THE UPPER-BOUND SOLUTION FOR BEARING CAPACITY FACTOR OF BY EMPLOYING THE EQUIVALENCE OF LIMIT ANALYSIS AND LIMIT EQUILIBRIUM METHOD
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摘要: 针对地基承载力系数N真实解答尚未获得的现状,提出一种计算N上限解的数值计算方法。在论证极限平衡法与极限分析法等效性的基础上,采用一组三角条块逼近满足机动许可的潜在破坏机构,通过极限平衡法建立条间力的递推公式,依据推力最大原理优化条块底线的倾角,得到最危险破坏机构及对应的地基承载力系数N的上限数值解,进而分析地表倾斜情况下的N及其修正方法;最后,为了便于工程应用,给出N及地表倾斜修正系数的近似表达式。通过与已有研究成果的比较,验证该方法的合理性。研究表明:该方法计算过程简单易于编程实现,能够得到相对小的上限解。研究成果可用于地基承载力的理论分析,为深入研究地基承载力系数N提供参考。Abstract: An approach for evaluating the upper-bound for bearing capacity factor N was presented.The equivalence of limit analysis and limit equilibrium method was analyzed,and then a kinematical admissible failure mechanism,which was composed of a sequence of rigid triangles,was considered in the framework of limit equilibrium method.The recursion formula of inter-slice force was deduced according to the force equilibrium conditions of slice,and optimal bottom inclination of each triangle also was obtained by employing the principle of maximum thrust force.Therefore,the critical failure mechanism and corresponding N value were obtained.Then,the influence of inclined ground surface on N value was discussed.These solutions,presented in the form of graphs,were compared against existing semi-empirical expressions and numerical solutions.Finally,approximate analytical expressions for N and (correction factor of inclined ground surface) were suggested.The present method,which was of simple principle and could be readily implemented into computer software,could solve a lower N value than other's the upper-bound solutions.The study results could be used in theoretical analysis of bearing capacity and provideed some beneficial references for further research on N.
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Terzaghi K. Theoretical soil Mechanics[M]. New York: JohnWiley & Sons,1943. [2] Meyerhof G G. The Ultimate Bearing Capacity of Foundations[J].Geotechnique,1951,2(4):301-332. [3] Kumbhojkar A S. Numerical Evaluation of Therzaghi s N[J].Journal of Geotechnical Engineering,1993,119(3):598-607. [4] Zhu D Y, Lee C F, Jiang H D. A Numerical Study of the BearingCapacity Factor N[J]. Canadian Geotechnical Journal,2001,38(1):1090-1096. [5] Sokolovskii V V. Statics of Soil Media[M]. London: ButterworthsPublications,1965. [6] Hansen J B. A Revised and Extended Formula for BearingCapacity[J]. Bulletin of the Danish Geotechnical Institute,1970,28:5-11. [7] Booker J R. Applications of Theories of Plasticity to CohesiveFrictional Soils[D]. Sydney: Sydney University,1969. [8] Bolton M D, Lau C K. Vertical Bearing Capacity Factors forCircular and Strip Footings on Mohr-Coulomb Soil[J]. CanadianGeotechnical Journal,1993,30(6):1024-1033. [9] Kumar J. Nfor Rough Strip Footing Using the Method ofCharacteristics[J]. Canadian Geotechnical Journal,2003,40(3):669-674. [10] 肖大平,朱维一,陈环.滑移线法求解极限承载力问题的一些进展[J].岩土工程学报,1998,20(4):25-29. [11] 韩冬冬,谢新宇,窦岩嵩.考虑土体重度的条形基础极限承载力半经验理论解[J].长江科学院院报,2009,26(8):54-58. [12] Chen W F. Limit Analysis and Soil Plasticity[M]. Amsterdam:Elsevier,1975. [13] Michalowski R L. An Estimate of the Influence of Soil Weight onBearing Capacity Using Limit Analysis[J]. Soils andFoundations,1997,37(4):57-64. [14] Soubra A H. Upper-Bound Solutions for Bearing Capacity ofFoundations[J]. Journal of Geotechnical and Geo-EnvironmentalEngineering,1998,125(1):59-68. [15] Wang Y J, Yin J H, Chen Z Y. Calculation of Bearing Capacity ofa Strip Footing Using an Upper Bound Method[J]. InternationalJournal for Numerical and Analytical Methods in Geomechanics,2001,25(8):841-851. [16] Zhu D Y. The Least Upper-Bound Solution for the BearingCapacity Factor N[J]. Soils and Foundations,2000,40(1):123-129. [17] 陈祖煜.