考虑初始地应力条件的边坡稳定分析方法研究
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摘要
边坡中的初始地应力长期处于不受重视的地位,即使考虑初应力,也只是用重力场来代替。传统的极限平衡方法与新近流行的强度折减法都不能考虑初始地应力的作用。增量有限元虽然可以考虑初应力,但它一般给出的是极限载荷;即使它借用极限平衡的概念,能给出一个基于过载定义的安全系数,但这个定义的物理意义不明确。本文研究了两种数值计算方法,既能考虑地应力的影响,又能给出一个工程师关心的安全系数。
本文在工程地质概念和经验的基础上,明确提出研究初始地应力状态和边坡稳定性之间的关系,并且找到了有效的定量分析方法(而不仅仅是靠概念性的分析)对这一问题进行研究。
发展完善了边坡稳定极限分析的单元集成法,发现这种方法对于需要考虑一个分布场变量对边坡稳定性的影响时所具有的特殊优越性。采用单元集成法对膨胀土边坡的稳定性,以及不同水平构造应力条件下边坡的稳定性进行了分析,得出在考虑土体膨胀变形和水平构造应力条件下,边坡稳定安全系数会显著降低的结果。这与实际工程中遇到的情况相符,并且避免了以稳定结果凑强度参数的人为性。当考虑土体膨胀变形和水平构造应力条件时,按照相同优化条件得到的临界破坏模式由普通的深层滑动变成了在浅层出现的一个局部滑动,它会牵动其上部的土体也相继出现局部滑动,从而形成一个较长范围的浅层滑动。这与膨胀土滑坡时所具有的牵引性的特点以及高地应力区一些水电工程的坝基和坝址岸坡开挖后出现的浅层破坏现象(岩层鼓曲)正好是相符合的。
把弹性补偿法引入到岩土工程领域,并对其算法过程进行了改造,特别是弹性模量调整公式中名义应力与等效应力的确定。通过编写用户子程序,在ABAQUS中成功实现了弹性补偿法的计算过程。在弹性迭代的过程中,可以同时生成满足极限定理的静力场和机动场,从而求出相应的极限载荷(安全系数)。弹性补偿法可以方便地考虑初始地应力的影响。
通过本文的研究,给初始地应力影响的边坡提供了一种有效的评价方法。
Initial stresses do not receive their deserved consideration in slope stability analysis for a long time. Engineers are used to considering gravity field instead of initial stresses. Initial stresses can not be included in conventional Limit Equilibrium Method (LEM) and recently popular Strength Reduction Method. Although incremental Finite Element Method (FEM) can take initial stresses into account, it only gives a limit load, not a Factor of Safety (FOS). Combining FEM and LEM can give a FOS based on an overload concept, but this definition does not have a straightforward physical meaning. Based on the two numerical methods proposed in this dissertation, both initial stresses and FOS concerned by engineers can be considered.
With the help of the concept and experience of engineering geology, research on the relationship between initial stresses and slope stability is done, and an efficient quantitative method (not conceptual analysis only) is also found.
The Element Integration Method (EIM) for limit analysis of slope stability is perfected. When considering the influence of a distributed field on the slope stability, EIM has an outstanding advantage. After stability analysis of expansive slopes and slopes under different horizontal tectonic stresses, it is found that the FOS of slopes could decrease dramatically. This agrees with the factual things, and avoids the arbitrariness of inferring strength parameters by results. Taking expansive deformations and horizontal tectonic stresses into consideration, the critical collapse pattern from the same optimization transforms from ordinary deep slide to local shallow slide, which will induce the upside soil mass into another small range of shallow slide. As a result, a larger range of shallow slide comes into being. This agrees well with the traction character of expansive soil slope and the phenomenon of shallow collapse after the excavation of slopes in some hydraulic engineering with high initial stresses.
Elastic Compensation Method (ECM) is introduced to geotechnical area. The author modifies the formulation of ECM, particularly in the determination of nominal stress and equivalent stress. By virtue of compiling user subroutines, the procedures of ECM are realized successfully in ABAQUS. In the elastic iterations, statically admissible stress and kinematically admissible velocity can be derived in the same time. Thus limit load or FOS can be attained by limit theorem. ECM can take initial stresses into consideration easily.
The research of this dissertation provides an efficient appraisable method for slopes influenced by initial stresses.
本文在工程地质概念和经验的基础上,明确提出研究初始地应力状态和边坡稳定性之间的关系,并且找到了有效的定量分析方法(而不仅仅是靠概念性的分析)对这一问题进行研究。
发展完善了边坡稳定极限分析的单元集成法,发现这种方法对于需要考虑一个分布场变量对边坡稳定性的影响时所具有的特殊优越性。采用单元集成法对膨胀土边坡的稳定性,以及不同水平构造应力条件下边坡的稳定性进行了分析,得出在考虑土体膨胀变形和水平构造应力条件下,边坡稳定安全系数会显著降低的结果。这与实际工程中遇到的情况相符,并且避免了以稳定结果凑强度参数的人为性。当考虑土体膨胀变形和水平构造应力条件时,按照相同优化条件得到的临界破坏模式由普通的深层滑动变成了在浅层出现的一个局部滑动,它会牵动其上部的土体也相继出现局部滑动,从而形成一个较长范围的浅层滑动。这与膨胀土滑坡时所具有的牵引性的特点以及高地应力区一些水电工程的坝基和坝址岸坡开挖后出现的浅层破坏现象(岩层鼓曲)正好是相符合的。
把弹性补偿法引入到岩土工程领域,并对其算法过程进行了改造,特别是弹性模量调整公式中名义应力与等效应力的确定。通过编写用户子程序,在ABAQUS中成功实现了弹性补偿法的计算过程。在弹性迭代的过程中,可以同时生成满足极限定理的静力场和机动场,从而求出相应的极限载荷(安全系数)。弹性补偿法可以方便地考虑初始地应力的影响。
通过本文的研究,给初始地应力影响的边坡提供了一种有效的评价方法。
Initial stresses do not receive their deserved consideration in slope stability analysis for a long time. Engineers are used to considering gravity field instead of initial stresses. Initial stresses can not be included in conventional Limit Equilibrium Method (LEM) and recently popular Strength Reduction Method. Although incremental Finite Element Method (FEM) can take initial stresses into account, it only gives a limit load, not a Factor of Safety (FOS). Combining FEM and LEM can give a FOS based on an overload concept, but this definition does not have a straightforward physical meaning. Based on the two numerical methods proposed in this dissertation, both initial stresses and FOS concerned by engineers can be considered.
With the help of the concept and experience of engineering geology, research on the relationship between initial stresses and slope stability is done, and an efficient quantitative method (not conceptual analysis only) is also found.
The Element Integration Method (EIM) for limit analysis of slope stability is perfected. When considering the influence of a distributed field on the slope stability, EIM has an outstanding advantage. After stability analysis of expansive slopes and slopes under different horizontal tectonic stresses, it is found that the FOS of slopes could decrease dramatically. This agrees with the factual things, and avoids the arbitrariness of inferring strength parameters by results. Taking expansive deformations and horizontal tectonic stresses into consideration, the critical collapse pattern from the same optimization transforms from ordinary deep slide to local shallow slide, which will induce the upside soil mass into another small range of shallow slide. As a result, a larger range of shallow slide comes into being. This agrees well with the traction character of expansive soil slope and the phenomenon of shallow collapse after the excavation of slopes in some hydraulic engineering with high initial stresses.
Elastic Compensation Method (ECM) is introduced to geotechnical area. The author modifies the formulation of ECM, particularly in the determination of nominal stress and equivalent stress. By virtue of compiling user subroutines, the procedures of ECM are realized successfully in ABAQUS. In the elastic iterations, statically admissible stress and kinematically admissible velocity can be derived in the same time. Thus limit load or FOS can be attained by limit theorem. ECM can take initial stresses into consideration easily.
The research of this dissertation provides an efficient appraisable method for slopes influenced by initial stresses.
引文
[1]黄润秋.中国西南岩石高边坡的主要特征及其演化.地球科学进展, 2005, 20(3):292-297.
[2]黄润秋.岩石高边坡发育的动力过程及其稳定性控制.岩石力学与工程学报, 2008, 27(8):1525-1544.
[3]姚宝魁,孙玉科,刘竹华.考虑地应力作用的边坡滑动块体稳定分析.金属矿山, 1984, (4):16-20.
[4]邹成杰.边坡作用地应力与边坡稳定分析计算.人民珠江, 1994, (5):28-31.
[5] Clough R W, Woodward R J. Analysis of embankment stresses and deformations. Journal of the Soil Mechanics and Foundations Divsion, ASCE, 1967, 93(SM4):529-549.
[6] Duncan J M. State of the Art: Limit Equilibrium and Finite-Element Analysis of Slopes. Journal of geotechnical engineering, 1996, 122(7):577-596.
[7]沈珠江.从学步走向自立的岩土力学.岩土工程界, 2003, 6(12):15-17.
[8] Taylor G. A connexion between the criterion of yield and the strain ratio relationship in plastic solids. Proceedings of the Royal Society of London Series a-Mathematical and Physical Sciences, 1947, 191(1027):441-446.
[9] Lubliner J. Plasticity theory. New York Macmillan, 1990.
[10] Lubliner J. A maximum-dissipation principle in generalized plasticity. Acta Mechanica, 1984, 52(3-4):225-237.
[11] Drucker D C. Some implications of work hardening and ideal plasticity. Quarterly of Applied Mathematics, 1950, 7(4):411-418.
[12] Drucker D C. A more fundamental approach to plastic stress-strain relations. // Proceedings of the First US National Congress of Applied Mechanics. 1951:487-491.
[13] Hill R. Mathematical theory of plasticity. New York: Oxford University Press, 1950.
[14] Drucker D C, Greenberg H J, Prager W. Safety factor of an elastic-plastic body in plane strain. Journal of Applied Mechanics, 1951:371-378.
[15] Drucker D C. Limit analysis of two and three dimensional soil mechanics problems. Journal of Mechanics and Physics of Solids, 1953, 1(4):217-226.
[16] Drucker D C, Prager W. Soil mechanics and plastic analysis or limit design. Quarterly of Applied Mathematics, 1952, 10(2):157-165.
[17] Drucker D C, Prager W, Greenberg H J. Extended limit design theorems for continuous media. Quarterly of Applied Mathematics, 1952, 9(4):381-391.
[18] Koiter W T. General theorems of elastic-plastic solids. // Sneddon I N, Hill R. Progress in Solids Mechanics. Amsterdam: North-Holland Publishing Company, 1960:167-221.
[19] Chen W F. Limit analysis and soil plasticity. New York: Elsevier Scientific Pub. Co., 1975.
