# Design Approach for Composite Pavement Structure Incorporating Reflective Crack Considerations
## 4 Derivation of Calculation Formula for Load Stress
### The Effect of Structural Parameters on Load Stress  
In previous studies [24], it has been demonstrated that the primary factors influencing load stress in asphalt layers include the elastic modulus \(E_{1}\), the asphalt layer thickness \(h_{1}\), the cement concrete slab elastic modulus \(E_{2}\), the cement concrete slab thickness \(h_{2}\), the length and width of cement concrete slab L * B, the foundation reaction modulus k, and the joint width \(\delta\). The analysis stress index encompasses the bending tensile stresses \(\sigma_{x}\) and \(\sigma_{z}\), at position 1 at the bottom of the asphalt layer, as well as the interlayer tensile stress \(\sigma_{y}\). (1) The influence of \(E_{1}\)  
As shown in Figure 11, increasing the elastic modulus \(E_{1}\) leads to a gradual rise in the values of \(\sigma_{x}\), \(\sigma_{y}\), and \(\sigma_{z}\). Specifically, when \(E_{1}\) increases from 500 MPa, each doubling of the modulus results in a 20-40% increase in \(\sigma_{x}\), a 6-8% increase in \(\sigma_{z}\), and a 7% increase in \(\sigma_{y}\). Previous studies [25; 26] have identified a direct correlation between a decrease in temperature and an increase in \(E_{1}\), with higher moduli contributing to greater load stresses. Additionally, cooling adversely affects the distribution of both temperature and load stresses in composite pavements. Figure 10: Schematic diagram of nodes of cement concrete slab. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Point** & **Spring Stiffness at Cement** & **Spring Stiffness in Cement** & **Spring Stiffness at Cement** \\  & **Concrete Slab Corner** & **Concrete Slab Center** & **Concrete SLAB Edge** \\ \hline Stiffness (N \(\times\) m\({}^{-1}\) ) & \(1.5\times 10^{7}\) & \(3.0\times 10^{7}\) & \(6.0\times 10^{7}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Joint stiffness at different points of the slab. (2) The influence of \(h_{1}\)  
As depicted in Figure 12, increasing the thickness \(h_{1}\) of the asphalt layer results in a decrease in the values of \(\sigma_{x}\), \(\sigma_{z}\), and \(\sigma_{y}\). When \(h_{1}\) increases to 12 cm, the reductions in \(\sigma_{z}\) and \(\sigma_{y}\) become more pronounced, reaching 50% and 30%, respectively. (3) The influence of \(E_{2}\)  
As shown in Figure 13, an increase in \(E_{2}\) leads to a gradual decrease in \(\sigma_{x}\) and \(\sigma_{z}\), while \(\sigma_{y}\) increases. For every 5000 MPa increase in the modulus of the cement board, \(\sigma_{x}\) increases by 6-10%, \(\sigma_{z}\) increases by 4-6%, and \(\sigma_{y}\) decreases by approximately 1%. Figure 11: Load stress at different \(E_{1}\) values. Figure 12: Load stress at different \(h_{1}\) values. (4) The influence of \(h_{2}\)  
Figure 14 demonstrates that, as the thickness \(h_{2}\) of the cement concrete slab increases, there is a gradual decrease in the values of \(\sigma_{x}\), \(\sigma_{z}\), and \(\sigma_{y}\), albeit not significantly. Specifically, for every 2 cm increase in \(h_{2}\), \(\sigma_{x}\) decreases by approximately 6-10%, \(\sigma_{z}\) decreases by 3-6%, and \(\sigma_{y}\) decreases by 1-4%. (5) The influence of L * B  
As shown in Figure 15, increasing L * B results in a gradual decrease in \(\sigma_{x}\), \(\sigma_{z}\), and \(\sigma_{y}\). Specifically, \(\sigma_{x}\) decreases by 15-20%, \(\sigma_{z}\) decreases by 2-7%, and \(\sigma_{y}\) decreases by 1.5-1.9%. Smaller dimensions of L * B in cement concrete slabs reduce load fatigue stress. For instance, the Weixu Expressway employs cement concrete slabs with dimensions of 4.0 m in length and 3.0 m in width, a design that minimizes load stress and prolongs the service life of the composite pavement by allowing vehicles to pass over cracks more effectively. Figure 14: Load stress at different \(h_{2}\) values. Figure 13: Load stress at different \(E_{2}\) values. (6) The influence of k  
As shown in Figure 16, an increase in k leads to a gradual decrease in \(\sigma_{x}\), \(\sigma_{z}\), and \(\sigma_{y}\).