径流条件下散粒体斜坡的颗粒冲刷启动机理
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摘要
为研究地表径流对散粒体斜坡的冲刷侵蚀效应,根据斜坡坡面径流和坡内渗流特征建立散粒体斜坡径流-渗流耦合模型。该模型利用Navier-Stokes方程描述淹没区坡面径流,利用Brinkman-extended Darcy方程描述散粒体斜坡坡内渗流。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Neal和Nader提出的流速相等和剪应力连续双边界条件。采用Navier-Stokes方程和Brinkman-extended Darcy方程分别联立连续性方程推求出径流区和渗流区的流速分布。分析流速理论表达式可知,影响斜坡表部径流流速和坡体内部渗流流速的主要因素有斜坡坡度、径流水深、斜坡散粒体的孔隙率和渗透率,且流速随其增大而增大。为探究在径流条件下散粒体斜坡坡面颗粒的冲刷启动机理,引入Newton内摩擦定律求得径流区和渗流区交界面上的切应力,并对颗粒发生滑动和滚动两种情况分别进行受力分析,给出颗粒滑动和滚动两种运动方式相应的失稳判据。分析两种判据可知:1)颗粒发生滑动时,其抗滑稳定安全系数主要受散粒体斜坡坡度、颗粒的内摩擦角、颗粒半径、径流水深、散粒体斜坡孔隙率和渗透率的影响,随颗粒的内摩擦角、颗粒半径、散粒体斜坡孔隙率和渗透率的增大而增大,随散粒体斜坡坡度和径流水深的增大而减小;2)颗粒发生滚动与否主要取决于散粒体斜坡坡度、径流水深、颗粒半径、散粒体斜坡孔隙率和渗透率,且其值越大,颗粒越容易失稳。
In order to study the scouring effect on particles in a loose granular slope with surface runoff,an analytical model was set up on the basis of the characteristics of slope runoff and seepage. A generalized equation known as the Brinkman-extended Darcy equation was solved inside the seepage zone,along with the incompressible Navier-Stokes equation in the upper runoff zone. The continuity equation was also used for both regions and a Neal-Nader boundary condition on the interface of the two regions. Combining Navier-Stokes equation and Brinkman-extended Darcy equation with the continuity equation can derive the flow velocity distributions of fluid in both regions. According to the flow velocity expressions,it was noted that the velocity mainly depends on slope gradient,runoff depth,porosity and permeability of the slope earth. In order to investigate the starting mechanism of particles on slope under the condition of runoff,Newton's law of friction was introduced,and the shear stress at the interface of the two regions was obtained. The two cases of particle sliding and rolling were analyzed,and the corresponding instability criterion of particle in sliding and rolling were presented in the two motion modes. Based on the analysis of the two criterions,it was concluded that for the sliding case,the anti-sliding stability coefficient is mainly affected by the slope gradient,friction angle,particle radius,runoff depth and the porosity and permeability of the slope earth,and increases with the rising of the internal friction angle,particle radius,porosity and permeability of the slope earth,and decreases with the drop of the slope gradient and runoff depth. Whether the particle rolls or not depends mainly on the slope gradient,runoff depth,particle radius,and the porosity and permeability of the slope earth,and the larger the value,the easier the instability of the particles.
In order to study the scouring effect on particles in a loose granular slope with surface runoff,an analytical model was set up on the basis of the characteristics of slope runoff and seepage. A generalized equation known as the Brinkman-extended Darcy equation was solved inside the seepage zone,along with the incompressible Navier-Stokes equation in the upper runoff zone. The continuity equation was also used for both regions and a Neal-Nader boundary condition on the interface of the two regions. Combining Navier-Stokes equation and Brinkman-extended Darcy equation with the continuity equation can derive the flow velocity distributions of fluid in both regions. According to the flow velocity expressions,it was noted that the velocity mainly depends on slope gradient,runoff depth,porosity and permeability of the slope earth. In order to investigate the starting mechanism of particles on slope under the condition of runoff,Newton's law of friction was introduced,and the shear stress at the interface of the two regions was obtained. The two cases of particle sliding and rolling were analyzed,and the corresponding instability criterion of particle in sliding and rolling were presented in the two motion modes. Based on the analysis of the two criterions,it was concluded that for the sliding case,the anti-sliding stability coefficient is mainly affected by the slope gradient,friction angle,particle radius,runoff depth and the porosity and permeability of the slope earth,and increases with the rising of the internal friction angle,particle radius,porosity and permeability of the slope earth,and decreases with the drop of the slope gradient and runoff depth. Whether the particle rolls or not depends mainly on the slope gradient,runoff depth,particle radius,and the porosity and permeability of the slope earth,and the larger the value,the easier the instability of the particles.
引文
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[2]He Na,Fu Ronghua,Bu Xianghang,et al.An experimental study on movement and accumulation characteristics of the sand-sliding slope[J].Journal of Geological Hazards&Environment Preservation,2012,23(1):50-53.[何娜,傅荣华,卜祥航,等.散粒体斜坡运动堆积特征试验研究[J].地质灾害与环境保护,2012,23(1):50-53.]
[3]Wang Chenghua,Zhang Xiaogang,Que Yun,et al.Formation and basic characteristics of sand-sliding slope composed of granular clasts(Part I of sand-sliding slope series)[J].Rock&Soil Mechanics,2007,28(1):29-35.[王成华,张小刚,阙云,等.粒状碎屑溜砂坡的形成和基本特征研究(溜砂坡系列研究之一)[J].岩土力学,2007,28(1):29-35.]
