基于平动加转动运动场的边坡稳定极限分析法
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摘要
边坡工程是工程中最常见的工程形式,边坡工程中遇到的滑坡问题是全球三大地质灾害之一,严重危害人类的生命财产安全。随着我国经济建设的高速发展,边坡失稳问题日益突出,对边坡稳定问题的研究具有重要意义。
本文首先对目前常用的边坡稳定安全系数的分析方法:极限平衡法、有限元强度折减法、极限分析方法进行了简单的归纳和总结,详细分析了分别基于纯转动(Chen,1975)和纯平动(Michalowski,1995)运动场的边坡稳定安全系数的塑性极限分析上限解法。在此基础上提出了满足塑性流动法则,平动加转动的运动场及相应的边坡稳定安全系数计算方法。纯平动和纯转动运动场是本文提出的运动模式的二个特例。
本文分别假设滑动面为圆弧、对数螺旋线和任意形状滑动面,采用改进的蒙特卡洛法(李育超等,2005)搜索最危险的滑动面,并编制了相应的分析程序。通过大量的数值分析得到如下结论:(1) 对于给定的滑动面,转动速度分量对条间能量耗散有很大的影响,不同的转动速度对应不同的安全系数,最可能的转动速度使得该滑动面对应的稳定安全系数最小。(2) 与纯平动运动场相比,对于给定滑动面,本文提出的平动加转动的运动场能给出更小、更接近真值的安全系数上限解,两者的相对差别甚至可以高达20%。(3) 对于均质边坡,最危险的滑动面并非总是如Chen提出的对数螺旋线,特别是当土体的粘聚力较小时。(4) 基于相关联流动法则,采用土体内摩擦角计算出的安全系数比基于非相关联流动法则,采用剪胀角计算出的安全系数要偏大。
最后,本文对七子山垃圾填埋场扩建工程进行了稳定分析,指出当垃圾填埋体沿基底或者衬垫滑动时主要是发生平动破坏。
Slope is one of the most familiar engineering. The slide slope is one of the three geologic disasters which may cause much property loss and also many deaths. As the fast development of the economy construction, the study on the stability of slope is of great significance.Firstly, this thesis introduces the most popular methods of the stability analysis of slope, including the Limit equilibrium approach, the finite element approach and limit analysis approach. Based on the rotation kinematical field and translation kinematical field, a particular study on the upper bound limit analysis of slope stability is made. A kinematical field considering both translation and rotation is proposed. And the rotation and translation kinematical field are just two particular examples of its.Assuming the critical slide surface are circle arc, logarithmic spiral and other arbitrary form, the thesis uses the improved Monte Carlo method to search the critical slide surface, and use the three kinematical approaches mentioned above to calculate the factor of safety. Based on a great number of numeric examples, the following conclusions can be made. (1) For a fixed slide surface, the angle velocity has great effect on the energy dissipation between the labor blocks. And the most possible angle velocity makes the minimum safety factor. (2)Comparing to the translation kinematical field, the approach proposed in the thesis can give a less value of safety factor which is more closed to the true value. (3)The critical surface is not always the one proposed by Chen for a homogeneous slope. (4)The safety factor is higher when non-associate flow rule is used. At last, the safety factor of a landfill is analysed.
