# Comparison of Lab vs. Backcalculated Moduli of Virgin Aggregate and Recycled Aggregate Base Layers
## 3 Results and Discussion
### Comparison of Laboratory-Measured \(M_{n}\) against Backcalculated \(E_{fwd}\)  
Table 2 shows the average values of the NCHRP 1-37A model coefficients based on the lab \(M_{R}\) and multi-load FWD testing of the different unbound materials used in this study. The actual distribution of the obtained model coefficients is also shown in Figure 4.  
Figure 3: Results of FWD testing: (**a**) backcalculated modulus of base and subbase layers; (**b**) backcalculated modulus of subgrade layer; (**c**) maximum deflection of pavement surface. It is noted that the samples of the laboratory-measured data were collected at the time of construction, while the FWD-based data were averaged more than 10 times, as multi-load FWD tests were carried out for three years. This can explain the significantly wider range of the model coefficients (\(k_{i}\) values) obtained from the multi-load FWD tests, especially for the base layers. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Material**} & \multicolumn{4}{c}{**Lab Tests**} & \multicolumn{4}{c}{**Multi-Load FWD Tests**} \\ \cline{2-9}  & \(k_{1}\) & \(k_{2}\) & \(k_{3}\) & \(\mathbf{S}M_{R}\) & \(\mathbf{k}_{1\text{-FWD}}\) & \(k_{2\text{-FWD}}\) & \(k_{3\text{-FWD}}\) & \(\mathbf{E}_{\text{FWD}}\) \\ \hline Coarse RCA & 913 & 0.44 & \(-\)0.07 & 18.1 & 4125 & 0.24 & \(-\)0.03 & 58.28 \\ \hline Fine RCA & 882 & 0.45 & \(-\)0.06 & 17.8 & 7616 & 0.17 & \(-\)0.03 & 107.7 \\ \hline VA & 762 & 0.32 & \(-\)0.05 & 13.9 & 894 & 0.14 & \(-\)0.05 & 12.08 \\ \hline RCA + RAP & 803 & 0.51 & \(-\)0.12 & 16.5 & 1310 & \(-\)0.01 & \(-\)0.06 & 19.75 \\ \hline Sand subgrade & 947 & 0.75 & \(-\)0.42 & 11.3 & 1558 & 0.07 & \(-\)0.05 & 20.4 \\ \hline Clay loam & 1005 & 0.33 & \(-\)2.59 & 8.6 & 810 & \(-\)0.08 & \(-\)0.06 & 13.35 \\ \hline \hline \end{tabular} Unit Conversion: 1 ksi = 6.895 MPa.  
\end{table} 
Table 2: Average model coefficients based on lab \(M_{R}\) tests and multi-load FWD tests. Figure 4: Comparison of the NCHRP 1-37A model coefficients based on laboratory and field data: (**a**) \(k_{1}\) coefficient of base + subbase layer; (**b**) \(k_{1}\) coefficient of subgrade layer; (**c**) \(k_{2}\) coefficient of base + subbase layer; (**d**) \(k_{2}\) coefficient of subgrade layer; (**e**) \(k_{3}\) coefficient of base + subbase layer; (**f**) \(k_{3}\) coefficient of subgrade layer. A comparison of the average modulus values of the different unbound layers in Table 2 shows that the backcalculated \(E_{FWD}\) values were generally higher than the laboratory-measured \(M_{R}\) values, except for the VA base layer. This observation further highlights the stiffening effect of hydration and the aging process of the RAB materials over time. According to this table, the RCA base layers were stiffer than the other unbound materials, which is in agreement with the previous findings. Also, the fine RCA was observed to achieve the highest \(E_{FWD}\) value, by an adequate margin, in the field; however, the lab results for \(M_{R}\) present the coarse RCA as a better material. This is generally due to less breakage of the hydration materials during the compaction of the fine RCA in the lab compared to that in the field [13]. The \(E_{FWD}\) values were around 3.2, 6.1, 0.9, and 1.2 times those of the lab \(M_{R}\) for the coarse RCA, fine RCA, limestone, and RCA + RAP, respectively. For the sand and clay loam subgrades, the \(E_{FWD}\) values were 1.8 and 1.6 times the \(M_{R}\) values. Figure 4a shows the distribution of the \(k_{1}\) coefficients from the lab \(M_{R}\) and backcalculated FWD test results. As this figure shows, the magnitude of the \(k_{1}\) coefficients obtained from the FWD data has a direct correlation with the backcalculated \(E_{FWD}\) values, where the RCA base layers possessed the highest values. The authors expected such a correlation as the \(k_{1}\) coefficient is a direct multiplier in the NCHRP 1-37A model.