A novel rigid-plastic finite element method for slope stability analysis incorporating tensile failure

Tensile failure is often neglected in classical slope stability analyses, which can lead to overestimation of stability and an incomplete understanding of the failure mechanisms. To address this limitation, this study introduces a novel lower-bound formulation that incorporates tensile failure into the Drucker–Prager criterion through an additional constraint on tensile strength. A key feature of the proposed approach is the use of linear inequalities derived from the Gershgorin circle theorem, which preserves convexity in three-dimensional stress space. The method effectively captures the influence of tensile failure on slope stability. Results indicate that steep slopes are most affected, showing the largest reduction in stability number compared with shear-only analyses. This trend is supported by the distributions of equivalent plastic strain rates and associated velocity fields, which reveal that as tensile strength decreases, the failure mode transitions from shear-slip to tensile-toppling, accompanied by crack initiation and significant changes in the sliding body geometry.