本文首先对目前常用的边坡稳定安全系数的分析方法:极限平衡法、有限元强度折减法、极限分析方法进行了简单的归纳和总结,详细分析了分别基于纯转动(Chen,1975)和纯平动(Michalowski,1995)运动场的边坡稳定安全系数的塑性极限分析上限解法。在此基础上提出了满足塑性流动法则,平动加转动的运动场及相应的边坡稳定安全系数计算方法。纯平动和纯转动运动场是本文提出的运动模式的二个特例。
本文分别假设滑动面为圆弧、对数螺旋线和任意形状滑动面,采用改进的蒙特卡洛法(李育超等,2005)搜索最危险的滑动面,并编制了相应的分析程序。通过大量的数值分析得到如下结论:(1) 对于给定的滑动面,转动速度分量对条间能量耗散有很大的影响,不同的转动速度对应不同的安全系数,最可能的转动速度使得该滑动面对应的稳定安全系数最小。(2) 与纯平动运动场相比,对于给定滑动面,本文提出的平动加转动的运动场能给出更小、更接近真值的安全系数上限解,两者的相对差别甚至可以高达20%。(3) 对于均质边坡,最危险的滑动面并非总是如Chen提出的对数螺旋线,特别是当土体的粘聚力较小时。(4) 基于相关联流动法则,采用土体内摩擦角计算出的安全系数比基于非相关联流动法则,采用剪胀角计算出的安全系数要偏大。
最后,本文对七子山垃圾填埋场扩建工程进行了稳定分析,指出当垃圾填埋体沿基底或者衬垫滑动时主要是发生平动破坏。
Slope is one of the most familiar engineering. The slide slope is one of the three geologic disasters which may cause much property loss and also many deaths. As the fast development of the economy construction, the study on the stability of slope is of great significance.Firstly, this thesis introduces the most popular methods of the stability analysis of slope, including the Limit equilibrium approach, the finite element approach and limit analysis approach. Based on the rotation kinematical field and translation kinematical field, a particular study on the upper bound limit analysis of slope stability is made. A kinematical field considering both translation and rotation is proposed. And the rotation and translation kinematical field are just two particular examples of its.Assuming the critical slide surface are circle arc, logarithmic spiral and other arbitrary form, the thesis uses the improved Monte Carlo method to search the critical slide surface, and use the three kinematical approaches mentioned above to calculate the factor of safety. Based on a great number of numeric examples, the following conclusions can be made. (1) For a fixed slide surface, the angle velocity has great effect on the energy dissipation between the labor blocks. And the most possible angle velocity makes the minimum safety factor. (2)Comparing to the translation kinematical field, the approach proposed in the thesis can give a less value of safety factor which is more closed to the true value. (3)The critical surface is not always the one proposed by Chen for a homogeneous slope. (4)The safety factor is higher when non-associate flow rule is used. At last, the safety factor of a landfill is analysed.
引文
[1] 陈祖煜.土质边坡稳定分析——原理·方法·程序[M].中国水利水电出版社.2003:23-84
[2] 赵明阶,何光春,王多根.边坡工程处治技术[M].北京:人民交通出版社.2003.6:19-5
[3] Fellenius, W. (1927). Erdstatische Berechnungen. Berlin: Ernst.
[4] Bishop, A. W, The use of the slip circle in the stability analysis of slopes [J]. Geotechnique, 1955. 5 (1): 7-17.
[5] Janbu N, Application of composite slip surface for stability analysis[J]. Proc Euro ConfStability of Earth Slopes, Stockholm, 1954, 3: 43-49.
[6] U. S. Army, Corps of Engineers. Stability of slopes and foundations, Engineering Manual, Visckburg, Miss. 1967.
[7] Lowe. J. III. & Karaflath. L, Stability of earth dams upon drawdown. Proc. 1st Panamer. Conf. Soil Mech. 1960. Mexico City 2. 537-552.
[8] Chen, Zuyu Random trials used in determining global minimum factors of safety of slopes. Canadian Geotechnical Journal. 1992. 29 (2): 225-233.
[9] Spencer. E, A method of analysis of embankments assuming parallel imer-slice forces, Geotechnique, 1967.
[10] Morgenstem, N. R. & Price, V. E. (1965). The analysis of the stability of general slip surfaces. Geotechnique 15, No. 1, 79-93.
[11] Sarma, S. K. Stability analysis of embankrnents and slopes. Geotechnique. 1973. 23(3): 423-433.
[12] Prandtl L. Uber die harte plasticher Korpe. Nach. K. Ges. Wiss. Gott., Mathphys. Klasse, 74-85.
[13] Chen W. F. Limit Analysis and Soil Plasticity. Elsevier: Amsterdam, 1975.
[14] Chen Z Y, Donald I. Comparison between the limit equilibrium and limit analysis method. Proceedings of the 10th Asian Regional Conference on Soil Mechanics and Foundation Engineering, 1995, 267～270.
[15] Michalowski, R. L. Slope stability analysis: a kinematical approach Geotechnique 45 (1995), No. 2, 283-293.
[16] Donald IB, Chen ZY. Slope stability analysis by the upper bound approach: fundamentals and methods. Canadian Geotechnical Journal 1997: 34(6): 853-862.
