小样本岩土参数下土质边坡可靠度分析的条件概率法

蒋良潍 赵晶 罗强 张文生 熊卫平 孔德惠

蒋良潍,赵晶,罗强,等. 2021.小样本岩土参数下土质边坡可靠度分析的条件概率法[J].工程地质学报,29(1):205-213. doi:10.13544/j.cnki.jeg.2020-302 doi: 10.13544/j.cnki.jeg.2020-302
引用本文: 蒋良潍,赵晶,罗强,等. 2021.小样本岩土参数下土质边坡可靠度分析的条件概率法[J].工程地质学报,29(1):205-213. doi:10.13544/j.cnki.jeg.2020-302 doi: 10.13544/j.cnki.jeg.2020-302
Jiang Liangwei, Zhao Jing, Luo Qiang, et al. 2021. Conditional probability method for soil slope stability with small sample[J]. Journal of Engineering Geology, 29(1): 205-213. doi: 10.13544/j.cnki.jeg.2020-302
Citation: Jiang Liangwei, Zhao Jing, Luo Qiang, et al. 2021. Conditional probability method for soil slope stability with small sample[J]. Journal of Engineering Geology, 29(1): 205-213. doi: 10.13544/j.cnki.jeg.2020-302

小样本岩土参数下土质边坡可靠度分析的条件概率法

doi: 10.13544/j.cnki.jeg.2020-302
基金项目: 

中央高校基本科研业务费专项资金 2682014CX064

国家自然科学基金 51878560

详细信息
    作者简介:

    蒋良潍(1974-),男,博士,副教授,从事岩土工程及路基路堤边坡可靠度研究. E-mail: 154999419@qq.com

  • 中图分类号: TU43

CONDITIONAL PROBABILITY METHOD FOR SOIL SLOPE STABILITY WITH SMALL SAMPLE

Funds: 

the Fundamental Research for the Central Universities 2682014CX064

the National Natural Science Foundation of China 51878560

  • 摘要: 岩土勘察取样数量有限是土工参数统计不确定性的重要来源,小样本条件下参数估计偏差向可靠度计算环节传递,导致分析结果呈现不确定性。针对小样本岩土参数 X ,围绕样本平均值X构造具有不同随机偏离程度的一系列假想参数总体均值 μ *,以μi*的不同取值为发生条件P(Bi)、对应的可靠度计算结果Pfi为条件概率P(A|Bi),基于Bayes全概率公式,建立了小样本岩土参数下计算边坡失效概率P(A)的条件概率分析方法。研究表明:参数正态总体的样本数量有限条件下,以t分布函数对总体均值μ发生抽样估计偏差(X-μ)的概率进行量化,以此作为权值对可靠度条件概率进行修正,得到更趋近可靠度真值的分析结果;由简单土坡算例验证,较之将样本平均值X替代总体均值μ进行可靠度计算的传统直接代入法,条件概率法能减小因参数估计偏差导致的计算结果离散性,一定程度上可提高小样本岩土参数下的边坡可靠性分析精准度。
  • 图  1  有限样本估计总体均值的偏差及其发生概率

    Figure  1.  Error and occurrence probability for the estimation of population mean based on limited samples

    图  2  条件概率法流程图

    Figure  2.  Flow chart of conditional probability method

    图  3  估计偏差的概率密度函数子区间划分

    Figure  3.  Subinterval division of the probability density function of estimation error

    图  4  简单土坡模型(单位:m)

    Figure  4.  Model of simple soil slope(unit: m)

    图  5  可靠指标散点图

    a.直接代入法;b.条件概率法

    Figure  5.  Scatter of reliability indices

    图  6  可靠指标的绝对误差与相对误差

    a.绝对误差;b.相对误差

    Figure  6.  Absolute error and relative error of reliability indices

    图  7  两种方法可靠指标相对误差直方图

    Figure  7.  Relative error histogram of the reliability indices from two methods

    图  8  子区间划分数目敏感性分析

    Figure  8.  Sensitivity analysis of subinterval numbers

    表  1  t分布子区间划分

    Table  1.   Subinterval division of the t distribution

    t分布子区间 TcjTφk μcj*/kPa μφk* /(°) P(Bcj)、P(Bφk)
    [-2.5706,-2.0706) -2.3206 15.054 26.553 0.0216
    [-2.0706,-1.5706) -1.8206 14.538 26.058 0.0420
    [-1.5706,-1.0706) -1.3206 14.021 25.563 0.0781
    [-1.0706,-0.5706) -0.8206 13.504 25.068 0.1298
    [-0.5706,-0.0706) -0.3206 12.988 24.573 0.1767
    [-0.0706,0.4294) 0.1794 12.471 24.078 0.1840
    [0.4294,0.9294) 0.6794 11.954 23.583 0.1451
    [0.9294,1.4294) 1.1794 11.438 23.088 0.0915
    [1.4294,1.9294) 1.6794 10.921 22.592 0.0503
    [1.9294,2.5706] 2.2500 10.331 22.027 0.0308
    下载: 导出CSV

    表  2  发生较大抽样偏差时两种方法可靠度分析结果对比

    Table  2.   Comparison of the reliability analysis results under large sampling bias

    抽样次序l 抽样误差/%
    c/φ
    β
    β2/β1
    绝对误差
    Δ21/(Δ21)
    相对误差/%
    e2/e1/(e2-e1)
    4# 8.69/15.40 2.85/1.72 1.70/0.57/(1.13) 147.83/49.56/(98.27)
    6# 19.69/9.67 2.29/1.71 1.14/0.56/(0.58) 99.13/48.69/(50.44)
    7# 21.59/9.54 1.81/1.24 0.66/0.09/(0.57) 57.39/7.83/(49.56)
    19# 12.90/15.86 2.55/1.78 1.40/0.63/(0.77) 121.74/54.78/(66.96)
    23# 9.97/9.48 2.32/1.27 1.17/0.12/(1.05) 101.74/10.43/(91.31)
    46# 21.39/12.68 2.33/1.80 1.18/0.65/(0.53) 102.61/56.52/(46.09)
    下载: 导出CSV
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  • 收稿日期:  2020-01-22
  • 修回日期:  2020-12-01
  • 刊出日期:  2021-02-01

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