极限平衡法和有限单元法分析复杂边坡的稳定性
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摘要
土坡稳定性分析是岩土工程中的一个热门课题。在土木工程中，边坡稳定分析十分重要，如各种各样的天然边坡、高速公路、机场、填埋场、土石坝工程、各种填方、挖方工程等等都需要进行稳定分析。滑坡往往又伴随着地震、暴雨发生，并引发泥石流等严重的自然灾害。
本文首先分析了各种因素对边坡稳定性的影响。通过应用目前研究较多的极限平衡法和有限单元法，结合简单边坡和复杂边坡进行稳定性计算，介绍了此两种方法的原理、现状和发展，总结了各自的优缺点和存在的问题。
本文结合富阳来龙山滑坡的工程实例，介绍了来龙山滑坡的概况，分析了滑坡产生的成因、滑坡要素及监测情况，并用极限平衡法和有限元法分别进行了安全系数的计算与分析，提出并验证了自己的观点。
本文的工作主要是对极限平衡法和有限单元法在边坡稳定性计算与研究中的应用进行分析和比较。
Analysis of slope stability is one of the most important problems in Geotechnical Engineering. The stability of all kinds of natural slope, higeway, airport, refuse dump, dam, fill, excavation need to be analysed .
Firstly, the simple slope either with the two-layered or three-layered soils were calculated with softwares based on limited equilibrium method and the finite element method. The principle,current situation and development of these two methods were introduced. And advantages and shortcomings of the two methods were summarized .
Secondly, the Fu Yang Lailong Mountain slope failure was introduced. The factors influcing the slope stability were analysed and the calculated results were compared with those obtained by insitu monitoring.
Finally, some conclutions were obtained, which are important to engineering application.
本文首先分析了各种因素对边坡稳定性的影响。通过应用目前研究较多的极限平衡法和有限单元法，结合简单边坡和复杂边坡进行稳定性计算，介绍了此两种方法的原理、现状和发展，总结了各自的优缺点和存在的问题。
本文结合富阳来龙山滑坡的工程实例，介绍了来龙山滑坡的概况，分析了滑坡产生的成因、滑坡要素及监测情况，并用极限平衡法和有限元法分别进行了安全系数的计算与分析，提出并验证了自己的观点。
本文的工作主要是对极限平衡法和有限单元法在边坡稳定性计算与研究中的应用进行分析和比较。
Analysis of slope stability is one of the most important problems in Geotechnical Engineering. The stability of all kinds of natural slope, higeway, airport, refuse dump, dam, fill, excavation need to be analysed .
Firstly, the simple slope either with the two-layered or three-layered soils were calculated with softwares based on limited equilibrium method and the finite element method. The principle,current situation and development of these two methods were introduced. And advantages and shortcomings of the two methods were summarized .
Secondly, the Fu Yang Lailong Mountain slope failure was introduced. The factors influcing the slope stability were analysed and the calculated results were compared with those obtained by insitu monitoring.
Finally, some conclutions were obtained, which are important to engineering application.
