# Study of the Dynamic Response of a Rigid Runway with Different Void States during Aircraft Taxing
## 3 Finite Element Calculation Model Building  
### Runway Structural Parameters and Dynamic Load Application  
In this paper, it was necessary to apply a sliding action load to the model. The runway finite element model was 30 m in length and 20 m in width. We simplified the runway structure into the surface, base, and soil layers. The single cement concrete slab size on the surface was 5 m \(\times\) 5 m \(\times\) 0.36 m, and there were 24 slabs in total. The base layer thickness was 0.4 m. When the runway finite element model is used for transient dynamic analysis, the thickness of soil base layer should be greater than 13 m to ensure that the results are not affected by constraints [12]. Therefore, the thickness of soil base layer of runway model was set to 13 m. The overall size of the model was 30 m \(\times\) 20 m \(\times\) 13.76 m. Dowel bars were set horizontally between cement concrete slabs, and tie bars were set longitudinally. According to the specification found in [32], the number of dowel bars and tie bars at the edge of the board was 17, and the number of tie bars was 8. The diameters of dowel bars and tie bars were 0.035 m and 0.02 m, respectively; the lengths were 0.5 m and 1 m, respectively; the elastic modulus was 21,000 MPa, the Shear modulus was 80,000 MPa, and Poisson's ratio was 0.3. They interacted with two adjacent slabs by embedding both ends into concrete, and the distance between two adjacent concrete slabs was 1 cm. Research has shown that, when a pavement structure is subjected to dynamic load, the static elastic modulus cannot be applied well to the dynamic analysis of the structure. The dynamic elastic modulus (DEM) of elasticity is the ratio of stress to strain of an object under dynamic load, which can adequately reflect the vibration characteristics of materials. Thus, the DEM of each layer of the runway was used for subsequent calculations and analyses [42]. The parameters of each structural layer of the runway are shown in Table 4.  
It was assumed that the runway structure was an elastic layer system. Each layer was completely continuous, the tie bound the surface layer and the base layer, and a hole dissected the base layer and the soil base. The direction of aircraft taxiing was the \(Z\)-direction, while the direction of perpendicular aircraft taxiing was the \(X\)-direction, and the direction of depth along the runway was the \(Y\)-direction. The boundary constraints were applied to the model, and the boundaries in the parallel and perpendicular aircraft taxiing \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Structural Layer**} & **Modulus of** & \begin{tabular}{c} **Dynamic** \\ **Elasticity \(E_{d}\)** \\ **(MPa)** \\ \end{tabular} & \begin{tabular}{c} **Density \(\rho\)** \\ **Elasticity \(E_{d}\)** \\ **(MPa)** \\ \end{tabular} & \begin{tabular}{c} **Poisson’s** \\ **Ratio** \\ **(kg:m\({}^{3}\))** \\ \end{tabular} & \begin{tabular}{c} **Damping** \\ **Ratio** \\ **(s = 1)** \\ \end{tabular} & \begin{tabular}{c} **Damping** \\ **Factor \(\beta\)** \\ **(s = 1)** \\ \end{tabular} & \begin{tabular}{c} **Thickness \(h\)** \\ **(m)** \\ \end{tabular} \\ \hline \begin{tabular}{c} Cement concrete top layer \\ Cement gravel base layer \\ Soil base layer \\ \end{tabular} & 36,000 & 49,820 & 2400 & 0.15 & 0.1 & 0.001 & 0.36 \\ \
\begin{tabular}{c} Cement gravel base layer \\ Soil base layer \\ \end{tabular} & 1500 & 2692 & 2000 & 0.25 & 0.1 & 0.002 & 0.4 \\
\begin{tabular}{c} Soil base layer \\ \end{tabular} & 80 & 242 & 1800 & 0.35 & 1 & 0.01 & 13 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Parameters of runway structural layers. directions were set in the \(X\)- and \(Z\)-directions. The bottom surface of the soil base was formed to be entirely fixed. The finite element model is shown in Figure 5(a). It is generally believed that the shape of the wheel print of the aircraft tire in contact with the road surface is a rectangle with a semicircle on both sides.