DRAFT
Characterization of Effective Built- in Curling and Concrete Pavement
Cracking on the Palmdale Test Sections
By:
Shreenath Rao and Jeffery Roesler, Ph. D., P. E.
University of Illinois at Urbana- Champaign
Urbana, Illinois
University of California Berkeley
Institute of Transportation Studies
Pavement Research Center
May 2005
ii
iii
TABLE OF CONTENTS
Table of Contents....................................................................................................................... ... iii
List of Figures ............................................................................................................................... ix
List of Tables .............................................................................................................................. xxv
List of Acronyms and Abbreviations........................................................................................ xxvii
Abstract....................................................................................................................... .............. xxix
Acknowledgement ..................................................................................................................... xxxi
1.0 Introduction................................................................................................................... ..... 1
1.1 Problem Statement .......................................................................................................... 3
1.1.1 Problem Statement One: Back- calculation of Effective Built- In Curling .................. 4
1.1.2 Problem Statement Two: Modeling Fatigue Damage in Concrete Pavements........... 5
1.1.3 Problem Statement Three: Modeling Fatigue Damage in Concrete Pavements......... 6
1.2 Research Objective ......................................................................................................... 7
1.3 Field Test Background.................................................................................................... 8
1.4 Calculation Engine— Finite Element Program ISLAB2000......................................... 10
1.5 Research Methodology and Chapter Organization ....................................................... 11
2.0 Field Project and Data Collection ..................................................................................... 15
2.1 Layouts and Details of Test Sections............................................................................ 15
2.2 Loading History ............................................................................................................ 17
2.3 Data Collection and Instrumentation ............................................................................ 18
2.4 Data Collection and Instrumentation ............................................................................ 20
2.4.1 Deflection Measurement Devices............................................................................. 21
2.4.2 Multi- Depth Deflectometers ..................................................................................... 22
2.4.3 Thermocouples.......................................................................................................... 22
iv
2.4.4 Data Acquisition System........................................................................................... 22
2.5 Material Properties........................................................................................................ 24
2.5.1 Concrete Flexural Strength ....................................................................................... 25
2.5.2 Concrete Compressive Strength................................................................................ 28
2.5.3 Coefficient of Thermal Expansion............................................................................ 30
2.5.4 Back- calculated Layer Elastic Modulus and Modulus of Subgrade Reaction.......... 30
2.5.5 Poisson’s Ratio of the Concrete................................................................................ 31
2.5.6 Concrete Shrinkage Properties.................................................................................. 32
2.6 Performance Summary of Test Sections....................................................................... 34
3.0 Curling in Concrete Slabs ................................................................................................. 39
3.1 Factors Affecting Slab Effective Built- In Temperature Difference ............................. 43
3.1.1 Factors Affecting Differential Shrinkage through the Depth of the Slab ................. 43
3.1.2 Factors Affecting Creep Due to Slab Restraints ....................................................... 46
3.1.3 Factors Affecting Built- In Curling from Ambient Conditions
during Concrete Set................................................................................................... 47
3.1.4 Effect of Modulus of Elasticity, Slab Thickness, and Joint Spacing ........................ 48
3.1.5 Support from Underlying Layers .............................................................................. 51
3.2 Estimating Slab Effective Built- In Temperature Difference ( EBITD)......................... 53
3.2.1 24- Hour Unloaded Slab Deflections for Palmdale Sections..................................... 55
3.2.2 24- Hour Unloaded Slab Deflection Analysis ........................................................... 57
3.2.3 24- Hour Loaded Slab Deflections for Palmdale Sections ........................................ 62
3.2.4 24- Hour Loaded Slab Deflection Analysis............................................................... 65
3.2.5 Multi- Depth Deflectometer Deflections ................................................................... 73
v
3.2.6 Validation with 20- 80 kN Incremental Load Deflections......................................... 76
3.2.7 Back- calculation of Effective Built- In Temperature Difference
Using Falling Weight Deflectometer ........................................................................ 82
3.3 Summary of Loaded Slab Deflections for Back- calculation of Effective Built- In
Temperature Difference................................................................................................ 84
3.4 Estimated Effective Built- In Temperature Difference for Palmdale Test Sections...... 87
3.5 Factors Affecting Effective Built- In Temperature Difference...................................... 89
4.0 Cumulative Fatigue Damage Modeling............................................................................ 91
4.1 Fatigue Cracking........................................................................................................... 91
4.2 Miner’s Hypothesis....................................................................................................... 92
4.3 Fatigue Models.............................................................................................................. 93
4.3.1 Stress Ratio ............................................................................................................... 93
4.3.2 Fatigue Models.......................................................................................................... 93
4.4 Evaluation of Applicability of Fatigue Models to Palmdale Field Data....................... 96
4.4.1 Fatigue Analysis Procedure ...................................................................................... 97
4.4.2 Fatigue Analysis Results......................................................................................... 103
4.5 Rolling Wheel Load Analysis and Location of Peak Stresses.................................... 113
4.5.1 Influence Charts ...................................................................................................... 113
4.5.2 Location of Maximum Slab Stresses ...................................................................... 116
4.5.3 Peak Stresses at Transverse Joint Edges versus Peak Stresses at
Lane- Shoulder Edges .............................................................................................. 117
4.6 Fatigue Model Using Stress Ranges and Peak Stresses.............................................. 118
4.6.1 Fatigue Model ......................................................................................................... 119
vi
4.6.2 Crack Locations ...................................................................................................... 129
4.7 Summary of Cumulative Fatigue Damage Modeling ................................................. 131
5.0 Modeling Size Effect and Initial Slab Cracking ............................................................. 135
5.1 Size Effect................................................................................................................... 136
5.1.1 Statistical Size Effect .............................................................................................. 137
5.1.2 Fracture Mechanics Size Effect .............................................................................. 137
5.2 Early- Age Surface Microcracking .............................................................................. 141
5.3 Modeling Size Effect and Early- Age Surface Microcracking .................................... 143
5.4 Size Effect Analysis for Palmdale Slabs..................................................................... 156
5.5 Early Age Surface Microcracking Analysis for Palmdale Slabs ................................ 160
5.6 Summary of Size Effect and Initial Slab Surface Microcracking............................... 165
6.0 Conclusions.................................................................................................................... 171
7.0 Suggestions for Future Research .................................................................................... 177
References..................................................................................................................... ............. 179
Appendix A: Deflection, Residuals, and Influence Chart Data from All Tests.......................... A- 1
Appendix B: Factors Affecting Differential Shrinkage through the Depth of the Slab.............. B- 1
Shrinkage Characteristics ....................................................................................................... B- 1
Cement Type and Quantity.................................................................................................. B- 4
Shrinkage- Reducing Admixtures......................................................................................... B- 5
Shrinkage- Compensating Cement ....................................................................................... B- 6
Mix Water.......................................................................................................................... . B- 7
Relative Humidity................................................................................................................. B- 11
Moisture from Underlying Layers ........................................................................................ B- 14
vii
Concrete Curing.................................................................................................................... B- 14
Factors Affecting Creep Due to Slab Restraint......................................................................... B- 17
viii
ix
LIST OF FIGURES
Figure 1- 1. Progress of truck and trailer unit across curled concrete slabs ( from Hveem, 1949). . 2
Figure 1- 2. Slab shapes deformed by curling ( side view). ............................................................. 3
Figure 1- 3. Diagram and specifications of the Heavy Vehicle Simulator ( adapted from Roesler et
al., 2000). ............................................................................................................................... 9
Figure 1- 4. Heavy Vehicle Simulator with temperature control chamber ( from du Plessis,
2002B)......................................................................................................................... ........... 9
Figure 2- 1. South Tangent layout and pavement structure diagram ( from Roesler et al., 2000). 16
Figure 2- 2. North Tangent layout and pavement structure diagram ( from Roesler et al., 2000). 16
Figure 2- 3. Instrumentation layout of North Tangent test Section 535FD ( adapted from du
Plessis, 2002B)...................................................................................................................... 20
Figure 2- 4. Placement of deflection measurement device ( DMD) sensors and multi- depth
deflectometers ( MDDs) relative to test section ( adapted from du Plessis, 2002B). ............. 21
Figure 2- 5. Schematic of multi- depth deflectometer array ( from Roesler et al., 2000). .............. 23
Figure 2- 6. Average flexural strength gain curve for South Tangent test sections....................... 26
Figure 2- 7. Average compressive strength gain for all test sections. ........................................... 29
Figure 2- 8. Poisson’s ratio test results with mean values for high- performance concrete with
basalt, granite, and gravel ( from Kliszczewicz and Ajdukiewicz, 2002). ............................ 32
Figure 2- 9. Average shrinkage of mortar bars using ASTM C596- 96. ........................................ 33
Figure 3- 1. Relationship between drying shrinkage of test specimens and the amount of curling
deflection of full- size test slabs for three different sections ( from Suprenant, 2002; Tremper
and Spellman, 1963). ............................................................................................................ 44
x
Figure 3- 2. Experimental dependency of free shrinkage strain, total strain under simultaneous
drying and loading by tensile stress of 1 MPa, and basic creep under same stress of concrete
cured 1 day ( from Kovler, 1999). ......................................................................................... 47
Figure 3- 3. Effect of concrete modulus of elasticity on curling of floor slabs ( from Al- Nasra and
Wang, 1994).......................................................................................................................... 49
Figure 3- 4. Percentage upward deflection f ( relative to 20- cm slabs) due to curling as a function
of slab thickness ( from Eisenmann and Leykauf, 1990)....................................................... 50
Figure 3- 5. Upward deflection f ( relative to 20 cm slabs) due to curling as a function of joint
spacing for various values of elastic moduli and shrinkage strains ( Eisenmann and Leykauf,
1990). ............................................................................................................................... .... 52
Figure 3- 6. Upward slab curling and sinking of slab into the subgrade ( from Ytterberg, 1987). 52
Figure 3- 7. Illustration of support condition under pavement slabs ( a) assuming flat foundation
and ( b) including the effects of settlement ( from Yu et al., 2004)........................................ 53
Figure 3- 8. 24- hour unloaded slab relative deflections with no HVS and no temperature control
box ( Section 535FD)............................................................................................................. 56
Figure 3- 9. 24- hour unloaded slab relative deflections with HVS and temperature control box
( Section 535FD).................................................................................................................... 56
Figure 3- 10. Predicted unloaded slab corner relative deflections assuming 0 º C, – 10 º C, – 25 º C,
and – 35 º C effective built- in temperature difference and measured deflections ( Section
535FD, DMD4) under ambient conditions. .......................................................................... 58
Figure 3- 11. Predicted unloaded slab deflection range versus effective built- in temperature
difference for DMD4 ( corner) of slab, Section 535FD......................................................... 60
xi
Figure 3- 12. Example of temperature profile through a 250- mm concrete slab for a typical spring
day ( from Yu et al., 2004)..................................................................................................... 60
Figure 3- 13. Estimation of slab surface temperature by extrapolation of embedded thermocouple
readings....................................................................................................................... ......... 61
Figure 3- 14. Effect of extrapolation on estimated effective built- in temperature difference using
unloaded slab deflection range.............................................................................................. 62
Figure 3- 15. 24- hour 40- kN dual- wheel half- axle loaded slab deflections without using the
temperature control box, Section 535FD. ............................................................................. 64
Figure 3- 16. 24- hour 40- kN dual wheel half- axle loaded slab deflections with use of the
temperature control box, Section 535FD. ............................................................................. 64
Figure 3- 17. Predicted loaded slab deflections under influence of 40- kN dual wheel for Section
535FD ( DMD4, slab corner deflection, slab corner loading), Section 537FD ( interior MDD
location deflection, slab corner loading), and widened lane Section 539FD ( DMD4, slab
corner deflection, interior loading) as a function of total effective linear temperature
difference. ............................................................................................................................. 66
Figure 3- 18. Residuals ( difference in measured deflections and predicted deflections) as a
function of temperature difference for DMD2, DMD3, and DMD4 measured with and
without temperature control for Section 535FD. .................................................................. 71
Figure 3- 19. Residuals ( difference in measured deflections and predicted deflections) as a
function of measured deflections for DMD2, DMD3, and DMD4 measured with and
without temperature control for Section 535FD. .................................................................. 71
xii
Figure 3- 20. Residuals ( difference in measured deflections and predicted deflections) as a
function of predicted deflections for DMD2, DMD3, and DMD4 measured with and without
temperature control for Section 535FD. ............................................................................... 72
Figure 3- 21. MDD deflections for Section 535FD measured over a loaded 24- hour cycle without
temperature control. .............................................................................................................. 74
Figure 3- 22. MDD deflections for Section 535FD measured over a loaded 24- hour cycle with use
of the temperature control box.............................................................................................. 75
Figure 3- 23. MDD deflections for Section 537FD measured over a loaded 24- hour cycle without
temperature control. .............................................................................................................. 77
Figure 3- 24. MDD deflections for Section 537FD measured over a loaded 24- hour cycle with use
of the temperature control box.............................................................................................. 77
Figure 3- 25. MDD deflections for Section 539FD measured over a loaded 24- hour cycle without
temperature control. .............................................................................................................. 78
Figure 3- 26. MDD deflections for Section 539FD measured over a loaded 24- hour cycle with use
of the temperature control box.............................................................................................. 78
Figure 3- 27. MDD deflections for Section 540FD measured over a loaded 24- hour cycle without
temperature control. .............................................................................................................. 79
Figure 3- 28. MDD deflections for Section 540FD measured over a loaded 24- hour cycle with use
of the temperature control box.............................................................................................. 79
Figure 3- 29. Measured and predicted corner ( DMD2 and DMD4) and edge ( DMD3) deflections
for Section 535FD under the influence of 20- to 80- kN loads in 10- kN increments with no
significant differences in slab temperature gradients............................................................ 81
xiii
Figure 3- 30. Predicted versus measured corner ( DMD2 and DMD4) and edge ( DMD3)
deflections for Section 535FD under the influence of 20- to 80- kN loads in 10- kN
increments. ............................................................................................................................ 81
Figure 3- 31. Predicted falling weight deflectometer loaded slab corner deflection versus total
effective linear temperature difference for a typical slab. .................................................... 83
Figure 4- 1. Stress distribution at the top of a test slab ( Section 535FD) with corner loading and
effective linear temperature difference of - 25 º C across the slab. ......................................... 98
Figure 4- 2. Core showing crack initiation at the surface of the slab at a Palmdale test section
( photograph from Heath and Roesler, 1999). ....................................................................... 99
Figure 4- 3. Flowchart depicting the steps for calculating cumulative fatigue damage. ............. 102
Figure 4- 4. Calculated cumulative damage to first field- observed crack using various fatigue
models for Palmdale test sections. ...................................................................................... 103
Figure 4- 5. Calibrated curve relating fatigue damage to percent slabs cracked using the 2002
Design Guide model. .......................................................................................................... 105
Figure 4- 6. Calculated cumulative damage with error bars to first field- observed crack using
Zero Maintenance, Calibrated Mechanistic Design, and ERES/ COE fatigue models for
Palmdale test sections. ........................................................................................................ 108
Figure 4- 7. Calculated cumulative damage with error bars to first field- observed crack using
Foxworthy, PCA, and 2002 Design Guide fatigue models for Palmdale test sections....... 108
Figure 4- 8. Change in shrinkage strains with depth over time ( from Lim et al., 2004). ............ 112
Figure 4- 9. Slab shrinkage gradient bilinear model ( from Rasmussen and McCullough, 1998).
