Unified rock strength theory incorporating holistic consideration of macro-meso-micro defect coupling effects

Abstract

The establishment of a unified rock strength theory under multi-scale defect coupling effects is beneficial for engineering disaster prevention. This paper first develops a microscopic damage analytical model for rocks based on the Weibull distribution of damage probability on element strength. Subsequently, by analyzing the co-deformation effect of rock matrix and fracture structures, and incorporating the fracture number and the power-law distribution indices (PDI) of the fracture length, a macro-meso damage analytical model is constructed. Building upon this foundation and combined with Lemaitre’s strain equivalence principle, a unified rock strength theory under multi-scale defect coupling effects is established. The strength of specimens under multi-scale defect coupling effects was simulated using Particle Flow Code (PFC^2D) to verify the proposed theory. The main results are as follows: (1) As the homogeneity coefficient increases, the element strength distribution demonstrates a significant convergence process, with both dispersion degree and distribution range gradually narrowing, while the corresponding uniaxial compressive strength (UCS) shows a decelerating growth trend. (2) The decrease of PDI corresponds to increased proportion of long fractures, weakened rock homogeneity, and enhanced damage degree. With increasing fracture quantity and decreasing PDI, UCS generally follows a decelerated reduction pattern after initial acceleration. (3) The flow law of specimen UCS under multi-damage parameters was obtained based on the unified strength theory. Fracture quantity exhibits relatively linear influence on specimen UCS, while smaller values of homogeneity coefficient and PDI demonstrate more significant weakening effects. (4) The unified strength theory results show high consistency with numerical simulations, achieving a correlation coefficient of 0.990, proving the theory’s effectiveness in describing the coupled influence of element strength and fracture distribution characteristics on rock UCS. (5) The proposed strength theory overcomes existing limitations that separately consider fracture angle or length and demonstrates stronger capability in reflecting both factors’ impacts on specimen strength.