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The mechanical response characteristics of rock under low-frequency perturbation loads and high-stress conditions are important factors affecting the stability of interlayer rock in the goaf during upward mining. Taking the coal-bearing sedimentary rock sandstone as the research object, the dynamic uniaxial compression tests were conducted on high-stress sandstone (80%UCS) under low-frequency perturbation loads (5 Hz) using a self-developed dynamic-static coupled electro-hydraulic servo testing machine. The progressive damage behavior and nonlinear mechanical dynamic response characteristics of high-stress rock under low-frequency perturbations were revealed. The results are as follows: ① During the process of small amplitude low-frequency disturbance load, high-stress sandstone does not experience dynamic failure, the threshold value of low-frequency disturbance load amplitude to induce sandstone damage is 15%UCS. Under the action of low-frequency disturbance load above the threshold value, the number of disturbance load cycles before the failure of high-stress sandstone decreases exponentially with the increase of amplitude. ② The progressive initiation and accumulation of randomly distributed microcracks within the sandstone, as well as their gradual extension, significantly affect the nonlinear evolution characteristics of dynamic secant modulus, strain peak, plastic deformation, dissipated energy density, and b-value. ③ During the low-frequency perturbation process, the b-value and dissipated energy density exhibit a three-stage evolution characteristic consistent with the strain. The exponential strain evolution curve has a distinct inflection point before the failure of the sandstone, which can serve as a precursor information of dynamic failure under low-frequency perturbations and be used for corresponding dynamic disaster warnings. ④ During the low-frequency perturbation load process beyond the threshold, the dynamic secant modulus evolution curve approximates an exponential decay. The parameters in the nonlinear fitting relationship can be used to quantify the degradation rate of the elastic modulus. And the degradation rate of secant modulus of sandstone changes nonlinearly with the increase of amplitude. ⑤ The magnitude of the RA value in the initial stage of disturbance load can be used to predict the dynamic failure of sandstone in advance. Correspondingly, the sudden increase of RA during the low-frequency disturbance load process can serve as a precursor warning of dynamic instability of high stress sandstone. During the process of small-amplitude disturbance load below the threshold value, the microcracks mainly undergo tensile or mixed fracture, with shear fracture accounting for only 12.15%. During the low-frequency disturbance load processes with amplitudes of 15%UCS, 20%UCS, and 25%UCS, the shear fracture accounts for 37.17%, 52.75%, and 53.62% respectively. The proportion of shear fractures exhibits a logarithmic increase with the increase of amplitude.

Hydraulic fracturing is an important technical means to relieve the pressure of coal seam roof. Better understanding of fracture propagation mechanism is of great significance to the safe mining of coal seam. In order to further explore the law of hydraulic fracture propagation, aiming at rock-like specimens commonly used in the laboratory, MatDEM, a particle discrete element numerical simulation software, was used to establish a two-dimensional discrete element numerical model of hydraulic fracturing, and various hydraulic fracturing tests with different injection pressure increments were carried out. The effect of injection pressure increment on the propagation of hydraulic fractures was studied, and the mechanism of model initiation was revealed. The law of fracture generation and propagation was analyzed from mesoscale, and the propagation characteristics of hydraulic fractures were discussed. The results show that ① the effect of injection pressure increment on the model initiation pressure and initiation time presents an opposite trend. With the increase of injection pressure, the increase trend of initiation pressure is slow and gradually approaches to 5.6 MPa. The initiation time decreases with the increase of injection pressure, and the decreasing trend slows down gradually. ② The cumulative number of fractures increases exponentially with time. The hydraulic fracturing process can be divided into four stages (Ⅰ−Ⅳ): no fracture stage, slow fracture growth stage, steady fracture growth stage and rapid fracture growth stage, which correspond to the pre-crack initiation, pre-crack formation, primary fracture propagation and secondary fracture propagation processes respectively. As the injection pressure increment increases, the durations of stage Ⅰ, Ⅱ and Ⅲ decrease, while the duration of stage Ⅳ increases in a fluctuating manner. The number of cracks in each stage is the highest in stage Ⅳ, followed by stage Ⅲ and stage Ⅱ. ③ As the injection pressure increment increases, the number of secondary fractures increases from 8 to 16, and the growth rate of fractures gradually slows down before the stage Ⅲ, and increases rapidly after the stage Ⅳ. When the injection pressure increment increases from 0.03 MPa to 0.70 MPa, the final fracture length increases by 1.79 times. ④ The internal energy of the model increases with the increase of the injection pressure increment, and the energy input speed gradually becomes faster. After the model initiation, high-pressure water forms stress concentration at the crack tip, which promotes the crack to continue to extend. At higher injection pressure increment, the fracture propagation speed becomes faster, and the particle displacement decreases gradually from the pressure hole to the outside of the model. The increment of injection pressure makes the secondary fracture forming position close to the pressure hole, which inhibits the formation and expansion of the primary fracture and promotes the formation and expansion of the secondary fracture. All fracture types are tensile fractures.