Critical damage threshold of brittle rock failure based on Renormalization Group theory

An in-depth understanding of damage threshold behavior during rock damage and failure is critical to predicting short- and long-term rock stability. The percolation theory was used to describe the rock damage threshold behavior and the Renormalization Group theory was used to accurately solve the theoretical solution of the critical threshold of brittle rock failure. By redefining the stress-transfer mechanism between rock blocks, the theoretical expression of the critical damage threshold of brittle rock failure was calculated based on the Renormalization Group theory. An experimental investigation of shale samples by in-situ micro-computed tomography was carried out to verify the theoretical expression. The values of damage calculated experimentally were consistent with the theoretical critical damage threshold of brittle rock failure. On this basis, the reasonable range limit of the critical damage threshold for rock mass failure was discussed. The laboratory test results on different lithologies and case studies of in-situ direct shear tests of rock and rockfalls in Mesnil-Val were analyzed to validate the feasibility of the threshold range and reveal the potential application of the research results.