# Comparison of Lab vs. Backcalculated Moduli of Virgin Aggregate and Recycled Aggregate Base Layers
## 4 Summary and Conclusions  
Developing a correlation between the laboratory-measured resilient modulus (\(M_{R}\)) and the backcalculated layer modulus (\(E_{FWD}\)) depends on various factors. The responses of a pavement's unbound layers (as vertical strains to an applied load) in virgin aggregate (VA) base and recycled aggregate base (RAB) test sections were studied to ascertain any relationship between the lab \(M_{R}\) and \(E_{FWD}\) values. After reviewing the strain distribution in different pavement cells, calibrated using finite element (FE) and layered elastic analysis (LEA)-based approaches, the following conclusions can be drawn:  
1. The application of fine recycled concrete aggregate (RCA) materials in the base layer showed the best results in the field with their high stiffness and low strain responses, followed by coarse RCA, the blend of RCA and recycled asphalt pavement (RAP) (RCA + RAP), and VA materials. 2. Laboratory-measured \(M_{R}\) values and their corresponding coefficients of the NCHRP 1-37A model cannot represent the stiffness state of RAB material in the field. They could result in overdesigning the pavement structure. This is attributed to the aging and hydration processes of the mortar components in RAB materials. 3. A comparison of the vertical strain responses between the mid-depth of the base and the top of the subgrade layer presented no correlation between the laboratory-measured \(M_{R}\) and the field-based backcalculated \(E_{FWD}\) for the RAB materials. However, such a correlation seems reasonable for Cell 188, with the VA base (limestone) and clay loam subgrade layers, as the laboratory-based and field-based vertical strains were reasonably close to each other. Therefore, the following conversion factors are proposed by the authors: \(M_{R}\) = 0.87 \(E_{FWD}\) (for limestone aggregate in the base layer); \(M_{R}\) = 1.55 \(E_{FWD}\) (for clay loam material in the subgrade layer). 4. Field-calibrated coefficients of the NCHRP 1-37A model, which were obtained using the LEA approach and multi-load FWD test data, were validated with the nonlinear FE-based pavement response. 5. The difference between the vertical strains obtained using the FE-based approach and those calculated via LEA tended to increase with depth. The FE approach remained conservative by giving higher strains for limestone and RCA + RAP at 20 in. The opposite was observed for the coarse and fine RCA. 6. By generating the pavement's response through nonlinear parameters or stress dependencies, obtained by using \(E_{FWD}\) in the NCHRP model, the FE-based approach provided a better solution to avoid conversions of the modulus and obtain the best estimate of material in the field. 7. This study examined the linear and nonlinear pavement responses to a single load level of 9000 lbs, establishing a foundation for future analyses of pavement responses under varying loads and their effects on the correlation between lab \(M_{R}\) and \(E_{FWD}\). \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Test Section**} & \multicolumn{2}{c}{**Average Relative Difference**} & \multicolumn{2}{c}{**Average Relative Difference**} \\  & **between** & **\(E_{FWD}\) and \(M_{R}\) Strains** & **between** & \(E_{FWD}\) and \(M_{R}\)** Strains** \\  & **at 9 Inches** & & & **at 20 Inches** \\ \cline{2-5}  & **FE** & **LEA** & **FE** & **LEA** \\ \hline Cell 185 & & & & \\ (coarse RCA base, sandy subgrade) & 0.45 & 0.43 & 0.40 & 0.45 \\ \hline Cell 186 & & & & \\ (fine RCA base, sandy subgrade) & 0.30 & 0.30 & 0.26 & 0.47 \\ \hline Cell 188 & & & & \\ (VA base, clay loam subgrade) & 0.93 & 0.96 & 0.91 & 0.63 \\ \hline Cell 189 & & & & \\ (RCA + RAP base, clay loam subgrade) & 0.76 & 0.76 & 0.72 & 0.56 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Relationship between strains obtained using \(E_{FWD}\) (FE approach and LEA) and lab \(M_{R}\) (FE approach). **Author Contributions:** Conceptualization, S.W.H., Q.Z. and B.C. ; methodology, Q.Z., S.W.H. and B.C. ; software, S.F.A. and Q.Z.