Objective A constitutive model is identified as the most effective method for describing the deformations and failure characteristics of rocks and characterizing their mechanical behavior. Developing the equation and constitutive model for the dynamic damage evolution of rocks based on changes in their damage rates under loading is an important part of rock mechanics.

Methods To further investigate the whole process of rock deformations and failure under loading, rocks were divided into the damaged and undamaged parts via abstraction, with the latter bearing effective stress and the former bearing residual stress. This study established the equation and constitutive model based on the evolutionary characteristics of the dynamic damage rate and verified the rationality of the model using conventional triaxial compression experiments on red sandstones. Results and Conclusions The results indicate that the theoretical curve derived from the model can effectively reflect the mechanical behavior of rock damage and failure under loading. The dynamic damage of rocks underwent four stages: unchanged damage, accelerated damage propagation, slowly increasing damage, and complete damage, which correspond to the compression and elastic deformation, plastic deformation, post-peak softening, and residual deformation stages of the theoretical curve, respectively. According to the curve, the cumulative dynamic damage rate of rocks slowed down with an increase in the confining pressure. This indicates that confining pressure can inhibit damage propagation, as manifested by an increase in the compressive strength of rocks and a gradual enhancement of their plastic properties. The maximum damage rate was present in the stress decrease stage to the right of the curve’s peak, approaching the peak. Furthermore, the damage variable corresponding to the maximum damage rate was roughly consistent under different confining pressures. An increase in model parameter f was associated with an increase in the strength and plastic deformation of rocks. In contrast, a decrease in model parameter m corresponded to an increase in the rock strength but had minor impacts on the damage and deformation of rocks. By establishing the equation and constitutive model for the dynamic damage evolution of rocks, this study explores the characteristics of the maximum damage rate and the impacts of the model parameters on rock strength and the damage and deformation of rocks, serving as a valuable reference for the development of rock mechanics.