............................................................................................................................... ............. 112
xiv
Figure 4- 10. Influence diagram showing effect of 90- kN half- axle moving load on stresses at two
critical locations on the slab ( Section 535FD, EBITD = – 33.3 º C, ΔT = 0 º C). ................... 114
Figure 4- 11. Influence diagram showing effect of 90- kN half- axle and 150- kN aircraft moving
load on stresses at two critical locations on the slab ( Section 540FD, EBITD = – 17.1 º C, ΔT
= 0 º C). ............................................................................................................................... . 114
Figure 4- 12. Influence diagram showing effect of 35- kN half- axle moving load on stresses at
edge and midslab locations ( Section 520FD, EBITD = – 25.5 º C, ΔT = + 2.5 º C)................. 116
Figure 4- 13. Stress distribution at the top of a test slab ( Section 520FD) with corner loading and
effective linear temperature difference of – 23 º C across the slab showing peak stress at
middle of the slab rather than the edge of the slab. ............................................................ 117
Figure 4- 14. Calculated cumulative damage to first field- observed crack for Palmdale test
sections....................................................................................................................... ........ 124
Figure 4- 15. Comparison of number of allowable load applications to failure between existing
fatigue models and Palmdale linear model using beam strength........................................ 126
Figure 4- 16. Comparison of number of allowable load applications to failure between existing
fatigue models and Palmdale linear model using slab strength. ......................................... 128
Figure 4- 17. Number of allowable load applications to damage of 1.0 for Palmdale bilinear
fatigue model using slab strength. ...................................................................................... 129
Figure 5- 1. Effect of size on tensile strength ( from Carpinteri and Ferro, 1994). ...................... 135
Figure 5- 2. The three principal modes of cracking ( from Van Mier, 1997)............................... 138
Figure 5- 3. Effect of size on strength of quasibrittle materials ( from Bazant, 1984). ................ 139
Figure 5- 4. Fracture mechanics size effect for ( a) blunt crack band and ( b) slit- like process zone
( from Bazant and Planas, 1997).......................................................................................... 140
xv
Figure 5- 5. Restrained shrinkage at early age ( from Folliard et al., 1993)................................. 142
Figure 5- 6. Edge cracked plate in combined bending and tension. ............................................ 144
Figure 5- 7. Effect of slab thickness and crack depth on stress intensity factor ( L = 3.35 m)..... 147
Figure 5- 8. Effect of slab thickness and crack depth on stress intensity factor ( L = 4.57 m)..... 147
Figure 5- 9. Effect of slab thickness and crack depth on stress intensity factor ( L = 5.79 m)..... 148
Figure 5- 10. Effect of joint spacing and crack depth on stress intensity factor ( h = 203 mm)... 149
Figure 5- 11. Modeling of stress intensity factors for various slab thicknesses using sixth- order
polynomials.................................................................................................................... .... 149
Figure 5- 12. Geometric factor as a function of crack depth to thickness ratio........................... 151
Figure 5- 13. Softening stress- separation curve of cohesive crack model and area representing Gf
( from Bazant and Becq- Giraudon, 2002)............................................................................ 154
Figure 5- 14. Effect of thickness and crack depth on nominal strength for Palmdale concrete using
the Universal Size Effect Law. ........................................................................................... 155
Figure 5- 15. Nominal strength of uncracked ( notchless) slabs of various thicknesses relative to
152- mm slab strength.......................................................................................................... 155
Figure 5- 16. Nominal strength of slabs of various thicknesses and crack depths relative to 152-
mm slab strength. ................................................................................................................ 156
Figure 5- 17. Calculated cumulative damage to first field- observed crack for Palmdale test
sections incorporating effect of thickness on concrete strength. ........................................ 159
Figure 5- 18. Calculated cumulative damage to first field- observed crack for Palmdale test
sections incorporating effect of thickness and early- age surface microcracking on concrete
strength....................................................................................................................... ........ 165
xvi
Figure 5- 19. Calculated cumulative damage to first field- observed crack for Palmdale test
sections incorporating effect of thickness and early- age surface microcracking on concrete
strength....................................................................................................................... ........ 166
Figure A- 1. 24- hour unloaded slab ( 537FD) relative deflections with no HVS and no temperature
control box. ......................................................................................................................... A- 1
Figure A- 2. 24- hour unloaded slab ( 537FD) relative deflections with HVS and temperature
control box. ......................................................................................................................... A- 1
Figure A- 3. 24- hour unloaded slab ( 538FD) relative deflections with no HVS and no temperature
control box. ......................................................................................................................... A- 2
Figure A- 4. 24- hour unloaded slab ( 539FD) relative deflections with no HVS and no temperature
control box. ......................................................................................................................... A- 2
Figure A- 5. 24- hour unloaded slab ( 539FD) relative deflections with HVS and temperature
control box. ......................................................................................................................... A- 3
Figure A- 6. 24- hour unloaded slab ( 540FD) relative deflections with no HVS and no temperature
control box. ......................................................................................................................... A- 3
Figure A- 7. 24- hour unloaded slab ( 540FD) relative deflections with HVS and temperature
control box. ......................................................................................................................... A- 4
Figure A- 8. 24- hour unloaded slab ( 541FD) relative deflections with no HVS and no temperature
control box. ......................................................................................................................... A- 4
Figure A- 9. 24- hour 40- kN dual- wheel half- axle loaded slab ( 537FD) deflections without using
the temperature control box. ............................................................................................... A- 5
Figure A- 10. 24- hour 40- kN dual wheel half- axle loaded slab ( 537FD) deflections with use of
the temperature control box. ............................................................................................... A- 5
xvii
Figure A- 11. 24- hour 40- kN dual- wheel half- axle loaded slab ( 538FD) deflections without using
the temperature control box. ............................................................................................... A- 6
Figure A- 12. 24- hour 40- kN dual- wheel half- axle loaded slab ( 539FD) deflections without using
the temperature control box. ............................................................................................... A- 6
Figure A- 13. 24- hour 40- kN dual wheel half- axle loaded slab ( 539FD) deflections with use of
the temperature control box. ............................................................................................... A- 7
Figure A- 14. 24- hour 40- kN dual- wheel half- axle loaded slab ( 540FD) deflections without using
the temperature control box. ............................................................................................... A- 7
Figure A- 15. 24- hour 40- kN dual wheel half- axle loaded slab ( 540FD) deflections with use of
the temperature control box. ............................................................................................... A- 8
Figure A- 16. 24- hour 40- kN dual- wheel half- axle loaded slab ( 541FD) deflections without using
the temperature control box. ............................................................................................... A- 8
Figure A- 17. Residuals ( difference in measured deflections and predicted deflections) as a
function of temperature difference ( box) for DMD2 measured with and without temperature
control for Section 537FD. ................................................................................................. A- 9
Figure A- 18. Residuals ( difference in measured deflections and predicted deflections) as a
function of measured deflections for DMD2 measured with and without temperature control
for Section 537FD............................................................................................................... A- 9
Figure A- 19. Residuals ( difference in measured deflections and predicted deflections) as a
function of predicted deflections for DMD2 measured with and without temperature control
for Section 537FD............................................................................................................. A- 10
xviii
Figure A- 20. Residuals ( difference in measured deflections and predicted deflections) as a
function of temperature difference ( box) for DMD2 and DMD4 measured without
temperature control for Section 538FD. ........................................................................... A- 10
Figure A- 21. Residuals ( difference in measured deflections and predicted deflections) as a
function of measured deflections for DMD2 and DMD4 measured without temperature
control for Section 538FD. ............................................................................................... A- 11
Figure A- 22. Residuals ( difference in measured deflections and predicted deflections) as a
function of predicted deflections for DMD2 and DMD4 measured without temperature
control for Section 538FD. ............................................................................................... A- 11
Figure A- 23. Residuals ( difference in measured deflections and predicted deflections) as a
function of temperature difference ( box) for DMD2, DMD3, and DMD4 measured with and
without temperature control for Section 539FD. .............................................................. A- 12
Figure A- 24. Residuals ( difference in measured deflections and predicted deflections) as a
function of measured deflections for DMD2, DMD3, and DMD4 measured with and
without temperature control for Section 539FD. .............................................................. A- 12
Figure A- 25. Residuals ( difference in measured deflections and predicted deflections) as a
function of predicted deflections for DMD2, DMD3, and DMD4 measured with and without
temperature control for Section 539FD. ........................................................................... A- 13
Figure A- 26. Residuals ( difference in measured deflections and predicted deflections) as a
function of temperature difference ( box) for DMD2, DMD3, and DMD4 measured with and
without temperature control for Section 540FD. .............................................................. A- 13
xix
Figure A- 27. Residuals ( difference in measured deflections and predicted deflections) as a
function of measured deflections for DMD2, DMD3, and DMD4 measured with and
without temperature control for Section 540FD. .............................................................. A- 14
Figure A- 28. Residuals ( difference in measured deflections and predicted deflections) as a
function of predicted deflections for DMD2, DMD3, and DMD4 measured with and without
temperature control for Section 540FD. ........................................................................... A- 14
Figure A- 29. Residuals ( difference in measured deflections and predicted deflections) as a
function of temperature difference ( box) for DMD2 and DMD4 measured without
temperature control for Section 541FD. ........................................................................... A- 15
Figure A- 30. Residuals ( difference in measured deflections and predicted deflections) as a
function of measured deflections for DMD2 and DMD4 measured without temperature
control for Section 541FD. ............................................................................................... A- 15
Figure A- 31. Residuals ( difference in measured deflections and predicted deflections) as a
function of predicted deflections for DMD2 and DMD4 measured without temperature
control for Section 541FD. ............................................................................................... A- 16
Figure A- 32. Measured and predicted corner ( DMD2) deflections for Section 537FD under the
influence of 20- to 80- kN incremental loads with no significant differences in slab
temperature gradients........................................................................................................ A- 16
Figure A- 33. Measured and predicted corner ( DMD2 and DMD4) deflections for Section 538FD
under the influence of 20- to 80- kN incremental loads with no significant differences in slab
temperature gradients........................................................................................................ A- 17
xx
Figure A- 34. Measured and predicted corner ( DMD2 and DMD4) and edge ( DMD3) deflections
for Section 539FD under the influence of 20- to 80- kN incremental loads with no significant
differences in slab temperature gradients. ........................................................................ A- 17
Figure A- 35. Measured and predicted corner ( DMD2 and DMD4) and edge ( DMD3) deflections
for Section 540FD under the influence of 20- to 80- kN incremental loads with no significant
differences in slab temperature gradients. ........................................................................ A- 18
Figure A- 36. Measured and predicted corner ( DMD2 and DMD4) deflections for Section 541FD
under the influence of 20- to 80- kN incremental loads with no significant differences in slab
temperature gradients........................................................................................................ A- 18
Figure A- 37. Influence diagram showing effect of 35- kN moving load on transverse stresses at
the transverse joint ( Section 520FD, 100- mm slab). ........................................................ A- 19
Figure A- 38. Influence diagram showing effect of 35- kN moving load on longitudinal stresses at
