Determination of soil mechanics parameters based on Bayes method and posterior distribution limit

Geotechnical parameters are of great randomness in spatial distribution, and the existing researches are to infer large samples from small ones, which will inevitably lead to some errors. If the number of samples is large enough, the normal distribution will become highly concentrated near a certain value. The influences of statistical errors of geotechnical parameters will become smaller and smaller resulting from the investigation errors or accidental factors, then the more accurate parameters will be provided during prospective design. According to the collected experimental data of the cohesive force $c$ and the internal friction angle $\phi$ of Dianchi Lake facies deposition peat soil, silt and clay with high dispersion, the Bayesian large sample method is used to analyze the mechanical parameters of several soils, the posterior information of mechanical parameters of soils is derived based on the prior information from the collected samples, and the Bayesian estimation interval is obtained. After the Fisher information is determined, the posterior distribution of the mean value $\mu$ of the normal distribution of mechanical parameters of soils can be approximated by a normal distribution independent of the prior distribution, and the reliable value of the parameters can be obtained when the sample size tends to infinity. The consistency and asymptotic normality of mechanical parameters of soils are tested and analyzed by the posterior distribution limit. A large sample analysis of the mechanical indexes of the sedimentary soils in Dianchi Lake is carried out. The reliable value of the mechanics index of soils is estimated to fall within the Bayesian evaluation interval, which fully proves the feasibility and reliability of the analytical method. The analysis results may provide reference for the compilation of regional norms and the accumulation of engineering experience, and also a test for the rationality of the design parameters.