6.2.2
Gravity/self-weight loading .................................................................................. 145
6.2.3
Pour sequencing.................................................................................................... 146
6.2.4
Concrete barrier walls .......................................................................................... 146
6.2.5
Concrete/soil friction at approach slabs............................................................... 147
6.2.6
Soil/structure interaction at the piles .................................................................... 149
6.2.7
Random load application for full bridge models .................................................. 153
6.3
Concrete Spread Box Beam Bridge ............................................................................. 156
6.3.1
Parts and element types ........................................................................................ 156
6.3.2
Concrete box beam equivalent section ................................................................. 159
6.3.3
Constraints, boundary conditions, and other model features ............................... 160
6.3.4
Parametric evaluation features............................................................................. 161
v

6.4
Steel Girder Bridge....................................................................................................... 162
6.4.1
Parts and element types ........................................................................................ 162
6.4.2
Constraints, boundary conditions and other model features ................................ 164
6.4.3
Parametric evaluation features............................................................................. 164
6.5
Results .......................................................................................................................... 166
6.5.1
Box Beam Bridge Model Overall Results ............................................................. 166
6.5.2
Steel Girder Bridge Model Overall Results .......................................................... 181
6.5.3
Concrete box beam bridge parametric study comparison results ........................ 197
6.5.3.1
Effect of Increasing Deck Reinforcement ...................................................... 206
6.5.4
Steel girder bridge parametric study comparison results..................................... 217
6.5.4.1
Effect of shear connector re-distribution....................................................... 227
6.5.5
Effect of concrete tensile strength ......................................................................... 230
6.5.6
Discussion ............................................................................................................. 233
7

CONCLUSIONS AND RECOMMENDATIONS .............................................................. 237
7.1
Conclusions .................................................................................................................. 237
7.2
Recommendations ........................................................................................................ 239

REFERENCES ........................................................................................................................... 241

vi

LIST OF TABLES
Table 1. Bridges visited for field investigation ............................................................................ 28
Table 2. Field investigation results .............................................................................................. 34
Table 3. Experimental Test Matrix for Sub-Assembly Evaluation of Shrinkage Effects ............ 40
Table 4. Test Unit Reinforcement Details (Derived from Reference) ......................................... 47
Table 5. Test Unit Design Summary............................................................................................ 53
Table 6. MDOT Grade D Concrete Mix Design.......................................................................... 71
Table 7. MDOT Modified Grade D Slag Replacement Mix Design ........................................... 71
Table 8. Concrete Fresh Property Characteristics........................................................................ 73
Table 9. Shrinkage strain calculation constants ......................................................................... 109
Table 10. Element types used in computational evaluation ....................................................... 111
Table 11. Material properties used in the computer analyses .................................................... 116
Table 12. Concrete spread box beam bridge properties [25] ..................................................... 141
Table 13. Steel girder bridge properties [24] ............................................................................. 142
Table 14. Analyses run for full bridge parametric study ........................................................... 143
Table 15. Values used to calculate shrinkage load temperatures............................................... 144
Table 16. Assumed soil foundation properties [9][28] .............................................................. 150
Table 17. Element types utilized for concrete box beam bridge................................................ 157
Table 18. Concrete box beam transformed section moment of inertia calculation ................... 159
Table 19. Concrete box beam parametric evaluation analyses details....................................... 161
Table 20. Concrete box beam reinforcement arrangements ...................................................... 161
Table 21. Element types utilized for concrete steel girder bridge ............................................. 162
Table 22. Steel girder parametric evaluation analyses details ................................................... 165
Table 23. Steel girder bridge reinforcement arrangement ......................................................... 165
Table 24. Nomenclature used for box beam parametric study results ....................................... 197
vii

Table 25. Box beam bridge parametric study overall results..................................................... 205
Table 26. Nomenclature used for steel girder parametric study results ..................................... 217
Table 27. Steel girder bridge parametric study overall results .................................................. 226
Table 28. Shear stud size and volume determination for parametric study ............................... 227

viii

LIST OF FIGURES
Figure 1. Jointless bridges vs. bridges with expansion joints (adapted from [6]) ......................... 1
Figure 2. Integral bridges vs. jointless decks (adapted from [10]) ................................................. 2
Figure 3. Jointless Bridge Abutment Details (Adapted from [10]) ............................................... 3
Figure 4. Shrinkage-induced stress development in concrete bridge decks [31]......................... 12
Figure 5. Simplified Shrinkage Cracking (adapted from ref. [17]) .............................................. 12
Figure 6. Cracking in continuously restrained concrete test unit (adapted from ref.[17])............ 13
Figure 7. Curling of concrete deck due to sealed bottom surface (adapted from ref. [17]) ......... 13
Figure 8. Development of Free Shrinkage Strain with Time (adapted from ref. [22]) ................ 23
Figure 9. Field investigation locations ......................................................................................... 29
Figure 10. Semi-integral abutment connection (Bridge No. 13, 26 Mile Rd. over M-53) .......... 31
Figure 11. Fully-integral abutment connection (Bridge No. 4, US-10 over Sanford Lake) ........ 31
Figure 12. Transverse cracking over pier/negative moment region (Bridge No. 13, 26 mile Rd.
over M-53) .................................................................................................................................... 32
Figure 13. Typical transverse cracking in deck surface (Bridge No. 5: M-57 over US-127) ...... 32
Figure 14. Typical longitudinal cracking (Bridge No. 11: Burlingame Rd. over M-6) ............... 33
Figure 15. Steel beams selected, with welded extension plates ................................................... 41
Figure 16. MDOT cross-bracing standard specifications (adapted from ref. [26]) ..................... 42
Figure 17. Halsted Bridge cross-bracing dimensions and SAP 2000 model ............................... 43
Figure 18. Cross-bracing displacement results ............................................................................ 43
Figure 19. Gusset Plate Dimensions ............................................................................................ 45
Figure 20. Shear Connector Spacing over Top Flange ................................................................ 46
Figure 21. Shear Connector Detail 1(Test units 1, 3, and 4) ....................................................... 46
Figure 22. Shear Connector Detail 2 (Test Unit 2) ...................................................................... 46
Figure 23. Deck Reinforcement Detail 1 (Test units 1, 2, and 4) ................................................ 48

ix

Figure 24. Deck Reinforcement Detail 2 (Test Unit 3) ............................................................... 48
Figure 25. Welded connection configurations ............................................................................. 50
Figure 26. Pin plate details........................................................................................................... 51
Figure 27. Pin connection setup ................................................................................................... 51
Figure 28. Ring Test Setup (adapted from ref. [5]) ..................................................................... 52
Figure 29. Example Ring Test Strain Output (adapted from ref. [5]).......................................... 53
Figure 30. Test Unit Overall View .............................................................................................. 54
Figure 31. Reinforcing steel top mat strain gage locations .......................................................... 55
Figure 32. Reinforcing steel bottom mat strain gage locations ................................................... 55
Figure 33. Steel beam strain gage locations................................................................................. 56
Figure 34. Diaphragm strain gage locations ................................................................................ 56
Figure 37. LVDT Locations ......................................................................................................... 57
Figure 36. X-Y orientation for instrumentation ........................................................................... 59
Figure 37. Depth locations for instrumentation ............................................................................ 59
Figure 38. Test Unit Steel Frame Assemblies (Test units 1, 2, and 4) ........................................ 60
Figure 39. Test Unit 3 Steel Frame Assembly .............................................................................. 61
Figure 40. SIP forms front view .................................................................................................. 62
Figure 41. SIP forms Styrofoam fillers ........................................................................................ 62
Figure 42. Spot-welding of the forms (typical) ........................................................................... 63
Figure 43. Schematic for the cantilevered section formwork (note these forms are removable) 63
Figure 44. Cantilever forms bottom section ................................................................................ 64
Figure 45. Completed cantilever forms ....................................................................................... 64
Figure 46. Completed formwork (all lumber forms are removable) ........................................... 65
Figure 47. Concrete spacers for reinforcing steel (typical).......................................................... 66
Figure 48. Spacing between reinforcing steel mats (typical) ....................................................... 66
x

Figure 49. Reinforcing steel side cover (typical) ......................................................................... 67
Figure 50. Example strain gage installation process (typical for all strain gages) ...................... 68
Figure 51. LVDT placed underneath mid-test unit ...................................................................... 69
Figure 52. LVDT in place (mid-span of beam) ........................................................................... 69
Figure 53. Placing and vibrating the concrete (test unit 3) .......................................................... 72
Figure 54. Bull floating the concrete surface (test unit 3) ........................................................... 72
Figure 55. Timeline of events between casting to the end of moist curing (typical) ................... 73
Figure 56. Completed test unit overall view (test unit 4) ............................................................ 74
Figure 57. Completed test unit cantilever section (test unit 3) .................................................... 75
Figure 58. Close-up of completed test unit top surface (test unit 4) ............................................ 75
Figure 59. Test unit cross-section (test unit 4) ............................................................................. 76
Figure 60. Overall view of shrinkage rings ................................................................................. 77
Figure 61. Concrete split tensile strength testing ......................................................................... 79
Figure 62. Concrete compressive strength testing ....................................................................... 79
Figure 63. Test units 1 and 2 (MDOT Grade D mix) .................................................................. 80
Figure 64. Test unit 3 (MDOT Grade D mix).............................................................................. 81
Figure 65. Test unit 4 (Modified MDOT Grade D mix) .............................................................. 82
Figure 66. Ambient temperature values, first set of tests ............................................................ 84
Figure 67. Relative humidity percentage, first set of tests ........................................................... 85
Figure 68. Ambient temperature values, second set of tests ........................................................ 86
Figure 69. Relative humidity percentage, second set of tests ...................................................... 87
Figure 70. Concrete deck temperatures at the bottom mat of reinforcing steel (test units 1 and 2)
....................................................................................................................................................... 89
Figure 71. Lab ambient temperature, first set of test units .......................................................... 90
Figure 72. Maximum temperature gradient through the depth of the test unit (test units 1 and 2)
....................................................................................................................................................... 90
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Figure 73. Concrete deck temperatures at the bottom mat of reinforcing steel (test units 3 and 4)
....................................................................................................................................................... 91
Figure 74. Lab ambient temperature, second set of test units...................................................... 92
Figure 75. Maximum temperature gradient through the depth of the test unit (test units 3 and 4)
....................................................................................................................................................... 93
Figure 76. Girder 1 mid-span displacement (L-G1-1/2) .............................................................. 94
Figure 77. Mid-test unit displacement (L-1/2-1/2) ...................................................................... 94
Figure 78. Mid-test unit quarter-span displacement (L-1/2-3/4) ................................................. 95
Figure 79. Top mat longitudinal rebar strains, middle of test unit (S-Tp-1/2-1/2-L) .................. 96
Figure 80. Bottom mat longitudinal rebar strains, middle of test unit (S-Bt-1/2-1/2-L) ............. 96
Figure 81. Top mat transverse rebar strains, middle of test unit (S-Tp-1/2-1/2-T) ..................... 97
Figure 82. Bottom mat transverse rebar strains, middle of test unit (S-Bt-1/2-1/2-T) ................ 97
Figure 83. Beam top flange, mid-span longitudinal strains (S-G1-Tf-M-G1-1/2-L) .................. 98
Figure 84. Beam mid-web longitudinal strains (S-G1-W-O-G1-1/2-L) ...................................... 98
Figure 85. Beam bottom flange, mid-span longitudinal strains (S-G1-Bf-M-G1-1/2-L) ............ 99
Figure 86. Beam bottom flange, mid-span longitudinal strain inside and outside comparison . 100
Figure 87. Diaphragm strain data comparison ........................................................................... 101
Figure 88. Maximum Strain Gradient, Test unit 3 ..................................................................... 102
Figure 89. Maximum Strain Gradient, Test unit 4 (tension plotted on the right) ...................... 102
Figure 90. Concrete ring crack growth, Rings 1 to 4 (Grade D Mix) ........................................ 103
Figure 91. Ring test cracking (Ring 2)....................................................................................... 104
Figure 92. Concrete ring crack growth, Rings 5 to 8 ................................................................. 104
Figure 93. Concrete free shrinkage block overall model ........................................................... 110
Figure 94. Free shrinkage model strains and deflected shape ................................................... 110
Figure 95. Schematic representation of elements used [38] ...................................................... 112
Figure 96. Concrete damaged plasticity stress/strain curves ..................................................... 115
xii

Figure 97. Concrete ring test assembly ...................................................................................... 117
Figure 98. Material Imperfection Assignment ........................................................................... 118
Figure 99. ACI 209 Temperature values (applied to outside surface of concrete ring) [2] ....... 118
Figure 100. Temperature distribution through the rings ............................................................ 119
Figure 101. Concrete Ring plastic strain PE, Max Principal at time of 17 days ....................... 120
Figure 102. Plastic strain magnitude outputs through for the region of damage ....................... 120
Figure 103. Steel ring strain output through time ...................................................................... 121
Figure 104. Concrete ring strain output through time................................................................ 121
Figure 105. Lab test unit test unit models overall view ............................................................. 123
Figure 106. Temperature loading values for lab test unit analyses............................................ 124
Figure 107. Test Unit Models Overall Deflected Shape and Vertical Displacement [37] ........ 125
Figure 108. Beam mid-span deflection data comparison (L-G1-1/2) ........................................ 126
Figure 109. Mid-test unit deflection data comparison (L-1/2-1/2) ............................................ 127
Figure 110. Reinforcing Steel Top Mat Long. Strain Data Comparison (S-Tp-1/2-1/2-L) ....... 128
Figure 111. Reinforcing Steel Bott. Mat Long. Strain Data Comparison (S-Bt-1/2-1/2-L) ...... 128
Figure 112. Reinforcing Steel Top Mat Trans. Strain Data Comparison (S-Tp-G1-1/2-T) ...... 129
Figure 113. Reinforcing Steel Bott. Mat Trans. Strain Data Comparison (S-Bt-G1-1/2-T) ..... 129
Figure 114. Beam Top Flange Strain Data Comparison (S-G1-Tf-M-G1-1/2-L) ..................... 130
Figure 115. Beam Mid-Web Strain Data Comparison (S-G1-W-O-G1-1/2-L) ......................... 130
Figure 116. Beam Bottom Flange Strain Data Comparison (S-Bf-M-G1-1/2-L) ...................... 131
Figure 117. Depth through beam/slab assembly slab strain data comparisons (time=20 days) 131
Figure 118. Computer model data comparison, beam mid-span deflection (L-G1-1/2) ........... 132
Figure 119. Computer model data comparison, test unit mid-span deflection (L-1/2-1/2) ....... 132
Figure 120. Computer model data comparison, rebar top mat long. strains (S-Tp-1/2-1/2-L).. 133
Figure 121. Computer model data comparison, rebar bott. mat long. strains (S-Bt-1/2-1/2-L) 133
xiii

Figure 122. Computer model data comparison, rebar top mat trans. strains (S-Tp-1/2-1/2-T) . 134
Figure 123. Computer model data comparison, rebar bott. mat trans. strains (S-Bt-1/2-1/2-T) 134
Figure 124. Computer model data comparison, beam top flange strains (S-G1-Tf-M-1/2-L) .. 135
Figure 125. Computer model data comparison, beam mid-web strains (S-G1-W-O-1/2-L) ..... 135
Figure 126. Computer model data comparison, beam bott. flange strains (S-G1-Bf-M-1/2-L) 136
Figure 127. Longitudinal Strains through the depth of the beam/test unit section .................... 136
Figure 128. Strain behavior through the depth of the slab ......................................................... 139
Figure 129. Concrete spread box beam bridge (M-57 over US-127) elevation and cross-section
[25] .............................................................................................................................................. 141
Figure 130. Steel beam bridge (Kensington Rd. over I-96) elevation and cross-section [24]... 142
Figure 131. Shrinkage load temperature values for bridge deck and barrier wall (standard mix)
..................................................................................................................................................... 145
Figure 132. Barrier wall equivalent rectangular cross section [24] ........................................... 147
Figure 133. Typical approach slab connection with bridge deck [26] ....................................... 147
Figure 134. Approach slab friction force-displacement curve for each 2’-wide segment ......... 149
Figure 135. P-Y curves for soil/pile interaction......................................................................... 151
Figure 136. Pile lateral displacement values (as-built box beam model) .................................. 152
Figure 137. Literature pile lateral displacement values (adapted from ref. [9]) ........................ 152
Figure 138. Deck top temperature values for random load approach (box beam bridge) [37].. 154
Figure 139. Deck max principal plastic strains with random load approach [37] ..................... 154
Figure 140. Deck max principal stresses with random load approach [37] ............................... 155
Figure 141. Correct random temperature distribution application for bridge slabs ................... 156
Figure 142. Concrete box beam bridge overall views ............................................................... 158
Figure 143. Concrete box beam bridge overall views ............................................................... 163
Figure 144. Box beam as-built model deflected shape and vertical displacements (t=45 days) 167
Figure 145. Box beam as-built model maximum principal tensile stresses (t=45 days) ........... 168
xiv

Figure 146. Box beam as-built model maximum principal plastic strains (t=45 days) ............. 169
Figure 147. Box beam as-built model plastic strain global X-direction (1-1) output ................ 171
Figure 148. Box beam as-built model plastic strain global Y-direction (2-2) output ................ 171
Figure 149. Box beam as-built model plastic strain global Z-direction (3-3) output ................ 172
Figure 150. Box beam as-built model plastic shear strain (1-3) output ..................................... 172
Figure 151. Vertical displacement through time in bridge longitudinal direction ..................... 174
Figure 152. Maximum principal tensile stresses through time in bridge longitudinal direction 174
Figure 153. Maximum principal plastic strains through time in bridge longitudinal direction . 175
Figure 154. Maximum principal plastic strain output in positive moment region (span 2)....... 175
Figure 155. Development of maximum principal tensile stresses in full bridge deck ............... 176
Figure 156. Development of maximum principal plastic strains in full bridge deck ................ 177
Figure 157. Maximum principal tensile stresses along longitudinal direction, bottom of deck 179
Figure 158. Maximum principal plastic strains along longitudinal direction, bottom of deck .. 179
Figure 159. Vertical displacements along bridge transverse direction (time=45 days)............. 180
Figure 160. Maximum principal tensile stresses along bridge transverse direction (t=45 days)180
Figure 161. Maximum principal plastic strains along bridge transverse direction (time=45 days)
..................................................................................................................................................... 181
Figure 162. Steel girder as-built model deflected shape and vertical displacements (t=45 days)
..................................................................................................................................................... 182
Figure 163. Steel girder as-built model maximum principal tensile stresses (t=45 days) ......... 183
Figure 164. Steel girder as-built model maximum principal plastic strains (t=45 days) ........... 184
Figure 165. Steel girder as-built model plastic strain global X-direction (1-1) output.............. 186
Figure 166. Steel girder as-built model plastic strain global Y-direction (2-2) output.............. 186
Figure 167. Steel girder as-built model plastic strain global Z-direction (3-3) output .............. 187
Figure 168. Steel girder as-built model plastic shear strain (1-3) output................................... 187
Figure 169. Vertical displacement through time in bridge longitudinal direction ..................... 189
xv

Figure 170. Maximum principal tensile stresses through time in bridge longitudinal direction 189
Figure 171. Maximum principal plastic strains through time in bridge longitudinal direction . 190
Figure 172. Maximum principal plastic strain output in positive moment region (span 2)....... 191
Figure 173. Development of maximum principal tensile stresses in full bridge deck ............... 192
Figure 174. Development of maximum principal plastic strains in full bridge deck ................ 193
Figure 175. Maximum principal tensile stresses along longitudinal direction, bottom of deck 195
Figure 176. Vertical displacements along bridge transverse direction (time=45 days)............. 195
Figure 177. Maximum principal tensile stresses along bridge transverse direction (t=45 days)196
Figure 178. Maximum principal plastic strains along bridge transverse direction (time=45 days)
..................................................................................................................................................... 196
Figure 179. Max principal tensile stresses through the depth of the slab, between beams (t=45)
..................................................................................................................................................... 198
Figure 180. Max principal plastic strains through the depth of the slab, between beams (t=45)
..................................................................................................................................................... 198
Figure 181. Max principal tensile stresses through depth of beam/slab assembly (t=45) ......... 199
Figure 182. Max principal plastic strains through depth of slab, over beams (t=45) ................ 199
Figure 183. Vertical displacements along the longitudinal direction, span 2 (t=45 days)......... 200
Figure 184. Max principal stresses along the longitudinal direction, span 2 (t=45 days) ......... 200
Figure 185. Max principal plastic strains along the longitudinal direction, span 2 (t=45 days) 201
Figure 186. Vertical displacements along the transverse direction (t=45 days) ........................ 201
Figure 187. Max principal stresses along the transverse direction (t=45 days) ......................... 202
Figure 188. Max principal plastic strains along the transverse direction (t=45 days) ............... 202
Figure 189. Vertical displacements through time, between beams, span 2 ............................... 204
Figure 190. Max principal stresses through time, between beams, span 2 ................................ 204
Figure 191. Max principal plastic strains through time, between beams, span 2 ...................... 205
Figure 192. Prism model setup for investigating effect of reinforcement ................................. 207

xvi

Figure 193. Maximum principal plastic strain output, unreinforced prism ............................... 208
Figure 194. Maximum principal plastic strain output, #3 embedded bar .................................. 209
Figure 195. Maximum principal plastic strain output, #8 embedded bar .................................. 210
Figure 196. Development of stresses with time in prism........................................................... 211
Figure 197. Prism with #3 reinforcement plastic strain output at various times ....................... 212
Figure 198. Prism with #8 reinforcement plastic strain output at various times ....................... 212
Figure 199. Prism plastic strain values with time in concentrated cracking areas .................... 213
Figure 200. Prism reinforcing bar longitudinal stresses with time ............................................ 214
Figure 201. #3 prism with ‘rebar layer’ approach maximum principal plastic strains (t=30 days)
..................................................................................................................................................... 215
Figure 202. #8 prism with ‘rebar layer’ approach maximum principal plastic strains (t=30 days)
..................................................................................................................................................... 215
Figure 203. Plastic strains along longitudinal path for prisms with rebar layer approach (t=30)
..................................................................................................................................................... 216
Figure 204. Max principal tensile stresses through the depth of the slab, between beams (t=45)
..................................................................................................................................................... 218
Figure 205. Max principal plastic strains through the depth of the slab, between beams (t=45)
..................................................................................................................................................... 218
Figure 206. Max principal tensile stresses through depth of beam/slab assembly (t=45) ......... 220
Figure 207. Max principal plastic strains through depth of slab, over beams (t=45) ................ 220
Figure 208. Vertical displacements along the longitudinal direction (t=45 days) ..................... 221
Figure 209. Max principal stresses along the longitudinal direction (t=45 days)...................... 221
Figure 210. Max principal plastic strains along the longitudinal direction (t=45 days) ............ 222
Figure 211. Vertical displacements along the transverse direction (t=45 days) ........................ 222
Figure 212. Max principal stresses along the transverse direction (t=45 days) ......................... 223
Figure 213. Max principal plastic strains along the transverse direction (t=45 days) ............... 223
Figure 214. Vertical displacements through time, between beams ........................................... 225

xvii

Figure 215. Max principal stresses through time, between beams ............................................ 225
Figure 216. Max principal plastic strains through time, between beams, span 2 ...................... 226
Figure 217. Maximum principal stress contours (time=30 days) .............................................. 228
Figure 218. Concrete maximum principal tensile stresses, middle of the slab on top............... 229
Figure 219. Vertical displacements, middle of slab on top........................................................ 229
Figure 220. Maximum principal tensile stress values through time, tensile strength comparison
..................................................................................................................................................... 231
Figure 221. Maximum principal plastic strain values through time, tensile strength comparison
..................................................................................................................................................... 231
Figure 222. Maximum principal plastic strain values along longitudinal direction (t=45 days) 232
Figure 223. Longitudinal stresses through the depth of the slab ............................................... 235

xviii

1
1.1

INTRODUCTION
Background
Traditionally, highway bridges have relied on a system of expansion joints, rocker bearings,

and other structural releases to accommodate expansion and contraction movements due to
temperature, creep, and shrinkage loading [10][30]. These expansion joints have been the cause
of many deterioration problems, as deicing chemicals and other debris prevent the joints from
functioning properly and lead to the corrosion of the structure beneath. This leads to high
maintenance and rehabilitation costs, and reduces the service level for the bridge [10][20]. Due
to these issues, recent measures have been taken to eliminate these joints and allow the bridge to
function as a continuous structural system. These are referred to as integral or jointless bridges
[10][15][42]. In jointless bridges, the expansion joints over the piers are eliminated and the deck
is made continuous, as shown in Figure 1.

Bridge Deck Expansion joint

Abutment

Pier

a) Schematic of bridge with expansion joints
Expansion joint
Approach Slab

Continuous
Deck Slab

Abutment

Pier
Flexible Piles

b) Jointless bridge layout
Figure 1. Jointless bridges vs. bridges with expansion joints (adapted from [6])
1

Newly designed bridges are connected with the abutment walls, thus allowing the structure to
act as a single system. Jointless bridge systems are either considered integral bridges (where the
girders are cast into the abutment wall), or non-integral bridges (where the substructure is
traditional, while the deck is continuous and cast with the abutment wall) [10], see Figure 2.

(b) Non-integral Bridge Abutment Detail

(a) Integral Bridge Abutment Detail

Figure 2. Integral bridges vs. jointless decks (adapted from [10])
Non-integral bridges do not have girders cast into the abutment wall, and the substructure is a
traditional design, typically with battered piles at the abutment, and roller, pin, or fixed supports.
The bridge deck either rests on top of the abutment wall and is allowed to slide, or is cast
monolithically with the abutment [21]. In either case, the movement is accommodated by
placing expansion joints beyond the abutment walls, and the deck behaves as a continuous
system.
While the design guidelines vary from state to state, integral bridges are grouped into two
major categories: (1) Fully-integral (full moment transfer) abutment systems, and (2) Semi-

2

integral (shear transfer only) abutment systems. In both cases, the girders are cast into the
abutment backwalls and the abutments are supported using flexible steel H-piles oriented in
weak-axis bending. In fully-integral systems, the abutment is connected rigidly to a single row
of flexible piles that move to accommodate full shear and moment transfer. In semi-integral
systems the backwall is allowed to move or rotate on top of the abutment wall, creating a shear
transfer but no moment transfer [10][30][42]., see Figure 3.
Abutment
Backwall

Abutment
Backwall
Girder

Girder
Neoprene
bearing

Abutment

Abutment

Dowel

Flexible
Piles

Flexible
Piles

(a) Fully-integral Abutment

(b) Semi-integral Abutment

Figure 3. Jointless Bridge Abutment Details (Adapted from [10])
A fully-integral abutment is designed by placing position bars in between the top and bottom
sections of the abutment backwall to preventing it from sliding. These bars are placed along the
centerline of each beam bearing. The bars provide added restraint between the abutment wall
and the backwall and full moment transfer. The entire abutment is designed to move and rotate
as a single system, transferring movements to the flexible piles oriented in weak-axis bending.
Semi-integral abutments are designed the same as fully-integral abutments, with the exception
that semi-integral abutments do not have the presence of position dowels. The bottom of the

3

backwall is allowed to move with frictional resistance, thus transferring only shear forces due to
the frictional resistance between the bottom of the backwall and the top of the abutment wall.
At least 32 states in the U.S. use jointless bridges. The overall designs consist of continuous
decks with capped pile stub-type abutments resting on steel H-piles oriented in weak-axis
bending [20]. While the maximum length constraints vary from state to state, typical ranges for
total bridge lengths are 200 to 500 ft for steel girders, and 150 to 800 ft for concrete girders [30].
Many types of jointless bridge systems have been studied, with varying designs regarding fullyintegral abutments, semi-integral abutments, concrete girders, steel girders, maximum skew
angle, span length, and number of spans [6][15][16][20][30][31][36].
1.2

Motivation
Jointless bridges are overall performing well, and they have alleviated the deterioration

problems experienced in conventional bridge design. Eliminating expansion joints has provided
increased ride quality, less required maintenance, and overall increased longevity of the structure
[10][21][30][42]. A survey conducted by the New York State Department of Transportation
(NYSDOT) found that at least 30 states use integral abutment bridges, and that most of them are
considered to be in ‘good’ or ‘excellent’ condition [20]. While jointless bridges are overall
performing as designed and are performing better than bridges with joints, there is interest in
investigating the various problems that have arisen in these new bridges [6][10][30][42]. Most
of the problems are attributed to the increased rigidity of the system, resulting in less freedom of
movement and higher stress levels due to temperature, creep, and shrinkage movements.
Problems that have arisen include settlement and cracking of approach slab, separation of the
approach slab with the abutment, cracking in abutment end diaphragms, and transverse cracking
in the deck [6][10][17][30][31][41][42].
4

Transverse cracking in bridge decks is a common problem for both jointless bridges and
bridges with joints, and has been studied extensively. However, transverse cracking in bridge
decks has been found to be the most common problem experienced by jointless bridges, when
the restrained mass of concrete experiences a change of volume and generates additional stresses
due to the restraint in movement. Transverse cracking occurs when the longitudinal tensile
stresses exceed the concrete modulus of rupture. Studies have shown that more than 100,000
bridges in the United States experience transverse deck cracking.[16][17][18][29][31][36][41].
Cracks often appear at an early age, sometimes before the bridge is open to traffic. The cracks
are often full-depth, spaced 3-9 ft apart, and continue growing with time. This could potentially
lead

to

further

deterioration

problems

within

the

deck

and

supporting

girders

[10][16][17][18][31][41]. Cracks are typically concentrated over the transverse rebar in negative
moment regions and along the longitudinal edge of girders. These areas are more susceptible to
forming a plane of weakness in the concrete [29]. Cracking is greater in longer spans and older
decks [16][29]. Additionally, cracking has often occurred in approach test units as soil backfill
settles and resultant forces are transferred into the approaches [20][21][30].

