考虑衬砌及注浆圈的任意埋深隧道渗流场解析解

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

摘要:

针对含衬砌及注浆圈隧道运营过程中发生全断面渗漏的稳态渗流工况,提出了一种新的适用于隧道衬砌和注浆圈的保角变换方法,结合分离变量法推导了该工况的水头通解,最后运用三角函数的正交性得出了水头及水压力解析解。通过与ABAQUS数值模拟结果及既有文献数据对比,验证了解析解的正确性及适用性。参数分析结果表明:隧道埋深的增加及注浆圈厚度的减小均会显著增加衬砌外部水压力及衬砌涌水量,而衬砌厚度减小则会降低衬砌外部孔隙水压力,并导致衬砌涌水量增加；土体渗透系数及注浆圈渗透系数增大均会增加隧道衬砌外部水压及衬砌涌水量,而衬砌渗透系数增大则会降低衬砌外部孔隙水压力,并增加衬砌涌水量。该解析解为隧道的衬砌及注浆圈尺寸设计和材料选择均提供了参考。

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.