## 1 Introduction  
High-speed railway lines run often through tunnels, on bridges, in cuts, and on embankments. The train-induced ground vibrations need to be predicted and--if necessary --mitigated. The aim of this contribution is to analyse the reduction effects of special track or line types and of mitigation measures in the propagation path by a unified approach. Tunnel and bridge lines have been calculated by large finite-element models. These analyses are usually for one line type only. Continuous bridge tracks (viaduct lines), which are quite a standard in China, Japan and Taiwan, have been treated in [1; 2; 3; 4; 5; 6; 7]. The numerical results are sometimes compared with measured ground vibrations, but not with calculations of surface lines. Tunnel lines have also been analysed by large finite-element models, for example in [8], and many tunnel studies exist for high-speed and metro lines [9; 10; 11; 12; 13]. Simplified methods, for example in wavenumber domain [14] or with substructuring [15; 16] have been developed where the tunnel is assumed as imbedded in an infinite soil medium (a full space). The original (full-space) boundary-element method can simplify the geometry of the model [17; 18]. According to the geometry of the tunnel, also 2-dimensional [19; 20; 21] and 2.5 dimensional [22; 23] finite-element and boundary-element methods have been applied. Moreover, simplified phenomenological soil-structure methods have been used in [24; 25]. A few publications deal with more than one type of railway line. In [26], tunnel and bridges have been analysed as substructures where little influence on the vehicle dynamics and considerable influence on the track dynamics has been found for models on a Winkler foundation. In [27], the ground vibrations from a bridge and an embankment line have been compared indicating that the bridge generates more low-frequency and a more specific high-frequency vibration whereas the embankment results in wider low and high frequency bands. In [28], railway lines on embankments, in cuts and on the plane surface have been compared with some similar results as will be demonstrated in the present contribution. Mitigation measures for railway induced vibrations are well known at the track (elastic elements, mass-spring systems) and at the building (base isolation). Mitigation in the propagation path (trenches, obstacles, groups of piles) have been proposed, for example in [29; 30; 31; 32; 33; 34; 35; 36; 37], and analysed in two or three dimensions. In the present contribution, the reduction effects of various measures in the propagation path are analysed in the same way as for the different types of railway lines. For the comparison of different railway situations, the 2-dimensional calculation is an advantageous approach as it reduces the number of parameters as well as the modelling and the calculation time. The article is structured as follows. The two methods that are used here to represent the infinitely large soil, the Thin Layer Method (TLM) and the Boundary-Element Method (BEM) are shortly outlined in Sections 2.1 and 2.2 by referring to previous publications. Both methods establish a boundary matrix which is coupled with the Finite-Element Method (FEM) for an inner soil region, a track, tunnel or building structure. The Boundary-Element Method uses the explicit full-space solution or--from integration in wavenumber domain--the half-space solution whereas the Thin Layer Method uses discrete wave modes from an eigenvalue problem. In Section 3, the results for the line load and the track load on the surface are given as the reference for the comparison of the special situations. Section 4 presents the reduction effects of different obstacles in the propagation path, open and infilled trenches, stiff walls, plates and blocks. The effects of different railway lines are discussed in the following two sections, in Section 5 for embankments and cuts with different slopes, and in Section 6 for tunnels and bridges.