Longitudinal

cracking has been a common problem in concrete girder bridges along the edges of the girders,
due to the formation of weak planes at the girder edges [17]. This type of cracking can be
attributed to the bridge geometry and is not due to restrained concrete shrinkage.
Overall, deck cracking can be attributed to the build-up of forces induced by the secondary
effects from temperature, creep, and shrinkage induced volume changes.

Current designs

account for dead and live loading, as well as for temperature loads. However, many agencies do
not account for concrete creep and shrinkage in bridge deck design, which may explain the
presence of cracking [20][30][41].

5

1.3

Research Objectives
The overall objective of this research project was to investigate the performance of jointless

bridges, identify the causes that lead to early-age deck cracking, and develop solution strategies
to minimize or eliminate this damage. This was accomplished through experimentally-calibrated
finite-element computer simulations and field assessment. The overall objective was completed
through the following tasks:
•

Task 1: Literature Review. This task’s aim was to determine the current state-of-theart on the behavior of jointless bridges to identify the existing knowledge on the causes
for deck cracking as well as any potential solution strategies.

•

Task 2: Field Inspection. The focus of this task was to perform field inspections on
jointless bridges in Michigan that are known to suffer from deck cracking. The
parameters and conditions that could predict the cause of the distress were identified and
a matrix of bridge design features and cracking patters was developed to summarize the
predominant parameters. This information was used to verify the findings from the
literature review and to develop a prototype system for the experimental and
computational evaluation.

•

Task 3: Experimental Evaluation. This task focused on experimentally evaluating the
behavior of jointless bridges at the sub-assembly level through four different test unit
systems. The relative differences between the test units were determined and the
experimental data was used to validate the computer modeling approach.

•

Task 4: Computational Evaluation. The aim of tis task was to evaluate the behavior
of jointless bridges through experimentally-calibrated finite element models. The
modeling approach was verified through smaller sub-assembly models, and implemented
on full bridge systems. Parametric studies were performed to evaluate the bridge
behavior for different bridge design features.

This research study provides an in-depth analysis of the behavior of jointless bridges and
identifies the predominant causes that lead to early-age deck cracking. Solution strategies for
future bridge design and construction are also developed and proposed.

The information

presented in this report is immediately applicable to the work of MDOT and bridge engineers.

6

1.4

Report Organization
This report is organized to highlight the results of each of the four tasks outlined in the

previous section. A literature review is presented in Chapter 2 to present the current state-of-theart on deck cracking in jointless bridges. Chapter 3 presents the results and conclusions of the
field investigation. Chapter 4 discusses the experimental evaluation, including the methods,
approach, and results. Chapter 5 discusses the computer modeling approach, and the verification
of the computer modeling through comparison with experimental data. Chapter 6 presents and
discusses the results from the series of finite-element computer simulations with different bridge
design parameters. The overall conclusions and recommendations are presented in Chapter 7.

7

2

LITERATURE REVIEW

2.1

Sources Contributing to Deck Cracking
Due to the increased rigidity created by eliminating expansion joints, jointless bridge systems

have less freedom of movement and thus less opportunity to relieve the stresses induced by
temperature, creep, and shrinkage effects. The behavior of jointless bridges is complex and
requires an investigation of many parameters affecting the stiffness of the overall system, which
dictates the amount of deck cracking. These parameters include material properties and mix
design, soil-structure interaction/abutment movement, temperature, creep, and shrinkage loading
effects, and bridge design features.
2.1.1

Material Properties and Mix Design

Much research has been performed on the effect concrete material properties and mix design
has on deck cracking. A study was performed on 40 steel girder bridges in Kansas to investigate
the relation of material properties to deck cracking [15]. While the bridges selected were not all
jointless, the effects of material properties apply to all types of bridges. The study found that the
amount of cracking increased with an increase in slump (although zero slump was found to be
worse due to the lack of consolidation), water content, compressive strength, and a decrease in
air content. Although this was not always the case, the study also found that the higher w/c ratio,
the more cracking. Most of the cracking occurred along transverse reinforcement, in the areas of
concrete settlement adjacent to the reinforcement [29][36]. Other studies suggested that cracking
increases with higher w/c ratio, cement content, and air content [16][18]. The same studies also
found that larger aggregate volume would minimize cracking due to the reduction in cement
content.

8

Overall, the underlying premise behind the effects of material properties and mix design is
that the higher content of water and cement, the more concrete shrinkage that will occur, which
will lead to higher restraint forces from volume changes and in turn increase the amount of
cracking [16][36]. Research has found that limiting the w/c ratio, lowering the cement content,
lowering the air content, and increasing the aggregate content will reduce the amount of deck
cracking [16][29][36]. Reduced cement paste volume and low cement contents are associated
with reduced heat of hydration, which leads to reduced thermal stresses and reduced cracking
[16]. Specifically, it has been found that low shrinkage aggregates with the largest possible size
should be used. Type II cement should be used due to its reduced early thermal gradient
[18][29]. Compressive strength should be limited. Finally, set retarding admixtures should be
used, as they reduce the rate of early temperature change [18].
2.1.2

Soil-Structure Interaction and Abutment Movement

Cracking in bridge decks relates heavily to the overall stiffness of the system, which is
partially dictated by the soil-structure interaction at the abutment and supporting piles. This
issue has been investigated to a moderate extent, although further research is needed. The largest
induced movement for jointless bridge systems is found to occur at the abutments. Therefore,
large stress concentrations develop in this region of the bridge deck [30]. The overall length
limitations for jointless bridges are often dependent on soil/structure interaction, and how much
lateral movement can be accommodated without compromising the structure serviceability
[9][15]. In addition to bridge decks, the approach slabs in jointless bridges also exhibit cracking
problems as stress levels increase due to the settlement of soil backfill and restrained movement
of the bridge system [20]. Since most approach slabs rest on top of the abutment backwalls and
extend longitudinally from the decks, stresses are induced due to load transfer at the abutment.
9

The behavior of a prototype integral abutment bridge in Minnesota was studied through
instrumentation during and after construction.

The bridge was a 3-span simply supported

concrete girder system with a continuous deck. The study found that abutment movement
behaved in translation instead of rotation, and that the tops of piles deformed in double
curvature. The study also found that the lower the freedom of movement, the higher the induced
stress levels and the higher the amount of cracking [21].
Most agencies simplify the soil pressure behind the abutment and supporting piles as a linear,
triangular pressure distribution.

The calculation of the soil stiffness involves an iterative

procedure, where the magnitude of the soil lateral loads are estimated and applied with linear
springs [15]. However, this is not the case, as the true soil reaction is non-linear and varies with
the depth, amount, and mode of pile displacement. The amount of soil pressure will increase as a
function of the pile displacement. Nonlinear p-y design curves, developed by the American
Petroleum Institute, can be used to model nonlinear soil behavior [4]. The behavior of soil is
very complex and current methods over-simplify soil/structure response.
A 3D Finite-Element model was used by researchers to study the Bemis Road Bridge in
Fitchburg, Massachusetts [15]. The Bemis Road Bridge is a 3-span fully-integral abutment steel
girder bridge that is 150 ft long. The soil response was modeled as a series of “Winkler” springs,
and p-y design curves were used to model the nonlinear springs at the abutment wall and pile
nodes.

The soil compaction levels were varied: loose/dense, loose/loose, dense/loose, and

dense/dense. The analysis results indicated the level of soil compaction behind the abutment
wall is of utmost importance, as the axial forces and bending moments in the deck more than
doubled when the soil compaction was varied from loose to dense [15]. Overall, it was found
that the larger the soil compaction level, the more rigidity within the system and the larger the

10

amount of cracking. While having looser soil may help mitigate some of the deck cracking
issues, it is necessary to have enough compaction to support the approach test unit. Soilstructure interaction is a parameter that is currently simplified and not much research has been
conducted on its behavior [9][15][21].
2.1.3

Temperature, Creep, and Shrinkage effects

Temperature effects have been studied in detail, and it is well known that both daily and
seasonal temperature fluctuations create movement within the structure.

Daily fluctuations

create a thermal gradient through the cross section of the structure, while seasonal fluctuations
lead to overall structural expansion and contraction. [21][30]. Temperature effects are taken into
account in current designs, and use the equation for thermal expansion, ∆L=L∆Tα [20]. The
effects of temperature have been found to be as much as the effects of live loading [21].
Volume change in concrete is unavoidable, resulting from drying of concrete materials and
internal chemical reactions that lead to concrete shrinkage. The amount of concrete shrinkage is
dictated by mix design and construction practices, and is considered to be the most dominant
source of deck cracking in jointless bridges due to the restraint in volume change
[10][16][17][29][36][41]. Restrained concrete shrinkage causes early-age cracking in particular,
since most shrinkage magnitude and strength gain occurs within the first few weeks
[16][17][21][40].

Concrete shrinkage is resisted by girder stiffness, shear connectors, and

reinforcing steel. The downward deflection of the deck-girder system due to composite action
with the deck creates restraint to concrete shrinkage, inducing tensile stresses within the deck,
which leads to cracking [17][18]. This is illustrated below in Figure 4.
Consider a regular reinforced concrete section supported on its two ends. When undergoing
restrained shrinkage, the specimen will first crack in the center, as shown in Figure 5. After this,
11

the two cracked pieces will act individually and shrinkage-induced cracking will continue at the
quarter points. Cracking will continue until the total shrinkage strain is accommodated, and the
length of the un-cracked section is small enough to allow tensile stresses to be accommodated by
the concrete. This is shown in Figure 6. This mechanism possibly explains the equal spacing of
early-age transverse cracks observed in the bridge deck systems.

a) Concrete cast b) Concrete shrinkage
c) Girder restraint produces a downward displacement d) Tensile stresses are induced

Figure 4. Shrinkage-induced stress development in concrete bridge decks [31]

a) Before Shrinkage
Tension Crack

b) After Shrinkage
Figure 5. Simplified Shrinkage Cracking (adapted from ref. [17])

12

a) Before Shrinkage

b) After Shrinkage
Figure 6. Cracking in continuously restrained concrete test unit (adapted from ref.[17])

In bridges, restraint is only provided at the bottom surface, and cracking initiates at the
bottom surface and increases in depth until the total shrinkage strains are accommodated. Since
the bottom surface is typically sealed by stay-in-place forms while the top surface is free to
shrink, differential shrinkage strains form through the depth of the deck, causing curling. This
creates additional tensile stresses in the bottom surface of the deck. These stresses are higher for
systems more susceptible to this differential shrinkage, such as bridges with steel girders,
concrete girder bridges with overlays, and bridges with stay-in-place deck forms [17].

Before Shrinkage

Sealed Surface

After Shrinkage
Figure 7. Curling of concrete deck due to sealed bottom surface (adapted from ref. [17])

13

There are four major types of concrete shrinkage, all of which contribute to inducing tensile
stresses. These include plastic shrinkage (moisture loss from concrete before it sets), autogenous
shrinkage (loss of water from capillary pores due to hydration), carbonation shrinkage (chemical
reaction of hydration with the air, which occurs on exposed concrete surfaces), and drying
shrinkage (long-term volumetric change due to concrete drying). While total shrinkage is the
sum of all four types, carbonation and autogenous shrinkage do not contribute significantly to
deck cracking [17][18][19][31][41]. Since early age cracking is of particular interest, the effects
of creep can be neglected. Creep is a long-term effect caused mainly by the deck self-weight,
and cracking most often occurs before creep is able to take place [19][31][41].
Concrete shrinkage is a parameter that is not always taken into account in design. A survey
performed by the NYSDOT revealed that 75% of agencies do not take into account shrinkage of
concrete in design, and those that do confine it only to prestressed-concrete bridge elements [20].
If shrinkage is evaluated, it is taken into account over the long-term, while short-term volume
changes due to shrinkage are overlooked and dismissed as insignificant. Current design practices
consider shrinkage as a secondary, long-term effect, and use only the long-term drying shrinkage
component as the ultimate shrinkage value. However, this is inaccurate since most concrete
shrinkage occurs at an early age and exceeds the amount of long-term shrinkage. Shrinkage
stresses can potentially exceed even traffic loading conditions, so it is therefore inappropriate to
consider shrinkage as a secondary effect [16][17][19][20][31][41]. Early age volume change due
to drying shrinkage is of great importance and should thus be considered in design. Drying
shrinkage magnitude is dependent on the amount of water lost during placement and the rate of
evaporation. Typical values are around 1 mm/m or less over the long-term, but short-term values

14

could be 5 mm/m or greater during accelerated drying. This is often equal to or greater than the
28-day drying shrinkage measurements [19].
The University of West Virginia performed a study to investigate the effects of early age
shrinkage stresses [41] in which researchers instrumented a 3-span continuous steel-girder bridge
with fully integral abutments. Sensors were placed along half the length of the first stage of the
bridge deck construction to monitor strain and temperature in the deck and reinforcing steel, and
the overall expansion and contraction of the bridge system. Strain data was taken every 30
minutes, which was used to analyze the induced stresses. It was discovered that the strain at the
top of the deck was higher than the strain at the bottom, since the bottom is more constrained to
due formwork and shear connectors. This produced tensile stresses at the top of the deck, which
exceeded the concrete modulus of rupture and led to cracking. The study found that as the
concrete ages the stresses due to shrinkage stabilize. However, it was discovered that the
magnitude of the shrinkage stresses exceeded the concrete modulus of rupture and produced
cracking. Overall, the study confirmed that volume changes and induced stresses from drying
shrinkage are of paramount importance and that the stresses that develop are relatively high,
even when compared to traffic loading. The study suggested that the effect of shrinkage be
considered in design as a primary load [41].
Research on the specific effects of concrete shrinkage on deck cracking is limited, and its
behavior is largely unknown [30]. However, all the studies agreed that the higher the shrinkage
rate

and

the

higher

amount

of

shrinkage,

the

more

deck

cracking

[10][16][17][18][19][30][31][41]. Gaining an understanding of early age shrinkage is of
increasing concern and studying it in more detail could help mitigate the problem of early-age
cracking.

15

2.1.4

Bridge Design Features

Many different types of bridge designs and the effects of those designs on early-age deck
cracking have been studied. There is much disparity in design requirements, which vary from
state to state.

A field investigation and parametric study performed by the Minnesota

Department of Transportation (MNDOT) investigated the effects of bridge design on deck
cracking. Seventy-two bridges were investigated, including 34 with concrete girders, 34 with
steel girders, and 4 with W-shaped steel beams [16]. The top and bottom deck crack patterns
were documented and summarized and the bridge decks were given a rating from ‘5’ to ‘9’, with
9 corresponding to a ‘no cracking’ condition. While the field investigation was able to consider
the system as a whole, the parametric study was used to isolate individual factors.
Overall, the more restraint that was present in the system, the more cracking that occurred.
The field study found that concrete girder bridges performed better than steel girder bridges. Of
the 34 concrete girder bridges studied, 25 had ratings of ‘8’ or better, while of the 38 steel girder
bridges studied, only 12 had ratings of ‘8’ or better. This was attributed to reduced end restraint
provided by simply supported concrete girders with continuous decks and the beneficial
shrinkage characteristics of the concrete girders [16]. Steel girder bridges have differential
shrinkage characteristics between the deck and the girders, while concrete girder bridges exhibit
shrinkage of both the deck and the girders. Since steel girders do not shrink, they create
increased rigidity in the system, thus leading to higher stresses and lower overall deck ratings.
This phenomenon can also be seen in deck reconstruction on concrete girder bridges, which had
more cracking than on new bridges. This is because the shrinkage characteristics of girders for
the reconstructed deck bridges had already been stabilized, thus restraining the shrinkage of the
deck and having a similar effect to steel girder bridges. Other conclusions drawn from the field

16

study was that longitudinal restraint should be limited by increasing girder spacing and the
number of shear connectors used should be limited. It was concluded that thicker decks should
also be used, and should be above 6.25 inches thick. Additionally, the transverse bar size should
be limited while the spacing should be maximized. It was recommended to use No. 5 bars
spaced at 5.5 inches or No. 6 bars spaced at 7 inches. Crack concentrations were found to occur
in the area of cross-frames and diaphragms. For steel structures, the larger the girder spacing the
less cracking that occurred. The field study found that multiple factors exist, making it difficult
to pinpoint individual parameters [16].
For the parametric study, computational analyses were performed using the finite-element
program PBEAM [16]. A fiber, or layered, analysis approach was used and the cross section of
the girders and test unit were divided into layers. The bridge boundary conditions were modeled
as fixed, pinned, or roller supports. A prestressed concrete girder bridge was modeled, as well as
a continuous steel girder bridge. Nonlinear static analysis were conducted by varying the key
parameters of shrinkage, end conditions, girder stiffness, cross-frames, splices, and the value of
the deck modulus [16]. Differential shrinkage between the concrete deck and supporting girders
was the primary cause of cracking, which was especially evident in steel and reconstructed
concrete bridges. Additionally, the rate of shrinkage had a large impact on deck cracking.
Reducing the initial rate of shrinkage reduced early transverse cracking. For end boundary
conditions, the most extensive cracking was found for an idealized fixed-fixed case. The end
boundary conditions had the greatest effect on the extent of cracking, while girder stiffness,
cross-frames, and splices dictated the crack locations. The study found that crack concentrations
were increased in areas of cross-frames and splices. Additionally, stiffer girders produced more
uniform cracking, while flexible girders exhibited increased crack concentrations at midspan.

17

The study also found that the smaller the value of the deck effective modulus the more allowed
shrinkage deformation and the less cracking. The parametric study correlated well with the field
study [16].
Purdue University also performed a field investigation and created laboratory models to
investigate the effect of design factors on bridge deck cracking [17]. The field investigation
involved visually inspecting twenty bridges, which included eleven steel-girder bridges and nine
concrete-girder bridges. The most transverse cracking was observed on steel girder bridges
incorporating composite action and SIP forms, while the least amount of cracking was observed
on bridge decks cast monolithically with concrete superstructures. More longitudinal cracking
was observed on concrete girder bridges than on steel girder bridges, likely due to the planes of
weakness formed along the edges of the concrete girders [17]. Nine of the eleven steel-girder
bridges experienced transverse cracking, while only four of the nine concrete-girder bridges had
transverse cracking. Interestingly, one of the concrete-girder bridges only experienced cracking
on a newly widened portion of the bridge deck. Since the original portion of the deck had
already undergone shrinkage, it created an additional restraint for the shrinkage movement in the
widened portion. The original portion prevented the widened portion from shrinking freely, thus
inducing cracking in that region. This observation is similar to the observations noted with
reconstructed decks cast on concrete-girder bridges in the MNDOT study, where new deck
portions experienced restrained shrinkage, leading to the build-up of tensile forces and deck
cracking [16][17].
The study performed at Purdue also included a field instrumentation and extensive laboratory
investigation into the effects of design factors on concrete shrinkage and deck cracking [17]. For
the field instrumentation, a series of strain gages were placed in the deck and supporting girders

18

of a new bridge to measure thermal and strain gradients through the deck and girders. A
dramatic increase in strain in the deck reinforcement was noted 19 days after casting, while there
was no change in the steel girder strain, likely indicating the development of transverse cracking.
It was determined that once the deck cracked, the stress in the concrete was transferred to the
reinforcing steel and eventually decreased over time due to force redistribution [17].

The

laboratory investigation consisted of three parts. The first part involved creating cut models
from the instrumented bridge deck, the second part involved creating small shrinkage models to
investigate various design parameters, and the third part involved creating reinforced concrete
test unit models to investigate the effect of reinforcing bar size, spacing, and epoxy-coating
thickness [17]. From the first part of the study it was determined that moisture loss and drying
shrinkage commenced at the completion of curing and that the primary cause of deck cracking
was the restraint of concrete drying shrinkage. From the study’s second part it was determined
that sealing the bottom surface of the deck (through SIP forms) significantly influences the
amount of concrete shrinkage, that increased deck thickness leads to reduced shrinkage, that and
increasing the reinforcement reduces the total shrinkage but increases the amount of curling. In
the third part of the work it was determined that as the reinforcement spacing was decreased, the
spacing and size of primary cracks decreased but the number of cracks increased.

As

reinforcement spacing was increased the number of cracks decreased but the crack width
increased. Additionally, it was determined that as epoxy coating thickness was increased, the
average and maximum crack widths also increased [17].
Another study developed 2D and 3D finite-element models to examine the effects of changing
various design factors and boundary conditions [31]. The computer program ANSYS was used to
model the Hackensack Avenue Bridge over New Jersey Route 4.

19

An increasing uniform

shrinkage loading was applied, and cracking was assumed to occur at sudden jumps in the
shrinkage strain curves. The study revealed that cracks develop suddenly from the bottom to the
top, and are full-depth. The more rigid the boundary conditions and end restraint conditions, the
lower the amount of shrinkage required to cause cracking [31]. Different design parameters
were varied in the 2D model for each boundary condition. An increase in overall stress levels
led to an increase in the amount of cracking. The analyses revealed the following:
•
•
•
•
•
•
•

Increasing boundary restraints increased tensile shrinkage stresses.
Span length had no effect on shrinkage stresses.
Increasing deck thickness reduced shrinkage stresses.
Increasing girder spacing reduced shrinkage stresses.
Increasing ratio of girder to deck moment of inertia increased shrinkage stresses. It is
desirable to have flexible supporting girders.
Increasing area of longitudinal reinforcement increased shrinkage stresses.
Changing the distribution of reinforcement had no effect on shrinkage stresses. [31]

The study also investigated the effect of shear connectors on deck cracking. It was determined
that reducing the number of connectors would be beneficial in reducing the rigidity of the
system. However, current amounts are required by design to allow for composite action. The
study proposed a mechanism to prevent composite action at the early stages (during early age
shrinkage), but that will initiate when higher service loads and ultimate loads are applied. The
proposed idea was to wrap the shear connectors in a hyperelastic material that would compress
during early age shrinkage and provide enough resistance at later times to provide full composite
action [31]. Overall, the study proposed the following conclusions:
•
•
•
•
•
•
•

Stresses between the deck and girders are concentrated at the two ends of the bridge.
Time-dependent volume changes due to shrinkage should be considered in bridge design.
Construction practices should not introduce unnecessary restraints on the girders.
The ratio of girder/deck stiffness should be minimized.
More flexible superstructures are recommended: have a minimum deflection requirement
and increase the maximum limit.
Uniform reinforcement is recommended, and increasing the reinforcement volume above
code levels was not found to be beneficial.
Controlled composite action (wrapped shear connectors) should be investigated. [31]
20

Most jointless bridges use piles in favor of spread footings, as translationally stiff foundations
induce greater superstructure loads due to less freedom of movement. Current designs assume
axial pile loads are distributed evenly, and over 50% of agencies design for vertical eccentric
loading at the tops of the piles [15][20]. Expansion for jointless bridges is provided at the far
end of the approach test unit or between the abutment and the approach test unit. For steel
structures, having expansion joints beyond the backwall produced less deck cracking [6][20].
A research study was also performed at Marquette University through the Wisconsin
Department of Transportation to investigate early-age deck cracking. The effects of design
parameters, construction practices, and concrete mix design on early-age cracking were all
investigated by means of a field investigation and finite-element computer modeling [40]. The
field investigation showed a varied trend in cracking patterns and not all bridge properties were
able to be investigated. However, the study found that bridges with concrete girders exhibited
the most cracking, which is in conflict with other research findings [40]. It was determined that
the type of superstructure can greatly influence the amount of cracking and that it is important to
consider.
Finite-element computer modeling was also performed to simulate concrete shrinkage and
traffic loading. Shrinkage loading was applied through temperature, while traffic loads were
simulated through pressure points. The analysis did not use full inelastic material behavior.
Instead, cracking was determined to occur when the concrete stress exceeded the concrete
modulus of rupture. The analysis found that longitudinal stresses were larger than transverse
stresses, so transverse cracking would dominate. It also found that even if deck cracking does
not occur due to shrinkage loading alone, the added stresses due to traffic loading may be high
enough to cause cracking [40].
21

Design criteria vary considerably from state to state, and every bridge investigated in the
literature contained different types of designs. Overall, it was determined that the more restraint
in the system, the more susceptible it was to deck cracking. In general, concrete girder bridges
experienced less cracking than steel girder bridges, larger skews produced more cracking
(especially in steel girder bridges), larger span lengths produced more cracking, and the closer
the girder spacing the more cracking that occurred [6][16][17][18][20][29][42].
2.2

Concrete Shrinkage Standard Tests

Many standard tests exist for studying concrete shrinkage and for determining restrained
shrinkage strain and cracking. The most common test is the “ring test.” Literature describing
ring test experiments is widely available, along with many results for comparison
[8][22][33][34]. The literature focuses mostly on the effects of concrete material properties,
fibers and shrinkage-reducing admixtures on shrinkage strain and crack width, which goes
beyond the scope of this research [33][34]. However, review of this literature revealed that most
free shrinkage strain occurs during the first month of drying and levels out with time
[22][33][34]. This is illustrated below in Figure 8. Additionally, the literature indicated that
cracking occurred fairly consistently at a steel ring strain of 100 to 120µ-strain [8][22][33][34].
While the literature obtained on concrete shrinkage standard testing focused on material
properties and mix design, it was determined that the ring test is able to predict cracking
potential and restrained shrinkage strain reasonably well

The results from the literature were

thus used further as a comparison for computer modeling and to verify modeling approaches.

22

0.001

Strain

0.0008
0.0006
0.0004
0.0002
0
0

10 20 30 40 50 60 70
Age (Days)

Figure 8. Development of Free Shrinkage Strain with Time (adapted from ref. [22])

2.3

Questions and Outstanding Issues Remaining
Overall, the behavior of jointless bridges has been considerably investigated, and research is

widely available on the effects of mix design and primary loading. However, more work and
research is needed for the behavior due to the secondary forces of temperature, creep, and
shrinkage, particularly in the area of shrinkage. While temperature effects have been studied to
some extent, the effects of concrete creep and shrinkage are still largely unknown, and need
further investigation. Specifically, the effect of bridge design factors on concrete shrinkage
needs further investigation, as the effect of mix design on concrete shrinkage has been studied in
more detail. Conducting more research in all these areas will shed light on the issues currently
facing jointless bridges, specifically in the area of deck cracking. This research can be used to
develop new designs that could help mitigate the problem of deck cracking in jointless bridges.

23

2.4

Conclusions, Recommendations, and Suggestions for Prototype Bridge System
It is hypothesized that evenly-spaced early-age transverse cracking in jointless bridge decks

are primarily caused by restrained concrete shrinkage. The amount of shrinkage is dictated
primarily by concrete material properties and mix design, but bridge design factors can also have
an effect. Overall, it is predicted that the more restraint present in the bridge system, the more
cracking that will occur. Bridge designs can be modified to reduce the amount of restraint,
which will decrease the amount of early-age cracking.
Deck cracking appears to be more prevalent in bridges supported by steel girders due to
differential shrinkage and temperature characteristics through the section depth, along with the
added restraint provided by the shear connectors. Reconstructed bridge decks supported by
concrete girders also experience deck cracking, as they behave similar to steel girder bridges.
Nonetheless, this research considers both steel and concrete girder brides.

The effects of

boundary conditions, girder spacing, rebar size and spacing, deck thickness and cover, and the
effects of shear connectors are studied.

