The effect of viscoelastic deformation in pipe cracks on leakage response to variations in pressure

Includes bibliographical references.Water is an important and increasingly scarce resource in the world today. Unfortunately, a lot of water is lost through leakage since most distribution systems are deteriorating. Therefore research in leakage management is necessary in order to improve the utilization of water resources. Leakage may be reduced by managing the water pressure in water distribution systems. One of the important factors affecting the pressure-leakage relationship is pipe material behaviour (Van Zyl & Clayton 2007; Greyvenstein & Van Zyl 2007). The pressure – leakage relationship has been described by several relationships such as the Torricelli equation, the Fixed and Variable Area Discharge (FAVAD) concept and the conventional equation. Pipe material behaviour affects leakage parameters in the pressure-leakage relationship such as the leak area and the leak exponent (Cassa et al. 2010). For this project, the pressure-leakage relationships in High Density Polyethylene (HDPE) and Polyvinylchloride (PVC) pipes are investigated. HDPE and PVC are polymeric materials and therefore exhibit a viscoelastic response to applied stress and applied strain. Viscoelastic responses include creep, relaxation, hysteresis and time dependency. When these pipes experience stresses due to water pressures, failure and fracture may occur as leaks. The viscoelastic properties of these materials therefore affect how the leaks respond to pressure change. The effect of viscoelastic deformations in leaks was investigated using Finite Element Analysis (FEA) software, Abaqus. Round holes and longitudinal cracks were represented as individual leaks in HDPE and PVC pipes in Abaqus. Pressure was applied to each pipe model for different time periods, and the deformed leak areas were obtained. Further analysis was carried out to determine the effects of pressure on leak parameters such as the gradient of the leak area-pressure relationship, leak exponent and the leakage number. The analysis shows that viscoelastic deformations have an effect on the pressure-leakage relationship. A linear relationship exists between the leak area and pressure for all time periods investigated and therefore gradients could be obtained. Deformed leak areas, gradients and leak exponents all increased with time and therefore confirmed that the time dependency of viscoelastic materials affected the pressure-leakage relationship. The leakage exponents for both materials were found to vary between 0.5 and 1.5 for both HDPE and PVC. HDPE also exhibited higher leak exponents, gradients and larger deformed leak areas than PVC for the same leaks. It was also found that leakage in viscoelastic materials may be analysed using the leakage number, developed for elastically deforming materials by Van Zyl & Cassa (2013)