# 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 \(E_{fwd}\)
However, the lab \(M_{R}\) presented a base + subbase \(k_{1}\) of the coarse and fine RCA higher than that of the VA and RCA + RAP, but the difference was significantly smaller than the observed difference in the field. This is mainly due to the hydration of cementitious materials over an extended period, resulting in an increased modulus in the field compared to the limited hydration in the lab environment. Figure 4b shows similar results for the two subgrade soils, where the variation in the \(k_{1}\) coefficient is considerably lower than those of the base layers. This is attributed to a higher stress state at the base layers and their stiffer behavior due to the higher angularity and aggregate interlocking. Figure 4c shows the distribution of the \(k_{2}\) coefficient in the NCHRP 1-37A model, which is the exponent of the bulk stress (\(\theta\)) term and an indicator of the material behavior with a change in the stress state. As this figure shows, all bases showed positive \(k_{2}\) coefficients in the laboratory, indicating the stress-hardening behavior. However, the magnitude of the calibrated \(k_{2}\) coefficients from the FWD test results was lower than those measured in the laboratory, which means the stress sensitivity of the materials in the field over time was reduced. In the case of the subgrade materials, Figure 4d shows that both the sandy and clayey subgrades had stress-hardening behavior in the laboratory. In contrast, the clay loam subgrade showed less stress sensitivity. Meanwhile, the FWD-based data presented significantly lower values of the \(k_{2}\) coefficients. Also, the clay loam subgrade had stress softening (negative \(k_{2}\) coefficient) in the field, which might be expected for clayey materials. The distribution of the \(k_{3}\) coefficients of the different base and subgrade layers is shown in Figure 4e,f. As these figures show, the obtained \(k_{3}\) coefficients based on the field data were very close to zero, which neglects the shear-softening term of the NCHRP 1-37A model. This observation can be attributed to the low magnitude of the shear stress at the mid-depth of the unbound layers. Therefore, the shear sensitivity of the model could not be captured during the calibration process. However, the material experienced a wide range of shear stresses in the laboratory to evaluate the effect of shear stresses on the \(M_{R}\). This can explain the significantly lower \(k_{3}\) coefficient of the clay loam subgrade based on the laboratory data, compared to the obtained values of almost zero based on the FWD test results. Finally, a comparison of the results for Cells 185 and 186 for the sandy subgrade and Cells 188 and 189 for the clay loam subgrade, in Figure 4b,d, and f, shows a reasonable reproducibility for the calibrated model coefficients (\(k_{i}\) values) from the multi-load FWD test data. In other words, although the base layer in all test sections was completely different, almost reproducible model coefficients were obtained for the sandy subgrade in Cells 185 and 186 and the clay loam subgrade in Cells 188 and 189.