Analytical method for calculation of ground vibration from a tunnel embedded in a multi-layered half-space

An analytical method is presented to calculate ground vibrations from a tunnel in a multi-layered half-space. Using the transfer matrix method, the dynamic system matrix for the multi-layered soil overlying a half-space or bedrock is obtained. The tunnel is coupled with the multi-layered soil via transformations between the cylindrical waves and plane waves. The proposed method provides a high-efficient tool to predict vibrations induced by underground railways. Numerical simulation suggests that the critical velocity under the moving harmonic load mainly depends on the properties of soils below the tunnel. There is no obvious critical velocity under the moving harmonic load.