## 5 Summary and Conclusions  
(1) The resultant force application point initially shifts downward as the upper earth pressure decreases faster than the lower portion under small wall-top displacements, progressively descending from the initial at-rest earth pressure height (1/3 relative height). During initial wall rotation, the resultant point rapidly lowers due to abrupt reduction in upper earth pressure. With further horizontal displacement, upper active earth pressure stabilizes while mid-section pressure continues to decrease. Ultimately, the earth pressure achieves a linear distribution at the active limit state, with the resultant point returning to the 1/3 wall height.  
(2) Key findings from parametric analyses: Overall, as the horizontal seismic acceleration coefficient increases from 0.1 to 0.4, the active earth pressure coefficient rises from 0.39 to 0.81. When the parameter \(\delta\) increases from 0.5 to 5.0, the non-limit active earth pressure coefficient decreases from 0.44 to 0.33. With the internal friction angle increasing from 33\({}^{\circ}\) to 42\({}^{\circ}\), the active earth pressure coefficient exhibits an approximately linear reduction from 0.39 to 0.32. Similarly, as the wall-soil interface friction angle grows from 0\({}^{\circ}\) to 33\({}^{\circ}\), the active earth pressure coefficient shows a near-linear decrease from 0.44 to 0.41. The position of the resultant force application point demonstrates minor variations, fluctuating slightly around 0.30 \(H\) (where \(H\) represents the retaining wall height).  
(3) Finally, it should be emphasized that the pseudo-static method cannot fully capture the nonlinear distribution characteristics of seismic earth pressure under earthquake loading. The assumption of linear pressure distribution in this method represents a conservative (safety-oriented) simplification. While the pseudo-static method exhibits both distinct advantages and limitations, its adoption in this study allows partial consideration of dynamic loading characteristics. However, it inherently neglects material-specific dynamic properties, inter-structural dynamic interactions, and dynamic coupling effects, thereby failing to account for time-dependent stress redistribution, damping effects, or authentic soil-wall dynamic interactions. Application constraints must be strictly observed: they may be inapplicable to scenarios involving significant soil stiffness degradation or liquefaction during seismic events, or limited to structures with low design accelerations and negligible dynamic interactions. However, the pseudo-static method demonstrates notable strengths: its clear physical conceptualization, the relative simplicity of its computational procedures compared to fully dynamic analysis, and its minimal computational demands, easily determinable parameters, and extensive empirical validation make it widely accepted by design engineers. Additionally, this study does not address the influence of soil arching  
Figure 15: Influences of wall top displacement on (**a**) seismic active earth pressure and (**b**) active earth pressure coefficient and resultant force position.  
effects on stress redistribution, which is a direction for future research on seismic earth pressure mechanisms.  
Conceptualization, Z.S. and W.W.; methodology, Z.S.; validation, Z.S. and W.W.; formal analysis, W.W.; investigation, W.W.; resources, W.W.; data curation, Z.S.; writing--original draft preparation, Z.S.; writing--review and editing, Z.S. and W.W.; supervision, Z.S.; project administration, W.W.; funding acquisition, W.W. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the Open Research Fund of Anhui Provincial Key Laboratory of Building Earthquake Disaster Mitigation and Green Operations, Anhui Institute of Building Research & Design, Grant NO. 2022-JKYL-002.  
Not applicable.  
The raw data supporting the conclusions of this article will be made available by the authors on request.  
The authors declare no conflicts of interest.