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

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I-1 Appendix I. Subgrade Subroutine for Flexible and Rigid Pavements The subgrade subroutine is used to produce the modulus of subgrade, which is both stress dependent and moisture dependent. Because of the moisture dependence, this will require the iteration of the elastic layer program (JULEA). The modulus will be able to change as frequently as the degree of saturation changes. The subgrade subroutine will also supply the base course subroutine with the equilibrium suction at the depth of constant suction. The subgrade subroutine outputs the models including:  Equilibrium suction model.  Suction Water Characteristics Curve (SWCC) model.  Resilient modulus model for subgrade. The regression equations for equilibrium suction for vegetation canopy and bare soil are given as: | 0.0199 0.0047 3.3976 (I.1) | 0.0214 0.00607 3.5318 (I.2) where is the equilibrium suction on a pF scale; PI is plasticity index; is the Thorthwaite moisture index. Table I.1 presents the inputs to equilibrium suction model. Table I.1. Input Variables to Equilibrium Suction Model. Input variables Description Unit TMI Thorthwaite 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 To identify the presence of vegetation in the soil surface, a vegetation cover map of continental United States is presented below.

I-2 Figure I.1. GIS Map of Vegetation Cover. The depth to constant suction is the depth below the surface of the natural soil at which there is no more annual and seasonal variations of moisture or suction. It is also called the depth of the moisture active zone. This depth has been observed in the field to vary between 9.4 and 21 feet, depending upon the depth of penetration of the roots of vegetation. The depth to constant suction must be used when a water table is deeper than 21 feet. In the absence of vegetation, the depth to constant suction is at the minimum. The subgrade subroutine sets the depth to constant suction at 9.4 feet where there is no vegetation at the surface and sets it at: zm = 9.4 + (21-9.4)* Vegetation Index (I.3) The equilibrium suction map in Figure 4.14 of the final report shows colored regions of ranges of suction expressed in cm. The conversion to the pF scale is as follows: pF = log10(suction, cm) (I.4) Table I.2 lists the conversion of typical ranges in Equilibrium suction map from cm scale to pF scale. Table I.2. Ranges of Equilibrium Suction in cm and pF Scale. Suction Range, cm Suction range, pF <3000 <3.47 3000–4000 3.47–3.6 4000–5000 3.6–3.69 5000–6000 3.69–3.77 >6000 >3.77

I-3 The Fredlund and Xing equation is used to estimate the relationship between matric suction and water content and expressed as: 1 ln (I.5) 1 ln 1 ln 1 1.45 10 (I.6) 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 models and are predicted by the input variables into SWCC models for plastic and non-plastic materials. Tables I.2 and I.3 present the associated inputs for SWCC model ( , , and ) of plastic and non-plastic subgrade materials, respectively. Table I.3. 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 I.4. 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 (I.7)

I-4 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 I.4 and I.5 present the input variables into ANN models ( , and ) of plastic and non-plastic materials. Table I.5. 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 g/cm3 Test MC tested moisture content % Table I.6. 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 g/cm3 Test MC tested moisture content % In addition, the inputs to program JULEA includes:  Loads.  Layer thickness and Poisson’s Ratio.  Layer Moduli. Figure I.1 presents the flowchart of incorporating the subgrade models into Pavement ME Design for flexible and rigid pavements.

I-5 Figure I.2. Flowchart of Incorporating the Subgrade Models into Pavement ME Design for Flexible and Rigid Pavements.