Numerical modeling of discrete multi-crack growth applied to pattern formation in geological brittle media

Paluszny, Adriana; Matthäi, Stephan

doi:10.1016/j.ijsolstr.2009.05.007

Cited by 75 publications

(24 citation statements)

References 91 publications

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“…A finite set of randomly oriented flaws with varying size initially populates a two‐dimensional region of the model, the “flaw area.” Mode I and II stress intensity factors, K I and K II , are computed using the quarter point displacement technique [ Lim et al , 1992]. Specifically, modeling simultaneous growth of multiple cracks relies on three locally determined criteria: failure, propagation, and angle [ Paluszny and Matthai , 2009]. Failure criteria control if a fracture tip propagates.…”

Section: Methodsmentioning

confidence: 99%

Impact of fracture development on the effective permeability of porous rocks as determined by 2‐D discrete fracture growth modeling

Paluszny

Matthäi

2010

J. Geophys. Res.

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[1] Fracture networks exert a strong influence on fluid flow in the subsurface. We present a 2-D linear elastic finite element model that generates fracture patterns in incremental iterative steps. A subcritical failure criterion is applied to simulate quasi-static multiple crack propagation. We study their impact on fluid flow as a function of fracture density. Fractures are represented by closed polygons. Geomechanical apertures are a by-product of growth and depend on the current stress state. Fracture arrest, closure, and coalescence are handled by a geometric kernel. Traction and cohesion along fracture walls are not taken into account. All patterns are generated assuming plane strain and applying displacement tensile boundary conditions. We assume randomly distributed flaw positions with a uniform probability distribution and Gaussian-distributed flaw lengths. A piecewise fracture permeability is derived from the parallel plate law. We measure the effective permeability, k eff , and fracture-matrix flux ratio, q f /q m across the percolation threshold. Before the percolation threshold we observe an increase in k eff of up to two orders of magnitude. Models with fixed apertures overpredict k eff by up to six orders of magnitude, as they disregard variations in the aperture distribution due to fracture interaction. After percolation our model predicts steady linear increase in effective permeability. The q f /q m ratio better captures the initial increase in hydraulic conductivity of the system as opposed to the k eff measurements. Results corroborate that fracture percolation and stress-dependent aperture distribution due to mechanical interactions control the evolution of the k eff of the system. Results depend on the number of initial flaws used for fracture set growth.Citation: Paluszny, A., and S. K. Matthai (2010), Impact of fracture development on the effective permeability of porous rocks as determined by 2-D discrete fracture growth modeling,

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Section: Methodsmentioning

confidence: 99%

Impact of fracture development on the effective permeability of porous rocks as determined by 2‐D discrete fracture growth modeling

Paluszny

Matthäi

2010

J. Geophys. Res.

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“…All procedures employed in this work were implemented into the Geomechanics module (Paluszny and Matthäi, 2009;Paluszny and Zimmerman, 2011) of the Complex System Modeling Platform (CSMP++), an object-oriented finite element based API developed for the simulation of complex geological processes (Matthai et al, 2001). The system of equations resulting from the finite element method accumulation is solved using the Fraunhofer SAMG Solver (Stüben, 2001).…”

Section: Finite Element Implementation Detailsmentioning

confidence: 99%

A disk-shaped domain integral method for the computation of stress intensity factors using tetrahedral meshes

Nejati

Paluszny

Zimmerman

2015

International Journal of Solids and Structures

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Please cite this article as: Nejati, M., Paluszny, A., Zimmerman, R.W., A disk-shaped domain integral method for the computation of stress intensity factors using tetrahedral meshes, International Journal of Solids and Structures (2015), doi: http://dx.doi.org/10. 1016/j.ijsolstr.2015.05.026 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.A disk-shaped domain integral method for the computation of stress intensity factors using tetrahedral meshes Abstract A novel domain integral approach is introduced for the accurate computation of pointwise Jintegral and stress intensity factors (SIFs) of 3D planar cracks using tetrahedral elements. This method is efficient and easy to implement, and does not require a structured mesh around the crack front. The method relies on the construction of virtual disk-shaped integral domains at points along the crack front, and the computation of domain integrals using a series of virtual triangular elements. The accuracy of the numerical results computed for through-the-thickness, penny-shaped, and elliptical crack configurations has been validated by using the available analytical formulations. The average error of computed SIFs remains below 1% for fine meshes, and 2 − 3% for coarse ones. The results of an extensive parametric study suggest that there exists an optimum mesh-dependent domain radius at which the computed SIFs are the most accurate. Furthermore, the results provide evidence that tetrahedral elements are efficient, reliable and robust instruments for accurate linear elastic fracture mechanics calculations.

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“…Modeling multiple crack growth relies on three locally defined criteria: failure, propagation magnitude, and angle [17]. A failure criterion determines if the fracture tip will advance.…”

Section: A Mechanical Modelmentioning

confidence: 99%

“…This is accomplished by a high-level Picard iteration allowing fractures to advance until there is insufficient strain to induce further propagation. Further details of the method, including its validation, can be found in Paluszny and Matthäi [15,17].…”

Section: -2mentioning

confidence: 99%

“…Thus, a fracture is always planar and its orientation predefines its connectivity. In mechanically informed simulations, this is not the case: fractures can grow in many shapes and patterns, and curving and coalescence can greatly enhance connectivity without significantly increasing density [17]. Therefore, while the stochastic method may reproduce the statistics of fracture data measured in the field, it does not capture the more subtle aspects of natural fracture distributions that depend on the rock deformation history and its material properties.…”

Section: Introductionmentioning

confidence: 99%

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Role of geomechanically grown fractures on dispersive transport in heterogeneous geological formations

et al. 2011

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A second order in space accurate implicit scheme for time-dependent advection-dispersion equations and a discrete fracture propagation model are employed to model solute transport in porous media. We study the impact of the fractures on mass transport and dispersion. To model flow and transport, pressure and transport equations are integrated using a finite-element, node-centered finite-volume approach. Fracture geometries are incrementally developed from a random distributions of material flaws using an adoptive geomechanical finite-element model that also produces fracture aperture distributions. This quasistatic propagation assumes a linear elastic rock matrix, and crack propagation is governed by a subcritical crack growth failure criterion. Fracture propagation, intersection, and closure are handled geometrically. The flow and transport simulations are separately conducted for a range of fracture densities that are generated by the geomechanical finite-element model. These computations show that the most influential parameters for solute transport in fractured porous media are as follows: fracture density and fracture-matrix flux ratio that is influenced by matrix permeability. Using an equivalent fracture aperture size, computed on the basis of equivalent permeability of the system, we also obtain an acceptable prediction of the macrodispersion of poorly interconnected fracture networks. The results hold for fractures at relatively low density.

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Numerical modeling of discrete multi-crack growth applied to pattern formation in geological brittle media

Cited by 75 publications

References 91 publications

Impact of fracture development on the effective permeability of porous rocks as determined by 2‐D discrete fracture growth modeling

Impact of fracture development on the effective permeability of porous rocks as determined by 2‐D discrete fracture growth modeling

A disk-shaped domain integral method for the computation of stress intensity factors using tetrahedral meshes

Role of geomechanically grown fractures on dispersive transport in heterogeneous geological formations

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