考虑平动–转动力学效应的露天矿山节理岩质边坡塑性极限分析
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摘要
露天矿山节理岩质边坡的失稳破坏一般同时包含平动和转动力学效应。本文将塑性极限分析理论、多自由度的刚性块体单元离散技术、拟静力法原理和数学规划方法结合起来,研究矿山节理岩质边坡平动滑移破坏或倾倒破坏时的稳定性。根据拟静力法原理计算单元形心地震惯性力,以结构面的法向力、剪力、弯矩为决策变量,构建节理岩质边坡静力许可应力场,建立节理岩质边坡稳定性分析的下限法数学规划模型;同时以单元形心的平动速度、转动速度为决策变量,构建节理岩质边坡机动许可速度场,建立节理岩质边坡稳定性分析的上限法数学规划模型;最后运用优化算法求解这两个数学模型,获得节理岩质边坡安全系数的上、下限解和对应的破坏机构。
The failure of open-pit mine jointed rock slope generally includes translational and rotational mechanical effects. The stability of jointed rock slope with sliding and toppling failure is studied,by combining plastic limit analysis theory,discrete technique of rigid block element with multiple degrees of freedom,the principle of pseudo-static method and mathematical programming method. The seismic inertia forces of elements are calculated according to the pseudo-static method. After that,taking internal force vector(normal force,shear force and bending moment) of interfaces as decision variables,the static admissible stress fields of jointed rock slope are constructed,and the mathematical programming model of lower bound method for jointed rock slope stability analysis is established. At the same time,taking the translational velocity and rotational velocity of element centroid as decision variables,the kinematically admissible velocity fields of jointed rock slope are constructed,and the mathematical programming model of upper bound method for jointed rock slope stability analysis is established. Lastly,the optimization algorithm are employed to solve these two models,and the upper and lower bound solution of the safety factor and corresponding failure mechanisms of jointed rock slopes can be obtained.
The failure of open-pit mine jointed rock slope generally includes translational and rotational mechanical effects. The stability of jointed rock slope with sliding and toppling failure is studied,by combining plastic limit analysis theory,discrete technique of rigid block element with multiple degrees of freedom,the principle of pseudo-static method and mathematical programming method. The seismic inertia forces of elements are calculated according to the pseudo-static method. After that,taking internal force vector(normal force,shear force and bending moment) of interfaces as decision variables,the static admissible stress fields of jointed rock slope are constructed,and the mathematical programming model of lower bound method for jointed rock slope stability analysis is established. At the same time,taking the translational velocity and rotational velocity of element centroid as decision variables,the kinematically admissible velocity fields of jointed rock slope are constructed,and the mathematical programming model of upper bound method for jointed rock slope stability analysis is established. Lastly,the optimization algorithm are employed to solve these two models,and the upper and lower bound solution of the safety factor and corresponding failure mechanisms of jointed rock slopes can be obtained.
引文
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[3]汪小刚,贾志欣,陈祖煜,等.岩质边坡倾倒破坏的稳定分析方法[J].水利学报,1996,(3):7-12.(WANG Xiaogang,JIA Zhixin,CHENZuyu,et al.The research of stability analysis of toppling failure of jointed rock slopes[J].Journal of Hydraulic Engineering,1996,(3):7-12.(in Chinese))
[4]LIU C H,JAKSA M B,MEYERS A G.A transfer coefficient method for rock slope toppling[J].Canadian Geotechnical Journal,2009,46(1):1-9.
[5]孙东亚,彭一江,王兴珍.DDA数值方法在岩质边坡倾倒破坏分析中的应用[J].岩石力学与工程学报,2002,21(1):39-42.(SUNDongya,PENG Yijiang,WANG Xingzhen.Application of DDAmethod in stability analyses of topple rock slope[J].Chinese Journal of Rock Mechanics and Engineering,2002,21(1):39-42.(in Chinese))
[6]张国新,雷峥琦,程恒.水对岩质边坡倾倒变形影响的DDA模拟[J].中国水利水电科学研究院学报,2016,14(3):161-170.(ZHANG Guoxin,LEI Zhengqi,CHENG Heng.DDA simulation of impact of water on toppling deformation of rock slope[J].Journal of China Institute of Water Resources and Hydropower Research,2016,14(3):161-170.(in Chinese))
[7]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.
