Simulation Of Cross-correlated Random Fields And Soil Slope Reliability Analysis Based On Copula Approach

Slope instability is one of the major geological disasters in the world.The study on slope stability has important economical and practical significances for the safety design,ecological environment,and life and property safety.Many uncertain factors affect slope stability.Among them,the uncertainties caused by uncertain probability distribution,spatial variability and cross-correlation of the rock and soil profiles are important sources of uncertainty in slope system.However,the random volatility in the real distribution of soil profiles is commonly neglected during estimating probability distribution.Furthermore,limited studies could be found on cross-correlated random fields which can characterize spatially variable soil profiles.The slope reliability analysis with considering cross-correlation needs to be deeply explored.Moreover,the computational efficiency of the random finite element method for slope reliability is seriously insufficient.In view of the above problems,this paper focuses on the characterization of spatial variability of cross-correlated soil profiles and the efficient method for slope reliability,with the help of reliability theory,probability theory and random field theory.The main works and conclusions are displayed as follows:(1)In view of the uncertainty caused by random volatility and cross-correlation of soil parameters in estimating probability distribution of soil profiles,the estimation method of probability distribution based on Copula function and information diffusion distribution is proposed.Firstly,the methods commonly used to estimate probability distribution of soil profiles are introduced.The information diffusion theory is adopted to estimate marginal distribution.The differences among information diffusion distribution and traditional models are discussed.The performance of the proposed marginal distribution is validated.Then,the estimation method of probability distribution for soil parameter based on information diffusion distribution and Copula function is proposed.The influence of soil parameter marginal distribution and dependence structure on joint distribution is analyzed.The effectiveness and accuracy of the proposed method are proved by an engineering case.It provides an effective tool for the representation of cross-correlated soil parameters and estimation of probability distribution.(2)In view of the uncertainties caused by cross-correlation and uncertain probability distributions of soil parameters in slope reliability analysis,a method of slope reliability analysis based on Copula and information diffusion distribution is proposed.The theory of slope reliability is introduced firstly.The commonly used Monte Carlo simulation(MCS)method and its derivative algorithm are reviewed.Based on MCS,the framework of the slope reliability analysis method based on Copula function and information diffusion distribution is put forward.The performance and effectiveness of the proposed method are verified by an engineering case.The influence of marginal distribution and Copula function on slope reliability is discussed.The performance of copula model coupling information diffusion distribution is demonstrated by comparing with the traditional joint distribution models.Results show that the marginal distribution and cross-correlation of soil parameters sievely affect slope reliability,which provides a basis for the probability analysis of slope stability with considering the cross-correlation of soil profiles.(3)Aiming at the characterization of spatially variable soil with considering cross-correlation,a simulation method based on Copula function is proposed.The basic theory of random field is introduced.The scale of fluctuation and correlation function of anisotropic random field are summarized.The influence of autocorrelation and cross-correlation of soil parameters on random field is analyzed.The simulation method of multivariate cross-correlated random fields based on Copula function is put forward.The proposed method is then validated by a classical slope model.The feasibility and effectiveness of the proposed method are discussed.The relationship between cross-correlation and spatial variability is discussed.The influence of Copula function and marginal distribution on the cross-correlated random fields is analyzed.Results show that the proposed simulation method for cross-correlated random fields based on Copula function can accurately simulate the distribution of soil parameters.The cross-correlation random fields generated by different Copulas are different,which provides theoretical basis and technical support for the random finite element method with considering the cross-correlation of soil profiles.(4)A random finite element method for slope reliability analysis based on cross-correlated random fields is proposed with considering cross-correlation and spatial variability of soil profiles.The principle and process of random finite element method are elaborated.The coupling method of cross-correlated random fields and finite element mesh is proposed.A data interactive program based on MATLAB-Python-ABAQUS is developed.An automatic random finite element analysis method is presented.The feasibility and effectiveness of the proposed method are verified by a classical slope model.The variation rules with scale of fluctuation,cross-correlation and coefficient of variation of soil profiles,and Copulas are discussed.The influences of spatial variability and cross-correlation on slope reliability is demonstrated.Results show that the proposed method can accurately calculate the slope reliability with considering cross-correlation and spatial variability.For cross-correlated and spatially variable soils,all the above factors are crucial to slope failure probability.(5)Aiming at the problem of computational efficiency of random finite element method based on MCS,an improved subset simulation method based on Hamiltonian Monte Carlo(HMC)method is proposed.The basic principle and calculation procedure of the subset simulation are introduced and the corresponding calculation method for slope reliability is established.Then the basic principle of HMC method is introduced.An improved subset simulation method based on HMC method is proposed.The framework of the proposed method is given.The feasibility and accuracy of the proposed method are validated by a classicial slope model and an engineering case.Results show that the HMC algorithm mitigates the random walk behavior of the Markov Chain Monte Carlo algorithm,and improves efficiency and precision of subset simulation method,which is more accurate and efficient for geotechnical engineering.These works can provide a support for slope reliability analysis more accuratly and efficiently.