Analytical layer element with a circular cavity and its application in predicting ground vibrations from surface and underground moving sources

Abstract The ground-borne vibrations caused by surface and underground moving trains have been recognized as an important environmental issue. There are good reasons to develop prediction models to compute the ground-borne vibration from moving sources. Underground sub-surface structures linked with infrastructure construction are always present in cities like cavities, tunnels, pipes and subways. When these inclusions exist in the ground, the solution to the wave field in a soil layer with inclusions is required for modelling the vibrations from moving sources on the ground surface or inside the inclusion. One of the simplest inclusions in the ground can be an empty infinitely-long circular cavity. In this paper the concept of analytical layer element with a circular cavity is proposed by using the wave function method aiming at providing a powerful tool to compute the vibrations from surface and underground moving sources. A complete solution to the wave field in a soil layer of finite thickness with a circular cavity is given, and the layer element can be easily assembled with other soil layers (with or without inclusions) by the formulations commonly used for a multi-layered ground. Moving sources can be located on the ground surface or inside the cavity. Two application examples are provided to show the capability of the proposed layer element: one is a theoretical investigation on the influence of a cavity/tunnel on ground vibrations due to a surface moving load. The other is an example to calculate ground vibrations from underground moving trains.