the lane- shoulder joint ( Section 520FD, 100- mm slab).................................................... A- 19
Figure A- 39. Influence diagram showing effect of 20- kN moving load on transverse stresses at
the transverse joint ( Section 520FD, 100- mm slab). ........................................................ A- 20
Figure A- 40. Influence diagram showing effect of 20- kN moving load on longitudinal stresses at
the lane- shoulder joint ( Section 520FD, 100- mm slab).................................................... A- 20
Figure A- 41. Influence diagram showing effect of 60- kN moving load on transverse stresses at
the transverse joint ( Section 520FD, 100- mm slab). ........................................................ A- 21
Figure A- 42. Influence diagram showing effect of 60- kN moving load on longitudinal stresses at
the lane- shoulder joint ( Section 520FD, 100- mm slab).................................................... A- 21
Figure A- 43. Influence diagram showing effect of 35- kN moving load on transverse stresses at
the transverse joint ( Section 524FD, 150- mm slab). ........................................................ A- 22
xxi
Figure A- 44. Influence diagram showing effect of 35- kN moving load on longitudinal stresses at
the lane- shoulder joint ( Section 524FD, 150- mm slab).................................................... A- 22
Figure A- 45. Influence diagram showing effect of 20- kN moving load on transverse stresses at
the transverse joint ( Section 524FD, 150- mm slab). ........................................................ A- 23
Figure A- 46. Influence diagram showing effect of 20- kN moving load on longitudinal stresses at
the lane- shoulder joint ( Section 524FD, 150- mm slab).................................................... A- 23
Figure A- 47. Influence diagram showing effect of 60- kN moving load on transverse stresses at
the transverse joint ( Section 524FD, 150- mm slab). ........................................................ A- 24
Figure A- 48. Influence diagram showing effect of 60- kN moving load on longitudinal stresses at
the lane- shoulder joint ( Section 524FD, 150- mm slab).................................................... A- 24
Figure A- 49. Influence diagram showing effect of 35- kN moving load on transverse stresses at
the transverse joint ( Section 530FD, 200- mm slab). ........................................................ A- 25
Figure A- 50. Influence diagram showing effect of 35- kN moving load on longitudinal stresses at
the lane- shoulder joint ( Section 530FD, 200- mm slab).................................................... A- 25
Figure A- 51. Influence diagram showing effect of 20- kN moving load on transverse stresses at
the transverse joint ( Section 530FD, 200- mm slab). ........................................................ A- 26
Figure A- 52. Influence diagram showing effect of 20- kN moving load on longitudinal stresses at
the lane- shoulder joint ( Section 530FD, 200- mm slab).................................................... A- 26
Figure A- 53. Influence diagram showing effect of 60- kN moving load on transverse stresses at
the transverse joint ( Section 530FD, 200- mm slab). ........................................................ A- 27
Figure A- 54. Influence diagram showing effect of 60- kN moving load on longitudinal stresses at
the lane- shoulder joint ( Section 530FD, 200- mm slab).................................................... A- 27
xxii
Figure B- 1. Comparison between computed distribution of
drying and measured distribution of shrinkage in 150- mm cubes of concrete drying from
one face only ( from Carlson, 1938). ................................................................................... B- 2
Figure B- 2. Average effect of adding 1 percent shrinkage- reducing admixture to high- strength
concrete on early age drying shrinkage after casting ( from Holt and Leivo, 2004). .......... B- 6
Figure B- 3. Mortar mixture bar expansions of shrinkage- compensating Type K cement ( MKM
and MKK), and Type I cement ( MOM and MOO) ( from Pittmann et al., 1999)............... B- 7
Figure B- 4. Effect of water- cement ratio on early age autogenous shrinkage of mortar after
casting ( from Holt and Leivo, 2004)................................................................................... B- 9
Figure B- 5. Correlation between autogenous strain and water- cement ratio for cement pastes
aged to 28 days ( from Baroghel- Bouny, 1996). ................................................................. B- 9
Figure B- 6. Relation between shrinkage and weight loss and between weight loss per unit
volume and paste volume ( from Bissonnette et al., 1999)................................................ B- 10
Figure B- 7. Effect of ambient humidity gradient through slab sections
( from Abrams and Orals, 1965). ....................................................................................... B- 11
Figure B- 8. One year of shrinkage data for a 380 mm slab as a function of relative
humidity with only the top surface exposed to drying ( from Keeton, 1979).................... B- 12
Figure B- 9. Drying shrinkage results of various 4 × 8 × 32 mm specimen
( from Bissonnette et al., 1999).......................................................................................... B- 13
Figure B- 10. Distribution of unit shrinkage deformation in prisms under different drying
conditions ( from Nagataki, 1970). .................................................................................... B- 15
Figure B- 11. Upward curvature of slab after initial drying cycle on dry granular subbase
and on a saturated subbase ( from Leonards and Harr, 1959). .......................................... B- 15
xxiii
Figure B- 12. Early- age evaporation and horizontal drying shrinkage from a slab at
three different wind speeds ( from Holt and Leivo, 2004). ............................................... B- 16
Figure B- 13. Shrinkage and creep strains after casting for plain concrete mixtures
( from Altoubat and Lange, 2001). .................................................................................... B- 17
Figure B- 14. Specific total tensile creep at 50 percent relative humidity of two concrete
mixtures ( ordinary and with silica fume) at two water- cement ratios ( 0.55 and 0.35)
( from Bissonnette and Pigeon, 1995)................................................................................ B- 18
Figure B- 15. Effect of applied load and age at loading on tensile creep ( from
Ostergaard et al., 2001)..................................................................................................... B- 19
xxiv
xxv
LIST OF TABLES
Table 2- 1 Summary of Design Features and Properties............................................................ 17
Table 2- 2 Construction Date, Fatigue Testing Dates, and Loading History ............................. 19
Table 2- 3 Target FSHCC Mix Design ( Stock Weights) ........................................................... 24
Table 2- 4 Average Flexural Strengths for South Tangent Sections.......................................... 27
Table 2- 5 Estimated Expected Average Flexural Strength for South Tangent Test Sections... 28
Table 2- 6 Average Compressive Strengths, Cylinder Specimens............................................. 29
Table 2- 7 Summary of First Crack Occurrence for South Tangent Test Sections.................... 35
Table 3- 1 Five components of curling in concrete pavement slabs. ......................................... 41
Table 3- 2 Individual and Cumulative Effects of Various Factors on Concrete Shrinkage
Assuming Constant Water- Cement Ratio ( Mather, 1964; Powers, 1959)............................ 45
Table 3- 3 Cumulative Effect of “ Adverse” Factors on Shrinkage
( Tremper and Spellman, 1963) ............................................................................................. 45
Table 3- 4 Summary of Estimated Effective Built- in Temperature Difference ( º C) for the North
Tangent Sections at JDMD Locations .................................................................................. 70
Table 3- 5 Summary of Estimated Effective Built- in Temperature Difference ( º C) for the North
Tangent Sections at MDD Locations.................................................................................... 74
Table 3- 6 Estimated Effective Built- in Temperature Difference ( Right Corner) in º C from
DMD Analysis and from FWD Analysis.............................................................................. 84
Table 3- 7 Summary of Back- calculated EBITD values ( º C) for Palmdale Test Sections......... 88
Table 4- 1 Summary of Concrete Fatigue Models ( Adapted from Smith and Roesler, 2003)... 96
Table 4- 2 Summary of Effectiveness of Various Fatigue Models as Applicable to the Cracked
Peak Stress Locations for Palmdale Test Sections ............................................................. 126
xxvi
Table 4- 3 Observed Crack Locations and Predicted Critical Damage Locations for
Palmdale Test Sections ....................................................................................................... 130
Table 5- 1 Effect of Thickness on Nominal Strength of Uncracked ( Notchless Slabs
for the Palmdale Test Sections............................................................................................ 157
Table 5- 2 Back- calculated Effective Initial Crack Depth at Transverse Joint Locations
for Palmdale Test Sections.................................................................................................. 162
Table 5- 3 Back- calculated Effective Initial Crack Depth at Lane- Shoulder Joint Locations
for Palmdale Test Sections.................................................................................................. 163
Table B- 1 Effect of Coarse Aggregate on Drying Shrinkage of
Concrete ( Meininger, 1966)................................................................................................ B- 2
Table B- 2 One- year Drying Shrinkage for Various Aggregate Types ( Burrows, 1998)..... B- 3
Table B- 3 Summary of Free Shrinkage Measurements and Restrained Shrinkage Ring
Cracking ( Folliard and Berke, 1997) .................................................................................. B- 5
xxvii
LIST OF ACRONYMS AND ABBREVIATIONS
AASHTO American Association of State Highway and Transportation Officials
AC Asphalt Concrete
APT Accelerated Pavement Testing
ASTM American Society for Testing and Materials
Caltrans California Department of Transportation
CB Corner Break
COV Coefficient of Variation
CSIR Council for Scientific and Industrial Research
DMD Deflection Measurement Devices
EBITD Effective Built- In Temperature Difference
EICM Enhanced Integrated Climatic Model
ESAL Equivalent Single Axle Load
FHWA Federal Highway Administration
FSHCC Fast- Setting Hydraulic Cement Concrete
FD Fatigue Damage
FWD Falling Weight Deflectometer
HRWR High- Range Water Reducer ( Superplasticizer)
HVS Heavy Vehicle Simulator
HWD Heavy Weight Deflectometer
LC Longitudinal Crack
LEFM Linear Elastic Fracture Mechanics
LLPRS Long Life Pavement Rehabilitation Strategies
LTE Load Transfer Efficiency
LVDT Linear Variable Displacement Transducer
MDD Multi Depth Deflectometer
MR Modulus of Rupture
PCA Portland Cement Association
PCC Portland Cement Concrete
RH Relative Humidity
RMS Root Mean Square
xxviii
SD Standard Deviation
SEL Size Effect Law
SR Stress Ratio
TC Transverse Crack
TELTD Total Effective Linear Temperature Difference
UCB University of California, Berkeley
xxix
ABSTRACT
Differential expansion and contraction between the top and bottom of a concrete slab
results in curling. Curling affects stresses and deflections and is an important component of any
mechanistic- empirical design procedure. A significant portion of curling can be attributed to the
combined effects of nonlinear “ built- in” temperature gradients, irreversible shrinkage, moisture
gradients, and creep, which can be represented by an effective built- in temperature difference
( EBITD).
Several instrumented test sections utilizing several design features were constructed and
evaluated using the Heavy Vehicle Simulator ( HVS) in Palmdale, California. These instrumented
slabs were loaded with a half- axle edge load without wander in order to study the effects of
curling and fail the slab sections under accelerated pavement testing. A procedure for estimating
EBITD using loaded slab deflections was developed using the HVS results. The advantages of
using loaded slab deflections are that they can be used for measuring EBITD of slabs with high
negative built- in curl and can also be adapted for a Falling Weight Deflectometer, making the
procedure efficient and cost- effective for the back- calculation of EBITD of in- service
pavements. Differences in restraints and variability in concrete material properties resulted in
EBITDs ranging from – 5 º C to greater than – 30 º C.
The HVS field tests were also used to examine Miner’s hypothesis along with various
fatigue damage models. Results indicate test slabs cracked at cumulative damage levels
significantly different from unity. New models that incorporate stress range and loading rate
along with peak stresses were developed. The coefficients for these models were developed to
incorporate transverse cracking, longitudinal cracking, and corner breaks. The models can also
be used for slabs that exhibit high negative EBITD. For slabs susceptible to high shrinkage
gradients, microcracking resulting from restraint stresses during early ages can significantly
xxx
reduce the slab’s nominal strength. Early- age restraint can vary considerably from one slab to
another, depending on restraint. A procedure to model slab strength reduction and slab size was
developed using nonlinear fracture mechanics principles. A parameter called the “ effective initial
crack depth” is introduced to characterize the early- age surface microcracking.
xxxi
ACKNOWLEDGEMENT
The research included in this paper was conducted under a grant from the University of
California at Berkeley Pavement Research Center and the support of the California Department
of Transportation ( Caltrans). Their support of the research effort is greatly appreciated.
xxxii
1
1.0 INTRODUCTION
Like many porous materials, concrete expands and contracts with changes in temperature
and moisture content. The influence of temperature and moisture gradients through the concrete
slab depth on slab responses has long been recognized by researchers. Hatt ( 1925) was one of the
first researchers to report that curling of the slab could occur due to temperature and moisture
differences within the concrete slab. Carlson ( 1934) conducted experiments on slabs drying from
the top and observed that greater moisture loss and shrinkage occurred near the exposed concrete
surface. Temperature and moisture gradients through the vertical profile of a slab result in
differential expansion and contraction between the top and the bottom of the slab. The expansion
of the top of the slab relative to the bottom results in a convex curvature ( downward curl) and is
equivalent to a void beneath the middle of the slab. Contraction of the top of the slab relative to
the bottom results in a concave curvature ( upward curl) and is equivalent to voids beneath the
corners and edges of the slab.
