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.

由地面和地下行驶的列车引起的地面振动已被认为是一个重要的环境问题。有充分的理由开发预测模型来计算来自移动源的地面振动。与基础设施建设相关的地下地下结构总是存在于城市中，如空洞、隧道、管道和地铁。当这些包裹体存在于地下时，需要求解包含包裹体的土层中的波场来模拟地表或包裹体内部移动源的振动。地面中最简单的包裹体之一可能是一个空的无限长的圆形空腔。在本文中，通过使用波函数方法提出了具有圆形腔的解析层元的概念，旨在为计算来自地表和地下运动源的振动提供强大的工具。给出了具有圆形空腔的有限厚度土层中波场的完整解决方案，并且层单元可以通过通常用于多层地面的公式轻松地与其他土层（有或没有夹杂物）组装. 移动源可以位于地表或空腔内。提供了两个应用示例来说明所提出的层单元的能力：一个是对空腔/隧道对地面移动载荷引起的地面振动影响的理论研究。