Modeling The Bivariate Distribution Of Shear Strength Parameters Using Maximum Entropy Principle And Its Application To Slope Reliability Analysis

Geotechnical engineering reliability analysis is based on the estimation of probability distribution.The precision of estimation will directly affect subsequent assessment and thus plays a critical role in reliability analysis.However,as a result of the limitation of technical and economic conditions,experiment data of rock and soil mass in practical geotechnical engineering often is very limited so that its probability model can't be uniquely identified.Therefore,engineers often need to make extra subjective judgment.This would introduces more uncertainty and further affects the objectivity of reliability analysis.So,facing the insufficient of information how to reduce subjective factors interference with parameter uncertainties in geotechnical engineering modeling is a meaningful issue.In addition,probability model based on limited geotechnical data inevitably contains larger uncertainty which will pass to the reliability analysis further.Uncertainty analysis of parameter model within small samples and its impact on the reliability analysis is also in urgent need of research.To address the above key issues,this thesis aims to introduce principle of maximum entropy into geotechnical engineering and discusses its differences with the traditional method on reliability analysis.The main work and study results are as follows:(1)This thesis briefly introduces the background and meaning of the estimation of probability distribution of getotechnical parameters.Then this thesis summarizes the existing estimation methods in the filed of geotechnical engineering,and discusses their limitations.Reviews of the applications of maximum entropy principle in natural language processing,financial,hydrology,and other fields,especially in geotechnical engineering are also presented.(2)The process of estimating probability distribution based on maximum entropy principle is introduced.Then the definition of entropy and maximum entropy principle is illustrated.The concrete modeling steps based on maximum entropy principle is given.And then this thesis discusses the meaning of sample information constraints and the specific selection scheme under the limitation of small sample.(3)For characterizing uncertainty in shear strength parameters of rock and soil mass within limited data,this thesis proposes a new method based on maximum entropy principle.The differences between the proposed method and traditional methods in distribution fitting and reliability analysis is explored.Results show that the probability distribution based on maximum entropy principle has better accuracy and stability in both one-dimensional and two-dimensional.They also show better performance in fitting effects and reliability analysis.It provides an effective method for characterizing uncertainty in shear strength parameters of rock and soil mass.(4)In view of the uncertainty of reliability analysis resulted from uncertainty of small samples,this thesis puts forward an idea that combing the principle of maximum entropy with the Bootstrap method.It firstly discussed the uncertainty of small sample data's statistics and its effect on reliability analysis.Then a reliability updating method was proposed based on the Bootstrap method,and its efficiency is illustrated through a simulation experiment.