Hveem ( 1949) defined curling as “ the tendency of a concrete pavement to bend or warp,
usually developing high joints” and was one of the first researchers to study the cracking and
failure of curled concrete pavement slabs in detail, as seen in his diagrammatic sketches showing
the progress of a truck and trailer unit across a series of 6.1- m slabs ( Figure 1- 1). He stated that
“… both moisture and temperature are prone to vary throughout the depth of the slab and it is
inevitable that the expansion or shrinkage of a concrete pavement will rarely be confined to
simple horizontal movement alone… It is almost certain that the expansion or contraction will be
greater either on the surface or on the underside of the slab with the result that any overall
expansion is invariably accompanied by warping or curling of the slabs.” He observed that the
length of the slab that departs from the plane of the pavement ( curled unsupported portion of the
slab) ranges from 1 to 2 m in length for California pavements. In referring to Figure 1- 1, Hveem
2
1 ft = 0.305 m
Figure 1- 1. Progress of truck and trailer unit across curled concrete slabs ( from Hveem,
1949).
added that “ The rapid progress of such a truck and trailer unit across each slab from left to right
produces many very complicated stresses and reaction in the slab.”
Curling of a concrete slab in the field is restrained by the slab’s self- weight, shoulder and
adjacent slabs through aggregate interlock, load transfer devices, and tie bars, and through
nonuniform friction between the base layer and concrete slab ( Poblete et al., 1987; Rao and
Roesler, 2005A). This restraint may vary from one location of the slab to another, resulting in
asymmetric curling of the slab as shown in Figure 1- 2, and from one slab to another, resulting in
variability in performance of the slabs. The resulting loss of contact between the slab and the
3
( c)
Asymmetric Concave
( b)
Concave
( a)
Convex
Figure 1- 2. Slab shapes deformed by curling ( side view).
base due to curling causes increased stresses and deflections, and consequently, increased slab
cracking, which is one of the primary modes of failure in jointed plain concrete pavements.
1.1 Problem Statement
It is widely accepted that curling is a significant factor that affects the cracking
performance of concrete pavements. One of the first procedures to include curling in concrete
pavement design was presented in the Zero- Maintenance study ( Darter and Barenberg, 1977) and
was also a key aspect in the 2002 Design Guide ( Yu et al., 2004). Curling is a crucial
consideration in the design of concrete pavements using mechanistic- empirical design
procedures ( Zollinger and Barenberg, 1989; Darter et al., 2001; Hiller and Roesler, 2002). As
such, a thorough characterization of curling and its influence on the long- term cracking
performance of a slab is imperative to understanding concrete pavement behavior for use in
design and construction of long- lasting concrete pavements.
4
1.1.1 Problem Statement One: Back- calculation of Effective Built- In Curling
As described in Chapter 3, curling is the result of a combination of five nonlinear
components. One of these components is the nonlinear temperature gradients in the slab, which
change over the course of a typical day, and can be measured using embedded thermocouples or
other temperature measuring instruments. They can also be modeled with reasonable accuracy
using programs such as the Enhanced Integrated Climatic Model ( EICM) ( Larson and Dempsey,
1997). The other four components— built- in temperature gradient, differential drying shrinkage,
moisture gradients, and creep— change to a smaller extent through the life of the pavement and
have traditionally been grouped together into an effective “ built- in” curl. These components
primarily develop during the early ages of the concrete.
Currently, no comprehensive procedure exists to model or estimate potential effective
built- in curl based on material properties, ambient conditions during concrete set, curing
conditions, and restraint mechanisms during set. Traditional methods of back- calculating built- in
curling of in- service pavements using unloaded slab deflections have been cumbersome and
involve instrumentation and measurement of movement of individual slabs over a 24- hour
period. As a result, very little information exists on the magnitude of effective built- in curl and
how various design features affect it. The available information on built- in temperature curling is
limited to a handful of research projects.
Due to this limitation, in the development of the 2002 Design Guide, while moisture
gradients were modeled using monthly/ seasonal fluctuations in ambient relative humidity, the
other three components of the effective built- in curl were grouped together as the “ permanent”
curl and obtained through calibration as – 5.6 º C ( Yu et al., 2004). While this value may be used
as an average value representative of a large number of test sections across the country, it would
5
likely have less validity for use in the analysis of individual sections, and more specifically,
individual slabs for which the magnitude of built- in curl can deviate significantly from the mean.
Another drawback of the traditional methods of back- calculating built- in curl is that they
cannot be used for slabs with high negative built- in curl because the slab corners never come in
contact with the base.
To overcome these drawbacks, a procedure to back- calculate built- in curl based on
loaded slab deflections was developed. The load can be either traffic loading, such as using a
Heavy Vehicle Simulator ( HVS), or simulated loading, such as using a Heavy Weight
Deflectometer ( HWD) or a Falling Weight Deflectometer ( FWD).
1.1.2 Problem Statement Two: Modeling Fatigue Damage in Concrete Pavements
Cracking in concrete pavements due to fatigue damage from repeated application of
thermo- mechanical loading is a complex problem, the mechanisms of which are not clearly
understood. It is generally accepted that high peak stresses contribute to early fatigue cracking.
Existing procedures to model fatigue cracking use a “ cumulative damage” approach, as detailed
in Chapter 4. For new construction, the slab is assumed to start with zero initial damage and the
damage due to each subsequent load application is added to the existing damage. The damage
due to each load application is calculated as a function of the ratio of peak stress to flexural
strength. The coefficients for this function are obtained through empirical calibration. In the
development of existing procedures to model fatigue cracking, the contribution of other aspects
of repeated loading, such as stress range, stress reversal, stress history, loading rate, variable load
amplitude, etc., have not been included. The result is a loss of generality of the models. Also, as
shown in Chapter 4, using peak stresses to calculate cumulative damage may result in
discrepancies between predicted locations of maximum damage and observed cracking locations.
6
Another concern regarding the use of existing fatigue models is that while some were
developed for failure of laboratory beam specimens, others do not incorporate curling stresses.
Only two models— the calibrated mechanistic design model ( Salsilli et al., 1993; Thompson and
Barenberg, 1992) and the 2002 Design Guide model ( Darter et al., 2001; Yu et al., 2004)—
incorporate both load and curling stresses. None of the existing design procedures were
calibrated for longitudinal cracking and corner breaks, or for slabs with high negative built- in
curl.
While developing a process that accounts for all of the above- mentioned shortcomings of
existing procedures is beyond the scope of this research, a model that incorporates stress range
and loading rate along with peak stresses was developed. The procedure was calibrated for
transverse cracking, longitudinal cracking, and corner breaks, and because of the inclusion of
stress range, can also be used for slabs that exhibit high negative built- in curl.
1.1.3 Problem Statement Three: Modeling Fatigue Damage in Concrete Pavements
In existing procedures for modeling fatigue cracking, for a given project, all slabs are
assumed to have equal strength. Variability within a project is incorporated through transfer
functions that relate fatigue damage to percent slabs cracked. The coefficients for the transfer
functions are obtained through calibration and typically correspond to 50 percent slab cracking
for cumulative damage of 1.0. However, this approach is not suitable for analysis of individual
slabs. For concrete slabs that are susceptible to high shrinkage gradients, restraint stresses during
early ages can significantly reduce the nominal strength of the slab, as elaborated in Chapter 5.
Early- age restraint can vary considerably from one slab to another, depending on slab self-weight,
slab- base friction, and load transfer with adjacent slabs and shoulders. Therefore, large
differences can exist in the performance of individual slabs. A secondary consideration is that
7
slabs of all thicknesses are assumed to have equal strength. However, fracture mechanics
principles suggest that the nominal strength of concrete decreases with increase in size.
A procedure to model slab strength reduction due to surface microcracking from early-age
restraint stresses and slab size was developed using nonlinear fracture mechanics principles.
A new parameter called the “ effective initial crack depth” is introduced to characterize the early-age
microcracking at the slab surface.
1.2 Research Objective
The principal objective of the research study was to characterize curling, particularly the
“ built- in” component of curling, and to develop a nondestructive procedure to back- calculate
effective built- in curling of in- service pavements. The second objective of the research was to
develop a fatigue cracking failure model that can be more generally applicable than current
fatigue models, and that is inclusive of slabs that exhibit significant curling and reduction in
strength due to microcracking caused by early- age restraint stresses that developed as a result of
differential shrinkage between the top and bottom of the slab. Field- test data of full- scale
instrumented test sections loaded past fatigue failure using a Heavy Vehicle Simulator ( HVS)
were used to accomplish the research objectives. The following three hypotheses are proposed,
developed, and validated through this research:
• Hypothesis 1: Back- calculation of built- in curl based on loaded slab deflections is an
enhancement over methods based on unloaded slab deflections.
• Hypothesis 2: A fatigue model that incorporates both peak stresses and stress ranges
is more generally applicable and is an improvement over existing fatigue models that
only use peak stresses.
8
• Hypothesis 3: A fracture mechanics- based approach can be used to account for the
large variability in performance of individual slabs due to disparities in nominal
strengths between slabs resulting from differences in early- age restrained
microcracking.
The product of this research is an improved procedure for back- calculation of effective
built- in curl and an enhanced understanding of cracking behavior in concrete pavement slabs due
to built- in curling and combined thermo- mechanical loading.
1.3 Field Test Background
As part of the Caltrans Long Life Pavement Rehabilitation Strategies ( LLPRS), a high
early strength hydraulic cement concrete pavement section was field tested using an HVS,
illustrated in Figure 1- 3 and shown in Figure 1- 4. Two full- scale test pavement sections, each
approximately 210 m in length, were constructed on State Route 14 about 8 km south of
Palmdale, California, using an 80/ 20 blend of Ultimax ® to Type II portland cement. The test
sections were located adjacent to the in- service pavement, one on the north side of the highway
(“ North Tangent”) and one on the south side of the highway (“ South Tangent”). The sections
were constructed using three different design thicknesses and design features ( dowels, tie bars,
and widened truck lanes). This fast- setting hydraulic cement concrete ( FSHCC) was designed to
gain enough strength to allow it to be opened to traffic within 4 hours of placement. The
objective of the HVS tests was to evaluate the performance of these full- scale pavement test
sections under the influence of controlled loading and both controlled and ambient temperature
conditions.
9
Overall weight 59,646 kg
Load weight of the test wheel tire 20- 100 kN with truck tire
20- 200 kN with aircraft tire
Dimensions of tested area of pavement 1.5 m × 8 m maximum
Velocity of the test wheel 10 km/ hr maximum
Maximum trafficking rate 1000 repetitions/ hr
Average trafficking rate 750 repetitions/ hr
Average daily repetitions 16,000
Dimensions: Length 22.56 m
Width, overall 3.73 m
Height 3.7 m
Wheel base 16.7m
Number of axles 3 ( 1 in rear, 2 in front)
Figure 1- 3. Diagram and specifications of the Heavy Vehicle Simulator ( adapted from
Roesler et al., 2000).
Figure 1- 4. Heavy Vehicle Simulator with temperature control chamber ( from du Plessis,
2002B).
10
1.4 Calculation Engine— Finite Element Program ISLAB2000
The finite element program ISLAB2000 ( Khazanovich et al., 2000), was used during
several stages of the research. ISLAB2000 is the latest version of ILLI- SLAB, a two-dimensional
finite element program developed at the University of Illinois ( Tabatabaie, 1977;
Tabatabaie and Barenberg, 1980). The program was developed for the analysis of one- and two-layer
jointed concrete pavement systems, with or without mechanical load transfer system at the
joints. ILLI- SLAB is based on medium- thick plate theory over a dense liquid or Winkler
foundation ( Timoshenko et al., 1959), and can be used to evaluate the structural response of a
pavement system with any slab size, joint locations, and load location, size, and configuration.
Through the years, ILLI- SLAB has undergone a number of improvements and additions,
including the incorporation of different subgrade support models and nonlinear temperature
gradients, resulting in a significant enhancement of its modeling capabilities ( Ioannides et al.,
1985; Khazanovich, 1994). ILLI- SLAB has been widely tested over the past 20 years. The
results of the finite element analysis using ILLI- SLAB were found to be comparable to available
theoretical solutions and experimental studies ( Tabatabaie et al., 1979; Ioannides et al., 1985).
The following assumptions are inherent in the use of plate theory, ILLI- SLAB, and
ISLAB2000 for the structural analysis of concrete pavements:
1. Slab and base layers are elastic, homogeneous, medium- thick plates.
2. All forces on the surfaces of the slab are normal to the surfaces— no shear forces are
present on surfaces.
3. The slab is of uniform stiffness— constant elastic modulus and thickness.
4. There are no in- plane forces.
5. Deformations within the elements normal to the slab surfaces are small and can be
ignored— slab will not change in thickness when load is applied.
11
6. Shear deformations are small compared with bending deformations and can be
ignored.
7. Full strain compatibility exists at a bonded interface, while shear stresses at unbonded
interfaces are zero.
8. Dowel bars are linear elastic and located at the neutral axis of the slab.
9. When the load transfer between adjacent slabs is through aggregate interlock, only
shear load is transferred from one slab to another. Both moment and shear are
transferred across joints when dowel bars are used.
The ILLI- SLAB Fortran code was rewritten for ISLAB2000 in C++ to take advantage of
the greater efficiency and power in the execution of mathematical functions, to increase analysis
capacity, and to fix some known bugs in ILLI- SLAB thus improving program reliability. A
graphical user interface was also included to process input data factorially, automate finite
element grid generation, and display output results. Recently, ISLAB2000 was extensively used
as the principal calculation engine for rigid pavement analysis in the 2002 Design Guide ( Darter
et al., 2001).
