Stability analysis of residual soil slope with partially buried solitary rock block under rainfall conditions

Residual soil slopes containing partially buried solitary rock blocks exhibit fundamentally different instability mechanisms compared to conventional soil slopes without such inclusions, presenting unique challenges for geotechnical engineering practice. Currently, no mature theoretical framework exists for analyzing the stability of these composite slope systems. This study proposes a novel analytical method for evaluating the stability of residual soil slopes with partially buried solitary rock blocks under rainfall conditions. A geomechanical model was established, three distinct failure modes were identified, and corresponding safety factor formulas were derived. The theoretical calculations were validated against a case study in Hongqiao village, Sichuan Province, China, showing strong agreement with both physical model experiments and three-dimensional discrete element method (3DEM) numerical simulations. Parametric analyses reveal that variations in burial depth and inclination angle of the solitary rock block govern the transition between different failure modes. The relative position of the rock block on the slope surface determines whether its presence enhances or diminishes overall slope stability. The safety factor against block sliding is most sensitive to slope gradient: at gradients between 25° and 60°, block toppling governs failure (exhibiting the lowest safety factor), whereas at gradients between 60° and 70°, global slope sliding becomes the dominant mechanism. The influence of the solitary rock block on slope stability diminishes with increasing slope height. While rainfall conditions exacerbate all three potential failure modes, they do not alter the most probable failure mechanism for a given slope configuration. Compared to resource-intensive physical experiments and numerical simulations, the proposed theoretical model offers an efficient tool for rapidly assessing potential failure modes and calculating safety factors for residual soil slopes containing partially buried solitary rock blocks.