模拟岩石边坡倾倒破坏的数值流形法
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摘要
倾倒破坏是岩石边坡破坏形式之一。对这种破坏形式的模拟要求计算方法能够正确模拟变形和应力、破坏面的发展、块体间的接触及块体的运动。数值流形法具备这种能力,可用于正确模拟岩石边坡的倾倒破坏。简单介绍了流形元法的基本原理、接触模拟的方法、接触力、接触应力的计算方法及用于倾倒破坏模拟的方法,并运用几个算例与Goodman和Bray提出的基于极限平衡原理的分析方法(以下简称G-B方法)、离心机模型试验方法进行了比较;给出了流形元结构计算的安全系数,并且用极限平衡原理结合流形元计算的应力得出了结构整体和单个块体的安全系数,同流形元结果进行了对比。结果表明:介绍的数值流形法可以正确计算边坡倾倒安全系数,模拟边坡的倾倒破坏过程。
As one type of rock slope failures,toppling could be correctly simulated only if deformation and stress,failure growth,contacts and movements of blocks were well taken into account.The numerical manifold method could be used for this purpose.The fundamental principles of manifold method,the contact simulation,the calculation method of contact forces and stress,and other methods simulating toppling failure were introduced.Several examples were used to illustrate the manifold method in comparison with G-B method put forward by Goodman and Bray and centrifuge model tests.The safety factor by manifold method was obtained.For comparison,the safety factors of the whole model and every block were also given by Limit Equilibrium Theory.It was shown that the numerical manifold method could be used to correctly simulate slope toppling failure and to calculate the safety factor as well.
As one type of rock slope failures,toppling could be correctly simulated only if deformation and stress,failure growth,contacts and movements of blocks were well taken into account.The numerical manifold method could be used for this purpose.The fundamental principles of manifold method,the contact simulation,the calculation method of contact forces and stress,and other methods simulating toppling failure were introduced.Several examples were used to illustrate the manifold method in comparison with G-B method put forward by Goodman and Bray and centrifuge model tests.The safety factor by manifold method was obtained.For comparison,the safety factors of the whole model and every block were also given by Limit Equilibrium Theory.It was shown that the numerical manifold method could be used to correctly simulate slope toppling failure and to calculate the safety factor as well.
引文
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[12]陈祖煜,汪小刚,杨健,等.岩石边坡稳定分析——原理.方法.程序[M].北京:中国水利水电出版社,2005.(CHEN Zu-yu,WANG Xiao-gang,YANG Jian,et al.Rock slope stability analysis—theory,method and programs[M].Beijing:China Water Power Press,2005.(in Chinese))
[2]CUNDALL P A,STACK O D L.A discrete numerical model granular assemblies[J].Geotechnique,1979,29(1):47–65.
[3]石根华.数值流形方法与非连续变形分析[M].裴觉民,译.北京:清华大学出版社,1997.(SHI Gen-hua.Numerical manifold method and discontinuous deformation analysis[M].PEI Jue-min,Trans.Beijing:Tsinghua University Press,1997.(in Chinese))
[4]张国新,彭静.二阶流形元与结构变形分析[J].力学学报,2002,34(2):261–269.(ZHANG Guo-xin,PENG Jing.Second-order manifold method in structure failure analysis[J].Acta Mechnica Sinica,2002,34(2):261–269.(in Chinese))
[5]ZHANG G X,SUGIURA Y,et al.The second order manifold with six node triangle mesh[J].J Struct Mech Earthquake Eng,JSCE,2002,696/Ⅰ-58:1–9.
[6]张国新,王光纶,裴觉民.基于流形元方法的结构体破坏分析[J].岩石力学与工程学报,2001,20(3):281–287.(ZHANG Guo-xin,WANG Guang-lun,PEI Jue-min.Structure failure analysis based on manifold method[J].Chinese Journal of Rock Mechanics and Engineering,2001,20(3):281–287.(in Chinese))
[7]ZHANG G X,YASUHITO Sugiura,KOZO Saito.Failure simulation of foundation by manifold method and comparison with experiment[J].Journal of Applied Mechaics,JSCE,1998,1:427–436.
[8]张国新,金峰,王光纶.用基于流形元的子域奇异边界元法模拟重力坝的地震破坏[J].工程力学,2001,18(4):18–27.(ZHANG Guo-xin,JIN Feng,WANG Guang-lun.Seismic failure simulation of gravity dam by manifold-based singular boundary element method[J].Engineering Mechanics,2001,18(4):18–27.(in Chinese))
[9]BRAY J W,GOODMAN R E.The theory of base friction models[J].Int J Rock Mech Min,Sci Geomech Abstr,1981,18:453–468.
[10]SEGASETA C.On the modes of instability of a rigid block on an inclined plane[J].Rock Mechanics and Rock Engineering,1986,19:261–266
[11]汪小刚,张建红,赵毓芝,等.用离心模型研究岩石边坡的倾倒破坏[J].岩土工程学报,1996,18(5):14–21.(WANG Xiao-gang,ZHANG Jian-hong,ZHAO Yu-zhi,et al.Investigations on mechanism of slope toppling failure by centrifuge model testing[J].Chinese Journal of Geotechnical Engineering,1996,18(5):14–21.)
[12]陈祖煜,汪小刚,杨健,等.岩石边坡稳定分析——原理.方法.程序[M].北京:中国水利水电出版社,2005.(CHEN Zu-yu,WANG Xiao-gang,YANG Jian,et al.Rock slope stability analysis—theory,method and programs[M].Beijing:China Water Power Press,2005.(in Chinese))
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