Quantitative Prediction of Blast-Induced Crack Length Around a Blasthole in Deep Rock Masses Under In Situ Stress

Deep rock blasting under high in situ stress is challenged by the suppression of stress wave propagation and the strong directional dependence of crack growth, which together make fragmentation control notoriously difficult. Existing studies remain largely qualitative and lack predictive mathematical relationships linking crack length to the in situ stress state. In this study, we combine theoretical analysis with LS-DYNA numerical simulations to investigate eight stress cases (σ = 10~40 MPa, lateral stress coefficient K = 0~2). For the first time, a dimensionless confinement parameter, χ = σm/σt* + αχΔσ/σc, combining mean and deviatoric stresses, is introduced. And a unified exponential scaling relationship is established: Lc/a = 122.54exp(−0.80χ) + 4.9(R2 = 0.94). This quantitative relationship reveals a hoop stress phase transition: the tensile phase vanishes completely when the hydrostatic stress reaches approximately 30 MPa, and provides a practical theoretical basis for optimizing blasting parameters and predicting fragmentation extents in deep, high-stress mining and tunneling.