Site Response To Obliquely Incident 3D Seismic Waves

Usually,the research on the seismic response of the site takes one of the three-component seismic waves for research and analysis.Study the dynamic response of the site under the action of a single body wave through numerical simulation or theoretical derivation.In order to study the seismic response of the site under the joint action of three-dimensional seismic waves,In this paper,based on the basic principles of seismology,the reflection and transmission coefficients of each component wave obliquely incident on the elastic interface and free surface are derived.The seismic superposition principle is used to obtain the theoretical solution of the seismic response of a uniform site under the action of any component wave.Then,the MATLAB calculation program is compiled,and the model response is studied based on the isochronous amplitude superposition principle to study the site response problem under the simultaneous action of three-dimensional seismic waves,and the effects of different factors on the seismic response are studied.Research indicates:(1)In the case of SH wave incidence,as the angle of incidence increases,the surface response amplitude gradually decreases.When the incident angle is less than 60°,the surface response amplitude is twice that of the incident wave.The thickness of the formation has no effect on the response amplitude.As the thickness of the formation increases,the maximum response amplitude of the surface moves backward in time.(2)In the case of P-wave incidence,as the angle of incidence increases,the horizontal vibration gradually increases,the vertical direction gradually decreases,and the rotational vibration increases.As the thickness of the formation increases,the maximum response amplitude of the vertical surface increases,and the maximum response amplitude of the horizontal surface decreases.(3)SV waves are obliquely incident.When the incident angle exceeds the critical angle,the reverse transmission coefficient is a complex number.As the angle of incidence increases,both horizontal and vertical vibrations tend to increase first and then decrease,and rotational vibrations increase.However,when the incident angle is close to the critical angle of 36°,the horizontal vibration suddenly increases,and the response amplitude is 3 times the amplitude of the incident wave.(4)When three-dimensional seismic waves act simultaneously,as the incident angle of the SV component wave increases and the incident angle of the P component wave decreases,the maximum response amplitude of the total horizontal and vertical seismic time history of the ground surface increases first and then decreases.The duration of the vibration does not change,and the overall rotational vibration gradually increases.When the incident angle of the SV component wave increases to the critical angle,the total response amplitude in the horizontal direction is four times the amplitude of the incident wave,showing that the vibration is stronger than the single body wave.As the thickness of the overlying soil layer increases,the maximum amplitude of the horizontal seismic response on the ground surface decreases first,then increases,and then decreases in a wave-like trend.The vertical vibration time course of the ground surface shows a trend of decreasing first and then increasing.The vertical direction does not change.