Dynamic Stress Concentration of Surrounding Rock of a Circular Tunnel Subjected to Blasting Cylindrical P-Waves

In blasting excavation, the operation is always close to existing tunnels. It is not suitable to treat blasting waves as plane waves. In this paper, blasting waves are simplified as cylindrical P-waves. The wave function expansion method and multi-polar coordinates are adopted to derive the formula for dynamic stress concentration factor (DSCF) of tunnel surrounding rock under cylindrical P-waves. Combined with a specific engineering case, the influence of frequency and scaled distance r* on DSCF is analyzed. Results show when when r* is small, the increasing frequency of the incident wave will result in a more complex distribution of DSCF and the change in the location of the maximum DSCF around the metro tunnel from θ = 0° to θ = 180°, but the maximum DSCF around the metro tunnel increases first and then decreases, and the highest value is at about 20 Hz; the distribution of DSCF induced by cylindrical P-waves is quite different from plane incident P-waves. With the increase of r*, the maximum DSCF around the metro tunnel tends to be a constant of about 2.39 and the distribution of DSCF changes towards to the case of plane P-waves; when r* ≥ 15, a cylindrical P-wave can be approximately treated as a plane P-wave.