[17] Donald IB, Chen ZY. Slope stability analysis by the upper bound approach: fundamentals and methods. Canadian Geotechnical Journal 1997: 34(6): 853-862.
[18] Solan S W. Lower bound limit analysis using finite elements and linear programming. International journal for Numerical and Analytical Method in Geomechanics, 1988, 12: 61～67.
[19] Solan S W. A steepest edge active set algorithm for solving sparse linear programming programs. International journal for Numerical method in Engineering, 1988, 26: 2671～282.
[20] Solan S W. Upper bound limit analysis using finite elements and linear programming. International journal for Numerical and Analytical Method in Geomechanics, 1989, 13: 263～282.
[21] 殷有泉固体力学非线性有限元引论.A北京.北京大学出版社和清华大学出版社,1993
[22] Baker R, Gather M. Variation approach to slope stability[J]. Proc. 9th Int. Conf. on Soil Mech. and Found. Engng. [C]. 1977, Vol. 2: 9-12.
[23] Castillo E, Revilla J. The calculus of variations and the stability of slopes[A]. Proc. 9th Int. Conf. oil Soil Mech. and Found. Engng.[C]. 1977, Vol. 2: 25-30.
[24] Revilla J, Castillo E. The calculus of variations applied to stability of slopes[J]. Geotechnique, 1977, 27(1): 1-11.
[25] Ramamurthy T, Narayan C G P, Bhatkar V P. Variational method for slope stability analysis[A]. Proc. 9th Int. Conf. on Soil Mech. And Found. Engng.[C]. 1977, Vol. 3: 139-142.
[26] De Josselin, De Jong G. Application of the calculus of variation to vertical cut offin cohesive frictioniess soil[J]. Geotechnique, 1980, 30(1): 1-16.
[27] Luceno A, C. astillo E. Evaluation of variational methods in slope analysis[A]. Proc. 1st Int. Syrup on Landslides[C]. Meerut: Sarita Prakashan, New De lhi, 1980. 255-258.
[28] Siegel R A. Computer analysis of general slope stability problems [M]. Res. Report No. JHRP-75-8, Engineering Experiment Station, Purdue University, West Lafayette, Ind., 1975.
[29] Nguyen V U, De termination of critical slope failure surface[J]. J Geotech. Engng., AsCE, 1985, 111(2): 238-250.
[30] De Natale J S, Raped identification of critical slip surface: structure[J]. J. Geotech. Engng., ASCE, 1991, 177(10): 1, 568-589.
[31] Celestino T B, Duncedl J M. Simplified search for non-circular slip surface [A]. Proc., 10th Int. Conf. on Soil Mech. and Found. Engin.[C]. A. A. Balkema, Rotterdam, The Netherlands, 1981. 3, 391-394.
[32] Arai K, TagyoK. De terminationof noncircular slip surface giving the minimum factor of safety in slope stability analysis[J]. Soils and Foun ddations, 1985, 25(1): 43-51.
[33] Li K S, Vghite W. Rapid evaluation of the critical surface in slope stability problems[J]. Int. J. for Numer. and Anal. Meth. In Geomech., 1987, 11(5): 449-473.
[34] 阎中华.均质土坝与非均质土坝稳定安全系数极值分布规律及电算程序简介[J].水利水电技术,1983,(7)
[35] 周文通.最优化方法在土坝稳定分析中的应用[J].土石坝工程,1984,(2)
[36] Yarnagami T, Ueta Y. Search for critical slip lines in finite element stress fields by dynamic programming. Pro:. of 6th Int. Conf. on Numerical Methods in Geomechanies[J]. Irmshruck,1988. 1347. 13-52.
[37] 陈祖煜,邵长明.最优化方法在确定边坡最小安全系数方面的应用[J].岩土工程学报,1988,(4):1-13
[38] Greco V R. Numerical methods for locating the critical slip surface in slope stability[A]. Proc. of 6 Int. Conf. on Numerical Methods in Geomechanics [C]. Innsbruck, 1988. 1219-1223.
[39] Baker R, Determination of critical slip surface in slope stability computation[J]. Int. J. for Numer. and Anal～ical Meth. In Geomech., 1980.4, 333-359.
