One fatigue damage constitutive model for rocks considering previously accumulated degradation and its engineering application on the fatigue life prediction

Cyclic loading from earthquakes, construction activities, blasting, or rock bursts can pose significant stability challenges to both surface and underground geotechnical projects. Understanding the fatigue properties and failure mechanisms of rocks under such loads is therefore essential. This study first reviews the deformation and microcracking characteristics, influencing factors, and current advances in the fatigue damage evolution laws, as well as the definitions of fatigue damage variables and constitutive relationships for rocks under cyclic loads. A novel fatigue damage variable is then proposed, accounting for accumulated damage from previous cycles and damage stress threshold attenuation, alongside a corresponding damage constitutive equation to describe the rock's behavior under varying cyclic loads. The proposed cyclic constitutive equations are validated using experimental data from diverse cyclic loading scenarios, and corresponding correlation coefficients both greater than 0.9 indicates reasonable agreement between experimental and theoretical curves. The fatigue damage evolution curve exhibits an inverse S-shape with three distinct features, and it effectively highlights the intrinsic relationship and difference between loading and unloading damage. Finally, a novel method to predict the fatigue damage is developed and proven to be feasible with test data and field data. Corresponding method for predicting fatigue life is derived, with potential application to evaluate the residual life of tunnels. Additionally, damage stress threshold, model parameters, ambiguous questions and prospective research are interpreted and discussed. This study provides a foundation for safety design and operations of rock engineering.