Study On The Characters Of Geotechnical Parameter's Estimation And Calculation Of Slope Reliability With Small Samples

Using reliability theory which based on probability theory and mathematical statistics method can consider the uncertain factors in engineering and quantitatively describe the degree of safety by reliability has become a trend in slope stability analysis.Among the uncertainty of geotechnical parameters,the inherent soil variability is a kind of objective existence.Although the population parameter has real probability distribution,the sampling test of engineering investigation can only estimate the population parameter with limited number of samples and the sample number and the confidence level will affect the size of statistical uncertainty.Because of the accuracy of reliability analysis depends greatly on the description precision of probability distribution and character of parameter for population parameter,the result of reliability analysis has discreteness if seting the sample mean as population mean when calculating the slope reliability.Therefore,the character of interval estimation of parameters,the influence factors and the correction method of reliability with small samples are urgent to research in the slope reliability analysis.The sample number and confidence level which will affect the estimation result of parameters were studied in this paper,and an improved method based on Bayes theorem and conditional probability principle was established by studying the estimation character of parameters.In addition,the evaluation system considering the influence of parameter variation and correlation for embankment slope stability was explored based on the corresponding relationship between safety factor and reliability.The main research woks and conclusions in this paper are as following:(1)The limited number of samples is an important source of statistical uncertainty for geotechnical parameters,and the practical investigation activities of slope engineering can be described as a random sampling of population parameter in mathematics.A mass of repeated sampling was done by using the numerical simulation experiment,and the discreteness of failure probability was investigated to determine the reasonable value of sample number based on the decreased amplitude of standard deviation of failure probability and variation characteristics of relative standard deviation.The analysis result shows that the discreteness of reliability degree could effectively reduce when the sample number increased to 15 with small parameter variation level or 20 for middle and big variation level.According to the discrete range of repeated sampling failure probability with the same number of samples under different confidence level,the reasonable value of confidence level was determined.The result shows that the confidence level can decrease for piratical slope design compared with 95%confidence level in code and the confidence can take 0.8 with small parameter variation level or 0.9 for middle and big variation level.(2)Under the condition of small sample statistics due to the overall average mean and the actual parameter does not explicitly exist between the distribution of random deviation,to survey and sample statistics as the inherent true value calculation will lead to the results of the reliability analysis is discrete.Based on the assumption that the geotechnical parameters obey normal distribution,the variables of random deviation between population mean and sample mean is subject to the theory of/-Distribution.With the different values of population mean given by the distribution of random deviation set as conditions and the failure probabilities as conditional probabilities,a calculation method for stability of slopes with geotechnical parameters of small samples is presented based on the Bayes' theorem and total probability formula.And under the influence of the variation of parameters and the statistical uncertainty,the relationship between reliability and safety factor of embankment slope is discussed.The results show that:the mathematical method of total probability formula,which can effectively reduce the effects of the contingency from small sample on the calculation results of reliability and improve the calculation accuracy,is a cost-effective way as a compensation for the limited amount of samples.Under confidence level 90%and 95%,since the standard value of strength parameters from small sample are lower than those from large sample,the reliability level of slope will have to be significantly raised to achieve the same safety factor.The parameter variability's influence on reliability of slope is particularly clear,but the difference of results with different confidence level 90%and 95%are not obvious.The presented calculation method based on conditional probability with small sample has a positive effect on improving the analysis theory about the reliability of geotechnical engineering structure.(3)The range of variation coefficient and correlation coefficient of c and ? were summarized according to related literatures.An example of reliability analysis for standard railway embankment slope section model was presented with the influence of parameter variation and correlation when the probability distribution and numerical characteristics were clear.Based on the relationship between the safety coefficient and reliability,an evaluation system of slope stability which set parameter variation coefficient,correlation coefficient and safety coefficient as indexes and the safety coefficients of homogeneous embankment slope with the reliability control idea were proposed.In addition,the supplementary calculation means of Rosenblueth method with correlated random variables whose probability distribution were deviated was introduced.