The study investigates the temporal and spatial evolution patterns of hydraulic fractures in rock during the hydraulic fracturing process for roof stress relief in coal mines. By employing the discrete element method, a model for hydraulic fracture propagation and particle displacement was constructed to analyze the responses of fracture quantity and morphology, particle displacement, and damage zone area to variations in water pressure, cohesion, porosity, and Young's modulus. The results show that an increase in water pressure causes the fractures to transition from linear to complex mesh or branched forms, providing more channels for particle displacement and increasing the damage zone area. However, excessive water pressure may induce compaction effects, reducing the effectiveness of fracture channels and inhibiting further damage zone expansion. An increase in cohesion makes fracture propagation more regular, with particle displacement transitioning from disordered to ordered. Porosity influences the complexity of fracture propagation and the amplitude of particle displacement, while an increase in Young's modulus results in more concentrated fracture paths and enhanced directional particle displacement. The temporal evolution of fractures can be divided into the initiation stage, micro-crack propagation stage, and rapid crack propagation stage. The temporal evolution curves of hydraulic fractures under different variables follow an exponential distribution. This study provides a theoretical basis for optimizing hydraulic fracturing construction processes and offers guidance for improving roof stress relief efficiency.