## 1 Introduction
[PERSON] et al. [10] considered P-waves, S-waves, and Rayleigh waves, using limit equilibrium methods to estimate the seismic active earth pressure on rigid retaining walls. Compared to the existing pseudo-static and pseudo-dynamic methods, the seismic influence zone when accounting for Rayleigh waves was approximately 22% and 17% larger, respectively. [PERSON] et al. [11; 12] proposed a kinematic analysis method based on discretization, dividing backfill soil into finite elements to account for temporal and spatial effects of seismic acceleration through the consideration of P- and S-waves. [PERSON] et al. [13] developed a novel framework by combining kinematic limit analysis with pseudo-dynamic methods to predict the 3D seismic active earth pressure in cohesive backfill with cracks. They found that 3D effects and the soil cohesion significantly reduce the active pressure, whereas cracks and seismic effects counteract this. [PERSON] et al. [14] employed a modifiedpseudo-dynamic method for the rotational stability analysis of gravity retaining walls. Under various seismic conditions, wall-soil interactions may exhibit in-phase or out-of-phase behavior during seismic excitation, depending on the backfill properties, wall material characteristics, and input motion frequency content. [PERSON] et al. [15] integrated lower-bound limit analysis, finite element discretization, and second-order cone programming to evaluate active/passive seismic earth pressure coefficients for retaining structures under pseudo-dynamic loads. They demonstrated that as the soil-wall frictional resistance increases, the interface friction angle exhibits progressively more pronounced influence on the limiting earth pressure coefficients. Beyond retaining wall analysis, the pseudo-dynamic method has been widely applied in seismic stability assessments of foundations [16; 17; 18; 19; 20; 21], slopes [22; 23; 24; 25], and other geotechnical systems. Although the pseudo-dynamic method has been widely applied, the existing research outcomes mentioned above exhibit the following limitations when applied to the most common engineering conditions: (1) The insufficient consideration of local site effects: when the backfill behind the retaining wall is non-horizontal, the amplification characteristics of the seismic acceleration along the wall height cannot be adequately addressed. (2) The underestimation of cohesive effects: The influence of the backfill cohesion, wall-soil adhesion, and friction angles is not fully accounted for. While engineering practice often recommends sand or gravel as backfill materials, most natural backfills possess cohesion due to the presence of fine-grained components (i.e., _c-\(\varphi\)_ backfill). (3) Limited experimental validation and practical applicability: There is a lack of sufficient experimental data to support theoretical findings. To address these issues, this study will begin by analyzing the seismic response characteristics of backfill soil behind retaining walls under earthquake action. Based on the pseudo-dynamic method, we will develop a generalized seismic earth pressure calculation framework that comprehensively incorporates the amplification (attenuation) effects of acceleration along the backfill height and the cohesive properties of the backfill. The rationality of the proposed method will be validated through experimental data.