摘要
基于目前未见对任意埋深情况下排水系统非对称堵塞隧道渗流场的解析研究,结合保角变换和分离变量法2种方法,推导出任意埋深情况下排水系统非对称堵塞后隧道渗流场的显式解析解,并利用正交性对解析解中的未知数进行求解,首次提出可以适用于浅埋隧道排水系统非对称堵塞后渗流场的显式解析解。该解析解经试算后发现,当级数项数N≥20时,解析解计算结果收敛程度已经很好,且在改变工程参数时仅需要对输入值进行调整,计算耗时远小于需要重新建模和划分网格的数值软件。深埋隧道算例和浅埋隧道算例情况下,分别将解析解水头和水压力计算结果与有限元软件计算结果进行对比,发现解析解计算结果与有限元软件均吻合很好,验证了解析解的正确性,说明解析解可以准确地预测任意埋深情况下隧道发生非对称堵塞时隧道周围渗流场情况。对不同埋深、不同地表水头情况下的隧道周围渗流场、衬砌水压力和渗流量进行分析,发现随着隧道埋深的增大,隧道周围总水头明显降低,而距离隧道较远位置的水头变化较小,隧道衬砌水压力逐渐增大,且最大衬砌水压力出现在隧道排水系统被堵塞一侧衬砌的中心,渗流量则会先减小后增大;随着地表水头的增大,总水头线分布情况一致,但水头线对应的水头值随着地表水头的增大会相应增大,隧道衬砌水压力和渗流量均逐渐增大,且渗流量最小值所对应的隧道埋深也会逐渐增大。
Given the absence of any analytical exploration on the seepage field of asymmetrically blocked tunnels with drainage systems at arbitrary burial depths,this study established an explicit analytical solution for the seepage field of asymmetrically obstructed tunnels with drainage systems at arbitrary burial depths by combining two methods(i.e.,the conformal mapping and the separation of variables method)and solved for the unknowns in the analytical solution by using orthogonality.For the first time,an explicit analytical solution for the seepage field after asymmetric blockage of a shallow buried tunnel drainage system was presented.The analytical solution was found to converge well when the number of terms N≥20,and only the input parameters need to be adjusted when changing the engineering parameters,which is much less time consuming than numerical software that requires re-modelling and re-gridding.The results of the head and water pressure calculations of the analytical solution of this paper were compared with those of the finite element software for the deeply buried tunnel case and the shallowly buried tunnel case,respectively.It was found that the results of the analytical solution of this paper were in good agreement with the finite element software,which verified the correctness of the analytical solution of this paper and showed that the analytical solution of this paper can accurately predict the seepage field around the tunnel when asymmetric blockage occurs at any burial depth.Analysis of the seepage field,lining water pressure,and seepage volume around the tunnel at different burial depths and surface heads indicate a significant decrease in total hydraulic head around the tunnel with increasing tunnel depth.Conversely,the hydraulic head at the more distant locations from the tunnel undergoes comparatively smaller changes.The tunnel lining water pressure gradually increases,and the maximum lining water pressure occurs at the centre of the lining on the side where the tunnel drainage system is obstructed,and the seepage volume decreases and then increases.As the surface head increases,the distribution of the total head line is consistent,but the head value corresponding to the head line increases as the surface head increases,and the tunnel lining water pressure and seepage volume both gradually increase,and the tunnel depth corresponding to the minimum value of seepage volume also gradually increases.
作者
余俊
李东凯
和振
郑靖凡
张志中
YU Jun;LI Dongkai;HE Zhen;ZHENG Jingfan;ZHANG Zhizhong(School of Civil Engineering,Central South University,Changsha 410075,China)
出处
《铁道科学与工程学报》
EI
CAS
CSCD
北大核心
2023年第12期4678-4689,共12页
Journal of Railway Science and Engineering
基金
国家自然科学基金资助项目(52078496)。
关键词
任意埋深
隧道
排水系统
非对称堵塞
显式解析解
渗流场
arbitrary burial depth
tunnels
drainage system
asymmetric blocked
explicit analytical solution
seepage field
