Abstract
This paper presents a novel rigorous procedure for assessing the lower bound of three dimensional (3D) slope stability based on the block element method. Within the framework of the lower bound theorem, a statically allowable stress field satisfying the equilibrium, stress boundary, and yield conditions is constructed. Six equilibrium conditions including force and moment equilibrium are strictly satisfied for every block element. Additionally, two possibilities in the direction of resultant shear resistance on the slip surface, including unique direction and non-unique direction, are considered. In contrast to the previous studies adopting the assumptions on the inter-block forces, these forces are explicitly calculated in this study. The proposed linear programming optimization technique is well applicable to both unique and non-unique direction models. The simplicity and robustness of the rigorous method proposed in this study have been validated, by comparing the results with those obtained from various existing theories, considering four different types of slopes. The proposed method is then applied to investigate the stability of the left bank rock slope at Jinping-I Hydropower Station.
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