The geometry of echelon fractures in rock: implications from laboratory and numerical experiments

Thomas, Andrew L.; Pollard, David D.

doi:10.1016/0191-8141(93)90129-x

Cited by 171 publications

(80 citation statements)

References 22 publications

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“…Thus fewer elements are needed in the present scheme for the same accuracy, or much greater accuracy can be achieved for the same N. Figure A1. Relative error e = |K num À K exact |/K exact in the numerically determined stress intensities K I and K II at the tips of a circular arc crack of angle 2a subject to uniform far-field tension for a = 45°(thin lines) and a = 90°(thick lines) as a function of the number of boundary elements N. The present scheme (solid lines) is much more accurate than that of Crouch and Starfield [1983] as described by Thomas and Pollard [1993] (dashed lines).…”

Section: A4 Verification and Accuracymentioning

confidence: 89%

“…1. The correction factor 0.806 used by Thomas and Pollard [1993] (0.798 is actually better) removes this leading-order error but still leaves numerical errors that are much greater than the present scheme ( Figure A1). Thus fewer elements are needed in the present scheme for the same accuracy, or much greater accuracy can be achieved for the same N. Figure A1.…”

Section: A4 Verification and Accuracymentioning

confidence: 91%

“…Various studies have considered how the presence of one or more neighboring cracks influences the stress field near another and hence the propagation path [e.g., Pollard et al, 1982;Sempere and Macdonald, 1986;Olson and Pollard, 1989;Cruikshank et al, 1991;Olson, 1993;Thomas and Pollard, 1993]. These analyses largely focus on crack curvature as a crack-crack interaction effect caused by the approach and overlap of echelon segments.…”

Section: Introductionmentioning

confidence: 99%

“…Several straight cracks can be dealt with by reflection techniques [Pollard et al, 1982] and small deflections from a straight path can be dealt using the analysis of Cotterell and Rice [1980] [Cruikshank et al, 1991]. However, previous calculations of propagation along more general curving trajectories [e.g., Olson and Pollard, 1989;Olson, 1993;Thomas and Pollard, 1993] have largely been based on the boundary element method of Crouch and Starfield [1983]. This method employs a simple discretization in which the dike shape is approximated by elements consisting of straight-line segments and the wall displacement on each element is taken to be constant.…”

Section: Introductionmentioning

confidence: 99%

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Calculation of dike trajectories from volcanic centers

Meriaux

Lister

2002

J. Geophys. Res.

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[1] Patterns of dike swarms around volcanic centers or above mantle plumes are interpreted by a mechanical analysis of regional and dike-induced stresses, in which dike emplacement is controlled and guided by the stress state. Comparisons of dike patterns with patterns of principal-stress trajectories caused by a source and a regional stress system are commonly used to infer paleostresses. However, dike trajectories are determined by a complex interaction between dike-induced stresses and the source/ regional stress system. We present numerical calculations based on a novel boundary-integral formulation, which examines the simultaneous effects of regional stresses, magma pressure, and dike injection on the local stress state around a continuously curving dike. Dike paths are calculated from the condition that dikes propagate by mode I failure. Our results suggest that the magnitude of the regional stresses would be 2 -5 times higher than previous estimates based on principal-stress trajectory analysis.

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Section: A4 Verification and Accuracymentioning

confidence: 89%

Section: A4 Verification and Accuracymentioning

confidence: 91%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Calculation of dike trajectories from volcanic centers

Meriaux

Lister

2002

J. Geophys. Res.

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“…The model is restricted by the following assumptions' (1) an effective tensile stress is required for joint growth, (2) there is no interaction between a growing cross joint and the preexisting joint, (3) there is no interaction between two adjacent cross joints, and (4) the tip of the growing cross joint will be aligned perpendicular to the local c• 3. The latter assumption, validated and discussed by Bergkvist Thomas and Pollard [1993], among others, enables us to construct cross-joint trajectories based on the orientation of local principal stresses near the preexisting joint.…”

Section: Theoretical Derivationmentioning

confidence: 99%

Theoretical analysis of cross‐joint geometries and their classification

Bai¹,

Gross²

1999

J. Geophys. Res.

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Abstract. One commonly observed bedrock joint pattern consists of cross joints that terminate against an older set of longer systematic joints. Dyer [ 1988] showed that unique cross-joint geometries may develop in response to a combination of remote stresses and local perturbations of the stress field in the vicinity of preexisting joints. We expand upon Dyer's analysis by providing the general solutions for cross-joint geometry as a function of remote principal stress orientations and ratios. Specific cross-joint geometries are determined by solving for the local cross-joint angle as a function of distance from the preexisting joint. On the basis of theoretical derivations, cross-joint geometries are grouped into five main categories: curving parallel, curving perpendicular, quasi-curving parallel, quasi-curving perpendicular and noncurving geometries. Furthermore, by discussing the stress state in the vicinity of the preexisting joint, a general expression for the dimension of compressive zone is derived, and a more detailed classification of cross-joint geometry is provided. Results from this study provide a method to estimate the relative magnitudes of remote principal stresses simply based on the observed cross-joint geometry, which may help constrain the tectonic history of a region. In addition, knowledge of precise cross-joint curvature and intersection geometries may provide important insights into their connectivity and fluid flow characteristics.

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Mechanics of two interacting magma‐driven fractures: A numerical study

2014

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To understand magma focusing from broad melting zones in the crust, propagation in brittle rocks of two interacting dikes ascending from a single deep source has been modeled using a time-dependent plane strain hydraulic fracturing model. The source is assumed to generate a constant influx rate to feed the dike growth, which is also aided by buoyancy effects. In contrast to uncoupled model results, the simultaneous parallel growth of two dikes to a certain distance is found to occur provided that the two dikes are initially of different heights, which might be produced either by previous magma intrusion or during nucleation. The shorter dike will chase the longer one and they can either progressively merge or continue subparallel growth at a reduced spacing, depending on the deviator stress between the vertical and horizontal stresses and the initial lateral separation, with parameters given in dimensionless forms. Numerical results reveal the mechanics for simultaneous ascents of two subparallel dikes, in that dike interaction can produce a low-stress field, which is just above the tip of the shorter dike, favorable to growth of the shorter dike. The energy analysis indicates that the energy required for two subparallel dikes is less than that for a single dike during the late-time buoyancy-viscosity propagation stage where considerable ascent occurs. This growth behavior might provide the mechanism for simultaneous, instead of sequential, growth of various dikes in a single set.

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The geometry of echelon fractures in rock: implications from laboratory and numerical experiments

Cited by 171 publications

References 22 publications

Calculation of dike trajectories from volcanic centers

Calculation of dike trajectories from volcanic centers

Theoretical analysis of cross‐joint geometries and their classification

Mechanics of two interacting magma‐driven fractures: A numerical study

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