Determining the Cohesive Length of Rock Materials by Roughness Analysis

Abstract

In this research, the cohesive length of various rock types is measured using quantitative fractography alongside a recently developed multifractal analysis. This length is then utilized to gauge material cohesive stress through the theory of critical distances. Furthermore, the fracture process zone length of different rings sourced from identical rocks is assessed as a function of ring dimensions and experimental measurements of fracture toughness, in accordance with the energy criterion of the finite fracture mechanics theory. Subsequently, employing the stress criterion within coupled finite fracture mechanics, the failure stress corresponding to the fracture process zone is determined for various rings. Ultimately, through interpolation, the critical stress corresponding to the cohesive length, quantified via quantitative fractography, is approximated. Remarkably, the cohesive stress values derived from both methodologies exhibit perfect alignment, indicating the successful determination of cohesive length for the analyzed rock materials. The study also delves into the significant implications of these findings, including the quantification of intrinsic tensile strength in quasi-brittle materials and the understanding of tensile strength variations under diverse stress concentrations and loading conditions.