Dynamic response of a partially sealed tunnel in porous rock under inner water pressure

In this paper, the dynamic response of the surrounding rock and structure of a tunnel that is subjected to an inner water pressure is investigated by taking hydraulic–mechanical coupling into account. A dimensionless permeable parameter defines the flow capacity of the lining, is introduced by considering the relative permeability of the lining of the tunnel and the surrounding rock. Further more, a dimensionless loading coefficient depending on the porosity of the medium, is introduced to determine approximately the quantity of the inner water pressure supported by the solid and the pore water at the boundary of tunnel. Therefore, the coupling property of partial sealing, porosity of tunnel material and geometry is developed. The analytical solutions of stress, displacement and pore pressure are derived in the Laplace transform domain with and without considering the stiffness of lining. Numerical results in time domain are obtained by Durbin’s inverse Laplace transform and are used to analyze the influence of the loading coefficient, permeable parameter, relative stiffness and thickness on stress, displacement and pore pressure in the rock mass. The available result without considering the coupling properties of partial sealing and porosity is only an extreme case of this paper.