Determination of Soil Mechanical Parameters From Posterior Distributions Under Different Prior Distributions

The values of soil layer parameters in geotechnical engineering were determined according to field and laboratory test data with classical statistical methods, without use of the prior information. Unlike classical statistical methods, the Bayes method combines samples from the perspective of prior distribution to deduce the posterior distribution, providing a new analytical method for the evaluation of geotechnical parameters. The geotechnical engineering survey makes a random sampling of the overall strata. The density function of the sample distribution is determined when the sampling is completed. Therefore, the posterior distribution in the Bayes method depends on the prior distribution, and 2 different sets of prior distributions were derived: the prior distribution and the conjugate prior distribution were determined with the prior information. Through calculation of the parameters in the posterior distribution, with the sample generally conforming to the normal distribution of N(μ,σ²), unknown parameters μ and σ were analyzed, the interval lengths of the posterior distribution under different prior distributions were comprehensively compared, and the prior distribution selected for the optimal posterior distribution in the Bayes inference of the geotechnical parameter was given. The results show that, the posterior distribution in the conjugate case is always shorter than that in the absence of information, and the probability density function distribution is more centralized and the value determination is more convenient. Under the overall normal situation, the extreme value method obtained based on the joint posterior distribution of unknown parameters μ and σ to determine maximum probability mean μ_max and variance σ_max in the sample as the adopted values in the engineering design, provides a way for the value determination of geotechnical parameters, and has engineering significance.