Effect of soft-end amplification on elastically supported bridges with bearings of unequal stiffnesses scanned by moving test vehicle

Abstract

Bearings are commonly inserted on bridge piers to mitigate the seismic forces transmitted upward. But they often become unequal in stiffness due to ageing, overloading, etc. This study made the first attempt to exploit the soft-end amplification (SEA) effect on scanning of frequencies of the bridges with unequal end bearings, using the novel technique of forward-backward scanning to detect the soft end of the bridge. The SEA effect was clearly interpreted by the closed-form solutions derived for the dynamic responses of the test vehicle modelled by a sprung mass moving over the elastically supported (ES) beam. Both the temporal and spectral features of the vehicle response in forward-backward scanning were analytically examined, and validated against various inequality ratios by the finite element method (FEM). It was shown that the bridge frequencies shift to lower values for bearings with lower stiffness, and that both vehicle's accelerations and bridge's frequency amplitudes are much enlarged for the vehicle moving from the softer end of the bridge. Both the down-shifting in bridge frequencies and SEA of the ES bridge are helpful to assess the overall health condition of the bridge. Besides, the contact point outperforms the vehicle in that its response allows more bridge frequencies to be identified, due to elimination of vehicle's frequency. Finally, the efficacy of the proposed technique is verified in a parametric study for factors such as surface roughness, vehicle speed and frequency, followed by a more realistic example that simultaneously considers the bridge and bearing damping, and environmental noise. The proposed technique is confirmed to be able to detect the first three frequencies and softer end of ES bridges in real conditions for vehicle speeds below 10 m/s, along with an accompanying vehicle.