颗粒接触无网格法及其在边坡成灾范围模拟中的应用
|
摘要
提出了一种基于颗粒接触的无网格方法(PCMM),并编制了相应的C++程序,解决了有限元等网格类方法在模拟边坡失稳滑动过程中的网格畸变问题。该方法利用颗粒离散元中的接触拓扑创建连续介质单元,通过颗粒的运动演化实现连续介质单元的自动删除及重建,通过在连续介质单元中引入考虑应变软化效应的Mohr-Coulomb模型及最大拉应力模型,实现边坡的弹塑性分析及失稳滑移过程的模拟。利用PCMM分析了均质边坡的弹塑性场、沙堆的形成过程及土质边坡的失稳过程。计算结果表明,PCMM在小变形下具有足够的精度,且在模拟材料大变形方面具有明显优势,是一种模拟边坡成灾范围的有效方法。
When simulate slope sliding process by grid-based methods such as FEM, element distortion will happen. To solve such problems, a particle contact-based meshfree method(PCMM) is proposed; and a corresponding C++ code is implemented. In this method, the continuous media elements are created based on contact topology of particle DEM; and the elements will be deleted or recreated according to the movement and evolvement of the particle system. The elastoplastic analysis and sliding process simulation of slope are realized by intruducing the softening Mohr-Coulomb model and maximal tensile stress model into continuous media elements. PCMM is uesed to simulate the elastoplastic deformation of homogeneous slope, formation process of sand pile and failure process of soil slope through cases. The results show that the PCMM is an effective approach to simulate disaster range of slope; and it owns enough accuracy when simulating small deformation and large deformation problems.
When simulate slope sliding process by grid-based methods such as FEM, element distortion will happen. To solve such problems, a particle contact-based meshfree method(PCMM) is proposed; and a corresponding C++ code is implemented. In this method, the continuous media elements are created based on contact topology of particle DEM; and the elements will be deleted or recreated according to the movement and evolvement of the particle system. The elastoplastic analysis and sliding process simulation of slope are realized by intruducing the softening Mohr-Coulomb model and maximal tensile stress model into continuous media elements. PCMM is uesed to simulate the elastoplastic deformation of homogeneous slope, formation process of sand pile and failure process of soil slope through cases. The results show that the PCMM is an effective approach to simulate disaster range of slope; and it owns enough accuracy when simulating small deformation and large deformation problems.
引文
[1]郑颖人,赵尚毅.有限元强度折减法在土坡与岩坡中的应用[J].岩石力学与工程学报,2004,23(19):3381-3388.ZHENG Ying-ren,ZHAO Shang-yi.Application of strength reduction FEM in soil and rock slope[J].Chinese Journal of Rock Mechanics and Engineering,2004,23(19):3381-3388.
[2]HUANG MAO-SONG,JIA CANG-QIN.Strength reduction FEM in stability analysis of soil slopes subjected to transient unsaturated seepage[J].Computers and Geotechnics,2009,36(1-2):93-101.
[3]李新平,郭运华,彭元平,等.基于FLAC3D的改进边坡极限状态确定方法[J].岩石力学与工程学报,2005,24(增刊2):5287-5291.LI Xin-ping,GUO Yun-hua,PENG Yuan-ping,et al.Improved method to determine the critical state of slopes based on FLAC3D method[J].Chinese Journal of Rock Mechanics and Engineering,2005,24(Supp.2):5287-5291.
[4]林杭,曹平,李江腾,等.基于Hoek-Brown准则的三维边坡变形稳定性分析[J].岩土力学,2010,31(11):3656-3660.LIN Hang,CAO Ping,LI Jiang-teng,et al.Deformation stability of three-dimensional slope based on Hoek-Brown criterion[J].Rock and Soil Mechanics,2010,31(11):3656-3660.
[5]曹琰波,戴福初,许冲,等.唐家山滑坡变形运动机制的离散元模拟[J].岩石力学与工程学报,2011,30(增刊1):2878-2887.CAO Yan-bo,DAI Fu-chu,XU Chong,et al.Discrete element simulation of deformation and movement mechanism for Tangjiashan landslide[J].Chinese Journal of Rock Mechanics and Engineering,2011,30(Supp.1):2878-2887.
[6]申通,王运生,吴龙科.重庆小南海滑坡形成机制离散元模拟分析[J].岩土力学,2014,35(增刊2):667-675.SHEN Tong,WANG Yun-sheng,WU Long-ke.Discrete element simulation analysis of formation mechanism of Xiaonanhai landslide in Chongqing city[J].Rock and Soil Mechanics,2014,35(Supp.2):667-675.
[7]刘君,王丽丽.鸡尾山滑坡全过程数值模拟[C]//颗粒材料计算力学研究进展.大连:大连理工大学出版社,2012:239-246.LIU Jun,WANG Li-li.Numerical simulation of Jiweishan landslide[C]//Advances in Computational Mechanics of Granular Materials.Dalian:Dalian University of Technology Press,2012:239-246.
