无黏性土坡滑动过程与接触网络演化分析
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摘要
基于离散元法建立边坡模型,将颗粒间的黏结强度降低为零来模拟边坡的滑动过程。通过记录不同时间步下边坡的破坏形态,从复杂网络的视角分别对边坡坡顶、坡中和坡脚的平均度、平均最短路径和网络密度进行了分析。结果表明:靠近边坡表面的颗粒沿着斜坡向下运动,且越靠近坡面的颗粒位移变化越大;失稳后的斜坡通过初始边坡的中点,形成新的稳定边坡的坡面倾角略小于初始边坡双轴压缩试验得到的峰值应力内摩擦角;在初始滑动阶段坡顶、坡中和坡脚颗粒的平均度均减小,接触网络结构的稳定性减弱,初始阶段边坡的抗剪强度降低,很容易发生失稳变形;随着时间步的增加,坡顶颗粒的平均最短路径减小,坡脚颗粒的平均最短路径增大,坡顶颗粒比坡脚颗粒更容易进行信息交流;随着时间步的增加,坡顶的接触网络变得越来越稠密,坡脚的接触网络变得越来越稀疏,这是滑坡发生后坡脚处土体变得松散的原因。
Based on the discrete element method, the geometrical model of slope was established here to investigate the slope failure during the landslide process by reducing the bond strength at all contacts between particles to be zero. By recording the slope failure configurations on different time steps, both slope failure on macro-scale and the slope failure from a complex network perspective, i.e., average degree, average path length and network density, of the slope top, the middle of the slope and slope toe were analyzed in detail. The result demonstrates that a) during the landslide process, the soil close to slope surface moves along downward slope. The displacements of particles will be larger when they are closer to the slope surface; b) the post-failure slope surface passes through the centre of the initial slope surface, and the post-failure inclination is slightly smaller than the peak internal friction angle of the material; c) the number of contacts between particles of the top/middle/toe of slope are all decrease at the beginning of slope sliding, which leads to the reducation of shear strength and causes landslide easily to occur; d) with the increase of time steps, the slope top of the average shortest path length decreases and the slope toe of the average shortest path length increases, which causes the slope top particles to exchange information more easily than those of slope toe and; e) with the increase of time steps, the contact networks of become denser, and the contact networks of slope toe becomes sparser, which can explain the reason that the soil at the slope toe after slope failure becomes looser.
Based on the discrete element method, the geometrical model of slope was established here to investigate the slope failure during the landslide process by reducing the bond strength at all contacts between particles to be zero. By recording the slope failure configurations on different time steps, both slope failure on macro-scale and the slope failure from a complex network perspective, i.e., average degree, average path length and network density, of the slope top, the middle of the slope and slope toe were analyzed in detail. The result demonstrates that a) during the landslide process, the soil close to slope surface moves along downward slope. The displacements of particles will be larger when they are closer to the slope surface; b) the post-failure slope surface passes through the centre of the initial slope surface, and the post-failure inclination is slightly smaller than the peak internal friction angle of the material; c) the number of contacts between particles of the top/middle/toe of slope are all decrease at the beginning of slope sliding, which leads to the reducation of shear strength and causes landslide easily to occur; d) with the increase of time steps, the slope top of the average shortest path length decreases and the slope toe of the average shortest path length increases, which causes the slope top particles to exchange information more easily than those of slope toe and; e) with the increase of time steps, the contact networks of become denser, and the contact networks of slope toe becomes sparser, which can explain the reason that the soil at the slope toe after slope failure becomes looser.
引文
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[18] JIANG M, MURAKAMI A. Distinct Element Method Analyses of Idealized Bonded-Granulate Cut Slope[J]. Granular Matter, 2012(14): 393-410.
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[2] WANG C, TANNANT D D, LILLY P A. Numerical Analysis of the Stability of Heavily Jointed Rock Slopes Using PFC2D[J]. International Journal of Rock Mechanics & Mining Sciences, 2003, 40(3): 415-424.
[3] SARMA S K. Stability Analysis of Embankments and Slopes[J]. Journal of Geotechnical Engineering Division, 1979, 105(12): 1511-1524.
[4] CLOUGH R W, WOODWARD R J. Analysis of Embankment Stresses and Deformations[J]. Soil Mechanics & Foundation Division, 1967, 93(4): 529-549.
[5] 郑颖人,赵尚毅,张鲁渝.用有限元强度折减法进行边坡稳定分析[J].中国工程科学,2002,4(10):57-61.
[6] CUNDALL P A. A Computer Model for Simulating Progressive, Large-Scale Movements in Block Rock Systems[C]// Nancy:Symposium of International Society of Rock Mechanics, 1971: 8-11.
[7] CHEN H, LIU S H. Slope Failure Characteristics and Stabilization Methods[J]. Canadian Geotechnical Journal, 2007, 44(4): 377-391.
[8] KIM J S, KIM J Y, LEE S R. Analysis of Soil Nailed Earth Slope by Discrete Element Method[J]. Computers & Geotechnics, 1997, 20(1): 1-14.
[9] JIANG M, JIANG T, CROSTA G B, et al. Modeling Failure of Jointed Rock Slope with Two Main Joint Sets Using a Novel DEM Bond Contact Model[J]. Engineering Geology, 2015, 193: 79-96.
[10] SCHOLTèS L, DONZé F V. A DEM Analysis of Step-Path Failure in Jointed Rock Slopes[J]. Comptes Rendus Mecanique, 2015(2): 155-165.
[11] 周健,王家全,曾远,等.颗粒流强度折减法和重力增加法的边坡安全系数研究[J].岩土力学,2009,30(6):1549-1554.
[12] 周健,王家全,曾远,等.土坡稳定分析的颗粒流模拟[J].岩土力学,2009,30(1):86-90.
[13] 曾锃,张泽辉,杨宏丽,等.基于边坡渐进破坏特征对传统极限平衡法几点假设的合理分析[J].岩土力学,2012,33(增刊1):146-150.
[14] ROTHENBURG L, KRUYT N P. Critical State and Evolution of Coordination Number in Simulated Granular Materials[J]. International Journal of Solids & Structures, 2004, 41(21): 5763-5774.
[15] PETERS J F, MUTHUSWAMY M, WIBOWO J, et al. Characterization of Force Chains in Granular Material[J]. Physical Review E, 2005, 72(4): 138-148.
[16] TORDESILLAS A, O’SULLIVAN P, WALKER D M, et al. Evolution of Functional Connectivity in Contact and Force Chain Networks: Feature Vectors, K-Cores and Minimal Cycles[J]. Comptes Rendus Mecanique, 2010, 338(10-11): 556-569.
[17] SILBERT L E, GREST G S, LANDRY J W. Statistics of the Contact Network in Frictional and Frictionless Granular Packings[J]. Physical Review E Statistical Nonlinear & Soft Matter Physics, 2002, 66(1): 114-129.
[18] JIANG M, MURAKAMI A. Distinct Element Method Analyses of Idealized Bonded-Granulate Cut Slope[J]. Granular Matter, 2012(14): 393-410.
[19] 李明哲,金俊,石瑞银.图论及其算法[M].北京:机械工业出版社,2010:4-5.
[20] DOROGOVTSEV S N, MENDES J F F. The Shortest Path to Complex Networks[J]. Physics, 2004, 71: 47-53.
[21] 王小帆,李翔,陈关荣.网络科学导论[M].北京:高等教育出版社,2012:87-88.
[22] 何大韧,刘宗华,汪秉宏.复杂系统与复杂网络[M].北京:高等教育出版社,2009:126-127.