引文
1. Anderson, S. A& Riemer, M. F. Collapse of saturated soil due to reduction in confinement. J. Geotech. EngngDiv., ASCE 121, No. 2, 216-220, 1995
2. Anderson, S. A& Sitar, N. Analysis of rainfall-induced debris flows. J. Geotech. EngngDiv., ASCE 121, No. 7, 544-552, 1999
3. Arai K and Tagyo K. Determination of noncircular slip surface giving the minimum factor of safety in slope stability analysis. Soil and Foundations, 1985, 25(1): 43～51
4. Baker R. Determination of critical slip surface in slope stability computations. Int J Num Anal Meth Geomech, 1980, 4(1): 333～359
5. Bishop A W. The use of the slip circle in stability analysis of slopes. Geotechnique, 1955, 5(1): 7～17
6. Bishop A W. The strength of soils as engineering materials. Geotechnique, 1966, 16(2): 91～128
7. Bishop A W. The influence of progressive failure on the choice of the method of stability. Geotechnique, 1971, 21(2): 168～172
8. Blight, G. interactions between the atmosphere and the Earth. Geotechnique 47, No. 4, 715-766, 1997
9. Burland, J. B. On the compressibility and shear strength of natural clays. Geotechnique 40, No. 3, 329-378, 1990
10．包承纲．非饱和土的特征及其抗剪强度问题。第八届土力学及岩土工程学术会议论文集。万国学术出版社。1999
11. Casagrande A. The structure of clay and its importance in foundation engineering. J Boston Soc Civ Engrs, 1932, 19(4): 168～209
12. Chen Z Y, Shao C M. Exaluation of minimum factor of safety in slope stability analysis. Can GeotechJ, 25: 735-748, 1988
13. Chen Z Y. Random trials used in determining global minimum factors of safety of slopes Can Geotech J, 29: 225-233, 1992
14．陈善雄，陈守义．考虑降雨的非饱和土边坡稳定分析方法．岩土力学．Vol．22
No(4)：447-450，2001
15．陈祖煜，汪小刚．极限分析数值方法。土工计算分析(龚晓南主编)．北京：中国建筑工业出版社，2000：234～258
16. Dawson E M, Roth W H, Drescher A. Slope stability analysis by strength reduction. Geotechnique, 49(6): 835-840, 1999
17. Demers. D, Leroueil, S. &DAstous. In situ testing in a landslide area at Maskinong, Quebec. Can. Geotech. J36, No. 6, 1001-1014, 1999
18. Donald I B and chen Z. Slope stability analysis by the upper bound approach: fundamentals and methods. Can Geotech J, 1997, 34(6): 853～862
19. Duncan, State of the art: Limit equilibrium and Finite-element analysis of slopes. Journal of Geotechnical Engineering 122(7): 577-595, 1996
20. D. V. Griffiths and P. A. lane. Slope stability analysis by finite elements. Geotechnique, 49(3): 387-403, 1999
21．戴福初，陈守义，李焯芬．从土的应力应变特性探讨滑坡发生机理。岩土工程学报。Vol．22 No(1)：127-130，2000
22. Fellenius W. Erdstatische berechnungen mit reinbung und kohasion und unter annahme kreissylindrischer gleitflachen(Earth static calculations with fiction and cohesion and use of circular sliding surfaces)). Berlin: Ernst, 1927
23. Fellenius W. Calculation of the stability of earth dams. Trans 2nd. Congr. Large Dams, Washington D C, 1936, 4: 445～462
24. Fredlund, D. G., Morgenstern, N. R&Widger, R. A. The shear strength of unsaturated expansiveclays. Can. Geotech. J. 15, No. 3, 313-321, 1978
