## 5 Conclusions  
This paper is based on [PERSON]'s theory of homogeneous foundation and extends it to a layered foundation using the unified sliding surface assumption and difference analysis method. In this paper, a theoretical formula for the ultimate bearing capacity of layered foundations with completely rough foundations is derived and compared and analyzed in relation to the classical semiempirical formula for layered foundations. On  
Figure 10: Correlation between different influencing parameters and ultimate bearing capacity of the foundation.  
the basis of verifying the reliability of the theoretical formula results, a numerical model is established to further explore and analyze the influence of relevant parameters of soil and foundation on the bearing capacity of the foundation. The main conclusions are as follows:  
1. In this paper, the unified assumption of logarithmic spiral sliding surface is adopted to derive the bearing capacity coefficient, which not only simplifies the calculation but also conforms to the actual situation of a unique sliding surface. [PERSON]'s theory of homogeneous foundations has been extended, and the derived theoretical formulas have a certain degree of credibility, providing a new approach for predicting the bearing capacity of layered foundations.
2. The numerical simulation results are in good agreement with the derived formulas, and the comparison with different theoretical formula solutions shows that the theoretical formula for the ultimate bearing capacity of layered foundations derived in this paper has certain rationality and applicability. [PERSON]'s semiempirical formula for a double-layer foundation overestimates the ultimate bearing capacity of the foundation. However, the results of the bearing capacity formula for the upper soft clay and lower sandy soil derived based on this correction in this paper are relatively close to the results of [PERSON]'s weighted average method.
3. The numerical simulation results obtained from the single factor analysis method show that the width to depth ratio of the foundation, the ratio of cohesive force of the double-layer soil, and the tangent ratio of the internal friction angle have a positive correlation with the ultimate bearing capacity of the foundation, and the influence is significant. The increase in the thickness of the overlying cohesive soil has an adverse effect on the ultimate bearing capacity of the foundation, manifested as the larger the thickness, the smaller the foundation bearing capacity. Among the four influencing factors mentioned above, grey correlation analysis shows that the width to depth ratio of the foundation has the greatest impact on the ultimate bearing capacity of the foundation, followed by the thickness of the overlying clay layer.  
Conceptualization, G.L. and C.L.; methodology, G.L.; software, G.L.; validation, G.L. and C.L.; resources, C.L.; data curation, G.L. and C.L.; writing--original draft preparation, G.L.; writing--review and editing, G.L. and C.L. All authors have read and agreed to the published version of the manuscript.  
This work is supported by National Natural Science Foundation of China project (No. 51508278).  
Not applicable.  
The original contributions presented in the study are included in the article, and further inquiries can be directed to the corresponding author.  
The completion of this paper is inseparable from the help of [PERSON] from Nanjing Forestry University and [PERSON] from Wenzhou University in China. Here, I sincerely thank [PERSON] for providing technical guidance. Thank you to [PERSON] and [PERSON] for providing knowledge guidance during the derivation of theoretical formulas in the paper, as well as for the review and revision suggestions provided after the completion of the paper writing.  
The authors declare no conflicts of interest.