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Publication Number: FHWA-HRT-08-073
Date: September 2009

Development of A Multiaxial Viscoelastoplastic Continuum Damage Model for Asphalt Mixtures

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Table of Contents

FOREWORD

The constitutive modeling of asphalt concrete behavior is a topic that has gained national importance in the past few years. Such modeling efforts have the explicit goal of providing for better design and analysis of asphalt pavement structures to resist failure and/or better predict when failure will occur. These efforts should thus provide the tools necessary to better utilize available resources and/or to gain maximum results from limited resources. One such modeling effort that encompasses the two main forms of pavement distress, cracking and permanent deformation, is the multiaxial viscoelastoplastic continuum damage (MVEPCD) model and finite element package, finite element program (FEP++). The MVEPCD model combines elements of viscoelasticity, continuum damage mechanics, and viscoplasticity to model the material behavior, and FEP++ is used to model the interaction of material and structure.

The MVEPCD model has been characterized and verified using asphalt concrete mixtures tested at the Federal Highway Administration's Accelerated Load Facility in McLean, VA. A novel approach to modeling this process is suggested and verified in this work. In light of practical concerns related to constant rate tests using the Asphalt Mixture Performance Tester and due to the complexities of performing true time-dependent analysis of cyclic fatigue tests, a refined and simplified viscoelastoplastic continuum damage model is presented. A robust FEP++ has been developed to account for the effects of loading and boundary conditions. Analysis can be performed in either two-dimensional or three-dimensional configurations. The resulting predictions are deemed reasonable and, thus, a reliable simulation of pavement response.

Cheryl Allen Richter
Acting Director, Office of Infrastructure
Research and Development

Notice

This document is disseminated under the sponsorship of the U.S. Department of Transportation in the interest of information exchange. The U.S. Government assumes no liability for the use of the information contained in this document.

The U.S. Government does not endorse products or manufacturers. Trademarks or manufacturers' names appear in this report only because they are considered essential to the objective of the document.

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The Federal Highway Administration (FHWA) provides high-quality information to serve Government, industry, and the public in a manner that promotes public understanding. Standards and policies are used to ensure and maximize the quality, objectivity, utility, and integrity of its information. FHWA periodically reviews quality issues and adjusts its programs and processes to ensure continuous quality improvement.

TECHNICAL REPORT DOCUMENTATION PAGE

1. Report No.

FHWA-HRT-08-073

2. Government Accession No.

3. Recipient's Catalog No.

4. Title and Subtitle

Development of a Multiaxial Viscoelastoplastic Continuum Damage Model for Asphalt Mixtures

5. Report Date

September 2009

6. Performing Organization Code

7. Author(s)

Y. Richard Kim, Ph.D. P.E., M.N. Guddati, Ph.D., B.S. Underwood, T.Y. Yun, V. Subramanian, S. Savadatti

8. Performing Organization Report No.

9. Performing Organization Name and Address

North Carolina State University
Department of Civil, Construction, and Environmental Engineering
Campus Box 7908
Raleigh, NC 27695

10. Work Unit No. (TRAIS)

11. Contract or Grant No.

DTFH61-05-H-00019

12. Sponsoring Agency Name and Address

Office of Research and Technology Services
Federal Highway Administration
6300 Georgetown Pike
McLean, VA 22101-2296

13. Type of Report and Period Covered

14. Sponsoring Agency Code

FHWA

15. Supplementary Notes

Project performed under FHWA DTFH61-05-H-00019; FHWA AOTR: Katherine Petros

16. Abstract

This report highlights findings from the FHWA DTFH61-05-H-00019 project, which focused on the development of the multiaxial viscoelastoplastic continuum damage model for asphalt concrete in both compression and tension. Asphalt concrete pavement, one of the largest infrastructure components in the United States, is a complex system that involves multiple layers of different materials, various combinations of irregular traffic loading, and various environmental conditions. The performance of this structure is closely related to the performance of asphalt concrete. To predict the performance of asphalt concrete with reasonable accuracy, a better understanding of its deformation behavior under realistic conditions is urgently needed. Over the past decade, the authors have been successful in developing uniaxial material models that can accurately capture various critical phenomena such as microcrack-induced damage that is critical in fatigue modeling, strain-rate temperature interdependence, and viscoplastic flow, which is critical for high temperature modeling. The resulting model is termed the viscoelastoplastic continuum damage model. However, to consider the complicated nature of in-service stress states, a multidimensional model is needed. To predict the performance of the real pavement structures, it is also important to incorporate the material model in a pavement model that considers the vehicle and climatic loads as well as the boundary conditions; the in-house finite element package has been developed for this purpose.