[8]张龙,唐辉明,熊承仁,等.鸡尾山高速远程滑坡运动过程PFC3D模拟[J].岩石力学与工程学报,2012,31(1):2601-2611.ZHANG Long,TANG Hui-ming,XIONG Cheng-ren,et al.Movement process simulation of high-speed long-distance Jiweishan landslide with PFC3D[J].Chinese Journal of Rock Mechanics and Engineering,2012,31(1):2601-2611.
[9]邬爱清,丁秀丽,李会中,等.非连续变形分析方法模拟千将坪滑坡启动与滑坡全过程[J].岩石力学与工程学报,2006,25(7):1297-1303.WU Ai-qing,DING Xiu-li,LI Hui-zhong,et al.Numerical simulation of startup and whole failure process of Qianjiangping landslide using discontinuous deformation analysis method[J].Chinese Journal of Rock Mechanics and Engineering,2006,25(7):1297-1303.
[10]WU J H,CHEN C H.Application of DDA to simulate characteristics of the Tsaoling landslide[J].Computers and Geotechnics,2011,38(5):741-750.
[11]LIU G R.Meshfree methods:Moving beyond the finite element method[M].[S.l.]:CRC press,2010.
[12]LUCY L B.A numerical approach to the testing of the fission hypothesis[J].The Astronomical Journal,1977,82:1013-1024.
[13]GINGOLD R A,MONAGHAN J J.Smoothed particle hydrodynamics——Theory and application to nonspherical stars[J].Monthly Notices of the Royal Astronomical Society,1977,181:375-389.
[14]LU Y Y,BELYTSCHKO T,GU L.A new implementation of the element-free Galerkin method[J].Computer Methods in Applied Mechanics Engineering,1994,113(3-4):397-414.
[15]ZHANG X,SZE K Y,MA S.An explicit material point finite element method for hyper-velocity impact[J].International Journal for Numerical Methods in Engineering,2006,66(4):689-706.
[16]BUI H H,FUKAGAWA R,SAKO K,et al.Slope stability analysis and discontinuous slope failure simulation by elasto-plastic smoothed particle hydrodynamics(SPH)[J].Geotechnique,2010,61(7):565-574.
[17]庞作会,葛修润,王水林.无网格伽辽金法(EFGM)在边坡开挖问题中的应用[J].岩土力学,1999,20(1):61-64.PANG Zuo-hui,GE Xiu-run,WANG Shui-lin.Application of element free Galerkin method(EFGM)to the slope excavation[J].Rock and Soil Mechanics,1999,20(1):61-64.
[18]ANDERSEN S,ANDERSEN L.Modelling of landslides with the material-point method[J].Computational Geosciences,2010,14(1):137-147.
[19]冯春,李世海,刘晓宇.一种基于颗粒接触的二维无网格方法及其在高速冲击模拟中的应用[J].爆炸与冲击,2014,34(3):292-299.FENG Chun,LI Shi-hai,LIU Xiao-yu.A 2D particle contact-based meshfree method and its application in hypervelocity impact simulation[J].Explosion and Shock Waves,2014,34(3):292-299.
[20]Itasca Consulting Group Inc.FLAC-3D(Fast Lagrangian Analysis of Continua in 3 Dimensions),Version 3.0,Users Manual[M].USA:Itasca Consulting Group Inc.,2005.
[21]赵啦啦,赵跃民,刘初升,等.湿颗粒堆力学特性的离散元法模拟研究[J].物理学报,2014,63(3):34501-34501.ZHAO La-la,ZHAO Yue-min,LIU Chu-sheng,et al.Discrete element simulation of mechanical properties of wet granular pile[J].Acta Physica Sinica,2014,63(3):34501-34501.
[22]FENG C,LI S H,LIU X Y,et al.A semi-spring and semi-edge combined contact model in CDEM and its application to analysis of Jiweishan landslide[J].Journal of Rock Mechanics and Geotechnical Engineering,2014,6(1):26-35.
[2]HUANG MAO-SONG,JIA CANG-QIN.Strength reduction FEM in stability analysis of soil slopes subjected to transient unsaturated seepage[J].Computers and Geotechnics,2009,36(1-2):93-101.
[3]李新平,郭运华,彭元平,等.基于FLAC3D的改进边坡极限状态确定方法[J].岩石力学与工程学报,2005,24(增刊2):5287-5291.LI Xin-ping,GUO Yun-hua,PENG Yuan-ping,et al.Improved method to determine the critical state of slopes based on FLAC3D method[J].Chinese Journal of Rock Mechanics and Engineering,2005,24(Supp.2):5287-5291.
[4]林杭,曹平,李江腾,等.基于Hoek-Brown准则的三维边坡变形稳定性分析[J].岩土力学,2010,31(11):3656-3660.LIN Hang,CAO Ping,LI Jiang-teng,et al.Deformation stability of three-dimensional slope based on Hoek-Brown criterion[J].Rock and Soil Mechanics,2010,31(11):3656-3660.
