Analytical Method of Spatiotemporal Evolution Characteristics of Unsteady Seepage Flow Pore Water Pressure in Front of Tunnel Face

To evaluate the spatiotemporal evolution of pore water pressure in unsteady seepage flow ahead of a tunnel face, a partial differential equation for unsteady seepage is established. The ranges and boundary conditions of the unsteady seepage flow are specified, and the analytical solution of the unsteady seepage flow is obtained by the eigenfunction method. The obtained analytical solution additionally considers the time factor, which can be used to study the influence of seepage time on the seepage flow. And the pressure transmitting coefficient is introduced to analyze the influence of water and soil characteristics on the unsteady seepage. The analysis shows that the spatiotemporal evolution of the unsteady seepage flow pore water pressure ahead of a tunnel face is reflected in two aspects, the dissipation of the water pressure and the diffusion of the influence range of the unsteady seepage. The dissipation captures the gradual reduction of pore water pressure at a specific location as time progresses. Meanwhile, diffusion characterizes the alteration in the spatial distribution of water pressure. The pressure transmitting coefficient promotes the rate of unsteady seepage, while the height of water table has a greater influence on the magnitude of water pressure change in unsteady seepage flow.