Fracture growth-I. Formulation and implementations

Wei, Kaihong; Bremaecker, J. Cl. De

doi:10.1111/j.1365-246x.1995.tb06832.x

Cited by 8 publications

(6 citation statements)

References 19 publications

(16 reference statements)

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“…8(a), where the separation is half the length of the cracks, there seems to be no coalescence by the propagation of the inner wing cracks. This result is consistent with a previous calculation by Wei & De Bremaecker ( 1995b), who used the boundary-element implementation of the repulsion scheme and the maximum strain-energy release-rate criterion (Wei & De Bremaecker 1995a) to compute the growth path of two right-stepping horizontal cracks under right-lateral shearing. Their geometry is comparable with ours since the vertical compression applied on inclined cracks resolves into left-lateral shearing on the crack planes, which makes our geometry of left-stepping cracks under left-lateral shearing the symmetrical geometry of Wei & De Bremaecker's (1995b) one.…”

Section: Results a N D Discussionsupporting

confidence: 91%

A theoretical approach to the propagation of interacting cracks

Baud¹,

Reuschlé²

1997

Geophysical Journal International

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S U M M A R YWe propose a scheme to compute interaction effects between two randomly oriented cracks under compressive stresses and we discuss the role crack interactions play in the crack coalescence process. Stress intensity factors are computed by using an iterative technique based on the method of successive approximations. Once crack propagation occurs, curved wing cracks grow from the initial crack tips. The stress intensity factors at the wing crack tips are calculated as the sum of two terms: a component for a single wing crack subjected to both the applied stresses and the interaction effect, and a component due to the sliding of the initial crack. We have applied our procedure to various crack geometries. Our results show that interaction effects act on the crack propagation path. For cracks under tension, our approach correctly predicts the curving, hook-shaped paths of interacting cracks that have been observed in various materials. For en echelon compressive cracks, interaction effects depend on the geometry of stepping. For right-stepping cracks, no mode I crack coalescence occurs. A mixedmode propagation criterion may be introduced to check whether coalescing secondary shear fractures initiate. For left-stepping cracks, depending on whether or not there is overlapping, crack coalescence is achieved by tension wing cracks at the inner crack tips. Without overlapping, the growing wing cracks delimit a region where a tensile secondary fracture may develop and lead to coalescence. These results are consistent with previous work and show that our procedure may be now extended to a population of cracks.

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Section: Results a N D Discussionsupporting

confidence: 91%

A theoretical approach to the propagation of interacting cracks

Baud¹,

Reuschlé²

1997

Geophysical Journal International

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“…We use a maximum strain‐energy release rate criterion (generalized Griffith criterion) to estimate whether and in which direction a fracture will grow. A similar criterion has been used by De Bremaecker & Wei (1994) and Wei & De Bremaecker (1995a,b) to simulate mixed‐mode fracture growth under shear load and compression. Other authors have used a maximum tensile or maxi‐mum circumferential stress (e.g.…”

Section: Methodsmentioning

confidence: 99%

“…This is because we do not account for sliding friction at the closed parts of the fracture that are moving under shear mode. We have also not included two independent fracture toughnesses for mode I and mode II fracture propagation (see also Wei & De Bremaecker 1995a; Shen & Stephansson 1995).…”

Section: Methodsmentioning

confidence: 99%

“…The numerical simulation of quasi‐static fracture growth has been performed previously (e.g. Sempere & MacDonald 1986; De Bremaecker & Swenson 1990; De Bremaecker & Wei 1994; Wei & De Bremaecker 1995a,b; Shen & Stephansson 1995). However, in our terminology these authors simulated empty fracture growth and not wholesale fracture motion, that is, the displacement of a whole fracture from one position to another (denoted as fracture propagation in the following).…”

Section: Introductionmentioning

confidence: 99%

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Numerical simulations of the propagation path and the arrest of fluid-filled fractures in the Earth

Dahm

2000

Geophysical Journal International

150

162

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Summary We use a boundary element method to study the growth and quasi‐static propagation of fluid‐filled fractures in regions with inhomogeneous and deviatoric stresses. The wholesale migration of fractures due to their opening at one end and closing at the other can be simulated when using a finite fluid mass contained in a fracture and considering fluid compression or expansion with changing fracture volume; these fractures are driven by stress gradients and by the density differences between the fluid and the surrounding rock. Contrary to commonly held beliefs, the fracture growth and the propagation directions are not controlled only by the direction of the principal stresses, but also by tectonic stress gradients, apparent buoyancy forces and the length of the fractures themselves. The models help to explain the formation of sills, the lateral migration of magmas under volcanoes and the absence of volcanoes under the shallow parts of the Nazca plate.

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“…. Finally, attempts have been made to arrive at the correct BC by more or less systematically decreasing the separation between the crack faces [3,6,7,29]. Absent a realization of the complementary nature of the BC, these attempts were only mildly successful.…”

Section: Theorymentioning

confidence: 99%

Compressional fractures considered as contact problems and mixed complementarity problems

Bremaecker

Ferris

Ralph

2000

Engineering Fracture Mechanics

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The boundary conditions on the faces of compressional fractures are not known a priori since these faces may or may not be in contact, but the product of the normal stress and the normal relative displacement is necessarily null; similar but more complex conditions may be written for the shear stress and displacement. These conditions can be expressed in the form of a mixed linear complementarity problem. We use the Displacement Discontinuity Method and the PATH algorithm to solve them. This scheme is faster and more accurate than the methods previously used. The shear stresses on two parallel cracks depend on their separation, their inclination with respect to the imposed maximum compressional stress, and their geometry. The shear stress on two horizontal cracks separated by a small upward or downward step Ð considering the imposed direction of motion Ð drops to zero very near the step; in the case of a downward step this region is surrounded by a small region where the stress increases by a factor of about 10. Many more cases must be investigated before general conclusions can be drawn. 7

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Fracture growth-I. Formulation and implementations

Cited by 8 publications

References 19 publications

A theoretical approach to the propagation of interacting cracks

A theoretical approach to the propagation of interacting cracks

Numerical simulations of the propagation path and the arrest of fluid-filled fractures in the Earth

Compressional fractures considered as contact problems and mixed complementarity problems

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