[40] BoutrupE, LovellCW. Searchtechnicalin slope stability analysis [J]. Engineering Geotechnical, 1980, 16(1): 51-61.
[41] SiegelRA, KovacsW D, LovellCW. Random sill-facegeneration in stability analysis[J]. J. Geoteeh. Engng., ASCEo 1981, 107(7): 996-1002.
[42] Greco Efficient Monte Carlo technique for locating critical slip surface [J]. J. Geotech. Engng., ASCE, 1996, 122(7): 517-525.
[43] Abdallah I H, Waleed FH, SaradaK S. Global searchmethod for locating general slip surface using Monte Carlo Techniques[J]. J. of Geotech. an d Geoenviro. Engng., ASCE, 2001, Vol. 127: 688-698.
[44] 李育超,凌道盛,陈云敏,张文杰,蒙特卡洛法与有限元相结合分析边坡稳定性.岩石力学与工程学报,2005.24卷11期:1933-1941
[45] 肖专文,张奇志,粱力.遗传进化算法在边坡稳定分析中的应用[J].岩 土工程学报,1998,20(1):44-46
[46] Anthony T G. Genetic algorithm search for critical slip surface in multiple-wedgestabilityanalysis[J]. Can. Geotech. J., 1999, Vol. 36: 382-391.
[47] 史恒通,王成华.土坡有限元稳定分析若干问题探讨[J].岩石力学.2000,22(2):152-155
[48] 陈昌富,刘齐建,杨明辉.沌蚁群算法及其工程应用.九届土力学及岩土工程学术会议论文集.2003,10:1355-1357
[49] Zhu D. Y, A method for locating critical slip surfaces in slope stability analysis, Canadian Geotechnical Journal, 2001, 38: 328-337.
[50] 李育超.基于实际应力状态的土质边坡稳定分析研究.浙江大学博士学位论文.2006
[51] Cheng Y. M. Location of critical failure surface and some further studies on slope stability analysis. Computers and Geotechnics, 2003, 30: 255-267.
[52] Chen Z. Y., Shao C. Evaluation of minimum factor of safety in slope stability analysis. Canadian Geotechnical Journal, 1988, 25: 735-748.
[53] Mandlt, G. and R. Femandez Luquet, R. Fully Developed Plastic Shear Flow of Granular Materials. Geotechnique. 1970. 20(3): 277-307.
[54] De Josselin, De Jong G. Application of the calculus of variation to vertical cut offin cohesive frictionless soil[J]. Geotechnique, 1980, 30(1): 1-16.
[55] Drescher, A. and Detoumey, E. Limit Load in Traslational Failure Mechanisms for Associative and Non-Associative Materials. Geotechnique. 1993. 43(3): 443-456.
[56] Zienkiewics, O. C. Humpheson, C. and Lewis, R W. Associated and Non-Associated Visco-Plasticity and Plasticity in Soil Mechanics. Geotechnique. 1975.25(4): 671-689.
[57] Davis, E. H. and Booker, J. R. Some Adaptations of Classic Plasticity Theory for Soil Stability Problems. Proceedings of Symposium on the Role of Plasticity in Soil Mechanics. 1973: 24-41.
[58] Mroz, Z. and Srymanslci, C. Z. Non-Associated Flow Rules in description of Plastic Flow of Granular Materials. Proceedings of Symposium on the Role of Plasticity in Soil Mechanics. 1973: 51-69.
[59] 郑颖人.广义塑性力学理论.岩土力学.2000,21(2):188-192
[60] 陈祖煜,汪小刚,杨健,贾志欣,王玉杰.岩质边坡稳定分析—原理·方法·程序.北京:中国水利水电出版社,2005
[61] Pham H.T.V., Fredlund D.G. The application of dynamic programming to slope stability analysis. Canadian Geotechnical Journal, 2003,40: 830-847.
[62] Malkawi A.I.H., Hassan W.F., Sarma S.K. Global search method for locating general slip surface using Monte Carlo Techniques. Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 2001,127(8): 688-698.
[63] Chen Z.Y. Random Trials used in determining global minimum factors of safety of slope. Canadian Geotechnical Journal, 1992, 29: 225-233.
