Fatigue Damage Characteristics and Metrics for Brittle Rocks under Different Cyclic Loading Patterns

Abstract

Understanding fatigue damage evolution of brittle rocks under cyclic loading is critical for assessing the stability of deep underground geo-systems, yet the loading-history dependence of damage indicators remains insufficiently studied. In this work, cyclic loading–unloading, multistage constant-amplitude loading, and constant-amplitude-cyclic loading tests were conducted on brittle rock specimens. The results show that the secant modulus exhibits an initial increase followed by degradation, while cumulative residual strain develops in three characteristic stages. Energy components (total, elastic, and dissipated energies) increase progressively with cycle number, with dissipated energy showing accelerated growth prior to failure. Fatigue damage was quantified using the modulus method, residual strain method, energy method (EM), and a newly proposed residual deformation–energy method (REM). A comparative analysis demonstrates that the EM provides stable damage characterization under cyclic loading–unloading and multistage loading, whereas the proposed REM more effectively captures damage evolution under constant-amplitude-cyclic loading. These findings clarify the loading-history dependence of fatigue damage metrics and provide guidance for selecting appropriate damage indicators in laboratory evaluation and engineering applications.