A 3D grain‐based reconstruction method from a 2D surface image for the Distinct Lattice Spring Model

Abstract

In this work, a surface image-based 3D grain-based model (GBM) reconstruction method based on the digital image processing (DIP) technique, periodic random packing and the simulated annealing algorithm is proposed. Taking a surface digital image of Beishan granite as an example, a K-means clustering algorithm is employed to extract the mineral compositions, the distribution of which is quantified by the two-point probability function (TPPF). Given the 3D volume fraction of each mineral composition, their corresponding 3D two-point probability functions can be evaluated from their 2D forms by the linear interpolation method. The 3D GBM reconstruction is generated by a simulated annealing algorithm, with the Monte Carlo algorithm extending the calculation of the two-point probability function as the target function to the random particle model. To improve the computational efficiency, the periodic boundary condition is applied to both the random particle generator and the evaluation of the two-point probability function, allowing large-scale GBM to be generated for the Distinct Lattice Spring Model (DLSM). The elastic response and advantages of the random particle model for the DLSM are investigated. Finally, the DLSM is further enriched with a tension-cutoff Mohr-Coulomb failure criterion, and the GBM reconstruction method is successfully tested for reproducing the mechanical behaviours of granite and interpreting the failure mechanism at the mesoscale under different loading conditions.