边坡稳定分析的非连续面拓扑优化技术

贾苍琴; 黄齐武; 王贵和

doi:10.11779/CJGE201804009

边坡稳定分析的非连续面拓扑优化技术 English Version

1. 中国地质大学（北京）工程技术学院,北京 100083;
2. 北京市轨道交通建设管理有限公司,北京 100068;

基金项目: 国家自然科学基金项目（40902085,41202219）; 中央高校基本科研业务费专项资金项目（2652013104）

详细信息

作者简介:
贾苍琴(1976- ),女,讲师,主要从事岩土力学数值分析等方面的教学和科研。E-mail：jiacangqin@cugb.edu.cn。

通讯作者:
黄齐武，E-mail：richardhuangqw@163.com

中图分类号: TU435
计量
- 文章访问数: 318
- HTML全文浏览量: 4
- PDF下载量: 299
出版历程
- 收稿日期: 2016-11-27
- 发布日期: 2018-04-24

Slope stability using discontinuity topology optimization technique

1. School of Engineering and Technology, China University of Geosciences, Beijing 100083, China;
2. Beijing MTR Construction Administration Corporation, Beijing 100068, China;

摘要

摘要: 土工结构稳定性的极限分析方法研究一直是热点问题。提出的非连续面拓扑优化技术（DTO）的主要特征之处在于稳定性问题的极限分析根据节点及其连线而不是单元或实体来进行构造。替代的近似过程主要采用适量的栅格节点来离散问题几何域,临界破坏机构则由节点间的连线集构造而成。基于Mohr-Coulomb屈服准则构造目标函数,并通过优化来确定极限荷载系数。结合离散构造特征,引入孔隙水压力和安全系数,DTO可拓展处理涉及地下水的边坡稳定问题。DTO是建立临界破坏模式和确定相应安全系数的有效工具,而无需考虑滑移面的入口/出口限界或点的约束与假设。本研究以复杂条件下的边坡稳定性为例,深入分析DTO和其他各种方法所得结果的一致性和差异性。相关比较表明,对于材料特性要求高、几何边界和荷载作用条件复杂的边坡稳定分析而言,DTO技术是一种可靠的替代分析手段。
- 上限法 /
- 拓扑优化 /
- 边坡 /
- 孔隙水压力 /
- 非连续面
Abstract: Many efforts have been focused on the stability problems of geotechnical structures with the limit analysis methods. A key advance of the proposed method is that the problem is described only in terms of nodes and discontinuities connecting those nodes rather than elements or bodies. The alternative approximation procedure might involve discretization of a given body under consideration using a suitably large number of nodes laid out on a grid, with the failure mechanism comprising the most critical subset of potential discontinuities interconnecting these nodes. The discontinuity topology optimization (DTO) technique using the Mohr-Coulomb failure criterion to formulate the objective function is developed and the collapse load multiplier is determined from optimization. Incorporating the pore-water pressure and factor of safety is consistent with the formulation of nodal grid and inter-node connections, and the ability of the DTO procedure extended to handle the slope problems involving ground water pressures is demonstrated. The use of DTO can be an effective tool for establishing a critical failure mechanism and its corresponding safety factor without the constraints or assumptions regarding entrance/exit limits or points of the slip surface. The uses of various methods and DTO for several examples that focus on complex geotechnical scenarios are compared to illustrate the agreement and difference between the analyses. The developed techniques are shown to provide a viable alternative to analyze the stability of slopes with demanding material behavior, complex geometry and loading conditions.
- upper bound theorem /
- topology optimization /
- slope /
- pore-water pressure /
- discontinuity

HTML全文

参考文献(30)

