半无限平面含注浆圈深埋隧道渗流场解析研究

Analytical study on seepage field of deep tunnel with grouting circle in half plane

基于复变函数和渗流力学理论,采用保角变换将半无限平面围岩渗流场解析问题转化为二维圆环域的Laplace方程求解问题.根据边界条件和流量连续条件,对围岩、衬砌及注浆圈的渗流场进行联立求解,推导出半无限平面含注浆圈深埋隧道渗流场解析解.通过与镜像法解析解及数值解进行对比,验证了该解析解的可靠性.运用该解析解分析含注浆圈深埋隧道渗流场对注浆参数变化的敏感性,结果表明:注浆参数变量可通过与注浆圈渗透系数负相关,与注浆圈厚度正相关的无量纲影响因子统一表示;隧道渗流量、衬砌外水头以及渗流场敏感性随着注浆参数影响因子的增大而减小;随着衬砌渗透系数减小,衬砌厚度增大,隧道渗流场对注浆参数变化的敏感性减弱,而隧道埋深与断面尺寸的变化则对其影响很小.

Based on the complex variables and the theory of seepage mechanics,the analytical problem for seepage field of surrounding rock in a half plane was transformed to solve the Laplace equation of a planar ring domain using the conformal transformation.According to the boundary conditions and the continuous condition of flow,the analytical solutions for seepage field of deep tunnel with grouting circle in a half plane were derived by solving seepage fields of surrounding rock,lining and grouting circle simultaneously.The proposed analytical solutions were compared with the analytical solutions derived with the method of image and the numerical solutions,which indicates that the proposed solutions are reliable.The sensitivity of seepage field of deep tunnel with grouting circle to the variation of grouting parameters was analyzed using the proposed analytical solutions.Results show that the grouting parametric variables can be integrated and described as a dimensionless impact factor,which is negatively correlated with the permeability coefficient of grouting circle,but positively correlated with the thickness of grouting circle.Furthermore,the water inflow into tunnel,the hydraulic head around lining and the sensitivity of seepage field decrease with the increase of this dimensionless impact factor.With the decrease of permeability coefficient of lining and the increase of thickness of lining,the sensitivity of seepage field to the variation of grouting parameters decreases,while,on which the variations of buried depth and section size of tunnel have little effect.