Bayesian Characterization Of Probabilistic Models Of Soil Parameters And Slope Reliability Analysis

The variabilities of soil parameters are inherent properties of natural soils,and have significant effects on the behaviors,reliability analysis and risk-based decision making for geotechnical structures.Probabilistic models of soil parameters are the bases for quantificationally characterizing the varibilties of soils.Based on the probabilistic models of soil parameters,the varying soils and geological profiles can be figured out by site-specific data from ground investigation.Multi-source data(e.g.,in-situ tests,laboratory tests and geophysical tests)can be obtained from site investigation,and interpretations based on single-source data may result in wasting the costs and even un-reliable results.The existing method for characterization of variability of soil parameter is usually limited to point estimation of parameter statistics or quantification of one-dimensional probabilitic model of soil parameter.However,in practice,a 2D/3D geologic design profile of soil parameter is usually required.Ideally,the profile should be constrained by the survey data and reflect the overall and local variation of the data.Therefore,how to use multi-source survey information to determine the 2D conditional random field model of soil parameter is a key problem in the characterization of soil geologic profiles.Based on the aforementioned probabilistic model of soil parameter and data from ground investigation,direct predictions of behaviors of a geotechnical structure(e.g.,embankmen)usually deviate from the monitored data(e.g.,settlements and pore pressures).Accurate prediction of the behaviour is of great significance for theoretical and practical study of prediction and early-warning for geotechnical structures.Uasage of information from field monitoring contributes to accurate preditions of behaviors of geotechnical structures.Bayes'rule is the basic theory for updating the probabilistic models of soil parameters and predicting the behaviours of geotechnical structures.Trational methods for embankment predictions based on Bayesian theory have several limations:(a)the physical(e.g.,numerical and constutive models)models are overly-simplified;(b)there is no effective fusion of survey and monitoring data;(c)the ability to solve high-dimensional nonlinear problems needs to be improved.Characterization of the high-dimensional random variable models of soil parameters via integrating the data from site investigation and field monitoring is critical for accurate prediction of structual behaviours.The capability of the method in coping with a practical problem(e.g.,Ballina embankment prediction)deserves to be investigated.The probabilistic models of soil parameters have significant effects on the critical failure modes and reliability analysis.Surrogate model-based method can improve the efficiency of reliability calculation.However,the advantages and disadvantages of different surrogate models are not systematically compared.The accuracy and efficiency of different surrogate models in dealing with different soil slope reliability problems are not clear,and there is no recommendation on how to choose rational surrogate models for different problems.The surrogate model has wide applications in the community of slope reliability analysis,however,it has the problem of losing efficiency and accuracy in coping with high-dimensional problem.When considering soil spatial variability,the curse of dimensionality becomes more prominent.There is an urgent need to develop methods for reducing the dimension of input variables to fully improve the accuracy of the surrogate model and the computational efficiency of reliability analysis.In addition,the failure mechnisium of slope becomes more complex accounting for soil spatial variability.Identifying key failure modes of slope has the potential for contributing to slope reinforcement.Key failure modes and reliability analysis are the key elements of risk assessment.Therefore,identification of key failure mode and efficient slope reliability analysis considering soil spatial variability are both important and challenging issues.For this reason,this thesis focuses on the following three key scientific issues:(1)Characterization of two-dimensional random field model of soil parameter integrating multi-source information from site investigation;(2)Behavior prediction of embankment via integrating information from site investigation and field monitoring;(3)Identification of key failure modes of soil slope and efficient slope reliability analysis considering soil spatial vaiability.Focusing on the above scientific issues,the main research contents and achievements of this thesis are as follows:(1)A probabilistic characterization approach for two-dimensional random field model of soil parameter via integrating multi-source data from ground investigation is proposedThe Bayes' rule is adopted to integrate multi-source information from site investigation,the posterior distribution of model parameters of soil parameters is formulated.On the whole,part of information from cone penetration test is used to characterize a priori random field.Indirect data of surface wave velocities are incorporated into the Bayesian formula through a transformation model to further update the model parameters of random field of soil.The Karhunen-Loeve expansion method is adopted for discretizating the random field of soil parameter,and the model parameters of random field are determined by model parameterization process.An efficient multi-chain Markov Chain Monte Carlo(MCMC)simulation technique is used to update the model parameters and obtain posterior distributions.Based on the updated posterior distribution of model paramters,the two-dimensional(2D)random field model is updated and the corresponding soil profile is further characterized.Data from Ballina test site in Australia are used to perform the characterization of soil profile,it is found that the uncertainty of the profile of soil parameter decreases with the increasing of the data from site investigation.The 2D soil profile after fusion of multi-source information is constraited by site data,and can capture the spatial variation of the data globally and locally;the "weak" area is also identified.