粒径及级配特性对土体渗透系数影响的细观模拟
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摘要
渗透系数是体现土体渗透特性的主要参数。已有关于粒径及级配特性对土体渗透系数影响的研究主要采用试验研究方法,在试验研究中各个变量相互影响,很难完全独立改变某一参数,从而造成已有研究结论差异较大。在其他参数不变条件下数值模拟基本可以独立改变某一参量,弥补试验研究方法的不足。采用离散元数值模拟方法,通过调节控制粒径的方式,随机生成不同粒径、不同孔隙率、不同级配的土体多孔介质。利用格子Boltzmann方法从细观孔隙流体尺度模拟了土中的渗流。研究结果表明,格子Boltzmann方法可以准确有效地模拟土中的渗流;在渗流过程中存在主通道现象和大粒径效应;计算结果与Kozeny-Carman(简称K-C)公式完全一致,且证明K-C公式适用于不同级配的土体;渗透系数随不均匀系数和曲率系数的增大而增大;给出了一个包含级配参数的渗透系数计算公式,该公式与K-C公式基本等价,但所含参数是工程中较易测量的,对实际工程有一定的参考意义。
Permeability coefficient is a main parameter to reflect the permeability of soil. Existent studies about influence of particle size and gradation on permeability coefficient of soil mainly focused on experiments. It is difficult to change a parameter completely independently because of the interaction of various variables in the experimental study, which results in considerable differences between the conclusions from different researchers. Under the condition that other parameters remain unchanged, numerical simulation can basically change a certain parameter independently to make up for the shortcomings of experimental methods. In this paper, the particle discrete element method is used to generate soil of porous media with different particle sizes, different porosities and gradations by adjusting the size of the control particles. Lattice Boltzmann method is used to simulate seepage in soil at meso-pore fluid scale. The results show that the lattice Boltzmann method can simulate soil seepage accurately and effectively. Main passageway phenomena and large particle size effect are found in the seepage process. The simulation results are in good agreement with those by Kozeny-Carman(K-C) formula, demonstrating the K-C formula is applicable to porous media with different gradations. The permeability coefficient increases with the increase of uniformity coefficient and the curvature coefficient. A formula for calculating permeability coefficient with gradation parameters is given. The formula is nearly equivalent to K-C formula, but the parameters in this formula can be measured easily.
Permeability coefficient is a main parameter to reflect the permeability of soil. Existent studies about influence of particle size and gradation on permeability coefficient of soil mainly focused on experiments. It is difficult to change a parameter completely independently because of the interaction of various variables in the experimental study, which results in considerable differences between the conclusions from different researchers. Under the condition that other parameters remain unchanged, numerical simulation can basically change a certain parameter independently to make up for the shortcomings of experimental methods. In this paper, the particle discrete element method is used to generate soil of porous media with different particle sizes, different porosities and gradations by adjusting the size of the control particles. Lattice Boltzmann method is used to simulate seepage in soil at meso-pore fluid scale. The results show that the lattice Boltzmann method can simulate soil seepage accurately and effectively. Main passageway phenomena and large particle size effect are found in the seepage process. The simulation results are in good agreement with those by Kozeny-Carman(K-C) formula, demonstrating the K-C formula is applicable to porous media with different gradations. The permeability coefficient increases with the increase of uniformity coefficient and the curvature coefficient. A formula for calculating permeability coefficient with gradation parameters is given. The formula is nearly equivalent to K-C formula, but the parameters in this formula can be measured easily.
引文
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[16]SANGANI A S,ACRIVOS A.Slow flow past periodic arrays of cylinder with application to heat-transfer[J].International Journal of Multiphase Flow,1982,8(3):193-206.
[17]唐文文,康秀英.格子Boltzmann方法模拟多孔介质内流体的流动[J].北京师范大学学报(自然科学版),2016,52(1):12-16.TANG Wen-wen,KANG Xiu-ying.Lattice Boltzmann method simulating flow in porous media[J].Journal of Beijing Normal University(Natural Science),2016,52(1):12-16.
