结点虚流量法理论基础阐释及改进算法
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摘要
含自由面的无压渗流问题本质上是一类非线性自由边值问题,固定网格的结点虚流量法在全域范围内不断扣除虚域流量贡献,从而使该问题得到求解。它具有网格依赖性小、出逸点收敛快等优点,但其内在理论基础尚未被完全揭示。通过引入互补型约束条件建立了结点虚流量法和Signorini型变分不等式提法的等价性桥梁,在此基础上引入过渡区放大系数(35)h对自由面判别准则进行优化,并以砂槽模型试验为例进行验证。对比结果表明,优化后算法数值稳定性更好,计算结果与试验数据吻合度更高。研究成果为超大规模网格的渗控结构优化设计提供了有效分析手段。
Seepage with free surface is essentially one type of nonlinear free boundary problems. In order to solve this problem in global domain, the nodal virtual flux method deducts the virtual flux gradually in each iteration. It has the advantages of weak mesh dependency, fast convergence rate, etc. To reveal its internal theoretical foundation, this paper builds an equivalent bridge between the nodal virtual flux method and variational inequality of Signorini type through a complementarity constraint. The criterion of free surface is optimized by introducing an amplification coefficient(35)h for transition region, verified through a sand flume model test. The comparisons show that the improved algorithm has better numerical stability and higher curvature tolerance, and provides an effective approach for optimization design of seepage control structure with large-scale grid.
Seepage with free surface is essentially one type of nonlinear free boundary problems. In order to solve this problem in global domain, the nodal virtual flux method deducts the virtual flux gradually in each iteration. It has the advantages of weak mesh dependency, fast convergence rate, etc. To reveal its internal theoretical foundation, this paper builds an equivalent bridge between the nodal virtual flux method and variational inequality of Signorini type through a complementarity constraint. The criterion of free surface is optimized by introducing an amplification coefficient(35)h for transition region, verified through a sand flume model test. The comparisons show that the improved algorithm has better numerical stability and higher curvature tolerance, and provides an effective approach for optimization design of seepage control structure with large-scale grid.
引文
[1]刘日成,蒋宇静,李博,等.岩体裂隙网络非线性渗流特性研究[J].岩土力学,2016,37(10):2817-2824.LIU Ri-cheng,JIANG Yu-jing,LI Bo,et al.Nonlinear seepage behaviors of fluid in fracture networks[J].Rock and Soil Mechanics,2016,37(10):2817-2824.
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[3]覃小华,刘东升,宋强辉,等.强降雨条件下基岩型层状边坡入渗模型及稳定性研究[J].岩土力学,2016,37(11):3156-3164.QIN Xiao-hua,LIU Dong-sheng,SONG Qiang-hui,et al.Infiltration model of bedrock laminar slope under heavy rainfall and its stability analysis[J].Rock and Soil Mechanics,2016,37(11):3156-3164.
[4]GAN L,SHEN X Z,QING W W.Seepage analysis of concrete face rockfill dam for material damage of water stop structure[J].Key Engineering Materials,2017,729.
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[7]熊勇林,朱合华,叶冠林,等.降雨入渗引起非饱和土边坡破坏的水-土-气三相渗流-变形耦合有限元分析[J].岩土力学,2017,38(1):284-290.XIONG Yong-lin,ZHU He-hua,YE Guan-lin,et al.Analysis of failure of unsaturated soil slope due to rainfall based on soil-water-air seepage-deformation coupling FEM[J].Rock and Soil Mechanics,2017,38(1):284-290.
[8]邓高阳,肖明,陈俊涛.基于变分不等式的地下洞室渗流边界模拟[J].岩土力学,2017,38(3):762-768.DENG Gao-yang,XIAO Ming,CHEN Jun-tao.Simulation of seepage boundary of underground cavern based on variational inequality[J].Rock and Soil Mechanics,2017,33(3):762-768.
[9]侯晓萍,徐青,陈胜宏.用空气单元法求解渗流场的逸出边界问题[J].岩土力学,2015,36(8):2345-2351.HOU Xiao-ping,XU Qing,CHEN Sheng-hong.An air element method for overflow boundary problem in seepage analysis[J].Rock and Soil Mechanics,2015,36(8):2345-2351.
[10]潘树来,王全凤,俞缙.利用初流量法分析有自由面渗流问题之改进[J].岩土工程学报,2012,34(2):202-209.PAN Su-lai,WANG Quan-feng,YU Jin.Improvement of analysis of free surface seepage problem by using initial flow method[J].Chinese Journal of Geotechnical Engineering,2012,34(2):202-209.
