Mean stress effects and energy-based modeling of fatigue behavior in artificially cemented rock-like materials under cyclic loading

Soft rocks are prevalent in construction environments and are frequently subjected to cyclic loading conditions, making them susceptible to fatigue failure. In practical applications, cyclic stresses often coexist with pre-existing static (mean) stresses, necessitating the explicit consideration of mean stress effects in fatigue life evaluation. Additionally, mean stress variations are inherently introduced when irregular cyclic loadings are idealized into regular waveform patterns in both experimental and analytical frameworks. This study investigates the influence of cyclic mean stress on the fatigue behavior of artificially prepared, weakly cemented sandstone specimens under uniaxial cyclic compression. Force-controlled fatigue tests with a constant amplitude were conducted at stress ratios (R = σ_min/σ_max) of 0.0, 0.1, and 0.2 with a loading frequency of 0.5 Hz. The maximum cyclic stress level ranged from 68 to 98% of the monotonic compressive strength. Stress-life (S–N) curves were established, accompanied by detailed analyses of dissipated and elastic energies accumulation per cycle. Results showed that, for a given maximum cyclic stress level, the fatigue life increases as the stress ratio increases, while the dissipated energy per cycle decreases. An empirical fatigue life prediction model was developed based on the cumulative dissipated energy at failure, explicitly incorporating mean stress effects. Model parameters were determined solely from the stress-life data at a stress ratio of R = 0.0. Validation indicates that the proposed model accurately captures the sensitivity of fatigue life to mean stress variations across different regimes, providing a robust tool for designing fatigue-resistant rock materials in cyclic loading conditions.