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Fractal behaviour of some geological media

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Abstract

 This paper describes the use of fractal geometry in determining the characteristics of some geological media, such as clayey and pumice soils. Attention is drawn to the determination of the specific surface of some clays of southern Italy and of pumice of the Vesuvius eruption of 79 a.d. The analysis proposed gives the Minkowski dimension of soils expressed by the power law, or the equation Mδ(F)≈Cδ–s; this is a dimensionless number. The values of Minkowski dimension obtained have been compared with the values obtained by physical methods (mercury porosimetry and the bottle helium test). The analyses conducted prove that, for the range of magnification adopted, the media examined behave as irregular or fractal sets.

Résumé

L'utilisation de la géométrie fractale a permis de déterminer certaines caractéristiques de matériaux tels que des sols argileux et des dépôts de ponces. En particulier, les surfaces spécifiques de quelques argiles de l'Italie du Sud et de ponces apportées par l'éruption du Vésuve de 79 a.d. ont été déterminées. L'analyse réalisée donne la dimension de Minkowski de ces sols, nombre sans dimension. Les valeurs de dimension de Minkowski ont été comparées avec des valeurs dérivées de méthodes physiques (porosimétrie au mercure et BHT). Les analyses réalisées prouvent que, dans la gamme, des grossissements utilisés, les matériaux examinés se comportent comme des ensembles irréguliers ou fractals.

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Received: 10 July 1999 · Accepted: 8 October 1999

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Esposito, L., Guadagno, F. Fractal behaviour of some geological media. Bull Eng Geol Env 58, 289–295 (2000). https://doi.org/10.1007/s100640000038

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  • DOI: https://doi.org/10.1007/s100640000038

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