17. Key Words

Constitutive modeling, Asphalt concrete, Viscoelastic, Viscoplastic, Multiaxial, VECD, Damage mechanics

18. Distribution Statement

No restrictions. This document is available through the National Technical Information Service, Springfield, VA 22161.

19. Security Classif. (of this report)

Unclassified

20. Security Classif. (of this page)

Unclassified

21. No. of Pages

264

22. Price

Form DOT F 1700.7 (8-72) Reproduction of completed page authorized


SI (Modern Metric) Conversion Factors


TABLE OF CONTENTS

LIST OF FIGURES

Figure 1. Graph. Schematic representation of dynamic modulus shifting process with unshifted data

Figure 2. Graph. Schematic representation of dynamic modulus shifting process with shifted data

Figure 3. Graph. Schematic representation of dynamic modulus shifting process with time-temperature shift factor

Figure 4. Graph. Constant crosshead test results in stress-strain space

Figure 5. Graph. Constant crosshead test results in stress-pseudo strain space

Figure 6. Graph. Comparison of refined and approximate damage calculation techniques

Figure 7. Graph. Comparison of refined and approximate damage characteristic relationship

Figure 8. Illustration. Mechanical analog for the viscoplastic model

Figure 9. Illustration. Isotropic hardening diagram

Figure 10. Illustration. Kinematic hardening diagram

Figure 11. Illustration. Strain decomposition from creep and recovery testing

Figure 12. Illustration. Typical yield surface of HISS model

Figure 13. Graph. Mixture gradation chart

Figure 14. Graph. Comparison of test lane and laboratory gradations

Figure 15. Graph. Stress history of VL testing (unconfined and 140 kPa confinement VL)

Figure 16. Graph. Stress history of VL testing (500 kPa confinement VL)

Figure 17. Graph. Stress history of VLT testing (140 kPa confinement)

Figure 18. Graph. Stress history of VLT testing (500 kPa confinement)

Figure 19. Graph. Effect of 500 kPa confining pressure on the dynamic modulus in semi-log space

Figure 20. Graph. Effect of 500 kPa confining pressure on the dynamic modulus in log-log space

Figure 21. Graph. Effect of 500 kPa confining pressure on observed elasticity in the Control mixture

Figure 22. Graph. Effect of 500 kPa confining pressure on the log shift factor function

Figure 23. Graph. Effect of confining pressure on the relaxation spectrum

Figure 24. Graph. Use of the uniaxial relaxation spectrum for multiaxial test results

Figure 25. Graph. Effect of performing confined temperature/frequency sweep testing on the unconfined dynamic modulus

Figure 26. Graph. Multiaxial equilibrium characterization results

Figure 27. Graph. Multiaxial dynamic modulus model strength

Figure 28. Graph. C11 versus S for tension for Control-2006 mixture (5 °C reference)

Figure 29. Graph. Effect of time-dependent Poisson's ratio on C12 calculation

Figure 30. Graph. C12 characteristic curve for Control-2006 mixture

Figure 31. Graph. C12 characteristic curve for Control-2006 mixture in semi-logarithmic space

Figure 32. Graph. Effect of different time-independent Poisson's ratio values on radial strain predictions

Figure 33. Graph. C12 versus S for tensile loading for Control-2006 mixture (5 °C reference)

Figure 34. Graph. S as a function of reduced time calculated by three different methodologies in arithmetic space for 5-1-T

Figure 35. Graph. S as a function of reduced time calculated by three different methodologies in arithmetic space for 5-3-T

Figure 36. Graph. S as a function of reduced time calculated by three different methodologies in arithmetic space for 5-4-T

Figure 37. Graph. S as a function of reduced time calculated by three different methodologies in arithmetic space for 5-5-T

Figure 38. Graph. S as a function of reduced time calculated by three different methodologies in logarithmic space for 5-1-T

