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

    CONDITIONAL PROBABILITY METHOD FOR SOIL SLOPE STABILITY WITH SMALL SAMPLE

    • 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。

       

      Abstract: As a significant source of uncertainty, the statistical uncertainty due to limited samples considerably affects the result of slope stability evaluation. In this paper, a conditional probability approach(CPA)was proposed to lower the effects of statistical uncertainty on slope stability evaluation without adding further samples. First, the bias between the mean (μ) of a Gaussian population and the averaged value (X) of a small sample ( X ) taken from the population obeys the t distribution. Based on this condition, given a set of survey sample data X , a series of potential mean values (μi*) of the corresponding unknown population with random deviations from the X can be created(denoted by event Bi, i=1, 2, …). The occurrence probability of each case is quantified and denoted by P(Bi). Then, the stability analysis for each case can be performed. The result(e.g., failure probability Pfi) is seen as the conditional probability of event Bi(denoted by P(A|Bi)), where A stands for the event of slope failure. Finally, from the law of total probability, the sum of the product of P(Bi) and P(A|Bi) for all cases is treated as the slope failure probability(denoted by P(A)). To investigate the established method, a series of case studies were carried out. The result indicates that the CPA can efficiently reduce the discretion of the stability analysis result (i.e. P(A)), thereby lead to a more precise outcome than the conventional analysis method where the sample mean is directly utilized.

       

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