The shadow effect on the ground surface due to vibration transmission from a railway tunnel

Abstract

Abstract The prediction of the ground vibration transmitted from tunnels to neighbouring buildings is a vital step in the assessment of the ground-borne noise in buildings. In empirical models it is commonly assumed that the level of ground vibration reduces monotonically with the distance away from the tunnel alignment. In reality, a ‘shadow’ zone is observed above the tunnel. This is first illustrated using measurements made above an operational railway line. To understand and characterise this effect, a study has then been carried out using various simulation models. Using an analytical model for the response to a point force acting in a homogeneous full-space, it is shown that the response is principally in the form of shear waves which radiate to the side rather than compressional waves which radiate in the direction of the load. This leads to a ‘shadow’ zone forming above a certain frequency, even in the absence of a tunnel and the absence of a free ground surface. The ground surface is next introduced by considering the response of a half-space to a point force, using a semi-analytical model. This is shown to exhibit similar behaviour although with differences caused by the free ground surface. Finally, a numerical 2.5-dimensional finite element/boundary element model is used to determine the response of a half-space ground to a force acting at the bottom of a concrete tunnel. The extent of the shadow is defined as the width to the point of maximum response. This depends largely on the depth of the excitation force and the shear wave speed of the soil. Although similar features are found with or without the tunnel, the presence of the tunnel structure causes a reduction in the shadow width, and the level difference within the shadow region is slightly increased. A tunnel with a smaller diameter leads to an increase in the frequency at which a given shadow effect occurs, but the tunnel lining thickness has negligible influence. The existence of shadow effect should be taken into account when making predictions of ground vibration using empirical models.