Determination of the Water Outflow Zone on the Ground Surface After a Pipe Failure Using Fractal Geometry

Uncontrolled water outflows from water supply pipes can pose a serious threat to human safety and infrastructure due to the washing out of soil particles and the formation of subsurface voids, leading to soil subsidence (suffosion). One way to mitigate these hazards is by determining water outflow zones (WOZ) around underground pipes, within which water may emerge on the soil surface. This paper presents the final stage of a broader study on the use of fractal geometry for determining WOZ. Suffosion hole locations form point structures that exhibit features of probabilistic fractals, and their parameters depend on the number of points in the structure. The objectives of the study were: (1) to determine the minimum number of points required for a structure to be considered representative; (2) to establish a relationship for calculating the WOZ radius; and (3) to empirically verify the theoretical WOZ radius values. Representative structures were identified and used to calculate the R fr parameter, which, after scaling to real conditions, enabled determination of the WOZ radius, ranging from 3.5 to 5.5 m. Empirical verification confirmed the method’s validity, as theoretical zones covered up to 100% of actual outflow points (96% overall). The developed method can be applied into decision-support systems for sustainable infrastructure planning, and more efficient use of water resources.