Characterization Of Variability Of Correlated Soil Properties And Geotechnical Reliability Analysis

The stability evaluations of slope,foundation and other geotechnical structures in hydropower projects is of great significance to ensure the safety of the project.Because of the variability of soil parameters,the reliability method to evaluate the safety performance of geotechnical engineering is gradually favored.The reliability evaluation of geotechnical structure depends on probability model of soil parameters.Two common probability models are random variable model and random field model.As to the random variable model,it is common that many soil parameters are statistically correlated,which should be considered in the process of constructing random variable models.The mathematical tools such as Nataf transformation and copula function provide effective tools to construct random variable model considering the correlation between soil parameters.Inferring probability models of soil parameters of a specific site depends on the soil investigation information of the site.This work,however,is blocked by the statistical uncertainty results from limited information of site investigation.The characterization of probability model of soil parameters under the condition of limited data is a necessary work for the reliability evaluation in specific sites.At present,methods for characterizing of the two-dimensional random variable model of soil parameters have some technical problems such as the low efficiency of reliability calculation and the imperfection of considering the statistical uncertainty.Therefore,how to improve the efficiency of characterizing probability model and estimating geotechnical reliability considering statistical uncertainty under the condition of limited data is a key problem to promote the application of reliability theory in geotechnical engineering.In addition,the reliability-based design of geotechnical engineering is an important application of variability characterization of soil parameters.The current reliability-based design method is mainly the semi probabilistic reliability-based design method.And the total probabilistic reliability-based method has also gained much attention.However,few reliability-based design research work consider the influence of statistical uncertainty of correlated soil parameters under the condition of limited data,which has become one of the main factors hindering the wide application of reliability theory in geotechnical engineering design.Therefore,how to consider the statistical uncertainty in reliability-based design is a key problem to improve the reliability-based design method.As to another probabilistic model,the construction of random field model is of great significance for reliability analysis considering the spatial variability of soil parameters.For the random field of a single soil parameter,the traditional random field analysis method based on the mean value,standard deviation,fluctuation range and correlation function cannot characterize the autocorrelation structure between spatial discrete points.For multivariable random fields,the traditional method based on Nataf transformation cannot characterize the spatial cross-correlation structure among different soil parameters.Therefore,how to quantitatively characterize the random field model considering the autocorrelation structure and the cross-correlation structure is a key problem in the application of random field to characterize spatial variability.In view of the above three key problems,this paper focus on the quantitative characterization of random variable model and random field model,and reliability estimation and design,during which the copula function for modelling joint probability distribution function,resampling method dealing with statistical uncertainty and the Bayesian method are involved.The current research includes six specific contents: the statistical uncertainty characterization of two-dimensional random variable model of soil parameters based on resampling method and Bayesian method;reliability analysis considering statistical uncertainty of two-dimensional random variable model of soil parameters;reliability-based design of foundation considering the statistical uncertainty of correlated soil parameters;quantitative characterization of univariate and multivariate random field model of soil parameters based on the Bayesian method.The main work and conclusions are as follows:(1)In view of the low efficiency of traditional methods in reliability calculation considering statistical uncertainty,a jackknife method is proposed to model the statistical uncertainty of two-dimensional random variable model of soil parameters.The accuracy and efficiency of the proposed method are verified by comparing with the traditional method.This method can greatly improve the efficiency of interval estimation of reliability index when considering the statistical uncertainty of joint probability model of two-dimensional soil parameters,especially in the complex reliability analysis of geotechnical engineering.It provides a feasible way to evaluate the structural safety considering the statistical uncertainty in practical engineering.(2)A Bayesian method is proposed to efficiently model the statistical uncertainty of the random variable model of soil parameters based on Copula function.Under Bayesian framework,the likelihood function is reconstructed by resampling method,which avoids the complex integration problem in the solution of Bayesian posterior distribution,and greatly improves the efficiency of the solution of Bayesian posterior distribution.The proposed method can take into account both the uncertainty of distribution parameters and the uncertainty of distribution types to quantitatively characterize the two-dimensional joint probability model based on Copula function.It provides an effective tool for probability model characterization of soil parameter and reliability analysis based on Copula function in geotechnical engineering.(3)Under Bayesian framework,a method is proposed to estimate the failure probability by considering the uncertainty of distribution type and distribution parameters based on copula function.The influence of the uncertainty of distribution type and distribution parameter on reliability estimation of shallow foundation is studied.In the case of limited soil samples,the way considering the two uncertainties to estimate the failure probability can consider the possibility of various parameter values as the actual parameters and the possibility of each alternative model as the best-fit model.Therefore the results are more reasonable.The proposed method provides an effective way to minimize the impact of statistical uncertainty by using all available site-specific information.(4)In view of the defect that the traditional reliability-based design method cannot deal with the statistical uncertainty caused by limited site-specific information,the full probabilistic reliability-based design method and the semi probabilistic reliability-based design method considering the statistical uncertainty of correlated soil parameters are proposed.By using bootstrap method to model the statistical uncertainty of probability model,a robust design scheme can be directly designed by considering the statistical uncertainty in the full probabilistic reliability-based design.For the semi probabilistic reliability-based design,the resistance partial coefficient obtained by calibration considering the statistical uncertainty is smaller,and therefore the scheme obtained with the calibrated resistance partial coefficient is more conservative.The calibration results show the recommended partial resistance coefficient for foundation design,classified according to different number of samples.The proposed method directly and clearly provides a robust design method.(5)In view of the defect that the traditional characterization method for random field of soil parameters cannot characterize the non-Gaussian autocorrelation structure,the framework of random field model based on vine copula function considering autocorrelation structure is improved.Considering the limited amount of data in geotechnical engineering,a Bayesian method for quantitative characterization of single variable random field model is proposed.This method can effectively estimate the random field model based on the limited site-specific information.The proposed method can characterize the spatial variability,including the autocorrelation structure between spatial discrete points.It allows the correlated variables with different spatial distances to have different correlation structure types,which,as a result,can more accurately model the spatial variability.It provides an effective way to estimate the random field considering the autocorrelation structure under the condition of limited survey information.(6)In order to solve the problem that the traditional characterization method of cross-correlation random field cannot consider the non-Gaussian cross-correlation structure,a new method for modelling the cross-correlation random field model based on vine copula function is proposed.Considering the limited number of samples used to infer the random field in geotechnical engineering,a Bayesian method based on the limited data is proposed to quantitatively characterize the cross-correlation random field model.This method can effectively estimate the cross-correlation random field model based on the limited survey information.Moreover,it can characterize the spatial variability including autocorrelation structure and cross-correlation structure,which,as a result,is more comprehensive than the traditional characterization method.It is an effective tool to estimate the cross-correlated random field model under the condition of limited data.