An Energy-Based Mixed-Mode Curved Crack Path Model for Empty Hole–Blasthole Spacing in Tunnel Peripheral Blasting

Peripheral empty holes can redirect blast-induced damage and improve tunnel contour formation, but the quantitative relationship between curved crack propagation and engineering hole spacing remains insufficiently characterized. Analytically, an equivalent curved crack path model combining mixed-mode linear elastic fracture mechanics (LEFM) and energy balance was developed, yielding a critical center-to-center spacing of approximately 302 mm between an empty hole and an adjacent blasthole. For a slightly weathered granite tunnel with 42 mm blastholes and empty holes at Entrance A of Changle Road Station on Qingdao Metro Line 5, deterministic two-dimensional LS-DYNA simulations compared empty hole spacings of 450, 600, and 750 mm. Among the investigated cases, the 600 mm condition—corresponding to a 300 mm center-to-center spacing between each empty hole and its adjacent blasthole—provided the most favorable balance among interhole crack-like failure path connectivity, contour formation, and surrounding rock damage control. Numerically, the crown peak stress decreased from 29.05 to 20.70 MPa, representing a reduction of 28.7% relative to the baseline. A single engineering blast at the same site provided qualitative photographic evidence of a more continuous and regular excavation contour with fewer visibly loose or locally spalled zones. Together, these results support comparative spacing assessment under similar geological, geometric, and blasting conditions.