Bayesian paradigm to assess rock compression damage models

Abstract

Energy extraction and waste storage in geological formations raise interest in developing systematic and reliable calibration methods to assess performance of rock models. A methodology is proposed to improve damage prediction in sandstone, based on finite element simulations coupled with the Bayesian paradigm. To illustrate this methodology, we defined parameters of a continuum damage mechanics model as random variables. (1) Probability density functions are formulated for each parameter (expert’s judgement) and sampled later independently to simulate likely random sandstone responses during a triaxial compression test (forward problem). (2) Experimental data are introduced (new evidence available), which allow updating the probability distributions depicting the model parameters (inverse problem). Results show that it is possible to quantify the impact of experimental evidence into the rock characterisation and that correlations between all rock damage parameters can be retrieved. Mechanically speaking, this means that (a) similar accuracy in the prediction of damage might be achievable with less model parameters, (b) and the input of energy released to initiate crack propagation is contingent on conditions external to the model (e.g., initial texture of the rock). Results from this investigation provide promising applications of the probabilistic calibration approach to damage models in multiphase porous medium.