[20]钱令希,钟万勰.论固体力学中的极限分析并建议一个一般变分原理.力学学报, 1963, 6(4):287-303.
[21]钟万勰.极限分析中新的上、下限定理.力学学报, 1983, (4):341-351.
[22]钟万勰.极限分析中新的上、下限定理及其算法.计算结构力学及其应用, 1984, 1(1):21-27.
[23]高扬,黄克智.塑性极限分析的统一理论.力学学报, 1989, 21(3):306-315.
[24] Koopman D C A, Lance R H. On linear programming and plastic limit analysis. Journal of the Mechanics and Physics of Solids, 1965, 13(2):77-87.
[25] Lysmer J. Limit analysis of plane problems in soil mechanics. Journal of the Soil Mechanics and Foundations Divsion, 1970, 96(4):1311-1334.
[26] Anderheggen E, Knoepfel H. Finite element limit analysis using linear programming. International Journal of Solids and Structures, 1972, 8(12):1413-1431.
[27] Bottero A, Negre R, Pastor J, et al. Finite element method and limit analysis theory for soil mechanics problems. Computer Methods in Applied Mechanics and Engineering, 1980, 22(1):131-149.
[28] Sloan S W. Steepest edge active set algorithm for solving sparse linear programming problems. International Journal for Numerical Methods in Engineering, 1988, 26(12):2671-2685.
[29] Sloan S W. Lower bound limit analysis using finite elements and linear programming. International Journal for Numerical and Analytical Methods in Geomechanics, 1988, 12(1):61-77.
[30] Sloan S W. Upper bound limit analysis using finite elements and linear programming. International Journal for Numerical and Analytical Methods in Geomechanics, 1989, 13(3):263-282.
[31]刘应华.结构极限与安定分析的数值方法研究及其工程应用[博士学位论文].北京:清华大学, 1995.
[32]钱令希,王志必.结构极限分析和安定分析——温度参数法.计算结构力学及其应用, 1989, 6(1):113-121.
[33] Lyamin A V. Three-dimensional lower bound limit analysis using nonlinear programming [D]. 1999.
[34] Zouain N, Herskovits J, Borges L A, et al. Iterative algorithm for limit analysis with nonlinear yield functions. International Journal of Solids and Structures, 1993,30(10):1397-1417.
[35] Lyamin A V, Sloan S W. Lower bound limit analysis using non-linear programming. International Journal for Numerical Methods in Engineering, 2002, 55(5):573-611.
[36]王均星,李泽.基于非线性规划的有限元塑性极限分析下限法研究.岩土力学, 2008, 29(6):1471-1476.
[37] Krabbenhoft K, Damkilde L. A general non-linear optimization algorithm for lower bound limit analysis. International Journal for Numerical Methods in Engineering, 2003, 56(2):165-184.
[38] Makrodimopoulos A, Martin C M. Lower bound limit analysis of cohesive-frictional materials using second-order cone programming. International Journal for Numerical Methods in Engineering, 2006, 66(4):604-634.
[39] Ciria H, Peraire J, Bonet J. Mesh adaptive computation of upper and lower bounds in limit analysis. International Journal for Numerical Methods in Engineering, 2008, 75(8):899-944.
[40] Mu?oz J J, Bonet J, Huerta A, et al. Upper and lower bounds in limit analysis: Adaptive meshing strategies and discontinuous loading. International Journal for Numerical Methods in Engineering, 2009, 77(4):471-501.
[41]黄齐武.基于锥形规划理论的数值极限分析下限法及其应用[博士学位论文].上海:同济大学, 2007.
[42] Chen S, Liu Y, Cen Z. Lower-bound limit analysis by using the EFG method and non-linear programming. International Journal for Numerical Methods in Engineering, 2008, 74(3):391-415.
[43] Hayes D J, Marcal P V. Determination of upper bounds for problems in plane stress using finite element techniques. International Journal of Mechanical Sciences, 1967, 9(5):245-251.
[44] Turgeman S, Pastor J. Limit analysis: a linear formulation of the kinematic approach for axisymmetric mechanic problems. International Journal for Numerical and Analytical Methods in Geomechanics, 1982, 6(1):109-128.
[45] Jiang G-L. Regularized method in limit analysis. Journal of Engineering Mechanics, 1994, 120(6):1179-1197.
[46] Jiang G-L. Non-linear finite element formulation of kinematic limit analysis. International Journal for Numerical Methods in Engineering, 1995, 38(16):2775-2807.
[47] Yu H S, Sloan S W, Kleeman P W. A quadratic element for upper bound limit analysis. Engineering Computations, 1994, 11(3):195-212.
[48] Sloan S W, Kleeman P W. Upper bound limit analysis using discontinuous velocity-fields. Computer Methods in Applied Mechanics and Engineering, 1995, 127(1-4):293-314.
[49] Liu Y H, Cen Z Z, Xu B Y. A numerical method for plastic limit analysis of 3-D structures. International Journal of Solids and Structures, 1995, 32(12):1645-1658.
[50] Lyamin A V, Sloan S W. Upper bound limit analysis using linear finite elements and non-linear programming. International Journal for Numerical and Analytical Methods in Geomechanics, 2002, 26(2):181-216.
[51]杨小礼.线性与非线性破坏准则下岩土极限分析方法及其应用[博士学位论文].长沙:中南大学, 2002.
[52] Krabbenhoft K, Lyamin A V, Hjiaj M, et al. A new discontinuous upper bound limit analysis formulation. International Journal for Numerical Methods in Engineering, 2005, 63(7):1069-1088.
[53] Makrodimopoulos A, Martin C M. Upper bound limit analysis using simplex strain elements and second-order cone programming. International Journal for Numerical and Analytical Methods in Geomechanics, 2007, 31(6):835-865.
[54] Makrodimopoulos A, Martin C M. Upper bound limit analysis using discontinuous quadratic displacement fields. Communications in Numerical Methods in Engineering, 2008, 24(11):911-927.
[55] Martin C M, Makrodimopoulos A. Finite-element limit analysis of Mohr-Coulomb materials in 3D using semidefinite programming. Journal of Engineering Mechanics-Asce, 2008, 134(4):339-347.
[56] Krabbenhoft K, Lyamin A V, Sloan S W. Three-dimensional Mohr-Coulomb limit analysis using semidefinite programming. Communications in Numerical Methods in Engineering, 2008, 24(11):1107-1119.
[57] Chen J, Yin J-H, Lee C F. Upper bound limit analysis of slope stability using rigid finite elements and nonlinear programming. Canadian Geotechnical Journal, 2003, 40(4):742-752.
[58] Maier G, Munro J. Mathematical programming applications to engineering plastic analysis. Applied Mechanics Reviews, 1982, 35(12):1631-1643.
[59] Maier G, Smith D L. Update to mathematical programming applications to engineering plastic analysis. // Steele C R, Springer G S. Applied Mechanics Update. New York: ASME, 1986:377-383.
[60] Mackenzie D, Boyle J T, Hamilton R. The elastic compensation method for limit and shakedown analysis: a review. Journal of Strain Analysis, 2000, 35(3):171-188.
[61] Jones G L, Dhalla A K. Classification of clamp induced stresses in thin-walled pipe. Proceedings of the ASME Pressure Vessels and Piping Conference, 1981:17-23.
[62] Babu S, Iyer P K. Inelastic analysis of components using a modulus adjustment scheme. Journal of Pressure Vessel Technology, Transactions of the ASME, 1998, 120(1):1-5.
[63] Babu S, Iyer P K. A robust method for inelastic analysis of components made of anisotropic material. Journal of Pressure Vessel Technology, Transactions of the ASME, 1999, 121(2):154-159.
[64] Marriott D L. Evaluation of deformation or load control of stresses under inelastic conditions using elastic finite element stress analysis. // Proceedings of the ASME Pressure Vessels and Piping Conference. New York: ASME, 1988:3-9.
[65] Seshadri R. Generalized Local Stress Strain (GLOSS) analysis. Theory and applications. Journal of Pressure Vessel Technology, Transactions of the ASME, 1991, 113(2):219-227.
[66] Seshadri R, Marriott D L. On relating the reference stress, limit load and the ASME stress classification concepts. International Journal of Pressure Vessels and Piping, 1993, 56(3):387-408.
[67] Mangalaramanan S P. Conceptual models for understanding the role of the R-nodes in plastic collapse. Journal of Pressure Vessel Technology, 1997, 119(3):374-378.
[68] Seshadri R. Inelastic evaluation of mechanical and structural components using the generalized local stress strain method of analysis. Nuclear Engineering and Design, 1995, 153(2-3):287-303.
[69] Seshadri R. In search of redistribution nodes. International Journal of Pressure Vessels and Piping, 1997, 73(1):69-76.
[70] Seshadri R, Mangalaramanan S P. Lower bound limit loads using variational concepts: the mα-method. International Journal of Pressure Vessels and Piping, 1997, 71(2):93-106.
[71] Seshadri R. Limit loads using extended variational concepts in plasticity. Journal of Pressure Vessel Technology, Transactions of the ASME, 2000, 122(3):379-385.
[72] Pan L, Seshadri R. Limit load estimation using plastic flow parameter in repeated elastic finite element analyses. Journal of Pressure Vessel Technology, 2002, 124(4):433-439.
[73] Pan L, Seshadri R. Limit loads for layered structures using extended variational principles and repeated elastic finite element analysis. Journal of Pressure Vessel Technology, 2002, 124(4):425-432.
[74] Reinhardt W D, Seshadri R. Limit load bounds for the mαmultiplier. Journal of Pressure Vessel Technology, 2003, 125(1):11-18.
[75] Adibi-Asl R, Seshadri R. Local limit-load analysis using the m-beta method. Journal of Pressure Vessel Technology, 2007, 129(2):296-305.
[76] Indermohan H, Reinhardt W D, Seshadri R. Limit load of anisotropic components using the M-beta multiplier method. Journal of Pressure Vessel Technology, Transactions of the ASME, 2004, 126(4):455-460.
[77] Seshadri R, Indermohan H. Lower bound limit load determination: The m-beta multiplier method. Journal of Pressure Vessel Technology, 2004, 126(2):237-240.
[78] Mangalaramanan S P, Seshadri R. Robust limit loads of symmetric and non-symmetric plate structures. Transactions of the Canadian Society for Mechanical Engineering, 1995, 19(3):227-246.
[79] Fernando C P D, Seshadri R. Limit loads of framed structures and arches using the GLOSS r-node method. Transactions of the Canadian Society for Mechanical Engineering, 1993, 17(2):197-214.
