基于块体单元法的岩石边坡安全系数研究
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摘要
岩石边坡因其结构面数量众多、块体系统及其滑动方式复杂,给危险块体组合的搜索及其安全系数计算带来很大困难。基于块体单元法,对岩石边坡中的危险块体组合搜索及其安全系数的计算方法进行了研究。首先,在块体元强度折减计算的成果下,根据屈服面贯通理论提出搜索危险块体组合的新方法;然后,对安全系数计算方法进行研究,建议在位移突变判据下采用双线性交叉法计算安全系数;最后,进行了单面、双面和多面滑动以及复杂块体系统的算例分析,并与刚体极限平衡法计算结果进行了对比。结果表明,由于块体单元法考虑了力与力矩的平衡及结构面上应力的非均匀分布,其计算结果更准确。该方法有望广泛应用于复杂岩石边坡稳定分析。
It is difficult to search the dangerous block combination and acquire the safety factor precisely because of the numerous planes of weakness,the complicated block system and the diverse slip modes in rock slopes.Based on block element method,the search of dangerous block combination and the calculation of stability safety factor are conducted.At first,a new method for searching dangerous block combination is proposed,according to the results of block element method through strength reduction calculation.Then,the method for computing safety factors is studied;and the double line intersection method is suggested to calculate the safety factor when the abrupt theory of displacement is adopted.At last,several typical examples are calculated with the proposed methods;and the results are compared with those obtained by using the rigid body limit equilibrium method.The results show that it is more accurate by adopting the block element method,because the force and bending moment equilibrium and the nonuniform distribution of stress on the planes of weakness are considered.The proposed method is expected to be widely used to solve stability problems in complicated rock slopes.
It is difficult to search the dangerous block combination and acquire the safety factor precisely because of the numerous planes of weakness,the complicated block system and the diverse slip modes in rock slopes.Based on block element method,the search of dangerous block combination and the calculation of stability safety factor are conducted.At first,a new method for searching dangerous block combination is proposed,according to the results of block element method through strength reduction calculation.Then,the method for computing safety factors is studied;and the double line intersection method is suggested to calculate the safety factor when the abrupt theory of displacement is adopted.At last,several typical examples are calculated with the proposed methods;and the results are compared with those obtained by using the rigid body limit equilibrium method.The results show that it is more accurate by adopting the block element method,because the force and bending moment equilibrium and the nonuniform distribution of stress on the planes of weakness are considered.The proposed method is expected to be widely used to solve stability problems in complicated rock slopes.
引文
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[14]汪卫明,丁刚.岩质边坡开挖过程动态仿真分析的块体单元法[J].岩石力学与工程学报,2011,30(3):540-546.WANG Wei-ming,DING Gang.Block element methodfor dynamically simulating excavation progress of rockslope[J].Chinese Journal of Rock Mechanics andEngineering,2011,30(3):540-546.
[15]陈胜宏.计算岩体力学与工程[M].北京:中国水利水电出版社,2006.
[16]郑惠峰,汪卫明,陈胜宏.弹粘塑性块体单元法在龙滩水电站右岸坝肩边坡稳定分析中的应用[J].岩土力学,2006,27(1):107-111.ZHENG Hui-feng,WANG Wei-ming,CHEN Sheng-hong.Application of elasto-viscoplastic block element methodto stability analysis of right abutment slope in Longtanhydropower project[J].Rock and Soil Mechanics,2006,27(1):107-111.
[17]汪卫明,陈胜宏.三维岩石块体系统的自动别方法[J].武汉水利电力大学学报,1998,31(5):51-55.WANG Wei-ming,CHEN Sheng-hong.Automaticidentification method for three-dimensional rock blocksystems[J].Journal of Wuhan University of Hydraulicand Electric Engineering,1998,31(5):51-55.
[18]OWEN D R J,HINTON E.Finite elements in plasticity:Theory and practice[M].Swansea,U.K.:Pineridge PressLtd.,1980.
[19]万文,曹平,冯涛,等.基于加速混合遗传算法搜索复杂边坡的最危险滑动面[J].岩土工程学报,2006,28(4):475-479.WAN Wen,CAO Ping,FENG Tao,et al.Searching forthe most dangerous failure surface of complex slopebased on accelerating hybrid genetic algorithm[J].Chinese Journal of Geotechnical Engineering,2006,28(4):475-479.
