Probabilistic Parameter Estimation Based On Polynomial Chaos Expansion For Slope Stability

The research on slope stability analysis is of great significance because of far-reaching landslide hazards.The coupling effect between seepage and stress needs to be considered in unsaturated slope stability analysis.Stability model of an unsaturated slope are high nonlinear and are commonly adopted with numerical model methods.Back analysis with field monitoring data is an effective approach for solving the uncertainties in geotechnical engineering.However,tremendous computational cost of numerical modeling is the main obstacle for probabilistic back analysis.In order to improve the computational efficiency of back analysis for unsaturated soil slopes,a probabilistic back analysis method based on Polynomial Chaos Expansion(PCE)is proposed in this study.the feasibility of the proposed method is verified by numerical experiments of an unsaturated soil slope.The main contents and results of this research are as follows:(1)The probabilistic parameter estimation method for unsaturated soil slope stability is proposed based on Polynomial Chaos Expansion.Polynomial Chaos Expansion method is used to construct the explicit functions between slope responses and estimated soil parameters.The expansion coefficients in PCE are calculated using the spectral projection method and Smolyak sparse grid collocation method.Parameter posterior inference are implemented using Bayesian theory and Markov Chain Monte Carlo(MCMC)simulation,with the Metropolis algorithm and the Different Evolution Adaptive Metropolis algorithm.(2)Performance comparison is implement by an illustrative example between the proposed method and the back analysis based on numerical model.An example of unsaturated slope under rainfall infiltration is presented,and the coupled hydro-mechanical numerical model is established in the finite element software ABAQUS.Weighing approximation accuracy and computation efficiency,2-degree PCE are used to surrogate the pore water pressure responses and 3-degree PCE for displacement responses.With pore water pressure and horizontal displacement measurement,hydraulic parameters and soil constitutive parameters are estimated with the two probabilistic back analysis respectively.Compared with the back analysis based on numerical model,the computational efficiency of single PCE surrogate model has improved7000 times than the numerical model.The statistics of posterior distribution and 95%uncertainty bounds obtained with the PCE-based method are close to the results of back analysis based on the original numerical model.The results show the proposed new method can significantly improve the efficiency of model calibration.(3)The effects of parameter prior information,measurement durations,measurement types and monitoring sites on parameter posterior estimation are discussed based on the proposed method.The performance of parameter posterior estimation is compared when cohesion c'are set to follow normal distribution and log-normal distribution.With the increase of measurement duration,the uncertainties of soil properties are significantly reduced.The reduction of uncertainty during a specific time is basically related with the variation of the response within this time interval.The uncertainties of permeability coefficient k_s and SWCC parameter?are reduced significantly using the pore water pressure data,while the uncertainties of Elasticity modulus E?internal friction angle?'and cohesion c'are reduced greatly using the measured displacement data.The back analysis using displacement responses can yield more reasonable correlations among soil parameters.Pore water pressure measurement of points at deeper location near slope top can reduce more uncertainties for hydraulic parameters and provides bigger positive correlations among them.For each type of responses(pore water pressure,horizontal displacement and vertical displacement)at different monitoring sites,the coverage of the uncertainty bounds for measurements are all larger than90%,indicating a good model performance with the proposed method based on PCE.