[64] Li K.S. White W. Rapid evaluation of the critical slip surface in slope stability problems. Journal for Numerical and Analytical methods in Geomechanics, 1987,11(5): 449-473.
[2] 赵明阶,何光春,王多根.边坡工程处治技术[M].北京:人民交通出版社.2003.6:19-5
[3] Fellenius, W. (1927). Erdstatische Berechnungen. Berlin: Ernst.
[4] Bishop, A. W, The use of the slip circle in the stability analysis of slopes [J]. Geotechnique, 1955. 5 (1): 7-17.
[5] Janbu N, Application of composite slip surface for stability analysis[J]. Proc Euro ConfStability of Earth Slopes, Stockholm, 1954, 3: 43-49.
[6] U. S. Army, Corps of Engineers. Stability of slopes and foundations, Engineering Manual, Visckburg, Miss. 1967.
[7] Lowe. J. III. & Karaflath. L, Stability of earth dams upon drawdown. Proc. 1st Panamer. Conf. Soil Mech. 1960. Mexico City 2. 537-552.
[8] Chen, Zuyu Random trials used in determining global minimum factors of safety of slopes. Canadian Geotechnical Journal. 1992. 29 (2): 225-233.
[9] Spencer. E, A method of analysis of embankments assuming parallel imer-slice forces, Geotechnique, 1967.
[10] Morgenstem, N. R. & Price, V. E. (1965). The analysis of the stability of general slip surfaces. Geotechnique 15, No. 1, 79-93.
[11] Sarma, S. K. Stability analysis of embankrnents and slopes. Geotechnique. 1973. 23(3): 423-433.
[12] Prandtl L. Uber die harte plasticher Korpe. Nach. K. Ges. Wiss. Gott., Mathphys. Klasse, 74-85.
[13] Chen W. F. Limit Analysis and Soil Plasticity. Elsevier: Amsterdam, 1975.
[14] Chen Z Y, Donald I. Comparison between the limit equilibrium and limit analysis method. Proceedings of the 10th Asian Regional Conference on Soil Mechanics and Foundation Engineering, 1995, 267～270.
[15] Michalowski, R. L. Slope stability analysis: a kinematical approach Geotechnique 45 (1995), No. 2, 283-293.
[16] Donald IB, Chen ZY. Slope stability analysis by the upper bound approach: fundamentals and methods. Canadian Geotechnical Journal 1997: 34(6): 853-862.
[17] Donald IB, Chen ZY. Slope stability analysis by the upper bound approach: fundamentals and methods. Canadian Geotechnical Journal 1997: 34(6): 853-862.
[18] Solan S W. Lower bound limit analysis using finite elements and linear programming. International journal for Numerical and Analytical Method in Geomechanics, 1988, 12: 61～67.
[19] Solan S W. A steepest edge active set algorithm for solving sparse linear programming programs. International journal for Numerical method in Engineering, 1988, 26: 2671～282.
[20] Solan S W. Upper bound limit analysis using finite elements and linear programming. International journal for Numerical and Analytical Method in Geomechanics, 1989, 13: 263～282.
[21] 殷有泉固体力学非线性有限元引论.A北京.北京大学出版社和清华大学出版社,1993
[22] Baker R, Gather M. Variation approach to slope stability[J]. Proc. 9th Int. Conf. on Soil Mech. and Found. Engng. [C]. 1977, Vol. 2: 9-12.
[23] Castillo E, Revilla J. The calculus of variations and the stability of slopes[A]. Proc. 9th Int. Conf. oil Soil Mech. and Found. Engng.[C]. 1977, Vol. 2: 25-30.
[24] Revilla J, Castillo E. The calculus of variations applied to stability of slopes[J]. Geotechnique, 1977, 27(1): 1-11.
[25] Ramamurthy T, Narayan C G P, Bhatkar V P. Variational method for slope stability analysis[A]. Proc. 9th Int. Conf. on Soil Mech. And Found. Engng.[C]. 1977, Vol. 3: 139-142.
[26] De Josselin, De Jong G. Application of the calculus of variation to vertical cut offin cohesive frictioniess soil[J]. Geotechnique, 1980, 30(1): 1-16.
