Multivariate probability distribution for some intact rock properties

A multivariate probability distribution model for nine parameters of intact rocks, including unit weight (gamma), porosity (n), L-type Schmidt hammer hardness (R-L), Shore scleroscope hardness (S-h), Brazilian tensile strength (sigma(bt)), point load strength index (Is(50)), uniaxial compressive strength (sigma(c)), Young's modulus (E), and P-wave velocity (V-p), is constructed based on the ROCK/9/4069 database that was compiled by the authors. It is shown that the multivariate probability distribution captures the correlation behaviors in the database among the nine parameters. This multivariate distribution model serves as a prior distribution model in the Bayesian analysis and can be updated into the posterior distribution of the design intact rock parameter when multivariate site-specific information is available. In this paper, the parameters for the posterior distribution of the design intact rock parameter are summarized into user-friendly tables so that engineers do not need to conduct the actual Bayesian analysis. Caution should be taken in extrapolating the results of this paper to cases that are not covered by ROCK/9/4069, because the resulting posterior distribution can be misleading.