# Study of the Dynamic Response of a Rigid Runway with Different Void States during Aircraft Taxing
## 3 Finite Element Calculation Model Building
### Void Settings and Mesh Division  
In a previous airport runway detection, it was found that the void position mainly occurs at the edge or corner of the concrete slab [43]. The research study showed that, before the pavement slab is completely separated from the base layer, in most cases, the base layer in the void area only loses some fine aggregate, which still has a certain supporting effect on the pavement slab. The response modulus of the base layer is only reduced compared with that without void base layer [44], which is a slight void. After the pavement is separated from the base layer, it becomes a serious void. This paper analyzes and discusses the situations presenting a slight void and a serious void. Considering the actual situation of the void, it is also necessary to ensure that the mesh division between void and no-void models is consistent to facilitate postprocessing analysis. When establishing the void model in the finite element model, the void location was set in the center of the model, as shown in Figure 6(a), located at the edges and corners of the four slabs. In the case of a slight void, the initial dimension of the void area was 5 m in length \(a\) and 2.4 m in width \(b\). \(S_{VA}\) is the corner void area of a single board, which remained unchanged at 3.00 m\({}^{2}\). When there is a slight void, in [44], the degree of the void was reflected by reducing the reaction modulus of the base layer under the slab. In this article, the difference in the pavement void degree was realized by reducing the DEM at the base layer, and \(\xi\) represents the reduction coefficient (RC) of the DEM at the base layer in the void area, with the reduced DEM at the base layer being equal to \(\xi\) multiplied by the original DEM at the base layer (\(E_{d}\)). The values of \(\xi\) were 0.75, 0.5, 0.25, 0.1, 0.01, 0.001, and 0.0001, indicating different degrees of void. \(\xi\) equal to 1 indicated a healthy pavement structure. The setting of a slight void is shown in Figure 6(b). For the case of a severe void, we deleted the corresponding base area and set the void size \(a\) to 5 m, \(b\) to 0.6 m, 1.2 m, 1.8 m, 2.4 m, 3.0 m, and 3.6 m, and the corresponding \(S_{VA}\) to 0 m\({}^{2}\), 0.75 m\({}^{2}\), 1.50 m\({}^{2}\), 2.25 m\({}^{2}\), 3.00 m\({}^{2}\), 3.75 m\({}^{2}\), and 4.5 m\({}^{2}\), respectively. The runway finite element models were established by taking \(\xi\) and \(S_{VA}\) as variables. A reasonable mesh division can reduce the usage of computational resources while ensuring computational accuracy. In the response analysis of the pavement, there are two or more layers of meshes on the surface layer thickness, which can meet the calculation requirements [45]. The mesh size of the runway model surface layer was 0.18 m \(\times\) 0.18 m \(\times\) 0.18 m.  
Figure 7: Void mode and mesh generation of model. In order to facilitate void setting and data extraction, the mesh size of the base layer was slightly larger than that of the surface layer, with the size of 0.3 m \(\times\) 0.3 m \(\times\) 0.2 m. The length and width of the soil base meshes are consistent with the base layer; referring to the method in [46], the thickness was gradually increased downward from 0.2 m to 1 m to reduce the amount of calculation. The element type used was C3D8R. The C3D8R unit is a reduced integration for eight-node solid elements with three translational degrees of freedom per node [47]. It is suitable for finite element analysis of road structure model [48]. The dowel bar and tie bar are shown in Figure 7d, and a two-node linear beam unit B31 was adopted. The mesh division of the overall runway model is shown in Figure 7e. Below, we present the analysis and processing of the runway structure's vertical dynamic displacement response and vibration acceleration signals under different void conditions when the aircraft taxied on the runway. According to the research requirements, seven points were taken from the runway center to both sides to extract the VDD of the pavement slab in the time domain.