董鸾花,李萍,夏增选,李同录,GRIFFITHS D V,侯晓坤.基于参数相关的Bayes估计及在黄土边坡可靠度分析中的应用[J].西北地质,2020,53(4):186-193 DONG Luanhua,LI Ping,XIA Zengxuan,LI Tonglu,GRIFFITHS D V,HOU Xiaokun.Parameters-based Bayes Estimation and Its Application in the Reliability Analysis of Loess Slope[J].Northwestern Geology,2020,53(4):186-193
基于参数相关的Bayes估计及在黄土边坡可靠度分析中的应用
Parameters-based Bayes Estimation and Its Application in the Reliability Analysis of Loess Slope
投稿时间:2019-11-06  修订日期:2020-08-14
DOI:10.19751/j.cnki.61-1149/p.2020.04.017
中文关键词:  黄土边坡;Bayes理论;可靠度;相关性
英文关键词:loess slope;Bayes theory;reliability;correlation
基金项目:国家自然科学基金项目“黄土台塬灌区边坡可靠度及其防治及稳健决策”(41877242)
作者单位E-mail
董鸾花 长安大学地测学院, 陕西 西安 710054  
李萍 长安大学地测学院, 陕西 西安 710054 dcdgx07@chd.edu.cn 
夏增选 长安大学地测学院, 陕西 西安 710054  
李同录 长安大学地测学院, 陕西 西安 710054  
GRIFFITHS D V Department of Civil and Environmental Engineering, Colorado School of Mines, Colorado Golden USA Colorado, 80401  
侯晓坤 长安大学地测学院, 陕西 西安 710054
中国科学院地质与地球物理研究所, 北京 100029 
 
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中文摘要:
      黄土强度参数具有一定的相关性。在传统的边坡稳定性计算中,常把黄土强度参数c、φ值视为独立的2个参数,忽略了其相关性,导致计算结果存在一定的偏差。笔者采用二维联合正态分布拟合黄土强度参数的概率密度函数,应用Bayes公式对函数参数的取值进行优化。以西安咸阳机场排污口潜在滑坡为例,计算该边坡可靠性指标。研究结果表明,利用Bayes考虑了工程经验,估计结果的方差减小,使得黄土强度参数估计结果更为稳健,同时也减小因样本数量太少而产生的误差。相关系数对稳定系数几乎没有影响,对可靠度指标和失效概率的影响较大。当利用可靠度理论评价边坡稳定性时,不考虑c、φ值正相关系数,边坡的稳定性则会被高估;不考虑c、φ负相关性时,将严重低估边坡的稳定性。采用二维联合正态分布的Bayes估计强度参数,可对黄土边坡稳定性进行更为准确的评价。
英文摘要:
      There is a correlation between each loess strength parameters. In the traditional slope stability calculation, the loess strength parameters c and φ are often seen as two independent random variables. The neglect of their correlation leads to calculation deviation. In this paper, the two-dimensional joint normal distribution is used as the distribution profile of the loess strength parameters, and the Bayes formula is to optimize the parameters. Taking as an example of the potential landslide in the sewage outlet of Xi'an Xianyang Airport, the reliability index of the slope is calculated. The results show that Bayes makes it possible to reduce the variance of the estimated results, to get more reliable estimated results of loess strength parameter and what’s more, to avoid errors caused by small sample size. Correlation coefficient nearly has no effect on stability coefficient, but has much effect on the reliability index and the failure probability. The stability of the slope will be over-estimated without considering the positive correlation coefficient of c and φ value. The stability of the slope will be seriously under-estimated when the c and φ negative correlation is not taken into account. The estimated strength parameters from Bayes of two-dimensional joint normal distribution evaluate accurately the stability of loess slope.
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