[18]申林方,王志良,李邵军.基于土体细观结构重构技术的渗流场数值模拟[J].岩土力学,2015,36(11):3307-3314.SHEN Lin-fang,WANG Zhi-liang,LI Shao-jun.Numerical simulation for seepage field of soil based on mesoscopic structure reconfiguration technology[J].Rock and Soil Mechanics,2015,36(11):3307-3314.
[19]罗忠贤,邱延峻,禹华谦.随机多孔介质流动的格子Boltzmann法模拟[J].西南交通大学学报,2014,49(1):93-96+118.LUO Zheng-xian,QIU Yan-jun,YU Hua-qian.Computational modeling of flows in random porous media using Lattice Boltzmann method[J].Journal of Southwest Jiaotong University,2014,49(1):93-96+118.
[20]崔冠哲,申林方,王志良,等.基于格子Boltzmann方法土体CT扫描切片细观渗流场的数值模拟[J].岩土力学,2016,38(5):1497-1502.CUI Guan-zhe,SHEN Lin-fang,WANG Zhi-liang,et al.Numerical simulation of mesoscopic seepage field of soil CT scanned slice based on lattice Boltzmann method[J].Rock and Soil Mechanics,2016,38(5):1497-1502.
[21]CHEN S,DOOLEN G D.Lattice Boltzmann method for fluid flows[J].Annual Review Fluid Mechanics,1998,30(1):329-364.
[22]QIAN Y H,D’HUMIèRES D,LALLEMAND P.Lattice BGK models for Navier-Stokes equation[J].Europhysics Letters,1992,17(6):479-484.
[23]GUO Z L,ZHENG C G,SHI B C.Non-equilibrium extrapolation method for velocity and boundry conditions in the lattice Boltzmann method[J].Chinese Physics,2002,11(4):366-374.
[2]TERZAGHI K,PECK R B,MESRI G.Soil mechanics in engineering practice[M].New York:John Wiley&Sons Inc.,1996.
[3]HAZEN A.Discussion of‘dams on sand foundation’by A.C.Koenig[J].Transactions American Society of Civil Engineers,1911,73(1):199-203.
[4]VUKOVIC M,SORO A.Determination of hydraulic conductivity of porous media from grain-size composition[M].Littleton:Water Resources Publications,1992.
[5]CARMAN P C.Fluid flow through granular beds[J].Chemical Engineering Research and Design,1937,75(1):32-48.
[6]刘杰.土的渗流稳定与渗流控制[M].北京:水利电力出版社,1992:297.LIU Jie.Soil seepage stability and seepage control[M].Beijing:Water Resources and Electric Power Press,1992:297.
[7]朱崇辉.筑坝土料的水利工程性质研究[D].杨凌:西北农林科技大学,2010.ZHU Chong-hui.Damming the soil properties of water conservancy projects[D].Yangling:Northwest Agriculture&Forestry University,2010.
[8]苏立君,张宜健,王铁行.不同粒径级砂土渗透特性试验研究[J].岩土力学,2014,35(5):1289-1294.SU Li-jun,ZHANG Yi-jian,WANG Tie-xing,Investigation on permeability of sands with different particle sizes[J].Rock and Soil Mechanics,2014,35(5):1289-1294.
[9]孔令伟,李新明,田湖南.砂土渗透系数的细粒效应与其状态参数关联性[J].岩土力学,2011,32(增刊2):21-26+41.KONG Ling-wei,LI Xin-ming,TIAN Hu-nan.Effect of fines content on permeability coefficient of sand and its correlation with state parameters[J].Rock and Soil Mechanics,2011,32(Supp.2):21-26+41.
[10]樊贵盛,邢日县,张明斌.不同级配砂砾石介质渗透系数的试验研究[J].太原理工大学学报,2012,43(3):373-378.FAN Gui-sheng,XING Ri-xian,ZHANG Ming-bin.Experimental study on permeability of sandy gravel media with different gradation[J].Journal of Taiyuan University of Technology,2012,43(3):373-378.
