# Calculation Method of Earth Pressure Considering Wall Displacement and Axial Stress Variations
## 3 Example Verification
### Model Experiment
The earth pressure acting behind the wall can be divided into six regions by using five special points. Specifically, the active failure zone is (\(-\infty\), \(-0.045z\)), the active earth pressure zone is (\(-0.045z\), 0), the passive earth pressure zone before the  
Figure 12: Comparison between the results in this study and the experimental model results. (**a**) Translation mode (T). (**b**) Rotation mode around wall top (RTT \(\lambda\) = 0). (**c**) Rotation mode around wall bottom (RBT \(\lambda\) = 0) [7]. major principal stress reversal (0, 0.451\(z\)), the passive earth pressure zone between the major and minor principal stress inflection points is (0.451\(z\), 1.894\(z\)), the passive earth pressure zone after the minor principal stress reversal is (1.894\(z\), 2.14\(z\)) and the passive failure zone is (2.14\(z\), +\(\infty\)). Under the T mode, the comparison between the method proposed in this study and the experimental results is shown in Figure 13. In the absence of wall displacement, the earth pressure has an almost linear distribution. However, once the wall is displaced, the earth pressure follows a parabolic distribution. As the displacement increases, the rate of increase in earth pressure gradually decreases until it reaches the passive limit. The comparison between the RBT modes (\(\lambda\) = 0, 0.21, 0.5 and 13.78) and the proposed method is shown in Figure 14. When \(\lambda\) = 0, the wall rotates around the base and the displacement at the bottom of the wall is zero. Consequently, there is no change in the earth pressure, and the variation of the earth pressure measured in the model test is also small. Although the displacement is the greatest at the top of the wall, the tangent modulus is zero, resulting in no change in earth pressure. In this mode, the earth pressure bulges in the direction away from the retaining wall. As \(\lambda\) increases, the center of rotation gradually moves away from the bottom of the wall and the displacement at the bottom of the wall gradually increases. The position of the maximum stress gradually moves downward, and the bulge gradually disappears. When \(\lambda\) = 13.78, the earth pressure distribution behind the wall is basically the same as in the T mode. The comparison between the RTT modes (\(\lambda\) = 0, 0.5, 1.81 and 7.43) and the proposed method is shown in Figure 15. In the case of \(\lambda\) = 0, the wall rotates around the top, which transforms the RTT mode into the RT mode. In this mode, the distribution of wall displacement along the soil depth gradually increases, so that the increase of earth pressure behind the wall to also gradually increases with depth. The earth pressure distribution in this mode shows a certain concavity toward the wall, and although the proposed method also captures this phenomenon, there are some numerical differences from the experiment conducted by [PERSON] [4]. As \(\lambda\) gradually increases, the center of rotation moves away from the top of the wall and the difference in displacement at different heights of the wall gradually decreases. The earth pressure distribution behind the wall gradually takes on a parabolic shape. When \(\lambda\) = 7.43, the influence of the difference in wall displacement at different heights on the earth pressure can be almost neglected, and the earth pressure distribution behind the wall in this mode is similar to that in the T mode. Figure 13: Comparison diagram under T mode [4]. In the RBT and RTT modes, when \(\lambda\) is small, there is a discrepancy between the results obtained in this study and the experimental findings. This discrepancy can be primarily attributed to the omission of the soil arching effect caused by wall-soil friction in this study [50,51]. As the value of \(\lambda\) gradually increases, the earth pressure distribution behind the wall tends toward the T mode, and the difference between the results of this study and the model test results gradually decreases.