Figure 39. Graph. S as a function of reduced time calculated by three different methodologies in logarithmic space for 5-3-T

Figure 40. Graph. S as a function of reduced time calculated by three different methodologies in logarithmic space for 5-4-T

Figure 41. Graph. S as a function of reduced time calculated by three different methodologies in logarithmic space for 5-5-T

Figure 42. Graph. Predicted and measured stress as a function of reduced time for different S calculation methodologies for 5-1-T

Figure 43. Graph. Predicted and measured stress as a function of reduced time for different S calculation methodologies for 5-3-T

Figure 44. Graph. Predicted and measured stress as a function of reduced time for different S calculation methodologies for 5-4-T

Figure 45. Graph. Predicted and measured stress as a function of reduced time for different S calculation methodologies for 5-5-T

Figure 46. Graph. C22 as a function of S calculated by different methodologies for 5-1-T

Figure 47. Graph. C22 as a function of S calculated by different methodologies for 5-3-T

Figure 48. Graph. C22 as a function of S calculated by different methodologies for 5-4-T

Figure 49. Graph. C22 as a function of S calculated by different methodologies for 5-5-T

Figure 50. Graph. Representative C22 versus S for tension using optimization methodology (5 °C reference)

Figure 51. Graph. Effect of confining pressure on coefficient Y

Figure 52. Graph. Results of MVEPCD model simple verification for constant crosshead rate tests under 500 kPa confinement at 25 °C

Figure 53. Graph. Results of MVEPCD model verification for constant crosshead rate tests under 250 kPa confinement at 40 °C

Figure 54. Graph. Results of MVEPCD model verification for constant crosshead rate tests under 250 kPa confinement at 5 °C

Figure 55. Illustration. Schematic representation of first step for verifying the t-TS principle under growing damage, finding stress for different tests at a consistent strain level

Figure 56. Illustration. Schematic representation of the second step for verifying the t-TS principle under growing damage, finding reduced time for the stress found in the first step for each test

Figure 57. Illustration. Schematic representation of the third step for verifying the t-TS principle under growing damage, plotting the stress from the first step against the reduced time from the second step

Figure 58. Graph. Strain levels examined for verifying the t-TS principle under growing damage and confining pressure for the Control-2006 mixture

Figure 59. Graph. t-TS with growing damage under confinement verification at a 0.0001ε level

Figure 60. Graph. t-TS with growing damage under confinement verification at a 0.0005ε level

Figure 61. Graph. t-TS with growing damage under confinement verification at a 0.001ε level

Figure 62. Graph. t-TS with growing damage under confinement verification at a 0.0022ε level

Figure 63. Graph. t-TS with growing damage under confinement verification at a 0.004ε level

Figure 64. Graph. t-TS with growing damage under confinement verification at a 0.007ε

Figure 65. Graph. Effect of 500 kPa confining pressure on strength mastercurves

Figure 66. Graph. Effect of 500 kPa confining pressure on ductility in constant crosshead rate tests

Figure 67. Illustration. A schematic representation of the concept of average dC/dt

Figure 68. Illustration. A schematic representation of the effect of the M factor on dC/dt used in calculation

Figure 69. Illustration. Mathematical equivalence of the formulation used by Lee, Daniel, and Kim

Figure 70. Illustration. Schematic representation of assumptions made for controlled stress cyclic loading to develop Q and M factors

Figure 71. Illustration. Schematic representation of assumptions made for controlled crosshead cyclic loading to develop Q and M factors

Figure 72. Graph. Damage characteristic comparison, cyclic to monotonic using equation 127 Control mixture

Figure 73. Graph. Damage characteristic comparison, cyclic to monotonic using equation 127 CRTB mixture

Figure 74. Graph. Damage characteristic comparison, cyclic to monotonic using equation 127 SBS mixture

Figure 75. Graph. Damage characteristic comparison, cyclic to monotonic using equation 127 Terpolymer mixture

Figure 76. Graph. Damage characteristic comparison, cyclic to monotonic using refined model Control mixture

Figure 77. Graph. Damage characteristic comparison, cyclic to monotonic using refined model CRTB mixture

Figure 78. Graph. Damage characteristic comparison, cyclic to monotonic using refined model SBS mixture

Figure 79. Graph. Damage characteristic comparison, cyclic to monotonic using refined model Terpolymer mixture

