考虑地表径流拖曳力效应多层边坡稳定性分析
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摘要
为研究地表径流拖曳力对多层边坡稳定性的影响,建立了多层边坡渗流-径流耦合模型。采用NavierStokes方程描述地表径流,用Brinkman-extended Darcy方程描述土层渗流,径流区和渗流区的流体运动均满足连续性方程,且在交界面处的流体满足流速相等和切应力连续双边界条件。根据上述条件推求出径流区和渗流区的流速分布,并引入Newton内摩擦定律求出坡面径流拖曳力。利用刚体极限平衡理论对径流状态下多层边坡的稳定性进行分析,得出每层土的稳定系数。并结合工程实例讨论径流水深、边坡坡度和上下部土层厚度分别对上下部土层稳定系数的影响。结果表明,考虑地表径流拖曳力效应时,上部土体的安全系数下降了9.95%,下部土体的安全系数下降了4.99%。因此,在进行多层边坡稳定性分析与计算中,应考虑地表径流拖曳力作用。
In order to study the effect of surface runoff drag on the stability of multi-story slopes,a multi-layered seepage-runoff coupled model is established. The model describes the surface runoff using the Navier-Stokes equation and the Brinkman-extended Darcy equation to describe the seepage of the soil. The fluid motion in the runoff region and the seepage region all satisfy the continuity equation,and the fluid at the interface satisfies the flow velocity equal and the shear stress continuous Double boundary conditions. According to the above conditions,the flow velocity distribution in runoff area and seepage area was deduced,and Newton's internal friction law was introduced to determine the drag force of slope runoff. The stability of multi-layered slope under runoff condition is analyzed by rigid body limit equilibrium theory,and the stability coefficient of each layer of soil is obtained. The effects of runoff depth,slope grade and thickness of upper and lower soil layers on the stability coefficient of upper and lower soil layers are discussed with engineering examples. The results show that considering the drag effect of surface runoff,the safety factor of the upper soil decreases by 9. 95% and that of the lower soil decreases by 4. 99%.Therefore,in the analysis and calculation of multi-story slope stability,the drag force of surface runoff should be considered.
In order to study the effect of surface runoff drag on the stability of multi-story slopes,a multi-layered seepage-runoff coupled model is established. The model describes the surface runoff using the Navier-Stokes equation and the Brinkman-extended Darcy equation to describe the seepage of the soil. The fluid motion in the runoff region and the seepage region all satisfy the continuity equation,and the fluid at the interface satisfies the flow velocity equal and the shear stress continuous Double boundary conditions. According to the above conditions,the flow velocity distribution in runoff area and seepage area was deduced,and Newton's internal friction law was introduced to determine the drag force of slope runoff. The stability of multi-layered slope under runoff condition is analyzed by rigid body limit equilibrium theory,and the stability coefficient of each layer of soil is obtained. The effects of runoff depth,slope grade and thickness of upper and lower soil layers on the stability coefficient of upper and lower soil layers are discussed with engineering examples. The results show that considering the drag effect of surface runoff,the safety factor of the upper soil decreases by 9. 95% and that of the lower soil decreases by 4. 99%.Therefore,in the analysis and calculation of multi-story slope stability,the drag force of surface runoff should be considered.
引文
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[19]Rumer RR,Drinker PA.Resistance to laminar flow through porous media[J].Journal of the Hydraulics Division,1966,92:155-163.
[20]Chai J.Drag forces applied on rock matrix by fluid flow through fracture network in rock mass[M]∥Computational Methods in Engineering&Science,2006:291.
[21]Neale G,Nader W.Practical significance of brinkman's extension of Darcy's law:Coupled parallel flows within a channel and a bounding porous medium[J].Canadian Journal of Chemical Engineering,2009,52(4):475-478.
[22]李仕雄,姚令侃,蒋良维.松散边坡演化特征及其应用[J].四川大学学报(工程科学版),2004,36(2):7-11.
