## 1 Introduction  
Slope instability (landslides and collapses) is the most common geological disaster worldwide, often resulting in casualties and property damage [1; 2; 3; 4]. The analysis of slope stability has consistently been a focal point of research in the field of engineering geology, with many scholars having conducted extensive work and achieved significant results [5; 6; 7; 8; 9]. The presence of soft interlayers has a significant impact on many engineering projects [10; 11]. The failure and instability of layered rock slopes containing these soft interlayers have become significant issues affecting engineering construction. Therefore, studying the deformation characteristics, failure mechanisms, and stability conditions of various types of layered rock slopes containing soft interlayers has significant practical implications. [PERSON] et al. [12] and [PERSON] [13] used the finite element strength reduction method to analyze the impact of the height, dip angle, spacing, cohesion, internal friction angle, and slope angle of the soft interlayers on the slope displacement, safety factor, and the location of potential failure surfaces. Other researchers [14; 15; 16; 17] employing the finite-difference-based shear strength reduction method conducted similar studies. [PERSON] et al. [18] utilized the actual failure process analysis and strength reduction method to study the impact of the depth, dip angle, thickness, cohesion, and internal friction angle of the soft interlayers on the slope failure process, safety factor, and displacement. [PERSON] et al. [19] utilized the theory of butterfly mutation to investigate the relationship of the safety factor of rock slopes with the dip angle, cohesion, internal friction angle, and thickness of soft interlayers. In Yunnan Province, China, situated between the Xiaojiang fault zone and the Puduhe fault zone, bedding cataclastic rock slopes containing multi-muddy interlayers are fairly common. If not promptly reinforced after excavation, these slopes frequently destabilize. The cut slope at the Yanhe domestic waste incineration power plant in Yuxi City, Yunnan Province, is a classic example of a bedding cataclastic rock slope with multiple muddy interlayers. Slope instability resulted from improper reinforcement, leading to an increase in investment and a six-month extension of the project timeline. The authors had conducted detailed studies on the spatial distribution of the muddy interlayers and the engineering geological characteristics of the cataclastic rock mass of this slope [20; 21]. Unlike soft interlayers, muddy interlayers were thinner, had lower strength, a larger Poisson's ratio, and the surrounding rock masses above and below the muddy interlayers were more fragmented [22; 23]. The form of failure and its developmental process in the rock mass containing interlayers were dependent on the interaction between the interlayers and the surrounding rock [24]. In summary, although extensive research had been conducted on the stability of layered rock slopes containing soft interlayers [25], the failure mode and stability of bedding cataclastic rock slope containing multi-muddy interlayers differed from those of layered rock slopes containing soft interlayers. Furthermore, there have been no reported studies on the stability of bedding cataclastic rock slopes containing multi-muddy interlayers. Due to varying geological conditions and structural environments, the influencing factors of rock slopes containing multi-muddy interlayers differ, and primarily include the following categories: (1) The physical and mechanical parameters of the rock mass and structural surfaces; (2) Geometric parameters of the slope (height, angle, rock layer dip angle, structural surface spacing); and (3) Initial geo-stress, hydro-meteorological conditions, earthquakes, and anthropogenic factors. The stability of layered rock slopes often varies significantly under different geometric and physico-mechanical parameter conditions, as well as under different load combinations.