Prediction of Mode I fracture toughness of porous rocks using rheological dynamics

Purpose The aim of this paper was to define the Mode I fracture toughness of porous dry rocks based on the rheological-dynamic theory (RDT). The topic is potentially relevant in the context of constitutive modeling and damage mechanics. Design/methodology/approach The fracture toughness is defined within the fracture process zone (FZZ) as a function of the void volume fraction (VVF), which represents existing pores and newly formed voids due to loading. The problem is formulated on a standard cylindrical specimen with a ring-shaped crack under unconfined compressive strength (UCS). Due to the differently defined cohesions in the RDT and Mohr-Coulomb (MC) material, a lateral principal stress appears in the cylinder. The conventional Griffith criterion is improved by introducing this lateral principal stress. Findings The improved Griffith criterion is consistent with the RDT at zero porosity when the rock is treated as elastic. However, differences occur within the inelastic FPZ. The fracture toughness within the FPZ is a function of: VVF, UCS, damage variables, porosity thresholds, creep coefficients, dynamic Poisson's ratio, elastic modulus ratios, cylinder diameter and geometric factor. Originality/value This study uses Zhang's empirical equation to confirm the accuracy of the results obtained by RDT. Evidence for the obtained Mode I fracture toughness is related to the FPZ. The applicability of RDT is confirmed by our own investigations of sandstone samples with ultrasonic P- and S-wave velocities, as well as on sandstone compositions of various minerals taken from the literature.