The combined finite-discrete element method (FDEM) has been widely used for various engineering applications including the field of rock engineering as one of the promising hybrid methods since this method can simulate the processes of intact/continuous rock deformation, transition from continuum to discontinuum (i.e., rock fracturing) and discontinuous interactions between material surfaces (e.g., rock fragmentation). However, this method is notorious for its computationally expensive nature, especially when modeling rock fracture processes under quasi-static loading. The authors have recently developed a 2-dimensional/3-dimensional(3D) Y-HFDEM code through a research collaboration between university of Tasmania and Hokkaido university. An important feature of this code includes the incorporation of parallelization scheme using a general-purpose-graphics-processing-unit (GPGPU) to achieve a good speed-up of FDEM simulations of rock fracture processes, and the 3D Y-HFDEM code can achieve up to 284 times speed-up compared with the sequential code if it is run on appropriate GPGPU accelerators. In addition, the code is free for non-commercial/non-military applications, which should be useful for many young researchers in the field of rock engineering.

This paper demonstrates our recent developments/achievements based on the Y-HFDEM code especially by introducing 3D modeling of rock fracture processes in uni- and tri-axial compression tests using 3D Y-HFDEM code since the number of applications of 3D FDEM for this class of problems has been very limited. One important issue regarding on the timing of contact activation is also discussed.

1. Introduction

Over recent two and half decades, the combined finite-discrete element method (FDEM), proposed by (Munjiza et al., 1995; Munjiza, 2004), has been further developed and applied in the field of rock engineering due to its capability of incorporating the advantages of both continuum- and discontinuum-based methods in terms of simulating rock fracture and fragmentation (Mohammadnejad et al., 2018). Transition from an assembly of continuum finite elements to discontinuum is facilitated by initially zero-thickness cohesive elements which are inserted along the boundaries of continuum finite elements. One of the most representative FDEM code is an open-source research code, Y code (Munjiza, 2004), and several attempts have been made to actively extend the original code into both open access and commercial codes. We have also self-developed Y-HFDEM IDE (Liu et al. 2016; Liu et al. 2016) code based on Y code. Since FDEM is notorious for its computational expensive characteristics, we have recently introduced the parallel computation scheme into the Y-HFDEM IDE code using the GPGPU accelerator controlled by CUDA C/C++ for both two-dimensional (2D) (Fukuda et al., 2019a) and threedimensional (3D) (Fukuda et al., 2019b) applications. Although there are many publications on applying the 2D FDEM to simulate the fracturing process of rocks especially under quasi static loading condition, there is a limited number of publications on the application of 3D FDEM in simulating the failure process of rocks under quasi-static and dynamic loading conditions, which is due to the intensive computational nature of the 3D FDEM. Brazilian indirect tensile strength (BTS) and uniaxial compressive strength (UCS) tests have frequently been utilized for the calibration of the 2D/3D FDEM simulations. While conducting experiments of UCS tests is not time-consuming, conducting 3D FDEM simulation of such tests requires significant computational effort since the involving process includes the intact deformation in the pre-peak regime, transition from continuum to discontinuum (emergence of non-linearity around the peak) and completely discontinuous deformation (post peak regime involving with sudden release of stress and significant contact process between newly created macro fractures) along with the fact that very slow loading must be applied to simulate the quasi-static loading. Considering that the FDEM is based on explicit finite element method (FEM), the simulation becomes more computationally expensive when 3D FDEM is applied to simulate triaxial compression tests with high confining pressures since, with the very slow loading rate being kept, more computational steps are needed to model the failure process of rock with higher compressive strength. Meanwhile, the 3D FDEM simulation of the triaxial compression test is necessary to calibrate the input parameters such as cohesion and internal friction angle of rocks along with the UCS and BTS tests. Therefore, some remedies should be used to make 3D FDEM simulation of triaxial compression tests more affordable.

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