Solution of moving-load-induced soil vibrations based on the Betti–Rayleigh Dynamic Reciprocal Theorem

Based on the Betti–Rayleigh Dynamic Reciprocal Theorem, the reciprocal property of the Green's functions is demonstrated, on the basis of which the analytical solution of soil vibration subjected to moving loads is derived. By application of the Betti–Rayleigh Dynamic Reciprocal Theorem, the moving source problem is converted to the fixed source problem with receiver point moving in opposite direction, which greatly simplifies the complex analytical solution of soil/ground vibration induced by a moving load. A computer code for solving the ground responses subjected to the moving constant load and harmonic load is developed via MATLAB and is employed to perform a case study. The analyzed results show that the ground vibration induced by moving constant load is of typical low-frequency feature; the frequency range of ground vibration is controlled by the Rayleigh's wave velocity of the top layer soil; when the receiver nears the source path, the R-wave contributes to the ground vibration more than the P-wave and the S-wave; while when the receiver is far from the source path, the contribution of the P-wave is more obvious.