Scattering Of Elastic Waves By Semi-cylindrical Canyon In Saturated Half Space

As disaster investigation and seismic observation shown: the local complex terrain is closely related to the degree of earthquake disaster,generally shown as the amplification effect of ground motion,which is also one of the important factors causing serious damage to the surface structure.In order to meet the needs of earthquake prevention and disaster reduction in complex terrain,relevant scholars have carried out research on local topographic effects of ground motion,which is essentially the study of elastic wave scattering problem in local topography.Most of the existing research results are based on single-phase media,but the research on two-phase media has not formed a complete system relatively.Therefore,the study of elastic wave scattering in local topography of saturated two-phase media has theoretical significance and engineering value.Based on the Biot’s saturated porous media wave theory,by means of complex function method and integral transformation method of Hankel function,the scattering problem of P wave and SV wave in semi-cylindrical canyon in saturated half-space is studied.Firstly,the semi-cylindrical canyon model of saturated half-space is constructed,whereafter the potential function of wave field and its general solution form in the medium are obtained.Secondly,the unknown coefficients in the potential function are obtained by substituting the corresponding stress boundary conditions.The wave potential function in the form of complex coordinates is transformed by the integral transformation method of Hankel function to meet the half-space horizontal boundary conditions in the cartesian coordinate system.Finally,the surface displacement amplitude at the semi-cylindrical canyon and its surrounding horizontal boundary is obtained by the total wave field potential function,moreover,the variation rule of surface displacement amplitude under the influence of different parameters,such as incident angle and dimensionless frequency,is analyzed.Combined with specific examples,the results show that: due to the existence of local topography,the amplitude of surface displacement at the semi-cylindrical canyon is more complex than that at the horizontal boundary on both sides.With the increase of incident angle,the amplitude of surface displacement decreases.When the incident wave is propagating at an oblique angle,the change of surface displacement amplitude is more complicated and the oscillation is more intense,however,energy transfer occurs in some cases.With the increase of the dimensionless frequency,the surface displacement amplitude increases and the oscillation degree becomes more severe.