24

3

FIELD INSPECTION
A field inspection was conducted to examine several jointless bridges in Michigan that are

known to have suffered from early-age deck cracking. Fifteen bridges with four different ypes of
superstructures were visited. The field inspection was used to identify the parameters and
conditions that could cause distress in bridge decks. The findings were compared to the results
from the literature review and used to develop a prototype bridge system for further research
tasks.
3.1

Past Field Investigation Studies that have been Performed
A number of field investigation studies have been performed to determine the parameters

causing deck cracking in jointless bridges. The study performed by the Minnesota Department
of Transportation outlined in the literature review involved an extensive field investigation [16].
Seventy-two bridges in the Minneapolis/St. Paul area were investigated, including 34 with
concrete girders, 34 with steel girders, and 4 with wide-flanged steel beams. A wide range of
roadway types, ages, lengths and deck conditions were chosen. The design, material, and
construction data were collected for each bridge and documented. This included information on
the year of construction, overlay/redecking, dimensions, average daily traffic, span lengths,
girder spacing, deck reinforcement and shear connector details, cement supplier and detailed mix
design, deck contractor, joint type, and high and low temperature during the day of deck
placement. The top crack patterns in the deck were examined, as well as the bottom crack
patterns by fascia girders, joints in parapets, cross frames, and field splices. Crack patterns were
documented and given a deck rating similar to the rating system used by MNDOT. The rating
was on a scale from ‘5’ to ‘9’. The detailed criteria are presented below: [16]
25

‘9’ – No cracks
‘8’ –A few single cracks less than 0.03’’ wide
‘7’ –Single cracks with crack width less than 0.03’’ and crack spacing greater than 6’
‘6’ –Areas with high crack density. Crack width less than 0.03’’ and crack spacing from
from 3’ to 6’
‘5’ –Areas with high crack density and large crack width. Crack with greater than 0.03’’
and crack spacing less than 3’
The deck condition rating was compared to the design, material, and construction data, and
relationships between the deck rating and various parameters were plotted on 2D graphs. Linear
regression was used to determine cracking tendency [16].
Another field investigation was conducted by researchers at Purdue University [17]. The
field investigation involved visually inspecting and documenting cracking tendencies on bridges
in two regional transportation districts. Bridges chosen were either newly constructed, or older
bridges known to be experiencing deck cracking. Both concrete and steel girder bridges were
investigated. Twenty bridges were inspected, which included 11 steel girder bridges and 9
concrete girder bridges. The top surface of the bridge deck was visually inspected by walking
the entire length of the bridge. Any type of cracking or deterioration was noted and documented.
The bottom surface of the bridge was also examined. Cracking was recorded for bridges not
using stay-in-place (SIP) forms, while the use of these forms was also noted. Photographs were
taken to capture the deterioration, and crack width/spacing was measured. Pertinent information
recorded was the Indiana Department of Transportation (INDOT) structure number, date of
construction, date of rehabilitation or widening (if applicable), date inspected, type of girder,
skew angle, use of SIP forms, and cracking type.
documented and summarized [17].

26

Major concerns observed were also

3.2

Bridge Information Provided by MDOT
MDOT provided information for this research on several bridges in Michigan that have

experienced deck cracking.

Information provided included bridge inspection reports and

photographs of damage. The bridge information was reviewed and a matrix of the deck cracking
was developed. General bridge information was recorded, including the bridge ID number,
location, date of construction, date of inspection, repair actions taken, skew angle, and type of
deck forms used. A description of the type of cracking was then provided, along with the
MDOT deck rating. A summary of the provided information was made to determine the
structures to visit for the field investigation. Please refer to reference [35] for a summary of the
bridge information provided by MDOT.
3.3

Parameters Considered and Bridges Visited
The bridge inspection reports and photographs provided by MDOT were used to predict

whether or not transverse cracking was evident. A decision was then made whether or not each
bridge was a potential candidate to visit. Bridges selected to visit were those that appeared to
have widespread transverse cracking, indicating restrained concrete shrinkage. Bridges with
recent deck replacements that were known to experience cracking were of particular interest,
since these would have early-age cracking. Bridges with large skew angles (greater than 20
degrees) were discarded, along with bridges known to have part-width construction. The bridges
visited are summarized below in Table 1. The bridge locations are shown in Figure 9.

27

Bridge Location
I-96 wb @ Lansing
Rd.
I-96 eb @ Lansing
Rd.
I-496
eb
@
Pennsylvania Ave.
I-496
wb
@
Pennsylvania Ave.
M-52 over Looking
Glass River
US-10
eb
over
Sanford Lake
M-57 over US-127
Halsted Rd. over
I-696
I-96 eb over
Grange Rd.
I-96 wb over Grange
Rd.
Kensington Rd. over
I-96
M-6 eb over
Buck Creek
th

44 Street over
US-131
Burlingame Rd. over
M-6
Milham Rd. over
US-131
26 Mile Rd. over
M-53
Walton Blvd. over
I-75
Hawkins Rd. over I94
I-94 over Sandstone
Creek

Table 1. Bridges visited for field investigation
Bridge ID
Girder
Reason to visit
Number
Type
1a
Side-by-side Cracking pattern of interest, close
box beams proximity to MSU
1b
Side-by-side Cracking pattern of interest, close
box beams proximity to MSU
2a
Side-by-side Cracking pattern of interest, close
box beams proximity to MSU
2b
Side-by-side Cracking pattern of interest, close
box beams proximity to MSU
3
Spread box Extensive transverse cracking is
beams
evident
4
Concrete
Extensive transverse cracking, spaced
I-beams
at 10’, interestingly the westbound
counterpart has no cracking
5
Spread box Based on photos and inspection
beams
report, there is extensive cracking
6
Steel girders Cracking evident prior to recent
concrete overlay
7a
Concrete
Cracking possibly widespread, close
I-beams
proximity to MSU
7b
Concrete
Cracking possibly widespread, close
I-beams
proximity to MSU
8
Steel girders Photos indicate possible transverse
cracking, has a high deck rating
9
Concrete I- Need photos to document the
beams
damage, extensive cracking not
evident
10
Steel
Widespread transverse cracking, may
Girders
be
affected
by
part-width
construction
11
Concrete
Transverse
cracking
appears
I-beams
concentrated at the piers
12
Spread box Photos and inspection report indicate
beams
widespread cracking
13
Spread box Some cracking over piers, recent
beams
deck replacement
14
Spread box Some cracking throughout, recent
beams
deck replacement
15
Spread box Inspection photos indicate cracking,
beams
recent deck replacement
16
Steel
Transverse cracking evident, recent
Girders
overlay and deck widening
28

4
4

5
5

10
11 9
11

10
9

3
3

7
7

1

2
2

1

8

8

15

6
6

14 13
15 13
14

15

16
16

12

12

Figure 9. Field investigation locations
(For interpretation of the references to color in this and all other figures, the reader is referred to
the electronic version of this thesis)

The field investigation examined a wide variety of bridge superstructure types and a variety
of locations. Most of the bridges indentified by MDOT are supported by concrete beams, since
that is the most common construction practice for new bridges.

29

3.4

Field Inspection Results
All of the bridges for the field investigation were visited during a one-week period in

October, 2011. The visits occurred between mid-morning to late-afternoon, in weather ranging
from sunny to overcast/light rain. Cracks were able to be observed on all days the bridges were
visited. Pertinent bridge information was recorded, such as superstructure type, number of
spans, type of abutment, use of stay-in-place forms, and skew angle. Next, photographs were
taken of the overall bridge deck top surface and elevation to verify the overall design parameters.
The bottom surface of the bridge deck was then inspected and photographed, and evidence of
visible cracks was documented. Most bridges had stay-in-place forms, which prevented seeing
evidence of cracking on the bottom surface.

Finally, the entire top surface was visually

inspected by walking the length of the bridge.
photographed.

All crack types were documented and

Based on the photographs, a qualitative assessment of the damage was

developed, and a prediction was made on whether or not cracking was onset by restrained
concrete shrinkage. Typical photographs of damage are shown below in Figure 10 to Figure 14.
Please refer to reference [35] for detailed photographs for each bridge.

30

Figure 10. Semi-integral abutment connection (Bridge No. 13, 26 Mile Rd. over M-53)

Figure 11. Fully-integral abutment connection (Bridge No. 4, US-10 over Sanford Lake)
31

Figure 12. Transverse cracking over pier/negative moment region (Bridge No. 13, 26 mile Rd.
over M-53)

Figure 13. Typical transverse cracking in deck surface (Bridge No. 5: M-57 over US-127)
32

Figure 14. Typical longitudinal cracking (Bridge No. 11: Burlingame Rd. over M-6)

The results of each bridge inspection are summarized below in Table 2.

33

Table 2. Field investigation results

Bridge

I-96 @ Lansing Rd.
I-496 @ Pennsylvania
M-52 over Looking
Glass River
M-57 over US-127*
I-96 over Grange Road
Hawkins Rd. over I-94
I-94 over Sandstone
Creek
US-10 over Sanford
Lake
Kensington Rd. over I96*
26-Mile Rd. over M-53
Walton Blvd. over I-75
Halsted Rd. over I-696
M-6 over Buck Creek
44th Street over US131
Burlingame Rd. over
M-6
Milham Rd. over US131*

Type

Abutment
Type

ShrinkageInduced?

Cracking Type
Longitudinal
Yes, evenly spaced
Yes

Not likely
Not likely

Recently
Reconstructed?
No
No

Adjacent Box Beam
Adjacent Box Beam

Integral
Integral

Transverse
Yes, at piers and joints
Yes, at piers and joints

Spread Box Beam
Spread Box Beam
I-beam
Spread Box Beam

Integral
Integral
Integral
Integral

Yes
Yes, widespread
Yes, only at piers
Yes, especially at piers

Yes
Not much
Not much
Yes, evenly spaced

Yes
Yes
No
Possibly

No
No
Yes
No

Steel beams

Non-integral

No

No

No

Yes

MI-1800 I-girder

Integral

Yes, at piers

Possibly

No

Steel beams
Spread Box Beam
Spread Box Beam
Steel beams
MI-1800 I-girder

Integral
Non-integral
Non-integral
Non-integral
Non-integral

Yes, at piers and joints
Yes, at pier
Yes, at pier
No
Yes, at piers and in-between

Yes
Yes, spaced
randomly
Yes, evenly spaced
Yes, evenly spaced
No
No

Yes
No
No
No
Yes

Yes
No
No
Yes
No

Steel beams

Non-integral

Yes, at piers

No

Yes

No

MI-1800 I-girder

Integral

Yes at piers

No

No

Spread Box Beam

Integral

Yes, widespread

Yes, evenly spaced
Yes, spaced
randomly

Yes

Yes

Note: "Integral" refers to beams cast into the abutment, while "non-integral" refers to beams not cast into abutment.

34

3.4.1

Transverse Cracking

Transverse cracking was evident in the negative moment regions (over the piers) in almost all
of the bridges inspected. Transverse cracks in these regions were likely caused by the negative
bending moment rather than induced tensile forces from restrained concrete shrinkage.
Restrained shrinkage cracking was indicative by the presence of evenly-spaced transverse cracks
throughout the entire bridge surface. This appeared to have occurred in bridges 5, 8, 9, 10, and
12. Interestingly, it was evident in bridges with three different superstructure types (spread box
beams, concrete I-beams, steel girders). It was only not evident in side-by-side box beam
bridges.
3.4.2

Longitudinal Cracking

Longitudinal cracking was common in bridges with side-by-side box beams and spread box
beams. The cracks typically spanned the entire length of the bridge and were spaced at the same
spacing of the beams. The longitudinal cracks in the side-by-side beam bridges were likely due
to either differential settlement between the beams and the grout filler, or loss of post-tension
force between the beams.

For the spread box beam bridges, longitudinal cracking likely

occurred due to a concentration of longitudinal shear forces at the edges of the beams. This is
assumed since the spacing of the cracks matches the beam spacing. These types of cracks are not
due to restrained concrete shrinkage.

35

3.5

Summary and Conclusions

Based on the field investigation, some general trends were observed and the following
conclusions can be made:
•

Bridges with fully integral abutments (beams cast directly into the abutment)
experienced more cracking than bridges with non-integral abutments (beams not
cast into the abutment). This is expected, since bridges with fully integral
abutments have more restraint.

•

Bridges with larger girders experienced more cracking.

•

Part-width construction on Bridge 12 may have had an influence on the extent of
cracking.

•

Bridges with spread box beams experienced both transverse cracking and
longitudinal cracking. Longitudinal cracking was evident along the beam edges
and transverse cracking was evident in both the positive and negative moment
regions.

•

Bridges with steel girders had extensive transverse cracking, but did not exhibit
longitudinal cracking.

•

Bridges with side-by-side box beams did not exhibit transverse cracking.

In general, the information obtained from the field inspection correlated well with the
information provided by MDOT. It is difficult to pin-point which type of bridge will experience
the most restrained shrinkage cracking, since transverse cracking was evident on a wide variety
of superstructure types and each bridge is unique. However, the field investigation was able to
confirm the hypothesis that increased restraint in the system will lead to more cracking. Overall,
it appears that bridges with spread box beams and steel girders are most susceptible to restrained
shrinkage cracking.
Based on the results of the field investigation, two prototype bridges were chosen to develop
finite-element computer modeling at the global/system level. It was initially understood that the
Halsted Rd. over I-696 bridge experienced a heavy amount of transverse cracking, and was
36

considered as a prototype for the steel-girder laboratory models. However, based on the field
investigation, that was not the case. Of the steel bridges visited, the Kensington Rd. over I-96
bridge (Bridge 8) appeared to be the best candidate to use as a prototype for computer modeling,
since it had the largest extent of transverse cracking among the steel girder bridges. Of the
spread box beam bridges visited, the M-57 over US-127 bridge had the most amount of cracking.
These two bridges were thus used as prototypes for further computer modeling.

37

4

EXPERIMENTAL EVALUATION
The experimental evaluation was used to investigate the influence of restrained shrinkage in

jointless bridges at the sub-assembly level. This was completed by constructing four different
full-scale test unit slabs. The data was used to compare the relative differences in the shrinkage
behavior of each test unit and to validate the computer modeling approach.
4.1

Approach
The causes behind restrained shrinkage cracking may be grouped at three levels: (i) material,

(ii) sub-assembly, and (iii) system. Material effects on concrete shrinkage have been studied
considerably and are not in the scope of the current project. Sub-assembly level effects include
structural design features such as girder type, diaphragms, deck forms, deck reinforcement
details, and shear connector configuration. System level effects include those from support
conditions, soil/structure interaction, and interaction between sub-assembly units.
Evaluating behavior at the global level is complex since it requires simulation of boundary
conditions and soil-structure interaction. Thus, the laboratory investigation was designed to
assess behavior at the sub-assembly level. The approach was similar to a laboratory investigation
performed at Purdue University, which consisted of square deck test unit segments attached to
longitudinal edge girders and incorporating relevant design features such as transverse
diaphragms, shear connectors and formwork panels [17].
The effects of restrained shrinkage were evaluated by means of the actual volume change of
the concrete in the deck test unit. Thus, no attempt was made to simulate restraining effects from
the rest of the bridge or to introduce mechanically equivalent shrinkage loads. Four beam/test
unit assemblies were designed to experimentally evaluate the effects of different design
38

parameters. The following parameters were considered be important to shrinkage restraint at the
sub-assembly level:
•

Deck-girder shear interaction: shear connector spacing and amount.

•

Transverse system stiffness: diaphragm type (i.e., channel vs. x-bracing).

•

Deck reinforcement: mainly transverse reinforcement size and spacing.

•

Deck thickness.

•

Formwork system.

Of these parameters, deck thickness was eliminated since it is constant for modern MDOT bridge
designs. Also, the effects of formwork were evaluated by the work at Purdue University [17] and
no repetition was needed. While the focus of the research was mainly on the effects of design
factors on restraining concrete shrinkage, MDOT was also interested in studying an optimized
concrete mix design, which would contain less cement and therefore theoretically experience less
shrinkage. Based on these considerations, the experimental test matrix shown in Table 3 was
developed. The baseline details for deck reinforcement, shear connector density, and size and
girder spacing was obtained from the Halsted Rd. over I-696 bridge.
The experimental data was used to calibrate material and shrinkage simulation finite element
models. The finite element models for the sub-assemblies were further used to evaluate
variations on the design parameters. Evaluation of system-level effects, such as soil-structure
interaction and skew angle were done on finite element models of full bridge systems using the
calibrated material and shrinkage modeling approach used for the sub-assembly models.

39

Table 3. Experimental Test Matrix for Sub-Assembly Evaluation of Shrinkage Effects
Test Girder Diaphragm
No. Type
Type
1
Steel
C-Channel
2

Steel

C-Channel

3

Steel

X-Bracing

4

Steel

C-Channel

4.2

Shear
Connectors
StudsDensity 1
StudsDensity 2
StudsDensity 1

Reinforcement
Detail
Detail 1

Concrete
Mix
Standard

Unique Parameter

Detail 1

Standard

Detail 2

Standard

StudsDensity 1

Detail 1

Optimized

Shear Connector
Density
Diaphragm Type
and Reinforcement
Density
Concrete Mix

Standard Design

Test Unit Design Parameters
Based on the revised approach described above, designs were developed for all four test units.

As previously stated, the originally-considered prototype bridge (Halsted Rd. over I-696) was
used as a basis for the designs. Each test unit consisted of a 10 ft by 10 ft test unit cast on two
beams, spaced apart by 7 ft on center. The Halsted Road Bridge has a girder spacing of 9’-4’’ on
center. However, due to laboratory size constraints and typical bridge girder spacing from the
literature, a 7 ft spacing was chosen. The overall test unit size was based on the beam spacing
and space constraints in the laboratory. The design development for each parameter shown in
Table 3 is described in the following sections.
4.2.1

Steel Beam Size Determination

The two parameters considered in determining the steel beam size was axial stiffness and top
flange width. The beams had to be as stiff or stiffer than the girders used in the Halsted Bridge,
and the top flange width had to be the same in order to match the interaction between the steel
and concrete. Since the span length of the test units were very small compared to the actual span
length in the prototype bridge, the governing criteria was to match the top flange width.
40

The

flange width of the girders used in the Halsted Bridge is 14’’, so the smallest wide flange beam
section with a 14 in. flange was desired. This led to select a W14x176 beam. However, this
section has a large cross-sectional area and would have produced much larger axial stiffness than
the actual prototype bridge. Therefore, the beam selection was modified by selecting a smaller
section and then welding extension plates to the top flange to obtain the correct width. A
W12x40 section was thus chosen, which is the smallest section with 8 in. wide flanges. In order
to reach the required 14 in. width on top, 3 in. extension plates were welded on either side of the
top flange, as shown below in Figure 15.

3 '' p la t e s
1

4 ''

1

3 ''- w id e p la t e
4

''
W12x40 Beam Top Flange
3 ''- w id e p la t e

W 1 2 x 4 0 B e a m

Cross-section View

Plan View

Figure 15. Steel beams selected, with welded extension plates

4.2.2

Diaphragm Section Determination

As shown in Table 3, two different types of diaphragms are used for the test units. The
diaphragms were selected to match the axial stiffness of the C-channels used in the prototype
2

bridge, which were C12x25 shapes with a cross-sectional area of 7.34 in . The transverse
spacing of the beams in the laboratory test units was the same as the actual bridge. Therefore,
the cross sectional area of the chosen diaphragm shape had to be the same to match the axial
stiffness. Double angle sections were used in lieu of C-channels, since the available C-channel
41

sections were too tall for the W12x40 beams. The diaphragm thus consisted of two back-to-back
2

angles (2L5x5x3/8) with a cross-sectional area of 7.3 in .
MDOT specifications and structural analyses were used to determine the angle size to
produce equivalent stiffness for the cross-bracing diaphragms. First, a cross-bracing design for
the Halsted Bridge was determined according to the MDOT standard specifications, as shown
below in Figure 16.

“L”

Min Angle Size

Less Than 6’-9’’

3x3x5/16

6’-9’’ to 9’-3’’

4x4x5/16

9’-3’’ to 11’-6’’

5x5x3/8

11’-6’’ to 13’-9’’

6x6x3/8

13’-9’’ to 18’-6’’

8x8x½

L
Figure 16. MDOT cross-bracing standard specifications (adapted from ref. [26])

Since the girder spacing (L) is 7 ft in the Halsted Bridge, the angle size that would be used in
a cross-bracing diaphragm is L4x4x5/16. This cross-bracing for the Halsted Bridge was then
modeled in SAP2000 [14] with a unit force, as shown in Figure 17.
displacements are shown in Figure 18.

42

The corresponding

F=1
H=42'’ (Halsted Bridge
girder height )

F=1
W=7'-0'’ (Halsted Bridge
girder spacing )
Note: MDOT specs. require two cross -members , as well
as a straight member across the bottom , as shown
Figure 17. Halsted Bridge cross-bracing dimensions and SAP 2000 model

delta=0.0012'’
Ave. delta=0.00095'’
delta=0.007'’
Figure 18. Cross-bracing displacement results

The shapes for the lab model cross-bracing were selected so that the overall axial stiffness
was equivalent to the prototype bridge. The process for determining the correct shapes is
summarized below in Equations 4-1 to 4-7.

43

Stiffness, k = F = 2

(4-1)

k = EA (axial stiffness)

(4-2)

δ

δ

L

F
kbottom = b =

δb

ktop =

kbottom = 1429 =
ktop = 833 =

1 = 1429
0.007

Ftop
= 1 = 833
δ top 0.0012

(4-3)
(4-4)

29000* Ab
→ Abottom = 3.73 sq. in.
L

(4-5)

29000* At
→ Atop = 2.18 sq. in.
L

(4-6)

Atotal = 5.49in2 ∴ 2.75in2 per angle in lab bracing

(4-7)

Note that two angles were chosen for the lab cross-bracing instead of three due to the height of
2

the beams. With 2.75 in required per angle, a shape of L3x3x1/2 was selected for the crossbracing members in the laboratory models.
Two sets of diaphragms were placed for each test unit, 1 ft inward from the ends of the
beams. The diaphragms were attached to the beams at gusset plates. The plate dimensions were
chosen to be 3/8 in. thick fit in between the top and bottom flanges of the beams. The gusset
plate details are shown below in Figure 19.

44

Figure 19. Gusset Plate Dimensions

4.2.3

Shear Connector Layout Determination

Two different shear connector configurations were welded to the top flange of the beams.
The shear stud spacing in the Halsted Bridge varied from 6 inches to 2 ft. Therefore, to examine
the effect of shear stud density, both extremes were used. The 6 in. spacing was used for test
unit 2, while the 2 ft spacing was used for test units 1, 3, and 4. The same 0.75 in. diameter by 6
in. tall shear connectors were used in the test units. In all cases three connectors were placed per
row (across the flange width), with a 5 in. distance between them.
configurations are shown in Figure 20 to Figure 22.

45

The shear connector

1

''x 6 '' S h e a r S t u d s
S p a c e d @ 5 ''
1

4

3
'' w e ld
1 6
( a ll a r o u n d )

Figure 20. Shear Connector Spacing over Top Flange

W 2x40 St eel Beam
1
2 L 5 x 5 x
3
8

D ia p h r a g m s ( w e ld e d )

Figure 21. Shear Connector Detail 1(Test units 1, 3, and 4)

W 2x40 St eel Beam
1
2 L 5 x 5 x
3
8

D ia p h r a g m s ( w e ld e d
)

Figure 22. Shear Connector Detail 2 (Test Unit 2)

46

4.2.4

Deck Reinforcing Steel Determination

Two different reinforcing steel configurations were used for the test units.

The first

configuration matched the MDOT specifications for the 7 ft beam spacing used in the lab test
units. This was used for test units 1, 2, 3, 5, and 6. The second configuration matched the
Halsted Bridge reinforcement, which was derived from the girder spacing of 9’-4’’ in the actual
bridge. This was used for test unit 4. The two reinforcement configurations are summarized
below in Table 4, and are visually represented in Figure 23 and Figure 24.

Table 4. Test Unit Reinforcement Details (Derived from Reference)
Reinforcement
Type
Detail 1

Detail 2

Top
Longitudinal
#3 Bars
Spa. @ 10.5’’
#3 Bars Spa. @
10’’

Top
Transverse
#5 Bars
Spa. @ 8’’
#6 Bars
Spa. @ 8.5’’

47

Bottom
Longitudinal
#4 Bars
Spa. @ 8.5’’
#5 Bars
Spa. @ 9’’

Bottom
Transverse
#5 Bars
Spa. @ 8’’
#6 Bars
Spa. @ 8.5’’

Longit udinal R orcem D ail
einf
ent et
# 5 T o p B a rs

# 5 B o tto m

B a rs

Transverse R orcem D ail
einf
ent et
# 3 T o p B a r s ( L o n g itu d in a l )
# 4 B o tto m

B a r s ( L o n g itu d in a l )

Figure 23. Deck Reinforcement Detail 1 (Test units 1, 2, and 4)

Longit udinal R orcem D ail
einf
ent et
# 5 T o p B a rs

# 5 B o tto m

Transverse R orcem D ail
einf
ent et
# 3 T o p B a r s ( L o n g it u d in a l )
# 4 B o tto m

B a r s ( L o n g it u d in a l )

Figure 24. Deck Reinforcement Detail 2 (Test Unit 3)

48

B a rs

4.2.5

Weld Design

The connections for the gusset plates, shear studs, and diaphragms were welded together
using the AISC minimum weld size specifications. According to the AISC manual, for a plate
and angle thickness of 3/8’’, the minimum weld size is 3/16’’ [3]. The weld strength is specified
below in Equation 4-8.

Pweld = 0.75(0.707 * t * L * 0.6 * 60 ksi ) = 19.089 * L * t (kips)

(4-8) [3]

Assuming 3/16’’-thick welds, the weld strength is:

Pweld = 3.58 * L

(4-9) [3]

The weld lengths were dictated by the required connection details. Using Equation 9, the weld
strength for each the connection is given as:

Pweld _ gusset = 3.58*(2 *[6''+ 6''+ 5'']) = 121.72 kips =121,720 lbs

(4-10)

Pweld _ diaphragms = 3.58* (2 *[2 *5.5'']) = 78.76 kips =78,760 lbs

(4-11)

Pweld _ x −bracing = 3.58* (2 *[2 *5.5'']) = 78.76 kips =78,760 lbs

(4-12)

Since these strengths are much higher than the anticipated forces expected for the lab models, it
was determined that using 3/16’’ welds would be adequate. The weld details are shown in
Figure 25.

49

S e c tio n A - A
A
3

3
1 6

''
3

3

1 6

''

1 6

1 6

2 L 5 x 5 x

''

2 L 5 x 5 x

''
3
3

3
8

1 6

''

1 6
3

A

''
3

3

1 6

''

1 6

3

S tiffe n e r
P la te

1 6

''

2 L 5 x 5 x3 8
D ia p h r a g m
'

3 '' p la t e s
( w e ld e d )
b) Diaphragm Connection Plan View
3
1 6 ''

''

3

3
1 6

1 6

''
3

''

3

i.

3

1 6

S tiffe n e r P la te
W 1 2 x 4 0 B e a m

1 6

''

''

a) Gusset Plate and Diaphragm Connection Cross-Section View

3

1 6

1 6

8

'' P la t e

''

Weld Detail

ii. Dimension Detail

c) Cross Bracing Connection
Figure 25. Welded connection configurations
50

''

3
8

4.2.6

Pin Support Design

The beams were set on pin supports at each end. The bases for the supports were made from
cut sections of W8x31 beams. Grooved steel plates and round steel bars were utilized to
simulate the rocker bearings used in bridges. Since the anticipated rotations at the supports were
small, the pin dimensions did not need to match the dimensions of the rocker bearings used in the
Halsted Bridge. The pin support details are shown below in Figure 26 and Figure 27. The
supports were placed 6 inches from the ends of each beam. Bolted connections were used so that
the plates could be re-used.

0 . 5 ''- d ia m e t e r s t e e l b o lt s
1 ''x 4 ''x 1 0 '' s t e e l p la t e s

1 . 5 ''- d ia m e t e r s t e e l r o d
0 . 5 ''- d ia m e t e r s t e e l b o lt s

Figure 26. Pin plate details

1 ''x 4 ''x 1 0 '' s t e e l p la t e s

W12x40 Beam
1 . 5 ''- d ia m e t e r s t e e l r o d
W 8 x 3 1 B e a m
( 1 0 '' D e e p )

W8x31 Base

Figure 27. Pin connection setup

51

4.2.7

Ring Test

In addition to the four test units, a concrete shrinkage ring test was performed to evaluate the
shrinkage properties and cracking potential of the concrete. The test setup was based on ASTM
C1581-04. In the test, a ring-shaped sample of concrete is cast between an instrumented steel
ring and a circular mold. After the specimens cure the circular mold is removed and the top
surface is sealed, which allows free shrinkage only on the exterior surface of the concrete ring.
The interior steel ring restrains the shrinkage of the concrete ring, and compressive strain and
stress is induced [5]. The test setup is shown in Figure 28.

