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The internal damage of red-bed soft rock induced by water is pervasive. The accumulation, growth, and localization of damage is a multi-scale process that can lead to significant strength loss in red-bed soft rock. Yet, research on the critical state of deterioration process considering multi-scale failure is limited due to high degree of system freedom. Renormalization group theory is an effective approach to find critical point of phase transition in a disordered system. To apply renormalization group theory in red-bed soft rocks, this article firstly analyzed their microstructures. Then, the granular unit model and stripy unit model are proposed to describe the self-similar characteristics of red-bed soft rocks. The calculation results based on renormalization group theory are consistent with the experimental results. The critical reductions of strength induced by water are 60% in light-yellow silty mudstone and 80% in grey silty mudstone. In addition, the critical state of damage propagation caused by stress is also studied and the analytical solution is derived. Results show that the renormalization group theory can effectively couple the micro damage and strength deterioration which provides guidance to the engineering.

The Critical Indicator of Red-Bed Soft Rocks in Deterioration Process Induced by Water Basing on Renormalization Group Theory