[8]袁志辉,陈志新,倪万魁,等.倾倒式岩质崩塌运动过程数值模拟分析[J].中国地质灾害与防治学报,2014,25(2):26-31.(YUANZhihui,CHEN Zhixin,NI Wankui,et al.Numerical analysis of the movement process of toppling fall[J].The Chinese Journal of Geological Hazard and Control,2014,25(2):26-31.(in Chinese))
[9]张国新,赵妍,彭校初.考虑岩桥断裂的岩质边坡倾倒破坏的流形元模拟[J].岩石力学与工程学报,2007,26(9):1 773-1 780.(ZHANG Guoxin,ZHAO Yan,PENG Xiaochu.Simulation of toppling failure of rock slope by numerical manifold method considering fracture of rock bridges[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(9):1 773-1 780.(in Chinese))
[10]刘红岩,秦四清.层状岩石边坡倾倒破坏过程的数值流形方法模拟[J].水文地质工程地质,2006,33(5):22-25.(LIU Hongyan,QIN Siqing.Simulation of stratified rock slope toppling failure process by numerical manifold method[J].Hydrogeology and Engineering Geology,2006,33(5):22-25.(in Chinese))
[11]陈孝兵,李渝生,赵小平.底摩擦重力试验在倾倒变形岩体稳定性研究中的应用[J].地学前沿,2008,15(2):300-304.(CHENXiaobing,LI Yusheng,ZHAO Xiaoping.The application of bottomfriction gravity test to the study of the stability of the toppling rock mass[J].Earth Science Frontiers,2008,15(2):300-304.(in Chinese))
[12]左保成,陈从新,刘小巍,等.反倾岩质边坡破坏机理模型试验研究[J].岩石力学与工程学报,2005,24(19):3 505-3 511.(ZUOBaocheng,CHEN Congxin,LIU Xiaowei,et al.Modeling experiment study on failure mechanism of counter-tilt rock slope[J].Chinese Journal of Rock Mechanics and Engineering,2005,24(19):3 505-3 511.(in Chinese))
[13]陈从新,郑允,孙朝燚.岩质反倾边坡弯曲倾倒破坏分析方法研究[J].岩石力学与工程学报,2016,35(11):2 174-2 187.(CHENCongxin,ZHENG Yun,SUN Chaoyi.An analytical approach on flexural toppling failure of counter-tilt slopes of layered rock[J].Chinese Journal of Rock Mechanics and Engineering,2016,35(11):2 174-2 187.(in Chinese))
[14]吴昊,赵维,年廷凯,等.反倾层状岩质边坡倾倒破坏的离心模型试验研究[J].水利学报,2018,49(2):223-231.(WU Hao,ZHAO Wei,NIAN Tingkai,et al.Study on the anti-dip layered rock slope toppling failure based on centrifuge model test[J].Journal of Hydraulic Engineering,2018,49(2):223-231.(in Chinese))
[15]宋京雷,郝社锋,岳翎,等.采矿引起的将军崖岩画区倾倒变形机理及治理措施分析[J].中国地质灾害与防治学报,2017,28(4):40-46.(SONG Jinglei,HAO Shefeng,YUE Ling,et al.Deformation mechanism and treatment measures of the mining-induced toppling deformation in rock painting area in Jiangjun cliff[J].The Chinese Journal of Geological Hazard and Control,2017,28(4):40-46.(in Chinese))
[16]林必挺,袁宝远,邹凯,等.水力作用下陡倾顺层岩质斜坡的倾倒破坏[J].中国煤炭地质,2016,28(12):55-61.(LIN Biting,YUANBaoyuan,ZOU Kai,et al.Toppling failure of steeply dipped bedding rock slope under hydraulic actions[J].Coal Geology of China,2016,28(12):55-61.(in Chinese))
