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To study the propagation characteristics of Rayleigh waves and the isolation mechanism of a single-row of piles by isolation effects, in this paper we draw a two-dimensional contour map of ζ (normalized acceleration amplitude relative to a measure close at the vibration source) using a vibration test carried out on a sand foundation. In this experiment, we study, in addition to the free field and the single pile cases, settings with two and three piles. The result shows that the vibration caused by the point source in the free field excites Rayleigh waves in a radial direction along the surface of the foundation. Meanwhile, the vibrations of the points along the propagation path on the surface of the foundation are gradually weakened. There is a steady transition when the ζ drops to 0.6 and a placid decline when ζ decreases to less than 0.25. The vibration-shielded region, the strengthened region, and the strengthened strips will appear on the surface of the foundation. The vibration-shielded region is located behind the piles, and the region presents a trumpet-shaped area that takes the pile as the vertex. Increasing the quantity of piles contributes to increasing the vibration isolation effect, not only that involving the degree of isolation but also for the area of the shielded area. The vibration-strengthened regions include the diffraction regions at the pile corners on both sides of the single-row of piles and the scattering region at the gaps of the piles. In addition, the composite regions are located among the vibration source and the scattering and diffraction-strengthened regions. Increasing the number of piles has little influence on the scattering and diffraction-strengthened regions but can significantly enhance the vibrations of the composite regions. In general, the vibration-strengthened strips are connected with the scattering-strengthened regions. However, in the test of a single pile, the pile is connected to the diffraction-strengthened regions near its two anterior angles.

Stress concentration occurs in the foundations of railway tracks where discontinuous components are located. The exacerbated stress under the expansion joints in slab tracks may trigger foundation failures such as mud pumping. Although the higher stress due to the discontinuities of track structures has been discussed in past studies, few focused on the stress response of roadbeds in slab tracks and quantitatively characterized the stress pattern. In this paper, we performed a dynamic finite element analysis of a track-formation system, incorporating expansion joints as primary longitudinal discontinuities. The configurations of CRTS III slab tracks and the contact conditions between concrete layers were considered. Numerical results show that longitudinal influencing length of induced stress on roadbed under wheel load relates to the contact conditions between concrete layers, increasing nonlinearly at a larger coefficient of friction. Given a measured coefficient of friction of 0.7, the calculated longitudinal influencing length (9.0 m) matches with field data. The longitudinal influencing length is not affected with the increasing velocity. As stress concentration arises with expansion joints, the worst-case scenario emerges when double-axle loads are exerted immediately above the expansion joints between concrete bases. A stress concentration factor Cv on the roadbed is proposed; it increases with the increasing velocity, changing from 1.33 to 1.52 at velocities between 5 and 400 km/h. The stress distribution on roadbeds transforms from a trapezoid pattern at continuous sections to a triangle pattern at points with longitudinal discontinuities. An explicit expression is finally proposed for the stress pattern on roadbed under expansion joints. Although structural discontinuities induce stress raiser, the extent of concentration is mitigated with increasing depth at different velocity levels.

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