Stresses around Pressure Tunnels with Semi-permeable Liners

Summary. The liner of a pressure tunnel needs to be designed such that it can withstand the loads from the ground, the internal pressure, and minimize the development of significant pore pressures at the liner-ground interface. Pore pressures behind the liner reduce the effective stresses in the ground immediately in contact with the liner and can ultimately produce loss of support from the ground. Deformations and loads of the liner are intimately connected to the interplay that exists between liner, ground, and pore pressures in the ground. A closed-form analytical solution has been derived that accounts for the inter-relation between liner, ground, and pore pressures. Elastic response of the liner and ground, and plane strain conditions at any cross-section of the tunnel are assumed. The solution shows that stresses in the ground depend on the following dimensionless factors: relative stiffness of the ground and liner, ground Poisson’s ratio, surface slope angle, coefficient of earth pressure at rest, relative tunnel depth, and magnitude of the pore pressure behind the liner relative to the internal pressure. The minimum ground effective tangential stresses at the ground-liner interface increase with the relative stiffness of the liner, with the coefficient of earth pressure at rest, and with tunnel depth. They decrease with increasing surface slope angle and pore pressures behind the liner. As leakage through the liner increases, the pore pressures in the ground increase. This results in a decrease of effective radial and tangential stresses in the ground while displacements and loads of the liner are relatively less affected.