A three-parameter permeability model for the cracking process of fractured rocks under temperature change and external loading

Abstract A three-parameter permeability model is proposed to describe the cracking effects of fractured rocks induced by changes in effective stress, temperature, or both. First, a fractured rock is a composite of fractures (soft part) and matrix (hard part). In the proposed model, the natural-strain-based Hooke's law and engineering-strain-based Hooke's law are used for the deformation of the soft and hard parts, respectively. Second, the compaction of fractured rocks and generation of new fractures in the matrix are analyzed based on the energy principle and Weibull distribution. Third, a three-parameter permeability model is established for the entire deformation process. The model has three parameters: the proportion of fracture aperture in the soft part, the evolution of mean fracture aperture, and the effect of temperature change and external loading on fracture density. Finally, the proposed model is applied to fit five sets of experimental data available in the public literature; these include a China shale, China coal, France granite, China red sandstone, and USA coal datasets. The fitting results show that this three-parameter permeability model can effectively describe the permeability behaviors of fractured rock throughout the deformation process under effective stress, temperature change, or both. It can also describe the heterogeneity and interaction of deformations in the fractures and matrix.