边坡稳定性塑性极限分析上限法研究
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摘要
极限分析上、下限定理是求解岩土工程问题的有效工具,极限分析上限法是岩土工程界的热点研究问题之一。解析解法和数值解法又是极限分析上限法的两种主要方法。论文围绕这两种方法在边坡稳定性方面的应用做了一些研究。在优化理论的基础上,研究了非线性破坏准则下边坡稳定性极限分析解析解法和边坡稳定性极限分析上限有限元法。具体研究内容如下：
(1)为了研究非线性破坏准则下的边坡稳定性极限分析上限法,介绍了线性和非线性破坏准则,阐述了极限分析法和数学规划法的基本理论。
(2)在非线性破坏准则下,引入外切直线法,采用条分法与极限分析上限法相结合的方法,推导出不同滑裂面边坡稳定性安全系数F的隐式表达式,采用序列二次规划技术,计算出非线性破坏准则下的边坡稳定性安全系数F和稳定性系数Ns。通过一具体算例,分析了非线性破坏准则对边坡稳定性的影响；将计算结果与已有研究成果进行了比较,结果表明本文方法的正确性。
(3)在上限定理的基础上,采用有限元离散法离散了边坡体,构建了单元速度模式,建立了线性规划模型；采用优化方法获得了边坡极限荷载p上和边坡稳定性安全系数F。为了验证理论的可行性,对一个具体算例进行了计算,分析了相关参数对计算结果的影响。
Upper and lower bound limit analysis methods are effective tools in solving Geotechnical Engineering problems. The former is one of the most popular issues in the field of Geotechnical Engineering and it includes two main methods:analytical method and finite elements method. In this paper, some researches which focus on these two methods have been done in the application of slope stability. Based on the optimization theory, slope stability upper bound limit analysis method with nonlinear failure criterion and upper bound limit finite elements method have been studied. Specific contents are as follows:
To study the slope stability upper bound limit analysis method with nonlinear failure criterion, the author first introduced the linear and nonlinear failure criteria and then described in detail the basic theory of limit analysis and mathematical programming.
Under the nonlinear failure criterion, circumscribed linear method was introduced. By combining the slice method and limit analysis upper bound method, the author has deduced the implicit expressions of stability safety factor in slopes with different sliding surface. Slope stability factor and safety factor with a nonlinear failure criterion were calculated by using sequential quadratic planning techniques. The impact of a nonlinear failure criterion on slope stability was analyzed by a concrete example. Finally, some comparison with existing researches have been done, and the result shows that the method introduced by the paper is correct.
In the upper bound theorem, slope was discreted by finite element discretizational method. The paper has obtained the ultimate load and the safety factor by the mathematical programming after constructing the unit speed mode and setting up a linear programming model. In order to verify the feasibility of the theory, the author has analyzed a specific example. The impacts of relevant parameters on the calculation results has already been analyzed.
(1)为了研究非线性破坏准则下的边坡稳定性极限分析上限法,介绍了线性和非线性破坏准则,阐述了极限分析法和数学规划法的基本理论。
(2)在非线性破坏准则下,引入外切直线法,采用条分法与极限分析上限法相结合的方法,推导出不同滑裂面边坡稳定性安全系数F的隐式表达式,采用序列二次规划技术,计算出非线性破坏准则下的边坡稳定性安全系数F和稳定性系数Ns。通过一具体算例,分析了非线性破坏准则对边坡稳定性的影响；将计算结果与已有研究成果进行了比较,结果表明本文方法的正确性。
(3)在上限定理的基础上,采用有限元离散法离散了边坡体,构建了单元速度模式,建立了线性规划模型；采用优化方法获得了边坡极限荷载p上和边坡稳定性安全系数F。为了验证理论的可行性,对一个具体算例进行了计算,分析了相关参数对计算结果的影响。
Upper and lower bound limit analysis methods are effective tools in solving Geotechnical Engineering problems. The former is one of the most popular issues in the field of Geotechnical Engineering and it includes two main methods:analytical method and finite elements method. In this paper, some researches which focus on these two methods have been done in the application of slope stability. Based on the optimization theory, slope stability upper bound limit analysis method with nonlinear failure criterion and upper bound limit finite elements method have been studied. Specific contents are as follows:
To study the slope stability upper bound limit analysis method with nonlinear failure criterion, the author first introduced the linear and nonlinear failure criteria and then described in detail the basic theory of limit analysis and mathematical programming.