[80] Mangalaramanan S P, Seshadri R. Limit loads of layered beams and layered cylindrical shells using the r-node method. // Proceedings of the 1997 ASME Pressure Vessels and Piping Conference. New York: ASME, 1997:201-215.
[81] Fanous L F Z, Adibi-Asl R, Seshadri R. Limit load analysis of pipe bend using the r-node method. Journal of Pressure Vessel Technology, 2005, 127(4):443-448.
[82] Mangalaramanan S P, Seshadri R, Reinhardt W. Limit loads of orthotropic structures using the R-node method. // Fracture, Design Analysis of Pressure Vessels, Heat Exchangers, Piping Components, and Fitness for Service. New York: ASME, 1999:241-249.
[83] Mangalaramanan S P, Seshadri R. Minimum weight design of pressure components using r-nodes. Journal of Pressure Vessel Technology, 1997, 119(2):224-231.
[84] Reinhardt W D, Mangalaramanan S P. Efficient tubesheet design using repeated elastic limit analysis technique. // Computer Technology (The ASME Pressure Vessels and Piping Conference). New York: ASME, 1999:141-149.
[85] Fanous I F Z, Seshadri R. Stress classification using the r-node method. Journal of Pressure Vessel Technology, Transactions of the ASME, 2007, 129(4):676-682.
[86] Seshadri R. Simplified methods in plasticity creep and fracture - some recent developments. Transactions of the Canadian Society for Mechanical Engineering, 1998, 22(4 B):419-433.
[87]王勖成,童瑞成.确定结构极限载荷的有限元简化算法.机械强度, 1997, 19(2):5-10.
[88] Mackenzie D, Boyle J T. Method of estimating limit loads by iterative elastic analysis. I - simple examples. International Journal of Pressure Vessels and Piping, 1993, 53(1):77-95.
[89] Nadarajah C, Mackenzie D, Boyle J T. Method of estimating limit loads by iterative elastic analysis. II - nozzle sphere intersections with internal pressure and radial load. International Journal of Pressure Vessels and Piping, 1993, 53(1):97-119.
[90] Shi J, Mackenzie D, Boyle J T. Method of estimating limit loads by iterative elastic analysis. III - torispherical heads under internal pressure. International Journal of Pressure Vessels and Piping, 1993, 53(1):121-142.
[91] Mackenzie D, Shi J, Boyle J T. Finite element modelling for limit analysis by the elastic compensation method. Computers and Structures, 1994, 51(4):403-410.
[92] Desquines J, Plancq D, Wielgosz C. In-plane limit moment for an elbow. Lower-boundanalytical solution and finite element processing by elastic compensation method. International Journal of Pressure Vessels and Piping, 1997, 71(1):29-34.
[93] Plancq D, Berton M N. Limit analysis based on elastic compensation method of branch pipe tee connection under internal pressure and out-of-plane moment loading. International Journal of Pressure Vessels and Piping, 1998, 75(11):819-825.
[94] Mangalaramanan P, Reinhardt W. On relating redistributed elastic and inelastic stress fields. International Journal of Pressure Vessels and Piping, 2001, 78(4):283-293.
[95] Mohamed A I, Megahed M M, Bayoumi L S, et al. Applications of iterative elastic techniques for elastic-plastic analysis of pressure vessels. Journal of Pressure Vessel Technology, 1999, 121(1):24-29.
[96]王飞,陈钢,刘应华,等.极限分析的弹性补偿法及其应用.应用力学学报, 2004, 21(4):147-150.
[97]王飞,陈钢,刘应华,等.内压下含局部减薄缺陷三通的极限分析.清华大学学报(自然科学版), 2004, 44(11):1517-1519.
[98] Marin-Artieda C C, Dargush G F. Approximate limit load evaluation of structural frames using linear elastic analysis. Engineering Structures, 2007, 29(3):296-304.
[99] Yang P, Liu Y, Ohtake Y, et al. Limit analysis based on a modified elastic compensation method for nozzle-to-cylinder junctions. International Journal of Pressure Vessels and Piping, 2005, 82(10):770-776.
[100]杨璞,刘应华,袁鸿雁,等.计算结构极限载荷的修正弹性补偿法.工程力学, 2006, 23(3):21-26.
[101]陈立杰,刘应华,杨璞,等.复杂结构塑性极限分析的修正弹性补偿法.机械工程学报, 2007, 43(05):187-193.
[102] Chen L, Liu Y, Yang P, et al. Limit analysis of structures containing flaws based on a modified elastic compensation method. European Journal of Mechanics a-Solids, 2008, 27(2):195-209.
[103] Desikan V, Sethuraman R. Analysis of material nonlinear problems using pseudo-elastic finite element method. Journal of Pressure Vessel Technology-Transactions of the Asme, 2000, 122(4):457-461.
[104] Upadrasta A, Peddieson J, Buchanan G R. Elastic compensation simulation of elastic/plastic axisymmetric circular plate bending using a deformation model. International Journal of Non-Linear Mechanics, 2006, 41(3):377-387.
[105] Shi J, Boyle J T, Mackenzie D, et al. Approximate limit design of frames using elastic analysis. Computers and Structures, 1996, 61(3):495-501.
[106] Boyle J T, Hamilton R, Shi J, et al. Simple method of calculating lower-bound limit loads for axisymmetric thin shells. Journal of Pressure Vessel Technology, 1997,119(2):236-242.
[107] Hamilton R, Boyle J T. Approximate calculation of upper bound limit loads for axisymmetric thin shells. // Proceedings of the 1998 ASME/JSME Joint Pressure Vessels and Piping Conference. New York: ASME, 1998:147-151.
[108] Hamilton R, Mackenzie D, Shi J, et al. Simplified lower bound limit analysis of pressurised cylinder/cylinder intersections using generalised yield criteria. International Journal of Pressure Vessels and Piping, 1996, 67(2):219-226.
[109] Hamilton R, Boyle J T. Simplified lower bound limit analysis of transversely loaded thin plates using generalised yield criteria. Thin-Walled Structures, 2002, 40(6):503-522.
[110] Adibi-Asl R, Fanous I F Z, Seshadri R. Elastic modulus adjustment procedures - Improved convergence schemes. International Journal of Pressure Vessels and Piping, 2006, 83(2):154-160.
[111] Martin J B. Plasticity : fundamentals and general results. The MIT Press, 1975.
[112] Gokhfeld D A, Cherniavsky O F. Limit analysis of structures at thermal cycling. Sijthoff and Noordhoff, 1980.
[113] Nadarajah C, Mackenzie D, Boyle J T. Limit and shakedown analysis of nozzle/cylinder intersections under internal pressure and in-plane moment loading. International Journal of Pressure Vessels and Piping, 1996, 68(3):261-272.
[114] Hamilton R, Boyle J T, Shi J, et al. Simple upper-bound method for calculating approximate shakedown loads. Journal of Pressure Vessel Technology, 1998, 120(2):195-199.
[115] Hardy S J, Gowhari-Anaraki A R, Pipelzadeh M K. Upper and lower bound limit and shakedown loads for hollow tubes with axisymmetric internal projections under axial loading. Journal of Strain Analysis for Engineering Design, 2001, 36(6):595-604.
[116] Fellenius W. Calculation of the stability of earth dams. // Transactions of the 2nd International Congress on Large Dams. Washington,D.C., 1937.
[117] Bishop A W. The use of the slip circle in the stability analysis of slopes. Geotechnique, 1955, 5(1):7-17.
[118] Janbu N. Application of composite slip surfaces for stability analysis. // Proceedings of the European Conference on Stability of Earth Slope. Stockholm, 1954:43-49.
[119] Janbu N. Stability analysis of slopes with dimensionless parameters // Harvard Soil Mechanics Series No46. 1954.
[120] Janbu N. Soil stability computations. // Embankment Dam Engineering. New York: Wiley, 1973:47-87.
[121] Spencer E. A method of analysis of stability of embankments assuming parallel inter-slice forces. Geotechnique, 1967, 17(1):11-26.
[122] Spencer E. Thrust line criterion in embankment stability analysis. Geotechnique, 1973, 23(1):85-100.
[123] Morgenstern N R, Price V E. Analysis of stability of general slip surfaces. Geotechnique, 1965, 15(1):79-93.
[124] Sarma S K. Stability analysis of embankments and slopes. Geotechnique, 1973, 23(3):423-433.
[125] Chen Z Y, Morgenstern N R. Extensions to the generalized method of slices for stability analysis. Canadian Geotechnical Journal, 1983, 20(1):104-119.
[126]陈祖煜.土质边坡稳定分析:原理·方法·程序北京:中国水利水电出版社, 2003.
[127] Fredlund D G, Krahn J. Comparison of slope stability methods of analysis. Canadian Geotechnical Journal, 1977, 14(3):429-439.
[128] Fredlund D G, Krahn J, Pufahl D E. The relationship between limit equilibrium slope stability methods. // Proceedings of the 10th ICSMFE. 1981:409-416.
[129] Chugh A K. Variable interslice force inclination in slope stability analysis. Soils and Foundations, 1986, 26(1):115-121.
[130] Espinoza R D, Bourdeau P L, Muhunthan B. Unified formulation for analysis of slopes with general slip surface. Journal of geotechnical engineering, 1994, 120(7):1185-1203.
[131] Zhu D Y, Lee C F, Jiang H D. Generalised framework of limit equilibrium methods for slope stability analysis. Geotechnique, 2003, 53(4):377-395.
[132] Cheng Y M, Zhu L J. Unified formulation for two dimensional slope stability analysis and limitations in factor of safety determination. Soils and Foundations, 2004, 44(6):121-127.
[133] Wright S G, Kulhawy F H, Duncan J M. Accuracy of equilibrium slope stability analysis. American Society of Civil Engineers, Journal of the Soil Mechanics and Foundations Division, 1973, 99(SM10):783-779.
[134] Fredlund D G. Analytical method of slope stability analysis // Proceedings of the 4th International Symposium on Landslides 1984:229-250
[135] Duncan J M, Wright S G. The accuracy of equilibrium methods of slope stability analysis. Engineering Geology, 1980, 16(1-2):5-17.
[136]朱大勇,邓建辉,台佳佳.简化Bishop法严格性的论证.岩石力学与工程学报, 2007, 26(3):455-458.
[137] Abramson L W, Lee T S, Sharma S, et al. Slope stability and stabilization methods. 2ed. New York: John Wiley & Sons, 2002.
[138] Krahn J. The 2001 R.M. Hardy Lecture: The limits of limit equilibrium analyses. Canadian Geotechnical Journal, 2003, 40(3):643-660.
[139] Michalowski R L. Slope stability analysis: a kinematical approach. Geotechnique, 1995,45(2):283-293.
