## 3 Numerical Simulation Verification and Comparative Analysis  
This paper uses the finite difference software FLAC3D 6.0 to model and analyze the bearing capacity of layered foundations with upper soft clay and lower sandy soil layers, verifying the rationality of the theoretical derivation in the previous text. Furthermore, the theoretical solution of this paper is compared with the existing formula results of previous scholars. For layered foundations considering burial depth, a numerical model in Figure 6 is established to verify the rationality of the previously derived formulas. The foundation consists of a double-layer soil composed of soft clay in the upper part and sandy soil in the lower part, both of which adopt the Mohr Coulomb constitutive model. The specific soil parameters are shown in Table 1. The basic material is concrete, set as a linear elastic model, and the Young's modulus and Poisson's ratio are taken as 20 GPa and 0.2, respectively. The friction angle between the side of the foundation and the soil is \(12^{\circ}\). The horizontal displacement at the bottom of the foundation is limited to simulate the situation where the bottom of the foundation is completely rough. The width of the foundation is 3 m. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Soil Mass** & **Weight** & **Cohesive Force** & **Internal Friction Angle** & **Young’s Modulus** & **Poisson’s Ratio** \\  & **(kN\(\cdot\)m\({}^{-3}\))** & **(kPa)** & **(\({}^{\circ}\))** & **(kPa)** & **Poisson’s Ratio** \\ \hline Upper soft clay & 14 & 30 & \(10\) & \(5\times 10^{3}\) & 0.3 \\ Lower sandy soil & 19 & 8 & 35 & \(1\times 10^{4}\) & 0.2 \\ \end{tabular}
\end{table} 
Table 1: Soil strength parameters. Figure 5: Force analysis of isolation body considering the weight of soil and passive soil pressure. Based on the above parameters, numerical simulation and theoretical formula calculations were conducted, and the results were compared with [PERSON]'s semiempirical Formula (1) and [PERSON]'s weighted average method. The comparison results are shown in Figure 7. From Figure 7, it can be seen that the numerical simulation results and the calculation results of Formula (28) in this paper are relatively similar to the results of [PERSON]'s weighted average method, with a maximum error of no more than 5%. The numerical simulation results are very close to the formula results in this paper, although both of them are lower than [PERSON]'s formula results, with a maximum error of about 20%, but the overall trend is basically consistent. Moreover, the larger the foundation burial depth and the thickness of the overlying soft clay layer, the more significant the error. The reason is as follows: as mentioned in the second section of the previous text, Formula (1) takes the difference in the bearing capacity of the foundation between soft clay and sandy soil based on the ratio of the thickness of the soft clay layer to the depth of the failure sliding surface. However, the normal stress \(\sigma_{0}\) on the equivalent free surface is derived from the equivalent conversion of frictional force and the weight of soil on both sides of the foundation, which is independent of the depth of the sandy soil in the bearing layer of the foundation. For the terms \(\sigma_{0}N_{q}\), the difference analysis method overestimates the ultimate bearing capacity of layered foundations. However, the Formula (28) derived in this paper is a correction to it, so the calculated foundation bearing capacity will be less than the result of Formula (1), which is reasonable. Therefore, the unified logarithmic spiral assumption adopted in this paper not only simplifies the calculation but also conforms to the actual situation of a unique sliding surface. The derived theoretical formula has a certain degree of credibility, and the established numerical model can accurately reflect the ultimate bearing capacity of layered foundations when the foundation is completely rough.