## 2 Theories and Methods
### Load Model of a Pavement Slab under an Aircraft Load
According to the principle of flight dynamics, the lifting force of the aircraft during taxiing is:  
\[Y_{v}=\frac{1}{2}\rho v^{2}C_{y}S \tag{6}\]  
where \(\rho\) is air density (kg/m\({}^{3}\)); \(C_{y}\) is the lift coefficient; \(S\) is the wing area (m\({}^{2}\)); \(v\) is the aircraft taxiing speed (m/s). Therefore, the vertical load on the pavement during aircraft taxiing can be expressed as:  
\[P=Mg(1+11.5c_{0} IRI\sqrt{v})-Y \tag{7}\]  
where \(M\) is the mass of the aircraft, \(P=Mg(1+11.5c_{0} IRI\sqrt{v})-\frac{1}{2}\rho v^{2}C_{y}S\)  
Based on Equations (2)-(7), the theoretical analytical expression of the stress component of the aircraft load along the \(z\) direction of the pavement slab is shown in Equation (8): \begin{table}
\begin{tabular}{c c} \hline
**Aircraft Parameters** & **Value** \\ \hline \hline Suspension system mass (\(m_{2}\))/kN & 328 \\ \hline Non-suspension system mass (\(m_{1}\))/kN & 74.55 \\ \hline Rear landing gear tire stiffness coefficient (\(k_{1}\))/kN\(\cdot\)m\({}^{-1}\) & 9600 \\ \hline Rear suspension stiffness factor (\(k_{2}\))/kN\(\cdot\)m\({}^{-1}\) & 4800 \\ \hline Rear landing gear tire damping factor (\(c_{1}\))/kN\(\cdot\)m\({}^{-1}\cdot\)s\({}^{-1}\) & 24 \\ \hline Rear suspension buffer damping factor (\(c_{2}\))/kN\(\cdot\)m\({}^{-1}\cdot\)s\({}^{-1}\) & 20 \\ \hline \end{tabular}
\end{table} 
Table 1: Parameters of B737-800 aircraft. \[\sigma_{d}=\sum_{i=1}^{n}\frac{3P_{i}}{2\pi\bullet z^{2}[({x_{i}}^{2}+{y_{i}}^{2})/ {z_{i}}^{2}+1]^{5/2}}=\sum_{i=1}^{n}\frac{3\times\left(Mg(1+11.5c_{0} IRI\sqrt{\upsilon})-\frac{1}{2}\rho v^{2}C_{y}S \right)_{i}}{2\pi\bullet z^{2}[({x_{i}}^{2}+{y_{i}}^{2})/{z_{i}}^{2}+1]^{5/2}} \tag{8}\]  
2. Aircraft wheel load simulation The impact of the aircraft load on the construction of the runway's foundation is investigated using the B737-800 as the research aircraft. Regarding the area of the pavement where the aircraft's wheels make contact, the shape of the wheel imprints is commonly represented by a graph consisting of a rectangle and two semicircles [42; 43; 44; 45]. In order to simplify the computation, as depicted in Figure 2, the area of the wheel impression is determined using Equation (9). It is assumed that the length of the aircraft's wheel imprint is L and its width is 0.6 L, which may be computed using Equations (9)-(11). The form of the main landing gear of the B737-800 aircraft is depicted in Figure 3, and the specific calculation parameters of the B737-800 aircraft are displayed in Table 2. \[A=\frac{P_{S}}{1000q}\] (9)  
\[A=\pi\times(0.3L)^{2}+0.4L\times 0.6L=0.5227L^{2} \tag{10}\]  
\[b=\frac{S}{0.6L}=\frac{0.5227L^{2}}{0.6L}=0.8712L \tag{11}\]  
where \(A\) is the area (m\({}^{2}\)) of the aircraft's single wheel imprint; \(P_{s}\) is the single wheel load of main landing gear (kN); \(Q\) is the single wheel contact pressure on the main landing gear of the aircraft, which can be the inflation pressure of the tire (MPa); \(B\) is the length of the combined wheel imprints (m). Figure 3: Schematic diagram of the wheel imprint of the main landing gear acting on airport pavement. Figure 2: Equivalent wheel imprint area of the rectangle, combined with the wheel imprints.