# Calculation Method of Earth Pressure Considering Wall Displacement and Axial Stress Variations
## 4 Conclusions  
Based on the non-linear elastic constitutive theory and assuming that the soil behind the wall is in a plane strain state, this study presents a predictive model for earth pressure under finite displacement conditions that takes into account the variation of axial stress. The axial stress considerations have a clear advantage over the static earth pressure assumption of [PERSON] [49]. The model incorporates the tangent modulus from the Duncan model to accurately capture the influence of confining pressure on the soil modulus. Notably, when the retaining wall has no displacement, the model automatically reduces to the static earth pressure. Moreover, leveraging the specific characteristics of the displacement distribution for each displacement mode, the study provides earth pressure calculation formulas for each respective mode.  
The movement of the retaining wall causes a change in the direction of principal stresses in the soil behind it, as the earth pressure increases. Considering the effect of axial stress changes at specific points, the formula for calculating the static earth pressure point (\(\sigma_{x}=\sigma_{y}\)) and the major principal stress inflection point (\(\sigma_{x}=\sigma_{z}\)) has been improved. In addition, the minor principal stress second inflection point (\(\sigma_{y}=\sigma_{z}\)) is introduced for the first time. However, the earth pressure at this point should be less than or equal to the passive limit earth pressure, otherwise this point does not exist. Based on this, the paper proposes conditions for judging the existence of this point for different soils. These points  
Figure 15: Comparison diagram under RTT mode [4].  
are then combined with the active and passive limit earth pressure points to divide the earth pressure behind the retaining wall into different zones.  
The discrete element tests have demonstrated that the method proposed in this study exhibits good agreement with experimental results in the limit state and at specific earth pressure points, particularly in the passive earth pressure zone. Furthermore, the earth pressure prediction models developed for different displacement modes can also effectively predict the results of the cohesionless soil and clay model tests. However, due to the omission of arching effects, there exists a deviation between the predicted results and the actual observations when the rotation center approaches the top or bottom of the wall. Addressing and refining this aspect will be a focus of the upcoming research phase.  
F.D.: Methodology, Conceptualization, Supervision, Writing review & editing, Funding acquisition, Project administration. X.W.: Formal analysis, Investigation, Formal analysis, Software, Validation, Writing original draft, Data curation. X.C.: Review & editing. J.G.: Review & editing. J.D.: Review & editing. Data curation. L.Z.: Data curation, Writing--review & editing. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (NSFC Grant No. 51979225), Key Research and Development Projects of Shaanxi Province (Grant No. 2022 ZDLSF07-02) and Shaanxi Provincial Key Laboratory Project of Department of Education (Grant No. 20 JS091).  
Not applicable.  
The dataset used to support the findings of this study is available from the corresponding author upon request.  
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.