25. Fredlund D G, Xing Anqing. The relationship of the unsaturated soil shear strength to the soil-water characteristic curve. Can. Geotech. J 33: 440-448, 1996
26. Fredlund D G, Xing A. Equations for the soil-water characteristic curve. Can. Geotech. J 31: 521-532, 1994
27．丰定详，吴家秀，葛修润．边坡稳定性分析中几个问题的探讨．岩土工程学报．Vol．12 No(3)：1-9，1990
28. Griffiths D V, Lane P A. Slope stability analysis by finite
elements. Genotechnique, 49(3): 387-403, 1999
29. Green V R. Efficient Monte-Carlo technique for locating critical slip surface. Can GeotechJ, 122(7): 517-525, 1994
30．郭志平．土坡稳定计算．土工原理与计算(上册，华东水利学院土力学教研室)．北京：水利电力出版社，1982：239～254
31．黄春娥，龚晓南．条分法与有限元法相结合分析渗流作用下的基坑边坡稳定性。水利学报。Vol．22 No(3)：6-10，2001
32．黄春娥，龚晓南，顾晓鲁．考虑渗流的基坑边坡稳定分析．V01．34 No(4)：98-101．2001
33. Janbu N. Application of composite slip surface for stability analysis. Proc Euro Conf Stability of Earth Slopes, Stockholm, 1954, 3: 43～49
34. Janbu N. Earth pressure and bearing capacity calculations by generalized procedure of sliees. Proc 4th hat Corf Soil Mech Fdn Engng, London, 1957, 2: 207～212
35. Janbu N. Slope stability computations. In: Embankment-dam engineering, Casagrand volume, Stockholm, London: John Wiley, 1973: 47～86
36．蒋刚，林鲁生，刘祖德，王钊．考虑非饱和土强度的边坡稳定分析方法及应用．岩石力学与工程学报．Vol．20 增(1)：1070-1074，2001
37. Leroueil S. Vaughan P. R. The General and Congruent Effects of Sstmcture in Natural Soil and Weak Rock. Geotechnique. 40(3): 467-488, 1990
38. Leroueil Natural slopes and cuts: movement and failure. mechanisms Geotechnique 51, No. 3, 197-243, 2001
39. Lim T T, Rahardjio H, Chang M F et. al Effect of rainfall on matric suctions in a residual soil slope. Can. Geotech. J 33: 618-628, 1996
40．林孝松，郭跃．滑坡与降雨的耦合关系研究．灾害学．Vol．16 No(2)：87-93，2001
41．连镇营，韩国城，孔宪京．强度折减有限元法研究开挖边坡的稳定性．岩土工程学报．Vol．23 No(4)：407-411，2001
42．李兆平，张弥．考虑降雨入渗影响的非饱和土边坡瞬态安全系数研究．土木工程学报．Vol．34 No(5)：57-61，2001
43．卢肇均等．非饱和土的抗剪强度与膨胀力。岩土工程学报。Vol．14 No(3)：1-8，1992
44．罗小杰，黄胜华．滑坡活动强度与几何要素之关系探讨．水文地质工程地质．No(1)：10-15，2001
45. Matsui T and San K. Finite element slope stability analysis by Shear Strength Reduction Technique. Soils and Foundations, 32(1): 59-70, 1992
46. Manzari M T, Nour M A. Significance of soil dilatancy in slope stability analysis. J. Geotech. EngngDiv. ASCE, 126(1): 75-80, 2000
47．毛昶熙，李吉庆，段祥宝．渗流作用下土坡圆弧滑动有限元计算。岩土工程学报。Vol．22 No(6)：746-752，2001
48. Potts, D. M., Kovacevic, N. &Vaughan, P. L. R. Delayed collapse of cut slopes in stiff clay. Geotechnique 47, No5, 953-982, 1997
49. Stark, T. D. &Eid, H. T. Drained residual strength of cohesive soils. J. Geotech. Engng Div, ASCE 120, No. 5, 856-871, 1994
50. Teruo Nakai, Hajime Matsuoka, Naomi Okuno, et al. Ture triaxial tests on normally consolidated clay and analysis of the observed shear behavior using elastoplastic constitutive models. Soils and Foundations 26(4): 67-78, 1986
