# Passive Earth Pressure and Soil Arch Shape: A Two-Dimensional Analysis
## 5 Comparison with Existing Theories and Experimental Data
The Coulomb, Caquot-Kerisel, and Zhu and Zhao theories all predict a similar, gradual monotonic increase in \(K_{p}\) with increasing \(\delta\). In contrast, the  
Figure 11: Comparison of passive earth pressure distribution with existing theories [1; 11; 12]. Figure 12: Comparison with existing theories [1; 11; 12] on the effect of internal friction angle on passive earth pressure: (**a**) passive earth pressure coefficient; (**b**) the height of application point. predicted by [PERSON] et al. [11] increases much more rapidly, showing significant amplification at higher \(\delta\) values. The \(K_{p}\) derived from the present study exhibits non-monotonic behavior, initially increasing with \(\delta\) before decreasing as \(\delta\) becomes larger. This unique non-monotonic trend is a significant differentiator of the proposed model, contrasting sharply with classical theories and other analyses. It suggests a complex interplay between interface friction and overall stability captured by the current approach. Figure 13b compares the effect of \(\delta\) on the application point height \(h_{p}\). Again, classical theories predict a constant \(h_{p}=H/3\). The other models, including the present work, show \(h_{p}\) generally decreasing as \(\delta\) increases from zero. The rate of decrease is most rapid in the results of Reference [11], followed by Reference [12]. The present study predicts the smallest decrease in \(h_{p}\), with the curve tending to flatten at higher \(\delta\) values. The application height \(h_{p}\) predicted by the proposed method generally falls between the constant value of \(H/3\) assumed by classical theories and the lower values obtained from other theories that account for nonlinear pressure distributions. This intermediate position for \(h_{p}\) leads to an assessment of overturning resistance that is potentially more balanced than other methods. This offers a potentially advantageous balance between ensuring structural stability and achieving design economy. Theoretical predictions are compared with experimental data from [PERSON] et al. [27] in Figure 14. The theories of [PERSON] and Caquot-Kerisel align reasonably well with the experimental results near the top of the wall, where other theories tend to underestimate the pressure. Predictions by [PERSON] et al. [11] and [PERSON] and [PERSON] [12] are similar to each other and provide a better fit for the pressure distribution in the mid-upper portion of the wall. Experimental data points are distributed on either side of the linear prediction from [PERSON], which reflects the general trend of increasing pressure with depth. However, this linear approach inherently cannot capture the observed non-linear pressure profile, particularly underestimating values near the wall base. The results from the present study show favorable agreement with the experimental data in the mid-lower sections of the wall, although some deviation is observed around the mid-height. Figure 13: Comparison with existing theories [1,11,12] on the effect of soil–wall friction angle on passive earth pressure: (**a**) passive earth pressure coefficient; (**b**) the height of application point. To quantitatively assess the prediction accuracy of the different theoretical methods against the experimental data from [PERSON] et al. [27], the Sum of Squared Errors (SSE) and the Coefficient of Determination (\(R^{2}\)) for the earth pressure distribution, along with the percentage error in the resultant force application height, were calculated (see Table 1). The statistical results indicate that the proposed method yields the lowest SSE and the highest \(R^{2}\) value (0.8108), suggesting the best overall agreement with the experimental earth pressure measurements among the compared theories. Notably, the linear Coulomb theory shows a poor fit to the experimental data (\(R^{2}\) < 0), while other methods achieve intermediate accuracy. Furthermore, the proposed method also exhibits the smallest percentage error in predicting the application height of the resultant force.