Analytical solution of steady seepage field of a lined tunnel with grouting ring at arbitrary buried depth

Abstract:

In order to solve steady seepage filed for full-sectional leakage of a lined tunnel with grouting ring, a new conformal transformation method for both tunnel lining and grouting ring is proposed, and the explicit analytical solution without infinite series for head and water pressure in tunnel surrounding rock is obtained by variable separation method and orthogonality of trigonometric functions. Results of this analytical solution is compared with numerical simulation data by ABAQUS and existing literature data, which shows a reasonable agreement and verifies the correctness and applicability of this analytical solution. Parameter analysis of this analytical solution demonstrates that an increase in tunnel buried depth and a decrease in grouting ring thickness both increase the external water pressure on tunnel lining and lining water influx, whereas a reduction in lining thickness reduces water pressure outside tunnel lining, but increases lining water influx. Increases both in soil permeability coefficient and grouting ring permeability coefficient will increase water pressure outside tunnel lining and lining water influx, whereas an increase in lining permeability coefficient reduces water pressure outside tunnel lining, but increases lining water influx. This analytical solution provides a reference for size design of tunnel lining and grouting ring as well as the selection of materials.