Selection of site-specific regression model for characterization of uniaxial compressive strength of rock

When there is no possibility of direct compression test, geotechnical engineers and practitioners may utilize regression models (i.e., equations) to estimate the uniaxial compressive strength, UCS, of rock from point load index, Is(50), since there are established relationships between the two properties. Different studies have shown, however, that there is no unique equation relating Is(50) to UCS for all rock types. This leads to the problem of how to select the most appropriate model for a particular rock deposit out of the numerous models available, since UCS of rock like other geomechanical properties are inherently variable as a result of different geological processes that rocks are subjected to. This study develops a method that rationally compares different regression models and selects the most appropriate model for a specific site or deposit. The most appropriate model is the model with the highest occurrence probability for the given set of observation data, and it is selected using only a limited number of Is(50) data obtained from the specific deposit or site. The methodology starts with the formulation of a general likelihood model to determine the occurrence probability of each model based on the limited number of Is(50) data available from a specific site. This is different from previous works that need both UCS and Is(50) data to draw comparison. Note that UCS data are generally not available when the use or selection of regression model is needed. The selected model is subsequently used in Bayesian framework to integrate the prior knowledge about UCS with the limited number of site-specific Is(50) data available for probabilistic characterization of UCS, such as obtaining its mean, standard deviation and full probabilistic distribution.