Micro-pressure wave radiation from tunnel portals in deep cuttings

The reflection and radiation of steep-fronted wavefronts at a tunnel exit to a deep cutting is studied and contrasted with the more usual case of radiation from over-ground portals. A well-known difference between radiation in odd and even dimensions is shown to have a significant influence on reflected wavefronts, notably causing increased distortion that complicates analyses, but that can have practical advantages when rapid changes are undesirable. Likewise, micro-pressure waves radiating from the portal into a cutting are shown to exhibit strong dispersion that does not occur in the corresponding radiation into an open terrain. In the latter case, formulae that represent the behaviour of monopoles and dipoles are commonly used to estimate conditions beyond tunnel portals, but no such simple formula exists (or is even possible) for cylindrical radiation that is characteristic of MPWs in cuttings. An important outcome of the paper is the development of an approximate relationship that predicts the maximum amplitudes of these MPWs with an accuracy that should be acceptable in engineering design, at least for initial purposes. The formula shows that peak pressure amplitudes decay much more slowly than those from an overground portal, namely varying approximately as r ^−0.5 compared with r ⁻¹, where r denotes the distance from the portal.