Response of a circular tunnel embedded in saturated soil to a series of equidistant moving loads

The dynamic response of an infinitely long circular tunnel embedded in the saturated soil to a series of equidistant moving loads (SEML) is investigated in this study. The saturated soil surrounding the tunnel is described by Biot’s theory. Two scalar potentials and one vector potential are introduced to represent the displacement of the solid skeleton and the pore pressure. Based on Biot’s theory, the Helmholtz equations for the potentials are derived using the Fourier transform method. Performing the Fourier transform with respect to the longitudinal coordinate on the Helmholtz equations gives the frequency–wavenumber domain general solutions for the potentials. With the general solutions and the boundary conditions along the tunnel surface, the solution for the circular tunnel subjected to a single moving load (SML) is obtained. Superposition of the solutions for SMLs gives the representation for the response of the tunnel to a SEML, with which the resonance and cancelation conditions for the SEML are derived. Numerical simulations suggest that for the circular infinite tunnel there is a critical velocity. When the load moves with the critical velocity, the frequency domain response of the tunnel exhibits some dominant peak. Further, for a SEML moving with the critical velocity, the resonance and cancelation phenomena in the time domain may occur when the aforementioned resonance and cancelation conditions are fulfilled.