2appendices_RR

LIST OF FIGURES

Figure 1. Conceptual depiction of relative uncertainties of components in pavement performance prediction system.....................................................6

Figure 2. Sand test pit for comparison of measured vs. predicted stresses. (Ullidtz, Askegaard, and Sjolin, 1996).....................................................8

Figure 3. Comparison of measured vs. predicted stresses for sand test pit. (Ullidtz, Askegaard, and Sjolin, 1996).....................................................8

Figure 4. Comparisons between backcalculated and measured asphalt tension strains at MnRoad (Dai et al., 1987).....................................................9

Figure 5. Comparisons between predicted and measured subgrade stresses at the Danish test road (Ertman, Larsen, and Ullidtz, 1987).....................................................9

Figure 6. Theoretical vs. measured pavement stresses and strains (Ullidtz, 1998). [Note: Low values (<50) are stresses on the subgrade in kPa; intermediate values (50-400) are asphalt tensile strains in με; higher values (100-600) are subgrade compressive strains in με; (P. Ullidtz, personal communication).].....................................................10

Figure 7. Nonlinear material behavior.....................................................11

Figure 8. Example of influence of nonlinear unbound material on predicted surface deflections (Chen et al., 1995).....................................................12

Figure 9. Comparison of measured subgrade vertical strain against predictions from linearly elastic pavement response models (Ullidtz, 1998).....................................................13

Figure 10. Computation times for KENLAYER.....................................................19

Figure 11. Computation times for JULEA.....................................................20

Figure 12. Coarse refinement mesh (396 elements).....................................................23

Figure 13. Medium refinement mesh (1584 elements).....................................................24

Figure 14. Fine refinement mesh (3564 elements).....................................................25

Figure 15. Surface displacements computed at different mesh refinements.....................................................26

Figure 16. Vertical stresses along centerline at different mesh refinements.....................................................26

Figure 17. Horizontal stresses along centerline at different mesh refinements.....................................................27

Figure 18. Comparison of finite element execution times.....................................................27

Figure 19. Medium refinement mesh with distant infinite boundary elements.....................................................29

Figure 20. Medium refinement mesh with close infinite boundary elements.....................................................30

Figure 21. Finite element solution times using infinite boundary elements.....................................................31

Figure 22. Overall program flow.....................................................46

Figure 23. Data flow from the 2002 Design Guide user interface program.....................................................47

Figure 24. Data flow for PRE-DSC pre-processor program.....................................................47

Figure 25. Data flow for DSC2D finite element program.....................................................48

Figure 26. Data flow for POST-DSC post-processor program.....................................................49

Figure 27. Data flow to 2002 Design Guide user interface program.....................................................49

Figure 28. Conceptual depiction of finite element model.....................................................52

Figure 29. Schematic of incremental iterative nonlinear solution technique.....................................................52

Figure 30. Definition of resilient modulus as a chord modulus.....................................................56

Figure 31. Normalized stress, tangent modulus, and secant modulus vs. strain (k₁=1000; k₂=0.25, 0.5, 0.75; k₃=-0.3; σ_c=0).....................................................62

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Foreword

The finite element code that is used for the non-linear assessment of flexible (AC) pavement systems in the analysis and design methodology of the Design Guide, and referred to in this Appendix, is a modified and enhanced version of the DSC2D finite element code originally developed by Dr. C. S. Desai at the University of Arizona, Tucson. Significant additions, modifications and enhancements were implemented by Dr. Schwartz and his research team in order to fully implement the DSC2D code properly into the 2002 Design Guide approach.

Some of the major enhancements, completed by the University of Maryland research team, dealt with the following issues:

• Formulation of the final non-linear Mr (resilient modulus) implementation scheme for all unbound base, subbase and subgrade layers characterized by the 3 parameter ki non-linear model function selected for use in the Design Guide analysis methodology.
• Development of an enhanced tension cutoff model and associated convergence routines.
• Development of practical user guidelines, including details of incorporating infinite elements at the boundaries of the mesh, as well as sensitivity studies to determine the appropriate locations for the infinite elements within the mesh.
• Restructuring the DSC2D model to efficiently predict pavement response values in the continuous, multi-seasonal analysis used in the cumulative incremental damage approach employed in both the linear or non-linear pavement analysis approaches of the 2002 Design Guide.
• Development of both pre and post processors for the DSC2D to generate finite element pavement models from the main program user interface and to extract salient pavement damages and distress quantities from the stresses and strains computed by the finite element program.
• Finally, the development of the detailed user documentation for the code formulation and implementation as presented in this Appendix.

