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《建筑科学与工程学报》[ISSN:1673-2049/CN:61-1442/TU]

卷:

41卷

期数:

2024年02期

页码:

163-172

栏目:

岩土工程

出版日期:

2024-03-30

文章信息/Info

Title:

Bayes estimation of mean and variance for shear strength parameters of loess and its application

文章编号:

1673-2049(2024)02-0163-10

作者:

李 萍^1,2,董鸾花³,赵枝艳^1,2,李金明^1,2,沈 伟^1,2,李同录^1,2

(1. 长安大学 地质工程与测绘学院,陕西 西安 710054; 2. 黄土高原水循环与地质环境教育部野外科学观测研究站,甘肃 正宁 745399; 3. 陕西省水利电力勘测设计研究院,陕西 西安 710005)

Author(s):

LI Ping^1,2, DONG Luanhua³, ZHAO Zhiyan^1,2, LI Jinming^1,2, SHEN Wei^1,2, LI Tonglu^1,2

(1. School of Geological Engineering and Geomatics, Chang'an University, Xi'an 710054, Shaanxi, China; 2. Water Cycle and Geological Environment Observation and Research Station for the Chinese Loess Plateau, Zhengning 745399, Gansu, China; 3. Shaanxi Province Institute of Water Resources and Electric Power Investigation and Design, Xi'an 710005, Shaanxi, China)

关键词:

黄土;  边坡;  Bayes理论;  先验分布;  正态-逆伽马分布

Keywords:

loess;  slope;  Bayes theory;  priori distribution;  normal inverse gamma distribution

分类号:

TU444

DOI:

10.19815/j.jace.2022.04123

文献标志码:

A

摘要:

为解决黄土强度参数估计问题,从工程勘察项目中共收集统计了3 384组Q₁、Q₂、Q₃黄土强度参数黏聚力c、内摩擦角φ值的测试数据,不考虑二者的相关性,将参数均值和方差都作为随机变量,建立起黄土强度参数c、φ的正态-逆伽马先验分布。基于Bayes理论,利用共轭先验法推导了参数后验分布和后验概率密度函数的期望值求解公式,确定了估计的误差。以陕西泾阳黄土边坡为例,利用所建立的先验分布和边坡土层测试强度指标,求取参数的后验分布,进一步估计了边坡失效概率的概率分布和稳定系数均值的概率分布。结果表明:在95%的置信度下,按稳定系数评价,边坡均处于基本稳定状态,且稳定系数置信区间小; 按失效概率评价,边坡接近稳定状态,但失效概率的置信区间较大,黄土强度参数的方差控制着边坡失效概率的置信区间,将方差作为随机变量,考虑方差变异性,能更科学地评估黄土工程的可靠度。

Abstract:

In order to solve the problem of estimating the strength parameters of loess, 3 834 sets of Q₁, Q₂, Q₃ loess strength parameters c(cohesive force), φ(internal friction angle)from engineering survey projects test data were collected and statistically analyzed. Without considering the correlation between the two, both the mean and variance of the parameters were used as random variables to establish normal inverse gamma priori distribution of the loess strength parameter c, φ. Based on Bayes theory, the expected value solution formulas for the posterior distribution of parameters and the posterior probability density function were derived using the conjugate prior method, and the estimation error was determined. Taking the loess slope of Jingyang in Shaanxi as an example, using the established prior distribution and the strength index of the slope soil layer test, the posterior distribution of the parameters was obtained, and the probability distribution of slope failure probability and the probability distribution of the mean stability coefficient were further estimated. The results show that at a 95% confidence level, according to the stability coefficient evaluation, the slopes are in a basically stable state, and the confidence interval of the stability coefficient is small. According to the evaluation of failure probability, the slope is close to a stable state, but the confidence interval of failure probability is relatively large. The variance of loess strength parameters controls the confidence interval of slope failure probability. Using variance as a random variable and considering variance variability can more scientifically evaluate the reliability of loess engineering.

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备注/Memo

备注/Memo:

收稿日期:2023-04-09
基金项目:国家自然科学基金项目(42041006,41877242); 中国电建集团西北勘测设计研究院有限公司资助项目(XBY-PTKJ-2022-8)
作者简介:李 萍(1971-),女,工学博士,教授,博士生导师,E-mail:dcdgx07@chd.edu.cn。

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更新日期/Last Update: 2024-03-25