| 先验概率分布及似然函数模型的选择对边坡可靠度评价影响的定量评估 |
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| 引用本文： | 蒋水华,刘源,章浩龙,黄发明,黄劲松.先验概率分布及似然函数模型的选择对边坡可靠度评价影响的定量评估[J].岩土力学,2020,41(9):3087-3097. |
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| 作者姓名： | 蒋水华 刘源 章浩龙 黄发明 黄劲松 |
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| 作者单位： | 1. 南昌大学 建筑工程学院，江西 南昌 330031；2. 中国科学院武汉岩土力学研究所 岩土力学与工程国家重点实验室，湖北 武汉 430071 |
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| 基金项目： | 国家自然科学基金项目（No.41867036，No.41972280，No.51679117）；江西省自然科学基金项目（No.20181ACB20008）；岩土力学与工程国家重点实验室资助课题（No.Z019019） |
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| 摘 要： | 受工程勘察成本及试验场地限制，可获得的试验数据通常有限，基于有限的试验数据难以准确估计岩土参数统计特征和边坡可靠度。贝叶斯方法可以融合有限的场地信息降低对岩土参数不确定性的估计进而提高边坡可靠度水平。但是，目前的贝叶斯更新研究大多假定参数先验概率分布为正态、对数正态和均匀分布，似然函数为多维正态分布，这种做法的合理性有待进一步验证。总结了岩土工程贝叶斯分析常用的参数先验概率分布及似然函数模型，以一个不排水黏土边坡为例，采用自适应贝叶斯更新方法系统探讨了参数先验概率分布和似然函数对空间变异边坡参数后验概率分布推断及可靠度更新的影响。计算结果表明：参数先验概率分布对空间变异边坡参数后验概率分布推断及可靠度更新均有一定的影响，选用对数正态和极值I型分布作为先验概率分布推断的参数后验概率分布离散性较小。选用Beta分布和极值I型分布获得的边坡可靠度计算结果分别偏于保守和危险，选用对数正态分布获得的边坡可靠度计算结果居中。相比之下，似然函数的影响更加显著。与其他类型似然函数相比，由多维联合正态分布构建的似然函数可在降低对岩土参数不确定性估计的同时，获得与场地信息更为吻合的计算结果。另外，构建似然函数时不同位置处测量误差之间的自相关性对边坡后验失效概率也具有一定的影响。
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| 关 键 词： | 边坡可靠度 贝叶斯方法 先验概率分布 似然函数 空间变异性 |
| 收稿时间： | 2019-11-07 |
| 修稿时间： | 2020-03-19 |
Quantitatively evaluating the effects of prior probability distribution and likelihood function models on slope reliability assessment |
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| JIANG Shui-hua,LIU Yuan,ZHANG Hao-long,HUANG Fa-ming,HUANG Jin-song.Quantitatively evaluating the effects of prior probability distribution and likelihood function models on slope reliability assessment[J].Rock and Soil Mechanics,2020,41(9):3087-3097. |
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| Authors: | JIANG Shui-hua LIU Yuan ZHANG Hao-long HUANG Fa-ming HUANG Jin-song |
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| Institution: | 1. School of Civil Engineering and Architecture, Nanchang University, Nanchang, Jiangxi 330031, China; 2. State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, Hubei 430071, China |
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| Abstract: | The number of available site-specific test data is often sparse because of limited budgets and inherent restrictions at the project sites. It is difficult to evaluate accurate statistics of geotechnical parameters and slope reliability based on such limited test data. Bayesian analysis method can effectively reduce the estimation of the uncertainties of geotechnical parameters and improve the slope reliability by integrating the limited site-specific information. However, currently most Bayesian updating studies assume the prior probability distributions of geotechnical parameters as normal, lognormal and uniform distributions, and assume the likelihood function as multivariate normal distribution. The rationale behind this assumption needs to be verified. To this end, this paper summarizes commonly-used prior probability distribution and likelihood function models for Bayesian analysis in geotechnical engineering. An undrained clay slope is investigated as an example to explore the influences of the prior probability distribution and likelihood function on the inference of posterior probability distributions of geotechnical parameters and reliability updating of spatially varying slopes based on an adaptive Bayesian updating approach. The results indicate that the prior probability distribution has an important influence on the inference of posterior probability distributions and reliability updating of spatially varying slopes. The obtained posterior probability distributions of geotechnical parameters are less spread when the lognormal and extreme value I distributions are selected as the prior probability distribution. The obtained slope reliability results are conservative and risky,
respectively, when the Beta and extreme value I distributions are chosen; while they are in the middle when the lognormal distribution is chosen. In contrast, the likelihood function has more significant effects. In comparison with the other types of likelihood function, the likelihood function constructed using joint multivariate normal distribution not only can reduce the estimation of the uncertainties of geotechnical parameters, but also can obtain more consistent results with the site-specific information. In addition, the autocorrelation of the measurement errors at different locations that used in constructing the likelihood function also has a certain effect on the posterior probability of slope failure. |
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| Keywords: | slope reliability Bayesian method prior probability distribution likelihood function spatial variability |
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