(2)A method for predicting embankment behaviors via integrating data from site investigation and field monitoring is proposedThe Bayesian formulas for updating random variable models of soil parameters integrating information from site investigation and field monitoring is constructed.The prior information is obtained by compiling the data from site investigation at Ballina site,literature and engineering experience.In conjuction with the widely-used Cam-Clay model,the consolidation of multi-layered embankment is simulated using finite element method.The multi-chain algithm,i.e.,MCMC(zs),is adopted for carrying out efficient MCMC sampling.The high-dimensional posterior distributions of model parameters are obtained,and the random variable models of soil parameters and profiles are updated.The behaviors of Ballina embankment are accurately predicted based on the updated soil parameters and profiles.For the Ballina embankment,the needed data for accurate predictions of settlement and pore water pressure,respectively,are determined.As the amount of monitored data increases,the predictions gradually converge to the monitored values.The statisticses of a priori distribution and monitoring error have different effects on the accuracy of prediction.(3)Selection criteria of surrogate model for soil slope reliability analysis considering variabilities of soil parameters is suggesttedThe probabilistic models of soil parameters are the bases for geotechnical reliability analysis.The influencial mechanisms of probabilistic models of soil parameters and soil stratification on slope failure are qualitatively analysed,and four types of typical soil slope reliability problems are summarized via mining and analyzing information from literature database.Type ?:single-layered slope considering random variable models of soil parameters;Type ?:single-layered slope considering random field models of soil parameters;Type III:multi-layered slope considering random variable models of soil parameters;Type IV:multi-layered slope considering random field models of soil parameters.The four surrogate models based on polynomials(see Chapter 5 for details)are quantificationally studied to solve the problems ?-?.In terms of computational accuracy and efficiency,the four types of RSMs are systematically compared in evaluating the reliability of cohesive and c-? soil slopes.SQRSM is recommended for single-layered slopes considering random variable models(Type ?);MSRSM is recommended when single-layered slopes consider random field models(Type ?);MQRSM is recommended for multi-layered slopes that consider random variable models(Type?).For the multi-layered slope considering random field models(Type ?),MSRSM is recommended.(4)A dimension reduction method is proposed for soil slope reliability analysis considering random field models of soil parametersBased on the probabilistic model of soil parameter,a large number of random variables are generated when using the traditional method(e.g.,mid-point method)to discretize the random field.The high-dimensional problem(i.e.,curse of dimensionality)is raised,which seriously restricts the accuracy and efficiency of the surrogate model under given training samples.A two-stage dimension reduction method allowing the surrogate to be constructed in a reduced low-dimension space is therefore proposed.This method can enhance the accuracy and also release the computational burden.The original high-dimensional input model is first represented with a low-dimensional random vector by a first-stage technique say KLE.Then this vector is mapped into a much lower dimensional space by a second-stage method(e.g.,sliced inverse regression).These allow the inexpensive surrogate construction with much less training samples.The results indicate that the input dimension after discreting random field is greatly reduced by the proposed method,and the surrogate model is constructed with low computational cost in the low-dimensional space,so that the efficient reliability analysis is realized without much loss of computational accuracy.(5)A method for quantifying correlations among slope failure models considering spatial variabilities of soil parameters is proposedWhen considering the random field models of soil parameters,the complex issue regarding to failure mechnisium of a soil slope with multiple failure modes is caused.The spatial variability has a significant influence on the identified key failure modes and slope system reliability.A new correlation coefficient(NCC)was proposed to evaluate the correlations between failure modes of a slope and to provide an effective tool for quantifying the correlations among multiple failure modes when considering soil spatial variability.Based on the NCC and Pearson correlation coefficients,the effects of soil spatial variability on the identified representative failure modes and the system probability of slope failure are investigated using a probabilistic network evaluation technique and a risk aggregation approach.The results indicate that compared with traditional approximate correlation coefficient,the NCC and Pearson correlation coefficients can effectively consider the influence of soil spatial variability on the correlations among slope failure modes.When soil spatial variability strengthens,the number of representative failure modes identified based on NCC and Pearson correlation coefficients gradually increasess,the failure mechnisim of slope becomes more complex,and the system probability of slope failure gradually decreases.