[20]谭儒蛟,李明生,张建根,等.岩质边坡最危险滑裂面的GA-Sarma算法研究[J].岩石力学与工程学报,2010,29(增刊1):2866-2871.TAN Ru-jiao,LI Ming-sheng,ZHANG Jian-gen,et al.Study of GA-Sarma algorithm of critical slip surface ofrock slope[J].Chinese Journal of Rock Mechanics andEngineering,2010,29(Supp.1):2866-2871.
[21]陈昌富,朱剑锋.基于Morgenstern-Price法边坡三维稳定性分析[J].岩石力学与工程学报,2010,29(7):1473-1480.CHEN Chang-fu,ZHU Jian-feng.A three-dimensionalslope stability analysis procedure based onMorgenstern-Price method[J].Chinese Journal of RockMechanics and Engineering,2010,29(7):1473-1480.
[22]徐明毅,汪卫明,陈胜宏.岩石边坡危险滑动块体组合研究[J].岩土力学,2000,21(2):148-151.XU Ming-yi,WANG Wei-ming,CHEN Sheng-hong.Research on the dangerous sliding-block combination ofrock slopes[J].Rock and Soil Mechanics,2000,21(2):148-151.
[23]迟世春,关立军.基于强度折减的拉格朗日差分方法分析土坡稳定性[J].岩土工程学报,2004,26(1):42-46.CHI Shi-chun,GUAN Li-jun.Slope stability analysis byLagrangian difference method based on shear strengthreduction[J].Chinese Journal of GeotechnicalEngineering,2004,26(1):42-46.
[2]陈胜宏,万娜.边坡稳定分析的三维剩余推力法[J].武汉大学学报(工学版),2005,38(3):69-73.CHEN Sheng-hong,WAN Na.Study of three-dimensionalresidual thrust method for slope stability analysis[J].Engineering Journal of Wuhan University,2005,38(3):69-73.
[3]李同录,王艳霞,邓宏科.一种改进的三维边坡稳定性分析方法[J].岩土工程学报,2003,25(5):611-614.LI Tong-lu,WANG Yan-xia,DENG Hong-ke.Animproved method for three-dimensional slope stabilityanalysis[J].Chinese Journal of GeotechnicalEngineering,2003,25(5):611-614.
[4]顾晓强,陈龙珠.边坡稳定分析的三维极限平衡法[J].上海交通大学学报,2007,41(6):970-977.GU Xiao-qiang,CHEN Long-zhu.A 3D limit equilibriummethod for slope stability analysis[J].Journal ofShanghai Jiaotong University,2007,41(6):970-977.
[5]卓家寿,赵宁.不连续介质静、动力分析的刚体-弹簧元法[J].河海大学学报,1993,21(5):34-43.ZHUO Jia-shou,ZHAO Ning.Piecewise rigidbody-interface spring method for problems ofdiscontinuous medium[J].Journal of Hohai University,1993,21(5):34-43.
[6]CUNDALL P A.Formulation of a three-dimensionaldistinct element model—part 1:A scheme to detect andrepresent contacts in system composed of manypolyhedral blocks[J].International Journal of RockMechanics and Mining Sciences and GeomechanicsAbstracts,1988,25(3):107-116.
[7]贺续文,刘忠,廖彪,等.基于离散元法的节理岩体边坡稳定性分析[J].岩土力学,2011,32(7):2199-2204.HE Xu-wen,LIU Zhong,LIAO Biao,et al.Stabilityanalysis of jointed rock slopes based on discrete elementmethod[J].Rock and Soil Mechanics,2011,32(7):2199-2204.
[8]石根华.数值流形方法与非连续变形分析[M].北京:清华大学出版社,1997.
[9]张国新,李海枫,黄涛.三维不连续变形分析理论及其在岩质边坡工程中的应用[J].岩石力学与工程学报,2010,29(10):2116-2126.ZHANG Guo-xin,LI Hai-feng,HUANG Tao.Three-dimensional discontinuous deformation analysistheory and its application to rock slopes[J].ChineseJournal of Rock Mechanics and Engineering,2010,29(10):2116-2126.
[10]赵宁,卓家寿.结构的三维非线性界面元分析[J].河海大学学报,1995,23(2):23-31.ZHAO Ning,ZHUO Jia-shou.3-D nonlinear interfaceelement analysis of structures[J].Journal of HohaiUniversity,1995,23(2):23-31.
