Theoretical study on dynamic responses of an unlined circular tunnel subjected to blasting P-waves

Abstract

Abstract In conventional studies, the blasting seismic wave is always treated as a time-harmonic wave, which is not suitable in some situations due to its short duration. In this paper, the blasting P-wave is simplified as a triangular impulse. The distribution functions of dynamic stress concentration factor (DSCF) and the radial and hoop vibration velocity scaling factors (RVSF and HVSF) around the circular tunnel are derived based on the Fourier–Bessel expansion method. Then, the effects of the rising duration, the total duration and Poisson's ratio on DSCF, RVSF and HVSF are discussed. Results show that (1) the maximum RVSF and HVSF are located at the incident side, and the location of the maximum DSCF will move from the incident side to the shadow side when the total duration increases; (2) the maximum DSCF increases with the increasing total duration, decreases with the increasing Poisson's ratio, but is immune to the ratio of the rising to total duration; (3) the maximum RVSF decreases with the increase of the total duration and the ratio of the rising to total duration, but increases with the increasing Poisson's ratio; (4) the maximum HVSF decreases with the increase of the total duration and the ratio of the rising to total duration, but is immune to Poisson's ratio; (5) the RVSF and HVSF under triangular impulses gradually change from less than those under time-harmonic waves to greater than those under time-harmonic waves with the increasing total duration, but the DSCF shows the opposite trend.