Influence of Ground Conditions on Intrusion Flows through Apertures in Distribution Pipes

Abstract

This paper presents a new, tractable analytical expression to describe the intrusion of fluids into buried pipes under steady-state conditions. The expression is validated with results from novel experiments. The derivation is based on the combination of the relevant existing models of flows through porous media and the losses through an orifice, with the resulting expression relating the intrusion flow rate to an applied driving pressure. The expression is shown to yield results directly equivalent to those generated from a full three-dimensional (3D) computational fluid dynamics (CFD) model of the intrusion process. Results from the experiments, quantifying volumetric intrusion from a realistic 3D porous media, presented here, compare favorably with calculated values, validating the expression. Although the experimental and analytical results show a high level of agreement, it was found that the analytical expression tends to slightly underestimate the intrusion rate seen experimentally. The absolute difference in the values is low and is thought to be attributed to preferential flow path at the porous media and pipe interface that the analytical expression and CFD model do not include. It is shown mathematically and verified experimentally that the viscous and inertial resistance to flow in the porous media reduces the intrusion (or leakage) flow over that predicted by the standard orifice equation and places additional dependencies of the flow on the size of the intrusion orifice. The values obtained from the expression should be considered as a lower bound to intrusion (and leakage) rates, with upper bounds being provided by the standard orifice equation. Although developed to aid in the quantification of intrusion risk, such as that associated with water distribution systems, the expression is also validated for leakage for the limited case that the external porous media is considered to be fully compacted, consolidated, and immobile.