Bayes estimation of mean and variance for shear strength parameters of loess and its application
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.
loessslopeBayes theorypriori distributionnormal inverse gamma distribution
万方数据
维普