[140] Donald I B, Chen Z. Slope stability analysis by the upper bound approach: fundamentals and methods. Canadian Geotechnical Journal, 1997, 34(6):853-862.
[141]徐千军,李明元,陆杨.边坡稳定极限分析的单元集成法.岩土力学, 2006, 27(7):1028-1032.
[142] Yu H S, Salgado R, Sloan S W, et al. Limit analysis versus limit equilibrium for slope stability. Journal of Geotechnical and Geoenvironmental Engineering, 1998, 124(1):1-11.
[143] Kim J, Salgado R, Yu H S. Limit analysis of soil slopes subjected to pore-water pressures. Journal of Geotechnical and Geoenvironmental Engineering, 1999, 125(1):49-58.
[144] Kim J. Limit analysis of soil slope stability using finite elements and linear programming [D]. Purdue University, 1998.
[145] Kim J, Salgado R, Lee J. Stability analysis of complex soil slopes using limit analysis. Journal of Geotechnical and Geoenvironmental Engineering, 2002, 128(7):546-557.
[146] Michalowski R L. Three-dimensional analysis of locally loaded slopes. Geotechnique, 1989, 39(1):27-38.
[147] Zienkiewicz O C, Humpheson C, Lewis R W. Associated and non-associated visco-plasticity and plasticity in soil mechanics. Geotechnique, 1975, 25(4):671-689.
[148] Matsui T, San K-C. Finite element slope stability analysis by shear strength reduction technique. Soils and Foundations, 1992, 32(1):59-70.
[149] Ugai K, Leshchinsky D. Three-dimensional limit equilibrium and finite element analyses: A comparison of results. Soils and Foundations, 1995, 35(4):1-7.
[150]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.
[151] Griffiths D V, Lane P A. Slope stability analysis by finite elements. Geotechnique, 1999, 49(3):387-403.
[152] Dawson E M, Roth W H, Drescher A. Slope stability analysis by strength reduction. Geotechnique, 1999, 49(6):835-840.
[153] Dawson E, Motamed F, Nesarajah S, et al. Geotechnical stability analysis by strength reduction. // Proceedings of Sessions of Geo-Denver 2000 - Slope Stability 2000. American Society of Civil Engineers, 2000:99-113.
[154]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, 2001, 23(4):407-411.
[155]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, 2002, (1):7-9.
[156]张鲁渝,时卫民,郑颖人.平面应变条件下土坡稳定有限元分析.岩土工程学报, 2002, 24(4):487-490.
[157]赵尚毅,郑颖人,时卫民,等.用有限元强度折减法求边坡稳定安全系数.岩土工程学报, 2002, 2002(5):343-346.
[158]郑颖人,赵尚毅.有限元强度折减法在土坡与岩坡中的应用.岩石力学与工程学报, 2004, 23(19):3381-3388.
[159]郑颖人,赵尚毅,张鲁渝.用有限元强度折减法进行边坡稳定分析.中国工程科学, 2002, 4(10):57-61.
[160]郑颖人,赵尚毅,孔位学,等.极限分析有限元法讲座——Ⅰ岩土工程极限分析有限元法.岩土力学, 26(1):163-168.
[161]郑宏,李春光,李焯芬,等.求解安全系数的有限元法.岩土工程学报, 2002, 24(5):626-628.
[162] Zheng H, Liu D F, Li C G. Slope stability analysis based on elasto-plastic finite element method. International Journal for Numerical Methods in Engineering, 2005, 64(14):1871-1888.
[163]宋二祥,高翔,邱玥.基坑土钉支护安全系数的强度参数折减有限元方法.岩土工程学报, 2005, 27(3):258-263.
[164] Xu Q J, Yin H L, Cao X F, et al. A temperature-driven strength reduction method for slope stability analysis. Mechanics Research Communications, 2009, 36(2):224-231.
[165] Kulhawy F H. Finite element analysis of the behavior of embankments [D]. University of California, 1969.
[166] Resendiz D. Discussion of 'Accuracy equilibrium slope stability analysis'. Journal of the Soil Mechanics and Foundations Divsion, 1974, 100(GT8):967-970.
[167] Adikari G S N, Cummins P J. An effective stress slope stability analysis method for dams. // Proceedings of the 11th International Conference on Soil Mechanics and Foundation Engineering. San Francisco, 1985:713-718.
[168] Naylor D J. Finite elements and slope stability. // Martins J B. Numerical Methods in Geomechanics:Proceedings of the NATO Advanced Study Institute. Dordrecht: D.Reidel Publishing Company, 1982:229-244.
[169] Farias M M, Naylor D J. Safety analysis using finite elements. Computers and Geotechnics, 1998, 22(2):165-181.
[170] Fredlund D G, Scoular R E G. Using limit equilibrium concepts in finite element slope stability analysis. // Yagi N, Yamagami T, Jiang J-C. Slope Stability engineering:Proceedings of the International Symposium on Slope Stability Engineering-IS-Shikoku'99. Rotterdam: Balkema, 1999:31-47.
[171] Pham H T V, Fredlund D G. The application of dynamic programming to slope stability analysis. Canadian Geotechnical Journal, 2003, 40(4):830-847.
[172]邓俊晔.边坡极限平衡有限元稳定分析的Dijkstra算法的理论及应用[硕士学位论文].南京:河海大学, 2006.
[173]徐卫亚,周家文,邓俊晔,等.基于Dijkstra算法的边坡极限平衡有限元分析.岩土工程学报, 2007, 29(8):1159-1172.
[174] Loehr J E. Development of a hybrid limit equilibrium-finite element procedure for three-dimensional slope stability analysis [D]. The University of Texas at Austin, 1998.
[175] Taylor D W. Stability of earth slopes. Boston Society of Civil Engineers, 1937, 24(3):197-246.
[176] Taylor D W. Fundamentals of soil mechanics. New York: Wiley, 1948.
[177] Gitirana Jr. G F N. Weather-related geo-hazard assessment model for railway embankment stability [D]. University of Saskatchewan, 2005.
[178] Chowdhury R N. Slope analysis. Amsterdam: Elsevier Scientific Publishing Company, 1978.
[179] Huang Y H. Stability analysis of earth slopes. New York: Van Nostrand Reinhold, 1983.
[180]郑宏,田斌,刘德富,等.关于有限元边坡稳定性分析中安全系数的定义问题.岩石力学与工程学报, 2005, 24(13):2225-2230.
[181]卓家寿.关于岩体稳定性问题的一点注记.河海大学学报, 2001, 29(增刊):1-5.
[182]邵国建,卓家寿,章青.岩体稳定性分析与评判准则研究.岩石力学与工程学报, 2003, 22(5):691-696.
[183]沈珠江.当前土力学研究中的几个问题.岩土工程学报, 1986, 8(5):1-8.
[184]丰定祥,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, 1990, 12(3):1-9.
[185]刘艳章,葛修润,李春光,等.基于矢量法安全系数的边坡与坝基稳定分析.岩石力学与工程学报, 2007, 26(10):2130-2140.
[186]邵龙潭,唐洪祥,韩国城.有限元边坡稳定分析方法及其应用.计算力学学报, 2001, 18(1):81-87.
[187]赵杰.边坡稳定有限元分析方法中若干应用问题研究[博士学位论文].大连:大连理工大学, 2006.
[188]赵杰,邵龙潭.平面应变条件下两类有限元边坡稳定分析方法比较研究.大连理工大学学报, 2007, 47(6):873-879.
[189]郑颖人,赵尚毅.边(滑)坡工程设计中安全系数的讨论.岩石力学与工程学报, 2006, 25(9):1937-1940.
[190] Janbu N. Earth pressure and bearing capacity calculations by generalized procedure of slices. // Proceedings of the 4th International Conference on Soil Mechanics and Foundation Engineering. 1957:207-212.
[191] Chugh A K. Variable factor of safety in slope stability analysis. Geotechnique, 1986, 36(1):57-64.
[192] Chugh A K. Variable factor of safety in slope stability analysis by limit equilibrium method. Journal of the Institution of Engineers (India): Civil Engineering Division, 1988, 69:149-155.
[193]卓家寿,邵国建,陈振雷.工程稳定问题中确定滑坍面、滑向与安全度的干扰能量法.水利学报, 1997, (8):80-84.
[194] Chen W F, Snitbhan N. On slip surface and slope stability analysis. Soils and Foundations, 1975, 15(3):41-49
[195] Chen Z, Wang X, Haberfield C, et al. A three-dimensional slope stability analysis method using the upper bound theorem Part I: Theory and methods. International Journal of Rock Mechanics and Mining Sciences, 2001, 38(3):369-378.
[196] Askari F, Farzaneh O. Upper-bound solution for seismic bearing capacity of shallow foundations near slopes. Geotechnique, 2003, 53(8):697-702.
[197] Farzaneh O, Askari F. Three-dimensional analysis of nonhomogeneous slopes. Journal of Geotechnical and Geoenvironmental Engineering, 2003, 129(2):137-145.
[198] Jiang G L, Magnan J P. Stability analysis of embankments: comparison of limit analysis with methods of slices. Geotechnique, 1997, 47(4):857-872.
[199] Chen W F, Liu X L. Limit analysis in soil mechanics. Elsevier Science: Amsterdam, 1990.
[200]殷建华,陈健,李焯芬.岩土边坡稳定性的刚体有限元上限分析.岩石力学与工程学报, 2004, 23(6):898-905.
[201] 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. Journal of Engineering Mechanics, 2004, 130(8):886-893.
[202]包承纲.非饱和土的性状及膨胀土边坡稳定问题.岩土工程学报, 2004, 26(1):1-15.
[203]孙小明,武雄,何满潮,等.强膨胀性软岩的判别与分级标准.岩石力学与工程学报, 2005, 24(1):128-132.
[204]殷宗泽,吕擎峰,袁俊平.膨胀土边坡的稳定性分析. //郑健龙.膨胀土处治理论、技术与实践.北京:人民交通出版社, 2004:61-69.
[205]尹宏磊,徐千军,李仲奎.膨胀变形对膨胀土边坡稳定性的影响.岩土力学, 2009, 30(8).
[206]陆杨,徐千军.交变载荷作用下边坡的安定性分析.岩土力学, 2004, 25(11):1693-1697.
[207]徐千军,陆杨.干湿交替对边坡长期安全性的影响.地下空间与工程学报, 2005, 1(7):1021-1024.
[208]尹宏磊,徐千军,李仲奎.抗剪强度随干湿循环变化对边坡安定性的影响.水利学报, 2008, 39(5):568-572.
[209]陈祖煜.土力学经典问题的极限分析上、下限解.岩土工程学报, 2002, 24(1):1-11.