51. Ugai K. A method of calculation of total factor of safety of slopes by elaso-plastic. Soils and Foundations, 29(2): 190-195, 1989
52. Ugai K, Leshchinsky D. Three-dimensional limit equilibrium and finite elementanalysis: a comparison of results. Soils and Foundations, 35(4): 1-7, 1995
53. Vanapalli S K, Fredlund D G, Pufahl D E, et al. Model for the prediction of shear strength with respect to soil suction. Can. Geotech. J 33: 379-392, 1996
54. Sarma S K. Stability analysis of embankments and slopes. J. Geotech. Engng Div. ASCE, 105(12): 392-398, 1979
55. Rahardjo H, Fredlund D G. General Limit Equilibrium Method for Lateral Earth Force. Can. Geotech. J. 21: 166-175, 1984
56．邵龙潭，唐洪祥，韩国城．有限远边坡稳定分析方法及其应用。计算力学学报。Vol．18 No(1)：81-87，2001
57．沈珠江．饱和粘土抗剪强度的变化规律及其在土工建筑物稳定分析中的应用．土木工程学报，1963，9(2)：29～36
58．沈珠江．理论土力学．北京：中国水利水电出版社，2000b
59．宋二祥．土工结构安全系数的有限元计算．岩土工程学报，1997，19(2)：1～7
60. Taylor D W. Stability of earth slopes. J Boston Soc Civ Engrs,1937, 24(3): 197～246
61. Taylor D W. Fundamentals of soil mechanics. New York: John Wiley and Sons, 1948
62. Terzaghi K. Critical height and factor of safety of slopes against sliding. Proc 1st Int Conf Soil Mech Fdn Engng, Cambridge, Massachusetts, 1936a, 1: 156～161
63. Terzaghi K. Undisturbed clay samples and undisturbed clays. J Boston Soc Civ Engrs, 1941, 28(3): 211～231
64. Terzaghi K. Theoretical soil mechanics. New York: John Wiley and Sons, Inc, 1943
65．汪自力，朱明霞，高青伟，岳瑜素．饱和-非饱和渗流作用下边坡稳定分析的混合法。郑州大学学报。Vol．23 No(1)：25-27，2002
66．魏汝龙，张凌．稳定分析中的强度指标问题．岩土工程学报，1993，15(5)：24～30
67．吴宏伟，陈守义，庞宇威．雨水入渗对非饱和土坡稳定性影响的参数研究．岩石力学．Vol．20 No(1)：1-14，1999
68．谢康和，周健．岩土工程有限元分析理论与应用。科学出版社，2002
69．谢守益，徐卫亚．降雨诱发滑坡机制研究．武汉水利电力大学学报．Vol．32No(1)：21-23，1999
70．姚海林，郑少河，陈守义．考虑裂隙及雨水入渗影响的膨胀土边坡稳定性分析．岩土工程学报．Vol．23 No(5)：606-609，2001
71．朱文彬，刘宝琛．降雨条件下土体滑坡的有限元数值分析．岩石力学与工程学报．Vol．21 No(4)：509-512，2002
72．郑颖人，赵尚毅．用有限元法求边坡稳定安全系数。公路交通技术。Vol．22 No(1)：7-10，2001
73．张季如．边坡开挖的有限元模拟和稳定性评价。岩石力学与工程学报。Vol．21 No(6)：843-847，2002
2. Anderson, S. A& Sitar, N. Analysis of rainfall-induced debris flows. J. Geotech. EngngDiv., ASCE 121, No. 7, 544-552, 1999
3. Arai K and Tagyo K. Determination of noncircular slip surface giving the minimum factor of safety in slope stability analysis. Soil and Foundations, 1985, 25(1): 43～51
4. Baker R. Determination of critical slip surface in slope stability computations. Int J Num Anal Meth Geomech, 1980, 4(1): 333～359
5. Bishop A W. The use of the slip circle in stability analysis of slopes. Geotechnique, 1955, 5(1): 7～17
6. Bishop A W. The strength of soils as engineering materials. Geotechnique, 1966, 16(2): 91～128
7. Bishop A W. The influence of progressive failure on the choice of the method of stability. Geotechnique, 1971, 21(2): 168～172
8. Blight, G. interactions between the atmosphere and the Earth. Geotechnique 47, No. 4, 715-766, 1997
9. Burland, J. B. On the compressibility and shear strength of natural clays. Geotechnique 40, No. 3, 329-378, 1990
