Combined finite-discrete element method has become one of the most powerful numerical methods 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.
The study on rock failure process has been a challenging but hot topic since rock fracture has applications in not only breaking the rock mass for extracting valuable natural resources in mining, geothermal, and oil & gas industries but also preventing geotechnical engineering structures such as tunnels, slopes and dams from failure and collapse. In recent decades, numerical method has been one of the most powerful tools for studying rock failure process and the combined finite-discrete element method initially proposed by Munjiza (2004) has become one of the most powerful numerical methods for modelling the rock failure process. Compared with the finite element method, the combined finite-discrete element method is more robust in modelling rock failure, especially fracture, fragmentation, and fragment movements resulting in tertiary fractures. Compared with the discrete element method, the combined finite-discrete element method is more versatile in dealing with irregular-shaped, deformable and breakable particles. However, most of studies in literatures focus on modelling the rock failure process using two-dimensional (2D) finite-discrete element methods (Mahabadi et al., 2010; Liu, 2013; Lisjak et al., 2014; Liu et al., 2015 and 2016; Mahabadi et al., 2016; An et al., 2017). Thanks to the rapid development of computing power, interactive computer graphics and topological data structure, three-dimensional (3D) finite-discrete element modelling of the rock failure process has attracted the attention of more and more researchers. Rougier et al. (2014) simulated the dynamic rock failure process in dynamic Brazilian test using a 3D combined finite-discrete element method, i.e. the so-called MUNROU (Munjiza-Rougier) code running on a supercomputer with a few hundreds of CPUs at Los Alamos National Laboratory. Mahabadi et al. (2014) implemented a 3D combined finite-discrete element method to investigate the rock failure process in Brazilian disc test and uniaxial compression test although their 3D modelling of the uniaxial compression test is far from satisfactory. Hamdi et al. (2014) simulated the complete 3D fracture process during conventional laboratory testing including Brazilian indirect tension and uniaxial and biaxial compression using a combined finite-discrete element method called ELFEN developed Rockfield Ltd. In this study, a hybrid finite-discrete element method proposed by Liu et al. (2015) on the basis of Munjiza's (2004) open-source combined finite-discrete element libraries are further developed for three-dimensional modelling of the rock failure processes in Brazilian tests and uniaxial compression test, which extends a recent study on the 3D hybrid finite-discrete element modelling conducted by the authors (Liu et al., 2018). Moreover, the further developed 3D hybrid finite-discrete element method is parallelized using the GPGPU (general purpose graphic processing unit) parallel method initially implemented in the DFPA (dynamic failure process analysis) code (Fukuda et al., 2016) to conduct a full-scale 3D modelling of the single Hopkinson pressure bar test on the rock spalling failure process. Unlike Rougier et al.'s (2014) and probably Hamdi et al.'s (2014) (although unclear since not stated in their paper) modellings completed in the supercomputer with hundreds of CPUs, all of 3D modellings reported in this paper are completed in PC although the rock spalling test is modelled using a PC with a powerful GPU.