O v e r a ll T e s t S e tu p ( P la n V ie w )
O u te r S te e l R in g
C o n c r e te R in g

t = 1 / 2 ''
t = 1 / 2 ''

B o lts w ith e c c e n tr ic w a s h e r s

In n e r S te e l R in g ( w ith s tr a in g a g e s
N o n - a b s o r p tiv e b a s e
( s e a le d o r c o v e r e d p ly w o o d )
O v e r a ll T e s t S e tu p ( S e c tio n V ie w )
S e a l
t = 1 2 ''
S tr a in
t = 1 2 ''
g a g e s

Figure 28. Ring Test Setup (adapted from ref. [5])

52

)

Strain gages were placed on the interior of steel ring to measure strains in the circumferential
direction. As the concrete shrinks it compresses the inner steel ring, inducing compressive
strains.

The steel ring restrains the shrinkage movement of the concrete ring and the

compressive strains increase until cracks form in the concrete [5]. Compressive strains were
measured from the time of casting, and cracking is indicated by a sudden decrease in strain. An

Steel Ring Strain (x10^-6)

example strain output is shown in Figure 29. Three rings were cast for each batch of concrete.

20
0
-20
-40
-60
-80
-100
0

2
4
6
8
Specimen Age, Days

10

Figure 29. Example Ring Test Strain Output (adapted from ref. [5])

The overall designs for all four test units are summarized in Table 5 and a three-dimensional
drawings of the test unit is shown in Figure 30.
Table 5. Test Unit Design Summary
Test Girder
No.
Type
1
W14x176

2
3
4

Diaphragm
Type
2L 5x5x3/8 angles

Shear
Reinforcement Concrete Mix
Connectors
Detail
1.25x6’’ studs
Detail 1
Standard
spa. @ 2’-0’’
W14x176 2L 5x5x3/8 angles 1.25x6’’ studs
Detail 1
Standard
spa. @ 6’’
W14x176 L 3x3x1/2 X-bracing 1.25x6’’ studs
Detail 1
Standard
spa. @ 2’-0’’
W14x176 2L 5x5x3/8 angles 1.25x6’’ studs
Detail 2
Optimized
spa. @ 2’-0’’
53

Figure 30. Test Unit Overall View

4.3

Instrumentation Layout

A combination of LVDTs, thermocouples, and strain gages were used to monitor the earlyage concrete behavior in the test units and to measure the effect of concrete shrinkage.
Instrumentation was placed so that an overall representative behavior of each test unit could be
obtained and used to calibrate the computer models.
4.3.1

Strain Gages

Wire-resistant strain gages were attached on both mats of reinforcing steel and through the
depth of the beams to determine the strain gradient through the depth of the test units. The strain
gage locations are shown below in Figure 31 to Figure 34.

54

5'-0''
#3 Longitudinal Bars
#5 Transverse Bars

2'-6''
5'-0''

10'-0''

2'-6''

Indicat es St rain G Locat ions
age
Figure 31. Reinforcing steel top mat strain gage locations

5'-0''
#4 Longitudinal Bars
#5 Transverse Bars

2'-6''
5'-0''

10'-0''

2'-6''

Indicat es St rain G Locat ions
age
Figure 32. Reinforcing steel bottom mat strain gage locations

55

St eel Beam St rain G Locat ions
age
(Test U s 1 4)
nit Support

Support

6''

3 Strain Gages
(see detail A)

5'-0''

2 Strain Gages
(see detail C)

6 Strain Gages
(see detail A)

9'-0''

Beam Midspan

Beam Midspan

2 Strain Gages
(see detail C)

2'-6''
Support

Support

6''

D ail A
et

D ail B
et

D ail C
et

Indicat es St rain G Locat ions
age

Figure 33. Steel beam strain gage locations

1'-7''

1'-7''
1'-8'' 1'-8''

2 L 5 x 5 x 3 /8 D ia p h r a g m s

L 3x3x12 Diaphragms

Indicat es St rain G Locat ions
age
Figure 34. Diaphragm strain gage locations

56

4.3.2

LVDTs

Several 0.05-in. LVDTs were used to measure the vertical deflection of the laboratory
models. The LVDTs were calibrated using plates with known heights, which was required to
convert output voltage to displacement. The LVDT layout is shown below in Figure 35. As
shown, the LVDT’s were placed underneath each beam at mid-span, as well as two locations in
the center of the test unit.

10'-0''
5'-0''
Support

Support

Support

Support

5'-0''

10'-0''

Indicat es LVD Locat ions
T
Figure 35. LVDT Locations

57

4.3.3

Thermocouples

Type K thermocouples were used to measure the temperature change in the concrete during
curing, as well as the ambient temperature. The thermocouples were positioned at the same level
as the top and bottom mats of reinforcing steel in the test unit, while the ambient thermocouple
was placed close to the test units.
4.3.4

Instrumentation Naming Scheme

The following naming scheme was used to identify the locations of each instrument. This
naming scheme was utilized in all the data outputs.
(Test Unit)-(Type)-(X-coordinate)-(Y-coordinate)-(Depth)-(Orientation)
•
•
•
•
•
•

Test Unit: 1, 2, 3, or 4
Type: LVDT (D), Strain gage (S), Thermocouple (T)
X-coordinate: See Figure 36
Y-coordinate: See Figure 36
Depth: See Figure 37
Orientation: Transverse (T), Longitudinal (L)

58

(X=Girder 1) (X=5'0'')
1
G1
2
(X=Girder 2)
(X=3'4'')
G2
1
Y
3

2'-6''
4

(Y=7'6'')

2

(Y=5'0'')

4

(Y=2'6'')

3

5'-0''

1

10'-0''

5'-0''

1

2'-6''
X

5'-0''
Figure 36. X-Y orientation for instrumentation

1 Tp (Top mat)
2 Bt (Bottom mat)
3 Tf (Top Flange)
4

W (Mid. Web)

5

Bf (Bottom Flange)

Figure 37. Depth locations for instrumentation

59

4.4

Test Unit Construction and Casting

The construction process of the laboratory test units is described in the following sections.
Please refer to reference [35] for detailed photographs of the construction process. Due to space
constraints in the laboratory, two test units were constructed and tested the same time. A local
fabricator assembled the steel girder/diaphragm assemblies and attached the shear studs. The test
unit steel frames were then brought into the laboratory and set on the supports as shown in
Figure 38 and Figure 39.

Figure 38. Test Unit Steel Frame Assemblies (Test units 1, 2, and 4)

60

Figure 39. Test Unit 3 Steel Frame Assembly

4.4.1

Formwork

Standard stay-in-place metal bridge deck forms were used in between the steel beams, and
were spot-welded in place on the beam top flanges. The corrugations of the forms were filled
with Styrofoam inserts, which is typical for MDOT bridges. The metal form installation is
shown in Figure 40 to Figure 42.

61

Figure 40. SIP forms front view

Figure 41. SIP forms Styrofoam fillers

62

Figure 42. Spot-welding of the forms (typical)

Removable lumber forms were used for the edges of the test units, as well as the cantilevered
sections. A schematic of the formwork for the cantilevered section is shown below in Figure 43.
Photos of the formwork construction are shown in Figure 44 to Figure 46.

¾’’ plywood
Steel beam

2'’x10'’
lumber

Support

2'’x4'’ lumber
braces
2'’x4'’
lumber

Figure 43. Schematic for the cantilevered section formwork (note these forms are removable)

63

Figure 44. Cantilever forms bottom section

Figure 45. Completed cantilever forms

64

Figure 46. Completed formwork (all lumber forms are removable)

4.4.2

Reinforcing Steel

The mats of reinforcing steel were tied together with steel wire and then positioned in the test
units. Each intersection of the bars was tied and secured, ensuring the bars did not move.
Concrete spacers were cut to provide the required cover for both mats of steel, as shown in
Figure 47 to Figure 49.

65

Figure 47. Concrete spacers for reinforcing steel (typical)

Figure 48. Spacing between reinforcing steel mats (typical)

66

Figure 49. Reinforcing steel side cover (typical)

4.4.3 Instrumentation Installation
Strain gages were attached directly to the reinforcing steel and structural steel.

The

installation followed the procedure outlined below.
•

The installation surface was ground smooth, and wiped with rubbing alcohol to ensure a
clean surface.

•

The strain gage was taped to the surface using cellophane tape

•

The tape was pulled back from one end to expose the bottom of the strain gage. Then, a
fast-cure adhesive was applied to the bottom of the strain gage, which was pressed down
for at least one minute.

•

The cellophane tape was removed, and the lead wires were adjusted, ensuring they did
not touch one another or the steel surface.

•

The entire assembly was covered with a protective acrylic paint.

•

Electrical tape was placed over the strain gage to provide further protection.

This process is shown below in Figure 50.
67

a) Ground and cleaned surface

b) Strain gage attached to steel bar

c) Lead wires adjusted so they do not
touch the steel

d) Assembly covered with M-Coat D

e) Electrical tape placed to protect strain
gage
Figure 50. Example strain gage installation process (typical for all strain gages)
68

LVDT’s were positioned directly underneath the bottom flanges of the beams to record
midspan deflections. Wooden stands were constructed to hold the LVDT’s in place. For the
LVDT’s in the middle of the test unit, a small steel rod with an aluminum plate was positioned
into the deck. The LVDT’s were positioned underneath the aluminum plate, so that deflections
of the concrete test unit could be directly measured. This was done in case the concrete deck and
formwork became separated. The LVDT placement is shown below in Figure 51 and Figure 52.

b) Steel bonding rod

a) LVDT stand setup

Figure 51. LVDT placed underneath mid-test unit

Figure 52. LVDT in place (mid-span of beam)

69

4.4.4

Test unit Casting

4.4.4.1 Concrete Mix Design
Two different types of concrete mixes were used in the test units. For the first three test units,
the MDOT standard Grade D concrete mix was used, while a modified Grade D mix was used
for the fourth test unit. Both mixes had a 28-day design compressive strength of 4,500 psi and
maximum aggregate size of 1 inch. The only differences between the two mixes were in the
cement content and aggregate gradation. The modified mix had a 30% slag cement replacement
and an optimized aggregate gradation. The interest in the modified mix is that its performance
should be better in terms of reduced shrinkage due to the lower cement content. The details for
each mix are summarized in Table 6 and Table 7.
4.4.4.2 Concrete casting
The first two test units were cast at the same time to ensure they experienced the same
shrinkage characteristics. The concrete was obtained from Shafer’s, a local redi-mix company.
The concrete was mechanically vibrated during casting to ensure proper consolidation. The test
unit surfaces were then finished with a bull float. The first two test units were cast in the
morning of February 10, 2012. The third test unit was cast in the morning of March 23, 2012,
and the fourth test unit was cast in the morning of March 26, 2012. Casting took about 30-45
minutes for each test unit. The casting and finishing work is shown below in Figure 53 and
Figure 54.

70

Table 6. MDOT Grade D Concrete Mix Design
Material
Quantity
3
Portland Cement
658 lb/yd
Fly Ash
None
Lafarge Slag
None
3
Sand (2NS)
1195 lb/yd
Gravel (26A)
None
3
Gravel (6AA)
1740 lb/yd
3
Water
270 lb/yd

W/C ratio
Air content (%)
Slump (in.)
Fine agg./total agg
percentage

0.41
6.5
4.5
0.41

Table 7. MDOT Modified Grade D Slag Replacement Mix Design
Material
Quantity
3
Portland Cement
461 lb/yd
Fly Ash
None
3
Lafarge Slag
197 lb/yd
3

Sand (2NS)

1088 lb/yd

Gravel (26A)

508 lb/yd

Gravel (6AA)

1306 lb/yd

Water

270 lb/yd
0.41
6.5
5.25
0.55

3
3

3

W/C ratio
Air content (%)
Slump (in.)
FA./TA percentage

71

Figure 53. Placing and vibrating the concrete (test unit 3)

Figure 54. Bull floating the concrete surface (test unit 3)

72

Fresh concrete properties (air and slump) were also tested for each concrete mix using the
standard test methods. The results are summarized in Table 8.
Table 8. Concrete Fresh Property Characteristics
Mix
Slump (in)
Air content (%)
Test unit 1 and 2
4.5
5.5
(Grade D)
Test unit 3
4.25
6.5
(Grade D)
Test unit 4
4.25
6.5
(Grade D-Mod.)

After the concrete initial set, the test unit surfaces were covered with wet burlap and plastic to
provide a seven-day wet cure in accordance with MDOT standard specifications [26]. This was
done four hours after the concrete surface was finished. The burlap was examined daily to
ensure it was kept saturated, and was re-wetted when necessary. All wooden forms were
removed after three days. A typical timeline of events from casting to the end of curing is shown
in Figure 55. The times listed are approximate and varied slightly for each test unit.

Figure 55. Timeline of events between casting to the end of moist curing (typical)

73

4.4.5

Completed test units

After the seven-day wet cure the burlap and plastic was removed and the top and outside
surfaces of the test units were exposed to drying shrinkage. The completed test units are shown
below in Figure 56 to Figure 59.

Figure 56. Completed test unit overall view (test unit 4)

74

Figure 57. Completed test unit cantilever section (test unit 3)

Figure 58. Close-up of completed test unit top surface (test unit 4)

75

Figure 59. Test unit cross-section (test unit 4)

4.4.6

Concrete Shrinkage Ring Tests

Concrete rings were cast for each mix in order to determine the shrinkage characteristics and
cracking potential at the material level. For the first two test units, three rings were moist-cured
for seven days, while one ring was moist-cured for 24 hours. For the second set of test units, two
rings were cast using the standard Grade D mix (test unit 3), and two rings were cast using the
modified Grade D mix (test unit 4). These four rings were moist-cured for seven days. The
rings were placed in a separate room where constant temperature and humidity was maintained,
as illustrated in Figure 66 and Figure 67. After the moist-cure period was completed, the top
surfaces of the rings were sealed with silicone, thus only allowing shrinkage from the outside
surface. An overall view of the completed rings is shown in Figure 60.
76

Figure 60. Overall view of shrinkage rings

4.5

Results

The data obtained from the laboratory investigation was used to: (1) calibrate the material and
shrinkage simulation of the finite element computer models, and (2) analyze the effect of bridge
design parameters at the sub-assembly level. The experimental data was used to verify the
computer modeling approach and validate its use for full bridge models at the global level.
4.5.1

Data Acquisition

Data was collected on a National Instruments SCXI-1001 data acquisition system. Data was
collected continuously, starting within two hours after the top surface of the concrete was
finished. Readings were taken every minute during the duration of the test; and the tests were
run for a period of three weeks, including the one week of wet curing.
77

4.5.2

Concrete Material Testing

Standard compressive and split tensile strength tests were performed on 4’’x8’’ concrete
cylinders at ages of 3, 7, 14, 21, and 28 days. The cylinders were de-molded three days after
casting and placed in a curing room with a constant temperature of 72⁰F and constant relative
humidity of 80%. The cylinder strength testing is shown in Figure 61 and Figure 62. The
compressive and split tensile strength gain curves for each mix are shown below in Figure 63 to
Figure 65.
As shown in Figures Figure 63 to Figure 65, the compressive and split tensile strength values
were fairly consistent for all of the concrete mixes. The peak compressive strength at 28 days
was approximately 7,000 psi for all mixes, which was 2,500 psi higher than the design strength.
The modified Grade D mix had similar material strength characteristics to the standard mix.
Thus, the mix design modifications did not have an effect on the concrete strength. The concrete
strength data was used further to develop the concrete inelastic material properties in the
computational evaluation.

The rest of this page was left blank intentionally.

78

Figure 61. Concrete split tensile strength testing

Figure 62. Concrete compressive strength testing

79

7000
6000
5000
4000
3000
2000
1000
0
0

5

10

15
20
Time (days)

25

30

a) Compressive

Split Tensile Strength (psi)

Compressive Strength (psi)

8000

450
400
350
300
250
200
150
100
50
0
0

5

10
15
Time (days)
b) Split Tensile

Figure 63. Test units 1 and 2 (MDOT Grade D mix)

80

20

25

7000
6000
5000
4000
3000
2000
1000
0
0

5

10

15
20
Time (days)

25

30

a) Compressive

700
Split Tensile Strength (psi)

Compressive Strength (psi)

8000

600
500
400
300
200
100
0
0

5

10

15
20
Time (days)

b) Split Tensile
Figure 64. Test unit 3 (MDOT Grade D mix)

81

25

30

7000
6000
5000
4000
3000
2000
1000
0
0

5

10

15
20
Time (days)

25

30

a) Compressive

600
Split Tensile Strength (psi)

Compressive Strength (psi)

8000

500
400
300
200
100
0
0

5

10

15
20
Time (days)

b) Split Tensile
Figure 65. Test unit 4 (Modified MDOT Grade D mix)

82

25

30

4.5.3

Ambient temperature and relative humidity

The ambient temperature and relative humidity was monitored daily in the laboratory main
test bay and in the ring test room. The data was used for developing the shrinkage loading
characteristics in the computational evaluation. The temperatures and relative humidity for the
first set of test units are shown below in Figure 66 and Figure 67. The temperatures and relative
humidity for the second set of test units are shown in Figure 68 and Figure 69. Note that 100%
relative humidity was assumed during the time of wet curing.
As shown in Figures Figure 66 to Figure 69, the temperature and relative humidity remained
fairly consistent in both the main lab and the ring test room. A humidifier was placed in the ring
test room to try to maintain a consistent humidity of 50%. However, due to the heaters running
and the large size of the room, this was difficult to achieve. The temperature and humidity data
were used further to calculate the required equivalent shrinkage loads for the computational
evaluation.

The rest of this page was left blank intentionally.

83

0

5

10
Time (days)

15

20

a) Main Lab

72
70

Temperature (F)

Temperature (F)

80
78
76
74
72
70
68
66
64
62
60

68
66
64
62
60
0

5

10

15
20
Time (days)

25

b) Ring Test Room
Figure 66. Ambient temperature values, first set of tests

84

30

120
100

60
40
20
0
0

5

10
15
Time (days)

20

25

a) Main Lab

60
55
50
45
%RH

% RH

80

40
35
30
25
20
0

5

10

15
20
Time (days)

25

b) Ring Test Room
Figure 67. Relative humidity percentage, first set of tests

85

30

80

Temperature (F)

75
70
65
60
55
50
0

5

10
15
Time (days)

20

25

a) Main Lab

80

Temperature (F)

75
70
65
60
55
50
0

5

10
15
Time (days)

20

b) Ring Test Room
Figure 68. Ambient temperature values, second set of tests

86

25

120
100

60
40
20
0
0

5

10
15
Time (days)

20

25

a) Main Lab

120
100
80
%RH

%RH

80

60
40
20
0
0

5

10

15
20
Time (days)

25

b) Ring Test Room
Figure 69. Relative humidity percentage, second set of tests

87

30

4.5.4

Thermocouples

Thermocouples were positioned at the top and bottom mats of reinforcing steel, the beam top
flange, and the beam bottom flange. This allowed temperature profiles through the depth of the
test units to be measured. An ambient thermocouple was also positioned next to the test units to
monitor the temperature variation in the lab. The temperature in the deck for test units 1 and 2
are shown in Figure 70, while the lab ambient temperature is shown in Figure 71.
The concrete temperatures of the two test units remained consistent. This was expected, since
the two test units contained the same concrete mix. The maximum deck temperature was
reached about 24 hours after casting, and the hydration period ended at about three days. The lab
ambient temperature remained fairly consistent for the duration of the test. The drops shown
were times when the door was opened and the lab was allowed to cool. The initial increase in
temperature was due to the thermocouple being placed underneath the plastic that was covering
the two test units. After the hydration period, the concrete temperature was about the same as
the ambient temperature of the lab.
The temperature gradient through the depth of the test unit is shown in Figure 72. As shown in
this figure, the temperatures at the top and bottom mats of steel were very similar, the beam top
flange was slightly cooler, and the beam bottom flange was very close to the ambient
temperature.

88

120.0

Temperature (F)

100.0
80.0
60.0
40.0
20.0
0.0
0

2

4
6
Time (days)

8

10

a) Test Unit 1

120.0

Temperature (F)

100.0
80.0
60.0
40.0
20.0
0.0
0

2

4
6
Time (days)

8

10

b) Test Unit 2
Figure 70. Concrete deck temperatures at the bottom mat of reinforcing steel (test units 1 and 2)

89

Temperature (F)

120.0
100.0
80.0
60.0
40.0
20.0
0.0
0

2

4
6
Time (days)

8

10

Temperature (F)

Figure 71. Lab ambient temperature, first set of test units

140
120
100
80
60
40
20
0

Temperature
Gradient
Average
Ambient
0

5

10
15
20
Depth (inches)

25

Figure 72. Maximum temperature gradient through the depth of the test unit (test units 1 and 2)

90

The temperature in the deck for test units 3 and 4 are shown below in Figure 73, while the lab
ambient temperature is shown in Figure 74. During the test, the data acquisition system was
accidently disconnected, so some of the values shown are predictions for the missing data.

120
Temperature (F)

100
80

Actual data

60

Predicted values for
missing data

40
20
0
0

2

4

6

8

10

Time (days)
a) Test Unit 3

120

Temperature (F)

100
80
60

Predicted values for
missing data

40

Actual Data

20
0
3

5

7
Time (days)

9

b) Test Unit 4
Figure 73. Concrete deck temperatures at the bottom mat of reinforcing steel (test units 3 and 4)

91

80

Temperature (F)

70
60
Actual Data

50
40

Predicted values for
missing data

30
20
10
0
0

2

4
6
Time (days)

8

10

Figure 74. Lab ambient temperature, second set of test units

The concrete temperature maximum range for the two mixes was about the same, while the
hydration period for the slag mix (test unit 4) was slightly longer and the concrete remained at
the peak temperature longer. The initial set time in test unit 4 also took longer than in the first
three test units. The concrete temperature distribution was very similar between test unit 3 and
the first two test units, since they were made with the same concrete mix. The lab ambient
temperature remained fairly consistent throughout the test, except during the casting of test unit
4. The large temperature drop shown is when the door to the lab was left open during the casting
of test unit 4, allowing the lab to cool. After the hydration period, the concrete temperature was
about the same as the ambient temperature of the lab. The temperature gradient through the
depth of the test unit is shown below in Figure 75.

92

140
Temperature (F)

120
100

Temperature
Gradient

80
60

Average
Ambient

40
20
0
0

5

10
15
20
Depth (inches)

25

Figure 75. Maximum temperature gradient through the depth of the test unit (test units 3 and 4)

As seen in Figure 75, the maximum temperature distribution through the depth of the test
units was very similar to the distribution for the first two test units. The concrete temperature at
the top and bottom mats of steel were similar, followed by a slight decrease at the top flange, and
the bottom flange was consistent with the average ambient temperature. Overall, the temperature
distribution was consistent with expectations.

4.5.5

LVDT’s

The vertical displacements for all four test units are shown below in Figure 76 to Figure 78.
Note that negative values indicate downward movement, while positive values indicate upward
movement. Also note that the LVDTs were not positioned until after the concrete initial set, so
they do not show an initial downward deflection that would have occurred due to the concrete
self-weight.
93

Vertical Displacement (inches)

0.015
0.01
0.005
Slab 1
Slab 2
Slab 3
Slab 4

0
-0.005
-0.01
-0.015
0

5

10
Time (days)

15

20

Vertical Displacement (Inches)

Figure 76. Girder 1 mid-span displacement (L-G1-1/2)

0.02
0.015
0.01
0.005
0
-0.005
-0.01
-0.015
-0.02
-0.025
-0.03
-0.035

Slab 1
Slab 2
Slab 3
Slab 4
0

5

10
Time (days)

15

20

Figure 77. Mid-test unit displacement (L-1/2-1/2)

94

Vertical Displacement (inches)

0.015
0.01
0.005
0

Slab 1

-0.005

Slab 2

-0.01

Slab 3

-0.015

Slab 4

-0.02
-0.025
0

5

10
15
Time (days)

20

Figure 78. Mid-test unit quarter-span displacement (L-1/2-3/4)

At each LVDT location the test units underwent the same general behavior. The upward
displacement corresponds well with the concrete temperature values. The concrete expanded
due to the temperature rise during hydration, causing an upward displacement. There was then a
slight drop in the displacement due to the removal of the wooden forms. The displacements then
leveled off while the concrete surface remained covered during the seven-day wet cure. When
the burlap was removed, there was a sudden drop in the displacements due to immediate drying
of the concrete. The displacements then decreased steadily due to drying shrinkage effects.
4.5.6

Strain Gages

There were several errors in the strain gage data for the first two test units. Since the data was
taken continuously and the system was not reset during the test, the system became saturated and
skewed the data points after the first few days. For test units 3 and 4, the system was stopped
and reset daily, and the strain data turned out much better overall. Selected strain plots for test
95

units 3 and 4 are presented below. Please refer to reference [35] for the full data output. Note
that in the following plots, compressive strains are negative and tensile strains are positive.

Microstrains

Recall that the instrumentation naming scheme is presented in Figure 36 and Figure 37.

150
100
50
0
-50
-100
-150
-200
-250
-300
-350
-400

Slab 3
Slab 4

0

5

10
Time (days)

15

20

Figure 79. Top mat longitudinal rebar strains, middle of test unit (S-Tp-1/2-1/2-L)

400

Microstrains

200
0
-200
-400

Slab 3
Slab 4

-600
-800
0

5

10
Time (days)

15

20

Figure 80. Bottom mat longitudinal rebar strains, middle of test unit (S-Bt-1/2-1/2-L)
96

50
0

Microstrains

-50
-100
-150
Slab 3

-200

Slab 4

-250
-300
0

5

10
Time (days)

15

20

Figure 81. Top mat transverse rebar strains, middle of test unit (S-Tp-1/2-1/2-T)

600

Microstrains

400
200
0
-200
Slab 3
-400

Slab 4

-600
-800
0

5

10
Time (days)

15

20

Figure 82. Bottom mat transverse rebar strains, middle of test unit (S-Bt-1/2-1/2-T)

97

50

Microstrains

0
-50
-100
Test Unit 3

-150
-200
-250
0

5

10
Time (days)

15

20

Strains

Figure 83. Beam top flange, mid-span longitudinal strains (S-G1-Tf-M-G1-1/2-L)

60
50
40
30
20
10
0
-10
-20
-30

Slab 3
Slab 4

0

5

10
Time (days)

15

20

Figure 84. Beam mid-web longitudinal strains (S-G1-W-O-G1-1/2-L)

98

100

Microstrains

80
60
40

Slab 3

20

Slab 4

0
-20
0

5

10
Time (days)

15

20

Figure 85. Beam bottom flange, mid-span longitudinal strains (S-G1-Bf-M-G1-1/2-L)

The strain output behavior is summarized below:
•

Longitudinal Strains: All of the longitudinal strain gages showed a large spike in
compressive strain during the concrete hydration period, followed by a leveling off
during the remainder of the wet-cure period, then a steady increase in compressive strain
due to drying shrinkage.

•

Transverse Strains: The transverse strains exhibited similar overall behavior to the
longitudinal strains but were smaller in magnitude. This was expected, since the bar size
for the transverse steel was larger than the longitudinal steel.

•

Top Flange Strains: The beam top flange strains were very similar to the rebar strains,
and also smaller in magnitude.

•

Mid-Web Strains: In the web, there was a large increase in tensile strain due to the beam
expansion during hydration. The strains then leveled off to close to zero and remained
there for the remainder of the test.

•

Bottom Flange Strains: Like the web, in the bottom flange there was a large increase in
tensile strain due to beam expansion during hydration. The strains then leveled off,
followed by a steady increase in tensile strain during drying shrinkage.

99

To determine if the beams were bending inward or outward, longitudinal strain gages were
placed at the inside and outside of the bottom flange. The bottom flange inside and outside
strains for test unit 3 are shown below in Figure 86.

60
50

Microstrains

40
30
Bottom Flange
Inside

20
10

Bottom Flange
Outside

0
-10
-20
0

5

10
15
Time (days)

20

Figure 86. Beam bottom flange, mid-span longitudinal strain inside and outside comparison

As shown in Figure 86, the strains at the outside of the bottom flange remained slightly higher
than the strains at the inside of the bottom flange. This indicates that the bottom flange not only
experienced positive bending, but also bent slightly inward.
To determine the effect of using straight diaphragms verses cross-bracing, the diaphragm
strain data was compared. The strains on the outside front surface are compared below in Figure
87. It can be seen that both sets of diaphragms were in tension during the initial deck expansion
from hydration, then undergo compression due to concrete shrinkage. The strain values were for
each diaphragm, although the straight diaphragm had slightly larger strain magnitudes. The
100

cross-bracing diaphragms likely created slightly more restraint in the system than the straight
diaphragms.

