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1. Modeling of rock inhomogeneity and anisotropy by explicit and implicit representation of microcracks

   Abedi, Reza; Clarke, Philip L. (January 2018, Proceedings of ARMA 2018)

   Fracture in rock as a heterogeneous brittle material, having significant inherent randomness, requires including probabilistic considerations at different scales. Crack growth in rocks is generally associated with complex features such as crack path oscillations, microcrack and crack branching events. Two methods will be presented to address rock inhomogeneity and anisotropy. First, microcracks are explicitly realized in a domain based on specific statistics of crack length and location. Second, a statistical model is used to implicitly represent an inhomogeneous field for fracture strength. Both approaches can be used for rocks in which the natural fractures are oriented in a specific angle, i.e. an aspect for modeling bedding planes in sedimentary rocks. 

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2. Random field realization and fracture simulation of rocks with angular bias for fracture strength

   Garrard, J. M.; Abedi, Reza; Clarke, P. L. (January 2018, 52nd U.S. Rock Mechanics/Geomechanics Symposium)

   Realistic fracture simulations in rock as a heterogeneous brittle material with significant inherent randomness 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. 

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3. Random field realization and fracture simulation of rocks with angular bias for fracture strength

   Garrard, J.M.; Abedi, R.; Clarke, P.L. (January 2018, Proceedings of ARMA 2018)

   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. 

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4. Comparison of Interfacial and Continuum Models for Dynamic Fragmentation Analysis

   https://doi.org/10.1115/IMECE2018-88294  

   Bahmani, Bahador; Clarke, Philip; Abedi, Reza (November 2018, Proceedings of ASME 2018 International Mechanical Engineering Congress and Exposition)

   The microstructural design has an essential effect on the fracture response of brittle materials. We present a stochastic bulk damage formulation to model dynamic brittle fracture. This model is compared with a similar interfacial model for homogeneous and heterogeneous materials. The damage models are rate-dependent, and the corresponding damage evolution includes delay effects. The delay effect provides mesh objectivity with much less computational efforts. A stochastic field is defined for material cohesion and fracture strength to involve microstructure effects in the proposed formulations. The statistical fields are constructed through the Karhunen-Loeve (KL) method. An advanced asynchronous Spacetime Discontinuous Galerkin (aSDG) method is used to discretize the final system of coupled equations. Application of the presented formulation is shown through dynamic fracture simulation of rock under a uniaxial compressive load. The final results show that a stochastic bulk damage model produces more realistic results in comparison with a homogenizes model. 

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5. Gap Test of Crack-Parallel Stress Effect on Quasibrittle Fracture and Its Consequences

   https://doi.org/10.1115/1.4047215  

   Nguyen, Hoang Thai; Pathirage, Madura; Cusatis, Gianluca; Bažant, Zdeněk P. (July 2020, Journal of Applied Mechanics)

   null (Ed.)

   Abstract In the standard fracture test specimens, the crack-parallel normal stress is negligible. However, its effect can be strong, as revealed by a new type of experiment, briefly named the gap test. It consists of a simple modification of the standard three-point-bend test whose main idea is to use plastic pads with a near-perfect yield plateau to generate a constant crack-parallel compression and install the end supports with a gap that closes only when the pads yield. This way, the test beam transits from one statically determinate loading configuration to another, making evaluation unambiguous. For concrete, the gap test showed that moderate crack-parallel compressive stress can increase up to 1.8 times the Mode I (opening) fracture energy of concrete, and reduce it to almost zero on approach to the compressive stress limit. To model it, the fracture process zone must be characterized tensorially. We use computer simulations with crack-band microplane model, considering both in-plane and out-of-plane crack-parallel stresses for plain and fiber-reinforced concretes, and anisotropic shale. The results have broad implications for all quasibrittle materials, including shale, fiber composites, coarse ceramics, sea ice, foams, and fone. Except for negligible crack-parallel stress, the line crack models are shown to be inapplicable. Nevertheless, as an approximation ignoring stress tensor history, the crack-parallel stress effect may be introduced parametrically, by a formula. Finally we show that the standard tensorial strength models such as Drucker–Prager cannot reproduce these effects realistically. 

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