Bayesian calibration of microCT-based DEM simulations for predicting the effective elastic response of granular materials

A novel approach is presented for calibrating discrete element method (DEM) simulations of granular materials based on the sequential Bayesian parameter estimation over the experimental stress–strain responses. The initial DEM packing is bridged with microscopic computed tomography (microCT) images by quantitative assessments of particle morphologies and configuration, which are offered by the image processing techniques suitable for fine particles with material imperfections. The aim of this work is twofold: to establish a calibration procedure which estimates the posterior probability for the micro-mechanical parameter sets given the macroscopic measurements, and to numerically investigate the elastic response of an assembly of glass bead particles that obey the Hertzian law.
We first introduce the feature-based watershed algorithm, which performs image filtering, geodesic reconstruction, feature-based segmentation, watershed separation and particle analysis on the microCT images of a glass bead packing cored at an isotropic pressure of five MPa. From the resulting particle morphologies and configuration, the contact force network within a representative volume of the packing in DEM simulations is inferred via a Monte Carlo inversion. By changing the interparticle friction coefficient and the size of the periodic cubic cell only, the effects of the micro-mechancial parameters on the inference are investigated, and the parameter sets that reproduce the initial bulk stress and void ratio with high accuracy are selected for a sequential Bayesian parameter estimation. The Bayesian estimation results in a posterior probability density function of the selected parameter sets, which is updated at each measurement step using the macroscopic measurements.
We applied the presented approach to calibrating the microCT-based DEM simulation of the glass bead packing under an isotropic loading path. The results of the DEM simulation using the parameter set with the highest posterior probability are in good agreement with the experimental data. The parameter set was used in the DEM simulations to calculate the elastic moduli of the same granular material, which was found to agree well with the moduli values inferred from wave velocities.