[17]张海娜,陈从新,郑允,等.地震作用下的层状岩质边坡块状-弯曲倾倒解析分析[J].中国公路学报,2018,31(2):75-85.(ZHANG Haina,CHEN Congxin,ZHENG Yun,et al.Analytical study on block-flexure toppling failure of rock slopes subjected to seismic loads[J].China Journal of Highway and Transport,2018,31(2):75-85.(in Chinese))
[18]郑允,陈从新,朱玺玺,等.地震作用下岩质边坡倾倒破坏分析[J].岩土力学,2014,35(4):1 025-1 032.(ZHENG Yun,CHEN Congxin,ZHU Xixi,et al.Analysis of toppling failure of rock slopes subjected to seismic loads[J].Rock and Soil Mechanics,2014,35(4):1 025-1 032.(in Chinese))
[19]SlOAN S W,KLEEMAN P W.Upper bound limit analysis using discontinuous velocity fields[J].Computer Methods in Applied Mechanics and Engineering,1995,127(1):293-314.
[20]SUTCLIFFE D J,YU H S,SLOAN S W.Lower bound solutions for bearing capacity of jointed rock[J].Computers and Geotechnics,2004,31(1):23-36.
[21]李泽,王均星,王汉辉.成组节理岩体的有限元塑性极限分析研究[J].岩土工程学报,2007,29(10):1 517-1 521.(LI Ze,WANGJunxing,WANG Hanhui.Plastic limit analysis on stability of jointed rock slopes using finite elements[J].Chinese Journal of Geotechnical Engineering,2007,29(10):1 517-1 521.(in Chinese))
[22]李泽,王均星.基于非线性规划的岩质边坡有限元塑性极限分析下限法研究[J].岩石力学与工程学报,2007,26(4):747-753.(LIZe,WANG Junxing.Lower bound limit study on plastic limit analysis of rock slope using finite elements based on nonlinear programming[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(4):747-753.(in Chinese))
[23]李春光,朱宇飞,刘丰,等.基于四边形网格的下限原理有限元法[J].岩石力学与工程学报,2012,31(3):461-468.(LI Chunguang,ZHU Yufei,LIU Feng,et al.Lower bound limit analysis using quadrilateral finite elements[J].Chinese Journal of Rock Mechanics and Engineering,2012,31(3):461-468.(in Chinese))
[24]孙聪,李春光,郑宏,等.基于四边形网格的边坡上限有限元法[J].岩石力学与工程学报,2015,34(1):114-120.(SUN Cong,LI Chunguang,ZHENG Hong,et al.Upper bound limit analysis of slopes using quadrilateral finite elements[J].Chinese Journal of Rock Mechanics and Engineering,2015,34(1):114-120.(in Chinese))
[25]ZHANG X.Slope stability analysis based on the rigid finite element method[J].Géotechnique,1999,49(5):585-593.
[26]CHEN J,YIN J H,LEE C F.Rigid finite element method for upper bound limit analysis of soil slopes subjected to pore water pressure[J].Journal of Engineering Mechanics,2004,130(8):886-893.
[27]LIU F,ZHAO J.Limit analysis of slope stability by rigid finite element method and linear programming considering rotational failure[J].International Journal of Geomechanics,2013,13(6):827-839.
[28]李泽,张小艳,王均星.基于刚性块体系统的岩质边坡稳定性下限法研究[J].岩土工程学报,2012,34(8):1 534-1 540.(LI Ze,ZHANG Xiaoyan,WANG Junxing.Lower bound method for stability of rock slopes based on rigid block assemblages[J].Chinese Journal of Geotechnical Engineering,2012,34(8):1 534-1 540.(in Chinese))
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