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Title: Computational model coupling mode II discrete fracture propagation with continuum damage zone evolution: A FRACTURE PROPAGATION COMPUTATION TOOL
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Publication Date:
Journal Name:
International Journal for Numerical and Analytical Methods in Geomechanics
Page Range or eLocation-ID:
223 to 250
Sponsoring Org:
National Science Foundation
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  1. In this work, we review and describe our computational framework for solving multiphysics phase-field fracture problems in porous media. Therein, the following five coupled nonlinear physical models are addressed: displacements (geo-mechanics), a phase-field variable to indicate the fracture position, a pressure equation (to describe flow), a proppant concentration equation, and/or a saturation equation for two-phase fracture flow, and finally a finite element crack width problem. The overall coupled problem is solved with a staggered solution approach, known in subsurface modeling as the fixed-stress iteration. A main focus is on physics-based discretizations. Galerkin finite elements are employed for the displacement-phase-field system and the crack width problem. Enriched Galerkin formulations are used for the pressure equation. Further enrichments using entropy-vanishing viscosity are employed for the proppant and/or saturation equations. A robust and efficient quasi-monolithic semi-smooth Newton solver, local mesh adaptivity, and parallel implementations allow for competitive timings in terms of the computational cost. Our framework can treat two- and three-dimensional realistic field and laboratory examples. The resulting program is an in-house code named IPACS (Integrated Phase-field Advanced Crack Propagation Simulator) and is based on the finite element library deal.II. Representative numerical examples are included in this document.
  2. Abstract. The continuum of behavior that emerges during fracturenetwork development in crystalline rock may be categorized into threeend-member modes: fracture nucleation, isolated fracture propagation, andfracture coalescence. These different modes of fracture growth producefracture networks with distinctive geometric attributes, such as clusteringand connectivity, that exert important controls on permeability and theextent of fluid–rock interactions. To track how these modes of fracturedevelopment vary in dominance throughout loading toward failure and thushow the geometric attributes of fracture networks may vary under theseconditions, we perform in situ X-ray tomography triaxial compressionexperiments on low-porosity crystalline rock (monzonite) under upper-crustalstress conditions. To examine the influence of pore fluid on the varyingdominance of the three modes of growth, we perform two experiments undernominally dry conditions and one under water-saturated conditions with 5 MPa ofpore fluid pressure. We impose a confining pressure of 20–35 MPa and thenincrease the differential stress in steps until the rock failsmacroscopically. After each stress step of 1–5 MPa we acquire athree-dimensional (3D) X-ray adsorption coefficient field from which weextract the 3D fracture network. We develop a novel method of trackingindividual fractures between subsequent tomographic scans that identifieswhether fractures grow from the coalescence and linkage of several fracturesor from the propagation of a single fracture. Throughout loadingmore »in all ofthe experiments, the volume of preexisting fractures is larger than that ofnucleating fractures, indicating that the growth of preexisting fracturesdominates the nucleation of new fractures. Throughout loading until close tomacroscopic failure in all of the experiments, the volume of coalescingfractures is smaller than the volume of propagating fractures, indicatingthat fracture propagation dominates coalescence. Immediately precedingfailure, however, the volume of coalescing fractures is at least double thevolume of propagating fractures in the experiments performed at nominallydry conditions. In the water-saturated sample, in contrast, although thevolume of coalescing fractures increases during the stage preceding failure,the volume of propagating fractures remains dominant. The influence ofstress corrosion cracking associated with hydration reactions at fracturetips and/or dilatant hardening may explain the observed difference infracture development under dry and water-saturated conditions.« less