Investigation of flow rate calculation and ground surface response prediction for a composite lined tunnel with grouted circle

In tunnel engineering, drainage systems can effectively reduce the external water pressure of the lining, but they can also cause environmental problems such as tunnel and surface settlement and groundwater loss. Currently, there is a lack of a reliable method to quickly calculate groundwater inflow and predict surface settlement. This paper proposes a set of analytical solutions for calculating the flow rate in composite lined tunnels with grouted circles and predicting the ground surface settlement due to long-term drainage from the waterproof and drainage systems. The analytical solutions were derived through the conformal transformation, the separated variables method and the Terzaghi’s effective stress principle considering the role of the grouted circle as well as the two-dimensional seepage characteristics inside the tunnel structure. The correctness of the solutions was verified by comparing with numerical simulations and existing solutions without considering the grouted circle. Finally, a series of parameter analyses were conducted based on the solutions. The results not only clarify the influence of the grouted circle parameters, the geotextile parameters and the spacing of the drainage pipes on the tunnel inflow and the surface settlement caused by the long-term drainage of the waterproof and drainage systems, but also prove the capability of the proposed analytical solutions. In addition, the proposed solutions have high computational efficiency and take less than 3 s for a single case, which demonstrates the practicality and feasibility of the proposed solutions for calculating the tunnel inflow and predicting the surface settlement in tunnel engineering.