80
60

Microstrains

40
20

Test Unit 3 (X-Bracing)

0
Test Unit 4 (Straight)

-20
-40
-60
-80

-100
0

2

4

6

8 10 12 14 16 18 20
Time (days)

Figure 87. Diaphragm strain data comparison

The maximum strain gradients through the depth of both test units were extracted at the midspan of Girder 1. They are presented below in Figure 88 and Figure 89. Note that tension is
plotted to the right (high) side of the x-axis.
As shown in Figures Figure 88 and Figure 89, both mats of reinforcing steel bent in
compression, while the beams deformed in positive bending, with compressive strains on top,
nearly zero strain in the web, and tensile strains on the bottom. The maximum strain gradient
was larger for test unit 4 than test unit 3, which was likely due to the smaller bar sizes that were
used.
101

-300

-200

Microstrains
-100

0

100

Depth through Beam/Slab
Assembly (inches)

0
5
10
15
20
25

Figure 88. Maximum Strain Gradient, Test unit 3

-400

-300

Microstrains
-200
-100
0

100

200

Depth through Beam/Slab
Assembly (inches)

0
5
10
15
20
25

Figure 89. Maximum Strain Gradient, Test unit 4 (tension plotted on the right)

102

4.5.7

Ring Test Crack Growth

The shrinkage rings were monitored daily for cracking. Once the presence of cracking was
detected, the cracks were measured and crack growth plots were developed. The crack growth
plots for Rings 1 to 4 (corresponding to the concrete used in Test units 1 and 2) are shown below
in Figure 90.

Crack Width (inches)

0.025
0.02
0.015

Ring 1 (7-day cure)

0.01

Ring 2 (7-day cure)
Ring 3 (7-day cure)

0.005

Ring 4 (24-hr cure)
0
0

20

40
60
Time (days)

80

Figure 90. Concrete ring crack growth, Rings 1 to 4 (Grade D Mix)

As expected, Ring 4 was the first ring to crack, since it only underwent moist curing for 24
hours. Rings 2 and 3 experienced a similar cracking trend for the first few days, while the crack
width for Ring 2 continued growing. Ring 1 did not crack until much later. In general, the rings
began to crack at around 15-20 days after casting. Each ring contained one vertical crack, which
kept growing as the rings continued to undergo shrinkage. An example ring crack is shown
below in Figure 91.

103

For test units 3 and 4, two rings were cast for each concrete mix and moist-cured for seven
days. Rings 7 and 8, the rings made with the modified Grade D mix did not crack. The rings
made with the standard Grade D mix began cracking at around 18 days, which was consistent
with the first set of rings. The crack growth plots for Rings 5 to 8 is shown below in Figure 92.

Crack Width (inches)

Figure 91. Ring test cracking (Ring 2)

0.01
0.009
0.008
0.007
0.006
0.005
0.004
0.003
0.002
0.001
0

Ring 5
(Standard Mix)
Ring 6
(Standard Mix)
Ring 7 (LowShrinkage Mix)
Ring 8 (LowShrinkage Mix)
0

10

20
30
Time (days)

40

Figure 92. Concrete ring crack growth, Rings 5 to 8

104

4.6

Data Analysis

Overall, the data matched what was expected for the testing. The data revealed the test units
initially expand due to the concrete heat of hydration and then leveled off while they remained
covered during wet curing. Once the wet burlap was removed, drying was initiated and the test
units steadily curled inward in a bowl-shaped pattern. The overall trends and analyses for each
type of instrument are presented below.

Variations in behavior due to different design

parameters at the sub-assembly level are presented in the computational analysis section.
4.6.1

Temperature

Overall, each test unit exhibited the same general temperature response. In the concrete, there
was a large increase in temperature during the first 24 hours of hydration, followed by a decrease
until the end of hydration at three days. The steel top flange temperature was slightly cooler than
the concrete, while the steel bottom flange temperature remained close to ambient. After the
hydration period, the concrete internal temperature was slightly warmer than the lab ambient
temperature.
All three test units made with the standard MDOT Grade D mix exhibited very similar
temperature trends, indicating consistency in the mix. The modified Grade D mix had a similar
temperature magnitude to the other mixes, but had a longer initial set time and remained at the
peak temperature longer.
4.6.2

Vertical Displacements

As expected, the overall deflection magnitudes were larger underneath the test unit than
underneath the steel beams, and were largest in the middle of the test unit. This behavior

105

matched the overall deflected “bowl-shaped” pattern of the beam/slab assembly due to concrete
shrinkage, with the largest displacement in the middle.
Overall, test units 2 and 4 exhibited very similar displacement trends, as well as test units 1
and 3. The high shear stud density in test unit 2 likely produced added restraint, thus limiting the
overall amount of displacement, and the low-shrinkage mix for test unit 4 also limited the
displacement.

Test units 1 and 3 had the same type of concrete, with different rebar

configurations and diaphragm types. From a deformation point of view, these design features do
not appear to have a large effect. Since test unit 2 had the smallest overall displacements, it can
be seen that increasing the shear stud density decreases the overall deformations.
4.6.3

Strains

Overall, the strain behavior was as expected and matched well with the deflection and
temperature data. All of the reinforcing steel strains remained in compression, which was
consistent with the expected “bowl-shaped” deformation of the test unit. The beams initially
showed a combination of positive bending (due to concrete self-weight) and expansion (due to
heat of hydration). After the hydration period was over, the beams continued to experience
positive bending, with compressive strain in the top flange, nearly zero strain in the web, and
tensile strain in the bottom flange. Based on the bottom flange strain gage data, the beams also
bent inward slightly. The overall strain magnitudes in test unit 4 were higher than in test unit 3.
This was slightly surprising, since test unit 4 had a lower-shrinkage concrete mix. However, test
unit 3 had a heavier reinforcement scheme, which may have caused lower values of strain. The
diaphragm strain values were similar for both types of diaphragms, although the cross-bracing
diaphragms likely created slightly more restraint than the straight diaphragms.
106

5

COMPUTATIONAL EVALUATION

Finite-element computer models were developed to simulate restrained concrete shrinkage in
jointless bridge systems. An approach was developed to simulate concrete shrinkage through
temperature loading. The approach was verified by comparing the experimental data to the
computer model data. The approach was then implemented for full bridge systems, and results
were compared for different bridge design features.
5.1

Modeling Approach

A method was developed for modeling and evaluating restrained concrete shrinkage through
finite-element analyses. The finite-element program ABAQUS was used for all computational
evaluations [37]. The method utilizes temperature loading on exposed concrete surfaces to
simulate free shrinkage strain. To develop the required temperature loading, the shrinkage strain
relationship given by ACI 209 was used [2]. This is a design code and is conservative by nature,
which would give shrinkage values on the higher end. This allows for a “worst-case” scenario to
be simulated. The free shrinkage strain at time

t is calculated using the relationship given by

ACI 209, as shown in Equation 5-1 below [2].
(5-1)

(ε sh )t = t * (ε sh )u
35+ t
In Equation 5-1,

(εsh)t is the free shrinkage strain, t is the time (in days), and (εsh)u is the

ultimate shrinkage strain. The ultimate shrinkage strain is based on a number of factors related
to relative humidity and mix design as shown in Equation 5-2 below.

(ε sh )u = 780 * λcp * λλ * λvs * λs * λΨ * λc * λα *10−6
107

(5-2)

In Equation 5-2,

λcp depends

on the number of days of moist curing,

λλ

depends on the

percentage of relative humidity, λvs depends on the volume/surface area ratio (in.), λs depends on
the slump (in.), λψ depends on the percentage of fine aggregate to total aggregate, λc depends on
the cement content (lb/yd3), and λa depends on the air content (%). Equations for each of these
parameters are listed below.
ߣ௖௣ ൌ 1.0 ݂‫ 7 ݎ݋‬െ ݀ܽ‫݁ݎݑܿ ݐݏ݅݋݉ ݕ‬

λλ =1.4−0.01*λ ,, for 40% ≤ λ ≤ 80%
3.0 −0.03*λ for 80% ≤ λ ≤ 100%

λvs = 1.2 * e

(5-3)
(5-4)

−0.12* v

s , where v

(5-5)

s

is volume to surface area (inches)

λs = 0.89 * 0.041* s , where s is the slump (in.)

(5-6)

0.3
for
λΨ =3.0+ 0.014*Ψ ,for λΨ ≤ 80%
>100 %
−0.03*Ψ ,

(5-7)

λc = 0.75 + 0.00036 * c, where c is the cement content ( lb
λα = 0.95 + 0.008 * α , where α is the air content (%)

yd

3)

(5-8)

(5-9)

Values for all these constants were calculated for each of the four laboratory test units, and
are listed below in Table 9.

108

Table 9. Shrinkage strain calculation constants
Constant
λcp
λλ
λvs
λs
λψ
λc
λa

Test units 1 and 2
(Standard Mix)
1.0
Varies, dependent on
humidity (see Figure 67)
1.114
1.075
0.874
0.987
0.986

Test Unit 3 (Standard
Mix)
1.0
Varies, depends on
humidity (see Figure 69)
1.114
1.064
0.874
0.987
1.002

Test Unit 4 (Modified
Mix)
1.0
Varies, depends on
humidity (see Figure 69)
1.114
1.064
0.874
0.916
1.002

After calculating the values shown in Table 9, the free shrinkage strain at time t, (εsh)t, was
determined. To apply this strain through temperature loading, Equation 5-1 was set equal to the
equation for free thermal expansion, as shown below in Equation 5-10.

(ε sh )t = α * T
In Equation 5-10,
(⁰F).

(5-10)

α is the coefficient of thermal expansion (1/⁰F) and T is the temperature

Finally, the temperature loading to be applied in the finite-element modeling was

determined by solving Equation 5-10 for T.
(ε )
T = − sh t

(5-11)

α

The temperature values calculated in Equation 5-11 were applied to exposed concrete
surfaces to simulate free shrinkage strain, while a temperature of zero degrees was applied to
restrained concrete surfaces.

The temperature values were applied using transient coupled

temperature-displacement loading in ABAQUS.

109

5.1.1

Free shrinkage model

To verify the approach in Equation 5-11, a simplified concrete block model was created and
simulated. The block model is shown below in Figure 93.

Figure 93. Concrete free shrinkage block overall model

Assuming a shrinkage strain ((εsh)t)of 100µ and concrete coefficient of thermal expansion
-6

(α) of 6.0*10 , the applied temperature loading was -16.67 ⁰F. This was applied to the outside
of the block on all surfaces. The strain values and deflected shape are shown below in Figure 94.

Figure 94. Free shrinkage model strains and deflected shape

As shown in Figure 94, the strain throughout the entire block was the assumed free shrinkage
strain of 100µ. Additionally, the stress throughout the block was zero since the block was
completely free to contract. This analysis indicated that the temperature equation (Equation 511) could be used to successfully simulate free shrinkage strain.
110

5.2

Computer Modeling Features

As previously stated, the finite-element program ABAQUS was used in all computational
evaluations [37].

Transient coupled temperature-displacement analysis was used to model

concrete shrinkage through temperature loading.

The analysis procedure allows for the

simultaneous solution of deformations with the changes in temperature. The system is solved by
using Newton’s method, as illustrated below in Equation 5-12 [38].

 Kuu
K
 θu

Kuθ
Kθθ

( ) ( )

 ∆u
Ru
 * ∆θ = Rθ


(5-12)

In Equation 5-12 above, ∆u and ∆θ are the corrections for incremental displacement and
temperature, Kxx are the stiffness values for the Jacobian matrix, and Ru and Rθ are the
mechanical and thermal vectors.
Different types of elements were used for the various parts in the models.

Reduced

integration was used for all analyses. The element types used for each part are summarized in
Table 10. Schematics and available degrees of freedom for each element type are illustrated in
Figure 95.
Table 10. Element types used in computational evaluation
Part

Element Type

ABAQUS Element
Designation

Number of Nodes
Per Element

Concrete Deck

3D ThermallyCoupled Solid Brick

C3D8T

8

Steel Beams & Diaphragms

2D Shell

S4R

4

Stay-in-place forms

2D Shell

S4R

4

Reinforcement

1D Truss

T3D2

2

Shear Connectors

1D Truss

T3D2

2

111

3

n2

1

i1
i5

2
n3

u3

n1

uR3

n4

uR1

i2

i4
i6 n6

u1

uR2

n5
i3

u2

n8

n7

ii) Nodal Degrees of Freedom

i) Element Nodes and Integration Points
a) C3D8T

u3

3

uR3

n2

1
2

uR1

n1
i1

n3

u1

uR2

n4

u2

i) Element Nodes and Integration Points

ii) Nodal Degrees of Freedom
b) S4R
u3

3

1

n2,i3

i1

n1,i1

2

u1

i) Element Nodes and Integration Points

ii) Nodal Degrees of Freedom
c) T3D2

Figure 95. Schematic representation of elements used [38]

112

5.3

Material Properties

Inelastic concrete behavior was implemented by using the ‘concrete damaged plasticity’
material model in ABAQUS [37]. The material is a plasticity-based damage model for concrete,
and is good to use for concrete in all types of structures under low confining pressures [38]. It
can be used in both plain and reinforced concrete models, although it is primarily used to model
reinforced concrete. It is able to model the irreversible damage that occurs when concrete cracks
through strain softening. While it does not introduce cracking directly at material integration
points, cracks can be visualized to occur in locations where the maximum principal plastic strain
outputs are larger than zero. To model the inelastic concrete behavior, it implements damaged
elasticity, along with tensile and compressive plasticity, and requires the input of uniaxial
concrete stress/strain curves in tension and compression.
The concrete stress-strain curves were generated by using the model proposed by Collins, et.
al. [13]. The compressive stress/strain equations are shown below in Equation 5-13 [13].

ε
fc
n
= c *
f 'c ε 'c (n − 1) + (ε c

(5-13)

ε 'c )

n*k

In Equation 5-13, fc is the compressive stress (psi),
the compressive strain (in/in),

ε’c is

f’c is the compressive strength (psi), εc is

the strain where fc reaches

f’c

(in/in), and

n

and

k

are

curve-fitting factors, as shown below in Equations 5-14 and 5-15. For εc/εc’>1,

k = 0.67 +
n = 0.8 +

(5-14)

f 'c
(psi)
9000

(5-15)

f 'c
(psi)
2500
113

The equation for ε’c is given as

ε 'c =

(5-16)

f 'c n
*
(in./in.)
Ec n−1

The concrete modulus of elasticity, Ec, was predicted using the ACI code.
(5-17)

Ec = 57,000 f 'c (psi)

The tensile stress-strain relation proposed by Vecchico and Collins [39] was used. The stressstrain behavior of the concrete in tension was assumed to be linear-elastic, with modulus Ec, up
to cracking. After cracking, the average tensile stress, including the effects of tension stiffening,
was defined by:

σc =

fcr
1+ 500*ε cr

(5-18)

(psi)

In Equation 5-18, σc is the concrete stress (psi), fcr is the concrete tensile strength (psi), and

εcr is the concrete strain after cracking.

The concrete tensile strength varies greatly, and several

different equations are proposed for calculating the tensile strength. For the computer modeling,
the following relationship in Equation 5-19 was used.
(5-19)

fcr = 7.5* f 'c

This relationship was used in lieu of actual strength data from the laboratory, due to the scatter in
the data output.
114

For the computer modeling, a concrete compressive strength of 7,000 psi was assumed for all
of the analyses, since all the concrete had a 28-day compressive strength of 7,000 psi or slightly
higher. The concrete stress/strain curves were generated using the method described above, and
are shown below in Figure 96. The “approximation” curves shown in Figure 96 were the values
inputted in ABAQUS since the simulations would not converge if all the values in the data sets

8000
7000
6000
5000
4000
3000
2000
1000
0

Compression
Curve
Approximation

0

0.0025
0.005
Strain (in/in)

0.0075

a) Compression

Stress (psi)

Stress (psi)

were inputted.

700
600
500
400
300
200
100
0

Tension Curve
Approximation

0

0.005
0.01
Strain (in/in)
b) Tension

Figure 96. Concrete damaged plasticity stress/strain curves

115

In addition to the concrete inelastic behavior, several elastic material properties were modeled
for both the concrete and the steel. Note that all steel was modeled as elastic. The material
properties for the steel and concrete are shown below in Table 11.

Table 11. Material properties used in the computer analyses
Material Property
Modulus of Elasticity E (psi)
Poisson’s Ratio ν
Mass density ρ (slugs/in3)
Coefficient of thermal expansion α (per ⁰F)
Thermal conductivity κ (Btu/in*hr*⁰F)

5.4

Concrete
4,768,962
0.2
0.00261
6.0 x 10-6
0.15

Steel
29,000,000
0.3
0.00881
6.5 x 10-6
2.5

Laboratory Models

Before implementing the loading approach to full bridge models (see Chapter 6), it had to
first be calibrated and validated. This was completed by comparing the computer model data to
the results obtained from the laboratory investigation. Models were created to simulate both the
ring test and the four test unit slabs.
5.4.1

Concrete Shrinkage Ring Test

A computer model was first created to simulate the shrinkage rings cast in the lab. Separate
parts were created for the concrete and steel rings, and the dimensions corresponded to those
shown in Figure 28. Both the concrete and steel were made of solid 3D elements, with six
elements through the depth of the concrete ring and five elements through the depth of the steel
ring. Friction interaction was implemented in the tangential direction between the concrete and
steel, with a friction coefficient of 0.45. “Hard” contact was used for the interaction between the
116

steel and concrete in the normal direction. Fixed boundary conditions were placed at the four
contact points where the bolts were located at the inner steel ring. The ring test assembly setup
is shown below in Figure 97

Figure 97. Concrete ring test assembly

A zero-degree boundary condition was implemented for the steel ring, as well as the inside,
top, and bottom surfaces of the concrete ring, since these drying was prevented from these
surfaces. The outside surface of the concrete ring had time-dependent tabular temperature values
applied, corresponding to the calculated ACI 209 free shrinkage strain values [2].

The

temperature values were calculated as described in Section 5.1.
Originally, the entire outside surface of the concrete ring had a uniform temperature
distribution applied. With this approach, instead of damage being concentrated in a specific
region of high stress, the entire ring would become damaged, since it has uniform material
properties and loading. Therefore, a material imperfection was created along a small strip in the
concrete ring. This was done to provide a stress concentration and produce cracking in a
117

specified region of damage. An arbitrary value of 8*10

-6

was chosen for the imperfection

region. This is illustrated below in Figure 98.

Figure 98. Material Imperfection Assignment

Temperature (F)

0
-10
-20
-30
-40
-50
-60
0

5

10
15
20
Time (days)

25

30

Figure 99. ACI 209 Temperature values (applied to outside surface of concrete ring) [2]

118

The calculated temperature values applied to the outside surface are shown in Figure 99. The
temperature values were applied as shown in Figure 100. The analysis was run for the entire
time period, and the plastic strains were monitored for cracking. According to the results,
cracking began at a temperature value of -45⁰F, corresponding to a time of 17 days. This was
very similar to the time for cracking in the actual laboratory models.

The plastic strain

magnitudes at that time are shown below in Figure 101.
The plastic strains through time in the region of imperfection were extracted and are shown in
Figure 102. The strains through time at the inside middle surface of the ring are shown in Figure
103. This is the same location where strain gages were placed for the ring test. Additionally, the
concrete ring strains in the location of damage were extracted and shown in Figure 104.

Figure 100. Temperature distribution through the rings

119

Figure 101. Concrete Ring plastic strain PE, Max Principal at time of 17 days

90
80

Microstrains

70
60
50
40
30
20
10
0
0

5

10

15
20
25
Time (Days)

30

35

Figure 102. Plastic strain magnitude outputs through for the region of damage

120

0

Microstrains

-50
-100
-150
-200
-250
-300
0

5

10

15
20
Time (days)

25

30

Figure 103. Steel ring strain output through time
10
0

Microstrains

-10
-20
-30
-40
-50
-60
-70
0

5

10

15
20
Time (Days)

25

30

35

Figure 104. Concrete ring strain output through time

121

As shown in Figure 102 to Figure 104, the steel ring compressive strains increased with time,
but did not experience a sudden drop, which would in reality happen when cracking occurs.
However, evaluation of the predicted concrete ring strains shows that softening does occur, and
that the strains drop after cracking occurs. The reason why the steel ring strains did not drop
may be due to the plastic strains not being full-depth, and the effect of a continuum-based plastic
assumption in the finite-element simulations.
The material imperfection approach was successfully able to concentrate the plastic strains in
one particular region where cracking would occur, instead of having evenly-distributed damage
throughout the entire ring. It can be seen that introducing random imperfections should be
considered in the full bridge parametric studies to produce accurate cracking distributions, and
prevent uniform damage from occurring throughout the entire model.
The time for cracking matched well with the experimental results and the steel ring strain
results matched the overall magnitude of the results from the lab. Overall the approach was
shown to be logical, and correctly implemented the concrete material properties and damage.

5.4.2

Lab Test Unit Test unit Models

Computer models were next created to simulate the test unit test units that were created in the
lab. Each model consisted of the same design and layout as the test units. The effect of different
design parameters at the sub-assembly level was examined, along with the validity of the overall
computer modeling approach. An overall view of the model is shown in Figure 105.

122

Figure 105. Lab test unit test unit models overall view

Tie constraints were used to simulate all welded connections. This included the connections
between the stiffener plates and beams, diaphragms and stiffener plates, metal forms and beam
top flanges, and the shear studs and beam top flanges. The reinforcing steel and shear studs were
embedded in the concrete using the ‘embedded region’ constraint option in ABAQUS. Friction
interaction was modeled between the steel and concrete parts with a friction coefficient of 0.45.
Since the effects of the concrete self-weight were not monitored during the laboratory testing,
self-weight loading was not included in the computational analyses. The pin bearings from the
experimental setup were simulated through boundary conditions along a path at the bottom
flanges of the beams, where rotation in the x-direction was allowed and all other degrees of
123

freedom were fixed. To simulate shrinkage, temperature loading was applied to the top and side
surfaces of the test units, while the bottom surface had a temperature of zero degrees. This
created a linear temperature distribution through the depth of the test units. The temperature

Shrinkage Temperature (degrees)

loading values that were applied are shown below in Figure 106.

0
-10
-20
-30
-40
-50
-60
-70
-80
-90

Slabs 1 and 2
Slab 3
Slab 4

0

5

10
15
20
Time (days)

25

30

Figure 106. Temperature loading values for lab test unit analyses

The overall deflected shape for the test unit models at the end of the analysis is shown in
Figure 107. Note the presence of the “bowl-shape” pattern which was discussed in Chapter 4.

124

2

3

1

Figure 107. Test Unit Models Overall Deflected Shape and Vertical Displacement [37]

To validate the computer modeling approach, the computational analysis results were
compared with the laboratory data. Selected comparison plots are shown in Figure 108 to Figure
117 (Refer to Figure 36 and Figure 37 for the instrumentation naming scheme.) As shown in the
noted figures, the computer model data corresponded to the laboratory data reasonably well. In
general, the computer model data slightly over-predicted the deflection outputs, while it slightly
under-predicted the strain data. Further discussion is provided in section 5.4.3.1.

125

Vertical Displacement (Inches)

Vertical Displacement (Inches)

0.01
0.005
0
-0.005
-0.01
-0.015
-0.02
-0.025
-0.03

Laboratory
Data
Computer Data

0

5

10
15
Time (days)

0.005
0
-0.005
-0.01
-0.015

-0.025
-0.03

20

Vertical Displacement (inches)

Vertical Displacement (inches)

5

0

5
10 15
Time (days)

20

b) Test Unit 2

Computer
Model Data
Experimental
Data
0

Laboratory
Data

-0.02

a) Test Unit 1
0.015
0.01
0.005
0
-0.005
-0.01
-0.015
-0.02
-0.025

Computer
Data

0.015
0.01
0.005
0
-0.005
-0.01
-0.015
-0.02
-0.025
-0.03

0
5
10
15
10
15
20
Time (days)
Time (days)
c) Test Unit 3
d) Test Unit 4
Figure 108. Beam mid-span deflection data comparison (L-G1-1/2)

126

Computer
Model Data
Experimental
Data
20

Laboratory
Data
5

10
15
Time (days)

20

Vertical Displacement (inches)

Computer
Data

0

0.01
0
-0.01
-0.02
-0.03
-0.04
-0.05
-0.06
-0.07

Computer
Model Data
Experimental
Data
0

Vertical Displacement (inches)

0.02
0.01
0
-0.01
-0.02
-0.03
-0.04
-0.05
-0.06

Computer
Data
Laboratory
Data
0

a) Test Unit 1

Vertical Displacement (inches)

Vertical Displacement (inches)

0.01
0
-0.01
-0.02
-0.03
-0.04
-0.05
-0.06
-0.07

5

10
15
Time (days)
b) Test Unit 2

0.02
0.01
0
-0.01
-0.02
-0.03
-0.04
-0.05
-0.06
-0.07

0
5
10
15
5
10
15
20
Time (days)
Time (days)
c) Test Unit 3
d) Test Unit 4
Figure 109. Mid-test unit deflection data comparison (L-1/2-1/2)
127

20

Computer
Model Data
Experimental
Data
20

Mictrostrains

Mictrostrains

200

50
0
-50
-100
-150
-200
-250
-300
-350

Computer
Model Data
Experimental
Data
0

5
10 15
Time (days)

100
0
-100

Computer
Model Data
Experimental
Data

-200
-300
-400
0

20

a) Test Unit 3

5
10
15
Time (days)

20

b) Test Unit 4

100
0
-100
-200
-300
-400
-500
-600
-700

400
Mictrostrains

Mictrostrains

Figure 110. Reinforcing Steel Top Mat Long. Strain Data Comparison (S-Tp-1/2-1/2-L)

Computer
Model Data
Experimental
Data
0

a) Test Unit 3

5

10
15
Time (days)

200
0
-200

Computer
Model Data
Experimental
Data

-400
-600
-800
0

20

5
10
15
Time (days)

20

b) Test Unit 4
Figure 111. Reinforcing Steel Bott. Mat Long. Strain Data Comparison (S-Bt-1/2-1/2-L)

128

Computer
Model Data

Mictrostrains

Mictrostrains

50
0
-50
-100
-150
-200
-250
-300

Experimental
Data
0

5
10
15
Time (days)

200
100
0
-100
-200
-300
-400

Computer
Model Data
Experimental
Data
0

20

a) Test Unit 3

5
10
15
Time (days)

20

b) Test Unit 4

1400
1200
1000
800
600
400
200
0
-200
-400

100
50

Computer
Model Data
Experimental
Data

Mictrostrains

Mictrostrains

Figure 112. Reinforcing Steel Top Mat Trans. Strain Data Comparison (S-Tp-G1-1/2-T)

0
-50
Computer
Model Data

-100
-150

Experimental
Data

-200
0

a) Test Unit 3

5
10 15
Time (days)

20

0

5
10
15
Time (days)
b) Test Unit 4

20

Figure 113. Reinforcing Steel Bott. Mat Trans. Strain Data Comparison (S-Bt-G1-1/2-T)
129

Computer
Model Data
Experimental
Data
0

5

10
15
Time (days)

Mictrostrains

Mictrostrains

200

50
0
-50
-100
-150
-200
-250

100
0
Computer
Model Data
Experimental
Data

-100
-200
-300

20

0

a) Test Unit 3

5
10 15
Time (days)

20

b) Test Unit 4
Figure 114. Beam Top Flange Strain Data Comparison (S-G1-Tf-M-G1-1/2-L)

60

20

40

0
-20

Computer
Model Data

-40

Experimental
Data

0

5

10
15
Time (days)

20

Mictrostrains

Mictrostrains

40

20
Computer
Model Data

0
-20

Experimental
Data

-40
0

a) Test Unit 3

5

10
15
Time (days)

b) Test Unit 4
Figure 115. Beam Mid-Web Strain Data Comparison (S-G1-W-O-G1-1/2-L)

130

20

150

Mictrostrains

Mictrostrains

150

100

100
50

Computer
Model Data
Experimental
Data

0
-50
0

5
10 15
Time (days)

50
Computer
Model Data

0
-50
0

20

a) Test Unit 3

5
10 15
Time (days)

20

Experimental
Data

b) Test Unit 4
Figure 116. Beam Bottom Flange Strain Data Comparison (S-Bf-M-G1-1/2-L)

Depth (inches)

5

Slab

10
15

-600
0

200

Computer
Model Data
Experimental
Data

Beam

20

5

Microstrains
-400 -200
0

200

Slab

10
15
Beam
20

b) Test Unit 4
Figure 117. Depth through beam/slab assembly slab strain data comparisons (time=20 days)
131

Computer
Model Data
Experimental
Data

25

25
a) Test Unit 3

Depth (inches)

-600
0

Microstrains
-400 -200
0

The computer model data for each test unit was also extracted to determine the relative
differences at the sub-assembly level. This is shown in selected results presented in Figure 118

Vertical displacement (Inches)

to Figure 126.