Note that general two and three dimensional disturbed state concept DSC codes, with many additional features, such as a wide selection of material models (elastic, plastic, HISS, creep, disturbance (damage), static, dynamic and repetitive loading, coupled fluid effects and thermal loading) have been developed by C.S.Desai and are available. These programs have been validated for a wide range of engineering problems, including pavement systems. For further information, one can visit the web site: dscfe.com; write to DSC, P.O. Box 65587, Tucson, Arizona 85728 or e-mail: support@dscfe.com

Acknowledgements

The research team for NCHRP Project 1-37A: Development of the 2002 Guide for the Design of New and Rehabilitated Pavement Structures consisted of Applied Research Associates, Inc. (ERES Division) as the prime contractor with Arizona State University (ASU) and Fugro-BRE, Inc. as subcontractors. University of Maryland and Advanced Asphalt Technologies, LLC served as subcontractors to the Arizona State University along with several independent consultants.

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Research into this subject area was conducted in ASU under the guidance of Dr. M. W. Witczak. Dr Witczak was assisted by Dr. C. W. Schwartz and Mr. Y.Y. Feng of the University of Maryland. Other contributors were Dr. Jacob Uzan of Technion University (Israel) and Dr. Waseem Mirza of ASU.

The pioneering work of Dr. C. S. Desai at the University of Arizona in developing the original version of the DSC2D finite element code is gratefully acknowledged.

