## 5 Analysis of Influence Parameters
### Internal Friction Angle \(\varphi_{1}\), \(\varphi_{2}\)  
Before parameter analysis, it is uniformly stipulated that the foundation width is 4 m and the upper soil height is 2 m, regardless of the ground overload. The soil parameters of the two-layered foundation are shown in Table 6 (except for specific modifications). The internal friction angle of foundation soil reflects its shear strength. At present, the internal friction angle of the current upper soil \(\varphi_{1}=10^{\circ}\), internal friction angle of subsoil \(\varphi_{2}=10^{\circ}\), \(20^{\circ}\), \(30^{\circ}\), \(40^{\circ}\), and \(50^{\circ}\), respectively, then \(\varphi_{1}/\varphi_{2}\) is 1, 2, 3, 4, 5 in turn; retrieving \(\varphi_{2}=10^{\circ}\), \(\varphi_{1}=10^{\circ}\), \(20^{\circ}\), \(30^{\circ}\), \(40^{\circ}\), and \(50^{\circ}\), respectively, then the ratio \(\varphi_{2}/\varphi_{1}\) is 1, 2, 3, 4, 5 in turn.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Soil Layer Classification** & \(\varphi\) (\({}^{\circ}\)) & **H (m)** & \(c\) (kPa) & \(\gamma\) (kN/m\({}^{3}\))** \\ \hline Upper soil & 22 & 2 & 20 & 19.5 \\ Lower soil & 22 & – & 20 & 19.5 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Soil parameter.  
The crucial sliding surface of the internal friction angle between the top soil and the lower soil is shown by Figure 16 in the ratio \(\varphi_{1}/\varphi_{2}\). Figure 17 shows the influence of the internal friction angle ratio of two-layered soil on the ultimate bearing capacity of the foundation.  
It is discovered that the essential sliding surface under search would deepen and expand when the internal friction angle ratio rises (Figure 16). In order to expand the area of the soil affected by the foundation and drive more soil to contribute to the instability of the foundation, the internal friction angle must be increased. This will raise the foundation's overall bearing capacity. As shown in Figure 17, when the internal friction angle of the subsoil is fixed, the internal friction angle of the upper soil increases, enhancing the ultimate bearing capacity of the foundation. The ultimate bearing capacity of the double-layer foundation will initially increase and then essentially remain unch  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Soil Layer Classification** & \(\varphi\) (\({}^{\circ}\)) & \(H\) (m) & \(c\) (kPa) & \(\gamma\) (kN/m\({}^{3}\)) \\ \hline Upper soil & 15 & 2 & 5 & 10 \\ Lower soil & 5 & – & 5 & 10 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Soil parameter.  
Figure 16: Search results of the critical sliding surface of the foundation under different ratios \(\varphi_{1}/\varphi_{2}\).  
Figure 17: Comparison of ultimate bearing capacity of foundation under different internal friction angle ratios.  
friction angle of the upper soil is fixed and the value of the internal friction angle of the lower soil is continuously increased. Therefore, in the actual project, appropriate measures should be taken to increase the ratio of the internal friction angle between the upper soil and the lower soil, so as to improve the ultimate bearing capacity of the foundation.