Mechanical behavior and failure modes of coal under unloading subjected to low-frequency dynamic disturbance

To address rib spalling and roof falls triggered by strong deep mining-induced disturbances, which limit the safe and efficient extraction of deep coal resources, we employed an in-house developed microcomputer-controlled electrohydraulic servo testing system for coal and rock, capable of combined static and dynamic loading with adaptive coupling. Three coupled loading paths were implemented: unloading of confining pressure (SX group), unloading under dynamic disturbance with a variable lower stress limit (BX group), and unloading under dynamic disturbance with a constant lower stress limit (HX group). We characterized the effects of low-frequency dynamic disturbance on the mechanical response and failure modes of coal during the unloading process. The results indicate that: (1) For SX group specimens, peak strain and peak stress positively correlate with confining pressure. After experiencing low-frequency dynamic disturbance, BX and HX group specimens exhibited reduced peak strain, with peak stress decreasing by 4.553% to 8.432% and 0.475% to 6.322%, respectively. Stress-volumetric-strain curves demonstrate dilatancy between 0 and 20 MPa, which initiates before the peak, followed by a compaction mechanism between 30 and 50 MPa. This transition is governed by confining pressure and remains independent of the stress path. (2) The deformation modulus experiences a three-stage evolution during unloading: a logarithmic decline, followed by linear attenuation, and finally an abrupt drop to failure. The instantaneous decay rate follows a U-shaped trajectory. When confining pressure is at or below 30 MPa, the rate of modulus degradation is highly sensitive to unloading. Under confining pressures of 40–50 MPa, low-frequency dynamic disturbances induce a sharp decline in modulus values into negative territory, followed by a rapid rebound. During unloading, the coal sample exhibits a damage mechanism characterized by transient strengthening and progressive deterioration. (3) Macroscopic failure modes are influenced by the level of confining pressure and the stress path. As confining pressure increases, SX group specimens transition from single shear to multiple shear failure, accompanied by a progressive reduction in surface tensile cracks. BX group specimens evolve from multiple shear failure to a combined multiple shear and transverse shear failure, characterized by lamellar scaly tensile and shear composite fragmentation. HX group specimens display multiple shear failure; however, at 30–50 MPa, they also exhibit significant tensile fragmentation and particle-scale pulverization. (4) Compared to SX group specimens, BX and HX group specimens show larger fluctuations in modulus values, with abrupt changes in modulus concentrated during disturbance stages I to II and III to IV, respectively. Based on analyses of acoustic emission RA and AF values, tensile cracking predominates in SX specimens. Along the BX group path, the fraction of tensile cracks increases progressively during confining pressure unloading and the early disturbance stage. Under HX group conditions，at stages III to IV, the proportions of tensile and shear cracks surge simultaneously.