Under the nonlinear failure criterion, circumscribed linear method was introduced. By combining the slice method and limit analysis upper bound method, the author has deduced the implicit expressions of stability safety factor in slopes with different sliding surface. Slope stability factor and safety factor with a nonlinear failure criterion were calculated by using sequential quadratic planning techniques. The impact of a nonlinear failure criterion on slope stability was analyzed by a concrete example. Finally, some comparison with existing researches have been done, and the result shows that the method introduced by the paper is correct.
In the upper bound theorem, slope was discreted by finite element discretizational method. The paper has obtained the ultimate load and the safety factor by the mathematical programming after constructing the unit speed mode and setting up a linear programming model. In order to verify the feasibility of the theory, the author has analyzed a specific example. The impacts of relevant parameters on the calculation results has already been analyzed.
引文
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[4]李泽.考虑孔隙压力的有限元塑性极限分析法研究：[硕士学位论文].武汉：武汉大学,2005
[5]Drucker D C, Prager W. Soil mechanics and plastic analysis in limit design[J]. Quarterly Journal of Applied Mathematics,1952,10(2): 157-165
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[12]肖成志,栾茂田,杨庆等.土工格栅均布加筋土坡稳定性分析的上限解法[J].岩石力学与工程学报,2005,24(增1)：5076-2080
[13]乔丽平,王钊.加筋土坡临界高度的研究[J].岩土力学,2006,27(1)：132-136
[14]崔新壮,姚占勇,商庆森,等.加筋土坡临界高度的极限分析[J].中国公路学报,2007,20(1)：1-6
[15]杨小礼.线性与非线性破坏准则下岩土极限分析方法及应用：[博士学位论文].长沙：中南大学,2002
[16]YANG Xiao-li, LI Liang, YIN Jian-hua. Stability analysis of rock slopes witli a modified Hoek-Brown failure criterion[J] International Journal for Numerical and Analytical Methods in Geomechanics,2004,28(2):181-190
[17]YANG Xiao-li, YIN Jian-hua. Slope stability analysis with nonlinear failure criterion[J]. Journal of Engineering Mechanics,2004, 130(3):267-273
[18]YANG Xiao-li, LI Liang, YIN Jian-hua. Seismic and static stability analysis for rock slopes by a kinematical approach [J]. Geotechnique, 2004,54 (8):543-549
[19]杨小礼,李亮,刘宝探.非线性破坏准则对竖直边坡稳定性分析的影响[J].岩石力学与工程学报,2004,23(4)：592-596
[20]杨小礼,李亮,刘宝深.岩土工程中极限分析数值模拟的研究进展[J].有色金属,2002,54(3)：107-112
[21]杨小礼,李亮,刘宝深.非线性破坏准则对竖直边坡稳定性分析的影响[J].岩石力学与工程学报,2004,23(4)：592-596
[22]Yang Xiao-Li, Yin Jian-Hua. Slope Equivalent Moch-Coulomb Strength Parameters for Rock Masses Satisfying the Hoek-Brown Creterion[J]. Rock Mech Rock Eng. DOI10.1007/s00603-009-0044-2,2009
[23]杨小礼.岩石极限分析非线性理论及应用[J].中南大学学报(自然科学版),2009,40(1)：225-229
[24]李新坡,何思明,徐骏,等.预应力锚索加固土质边坡的稳定性极限分析[J].四川大学学报(工程科学版),2006,38(5)：82-85
[25]李新坡,张正波,吴永,等.非线性破坏准则的竖直边坡稳定性分析[J].四川大学学报(工程科学版),2009,41(增)：80-83
[26]Miller T W. Hamilton J H. Discussion on a new analysis procedure to explain a slope failure at the Martin Lake mine[J]. Geotechnique, 1990,40(1):145-147
[27]Michalowski R L. Slope stability analysis:a kinematical approach[J] Geotechnique,1995,45(2):283-293
[28]梁仕华,应宏伟,谢康和,等.能量法在土钉支护结构分析中的应用[J].岩石力学与工程学报,2005,24(4)：721-728.
[29]Li X P, He S M, Wang C H. Stability analysis of slopes reinforced with piles using limit analysis method[C]. Geo-Shanghai International Conference, Geotechnical Special Publication,2006
[30]年廷凯,栾茂田,杨庆.抗滑桩加固土坡稳定性分析与桩基的简化设计 [J].岩石力学与工程学报,2005,24(19)：3427-3433
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