A Simplified Model of the Ground Surface Vibration Arising from a Leaking Pipe

Acoustic techniques remain the bedrock of pipeline leak detection, particularly for the water industry. The correlation technique, in which leak noise measurements are made at accessible locations on the pipe, either side of the leak, is used world-wide. Unfortunately, especially in the case of plastic pipes, access points are often not spaced closely enough for effective leak detection to take place. An alternative to sensing on the pipe is to measure directly on the ground surface, using discrete sensors such as geophones or accelerometers. However, to do this, the vibrational field on the ground, produced by the leak, needs to be fully understood. The present author, alongside colleagues, has developed an analytical model to show how axisymmetric elastic waves propagating within the pipe radiate to the ground surface. The model, only valid directly above the pipe, shows that, dependent on the soil properties, both a conical shear wave and a conical compressional wave may radiate into the soil, and thence propagate to the ground surface. Moreover, the axial dependence of the ground surface response mirrors the axial dependence of the waves propagating within the pipe. Here, a simplified analytical model of the conical pipe-radiated waves, which encapsulates the essential phase-related features of the more complex development described previously, is presented. This then allows a relatively simple extension to predict the off-axis ground surface as well as that directly above the pipe. Numerical simulations and experimental investigations are also carried out to demonstrate the potentialities of the proposed model to reveal the underlying physics through a simple way.