0
-0.005
-0.01
1-L-G1-1/2

-0.015

3-L-G1-1/2

-0.02

4-L-G1-1/2

-0.025

2-L-G1-1/2

-0.03
0

5

10 15 20
Time (days)

25

30

Vertical displacement (Inches)

Figure 118. Computer model data comparison, beam mid-span deflection (L-G1-1/2)

0
-0.01
-0.02
-0.03

1-L-G1-1/2

-0.04

3-L-G1-1/2

-0.05

4-L-G1-1/2
2-L-G1-1/2

-0.06
-0.07
0

5

10 15 20
Time (days)

25

30

Figure 119. Computer model data comparison, test unit mid-span deflection (L-1/2-1/2)

132

0

Microstrains

-50
-100

Test Unit 1
Test Unit 2

-150

Test Unit 3
-200

Test Unit 4

-250
0

5

10
15
20
Time (days)

25

30

Figure 120. Computer model data comparison, rebar top mat long. strains (S-Tp-1/2-1/2-L)

0
-20

Microstrains

-40
-60
Test Unit 1

-80

Test Unit 2

-100

Test Unit 3

-120

Test Unit 4

-140
-160
0

5

10

15
20
Time (days)

25

30

Figure 121. Computer model data comparison, rebar bott. mat long. strains (S-Bt-1/2-1/2-L)

133

0

Microstrains

-50
-100
-150

Test Unit 1

-200

Test Unit 2
Test Unit 3

-250

Test Unit 4
-300
-350
0

5

10
15
20
Time (days)

25

30

Figure 122. Computer model data comparison, rebar top mat trans. strains (S-Tp-1/2-1/2-T)

0

Microstrains

-20
-40
Test Unit 1

-60

Test Unit 2
Test Unit 3

-80

Test Unit 4
-100
-120
0

5

10

15
20
Time (days)

25

30

Figure 123. Computer model data comparison, rebar bott. mat trans. strains (S-Bt-1/2-1/2-T)

134

0
-20

Microstrains

-40
-60
-80

Test Unit 1

-100

Test Unit 2

-120

Test Unit 3

-140

Test Unit 4

-160
-180
0

5

10

15
20
Time (days)

25

30

Figure 124. Computer model data comparison, beam top flange strains (S-G1-Tf-M-1/2-L)

0

Microstrains

-1
-2
Test Unit 1

-3

Test Unit 2

-4

Test Unit 3

-5

Test Unit 4

-6
0

5

10

15
20
Time (days)

25

30

Figure 125. Computer model data comparison, beam mid-web strains (S-G1-W-O-1/2-L)

135

70

Microstrains

60
50
40

Test Unit 1

30

Test Unit 2

20

Test Unit 3

10

Test Unit 4

0
0

5

10
15
20
Time (days)

25

30

Figure 126. Computer model data comparison, beam bott. flange strains (S-G1-Bf-M-1/2-L)

The strains through the depth of the beam/test unit sections were also determined, and are
shown below in Figure 127. Compression is plotted to the left and tension is plotted to the right.

Depth Through Beam/Slab
Assembly (inches)

0
5
10
15
Test Unit 1

20

Test Unit 2
25
-400

Test Unit 3
-200

0

200

Test Unit 4

Microstrains
Figure 127. Longitudinal Strains through the depth of the beam/test unit section

136

5.4.3

Discussion

5.4.3.1 Validation of Computer Modeling Approach
As shown in Figure 108 to Figure 117, the computer model data correlated reasonably well
with the experimental data. In general, the computer model data slightly over-predicted the
deflection outputs, while it slightly under-predicted the strain data.
The computer modeling approach did not take into account the spike in strains and deflections
caused by the expansion of the concrete due to the heat of hydration. Instead, the model
assumed zero loading during the initial seven-day wet cure, followed by the temperature loads to
simulate drying shrinkage (see Figure 106). After the initial spike in strains and deflections due
to hydration most of the experimental data leveled off to around zero, followed by a steady
increase/decrease due to shrinkage. Overall the data had similar trends/slopes, but different
magnitudes. The difference in the magnitudes between the computer simulations and lab data
was likely due to assuming that strains and deflections were equal to zero after the hydration
period is over.

This behavior is especially prevalent in the results shown in Figure 110. The

data matches the best when the experimental readings dropped back to zero following the initial
spike due to hydration. This can be seen in Figure 112.
Overall, the computer model data matched reasonably well with the experimental data. The
data followed the same trends and were close to the same magnitude. The biggest discrepancy is
likely due to the absence of modeling concrete hydration, as this creates an initial jump in some
of the strain data. Other reasons for the discrepancy could have been due to small changes in the
lab ambient temperature not being taken into account, friction behavior at the pin supports, and
other areas where the computer modeling simplified actual experimental behavior. Despite the
137

discrepancies, the computer modeling approach was shown to be valid, and comparing to the
experimental data proved the approach and implementation was valid. Since the ring test and
test unit slab data matched with the experimental data, the computer modeling approach was
justified to be applied to the parametric study on full bridge models (See Chapter 6).
5.4.3.2 Effects of Design Parameters at the Sub-assembly level
While the overall trends and effects of design parameters at the sub-assembly level can be
evaluated using the lab shrinkage test unit models, their effect on the cracking potential for full
jointless bridges cannot be evaluated until the parametric study on the full bridge models.
In general, the reinforcing steel top and bottom mat strains were very similar for test units 1
and 2, and also test units 3 and 4. In general, the rebar strains in test units 1 and 2 were higher
than in test units 3 and 4. Test unit 3 most likely had lower strain values since it had a denser
reinforcement configuration, and test unit 4 most likely had lower strain values since it had a
lower-shrinkage concrete mix. It was expected that test units 1 and 2 would have similar strain
demands in the reinforcement since they had the same concrete mix and reinforcement
arrangement. For the strains in the beam top flange, test unit 2 had the lowest values. This was
likely due to the added restraint caused by the denser shear stud configuration. Test units 1 and 3
had similar top flange strain values, while test unit 4 had lower values due to the lower-shrinkage
mix. The strains in the web were nearly zero for all of the test units. For the bottom flange
strains, test unit 4 had the lowest values, while test unit 1 had the highest values. This was likely
because test unit 1 had the least amount of overall restraint with the regular Grade D mix, while
test unit 4 had the low-shrinkage mix.

138

Analysis of the strain data through the depth of the test units shows that both mats of steel
were in compression; while the beams behaved in positive bending, with compressive strains on
the top flange, nearly zero strains in the web, and tensile strains on the bottom flange. The
compressive strain in the reinforcing steel was due to the compression caused by the concrete
shrinkage as well as by the bending strain induced by the curling of the deck. A schematic of
this is illustrated in Figure 128 for test unit 1. Note that all the test units had a similar behavior.

Depth Through Beam/Slab
Assembly (inches)

0
5
Slab
10
15

Beam

20
25
-400

-200

0

200

Microstrains

Bending

Compression

Figure 128. Strain behavior through the depth of the slab

As shown in Figure 128, the strains through the depth of the slab are due to a combination of
bending and compression. It can be seen that most of the strains are compressive, caused by the
shrinkage of the concrete. The bending effect due to the curling of the deck has a much smaller
contribution. Overall, all test units behaved in a similar manner.
139

6

PARAMETRIC STUDY ON FULL BRIDGE MODELS

To evaluate the effect of bridge design factors on restraining concrete shrinkage and
producing cracking at the global level, a parametric study was performed on full bridge models.
Two bridges in lower central Michigan were studied: one concrete spread box beam bridge (M57 over US-127) and one steel girder bridge (Kensington Rd. over I-96). These bridges were
selected due to their similarity in size and layout, and due to the presence of transverse deck
cracking discovered in the field investigation. Elevation and cross-section views of both bridges
are shown below in Figure 129 and Figure 130. Details for each bridge are summarized below in
Table 12 and Table 13.

The rest of this page was left blank intentionally.

140

Table 12. Concrete spread box beam bridge properties [25]
Beam Type
Beam Spacing
Beam Support
Conditions
Number of Spans
Bridge Length
Bridge Width
Abutment Type
Skew Angle

60’’ Prestressed Concrete Box Beams
90’’ on center
Simply Supported on Elastomeric
Bearings
Four
322’-6’’
58’-8’’
Fully Integral, with piles oriented in
weak axis bending
Zero Degrees

322'-6''
37'-9'' Span 1

122'-3'' Span 2

122'-3'' Span 3

37'-9'' Span 4
20' Approach Slab

20' Approach Slab

Flexible Piles

Pier 1

Pier 2

Pier 3

Flexible Piles

a) Elevation

58'-8''

2'-10'' Barrier

9'' deck
60'' Box Beams Spa. @ 90'' on Center
b) Cross-section
Figure 129. Concrete spread box beam bridge (M-57 over US-127) elevation and cross-section
[25]

141

Table 13. Steel girder bridge properties [24]

39’’ Continuous Plate Girders
5’-5 1/2’’ on center
Rocker Bearings at abutments,
Fixed at the central pier
Two
260’-0’’
85’-11’’
Fully Integral, with rigid piles
oriented in strong axis bending
22 Degrees

Girder Type
Girder Spacing
Girder Support Conditions
Number of Spans
Bridge Length
Bridge Width
Abutment Type
Skew Angle

130'-0'' Span 1

20' Approach Slab

260'-0''

Exp

130'-0'' Span 2

Fix

20' Approach Slab
Exp
Rigid Piles

Rigid Piles

a) Elevation
85'-11''

2'-10'' Barrier

9'' deck
39'' Continuous Plate Girders Spa. @ 5'-5 1/2'' on Center

b) Cross-section
Figure 130. Steel beam bridge (Kensington Rd. over I-96) elevation and cross-section [24]

142

6.1

Parameters Considered

The full bridge finite element analyses were conducted with the program ABAQUS and the
cracking potential was determined for various design parameters.

The following design

parameters were investigated:
•

Reinforcement density/distribution

•

Shear connector density

•

Girder and diaphragm axial stiffness

•

Skew angle

•

Abutment Details (Integral vs. Non-Integral)

•

Concrete mix (standard D mix vs. modified D mix)

The parameters were studied by conducting the analysis cases listed in Table 14.

Table 14. Analyses run for full bridge parametric study
Bridge Type
Box Beam
Box Beam

Analysis Type
As-built
Different reinforcement
configuration

Box Beam
Box Beam

Denser reinforcement
configuration
Low-shrinkage

Steel Girder

As-built

Steel Girder

Shear connector spacing

Steel Girder

Abutment Detail

Steel Girder

Skew

143

Parameter Studied
Overall bridge performance
Effect of keeping same
reinforcement ratio, different
configuration
Effect of increasing the
reinforcement
Effect of using the lowshrinkage slag mix
Effect of girder and diaphragm
axial stiffness
Effect of changing the spacing
of shear connectors
Effect of changing abutment
connection from integral to
non-integral
Effect of changing the skew
angle

6.2

Loading method

6.2.1 Shrinkage loading
The loading method utilized to simulate concrete shrinkage was as described and validated in
Sections 5.1 and 5.2. Shrinkage was simulated through time-dependent negative temperature
loading applied to the exposed concrete surfaces. A uniform average relative humidity value
was assumed for the entire analysis process. The overall average was taken for humidity values
in the cities of Lansing and in Detroit for the months of May through October, during which deck
casting would most likely occur. Humidity values were obtained from the National Climactic
Data Center [27]. The average humidity calculated for the analyses was 71%. The other values
that were implemented to calculate the shrinkage loading are summarized below in Table 15.

Table 15. Values used to calculate shrinkage load temperatures
Parameter
Wet Cure Time
Percent Relative Humidity
Deck Volume/Surface Area
Barrier Wall Volume/Surface Area
Cement Content (Grade D Mix)

Value
7 days
71% (calculated average value for lower Michigan)
1.2 inches
5.7 inches
3
658 lb/yd

Cement Content (Low Shrinkage Mix)

461 lb/yd
4.5 inches
41%
6.5%

3

Slump
Fine Agg./Total Agg. Percentage
Air Content

Using the values from Table 15, (εsh)u (Equation 5-2) was calculated to be 514 microstrains
for the deck, and 299 microstrains for the barrier wall. These values varied slightly for the lowshrinkage mix. Plots of the temperature load applied for the deck and barrier walls in the full
144

bridge models are shown in Figure 131. Note that these values are different for the low
shrinkage mix.

0

Temperature (F)

-10
-20
-30

Bridge Deck Shrinkage
Barrier Wall Shrinkage

-40
-50
-60
0

10

20
30
Time (days)

40

50

Figure 131. Shrinkage load temperature values for bridge deck and barrier wall (standard mix)

6.2.2 Gravity/self-weight loading
Gravity loading and the effects of self-weight were ignored in the finite element simulations.
The reasoning behind this was because the camber of the beams and girders would account for
the deflections due to self-weight and bridge dead load.

Since early-age shrinkage is the

parameter of interest, the effects of traffic loading were neglected.

145

6.2.3 Pour sequencing
Pour sequencing is an important parameter affecting bridge deck performance, and was
included in the modeling. While the exact pour sequences vary for different bridge plans,
MDOT specifies that positive moment regions be cast 24 hours prior to negative moment regions
[26]. This is implemented to reduce the amount of negative moment that is induced by pouring
over the supports. Shrinkage will begin to occur in the region of the first pour one day prior to
shrinkage in the second pour, after the seven-day wet curing period. Therefore, pour sequencing
was implemented in the computer models using the ‘model change’ feature in ABAQUS [37].
The sections of the bridge deck were partitioned into different segments to account for the
different pour sequence regions. The elements associated with the second pour were then deactivated until one day after the first pour.
6.2.4 Concrete barrier walls
In Michigan, concrete barrier walls are typically cast immediately after the seven-day wet
cure for the decks [26]. At this time, the deck concrete has cured sufficiently and gained enough
strength to handle the load of the barrier walls. Like the deck, the walls are cast continuously,
with expansion provided at the two ends of the bridge. Since barrier walls are cast during the
early-age time region of interest, they were included in the modeling. To simplify the mesh, the
actual barrier wall cross section was simplified to a rectangular section, as shown below in
Figure 132. The same ‘model change’ feature was utilized to implement the barrier wall
elements after the initial seven-day wet cure [37]. Shrinkage was assumed to commence at a
time of three days, when the forms would be removed.

146

14''

9 13/16''
7''

34''

34''

13''
19''

b) Equivalent Dimensions used in
Computer Modeling

a) Original (per plan) Dimensions

Figure 132. Barrier wall equivalent rectangular cross section [24]

6.2.5 Concrete/soil friction at approach slabs
Since the approach slab is cast monolithically with the bridge for both the box beam bridge
and the steel girder bridge, the friction between the approach slab surface and approach fill has
an effect on the bridge restraint and needed to be accounted for in modeling. The connection
detail is shown in Figure 133.

Approach Slab

Bridge Deck

Reinforcement
Bottom Mat
(extends into
approach slab)

Abutment Wall

Figure 133. Typical approach slab connection with bridge deck [26]

147

The friction between the approach slab and soil backfill was implemented by using a series of
nonlinear springs at the bottom of the deck slab. The springs spaced at two-foot increments, and
were modeled using a nonlinear force-displacement response. The force-displacement behavior
was determined as follows.

Slab Weight = γ concrete * ( w * L * t )

(6-1)
3

In Equation 6-1, γ is the unit weight of concrete (taken to be 145 lb/ft ), w is the width of the
strip in consideration (taken to be 2 ft), and

t is the slab thickness (taken to be 0.75 ft).

The

friction force due to the weight of the slab is shown below in Equation 6-2.

F friction = µ *Slab Weight

(6-2)

In Equation 6-2, the coefficient of friction, µ, between the concrete and approach fill was
taken to be 0.6. Note that this relationship assumed that the soil was densely compacted for the
approach fill. Solving for equations 6-1 and 6-2, the friction force (Ffriction) for each 2’-wide
segment was calculated to be 2,610 lbs.
Once the friction force was determined the soil spring curve was able to be developed. A
non-linear force-displacement relationship was assumed, where the displacement was zero up to
the calculated friction force, after which nearly free deformation can occur. An arbitrary small
slope of 0.25 was assigned to the curve after the force exceeded the calculated friction force.
The developed spring curve for each 2 ft wide segment of the approach slab is shown below in
Figure 134.
Tabular values from the force-displacement response were applied to the bottom of the deck
slab by using the ‘connector builder’ feature in ABAQUS. CONN3D2 elements were applied at
148

various nodal locations, representing the center of each 2 ft wide strip. The force-displacement
response was activated for the global Z-direction (bridge longitudinal direction).

3000
2500

Force (lbs)

2000
1500
1000
500
0
0

0.25

0.5
0.75
1
Displacement (inches)

1.25

1.5

Figure 134. Approach slab friction force-displacement curve for each 2’-wide segment

6.2.6 Soil/structure interaction at the piles
Soil-structure interaction at the piles was modeled through nonlinear soil springs with varying
force-displacement responses for different depths. Piles were considered to be 50 ft deep as
stated in the bridge design plans [25]. The natural soil properties were assumed to vary from
‘loose’ to ‘dense’ below the abutments. The assumed soil characteristics for each type of soil
were obtained from the National Cooperative Highway Research Program design curves [28]
and are summarized below in Table 16.
149

Table 16. Assumed soil foundation properties [9][28]
Depth
0’ to 15’
15’ to 30’
30’ to 50’

Friction Angle
29 degrees
35 degrees
40 degrees

Density
110 pcf
125 pcf
140 pcf

From the assumed soil properties, nonlinear force-displacement responses could be developed
for varying depths through the soil. The p-y design curves recommended by the American
Petroleum Institute were utilized to model the soil behavior [4].

P = A * pu * tanh  k *H * y 
 A* pu




(6-3)

In Equation 6-3, P is the soil resistance force (lb), A is a factor to account for cyclic or static
loading (see equation 5-16), pu is the ultimate soil bearing capacity at various depths (lb/in.), k is
3

the initial modulus subgrade reaction (lb/in ), determined from Figure 6.8.7-1 in reference [4], y
is the lateral pile deflection (in.), and H is the depth below the surface (in.). The ultimate soil
bearing capacity, pu, varies for shallow depths verses deep depths. It is given as the smallest of

pus and pud, shown below in Equations 6-4 and 6-5.
pus = (C1* H + C 2 * D ) * γ * H

(6-4)

pud = C 3 * D * γ * H

(6-5)

In Equations 6-4 and 6-5, pus is the ultimate soil resistance (lb/in.) at shallow depths, pud is
the ultimate soil resistance (lb/in.) at deep depths, γ is the soil unit weight (lb/in ), H is the depth
3

(in.), D is the average pile diameter (in.), and C1, C2, and C3 are coefficients determined from

150

Figure 6.8.6-1 in reference [4]. The factor to account for cyclic or static loading, A, is given
below in Equation 6-6.

A=

(6-6)

0.9
for dynamic loading
H ≥ 0.9 for static loading
(3.0−0.8*
D

P-y design curves were developed at 2 ft incremental depths along the length of the piles.
The developed curves are shown below in Figure 135.

1200000

Force (lbs)

1000000
800000
600000
400000
200000
0
0

0.2
0.4
0.6
0.8
Pile Lateral Deflection (inches)

1

2
4
6
8
10
12
14
16
18
20
22
24
26
28

Figure 135. P-Y curves for soil/pile interaction

To determine the accuracy of the developed p-y design curves, the pile displacement results
for the as-built box beam model was compared to results obtained from reference [9]. In the
literature, various temperature values were monitored on a fully-integral bridge in the field, and
the pile displacement profiles were developed. The pile lateral displacements are compared in
Figure 136 and Figure 137.
151

Depth (Feet)

0
5
10
15
20
25
30
35
40
45
50
-0.02

0

0.02

0.04

0.06

0.08

0.1

Pile Lateral Displacement (Inches)
Figure 136. Pile lateral displacement values (as-built box beam model)

0

Depth (ft.)

5
10
15
20
25
30
-0.2

0

0.2

0.4

Deflection (inches)
Figure 137. Literature pile lateral displacement values (adapted from ref. [9])

152

As shown in Figures Figure 136 and Figure 137, the piles experience lateral displacement up
to a depth of around 10 feet, after which the piles bend in double curvature, followed by
remaining essentially rigid in the deeper soil strata. Since the pile behavior in the computational
analysis follows closely with literature values, and has a deflection profile as expected, it can be
seen that the p-y curves are correctly implemented.
6.2.7 Random load application for full bridge models
As described in Section 5.4.1, it was necessary to investigate a random load distribution for
correctly implementing stress concentrations and damage in the deck due to shrinkage loading.
With a uniform load application, it was expected that uniform plastic strains would be present
throughout the entire deck, and damage would not be concentrated in specified regions. To
apply random loading, a code was developed to randomly select half of the nodes in the sets
where temperature is applied. These randomly-selected nodes had time-dependent temperature
values of 1.5-times larger than the standard temperature according to the ACI 209 equations. It
was anticipated that this approach would concentrate stresses randomly throughout the entire
model, allowing for areas of restraint to dominate cracking behavior. To determine the accuracy
of this approach, it was only utilized for the “first pour” region. Selected output is given below
in Figure 138 to Figure 140.
As shown in Figure 139 and Figure 140, the approach did not produce the expected results. It
was thought that the random temperature loading would allow for stress concentrations and
cracking in the areas of restraint in the bridge. However, it can be seen that cracking occurs
randomly, at the same locations where the higher temperature values are applied. Instead of the

153

areas of restraint dominating the bridge behavior, the random locations where higher temperature
load is applied dominate the behavior.

Figure 138. Deck top temperature values for random load approach (box beam bridge) [37]

Figure 139. Deck max principal plastic strains with random load approach [37]

154

Figure 140. Deck max principal stresses with random load approach [37]

In order to correctly use a random load distribution, each element would have to have a
completely different temperature application. The temperatures would need to be applied such
that the overall collective average temperature of all the elements followed a normal distribution,
with the highest frequency matching the ACI 209 temperature equivalent values.

This is

illustrated below in Figure 141.
In the approach implemented, half of the elements followed the ACI 209 temperature
equivalent, while the other half had higher temperature values. Creating a random temperature
distribution that follows a normal bell-curve collectively for all the elements would be very
complicated, as each element would require its own set of time-dependent temperature values.
While this would be possible to implement, it may still produce incorrect results, and the same
155

random cracking patterns, and would also be time-consuming. Therefore, it was determined to
use the uniform temperature application to simulate shrinkage in the full bridge systems. While
the uniform application would not yield completely correct results, it could still be utilized for

Frequency

comparison-sake for different design parameters in the parametric evaluation.

ACI 209 Temperature Equivalent
Temperature
Figure 141. Correct random temperature distribution application for bridge slabs

6.3

Concrete Spread Box Beam Bridge

6.3.1 Parts and element types
A model was first developed for the “as-built” concrete spread box beam bridge (M-57 over
US-127). The model followed the geometry and design details specified in Figure 129 and Table
12. Separate parts were created for the deck, abutment, piles, box beams, deck reinforcement,
and piers. The element types utilized in the model are summarized below in Table 17. The

156

elements were meshed so that the global element size was 20’’. Overall views of the model are
shown in Figure 142.
Table 17. Element types utilized for concrete box beam bridge
Part

Element Type

ABAQUS Element
Designation

Mesh Size

Concrete Deck and

3D ThermallyCoupled Solid Brick

C3D8T

6 elements through
depth

Box Beams

3D ThermallyCoupled Solid Brick

C3D8T

1 element through
thickness, 3 elements
through the depth

Abutment

3D ThermallyCoupled Solid Brick

C3D8T

2 elements through
thickness, 6 elements
through height

Piles

2D Shell

S4R

25 elements through
height

Reinforcement

2D Shell, with
‘Rebar Layer’
Option

S4R

Global element size
of 20’’

Piers

1D Beam

B31

8 elements through
column height

Barrier Wall

157

a) Isometric view of meshed assembly

Y

X

b) End view (piles not shown)

Y

Z
c) Elevation view (piles not shown)
Figure 142. Concrete box beam bridge overall views

158

6.3.2 Concrete box beam equivalent section
In lieu of modeling the actual reinforcement in the concrete box beams, the beams were
modeled by using the equivalent stiffness of the concrete/steel composite beam. The calculation
for the equivalent stiffness involved calculating the transformed section modulus of elasticity and
moment of inertia, as outlined below.
(6-7)

A
A
Etransformed = ( c * Ec ) + ( s * Es )
Atot
Atot

In Equation 6-7, Etransformed is the modulus of the transformed section (psi), Ec is the
concrete modulus of elasticity (psi), Es is the steel modulus of elasticity (psi), Ac is the concrete
2

2

2

area (in. ), As is the steel area (in. ), and Atot is the total area (in. ).

Table 18. Concrete box beam transformed section moment of inertia calculation

n (Es/Ec)

A
2
(in. )

2)

n*A (in.

Top
6.080988 1.4 8.513382726
Steel
Bottom 6.080988 9.548 58.06127019
Steel
Conc.
1
1104
1104
Σ

-

-

1170.574653

2

depth
(in.)

d*n*A

Isection

ybar (in.)

ybar *n*A

3

25.54015

(in. )
0

-25.8571

5691.981

57

3309.492

0

28.14285

45985.69

30

33120

600768 -1.14285

1441.945

-

4

36455.03 600768

-

53119.62

The transformed section moment of inertia was calculated according to Equation 6-8 below.

Isec tion = ∑ I i + ∑ ( A * n * y bar 2 )

(6-8)

159

4

This yielded a calculated section moment of inertia of 653,888 in .

The beam side

thicknesses were changed to 4.5’’ (instead of 4’’ per plan), and the beam top and bottom
thicknesses were changed to 6.75’’ (instead of 6’’ per plan). This yielded a section moment of
4

inertia of 652,685 in , which is an error of only 0.18%.

6.3.3

Constraints, boundary conditions, and other model features

Surface-to-surface tie constraints were implemented to model the connection between the
bottom of the deck and the top of the abutment. Node-to-surface tie constraints were also used to
model the shear stirrups in lieu of actual embedded truss elements. The elastomeric bearings
were modeled using a multi-point-constraint (MPC) link. This allows for free translation in the
longitudinal direction, and creates rollers at the supports. Embedded region constraints were
implemented for the deck reinforcement rebar layers, the beam end embedment into the
abutment, and the pile top embedment into the abutment. The piles were oriented such that
bending occurs about their weak axis, as stated in the design plans. Connector sections were
implemented at locations spaced at 2 ft along the length of the piles to simulate nonlinear soil
response. The force-displacement response followed the developed p-y design curves shown in
Figure 135, and activated for the global Z-direction (bridge longitudinal direction). Fully-fixed
boundary conditions were applied at the bottom of the pier columns and the bottom of the piles.
Additionally, vertical displacements were restrained for the bottom of the abutment, since
abutment movement behaves mostly in translation [9][15][18].

160

6.3.4 Parametric evaluation features
The parametric evaluation for the concrete box beam bridge studied the effects of the lowshrinkage concrete mix and reinforcement arrangement. The design details for each parametric
study are summarized below in Table 19. The reinforcement arrangements are summarized in
Table 20. Deck reinforcement was implemented using the ‘rebar layer’ feature in ABAQUS.

Table 19. Concrete box beam parametric evaluation analyses details
Analysis

Shear Stirrup
Spacing
12’’

As-built

Reinforcement Redistribution

12’’

Reinforcement
Density

12’’

Low-Shrinkage Mix

Reinforcement
Detail
Detail 1
(see
Table 20)
Detail 2
(see
Table 20)
Detail 3
(see
Table 20)
Detail 1
(see
Table 20)

12’’

Concrete Mix

Standard D-mix

Standard D-mix

Standard D-mix

Low-shrinkage mix

Table 20. Concrete box beam reinforcement arrangements
Reinforcement

Top Mat

Top Mat

Bottom Mat

Bottom Mat

Detail

Transverse

Longitudinal

Transverse

Longitudinal

Detail 1

#5 Spa. @ 9’’

#3 Spa. @ 10’’

#5 Spa. @ 9’’

#5 Spa. @ 9’’

Detail 2 (increased

#6 Spa. @ 9’’

#4 Spa. @ 10’’

#6 Spa. @ 9’’

#6 Spa. @ 9’’

#6 Spa. @

#4 Spa. @ 18’’

#6 Spa. @

#6 Spa. @ 13’’

by 50%)
Detail 3 (same ρ)

12.75’’

12.75’’

161

6.4

Steel Girder Bridge

6.4.1 Parts and element types
A model was then developed for the steel girder bridge (Kensington Road over I-96). The asbuilt model followed the geometry and design details specified in Figure 130 and Table 13.
Separate parts were created for the deck, abutment, steel girders, deck reinforcement, and piers.
The element types utilized in the model are summarized below in Table 21. The elements were
meshed so that the global element size was 20’’. Overall views of the model are shown below in
Figure 143.

