摘要
在多层地基区域地下水流动的数值模拟中,假设地下水在强透水层内为水平流动、在弱透水层内为垂向流动的传统准三维方法计算效率高,但多适用于强弱透水层隔层分布的多层情况,不利于推广。对准三维计算理论进行扩展以适用于一般的多层情况,推导了各层土层内以平均水头为控制变量、且考虑上下界面入渗的平面二维流动控制方程,利用界面处的流速连续条件耦合各层控制方程,并在各土层内对平均水头与上下界面水头进行二次插值获取水头分布的垂向变化。基于扩展的计算理论建立相应的准三维有限元模型,各土层内划分相同的水平面二维网格,并在各节点处建立流量平衡关系。经算例验证,扩展后的准三维方法打破了传统方法的局限,允许各土层的水平和垂向流动同时得到合理的模拟,具有更高的精度和通用性,并且保持了计算效率的优势。由于方便求解自由面问题和处理地下结构奇异问题,且可以获取较高精度的三维水头分布结果,该方法在分析多层地基区域地下水流动问题中可以成为一个高效和有竞争力的方案。
The conventional quasi-three-dimensional technique has a high efficiency in the simulation of regional groundwater flow in multilayered subsoils,with the assumption that groundwater flow is essentially horizontal in the aquifers and vertical in the aquitards.This assumption requires a two orders of magnitude permeability contrast between the adjacent soils,which is not conducive to a wide application of the conventional technique.In this study,calculation theory is extended to be applied to regional groundwater flow in general multi-layered subsoils.Firstly,the partial differential equation governing two-dimensional horizontal flow in each soil is derived with the average hydraulic head as the main variable and considering the infiltration at the upper and lower interfaces.The velocity continuity conditions at the soil interfaces provide the coupling condition among the soils.Then,the vertical variation of the hydraulic head in individual soil is obtained by quadratic interpolation between the average head and the head at the upper and lower interfaces.A quasi-three-dimensional finite element model is presented based on the extended calculation theory.Each soil is discretized with the same two-dimensional horizontal grids,and the fluid mass balance is established at each node.The extended quasi-three-dimensional technique has a higher accuracy and greater applicability,as it can overcome the limitations of the conventional technique,and simultaneously get a reasonable simulation of the horizontal and vertical flow in each layer without sacrificing the calculation efficiency.The extended technique provides an efficient and competitive scheme to simulate regional groundwater flow in multilayered subsoils,because it is convenient to solve free surface problems and deal with singular problems of underground structures,and compute a high-precision three-dimensional representation of the hydraulic head distribution.
作者
梅锦玲
曹洪
骆冠勇
潘泓
MEI Jin-ling;CAO Hong;LUO Guan-yong;PAN Hong(School of Civil Engineering and Transportation,South China University of Technology,Guangzhou,Guangdong 510640,China;The 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
2021年第12期3428-3439,共12页
Rock and Soil Mechanics
基金
国家自然科学基金(No.51978282)
广东省自然科学基金(No.2018A030313383,No.2020A1515010583)。
关键词
渗流
数值模拟
多层地基
区域地下水流动
准三维模型
seepage
numerical simulation
multilayered subsoils
regional groundwater flow
quasi-three-dimensional model