[23]杨进良.土力学[M].4版.北京:中国水利水电出版社,2009:76-77.
[2]徐永强,祁小博,张楠.基于降雨与库水位耦合的三舟溪滑坡渗流模拟及稳定性分析[J].水文地质工程地质,2016,43(5):111-118.
[3]李媛,孟晖,董颖,等.中国地质灾害类型及其特征——基于全国县市地质灾害调查成果分析[J].中国地质灾害与防治学报,2004,15(2):29-34.
[4]许建聪,尚岳全,陈侃福,等.强降雨作用下的浅层滑坡稳定性分析[J].岩石力学与工程学报,2005,24(18):3 246-3 251.
[5]闻越.解读四川茂县“6·24”特大山体滑坡灾害成因[J].中国减灾,2017,(7):26-29.
[6]胡其志,周辉,肖本林,等.水力作用下顺层岩质边坡稳定性分析[J].岩土力学,2010,31(11):3 594-3 598.
[7]Ng C W,Wang B,Tung Y K.Three-dimensional numerical investigations of groundwater responses in an unsaturated slope subjected to various rainfall patterns[J].Canadian Geotechnical Journal,2001,38(5):1 049-1 062.
[8]Ng C W W,Shi Q.A numerical investigation of the stability of unsaturated soil slopes subjected to transient seepage[J].Computers&Geotechnics,1998,22(1):1-28.
[9]Rahardjo H,Li X W,Toll D G,et al.The effect of antecedent rainfall on slope stability[M]∥Unsaturated Soil Concepts and Their Application in Geotechnical Practice.Springer Netherlands,2001:371-399.
[10]Tsaparas I,Rahardjo H,Toll D G,et al.Controlling parameters for rainfall-induced landslides[J].Computers&Geotechnics,2002,29(1):1-27.
[11]杨涛,周德培,罗阳明,等.考虑层间作用的多层滑坡分析方法[J].岩石力学与工程学报,2005,24(7):1 129-1 133.
[12]Lyle W M,Smerdon E T.Relation of compaction and other soil properties to erosion resistance of soils[J].Transactions of the ASAE,1965,8(3):419-422.
[13]Foster G R,Meyer L D.Transport of soil particles by shallow flow[J].Amer Soc Agr Eng Trans Asae,1972,51(5):99-102.
[14]杨春霞,姚文艺,肖培青,等.坡面径流剪切力分布及其与土壤剥蚀率关系的试验研究[J].中国水土保持科学,2010,8(6):53-57.
[15]吴卿,杨春霞,甄斌,等.草被覆盖对坡面径流剪切力影响的试验研究[J].人民黄河,2010,32(8):96.
[16]盛贺伟.黄土区土壤类型和坡度对坡面片蚀和细沟侵蚀的影响研究[D].陕西杨凌:西北农林科技大学,2016.
[17]边锋,郑粉莉,徐锡蒙,等.东北黑土区顺坡垄作和无垄作坡面侵蚀过程对比[J].水土保持通报,2016,36(1):11-16.
[18]Wilson HJ.Stokes flow past three spheres[J].Journal of Computational Physics,2013,245:302-316.
[19]Rumer RR,Drinker PA.Resistance to laminar flow through porous media[J].Journal of the Hydraulics Division,1966,92:155-163.
[20]Chai J.Drag forces applied on rock matrix by fluid flow through fracture network in rock mass[M]∥Computational Methods in Engineering&Science,2006:291.
[21]Neale G,Nader W.Practical significance of brinkman's extension of Darcy's law:Coupled parallel flows within a channel and a bounding porous medium[J].Canadian Journal of Chemical Engineering,2009,52(4):475-478.
[22]李仕雄,姚令侃,蒋良维.松散边坡演化特征及其应用[J].四川大学学报(工程科学版),2004,36(2):7-11.
[23]杨进良.土力学[M].4版.北京:中国水利水电出版社,2009:76-77.