Table 21. Element types utilized for concrete steel girder bridge
Part

Element Type

ABAQUS Element
Designation

Mesh Size

Concrete Deck and

C3D8T

Barrier Wall

3D ThermallyCoupled Solid Brick

6 elements through
depth

Steel Girder

2D Shell

S4R

2 elements through
height and width

Diaphragms

2D Shell

S4R

1 element through
height and width

Abutment

3D ThermallyCoupled Solid Brick

C3D8T

2 elements through
thickness, 9 elements
through height

Reinforcement

2D Shell, with
‘Rebar Layer’
Option

S4R

Global element size
of 20’’

Piers

1D Beam

B31

8 elements through
column height

162

a) Isometric view of meshed assembly

Y

X

b) End view

Y

Z
c) Elevation view
Figure 143. Concrete box beam bridge overall views

163

6.4.2 Constraints, boundary conditions and other model features
Surface-to-surface tie constraints were implemented to model the connection between the
bottom of the deck and the top of the abutment. Node-to-surface tie constraints were also used to
model the shear studs at individual points in lieu of actual embedded beam elements (as used in
the laboratory test unit models). The rocker bearings were modeled using MPC link constraints.
This allows for free translation in the longitudinal direction, and creates pins at the supports. The
fixed bearings at the pier were modeled using MPC rigid constraints.

Embedded region

constraints were implemented for the deck reinforcement rebar layers and the girder end
embedment into the abutment. Fully-fixed boundary conditions were applied at the bottom of
the pier columns and at the bottom surface of the abutment footings. Since the piles for this
bridge are oriented in strong axis bending, it was assumed that the abutment footing would
remain fully fixed and that abutment translation would be restrained.
6.4.3

Parametric evaluation features

The parametric evaluation for the steel girder bridge studied the effects of the girder axial
stiffness and diaphragms, shear connector density, abutment type (integral vs. non-integral), and
skew angle. The design details for each parametric study are summarized below in Table 22.
Note that the Standard Grade D concrete mix was used for all steel girder bridge analyses.

164

Table 22. Steel girder parametric evaluation analyses details
Analysis

Shear Stud Spacing

Skew Angle

Abutment Type

As-built

6’’ in positive moment,

Zero Degrees

Integral

Zero Degrees

Integral

Zero Degrees

Non-integral

22 Degrees

Integral

2’ in negative moment
Shear Connector

12’’ in positive moment,

Density

2’ in negative moment

Abutment

6’’ in positive moment,

Configuration

2’ in negative moment

Skew Angle

6’’ in positive moment,
2’ in negative moment

In Table 22, “Integral” refers to the girder ends being embedded into the abutment, while
“Non-integral” refers to the girder ends not being embedded into the abutment.

This is

illustrated in Figure 2.
The deck reinforcement arrangement followed the arrangement specified in the bridge plans,
and was implemented using the ‘rebar layer’ feature.

The reinforcement configuration is

summarized below in Table 23.

Table 23. Steel girder bridge reinforcement arrangement
Top Longitudinal Top Transverse Bottom Longitudinal Bottom Transverse

#3 Bars

#5 Bars

#5 Bars

#5 Bars

Spa. @ 10’’

Spa. @ 8.5’’

Spa. @ 5’’

Spa. @ 8.5’’

165

6.5

Results

6.5.1 Box Beam Bridge Model Overall Results
The overall behavior of the box beam bridge was similar for each parametric analysis that was
simulated. The bridge deflected shape and vertical displacements for the as-built model are
shown below in Figure 144. It can be seen that the ends of the bridge move inward, while the
two central spans deflect in a “bowl-shaped” pattern.
To examine the cracking behavior for the deck, the maximum principal tensile stresses and
plastic strain outputs for the concrete deck at the end of the analysis were extracted and they are
shown in Figure 145 and Figure 146, respectively.
The overall behavior shown in Figure 144 to Figure 146 was similar for all parametric
analyses. Interestingly, although the deflected shape of the deck indicates positive bending in
Figure 144, the top of the deck shows the presence of tensile stresses, not the expected
compressive stresses.

This indicates that restraints within the bridge are inducing tensile

stresses, even though the bridge deflects in positive bending.
The regions of damage in the deck can be seen by examining the maximum principal plastic
strain output. As shown in Figure 146, most of the damage occurs on the top of the deck, while
the bottom of the deck experiences some damage at the piers. The highest levels of damage are
concentrated at the piers and the abutment, in the negative moment region.

Additionally,

damage can be seen in-between the piers, throughout the entire deck. As expected, the stresses
are higher in the regions over the beams and lower in-between the beams. The stresses are lower
in regions corresponding to higher plastic strains, indicating softening behavior.

166

a) Isometric View (deformation scale factor=500)

b) Elevation View (deformation scale factor=500)
Figure 144. Box beam as-built model deflected shape and vertical displacements (t=45 days)

167

a) Top of Deck

b) Bottom of Deck
Figure 145. Box beam as-built model maximum principal tensile stresses (t=45 days)

168

a) Top of Deck

b) Bottom of Deck
Figure 146. Box beam as-built model maximum principal plastic strains (t=45 days)

169

While the maximum principal tensile stress and plastic strain output is able to show overall
regions of damage, the directions of cracking cannot be determined. In order to determine the
cracking directions, the plastic strain outputs for the different components needed to be extracted
to derive the direction of the maximum principal plastic strains.

Cracking would occur

perpendicular to the direction of maximum principal plastic strains.

The plastic strain

component outputs at a time of 45 days are shown below in Figure 147 to Figure 150.
As shown in Figure 147 to Figure 150, the maximum principal plastic strains are mostly
influenced by the longitudinal (PE33) plastic strains in the positive moment regions, and are
mostly influenced by the transverse (PE11) plastic strains in the negative moment regions
(shown in Figure 147 and Figure 148). The vertical plastic strains (PE22) are nearly zero, and
therefore do not contribute heavily to the maximum principal plastic strains (shown in Figure
149). It can also be seen that shear strain (PE13) contributes in four corners of the bridge, by the
abutment (shown in Figure 150). The transverse restraint is highest at these locations, which
produces damage due to shear stresses.
Since cracking occurs perpendicular to the direction of plastic strain, it can be seen that
transverse cracking is predicted in the positive moment regions (since the plastic strain is mostly
in the longitudinal direction), and both longitudinal and transverse cracking occurs in the
negative moment regions, by the piers and the abutment (since the plastic strain is in both the
longitudinal and transverse direction). Additionally, the transverse plastic strain output (PE11)
predicts longitudinal cracking along the beams, across the entire length of the bridge. There is
also a concentration of shear cracking at the corners of the deck, near the abutment, as predicted
by the shear strain (PE13) output. These cracking patterns match well with the overall field
observations (see Section 3.4).
170

Figure 147. Box beam as-built model plastic strain global X-direction (1-1) output

Figure 148. Box beam as-built model plastic strain global Y-direction (2-2) output
171

Figure 149. Box beam as-built model plastic strain global Z-direction (3-3) output

Figure 150. Box beam as-built model plastic shear strain (1-3) output

172

To determine overall bridge behavior through time, the vertical displacements, maximum
principal stresses, and maximum principal strains were extracted along a longitudinal path in
along the middle of the bridge at various times. These outputs are shown below in Figure 151 to
Figure 153.
As shown in Figure 151, the overall vertical displacement profile remains the same for each
time step, while the magnitudes continue to increase.

This is expected since the overall

deflections increase as the amount of shrinkage increases. As indicated in Figure 152, the
maximum principal tensile stresses continuously grow with time up until the point of cracking,
when they decrease due to concrete softening. The tensile stresses are highest in the negative
moment regions at the piers and the abutments during the first part of the analysis, after which
the tensile stress becomes uniform due to cracking throughout the deck. As shown in Figure
153, the plastic strains remain zero up until the point of cracking, where they steadily continue to
grow. The negative moment regions over the piers and the abutments experience cracking
before the other regions, and have the highest overall plastic strain magnitudes.
To determine the presence of localization of damage and evenly-spaced transverse cracking,
the maximum principal plastic strain outputs were extracted in the positive moment region at the
end of the analysis. Jumps in the strain outputs would indicate presence of local cracking. The
output is shown in Figure 154, from which it can be seem that there is a steady increase in plastic
strains towards the central pier as expected due to negative moment demands. Transversely, the
jumps are spaced at 3 to 5 ft, which is consistent with the spacing of transverse cracks observed
in the field (see Section 3.4).
The development of maximum principal stresses and plastic strains in the deck through time
are shown with full contour plots in Figure 155 and Figure 156.
173

Vertical Displacement (Inches)

0.05
0
-0.05
-0.1
-0.15
-0.2
-0.25
-0.3
-0.35

Time
7 days
10 days
14 days
21 days
28 days
35 days
45 days
0

100

200

300

Longitudinal Distance (Feet)
Figure 151. Vertical displacement through time in bridge longitudinal direction

Max Principal Stress (psi)

700
Time
7 days

600
500

10 days

400

14 days

300

21 days

200

28 days
35 days

100

45 days

0
0

100

200

300

Longitudinal Distance (Feet)
Figure 152. Maximum principal tensile stresses through time in bridge longitudinal direction

174

300

Microstrain

250

Time
7 days
10 days
14 days
21 days
28 days
35 days
45 days

200
150
100
50
0
0

100

200

300

Longitudinal Distance (Feet)
Figure 153. Maximum principal plastic strains through time in bridge longitudinal direction

Microstrain

100
99
98
97
96
95
94
93
92
91
90
50

75

100

125

150

Longitudinal Distance (Feet)
Figure 154. Maximum principal plastic strain output in positive moment region (span 2)

175

b) Time=7 days

c) Time=10 days

d) Time=14 days

e) Time=21 days

f) Time=28 days

g) Time=35 days

h) Time=45 days

a) Legend

Figure 155. Development of maximum principal tensile stresses in full bridge deck

176

a) Legend

b) Time=7 days

d) Time=14 days

e) Time=21 days

g) Time=35 days

c) Time=10 days

h) Time=45 days

f) Time=28 days

Figure 156. Development of maximum principal plastic strains in full bridge deck

177

As shown in Figure 155 and Figure 156, the maximum principal tensile stresses and plastic
strains begin to grow in the negative moment regions near the beginning of the analysis, and then
continue to propagate through the deck. Transverse and longitudinal cracking begins over the
piers at around 14 days and then continues into the deck at 21 days.
The maximum principal stresses and plastic strains were also extracted along the longitudinal
direction at the bottom of the deck at the end of the analysis (time=45 days). The outputs are
shown in Figure 157 and Figure 158. It can be seen that that the regions over the piers and the
abutments show the highest levels of stress. The plastic strains are around zero through the
entire length of the bridge, except at the abutment connection. These areas show increased
damage, since they are areas of high restraint due to the deck connection with the abutment
backwall.
The maximum principal stresses, maximum principal strains, and deflections were also
extracted along the transverse direction midway between Pier 1 and Pier 2. The plots are shown
in Figure 159 to Figure 161.
As shown in Figure 159, the bridge deck displaces in a “bowl-shaped” pattern along the
transverse direction, with maximum displacement in the middle. As seen in Figure 160 and
Figure 161, the jumps in the plastic strain and tensile stresses at the two ends are likely due to the
restraint provided by the concrete barrier walls. Additionally, jumps can be seen in the plastic
strain plot through the width of the deck, indicating longitudinal cracking between beams.

178

800
Tensile Stress (psi)

700
600
500
400
300
200
100
0
0

100

200

300

Longitudinal Distance (Feet)
Figure 157. Maximum principal tensile stresses along longitudinal direction, bottom of deck

25

Microstrains

20
15
10
5
0
0

100

200

300

Longitudinal Distance (Feet)
Figure 158. Maximum principal plastic strains along longitudinal direction, bottom of deck

179

Vertical Displacement (Inches)

0
-0.05
-0.1
-0.15
-0.2
-0.25
-0.3
-0.35
0

10

20

30

40

50

60

Transverse Distance (Feet)

Max Principal Tensile Stresses (psi)

Figure 159. Vertical displacements along bridge transverse direction (time=45 days)

700
600
500
400
300
200
100
0
0

10

20

30

40

50

60

Transverse Distance (Feet)
Figure 160. Maximum principal tensile stresses along bridge transverse direction (t=45 days)

180

120
Microstrains

100
80
60
40
20
0
0

10

20

30

40

50

60

Transverse Distance (Feet)
Figure 161. Maximum principal plastic strains along bridge transverse direction (time=45 days)

6.5.2 Steel Girder Bridge Model Overall Results
The overall behavior of the steel girder bridge was also similar for each parametric analysis
that was simulated. The bridge deflected shape and vertical displacements for the as-built model
are shown in Figure 162. The two spans deflect in a similar “bow-shaped” pattern as the box
beam bridge. Since the abutments are more rigid due to the pile configuration, there is less
inward movement than in the box beam bridge. To examine the cracking behavior for the deck,
the maximum principal tensile stresses and plastic strain outputs at the end of the analysis were
extracted and are shown in Figure 163 and Figure 164, respectively.

181

a) Isometric View (deformation scale factor=500)

c) Elevation View (deformation scale factor=500)
Figure 162. Steel girder as-built model deflected shape and vertical displacements (t=45 days)

182

a)

Top of Deck

b) Bottom of Deck
Figure 163. Steel girder as-built model maximum principal tensile stresses (t=45 days)

183

a) Top of Deck

b) Bottom of Deck
Figure 164. Steel girder as-built model maximum principal plastic strains (t=45 days)
184

The overall behavior shown in Figure 162 to Figure 164 was similar for all parametric
analyses for the steel girder bridge. Like in the box beam bridge, although the deflected shape of
the deck indicates positive bending in Figure 162, deck shows the presence of tensile stresses,
not compressive stresses.
The regions of damage in the deck can be seen by examining the maximum principal plastic
strain output. As shown in Figure 164, almost all of the damage occurs on the top of the deck,
while the bottom of the only experiences damage at the corners by the connection with the
abutment. The highest levels of damage are concentrated at the pier and abutments in the
negative moment region. Additionally, some damage is being captured in-between the piers,
throughout the entire deck. The stresses are higher in the regions over the beams, and lower inbetween the beams. Regions where the plastic strains are higher correspond with lower stresses,
which indicate softening behavior.
As with the box beam bridge output, the plastic strains were extracted for each component to
derive the directions of the maximum principal tensile stresses and determine the directions for
cracking. The plastic strain component outputs at a time of 45 days are shown in Figure 165 to
Figure 168. The results in these figures show that the maximum principal plastic strains are
mostly influenced by the longitudinal (PE33) plastic strains in the positive moment regions and
over the pier, and are mostly influenced by the transverse (PE11) plastic strains in the regions
over the abutments. It can also be seen that shear plastic strain (PE13) contributes in four corners
of the bridge, by the abutment, as well as on the two edges of the bridge, by the pier.

185

Figure 165. Steel girder as-built model plastic strain global X-direction (1-1) output

Figure 166. Steel girder as-built model plastic strain global Y-direction (2-2) output
186

Figure 167. Steel girder as-built model plastic strain global Z-direction (3-3) output

Figure 168. Steel girder as-built model plastic shear strain (1-3) output
187

Since cracking occurs perpendicular to the direction of plastic strain, it can be seen that
transverse cracking is predicted in the positive moment regions and over the pier, and
longitudinal cracking is predicted over the abutments. The concentration of transverse cracking
is predicted to be highest over the pier. This matched the field observations of closer-spaced
cracking over the pier (see Section 3.4). Unlike the box beam bridge output, the steel bridge
simulation does not predict the presence of longitudinal cracking along the entire length of the
bridge, which is consistent with field observations. Shear cracking is concentrated at the corners
of the deck and near the edges of the piers, as predicted by the shear strain (PE13) output.
Cracking is concentrated in these regions due to the added transverse restraint provided by the
abutment and the pier. Overall, the cracking patterns are consistent with the field observations.
To determine overall bridge behavior through time, the vertical displacements, maximum
principal stresses, and maximum principal strains were extracted along a longitudinal path in
along the middle of the bridge at various times. These outputs are shown in Figure 169 to Figure
171. As shown in Figure 169, the overall vertical displacement profile remains the same for each
time step, while the magnitudes continue to increase. This is as expected, since the overall
deflections increase as the amount of shrinkage increases. From Figure 170 it can be seen that
the maximum principal tensile stresses grow with time up until the point of cracking, when they
decrease due to softening. Tensile stresses are highest in the negative moment regions at the pier
and the abutments during the first part of the analysis, after which they become uniform due to
cracking throughout the deck. Figure 171 shows that the plastic strains remain zero up until the
point of cracking, where they steadily continue to grow. The negative moment regions over the
pier and the abutments experience cracking before the other regions, and have the highest overall
plastic strain magnitudes.
188

Vertical Displacement (Inches)

0.05
0
Time
-0.05

7 days
10 days
14 days
21 days
28 days
35 days
45 days

-0.1
-0.15
-0.2
-0.25
-0.3
0

50

100

150

200

250

Longitudinal Distance (Feet)
Figure 169. Vertical displacement through time in bridge longitudinal direction

Max Principal Stress (psi)

700
600
Time
7 days
10 days
14 days
21 days
28 days
35 days
45 days

500
400
300
200
100
0
0

50

100

150

200

250

Longitudinal Distance (Feet)
Figure 170. Maximum principal tensile stresses through time in bridge longitudinal direction

189

Microstrain

180
160
140
120
100
80
60
40
20
0

7 days
Time
10 days
14 days
21 days
28 days
35 days
45 days
0

50

100

150

200

250

Longitudinal Distance (Feet)
Figure 171. Maximum principal plastic strains through time in bridge longitudinal direction

To determine the presence of localization of damage and evenly-spaced transverse cracking,
the maximum principal plastic strain outputs were extracted in the positive moment region at the
end of the analysis. Jumps in the strain outputs would indicate presence of local cracking. The
output is shown in Figure 172, where it can be seen that there is a steady increase in plastic strain
towards the pier, since that region has more restraint. There is not an obvious presence of jumps
in the strain data as there was for the box beam bridge output. Rather, the analysis is capturing
uniform damage throughout the entire deck instead of evenly-spaced localized areas of cracking.
The development of maximum principal stresses and plastic strains in the deck through time
are shown with full contour plots in Figure 173 and Figure 174.

190

Microstrain

100
99
98
97
96
95
94
93
92
91
90
30

40

50

60

70

Longitudinal Distance (Feet)
Figure 172. Maximum principal plastic strain output in positive moment region (span 2)

As shown in Figure 173 and Figure 174, the maximum principal tensile stresses and plastic
strains begin to grow in the negative moment regions near the beginning of the analysis, and then
propagate through the deck. At 14 days, the plastic strains originate as shear cracks at the
corners of the deck, by the abutment, and as transverse cracks in the negative moment region
over the pier. Longitudinal cracking then develops over the abutments, followed by transverse
cracking in the positive moment regions at 21 days. It can be seen that less localization of
damage is being captured in this model as the tensile stresses remain fairly uniform throughout
the deck.

191

a) Legend

b) Time=7 days

c) Time=10 days

d) Time=14 days

e) Time=21 days

f) Time=28 days

g) Time=35 days

h) Time=45 days

Figure 173. Development of maximum principal tensile stresses in full bridge deck

192

a) Legend

b) Time=7 days

d) Time=14 days

e) Time=21 days

g) Time=35 days

h) Time=45 days

Figure 174. Development of maximum principal plastic strains in full bridge deck

193

c) Time=10 days

f) Time=28 days

The maximum principal stresses were also extracted along the longitudinal direction at the
bottom of the deck at the end of the analysis (time=45 days), as shown below in Figure 175. The
regions over the piers abutments show the highest levels of stress due to the high restraint present
in these regions. The plastic strains were zero along the bottom middle of the deck, indicating
that cracking did not occur on the bottom surface.
The maximum principal stresses, maximum principal strains, and deflections were also
extracted along the transverse direction, midway between Abutment A and Pier 1. The plots are
shown below in Figure 176 to Figure 178.
As shown in Figure 176, the bridge deck displaces in a “bowl-shaped” pattern along the
transverse direction with maximum displacement in the middle. As seen in Figure 177 and
Figure 178, the jumps in the plastic strain and tensile stresses through the width of the deck are
likely due to the restraint provided by the girders and diaphragms. The overall stiffness of the
steel girder bridge is increased due to the presence of diaphragms.

194

Tensile Stress (psi)

450
400
350
300
250
200
150
100
50
0
0

50

100

150

200

250

Longitudinal Distance (Feet)
Figure 175. Maximum principal tensile stresses along longitudinal direction, bottom of deck

Vertical Displacement (Inches)

0.15
0.1
0.05
0
-0.05
-0.1
-0.15
-0.2
-0.25
-0.3
0

20

40

60

80

Transverse Distance (Feet)
Figure 176. Vertical displacements along bridge transverse direction (time=45 days)

195

Max Principal Tensile Stresses (psi)

700
650
600
550
500
450
400
0

20

40

60

80

Transverse Distance (Feet)
Figure 177. Maximum principal tensile stresses along bridge transverse direction (t=45 days)

Figure 178. Maximum principal plastic strains along bridge transverse direction (time=45 days)
196

6.5.3 Concrete box beam bridge parametric study comparison results
As stated previously, the overall global behavior of the bridge was the same for all the box
beam bridge parametric analyses. To compare the outputs, maximum principal tensile stresses,
maximum principal plastic strains, and vertical displacements were extracted at various locations
and paths in the bridge deck. The nomenclature used in the results is summarized in Table 24.

Table 24. Nomenclature used for box beam parametric study results
Parameter

Nomenclature used in plots of results

As-built model

“As-built”

Effect of using low-shrinkage slag mix

“Low-Shrinkage”

Effect of increasing the reinforcement

“Rebar Denser”

Effect of keeping the same reinforcement ratio

“Rebar Re-Distribution”

with different configuration

Figure 179 and Figure 180 show that the tensile stresses are higher near the top of the deck,
and decrease through the depth. The plastic strains penetrate roughly halfway through the depth
of the deck. Re-configuring the reinforcement arrangement had no effect on the stresses or
plastic strains, while increasing the density produced slightly higher stresses and plastic strains.
The lower-shrinkage mix had lower stress and strain values overall.
Results in Figure 181 and Figure 182 show that the maximum principal tensile stresses are
high at the top of the deck and then drop off significantly and remain fairly constant in the
beams. As it was the case in-between beams, the plastic strains penetrate to about halfway
through the depth of the deck. The stresses were slightly higher for the denser reinforcement
configuration, while the plastic strains were lower for the lower-shrinkage mix.
197

Depth Through Slab (Inches)

0
1
2
3
4
5
6
7
8
9
10

Rebar Denser
Low-Shrinkage
As-Built

0

200

400
600
800
Tensile Stress (psi)

Depth Through Slab (Inches)

Figure 179. Max principal tensile stresses through the depth of the slab, between beams (t=45)

0
1
2
3
4
5
6
7
8
9
10

Rebar Denser
Low-Shrinkage
As-Built

0

20

40
60
80
Microstrains

100

Figure 180. Max principal plastic strains through the depth of the slab, between beams (t=45)

198

Depth Through Beam/Slab (Inches)

0
10
20
30
40
50
60
70
80
90
100

As-Built
Low-Shrinkage
Rebar ReDistribution
Rebar Denser
0

200

400

600

Tensile Stress (psi)
Figure 181. Max principal tensile stresses through depth of beam/slab assembly (t=45)

Depth Through Slab (Inches)

0
1
2
3

As-Built

4
Low-Shrinkage

5
6

Rebar ReDistribution
Rebar Denser

7
8
9

10
0

20

40
60
80
Microstrains

100

Figure 182. Max principal plastic strains through depth of slab, over beams (t=45)
199

Vertical Displacement (Inches)

-0.25
Rebar Denser

-0.26
-0.27

Rebar
Re-Distribution
Low Shrinkage

-0.28
-0.29
-0.3

As-Built

-0.31
-0.32
50

70

90

110

130

150

Longitudinal Distance (Feet)
Figure 183. Vertical displacements along the longitudinal direction, span 2 (t=45 days)

Tensile Stress (psi)

569
567
563

Rebar ReDistribution
Rebar Denser

561

Low Shrinkage

565

559
As-Built

557
555
50

70

90

110

130

150

Longitudinal Distance (Feet)
Figure 184. Max principal stresses along the longitudinal direction, span 2 (t=45 days)

200

Vertical Displacement (Inches)

direction,
Figure 185. Max principal plastic strains along the longitudinal direction, span 2 (t=45 days)

-0.28
-0.285

Rebar ReDistribution
Rebar Denser

-0.29
-0.295

Low-Shrinkage

-0.3
-0.305

As-Built

-0.31
20

25

30

35

40

Transverse Distance (Feet)
Figure 186. Vertical displacements along the transverse dir
direction (t=45 days)

201

Max Principal Tensile Stresses (psi)

620
Rebar ReDistribution

610
600

Rebar Denser

590
Low-Shrinkage

580
570

As-Built

560
20

25

30

35

40

Transverse Distance (Feet)
Figure 187. Max principal stresses along the transverse direction (t=45 days)

100

Microstrains

95
90

Rebar ReDistribution
Rebar Denser

85
80

Low-Shrinkage

75
70

As-Built

65
20

25

30

35

40

Transverse Distance (Feet)
Figure 188. Max principal plastic strains along the transverse direction (t=45 days)

202

As shown in Figure 183 to Figure 188 above, reconfiguring the reinforcement had no effect
on the vertical displacements, maximum principal stresses, or maximum principal plastic strains.
The low-shrinkage mix had the lowest plastic strain values and the highest maximum principal
stress values, which indicates the least amount of damage.

The denser reinforcement

configuration produced higher plastic strain values and lower stress values, indicating slightly
more damage. The vertical displacements were lowest for the low-shrinkage mix, since induced
loads are smaller.

The denser reinforcement configuration also yielded slightly lower

displacement values, due to the added restraint caused by the reinforcement.
Outputs through time on the top surface of the deck in the middle of span 2 are shown in
Figure 189. It can be seen that there is initial deformation at beginning of shrinkage, followed by
a steady increase as shrinkage continues. This trend matches the behavior seen in the laboratory
models (see Section 4.6). Overall, the as-built model has the highest displacement values, while
the low-shrinkage mix has the lowest displacement values. Adding more reinforcement created
additional restraint in the slabs, which also lowered the displacement values.
As shown in Figure 190, the maximum principal tensile stresses steadily grow until the
concrete tensile strength is reached. At that point cracking occurs, and the stresses steadily
decrease due to softening. Results in Figure 191, the decrease in stress matches the increase in
plastic strains, as the cracks continue to open.

203

Vertical Displacement (Inches)

0
-0.05
Rebar ReDistribution

-0.1
-0.15

Rebar Denser

-0.2

Low-Shrinkage

-0.25
As-Built
-0.3
-0.35
0

10

20
30
Time (days)

40

Figure 189. Vertical displacements through time, between beams, span 2

Tensile Stress (psi)

600
500

Rebar ReDistribution
Rebar Denser

400
300
200

Low-Shrinkage

100

As-Built

0
0

10

20
30
Time (days)

40

Figure 190. Max principal stresses through time, between beams, span 2

204

Microstrains

100
90
80
70
60
50
40
30
20
10
0

Rebar ReDistribution
Rebar Denser
Low-Shrinkage
As-Built
0

10

20
30
Time (days)

40

Figure 191. Max principal plastic strains through time, between beams, span 2

The overall results of the parametric study for the box beam bridges are shown below in
Table 25. Note that “time for cracking” is taken as the time for plastic strains to first begin to
appear in the deck. This location was over the central pier.
Table 25. Box beam bridge parametric study overall results
Analysis

Time for

Maximum Plastic

Maximum

cracking

Strain Value

Vertical
Displacement

As-Built

13 days

281 µ-strain

-0.308 inches

Low-Shrinkage

16 days

249 µ-strain

-0.293 inches

Denser Rebar

12 days

284 µ-strain

-0.305 inches

Rebar Re-

13 days

281 µ-strain

-0.308 inches

Distribution

205

Overall, the bridge with the low-shrinkage mix exhibited the best behavior. It had the lowest
value of plastic strains at the end of the analysis as well as the latest time for cracking to occur.
Re-distributing the deck reinforcement did not have a large effect on the bridge overall behavior.
This is likely due to the way reinforcement was modeled in the simulation. The ‘rebar layer’
option in ABAQUS uses the reinforcement information to modify the overall stiffness of the
section, rather than implementing discrete reinforcement locations. Since the re-distribution of
the reinforcement kept the same reinforcement ratio, the overall deck stiffness remained the same
as in the as-built model, thus not having a large effect on the behavior.
6.5.3.1 Effect of Increasing Deck Reinforcement
Increasing the amount of reinforcement by 50% created more restraint in the bridge deck,
which lowered the time for cracking and increased the maximum plastic strain value at the end of
the analysis. While this effect was very minimal, the results conflict with the conventional
wisdom for the effects of adding reinforcing steel. It would be expected that increasing the
reinforcement in the deck would allow for more stresses to be accommodated by the steel, and
thus produce less cracking. However, the full bridge analyses show the opposite effect.
To investigate the effect of reinforcing steel on concrete shrinkage cracking, small fixed
“prism” models were created in ABAQUS. The models were fully fixed at both ends, with
uniform shrinkage temperature applied to the outside surfaces. The temperature followed the
same temperature loading used for the ring test models, as shown in Figure 99. A schematic of
the model is shown below in Figure 192.

