Quantitative Calculation of Crack Stress Thresholds Based on Volumetric Strain Decomposition for Siltstone and Granite

Abstract

Crack stress thresholds in rocks have long been a popular subject in rock mechanics and engineering research. In this study, the applicability of existing methods for determining the crack stress thresholds of granite and weakly cemented porous siltstone is investigated using step loading and unloading tests. In addition, a novel method for decomposing the volumetric strain into solid-phase linear elastic strain, gas-phase nonlinear elastic strain, and plastic volumetric strain is presented. A quantitative calculation method for determining these thresholds is proposed based on the evolution law of the gas-phase volumetric strain and the physical significance of crack stress thresholds. The initiation and termination points of the stationary stage of the gas-phase volumetric strain are determined as σcc and σci; the point at which the gas-phase strain changes from positive to negative is determined as σcd. To validate the proposed method, statistical results of the existing methods after screening are compared with the results of the proposed method. The results show that the proposed method provides reasonable crack stress thresholds for siltstone and granite and is applicable to rocks with similar stress–strain behaviors. The proposed method offers the advantages of independence from other methods, suitability across high and low confining pressures, and the capability for the quantitative calculation and processing of numerous samples.