# Calculation Method of Earth Pressure Considering Wall Displacement and Axial Stress Variations
## 1 Introduction  
Accurate earth pressure calculations are of paramount importance in engineering. Deviations from reality can make the design of retaining walls unreasonable. In practice, the earth pressure theory of [PERSON] [1] and [PERSON] [2] is commonly used, which gives the earth pressure at the limit state. However, experiments by [PERSON] [3] and [PERSON] [4] showed a robust correlation between the earth pressure behind the retaining wall and the wall displacement. Subsequent experiments have shown that the soil arching effect [5, 6] and the displacement pattern [7, 8, 9] also affect the earth pressure distribution. Advances in computational science have brought the finite element method [10] and the discrete element method [11] into focus. The finite element method can account for the constitutive relation of the soil [12, 13, 14], forecast localized deformations along the slip surface [15, 16], and predict the variation of earth pressure under seismic conditions [17]. Nevertheless, appropriate parameter selection [18] largely determines the accuracy of the finite element method, and mesh division has an impact as well [19]. In contrast, the use of the discrete element method requires more complex process for selecting contact models [20, 21] and their microscale parameters [22]. These considerations make itsapplication in engineering contexts more challenging [23]. Additionally, due to the limitations of previous contact models, the method is mainly used to investigate non-cohesive soils [24; 25; 26; 27]. Furthermore, there are researchers who explore the laws of variation in retaining wall displacement and earth pressure using analytical methods [28; 29]. The experiments of [PERSON] [30] demonstrated the variation of the friction angle with the displacement of the retaining wall. [PERSON] [31] proposed a method to determine the non-limit active earth pressure in the cohesionless soil. The findings of [PERSON] [32] and [PERSON] [13] further support this view and indicate that the external friction angle between the wall and the soil reaches its peak prior to the internal friction angle of the soil. [PERSON] [33] presented a semi-empirical approach for estimating the non-limit passive earth pressure. [PERSON] [34] assumed that the mobilized friction angle is non-linear, based on the work of [PERSON] [13]. [PERSON] [35] not only considered the effective internal friction angle of the soil, but also considered the impact of seepage on the active earth pressure. However, establishing the correlation between soil strength parameters and wall displacement remains a challenge. Meanwhile, the limit equilibrium theory and the horizontal thin layer method are common approaches to investigate the non-limit earth pressures [36; 37]. [PERSON] [38] developed a predictive approach for the active earth pressure in the translational mode by incorporating the soil arching effect. [PERSON] [39] applied the limit equilibrium method and the Kotter equation to determine the slip surface for solving the passive earth pressure on an inclined retaining wall. [PERSON] [40] developed a calculation method for active earth pressure by considering the moment equilibrium of the soil wedge. Regarding the rotation mode around the wall base, [PERSON] [41] proposed that the soil slip surface behind the wall is a log-spiral surface [36]. Then, both the horizontal slice method and the graphical procedure were used to estimate the displacement-dependent earth pressure. By using the curvilinear thin layer element method, [PERSON] [42] included the effect of soil arching on active earth pressure. In addition, some researchers have investigated the non-limit state earth pressure using the curve-fitting method. [PERSON] [43; 44] used exponential and hyperbolic models for prediction, but did not consider the effect of the retaining wall displacement mode. On this basis, [PERSON] [45] investigated the influence of the displacement mode and the center of rotation on the earth pressure distribution pattern.