A theoretical strain relationship for identifying the failure of laboratory-scale rocks under triaxial compression

Abstract

ABSTRACT A theoretical strain relationship between peak strain (ε peak) and crack damage strain (ε cd) is established for identifying the failure of the rock under triaxial compression. The relationship is derived from the two-dimensional renormalisation group theory with consideration of the rock heterogeneous microstructures. It is afunction of five parameters, including the confining stress (σ 3), Young’s modulus (E), friction angle (φ), Poisson’s ratio (γ) and homogeneity index of Weibull distribution (m). The σ 3, E, φ and γ values can be readily obtained from the stress–strain data, and amethod for obtainingmvalue using σ 3, σ cd, ε cd, E, φ and γ values is proposed. Comparison with the triaxial compression test results of 48 shale specimens with four bedding dip angles shows the failure identifications using the established relationship well agree with the experimental measurements, demonstrating the ability of the established relationship to identify the failure of the laboratory-scale rock specimens under triaxial compression. Single-parameter sensitivity analysis shows that the established relationship between the ε cd and ε peak is affected by the parameters with different sensitivity. The highest to lowest sensitivity of the parameters are φ, σ 3, E, γ andm, respectively.