Rotational–translational failure mechanism of multi-layered soil slopes using upper bound limit analysis

This study presents a closed-form analytical approximation for the stability of multi-layered cohesive–frictional slopes based on a kinematically admissible upper-bound formulation. A three-block mechanism composed of two rotational log-spiral zones connected by a translational block moving parallel to the slope face is proposed to capture the compound rotational–translational failure patterns characteristic of multi-layered slopes. Closed-form expressions for the critical height are derived by incorporating layer-specific strength parameters and energy dissipation while preserving analytical tractability. A homogeneous slope is included solely as a baseline verification to confirm that the formulation correctly reduces to the classical rotational solution in the absence of layering. Further, the optimal kinematic parameters are determined using an optimization procedure implemented through the OPTUNA framework based on the Tree-structured Parzen Estimator algorithm. The analytical predictions are validated against finite element simulations in PLAXIS 2D, showing deviations of less than 2% for the homogeneous baseline and the three-layer compound slope, and 5.6% for the two-layer clay–rock case where shallow localized failure lies at the boundary of the mechanism’s applicability. As a result, parametric analyses indicate that partition geometry is the dominant factor controlling the failure mechanism, while friction contrast and slope angle have secondary influence; the spiral center constraint and kinematic mode produce only minor variations in the stability number. The proposed framework offers a computationally efficient analytical tool for optimization-based slope stability assessment of layered slopes with a single evaluation completing in under six seconds. The mechanism is most reliable for slopes with moderate strength contrasts and a limited number of layers; cases involving thin weak caps overlying stiff interfaces may fall outside the applicable range and require additional verification using simplified rotational mechanisms or numerical methods.