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J-1 Appendix J. Unbound Base Course Subroutine for Flexible Pavements The base course subroutine is used to calculate the equilibrium suction in the base course and the change of suction relative to the equilibrium suction. The outputs of the base course subroutine will be the modulus of base course that is anisotropic, stress dependent and moisture dependent, and the permanent deformation that is stress and moisture dependent. These will be supplied as inputs to the material properties in the current Pavement ME Design. The base subroutine outputs the models including: ï· Equilibrium suction model. ï· SWCC model. ï· Resilient modulus model for base course. ï· Permanent deformation. The regression equation for equilibrium suction is given as: | 0.0199 0.0047 3.3976 (J.1) | 0.0214 0.00607 3.5318 (J.2) where is the equilibrium suction on a pF scale; PI is plasticity index; is the Thorthwaite moisture index. The inputs to equilibrium suction model are presented in Table J.1 Table J.1. Input Variables to Equilibrium Suction Model. Input variables Description Unit TMI Thornthwaite moisture index Zm depth to moisture active zone cm PI plasticity index thickness of surface layer in thickness of base layer in thickness of subgrade in The Fredlund and Xing equation is used to estimate the relationship between matric suction and water content and expressed as: 1 ln (J.3) 1 ln 1 ln 1 1.45 10 (J.4) where S is the degree of saturation (unit is %); is soil matric suction (unit is psi); and , , , and are soil fitting parameters. These four fitting parameters are the outputs of ANN
J-2 models and are predicted by the input variables into SWCC models for plastic and non-plastic materials. Tables J.2 and J.3 present the associated inputs for SWCC model ( , , , and ) of plastic and non-plastic base materials. Table J.2. Input Variables to SWCC Model Parameters for Plastic Materials. Input variables Description Unit % passing # 4 percent passing No. 4 sieve size % % passing # 200 percent passing No. 200 sieve size % LL liquid limit PI plasticity index Sat.vol.wc saturated volumetric water content % Table J.3. Input Variables to SWCC Model Parameters for Non-plastic Materials. Input variables Description Unit D30 (mm) particle size corresponding to 30% passing mm D60 (mm) particle size corresponding to 60% passing mm D90 (mm) particle size corresponding to 90% passing mm scale parameter in aggregate gradation shape parameter in aggregate gradation Sat.vol.wc saturated volumetric water content % The resilient modulus of subgrade considering the moisture and suction dependency is given: 3 (J.5) where is the resilient modulus (unit is MPa); is first invariant of the stress tensor (kPa); is volumetric water content; is matric suction; is octahedral shear stress; is atmospheric pressure (101.325 kPa); is saturation factor (1 ); , and are regression coefficients that can be predicted by ANN models for plastic and non-plastic materials. Tables J.4 and J.5 present the input variables into ANN models ( , and ) of plastic and non-plastic materials.
J-3 Table J.4. Input Variables into ANN Model of Plastic Materials. Input variables Description Unit % passing 3/8" percent passing 3/8" sieve size % % passing # 200 percent passing No. 200 sieve size % PL Plasticity limit PI plasticity index OMC Optimum moisture content % MDD Maximum dry density / Test MC tested moisture content % Table J.5. Input Variables into ANN Model of Non-plastic Materials. Input variables Description Unit % passing 3/8" percent passing 3/8" sieve size % % passing # 200 percent passing No. 200 sieve size % scale parameter in aggregate gradation shape parameter in aggregate gradation OMC Optimum moisture content % MDD Maximum dry density / Test MC tested moisture content % The new mechanistic-empirical permanent deformation model for unbound materials was proposed, which can predict the permanent deformation behavior at different stress state using the single stage test protocol. The formulation of the model is given as: (J.6) 2 â3 3 (J.7) 6 â² â3 3 (J.8) Table J.6. Input Variables into Permanent Deformation Parameters. Input variables Description Unit % passing # 4 percent passing No. 4 sieve size % % passing # 200 percent passing No. 200 sieve size % MDD Maximum dry density / saturated volumetric water content % OMC Optimum moisture content % PI plasticity index Gs specific gravity
J-4 In addition, the inputs to program JULEA include: ï· Loads. ï· Layer thickness and Poissonâs Ratio. ï· Layer Moduli. Figure J.1 presents the flowchart of incorporating the base course models into Pavement ME design for flexible pavements. Pavement ME Design Traffic Pavement structure Materials Loads Layer thickness Variation of degree of saturation around equilibrium Program JULEA Calculate stress state in base course Calculate Equilibrium suction in base course Variation of volumetric water content Suction at varying degrees of saturation Modulus of base course Anisotropic, stress and suction dependent New Input to Base Course Subroutine Suction vs water content coefficients, levels of input I, II, III Base course porosity Modulus model coefficients, levels of input I, II, III Pavement deformation model coefficients, levels of input I, II, III Ite ra te Modulus of base course Permanent deformation properties Pavement ME Design Materials Permanent deformation properties Figure J.1. Flowchart of Incorporating the Base Course Models into Pavement ME Design for Flexible Pavements.