A new modified maximum principal stress criterion for predicting rock fracture toughness under mixed-mode I/III loading

Fracture toughness (i.e., critical stress intensity factor) is recognized as an inherent strength property representing rock resistance to crack growth. Under pure mode-III loading, the edge-notched disk bending (ENDB) specimen exhibits a completely twisted fracture trajectory with anti-symmetry, whereas the fracture morphology of the double-edge notched disk compression (DENDC) specimen is almost co-planar and mirror-like. The pure mode-III fracture toughness obtained from the shear-based DENDC specimen is apparently higher than that obtained from the tension-based ENDB specimen. Consequently, the ENDB and DENDC specimens can serve as appropriate specimens for determining the lower- and upper-bound benchmarks of rock mixed-mode I/III fracture toughness, thus providing crucial design parameters for rock engineering projects. To theoretically predict the onset of mixed-mode I/III fracture in rocks subjected to combined tension-torsion loads, a 3D modified maximum principal stress (3D-MMPS) criterion is established by differentiating the contributions of volumetric and deviatoric stresses to crack propagation. The proposed fracture criterion is validated against mixed-mode I/III test data from the published literature. Based on the commonly used fracture criteria, the maximum ratio of mode-III fracture toughness to mode-I fracture toughness predicted is only 1, demonstrating that the derivation and establishment of existing fracture models are based on tensile-type conceptual frameworks. The developed fracture criterion has a profound physical meaning: the spherical stress tensor represents volumetric variation, while the deviatoric stress tensor represents shape change, effectively reflecting the fracture mechanisms of different rock specimens.