206

1’’
10’’

Single
Embedded Bar

Figure 192. Prism model setup for investigating effect of reinforcement

As shown in Figure 192, the effect of reinforcement was investigated by means of a single
embedded bar in the middle of the prism.

The analyses included a plain prism with no

reinforcement, an embedded #3 bar, and an embedded #8 bar. Maximum principal plastic strain
outputs for each analysis are shown below in Figure 193 to Figure 195.
As shown above in Figure 193 to Figure 195, plastic strains begin to appear through the entire
prism at a time of 13.5 days for all three models. This corresponded to a shrinkage strain of
175µ-strain, and a temperature value of -30⁰F. The plastic remain uniform until a time of 23
days, after which high values and concentrations can be seen evenly-spaced through the length of
the prism. When comparing the results at the end of the analysis, it can be seen that increasing
the bar size produces slightly lower plastic strain values at a closer spacing.

207

a) Time=30 days (end of analysis)

b) T=13.5 days (plastic strains begin to appear)
Figure 193. Maximum principal plastic strain output, unreinforced prism

208

a) Time=30 days (end of analysis)

b) T=13.5 days (plastic strains begin to appear)
Figure 194. Maximum principal plastic strain output, #3 embedded bar

209

a) Time=27 days (end of analysis)

b) T=13.5 days (plastic strains begin to appear)
Figure 195. Maximum principal plastic strain output, #8 embedded bar

210

To further determine the effects of increasing the bar size, plots through time were extracted
for the maximum principal plastic strain and stress values. The stresses through time at the
outside middle point of the prism are shown below in Figure 196.

700
600

Stress (psi)

500
400
#3 Bar
300

#8 Bar

200

No Reinforcement

100
0
0

5

10
15
20
Time (days)

25

30

Figure 196. Development of stresses with time in prism

As shown in Figure 196, the most concrete softening occurred in the unreinforced model,
which is indicated by the largest drop in stress. The prism with the #3 bar experienced slightly
more softening than the prism with the #8 bar. Plastic strains were extracted along a longitudinal
path on the outside edge of the prism at different times to determine the development of
cracking, as shown in Figure 197 and Figure 198.

211

T=7 days
T=13.5 days
T=18 days
T=22 days
T=26 days
T=30 days
0

2
4
6
8
Longitudinal Distance (Inches)

10

Figure 197. Prism with #3 reinforcement plastic strain output at various times

600
Plastic Strains (Microstrains)

Plastic Strains (Microstrains)

1800
1600
1400
1200
1000
800
600
400
200
0

500
T=7 days

400

T=13.5 days

300

T=18 days

200

T=22 days
T=26 days

100

T=30 days
0
0

2
4
6
8
Longitudinal Distance (Inches)

10

Figure 198. Prism with #8 reinforcement plastic strain output at various times

212

As seen above in Figure 197 and Figure 198, the prism with the #3 reinforcement had higher
plastic strain values, with less cracking locations. The prism with the #8 reinforcement had more
cracking locations but lower plastic strain values than the prism with the #3 reinforcement. This
behavior matches what is expected. If the bar size is increased, it would be expected that the
crack widths would decrease, but the number of cracks would increase; which is seen in the
plots. Comparing the plastic strains at the concentrated areas of cracking, the larger plastic strain
values in the model with the #3 bar can be seen; which is illustrated below in Figure 199.

Plastic Strain (Microstrain)

2500
2000
1500
#3 Bar
1000
#8 Bar
500
0
0

5

10
15
20
Time (Days)

25

30

Figure 199. Prism plastic strain values with time in concentrated cracking areas

213

The longitudinal stresses through time in the bars were also extracted. It would be expected
that the #8 bar would have lower stress values due to its increased area. The bar stress output is
shown below in Figure 200.

800
700

Stress (psi)

600
500
400

#3 Bar

300

#8 Bar

200
100
0
0

10

20

30

Time (days)
Figure 200. Prism reinforcing bar longitudinal stresses with time

Based on these analyses, it can be seen that the modeling approach is correct in terms of load
sharing between the steel and the concrete. It was expected that for a larger the bar size, the the
stresses in the bar would be lower, the crack width would decrease, and the distance between
cracks would tighten, all of which was captured by the simulation.
To investigate this issue further, the same prism models were run with a shell element and
‘rebar layer’ approach used to simulate the steel reinforcement. This was done since the ‘rebar
layer’ approach was used in the full bridge models. The maximum principal plastic strain
outputs at the end of the analysis are shown below in Figure 201 and Figure 202.
214

Figure 201. #3 prism with ‘rebar layer’ approach maximum principal plastic strains (t=30 days)

Figure 202. #8 prism with ‘rebar layer’ approach maximum principal plastic strains (t=30 days)
215

As seen in Figure 201 and Figure 202, using the rebar layer approach yields a slightly
different plastic strain output. Since the rebar layer uses a smeared reinforcement approach,
where the reinforcement stiffness is spread across the entire shell section, the plastic strain values
become concentrated at the location where the reinforcement is embedded. Even with this
approach, it can still be seen that increasing the reinforcement bar size yields lower plastic strain
values and more cracking locations. To verify this, the plastic strains along the top edge of the
prism were extracted at the end of the analysis and compared, as shown below in Figure 203.

Plastic Strains (Microstrains)

600
500
400
300

#3 Rebar Layer
#8 Rebar Layer

200
100
0
0

2
4
6
8
Longitudinal Distance (Inches)

10

Figure 203. Plastic strains along longitudinal path for prisms with rebar layer approach (t=30)

As seen above in Figure 203, the plastic strain values are higher for the prism with the #3
rebar layer than the prism with the #8 rebar layer, which was expected. Although it is not as
obvious as in the approach using the discrete embedded bar, it can be seen that the prism with the
#8 rebar layer has more cracking locations with lower overall plastic strain values.
216

In the full bridge models, the increase in plastic strain magnitudes that is seen with the
increase in reinforcement can be attributed to the increased stiffness of the deck/girder system.
In the full bridge deck, the girders create additional restraint, which produces higher plastic strain
values with an increase in deck stiffness. The plastic strains are developed as a result of the
restrained volume change from shrinkage. In a real bridge deck, an increase in the reinforcement
would lead to more discrete cracking locations, and lower overall crack widths. However, the
computational analysis uses a continuum model with strain/deformation control. When the
stresses are high enough to induce plastic strains, cracking occurs throughout the entire model
and the analysis does not capture discrete crack locations. Therefore, while the models predict
increased plastic strain values with added reinforcement, the crack widths and spacing would in
reality be reduced with added reinforcement.
6.5.4 Steel girder bridge parametric study comparison results
As with the box beam bridge, the overall global behavior of the steel girder bridge remained
the same for all the parametric analyses. To compare the outputs, maximum principal tensile
stresses, maximum principal plastic strains, and vertical displacements were extracted at various
locations and paths in the bridge deck. The nomenclature used in the results is summarized
below in Table 26.
Table 26. Nomenclature used for steel girder parametric study results
Parameter
As-built model
Effect of changing abutment connection
Effect of changing the shear connector
distribution
Effect of changing the skew angle

Nomenclature used in plots of results
“As-built”
“Non-integral”
“Shear Stud”

“Skew Angle”
217

Depth Through Slab (Inches)

0
1
2
3
4
5
6
7
8
9

Shear Stud
Skew Angle
Non-Integral
As-Built

0

250
500
750
Tensile Stress (psi)

Depth Through Slab (Inches)

Figure 204. Max principal tensile stresses through the depth of the slab, between beams (t=45)

0
1
2
3
4
5
6
7
8
9

Shear Stud
Skew Angle
Non-Integral
As-Built

0

20

40 60 80 100
Microstrains

Figure 205. Max principal plastic strains through the depth of the slab, between beams (t=45)

218

As shown in Figure 204 and Figure 205, the tensile stresses are higher near the top of the deck
and decrease through the depth. The plastic strains penetrate roughly halfway through the depth
of the deck, as in the box beam bridge. Increasing the shear connector spacing slightly lowered
the maximum principal plastic strain values, as well as creating a non-integral connection at the
abutment. Increasing the skew angle yielded slightly higher plastic strain values.
As shown in Figure 206 and Figure 207, the maximum principal tensile stresses are high at
the top of the deck and then drop off significantly and remain fairly constant in the beams. Like
response in-between the beams, plastic strains penetrate to about halfway through the depth of
the deck. The tensile stresses were slightly higher for the non-integral abutment connection and
higher shear connector spacing, which corresponded to lower plastic strains. Increasing the skew
angle also yielded slightly lower tensile stresses and higher plastic strains.
Results plotted in Figure 208 to Figure 213 show that a non-integral abutment configuration
yielded higher displacements, higher stresses, and lower plastic strains. The increased shear
connector spacing configuration also yielded slightly higher displacements, higher stresses, and
lower plastic strains, although not to the extent of the non-integral abutment configuration.
Increasing the skew angle yielded lower displacements, lower stresses, and higher plastic strain
values. The amount of overall restraint created by the non-integral abutment connection and
increased shear connector spacing was lower than the as-built case, while increasing the skew
angle produced a higher amount of restraint in the system.
Outputs through time on the top surface of the deck in the middle of span 2 are shown below.

219

Depth Through Beam/Slab (Inches)

0
10
20
Shear Stud
Skew Angle
Non-Integral
As-Built

30
40
50
60
0

250

500

750

Tensile Stress (psi)

Depth Through Slab (Inches)

Figure 206. Max principal tensile stresses through depth of beam/slab assembly (t=45)

0
1
2
3
4
5
6
7
8
9
10

Shear Stud
Skew Angle
Non-Integral
As-Built

0

20

40

60 80 100 120
Microstrains

Figure 207. Max principal plastic strains through depth of slab, over beams (t=45)

220

Vertical Displacement (Inches)

0.05
0
-0.05
-0.1
-0.15
-0.2
-0.25
-0.3
-0.35

Shear Stud
Skew Angle
Non-Integral
As-Built

0

50 100 150 200 250
Longitudinal Distance (Feet)

Max Principal Stress (psi)

Figure 208. Vertical displacements along the longitudinal direction (t=45 days)

610
605
600
595
590
585
580
575
570
565
560

Shear Stud
Skew Angle
Non-Integral
As-Built
0

50

100 150 200 250

Longitudinal Distance (Feet)
Figure 209. Max principal stresses along the longitudinal direction (t=45 days)

221

Microstrain

180
160
140
120
100
80
60
40
20
0

Shear Stud
Skew Angle
Non-Integral
As-Built
0

50

100 150 200 250

Longitudinal Distance (Feet)

Vertical Displacement (Inches)

Figure 210. Max principal plastic strains along the longitudinal direction (t=45 days)

0.25
0.2
0.15
0.1
0.05
0
-0.05
-0.1
-0.15
-0.2
-0.25
-0.3

Shear Stud
Skew Angle
Non-Integral
As-Built
0

25

50

75

Transverse Distance (Feet)
Figure 211. Vertical displacements along the transverse direction (t=45 days)
222

Max Principal Tensile Stresses (psi)

700
650
600
550

Shear Stud
Skew Angle
Non-Integral
As-Built

500
450
400
0

25

50

75

Transverse Distance (Feet)
Figure 212. Max principal stresses along the transverse direction (t=45 days)

140

Microstrains

120
100
80

Shear Stud
Skew Angle
Non-Integral
As-Built

60
40
20
0
0

25

50

75

Transverse Distance (Feet)
Figure 213. Max principal plastic strains along the transverse direction (t=45 days)

223

Results in Figure 214 show that there is an initial deformation at beginning of shrinkage,
followed by a steady increase in displacement as shrinkage continues. This trend matches the
behavior experienced for the laboratory models (see Section 5.4). Overall, the bridge with the
non-integral abutment configuration had highest displacement values while the bridge with the
skew had the lowest displacement values. The bridge with the higher shear stud spacing also had
slightly higher displacement values. This occurred because the bridge with the non-integral
connection had the lowest amount of overall restraint, which allowed for increased
displacements. The skew angle created additional restraint in the bridge, which limited the
displacement values.
As shown in Figure 215, the maximum principal tensile stresses steadily grow until the
concrete tensile strength is reached. At that point, cracking occurs, and the stresses steadily
decrease due to softening. As seen in Figure 216, the decrease in stress matches the increase in
plastic strains as the cracks continue to open. Overall, the non-integral abutment connection
bridge had lower plastic strain values and higher stress values. The higher shear connector
spacing bridge also had slightly lower plastic strain values and slightly higher stress values.
Since the overall restraint in these configurations are slightly less than the as-built model, less
cracking occurred, which yielded lower plastic strain values. The stress values were higher since
less concrete softening took place. The skew angle bridge had higher plastic strain values and
lower stress values. This bridge had more restraint than the as-built model, leading to more
cracking and increased plastic strain values.

224

Vertical Displacement (Inches)

0
-0.05
-0.1
Shear Stud
Skew Angle
Non-Integral
As-Built

-0.15
-0.2
-0.25
-0.3
0

10

20
30
Time (days)

40

Figure 214. Vertical displacements through time, between beams

Tensile Stress (psi)

600
500
400

Shear Stud
Skew Angle
Non-Integral
As-Built

300
200
100
0
0

10

20
30
Time (days)

40

Figure 215. Max principal stresses through time, between beams

225

120

Microstrains

100
80
Shear Stud
Skew Angle
Non-Integral
As-Built

60
40
20
0
0

10

20
30
Time (days)

40

Figure 216. Max principal plastic strains through time, between beams, span 2

The overall results of the parametric study for the steel girder bridges are shown below in
Table 27. Note that “time for cracking” was taken as the time for plastic strains to first begin to
appear in the deck. This occurred in the region over the pier.

Table 27. Steel girder bridge parametric study overall results
Analysis

Time for
cracking

Maximum Plastic
Strain Value

As-Built

13 days

170 µ-strain

Maximum
Vertical
Displacement
-0.263 inches

Non-Integral

14 days

160 µ-strain

-0.301 inches

Shear Stud

13 days

167 µ-strain

-0.262 inches

Skew Angle

12 days

172 µ-strain

-0.281 inches

226

Increasing the shear stud spacing slightly improved the bridge performance, while skew angle
produced more restraint and increased the maximum plastic strain value. Overall, the bridge
with the non-integral abutment connection exhibited the best behavior. This bridge had the least
overall amount of restraint, so it had the smallest plastic strain values at the end of the analysis
and longest time for cracking to occur. Additionally, it had the largest maximum vertical
displacement values, indicating the least amount of movement restraint.
6.5.4.1 Effect of shear connector re-distribution
In the full bridge models for the parametric study the actual discrete shear studs were not
modeled, so the full effect of shear stud size and volume was not able to be examined.
Therefore, the lab sub-assembly models were utilized to examine the effect of size and volume.
The shear stud size and spacing was compared between the as-built laboratory models (1.25’’diameter studs, spaced at 6’’) with an arrangement with larger studs at greater spacing. The new
size and spacing was calculated so that the total overall shear stud volume for each beam
remained the same. The shear stud size and spacing examined using the lab sub-assembly
models are summarized below in Table 28. Results from the analysis are shown in Figure 218 to
Figure 219.

Table 28. Shear stud size and volume determination for parametric study
Stud Diameter

Stud Height

Stud Spacing

Detail 1 (as built)

1.25’’

6’’

6’’

Stud Volume
Per Beam
419.71 in3

Detail 2 (larger studs,

1.5’’

7’’

10’’

408.21 in3

larger spacing)

227

a) Detail 1-Smaller Size and Spacing

b) Detail 2-Larger Size and Spacing
Figure 217. Maximum principal stress contours (time=30 days)

228

450
400
350

Stress (psi)

300
250

Smaller Size and
Spacing

200

Larger Size and
Spacing

150
100
50
0
0

10

20

30

Time (Days)
Figure 218. Concrete maximum principal tensile stresses, middle of the slab on top

0
-0.01

Stress (psi)

-0.02
-0.03
-0.04

Smaller Size and
Spacing

-0.05

Larger Size and
Spacing

-0.06
-0.07
0

10
20
Time (Days)

30

Figure 219. Vertical displacements, middle of slab on top

229

As shown in Figures Figure 217 to Figure 219, the stresses in the concrete were higher using
the smaller shear studs at a closer spacing, while the overall vertical displacement values
remained about the same. The additional amount of shear studs in the “as-built” model created
more locations of restraint, which led to higher overall stresses in the concrete.
6.5.5 Effect of concrete tensile strength
As described in section 5.3, a tensile strength of 7.5√f’c was defined for the concrete in the
computational evaluations. Since the true tensile strength of concrete varies and is largely
unknown, the effect of lowering the tensile strength was examined for the box beam “as-built”
model. Instead of the original tensile strength of 7.5√f’c, a lower value of 6.3√f’c was used. The
two analyses are compared in Figure 220 to Figure 222. It can be seen that the overall bridge
behavior remains the same when the concrete tensile strength is lowered. Lowering the tensile
strength decreases the tensile stress values, since the maximum value that the stresses can reach
before cracking occurs is lower.

Additionally, lowering the tensile strength increases the

magnitude of the plastic strain values, while reducing the time for cracking to occur.

230

Tensile Stress (psi)

600
500
400
Lower Tensile
Strength
Higher Tensile
Strength

300
200
100
0
0

10

20
30
Time (days)

40

Figure 220. Maximum principal tensile stress values through time, tensile strength comparison

120

Microstrains

100
Lower
Tensile
Strength

80
60

Higher
Tensile
Strength

40
20
0
0

10

20
30
Time (days)

40

Figure 221. Maximum principal plastic strain values through time, tensile strength comparison

231

300

Microstrain

250
Higher
Tensile
Strength

200
150

Lower
Tensile
Strength

100
50
0
0

100
200
300
400
Longitudinal Distance (Feet)
a) Entire length of bridge

120

Microstrain

115
Higher
Tensile
Strength

110
105

Lower
Tensile
Strength

100
95
90
50

100
150
Longitudinal Distance (Feet)
b) Span 1

Figure 222. Maximum principal plastic strain values along longitudinal direction (t=45 days)

232

6.5.6 Discussion
Overall, the simulations were able to capture the damage and cracking patterns that were
prevalent in the two prototype bridges in the field.

The box beam model predicted both

transverse cracking and longitudinal cracking throughout the bridge. Transverse cracking was
predicted along the length of the entire bridge, with 3’-5’ spacing between cracks. Longitudinal
cracking was predicted between beams. Cracking originated in the negative moment regions,
and then propagated to the rest of the bridge. These cracking patterns were observed during the
field inspection of the M-57 over US-127 bridge. The steel girder model predicted longitudinal
and diagonal cracking at the abutments, and transverse cracking throughout the entire deck.
Unlike the box beam bridge model, longitudinal cracking was not predicted. This also matched
the field observations during the inspection of the Kensington Road over I-96 bridge.
The steel and concrete “as-built” models exhibited similar behavior, and one bridge type did
not perform significantly better than the other. Both bridges showed signs of cracking over the
central pier at a time of around 13 days. Both bridges showed evidence of transverse cracking in
the negative moment regions (over the piers) and also showed evidence of transverse cracking
along the length of the spans.

The steel girder bridge showed a higher concentration of

transverse cracking in the regions over the piers, while the box beam bridge showed cracking
that was more evenly-spaced. Both bridges also showed signs of longitudinal cracking and
diagonal cracking at the two ends, over the abutments. Unlike the steel girder bridge model,
however, the box beam bridge simulation predicted longitudinal cracking along the length of the
bridge, over the edges of the beams. Even with diaphragms, the steel girder bridge is much more
flexible than the concrete bridge in the transverse direction, thus this type of cracking did not
occur.
233

For the parameters considered in the spread box beam bridge simulations, the use of a lowshrinkage mix had the greatest effect on improving bridge behavior, as expected. Changing the
distribution of reinforcement, while keeping the same reinforcement ratio, did not influence
bridge behavior. Although the reinforcement was not discretely modeled which may have
affected the results, it is predicted that changing the distribution will not influence the overall
bridge performance. Increasing the amount of reinforcement created additional restraint in the
bridge deck, leading to an increase in the plastic strain values. This effect did not influence
bridge behavior to a significant extent, and the changes in behavior produced by increasing the
amount of reinforcement were small.
For the parameters considered in the steel girder bridge simulations, changing the abutment
connection from fully-integral to non-integral had the greatest effect on the bridge behavior.
Changing the abutment to non-integral greatly reduced the total restraint present in the bridge,
and improved the overall performance. Fully-integral abutments only appear to work well if the
foundation is supported by flexible piles, oriented in weak-axis bending. As expected, increasing
the shear stud density also slightly improved the bridge performance, since it eliminated some of
the areas of restraint. However, this did not have a very large effect on the overall bridge
behavior. Increasing the bridge skew angle produced higher plastic strain values and reduced the
time for cracking to occur. The skew angle likely created additional restraint in the bridge,
which lowered the overall performance.
Overall, it can be seen that the restraint of concrete shrinkage is governed by both axial
behavior and bending behavior. The axial behavior is caused by the end restraint conditions at
the abutment, while the bending behavior is caused by the curling motion that is induced by the

234

restraint caused by the girders, shear connectors, and reinforcement. This is illustrated in Figure

Depth through deck (inches)

223 below, and was illustrated for the lab models in Figure 128.

0
2
4
6
8

10
-500

-250
0
250
500
750
Longitudinal Stresses (S33), psi

Bending

1000

Tension

Figure 223. Longitudinal stresses through the depth of the slab

Figure 223 shows that the stresses in the top half of the deck, where cracking occurs in the
simulations, are caused by both axial and bending behavior. The bottom half of the deck can be
seen to be in bending, with tensile stresses switching to compressive stresses. If the stresses
through the top half of the deck are extracted, it can be seen that most of the stress is due to axial
behavior, and the contribution of the bending stresses are minimal. This shows that the bending
235

behavior of the slab due to curling does not control the cracking behavior, but it is instead
governed by the axial effects due to the end restraint conditions. This explains why changing the
design parameters at the global level (such as changing the abutment configuration and the
bridge skew angle) had a greater impact than changing the design parameters at the sub-assembly
level (such as the reinforcement arrangement and shear connector spacing).
Since the behavior is mostly dominated by axial restraint, this problem can be simplified to be
analyzed as a slab on grade, with restraints at the ends. As shrinkage is induced in the slab,
cracking will occur at the mid-point, and then propagate to the quarter-points, until all of the
stresses are relieved. This explains the presence of evenly-spaced transverse cracking in the
bridge decks.

236

7

CONCLUSIONS AND RECOMMENDATIONS

7.1

Conclusions

While there are many factors that influence early-age deck cracking in jointless bridges, the
most dominant source is restrained concrete shrinkage. As the concrete is restrained from
movement, tensile stresses build up in the deck, causing cracking. Restrained concrete shrinkage
is dominated primarily by the concrete mix design, but bridge design factors can also greatly
influence the amount of shrinkage restraint.
Overall, the research confirmed the hypothesis that the more restraint that is present in the
bridge system, the greater the build-up of restrained tensile forces, and the more cracking that
will occur. A field investigation showed that early-age transverse cracking occurs on both steel
and concrete girder bridges, and that cracking is most prevalent in negative moment regions.
Concrete box beam bridges also experience longitudinal cracking.
Computational simulations based on the finite element method were conducted to evaluate the
effect of concrete shrinkage in full bridge systems, which were used to study the effects of
design factors at the global level. The simulation approach was verified through experimentallycalibrated finite-element models. The following conclusions were drawn from the simulation
parametric study on prototype jointless bridges.
•

Shrinkage cracking was prevalent in both steel and concrete girder bridges. Concrete
girder bridges experience both transverse and longitudinal cracking, while steel girder
bridges experience only transverse cracking.

With respect to restrained shrinkage

cracking, one bridge type did not perform better than the other, and the overall behavior
was similar.
237

•

Higher inelastic strain values and more cracking occurred in bridges with more spans and
more negative moment (pier) regions.

•

Using a lower-shrinkage concrete mix reduced the magnitude of shrinkage loads, and
thus reduced the amount of cracking. Changing the concrete mix had a larger influence
on bridge behavior than changing global bridge design parameters.

•

The effect of changing the amount of reinforcement and the reinforcement distribution
was found to be minimal and did not greatly influence the expected level of deck
cracking.

•

Designing a bridge with integral abutments and a rigid foundation greatly increased the
restraint in the system and increased the amount of predicted cracking. This was seen in
both the field investigation and the computational analyses of full bridge models.

•

Using larger shear studs at a larger spacing lowered the amount of restraint locations in
the bridge, and slightly improved performance.

•

Increasing the skew angle slightly lowered the overall bridge performance as indicated by
an increase in the predicted deck cracking region near the abutment.

•

Soil compaction level and foundation configuration greatly influences the overall
stiffness of the bridge system, and is important to consider.

•

The cracking behavior of the deck was primarily governed by the axial effects caused by
the end restraint conditions and was not influenced greatly by the bending behavior and
curling of the slab. For this reason, the bridge design parameters at the global level
(abutment configuration and skew angle) have a much larger effect on bridge
performance than the design parameters at the sub-assembly level (reinforcement
arrangement and shear connector spacing).
238

7.2

Recommendations

The following is recommended as a result of this research:
•

Measures should be taken to provide the least amount of restraint possible in the bridge.
The bridge simulations conducted in this study showed that the more restraint that is
present, the more cracking that will occur in the deck. The shear connector density
should be minimized as much as possible, although it should clearly be high enough to
maintain composite action.

•

Overall, cracking behavior is dominated by the axial demands caused by the end restraint
conditions at the global level. Therefore, the global restraint features, such as the skew
angle and abutment configuration, have a much larger effect on bridge performance than
the restraint features at the sub-assembly level.

•

Bridges supported by both steel and concrete beams are susceptible to deck cracking due
to restrained concrete shrinkage. Thus, one bridge type is not seen as superior over the
other with respect to this type of damage.

•

The negative retraining effect when using fully-integral abutments (where the girders are
cast into the abutment backwall) may be minimized by using a foundation supported on
flexible piles oriented in weak-axis bending.

•

Changing the reinforcement amount and distribution had a minimal effect on bridge
performance, and maintaining the current design guidelines is recommended.

•

Lowering the shear connector density slightly improved bridge performance. Increasing
the shear stud size and spacing is recommended to provide less areas of restraint within
the deck, and provide overall lower stress levels. However, the overall improvement
239

was minimal, and care should be taken to ensure that composite action between the slab
and beams is maintained.
•

Increasing the bridge skew angle slightly reduces the overall performance of the bridge.
Thus, large skew angles should be avoided as much as possible.

•

Concrete mixture designs optimized for low shrinkage, such as the modified MDOT
Grade D mix with the slag cement replacement, or the use of shrinkage reducing
admixtures should be evaluated for their effect on minimizing early-age deck cracking
on a full-scale bridge. However, care should be taken when evaluating the use of
shrinkage reducing admixtures, as MDOT has found them to be detrimental in
applications requiring entrained air for freeze-thaw durability. The strength behavior of
the modified MDOT Grade D concrete mix was very similar to the normal Grade D mix,
while the shrinkage characteristics were much better. Additionally, the cost of the mix
was comparable to the standard Grade D mix. The cracking potential and shrinkage
magnitude was much smaller for the modified Grade D mix, and it is thus recommended
for future construction.

240

REFERENCES

241

REFERENCES
[1] AASHTO, LRFD Bridge Design Specifications, American Association of State and Highway
Transportation Officials, Washington, D.C., 2007
[2] ACI Committee 209, 1992, “Prediction of Creep, Shrinkage, and Temperature Effects in
Concrete Structure,” American Concrete Institute, Farmington Hills, MI, USA
[3] American Institute of Steel Construction, “Steel Construction Manual”, American Institute of
Steel Construction, 13th ed., 2005
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