A 3D Voronoi clump based model for simulating failure behavior of brittle rock

Abstract

Particle-based model (PBM) has been extensively used to investigate progressive failure process of rock due to its advantage in modeling fracture development. In order to make the PBM reproduce rock failure behavior more realistically, this study develops an advanced clumped particle model for rock based on 3D Voronoi tessellation (VCPM). In the newly developed model, irregular clumps are identified by using an ergodic algorithm similar with that adopted by the Voronoi tessellation. Thus, structural similarity between convex clumps and Voronoi cells is guaranteed while computational efficiency of the clump logic is remained by the VCPM. The clump size and coordination number of the VCPM obey Inverse Gaussian and Gaussian distributions, respectively. Such characteristics enable the VCPM to simulate rock micro-cracking and macro-fracturing behaviors even in large-scale engineering problems. A comprehensive parametric study indicates both micro-geometric and micro-mechanical properties have significant influences on macro-mechanical properties of the VCPM. Linear or nonlinear mode of the predicted strength envelope can be controlled by the average particle number involved in the clump. Based on the revealed relationship between macro-mechanical responses and micro-properties, a calibration procedure is moreover established for the VCPM. The calibrated VCPM is then applied to simulate failure behavior of Lac du Bonnet granite to investigate its modeling capability. The predicted stress–strain response and strength envelope are in good accordance to the experimental data. The large magnitudes of the UCS-to-TS ratio and strength envelope slope imply the interlocking effect is greatly strengthened in the VCPM. In addition, the influences of the minor principal stress on the ductility, volumetric dilation and failure pattern of the granite as well as its splitting failure in the Brazilian test are also accurately captured by the VCPM. Such capabilities indicate the VCPM is of great potential in further investigation of rock fracturing behavior under more complex stress environment.