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  1. Fracture patterns experienced under a dynamic uniaxial compressive load are highly sensitive to rock microstructural defects due to its brittleness and the absence of macroscopic stress concentration points. We propose two different approaches for modeling rock microstructural defects and inhomogeneity. In the explicit realization approach, microcracks with certain statistics are incorporated in the computational domain. In the implicit realization approach, fracture strength values are sampled using a Weibull probability distribution. We use the Mohr-Coulomb failure criterion to define an effective stress in the context of an interfacial damage model. This model predicts crack propagation at angles ±ɸch = ±(45 − ɸ/2) relative to the direction of compressive load, where ɸ is the friction angle. By using appropriate models for fracture strength anisotropy, we demonstrate the interaction of rock weakest plane and ɸch. Numerical results demonstrate the greater effect of strength anisotropy on fracture pattern when an explicit approach is employed. In addition, the density of fractures increases as the angle of the weakest planes approaches ±ɸch. The fracture simulations are performed by an h-adaptive asynchronous spacetime discontinuous Galerkin (aSDG) method that can accommodate crack propagation in any directions.
  2. Realistic fracture simulations in rock as a heterogeneous brittle material with significant inherent ran- domness require the use of models that incorporate its inhomogeneities and statistical variability. The high dependence of their fracture progress on microstructural defects results in wide scatter in their ultimate strength and the so-called size effect. This paper proposes an approach based on statistical volume elements (SVEs) to characterize rock fracture strength at the mesoscale. The use of SVEs ensures that the material randomness is maintained upon averaging of microscale features. Because the fracture strength varies not just spatially, but also by the angle of loading, this work includes angular variability to properly model a heterogeneous rock domain. Two different microcrack distributions, one angularly uniform and one angularly biased towards a specific angle, are used to show that implementing angle into the random field provides the most realistic fracture simulation. An adaptive asynchronous spacetime discontinuous Galerkin (aSDG) finite element method is used to perform the dynamic fracture simulations.