[5]曹琰波,戴福初,许冲,等.唐家山滑坡变形运动机制的离散元模拟[J].岩石力学与工程学报,2011,30(增刊1):2878-2887.CAO Yan-bo,DAI Fu-chu,XU Chong,et al.Discrete element simulation of deformation and movement mechanism for Tangjiashan landslide[J].Chinese Journal of Rock Mechanics and Engineering,2011,30(Supp.1):2878-2887.
[6]申通,王运生,吴龙科.重庆小南海滑坡形成机制离散元模拟分析[J].岩土力学,2014,35(增刊2):667-675.SHEN Tong,WANG Yun-sheng,WU Long-ke.Discrete element simulation analysis of formation mechanism of Xiaonanhai landslide in Chongqing city[J].Rock and Soil Mechanics,2014,35(Supp.2):667-675.
[7]刘君,王丽丽.鸡尾山滑坡全过程数值模拟[C]//颗粒材料计算力学研究进展.大连:大连理工大学出版社,2012:239-246.LIU Jun,WANG Li-li.Numerical simulation of Jiweishan landslide[C]//Advances in Computational Mechanics of Granular Materials.Dalian:Dalian University of Technology Press,2012:239-246.
[8]张龙,唐辉明,熊承仁,等.鸡尾山高速远程滑坡运动过程PFC3D模拟[J].岩石力学与工程学报,2012,31(1):2601-2611.ZHANG Long,TANG Hui-ming,XIONG Cheng-ren,et al.Movement process simulation of high-speed long-distance Jiweishan landslide with PFC3D[J].Chinese Journal of Rock Mechanics and Engineering,2012,31(1):2601-2611.
[9]邬爱清,丁秀丽,李会中,等.非连续变形分析方法模拟千将坪滑坡启动与滑坡全过程[J].岩石力学与工程学报,2006,25(7):1297-1303.WU Ai-qing,DING Xiu-li,LI Hui-zhong,et al.Numerical simulation of startup and whole failure process of Qianjiangping landslide using discontinuous deformation analysis method[J].Chinese Journal of Rock Mechanics and Engineering,2006,25(7):1297-1303.
[10]WU J H,CHEN C H.Application of DDA to simulate characteristics of the Tsaoling landslide[J].Computers and Geotechnics,2011,38(5):741-750.
[11]LIU G R.Meshfree methods:Moving beyond the finite element method[M].[S.l.]:CRC press,2010.
[12]LUCY L B.A numerical approach to the testing of the fission hypothesis[J].The Astronomical Journal,1977,82:1013-1024.
[13]GINGOLD R A,MONAGHAN J J.Smoothed particle hydrodynamics——Theory and application to nonspherical stars[J].Monthly Notices of the Royal Astronomical Society,1977,181:375-389.
[14]LU Y Y,BELYTSCHKO T,GU L.A new implementation of the element-free Galerkin method[J].Computer Methods in Applied Mechanics Engineering,1994,113(3-4):397-414.
[15]ZHANG X,SZE K Y,MA S.An explicit material point finite element method for hyper-velocity impact[J].International Journal for Numerical Methods in Engineering,2006,66(4):689-706.
[16]BUI H H,FUKAGAWA R,SAKO K,et al.Slope stability analysis and discontinuous slope failure simulation by elasto-plastic smoothed particle hydrodynamics(SPH)[J].Geotechnique,2010,61(7):565-574.
[17]庞作会,葛修润,王水林.无网格伽辽金法(EFGM)在边坡开挖问题中的应用[J].岩土力学,1999,20(1):61-64.PANG Zuo-hui,GE Xiu-run,WANG Shui-lin.Application of element free Galerkin method(EFGM)to the slope excavation[J].Rock and Soil Mechanics,1999,20(1):61-64.
[18]ANDERSEN S,ANDERSEN L.Modelling of landslides with the material-point method[J].Computational Geosciences,2010,14(1):137-147.
[19]冯春,李世海,刘晓宇.一种基于颗粒接触的二维无网格方法及其在高速冲击模拟中的应用[J].爆炸与冲击,2014,34(3):292-299.FENG Chun,LI Shi-hai,LIU Xiao-yu.A 2D particle contact-based meshfree method and its application in hypervelocity impact simulation[J].Explosion and Shock Waves,2014,34(3):292-299.
[20]Itasca Consulting Group Inc.FLAC-3D(Fast Lagrangian Analysis of Continua in 3 Dimensions),Version 3.0,Users Manual[M].USA:Itasca Consulting Group Inc.,2005.
[21]赵啦啦,赵跃民,刘初升,等.湿颗粒堆力学特性的离散元法模拟研究[J].物理学报,2014,63(3):34501-34501.ZHAO La-la,ZHAO Yue-min,LIU Chu-sheng,et al.Discrete element simulation of mechanical properties of wet granular pile[J].Acta Physica Sinica,2014,63(3):34501-34501.
[22]FENG C,LI S H,LIU X Y,et al.A semi-spring and semi-edge combined contact model in CDEM and its application to analysis of Jiweishan landslide[J].Journal of Rock Mechanics and Geotechnical Engineering,2014,6(1):26-35.