Abstract:Considering the compression of soil grain and pore fluid, and viscid coupling of pore fluid with soil skeleton, adopting the amended Biot model, the amplitudes of P1 wave, P2 wave and SV wave which are reflected from the planc PI wave are calculated when the semi-infinite space surface is impervious. The semi-infinite surface is taken as a large curved arc, the potential functions of incident waves, reflected waves from the semi-infinite surface, scattered waves from the circular cavity and the curved arc are all expanded to the infinite serials of Fourier-Bessel functions based on the expansion method of wave functions, and then the single scattering problem of a cavity in semi-infinite space is turned to a multiple scattering problem of cavity and curved arc based on the Graf＇s addition theorem. According to the boundary conditions that the semi-infinite space surface and cavity are all free, the theoretical solutions the complex coefficients of the potential functions are obtained. The influence of the normalized incident frequency and the cavity depth on the normalized horizontal, vertical displacements of the semi-infinite space surface and the dynamic stress concentration factor of the cavity are studied by theoretical simulation when the P1 waves are vertically incident.
