# Comparison of Lab vs. Backcalculated Moduli of Virgin Aggregate and Recycled Aggregate Base Layers
## 2 Methodology
### Analysis Method  
The FWD test results were used to backcalculate the layer modulus (\(E_{FWD}\)) of the test sections using the Modulus 7.0 computer program. This program was developed by the Texas A&M Transportation Institute (TTI) and uses deflections from seven sensors for backcalculation procedures. Therefore, deflection data from the 0, 8, 12, 18, 24, 36, and 60-inch sensors were used as the input. Furthermore, the base and subbase layers were modeled as a single layer with a thickness of 15.5 inches [13].  
The nonlinear stress-dependent behavior of the unbound materials was captured using the NCHRP 1-37A model, the coefficients of which were estimated for the unbound materials in the laboratory using the \(M_{R}\) test results [23]. Additionally these model coefficients were also calibrated each time the multi-load FWD test was carried out in the field. The stresses for the model were found at 9.5 inches (from the surface) for the base and 25 inches (from the surface) for the subgrade modulus using a linear elastic solution (KENLAYER) [27].  
The pavement strain responses were calculated in the next step by inputting the laboratory-measured \(M_{R}\) and backcalculated \(E_{FWD}\) coefficients of the NCHRP 1-37A model into the MatFEA program as a nonlinear pavement response. In addition, as the current ME-based pavement analysis/design procedures use LEA-based pavement response models, the KENLAYER program was also used to obtain the strain response of the test sections. In this regard, the flowchart of such an analysis is shown in Figure 2. It is noted that MatFEA is a 2D FE-based pavement response model developed at Michigan State University to analyze pavement structures with nonlinear stress-dependent unbound layers. This program uses a dynamically adjustable mesh size algorithm to improve the runtime efficiency of the program while maintaining the accuracy of the FE approach in calculating the pavement responses. The nonlinearity of the unbound layers was captured through an iterative process until the average error in the elemental moduli was reduced to less than 2% with 95% reliability. More details about the MatFEA program can be found elsewhere [28].  
An additional step of the analysis method was the validation of the NCHRP 1-37A model coefficients, which were calibrated using the multi-load FWD testing. For this purpose, the test sections were modeled using the MatFEA program with the calibrated NCHRP 1-37A model coefficients, and the nonlinear pavement responses at the mid-depth of the unbound layers were obtained to calculate the corresponding modulus. It is noted that the MatFEA program uses the same modulus value to generate the stiffness matrix for a specific element at the mid-depth of the unbound layer under the loading center. The calculated modulus from the MatFEA program was compared with the backcalculated \(E_{FWD}\) value for that layer to validate the calibrated NCHRP 1-37A model coefficients.  
Finally, the pavement responses, as the vertical strains at the middle of the base (9.5 inches) and top of the subgrade layer (20 inches), were compared to assess if a workable conversion between the lab \(M_{R}\) and the \(E_{\text{FWD}}\) exists.