## 4 Numerically Simulated Dynamic Response of JPCP
### Computing Procedure  
The dynamic response of JPCP is influenced by numerous factors which can be roughly divided into the pavement structure parameters and the dynamic load parameters. The pavement structure parameters mainly include the dimensions of each structural layer and the elastic modulus of different materials. The dynamic load parameters mainly include the vehicle speed, the axle weight, and the pavement roughness level.  
A comprehensive but simplified procedure is critical for accurately assessing the dynamic response of JPCP in relation to various factors, which includes the following steps. First, determining the input values of both the structure and the dynamic load parameters: the pavement structure and materials parameters are determined as the values shown in Table 4, which are the recommended values in the Chinese PCC pavement design guidebook [3]. The dynamic load parameters are considered for a total of 36 cases (36 = 3 vehicle speed \(\times\) 3 axle weight \(\times\) 4 roughness level), as shown in Table 5. It is worth mentioning that the roughness level of many real pavements is A or B [28], and it is difficult for a vehicle to travel at 100 km/h on a pavement with roughness level D. The purpose of calculating such conditions is to demonstrate the methodology proposed in this study and to comprehensively analyze the influence of roughness level and vehicle speed on PCC pavement. The second step is to selecting the critical dynamic load parameters (100 km/h-30 tons-D, as illustrated in Section 5.3) based on which the large tensile stresses in JPCP are calculated with the structure parameters shown in Table 4. Finally, the effect of the pavement structure parameters on the dynamic response of JPCP is investigated using the critical dynamic load parameters (100 km/h-30 tons-D). For this purpose, the values of the typical pavement structure parameters are varied as shown in Table 6, including three values of the thicknesses and the elastic moduli for each structure layer and the existence of bowel bars (23 cases). The materials parameters of different layers are shown in Table 4. It should be noted that the case corresponding to the values in bold in Table 6 was computed in the first step. By design, one pavement structure parameter in Table 6 increases or decreases relative to the bolded value, and other pavement structure parameters (bold values) remain unchanged. The computing procedure is illustrated in Figure 6. It is seen that the total number of computing cases is 51.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{2}{c}{**Slab**} & \multicolumn{3}{c}{**Base Layer**} & \multicolumn{2}{c}{**Subbase Layer**} & \multicolumn{2}{c}{**Foundation**} & \multicolumn{1}{c}{**Dowel Bar**} \\ \hline \multirow{3}{*}{\begin{tabular}{c} **Thickness** \\ **(m)** \\ \end{tabular} } & **Elastic** & \multirow{3}{*}{\
\begin{tabular}{c} **Thickness** \\ **Modulus** \\ **(GPa)** \\ \end{tabular} } & **Elastic** & \multirow{3}{*}{
\begin{tabular}{c} **Elastic** \\ **Modulus** \\ **(GPa)** \\ \end{tabular} } & **Elastic** & \multirow{3}{*}{**Elastic** & \multirow{3}{*}{**Modulus**} & **Modulus** \\  & & & **(GPa)** & & **(GPa)** \\ \hline
0.22 & 20 & 0.10 & 0.3 & 0.10 & 0.4 & 20 \\
**0.26** & **31** & **0.20** & **1.3** & **0.20** & **1.0** & **60** \\
0.30 & 40 & 0.30 & 2.3 & 0.30 & 1.6 & 100 \\ \hline \hline \end{tabular} Note: The values in bold for each of the pavement structure parameters are the same as the values in Table 4.  
\end{table}
Table 5: Dynamic loading parameters for calculation of stress in JPCP.