Investigation on the Expression Ability of a Developed Constitutive Model for Rocks Based on Statistical Damage Theory

Abstract

Abstract The three-parameter Weibull distribution has a strong ability to fit many kinds of experimental data, which provides a solution for using a unified expression to characterize the elastic-brittle, strain softening, elastic-plasticity, and other constitutive behaviors of rocks. Therefore, a statistical damage constitutive model based on three-parameter Weibull distribution was constructed through theoretical analysis and derivation. Its expression ability was verified by combining with the conventional triaxial compression test data of marble. Meanwhile, the application effect of this statistical damage constitutive model on granite and sandstone was analyzed. The results show that the statistical damage constitutive model of rock based on three-parameter Weibull distribution can well express elastic-brittle, elastic-plastic, strain softening behaviors of rock by setting reasonable constitutive parameters, which lays a theoretical foundation for constructing a unified rock constitutive model. Conventional triaxial tests of marble show that with the increasing of confining pressure (σ3= 5, 15, 25, 35 MPa), the plastic deformation increases and the failure mode gradually changes from brittle tensile failure to shear failure, showing brittle-ductile and brittle-plastic transition characteristics. And its constitutive behaviors are characterized by elastic-brittleness, strain softening, and elastic-plasticity, which can be well expressed by the statistical damage constitutive model. When σ3 is 25 and 35 MPa, sandstone samples show elastic-brittle behavior. And for granite samples, they show strain softening behavior when σ3 is 5 MPa. The statistical damage constitutive model is also suitable for describing both sandstone elastic-brittle behavior and granite strain softening behavior. It is concluded that the three-parameter Weibull distribution provides a useful approach to characterize various constitutive behaviors of rock, and the model has a wide potential in numerical simulation for mining engineering, geoengineering, and other rock engineering.