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TABLE OF CONTENTS

TABLE OF CONTENTS....................................................................................................iv

LIST OF FIGURES ....................................................................................................vi

LIST OF TABLES ....................................................................................................x

1. INTRODUCTION ....................................................................................................1

1.1 Objectives of Pavement Response Models ....................................................1

1.2 Accuracy of Pavement Performance Predictions............................................4

1.2.1 Sources of Error in Performance Predictions............................................4

1.2.2 Validation of Pavement Response Models ................................................6

1.3 Selection of Analysis Method ........................................................................10

1.3.1 Material Behavior ....................................................................................10

1.3.2 Problem Dimensionality ..........................................................................13

1.3.3 Computational Practicality........................................................................14

1.3.4 Implementation Considerations ..............................................................33

1.3 Summary of Finite Element Advantages and Disadvantages ......................34

2. SELECTION OF FINITE ELEMENT PROGRAM............................................................37

2.1 Key Issues ......................................................................................................37

2.1.1 Efficiency Issues ......................................................................................37

2.1.2 Operational Issues ....................................................................................39

2.2 Key Features Of Candidate Programs..........................................................40

2.3 Final Selection ..............................................................................................42

3. ORGANIZATION OF THE FINITE ELEMENT PROGRAMS............................................45

4. DSC2D FINITE ELEMENT PROGRAM............................................................................50

4.1 Basic Formulation ..........................................................................................50

4.2 Nonlinear Resilient Modulus Model..............................................................53

4.2.1 Finite Element Implementation..................................................................57

4.2.2 Importance of Nonlinear Behavior ............................................................64

4.2.3 Nonlinear Superposition ..........................................................................89

4.3 Infinite Boundary Element............................................................................107

4.3.1 Finite Element Formulation ....................................................................107

4.3.2 Guidelines for Infinite Boundary Element Location ..............................115

5. PRE-DSC PREPROCESSOR PROGRAM........................................................................127

6. POST-DSC POSTPROCESSING PROGRAM..................................................................130

7. PROGRAM INPUT/OUTPUT FILES ..............................................................................131

7.1 Overview........................................................................................................131

7.1.1 PRE-DSC Pre-Processor Program ..........................................................131

7.1.2 DSC2D Finite Element Program ............................................................132

7.1.3 POST-DSC Post-Processor Program ......................................................132

7.2 PRE-DSC Input/Output Files........................................................................133

LAYERS.CSV ....................................................................................................133

LAYERS.INI ......................................................................................................135

LOADLEVELS.CSV ............................................................................................137

PREPOST.DAT ..................................................................................................138

PROJECT_TANDEMAXLEOUTPUT.CSV ........................................................140

PROJECT_TRIDEMAXLEOUTPUT.CSV ..........................................................140

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PROJECT_QUADAXLEOUTPUT.CSV	140
7.3 DSC2D Input/Output Files	142
DSC.IN	143
Emmmm-nn.OUT	154
7.4 POST-DSC Input/Output Files	155
FATIGUE.OUT	155
PERMDEF.OUT	156
8. PROGRAMMER DOCUMENTATION FOR FINITE ELEMENT PROGRAMS	157
8.1 Subroutine Calls for DSC2D	158
8.1.1 Linear Solution	159
8.1.2 Nonlinear Solution	161
8.2 COMMON Variables in DSC2D	163
8.3 Array Pointers in DSC2D	166
9. REFERENCES	168
10. ALTERNATIVE FORMULATION FOR NONLINEAR MR	174

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LIST OF FIGURES

Figure 1. Conceptual depiction of relative uncertainties of components in pavement performance prediction system.....................................................6

Figure 2. Sand test pit for comparison of measured vs. predicted stresses. (Ullidtz, Askegaard, and Sjolin, 1996).....................................................8

Figure 3. Comparison of measured vs. predicted stresses for sand test pit. (Ullidtz, Askegaard, and Sjolin, 1996).....................................................8

Figure 4. Comparisons between backcalculated and measured asphalt tension strains at MnRoad (Dai et al., 1987).....................................................9

Figure 5. Comparisons between predicted and measured subgrade stresses at the Danish test road (Ertman, Larsen, and Ullidtz, 1987).....................................................9

Figure 6. Theoretical vs. measured pavement stresses and strains (Ullidtz, 1998). [Note: Low values (<50) are stresses on the subgrade in kPa; intermediate values (50-400) are asphalt tensile strains in με; higher values (100-600) are subgrade compressive strains in με; (P. Ullidtz, personal communication).].....................................................10

Figure 7. Nonlinear material behavior.....................................................11

Figure 8. Example of influence of nonlinear unbound material on predicted surface deflections (Chen et al., 1995).....................................................12

Figure 9. Comparison of measured subgrade vertical strain against predictions from linearly elastic pavement response models (Ullidtz, 1998).....................................................13

Figure 10. Computation times for KENLAYER.....................................................19

Figure 11. Computation times for JULEA.....................................................20

Figure 12. Coarse refinement mesh (396 elements).....................................................23

Figure 13. Medium refinement mesh (1584 elements).....................................................24

Figure 14. Fine refinement mesh (3564 elements).....................................................25

Figure 15. Surface displacements computed at different mesh refinements.....................................................26

Figure 16. Vertical stresses along centerline at different mesh refinements.....................................................26

Figure 17. Horizontal stresses along centerline at different mesh refinements.....................................................27

Figure 18. Comparison of finite element execution times.....................................................27

Figure 19. Medium refinement mesh with distant infinite boundary elements.....................................................29

Figure 20. Medium refinement mesh with close infinite boundary elements.....................................................30

Figure 21. Finite element solution times using infinite boundary elements.....................................................31

Figure 22. Overall program flow.....................................................46

Figure 23. Data flow from the 2002 Design Guide user interface program.....................................................47

Figure 24. Data flow for PRE-DSC pre-processor program.....................................................47

Figure 25. Data flow for DSC2D finite element program.....................................................48

Figure 26. Data flow for POST-DSC post-processor program.....................................................49

Figure 27. Data flow to 2002 Design Guide user interface program.....................................................49

Figure 28. Conceptual depiction of finite element model.....................................................52

Figure 29. Schematic of incremental iterative nonlinear solution technique.....................................................52

Figure 30. Definition of resilient modulus as a chord modulus.....................................................56

Figure 31. Normalized stress, tangent modulus, and secant modulus vs. strain (k₁=1000; k₂=0.25, 0.5, 0.75; k₃=-0.3; σ_c=0).....................................................62

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