Multiscale damage constitutive model of rock based on the energy evolution of mineral grains and its application

This study employs a phase-field method that considers mineral distribution to analyze the energy evolution of grains, establishing a multiscale damage constitutive model of rock on the basis of the energy laws of mineral grains. The proposed constitutive model is applied to analyze slope stability, achieving multiscale coverage from the mineral grain scale to the engineering scale. Random classification of Voronoi polygons is used for mineral-scale modeling, incorporating the coupling of mineral plasticity and damage. The evolution of macroscopic damage is obtained through statistical analysis of mineral grain energy. By deriving the relationships between the statistical parameters and the macroscopic mechanical variables, the statistical laws of mineral grain energy are applied to constitutive modeling at the sample scale. A corresponding numerical algorithm is developed and applied to strength reduction deformation calculations for slopes. The results indicate that the mineral-scale simulation method effectively captures the nonlinear mechanical behavior and progressive failure process of rock. The stress and strain concentrations result in a right-skewness in the data distribution of the mineral grain strain energy density, which can be accurately described by a log-normal distribution. The mean parameter of the grain strain energy density is equal to the macroscopically homogenized strain energy density, whereas the variance parameter reflects the mesoscopic heterogeneity and can be linearly represented by the macroscopic damage variable. The constitutive model based on mineral grain energy evolution accurately captures damage evolution at the sample scale and closely fits the measured stress–strain curves. This research provides a reference for evaluating the mechanical properties of rock masses and for disaster prevention and control.