Application of Graph Theory for Robust and Efficient Rock Bridge Analysis

Rock bridge analysis is a fundamental task in numerical modeling of rock slope failure, and other rock stability analyses. However, the question of what constitutes a rock bridge is quite complex and it depends on whether a definition is given based on a geometrical characterization of the fracture network, or whether the definition is given to also incorporate an analysis of failure mechanisms. The former is the focus of this paper. From a geometrical perspective, rock bridges could be defined as the shortest distance between two existing fractures; however, for a fractured rock mass even this simple definition would yield multiple complex critical paths. In the literature, several probabilistic limit equilibrium methods exist incorporating step-path analysis into rock slope design. In this paper, a novel and efficient method is presented that analyzes the rock mass in any complexity for all potential rock bridges. The output is not limited to the optimum pathway, rather it includes a detailed analysis of the network connectivity by considering multiple pathways. By using Graph theory models and tools, the proposed approach provides significant flexibility to incorporate multiple scenarios such as weighted rock bridges and classes of rock bridges.