1.5 Research Methodology and Chapter Organization
The field data and laboratory data used in this research were collected by the Pavement
Research Center at the University of California at Berkeley ( UCB) and its subcontractors,
Dynatest, Inc., and the Roads and Transport Technology Division of the Council for Scientific
and Industrial Research ( CSIR) of South Africa as part of the Accelerated Pavement Testing
( APT) program undertaken by Caltrans. Details of the field project, instrumentation, data
collection, results of relevant laboratory testing, and a performance summary of test sections, are
included in Chapter 2.
12
The objective of characterizing curling and the modeling of fatigue cracking in curled
concrete pavements were achieved in three stages. The first stage, covered in Chapter 3, entailed
development of a non- destructive procedure to estimate effective built- in curling of existing
slabs and identification of factors that affect curling in field concrete slabs. Field- measured
loaded and unloaded slab deflections, vertical slab temperature profiles, and joint load transfers,
along with slab geometries, subgrade support conditions, and layer material properties, were
used as inputs to ISLAB2000. The results of the finite element analysis were used to develop a
detailed procedure to back- calculate built- in curling at several slab locations. The procedure was
also adapted for slab corner loading using the deflections from a falling weight deflectometer
( FWD). The 20 to 80 kN incremental loading data from the test sections along with the FWD
results were used to validate the built- in curling back- calculation procedure. The back- calculated
curling results from the test slabs were used to quantify the influence of various design features
such as slab thickness, joint spacing, use of load transfer devices, tied concrete shoulders, etc., on
effective built- in curl, and to identify factors that affect it.
Chapter 4 presents the second part of the research study: the development of a new
procedure for modeling fatigue cracking. Several existing fatigue cracking models were first
evaluated using the repeated loading results of the field test sections. Peak stresses at critical
locations for each load application on a particular test slab were computed using ISLAB2000 for
all test slabs. The peak stresses were used in the fatigue models to calculate damage at the critical
location due to that single load application. For each field test section, the cumulative damage
was calculated for all load applications until the first observed crack. For the development of the
new procedure, a static rolling wheel analysis was used to compute peak stresses and stress
ranges, which were then used to obtain coefficients for an improved fatigue model that
13
incorporates nonlinearity of temperature and moisture gradients, stress range due to moving load,
and loading frequency.
Chapter 5 presents the third segment of the research. In this segment, fracture mechanics
principles were used in the new fatigue cracking model to account for size effect due to slab
thickness and the reduction in strength resulting from early- age surface microcracking due to
restrained differential shrinkage. A finite element program that models cracked slabs, ILSL962,
was used to develop the geometric factor, which in turn, was used to model the effect of size and
crack depth on the slab nominal strength. A parameter called the “ effective initial crack depth”
was introduced to represent the early- age microcracking at the slab surface. The effective initial
crack depth for the field test slabs were used to modify the fatigue model to incorporate the
effect of differences in restraints among slabs.
Chapter 6 presents the conclusions from all three stages of the research project and
recommendations for further research.
14
15
2.0 FIELD PROJECT AND DATA COLLECTION
Two full- scale test pavement sections incorporating multiple slab thicknesses and design
features were constructed near Palmdale, California. These sections are located on the north and
south sides adjacent to State Route 14, and are referred to as the North Tangent and the South
Tangent. The sections were constructed to evaluate the performance of full- scale instrumented
concrete pavement test slabs under the influence of controlled loading using the HVS, and both
controlled and ambient temperature conditions. The experiment design, along with construction,
instrumentation, collection and documentation of all laboratory and field data, were performed
by the Pavement Research Center at UCB and its subcontractors. A summary of the experimental
layout, loading history, instrumentation and field data collection relevant to this research, is
included in this chapter. Also included are summaries of relevant material properties obtained
from laboratory tests and the field- observed cracking performance of all test sections.
2.1 Layouts and Details of Test Sections
Various test sections, consisting of combinations of concrete slab thicknesses, base types,
tied concrete shoulders, doweled transverse joints, and widened lanes, were constructed and
evaluated using the HVS over a 2- year period. The slab widths on the test sections were 3.7 m
except for the widened lane sections, which were 4.2 m. The slabs had perpendicular transverse
joints with joint spacing varying from 3.7 m to 5.8 m. The South Tangent was constructed with
100-, 150-, and 200- mm nominal thickness concrete slabs on 150- mm thick Class 2 aggregate
base over a compacted granular subgrade. None of the pavement structures on the South Tangent
had dowel bars, tie bars, or widened lanes.
The North Tangent sections were 200- mm nominal thickness concrete over 100- mm
nominal thickness cement treated base with three design features: no dowels + asphalt concrete
16
shoulders, dowels + PCC shoulders, and dowels + widened lanes. Figure 2- 1 and Figure 2- 2
show the pavement structure diagrams for the South Tangent and North Tangent sections,
respectively. A brief summary of the design features of all test sections is shown in Table 2- 1.
Figure 2- 1. South Tangent layout and pavement structure diagram ( from Roesler et al.,
2000).
Figure 2- 2. North Tangent layout and pavement structure diagram ( from Roesler et al.,
2000).
17
Table 2- 1 Summary of Design Features and Properties
Section
Location
and Base
Type
Section
ID
Load
Transfe
r
Devices
Shoulder
Type
Nominal
Design
Thickness,
mm
Actual
Slab
Thickness,
mm
Concrete
Density,
kg/ m3
Joint Spacing:
Left Slab- Test
Slab- Right Slab, m
519FD 94 2,480 5.42 5.81 3.97
520FD 109 2,450 5.45 5.78 4.03
521FD 129 2,440 5.51 5.77 3.78
522FD*
None AC 100
114 2,390 3.98 3.69 5.51
523FD 171 2,370 3.63 5.49 5.83
524FD 165 2,420 5.60 5.72 3.98
525FD 175 2,400 5.78 3.89 3.61
526FD 185 2,390 5.80 4.01 3.56
527FD
None AC 150
170 2,400 3.89 3.61 5.60
528FD 195 2,420 5.73 4.03 3.60
529FD 188 2,400 5.84 3.95 3.65
530FD 220 2,440 5.78 3.96 3.67
South
Tangent
150mm
aggregate
base
531FD
None AC 200
204 2,420 3.93 3.70 5.39
532FD 225 2,350 5.82 3.95 3.64
533FD 220 2,240 5.79 4.03 3.65
534FD 228 2,310 5.91 3.86 3.90
535FD
None AC 200
220 2,470 4.11 3.71 5.35
536FD 220 2,350 5.81 3.96 3.62
537FD 213 2,290 5.78 3.94 3.66
538FD
Dowel
bars Tied concrete 200
221 2,390 5.86 3.92 3.75
539FD 203 2,420 5.86 3.85 3.71
540FD 223 2,420 5.86 3.80 3.80
North
Tangent
100mm
cement-treated
base over
150mm
aggregate
base 541FD
Dowel
bars
600 mm
widened lane
with AC
200
244 2,390 5.91 3.89 3.67
* Static load test – not used in analysis
2.2 Loading History
All dynamic data was collected with the HVS wheel running at creep speed ( 2 km per
hour) for the South Tangent sections and two North Tangent sections ( 532FD and 533FD), and
10 km per hour for the rest of the North Tangent sections. The loads were applied through a dual
truck wheel ( tire pressure = 690 kPa) or single aircraft wheel configuration ( tire pressure = 1,100
kPa), typically bi- directionally ( with the exception of two North Tangent sections run uni-directionally),
and without any wheel wander. HVS tests were run past fatigue failure to observe
the performance of the slabs after the initial crack. Temperature control was used on some of the
tests while others were performed under ambient conditions. Prior to fatigue loading, some of the
18
North Tangent slabs were monitored over a 24- hour cycle without any applied load, and over a
24- hour cycle under a slow- moving 40- kN rolling load using the HVS. The construction date,
fatigue testing dates, testing conditions, and loading history for all test sections are shown in
Table 2- 2.
2.3 Data Collection and Instrumentation
Data collected at two- hour intervals included visual distress surveys, vertical temperature
profile measured using thermocouples, mid- slab edge and corner surface deflections measured
using Deflection Measuring Devices ( DMDs), and vertical deflections ( interior slab location) at
multiple depths of the pavement structure measured using Multi- Depth Deflectometers ( MDDs).
Thermocouples were taped and spaced on wooden dowels in order to measure the temperature at
the top, mid- depth, and bottom of the concrete slab. For North Tangent sections, thermocouple
stacks were placed at four locations on each test section: in the sun, in the shade of the HVS,
inside the temperature control area, and near the traffic barrier ( k- rail). A typical instrumentation
layout for a North Tangent test section ( Section 535FD) is shown in Figure 2- 3. Other
environmental data such as rainfall, wind direction, and wind speed were continuously recorded
using a Davis automatic weather station. Detailed descriptions of all devices, including their
placement and installation at the Palmdale test site, are covered in Roesler et al. ( 2000).
Instrumentation layout details specific to individual test sections are included in du Plessis
( 2002A and 2002B).
19
Table 2- 2 Construction Date, Fatigue Testing Dates, and Loading History
Section
ID
Construction
Date
Testing Start
Date
Testing End
Date
Temperature
Control Box
Used During
Testing?
Load,
kN
Load
Repetitions
Cumulative Load
Repetitions
519FD 06/ 11/ 98 07/ 15/ 98 ( 34) 07/ 19/ 98 ( 38) Yes
25
50
100
55,448
984
3,731
55,448
56,432
60,163
520FD 06/ 11/ 98 07/ 23/ 98 ( 42) 07/ 30/ 98 ( 49) Yes 35
100
51,240
23,080
51,240
74,320
521FD 06/ 11/ 98 08/ 10/ 98 ( 60) 08/ 28/ 98 ( 78) Yes 20
80
157,719
10,600
157,719
168,319
522FD* 06/ 11/ 98 09/ 02/ 98 ( 83) 09/ 02/ 98 ( 83) Ambient n/ a n/ a n/ a
523FD 06/ 11/ 98 09/ 14/ 98 ( 95) 09/ 29/ 98 ( 110) Yes 45 151,151 151,151
524FD 06/ 11/ 98 10/ 02/ 98 ( 113) 10/ 13/ 98 ( 124) Yes 45 119,784 119,784
525FD 06/ 11/ 98 10/ 15/ 98 ( 126) 10/ 18/ 98 ( 129) Ambient 45 5,000 5,000
526FD 06/ 11/ 98 10/ 19/ 98 ( 130) 10/ 22/ 98 ( 133) Yes 85 23,625 23,625
527FD 06/ 11/ 98 10/ 26/ 98 ( 137) 01/ 21/ 99 ( 224) Ambient 35 1,233,969 1,233,969
528FD 06/ 11/ 98 01/ 27/ 99 ( 230) 02/ 02/ 99 ( 236) Yes 40 83,045 83,045
529FD 06/ 11/ 98 02/ 07/ 99 ( 241) 03/ 04/ 99 ( 266) Ambient 40
60
88,110
264,214
88,110
352,324
530FD 06/ 10/ 98 03/ 10/ 99 ( 273) 05/ 14/ 99 ( 338) Yes
40
60
90
64,227
752,447
30,170
64,227
816,674
846,844
531FD 06/ 10/ 98 05/ 19/ 99 ( 343) 05/ 21/ 99 ( 345) Yes 40
60
31,318
33,997
31,318
65,315
532FD 06/ 18/ 98 06/ 07/ 99 ( 354) 07/ 26/ 99 ( 403) Yes 40
70
24,337
177,965
24,337
202,302
533FD 06/ 18/ 98 08/ 06/ 99 ( 414) 11/ 01/ 99 ( 501) Yes
40
70
90
44,164
210,003
116,983
44,164
254,167
371,150
534FD 06/ 17/ 98 12/ 15/ 99 ( 546) 03/ 14/ 00 ( 636) Yes
40
70
90
126,580
858,022
299,758
126,580
984,602
1,284,360
535FD 06/ 17/ 98 03/ 29/ 00 ( 651) 04/ 04/ 00 ( 657) Yes 90 80,002 80,002
Yes
90
70A
90A
110A
130A
150A
750,000
500
500
500
500
88,450
536FD 06/ 17/ 98 04/ 17/ 00 ( 670) 07/ 12/ 00 ( 756)
Ambient 150A 152,332
750,000
750,500
751,000
751,500
752,000
840,450
992,782
537FD 06/ 17/ 98 07/ 20/ 00 ( 764) 08/ 21/ 00 ( 796) Ambient
40
70
90
150A
13,230
500
310,004
65,002
13,230
13,730
323,734
388,736
538FD 06/ 17/ 98 01/ 03/ 01 ( 931) 01/ 18/ 01 ( 946) Ambient 70
90
500
188,882
500
189,382
539FD 06/ 16/ 98 09/ 01/ 00 ( 808) 09/ 29/ 00 ( 836) Ambient
40
70
90
13,342
500
305,004
13,342
13,842
318,846
540FD 06/ 16/ 98 10/ 07/ 00 ( 844) 11/ 28/ 00 ( 896) Yes
40
90
150A
13,003
392,062
142,398
13,003
405,065
547,463
541FD 06/ 16/ 98 12/ 02/ 00 ( 900) 12/ 27/ 00 ( 925) Ambient
70
90
150A
500
167,777
110,011
500
168,277
278,288
* Static load test – not used in analysis
Number in parenthesis following start and end dates are days since construction
A = Aircraft load
20
MDD
JDMD
Slab 31 ( 4.1m) Slab 32 ( 3.7m) Slab 33 ( 5.3m)
TC/ Sun TC/ Shade
TC/ K- rail
TC/ Box
Temperature Chamber
Slab width 3.7m
8.0m
0.6m
Test Section
HVS outline
5 4 3 2 1
6
Thermocouple
Figure 2- 3. Instrumentation layout of North Tangent test Section 535FD ( adapted from du
Plessis, 2002B).