Figure 80. Graph. Damage characteristic comparison, cyclic to monotonic using refined simplified model Control mixture

Figure 81. Graph. Damage characteristic comparison, cyclic to monotonic using refined simplified model CRTB mixture

Figure 82. Graph. Damage characteristic comparison, cyclic to monotonic using refined simplified model SBS mixture

Figure 83. Graph. Damage characteristic comparison, cyclic to monotonic using refined simplified model Terpolymer mixture

Figure 84. Graph. Damage characteristic comparison, cyclic to monotonic using refined simplified model 9.5-mm Fine mixture

Figure 85. Graph. Stress-strain curves for unconfined constant strain-rate tests

Figure 86. Graph. Stress-strain curves for 500 kPa confinement constant strain-rate tests

Figure 87. Graph. Comparison of 500 kPa confinement and unconfined constant rate tests for 5 °C

Figure 88. Graph. Comparison of 500 kPa confinement and unconfined constant rate tests for 25 °C

Figure 89. Graph. Comparison of 500 kPa confinement and unconfined constant rate tests for 40 °C

Figure 90. Graph. Comparison of 500 kPa confinement and unconfined constant rate tests for 55 °C

Figure 91. Graph. Viscoplastic strain versus cumulative loading time (unconfined VL)

Figure 92. Graph. Viscoplastic strain versus cumulative loading time (140 kPa confinement VL)

Figure 93. Graph. Viscoplastic strain versus cumulative loading time (500 kPa confinement VL)

Figure 94. Graph. Viscoplastic strain versus cumulative loading time (unconfined VT testing)

Figure 95. Graph. Viscoplastic strain versus cumulative loading time (500 kPa confinement for VT and RVT testing)

Figure 96. Graph. Incremental viscoplastic strain rate versus viscoplastic strain (500 kPa confinement, 1,600 kPa deviatoric)

Figure 97. Graph. Viscoplastic strain versus cumulative loading time (500 kPa confinement CLT)

Figure 98. Graph. Viscoplastic strain versus cumulative loading time (140 kPa confinement VT)

Figure 99. Graph. Stress-time curves for the Control mixture before the application of time-temperature shift factors at a 0.0001 strain level under uniaxial conditions

Figure 100. Graph. Stress-time curves for the Control mixture before the application of time-temperature shift factors at a 0.0005 strain level under uniaxial conditions

Figure 101. Graph. Stress-time curves for the Control mixture before the application of time-temperature shift factors at a 0.001 strain level under uniaxial conditions

Figure 102. Graph. Stress-time curves for the Control mixture before the application of time-temperature shift factors at a 0.003 strain level under uniaxial conditions

Figure 103. Graph. Stress-time curves for the Control mixture before the application of time-temperature shift factors at a 0.005 strain level under uniaxial conditions

Figure 104. Graph. Stress-time curves for the Control mixture before the application of time-temperature shift factors at a 0.01 strain level under uniaxial conditions

Figure 105. Graph. Stress-time curves for the Control mixture before the application of time-temperature shift factors at a 0.015 strain level under uniaxial conditions

Figure 106. Graph. Stress-time curves for the Control mixture before the application of time-temperature shift factors at a 0.02 strain level under uniaxial conditions

Figure 107. Graph. Stress-time curves for the Control mixture before the application of time-temperature shift factors at a 0.0001 strain level under 500 kPa conditions

Figure 108. Graph. Stress-time curves for the Control mixture before the application of time-temperature shift factors at a 0.0005 strain level under 500 kPa conditions

Figure 109. Graph. Stress-time curves for the Control mixture before the application of time-temperature shift factors at a 0.001 strain level under 500 kPa conditions

Figure 110. Graph. Stress-time curves for the Control mixture before the application of time-temperature shift factors at a 0.003 strain level under 500 kPa conditions

Figure 111. Graph. Stress-time curves for the Control mixture before the application of time-temperature shift factors at a 0.005 strain level under 500 kPa conditions

Figure 112. Graph. Stress-time curves for the Control mixture before the application of time-temperature shift factors at a 0.01 strain level under 500 kPa conditions

Figure 113. Graph. Stress-time curves for the Control mixture before the application of time-temperature shift factors at a 0.015 strain level under 500 kPa conditions

