Fracture propagation law of hydraulic fracturing of rock-like materials based on discrete element method

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.