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A three-dimensional (3D) fracture algorithm is implemented into a hybrid finite-discreteelement method previously developed by the authors using a cohesive cracking model with an energy failure criterion to model the 3D transition from continuum to discontinuum during rock fracture. The newly developed 3D hybrid continuous-discontinuous method is then applied to model the fracture process of rock in the Brazilian tensile strength tests. After that, the obtained results are compared with those well documented in literatures to calibrate the development of the 3D fracture algorithm for the transition from continuum to discontinuum. Throughout this study, it is shown that the 3D hybrid continuous-discontinuous method is a valuable tool to investigate rock fracture and resultantfragment grinding behaviour. Compared with finite element method, the hybrid method is more robust in modelling rock failure, especially fracture, fragmentation, and fragment movements resulting in tertiary fractures while compared with discrete element method, the hybrid method is more versatile in dealing with irregular-shaped, deformable and breakable particles.

In the field of geotechnical engineering, the number of applications of combined/hybrid finite-discrete-element method(HFDEM) to both the lab-scale and field-scale problems has increased recently. In author’s research group at universityof Tasmania, 2-D/3-D HFDEM code has also been successfully developed [e.g. Liu et al. 2015, Int. J. Geotech. Eng.9:115-131] and applied to some geotechnical engineering problems such as rock blasting, fracture processes in a seriesof lab-scale rock testing methods and asperity degradation and gouge grinding during direct shearing of rough rock joints.However, since the HFDEM code was implemented by sequential programming, its main application mentioned abovewas limited to 2-D problems owing to the computationally expensive nature of HFDEM. To overcome this situation, theparallel programming scheme using “general-purpose-graphic-processing-unit (GPGPU)” and “CUDA (Compute UnifiedDevice Architecture) C” was recently incorporated into the HFDEM code and significant speed-up has been achieved.This paper briefly describes the theory and newly incorporated features of the GPGPU-based HFDEM code along withsome important issues which have not been addressed clearly in the previous publications using HFDEM. Then, this paperdemonstrates some examples of 3-D numerical modelling of rock fracture process using various lab-scale rock testingmethods such as quasi-static Brazilian test, quasi-static uniaxial compression test, dynamic Brazilian test using SplitHopkinson Pressure Bar (SHPB) apparatus. Through these demonstrations, the applicability of the newly developed 3-DHFDEM code is shown.

Combined finite-discrete element method has become one of the most powerful numericalmethods for modelling rock failure process in recent decades. However, most of studies focus on two-dimensional combined finite-discrete element modelling of the rock failure process. This paper further develops a hybrid finite-discrete element method proposed early by the authors for three-dimensional modelling of the rock failure processes in Brazilian tests and uniaxial compression test. The further developed three-dimensional hybrid finite-discrete element method is then parallelized using compute unified device architecture – based general purpose graphic processing unit parallel method to conduct a full-scale three-dimensional modelling of rock spalling failure process in the single Hopkinson pressure bar test. It is concluded that the three-dimensional hybrid finite-discrete element method provides a valuable numerical tools for modelling rock fracture and fragmentation and the parallelization makes it possible to be applied in the large-scale rock mass instability engineering application.

A three-dimensional (3D) fracture algorithm is implemented into a hybrid finite-discreteelement method previously developed by the authors using a cohesive cracking model with an energy failure criterion to model the 3D transition from continuum to discontinuum during rock fracture. The newly developed 3D hybrid continuous-discontinuous method is then applied to model the fracture process of rock in the Brazilian tensile strength tests. After that, the obtained results are compared with those well documented in literatures to calibrate the development of the 3D fracture algorithm for the transition from continuum to discontinuum. Throughout this study, it is shown that the 3D hybrid continuous-discontinuous method is a valuable tool to investigate rock fracture and resultantfragment grinding behaviour. Compared with finite element method, the hybrid method is more robust in modelling rock failure, especially fracture, fragmentation, and fragment movements resulting in tertiary fractures while compared with discrete element method, the hybrid method is more versatile in dealing with irregular-shaped, deformable and breakable particles.

Fine-grained infilling materials in rock fractures cannot be penetrated by cement-based grout, while high water velocities in the unfilled parts of the fracture can impose erosion of the infilling materials. Understanding the erosion process of the infilling materials is, therefore, essential for the design of grout curtains. In this paper, the incipient motion of infilling particles in a three-dimensional rock fracture is predicted by a coupled Computational Fluid Dynamics (CFD)-Discrete Element Method (DEM) approach. A fracture model is built based on high-resolution optical scanning data of a natural rock joint surface. Infilling particles are modelled as non-cohesive spheric particles in a range of fine-sand sizes. The motion of particles is produced by coupling the CFD, solving the Navier-Stokes equations, with the DEM, prescribing the contact forces between particles. The model could capture the particle-particle and particle-fluid interaction behaviours during particle movement. Simulation results of the fracture model are compared with a parallel-plate model, which shows that the fracture geometry significantly affects the transport and distribution of the infillings. The dimensionless critical shear stress of the fracture model for the studied fracture is 11% larger than the values obtained from the parallel-plate model. Furthermore, the simulations are compared with the Hjulström and Shields diagrams, showing that the use of these two diagrams to predict the infilling erosion in the fracture results in a significant discrepancy. In contrast, a previous equation derived from flume experiments under laminar flows agrees better with the simulations. The present study visualises and quantitatively analyses the erosion process of the fracture infillings, which provides a reference to predict the threshold of the infilling erosion., QC 20210527