Figure 114. Graph. Stress-time curves for the Control mixture before the application of time-temperature shift factors at a 0.02 strain level under 500 kPa conditions

Figure 115. Graph. Stress mastercurves for the Control mixture under uniaxial conditions

Figure 116. Graph. Stress mastercurves for the Control mixture under triaxial conditions (500 kPa)

Figure 117. Graph. Variation of strain rate during unloading

Figure 118. Graph. Viscoplastic strain versus cumulative loading time (140 kPa confinement VT at 40 and 55 °C)

Figure 119. Graph. Confining stress effect on the relaxation modulus

Figure 120. Graph. Comparison of zero-mean and zero-maximum deviatoric stress dynamic modulus mastercurves in semi-logarithmic scale

Figure 121. Graph. Comparison of zero-mean and zero-maximum deviatoric stress dynamic modulus mastercurves in logarithmic scale

Figure 122. Graph. Effect of test method on shift factor functions

Figure 123. Graph. Comparison of zero-mean and zero-maximum deviatoric stress phase angle mastercurves

Figure 124. Graph. Application of stress state-dependent model to zero-maximum deviatoric stress tests

Figure 125. Diagram. MVECD model characterization

Figure 126. Graph. C11 versus S for compression for Control mixture (5 °C reference)

Figure 127. Graph. C12 versus S for compression for Control mixture (5 °C reference)

Figure 128. Graph. C22 versus S for compression for Control mixture (5 °C reference)

Figure 129. Graph. Comparison of tension and compression of C11 damage function

Figure 130. Graph. Comparison of tension and compression of C12 damage function

Figure 131. Graph. Comparison of tension and compression of C22 damage function

Figure 132. Graph. Incremental viscoplastic strain rate versus viscoplastic strain (500 kPa confinement, 2,000 kPa)

Figure 133. Graph. Determined fitting results and coefficients of function a(tp)

Figure 134. Graph. Determined fitting results and coefficients of function D(tp σ)

Figure 135. Graph. VT predictions

Figure 136. Graph. VL predictions

Figure 137. Graph. CLT predictions (2.0 MPa deviatoric stress-0.1-s pulse time)

Figure 138. Graph. CLT predictions (2.0 MPa deviatoric stress-0.4-s pulse time)

Figure 139. Graph. CLT predictions (2.0 MPa deviatoric stress-1.6-s pulse time)

Figure 140. Graph. CLT predictions (2.0 MPa deviatoric stress-6.4-s pulse time)

Figure 141. Graph. CLT predictions (1.8 MPa deviatoric stress-1.6-s pulse time)

Figure 142. Graph. CLT predictions (2.2 MPa deviatoric stress-1.6-s pulse time)

Figure 143. Graph. Compressive and tensile peak stress in SQRT(J2) - I1 space

Figure 144. Graph. Determined γ0 parameter function

Figure 145. Graph. Determined R parameter function

Figure 146. Graph. Determined n parameter function

Figure 147. Graph. Determined α0 parameter function

Figure 148. Graph. Rate-dependent initial yield surface

Figure 149. Graph. Variation of α for 1,800 kPa CLT loading (500 kPa confinement)

Figure 150. Graph. Viscoplastic strain predictions for VT tests (500 kPa confinement)

Figure 151. Graph. Viscoplastic strain predictions for CLT tests (500 kPa confinement)

Figure 152. Graph. Viscoplastic strain predictions for RVT tests (500 kPa confinement)

Figure 153. Illustration. Variation of yield stress (Standard Linear Solid model)

Figure 154. Graph. Stress histories for rest period analysis

Figure 155. Graph. Yield stress versus cumulative loading time (rest period analysis)

Figure 156. Graph. Viscoplastic strain versus cumulative loading time (rest period analysis)

Figure 157. Graph. Stress history for loading time analysis

Figure 158. Graph. Viscoplastic strain versus cumulative loading time (loading time analysis)

Figure 159. Graph. Viscoplastic strain versus cumulative loading time (140 kPa confinement VT)

Figure 160. Graph. Viscoplastic strain versus cumulative loading time (140 kPa confinement VL)

Figure 161. Graph. Viscoplastic strain versus cumulative loading time (500 kPa confinement VT)

