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 rock models performance. A methodology is proposed to improve damage prediction in sandstone, based on Finite Element simulations coupled with the Bayesian paradigm. To illustrate this methodology, parameters of a Continuum Damage Mechanics model are defined as random variables. (1) First, 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) Second, experimental data is introduced (new evidence available), which allows 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 characterization, 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 upon 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 multi-phase porous media.

Probabilistic calibration of a damage rock mechanics model

“…The Bayesian approach has been used to calibrate numerous geomechanical models such as liquefaction (Cetin et al, 2002), snow avalanches (Gauer et al, 2009), landslides (Ranalli et al, 2009(Ranalli et al, , 2013, tsunamigenic rockslides (Eidsvig et al, 2009), mudslides (Medina-Cetina & Cepeda, 2012, soils' constitutive models (Medina-Cetina, 2006;Medina-Cetina & Rechenmacher, 2009) and foundations (Yu et al, 2011;Briaud et al, 2011) and, more recently, multi-physics geophysical inversions (MedinaCetina et al, 2013) and probabilistic damage prediction in rocks (Arson & Medina-Cetina, 2013). However, the Bayesian paradigm has never been used to maximise damage model performance.…”