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Fracture coalescence is a critical phenomenon for creating large fractures from smaller flaws, affecting fracture network flow and seismic energy release potential. In this paper, simulations of fracture coalescence processes in granite specimens with pre-existing cracks are performed. These simulations utilize an in-house implementation of the Combined Finite-Discrete Element method (FDEM) known as the Hybrid Optimization Software Suite (HOSS). The pre-existing cracks within the specimens follow two geometric patterns: 1) a single crack oriented at different angles with respect to the loading direction, and 2) two cracks, where one crack is oriented perpendicular to the loading direction and the other crack is oriented at different angles. The intent of this study is to demonstrate the suitability of FDEM for modeling fracture coalescence processes including: crack initiation and propagation, tensile and shear fracture behavior, and patterns of fracture coalescence. The simulations provide insight into the evolution of fracture tensile and shear fracture behavior as a function of time. The single-crack simulations accurately reproduce experimentally measured peak stresses as a function of crack inclination angle. Both the single- and double-crack simulations exhibit a linear increase in strength with increasing crack angle; the double-crack specimens are systematically weaker than the single-crack specimens.

In this paper, the Combined Finite-Discrete Element Method (FDEM) has been applied to analyze the deformation of anisotropic geomaterials. In the most general case geomaterials are both non-homogeneous and non-isotropic. With the aim of addressing anisotropic material problems, improved 2D FDEM formulations have been developed. These formulations feature the unified hypo-hyper elastic approach combined with a multiplicative decomposition-based selective integration for volumetric and shear deformation modes. This approach is significantly different from the co-rotational formulations typically encountered in finite element codes. Unlike the co-rotational formulation, the multiplicative decomposition-based formulation naturally decomposes deformation into translation, rotation, plastic stretches, elastic stretches, volumetric stretches, shear stretches, etc. This approach can be implemented for a whole family of finite elements from solids to shells and membranes. This novel 2D FDEM based material formulation was designed in such a way that the anisotropic properties of the solid can be specified in a cell by cell basis, therefore enabling the user to seed these anisotropic properties following any type of spatial variation, for example, following a curvilinear path. In addition, due to the selective integration, there are no problems with volumetric or shear locking with any type of finite element employed.

Large continental earthquakes activate multiple faults in a complex fault system, dynamically inducing co-seismic damage around them. The 2016 Mw 7.8 Kaikoura earthquake in the northern South Island of New Zealand has been reported as one of the most complex continental earthquakes ever documented1, which resulted in a distinctive on and off-fault deformation pattern. Previous geophysical studies confirm that the rupture globally propagated northward from epicenter. However, the exact rupture- propagation path is still not well understood because of the geometrical complexity, partly at sea, and the possibility of a blind thrust. Here we use a combination of state-of- the-art observation of surface deformation, provided by optical image correlation, and first principle physics-based numerical modeling to determine the most likely rupture path. We quantify in detail the observed horizontal co-seismic deformation and identify specific off-fault damage zones in the area of the triple junction between the Jordan, the Kekerengu and the Papatea fault segments. We also model dynamic rupture propagation, including the activation of off-fault damage, for two alternative rupture scenarios through the fault triple junction. Comparing our observations with the results from the above two modeled scenarios we show that only one of the scenarios best explains both the on and off-fault deformation fields. Our results provide a unique insight into the rupture pathway, by observing, and modeling, both on and off-fault deformation. We propose this combined approach here to narrow down the possible rupture scenarios for large continental earthquakes accompanied by co-seismic off-fault damage., Comment: 32 pages, 11 figures