# Application of Finite Layer Method in Pavement Structural Analysis
## 4 Numerical Analysis Using EasyFEM and EEP Techniques  
### Analytical Verification of EasyFEM  
The analytical verification of the EasyFEM without EEP post-processing was carried out. The models of the asphalt pavement were created in BISAR, ABAQUS and EasyFEM, which are representative software applications developed based on LET, FEM and FLM, respectively. The pavement type is widely used in Germany according to the guidelines RStO-12 [40] and RDO-Asphalt-09 [1], as shown in Figure 4. The thicknesses of all layers except for the sub-grade were derived from RstO-12 [40]. The thickness of the sub-grade was defined to be 2000 mm in ABAQUS and EasyFEM after a previous mesh study in order to minimize the influence of the boundary on the computational results. Furthermore, the length and width of the pavement in the full-scale model were set to be 6000 mm based on the same reason. A full-scale model was created in the EasyFEM while the model in ABAQUS was one-fourth symmetrical model. The full-scale model exhibits advantages for the simulation of nonsymmetrical models with complex loading conditions in the further development of the EasyFEM. In BISAR, the thickness of the sub-grade as well as the length and width of the pavement were set to be infinite according to the LET. The pavement surface temperatures of \(-12.5\) (winter) and \(27.5\)\({}^{\circ}\)C (summer) were assumed, and then the associated material properties were determined according to RDO-Asphalt-09 [1], as listed in Figure 4.  
The square load with the side length of 264 mm and uniformly distributed contact stress of 0.7 MPa was applied at the center of the full-scale pavement surface in the EasyFEM and a corresponding set-up was applied in ABAQUS. In BISAR, only circular loads can be defined and thus a uniform contact load of 0.7 MPa with a radius of 150 mm was applied. In all models, the three asphalt layers were totally bound; the two contact layers among the asphalt base course, road base course, sub-base and sub-grade were defined as being partially bound. In order to attain a high accuracy, a very fine mesh was adopted in ABAQUS and EasyFEM after a mesh study. The mesh size in EasyFEM was uniformly set as 10 mm and thus 275 3-node quadratic elements with 551 nodes were generated. In order to reduce the computational consumption, the mesh size increases gradually from the top to the bottom and from the loading center to the boundary in the one-fourth symmetrical model in ABAQUS, as shown in Figure 5. The number of elements and nodes in ABAQUS are 162,728 and 193,601, respectively. There was no mesh generated from the BISAR. The computational results shown in Figure 6 are derived from five series of response points offset from the loading center to the boundary. Figure 4: Geometrical data and material properties of the pavement. Figure 5: Mesh generated from ABAQUS. Figure 6: _Cont._  
Given these figures, it can be concluded that the results derived from ABAQUS and EasyFEM are consistent with each other, yet the results from BISAR exhibit great deviations from those from the other two software applications, especially along the first two series of response points. The underlying reasons for the differences can be attributed to the different geometrical definitions of the models in BISAR due to its intrinsic limitation (circular load, infinite length and width of the layers and infinite thickness of the sub-grade); the deviations are the largest at the response points that are closest to the load. In Table 1, the computational results from ABAQUS and EasyFEM are considered at five critical locations directly below the loading center shown in Figure 6, where maximum compressive or tensile values may occur.