Numerical modelling of the rock fracture process under mechanical loading

Abstract: The fracture of rock has been the subject of the extensive research in the mechanical fragmentation. With the rapid development of computing power, interactive computer graphics and topological data structure, numerical tool has become a good tool to gain some insights into the problem of rock fracture. However, most of the commercial programs are not so robust that they can model the fracture progressive process with rock fabric characteristics (heterogeneity) considered. Based on this background, a novel numerical code, rock and tool interaction code (R-T2D) has been developed to understand the fracture progressive process of heterogeneous rock. The research, development (R & D) and calibration of R-T2D code (Paper A and B) mainly consists of (1) characterization of rock heterogeneity, (2) mesoscopic constitutive law, nonlinear behaviour and associated seismicity, (3) Mohr-coulomb and double elliptic strength criterion, and (4) calibration of R-T2D code by simulating basic rock mechanics experiments. In the second part of the thesis (Paper C and D), preliminary industrial applications of R-T2D code in mechanical fragmentation are conducted. In rock cutting, the peculiarities in cutting heterogeneous brittle materials are investigated. Besides, the fracture processes induced by cutters with different back rake angles are examined and compared with each other. In indentation, indentation-induced fractures are researched by R-T2D code. The influences of confining pressure on the formation of side cracks are discussed. In the simultaneous loading by multiple indenters, the propagation, interaction and coalescence of side cracks induced by neighbour indenters are simulated to check how the side cracks propagate, interact and coalesce to form large rock chips. At last, the indexing-effect in the simultaneous loading is discussed. The major results for the two parts can be summarized as the following: On the basis of Weibull distribution, a heterogeneous material model is proposed to characterize the heterogeneity in rock, where rock is specified by a few characteristic parameters: the homogeneous index and the elemental seed parameters. Corresponding to the specific rock, the homogeneous index can be determined based on the defects distribution of microstructure and the elemental parameters can be gotten from the laboratory tests. Rock heterogeneity has an important influence on the crack initiation location and subsequent propagation path. Compared with the traditional Mohr-coulomb and Hoek-Brown strength criterion, the double elliptic strength criterion is more useful to model the fracture in mechanical fragmentation, which can represent the transition from brittle failure to ductile cataclastic failure with increasing confining pressure. A series of numerical experiments including both the intact rock and the notched rock are conducted by R-T2D code to obtain the physical-mechanical properties and fracture toughness, and to simulate the crack initiation, propagation and the whole fracture progressive process. The developed R-T2D code seems to have built a bridge between the physical-mechanical parameters and fracture toughness. The detailed visually shown stress distribution and redistribution; crack nucleation, initiation, stable and unstable propagation, interaction and coalescence; and corresponding load-displacement curves can be proposed as benchmarks for numerical programs for crack propagation. In mechanical fragmentation, a crushed zone is always available near the tool. The crushed zone has an important influence on the chipping process and energy utilization. The crushed zone is in fact the zone with a high density of microcracks and some of the rocks in this zone behave in a ductile manner with stress satisfying the ductile failure surface of the double elliptic strength criterion. A simple description and qualitative model of the rock fragmentation process induced by truncated indenters are summarized as follows: Little damage to the rock was observed at the linear elastic deformation stage. Then conical Hertzian cracks were initiated adjacent to both corners of the truncated indenter and propagated in the well-known conical Hertzian manner. As the loading displacement increased, some of the elements in the high confining pressure zone immediately under the indenter failed in the ductile cataclastic mode with the stress satisfying the ductile failure surface of the double elliptic strength criterion. With the cataclastic failures and tensile conical cracks releasing the confining pressure, the elements in the confining pressure zone were compressed into failure and the crushed zone came into being. In the crushed zone, microcracking was pervasive. The intensity of the microcracking within the zone increased and a re-compaction behaviour occurred with increasing loading displacement. Associated with this microcracked region there was a volumetric expansion and a tensile stress field, which drove side cracks to propagate in a curvilinear path. It is thought that the curvilinear path was caused by the heterogeneity of the rock. With an increased loading displacement, the side cracks rapidly propagated and intersected with the free rock surface to form rock chips. The confining pressure has an important influence on the failure mode in indentation test. As the confining pressure increases, a small but noticeable increase in the indentation strength was measured. With decreasing confining pressure, of particular interest is a change in the rock failure mode when the confining stress is reduced below a critical value. Instead of the usual formation of rock chips adjacent to the punch, vertical cracks are propagated beneath the punch, causing the specimen to be split in half when the confining pressure on the sample is less than a critical value. This result is of practical interest. In boring hard rock at low confining stresses, the creation of such tensile fractures beneath an indenter may serve to fragment the rock sufficiently to facilitate its removal. The simultaneous loading of the rock surface by multiple indenters seems to provide a possibility of forming larger rock chips, controlling the direction of subsurface cracks and consuming a minimum total specific energy. The simulated results by R-T2D code reproduce the progressive process of rock fragmentation under mechanical loading: the build-up of the stress field, the formation of the crushed zone, surface chipping, and the formation of the crater and subsurface cracks. Therefore, R-T2D code is indeed a valuable numerical tool to research rock fracture, which can be utilized to improve our understanding of rock-tool interaction and the rock failure mechanisms under the action of mechanical tools, which, in turn, will be useful in assisting the design of fragmentation equipment and fragmentation operations. Based on the above researches, a number of interesting problems are discussed and the future studies are suggested in the last part of the thesis.