## 4 Parametric Analysis and Discussion  
As indicated by Equations (2) and (7), the mobilized friction angles \(\varphi_{\rm m}\) and \(\delta_{\rm m}\) under the non-limit active state in the RB displacement mode are related to the wall displacement \(S\), the soil friction angle \(\varphi\), and the soil-wall interface friction angle \(\delta\). Consequently, the mobilized values of these friction angles directly influence the magnitude of seismic non-limit lateral earth pressure. Equations (8) and (13) further reveal that the horizontal acceleration coefficient \(k_{\rm h}\) and the horizontal acceleration amplification factor \(f_{\rm a}\) are critically linked to the lateral earth pressure coefficient. The following analysis evaluates the effects of key parameters on the seismic non-limit active earth pressure under the RB mode. (1) Influence of friction angle on non-limit earth pressure distribution in RB mode. Calculation parameters: \(H=4.0\) m, \(\gamma=17.6\) kN/m\({}^{3}\), \(\varphi_{0}=11^{\circ}\), \(\delta=22^{\circ}\), \(\delta_{0}=11^{\circ}\), \(k_{\rm h}=0.1\), \(f_{\rm a}=1.1\), \(R_{\rm f}=0.85\), and \(S/S_{\delta}=1.0\). The internal friction angle of the backfill \(\varphi\) varies, and may be \(33^{\circ}\), \(36^{\circ}\), \(39^{\circ}\), or \(42^{\circ}\). The calculated earth pressure distributions are shown in Figure 12a, while the effects of \(\varphi\) on the active earth pressure coefficient and the acting point position of the resultant force are illustrated in Figure 12b. From Figure 12a, has been is observed that the seismic non-limit active earth pressure under the RB mode exhibits a concave nonlinear distribution, with the intensity of the pressure increasing with depth. As the internal friction angle increases from \(33^{\circ}\) to \(42^{\circ}\), the active earth pressure coefficient exhibits an approximately linear reduction from \(0.39\) to \(0.32\), while the point of application of earth pressure slightly shifts downward from \(0.29\)\(H\) to \(0.27\)\(H\) (where \(H\) denotes wall height), demonstrating limited positional variation (see Figure 12b). Figure 11: A comparison between the calculated values and the experimental values of (**a**) maximum horizontal dynamic earth pressure distribution and (**b**) minimum horizontal dynamic earth pressure distribution in the RB mode from Reference [45]. It should be noted that this study does not account for the influence of the dilatancy angle, which may significantly affect earth pressure on retaining walls and requires dedicated investigation. Consequently, restricting the validity of the internal friction angle conclusions to non-dilative soils or soils with limited dilatancy constitutes a prudent approach. (2) Influence of soil-wall friction angle on non-limit earth pressure distribution in RB mode. Calculation parameters: \(H=4.0\) m, \(\gamma=17.6\) kN/m\({}^{3}\), \(\varphi=33^{\circ}\), \(\varphi_{0}=11^{\circ}\), \(\delta_{0}=0^{\circ}\), \(k_{\text{h}}=0.1\), \(f_{\text{a}}=1.1\), \(R_{\text{f}}=0.85\), and \(S/S_{\delta}=1.0\). The soil-wall friction angle \(\delta\) varies, and may be \(0^{\circ}\), \(11^{\circ}\), \(22^{\circ}\), or \(33^{\circ}\). The calculated earth pressure distributions are shown in Figure 13a, and the influence of the soil-wall interface friction angle \(\delta\) on the active earth pressure coefficient and resultant force position is illustrated in Figure 13b. From Figure 13a, under identical parameters, within the depth range of 0-3 m, the earth pressure intensity at the same depth decreases as \(\delta\) increases. However, in the 3-4 m depth range, the earth pressure intensity remains largely unaffected by variations in \(\delta\). This is because the mobilized value of the wall-soil interface friction angle near the wall base remains nearly constant under the given conditions (\(S/S_{\delta}=1.0\)). As shown in Figure 13b, both the active earth pressure coefficient and the acting point position of the resultant force decrease as \(\delta\) increases.