Set of Suffosion Holes Occurring After a Water Supply Failure as a Structure with Fractal Features

• Autorzy: Iwanek Małgorzata

Identyfikatory

DOI

10.12911/22998993/147808

• Języki publikacji: EN

Abstrakty

EN

As a result of a buried water pipe unsealing, water often flows from the pipe to the soil surface, washing out the solid particles of soil and creating the so-called suffosion holes. It is a dangerous phenomenon, especially in urbanized areas, where it poses a threat to human safety and the stability of infrastructure. Uncontrolled outflows of water from water pipes belong to the main causes of suffosion in cities, occur in all water networks around the world and are difficult to predict. Therefore, it seems to be important to determine the size of the so-called the protection zone, which is the area around the potential leak where, in the event of a water pipe failure, it would be possible for water to flow in the soil. The analysis of the suffosion holes distribution around the place of leakage may be helpful in determining the size of the protection zone. Previous studies have shown that this distribution is random. Thus, the structure consisting of suffusion holes creates a certain geometric shape, which is difficult to describe using the classical concepts of Euclidean geometry. The study showed that this structure meets the conditions for probabilistic fractals, which means that elements of fractal geometry can be used to determine the size of the protection zone.

Słowa kluczowe

EN

water pipe failure; suffosion hole; fractal feature

• Wydawca: Polskie Towarzystwo Inżynierii Ekologicznej ; Lublin University of Technology
• Czasopismo: Journal of Ecological Engineering
• Rocznik: 2022
• Tom: Vol. 23, nr 6
• Strony: 164--171
• Opis fizyczny: Bibliogr. 29 poz., rys., tab.

Twórcy

autor

Iwanek Małgorzata

• Faculty of Environmental Engineering, Lublin University of Technology, ul. Nadbystrzycka 40B, 20-618 Lublin, Poland

• https://orcid.org/0000-0003-2761-0100

Bibliografia

• 1. Barnsley M.F. 2012. Fractals Everywhere. Dover Publications Inc., New York.
• 2. Barnsley M., Hutchinson J., Stenflo Ö. 2005. A fractal valued random iteration algorithm and fractal hierarchy. Fractals, 13(02), 111–146.
• 3. Empacher A.B., Sęp Z., Żakowska A., Żakowski W. 1975. Short Dictionary of Mathematics. Wiedza Powszechna, Warsaw. (in Polish)
• 4. Falconer K.J. 2014. Fractal Geometry: Mathematical Foundations and Applications. Wiley Academic.
• 5. Gdawiec K., Kotarski W. 2008. Fractal recognition of two-dimensional objects. In: Decision support systems. Institute of Computer Science of the University of Silesia, Katowice, 261–268. (in Polish)
• 6. Ghanbarian B., Hunt A.G., Ewing R.P., Sahimi M. 2013. Tortuosity in porous media: a critical review. Soil Science Society of America Journal, 77(5), 1461–1477.
• 7. Hassan M.K., Kurths J. 2002. Can randomness alone tune the fractal dimension? Physica A, 315, 342–352.
• 8. Hutchinson J.E. 1981. Fractals and self-similarity. Indiana Univ. Math. J., 30(5), 713–747.
• 9. Iwanek M. 2021. Application of Ripley’s K -function in research on protection of underground infrastructure against selected effects of suffosion. International Journal of Conservation Science, 12, 827–834.
• 10. Iwanek M., Kowalski D., Kowalska B., Suchorab P. 2020. Fractal geometry in designing and operating water networks. Journal of Ecological Engineering, 21(6), 229–236.
• 11. Iwanek M., Suchorab P., Sidorowicz Ł. 2019. Analysis of the width of protection zone near a water supply network. Architecture Civil Engineering – Environment, 12(1), 123–128.
• 12. Khabbazi A.E., Hinebaugh J., Bazylak A. 2015. Analytical tortuosity-porosity correlations for Sierpinski carpet fractal geometries. Chaos, Solitons & Fractals, 78, 124–133.
• 13. Khomenko V.P. 2009. Suffosion hazard: today’s and tomorrow’s problem for cities. In: Culshaw M.G., Reeves H.J., Jefferson I. Spink T.W. (eds) Engineering geology for tomorrow’s cities. Geological Society, Engineering Geology Special Publication, London.
• 14. Kowalski D., Kowalska B., Kwietniewski M. 2015. Monitoring of water distribution system effectiveness using fractal geometry. Bulletin of the Polish Academy of Sciences: Technical Sciences, 63(1), 155–161.
• 15. Kowalski D., Kowalska B., Suchorab P. 2014. A proposal for the application of fractal geometry in describing the geometrical structures of water supply networks. In: Brebbia C.A., Mambretti S. (eds) WIT Transactions on The Built Environment, 139. Urban Water II, Southampton, Boston, UK: WIT Press, 75–90.
• 16. Kowalski, D. 2010. Is the water network a fractal? Gaz, Woda i Technika Sanitarna, 3, 29–33. (in Polish)
• 17. Kudrewicz J. 2015. Fractals and Chaos. WNT, Warsaw.
• 18. Kwietniewski M., Rak J.R. 2010. Reliability of water supply and sewage infrastructure in Poland. Committee of Civil and Water Engineering of the Polish Academy of Sciences. (in Polish)
• 19. Mandelbrot B.B. 1982. The Fractal Geometry of Nature. WH Freeman and Co., New York.
• 20. Martyn T. 2011. Geometric algorithms in the fractal visualization of iterated mapping systems. Scientific Works of the Warsaw University of Technology. Electronics, 178. (in Polish)
• 21. Nowak P. 1992. Fractal theory – a new way of describing geometrically irregular objects. Physicochemical problems of mineral processing, 25, 13–24. (in Polish)
• 22. Oleschko K., Figueroa B.S., Miranda M.E., Vuelvas M.A., Solleiro E.R. 2000. Mass fractal dimensions and some selected physical properties of contrasting soils and sediments of Mexico. Soil and Tillage Research, 55(1–2), 43–61.
• 23. Palais R.S. 2007. A simple proof of the Banach contraction principle. J. Fixed Point Theory Appl., 2(2), 221–223.
• 24. Pfeifer P. 1984. Fractal dimension as working tool for surface-roughness problems Fractal dimensions as working tool for surface-roughness problems. Applications of Surface Science, 18(1–2), 146–164.
• 25. PN-B-04481:1988. Building soils. Laboratory tests (Polish Standard; in Polish).
• 26. Ratajczak W. 1998. Methodological aspects of fractal modeling of reality. Adam Mickiewicz University, Poznań. (in Polish)
• 27. Suchorab P., Kowalska B., Kowalski D. 2016. Numerical investigations of water outflow after the water pipe breakage. Annual Set The Environment Protection, 18(2), 416–427.
• 28. Tucker H.G. 2014. An introduction to probability and mathematical statistics. Academic Press.
• 29. Xu P. 2015. A discussion on fractal models for transport physics of porous media. Fractals, 23(3), 1530001.