Fractal Geometry in Designing and Operating Water Networks

Fractals are self-similar sets that cannot be easily described by classical geometry. Fractal sets have been implemented in almost all areas of human activity since they were introduced to science by Mandelbrot in 1982. For the last 10 years, the interest in fractal geometry has increased by the issues connected with water distribution networks (WDNs). The aim of this paper was to review the application of fractal geometry in designing and operating WDNs. Treating a WDN as a fractal pattern enables its description and classification, simplifies the assessment of a network reliability, helps to solve the problems of routing and dimensioning WDN, as well as enables to select the places to locate measurement points in a network to control water quality, pressure in pipes and water flow rate. Moreover, the application of tree-shaped fractal patterns to reflect WDNs helps to solve the problems of their optimization. Fractal geometry can be also applied to investigate the results of WDNs failures connected with leakage of water to the ground. Using fractal dimension of a pattern created by points reflecting places of water outflow on the soil surface after a prospective pipe breakage enables to determine the zone near a pipe, where the outflow of water on the soil surface is possible. It is an important approach for the security of humans and existing infrastructure. Usage of fractal geometry in description, optimisation and operation analysis of WDNs still continues, which confirms the efficiency of fractal geometry as a research tool. On the other hand, it can be supposed that fractal geometry possibilities have still not been fully used.