An analytical solution for determination of pore pressure distribution around non-circular deep tunnels

In design and evaluation of the stability of deep tunnels placed in a saturated formation, the stress – strain state of the formation and the tunnel lining depends on the distribution of the pore water pressure and seepage flow in the medium. In some cases, a water collection system is installed at the extrados of the tunnel liner. The design of this drainage system also requires determining the ground-water inflow into the tunnels. Moreover, in many cases, a large rate of ground- water inflow into the tunnels during tunneling results in trouble for the construction. The problem is what is pump capacity needed to handle the water volume. This paper presents analytical solution to determine the pore water pressure field at steady-state around non-circular cross-section deep tunnels in a homogeneous, isotropic and saturated rock. Two specific cases are considered, elliptical cross-section and semicircular cross-sections tunnels. The solution is developed based on the conformal mapping technique of the complex variable method. The present solution is validated by comparing its results with the ones of numerical simulations based on the finite element method. The obtained analytical solution could be considered a quick and accurate tool for determination of the pore water pressure around the tunnels and, could be used for the preliminary design of the drainage system as well as for validation of numerical models.