Proposed Enhancements to Pavement ME Design: Improved Consideration of the Influence of Subgrade and Unbound Layers on Pavement Performance (2019)

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D-1 Appendix D. Moisture-Sensitive, Stress-Dependent, and Cross- Anisotropic Resilient Modulus Researchers have recently developed a new constitutive model (66) for unbound base courses considering both nonlinear cross-anisotropic behavior and moisture-sensitive characteristics, and incorporating the proposed constitutive model into the finite element model of the base layer to quantify the influence of moisture content on the pavement performance. More specifically, the saturation factor and the matric suction of the unsaturated unbound aggregates are applied to the proposed constitutive model to reflect the moisture dependence. Additionally, a new user-defined material subroutine (UMAT) is developed to characterize the moisture-sensitive and stress-dependent nonlinear cross-anisotropic behavior of base materials in the software ABAQUS. The formulation of the model is given as follows: 2 3 1 1 3 k k V m oct R a a a I fhM k P P P               (D.1) ; H R VH V V R R M Gs r M M   (D.2) where V RM is the resilient modulus in the vertical direction; 1I is the first invariant of stress tensor; oct is the octahedral shear stress; aP is the atmospheric pressure;  is the volumetric water content; f is the saturation factor, 11 f    ; mh is the matric suction; 1k , 2k , and 3k are regression coefficients; H RM is the resilient modulus in the horizontal direction; VHG is the shear modulus in the horizontal–vertical plane; and s r are the modulus ratios. In order to verify the accuracy of the modulus model in Equation D.1, researchers used the repeated load triaxial test (Figure D.1) measurements on three selected materials at three different moisture contents. The matric suction value in Equation 4.1 is obtained from the filter paper test, required as Level 1 input. For Level 2, the suction will be calculated from the relation between the Thornthwaite moisture index (TMI) and the equilibrium suction value (details are presented in Appendix I, “Subgrade Subroutine for Flexible and Rigid Pavements”). Figure D.2 presents the comparison between the predicted moduli using Equation 4.1 and the measured moduli from the triaxial tests. The model prediction provides a good agreement with the test measurements. This indicates that the constitutive model proposed in Equation D.1 can reflect the moisture-sensitive and stress-dependent behavior of unbound aggregates. After verification, Equations D.1 and D.2 are coded into a UMAT to develop a moisture-sensitive and stress- dependent nonlinear program that incorporates cross-anisotropy.

D-2 Figure D.1. Configuration of Repeated Load Triaxial Test. Figure D.2. Comparison of Predicted and Measured Resilient Moduli for Unbound Base Materials. (A, B, C stand for 3 types of unbound aggregates) Using this moisture-sensitive and stress-dependent nonlinear cross-anisotropic program, the numerical study is conducted on a typical flexible pavement structure to examine its capability to reflect the influence of unbound base on the pavement performance. The pavement structure, finite element model, and modeling parameters are given in Figure D.3. 0 200 400 600 800 1000 0 200 400 600 800 1000 Pr ed ic te d  Re si lie nt  M od ul us   (M Pa ) Measured Resilient Modulus (MPa) A @ Optimum Moisture Content (OMC) A @ 1.5% Above OMC A @ 1.5% Below OMC B @ OMC B @ 1.5% Above OMC B @ 1.5% Below OMC C @ OMC C @ 1.5% Above OMC C @ 1.5% Below OMC

D-3 (a) Schematic Plot of Pavement Structure (b) Meshed Finite Element Model Traffic Load   565 kPa (9 kips)  Base Moisture Conditions  Moist (1.5% above optimum)  Optimum  Dry (1.5 below optimum)  Material Properties  HMA layer  Viscoelastic  Unbound base course  Nonlinear cross‐anisotropic & moisture‐sensitive  Subgrade  Elastic  (c) Modeling Parameters Figure D.3. Finite Element Modeling Using Moisture-Sensitive and Stress-Dependent Nonlinear Cross-Anisotropic Program. The tensile strain at the bottom of the asphalt layer and the compressive strain in the base course are obtained from the numerical modeling, as shown in Figures D.4 and D.5. The increase of the moisture content in the base course significantly increases the tensile strain at the bottom of the asphalt layer; it also leads to a raise of the compressive strain in the base course. The incorporation of cross-anisotropy of base materials results in an increase of both tensile strain at the bottom of the asphalt layer and compressive strain in the base course. According to the fatigue life prediction equation and rut depth equation in Pavement ME Design, the fatigue life and the rut depth of this pavement change accordingly. The results of these pavement responses indicate that the proposed model and program can properly reflect the influence of moisture of base materials and the resulting change of the stress state in the base course on pavement performance. The model and program also reflect the fact that granular base materials exhibit cross-anisotropic behaviors that affect the performance of pavements.

D-4 (a) Tensile Strain at Bottom of Asphalt Layer to Predict Fatigue Life (b) Compressive Strain in Unbound Base to Predict Rutting Figure D.4. Demonstration of Effect of Moisture on Pavement Performance. 200 250 300 350 400 450 Dry Opt Moist Te ns ile  S tr ai n  at  th e  bo tt om   of  A sp ha lt  La ye r ( µε ) 200 300 400 500 600 700 800 Dry Opt Moist Av er ag e  co m pr es si ve   st ra in  in  B as e  (µ ε)

D-5 (a) Tensile Strain at Bottom of Asphalt Layer to Predict Fatigue Life (b) Compressive Strain in Unbound Base to Predict Rutting Figure D.5. Demonstration of Effect of Cross-Anisotropy on Pavement Performance. Table D.1. Ranges of Input Parameters Used in ANN Models for Plastic and Non-plastic Base Materials. Plastic Soil Non-plastic Soil Input parameters Range Input parameters Range Percent passing No. 3/8" sieve 42–83 Percent passing No. 3/8" sieve 34–80 Percent passing No. 200 sieve 7.5–33.3 Percent passing No. 200 sieve 4–44.7 PL 12–48 Scale parameter, ϴ 13.7–51 PI 1–23 Shape parameter, Ѱ 0.165–0.47 OMC 5–20 OMC 4–20 MDD 103–151 MDD 98–153 Test MC 4.5–20 Test MC 3.4–19.8 200 240 280 320 360 400 Nonlinear Anisotropic Model Nonlinear Isotropic Model Te ns ile  S tr ai n  at  th e  bo tt om   of  A sp ha lt  La ye r( µε ) 200 300 400 500 600 Nonlinear Anisotropic Model Nonlinear Isotropic Model Av er ag e  co m pr es si ve  st ra in   in  B as e  (µ ε)

D-6 Table D.2. Ranges of Input Parameters Used in ANN Models for Plastic and Non-plastic Subgrade Materials. Plastic Soil Non-plastic Soil Input parameters Range Input parameters Range Percent passing No. 3/8" sieve 50–100 Percent passing No. 3/8" sieve 53–100 Percent passing No. 200 sieve 1.8–98.4 Percent passing No. 200 sieve 1.7–96.7 PL 8–44 Scale parameter, ϴ 18.8–98.7 PI 1–75 Shape parameter, Ѱ 0.004–0.55 OMC 7–32 OMC 7–26 MDD 86–139 MDD 94–139 Test MC 6.4–35 Test MC 5.4–25.3