Renormalization-inspired modeling of rock mass failure: an AI-based alternative to graphical methods with a novel stress-transfer configuration

Understanding the cross-scale relationship of rock mass failure is essential for the instability of rock engineering. In this paper, the rock mass critical failure criterion under load is deduced by employing renormalization group technology and knowledge-mining technology based on machine learning. Firstly, we analyzed the relationship between the tipping point and the yield point. Secondly, we proposed a novel stress-transfer mechanism based on the equilateral triangle cell arrangement of rock representative elementary area to establish the rock mass cross-scale relationship. Thirdly, combined with the symbolic regression technique, an alternative to the graphical method is proposed to find the relationship between the homogeneity index \(m\)$m$ of Weibull distribution and the critical failure point \({p}_{*}\)$p_{\ast }^{}$. Finally, based on the tipping point in the renormalization group method, the compression/shear criterion for yield response are established and verified by a series of laboratory tests. The theoretical analysis and laboratory tests show that the results of our proposed method are consistent with the real physical situation. The research provides a new perspective on the critical failure of rock mass materials by the renormalization group method.