Quantifying the cohesive strength of rock materials by roughness analysis using a domain based multifractal framework

Abstract

Cohesive strength or intrinsic tensile strength as well as cohesive length are two important unknowns for cohesive modelling of fracture and failure analysis of quasi-brittle materials including rocks. There is no direct method for measuring these parameters and their quantification is always challenging and controversial. In this study, a novel multifractal framework is employed to quantify the cohesive length of four different rock types including sandstone, marble, fine-grained granite and coarse-grained granite by analysing the roughness of their fracture surfaces in a wide range of length scales. On the one hand, microstructural heterogeneities of rock material at small enough length scales will cause multifractality of the roughness of its fractured surface. On the other hand, this intrinsic heterogeneity together with extrinsic features including loading and environmental conditions as well as geometrical features including shape and size of a quasi-brittle specimen or structure are forming a fracture process zone (FPZ) in front of any stress concentrators before crack propagation. Therefore, it is proposed that locating the transition from multifractality to mono-fractality of a rough rock fractured surface using the employed statistical mechanics method leads to quantifying the effective length of FPZ of a sharp crack or the cohesive length. This length is quantified for the studied rocks ranging from 0.4 to 1.1 mm. Moreover, by employing the theory of critical distances, the cohesive strength σc of these rocks is also quantified ranging from 15 to 36 MPa.