Solution to transient response of a cylindrical lined tunnel in an infinite elastic medium under internal blast load

The vibration response resulting from internal explosion load is very important for the safety of the underground lined tunnels. The dimensionless dynamic transient solution to a cylindrical lined cavity under an internal blast load in an infinite elastic medium is derived by the Fourier transform and the Laplace transform. Utilizing the inverse Fourier transform and the inverse Laplace transform, the distribution and propagation attenuation laws of the vibration response generated by the internal explosion load in the lining and the surrounding elastic medium are calculated and analyzed. The results show that the radial displacement and the hoop stress on the internal lining surface and those of the soil on the interface between the lining and the soil reach the maximum at the explosion source center. The radial displacement and the hoop stress decrease rapidly with z* at both sides of the center, and eventually decay to zero at z*= 6. The peak value of the time history of the radial displacement and the hoop stress at the internal and outer lining surfaces are the maximum at the explosion source center. The further away from the explosion source center, the smaller the peak value. When t^*=10, the radial displacement and the hoop stress decay to zero.