Insights into the dimensionless stability analysis of homogeneous slopes

The paper explores the relationship between the normalised safety factor and the non-dimensional material parameter of homogeneous slopes. It introduces a novel non-dimensional slip geometry parametrisation within Bishop limit equilibrium solution, which is defined by the entry tangent, entry point and exit point. These parameters are directly linked to the physical viability of the slip surface and can therefore be mathematically constrained to account for all and only admissible failure mechanisms. The relationship between the normalised safety factor and the non-dimensional material parameter is decomposed into linear and non-linear components, which respectively describe the contributions of cohesion and friction to slope stability. These components vanish as the material parameter approaches zero and infinity, respectively, thus recovering the two limit cases of purely frictional and purely cohesive slopes. The relationship is interpolated by a closed-form equation, allowing the direct calculation of the factor of safety for virtually any cohesive-frictional slope, including vertical cuts, without requiring further analysis. Non-dimensional charts are derived to readily identify the critical slip surface based on the novel parameter triplet. The transition between shallow and deep failures is marked by a threshold value of the non-dimensional material parameter, which increases for steeper slopes.