A Mechanical Model for the Progressive Failure of Slabbing Roadway-Side Backfill Bodies

Slabbing failure of roadway-side backfill bodies critically threatens gob-side entry retaining stability. This study establishes an elastic thin-plate model with edge cracks, employing an innovative load transformation to reduce the three-dimensional in situ stress state to the combined action of roof–floor uniform load and equivalent axial bending moment. Based on fracture mechanics and elastic-plastic theory, the stress intensity factor K1 and crack initiation load q are derived in closed form. Results show that q is positively correlated with plate thickness t and bending moment M and negatively with crack length a in the dominant range. Applying the nonlinear Hoek–Brown criterion, the failure zone width rp at the crack tip is shown to exhibit an approximately exponential relationship with K1 for unbolted backfill. Introduction of tensioned bolts via a stress concentration factor η transforms the failure zone growth from exponential to asymptotic saturation, quantitatively confirming the crack-arresting effect. A sensitivity analysis identifies plate thickness as the dominant parameter. The model bridges the gap between initial slabbing and progressive V-shaped notch formation.