On a formula finding fractal dimension

• Autorzy: Kamilov Kh. , Zaitov A. , Tulaganov A.

Identyfikatory

DOI

10.5604/01.3001.0014.3865

• Języki publikacji: EN

Abstrakty

EN

Purpose: The article is devoted to the determination of the fractal dimension of cellular concrete, in particular foam concrete, and the further clarification of the relationship between fractal dimension and porosity and average density of cellular concrete. Design/methodology/approach: In the theoretical description of disordered systems, the fundamentals of fractal theory are actively used, which allow obtaining statistical indicators of chaotic natural and artificially disordered systems, which include cellular concrete. The parameters of the pore structure are difficult to quantify by conventional methods because of the complexity and irregularity of the pore structure due to their random distribution. Findings: Formulas for calculating the fractal dimension and average density of highly porous material are calculated and proposed. The formula for calculating the average density takes into account the density of the material between the pore walls. Research limitations/implications: The calculation of the fractal dimension is one of the main factors affecting the practical application of the theory of fractals, a natural problem arises on a theoretical basis to justify these calculations. Practical implications: The formulas proposed in this work for calculating the fractal dimension and density of a highly porous structure improve research on methods for producing substances with a controlled fractal structure, which will help create materials with unusual mechanical properties, density, and porosity. Originality/value: The formula for calculating the fractal dimension obtained in the work improves the well-known Hausdorff-Bezikovich formula. On the other hand, it makes it possible to obtain a highly porous structure with a given density of the material under study.

Słowa kluczowe

EN

fractal dimension; cellular concrete; structure; mineral binder; porosity; density

PL

wymiar fraktalny; beton komórkowy; struktura; spoiwo mineralne; porowatość; gęstość

• Wydawca: International OCSCO World Press
• Czasopismo: Archives of Materials Science and Engineering
• Rocznik: 2020
• Tom: Vol. 104, nr 1
• Strony: 19--22
• Opis fizyczny: Bibliogr. 19 poz.

Twórcy

autor

Kamilov Kh.

• Tashkent Institute of Architecture and Civil Engineering (TACI), Kichik Xalqa yuli Street, 7, Tashkent 100084, Uzbekistan

autor

Zaitov A.

• Tashkent Institute of Architecture and Civil Engineering (TACI), Kichik Xalqa yuli Street, 7, Tashkent 100084, Uzbekistan

autor

Tulaganov A.

• Tashkent Institute of Architecture and Civil Engineering (TACI), Kichik Xalqa yuli Street, 7, Tashkent 100084, Uzbekistan

Bibliografia

• [1] Yu.M. Bajenov, Texnologiya betona: Ucheb. posobie dlya texnol. spes. stroit, vuzov. 2-ye izd., pererab. — M.: Vissh. shk., 1987 (in Russian).
• [2] A. M. Neville, Properties of concrete, 5th Edition, Pearson Education Limited, London, 2011.
• [3] Yu.M. Bajenov, Texnologiya betona. Uchebnik, M.: Izd-vo ASV, 2011 (in Russian).
• [4] I.A. Ribev, Stroitelnoe materialovedenie. Ucheb. posobie dlya stroit, spes. vuzov: M., VSh, 2003. (in Russian).
• [5] V.I. Solomatov, V.N. Virovoy, Fizicheskie osobennosti formirovaniya strukturi kompozitsionnix stroitelnix materialov, Izvestiya VUZov. Stroitelstvo i arxitektura 8 (1984) 48-52 (in Russian).
• [6] Ye.M. Chernishev, A.I. Makeev, Sintez i konstruiro- vanie struktur betonov novogo pokoleniya s pozitsiy upravleniya odnorodnostyu-neodnorodnostyu ix stroe- niya: Sb. tr. 8-ye akad. chteniy. Sovremennoe sostoya- nie i perspektiva razvitiya stroitelnogo materialove- deniya: Samara, SGASU, 2004, 561-567 (in Russian).
• [7] J. Konkol, G. Prokopski, The use of fractal geometry for the assessment of the diversification of macropores in concrete, Image Analysis & Stereology 30/2 (2011) 89-100. DOI: https://doi.org/10.5566/ias.v30.p89-100
• [8] B. Mandelbrot, Fraktalnaya geometriya prirodi: [per. s angl.], M.: In-t kompyuternix issled., 2002 (in Russian).
• [9] Ye. Feder, Fraktali: [per. s angl.], M.: Mir, 1991 (in Russian).
• [10] B.M. Smirnov, Fizika fraktalnix klasterov, M.: Nauka. Gl. red. fiz.-mat. lit., 1991, 10 l. (Sovrem, probl. fiziki) (in Russian).
• [11] V.K. Balxanov, Osnovi fraktalnoy geometrii i fractal- nogo ischisleniya, Yu.B. Bashkuev (red.), Ulan-Ude: Izd-vo Buryatskogo gosuniversiteta, 2013 (in Russian).
• [12] M. Prigarin, K. Hahn, G. Winkler, Comparative analysis of two numerical methods to measure Hausdorff dimension of the fractional Brownian motion, Numerical Analysis and Applications 1/2 (2008) 163-178. DOI: https://doi.org/10.1134/S1995423908020079
• [13] H. Wang, Y. Liu, Y. Song, Y. Zhao, J. Zhao, D. Wang, Fractal analysis and its impact factors on pore structure of artificial cores based on the images obtained using magnetic resonance imaging, Journal of Applied Geophysics 86 (2012) 70-81. DOI: https://doLorg/10J016jjappgeo2Q12J07.01.5
• [14] L. Zhao, W. Wang, Z. Li, Y.F. Chen, Microstructure and pore fractal dimensions of recycled thermal insulation concrete, Materials Testing 57/4 (2015) 349-359. DOI: https://doi.org/10.3139/120.110713
• [15] S. Ebrahimi, M.B. Tavakolii, F. Setoudeh, Iris recognition system based on fractal dimensions using improved box counting, Journal of Information Science and Engineering 35/2 (2019) 275-290. DOI: https://doi.org/10.6688/JISE.201903 35(2).0002
• [16] R.D. Peng, H.P. Xie, Y. Ju, Computation method of fractal dimension for 2D digital image, Journal of China University of Mining & Technology 33/1 (2004) 19-24.
• [17] I. Alfonso, A. Beltran, M. Abatal, I. Castro, A. Fuentes, L. Vazquez, A. Garc^a, Fractal dimension determi- nation of rock pores by multi-scale analysis of images obtained using OM, SEM and XCT, Fractals-Complex Geometry Patterns and Scaling in Nature and Society 26/5 (2018) 1850067. DOI: https://doi.org/10.1142/S0218348X18500676
• [18] B. Pramanik, T. Tadepalli, P.R. Mantena, Surface fractal analysis for estimating the fracture energy absorption of nanoparticle reinforced composites, Materials 5/5 (2012) 922-936. DOI: https://doi.org/10.3390/ma5050922
• [19] C. Lee, T.A. Kramer, Prediction of three-dimensional fractal dimensions using the two-dimensional properties of fractal aggregates, Advanced in Colloid and Interface Science 112/1-3 (2004) 49-57. DOI: https://doi.org/10.1016/j.cis.2004.07.001

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021)