Analytical solution for stress distribution around deep lined pressure tunnels under the water table

Existing models on the stress distribution around deep buried tunnels pay little attention to the impact of rock-liner interaction and seepage variation. The conventional solution for deep lined tunnels has an inherent mathematical restriction since it is limited to thin liners. In this paper, we solve the poro-mechanical problem of stress and pore pressure distribution using the complex variable method and the conformal mapping technique. The proposed solution relaxes the assumptions of thin liner and negligible stresses that limit the usefulness of existing approaches. To derive the solution, the stress function is expanded into Laurent series in the complex plane. Analytic expressions for both with and without gravity conditions are obtained. The proposed solution is compared with the Finite Element Method; a good agreement has been obtained between the numerical simulations and proposed analytical solution. It is found that with the liner installation, the effective maximum principal stress (MPS) decreases by about 50% for the given case condition. In addition, the pore pressure distribution around the tunnel increases sharply compared to the no liner condition. The parametric study shows that the effective MPS value is highly affected by the liner relative thickness, stiffness and permeability. Its location on the tunnel boundary moves from the horizontal direction to the invert with the increase of the liner thickness and stiffness. Furthermore, the results show that low liner permeability results in high pore pressure around the tunnel, which reduces the effective stress within the rock mass.