Accurate predictions of ground-borne vibration levels in the vicinity of an underground railway are greatly sought after in modern urban centers. Yet the complexity involved in simulating the underground environment means that it is necessary to make simplifying assumptions about this system. One such commonly made assumption is to ignore the effects of nearby embedded structures such as piled foundations and neighbouring tunnels.Through the formulation of computationally efficient mathematical models, this dissertation examines the dynamic behaviour of these two particular types of structures. The effect of the dynamic behaviour of these structures on the ground-borne vibration generated by an underground railway is considered. The modelling of piled foundations begins with consideration of a single pile embedded in a linear, viscoelastic halfspace. Two approaches are pursued: the modification of an existing plane-strain pile model; and the development of a fully three-dimensional model formulated in the wavenumber domain. Methods for adapting models of infinite structures to simulate finite systems using mirror-imaging techniques are described. The interaction between two neighbouring piles is considered using the method of joining subsystems, and these results are extended to formulate models for pile groups. The mathematical model is validated against existing numerical solutions and is found to be both accurate and efficient. A building model and a model for the pile cap are developed, and are attached to the piled foundation. A case study is used to illustrate a procedure for assessing the vibration performance of pile groups subject to vibration generated by an underground railway.The two-tunnel model uses the superposition of displacement fields to produce a fully coupled model of two infinitely long tunnels embedded in a homogeneous, viscoelastic fullspace. The significance of the interactions occurring between the two tunnels is quantified by calculating the insertion gains that result from the existence of a second tunnel. The results show that a high degree of inaccuracy exists in any underground-railway vibration prediction model that includes only one of the two tunnels present.
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