## 5 Conclusions  
This paper derives a calculation method for determining seismic active earth pressure based on the pseudo-dynamic method. Considering the most general engineering conditions (including the cohesive backfill, acceleration amplification (attenuation) effects behind the wall, non-horizontal backfill surface, and non-vertical retaining wall backface), the proposed method enhances the practical relevance and applicability of seismic active earth pressure calculations, demonstrating significant engineering value. Subsequently, the rationality and reliability of the derived seismic active earth pressure calculation formula were validated through model test data from the relevant literature. The most unfavorable working conditions are calculated by the compiled program, and the influence of various factors as \(f_{\mathrm{a}}\), \(\delta\), \(\varphi\), \(\theta\), \(i\), \(T\), \(k_{\mathrm{h}}\), \(k_{\mathrm{v}}\), and \(c/\gamma H\) on the earth pressure coefficient, failure wedge angle, earth pressure distribution, and critical tension depth are considered in detail. Under special conditions, the earth pressure calculation formula of this paper can be degraded to the same formula as the Rankine theory. The critical depth \(z_{\mathrm{c}}\) behind the rigid retaining wall needs to be determined before calculating the seismic active earth pressure due to the existence of cohesion in \(c\)-\(\varphi\) backfill. The critical depth decreases with an increase of \(\theta\), and increases with an increase in \(i\) and \(c\). The acceleration amplification effect of the backfill soil behind the retaining wall significantly influences the magnitude of the seismic active earth pressure. When the amplification factor \(f_{\mathrm{a}}\) increases from 1.0 to 1.8 (under conditions of \(c/\gamma H=0\), \(\varphi=30^{\circ}\), \(\delta=\varphi/2\), \(\theta=20^{\circ}\), \(i=8^{\circ}\), and \(k_{\mathrm{v}}=0\)), the seismic active earth pressure coefficient rises from 0.9745 to 1.5852, marking a 63% increase. Conversely, the presence of cohesion notably reduces the seismic active earth pressure. For instance, when \(c/\gamma H=0.05\) (with \(\varphi=30^{\circ}\), \(\delta=\varphi/2\), \(\theta=20^{\circ}\), \(i=8^{\circ}\), and \(k_{\mathrm{v}}=0\)), the seismic active earth pressure coefficient drops to 1.1615, representing a 27% reduction compared to that of cohesionless backfill (1.5852). Current seismic design practices for retaining walls inadequately account for these two factors. This study recommends that the seismic design of retaining walls should appropriately evaluate both the acceleration amplification effect under seismic loading and the actual cohesion of backfill materials. The earth pressure calculation method proposed in this study can be extended to scenarios that involve layered backfill behind retaining walls. However, the fundamental assumptions of the model are incompatible with flexible retaining wall configurations. The following aspects require further improvement: (1) The formula derivation assumes a straight-line sliding surface for the soil wedge behind the wall, simplifying the inclination angle \(\alpha\). Actual engineering scenarios may involve curved sliding surfaces, which could affect the accuracy of the seismic active earth pressure results. (2) The amplification factor of the seismic acceleration of the backfill behind the retaining wall may have a coupling relationship with the magnitude of the seismic wave acceleration input at the base. This effect is not considered in this paper. (3) The simplification of seismic loading into equivalent sinusoidal waves based on the predominant frequency requires further in-depth research on the equivalence of dynamic responses in retaining walls under these two excitation patterns. **Author Contributions:** Conceptualization, Z.S. and W.W.; methodology, Z.S. ; validation, Z.S. and H.L. ; formal analysis, W.W.; investigation, H.L. ; resources, W.W.; data curation, Z.S. ; writing--original draft preparation, Z.S.