[11]钱琨,王新志,陈剑文,等.南海岛礁吹填钙质砂渗透特性试验研究[J].岩土力学,2017,38(6):1-8.QIAN Kun,WANG Xin-zhi,CHEN Jian-wen,et al.Experimental study on permeability of calcareous sand for islands in the South China Sea[J].Rock and Soil Mechanics,2017,38(6):1-8.
[12]杨兵,刘一飞,万奋涛,等.级配特性对砂土渗透系数影响试验研究[J].西南交通大学学报,2016,51(5):855-861.YANG Bing,LIU Yi-fei,WAN Fen-dou,et al.Experimental study on influence of particle-size distribution on permeability coefficient of sand[J].Journal of Southwest Jiaotong University,2016,51(5):855-861.
[13]MCNAMARA G R,ZANETTI G.Use of the Boltzmann equation to simulate lattice gas automata[J].Physical Review Letters.1988,61(20):2332-2335.
[14]何雅玲,王勇,李庆.格子Boltzmann方法的理论及应用[M].北京:科学出版社,2009.HE Ya-ling,WANG Yong,LI Qing.Theory and application of grid Boltzmann method[M].Beijing:Science Press,2009.
[15]LEE S L,YANG J H.Modeling of Darcy-Forchheimer drag for fluid flow across a bank of circular cylinders[J].International Journal of Heat and Mass Transfer,1997,40(13):3149-3155.
[16]SANGANI A S,ACRIVOS A.Slow flow past periodic arrays of cylinder with application to heat-transfer[J].International Journal of Multiphase Flow,1982,8(3):193-206.
[17]唐文文,康秀英.格子Boltzmann方法模拟多孔介质内流体的流动[J].北京师范大学学报(自然科学版),2016,52(1):12-16.TANG Wen-wen,KANG Xiu-ying.Lattice Boltzmann method simulating flow in porous media[J].Journal of Beijing Normal University(Natural Science),2016,52(1):12-16.
[18]申林方,王志良,李邵军.基于土体细观结构重构技术的渗流场数值模拟[J].岩土力学,2015,36(11):3307-3314.SHEN Lin-fang,WANG Zhi-liang,LI Shao-jun.Numerical simulation for seepage field of soil based on mesoscopic structure reconfiguration technology[J].Rock and Soil Mechanics,2015,36(11):3307-3314.
[19]罗忠贤,邱延峻,禹华谦.随机多孔介质流动的格子Boltzmann法模拟[J].西南交通大学学报,2014,49(1):93-96+118.LUO Zheng-xian,QIU Yan-jun,YU Hua-qian.Computational modeling of flows in random porous media using Lattice Boltzmann method[J].Journal of Southwest Jiaotong University,2014,49(1):93-96+118.
[20]崔冠哲,申林方,王志良,等.基于格子Boltzmann方法土体CT扫描切片细观渗流场的数值模拟[J].岩土力学,2016,38(5):1497-1502.CUI Guan-zhe,SHEN Lin-fang,WANG Zhi-liang,et al.Numerical simulation of mesoscopic seepage field of soil CT scanned slice based on lattice Boltzmann method[J].Rock and Soil Mechanics,2016,38(5):1497-1502.
[21]CHEN S,DOOLEN G D.Lattice Boltzmann method for fluid flows[J].Annual Review Fluid Mechanics,1998,30(1):329-364.
[22]QIAN Y H,D’HUMIèRES D,LALLEMAND P.Lattice BGK models for Navier-Stokes equation[J].Europhysics Letters,1992,17(6):479-484.
[23]GUO Z L,ZHENG C G,SHI B C.Non-equilibrium extrapolation method for velocity and boundry conditions in the lattice Boltzmann method[J].Chinese Physics,2002,11(4):366-374.