Limit-state geometry of trailing-edge tensile cracks in soil slopes with a tensile strength threshold

Abstract Trailing-edge tensile cracks can contribute to tensile–shear slope failure. Many analytical models prescribe a vertical crack and solve only for depth, and tensile strength, σₜ , is also often neglected or treated indirectly. This study develops a limit-state formulation for an initially intact, homogeneous cemented soil slope under drained conditions. Shear resistance follows the Mohr–Coulomb criterion, while tensile failure is governed independently by \(\:{\sigma\:}_{t}\). The formulation treats the limit-state crack depth L and inclination δ as coupled unknowns of the tensile–shear limit-state problem rather than prescribing the crack inclination in advance. The solution satisfies tensile and shear failure conditions, equilibrium, and geometric constraints. The formulation is examined using theoretical benchmarks, a bounded loess field comparison, and simulations using MatDEM. The benchmarks reproduce established depth trends. The field measurement falls within the calculated range for the adopted tensile-strength ratio. The simulations preserve the crack/no-crack distinction and show closer correspondence in inclination than in depth, with mean absolute differences of 4.22° and 1.66 m, respectively. Increasing σₜ reduces L and δ and may suppress a positive-depth solution. The cohesion intercept generally increases both, while unit weight mainly reduces L . Global Sobol analysis ranks cohesion > tensile strength > friction angle > unit weight for the zero-including depth response.