Study of crushing of grains of limestone under the effect of cyclic loading with the fractal dimension
Abstract
The grains can be of very diverse nature (size, shape, mineralogy, etc), indeed even if each grain is a fairly simple object, the set of grains is a very complex system in which the geometrical and physical properties of the grains, their forces and their orientations play a crucial role in their mechanical behavior. The measurement of their shape in soil mechanics has historically required the use of standards and diagrams to which the different grains can be compared. However, these methods are approaches and remain insufficient and incomplete for the actual measurement of their form and the understanding of their behavior remains a task far from being completed.
This work is in this context and proposes to analyze the shape and size of the grains with the fractal theory using the Box Counting method. It also makes it possible to study their influence on the crushing of the grains of the calcareous material under the effect of the cyclic loading-unloading during the oedometer test. The obtained results show that the variation of the fractal dimension, corresponding to the crushing effect of the grains, is strongly influenced by their shape, their size, their particle size distribution and the variation in the number of loading-unloading cycles.
References
AFNOR (1997). Essai oedométrique. Essai de compressibilité sur les matériaux fins quasi saturés avec chargement par paliers. XPP 94-090-1, p 24.
Bouzeboudja, A., & Melbouci, B. (2016a). Study of the evolution of the fractal dimension of a granular material’s grains during mechanical tests. Bulletin of Engineering Geology and the Environment, Volume 75, Issue 2, pp 821-839.
Bouzeboudja, A. , Melbouci, B., & Bouzeboudja, H. (2016b). Characterization of aggregates fragmentation using the calculation of fractal dimension” 16th International Conference on New Trends in Fatigue and Fracture (NT2F16), May 24-27, 2016, Dubrovnik, Croatia, ISBN 978-953-7738-39-6, pp. 211-213.
Chen, J., Lo, K.Y., Leung, H., & Litva, J. (1996). The Use of Fractals for Modeling EM Waves Scattering from Rough Sea Surface. IEEE Transactions On Geoscience and Remote Sensing, Vol. 34, NO. 4.
Einav, I. (2007a). Breakage mechanics. Part I: Theory. J. Mech. Phys. Solids 55(6), 1274-1297.
Falconer, K., Chichester, Wiley, J., & Sons. (1990). Fractal Geometry: Mathematical Foundations and Applications. 2e éd, poche (ISBN 978-0 470-84862-3) (LCCN 2004271361).
Huang, G.H., & Zhan, W.H. (2002). Fractal property of soil particle size distribution and its application. Acte Pedologica Sinica, 39, pp. 490-497.
Lade, P.V., Yamamuro, J.A., et al. (1996). Significance of particule crushing in granular materials. Journal de la technologie géotechnique, vol.122, N° 4, pp. 3109-3116.
Mandelbrot, B. (1983). The fractal geometry of nature. Edition W.II. Freeman, San Francisco, 461 pp.
Ovalle, C. (2013). contribution a l’étude de la rupture des grains dans les matériaux granulaires. MECHANICS OF MATERIALS. Ecole Centrale de Nantes (ECN), French.
Ramamurthy, T. (1969). Crushing Phenomena in Granular Soils. Journal of the Indian National Society of Soil Mechanics and Foundation Eng. Vol. 8.
Russel, D., Hanson, J., & OTT, E. (1980). Dimension of strange attractors. Physical review Letters 45, 1175-1178.
Sezer, A., Altun, S., & Erdogan, D. (2008). Correlation between CBR Strength and fractal Dimensions of Sands. 12eme Conference international de (IACMAG), 1-6 October, Goa Indian.
Wang, X., LI, M-H., Lui, S., & Lui, G. (2006). Fractal characteristics of soils under different land-usepatterns in the arid and semiarid regions of the Tibetan plateau. China, Geoderma, 134 (1-2), pp. 56-61.
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