# Evaluating Pile-Supported Embankment Considering the Soil Anisotropy Effect
## 7 Conclusions  
In this study, the significance of anisotropic behavior in embankment fill materials was addressed. An anisotropic calculation formula incorporating strength parameters was proposed, and a modified Mohr-Coulomb criterion was introduced. To investigate the influence of anisotropy on the stress and settlement of embankments, a customized user-defined subroutine (UMAT) was developed. The key findings and research contributions of this study were summarized as follows:  
1. The Mohr-Coulomb yield criterion incorporates anisotropic considerations for cohesion, treating cohesion as a function of the direction of the principal stress. This approach enables dynamic updates of cohesion with changes in the direction of major principal stress in the code. When examining the effects of anisotropy on pile-soil stress ratios with a cohesive strength of 5 kPa, it was observed that as the anisotropy of cohesion intensifies and the anisotropy coefficient diminishes from 1 to 0.3, the ratio decreases from 36.1 to 28.8. Additionally, there is a notable 12.1% increase in settlement at the top of the embankment, highlighting the impact of cohesion anisotropy on geotechnical structural performance. 2. This paper presents an advancement of the Mohr-Coulomb criterion by incorporating a variable function that represents the dependence of friction angles on the direction of shear stress. This extension allows for the consideration of friction angle anisotropy in the material subroutine, enhancing the accuracy and adaptability of the yield criterion. Through an investigation of cases with a fixed friction angle of 30\({}^{\circ}\), it was observed that as the coefficient of friction angle anisotropy increased from 1 to 1.48, resulting in heightened anisotropy, the pile-soil stress ratio experienced a significant decrease, dropping from 23.7 to 17.4. Additionally, the friction angle anisotropy exhibited a correspondence with an increased settlement at the pinnacle of the embankment, with the settlement of the top surface of the embankment increasing by 21.2%. 3. A numerical model consistent with the existing model test and field test is established. By comparing the field test results with the numerical calculation results using the anisotropic Mohr-Coulomb yield criterion, it is found that the calculation results under anisotropic conditions are closer to the actual situation than isotropic, which verifies the accuracy and applicability of the anisotropic numerical calculation method in this paper. Conceptualization, Y.Z. ; writing--original draft preparation, Y.Z. and H.F.; writing--review and editing, Y.W. and J.L. ; visualization, Y.Z. and J.C.; funding acquisition, Y.Z. and Z.C. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Natural Science Foundation for the General Program of China (Grant No. 52178316) and the National Science Fund for Excellent Young Scholars of China (Grant No. 51922029). Not applicable. **Data Availability Statement**: All data that support the findings of this study are included within the article. **Conflicts of Interest**: The authors declare no conflict of interest.