Dynamic Response of Twin Circular Unlined Tunnels Subjected to Blasting P Waves

The dynamic response of twin circular unlined tunnels is studied by indirect boundary integral equation method (IBIEM). The twin tunnels are assumed to lie in an unbounded elastic space subjected to blasting P waves. The influence of incident angle on the distribution of DSCF around the twin tunnels is analyzed. Besides, the influences of normalized wave number αa and normalized distance d* (ratio of spacing distance to tunnel radius) on the reference DSCF, that is, the peak DSCF for different incident angles with an assurance rate of 95%, are discussed. Results show that 1) the IBIEM is a high-precision method analyzing the DSCF around twin circular unlined tunnels induced by blasting P waves; 2) the incident angle θ0, αa, and d* all have significant influences on the distribution of DSCF; 3) for a constant d*, the peak DSCF around the right tunnel is slightly greater than the left one; 4) the reference DSCF decreases exponentially with the increasing of αa or d*, and the corresponding fitting functions are proposed.