半无限含水层中带衬砌隧洞渗流解析研究

现有关于半无限含水层中隧洞渗流的解析解不能考虑衬砌部分排水的特性。假定土体和衬砌均为饱和均匀连续介质，采用土体与衬砌分算；利用复变函数解决孔口问题基本方法，对土体采用共形映射坐标变换，将土体中的渗流方程转换为与衬砌部分类似的二维Laplace方程圆环域的Dirichlet问题；通过Fourier解法，根据边界条件并利用流量连续条件，求得半无限空间中带衬砌隧洞渗流量和衬砌周边水头解析解答。分析了径深比、土体与衬砌渗透系数相对值、内壁水压力等因素对渗流量和衬砌周边水头的影响，并与数值算例进行了比较。结果表明，对浅埋隧洞该解析解仍具有较好的精度，是简便、实用的计算方法。

Analytical study of seepage flow into a lined tunnel in a semi-infinite aquifer

An analytical solution is derived for seepage flow into a lined tunnel in a semi-infinite aquifer by assuming the soil and lining are saturated, homogeneous and isotropic media. Using the conformal mapping, the soil region is transferred into a cirque, and the flow in the soil region, as well as in the lining region, can be described by Laplace equation in a ring domain. The seepage inflow volume and hydraulic head along the tunnel circumference are solved by Fourier method for the Dirichlet problem. The influence of radius, hydraulic conductivity and internal water pressure on the seepage inflow volume and hydraulic head along the tunnel circumference is discussed and compared with numerical simulation. The comparison shows the analytical solution is a simple, convenient and practical calculation for shallow tunnels.