Theoretical and experimental study on the spalling law of tunnels subjected to underground explosions

Spalling is a predominant failure mode observed in underground tunnels subjected to explosion waves. The spalling laws of underground tunnels in homogeneous hard rock and fractured rock masses were analyzed using a one-dimensional wave model and a block instability model，respectively. The calculation formulas for spalling block size，spalling velocity and critical scaled distance for spalling under different conditions were obtained. Existing explosion tests conducted on underground tunnels were evaluated using the proposed theoretical methods. To obtain empirical spalling data and validate the theoretical methods，a prototype explosion experiment was conducted on a U-shaped tunnel in granite. The experiment demonstrated the spalling damage phenomenon of the tunnel at a scaled distance of 1.03 m/kg^1/3，and measured the peak particle velocities at the tunnel top，the ejection velocities of spalling blocks，and the irreversible displacements of the tunnel wall. The measured results show good agreement with the theoretical calculation results，which verified the scientific reliability of the proposed theoretical method.