This paper presents a new algorithm for assessing the reliability of three-dimensional (3D) slope stability considering the spatial variability of soil based on the Particle Swarm Optimization (PSO) algorithm. First, a 3D random field is generated using the Karhunen–Loève (K-L) expansion method. Then, the simplified Bishop method of limit equilibrium is coupled with the PSO algorithm to calculate safety factors of the slope. Finally, the failure probability of the slope is determined using the Monte Carlo Simulation method. After validating the rationality of the proposed method through a typical case study, this paper offers an in-depth examination of how soil spatial variability affects the stability of 3D slopes. It is observed that, given identical soil correlation lengths, slope geometric parameters, and failure surface widths, the failure probability is positively correlated with soil spatial variability parameters, while the mean safety factor demonstrates an inverse relationship with these variability parameters. Additionally, the failure probability tends to increase as the soil correlation lengths increase, and it also escalates with the expansion of the failure surface width. In contrast, the mean safety factor exhibits an upward trend with the augmentation of the horizontal correlation length, while it diminishes progressively as the vertical correlation length grows, and it also shows a decline with the widening of the failure surface width. The proposed algorithm significantly improves computational efficiency while ensuring accuracy, making it suitable for the reliability analysis of three-dimensional slopes.

The determination of the optimal random field element (RFE) size is crucial in soil slope reliability analysis as it governs the trade-off between precision in failure probability calculations and computational efficiency. Given the substantial computational burden associated with smaller RFE sizes, studies on their impact on slope failure probability are scarce. This research examines the influence of RFE size on failure probability and safety factor, employing the Karhunen–Loève expansion to generate random fields and integrating the simplified Bishop method with particle swarm optimization (PSO) to assess slope stability. Through Monte Carlo Simulation (MCS), this study investigates the effects of the ratio of slope height to RFE size (H/D_e) on slope reliability metrics across two illustrative cases. Results reveal a notable influence of H/D_e on the distribution of safety factors (F_s) and failure probability (PF), with overestimation observed at smaller H/D_e ratios. When H/D_e exceeds 10 for Example 1 and 15 for Example 2, the F_s distribution patterns in both scenarios stabilize significantly, displaying minimal variability. The PF of Example 1 and Example 2 decreases with the increase of H/D_e and remains basically unchanged when H/D_e exceeds 10 and 15, respectively. Consequently, a recommended H/D_e ratio of 20 is proposed based on the analyzed cases, facilitating accurate calculations while mitigating computational overhead.