# Application of Finite Layer Method in Pavement Structural Analysis
## 4 Numerical Analysis Using EasyFEM and EEP Techniques
### Application of EasyFEM  
The EasyFEM was used to predict the mechanical responses and the predictions were compared with the data derived from field measurements on the test track of the German Federal Highway Research Institute (BASt), as shown in Figure 8a. A truck driving at a speed of approximately 30 km/h was selected for the measurement to apply the loads, as shown in Figure 8b.  
During the test track construction, strain gauges and pressure load cells were embedded at different depths of the test track along the center of the wheel path, which can measure strains and stresses along the corresponding directions when the truck passes. Due to the low speed of loads and the suggestion from [17], a static analysis with stationary loads is precise enough to compute the pavement responses. The material parameters of the pavement layers were derived from the laboratory tests on the specimens drilled from the test track. The thicknesses and the material properties of the test track are listed in Table 2[17]. The length longitudinal to the direction of traffic (both directions) was defined as 20 times the loading radius to limit the time required for the computational calculation. The width of the pavement was defined to be 3750 mm.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Layer** & **Thickness [mm]** & \(\mu\) & **E [MPa]** \\ \hline Surface course & 40 & 0.35 & 11150 \\ Binder course & 50 & 0.35 & 10435 \\ Asphalt base course & 110 & 0.35 & 6893 \\ Gravel base layer & 150 & 0.49 & 157.8 \\ Frost protection layer & 570 & 0.49 & 125.7 \\ Sub-grade & 2000 & 0.49 & 98.9 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Layer thickness and material properties of the test track.  
Figure 8: (a) The test track in BASt (the German Federal Highway Research Institute); (b) geometrical data and tires of the truck S23.  
The loading parameters are listed in Table 3[17]. All of the contact areas are assumed as squares with a side length of 264 mm. The distance between the center of the first left tire and the left edge of the test track along the traffic direction is 1100 mm.  
The upper three asphalt layers were totally bound. The two contact layers between the asphalt base course, gravel base layer, frost protection layer and sub-grade were defined as being partially bound. The 3-node quadratic elements with the mesh size of 10 mm were applied in the EasyFEM with the EEP technique.  
The following computational values were compared with the measured data, which is used to verify the EasyFEM. The strain along the traffic direction at the bottom of the asphalt base course and the vertical tensile stress at the top of the gravel base layer from the location below the center of the left tire of each axle were used in the validation process. The values from the measurement and simulation can be seen in Figure 9. All computational strains are higher than the measured values and all computational stresses are lower than those obtained from the measurements. Due to the uncertainties and fluctuations, the error range is considered to be \(\pm\)20% [17]. The computational values are all within this range. Thus, the EasyFEM is suited to simulate the response of the asphalt pavement under the traffic load with sufficient accuracy.