# Evaluating Pile-Supported Embankment Considering the Soil Anisotropy Effect
## 1 Introduction  
Soil anisotropy refers to the difference in strength of soil in different principal stress directions. It is worth noting that geological materials such as natural rocks and soils usually exhibit anisotropy under the interaction of evolving particle composition and environmental factors [1; 2]. Several studies have indicated that [3; 4; 5; 6; 7; 8; 9; 10], the friction angle of soil is closely related to the direction of principal stress, and the strength values of soil in different loading directions are obviously different. The cohesion of the soil is also strongly dependent on the angle between the direction of the major principal stress and the direction of the soil deposition, showing significant anisotropy. Therefore, anisotropy is a basic and inherent characteristic of geotechnical materials [11], which should be taken into consideration in the design and analysis of geotechnical engineering. However, the existing ideal elastic-plastic model is not sufficient to describe the anisotropy of geotechnical materials. In many commercial software programs (FALC3D 6.0 [12], ABAQUS [13],MeshFree 2023 [14; 15; 16; 17; 18; 19; 20], etc.), theoretical models are also only designed for isotropic materials. Therefore, it is necessary to conduct extensive research on the anisotropic mechanical behavior of soil. Some scholars have simulated the stress distribution of soil through deep learning, artificial neural networks, and artificial intelligence algorithms [21; 22; 23; 24; 25; 26; 27; 28; 29]. [PERSON] and [PERSON] [30] used an improved constitutive model to characterize the anisotropic behavior of strength and stiffness of cohesive soil resulting from the rotation of the principal stress directions in order to calculate the safety factor of an undrained clay slope. [PERSON] and [PERSON] [31] established an anisotropic unified hardening (UH) model under the framework of elastoplastic theory for simulating the response of soils under principal stress rotation. By introducing an anisotropic transformation stress method, [PERSON] and [PERSON] [32] extended the isotropic failure criterion to the anisotropic failure criterion. [PERSON] and [PERSON] [33] established a failure criterion and constitutive model appropriate for anisotropic soils by modifying the stress components in different directions. [PERSON] [34] experimentally analyzed the development and disappearance of stress-induced anisotropy in normally consolidated clay, anisotropically consolidated clay, and overconsolidated clay under different stress history conditions. However, the previous studies were focused on stability evaluations of slopes [35; 36; 37]. In traffic geotechnical engineering, the anisotropy of the filler is usually not considered in the existing research on the settlement and stress analysis of the embankment filler, but the anisotropy has a significant effect on the strength and deformation of the filler [38]. Some researchers have found that failing to consider the anisotropy of geotechnical materials may result in unsafe designs [39; 40; 41]. Therefore, it is of great engineering significance to consider the anisotropy of embankment fill in the design of traffic geotechnical engineering. However, there are relatively few studies in this direction. This paper aims to incorporate the calculation formulas for anisotropic cohesion and friction angle into a Mohr-Coulomb material subroutine. This will facilitate the convenient representation of anisotropic changes in cohesion and friction angle. Furthermore, the three-dimensional model of pile-supported embankments is established by using the finite element software ABAQUS, and the influence of anisotropy on the distributions of stress and settlement deformations of embankments is analyzed. Finally, through the comparison of engineering examples, the accuracy and applicability of the model presented in this paper are verified. The research results can provide theoretical guidance for the analysis of embankment stability.