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A rigid block based lower bound limit analysis method for analyzing stability of fractured rock mass in 2D and 3D conditions is proposed. The rock bridge effects are considered in the general formation. No assumptions are imposed on the inter-element forces, and the solution obtained is statically admissible. The proposed method is theoretically rigorous and simple. The validation and efficiency of the proposed method have been demonstrated through three typical types of slopes, indicating that apart from the fractures, rock bridge plays a key role in stabilizing rock blocks, which should be greatly concerned in stability analysis of rock mass. [ABSTRACT FROM AUTHOR]