Damage constitutive model of brittle rock under uniaxial compression based on linear energy dissipation law

Abstract

Considering the linear energy dissipation law under uniaxial compression, a damage characterization of rocks including the compression energy dissipation coefficient is proposed, which can make the existing damage calculation formula more quantitative. Damage variables of brittle rocks can be directly calculated by using the compression energy dissipation coefficient and the input strain energy of rock under uniaxial compression. Furthermore, because the classical strain equivalence hypothesis has a large error in describing the constitutive relation of rock, a correction coefficient considering the compaction effect is introduced to modify the classical model. The modified model is extended to single-cyclic loading–unloading conditions, and the corresponding constitutive equation is established to further verify the applicability of the damage model and correction coefficient. The conventional uniaxial compression and single-cyclic loading–unloading uniaxial compression models are validated with experimental results of four typical brittle rocks. The results show that the theoretical curves are highly coincident with the actual stress–strain curves, indicating that the established damage constitutive model can accurately reflect the conventional uniaxial compression and single-cyclic loading–unloading processes of rocks. The new model in this paper considers the linear energy dissipation and compaction effect, which provides an insight for the study of brittle rock constitutive model from the perspective of energy.