[11]崔浩东,朱岳明.有自由面渗流分析的改进节点虚流量全域迭代法[J].武汉理工大学学报,2009,33(2):238-241.CUI Hao-dong,ZHU Yue-ming.Improved procedure of nodal virtual flux of global iteration to solve seepage free surface[J].Journal of Wuhan University of Technology,2009,33(2):238-241.
[12]ZHENG H,DAI H C,LIU D F.A variational inequality formulation for unconfined seepage problems in porous media[J].Applied Mathematical Modelling,2009,33(1):437-450.
[13]张乾飞,吴中如.有自由面非稳定渗流分析的改进截止负压法[J].岩土工程学报,2005,27(1):48-54.ZHANG Qian-fei,WU Zhong-ru.The improved cut-off negative pressure method for unsteady seepage flow with free surface[J].Chinese Journal of Geotechnical Engineering,2005,27(1):48-54.
[14]LACY S J,PREVOST J H.Flow through porous media:a procedure for locating the free surface[J].International Journal for Numerical and Analytical Methods in Geomechanics,1987,11(6):585-601.
[15]ZHENG H,LIU D F,LEE C F,et al.A new formulation of Signorini’s type for seepage problems with free surfaces[J].International Journal for Numerical Methods in Engineering,2005,64(1):1-16.
[16]周斌,刘斯宏,姜忠见,等.洪屏抽水蓄能电站渗控效果数值模拟与评价[J].水力发电学报,2015,34(5):131-139.ZHOU Bin,LIU Si-hong,JIANG Zhong-jian,et al.Numerical assessment of seepage control effects of Hongping pumped storage power station[J].Journal of Hydroelectric Engineering,2015,34(5):131-139.
[17]郑铁生,张文,马建敏,等.滑动轴承非线性油膜力的几个理论问题及应用[J].水动力学研究与进展,2003,18(6):761-768.ZHENG Tie-sheng,ZHANG Wen,MA Jian-min,et al.Some theoretical problems on the nonlinear oil-film forces of sliding bearing and their applications[J].Journal of Hydrodynamics,2003,18(6):761-768.
[18]YAN J,LIU S H.The improved node virtual method for the seepage problem with free surface[C]//International Conference on Electric Technology and Civil Engineering.Wuhan:[s.n.],2011:2760-2765.
[19]YAN J,LIU S H,ZHOU B.Numerical analysis of the anti-seepage measures for high earth rockfill dam on deep overburden[J].Applied Mechanics&Materials,2012,170(5):1872-1877.
[20]白正雄,陈益峰,胡冉,等.排水砂槽渗流试验与Signorini型变分不等式方法验证[J].岩土力学,2012,33(9):2829-2836.BAI Zheng-xiong,CHEN Yi-feng,HU Ran,et al.Seepage flow test on drain sand flume and validation of variation inequality method of Signorini condition[J].Rock and Soil Mechanics,2012,33(9):2829-2836.
[2]李文涛,马田田,韦昌富.基于自适应松弛Picard法的高效非饱和渗流有限元分析[J].岩土力学,2016,37(1):256-262.LI Wen-Tao,MA Tian-tian,WEI Chang-fu.An efficient finite element procedure for unsaturated flow based on adaptive relaxed Picard method[J].Rock and Soil Mechanics,2016,37(1):256-262.
[3]覃小华,刘东升,宋强辉,等.强降雨条件下基岩型层状边坡入渗模型及稳定性研究[J].岩土力学,2016,37(11):3156-3164.QIN Xiao-hua,LIU Dong-sheng,SONG Qiang-hui,et al.Infiltration model of bedrock laminar slope under heavy rainfall and its stability analysis[J].Rock and Soil Mechanics,2016,37(11):3156-3164.
[4]GAN L,SHEN X Z,QING W W.Seepage analysis of concrete face rockfill dam for material damage of water stop structure[J].Key Engineering Materials,2017,729.
[5]LIU C,DING L,NING B,et al.Element-free Galerkin method simulation of the seepage field in embankment dam with core wall[J].Journal of Hydroelectric Engineering,2012,31(3):182-187.
[6]杨连枝,何蕃民,高阳.模拟排水孔列渗流行为的以沟代孔列延长渗径法研究[J].岩土力学,2017,38(1):180-188.YANG Lian-zhi,HE Fan-min,GAO Yang.An extended seepage tracking method by slot instead of hole curtain for modeling seepage behaviors of drainage holes curtains[J].Rock and Soil Mechanics,2017,38(1):180-188.