[210] Chen Z Y. The limit analysis in soil and rock: a mature discipline of geomechanics. Journal of Zhejiang University, 2007, (11):1712-1724.
[211] Berak E G, Gerdeen J C. A Finite Element Technique for Limit Analysis of Structures. Journal of Pressure Vessel Technology, 1990, 112(2):138-144.
[212] Ponter A R S, Chen H F, Boulbibane M, et al. The linear matching method for the evaluation of limit loads, shakedown limits and related problems. // Mang H A, Rammerstorfer F G, Eberhardsteiner J. Proceedings of the Fifth World Congress on Computational Mechanics. Vienna, 2002.
[213] Ponter A R S, Engelhardt M. Shakedown limits for a general yield condition: implementation and application for a Von Mises yield condition. European Journal of Mechanics a-Solids, 2000, 19(3):423-445.
[214] Ponter A R S, Fuschi P, Engelhardt M. Limit analysis for a general class of yield conditions. European Journal of Mechanics a-Solids, 2000, 19(3):401-421.
[215] Boulbibane M, Ponter A R S. Linear matching method for limit load problems using the Drucker-Prager yield condition. Geotechnique, 2005, 55(10):731-739.
[216] Boulbibane M, Ponter A R S. Extension of the linear matching method to geotechnical problems. Computer Methods in Applied Mechanics and Engineering, 2005, 194(45-47):4633-4650.
[217] Boulbibane M, Ponter A R S. The linear matching method for the shakedown analysis of geotechnical problems. International Journal for Numerical and Analytical Methods in Geomechanics, 2006, 30(2):157-179.
[218] Chen H F, Ponter A R S. Shakedown and limit analyses for 3-D structures using the linear matching method. International Journal of Pressure Vessels and Piping, 2001, 78(6):443-451.
[219] Chen H F, Ponter A R S. Integrity assessment of a 3D tubeplate using the linear matching method. Part 1. Shakedown, reverse plasticity and ratchetting. International Journal of Pressure Vessels and Piping, 2005, 82(2):85-94.
[220] Chen H F, Ponter A R S, Ainsworth R A. The linear matching method applied to the high temperature life integrity of structures. Part 2. Assessments beyond shakedown involving changing residual stress fields. International Journal of Pressure Vessels and Piping, 2006, 83(2):136-147.
[221] Chen H F, Ponter A R S, Ainsworth R A. The linear matching method applied to the high temperature life integrity of structures. Part 1. Assessments involving constant residual stress fields. International Journal of Pressure Vessels and Piping, 2006, 83(2):123-135.
[222] Chen H F, Ponter A R S. Integrity assessment of a 3D tubeplate using the linear matchingmethod. Part 2: Creep relaxation and reverse plasticity. International Journal of Pressure Vessels and Piping, 2005, 82(2):95-104.
[223] Chen H, Ponter A R S. Linear matching method on the evaluation of plastic and creep behaviours for bodies subjected to cyclic thermal and mechanical loading. International Journal for Numerical Methods in Engineering, 2006, 68(1):13-32.
[224] Chen H F, Engelhardt M J, Ponter A R S. Linear matching method for creep rupture assessment. International Journal of Pressure Vessels and Piping, 2003, 80(4):213-220.
[225]余同希.塑性力学.北京:高等教育出版社, 1989.
[226]陈钢,刘应华.结构塑性极限与安定分析理论及工程方法.北京:科学出版社, 2006.
[227] Ponter A R S, Carter K F. Limit state solutions, based upon linear elastic solutions with a spatially varying elastic modulus. Computer Methods in Applied Mechanics and Engineering, 1997, 140(3-4):237-258.
[228]王仁,黄文彬,黄筑平.塑性力学引论.北京:北京大学出版社, 1992.
[229] Mackenzie D, Nadarajah C, Shi J, et al. Simple bounds on limit loads by elastic finite element analysis. Journal of Pressure Vessel Technology, Transactions of the ASME, 1993, 115(1):27-31.
[230] Hibbitt K S, Inc. ABAQUS Analysis User's Manual (version 6.5), 2004.
[231]黄正中.高等数学. 2版.北京:人民教育出版社, 1978.
[2]黄润秋.岩石高边坡发育的动力过程及其稳定性控制.岩石力学与工程学报, 2008, 27(8):1525-1544.
[3]姚宝魁,孙玉科,刘竹华.考虑地应力作用的边坡滑动块体稳定分析.金属矿山, 1984, (4):16-20.
[4]邹成杰.边坡作用地应力与边坡稳定分析计算.人民珠江, 1994, (5):28-31.
[5] Clough R W, Woodward R J. Analysis of embankment stresses and deformations. Journal of the Soil Mechanics and Foundations Divsion, ASCE, 1967, 93(SM4):529-549.
[6] Duncan J M. State of the Art: Limit Equilibrium and Finite-Element Analysis of Slopes. Journal of geotechnical engineering, 1996, 122(7):577-596.
[7]沈珠江.从学步走向自立的岩土力学.岩土工程界, 2003, 6(12):15-17.
[8] Taylor G. A connexion between the criterion of yield and the strain ratio relationship in plastic solids. Proceedings of the Royal Society of London Series a-Mathematical and Physical Sciences, 1947, 191(1027):441-446.
[9] Lubliner J. Plasticity theory. New York Macmillan, 1990.
[10] Lubliner J. A maximum-dissipation principle in generalized plasticity. Acta Mechanica, 1984, 52(3-4):225-237.
[11] Drucker D C. Some implications of work hardening and ideal plasticity. Quarterly of Applied Mathematics, 1950, 7(4):411-418.
[12] Drucker D C. A more fundamental approach to plastic stress-strain relations. // Proceedings of the First US National Congress of Applied Mechanics. 1951:487-491.
[13] Hill R. Mathematical theory of plasticity. New York: Oxford University Press, 1950.
[14] Drucker D C, Greenberg H J, Prager W. Safety factor of an elastic-plastic body in plane strain. Journal of Applied Mechanics, 1951:371-378.
[15] Drucker D C. Limit analysis of two and three dimensional soil mechanics problems. Journal of Mechanics and Physics of Solids, 1953, 1(4):217-226.
[16] Drucker D C, Prager W. Soil mechanics and plastic analysis or limit design. Quarterly of Applied Mathematics, 1952, 10(2):157-165.
[17] Drucker D C, Prager W, Greenberg H J. Extended limit design theorems for continuous media. Quarterly of Applied Mathematics, 1952, 9(4):381-391.
[18] Koiter W T. General theorems of elastic-plastic solids. // Sneddon I N, Hill R. Progress in Solids Mechanics. Amsterdam: North-Holland Publishing Company, 1960:167-221.
[19] Chen W F. Limit analysis and soil plasticity. New York: Elsevier Scientific Pub. Co., 1975.
[20]钱令希,钟万勰.论固体力学中的极限分析并建议一个一般变分原理.力学学报, 1963, 6(4):287-303.
[21]钟万勰.极限分析中新的上、下限定理.力学学报, 1983, (4):341-351.
[22]钟万勰.极限分析中新的上、下限定理及其算法.计算结构力学及其应用, 1984, 1(1):21-27.
[23]高扬,黄克智.塑性极限分析的统一理论.力学学报, 1989, 21(3):306-315.
[24] Koopman D C A, Lance R H. On linear programming and plastic limit analysis. Journal of the Mechanics and Physics of Solids, 1965, 13(2):77-87.
[25] Lysmer J. Limit analysis of plane problems in soil mechanics. Journal of the Soil Mechanics and Foundations Divsion, 1970, 96(4):1311-1334.
[26] Anderheggen E, Knoepfel H. Finite element limit analysis using linear programming. International Journal of Solids and Structures, 1972, 8(12):1413-1431.
[27] Bottero A, Negre R, Pastor J, et al. Finite element method and limit analysis theory for soil mechanics problems. Computer Methods in Applied Mechanics and Engineering, 1980, 22(1):131-149.
[28] Sloan S W. Steepest edge active set algorithm for solving sparse linear programming problems. International Journal for Numerical Methods in Engineering, 1988, 26(12):2671-2685.
[29] Sloan S W. Lower bound limit analysis using finite elements and linear programming. International Journal for Numerical and Analytical Methods in Geomechanics, 1988, 12(1):61-77.
[30] Sloan S W. Upper bound limit analysis using finite elements and linear programming. International Journal for Numerical and Analytical Methods in Geomechanics, 1989, 13(3):263-282.
[31]刘应华.结构极限与安定分析的数值方法研究及其工程应用[博士学位论文].北京:清华大学, 1995.
[32]钱令希,王志必.结构极限分析和安定分析——温度参数法.计算结构力学及其应用, 1989, 6(1):113-121.
[33] Lyamin A V. Three-dimensional lower bound limit analysis using nonlinear programming [D]. 1999.
[34] Zouain N, Herskovits J, Borges L A, et al. Iterative algorithm for limit analysis with nonlinear yield functions. International Journal of Solids and Structures, 1993,30(10):1397-1417.
[35] Lyamin A V, Sloan S W. Lower bound limit analysis using non-linear programming. International Journal for Numerical Methods in Engineering, 2002, 55(5):573-611.
[36]王均星,李泽.基于非线性规划的有限元塑性极限分析下限法研究.岩土力学, 2008, 29(6):1471-1476.
[37] Krabbenhoft K, Damkilde L. A general non-linear optimization algorithm for lower bound limit analysis. International Journal for Numerical Methods in Engineering, 2003, 56(2):165-184.
[38] Makrodimopoulos A, Martin C M. Lower bound limit analysis of cohesive-frictional materials using second-order cone programming. International Journal for Numerical Methods in Engineering, 2006, 66(4):604-634.
[39] Ciria H, Peraire J, Bonet J. Mesh adaptive computation of upper and lower bounds in limit analysis. International Journal for Numerical Methods in Engineering, 2008, 75(8):899-944.
[40] Mu?oz J J, Bonet J, Huerta A, et al. Upper and lower bounds in limit analysis: Adaptive meshing strategies and discontinuous loading. International Journal for Numerical Methods in Engineering, 2009, 77(4):471-501.
[41]黄齐武.基于锥形规划理论的数值极限分析下限法及其应用[博士学位论文].上海:同济大学, 2007.
[42] Chen S, Liu Y, Cen Z. Lower-bound limit analysis by using the EFG method and non-linear programming. International Journal for Numerical Methods in Engineering, 2008, 74(3):391-415.
[43] Hayes D J, Marcal P V. Determination of upper bounds for problems in plane stress using finite element techniques. International Journal of Mechanical Sciences, 1967, 9(5):245-251.
[44] Turgeman S, Pastor J. Limit analysis: a linear formulation of the kinematic approach for axisymmetric mechanic problems. International Journal for Numerical and Analytical Methods in Geomechanics, 1982, 6(1):109-128.
