## 1 Introduction
To account for this amplification effect, an improved methodology is presented that integrates the Swedish slice technique with the Newmark method for the simplified stability analysis of unsaturated slopes [17]. The conventional proposed static method cannot accurately simulate the temporal and spatial effects of seismic wave propagation in slopes, and it is difficult to truly reflect the seismic loads. [PERSON] et al. [18] used the proposed dynamic method to simulate the input of ground-shaking loads, and based on the lower limit theorem of plastic limit analysis, combined with finite element discretization technology, they established a mathematical design model for the finite element limit analysis of seismic slope stability, which satisfies the conditions of static equilibrium, yielding conditions, stress boundary conditions, and intermittent conditions. This shift in focus emphasizes the necessity of investigating the impact of non-uniform seismic excitation on slope stability. In order to meet the demand for non-uniform seismic response analysis of high dam-foundation systems, a deterministic non-uniform seismic motion field (DNSMF) model based on a wave input model has already been proposed [19]. The non-uniform spatio-temporal dynamic response of seismic motion fields, including time delay, complex amplitude variation and shape change of motion time history, can be expressed by the DNSMF model. Furthermore, the seismic response of gravity dams is significantly influenced by the DNSMF in comparison to the motion field of the vertical incident wave model. In view of the spatial difference of the seismic response of the wide valley non-uniform engineering site, a large-scale slope model for the nonlinear seismic response of a non-uniform site was developed. There are obvious differences in the ground vibration parameters at different locations on the surface of the site, and the response spectrum of the site surface shows the characteristics of multiple peaks and a wide period [20; 21]. The traditional uniform seismic motion input method would overestimate the responses of the dam. From the perspective of seismic safety evaluation [22], the overestimations would disturb the reasonable assessment of the stability of the large-scale slope. Accordingly, further research is required to explore the factors influencing the non-uniform seismic incidence. The results show that the factors affecting the non-uniform excitation of a slope include the time delay between the arrival times of waves arriving at different depths, causing a phase difference, and the coherence function [23]. This paper endeavors to study the relationship between the slope scale and the dynamic response under non-uniform incidence, drawing upon both theoretical and numerical approaches. In order to analyze the dynamic response of large-scale slopes under non-uniform seismic excitation, this paper is organized in the following way: Section 2 begins by laying out the theoretical methods of the non-uniform seismic excitation, and looks at how to obtain the numerical models for simulating the non-uniform incidence of seismic waves. Section 3 proposes the Stoneley equation considering the scale of the slope on the interface. Numerical models are established to simulate the dynamic response of uniform and non-uniform seismic activity, and the non-uniform spatio-temporal dynamic responses are analyzed by comparison. In Section 4, the Knott equation subjected to the non-uniform seismic waves is proposed to describe the scattering of elastic waves at rock interfaces. Different scale models are established to simulate the acceleration amplification effect. Section 5 identifies areas for improvement in the thesis and proposes future research directions. The last section is devoted to the conclusions.