## 1 Introduction  
Slope stability analysis and evaluation is one of the key issues in earth rock dam design. Currently, the analysis is predominantly based on the single safety factor method derived from the rigid body limit equilibrium approach. This method determines the minimum safety factor using fixed material parameters; if the computed value exceeds the permissible safety factor specified by design codes, the slope stability is deemed acceptable. However, due to the variability of mineral composition, particle gradation, and compaction degree, as well as measurement errors and scale effects in laboratory testing, the shear strength parameters of dam construction materials are inherently uncertain and should be treated as random variables. Therefore, it is essential to assess the impact of uncertainties in dam material strength parameters on the reliability of slope stability.  
Several scholars have studied the reliability analysis of earth rock dam slope stability, but their research has primarily focused on the reliability calculation of a single slip mode (i.e., a single slip surface) [1, 2, 3, 4, 5, 6]. In reality, the slip mode of the slope is also uncertain, and multiple potential slip modes may exist. This necessitates a system reliability analysis of slope stability, but related studies remain scarce. Earth rock dam slopes fall within the broader category of soil slopes, on which significant research on system reliability analysis has been conducted [7; 8; 9; 10; 11; 12; 13]. These studies have addressed the system reliability analysis of slopes with multiple slip modes (slip surfaces), but the calculations were primarily based on the rigid body limit equilibrium method, which mainly considers circular slip surfaces.  
The rigid body limit equilibrium method is widely used in practical engineering due to its simplicity and practicality. However, it cannot account for the influence of the nonlinear stress-strain relationship of soil on the internal stress state and stability of the slope, and the assumed slip surface location and shape are predefined rather than derived from the analysis. To address these limitations, [PERSON] proposed the finite element strength reduction method (FEM-SRM), which progressively reduces the strength parameters (internal friction angle and cohesion) of geotechnical materials in an elastoplastic finite element framework until the soil mass reaches a limiting equilibrium state. This approach allows for the consideration of the nonlinear stress-strain behavior of soil, eliminates the need to predefine the slip surface location and shape, and provides a means to describe the entire process of slope failure development [14]. Some researchers have applied FEM-SRM to slope and earth rock dam slope reliability analyses [15; 16; 17], but none have extended it to system reliability analysis.  
Due to the use of natural construction materials, the shear strength parameters of earth rock dam bodies exhibit significant randomness, while slope failure mechanisms and slip modes are highly complex. This necessitates a system reliability analysis of slope stability. This study proposes a novel system reliability analysis method for earth rock dam slope stability based on FEM-SRM. The core concept involves first identifying slope slip pathways using FEM-SRM, where each pathway consists of multiple elements undergoing shear failure. Each slip pathway is treated as a parallel system composed of failure elements, and the response surface method is used to compute the reliability of individual failure elements and their correlation coefficients. The stepwise equivalent linearization method is then employed to evaluate the reliability of slip pathways and their interdependencies. Since each slip pathway represents a failure mode of the slope, the overall system reliability of slope stability is determined using a series system composed of slip pathways. In this study, the Ditlevsen narrow bound method is used to compute the system reliability of slope stability.