边坡工程可靠性分析的最大熵方法

王宇; 张慧; 贾志刚

边坡工程可靠性分析的最大熵方法

王宇¹,
张慧²,
贾志刚^1,2

1.
中国地质大学武汉工程学院武汉 430074;
2.
黄淮学院驻马店 463000

基金项目:

国家十一五科技支撑计划项目(2008BAC47B0)和交通部西部交通建设科技项目(200906)

详细信息

作者简介:
王宇,主要从事地质灾害评估,边坡及滑坡工程治理研究.Email: good541571889@126.com

中图分类号: TU457
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出版历程
- 收稿日期: 2011-05-20
- 修回日期: 2011-11-15
- 刊出日期: 2012-02-25

THE MAXIMUM ENTROPY METHOD FOR RELIABILITY ANALYSIS OF SLOPE ENGINEERING

1.
School of Engineering, China University of Geosciences, Wuhan 430074;
2.
Huanghuai University, Zhumadian 463000

摘要

摘要: 边坡工程可靠性分析的最大熵方法,利用已有样本的部分信息来使熵最大化,充分利用了随机变量的高阶矩信息,由样本矩来推断边坡可靠性功能函数的概率密度函数,求解边坡的破坏概率。该方法对基本随机变量的分布没有特别要求,避免了常规方法计算过程中在迭代点处对非正态随机变量进行近似当量正态化处理的缺陷。通常,功能函数的真实概率密度函数很难、甚至无法求得,将Pearson曲线族引入岩土参数随机变量高阶矩的求解当中,可以很容易地得到功能函数的高阶中心矩,然后,基于最大熵原理拟合得到功能函数的最大熵密度函数,采用区间截断法和高斯-克朗罗德数值积分法分别确定最大熵密度函数的拉格郎日系数和边坡的破坏概率。算例分析结果表明:该方法计算效率高,结果可靠,克服了传统方法求解过程复杂、精度低的缺点,将其应用于工程边坡的可靠性分析当中,发展潜力大,具有一定的应用前景和实用价值。
- 边坡工程 /
- 最大熵方法 /
- 可靠性分析 /
- Pearson曲线族 /
- 破坏概率
Abstract: The maximum entropy method is used to conduct the reliability analysis for slope engineering.The entropy is enlarged by the partial information of the existed samples.The high order moment information of the random variables fully uses the sample moment to infer the slope reliability probability density function.Then the slope failure probability is calculated.This method is for the distribution of basic random variables without special requirement.It avoids the conventional method in the process of computation in the iteration points for non-normal random variables to approximate the yield of the normal processes defects.Usually,the function of real probability density function is difficult to obtain,even cant be calculated.So the Pearson curve clan is introduced to solve the high-order moment for geotechnical parameter random variable.It can easily get the function of high order center.It is based on the maximum entropy principle moment fitting get function of maximum entropy density function.It uses the interval truncation method and Gauss-Kronrod respectively to determine the maximum entropy density function.An example is analyzed.The results show that this method is of high efficiency,reliable.It overcomes the problem of the traditional methods that the solving process is complicated and low accuracy of faults.The new method is applied in the reliability analysis of slope engineering.It has certain application prospect and practical value.
- Slope engineering /
- Maximum entropy method /
- Reliability analysis /
- Pearson Curve clan /
- Failure probability

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参考文献(1)

[1] Christian JT,Ladd CC,Baecher GB.Reliability applied to slope stability analysis.Journal Geotechnical Engineering Division, 1994, 120 (12): 2180～2207.

[2] 谭晓慧. 边坡稳定可靠度分析方法的探讨[J].重庆大学学报(自然科学版), 2001, 24 (6): 40～44.

Tan Xiaohui.Discussion of reliability analysis methods of slope stability.Journal of Chongqing University(Natural Science Edition), 2001, 24 (6): 40～44.

[3] 王宇, 王春磊,汪灿,等.边坡可靠性评价的向量投影响应面研究及应用[J].岩土工程学报, 2011, 33 (9): 1435～1439.

Wang Yu,Wang Chunlei,Wang Can,et al.Reliability evaluation of slopes based on vector projection response surface and its application.Chinese Journal of Geotechnical Engineering, 2011, 33 (9): 1435～1439.

[4] 宋云连, 汲敏,李树军.高边坡结构可靠度的二次处理有限元分析[J].工程地质学报, 2008, 16 (4): 522～527.