[45] Jiang G-L. Regularized method in limit analysis. Journal of Engineering Mechanics, 1994, 120(6):1179-1197.
[46] Jiang G-L. Non-linear finite element formulation of kinematic limit analysis. International Journal for Numerical Methods in Engineering, 1995, 38(16):2775-2807.
[47] Yu H S, Sloan S W, Kleeman P W. A quadratic element for upper bound limit analysis. Engineering Computations, 1994, 11(3):195-212.
[48] Sloan S W, Kleeman P W. Upper bound limit analysis using discontinuous velocity-fields. Computer Methods in Applied Mechanics and Engineering, 1995, 127(1-4):293-314.
[49] Liu Y H, Cen Z Z, Xu B Y. A numerical method for plastic limit analysis of 3-D structures. International Journal of Solids and Structures, 1995, 32(12):1645-1658.
[50] Lyamin A V, Sloan S W. Upper bound limit analysis using linear finite elements and non-linear programming. International Journal for Numerical and Analytical Methods in Geomechanics, 2002, 26(2):181-216.
[51]杨小礼.线性与非线性破坏准则下岩土极限分析方法及其应用[博士学位论文].长沙:中南大学, 2002.
[52] Krabbenhoft K, Lyamin A V, Hjiaj M, et al. A new discontinuous upper bound limit analysis formulation. International Journal for Numerical Methods in Engineering, 2005, 63(7):1069-1088.
[53] Makrodimopoulos A, Martin C M. Upper bound limit analysis using simplex strain elements and second-order cone programming. International Journal for Numerical and Analytical Methods in Geomechanics, 2007, 31(6):835-865.
[54] Makrodimopoulos A, Martin C M. Upper bound limit analysis using discontinuous quadratic displacement fields. Communications in Numerical Methods in Engineering, 2008, 24(11):911-927.
[55] Martin C M, Makrodimopoulos A. Finite-element limit analysis of Mohr-Coulomb materials in 3D using semidefinite programming. Journal of Engineering Mechanics-Asce, 2008, 134(4):339-347.
[56] Krabbenhoft K, Lyamin A V, Sloan S W. Three-dimensional Mohr-Coulomb limit analysis using semidefinite programming. Communications in Numerical Methods in Engineering, 2008, 24(11):1107-1119.
[57] Chen J, Yin J-H, Lee C F. Upper bound limit analysis of slope stability using rigid finite elements and nonlinear programming. Canadian Geotechnical Journal, 2003, 40(4):742-752.
[58] Maier G, Munro J. Mathematical programming applications to engineering plastic analysis. Applied Mechanics Reviews, 1982, 35(12):1631-1643.
[59] Maier G, Smith D L. Update to mathematical programming applications to engineering plastic analysis. // Steele C R, Springer G S. Applied Mechanics Update. New York: ASME, 1986:377-383.
[60] Mackenzie D, Boyle J T, Hamilton R. The elastic compensation method for limit and shakedown analysis: a review. Journal of Strain Analysis, 2000, 35(3):171-188.
[61] Jones G L, Dhalla A K. Classification of clamp induced stresses in thin-walled pipe. Proceedings of the ASME Pressure Vessels and Piping Conference, 1981:17-23.
[62] Babu S, Iyer P K. Inelastic analysis of components using a modulus adjustment scheme. Journal of Pressure Vessel Technology, Transactions of the ASME, 1998, 120(1):1-5.
[63] Babu S, Iyer P K. A robust method for inelastic analysis of components made of anisotropic material. Journal of Pressure Vessel Technology, Transactions of the ASME, 1999, 121(2):154-159.
[64] Marriott D L. Evaluation of deformation or load control of stresses under inelastic conditions using elastic finite element stress analysis. // Proceedings of the ASME Pressure Vessels and Piping Conference. New York: ASME, 1988:3-9.
[65] Seshadri R. Generalized Local Stress Strain (GLOSS) analysis. Theory and applications. Journal of Pressure Vessel Technology, Transactions of the ASME, 1991, 113(2):219-227.
[66] Seshadri R, Marriott D L. On relating the reference stress, limit load and the ASME stress classification concepts. International Journal of Pressure Vessels and Piping, 1993, 56(3):387-408.
[67] Mangalaramanan S P. Conceptual models for understanding the role of the R-nodes in plastic collapse. Journal of Pressure Vessel Technology, 1997, 119(3):374-378.
[68] Seshadri R. Inelastic evaluation of mechanical and structural components using the generalized local stress strain method of analysis. Nuclear Engineering and Design, 1995, 153(2-3):287-303.
[69] Seshadri R. In search of redistribution nodes. International Journal of Pressure Vessels and Piping, 1997, 73(1):69-76.
[70] Seshadri R, Mangalaramanan S P. Lower bound limit loads using variational concepts: the mα-method. International Journal of Pressure Vessels and Piping, 1997, 71(2):93-106.
[71] Seshadri R. Limit loads using extended variational concepts in plasticity. Journal of Pressure Vessel Technology, Transactions of the ASME, 2000, 122(3):379-385.
[72] Pan L, Seshadri R. Limit load estimation using plastic flow parameter in repeated elastic finite element analyses. Journal of Pressure Vessel Technology, 2002, 124(4):433-439.
[73] Pan L, Seshadri R. Limit loads for layered structures using extended variational principles and repeated elastic finite element analysis. Journal of Pressure Vessel Technology, 2002, 124(4):425-432.
[74] Reinhardt W D, Seshadri R. Limit load bounds for the mαmultiplier. Journal of Pressure Vessel Technology, 2003, 125(1):11-18.
[75] Adibi-Asl R, Seshadri R. Local limit-load analysis using the m-beta method. Journal of Pressure Vessel Technology, 2007, 129(2):296-305.
[76] Indermohan H, Reinhardt W D, Seshadri R. Limit load of anisotropic components using the M-beta multiplier method. Journal of Pressure Vessel Technology, Transactions of the ASME, 2004, 126(4):455-460.
[77] Seshadri R, Indermohan H. Lower bound limit load determination: The m-beta multiplier method. Journal of Pressure Vessel Technology, 2004, 126(2):237-240.
[78] Mangalaramanan S P, Seshadri R. Robust limit loads of symmetric and non-symmetric plate structures. Transactions of the Canadian Society for Mechanical Engineering, 1995, 19(3):227-246.
[79] Fernando C P D, Seshadri R. Limit loads of framed structures and arches using the GLOSS r-node method. Transactions of the Canadian Society for Mechanical Engineering, 1993, 17(2):197-214.
[80] Mangalaramanan S P, Seshadri R. Limit loads of layered beams and layered cylindrical shells using the r-node method. // Proceedings of the 1997 ASME Pressure Vessels and Piping Conference. New York: ASME, 1997:201-215.
[81] Fanous L F Z, Adibi-Asl R, Seshadri R. Limit load analysis of pipe bend using the r-node method. Journal of Pressure Vessel Technology, 2005, 127(4):443-448.
[82] Mangalaramanan S P, Seshadri R, Reinhardt W. Limit loads of orthotropic structures using the R-node method. // Fracture, Design Analysis of Pressure Vessels, Heat Exchangers, Piping Components, and Fitness for Service. New York: ASME, 1999:241-249.
[83] Mangalaramanan S P, Seshadri R. Minimum weight design of pressure components using r-nodes. Journal of Pressure Vessel Technology, 1997, 119(2):224-231.
[84] Reinhardt W D, Mangalaramanan S P. Efficient tubesheet design using repeated elastic limit analysis technique. // Computer Technology (The ASME Pressure Vessels and Piping Conference). New York: ASME, 1999:141-149.
[85] Fanous I F Z, Seshadri R. Stress classification using the r-node method. Journal of Pressure Vessel Technology, Transactions of the ASME, 2007, 129(4):676-682.
[86] Seshadri R. Simplified methods in plasticity creep and fracture - some recent developments. Transactions of the Canadian Society for Mechanical Engineering, 1998, 22(4 B):419-433.
[87]王勖成,童瑞成.确定结构极限载荷的有限元简化算法.机械强度, 1997, 19(2):5-10.
[88] Mackenzie D, Boyle J T. Method of estimating limit loads by iterative elastic analysis. I - simple examples. International Journal of Pressure Vessels and Piping, 1993, 53(1):77-95.
[89] Nadarajah C, Mackenzie D, Boyle J T. Method of estimating limit loads by iterative elastic analysis. II - nozzle sphere intersections with internal pressure and radial load. International Journal of Pressure Vessels and Piping, 1993, 53(1):97-119.
[90] Shi J, Mackenzie D, Boyle J T. Method of estimating limit loads by iterative elastic analysis. III - torispherical heads under internal pressure. International Journal of Pressure Vessels and Piping, 1993, 53(1):121-142.
[91] Mackenzie D, Shi J, Boyle J T. Finite element modelling for limit analysis by the elastic compensation method. Computers and Structures, 1994, 51(4):403-410.
[92] Desquines J, Plancq D, Wielgosz C. In-plane limit moment for an elbow. Lower-boundanalytical solution and finite element processing by elastic compensation method. International Journal of Pressure Vessels and Piping, 1997, 71(1):29-34.
[93] Plancq D, Berton M N. Limit analysis based on elastic compensation method of branch pipe tee connection under internal pressure and out-of-plane moment loading. International Journal of Pressure Vessels and Piping, 1998, 75(11):819-825.
[94] Mangalaramanan P, Reinhardt W. On relating redistributed elastic and inelastic stress fields. International Journal of Pressure Vessels and Piping, 2001, 78(4):283-293.
[95] Mohamed A I, Megahed M M, Bayoumi L S, et al. Applications of iterative elastic techniques for elastic-plastic analysis of pressure vessels. Journal of Pressure Vessel Technology, 1999, 121(1):24-29.
[96]王飞,陈钢,刘应华,等.极限分析的弹性补偿法及其应用.应用力学学报, 2004, 21(4):147-150.
[97]王飞,陈钢,刘应华,等.内压下含局部减薄缺陷三通的极限分析.清华大学学报(自然科学版), 2004, 44(11):1517-1519.
[98] Marin-Artieda C C, Dargush G F. Approximate limit load evaluation of structural frames using linear elastic analysis. Engineering Structures, 2007, 29(3):296-304.
[99] Yang P, Liu Y, Ohtake Y, et al. Limit analysis based on a modified elastic compensation method for nozzle-to-cylinder junctions. International Journal of Pressure Vessels and Piping, 2005, 82(10):770-776.
[100]杨璞,刘应华,袁鸿雁,等.计算结构极限载荷的修正弹性补偿法.工程力学, 2006, 23(3):21-26.
