Characterization Of Statistical Uncertainty And Reliability Analysis For Geotechnical Parameters Using Bayesian Theory

The existence of complex spatial variability in rock and soil is the root cause of uncertainty in rock and soil.Since the safety of geotechnical structures is of paramount importance in geotechnical engineering,geotechnical reliability analysis is necessary.A large number of studies have shown that there is a significant correlation between geotechnical parameters.In order to accurately express the properties of geotechnical parameters,it is of great significance to establish a joint probability distribution model of geotechnical parameters.However,due to various economic and technical constraints,the available geotechnical parameters test data is very limited,and it is difficult to determine the joint probability distribution model of geotechnical parameters based on limited experimental data.Therefore,how to reduce the uncertainty of model selection and accurately establish the two-dimensional distribution model of rock and soil parameters under the condition of limited experimental data is a problem worth studying.At the same time,how to use the model to accurately analyze the reliability of geotechnical engineering is also a problem worth exploring.In view of the above problems,this paper combines Bayesian theory with Copula theory and applies it to the field of geotechnical reliability.Firstly,a parameter two-dimensional distribution model recognition method based on Bayesian theory is proposed to reduce the selection uncertainty of the parameter model.Secondly,a reliability analysis method based on Bayesian theory is proposed and combined with the parameter model identification method.It is applied to the reliability analysis of the foundation pile model and the foundation pit excavation model respectively.The main work and conclusions are as follows:(1)The identification method of optimal two-dimensional distribution model based on Bayesian theory is proposed,which verifies the effectiveness of Bayesian theory in identifying the optimal two-dimensional distribution model.The results show that Bayesian theory can effectively identify the optimal two-dimensional distribution model of soil shear strength parameters;Bayesian dependent identification method is the best representation method;the number of parameters,the correlation between parameters,preparation Selecting the two-dimensional distribution model set and the prior information all significantly affect the recognition accuracy of Bayesian theory.(2)Bayesian theory is applied to the statistical uncertainty analysis and reliability analysis of the probabilistic model parameters of the pile.The reliability of the normal use limit state(SLS)of the pile is used to verify the Marco based on Bayesian theory.The results show that the Markov chain Monte Carlo simulation method can effectively characterize the statistical uncertainty of the parameters of the small sample probability model,and can use a confidence interval with a specified confidence level to represent the failure probability of the pile.(3)The Bayesian theory is applied to the foundation pit excavation project to evaluate the applicability failure probability of the foundation pit during excavation,and the influence of the statistical uncertainty of the excavation model parameters on the failure probability of foundation pit excavation is characterized.The results show that the mean value of the failure probability of foundation pit excavation calculated by Markov chain Monte Carlo simulation method is larger than that obtained by the traditional reliability analysis method.The failure probability obtained by the traditional method is somewhat underestimated.