Abstract The paper presents a numerical study of the three-dimensional problem of cracks interacting with a cylindrical uniformly pressurized borehole. The theoretical developments describe general case in which the axis of the borehole can be inclined to the vertical direction, the cracks are either located outside of the borehole or emanate from it, and the in-situ stresses are uniform with major principal stress acting in vertical direction. The tractions are prescribed at the cracks surfaces that includes two limiting cases of traction-free cracks (“fast pressurization”) or cracks subjected to uniform load equal to that applied at the surface of the borehole (“slow pressurization”). The study is based on the complex integral representations for the three-dimensional fields around the borehole-crack system. The boundary surfaces are approximated using triangular mesh and quadratic polynomials are employed for approximating the boundary unknowns. The prescribed boundary conditions are met using “limit after discretization” procedure. The linear algebraic system to find the unknowns is set up by the collocation method. Two numerical benchmarks are presented.

Last. John McLennan(UofU: University of Utah)H-Index: 19

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Abstract Mode-I stress intensity factor (SIF) for symmetrical radial cracks emanating from hollow cylinder in an infinite plane under complex nonlinear loadings is firstly solved with the weight function method. A weight function providing wide-spectrum expressions for such fractures is developed. The weight function based SIFs are validated against different boundary collocation based SIFs. Three correlations of weight function parameters are derived for simplifying engineering applications and...

Last. Joseph F. Labuz(UMN: University of Minnesota)H-Index: 32

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Abstract This paper reports new developments on the complex variables boundary element approach for solving three-dimensional problems of cracks in elastic media. These developments include implementation of higher order polynomial approximations for the boundary displacement discontinuities and more efficient analytical techniques for evaluation of integrals. The approach employs planar triangular boundary elements and is based on the integral representations written in a local coordinate syste...

This paper examines major techniques for modeling elastostatic crack problems. The foundations of these techniques and fundamental papers that introduced, developed, and applied them are reviewed. The goal is to provide a “translation” between the different academic languages that describe the same problem.

#1P. Gupta(UIUC: University of Illinois at Urbana–Champaign)H-Index: 7

#2Carlos Armando Duarte(UIUC: University of Illinois at Urbana–Champaign)H-Index: 29

SUMMARY Hydraulic fracturing is the method of choice to enhance reservoir permeability and well efficiency for extraction of shale gas. Multi-stranded non-planar hydraulic fractures are often observed in stimulation sites. Non-planar fractures propagating from wellbores inclined from the direction of maximum horizontal stress have also been reported. The pressure required to propagate non-planar fractures is in general higher than in the case of planar fractures. Current computational methods fo...

Summary The article presents a new complex variables-based approach for analytical evaluation of threedimensional integrals involved in boundary element method (BEM) formulations. The boundary element is assumed to be planar and its boundary may contain an arbitrary number of straight lines and/or circular arcs. The idea is to use BEM integral representations written in a local coordinate system of an element, separate in-plane components of the fields involved, arrange them in certain complex c...

Last. Joseph F. Labuz(UMN: University of Minnesota)H-Index: 32

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Abstract This paper presents a new boundary element-based approach for solving three-dimensional problems of an elastic medium containing multiple cracks of arbitrary shapes. The medium could be loaded by far-field stress (for infinite domains), surface tractions (including those at the cracks surfaces), or point loads. Constant body forces are also allowed. The elastic fields outside of the cracks are represented by integral identities. Triangular elements are employed to discretize the boundar...

We provide a brief historical background of the development of hydraulic fracturing models for use in the petroleum and other industries. We discuss scaling laws and the propagation regimes that control the growth of hydraulic fractures from the laboratory to the field scale. We introduce the mathematical equations and boundary conditions that govern the hydraulic fracturing process, and discuss numerical implementation issues including: tracking of the fracture footprint, the control of the gro...

The complex variables boundary element method (CVBEM) is used to study interaction between a circular opening and fractures originating from its boundary in a piecewise homogeneous plane. A new complex hypersingular equation for piecewise homogeneous media with a circular opening is obtained. The equation is solved using the CVBEM technique with circular and straight boundary elements and polynomial approximations (with square root asymptotics for crack tip elements) for the unknown functions. T...

Growth of pressure-induced fractures originating from a wellbore at an arbitrary angle to the direction of far field stresses is considered. A parametric study of hydraulic fracturing process from the point of view of fracture mechanics is presented in conditions of slow and fast pressurization rate. The study is based on the linear elastic fracture mechanics formulation that involves a complex hypersingular equation (CHSIE) for a plane with a circular opening and a system of arbitrary curviline...

Abstract null null The work aims to increase the efficiency of finding local fields in problems, like those of fracture mechanics, for which extreme, rather than average, values of fields are of prime significance. We focus on using kernel independent fast multipole methods (KI-FMM) when a problem is solved by a boundary element method. To accurately calculate local fields, we employ smooth equivalent surfaces (SES), used in translations of a KI-FMM, instead of non-smooth surfaces having singula...