[101]陈立杰,刘应华,杨璞,等.复杂结构塑性极限分析的修正弹性补偿法.机械工程学报, 2007, 43(05):187-193.
[102] Chen L, Liu Y, Yang P, et al. Limit analysis of structures containing flaws based on a modified elastic compensation method. European Journal of Mechanics a-Solids, 2008, 27(2):195-209.
[103] Desikan V, Sethuraman R. Analysis of material nonlinear problems using pseudo-elastic finite element method. Journal of Pressure Vessel Technology-Transactions of the Asme, 2000, 122(4):457-461.
[104] Upadrasta A, Peddieson J, Buchanan G R. Elastic compensation simulation of elastic/plastic axisymmetric circular plate bending using a deformation model. International Journal of Non-Linear Mechanics, 2006, 41(3):377-387.
[105] Shi J, Boyle J T, Mackenzie D, et al. Approximate limit design of frames using elastic analysis. Computers and Structures, 1996, 61(3):495-501.
[106] Boyle J T, Hamilton R, Shi J, et al. Simple method of calculating lower-bound limit loads for axisymmetric thin shells. Journal of Pressure Vessel Technology, 1997,119(2):236-242.
[107] Hamilton R, Boyle J T. Approximate calculation of upper bound limit loads for axisymmetric thin shells. // Proceedings of the 1998 ASME/JSME Joint Pressure Vessels and Piping Conference. New York: ASME, 1998:147-151.
[108] Hamilton R, Mackenzie D, Shi J, et al. Simplified lower bound limit analysis of pressurised cylinder/cylinder intersections using generalised yield criteria. International Journal of Pressure Vessels and Piping, 1996, 67(2):219-226.
[109] Hamilton R, Boyle J T. Simplified lower bound limit analysis of transversely loaded thin plates using generalised yield criteria. Thin-Walled Structures, 2002, 40(6):503-522.
[110] Adibi-Asl R, Fanous I F Z, Seshadri R. Elastic modulus adjustment procedures - Improved convergence schemes. International Journal of Pressure Vessels and Piping, 2006, 83(2):154-160.
[111] Martin J B. Plasticity : fundamentals and general results. The MIT Press, 1975.
[112] Gokhfeld D A, Cherniavsky O F. Limit analysis of structures at thermal cycling. Sijthoff and Noordhoff, 1980.
[113] Nadarajah C, Mackenzie D, Boyle J T. Limit and shakedown analysis of nozzle/cylinder intersections under internal pressure and in-plane moment loading. International Journal of Pressure Vessels and Piping, 1996, 68(3):261-272.
[114] Hamilton R, Boyle J T, Shi J, et al. Simple upper-bound method for calculating approximate shakedown loads. Journal of Pressure Vessel Technology, 1998, 120(2):195-199.
[115] Hardy S J, Gowhari-Anaraki A R, Pipelzadeh M K. Upper and lower bound limit and shakedown loads for hollow tubes with axisymmetric internal projections under axial loading. Journal of Strain Analysis for Engineering Design, 2001, 36(6):595-604.
[116] Fellenius W. Calculation of the stability of earth dams. // Transactions of the 2nd International Congress on Large Dams. Washington,D.C., 1937.
[117] Bishop A W. The use of the slip circle in the stability analysis of slopes. Geotechnique, 1955, 5(1):7-17.
[118] Janbu N. Application of composite slip surfaces for stability analysis. // Proceedings of the European Conference on Stability of Earth Slope. Stockholm, 1954:43-49.
[119] Janbu N. Stability analysis of slopes with dimensionless parameters // Harvard Soil Mechanics Series No46. 1954.
[120] Janbu N. Soil stability computations. // Embankment Dam Engineering. New York: Wiley, 1973:47-87.
[121] Spencer E. A method of analysis of stability of embankments assuming parallel inter-slice forces. Geotechnique, 1967, 17(1):11-26.
[122] Spencer E. Thrust line criterion in embankment stability analysis. Geotechnique, 1973, 23(1):85-100.
[123] Morgenstern N R, Price V E. Analysis of stability of general slip surfaces. Geotechnique, 1965, 15(1):79-93.
[124] Sarma S K. Stability analysis of embankments and slopes. Geotechnique, 1973, 23(3):423-433.
[125] Chen Z Y, Morgenstern N R. Extensions to the generalized method of slices for stability analysis. Canadian Geotechnical Journal, 1983, 20(1):104-119.
[126]陈祖煜.土质边坡稳定分析:原理·方法·程序北京:中国水利水电出版社, 2003.
[127] Fredlund D G, Krahn J. Comparison of slope stability methods of analysis. Canadian Geotechnical Journal, 1977, 14(3):429-439.
[128] Fredlund D G, Krahn J, Pufahl D E. The relationship between limit equilibrium slope stability methods. // Proceedings of the 10th ICSMFE. 1981:409-416.
[129] Chugh A K. Variable interslice force inclination in slope stability analysis. Soils and Foundations, 1986, 26(1):115-121.
[130] Espinoza R D, Bourdeau P L, Muhunthan B. Unified formulation for analysis of slopes with general slip surface. Journal of geotechnical engineering, 1994, 120(7):1185-1203.
[131] Zhu D Y, Lee C F, Jiang H D. Generalised framework of limit equilibrium methods for slope stability analysis. Geotechnique, 2003, 53(4):377-395.
[132] Cheng Y M, Zhu L J. Unified formulation for two dimensional slope stability analysis and limitations in factor of safety determination. Soils and Foundations, 2004, 44(6):121-127.
[133] Wright S G, Kulhawy F H, Duncan J M. Accuracy of equilibrium slope stability analysis. American Society of Civil Engineers, Journal of the Soil Mechanics and Foundations Division, 1973, 99(SM10):783-779.
[134] Fredlund D G. Analytical method of slope stability analysis // Proceedings of the 4th International Symposium on Landslides 1984:229-250
[135] Duncan J M, Wright S G. The accuracy of equilibrium methods of slope stability analysis. Engineering Geology, 1980, 16(1-2):5-17.
[136]朱大勇,邓建辉,台佳佳.简化Bishop法严格性的论证.岩石力学与工程学报, 2007, 26(3):455-458.
[137] Abramson L W, Lee T S, Sharma S, et al. Slope stability and stabilization methods. 2ed. New York: John Wiley & Sons, 2002.
[138] Krahn J. The 2001 R.M. Hardy Lecture: The limits of limit equilibrium analyses. Canadian Geotechnical Journal, 2003, 40(3):643-660.
[139] Michalowski R L. Slope stability analysis: a kinematical approach. Geotechnique, 1995,45(2):283-293.
[140] Donald I B, Chen Z. Slope stability analysis by the upper bound approach: fundamentals and methods. Canadian Geotechnical Journal, 1997, 34(6):853-862.
[141]徐千军,李明元,陆杨.边坡稳定极限分析的单元集成法.岩土力学, 2006, 27(7):1028-1032.
[142] Yu H S, Salgado R, Sloan S W, et al. Limit analysis versus limit equilibrium for slope stability. Journal of Geotechnical and Geoenvironmental Engineering, 1998, 124(1):1-11.
[143] Kim J, Salgado R, Yu H S. Limit analysis of soil slopes subjected to pore-water pressures. Journal of Geotechnical and Geoenvironmental Engineering, 1999, 125(1):49-58.
[144] Kim J. Limit analysis of soil slope stability using finite elements and linear programming [D]. Purdue University, 1998.
[145] Kim J, Salgado R, Lee J. Stability analysis of complex soil slopes using limit analysis. Journal of Geotechnical and Geoenvironmental Engineering, 2002, 128(7):546-557.
[146] Michalowski R L. Three-dimensional analysis of locally loaded slopes. Geotechnique, 1989, 39(1):27-38.
[147] Zienkiewicz O C, Humpheson C, Lewis R W. Associated and non-associated visco-plasticity and plasticity in soil mechanics. Geotechnique, 1975, 25(4):671-689.
[148] Matsui T, San K-C. Finite element slope stability analysis by shear strength reduction technique. Soils and Foundations, 1992, 32(1):59-70.
[149] Ugai K, Leshchinsky D. Three-dimensional limit equilibrium and finite element analyses: A comparison of results. Soils and Foundations, 1995, 35(4):1-7.
[150]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.
[151] Griffiths D V, Lane P A. Slope stability analysis by finite elements. Geotechnique, 1999, 49(3):387-403.
[152] Dawson E M, Roth W H, Drescher A. Slope stability analysis by strength reduction. Geotechnique, 1999, 49(6):835-840.
[153] Dawson E, Motamed F, Nesarajah S, et al. Geotechnical stability analysis by strength reduction. // Proceedings of Sessions of Geo-Denver 2000 - Slope Stability 2000. American Society of Civil Engineers, 2000:99-113.
[154]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, 2001, 23(4):407-411.
[155]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, 2002, (1):7-9.
[156]张鲁渝,时卫民,郑颖人.平面应变条件下土坡稳定有限元分析.岩土工程学报, 2002, 24(4):487-490.
[157]赵尚毅,郑颖人,时卫民,等.用有限元强度折减法求边坡稳定安全系数.岩土工程学报, 2002, 2002(5):343-346.
[158]郑颖人,赵尚毅.有限元强度折减法在土坡与岩坡中的应用.岩石力学与工程学报, 2004, 23(19):3381-3388.
[159]郑颖人,赵尚毅,张鲁渝.用有限元强度折减法进行边坡稳定分析.中国工程科学, 2002, 4(10):57-61.
[160]郑颖人,赵尚毅,孔位学,等.极限分析有限元法讲座——Ⅰ岩土工程极限分析有限元法.岩土力学, 26(1):163-168.
[161]郑宏,李春光,李焯芬,等.求解安全系数的有限元法.岩土工程学报, 2002, 24(5):626-628.
[162] Zheng H, Liu D F, Li C G. Slope stability analysis based on elasto-plastic finite element method. International Journal for Numerical Methods in Engineering, 2005, 64(14):1871-1888.
[163]宋二祥,高翔,邱玥.基坑土钉支护安全系数的强度参数折减有限元方法.岩土工程学报, 2005, 27(3):258-263.
[164] Xu Q J, Yin H L, Cao X F, et al. A temperature-driven strength reduction method for slope stability analysis. Mechanics Research Communications, 2009, 36(2):224-231.
[165] Kulhawy F H. Finite element analysis of the behavior of embankments [D]. University of California, 1969.
[166] Resendiz D. Discussion of 'Accuracy equilibrium slope stability analysis'. Journal of the Soil Mechanics and Foundations Divsion, 1974, 100(GT8):967-970.