[11]薛翊国,陈剑平,王清.基于界面元的岩体裂隙网络渗流模型中不稳定块体预测[J].岩石力学与工程学报,2008,27(7):1485-1491.XUE Yi-guo,CHEN Jian-ping,WANG Qing.Predictionof instability block in rock fracture network seepagemodel based on interface stress element[J].ChineseJournal of Rock Mechanics and Engineering,2008,27(7):1485-1491.
[12]任青文,余天堂.块体单元法的理论和计算模型[J].工程力学,1999,16(1):67-77.REN Qing-wen,YU Tian-tang.Theory and calculatingmodel of block element method[J].EngineeringMechanics,1999,16(1):67-77.
[13]陈胜宏,汪卫明,邹丽春.岩石边坡开挖及加固分析的弹黏塑性块体元方法[J].岩石力学与工程学报,2002,21(7):953-958.CHEN Sheng-hong,WANG Wei-ming,ZOU Li-chun.Elasto-viscoplastic block element method for excavationand reinforcement analysis of rock slope[J].ChineseJournal of Rock Mechanics and Engineering,2002,21(7):953-958.
[14]汪卫明,丁刚.岩质边坡开挖过程动态仿真分析的块体单元法[J].岩石力学与工程学报,2011,30(3):540-546.WANG Wei-ming,DING Gang.Block element methodfor dynamically simulating excavation progress of rockslope[J].Chinese Journal of Rock Mechanics andEngineering,2011,30(3):540-546.
[15]陈胜宏.计算岩体力学与工程[M].北京:中国水利水电出版社,2006.
[16]郑惠峰,汪卫明,陈胜宏.弹粘塑性块体单元法在龙滩水电站右岸坝肩边坡稳定分析中的应用[J].岩土力学,2006,27(1):107-111.ZHENG Hui-feng,WANG Wei-ming,CHEN Sheng-hong.Application of elasto-viscoplastic block element methodto stability analysis of right abutment slope in Longtanhydropower project[J].Rock and Soil Mechanics,2006,27(1):107-111.
[17]汪卫明,陈胜宏.三维岩石块体系统的自动别方法[J].武汉水利电力大学学报,1998,31(5):51-55.WANG Wei-ming,CHEN Sheng-hong.Automaticidentification method for three-dimensional rock blocksystems[J].Journal of Wuhan University of Hydraulicand Electric Engineering,1998,31(5):51-55.
[18]OWEN D R J,HINTON E.Finite elements in plasticity:Theory and practice[M].Swansea,U.K.:Pineridge PressLtd.,1980.
[19]万文,曹平,冯涛,等.基于加速混合遗传算法搜索复杂边坡的最危险滑动面[J].岩土工程学报,2006,28(4):475-479.WAN Wen,CAO Ping,FENG Tao,et al.Searching forthe most dangerous failure surface of complex slopebased on accelerating hybrid genetic algorithm[J].Chinese Journal of Geotechnical Engineering,2006,28(4):475-479.
[20]谭儒蛟,李明生,张建根,等.岩质边坡最危险滑裂面的GA-Sarma算法研究[J].岩石力学与工程学报,2010,29(增刊1):2866-2871.TAN Ru-jiao,LI Ming-sheng,ZHANG Jian-gen,et al.Study of GA-Sarma algorithm of critical slip surface ofrock slope[J].Chinese Journal of Rock Mechanics andEngineering,2010,29(Supp.1):2866-2871.
[21]陈昌富,朱剑锋.基于Morgenstern-Price法边坡三维稳定性分析[J].岩石力学与工程学报,2010,29(7):1473-1480.CHEN Chang-fu,ZHU Jian-feng.A three-dimensionalslope stability analysis procedure based onMorgenstern-Price method[J].Chinese Journal of RockMechanics and Engineering,2010,29(7):1473-1480.
[22]徐明毅,汪卫明,陈胜宏.岩石边坡危险滑动块体组合研究[J].岩土力学,2000,21(2):148-151.XU Ming-yi,WANG Wei-ming,CHEN Sheng-hong.Research on the dangerous sliding-block combination ofrock slopes[J].Rock and Soil Mechanics,2000,21(2):148-151.
[23]迟世春,关立军.基于强度折减的拉格朗日差分方法分析土坡稳定性[J].岩土工程学报,2004,26(1):42-46.CHI Shi-chun,GUAN Li-jun.Slope stability analysis byLagrangian difference method based on shear strengthreduction[J].Chinese Journal of GeotechnicalEngineering,2004,26(1):42-46.