岩土强度参数正态–逆伽马分布的最大后验估计

doi:10.13722/j.cnki.jrme.2018.1385

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摘要岩土强度参数的概率分布特征参数是确定强度参数标准值和可靠度分析及风险评估的基础，目前采用现场数据进行估计的方法存在小样本信息量不足的问题，为此，基于贝叶斯统计理论提出服从正态分布的岩土强度参数的概率特征参数服从于一个二维联合先验分布，并根据贝叶斯公式推导相应的共轭后验分布函数，以及岩土强度参数概率特征参数的最大后验估计量计算公式。以重庆万州区域内若干工程的泥岩和砂岩的黏聚力、内摩擦角的历史数据为例，建立先验分布函数，先统计单个工程的现场样本均值和方差，然后将若干工程的均值和方差组成新的样本，以此样本为基础采用参数估计得到理论推导确定的先验分布中的超参数，从而确定该区域泥岩和砂岩黏聚力及内摩擦角的先验分布函数，结合该区域内一个工程算例的现场数据，得到该工程在现场样本情况下泥岩和砂岩黏聚力及内摩擦角的概率分布特征参数的后验分布函数和最大后验估计值，并计算相应的黏聚力及内摩擦角的标准值，与传统方法确定的标准值进行比较，表明提出的贝叶斯方法综合了历史数据和现场数据的信息，更为科学合理。

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	吴越1
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	刘东升3
	孙树国3
	秦宗兴3
	吴同情1
	2

关键词 ：岩土工程, 岩土强度参数, 先验分布, 正态&ndash, 逆伽马分布, 最大后验估计

Abstract：The probability distribution characteristic parameters of geotechnical strength indices are necessary for determining the standard values of geotechnical strengths，analyzing reliability and evaluating risk. Existing method using in-situ data has the problem of insufficient information due to small samples. Based on Bayesian theory，in this paper，it is proposed that the probability characteristic parameters of geotechnical strengths obey a 2D Joint Prior Distribution，and a posterior distribution function and an equation for calculating the maximum posteriori estimator were deduced. Taking the cohesion and internal friction angle of mudstone and sandstone from Wanzhou for example，the hyper-parameter of the Prior Distribution Function was obtained based on the sample of means and variance of geotechnical strengths from different projects and consequently，the Prior Distribution Function of the cohesion and internal friction angle of mudstone and sandstone in Wanzhou was determined. By using the field data of an actual project，the posterior distribution and the maximum posteriori estimator of the probability characteristic parameters of mudstone and sandstone strengths were determined，and the standard values of the cohesion and the internal friction angle were calculated. Comparison with conventional methods shows that the new Bayesian method containing the information of historical and field data is more scientific and reasonable.

Key words： geotechnical engineering geotechnical strength parameters prior distribution normal-inverse gamma distribution maximum posteriori estimation

引用本文:

吴越1，2，刘东升3，孙树国3，秦宗兴3，吴同情1，2. 岩土强度参数正态–逆伽马分布的最大后验估计[J]. 岩石力学与工程学报, 2019, 38(6): 1188-1196.
WU Yue1，2，LIU Dongsheng3，SUN Shuguo3，QIN Zongxing3，WU Tongqing1，2. Maximum posteriori estimation of strength parameters for geotechnical material obeying normal-inverse Gamma distribution. , 2019, 38(6): 1188-1196.

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http://www.rockmech.org/CN/10.13722/j.cnki.jrme.2018.1385 或 http://www.rockmech.org/CN/Y2019/V38/I6/1188

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