Investigation on an improved endochronic damage constitutive model accounting for micro-damage in brittle rocks.

Revealing the internal damage caused by changes in internal pores and other factors, as well as the deformation characteristics at various stages, is key to the multi-stage failure analysis of rocks. To more accurately describe the influence of damage evolution on deformation in different rock deformation stages (compaction, linear elasticity, elastoplasticity, and residual deformation) and to address the complexity in defining the relationship between the traditional elastoplastic constitutive yield surface hardening criterion and rock damage at different stages, this study proposes an improved internal time damage constitutive model that considers rock micro-damage. This model aims to better capture the damage evolution process from the compaction stage to the initiation of micro-damage in the linear elastic stage and ultimately to rock failure, as well as its impact on deformation at each stage.First, based on the endochronic constitutive model, which does not require yield surface calculations, improvements were made to address the traditional model’s limitations in reflecting the rock compaction stage. A compaction parameter in the internal time framework was introduced to represent the nonlinear characteristics caused by pore closure. Subsequently, the accumulation of micro-damage from the onset of the linear elastic stage was considered, and a damage equation was established using the internal time measure as the infinitesimal failure variable in the Weibull distribution. This equation describes the accumulation of rock damage at each stage, and the physical significance of the Weibull distribution parameters in the damage evolution equation was analyzed. Finally, the model was validated against experimental results and compared with the traditional internal time constitutive model and the statistical damage constitutive model. The results show that the proposed constitutive model exhibits a high degree of agreement with experimental data. Compared to the traditional internal time constitutive model and the statistical damage constitutive model, the improved internal time damage constitutive model demonstrates superior performance in capturing rock deformation during the compaction stage. Furthermore, in contrast to the statistical damage model, the proposed model more accurately reflects the damage evolution trends caused by rock fracture propagation, providing a more precise representation of how damage evolution at different deformation stages influences overall deformation. This effectively validates the rationality and superiority of the proposed model.