深埋隧道排水系统非对称堵塞后渗流场的解析研究

发布时间：2018-05-12 01:13

本文选题：隧道工程 + 排水系统　；参考：《岩石力学与工程学报》2017年05期

【摘要】：基于目前未见对隧道排水系统非对称堵塞渗流场进行解析研究,通过对研究区域进行简化假设,求解代表渗流场的Laplace方程。对研究区域内未知边界条件,采用PDE工具进行数值解后,得到近似的非齐次边界条件。基于此,再运用复平面内的保角变换、坐标变换、微分方程定解问题的分解等方法,将边界条件齐次化,在Hilbert空间中将最后唯一的非齐次边界条件表达为正交函数族的级数和,从而得到了此情况下的隧道周边渗流场解析级数,其后考查了级数项的多少对计算结果的影响。研究结果表明:(1)隧道排水系统非对称堵塞后渗流场可以表达为解析后级数,可简化将来针对这一情况下渗流场的求解难度;(2)隧道排水系统非对称堵塞后渗流场大致呈漏斗状,但在堵塞侧水头较高;(3)求和项数对计算精度的影响至多到100项,多数情况下只需50项;(4)考查了隧道可能受到的水压力分布和渗流量,分别与相同条件下的数值模拟结果进行对比,两者相差仅4.28%和4.05%。
[Abstract]:Based on the analysis of unsymmetrical blockage seepage field in tunnel drainage system, the Laplace equation representing seepage field is solved by simplifying the hypothesis of the study area. For the unknown boundary conditions in the studied region, the approximate inhomogeneous boundary conditions are obtained by using the PDE tool. Based on this, the conformal transformation, coordinate transformation and the decomposition of the definite solution of differential equation are used in the complex plane to homogenize the boundary conditions. The last inhomogeneous boundary condition is expressed as the series sum of the family of orthogonal functions in Hilbert space. The analytic series of seepage field around the tunnel are obtained, and the influence of the series term on the calculation results is investigated. The results show that the seepage field after asymmetric blockage of tunnel drainage system can be expressed as analytic series, which can simplify the difficulty of solving seepage field in the future. However, the influence of summation terms on the accuracy of the calculation is up to 100 items at most, and in most cases only 50 items are needed.) the distribution of water pressure and seepage flow to which the tunnel may be subjected has been investigated. Compared with the numerical simulation results under the same conditions, the difference between them is only 4.28% and 4.05%.
【作者单位】：重庆大学土木工程学院;
【基金】：中央高校基本科研业务费资助(CDJXS12200003) 重庆市基础与前沿研究计划项目(cstc2013jcyjA30005)~~
【分类号】：U453.6

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