Progressive failure mechanism and the effects of rockbolt support on deep pillars using continuous-discontinuous method

To study the failure mechanism of deep pillars and the reinforcement effect of rockbolts, a Voronoi breakable block model (VBBM) on the basis of the combined finite-discrete element method (FDEM) was proposed to characterize rock pillars. Laboratory- and field-scale uniaxial compression tests were conducted to develop a parameter calibration method and to validate the model. Combined with the fully grouted rockbolt model, the study explored the progressive damage mechanism of the pillar and the supporting effect of rockbolts. The results show that the proposed parameter calibration method effectively utilizes laboratory data to determine the model parameters for rock pillars at different scales. Based on reasonable parameter settings, it is found that the model can effectively capture the macroscopic failure mechanisms, including initial edge spalling, shallow-surface spalling, and deep conjugate shear failure within pillars. The width-to-height ratio (W/H) is identified as the fundamental factor influencing the transition from strain-softening behavior to pseudo-ductility behavior of pillars and the deformation differences in the core zone. Passive confinement from rockbolts activates when the pillar undergoes sufficient volumetric expansion. The constraints generated by rockbolts significantly affect the post-peak deformation behavior of pillars. The deformations of pillars exhibit a gradient feature from the shallow surface toward the core. The crack aperture and kinetic-energy release rate are negatively correlated with rockbolt support pressures, which shows a strong power-law relationship. This indicates a transitional range of supporting pressure and an optimal rockbolt spacing. The study provides a powerful analytical framework for elucidating the progressive failure mechanism in deep rock mass, and offers theoretical support for disaster risk assessment and rock-support reliability evaluation in deep mining.