## 4 Parametric Analysis and Discussion
As the wall-soil interface friction angle increases from \(0^{\circ}\) to \(33^{\circ}\), the active earth pressure coefficient shows an approximately linear decrease from 0.44 to 0.41, while the point of application of earth pressure shifts downward slightly from 0.29 \(H\) to 0.27 \(H\). Figure 12: Influences of internal friction angle on (**a**) seismic non-limit active earth pressure and (**b**) active earth pressure coefficient and resultant force position. Figure 13: Influences of soil–wall interface friction angle on (**a**) seismic non-limit active earth pressure and (**b**) active earth pressure coefficient and resultant force position. Comparing the effects of the internal friction angle \(\varphi\) and the wall-soil interface friction angle \(\delta\) on the active earth pressure coefficient and resultant force position, it is found that their trends are consistent. However, the influence of \(\varphi\) is more pronounced than that of \(\delta\). (3) Influence of seismic horizontal acceleration \(k_{\rm h}\) 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\({}^{\circ}\), \(f_{\rm a}\) = 1.1, \(R_{\rm f}\) = 0.85, and \(S/S_{\delta}\) = 1.0. \(k_{\rm h}\) is varied as 0.1, 0.2, 0.3 and 0.4. The influence of the horizontal seismic acceleration coefficient \(k_{\rm h}\) on non-limit active earth pressure under the RB displacement mode is investigated, excluding vertical seismic acceleration effects. The impacts of \(k_{\rm h}\) on earth pressure distribution curves, the active earth pressure coefficient, and resultant force position are presented in Figure 14.  
From Figure 14a, it is evident that \(k_{\rm h}\) significantly affects the lateral earth pressure intensity, notably increasing the pressure near the wall base. As indicated by Equation (8), a larger \(k_{\rm h}\) enlarges the failure wedge volume, thereby increasing the active earth pressure coefficient. As shown in Figure 14b, when the horizontal seismic acceleration coefficient increases from 0.1 to 0.4, the active earth pressure coefficient rises significantly from 0.39 to 0.81, demonstrating a pronounced growth trend with the amplification of seismic acceleration. Meanwhile, the application point of earth pressure only slightly shifts from 0.29 to 0.30 times the retaining wall height, remaining essentially stable. (4) Influence of wall top displacement \(S/S_{\delta}\) on non-limit earth pressure distribution. 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. The relative wall top displacements \(S/S_{\delta}\) are set to 0.5, 1.0, 2.0, and 5.0. Under non-limit conditions, the influences of wall top displacement on seismic lateral earth pressure, the active earth pressure coefficient, and the resultant force position are illustrated in Figure 15.  
As shown in Figure 15a, when \(S/S_{\delta}\) = 0.5, the upper section of the wall exhibits active earth pressure under horizontal seismic loading, as both the internal friction angle of the upper soil and the wall-soil interface friction angle reach their limit states. In the RB displacement mode, as the wall top displacement increases, the earth pressure in the lower wall section further decreases, the zone of upper soil in the limit state gradually expands, and the active earth pressure decreases significantly. Due to the rotation about the wall base in the RB mode, the displacement at the wall base remains minimal, resulting in nearly identical base earth pressures across different displacement conditions.