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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。
The existing analytical solutions for the seepage of tunnels in the semi-infinite aquifer can not consider the characteristics of drainage of the lining. Assuming that the soil and the lining are both saturated and uniform continuous media, the soil and the lining are used to calculate. The basic method of solving the orifice problem by the complex variable function is adopted. The conformal mapping coordinate transformation is applied to the soil and the seepage equation in the soil is converted to The Dirichlet problem of two-dimensional Laplace equation torus with lining is similar to that of the lining. By Fourier method, the seepage volume of the tunnel with the lining in the semi-infinite space and the analytical solution of the head around the lining are obtained by using the continuous flow conditions. The effects of depth-to-depth ratio, relative permeability coefficient between soil and lining, inner wall water pressure and other factors on seepage volume and head circumference of lining were analyzed. Numerical examples were also compared. The results show that the analytical solution of shallow tunnel still has good accuracy and is a simple and practical method of calculation.