# Calculation Method of Earth Pressure Considering Wall Displacement and Axial Stress Variations
## 3 Example Verification
### Model Experiment  
To explore the effect of wall displacement on earth pressure, [PERSON] [7] conducted model experiments using clay under different displacement modes, as shown in Figure 6, with \(\lambda\) = 0. The model was constructed with a length of 1.9 m and a width of 1 m, while the soil inside had a height of 0.95 m. The clay used had a friction angle of 34\({}^{\circ}\), a cohesion of 5 kPa, and a unit weight of 15.73 kN/m\({}^{3}\). In the Duncan model, the failure ratio \(R_{f}\) was set to 0.95, the modulus parameter \(K\) was set to 145, the dimensionless index \(n\) was set to 0.75 and the Poisson's ratio was set to 0.3. According to Equation (24), it can be concluded that the minor principal stress second inflection point exists. The earth pressure acting behind the wall can be divided into six regions by using five special points. Specifically, the active failure zone is \((-\infty,\)\(-0.57z-0.75)\), the active earth pressure zone is \((-0.57z-0.75,\) 0), the passive earth pressure zone before the major principal stress reversal is (0, 1.012), the passive earth pressure zone between the major and minor principal stress inflection points is (1.012, 3.142), the passive earth pressure zone after the minor principal stress reversal is (3.14z, 3.49z+2.52) and the passive failure zone is (3.49z+2.52, +\(\infty\)). The results extracted from Figure 12 clearly show that, in the T mode, the wall displacement is not affected by the soil depth. The earth pressure exhibits a parabolic distribution, and the magnitude of the earth pressure increment is positively correlated with the soil depth. In the RTT mode, there exists a positive correlation between wall displacement and the soil depth. The magnitude of the earth pressure increment is also positively correlated with the soil depth. In the RBT mode, there is a negative correlation between the wall displacement and the soil depth. In addition, the earth pressure initially has a positive correlation and then changes to a negative correlation with the soil depth. At the bottom of the wall, where the retaining wall displacement is zero, the soil strain is also zero, so the earth pressure has not changed. Figure 11: Earth pressure versus strain curves under different vertical loads [49]. For a given soil, it is established by Equation (8) that the variation in earth pressure due to the wall displacement is governed by two factors: the tangent modulus \(E_{t}\) and the soil strain \(\varepsilon_{x}\). The wall displacement affects the \(\varepsilon_{x}\), while the soil depth affects the soil confining pressure and hence the tangent modulus \(E_{t}\). The absence of changes in surface earth pressure during the wall displacement process can be attributed to the fact that the confining pressure of the surface soil is zero, indicating that the tangent modulus is zero. In the T mode, the strain \(\varepsilon_{x}\) remains constant, and only the tangent modulus \(E_{t}\) increases with soil depth. In the RTT mode, both \(\varepsilon_{x}\) and \(E_{t}\) increase with soil depth. In the RBT mode, \(\varepsilon_{x}\) decreases with soil depth, while \(E_{t}\) increases with soil depth. The interaction of these two factors results in an increase followed by a decrease in earth pressure. Overall, the results of this paper are in close agreement with the findings of [PERSON] [7]. The Pearson correlation coefficients for each displacement mode surpass 0.75, affirming the rationality of the proposed approach. [PERSON] [4] carried out a study of the earth pressure distribution using a cohesionless soil under different displacement modes. The model is 2 m long, 1 m wide and 0.5 m high. The cohesionless soil has a unit weight of 15.5 kN/m\({}^{3}\) and a friction angle of 30.9\({}^{\circ}\). The Duncan model was used with a failure ratio of 0.65, a modulus parameter of 550, a dimensionless index of 0.45 and a Poisson's ratio of 0.26. According to Equation (24), it can be concluded that the minor principal stress second inflection point exists.