Figure 162. Graph. Viscoplastic strain versus cumulative loading time (500 kPa confinement VL)

Figure 163. Graph. Viscoplastic strain versus cumulative loading time (140 kPa confinement VT)

Figure 164. Graph. Viscoplastic strain versus cumulative loading time (140 kPa confinement VLT)

Figure 165. Graph. Viscoplastic strain versus cumulative loading time (140 kPa confinement VT)

Figure 166. Graph. Viscoplastic strain versus cumulative loading time (140 kPa confinement VT + flow)

Figure 167. Graph. Viscoplastic strain versus cumulative loading time (500 kPa confinement 1,600 deviatoric VT)

Figure 168. Graph. Viscoplastic strain versus cumulative loading time (500 kPa confinement 2,000 deviatoric VT)

Figure 169. Graph. Viscoplastic strain versus cumulative loading time (500 kPa confinement 0.4 s CLT)

Figure 170. Graph. Viscoplastic strain versus cumulative loading time (500 kPa confinement 1.6 s CLT)

Figure 171. Graph. Viscoplastic strain versus cumulative loading time (500 kPa confinement 6.4 s CLT)

Figure 172. Graph. Viscoplastic strain versus cumulative loading time (500 kPa confinement VLT)

Figure 173. Graph. Damage characteristic relationship used in the finite element implementation of one-dimensional VECD model

Figure 174. Graph. Layout of the numerical experiment specimen

Figure 175. Graph. Effect of continuum damage evolution on the vertical displacement of the test specimen at point A in the test simulation

Figure 176. Graph. Verification of strain prediction for monotonic uniaxial test using the new continuum damage material model

Figure 177. Graph. Evolution of damage parameter, S, for the monotonic test

Figure 178. Graph. Plot of function C(S) with time

Figure 179. Diagram. Domain module

Figure 180. Illustration. Infinite elastic layer on a rigid base

Figure 181. Illustration. Finite element mesh required to model the physical problem with 1-percent accuracy without special elements

Figure 182. Illustration. Finite element mesh required to model the physical problem with 1-percent accuracy with special elements

