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

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。

There is a correlation between each loess strength parameters.In the traditional slope stability calculation,the loess strength parameters c andφare 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 andφvalue.The stability of the slope will be seriously under-estimated when the c andφnegative 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.