## 3 Dynamic Load Generation
### Dynamic Load Generation  
Although the quarter-car model cannot simulate some conditions including the contact between tires and pavement surface, the acceleration, the steering, and so on, existing research shows that it can be well used for pavement dynamic response analysis, with the advantages of simplicity and efficiency [13,14]. The quarter-car model has two degrees of freedom with the vertical displacements of the suspension mass and the nonsuspension mass. The schematic diagram of the quarter-car model is shown in Figure 4, and its motion differential equations are shown in Equations (11)-(13):  
\[m_{1}\ddot{x}_{1}=-k_{1}(x_{1}-x_{2})-c_{1}\big{(}\dot{x}_{1}-\dot{x}_{2}\big{)} \tag{11}\]  
\[m_{2}\ddot{x}_{2}=k_{1}(x_{1}-x_{2})+c_{1}\big{(}\dot{x}_{1}-\dot{x}_{2}\big{)} -k_{2}(x_{2}-q)-c_{2}\big{(}\dot{x}_{2}-\dot{q}\big{)} \tag{12}\]  
\[F_{d}=k_{2}(x_{2}-q)+c_{2}\big{(}\dot{x}_{2}-\dot{q}\big{)} \tag{13}\]  
Figure 2: PSD of (**a**) simulated level A roughness data, (**b**) simulated level B roughness data, (**c**) simulated level C roughness data, and (**d**) simulated level D roughness data, where the straight lines represent theoretical PSD functions of level A, B, C, and D pavements, obtained based on Equation (1). where \(m_{1}\) is suspension mass; \(m_{2}\) is nonsuspension mass; \(k_{1}\) is stiffness of suspension system; \(k_{2}\) is stiffness of tire; \(c_{1}\) is damping coefficient of suspension system; \(c_{2}\) is damping coefficient of tire; \(x_{1}\) is vertical displacements of suspension mass; \(x_{2}\) is vertical displacements of nonsuspension mass; \(q\) is vertical displacement caused by pavement roughness; \(\dot{x}_{1}\) and \(\dot{x}_{2}\) are the speed of the suspended mass and the non-suspended mass, respectively; \(\dot{x}_{1}\) and \(\dot{x}_{2}\) are the acceleration of the suspended mass and the non-suspended mass, respectively; \(F_{d}\) is the dynamic load of the tire; and \(q\) is the pavement roughness, which can be generated by the method discussed in Section 2. The wheel total random dynamic load applied to the pavement can be obtained based on the summation of \(F_{d}\) and the system static load (\(G\)), as shown in Equations (14) and (15):  
\[F_{t}=F_{d}+G \tag{14}\]  
Figure 4: Schematic diagram of the quarter-car model. Figure 3: (**a**) The elevation of an actual PCC pavement referring to LTPP database, and PSD of pavements in (**b**) good condition and (**c**) poor condition. \[G=(m_{1}+m_{2})g \tag{15}\]  
where \(F_{t}\) is the total random dynamic load; \(G\) is the system static load; \(g\) is the acceleration of gravity, taken as 9.8 m/s\({}^{2}\). The value of the standard axle weight specified in Chinese PCC pavement design guidebook is 10 tons [3], and by referring to the study by [PERSON] et al. [24], the values of the vehicle mass, the bogie mass, and the wheel mass are set as 4450 kg, 500 kg, and 50 kg, respectively. Normally, the vehicle body mass is treated as the suspension mass, and the nonsuspension mass includes the bogie mass and the wheel mass [15], this means that the suspension mass (\(m_{1}\)) and the nonsuspension mass (\(m_{2}\)) are 4450 kg, and 550 kg, respectively, in this study. To analyze the effect of overloading on the stress generated in the pavement, the value of the nonsuspension mass (\(m_{2}\)) is fixed as 550 kg, and the value of the suspension mass (\(m_{1}\)) increases from 4450 kg to 9450 kg and 14,450 kg, which corresponds to axle loads of 200 kN and 300 kN, respectively. The parameters of the quarter-car vehicle model used in this study are listed in Table 3. The first natural frequency in Table 3 is calculated according to reference [25].