[4]Wu Guoxiong,Zeng Rongbin,Wang Chenghua,et al.The inducing factors and the collapse conditions of sand-sliding slope[J].China Railway Science,2006,27(5):7-12.[吴国雄,曾榕彬,王成华,等.溜砂坡的形成诱发因素及失稳破坏条件[J].中国铁道科学,2006,27(5):7-12.]
[5]Sass O.Bedrock detection and talus thickness assessment in the European Alps using geophysical methods[J].Journal of Applied Geophysics,2007,62(3):254-269.
[6]Alastair M C,Chris J M.Lateglacial and Holocene talus slope development and rockwall retreat on Mynydd Du,UK[J].Geomorphology,2004,58(1/2/3/4):85-106.
[7]Sass O,Krautblatter M.Debris flow-dominated and rockfall-dominated talus slopes,genetic models derived from GPR measurements[J].Geomorphology,2007,86(1/2):176-192.
[8]Liang Guangmo,Wang Chenghua,Zhang Xiaogang.The formation of sand-sliding slope and its controlling countermeasure for Zhongba section of Sichuan-Tibet Highway[J].Chinese Journal of Geological Hazard&Control,2003,14(4):33-38.[梁光模,王成华,张小刚.川藏公路中坝段溜砂坡形成与防治对策[J].中国地质灾害与防治学报,2003,14(4):33-38.]
[9]Que Yun,Wang Chenghua,Zhang Xiaogang.Formative mechanism and control of typical sand-sliding slope along Sichuan-Tibet Highway[J].Journal of Mountain Research,2003,21(5):595-598.[阙云,王成华,张小刚.川藏公路典型溜砂坡形成机理与整治[J].山地学报,2003,21(5):595-598.]
[10]Xu Haiyang,Xia Keqin,Zhang Xiaoguang.Prevention countermeasures of the typical sand-sliding slope along the Tianshan Highway[J].Journal of Geological Hazards&Environment Preservation,2008,19(4):25-28.[徐海洋,夏克勤,张晓光.天山公路典型溜砂坡防治措施研究[J].地质灾害与环境保护,2008,19(4):25-28.]
[11]Wang Chenghua,Que Yun,Li Xinpo,et al.Movement characteristics and dynamical numerical analysis of sandsliding slope composed by granular clastics(Part II of sand-sliding slope series)[J].Rock&Soil Mechanics,2007,28(2):219-223.[王成华,阙云,李新坡,等.粒状碎屑溜砂坡运动特征与动力数值分析(溜砂坡系列研究之二)[J].岩土力学,2007,28(2):219-223.]
[12]Wang Chenghua,Que Yun,Xu Jun,et al.Equation of motion and soil pressure for sand-sliding slope composed by granular clast(Part III of sand-sliding slope series)[J].Rock&Soil Mechanics,2007,28(7):1299-1303.[王成华,阙云,徐骏,等.粒状碎屑溜砂坡运动方程与砂坡土压力计算(溜砂坡系列研究之三)[J].岩土力学,2007,28(7):1299-1303.]
[13]Wei Lina,Li Chuan,Fu Ronghua.Experimental research on related factors for stability of granular mixture slope[J].Journal of Water Resources and Architectural Engineering,2014,12(1):55-61.[魏丽娜,李川,傅荣华.散粒体斜坡稳定性相关因素试验研究[J].水利与建筑工程学报,2014,12(1):55-61.]
[14]He Wenshe,Lei Xiaozhang,Liu Xingnian,et al.Equivalent grain with incipient motion of non-uniform sediment[J].Mechanics in Engineering,2003,25(6):21-22.[何文社,雷孝章,刘兴年,等.等效粒径与非均匀沙起动条件研究[J].力学与实践,2003,25(6):21-22.]
[15]Deepak D.Theoretical studies of self-organized criticality[J].Physica A:Statistical and Theoretical Physics,2006,369(1):29-70.
[16]Li Yuanfu,Yao Lingkan,Deng Yucai.An experimental study on the self-organized criticality of sand pile model with one-grade slope[J].Journal of Southwest Jiaotong University,2000,35(2):121-125.[李远富,姚令侃,邓域才.单面坡沙堆模型自组织临界性实验研究[J].西南交通大学学报,2000,35(2):121-125.]
[17]Yao Lingkan,Li Shixiong,Jiang Liangwei.Self-organized criticality and its application in granular mixtures[J].Journal of Sichuan University(Engineering Science Edition),2003,35(1):8-14.[姚令侃,李仕雄,蒋良潍.自组织临界性及其在散粒体研究中的应用[J].四川大学学报(工程科学版),2003,35(1):8-14.]
[18]Li Shixiong,Yao Lingkan,Jiang Liangwei.Evolution features and application of loose slope[J].Journal of Sichuan University(Engineering Science Edition),2004,36(2):7-11.[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.]
[19]吴持恭.水力学(上册)[M].4版.北京:高等教育出版社,2008.
[20]Deng C,Martinez D M.Viscous flow in a channel partially filled with a porous medium and with wall suction[J].Chemical Engineering Science,2005,60(2):329-336.
[21]Zhou Shuang,Zhang Genguang,Xing Ru,et al.Determination of drag and lift coefficients of uniform sediment on the bed surface[J].Journal of Sediment Research,2016(2):1-6.[周双,张根广,邢茹,等.床面均匀沙拖曳力及上举力系数的确定[J].泥沙研究,2016(2):1-6.]