Generalized crack damage stress thresholds of hard rocks under true triaxial compression

The rock failure process can be characterized by several distinct stress thresholds: the crack closure stress sigma(cc), crack initiation stress sigma(ci), crack damage stress sigma(cd) and peak stress sigma(p). Seventy-one true triaxial compression tests were conducted to investigate the crack damage stress sigma(cd), which is the stress at the onset of unstable crack development and dilation. Two empirical models are developed to predict the crack damage stress sigma(cd) using the intermediate principal stress sigma(2) and the minimum principal stress sigma(3). In addition, the proposed models are validated by ten results derived from the German Continental Deep Drilling Program (KTB) deep hole amphibolite. A comparison with other failure criteria also indicates the accuracy and simplicity of the proposed models. The proposed composite models show that the crack damage stress sigma(cd) gradually increases with increasing intermediate principal stress sigma(2) and minimum principal stress sigma(3). The physical meanings and ranges of six material parameters are analyzed and explained. Both the influence of the tangent Young's modulus E and strain characteristics on the crack damage stress sigma(cd) and the inhomogeneity of the tested specimens are discussed in this paper.