摘要
减压井是渗流控制的重要手段,减压浅井井底的入渗量不可忽略。在渗流场有限元有关井的计算中,含水层与井半径有巨大尺寸差异,只有将井周围的网格尺寸限制在厘米级或更少,才能达到合理的精度,但效率过低。为提高效率,分析时通常将井底简化为点源。由于点源附近的水头梯度极大,是奇异点,有限元中通常要进行等效处理才能保证全局的精度。提出了以零体积点元模拟点源的方法,该方法基于修正井水位法,利用点源解析解及四面体渗流单元,推导了点元单元的显式解。使用该点元单元模拟井底,可以在不失全局精度的条件下用大网格对点源进行模拟,避免了迭代计算,极大提高了利用三维有限元模拟点源的效率。详细介绍了该点元显式解的推导过程,验证其计算精度,并探究出简化计算方法的适用范围。最后介绍了该方法在实际排水减压抗浮工程中的应用。
Relief wells are an important means of seepage control,and the infiltration at the bottom of shallow relief wells cannot be ignored.When utilizing the finite element method for seepage field analysis in relation to wells,a significant disparity exists between the aquifer's dimensions and the well's radius.Achieving reasonable accuracy necessitates limiting the mesh size around the well to centimeters or less,albeit at the cost of reduced efficiency.To enhance efficiency,the well bottom is commonly approximated as a point source in analytical models.The head gradient near the point source is extremely large,which is a singular point.In the finite element method,equivalent treatment is usually required to ensure the global accuracy.This paper presents a method for simulating point sources with zero-volume point elements which is based on the correction well water level method,the method uses the point source analytical solution and the tetrahedral seepage element to deduce the explicit solution of the point source element.By using this point source element to simulate the bottom of well,the point source can be simulated by using a large grid without losing the global accuracy,which greatly improves the efficiency of simulating the point source by using the three-dimensional finite element.
作者
潘泓
许嘉显
骆冠勇
彭斯格
曹洪
PAN Hong;XU Jia-xian;LUO Guan-yong;PENG Si-ge;CAO Hong(School of Civil Engineering and Transportation,South China University of Technology,Guangzhou,Guangdong 510640,China;State Key Laboratory of Subtropical Building Science,South China University of Technology,Guangzhou,Guangdong 510640,China)
出处
《岩土力学》
EI
CAS
CSCD
北大核心
2024年第8期2483-2491,共9页
Rock and Soil Mechanics
基金
国家自然科学基金(No.52308353,No.51978282)
广东省自然科学基金(No.2023A1515011571,No.2023A1515011683)
华南理工大学亚热带建筑科学国家重点实验室开放研究项目(No.2022ZB21)。
关键词
渗流
有限元法
井点
奇异点单元
seepage
finite element method
well point
singular point element
