## 4 Sensitivity Analysis of Bearing Capacity Parameters of a Layered Foundation
### The Width to Depth Ratio of the Foundation and the Thickness of the Overlying Soft Clay Layer  
Figure 8a shows the variation of the ultimate bearing capacity of the foundation under different width to depth ratios. It can be seen from the figure that when the foundation burial depth is kept constant, the ultimate bearing capacity of the foundation increases approximately linearly with the increase of the foundation width to depth ratio, and the larger the foundation burial depth, the higher the growth rate of the foundation's ultimate  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Condition Number** & _B/D_ & \(\epsilon_{1}\)/\(c_{2}\) & \(\tan\)\(\varphi_{1}\)/\(tan\)\(\varphi_{2}\) & \(H\) **(m)** \\ \hline
3 & 2 & & & \\
4 & 2.5 & & & \\ \hline
5 & & 1 & & \\
6 & & 1.5 & & \\
7 & 1.5 & 2 & 0.2 & 1 \\
8 & & 3 & & \\ \hline
9 & & & & 0.2 & \\
10 & & & & 0.4 & \\
11 & & 3 & 0.6 & 1 \\
12 & & & & 0.8 & \\ \hline
13 & & & & 0.5 \\
14 & & & & 1 \\
15 & & 3 & 0.2 & 1.5 \\
16 & & & & 2 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Numerical Simulation Scheme.  
Figure 7: Comparison between numerical and theoretical results of ultimate bearing capacity of completely rough foundation. (**a**) Different burial depths of foundations; (**b**) Different thicknesses of overlying soft clay.  
bearing capacity. The reason is as follows: the increase in foundation width and burial depth expands the contact area between the side and bottom of the foundation and the soil, thereby increasing the lateral constraint force of the soil on the foundation and the friction force on the bottom. In addition, increasing the width of the foundation can effectively reduce the bearing pressure of the soil per unit area, avoid stress concentration in the soil, and thus improve the ultimate bearing capacity of the foundation.  
Figure 8b shows the variation of the ultimate bearing capacity of the foundation under different thicknesses of overlying soft clay layers. It can be seen from the figure that the ultimate bearing capacity of the foundation decreases approximately linearly with the increase of the thickness of the overlying cohesive soil under the foundation. When the burial depth of the foundation is 2 m, the thickness of the overlying soft clay layer increases from 0.5 m to 2 m, and the ultimate bearing capacity of the foundation decreases from 1751 kN to 440 kN, with a decrease of nearly 74.7%. It can be seen that the thickness of the soft clay layer has a significant adverse effect on the ultimate bearing capacity of the foundation. The reasoning is as follows: the deformation modulus and internal friction angle of the overlying cohesive soil layer are smaller compared to sandy soil. As its thickness increases, the ability of the overlying soil to resist loads weakens, leading to a downward trend in the ultimate bearing capacity of the foundation. Furthermore, it can be observed from Formula (13) that the thicker the soft clay under the foundation, the smaller the coefficient n, which in turn leads to a decrease in the bearing capacity coefficient, ultimately resulting in a decrease in the bearing capacity of the layered foundation. In practical engineering, reinforcement should be considered for the soil with weak bearing layers to reduce engineering costs.