Inference method for optimal probability distribution function of shear strength parameters in geotechnical engineering

The inference of optimal probability distribution of shear strength parameters is the basis and premise to ensure the accuracy of reliability calculation in geotechnical engineering. The existing studies suggest that most of the shear strength parameters obey the normal or logarithmic normal distribution. However, because the actual distribution range of geotechnical parameters is very limited, the problem that range mismatches between the defined interval of normal distribution or logarithmic normal distribution and the actual distribution interval of geotechnical parameters is inevitable. Considering the fact that there is a certain degree of skewness for the distribution of most geotechnical parameters, based on the "3" principle, a distributed interval determination method adjusted with the skewness is proposed. Three groups of samples of the internal friction angle of batholiths from water conservancy and hydropower projects are treated as examples, and the normal information diffusion method (NID method) is used to infer their respective probability distribution function. The K-S test method is also introduced to test the fitting degree. At the same time, in order to investigate the influence of sample sizes on the fitting accuracy of the normal information diffusion method and the typical distribution fitting method, eight groups of samples are produced using the Monte-Carlo method, and the sample size is 15, 20, 30, 50, 100, 200, 500 and 1000. The results show that, regardless of the actual or simulated samples, compared with the logarithmic normal distribution (obtained by the typical distribution fitting method), all the test values of the normal information diffusion distribution are lower than those of lognormal distribution, and tend to converge with the increase of the sample sizes.