边坡的极限分析上限法具有较严谨的理论基础和物理意义,且可以在得到安全系数的同时找到最危险的临界失稳速度场,因此具有较广阔的应用前景。针对目前上限有限元法中被广泛采用的外切多边形逼近摩尔库伦屈服圆所带来的收敛速度慢的缺点,放松边坡内任一点需严格满足上限性质的要求,将多边形采用最佳平方逼近的形式逼近屈服圆,并系统地推导出了最佳平方逼近形式的上限有限元法的整个计算模型。算例表明该方法不仅继承了外接多边形从上方逼近解析解的优点,而且采用较少的多边形边数即可得到较为精确的结果,收敛速度大大提高。
Abstract
The upper bound limit analysis has broad application prospect as it has rigorous theoretical basis and clear physical meaning, and could give the safety factor as well as the critical velocity field at the same time. But it has slow convergence speed because of circumscribed polygon approximation (which is widely used) to Mohr-Coulomb yield circle. In view of this, we alleviated the requirement that all the points must strictly meet the limit properties, adopted the optimal square polygon approximation to the yield circle, and finally obtained the systematic calculation model of upper bound finite element based on optimal square polygon approximation. Numerical example shows that the method not only inherits the advantage circumscribed polygon have which approximates analytic solution from the upper, but also gets a precise result by less number of polygon edges, and also greatly improves the convergence speed.
关键词
极限分析 /
上限有限元法 /
摩尔库伦屈服圆 /
多边形最佳平方逼近 /
解析解 /
边坡稳定
Key words
limit analysis /
upper bound finite element method /
Mohr-Coulomb yield circle /
optimal square approximation /
analytical solution /
slope stability
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
参考文献
[1] 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.
GRIFFITHS D V, LANE P A. Slope Stability Analysis by Finite Elements. Geotechnique, 1999, 49(3):387-403.
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(1):1-7.(SONG Er-xiang. Finite Element Analysis of Safety for Soil Structure. Chinese Journal of Geotechnical Engineering, 1997, 19(1):1-7.(in Chinese))
DRUCKER D C, GREENBERG H J, PRAGER W. The Safety Factor of an Elastic-plastic Body in Plane Strain. Journal of Applied Mechanics Transactions of the ASME, 1951, 18(4): 371-378.
CHEN W F. Soil Mechanics and Theorems of Limit Analysis. Journal of Soil Mechanics & Foundations Division, 1969, 95(2): 493-518.
MICHALOWSKI R L. Slope Stability Analysis: A Kinematical Approach. Geotechnique, 1995, 45(2):283-293.
FARZANEH O, ASKARI F. Three Dimensional Analysis of Nonhomogeneous Slopes. Journal of Geotechnical and Geoenvironmental Engineering, 2003, 129(2): 137-145.
陈祖煜.土质边坡稳定分析.北京:中国水利水电出版社,2003. (CHEN Zu-yu. Stability Analysis on Soil Slope. Beijing: China Water Power Press, 2003. (in Chinese))
SLOAN S W. Upper Bound Limit Analysis Using Finite Element and Linear Programming. International Journal of Analytical Methods in Geomechanics, 1989,13(3): 263-282.
SLOAN S W. Upper Bound Limit Analysis Using Discontinuous Velocity Fields. Journal of Computer Methods in Applied Mechanics and Engineering, 1995, 127(4): 293-314.
王均星,王汉辉,张优秀,等.非均质土坡的有限元塑性极限分析.岩土力学,2004,25(3):415-421.(WANG Jun-xing, WANG Han-hui, ZHANG You-xiu, et al. Plastic Limit Analysis of Heterogeneous Soil Slope Using Finite Elements. Rock and Soil Mechanics, 2004, 25(3):415-421. (in Chinese))
杨小礼,李 亮,李克坤.上限原理法及其在陆地稳定性分析中的应用.长沙铁道学院学报,2002,20(l):41-45. (YANG Xiao-li, LI Liang, LI Ke-kun. Bearing Capacity Analysis of Subgrade Soil Using Upper Bound Finite Element Method. Journal of Changsha Railway University, 2002, 20(l):41-45. (in Chinese))
王敬林,钱开东,陈壁强.广义塑性理论上限法及其在边坡工程中的应用.重庆建筑,2002,(2):20-23. (WANG Jing-lin, QIAN Kai-dong, CHEN Bi-qiang. Generalized Plastic Upper Bound Method and Its Application in Slope Engineering. Chongqing Architecture, 2002, (2):20-23. (in Chinese))
李庆扬,王能超,易大义. 数值分析. 北京:清华大学出版社,2001. (LI Qing-yang, WANG Neng-chao, YI Da-yi. Numerical Analysis. Beijing: Tsinghua University Press, 2001. (in Chinese))
李国英, 沈珠江.下限原理有限单元法及其在土工问题中的应用. 岩土工程学报, 1997, 19(5): 84-89. (LI Guo-ying, SHEN Zhu-jiang. Lower Bound Finite Element Method and Its Application in Geotechnical Problems. Chinese Journal of Geotechnical Engineering, 1997, 19(5): 84-89. (in Chinese))
ABRAMSON L W, LEE T S, SHARMA S. Slope Stability and Stabilization Methods. New York: Wiley, 1996.
PDF(1250 KB)