Figure 183. Diagram. Analysis module

Figure 184. Screen capture. Main window of the preprocessor

Figure 185. Screen capture. Control panel

Figure 186. Screen capture. Mesh discretization

Figure 187. Screen capture. Zoom operation on a mesh

Figure 188. Diagram. Stages involved in an FEP++ analysis

Figure 189. Screen capture. Sample data entry window

Figure 190. Screen capture. Error dialog for a semantic error

Figure 191. Screen capture. Analysis run-time window

Figure 192. Graph. Temperature variations used for simulations

Figure 193. Illustration. Vertical strains in winter

Figure 194. Illustration. Vertical strains in summer

Figure 195. Illustration. Longitudinal strains in winter

Figure 196. Illustration. Longitudinal strains in summer

Figure 197. Illustration. Transverse strains in winter

Figure 198. Illustration. Transverse strains in summer

Figure 199. Illustration. Vertical strains for Control mixture

Figure 200. Illustration. Vertical strains for SBS mixture

Figure 201. Illustration. Longitudinal strains for Control mixture

Figure 202. Illustration. Longitudinal strains for SBS mixture

Figure 203. Illustration. Transverse strains for Control mixture

Figure 204. Illustration. Transverse strains for SBS mixture

Figure 205. Illustration. Vertical strains for a wheel speed of 13.41 m/s

Figure 206. Illustration. Vertical strains for a wheel speed of 26.82 m/s

Figure 207. Illustration. Longitudinal strains for a wheel speed of 13.41 m/s

Figure 208. Illustration. Longitudinal strains for a wheel speed of 26.82 m/s

Figure 209. Illustration. Transverse strains for a wheel speed of 13.41 m/s

Figure 210. Illustration. Transverse strains for a wheel speed of 26.82 m/s

Figure 211. Screen capture. General Information dialog

Figure 212. Screen capture. Material Properties dialog

Figure 213. Screen capture. Elastic material properties dialog

Figure 214. Screen capture. Viscoelastic material properties dialog

Figure 215. Screen capture. Prony Coefficients dialog

Figure 216. Screen capture. Layer properties dialog

Figure 217. Screen capture. Mesh properties dialog

Figure 218. Screen capture. Load properties dialog

Figure 219. Screen capture. Analysis Parameters dialog

Figure 220. Screen capture. Summary dialog

Figure 221. Screen capture. FEP++ analysis in progress

LIST OF TABLES

Table 1. Relevant asphalt binder information

Table 2. Summary of constructed lanes' air void and asphalt content

Table 3. Controlled crosshead testing matrix for Control-2006 in tension

Table 4. Controlled crosshead testing matrix for Control in compression

Table 5. Creep and recovery testing matrix for Control mixture in compression

Table 6. Test conditions for the VT and RVT tests

Table 7. Loading times for VLT test

Table 8. Linear viscoelastic characterization and variation for Control-2006 in unconfined state at selected frequencies and temperatures

Table 9. Linear viscoelastic characterization and variation for Control-2006 in 250 kPa confined state at selected frequencies and temperatures

Table 10. Linear viscoelastic characterization and variation for Control-2006 in 500 kPa confined state at selected frequencies and temperatures

Table 11. Effect of confining pressure on shift factor function coefficients for Control-2006 mixture

Table 12. Cyclic tests performed

Table 13. Summary of cyclic correction factors

Table 14. Summary of αvalues for refined model

Table 15. Cyclic tests performed for 9.5-mm Fine mixture

Table 16. Linear viscoelastic characterization and variation for the Control mixture in unconfined compression state at selected frequencies and temperatures

Table 17. Linear viscoelastic characterization and variation for the Control mixture in 140 kPa confined compression state at selected frequencies and temperatures

Table 18. Linear viscoelastic characterization and variation for the Control mixture in 500 kPa confined compression state at selected frequencies and temperatures

Table 19. Effect of confining pressure on shift factor function coefficients for the Control mixture in compression state

Table 20. Delft material model coefficients functions

Table 21. Material coefficients used for the developed model analysis

Table 22. Compression viscoplastic material model coefficients

Table 23. Properties of pavement

Table 24. Properties of moving wheel load

List of Acronyms and Symbols

Abbreviations

2D

Two-dimensional

3D

Three-dimensional

ALF

Accelerated Load Facility

AMPT

Asphalt Mixture Performance Tester

CLT

Constant loading level and time test

CR-TB

Crumb Rubber Terminal Blend

CS

Controlled stress

CX

Controlled crosshead

EICM

Enhanced Integrated Climatic Model

FEM

Finite element method

FEP++

Finite element package (proper name)