Song Yunlian,Ji Min,Li Shujun.Response surface methods for reliability analysis and its engineering application.Journal of Engineering Geology, 2008, 16 (4): 522～527.

[5] 张亚国, 张波,李萍,等.基于点估计法的黄土边坡可靠度研究[J].工程地质学报, 2011, 19 (4): 615～619.

Zhang Yaguo,Zhang Bo,Li Ping,et al.Research on loess slope reliability based on the point estimate method.Journal of Engineering Geology, 2011, 19 (4): 615～619.

[6] 章光, 朱维申,白世伟.计算近似失效概率的最大熵密度函数法[J].岩石力学与工程学报, 1995, 14 (2): 120～127.

Zhang Guang,Zhu Weishen,Bai Shiwei.A method of maximum entropy density function for calculation of approximate failure probability.Chinese Journal of Rock Mechanics and Engineering, 1995, 14 (2): 120～127.

[7] 邓建, 李夕兵,古德生.工程结构可靠性分析的最佳平方逼近法[J].计算力学学报, 2002, 19(2) 212～216.

Deng Jian,Li Xibing,Gu Desheng.Numerical approximation method in reliability analysis of engineering structure.Chinese Journal of Computational Mechanics, 2002, 19(2) 212～216.

[8] Siddal JN.Probabilistic Engineering Design: Principles and Applications.New York: Marcel Dekker Inc.1983, 92～125.

[9] 章光, 朱维申,白世伟.计算近似失效概率的最大熵密度函数法[J].岩石力学与工程学报, 1995, 14 (2): 119～129.

Zhang Guang,Zhu Wenshen,Bai Shiwei.A method of maximum entropy density function for calculation of approximate failure probability.Chinese Journal of Rock Mechanics and Engineering, 1995, 14 (2): 119～129.

[10] Zografos K.On maximum entropy characterization of Pearsons type Ⅱ and Ⅶ multivariate distribution.Journal of Multivariate Analysis, 1999, 71 (1): 67～75.

[11] 赵国藩. 工程结构可靠性理论与应用[M].大连: 大连理工大学出版社, 1996.

Zhao Guofan.Engineering Structure Reliability Theory and Application.Dalian: Dalian University of Technology Press, 1996.

[12] 吕震宙, 冯蕴雯,岳珠峰.改进的区间截断法及基于区间分析的非概率可靠性分析方法[J].计算力学学报, 2002, 19 (3): 260～264.

Lv Zhenzhou,Feng Yunwen,Yue Zhufeng.An advanced interval-truncation approach andnon-probabilistic reliability analysis based on interval analysis.Chinese Journal of Computation Mechanics, 2002, 19 (3): 260～264.

[13] 曹文贵, 张永杰.基区间截断法的地下结构模糊能度可靠性模型研究[J].岩土工程学报, 2007, 29 (10): 1456～1459.

Cao Wengui,Zhang Yongjie.Study on reliability model of fuzzy probability of underground structure with interval-truncation approach.Chinese Journal of Geotechnical Engineering, 2007, 29 (10): 1456～1459.

[14] 段永胜, 王宇,余宏明.基于正交设计和数值模拟的边坡稳定敏感性研究[J].公路交通科技(应用技术版), 2010,(9): 165～168.

Duan Yongsheng,Wang Yu,Yu Hongming.Sensitivity research of slope stability based on orthogonal design and numerical simulation.Journal of Highway and Transportation Research and Development(Application Technology Version), 2010,(9): 165～168.

[15] 王宇, 宋新龙,张行,等.边坡工程模糊随机可靠度分析[J].长江科学院院报, 2011, 28 (9): 31～34.

Wang Yu,Song Xinlong,Zhang Hang,et al.Fuzzy stochastic reliability analysis of slope engineering.Journal of Yangtze River Scientific Research Institute, 2011, 28 (9): 31～34.

[16] 苏永华, 赵明华,蒋德松,等.响应面方法在边坡稳定可靠度分析中的应用[J].岩石力学与工程学报, 2006, 25 (7): 1417～1424.

Su Yonghua,Zhao Minghua,Jiang Desong,et al.The response surface method in the slope stability reliability analysis.Chinese Journal of Rock Mechanics and Engineering, 2006, 25 (7): 1417～1424.

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