2.4 Data Collection and Instrumentation
Data collected at two- hour intervals included visual distress surveys, vertical temperature
profile measured using thermocouples, mid- slab edge and corner surface deflections measured
using Deflection Measuring Devices ( DMDs), and vertical deflections ( interior slab location) at
multiple depths of the pavement structure measured using Multi- Depth Deflectometers ( MDDs).
Thermocouples were taped and spaced on wooden dowels in order to measure the temperature at
the top, mid- depth, and bottom of the concrete slab. For North Tangent sections, thermocouple
stacks were placed at four locations on each test section: in the sun, in the shade of the HVS,
inside the temperature control area, and near the traffic barrier ( k- rail). A typical instrumentation
layout for a North Tangent test section ( Section 535FD) is shown in Figure 2- 3. Other
environmental data such as rainfall, wind direction, and wind speed were continuously recorded
using a Davis automatic weather station. Detailed descriptions of all devices, including their
placement and installation at the Palmdale test site, are covered in Roesler et al. ( 2000).
Instrumentation layout details specific to individual test sections are included in du Plessis
( 2002A and 2002B).
21
2.4.1 Deflection Measurement Devices
DMDs were used to measure vertical and horizontal joint displacement under dynamic
loads and temperature changes. The DMDs consisted of Linear Variable Displacement
Transducers ( LVDTs), and were used to measure vertical displacements under combined rolling
wheel and temperature loading. To measure vertical deflections, an anchor rod was driven into
the ground adjacent to the slab for absolute deflection measurement at the slab edges and
corners. An illustration of the placement of DMDs with respect to the test section is shown in
Figure 2- 4. DMDs were installed at the lane- shoulder edge and at only one of the two slab
corners for the South Tangent Sections 519FD through 531FD, and the two North Tangent
Sections 532FD and 533FD. For North Tangent Sections 534FD through 541FD, all DMDs
shown in Figure 2- 4 were installed.
DMD1
DMD2
DMD3
DMD4
DMD5
Corner MDD
Edge MDD
Load Wheel Path
DMD6
Sections 519FD – 533FD: DMD1 through DMD3.
Section 534FD: DMD1 through DMD5.
Sections 535FD – 541FD: DMD1 through DMD6.
Figure 2- 4. Placement of deflection measurement device ( DMD) sensors and multi- depth
deflectometers ( MDDs) relative to test section ( adapted from du Plessis, 2002B).
22
2.4.2 Multi- Depth Deflectometers
For some of the test sections, MDDs were installed after pavement construction by
drilling a 3.3- m deep hole from the surface of the pavement into the subgrade. An anchor was
fixed with concrete at the bottom of the hole in the subgrade. A center rod consisting of ferrous
material “ slugs” that served as targets for the MDD modules was connected to the anchor. Each
MDD module contained an LVDT that read displacement relative to the slugs. Each module was
affixed to the sides of the hole at specified depths, to measure total pavement deflection above
that location. A schematic of the MDD setup is shown in Figure 2- 5. Figure 2- 4 shows the
typical location of MDDs on a test section relative to the DMD sensors and HVS wheel path.
2.4.3 Thermocouples
Type K thermocouples were placed in the test sections to read temperature at multiple
depths. The thermocouples were continuously monitored by the data acquisition system.
2.4.4 Data Acquisition System
Deflection and temperature data under HVS loading was primarily collected using a
National Instrument SCXI data acquisition system. The dynamic data system was triggered on
and off by laser sensors at a fixed repetition interval. The dynamic system included a rotary
encoder input from the HVS wheel in order to determine the position of the wheel relative to the
deflection sensors on the pavement. The static data was collected using the CR10X system
manufactured by Campbell Scientific. Four CR10X units were installed at the Palmdale test site:
one on the South Tangent and three on the North Tangent. The units were placed approximately
4 m from the edge of the pavement. Each unit was placed in the ground and surrounded by a
concrete containment box with a steel cover to prevent damage to the unit during construction.
23
Figure 2- 5. Schematic of multi- depth deflectometer array ( from Roesler et al., 2000).
24
The system was used to continuously monitor and record data from thermocouples, LVDTs,
MDDs, etc., due to the environment only. The stored data was then downloaded to a PC. Details
of the data acquisition system and instrumentation of each section are included in Roesler et al.
( 2000) and du Plessis ( 2002A).
2.5 Material Properties
The concrete placed at the Palmdale test sections contained an 80/ 20 blend of Ultimax ®
to Type II portland cement, and included one coarse aggregate, one fine aggregate, water, air
entraining agent, and a retarder. The main chemical constituent of Ultimax cement is calcium
sulfoaluminate. The proportion of each mix constituent ( stock weights) for one cubic meter of
mix is shown in Table 2- 3. The coarse and fine aggregate had moisture contents of 1 and 4
percent greater than their saturated surface dry condition, respectively. The water- to- cement ratio
was 0.39, which includes the mix water and excess water from the coarse and fine aggregate.
Table 2- 3 Target FSHCC Mix Design ( Stock Weights)
Mix Constituent Batch Weight, kg/ m3
Coarse aggregate ( 25 mm maximum size) 1,080
Fine aggregate 848
Ultimax ® cement 332
Type II portland cement 83
Water 117
Delvo ® retarder ( oz) 95.5
Micro- Air ® air entraining agent ( oz) 1.36
Inputs for finite element analysis and fatigue damage analysis of concrete slabs include
material properties such as layer moduli, modulus of subgrade reaction, concrete coefficient of
thermal expansion, and concrete modulus of rupture ( flexural strength). These and other relevant
properties such as concrete compressive strength and shrinkage characteristics for the Palmdale
25
concrete slabs were tested and reported by personnel at UCB and are summarized in the
following sections.
2.5.1 Concrete Flexural Strength
The FSHCC used for the Palmdale test site construction was a blend of Ultimax ® and
Type II cement. The consistency of the concrete mix varied considerably from one truck to
another. Many of the mixes arriving at the site were fairly inconsistent and often required the
addition of water. Each of the six groups of sections ( South Tangent groups 1, 3, and 5, and
North Tangent groups 7, 9, and 11) required approximately 10 truckloads of concrete. For each
group, two of these trucks were selected at random to cast beams for 8- hour, 7- day, and 90- day
flexural strength tests. Two beams were tested at each of these ages for each truckload.
For the South Tangent sections, the average flexural strength increased over 90 percent
from the 8- hour to the 7- day test. The 7- to 90- day average flexural strength gain was 30 percent.
The variability in the 90- day flexural strength ranged from 11 to 22 percent. Much of the
variation was due to the variation in strengths between beams taken from two separate trucks.
Since several different truckloads were used for each test section, and only two trucks were
tested for flexural strength, it was not possible to ascertain the flexural strength characteristics
for each section on an individual basis. Because the variation in strength between trucks was
higher than ( or of the order of) the variation in strength between section groups, the average
flexural strength values representative of all South Tangent test sections was used in the analysis.
The average flexural strength of the beam specimens tested is summarized in Table 2- 4. The
strength gain curve based on the average for all South Tangent sections is shown in Figure 2- 6. A
strength gain model developed using the average laboratory flexural strength data is shown in
Equation 2- 1.
26
0.0
1.0
2.0
3.0
4.0
5.0
6.0
0 120 240 360 480 600
Age ( days)
Flexural Strength ( MPa)
Figure 2- 6. Average flexural strength gain curve for South Tangent test sections.
FSHCC Flexural Strength ( MPa) = 0.0075A3 – 0.2562A2 + 1.491A + 2.858 ( 2- 1)
where,
A = Log ( Age since construction, days).
This strength gain curve was used to estimate the expected average strength for the South
Tangent sections at the time of HVS testing based on age during testing as shown in Table 2- 5.
For simplicity of analysis and because of the high variability in FSHCC strength between
different truckloads relative to the effect of average strength gain over time, the FSHCC
strengths are combined into the three groups based on the nominal thicknesses. For the 100- mm
nominal thickness sections, the average age during testing ranged from 36 days to 83 days,
during which the average flexural strength is estimated as 4.71 MPa. For the 150- mm nominal
27
Table 2- 4 Average Flexural Strengths for South Tangent Sections
Nominal 8 Hours 7 Days 90 Days 575 Days ( North Tangent)
Thickness
( mm)
Mean
( MPa)
SD
( MPa)
COV
(%)
Mean
( MPa)
SD
( MPa)
COV
(%)
Mean
( MPa)
SD
( MPa)
COV
(%)
Mean
( MPa)
SD
( MPa)
COV
(%)
100 1.87 0.14 7 3.48 0.37 10 4.34 0.50 11
150 1.92 0.60 31 3.86 0.71 18 4.92 1.10 22
200 2.45 0.16 7 4.48 0.49 11 5.31 0.97 18
All Sections 2.08 0.39 19 3.94 0.65 17 4.85 0.90 19 5.18 0.25 5
28
Table 2- 5 Estimated Expected Average Flexural Strength for South Tangent Test
Sections
Section ID Average Age During
HVS Testing ( days)
Flexural Strength,
MPa
Average Flexural
Strength ( MPa)
519FD 36 4.59
520FD 46 4.66
521FD 69 4.78
522FD 83 4.83
4.71
523FD 103 4.88
524FD 119 4.92
525FD 128 4.93
526FD 132 4.94
527FD 181 5.00
4.93
528FD 233 5.05
529FD 254 5.07
530FD 306 5.10
531FD 344 5.11
5.08
thickness sections, the average age during testing ranged from 103 days to 181 days, with the
average flexural strength estimated as 4.93 MPa. The average flexural strength for the 200- mm
nominal thickness South Tangent test sections is estimated as 5.08 MPa. These slabs were tested
at ages ranging from 233 to 344 days. The average age during HVS testing for the North Tangent
sections ranged from 379 days to 913 days since construction. Therefore, the average long- term
strength of 5.20MPa was used in analysis as the flexural strength for all North Tangent sections.
2.5.2 Concrete Compressive Strength
For each of the six groups of sections ( South Tangent section groups 1, 3, and 5, and
North Tangent section groups 7, 9, and 11) twelve cylinders were sampled from two random
trucks per section. Of the six cylinders sampled per truck, two cylinders were tested for
compressive strength ( ASTM C 39) at 8 hours, two at 7 days, and two at 90 days. The results of
the compressive strength testing are shown in Table 2- 6. The average long- term compressive
strength based on cores taken from test sections after completion of HVS testing was 61.7 MPa.
29
The gain in compressive strength shown in Figure 2- 7 can be modeled using the following
equation:
FSHCC Compressive Strength ( MPa) = – 0.0023A3 + 1.555A2 + 10.826A + 18.42 ( 2- 2)
where,
A = Log ( Age since construction, days).
Table 2- 6 Average Compressive Strengths, Cylinder Specimens
8 hours 7 days 90 days
Location
Mean
( MPa)
SD
( MPa)
COV
(%)
Mean
( MPa)
SD
( MPa)
COV
(%)
Mean
( MPa)
SD
( MPa)
COV
(%)
South Tangent 12.95 3.43 26 26.22 5.37 20 45.99 8.24 15
North Tangent 14.19 1.47 10 31.15 3.65 12 45.02 7.54 17
All Sections 13.57 2.65 20 28.68 5.15 18 45.50 7.74 17
0
10
20
30
40
50
60
70
0 100 200 300 400 500 600 700
Age, days
Compressive Strength, MPa
Figure 2- 7. Average compressive strength gain for all test sections.
30
Using Equation 2- 2, the average 28- day compressive strength was estimated as 37.34
MPa.
2.5.3 Coefficient of Thermal Expansion
The concrete coefficient of thermal expansion was determined using two different test
methods: American Society for Testing and Materials, ASTM C531- 85 and United States Army
Corp of Engineers, USACE test method CRD- C39- 81. The coefficient of thermal expansion was
measured after curing at 20 º C either under water or in a temperature- controlled room with a
relative humidity of approximately 40 percent. Tests were performed after 28 days of curing and
after 90 days of curing with three replicates for each test. The average value for the coefficient of
thermal expansion of the FSHCC was 8.14 × 10- 6 mm/ mm/ º C. Details of the tests are described
in Heath and Roesler ( 1999).
2.5.4 Back- calculated Layer Elastic Modulus and Modulus of Subgrade Reaction
Elastic modulus for concrete slabs was back- calculated using FWD ( Falling Weight
Deflectometer) deflections at the Palmdale test site on both the South Tangent and the North
Tangent sections at several concrete ages ( 1 day, 7 day, 50 day, and 90 day) by Roesler et al.