10．包承纲．非饱和土的特征及其抗剪强度问题。第八届土力学及岩土工程学术会议论文集。万国学术出版社。1999
11. Casagrande A. The structure of clay and its importance in foundation engineering. J Boston Soc Civ Engrs, 1932, 19(4): 168～209
12. Chen Z Y, Shao C M. Exaluation of minimum factor of safety in slope stability analysis. Can GeotechJ, 25: 735-748, 1988
13. Chen Z Y. Random trials used in determining global minimum factors of safety of slopes Can Geotech J, 29: 225-233, 1992
14．陈善雄，陈守义．考虑降雨的非饱和土边坡稳定分析方法．岩土力学．Vol．22
No(4)：447-450，2001
15．陈祖煜，汪小刚．极限分析数值方法。土工计算分析(龚晓南主编)．北京：中国建筑工业出版社，2000：234～258
16. Dawson E M, Roth W H, Drescher A. Slope stability analysis by strength reduction. Geotechnique, 49(6): 835-840, 1999
17. Demers. D, Leroueil, S. &DAstous. In situ testing in a landslide area at Maskinong, Quebec. Can. Geotech. J36, No. 6, 1001-1014, 1999
18. Donald I B and chen Z. Slope stability analysis by the upper bound approach: fundamentals and methods. Can Geotech J, 1997, 34(6): 853～862
19. Duncan, State of the art: Limit equilibrium and Finite-element analysis of slopes. Journal of Geotechnical Engineering 122(7): 577-595, 1996
20. D. V. Griffiths and P. A. lane. Slope stability analysis by finite elements. Geotechnique, 49(3): 387-403, 1999
21．戴福初，陈守义，李焯芬．从土的应力应变特性探讨滑坡发生机理。岩土工程学报。Vol．22 No(1)：127-130，2000
22. Fellenius W. Erdstatische berechnungen mit reinbung und kohasion und unter annahme kreissylindrischer gleitflachen(Earth static calculations with fiction and cohesion and use of circular sliding surfaces)). Berlin: Ernst, 1927
23. Fellenius W. Calculation of the stability of earth dams. Trans 2nd. Congr. Large Dams, Washington D C, 1936, 4: 445～462
24. Fredlund, D. G., Morgenstern, N. R&Widger, R. A. The shear strength of unsaturated expansiveclays. Can. Geotech. J. 15, No. 3, 313-321, 1978
25. Fredlund D G, Xing Anqing. The relationship of the unsaturated soil shear strength to the soil-water characteristic curve. Can. Geotech. J 33: 440-448, 1996
26. Fredlund D G, Xing A. Equations for the soil-water characteristic curve. Can. Geotech. J 31: 521-532, 1994
27．丰定详，吴家秀，葛修润．边坡稳定性分析中几个问题的探讨．岩土工程学报．Vol．12 No(3)：1-9，1990
28. Griffiths D V, Lane P A. Slope stability analysis by finite
elements. Genotechnique, 49(3): 387-403, 1999
29. Green V R. Efficient Monte-Carlo technique for locating critical slip surface. Can GeotechJ, 122(7): 517-525, 1994
30．郭志平．土坡稳定计算．土工原理与计算(上册，华东水利学院土力学教研室)．北京：水利电力出版社，1982：239～254
31．黄春娥，龚晓南．条分法与有限元法相结合分析渗流作用下的基坑边坡稳定性。水利学报。Vol．22 No(3)：6-10，2001
32．黄春娥，龚晓南，顾晓鲁．考虑渗流的基坑边坡稳定分析．V01．34 No(4)：98-101．2001
33. Janbu N. Application of composite slip surface for stability analysis. Proc Euro Conf Stability of Earth Slopes, Stockholm, 1954, 3: 43～49
34. Janbu N. Earth pressure and bearing capacity calculations by generalized procedure of sliees. Proc 4th hat Corf Soil Mech Fdn Engng, London, 1957, 2: 207～212
