A novel cyclic loading-unloading constitutive model for marble considering time effects during unloading

Deep rocks subjected to cyclic loading under high-stress conditions exhibit both load-dependent and time-dependent behavior. This study proposes a novel cyclic loading-unloading constitutive model that accounts for time effects during unloading. Cyclic loading-unloading tests at three loading rates were performed on marble specimens, with acoustic emission (AE) monitoring used to validate the model. The results show that lower loading rates produce shorter fatigue lives and more pronounced time effects. Before failure, AE signals are concentrated primarily near the upper stress limit in each cycle, although substantial AE activity is also detected during the early unloading stage. The proposed model accurately reproduces the stress-strain response throughout loading and unloading. For loading rates of 250, 500, and 1000 N/s, the maximum peak-stress errors are 1.5 %, 0.35 %, and 0.6 %, respectively. The calculated cumulative plastic strains also agree closely with the experimental value, with errors ranging from –3 % to 6 %. In addition, the model parameters exhibit clear and consistent evolutionary trends.