Keywords: microtremor, railway traffic effects on structures, prediction dynamic, half space and structure response models, in situ experimental tests, ground vibration and structure response spectra, spectral analysis.

The dynamic train-track interaction is a coupled problem, contrary to vehicle-road interaction problems, that requires the simultaneous solution of the equations of motion of the train and the track. The train-track interaction forces arising from the track unevenness are computed using a flexibility formulation. A two-dimensional linear vehicle model with a limited number of degrees-of-freedom is coupled to a linear elastic longitudinal invariant track model, which allows the solution of the equations of motion in the frequency-wavenumber domain. The transfer functions between the track and the soil and the computed interaction forces are used to compute the response at any arbitrary point in the free field [1].

An analytical expression for the spectral density of ground vibration as functions of distance from both roadways and railways respectively is formulated in terms of rail and wheel roughness, vehicle characteristics, track-soil interaction forces and the frequency response function for the ground. The use of the random process theory to predict the level of ground vibration in the vicinity of railways using the calculation of the spectrum of vibration at the half-space point is possible using the two principal ways: (i) using a computer implementation of the theoretical expression for the rail roughness spectrum, the vehicle mass distribution spectrum and a model of vehicle dynamics and track-soil interaction and the frequency response function (FRF) of the ground by a method involving an integral transform, (ii) using the average response force spectrum derived from experimental data for authorized railway category with corresponding track profile and the FRF of the ground and calculate response spectrum vibration at a point by the same way as mentioned in (i).

The random process theory in the dynamic ground properties investigation can be utilized as well. Using the input signal (arising from traffic) measurement into the ground and the output signal measurement passing through the ground, the frequency response function, and the elastic and attenuation characteristics of the ground can be obtained. Finally, the building structure dynamic response at the distance point calculation is carried out using half-space output data (PSD, time history, etc.) for the input data into the building structure foundations.

1

T. Fujikake, "A prediction method for the propagation of ground vibration from railway trains", Journal of sound and Vibration, 111(2), 357-360, 1986. doi:10.1016/S0022-460X(86)80168-7

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