Relability Analysis Methods For Rockfill Dam Slope Stability Considering Statistical Uncertainty

Landslide is a common geological disaster in the construction of hydropower engineering,the landslides of reservoir dam will bring great threat to people’s lives and property.The rockfill dam area often has complex engineering geological environment.Earthquake,rainstorm and sudden drop of reservoir water level will induce landslides of the rockfill dam.The reliability analysis of the dam slope is an important part of the design and risk assessment of the rockfill dam.Due to the restriction of technical and economic conditions,test data of rock and soil parameters in geotechnical site(e.g.,cohesion c and internal friction angle φ)are very limited.It is impossible to obtain the actual values for the mean value μ,standard deviation σ,rank correlaton coefficient τ of shear strength parameters.The uncertainty in these model parameters θ=(μ1,σ1,μ2,σ2,τ)is called statistical uncertainty.There would be huge deviations in dam slope reliability analysis if statistical uncertainty was ignored.How to cover the reliability analysis of the rockfill dam slopes considering statistical uncertainty in a proper and robust manner remains a key issue to be solved in risk assessment of rockfill dams.In order to tackle the problem mentioned above,the reliability analysis of rockfill dam slopes considering statistical uncertainty is studied by using two schools of methods:frequentist method and Bayesian method.The joint probabilistic models of shear strength parameters of the main rockfill dam materials are constructed based on Copula theories.The approaches for model selection and parameters identification considering statictical uncertainty using frequentist and Bayesian thought are proposed,respectively.In frequentist method,statistical uncertainty of model parameters is simulated using Bootstrap resampling technique and the sampling distribution is obtained,and based on this method,models are identified considering the uncertainty of AIC values;In Bayesian method,a structural reliability-based Bayesian updating algorithm is employed to obtain model probability,which is not only able to identify the optimal probability model of shear strength parameters,but also to obtain the posterior distribution samples of the model parameters that reflect statistical uncertainty.Taking the test data of the Nuozhadu core rockfill dam as example,the model selection and model parameter identification are carried out by using two methods mention above.The failure probability and reliability index of the rockfill dam are also calculated based on the respective identified probability models and parameters,and the failure probability of rockfill dam is characterized as a confidence interval with a certain level of confidence,which can reasonably quantify the statistical uncertainty in the probability model parameters and its influence on the reliability of rockfill dam.Firstly,this paper briefly introduces the background,significance,purposes and contents of the research.Then the Copula theories and the reliability analysis methods of the rockfill dam are introduced in detail.The approaches for model selection and parameters identification considering statictical uncertainty using frequentist and Bayesian thought are proposed,respectively.And the validity of the frequency method and the Bayesian method are verified by the simulated data and an infinite slope model,the differences between the two methods in model parameter identification and reliability calculation are compared as well.Whereafter,the methods mention above are applied to the test data of the Nuozhadu core wall rockfill dam.The reliability analysis of the dam slope considering statistical uncertainty is carried out based on the frequency method and the Bayesian method,respectively,and the failure probability of the rockfill dam is presented as a 95% confidence interval.Finally,A software “Wuhan University Probabilitic Slope Stability Analysis of Rockfill Dam”(WHUPSSARD)is developed based on Matlab programming language.Results indicate that: both frequentist method and Bayesian method can complete the model selection and parameters identification considering the statistical uncertainty of model parameters,and effectively simulate the statistical uncertainty of dam slope’s failure probability.Ignoring the statistical uncertainty in model parameters may underestimate the failure probability of dam slope,leading to an unconservative reliability assessment result,therefore it is necessary to take statistical uncertainty into consideration;Bayesian method is more accurate and consistent than frequentist method in model parameter identification and reliability calculation,the model parameters identified and models selected by Bayesian method make the reliability calculation more conservative.WHUPSSARD software is applied for reliability analysis of rockfill dams considering statistical uncertainty,and provides a practical tool for reliability design and risk assessment of rockfill dams.