Performance analysis of empirical models for predicting rock mass deformation modulus using regression and Bayesian methods

Abstract

Deformation modulus of rock mass is one of the input parameters to most rock engineering designs and constructions. The field tests for determination of deformation modulus are cumbersome, expensive and time-consuming. This has prompted the development of various regression equations to estimate deformation modulus from results of rock mass classifications, with rock mass rating (RMR) being one of the frequently used classifications. The regression equations are of different types ranging from linear to nonlinear functions like power and exponential. Bayesian method has recently been developed to incorporate regression equations into a Bayesian framework to provide better estimates of geotechnical properties. The question of whether Bayesian method improves the estimation of geotechnical properties in all circumstances remains open. Therefore, a comparative study was conducted to assess the performances of regression and Bayesian methods when they are used to characterize deformation modulus from the same set of RMR data obtained from two project sites. The study also investigated the performance of different types of regression equations in estimation of the deformation modulus. Statistics, probability distributions and prediction indicators were used to assess the performances of regression and Bayesian methods and different types of regression equations. It was found that power and exponential types of regression equations provide a better estimate than linear regression equations. In addition, it was discovered that the ability of the Bayesian method to provide better estimates of deformation modulus than regression method depends on the quality and quantity of input data as well as the type of the regression equation.

Keywords

• Deformation modulus
• Rock mass
• Regression equation
• Bayesian method
• Performance analysis
• Rock mass rating (RMR)