( 2000) using the Dynatest ELCON program ( Ullidtz, 1987). The elastic modulus back- calculated
for the 200- mm nominal thickness sections on the South Tangent averaged 37,600 MPa. Back-calculation
for the 100- mm and 150- mm nominal thickness sections on the South Tangent
produced unreliable results due to the thin slabs. The average elastic modulus of the concrete
slabs on the North Tangent was approximately 42,500 MPa. Because of the uniform FSHCC
thickness on the North Tangent sections, the FWD data for the North Tangent was more
consistent than that of the South Tangent. The elastic modulus of the cement- treated base on the
31
North Tangent sections back- calculated from FWD data measured directly on the base layer was
1,400 MPa.
The average dynamic modulus of subgrade reaction for the North Tangent test sections
using the 50- day and 90- day FWD data was back- calculated as 100 MPa/ m by Roesler et al.
( 2000). For the South Tangent sections, the average dynamic modulus of subgrade reaction was
back- calculated as 120 MPa/ m. As part of this research, the values for elastic modulus and
modulus of subgrade reaction calculated by Roesler et al. were compared with those obtained
using AREA7, a procedure for back- calculation of concrete pavement properties developed by
Hall et al. ( 1997). The results were consistent with those obtained by Roesler et al., with less
than 10 percent difference between the two procedures. The static modulus of subgrade reaction,
which is about 50 percent of the dynamic modulus of subgrade reaction, was used in the analysis
conducted in this research.
2.5.5 Poisson’s Ratio of the Concrete
Laboratory tests were not conducted to measure the Poisson’s ratio of the FSHCC. The
FSHCC for the Palmdale test sections consisted of Gabbro coarse aggregate ( Heath and Roesler,
1999). Gabbro is formed by magma that cools very slowly into hard rock below or within the
Earth’s crust. It is an igneous rock with properties similar to basalt and granite. Kliszczewicz and
Ajdukiewicz ( 2002) performed laboratory tests to measure Poisson’s ratio of high- performance
concrete made with various kinds of aggregates. The results of their study, shown in Figure 2- 8,
indicate average Poisson’s ratio of 0.173 for high- performance concrete with granite coarse
aggregate and 0.205 for high- performance concrete with basalt coarse aggregate. For analysis
purposes in the present study, a Poisson’s ratio of 0.18 was used for the FSHCC at Palmdale.
32
Figure 2- 8. Poisson’s ratio test results with mean values for high- performance concrete
with basalt, granite, and gravel ( from Kliszczewicz and Ajdukiewicz, 2002).
2.5.6 Concrete Shrinkage Properties
The shrinkage properties of the cement used at the Palmdale test sections were also tested
by personnel at UCB. Three different methods of assessing drying shrinkage were used to
compare shrinkage characteristics of the cement used in Palmdale against a commercially
available Type II cement. The first and second methods measured the shrinkage of cement
mortar according to ASTM C596- 96 and California Test CT527, respectively. The third method
measured the shrinkage of small concrete beams according to ASTM C157- 93. All three test
methods involve measuring the length change of replicate unrestrained samples after curing for
7, 14, 21, 28 and 90 days under different curing conditions. Details of the shrinkage tests are
described in Heath and Roesler ( 1999). The results of the ASTM C596- 96 shrinkage tests are
shown in Figure 2- 9.
33
- 1800
- 1600
- 1400
- 1200
- 1000
- 800
- 600
- 400
- 200
0
200
400
0 20 40 60 80 100 120 140
Age, days
Shrinkage, microstrains
Pamdale blend, w/ c= 0.5, 50% RH
Pamdale blend, w/ c= 0.5, 30– 40% RH
Pamdale blend, w/ c= 0.4, 50% RH
Pamdale blend, w/ c= 0.4, 30– 40% RH
Type II, w/ c= 0.5, 30– 40% RH Type II, w/ c= 0.5, 50% RH
Type II, w/ c= 0.4, 30– 40% RH
Type II, w/ c= 0.4, 50% RH
Type II, w/ c= 0.5, underwater
Type II, w/ c= 0.4, underwater
Pamdale blend, w/ c= 0.5, underwater
Pamdale blend, w/ c= 0.4, underwater
Figure 2- 9. Average shrinkage of mortar bars using ASTM C596- 96.
The Palmdale blend cement bars had between 130 to 200 percent more shrinkage than the
Type II cement bars after 7 days ( early age), and between 63 to 80 percent more shrinkage after
90 days ( longer term). The differential shrinkage ( difference between 30- 50 percent relative
humidity and underwater tests) for the Palmdale blend was almost twice that of the Type II
cement and as high as 1,680 microstrains after 90 days. The results of California Test CT527
were similar. The results of shrinkage tests on concrete beams from ASTM C157- 93 also showed
significantly higher shrinkage ( particularly differential shrinkage) for the concrete with the
Palmdale blend cement as compared to the concrete with Type II cement. All of the laboratory
shrinkage tests confirm that the Palmdale slabs were highly vulnerable to shrinkage and to
differential shrinkage ( between top of the slab and bottom of the slab).
34
2.6 Performance Summary of Test Sections
A summary of slab cracking for the Palmdale test sections until the appearance of the
first crack along with the associated load and number of repetitions is shown in Table 2- 7. Since
no dynamic loading was applied to Section 522FD, the corresponding visual observations are not
included. For the sake of comparison with historic traffic information, the equivalent 80- kN
single axle loads ( ESALs) are also shown. The ESALs were estimated in order to determine the
approximate magnitude of traffic- induced damage. Caution must be used in interpreting ESALs
since temperature and moisture curling are not considered in the calculation of ESALs. The same
load on different sections could produce failure at different ESAL levels due to the changes in
temperature curling during the testing. This would not necessarily be accounted for if ESALs are
used, and therefore, an approach based on load spectra and cumulative damage is preferred in the
analysis of the results. For each test section, the ESALs were calculated using the formula:
k 4.2
i 1
i
i 40
P n 20 ESALs Σ=
 

 
=  ( 2- 3)
where:
Pi = Half- axle wheel load, kN
ni = Number of applications of load Pi
k = Number of unique loads Pi
The ratio of Pi to 40 was used because 40 kN is the half- axle load for an 80- kN single
axle load and the test sections at Palmdale were loaded with half axle edge loads. The
multiplicative factor of 20 was used to convert the edge loaded HVS trafficking without wander
into wheelpath loaded highway trafficking with wander ( Zollinger and Barenberg, 1989; Packard
and Tayabji, 1983).
All three 100- mm nominal thickness sections had corner breaks or cracks on adjacent
slabs prior to HVS loading. In addition, Section 520FD had a corner crack on the leave end of
35
Table 2- 7 Summary of First Crack Occurrence for South Tangent Test Sections
Section
ID
Crack
Type
Load,
kN ** Repetitions
Estimated
Equivalent Single
Axle Loads,
ESALs
Transverse
Distance from
Corner Measured
on Transverse
Joint, m
Longitudinal
Distance from
Corner Measured
on Lane- Shoulder
Joint, m
519FD LC 25 2,105 5,800 1.1, 1.3 -
520FD LC 35 1,000 11,400 1.1, 1.2 -
521FD LC* 20 500 500 1.3 -
523FD CB 45 89,963 2.951,000 1.8 2.4
524FD LC* 45 64,332 2,110,000 1.8 -
525FD CB 45 1,000 32,800 1.7 1.8
526FD CB 85 100 47,400 1.4 1.8
527FD LC 35 129,805 1,482,000 1.5 -
528FD TC 40 56,912 1,138,000 - 2.1
529FD LC* 40
60
88,110
234,423 25,740,000 1.7 -
530FD CB
40
60
90
64,227
752,448
13,789
92,218,000 1.4 1.4
531FD CB 40
70
31,318
31,495 7,234,000 1.3 1.4
532FD CB 40
70
24,337
124,990 26,709,000 1.4 1.6
533FD Did not
fail
40
70
90
44,164
210,003
116,983
115,461,000 - -
534FD CB
40
70
90
126,580
858,022
288,932
356,716,000 1.8 1.9
535FD CB 90 67,935 40,953,000 1.6 3.2
536FD Did not
fail
90
70A
90A
110A
130A
150A
750,000
500
500
500
500
240,782
1,695,110,000 - -
537FD TC
40
70
90
13,230
500
30,000
18,454,000 - 1.3
538FD Did not
fail
70
90
500
188,882 113,969,000 - -
539FD TC
40
70
90
13,342
500
207,522
125,473,000 - 1.6
540FD CB
40
90
150A
13,003
392,062
65,000
571,477,000 1.7 2.0
541FD Did not
fail
70
90
150A
500
167,777
110,011
668,004,000 - -
* Progressed after additional loading to CB.
** A = aircraft wheel ( for loads above 100 kN)
LC = Longitudinal crack, CB = Corner break, TC = Transverse crack
36
the test slab prior to loading. However, the first crack to occur on all of the test slabs after HVS
loading was a longitudinal crack at a distance of between 1.1 and 1.4 m from the slab corners.
Some of the 150- mm nominal thickness test sections had corner breaks or cracks on
adjacent slabs prior to HVS loading. However, the first crack to occur on all test slabs after HVS
loading was a longitudinal crack or a corner break at a transverse distance of between 1.5 and 1.7
m from the slab corners.
For the 200 mm nominal thickness sections, none of the test sections or the adjacent slabs
had any cracks prior to HVS loading. However, the first crack to occur on three of the 200- mm
test slabs after HVS loading was a longitudinal crack ( or a corner break) at a transverse distance
of between 1.4 and 1.7 m from the slab corners. Section 528FD never developed a corner break
or a longitudinal crack through the course of the HVS loading. The only crack on this section
was a short transverse crack.
Three of the four undoweled sections on the North Tangent failed via corner breaks at a
transverse distance between 1.4 and 1.8 m. The fourth undoweled section, Section 533FD, did
not fail at the point testing was terminated. Two of the three doweled sections with tied concrete
shoulders did not fail at the point the testing was terminated. Only Section 537FD exhibited
transverse cracking after approximately 44,000 repetitions. Of the three doweled sections with
widened lanes, Section 541FD did not fail. Section 540FD failed via a corner break and Section
539FD exhibited transverse cracking.
A large amount of variability was observed between the fatigue performance of
individual test sections with the same design and identical load levels. For example, while a
longitudinal crack was observed on Section 524FD after more than 64,000 repetitions of 45- kN
loading, a replicate section, 525FD, had a corner break after only 1,000 repetitions of 45- kN
37
loading. Similarly, while Section 535FD cracked after less than 68,000 repetitions of 90- kN
loading, Section 534FD ( a similar section) carried more than a million repetitions of 40-, 70-,
and 90- kN loading before the first crack was observed. Similar differences were observed
between other replicate sections ( i. e., Sections 536FD and 537FD).
38
39
3.0 CURLING IN CONCRETE SLABS
Curling in concrete slabs is a combination of 5 nonlinear components ( summarized in
Table 3- 1):
• Temperature gradient through the slab— During daytime, the top of the concrete
slab is typically warmer than the bottom, resulting in a positive temperature gradient
through the slab. During nighttime, the top of the concrete slab is typically cooler
than the bottom, resulting in a negative temperature gradient through the slab.
Temperature gradients through the depth of the slab cause differences in elongation
strains between the top of the slab and the bottom of the slab, resulting in curling.
Field studies ( Armaghani et al., 1986; Yu et al., 1998) have shown that these
temperature gradients are nonlinear, and that the daily fluctuation in temperature is
greater on the surface than at the bottom of the slab. Air temperature, solar radiation,
cloud cover, and precipitation affect temperature gradients in concrete slabs.
• Built- in temperature gradient— Concrete paving is typically performed during the
daytime in warmer months of the year. During daytime paving, the top of the slab is
typically warmer than the bottom of the slab at the concrete set time. Since the
concrete slab sets under this condition, the flat slab condition is not associated with a
zero temperature gradient. When the temperature gradient in the slab is zero, the slab
curls upward rather than remaining flat. Thus, an effective negative temperature
gradient is “ built into” the slab, and is referred to as the built- in construction
temperature gradient. The magnitude of the built- in temperature gradient is affected
by air temperature and weather conditions during set and curing conditions
( Eisenmann and Leykauf, 1990; Yu et al., 1998).
40
• Moisture gradient through the slab— The surface of the slab ( depth < 50 mm) is
typically only partially saturated compared to the bottom, which is usually saturated
( Janssen, 1986; Grasley, 2003; Lim et al., 2004). The difference in internal relative
humidity in concrete pores between the top of the slab and the bottom of the slab
causes differential shrinkage strains, resulting in curling. The curling associated with
these reversible shrinkage strains is primarily affected by changes in atmospheric
temperature and relative humidity, weather phenomenon such as rainfall, snow, etc.,
and design factors such as pavement layer materials ( permeable base vs. poorly
draining base).