土力学经典问题的极限分析上、下限解[J].岩土工程学报,2002,24(1):1-11. [18] 朱大勇.复杂条件下承载力系数 N的上限解[J].力学与实践,1999,21(4):24-27. [19] 黄茂松,秦会来,郭院成.非均质和各向异性黏土地基承载力的上限解[J].岩石力学与工程学报,2008,27(3):511-518. [20] Sloan S W. Lower Bound Limit Analysis Using Finite Elementsand Linear Programming[J]. International Journal for Numericaland Analytical Methods in Geomechanics,1988,12(8):61-77. [21] Ukritchon B, Whittle A W, Klangvijit C. Calculations of BearingCapacity Factor NUsing Numerical Limit Analyses[J]. Journal ofGeotechnical and Geoenviron mental Engineering,2003,129(6):468-474. [22] Hjiaj M, Lyamin A V, Sloan S W. Numerical Limit AnalysisSolutions for the Bearing Capacity Factor N[J]. InternationalJournal of Solids and Structures,2005,42(5/6):1681-1704. [23] Smith C C. Complete Limiting Stress Solutions for the BearingCapacity of Strip Footings on a Mohr-Coulomb Soil[J].Geotechnique,2005,55(8):607-612. [24] Griffiths D V. Computation of Bearing Capacity Factors UsingFinite Elements[J]. Geotechnique,1982,32(3):195-202. [25] Manoharan N, Dasgupta S P. Bearing Capacity of Surface Footingsby Finite Elements[J]. Computers and Structures,1995,54(4):563-586. [26] Day R A, Potts D M. Discussion of Observations on theComputation of the Bearing Capacity Factor Nby FiniteElements by P K Woodward and D V Griffith[J]. Geotechnique,2000,50(3):301-303. [27] Woodward P K, Griffiths D V. Observations on the Computation ofthe Bearing Capacity Factor Nby Finite Elements[J].Geotechnique,1998,48(1):137-141. [28] 詹云刚,袁凡凡,栾茂田,等.均质土地基上埋深条形基础极限承载力系数数值研究[J].岩石力学与工程学报,2008,27(S2):3408-3415. [29] 赵少飞,栾茂田,范庆来,等.非均质地基承载力及破坏模式的 FLAC 数值分析[J].岩土力学,2006,27(11):1909-1914. [30] Enoki M, Yagi N, Yatabe R, et al. Relation of Limit EquilibriumMethod to Limit Analysis Method[J]. Soils and Foundations,1991,31(4):37-47. [31] Drescher A, Detournay E. Limit Load in Translational FailureMechanisms for Associative and Non-Associative Materials[J].Geotechnique,1993,43(3):443-456. [32] Zhu D Y. A Method for Locating Critical Slip Surfaces in SlopeStability Analysis[J]. Canadian Geotechnical Journal,2001,38(2):328-337. [33] Khatri V N, Kumar J, Kouzer K M. Determination of the BearingCapacity Factor NUsing Upper and Lower Bound Limit AnalysisIncluding Slip Line Method[C]//The 12 th InternationalConference of International Association for Computer Methods andAdvances in Geomechanics.2008:3191-3198. [34] Kumar J, Khatri V N. Bearing Capacity Factors of CircularFoundations for a General c- Soil Using Lower Bound FiniteElements Limit Analysis[J]. International Journal for Numericaland Analytical Methods in Geomechanics,2011,35(3):393-405. [35] Kumar J, Khatri V N. Effect of Footing Roughness on LowerBound NValues[J]. International Journal of Geo-Mechanics,2008,8(3):176-187. [36] Vesic A S. Analysis of Ultimate Loads of Shallow Foundation[J].Journal of the Soil Mechanics and Foundation Division, ASCE,1973,99(1):45-73. [37] Dewaikar D M, Mohapatra B G. Computation of Bearing CapacityFactors NPrandtl s Mechanism[J]. Soils and Foundations,2003,43(3):1-10. [38] Caquot A, Kerisel J. Sur le Terme de Surface Dans le CalculdesFoundations en Milieu Pulverulent[C]//Proceedings of the 3 rdInternational Conference on Soil Mechanics and FoundationEngineering.1953:336-337. [39] Martin C M. New Software for Rigorous Bearing CapacityCalculations[C]//Proceedings of the British GeotechnicalAssociation International Conference on Foundations. Dundee:Thomas Telford,2003:581-592. [40] 杨峰,阳军生,张学民,等.斜坡地基单侧滑移破坏模式及承载力上限解[J].工程力学,2010,27(6):162-168. [41] 钱家欢,殷宗泽.土工原理与计算[M].2版.北京:水利水电出版社,1996.
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