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

Abstract

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.

Fractal Characteristics of Water Outflows on the Soil Surface after a Pipe Failure

“…• Approximate self-similarity: This feature has been improved for RSs by enlarging individual frames of the recordings of water outflow and the formation of a suffosion hole [7]. The stages of formation of the suffosion hole were the same regardless of the location of the hole, so it can be concluded that the self-similarity condition is also met by the TLS structure.…”

“…The water outflow locations obtained as a result of laboratory tests created real geometric structures (RSs), which were analyzed in this article. Since it was previously shown that RSs have fractal features [7], the analyses focused on their fractal dimensions (D b ). To simplify the research, an RS was reduced first to a plane form (Theoretical Planar Structure, TPS) and then to a linear form (Theoretical Linear Structure, TLS) using isometric transformations.…”

“…Laboratory investigations of water outflow on the soil surface after an induced water pipe failure were conducted on the research setup reflecting natural conditions at a scale of 1:10. The 3D scheme of the laboratory setup is presented in Figure 3 and consisted of a cuboid box (1) filled with medium sand (7), an intentionally damaged water pipe (2) supplied with water through an elastic hose (4) from a container (3) located at the assumed height. The pipe failure was presented as a bell-and-spigot joint (7) disconnection.…”

“…Due to the random distribution of points, as presented in the article [6], it was difficult to characterize RSs using classical concepts of Euclidean geometry. However, the analyses performed showed that RSs have the features of random fractals [7].…”

“…One way to determine the outflow zone is through a geometrical analysis of th tribution of points corresponding to the places of water outflow onto the soil surfa it was shown in previous research, these points create irregular sets that are diffic describe based on the concepts of classical Euclidean geometry [6]. Simultaneously, sets meet the conditions for random fractals [7], so it is possible to determine their f dimensions. The aim of the article is to check the possibility of using a fractal dime to estimate the size of the water outflow zone on the soil surface as a result of leakage a water pipe.…”