## 1 Introduction
The analysis then focuses on the sliding within the upper soil mass and along the soil-rock interface using traditional limit equilibrium or finite element methods [16; 17]. However, this approach neglects possible damage within the lower rock body and does not reflect the actual stability of the slope accurately [18]. The Finite Difference Method (FDM) is another technique in geotechnical engineering that approximates differential equations with finite differences, converting them into discrete algebraic systems. FLAC, which uses an explicit finite difference scheme, is effective for modeling nonlinear behavior and large deformation problems in geotechnical materials, and it has been widely applied in practical projects [19]. Some researchers have used FLAC to analyze the overall stability of soil-rock binary structure slopes. This approach considers multiple failure modes more accurately by including sliding within the soil, along the soil-rock contact surfaces, and within the rock body structure [2]. Despite this, using the safety coefficient from traditional slope stability analyses to assess the reliability of these slopes presents challenges in computational efficiency. FLAC has several drawbacks. First, it usually requires command flow for pre-processing, which means that complex models need to be created in external software (e.g., the pre-processing module of ANSYS (2025 R1)) and then imported into FLAC, significantly increasing analysis time. Second, its explicit difference algorithm, although suitable for dynamic problems and nonlinear static problems with large deformations [19], demands a smaller time step for slope stabilization problems that mostly involve linear and small deformations. This requirement increases computational time compared to the finite element method. Moreover, the convergence rate of the Finite Difference Method drops when the finite element size or the material'selastic modulus is large. In post-processing, FLAC's finite difference strength reduction technique, using the built-in SOLVE fos command, converges more slowly for complex slope models. Consequently, while FLAC excels in analyzing instability mechanisms and damage modes in soil-rock binary structure slopes, its lower efficiency in safety factor calculation limits its broader application in reliability analysis. Developing a numerical simulation method that can accurately reproduce the complex instability patterns of soil-rock binary structure slopes and improving computational efficiency is therefore critical. The PRE-IE method efficiently simulates sliding along structural planes in rock masses by discretizing the rock into rigid elements and employing interface elements to handle contact nonlinearities [15]. However, it cannot describe the continuous elastic deformation of the soil body. Therefore, building on the PRE-IE method [15], this study proposes the Partitioned Rigid Element-Interface Element-Finite Element (PRE-IE-FE) method, which integrates the finite element method (FEM) to simulate the continuum medium behavior of the overlying soil body, while coupling with the PRE-IE method to rigorously capture the discontinuous and nonlinear interactions at soil-rock contact surfaces and structural planes within the rock mass. This combined approach enables full-process modeling of composite failure modes in soil-rock binary structure slopes. We also combine the PRE-IE-FE method with the strength reduction method to create a slope instability criterion that better ensures the stability of soil-rock binary structure slopes. The effectiveness of this new method is verified through several examples [12; 13; 14; 15].