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| Titel |
Self-similar pattern formation and continuous mechanics of self-similar systems |
| VerfasserIn |
A. V. Dyskin |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1027-5606
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| Digitales Dokument |
URL |
| Erschienen |
In: Hydrology and Earth System Sciences ; 11, no. 2 ; Nr. 11, no. 2 (2007-01-17), S.665-676 |
| Datensatznummer |
250009206
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| Publikation (Nr.) |
 copernicus.org/hess-11-665-2007.pdf |
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| Zusammenfassung |
| In many cases, the critical state of systems that reached the threshold is
characterised by self-similar pattern formation. We produce an example of
pattern formation of this kind – formation of self-similar distribution of
interacting fractures. Their formation starts with the crack growth due to
the action of stress fluctuations. It is shown that even when the
fluctuations have zero average the cracks generated by them could grow far
beyond the scale of stress fluctuations. Further development of the fracture
system is controlled by crack interaction leading to the emergence of
self-similar crack distributions. As a result, the medium with fractures
becomes discontinuous at any scale. We develop a continuum fractal mechanics
to model its physical behaviour. We introduce a continuous sequence of
continua of increasing scales covering this range of scales. The continuum
of each scale is specified by the representative averaging volume elements
of the corresponding size. These elements determine the resolution of the
continuum. Each continuum hides the cracks of scales smaller than the volume
element size while larger fractures are modelled explicitly. Using the
developed formalism we investigate the stability of self-similar crack
distributions with respect to crack growth and show that while the
self-similar distribution of isotropically oriented cracks is stable, the
distribution of parallel cracks is not. For the isotropically oriented
cracks scaling of permeability is determined. For permeable materials
(rocks) with self-similar crack distributions permeability scales as cube of
crack radius. This property could be used for detecting this specific
mechanism of formation of self-similar crack distributions. |
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