# Impacts of Material Orthotropy on Mechanical Behaviors of Asphal Pavements
## 3 Model Verification  
The established model was verified by comparing its results with the FWD data and using two typical types of pavement structure in southern China: semi-rigid and inversed pavements. Back-calculated moduli of the two types of pavements are used as the vertical moduli \(E_{z}\) (Table 3). Based on the material parameters obtained in this paper, the anisotropy degrees \(k_{1}\) of the surface layer, base layer, and subgrade layer were 0.75, 0.8, and 0.8, respectively, and the \(k_{2}\) of the mentioned layer was 0.9 for all layers. According to Equations (6) and (7), the input parameters of the anisotropic material of each layer can be calculated, as shown in Table 3.  
Figure 5: Load model in this paper: (**a**) Load distribution. (**b**) Vertical stress over time.  
There were nine deflection sensors on the FWD, which were distributed in a straight line. The distance between each deflection sensor and the center of load action is shown in Table 4. To reduce the test error, each measuring point was hammered three times. The first two loads were mainly used to ensure the deflection bearing plate was closely in contact with the road surface and to eliminate the influence of residual loose particles on the measured deflection basin. The values obtained by the third load were recorded as valid data. The deflection basin results using the developed FE model were compared to the FWD data, as shown in Figure 6. The deflection at the distance \(x=0.15\) m of the developed FE model was compared to the FWD data in the location of the sensor number \(d_{1}\). The difference in the surface defection changing rate between the field data and the FE model are shown in Figure 7.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Sensor Number** & \(d_{1}\) & \(d_{2}\) & \(d_{3}\) & \(d_{4}\) & \(d_{5}\) & \(d_{6}\) & \(d_{7}\) & \(d_{8}\) & \(d_{9}\) \\ \hline Distance (m) & 0.15 & 0.35 & 0.45 & 0.60 & 0.75 & 1.05 & 1.35 & 1.65 & 1.95 \\ \hline \hline \end{tabular}
\end{table}
Table 4: The distance from sensor to coordinate origin.  
Figure 6: Comparison between the FWD data and anisotropy model of surface defection: (**a**) Structure A. (**b**) Structure B.  
As noted in Figure 6, almost all of the peak deflections obtained by the FE model were smaller than the measured values for the two pavement structures. In addition, in Figure 6a, the deflection-basin values of Structure A, a semi-rigid asphalt pavement, were close to the measured values, while those of Structure B in Figure 6b were not. This is because the base layer of Structure B was flexible, and thus more sensitive to the surrounding environment in the process of the field tests and, thereby, prone to generating larger surface deflections.  
As noted, compared with the measured surface deflections, the change rates of the isotropy and transverse isotropy by the anisotropy FE model for Structure A were 20.8% and 18.5%, respectively, while the corresponding change rates for Structure B were 24.4% and 21.3%, respectively. The change rate of surface deflection of Structure A for the orthotropy was significantly reduced, at no more than 5% and that of Structure B for the orthotropy was 10.6%, showing a satisfying error level using the proposed anisotropy FE model. Therefore, the developed model can be used to predict pavement mechanical behavior effectively.