Applying Bayesian Models to Forecast Rock Mass Modulus

The deformation modulus of a rock mass (E_m) is one of the most significant properties used by designers for estimating deformation behavior of rock masses encountered in rock engineering projects (slopes, foundations and tunnels). The E_m can only be determined by employing large-scale in situ tests on the rock mass, itself, for example, plate jacking, plate loading, pressuremeter, flat dilatometer, and Goodman jacking. It is sometimes difficult to apply the large scale in situ tests because of time consuming processes and installation required. To overcome this difficulty, the current study aims at predicting the E_m on the basis of the rock parameters including the uniaxial compressive strength of intact rock, rock mass rating, Depth and elastic modulus of intact rock (E_i). The Bayesian inference approach is implemented to identify the most appropriate models for estimating the E_m among six candidate models that have been proposed. The models were applied to available data given in open source literature. The unknown parameters of the models are considered as random variables. The WinBUGS software which uses Bayesian analysis of complex statistical models and Markov chain Monte Carlo (MCMC) techniques is employed to compute the posterior predictive distributions. The mean values of the model parameters obtained via MCMC simulations are considered for the model prediction performance evaluation. Various statistical performance indexes indexes [mean squared error, root mean squared error, squared correlation coefficient (R²) and mean absolute percentage error] were utilized to compare the performance of estimation models. Overall, the results indicate that the proposed E_m model possesses satisfactory predictive performance.