隧道拱顶渗漏稳态渗流场的解析研究

Analytical study of steady state seepage field of tunnel vault leakage

针对隧道运营中发生拱顶渗漏且无泥沙涌入的稳态渗流情况,结合保角变换法和分离变量法推导出隧道拱顶渗漏稳态渗流场的显式解析解.应用PLAXIS有限元软件建立数值模型,从渗流场分布、衬砌水压力两方面验证所得解的正确性,通过与现有解析解、数值解、试验结果的渗流量对比来验证所得解的准确性.进行参数分析,探究隧道埋深、渗漏宽度对衬砌水压力和渗流量的影响规律.结果表明,衬砌水压力在以渗漏位置为中心±60°范围内明显降低;随着隧道埋深的增大,衬砌最大水压力减小,渗流量先减小后增大,且渗流量最小值对应的隧道埋深随着地表水头的增大而增大;随着渗漏宽度的增大,衬砌最大水压力减小,渗流量增大,当渗漏宽度大于0.05 m时,渗漏宽度变化对水压力和渗流量的影响较小;在渗漏宽度较小时进行渗漏控制的效果明显.

In order to solve the steady state seepage flow of tunnel vault leakage without sediment influx,an explicit analytical solution of the steady state seepage field of the vault leakage was derived by combining the conformal mapping method and the separate variable method.The PLAXIS finite element software was applied to establish a numerical model to verify the correctness of the solution obtained in terms of the seepage field distribution and the lining water pressure,and the accuracy of the solution was illustrated by comparing the seepage volume with the existing analytical solutions,the numerical solutions and the experimental results.A parametric analysis was carried out to investigate the effect laws of the tunnel burial depth and the seepage width on the lining water pressure and the seepage volume.Results show that the lining water pressure decreases significantly within±60°of the centre of the leakage location,with the increase in the tunnel burial depth the maximum lining water pressure decreases,the seepage volume first decreases and then increases,and the tunnel burial depth corresponding to the minimum value of the seepage volume increases with the increase in the surface water head.As the leakage width increases the maximum lining water pressure decreases and the seepage volume increases.When the leakage width exceeds 0.05 m,the effect of changes in the width on the water pressure and the seepage volume is less.Leakage control at low leakage widths is effective.