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

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.

Key words: slope reliability, Bayesian method, prior probability distribution, likelihood function, spatial variability