Damage and energy evolution characteristics of pre-cracked sandstone under multi-stage amplitude-increasing cyclic loading

Abstract

To systematically investigate the damage evolution and energy dissipation mechanisms associated with rock fracture induced by cyclic disturbance, a series of multi-stage amplitude-increasing cyclic loading tests are conducted on red sandstone specimens containing elliptical pre-existing flaws. The results indicate that, under low-cycle fatigue loading, the peak stress of red sandstone specimens shows a V-shaped variation with increasing defect inclination, with a minimum-to-maximum difference of 26.3 %. In contrast, the peak stress exhibits a W-shaped variation with increasing defect size, with a difference of 18.9 %. Under low-cycle fatigue loading, the elastic modulus exhibits significant hardening and can be modeled accurately with a quadratic function. Furthermore, the evolution of damage with respect to the fatigue life ratio (N/N_f, where N represents the current cycle count and N_f denotes the total number of cycles) can be categorized into three stages: an initial rapid increase stage (0 ≤ N/N_f < 0.2), a middle steady increase stage (0.2 ≤ N/N_f ≤ 0.8), and a late rapid increase stage (0.8 < N/N_f ≤ 1). Additionally, a one-dimensional constitutive equation describing the fatigue damage evolution of red sandstone is established. Energy calculation results demonstrate that both dissipated energy and elastic strain energy exhibit a trend of slow growth followed by sharp increases during the progression of fatigue life ratio. This change can be quantitatively characterized using an exponential function model. The ratio K, defined as the dissipated energy (density) to elastic strain energy (density), remains consistently below 0.7 throughout the evolution of low-cycle fatigue damage. It exhibits three distinct stages of variation as the fatigue life ratio increases. These research findings not only enhance the understanding of rock mass failure mechanisms induced by cyclic disturbances but also provide critical experimental evidence and theoretical support for the design, construction, and long-term stability assessment of deep rock mass engineering.