[167] Adikari G S N, Cummins P J. An effective stress slope stability analysis method for dams. // Proceedings of the 11th International Conference on Soil Mechanics and Foundation Engineering. San Francisco, 1985:713-718.
[168] Naylor D J. Finite elements and slope stability. // Martins J B. Numerical Methods in Geomechanics:Proceedings of the NATO Advanced Study Institute. Dordrecht: D.Reidel Publishing Company, 1982:229-244.
[169] Farias M M, Naylor D J. Safety analysis using finite elements. Computers and Geotechnics, 1998, 22(2):165-181.
[170] Fredlund D G, Scoular R E G. Using limit equilibrium concepts in finite element slope stability analysis. // Yagi N, Yamagami T, Jiang J-C. Slope Stability engineering:Proceedings of the International Symposium on Slope Stability Engineering-IS-Shikoku'99. Rotterdam: Balkema, 1999:31-47.
[171] Pham H T V, Fredlund D G. The application of dynamic programming to slope stability analysis. Canadian Geotechnical Journal, 2003, 40(4):830-847.
[172]邓俊晔.边坡极限平衡有限元稳定分析的Dijkstra算法的理论及应用[硕士学位论文].南京:河海大学, 2006.
[173]徐卫亚,周家文,邓俊晔,等.基于Dijkstra算法的边坡极限平衡有限元分析.岩土工程学报, 2007, 29(8):1159-1172.
[174] Loehr J E. Development of a hybrid limit equilibrium-finite element procedure for three-dimensional slope stability analysis [D]. The University of Texas at Austin, 1998.
[175] Taylor D W. Stability of earth slopes. Boston Society of Civil Engineers, 1937, 24(3):197-246.
[176] Taylor D W. Fundamentals of soil mechanics. New York: Wiley, 1948.
[177] Gitirana Jr. G F N. Weather-related geo-hazard assessment model for railway embankment stability [D]. University of Saskatchewan, 2005.
[178] Chowdhury R N. Slope analysis. Amsterdam: Elsevier Scientific Publishing Company, 1978.
[179] Huang Y H. Stability analysis of earth slopes. New York: Van Nostrand Reinhold, 1983.
[180]郑宏,田斌,刘德富,等.关于有限元边坡稳定性分析中安全系数的定义问题.岩石力学与工程学报, 2005, 24(13):2225-2230.
[181]卓家寿.关于岩体稳定性问题的一点注记.河海大学学报, 2001, 29(增刊):1-5.
[182]邵国建,卓家寿,章青.岩体稳定性分析与评判准则研究.岩石力学与工程学报, 2003, 22(5):691-696.
[183]沈珠江.当前土力学研究中的几个问题.岩土工程学报, 1986, 8(5):1-8.
[184]丰定祥,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, 1990, 12(3):1-9.
[185]刘艳章,葛修润,李春光,等.基于矢量法安全系数的边坡与坝基稳定分析.岩石力学与工程学报, 2007, 26(10):2130-2140.
[186]邵龙潭,唐洪祥,韩国城.有限元边坡稳定分析方法及其应用.计算力学学报, 2001, 18(1):81-87.
[187]赵杰.边坡稳定有限元分析方法中若干应用问题研究[博士学位论文].大连:大连理工大学, 2006.
[188]赵杰,邵龙潭.平面应变条件下两类有限元边坡稳定分析方法比较研究.大连理工大学学报, 2007, 47(6):873-879.
[189]郑颖人,赵尚毅.边(滑)坡工程设计中安全系数的讨论.岩石力学与工程学报, 2006, 25(9):1937-1940.
[190] Janbu N. Earth pressure and bearing capacity calculations by generalized procedure of slices. // Proceedings of the 4th International Conference on Soil Mechanics and Foundation Engineering. 1957:207-212.
[191] Chugh A K. Variable factor of safety in slope stability analysis. Geotechnique, 1986, 36(1):57-64.
[192] Chugh A K. Variable factor of safety in slope stability analysis by limit equilibrium method. Journal of the Institution of Engineers (India): Civil Engineering Division, 1988, 69:149-155.
[193]卓家寿,邵国建,陈振雷.工程稳定问题中确定滑坍面、滑向与安全度的干扰能量法.水利学报, 1997, (8):80-84.
[194] Chen W F, Snitbhan N. On slip surface and slope stability analysis. Soils and Foundations, 1975, 15(3):41-49
[195] Chen Z, Wang X, Haberfield C, et al. A three-dimensional slope stability analysis method using the upper bound theorem Part I: Theory and methods. International Journal of Rock Mechanics and Mining Sciences, 2001, 38(3):369-378.
[196] Askari F, Farzaneh O. Upper-bound solution for seismic bearing capacity of shallow foundations near slopes. Geotechnique, 2003, 53(8):697-702.
[197] Farzaneh O, Askari F. Three-dimensional analysis of nonhomogeneous slopes. Journal of Geotechnical and Geoenvironmental Engineering, 2003, 129(2):137-145.
[198] Jiang G L, Magnan J P. Stability analysis of embankments: comparison of limit analysis with methods of slices. Geotechnique, 1997, 47(4):857-872.
[199] Chen W F, Liu X L. Limit analysis in soil mechanics. Elsevier Science: Amsterdam, 1990.
[200]殷建华,陈健,李焯芬.岩土边坡稳定性的刚体有限元上限分析.岩石力学与工程学报, 2004, 23(6):898-905.
[201] 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. Journal of Engineering Mechanics, 2004, 130(8):886-893.
[202]包承纲.非饱和土的性状及膨胀土边坡稳定问题.岩土工程学报, 2004, 26(1):1-15.
[203]孙小明,武雄,何满潮,等.强膨胀性软岩的判别与分级标准.岩石力学与工程学报, 2005, 24(1):128-132.
[204]殷宗泽,吕擎峰,袁俊平.膨胀土边坡的稳定性分析. //郑健龙.膨胀土处治理论、技术与实践.北京:人民交通出版社, 2004:61-69.
[205]尹宏磊,徐千军,李仲奎.膨胀变形对膨胀土边坡稳定性的影响.岩土力学, 2009, 30(8).
[206]陆杨,徐千军.交变载荷作用下边坡的安定性分析.岩土力学, 2004, 25(11):1693-1697.
[207]徐千军,陆杨.干湿交替对边坡长期安全性的影响.地下空间与工程学报, 2005, 1(7):1021-1024.
[208]尹宏磊,徐千军,李仲奎.抗剪强度随干湿循环变化对边坡安定性的影响.水利学报, 2008, 39(5):568-572.
[209]陈祖煜.土力学经典问题的极限分析上、下限解.岩土工程学报, 2002, 24(1):1-11.
[210] Chen Z Y. The limit analysis in soil and rock: a mature discipline of geomechanics. Journal of Zhejiang University, 2007, (11):1712-1724.
[211] Berak E G, Gerdeen J C. A Finite Element Technique for Limit Analysis of Structures. Journal of Pressure Vessel Technology, 1990, 112(2):138-144.
[212] Ponter A R S, Chen H F, Boulbibane M, et al. The linear matching method for the evaluation of limit loads, shakedown limits and related problems. // Mang H A, Rammerstorfer F G, Eberhardsteiner J. Proceedings of the Fifth World Congress on Computational Mechanics. Vienna, 2002.
[213] Ponter A R S, Engelhardt M. Shakedown limits for a general yield condition: implementation and application for a Von Mises yield condition. European Journal of Mechanics a-Solids, 2000, 19(3):423-445.
[214] Ponter A R S, Fuschi P, Engelhardt M. Limit analysis for a general class of yield conditions. European Journal of Mechanics a-Solids, 2000, 19(3):401-421.
[215] Boulbibane M, Ponter A R S. Linear matching method for limit load problems using the Drucker-Prager yield condition. Geotechnique, 2005, 55(10):731-739.
[216] Boulbibane M, Ponter A R S. Extension of the linear matching method to geotechnical problems. Computer Methods in Applied Mechanics and Engineering, 2005, 194(45-47):4633-4650.
[217] Boulbibane M, Ponter A R S. The linear matching method for the shakedown analysis of geotechnical problems. International Journal for Numerical and Analytical Methods in Geomechanics, 2006, 30(2):157-179.
[218] Chen H F, Ponter A R S. Shakedown and limit analyses for 3-D structures using the linear matching method. International Journal of Pressure Vessels and Piping, 2001, 78(6):443-451.
[219] Chen H F, Ponter A R S. Integrity assessment of a 3D tubeplate using the linear matching method. Part 1. Shakedown, reverse plasticity and ratchetting. International Journal of Pressure Vessels and Piping, 2005, 82(2):85-94.
[220] Chen H F, Ponter A R S, Ainsworth R A. The linear matching method applied to the high temperature life integrity of structures. Part 2. Assessments beyond shakedown involving changing residual stress fields. International Journal of Pressure Vessels and Piping, 2006, 83(2):136-147.
[221] Chen H F, Ponter A R S, Ainsworth R A. The linear matching method applied to the high temperature life integrity of structures. Part 1. Assessments involving constant residual stress fields. International Journal of Pressure Vessels and Piping, 2006, 83(2):123-135.
[222] Chen H F, Ponter A R S. Integrity assessment of a 3D tubeplate using the linear matchingmethod. Part 2: Creep relaxation and reverse plasticity. International Journal of Pressure Vessels and Piping, 2005, 82(2):95-104.
[223] Chen H, Ponter A R S. Linear matching method on the evaluation of plastic and creep behaviours for bodies subjected to cyclic thermal and mechanical loading. International Journal for Numerical Methods in Engineering, 2006, 68(1):13-32.
[224] Chen H F, Engelhardt M J, Ponter A R S. Linear matching method for creep rupture assessment. International Journal of Pressure Vessels and Piping, 2003, 80(4):213-220.
[225]余同希.塑性力学.北京:高等教育出版社, 1989.
[226]陈钢,刘应华.结构塑性极限与安定分析理论及工程方法.北京:科学出版社, 2006.
[227] Ponter A R S, Carter K F. Limit state solutions, based upon linear elastic solutions with a spatially varying elastic modulus. Computer Methods in Applied Mechanics and Engineering, 1997, 140(3-4):237-258.
[228]王仁,黄文彬,黄筑平.塑性力学引论.北京:北京大学出版社, 1992.
[229] Mackenzie D, Nadarajah C, Shi J, et al. Simple bounds on limit loads by elastic finite element analysis. Journal of Pressure Vessel Technology, Transactions of the ASME, 1993, 115(1):27-31.
[230] Hibbitt K S, Inc. ABAQUS Analysis User's Manual (version 6.5), 2004.
[231]黄正中.高等数学. 2版.北京:人民教育出版社, 1978.