[27] Luceno A, C. astillo E. Evaluation of variational methods in slope analysis[A]. Proc. 1st Int. Syrup on Landslides[C]. Meerut: Sarita Prakashan, New De lhi, 1980. 255-258.
[28] Siegel R A. Computer analysis of general slope stability problems [M]. Res. Report No. JHRP-75-8, Engineering Experiment Station, Purdue University, West Lafayette, Ind., 1975.
[29] Nguyen V U, De termination of critical slope failure surface[J]. J Geotech. Engng., AsCE, 1985, 111(2): 238-250.
[30] De Natale J S, Raped identification of critical slip surface: structure[J]. J. Geotech. Engng., ASCE, 1991, 177(10): 1, 568-589.
[31] Celestino T B, Duncedl J M. Simplified search for non-circular slip surface [A]. Proc., 10th Int. Conf. on Soil Mech. and Found. Engin.[C]. A. A. Balkema, Rotterdam, The Netherlands, 1981. 3, 391-394.
[32] Arai K, TagyoK. De terminationof noncircular slip surface giving the minimum factor of safety in slope stability analysis[J]. Soils and Foun ddations, 1985, 25(1): 43-51.
[33] Li K S, Vghite W. Rapid evaluation of the critical surface in slope stability problems[J]. Int. J. for Numer. and Anal. Meth. In Geomech., 1987, 11(5): 449-473.
[34] 阎中华.均质土坝与非均质土坝稳定安全系数极值分布规律及电算程序简介[J].水利水电技术,1983,(7)
[35] 周文通.最优化方法在土坝稳定分析中的应用[J].土石坝工程,1984,(2)
[36] Yarnagami T, Ueta Y. Search for critical slip lines in finite element stress fields by dynamic programming. Pro:. of 6th Int. Conf. on Numerical Methods in Geomechanies[J]. Irmshruck,1988. 1347. 13-52.
[37] 陈祖煜,邵长明.最优化方法在确定边坡最小安全系数方面的应用[J].岩土工程学报,1988,(4):1-13
[38] Greco V R. Numerical methods for locating the critical slip surface in slope stability[A]. Proc. of 6 Int. Conf. on Numerical Methods in Geomechanics [C]. Innsbruck, 1988. 1219-1223.
[39] Baker R, Determination of critical slip surface in slope stability computation[J]. Int. J. for Numer. and Anal～ical Meth. In Geomech., 1980.4, 333-359.
[40] BoutrupE, LovellCW. Searchtechnicalin slope stability analysis [J]. Engineering Geotechnical, 1980, 16(1): 51-61.
[41] SiegelRA, KovacsW D, LovellCW. Random sill-facegeneration in stability analysis[J]. J. Geoteeh. Engng., ASCEo 1981, 107(7): 996-1002.
[42] Greco Efficient Monte Carlo technique for locating critical slip surface [J]. J. Geotech. Engng., ASCE, 1996, 122(7): 517-525.
[43] Abdallah I H, Waleed FH, SaradaK S. Global searchmethod for locating general slip surface using Monte Carlo Techniques[J]. J. of Geotech. an d Geoenviro. Engng., ASCE, 2001, Vol. 127: 688-698.
[44] 李育超,凌道盛,陈云敏,张文杰,蒙特卡洛法与有限元相结合分析边坡稳定性.岩石力学与工程学报,2005.24卷11期:1933-1941
[45] 肖专文,张奇志,粱力.遗传进化算法在边坡稳定分析中的应用[J].岩 土工程学报,1998,20(1):44-46
[46] Anthony T G. Genetic algorithm search for critical slip surface in multiple-wedgestabilityanalysis[J]. Can. Geotech. J., 1999, Vol. 36: 382-391.
[47] 史恒通,王成华.土坡有限元稳定分析若干问题探讨[J].岩石力学.2000,22(2):152-155
[48] 陈昌富,刘齐建,杨明辉.沌蚁群算法及其工程应用.九届土力学及岩土工程学术会议论文集.2003,10:1355-1357
[49] Zhu D. Y, A method for locating critical slip surfaces in slope stability analysis, Canadian Geotechnical Journal, 2001, 38: 328-337.
[50] 李育超.基于实际应力状态的土质边坡稳定分析研究.浙江大学博士学位论文.2006
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