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.

从隧道传输到相邻建筑物的地面振动的预测是评估建筑物中地面传播噪声的重要步骤。在经验模型中，通常假设地面振动的水平随着远离隧道路线的距离而单调降低。实际上，在隧道上方观察到“阴影”区域。首先使用在运营的铁路线上进行的测量来说明这一点。为了理解和表征这种影响，然后使用各种仿真模型进行了研究。使用解析模型对在均匀全空间中作用的点力的响应进行分析，结果表明，该响应主要为向侧面辐射的剪切波形式，而不是沿载荷方向辐射的压缩波形式。 。即使在没有隧道和自由地面的情况下，这也会导致在一定频率以上形成“阴影”区域。接下来，使用半解析模型通过考虑半空间对点力的响应来引入地面。尽管这是由自由地面引起的，但显示出类似的行为。最后，使用数值2.5维有限元/边界元模型确定半空间地面对作用于混凝土隧道底部的力的响应。阴影的程度定义为到最大响应点的宽度。这在很大程度上取决于激励力的深度和土壤的剪切波速度。尽管无论有无隧道都可以找到类似的功能，隧道结构的存在导致阴影宽度减小，并且阴影区域内的水平差略有增加。直径较小的隧道会导致出现给定阴影效应的频率增加，但是隧道衬砌厚度的影响可以忽略不计。使用经验模型预测地面振动时，应考虑阴影效应的存在。