Phenomenological model of crack closure in triaxial compression of porous rock-like materials

Compared to hard rocks with low porosity, natural porous rocks and rock-like materials subjected to various weathering processes exhibit more pronounced nonlinear mechanical characteristics during compression, particularly during the initial stage of pore and crack closure. To characterize the influence of radial pressure on the nonlinearity in the mechanical behavior of porous rock-like materials, a phenomenological elastoplastic damage constitutive model under triaxial compression is proposed based on the Effective Medium Theory (EMT). By introducing the minimum principal stress as an independent variable to describe crack closure, this model overcomes the limitation of previous models, which require different material parameters for different confining pressure conditions. Furthermore, an initial damage state is defined, and a damage healing function, with the equivalent crack strain as an independent variable, is introduced to account for the variation in elastic modulus during the linear stage of uniaxial loading under different compression conditions. A stress-strain analytical algorithm for the two-stage (confining pressure-uniaxial compression process) is proposed based on the Newton-Raphson iteration method to determine the evolution of state variables prior to uniaxial loading, thus reflecting the impact of the confining pressure loading process. The model is validated as effective by this algorithm, and the stress-strain curve shows a good fit with experimental data, indicating that the model can effectively reflect both pore compaction and brittle-ductile transition behaviors of porous rock-like materials during the compaction stage under varying compression conditions using a single set of parameters.