• Differential irreversible shrinkage— Drying shrinkage is defined as “ the reduction
in concrete volume resulting from a loss of water from the concrete after hardening”
( Mather, 1964). Significant irreversible drying occurs in a concrete pavement only to
a shallow depth ( approx. 50 mm) ( Janssen, 1986; Suprenant, 2002). The drying
shrinkage at the surface is affected by early- age curing conditions. The drying
shrinkage at the bottom of the slab is significantly lower due to the high relative
humidity in the pores at that portion of the slab. Autogenous shrinkage, which is a
special case of drying shrinkage, is due to self- desiccation when insufficient
hydration moisture is not present in the concrete. Differences in irreversible shrinkage
between the top of the slab and the bottom of the slab result in permanent differences
in shrinkage strains between the top of the slab and the bottom of the slab, which
causes the slab to curl or warp.
• Creep— Creep is defined as the increase in strain over time of concrete subjected to
constant stress and is inversely proportional to the strength of the concrete at the time
41
of applied stress ( Neville and Meyers, 1964). For a curled slab, stresses caused by
restraints from shoulder and adjacent slabs, as well as from slab self- weight, result in
creep, particularly during the early ages of concrete strength development.
Differential creep strains between the top of the slab and the bottom of the slab
effectively result in the recovery of a portion of the fixed curling in the slab ( built- in
temperature gradient + differential irreversible shrinkage) ( Schmidt, 2000; Rao et al.,
2001). Tensile creep mechanisms reduce shrinkage strain in restrained concrete by at
least 50 percent ( Altoubat and Lange, 2001).
Table 3- 1 Five Components of Curling in Concrete Pavement Slabs
Cause of
Slab Curling
Frequency
( Best Description) Comments
Temperature
gradient
Intraday variation +
weather ( e. g., snow, wind,
rainfall, cloud cover)
Result of differential temperature changes through the slab;
affected by intraday fluctuations in air temperature, solar
radiation, and weather phenomena.
Built- in
temperature
gradient
Fixed
Result of temperature gradients during concrete set;
affected by cement heat of hydration, air temperature and
weather phenomena during set.
Moisture
gradient
Seasonal variation +
weather ( e. g. rainfall)
Result of differential changes in slab moisture/ internal
relative humidity; affected by atmospheric temperature and
humidity, weather phenomena, and drainage.
Differential
drying
shrinkage
Majority develops during
early- age
Result of the irreversible differential loss of moisture in
concrete; affected by curing conditions, concrete material
constituents, and environmental conditions.
Creep Short + long- term change
Result of stresses arising from restraints and slab self-weight;
affected by magnitude of stresses and concrete
material constituents.
These components are affected by material properties such as coefficient of thermal
expansion, thermal conductivity, permeability, etc., and depend on mix design parameters such
as aggregate type, cement content and type, water content, admixtures, etc. ( Ytterberg, 1987;
Tremper and Spellman, 1963).
42
The total amount of curling in a slab due to a combination of these five factors can be
represented as a temperature difference— the total effective linear temperature difference
( TELTD), ΔTtot:
ΔTtot = ΔTtg + ΔTmg + ΔTbi + ΔTshr – ΔTcrp ( 3- 1)
where,
ΔTtg = Temperature difference between top and bottom of a slab equivalent to
( producing similar deflection response to) nonlinear vertical temperature
gradients in the slab.
ΔTmg = Temperature difference between top and bottom of a slab equivalent to
( producing similar deflection response to) nonlinear vertical moisture
gradients in the slab. This represents the reversible portion of the
differential drying shrinkage between the top and the bottom of the slab.
ΔTbi = Temperature difference between top and bottom of a slab equivalent to
( producing similar deflection response to) nonlinear built- in construction
temperature gradient.
ΔTshr = Temperature difference between top and bottom of a slab equivalent to
( producing similar deflection response to) irreversible differential drying
shrinkage between the top and the bottom of the slab.
ΔTcrp = Portion of ΔTbi and ΔTshr recovered through creep.
The cumulative effect of built- in temperature gradient, drying shrinkage gradient,
moisture gradient, and creep can be defined as an effective built- in temperature difference
( EBITD), ΔTebi. The EBITD is the linear temperature difference between the top and bottom of a
concrete slab that produces the same deflection response as the cumulative effects of nonlinear
built- in temperature gradient, nonlinear moisture gradient, and nonlinear shrinkage gradient,
reduced over time by creep ( Rao and Roesler, 2005A).
ΔTebi = ΔTbi + ΔTshr + ΔTmg – ΔTcrp ( 3- 2)
ΔTtot = ΔTtg + ΔTebi ( 3- 3)
TELTD = ΔTtg + EBITD ( 3- 4)
43
The four components of EBITD are generally grouped together because they are
relatively stable over a longer time period as compared to ΔTtg, which changes intraday to a
considerably greater extent. The EBITD has traditionally been reported by researchers as
“ locked- in curvature” ( Byrum, 2000), “ zero- stress temperature” ( Eisenmann and Leykauf, 1990),
“ equivalent temperature gradient” ( Rao et al., 2001; Fang, 2001), and “ built- in curl” ( Yu et al.,
1998; Beckemeyer et al., 2002). EBITD is also the sum of the “ permanent curl” defined in the
2002 Design Guide ( Yu et al. 2004) and ΔTmg.
3.1 Factors Affecting Slab Effective Built- In Temperature Difference
Wide ranges of factors affect the various components of EBITD. As discussed in Section
2.4.5, the cement used at Palmdale resulted in the concrete slab being highly vulnerable to
shrinkage and to differential shrinkage strains through the depth of the slab. Because of this, as is
typically the case, irreversible differential shrinkage was the primary component responsible for
EBITD for the test slabs. A brief discussion on the factors affecting the various components of
EBITD follows in this section. A comprehensive literature review describing these factors is
included in Appendix B.
3.1.1 Factors Affecting Differential Shrinkage through the Depth of the Slab
Tremper and Spellman ( 1963) measured curling in the field from profilograms of various
highway pavements. Curling was taken as the maximum distance along a perpendicular from the
slab profile to a straight line drawn between profile high points at either adjacent slab joints.
Prisms were made at the same time the slabs were cast, and were tested in the laboratory for
shrinkage. Figure 3- 1, developed by Suprenant ( 2002) using data from Tremper and Spellman,
shows that for a given project, curling deflection increases as drying shrinkage increases.
44
1 in = 25.4 mm
Figure 3- 1. Relationship between drying shrinkage of test specimens and the amount of
curling deflection of full- size test slabs for three different sections ( from Suprenant, 2002;
Tremper and Spellman, 1963).
However, due to the influence of other factors such as material properties, concrete mix
properties, ambient relative humidity, moisture content of underlying layers, slab geometry, etc.,
the magnitude of the effect of drying shrinkage on slab curling differs among projects. Because
of the significant effect of drying shrinkage on effective built- in curl, these factors that affect
drying shrinkage, and in particular, drying shrinkage gradients, are also factors that affect
EBITD. These issues and how they affect drying shrinkage and drying shrinkage differentials are
discussed in detail in Appendix B.
The factors involved in shrinkage potential of a concrete mix can have a cumulative
effect as shown in the example in Table 3- 2 developed by Mather ( 1964) using results from
Powers ( 1959). A similar analysis was presented by Tremper and Spellman ( 1963) as shown in
Table 3- 3. These tables suggest that up to a 5- to 7- fold increase in slab shrinkage can occur,
depending on presence/ absence of various factors that affect shrinkage. Although both these
45
Table 3- 2 Individual and Cumulative Effects of Various Factors on Concrete
Shrinkage Assuming Constant Water- Cement Ratio ( Mather, 1964; Powers,
1959)
Factor Effect*
Favorable Unfavorable Individual Cumulative
Cement of optimum SO3 SO3 deficiency 1.5 1.5
Cement with 15 percent
retained on No. 200 0 percent retained on No. 200 1.25 1.9
Less compressible aggregate
( quartz)
More compressible ( Elgin
gravel) 1.25 2.4
Large aggregate
( 38 mm [ 1 ½ in.] max. size)
Small aggregate
( 6 mm ( ¼ in) max. size) 1.3 3.1
More aggregate ( stiff mixture) Less aggregate ( wet mixture) 1.2 3.7
No clay in aggregate Much bad clay in aggregate 2.0 7.4
* Multiplication factor for potential increase in shrinkage
Table 3- 3 Cumulative Effect of “ Adverse” Factors on Shrinkage ( Tremper and
Spellman, 1963)
“ Poor” Practices That Can Cause Increased
Shrinkage in Concrete Slabs
Equivalent
Increase in
Shrinkage,
Percent Cumulative Effect
Temperature of concrete at discharge allowed to
reach 27 ° C ( 80 ° F), whereas with reasonable
precautions, a temperature of 16 ° C ( 60 ° F) could
have been maintained
8 1.00 × 1.08 = 1.08
Use of 150 to 180 mm ( 6 to 7 in) slump where 75
to 100 mm ( 3 to 4 in) slump could have been used 10 1.08 × 1.10 = 1.19
Excessive haul in transit mixer, too long a waiting
period at job site, or too many revolutions at
mixing speed
10 1.19 × 1.10 = 1.31
Use of 19 mm ( 3/ 4 in) maximum size aggregate
under conditions where 38 mm ( 1- 1/ 2 in)
aggregate could have been used
25 1.31 × 1.25 = 1.64
Use of cement having relatively high shrinkage
characteristics 25 1.64 × 1.25 = 2.05
Excessive “ dirt” in aggregate due to insufficient
washing or contamination during handling 25 2.05 × 1.25 = 2.56
Use of aggregates of poor inherent quality with
respect to shrinkage 50 2.56 × 1.50 = 3.84
Use of an admixture that produces high shrinkage 30 3.84 × 1.30 = 5.00
TOTAL INCREASE ( percent) Summation = 183 Cumulative = 400
46
tables suggest that the effects listed are independent ( which is likely an incorrect assumption),
they do point to the large effect that adverse factors can have on concrete shrinkage.
3.1.2 Factors Affecting Creep Due to Slab Restraints
Restraint of shrinkage leads to stress development, which in turn causes the material to
creep, particularly at early age following concrete placement. The shrinkage of concrete usually
occurs simultaneously with creep ( Kovler, 1999). Creep strains due to tensile restraint stresses
tend to counteract the effect of shrinkage. Tensile creep tests, in parallel with free shrinkage tests
and basic creep tests, were carried out by Kovler ( 1999) on replicate 40 × 40 × 1000 mm
specimens. Figure 3- 2 shows that total strain of specimen with 1 MPa applied tensile stress was
lower in magnitude than the free shrinkage strain. The difference between the free shrinkage
strain and the total strain is the total creep contributing to an effective reduction in shrinkage.
The total creep during drying was greater than the creep under conditions of no moisture
movement, also known as basic creep, as first observed by Pickett ( 1942), who introduced the
idea of “ drying creep” to denote the difference between the total creep and the basic creep.
Curling in field slabs is reduced by creep stresses from restraints caused by several
factors including: weight of the slab, load transfer between the slab and adjacent slabs and/ or
shoulder, and friction between the slab and underlying base layer. At early ages, these restraints
cause tensile creep at the top of the slabs, which results in an effective reduction in the EBITD.
Suprenant ( 2002) states that “ Generally, the length of lost subbase contact is about 10 percent of
the slab length ( measured between joints) at joints that have load transfer ( doweled or sawcut
joints), and about 20 percent at joints with no load transfer,” suggesting more curling in slabs
without load transfer as compared to slabs with load transfer. One of the effects of the restraint
due to load transfer and slab- base friction is that different corners of the same slab can have
47
Figure 3- 2. Experimental dependency of free shrinkage strain, total strain under
simultaneous drying and loading by tensile stress of 1 MPa, and basic creep under same
stress of concrete cured 1 day ( from Kovler, 1999).
different amounts of curling deflections and EBITD, particularly for undoweled pavements
( depending on local conditions) which will result in asymmetric slab curvature as shown in
Figure 1- 2. A discussion on some of the factors that affect creep is included in Appendix B.
3.1.3 Factors Affecting Built- In Curling from Ambient Conditions during Concrete Set
Pavement slabs are typically placed during the daytime, and often in the hot summer
months. In this case, a positive temperature gradient exists through the depth of the slab at the
48
time of concrete set. Because the concrete is fluid prior to set, it hardens flat on the base/ subbase
layer. The flat slab condition then corresponds to a positive temperature gradient in the slab.
After set, the slab will be flat only when the same positive temperature gradient is applied to the
slab. When the actual temperature gradient through the slab is zero, the slab will be in a concave
condition analogous to a slab with a negative temperature gradient through the depth of the slab.
This negative temperature gradient is the built- in curling in the slab, and an equivalent positive
temperature gradient through the depth of the slab is required for the slab to come in contact with
the base ( Yu et al. 1998; Hansen et al., 2002).
The magnitude of built- in curling due to hot weather construction can be as high as -
0.055 º C/ mm on many highway pavements ( Eisenmann and Leykauf, 1990). The built- in curling
is affected by air temperature, solar radiation, base/ subbase thermal conductivity and
temperature, weather conditions during set, and concrete curing procedure. Also, temperatures in
the slab during set and the time to set are functions of heat of hydration, and depend on mix and
material properties such as cement type, cement fineness, water/ cement ratio, admixtures, etc.
3.1.4 Effect of Modulus of Elasticity, Slab Thickness, and Joint Spacing
3.1.4.1 Modulus of Elasticity
The concrete’s modulus of elasticity can affect the magnitude of the concrete curling. The
higher the modulus, the greater is