In deeply buried rock engineering, mechanical drilling, remote blasting, continuous low-frequency vibration of heavy machinery, and natural earthquakes often cause cyclic disturbance of the surrounding rocks. These cyclic disturbance loads have the characteristics of long transmission distances and high carrying energies, which may trigger damage, failure, or instability of the surrounding rocks (Zhu et al. in Tunn Undergr Space Technol 25(5):587–599, 2010; Du et al. in Rock Mech Rock Eng 49(9):3437–3453, 2016). Under these cyclic disturbances, the free faces of the surrounding rock that simultaneously bears a high geostress may pose potential engineering hazards related to large deformation or displacement (Kaiser et al. in Int J Rock Mech Min Sci 38(2):167–180, 2001), such as swelling, spalling, breaking, and relaxing of the free faces of the surrounding rock. Considering that there is still no universal agreement as to how high geostress affects the characteristics of rock deformation, damage, and failure during cyclic disturbance, it is hard to accurately predict and effectively prevent and control those potential disturbance-triggered engineering hazards, which may pose a risk to workers’ safety and cause economic losses.