A logistic-based constitutive model for rocks under uniaxial compression considering the initial damage recovery characteristics

The damage process is categorized into two phases from the perspective of crack evolution, damage recovery induced by the closure of primary cracks and damage growth induced by the propagation of new cracks, to establish a damage evolution equation and constitutive relationship that accounts for the initial damage recovery characteristics of rocks. The damage recovery and growth variables are determined through coordinate transformation and the deformation modulus attenuation method, using the damage stress threshold as the critical point. The corresponding theoretical damage evolution equation is developed using the logistic model. In addition, based on the strain equivalence hypothesis, a comprehensive damage evolution equation and constitutive model incorporating the rock’s initial compaction process are developed. Finally, the validity of the proposed model is confirmed using uniaxial compression data from gabbro, granite, red sandstone, and yellow sandstone. The results show that the model curve closely aligns with the experimental data. • The rock damage process includes damage recovery and damage growth. • A logistic-based model is developed to describe rock damage process. • The proposed model simulates the uniaxial compression results effectively.