Deformation and hysteresis behaviors of sandstone exposed to distinct sequences of variable-frequency compressive cyclic stresses

The response of rock to dynamic loading is critical to the stability of underground engineering. This study experimentally investigated the mechanical responses of sandstone exposed to incremental and decremental frequency under compressive cyclic loading. The impact of loading frequency on amplitude of strain variation between the upper and lower bounds of cyclic stresses are revealed. The result shows that a higher frequency can incur a larger-amplitude variation of axial and volumetric strains between two bounds of cyclic stresses. The inelastic axial and radial strain ratios (defined in text) both exhibit good performance in early warning of rock failure. The cyclic loading stage (CLS) with the lowest inelastic strain ratio can be defined as the critical phase. This also applies to the evolution of secant modulus, the CLS with the peak secant modulus is used as the point to emit warning signals. The phase shift between stress–strain is frequency-dependent, a lower frequency results in a larger phase-shift. The evolution of damping ratio and dissipated energy ratio are almost frequency independent and both decrease with the ongoing of cycle.