Analytical solution for calculating the water inflow in composite lined tunnels with waterproof and drainage systems

Abstract

In the design of waterproof and drainage systems for composite lined tunnels, water inflow is an important parameter. As the main method for predicting tunnel inflow at present, the existing analytical solutions tend to ignore the influence of seepage in the surrounding rock around the tunnel and the two-dimensional seepage characteristics inside the tunnel structure. This study addresses these two issues and derives an analytical solution for the water inflow of a composite lined tunnel with waterproof drainage system using the conformal transformation and the sub-regional separation of variables method. Comparison with numerical simulations and existing solutions shows that the analytical solution has good accuracy under any geotextile permeability coefficient k_g, soil permeability coefficient and primary lining permeability coefficient, which is obviously superior to the existing solutions. Finally, parameter analyses based on actual projects are carried out to investigate the relationship between geotextile parameters, drainage pipe spacing, and tunnel groundwater discharge. It is found that as k_g decreases, the level of groundwater inflow into the tunnel decreases. For a fixed k_g, smaller drainage pipe spacing and larger geotextile thickness increase groundwater inflow. In addition, when the surrounding rock and lining parameters are fixed, it is feasible to adjust the geotextile parameters and drainage pipe spacing to regulate the tunnel groundwater discharge, and this study can provide a reference for the design of the waterproof and drainage systems of composite lined tunnels.