Response Spectra of Structures under Subway Induced Vibrations

Passing underground trains induce vibrations transmitted to the ground surface and the nearby structures. Ordinarily, these vibrations do not result in structural damage but can harm nonstructural elements and disturb the occupants. These effects are more pronounced when evaluating buildings like hospitals, laboratories, museums, etc., and their assessment is an important design need. To respond to this requirement, in this paper response spectra for passing trains moving with different velocities are calculated. Using these spectra, without resorting to the time consuming and costly analysis of a tunnel-soil system under moving loads, the maximum structural responses can be calculated rapidly. To make this end, the soil-tunnel interaction is modeled using a three dimensional (3D) finite difference scheme under the standard moving train loads. The dynamic analysis of such a system results in the ground surface vibration time histories at different distances from the tunnel axis. Then the maximum values of acceleration, velocity, and displacement responses are calculated for a single degree of freedom (SDOF) dynamical system. The above calculations are accomplished for different standard trains, train velocities, tunnel depths, distances from tunnel, and soil types, and are presented as response acceleration, velocity, and displacement spectra.