Statisitical Characters Estimation For Geotechnical Parameters Of Small Samples And Reliability Analysis Of Slope Stability

Compared with the traditional safety factor method for slope stability,the reliability analysis method can quantitatively describe the uncertain factors in the slope engineering,and the reliability of the slope is truly reflected by the reliability index or failure probability,which has become the future development direction of the slope stability analysis.The reliability calculation should be based on the known statistical characteristics of the geotechnical parameters.However,in the actual slope engineering,with the limitation of inherent variability of the rock and soil and the number of geotechnical survey sampling,the statistical characteristics of the geotechnical parameters are usually deduced from the small sample data.There is some deviation between the statistical results and the true distribution of the parameters,which has a great influence on the accuracy of the engineering survey results.Therefore,it is necessary to study the statistical characteristics and its estimation method of geotechnical parameters under the condition of small sample,so as to evaluate the slope safety more reasonably.The main research work and achievements are as follows:(1)Based on the problem that traditional limit equilibrium methods of slope stability fail to reasonably consider the influence from variability of soil strength parameters,in the view of probability analysis principle of limit state,Monte-Carlo method was used to calculate the reliability of slope stability.The change rule between the slope failure probility with variation level of soil strength parameters was discussed under the condition of certain stability safety factor.The corresponding relationship between safety factor and reliability index of slope and its change characteristics with variation levels of soil strength parameters were analyzed.Research shows that the reliability index of slope is influenced significantly by the variability of soil strength parameters,showing sharp decrease with the increase of variation level of soil strength parameters.In order to ensure the slope has the identical reliability,safety factor should be adapt to the variability of soil strength parameters.Based on this,the principle of safety factor based on reliability index and variation level of soil strength parameters and the corresponding three-parameter function are proposed.(2)The discrimination for the probility distribution of geotechnical parameters was a basic work to carry out risk assessment and reliability analysis of geotechnical engineering.The basic contents,advantages and disadvantages of distribution identification methods such as ?2,K-S,A-D and AIC criterion were briefly summarized.Based on the identification for distribution of geotechnical parameters survey data from a railway station,the discriminant analysis results of each distribution identification method were compared and analyzed.Research shows that the traditional method of distribution fitting based on hypothesis test needs to consider the significance level and the critical value,it is inconvenient to use and has the problem that satisfying multiple probability distributions at the same significance level.The probability distribution of the minimum test statistic for ?2,K-S,A-D method is also inconsistent.The method of distribution identification based on the AIC criterion select the candidate alternative distribution which obtains the minimum AIC value as the optimal distribution,and its physical meaning is clear and easy to calculate.It has a great advantage in the application of geotechnical parameter identification.(3)Based on the problem that the estimated interval of mean value for geotechnical parameters using t-distribution method with limited samples varied in a wide range,and the deviation between the standard value of design parameters and the true value was large.Computer stochastic simulation is carried out to model the site-investigate sampling with known distribution type of geotechnical parameters.Based on the distribution space of standard value constructed from replicates with sufficient batches,the estimated interval available from nonparametric Bootstrap method and traditional t-distribution method was compared,and the changing law of standard value of geotechnical parameters by Bootstrap method versus statistics and size of sample was discussed.Research shows that Bootstrap method can make full use of empirical distribution contained in insufficient information,and thus to effectively narrow the mean confidence interval of geotechnical parameter under the same confidence level,which makes the standard value obtained closer to the true value than t-distribution method.The width of mean confidence interval for geotechnical parameters using Bootstrap method decreases with the increase of sample size,and the standard value shows a satisfied negative power functioning relationship with the sample size.A mean-based expression of standard value considering the effect of sample size and standard deviation is proposed.The advantage of the Bootstrap method to reduce the deviation between the standard value and the true is more obvious when the sample size is smaller than 20.(4)The scattered points of sample statistics were obtained by ample repeated sampling with small samples from c?? population of small,medium and large levels of variance.The distribution space of standard value was constructed using calculation formula of t distribution method and Bootstrap method,and the discrete characteristic of result space of safety factor and reliability index are analyzed.Research shows that the two methods display the same point estimation results of average value and variance,namely their reliability indexes of slope stability are equal,but the average value of safety factors of slope stability calculated by the standard value using Bootstrap method are relatively large,the discreteness of safety factors decrease,and the improvement trend becomes more obvious with the increase of variance level of parameters.On the condition of the same reliability,Bootstrap method can reasonably compensate the safety risk of slope caused by the statistical uncertainty from small samples.