[7]熊勇林,朱合华,叶冠林,等.降雨入渗引起非饱和土边坡破坏的水-土-气三相渗流-变形耦合有限元分析[J].岩土力学,2017,38(1):284-290.XIONG Yong-lin,ZHU He-hua,YE Guan-lin,et al.Analysis of failure of unsaturated soil slope due to rainfall based on soil-water-air seepage-deformation coupling FEM[J].Rock and Soil Mechanics,2017,38(1):284-290.
[8]邓高阳,肖明,陈俊涛.基于变分不等式的地下洞室渗流边界模拟[J].岩土力学,2017,38(3):762-768.DENG Gao-yang,XIAO Ming,CHEN Jun-tao.Simulation of seepage boundary of underground cavern based on variational inequality[J].Rock and Soil Mechanics,2017,33(3):762-768.
[9]侯晓萍,徐青,陈胜宏.用空气单元法求解渗流场的逸出边界问题[J].岩土力学,2015,36(8):2345-2351.HOU Xiao-ping,XU Qing,CHEN Sheng-hong.An air element method for overflow boundary problem in seepage analysis[J].Rock and Soil Mechanics,2015,36(8):2345-2351.
[10]潘树来,王全凤,俞缙.利用初流量法分析有自由面渗流问题之改进[J].岩土工程学报,2012,34(2):202-209.PAN Su-lai,WANG Quan-feng,YU Jin.Improvement of analysis of free surface seepage problem by using initial flow method[J].Chinese Journal of Geotechnical Engineering,2012,34(2):202-209.
[11]崔浩东,朱岳明.有自由面渗流分析的改进节点虚流量全域迭代法[J].武汉理工大学学报,2009,33(2):238-241.CUI Hao-dong,ZHU Yue-ming.Improved procedure of nodal virtual flux of global iteration to solve seepage free surface[J].Journal of Wuhan University of Technology,2009,33(2):238-241.
[12]ZHENG H,DAI H C,LIU D F.A variational inequality formulation for unconfined seepage problems in porous media[J].Applied Mathematical Modelling,2009,33(1):437-450.
[13]张乾飞,吴中如.有自由面非稳定渗流分析的改进截止负压法[J].岩土工程学报,2005,27(1):48-54.ZHANG Qian-fei,WU Zhong-ru.The improved cut-off negative pressure method for unsteady seepage flow with free surface[J].Chinese Journal of Geotechnical Engineering,2005,27(1):48-54.
[14]LACY S J,PREVOST J H.Flow through porous media:a procedure for locating the free surface[J].International Journal for Numerical and Analytical Methods in Geomechanics,1987,11(6):585-601.
[15]ZHENG H,LIU D F,LEE C F,et al.A new formulation of Signorini’s type for seepage problems with free surfaces[J].International Journal for Numerical Methods in Engineering,2005,64(1):1-16.
[16]周斌,刘斯宏,姜忠见,等.洪屏抽水蓄能电站渗控效果数值模拟与评价[J].水力发电学报,2015,34(5):131-139.ZHOU Bin,LIU Si-hong,JIANG Zhong-jian,et al.Numerical assessment of seepage control effects of Hongping pumped storage power station[J].Journal of Hydroelectric Engineering,2015,34(5):131-139.
[17]郑铁生,张文,马建敏,等.滑动轴承非线性油膜力的几个理论问题及应用[J].水动力学研究与进展,2003,18(6):761-768.ZHENG Tie-sheng,ZHANG Wen,MA Jian-min,et al.Some theoretical problems on the nonlinear oil-film forces of sliding bearing and their applications[J].Journal of Hydrodynamics,2003,18(6):761-768.
[18]YAN J,LIU S H.The improved node virtual method for the seepage problem with free surface[C]//International Conference on Electric Technology and Civil Engineering.Wuhan:[s.n.],2011:2760-2765.
[19]YAN J,LIU S H,ZHOU B.Numerical analysis of the anti-seepage measures for high earth rockfill dam on deep overburden[J].Applied Mechanics&Materials,2012,170(5):1872-1877.
[20]白正雄,陈益峰,胡冉,等.排水砂槽渗流试验与Signorini型变分不等式方法验证[J].岩土力学,2012,33(9):2829-2836.BAI Zheng-xiong,CHEN Yi-feng,HU Ran,et al.Seepage flow test on drain sand flume and validation of variation inequality method of Signorini condition[J].Rock and Soil Mechanics,2012,33(9):2829-2836.