## 2 Theories and Methods
### Finite Element Numerical Model of Runway Foundation  
Using the C3D20R 20-node secondary hexahedron element, the size of the partition mesh is 0.2 m \(\times\) 0.2 m \(\times\) 0.2 m. The model of the airport runway's concrete precast pavement slab and the base course is constructed. The length and width of the precast pavement slab have been fixed to 5 m \(\times\) 4 m, and Figure 4 depicts the mesh creation of the finite element model of the pavement structure. The contact between the base of the slab's surface and the layers of the structure utilizes Surface--Surface Contact (Standard), and it defines tangential behavior and normal behavior, where the friction Coeff is 0.6. The structural layer of the base is called the Elastic Foundation. Then, the base course material and pavement slab are assumed to have a linear elastic constitutive relationship, and the parameters of this model are assumed to be constant in temperature. Furthermore, the effect of temperature on pavement slabs is not discussed in this research. The airport runway's precast concrete pavement and foundation material specifications are found in the specifications for the Cement Concrete Pavement Design for Civil Airports [46; 47], and the particular pavement structural specifications are displayed in Table 3. The elastic modulus of the dowel bar is 200,000 MPa, and it has a Poisson's ratio of 0.3. It is made of a light round steel bar with a 13 mm diameter. The mechanical response changes caused by the dowel bar are ignored, and the interaction between the slab and the dowel bar adopts embedded region constraints. According to the distance requirements between engineering experience and the construction surface, the dowel bar is simulated by an optical circular reinforcement column, with a spacing of 0.3 m, and a total of 13 bars arranged in the transverse section of the pavement slab, 0.2 m away from the slab edge, and 0.2 m embedded at both ends. As illustrated in Figure 5, the aircraft wheel loads are applied in the center of the pavement slab, at the edge of the adjacent slab and the joint, based on the aircraft wheel \begin{table}
\begin{tabular}{c c c c} \hline Maximum ramp weight & 792.60 kN & Main landing gear spacing & 5.72 m \\ Maximum takeoff weight & 790.04 kN & Number of main landing gear & 2 \\ Maximum landing weight & 663.80 kN & Landing-gear tread & 0.86 \\ Maximum fuel-free weight & 627.50 kN & Main landing gear configuration & Double round \\ Empty weight & 414.30 kN & Main landing gear tire pressure & 1.47 MPa \\ \hline Main landing gear load distribution factor & & 0.950 & \\ \hline \end{tabular}
\end{table} 
Table 2: B737-800 model calculation reference data. Figure 4: Schematic diagram of the aircraft load pavement slab and quarter aircraft wheel load vibration model. Schematic diagram of finite element meshing model of pavement slab structure. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Cement Concrete Pavement** & **Cement-Stabilized Macadam** & **Base** \\ \hline Thickness/m & 0.24 & 0.3 & – \\ \hline Elasticity modulus/MPa & 38,000 & 1500 & 2000 \\ \hline Poisson’s ratio & 0.15 & 0.25 & 0.3 \\ \hline \end{tabular}
\end{table} 
Table 3: Parameters of the pavement structure layer. imprint area shown in Figure 3. The contact friction behavior between the bottom surface of the pavement slab and the top surface of the base layer, which is known as Tangential Behavior, expresses the contact property between the pavement slab and the base layer. In order to take into account the actual degree to which the surface layer and the base layer combine, as well as the actual stress conditions, the friction formula uses a penalty and the friction coefficient is 0.6, which makes the numerical computation of the finite element analysis more reasonable.