[1]	CHENG Y M, LAU C K.Slope stability analysis and stabilization: new methods and insight[M]. Abingdon: Routledge, 2008.
[2]	KRABBENHOFT K, LYAMIN A V, HJIAJ M, et al.A new discontinuous upper bound limit analysis formulation[J]. International Journal for Numerical Methods in Engineering, 2005, 63: 1069-1088.
[3]	ALWIS W A M. Discrete element slip model of plasticity[J]. Engineering Structures, 2000, 22:1494-1504.
[4]	SMITH C C, GILBERT M.Application of discontinuity layout optimization to plane plasticity problems[J]. Proceedings of the Royal Society A- Mathematical, Physical and Engineering Sciences, 2007, 463(2086): 2461-2484.
[5]	LYSMER J.Limit analysis of plane problems in soil mechanics[J]. Journal of the Soil Mechanics and Foundations Division, ASCE, 1970, 96(4): 1311-1334.
[6]	SLOAN S W, KLEEMAN P W.Upper bound limit analysis using discontinuous velocity fields[J]. Computer Methods in Applied Mechanics and Engineering, 1995, 127(1/2/3/4): 293-314.
[7]	MAKRODIMOPOULOS A, MARTIN C M.Lower bound limit analysis of cohesive-frictional materials using second-order cone programming[J]. International Journal for Numerical Methods in Engineering, 2006, 66(4): 604-634.
[8]	CHRISTIANSEN E, PEDERSEN O S.Automatic mesh refinement in limit analysis[J]. International Journal for Numerical Methods in Engineering, 2001, 50: 1331-1346.
[9]	BORGES L A, ZOUAIN N, COSTA C, FEIJOO R.An adaptive approach to limit analysis[J]. International Journal of Solids Structures, 2001, 38: 1707-1720.
[10]	FRANCO J R Q, PONTER A R S, BARROS F B. Adaptive F E method for the shakedown and limit analysis of pressure vessels[J]. European Journal of Mechanics (A/Solids), 2003, 22: 525-533.
[11]	LYAMIN A V, SLOAN S W.Mesh generation for lower bound limit analysis[J]. Advances in Engineering Software, 2003, 34: 321-338.
[12]	CIRIA H, PERAIRE J, BONET J.Mesh adaptive computation of upper and lower bounds in limit analysis[J]. International Journal for Numerical Methods in Engineering, 2008, 75: 899-944.
[13]	CHRISTIANSEN E.Computation of limit load[J]. International Journal for Numerical Methods in Engineering, 1981, 7: 1547-1570.
[14]	ANDERSEN K D, CHRISTIANSEN E.Limit analysis with the dual affine scaling algorithm[J]. Journal of Computational and Applied Mathematics, 1995, 59: 233-243.
[15]	GONDZIO J, SARKISSIAN R.Column generation with a primal-dual method[R]. Geneva: University of Geneva, 1997.
[16]	HUANG Q W, JIA C Q, XIA B R, WANG G H. Novel computational implementations for stability analysis[J]. Applied Mechanics and Materials, 2011, 90-93: 778-785.
[17]	DORN W C, GOMORY R E, GREENBERG H J.Automatic design of optimal structures[J]. J De Mechanique, 1964, 3(1): 25-52.
[18]	GILBERT M, TYAS A.Layout optimization of large-scale pin-jointed frames[J]. Engineering Computations, 2003, 20(8): 1044-1064.
[19]	SMITH C C, GILBERT M.New upper bound solutions for layered soil bearing capacity problems using discontinuity layout optimization[C]// 10th Australia New Zealand Conference on Geomechanics. Brisbane, 2007: 250-255.
[20]	GRIFFITHS D V, LANE P A.Slope stability analysis by finite elements[J]. Géotechnique, 1999, 49(3): 387-403.
[21]	BAKER R.Determination of the critical slip surface in slope stability computations[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 1980, 4(4): 333-359.
[22]	DONALD I, GIAM P.The ACADS slope stability programs review[C]// Proceedings of the 6th International Symposium on Landslides. Christchurch, New Zealand, 1992: 1665-1670.
[23]	DUNCAN J M.State of the art: Limit equilibrium and finite element analysis of slopes[J]. Journal of Geotechnical Engineering, 1996, 122(7): 577-596.
[24]	DAWSON E M, ROTH W H, DRESCHER A.Slope stability analysis by strength reduction[J]. Géotechnique, 1999, 49(6): 835-840.
[25]	CHENG Y M.Location of critical failure surface and some further studies on slope stability analysis[J]. Computers and Geotechnics, 2003, 30(3): 255-267.
[26]	KIM J, SALGADO R, LEE J.Stability analysis of complex soil slopes using limit analysis[J]. Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 2002, 128(7): 546-557.
[27]	GRECO V R.Efficient Monte Carlo technique for locating critical slip surface[J]. Journal of Geotechnical Engineering, 1996, 122(7): 517-525.
[28]	MALKAWI H A I, HASSAN W F, SARMA S K. Global search method for locating general slip surface using Monte Carlo techniques[J]. Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 2001, 127(8): 688-698.
[29]	CHENG Y M, LI L, CHI S C.Performance studies on six heuristic global optimization methods in the location of critical slip surface[J]. Computers and Geotechnics, 2007, 34(6): 462-484.
[30]	LIU J, ZHAO J.Limit analysis of slope stability by rigid finite-element method and linear programming considering rotational failure[J]. International Journal of Geomechanics, 2013, 13(6): 827-839.