FHWA

Federal Highway Administration

GUI

Graphical user interface

HISS

Hierarchical single surface

HMA

Hot mix asphalt

IDT

Indirect tension test

LVDT

Linear variable displacement transducers

LVE

Linear viscoelastic

MVECD

Multiaxial viscoelastic continuum damage

MVEPCD

Multiaxial viscoelastoplastic continuum damage

NCHRP

National Cooperative Highway Research Program

NCSU

North Carolina State University

NMSA

Nominal maximum size aggregate

RVT

Reversed variable loading time test

SBS

Styrene-butadiene-styrene

SHRP

Strategic Highway Research Program

SPT

Simple Performance Tester

t-TS

Time-temperature superposition

TFHRC

Turner-Fairbank Highway Research Center

TRS

Thermorheologically simple

UVECD

Uniaxial viscoelastic continuum damage

UVEPCD

Uniaxial viscoelastoplastic continuum damage

VECD

Viscoelastic continuum damage

VECD-FEP++

Viscoelastic continuum damage model included in finite element package

VEPCD

Viscoelastoplastic continuum damage

VP

Viscoplastic

VL

Variable loading level test

VLT

Variable loading level and time test

VT

Variable loading time test

VTK

Visualization Toolkit

Symbols

εeif elastic strain
εpif plastic strain
εcif creep strain
εvif viscoplastic strain
εvpif elastic plus linear viscoelastic strain due to damage
εve elastic plus linear viscoelastic strain due to damage
R reduced physical frequency (Hz)
ωR reduced angular frequency (=2π∫RΔt)
αt time-temperature shift factor at specific temperature, T
π 3.141593---
σ stress
ε strain
εx strain in direction x
με microstrain
Ε(t) relaxation modulus
D(t) creep compliance
τ dummy integration variable
Ρ subscript i relaxation time (fitting coefficient)
τj retardation time (fitting coefficient)
Ε relaxation modulus at infinite time
Εi Prony coefficient for relaxation modulus
Dε glassy compliance
DjProny coefficient for creep compliance
Ε' storage modulus
| Ε* | dynamic modulus
Φ phase angle
t time
ξ reduced time
partial derivative
ΔX delta, finite difference in X
X delta, finite difference in X
εR pseudo strain
ΕR reference modulus
C normalized pseudo secant modulus
I normalization parameter
S damage
W strain energy density
W dR pseudo energy density
α viscoelastic damage growth rate
Cikl general stiffness matrix
ν Poisson's ratio
Ε elastic elongational modulus
G elastic shear modulus
Zij stiffness matrix for transversely isotropic material
Ε3 modulus along axis of symmetry
Ε modulus perpendicular to axis of symmetry
v3132 Poisson's ratio between axis of symmetry and perpendicular plane
v1323 Poisson's ratio between perpendicular plane and axis of symmetry
v12 Poisson's ratio on perpendicular plane
Υ Poisson's ratio term
Si compliance matrix for transversely isotropic material
Aj alterative stiffness matrix terms for transversely isotropic material
evvolumetric strain (dilation)
e3major deviatoric strain
e2 strain difference
Ρ pressure
C11 first material integrity term
C12 second material integrity term
C22 third material integrity term
υ dilation
υR pseudo dilation
Qi generalized loads
qi generalized displacements
υs complementary strain energy
εvp viscoplastic strain rate
λ positive scalar factor
g plastic potential function (general viscoplasticity)
Φ overstress function
η viscosity
Γ fluidity
I1 first stress invariant
J2 second deviatoric stress invariant
J3 third deviatoric stress invariant
sij deviatoric stress
δIJ Kroneker delta
Κ isotropic hardening parameter
αIJ viscoplastic kinematic hardening parameter
g stress function (strain hardening model specific)
Pα atmospheric pressure
R tensile strength parameter
n yield stress shape parameter
β parameter determining shape of yield stress in deviatoric stress space
εin inelastic strain rate
κ isotropic hardening function
α viscoplastic back stress parameter (kinematic hardening)
D drag stress
R isotropic hardening function
H kinematic hardening function
G back stress (viscoplastic model)
ζ viscoplastic strain trajectory
θ angular direction in axisymmetric coordinate system
α 1 time-temperature shift factor function coefficient 1
α2 time-temperature shift factor function coefficient 2
α3 time-temperature shift factor function coefficient 3
θ bulk stress
εRpressure pseudo strain due to pressure
υRpressure pseudo dilation due to pressure
εRe effective pseudo strain
εRs permanent pseudo strain
εRm total maximum pseudo strain
εRme total effective pseudo strain at peak of loading
M time change correction factor
tp pulse time
ζpreduced pulse time
N number of points in a calculation
F pseudo strain slope function
G pseudo strain hysterisis function
H healing function
Epsilon hat superscript r parenthesis t close parenthesis analytical expression for pseudo strain as a function of time
Q pseudo strain shape factor
Z combined pseudo strain shape and pseudo stiffness time factor
εR0,ta pseudo strain tension amplitude only
σ0,ta stress tension amplitude only
σpp peak-to-peak stress magnitude
β factor quantifying time under tensile loading
σpeak maximum value of stress in a cycle
σvalley minimum value of stress in a cycle
ζi reduced time within a cycle when tension loading begins
ζf reduced time within a cycle when tension loading ends
Rt form adjustment factor for characterization
κl form adjustment factor for prediction
ε0,ta strain tension amplitude only
α(tp) phenomenological viscoplastic model slope pulse time function
D phenomenological viscoplastic model intercept function
γ viscoplastic softening parameter
Il,dilation first stress invariant value at the beginning of dilation
J2,dilation second deviatoric stress invariant value at the beginning of dilation
εreduced reduced strain rate
D viscosity parameter (final viscoplastic model)
G orientation-dependent isotropic hardening function
Gn+1 value of hardening function at next time step
Gn value of hardening function at current time step
ζon value of elastic state variable at current time step
ζon+l value of elastic state variable at next time step
ζin value of state variable for element i at current time step
ζin+l value of state variable for element i at next time step
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