Upper bound method for three hinge buckling failure of layered rock slopes

Layered rock slopes naturally formed or excavated are prone to buckling failure. Current assessment methods predominantly rely on flexural buckling theory (i.e., elastic instability), but in fact this type of destabilization rarely occurs. Thus, an applicable stability evaluation method is urgently needed. Based on the upper bound theorem, this study develops a three-hinge buckling (THB) kinematic mechanism for layered rock slopes, incorporating translational/rotational rigid blocks and triangular plastic hinges. An efficient solution scheme combining a two-step searching genetic algorithm and the strength reduction method is proposed to determine both the minimum factor of safety (FoS) and critical failure mechanism. The validity of the upper bound solutions is verified through discrete element method (DEM) simulations of THB experiments. Furthermore, two buckling events on the Lavini di Marco slope are analyzed using the presented method and the effects of pore water pressure, thickness of the sliding mass and spacing of bedding joints on stability are systematically investigated. The derived critical failure mechanisms align closely with field-observed buckling phenomena, reinforcing the method's reliability. This study advances the understanding of THB failure while providing engineers with a practical tool for assessing buckling stability in stratified rock slopes.