An extended finite element method for hydraulic fracture problems

By Brice Lecampion. 2009

283 citations recorded by the source corpus.

In this paper, the extended finite element method (X-FEM) is investigated for the solution of hydraulic fracture problems. The presence of an internal pressure inside the crack is taken into account. Special tip functions encapsulating tip asymptotics typically encountered in hydraulic fractures are introduced. We are especially interested in the two limiting tip behaviour for the impermeable case: the classical LEFM square root asymptote in fracture width for the toughness-dominated regime of propagation and the so-called ⅔ asymptote in fracture width for the viscosity-dominated regime. Different variants of the X-FEM are tested for the case of a plane-strain hydraulic fracture propagation in both the toughness and the viscosity dominated regimes. Fracture opening and fluid pressure are compared at each nodes with analytical solutions available in the literature. The results demonstrate the importance of correcting for the loss of partition of unity in the transition zone between the enriched part and the rest of the mesh. A point-wise matching scheme appears sufficient to obtain accurate results. Proper integration of the singular terms introduced by the enrichment functions is also critical for good performance. Copyright © 2008 John Wiley & Sons, Ltd.

Subfields: Civil and Structural Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/47395a7c5e3eae87935f9aa2f3edc81819686954

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In Mechanics of Materials

Citations in the corpus

Enrichment strategies and convergence properties of the XFEM for hydraulic fracture problems (2015, methodology): “The new enrichment is distinct from the Lecampion enrichment [36] for λ ≠ 1/2.”
Phase-field modeling of fluid-driven dynamic cracking in porous media (2019, methodology): “Lecampion [43] employed the extended finite element method to simulate hydraulic fracturing by applying fluid pressure along a line fracture.”
Numerical modeling of hydraulic fracture problem in permeable medium using cohesive zone model (2012, background): “Fluid-driven fractures were studied by many contributors during the last decades from an analytical perspective [3, 7, 14, 21, 35, 34, 41, 25, 27, 22, 38, 36] as well as from a numerical point of view [10, 23, 29, 31, 42, 43].”
Material point method with enriched shape function for crack problems (2017, methodology): “Recently, the XFEM has been enhanced to simulate many challenges in computational fracture mechanics and composite modelling such as fracture in shell structures [9], band structure of metamaterials with microstructures [10], hydraulic fracture propagation [11,12], etc.”
A review of mechanical models of dike propagation: Schools of thought, results and future directions (2015, background): “…specific functions to enrich the finite element basis that1378 ensure accurate and efficient computation when under strong fluid-solid1379 coupling (Lecampion, 2009; Gordeliy and Peirce, 2013; Chen, 2013).1380 • Damage mechanics-FEM based models for three-dimensional growth of1381 hydraulic…”
A phase-field modeling approach of fracture propagation in poroelastic media (2018, methodology): “Lecampion [17] applied the extended finite element method to hydraulic fracturing.”
Hydraulic fracture revisited: Particle velocity based simulation (2015, methodology): “…been attempts to develop full 3D models utilizing various numerical techniques, e.g. finite element method (Chen, 2013; Hunsweck, Shen, & Lew, 2012; Lecampion, 2009; Wangen, 2013), boundary element method (or combination of the two (Carter, Desroches, Ingraffea, & Wawrzynek, 2000; Yamamoto,…”
Thermo-hydro-mechanical modeling of impermeable discontinuity in saturated porous media with X-FEM technique (2012, methodology): “The technique was also employed by Lecamipon [51] in hydraulic fracture problems using the special crack-tip functions in the presence of internal pressure inside the crack.”
Generalized Duffy transformation for integrating vertex singularities (2009, background): “We choose α = {1, 1/2, 1/3, 2/3, 4/3}, which appear in various applications: α = 1/2, 1 for cracks in isotropic media [10], α = 1/2, 2/3 in hydraulic fracture [18], and α = 1/3, 2/3, 4/3 in the solution of Laplace equation in an L-shaped domain with a re-entrant corner (see Section 3.”