## 1 Introduction  
A waste dump is a massive artificial loose accumulation structure. Once destabilized, it may trigger mining disasters and major engineering accidents, which not only disrupt normal mining operations but also result in substantial economic losses and threaten downstream facilities and personnel safety [1, 2, 3]. In practical engineering, rainfall is one of the primary factors affecting slope stability. Globally, thousands of landslides are triggered by rainfall each year [4, 5, 6]. Rainfall infiltration saturates the soil, increases its weight, and reduces its shear strength, thereby inducing slope instability [7]. Prolonged or intense rainfall events significantly heighten the risk of slope failure, particularly in loose, poorly drained soils. For instance, the Three Gorges Reservoir area has experienced multiple rainfall-induced landslides [8]. Therefore, studying the stability of steep high slopes under rainfall conditions, especially under varying slope ratios, is crucial for preventing and mitigating geological disasters. In recent years, progress has been made in understanding slope stability, particularly the effects of rainfall infiltration. [PERSON] [9] demonstrated that the stability of heterogeneous slopes under different water-level drawdown conditions is significantly influenced by the heterogeneity coefficient of soil properties. [PERSON] and [PERSON] [10, 11] investigated the impact of rainfall infiltration on slope stability, finding that rainfall rapidly increases surface saturation and causes water accumulation at the interface between weak interlayers and bedrock, leading to shear failure. [PERSON] [12] conducted simulation experiments on slopes with varying basal inclinations and concluded that displacement and strain increments positively correlate with basal inclination. [PERSON] [13] proposed a novel three-dimensional stability calculation method, integrating the shear resistance and sliding force of micro-column units to establish a spatial shape equation for composite slopes. Numerous researchers have employed numerical simulation software, such as FLAC 3D and GeoStudio, to explore slope stability under various conditions [14; 15; 16]. [PERSON] [17] addressed the stability control requirements for reverse stacking in weak foundation dumps, establishing a relationship between stacking height rate and weak soil layer strength parameters, and proposed a stability analysis method for dump slopes under different stacking height rates. [PERSON] [18] developed a slope stability prediction model based on a genetic algorithm-optimized BP neural network, considering six key slope characteristics: unit weight (\(\gamma\)), cohesion (c), internal friction angle (\(\varphi\)), slope angle (\(\alpha\)), slope height (H), and pore water pressure (ru). [PERSON] [19] conducted model experiments to study the response of weathered rock slopes to rainfall infiltration under different conditions, concluding that excavation angle and moisture distribution are critical factors influencing slope stability. The finite element method (FEM) is widely used due to its advantages in handling complex geometries and heterogeneous materials [20]. In recent years, the strength reduction method based on FEM has become an important tool for slope stability assessment. [PERSON] [12] proposed a new three-dimensional slope stability analysis method based on finite element stress calculations. This method aligns with the rigid limit equilibrium assumption regarding the sliding direction, making it convenient for calculating three-dimensional sliding directions. [PERSON] [21] assessed the stability of slopes with complex geometries composed of hyaloclastite basalt, porphyritic basalt, ignimbrite, and debris layers (poorly sorted clayy sand to silty sand) using both the limit equilibrium method and the shear strength reduction method based on finite element analysis. Many studies rely on limited sample data, which may restrict the generalization ability and predictive accuracy of models.