考虑渗透各向异性的水下非圆形隧道渗流场解析

Analytical Solution on Seepage Field of Underwater Non-circular Tunnel Considering Seepage Anisotropy

矩形、直墙曲拱形等非圆形断面隧道在工程建设中越来越常见,自然界土体受地质运动和自身重力作用多为渗透各向异性介质。现有关于水下隧道渗流场的解析研究理论常将隧道截面形状假设为圆形,以使水下隧道渗流场的计算得到简化,少数关于非圆形断面隧道的解析研究也未能考虑隧道周围介质渗透各向异性对隧道渗流场的影响。基于此,以2个相互垂直的渗透系数表示隧道洞周土的渗透各向异性,基于地下水渗流理论、坐标变换、保角映射、最优化技术,将水下非圆形隧道渗流域分区域映射为同心圆环,在此基础上分别求解稳定渗流连续方程,再按照渗流连续性原则进行联立求解,推导出在渗透各向异性半无限多孔介质中水下非圆形隧道渗流量及水头的解析式。以某椭圆形水下隧道为依托,通过数值模拟验证了该解析解的正确性,且与等效周长法和等效面积法对比发现本文方法更符合数值模拟结果。研究发现:不考虑洞周土渗透各向异性将会低估隧道渗流量和衬砌外水头,给隧道支护结构设计带来安全隐患,在隧道工程建设中适当考虑洞周土渗透各向异性的影响符合实际情况。本文提供的方法适用于考虑渗透各向异性下的任意形状水下隧道渗流场的解析研究,为非圆形断面隧道渗流量、支护结构外水压力的快速、准确预测提供支撑。

Tunnels with non-circular cross-sections such as rectangles,straight walls,and arches are becoming more and more common in engin-eering construction.It is also a basic fact that natural soils are mostly permeable anisotropic media due to geological movement and their own gravity.The existing analytical research theories on the seepage field of underwater tunnels often assume that the shape of the tunnel cross-sec-tion is circular,to simplify the calculation of the seepage field of underwater tunnels.Few analytical studies on tunnels with non-circular cross-sections also fail to consider the effect of anisotropy of permeation of the surrounding medium on the seepage field.Based on this,two mutually perpendicular permeability coefficients are used to represent the permeability anisotropy of the surrounding soil of the tunnel.Based on ground-water seepage theory,coordinate transformation,conformal mapping,and optimization techniques,the sub-regions of the seepage area of under-water non-circular tunnels are mapped into concentric rings.On this basis,the steady seepage continuity equations are solved separately,and then simultaneously solved according to the seepage continuity principle,and the analytical formulas of seepage flow and water head in underwater non-circular tunnels in semi-infinite porous media with the permeation anisotropy are derived.Based on an elliptical underwater tunnel,the cor-rectness of the analytical solution is verified by numerical simulation,and compared with the equivalent perimeter method and the equivalent area method,it is found that this method is more consistent with the numerical simulation results.The study also finds that if the seepage anisotropy of the surrounding soil is not considered,the seepage flow of the tunnel and the water head outside the lining will be underestimated,which will bring safety hazards to the design of the tunnel support structure.The method is suitable for the analytical study of the seepage field of any shape underwater tunnel considering the seepage anisotropy and provides support for the rapid and accurate prediction of the seepage flow of the non-circular section tunnel and the external water pressure of the support structure.