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| Dynamic responses of layered foundation-track coupled system due to moving harmonic loads |
| Ba zhenning1,2, Jin wei1, Liang Jianwen1,2 |
1.Department of Civil Engineering, Tianjin University, Tianjin 300072,China;
2.Tianjin Municipal Key Laboratory of Coast Civil Structure Safety, Tianjin University, Tianjin 300072,China |
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Abstract The dynamic responses of layered foundation-track coupled system due to moving harmonic loads are evaluated by using the Green’s Functions method. The results are firstly obtained in the frequency-wave number domain and then results in the time-space domain are obtained by using the inverse Fourier transformation, and to do this, the Green’s Functions of moving distributed vertical loads acting on the surface of a layered half-space are deduced based on the three-dimensional exact dynamic stiffness matrix. The validity of the method are confirmed by comparing results with published ones, and the effects of the frequencies and velocities of the moving load, and in particular, some effects of layering on the dynamic responses are studied by taking layered ground-track coupled system and uniform ground-track coupled system as examples. The results show that the maximum ground surface displacements for the moving harmonic loads may not occur at the transonic speed compared to the moving static loads cases. The dynamic responses of layered foundation-track coupled system are significantly different from those of the uniform case. The amplitudes of the surface ground displacement are much larger when the frequency of the load is close to the natural frequency of the layered ground. The displacement amplitudes of the ground vibrate more serious with much longer duration when the load past by with a supersonic speed as the shear wave velocity ratio between the bedrock and the soil layer become larger. And the frequency spectrums of the displacement amplitudes migrate to the low frequency regions as the depth of the layer becomes thicker.
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Received: 27 April 2015
Published: 15 June 2016
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