Use of PiP to investigate the effect of a free surface on ground vibration due to underground railways

The Pipe-in-Pipe model (PiP) is a quick and accurate tool for calculating vibration from underground railways and for assessing the performance of vibration countermeasures. The original model formulation simulates a tunnel buried in a fullspace but has recently been extended to account for a free-surface (i.e. halfspace). Results from the two versions are compared to quantify the effect of the free-surface on soil power spectral density (PSD) values. The study suggests that it is reasonable to assume the PSD surface results predicted from the free-surface model will be approximately 6dB more than those predicted by the fullspace model when the tunnel is at a depth of two tunnel-diameters or more. For tunnel depths less than two tunnel-diameters it seems beneficial to account for the free surface in the simulation as there is significant variation in the results invalidating the 6dB assumption.