Realistic fracture simulations in rock as a heterogeneous brittle material with significant inherent randomness, requires the use of models that incorporate its inhomogeneities and statistical variability. Dynamic crack growth in rocks is generally associated with complex features such as crack path oscillations, microcracking and crack branching. We employ two approaches to address rock inhomogeneities for dynamic fracture simulations. First we model fractures explicitly with random size, location and orientation as natural pre-existing crack-like defects. Second, we use a probabilistic nucleation technique based on the Weibull model to implicitly incorporate creation of new cracks during the analysis. Both approaches can be used for the simulation of rocks for which the natural fractures are oriented in a specific angle, as in sedimentary rocks. We use the Spacetime Discontinuous Galerkin (SDG) method to efficiently and accurately capture complex fracture patterns observed in dynamic rock fracture. Specifically we employ a novel crack path tracking method, offered by the SDG method's powerful adaptive operations, to accurately model crack path oscillations, microcracking, and crack bifurcation. Our approach is applicable to rock fracture as well as problems where an induced major crack propagates and intersects natural fractures. Incorporation of macro-micro crack interactions can provide a more accurate estimation in hydrocarbon recovery in tight formations.
Rocks are heterogeneous at different scales. At small grain scale, they are characterized by the presence of microcracks and granular microstructures. In fact, rocks contain a large number of randomly oriented zones of potential failure in the form of grain boundaries. At large mass scale, they are described by the presence of different rock types, faults and weak features such as fracture networks. These inhomogeneities affect the continuum level mechanical characteristics of rocks such as strength, toughness, and elasticity properties. However, mechanical properties of a solid can also be estimated by simulating its microstruc-ture while it is loaded. In this context, failure in rock can be considered as the consequence of tensile and shear micro-fractures which progress within the microstructure and finally result in macro-fractures known as a failure state.
In many applications it is important to consider the natural discontinuities of rocks at different observation scales. Microcracks and pores in micro-scale or pre-existing fracture networks and faults in macroscale influence the formation of new discontinuities by joining and interacting with them. Rock blasting and hydraulic fracturing in tight formations are two examples in which the goal of induced dynamic loadings is to increase the discontinuities. This issue needs to be properly addressed in computational simulations. The consequences of rock blasting which includes fracturing of the rock and fragment size distributions should be well estimated in design process. In hydraulic fracturing, an induced major crack propagates and intersects natural fractures which in turn are hydraulically loaded and extended to intersect other fissures and finally results in a new complicated fracture network. Incorporation of macro-micro crack interactions can highly improve computational estimations for the problems dealing with fracture in rocks. For example, models that do not include the interactions of main hydraulically loaded and propagated cracks with natural fissures often underestimate the hydrocarbon recovery from a tight reservoir. In contrast to these problems at which the aim of numerical evaluation is to maximize the fractures and cracks in rock, there are some events aiming to limit the formation of new fractures and prevent rock failure. Natural slopes, dams and underground openings are among the examples in which the existing natural fractures should be included in the simulations for their stability assessments.