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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 ï± ï´ï¦ ï¶ ï¦ ï¶ï ï½ ï§ ï· ï§ ï· ï¨ ï¸ ï¨ ï¸ (D.1) ; H R VH V V R R M Gs r M M ï½ ï½ (D.2) where V RM is the resilient modulus in the vertical direction; 1I is the first invariant of stress tensor; octï´ is the octahedral shear stress; aP is the atmospheric pressure; ï± is the volumetric water content; f is the saturation factor, 11 f ï± ï£ ï£ ; 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 horizontalâvertical 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, âSubgrade Subroutine for Flexible and Rigid Pavementsâ). 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 dÂ Re si lie nt Â M od ul us Â (M Pa ) MeasuredÂ ResilientÂ ModulusÂ (MPa) AÂ @Â OptimumÂ Moisture ContentÂ (OMC) AÂ @Â 1.5%Â AboveÂ OMC AÂ @Â 1.5%Â BelowÂ OMC BÂ @Â OMC BÂ @Â 1.5%Â AboveÂ OMC BÂ @Â 1.5%Â BelowÂ OMC CÂ @Â OMC CÂ @Â 1.5%Â AboveÂ OMC CÂ @Â 1.5%Â BelowÂ OMC
D-3 (a) SchematicÂ PlotÂ ofÂ PavementÂ Structure (b) MeshedÂ FiniteÂ ElementÂ Model TrafficÂ LoadÂ Â 565Â kPaÂ (9Â kips)Â BaseÂ MoistureÂ ConditionsÂ MoistÂ (1.5%Â aboveÂ optimum)Â OptimumÂ DryÂ (1.5Â belowÂ optimum)Â MaterialÂ PropertiesÂ HMAÂ layerÂ ViscoelasticÂ UnboundÂ baseÂ courseÂ NonlinearÂ crossâanisotropicÂ &Â moistureâsensitiveÂ SubgradeÂ ElasticÂ (c) ModelingÂ 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 Â S tr ai nÂ at Â th eÂ bo tt om Â of Â A sp ha ltÂ La ye rÂ ( ÂµÎµ ) 200 300 400 500 600 700 800 Dry Opt Moist Av er ag eÂ co m pr es si ve Â st ra in Â in Â B as eÂ (Âµ Îµ)
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 42â83 Percent passing No. 3/8" sieve 34â80 Percent passing No. 200 sieve 7.5â33.3 Percent passing No. 200 sieve 4â44.7 PL 12â48 Scale parameter, Ï´ 13.7â51 PI 1â23 Shape parameter, Ñ° 0.165â0.47 OMC 5â20 OMC 4â20 MDD 103â151 MDD 98â153 Test MC 4.5â20 Test MC 3.4â19.8 200 240 280 320 360 400 NonlinearÂ Anisotropic Model NonlinearÂ Isotropic Model Te ns ile Â S tr ai nÂ at Â th eÂ bo tt om Â of Â A sp ha ltÂ La ye r( ÂµÎµ ) 200 300 400 500 600 NonlinearÂ Anisotropic Model NonlinearÂ IsotropicÂ Model Av er ag eÂ co m pr es si ve Â st ra in Â in Â B as eÂ (Âµ Îµ)
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 50â100 Percent passing No. 3/8" sieve 53â100 Percent passing No. 200 sieve 1.8â98.4 Percent passing No. 200 sieve 1.7â96.7 PL 8â44 Scale parameter, Ï´ 18.8â98.7 PI 1â75 Shape parameter, Ñ° 0.004â0.55 OMC 7â32 OMC 7â26 MDD 86â139 MDD 94â139 Test MC 6.4â35 Test MC 5.4â25.3