35. Janbu N. Slope stability computations. In: Embankment-dam engineering, Casagrand volume, Stockholm, London: John Wiley, 1973: 47～86
36．蒋刚，林鲁生，刘祖德，王钊．考虑非饱和土强度的边坡稳定分析方法及应用．岩石力学与工程学报．Vol．20 增(1)：1070-1074，2001
37. Leroueil S. Vaughan P. R. The General and Congruent Effects of Sstmcture in Natural Soil and Weak Rock. Geotechnique. 40(3): 467-488, 1990
38. Leroueil Natural slopes and cuts: movement and failure. mechanisms Geotechnique 51, No. 3, 197-243, 2001
39. Lim T T, Rahardjio H, Chang M F et. al Effect of rainfall on matric suctions in a residual soil slope. Can. Geotech. J 33: 618-628, 1996
40．林孝松，郭跃．滑坡与降雨的耦合关系研究．灾害学．Vol．16 No(2)：87-93，2001
41．连镇营，韩国城，孔宪京．强度折减有限元法研究开挖边坡的稳定性．岩土工程学报．Vol．23 No(4)：407-411，2001
42．李兆平，张弥．考虑降雨入渗影响的非饱和土边坡瞬态安全系数研究．土木工程学报．Vol．34 No(5)：57-61，2001
43．卢肇均等．非饱和土的抗剪强度与膨胀力。岩土工程学报。Vol．14 No(3)：1-8，1992
44．罗小杰，黄胜华．滑坡活动强度与几何要素之关系探讨．水文地质工程地质．No(1)：10-15，2001
45. Matsui T and San K. Finite element slope stability analysis by Shear Strength Reduction Technique. Soils and Foundations, 32(1): 59-70, 1992
46. Manzari M T, Nour M A. Significance of soil dilatancy in slope stability analysis. J. Geotech. EngngDiv. ASCE, 126(1): 75-80, 2000
47．毛昶熙，李吉庆，段祥宝．渗流作用下土坡圆弧滑动有限元计算。岩土工程学报。Vol．22 No(6)：746-752，2001
48. Potts, D. M., Kovacevic, N. &Vaughan, P. L. R. Delayed collapse of cut slopes in stiff clay. Geotechnique 47, No5, 953-982, 1997
49. Stark, T. D. &Eid, H. T. Drained residual strength of cohesive soils. J. Geotech. Engng Div, ASCE 120, No. 5, 856-871, 1994
50. Teruo Nakai, Hajime Matsuoka, Naomi Okuno, et al. Ture triaxial tests on normally consolidated clay and analysis of the observed shear behavior using elastoplastic constitutive models. Soils and Foundations 26(4): 67-78, 1986
51. Ugai K. A method of calculation of total factor of safety of slopes by elaso-plastic. Soils and Foundations, 29(2): 190-195, 1989
52. Ugai K, Leshchinsky D. Three-dimensional limit equilibrium and finite elementanalysis: a comparison of results. Soils and Foundations, 35(4): 1-7, 1995
53. Vanapalli S K, Fredlund D G, Pufahl D E, et al. Model for the prediction of shear strength with respect to soil suction. Can. Geotech. J 33: 379-392, 1996
54. Sarma S K. Stability analysis of embankments and slopes. J. Geotech. Engng Div. ASCE, 105(12): 392-398, 1979
55. Rahardjo H, Fredlund D G. General Limit Equilibrium Method for Lateral Earth Force. Can. Geotech. J. 21: 166-175, 1984
56．邵龙潭，唐洪祥，韩国城．有限远边坡稳定分析方法及其应用。计算力学学报。Vol．18 No(1)：81-87，2001
57．沈珠江．饱和粘土抗剪强度的变化规律及其在土工建筑物稳定分析中的应用．土木工程学报，1963，9(2)：29～36
58．沈珠江．理论土力学．北京：中国水利水电出版社，2000b
59．宋二祥．土工结构安全系数的有限元计算．岩土工程学报，1997，19(2)：1～7
60. Taylor D W. Stability of earth slopes. J Boston Soc Civ Engrs,1937, 24(3): 197～246
61. Taylor D W. Fundamentals of soil mechanics. New York: John Wiley and Sons, 1948
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