Site Response Under Seismic SV Wave Total Reflection

In the study of the response of earthquake engineering site,more and more studies show that the seismic waves from the source are tilted upwards to the surface at a certain incidence angle,so it may produce stronger vibration than the vertical incident.In various incident seismic body waves,because the total reflection phenomenon may occur when the incident wave of SV wave reaches the ground,the seismic motion caused by SV wave will be more complex,and the seismic response will be different at different incident angles.At present,the research on seismic SV wave is more inclined to the situation without total reflection,while the research on site response is less under total reflection.In order to reveal the seismic response of oblique incident seismic SV wave when it is totally reflected at the ground,assuming that the seismic wave is a plane wave from an infinite distance,the stratum is a transversely infinite isotropic homogeneous elastomer,and the ground is an unconstrained free interface,a ground motion model is established under the conditions of no total reflection and total reflection;According to this theoretical model,the reflection coefficient of SV wave on the ground is derived by using the elastic wave theory,and the formula for calculating the time history of ground motion is derived by using the wave field superposition principle.Based on this,the corresponding matlab calculation program is compiled,and the correctness of the program is verified by comparing with the finite difference method;The program is used to calculate and analyze the time history of ground displacement,particle trajectory and the general variation of ground sliding wave with incident angle,and further study the influence of critical angle on site response.The results show that:(1)When the SV wave is incident at less than the critical angle,the site response caused by the SV wave can be directly obtained by using the wave field superposition method in the time domain;When the incident angle is greater than the critical angle,it needs to be calculated in the frequency domain by Fourier transform.(2)When the total reflection of seismic SV wave does not occur,the horizontal ground motion decreases slightly with the increase of incident Angle,and its value is about twice that of incident wave,while the vertical ground motion increases slowly with the increase of incident angle,and the maximum value is close to 1.In this case,the particle vibration trajectory is a straight line segment crossing the origin of coordinates,and the ground motion shows linear body wave vibration characteristics.(3)When the total reflection of the seismic SV wave is close to the critical angle,the horizontal ground motion increases rapidly and reaches the maximum value when the incident angle is equal to the critical angle,which is about 4 times of the incident wave,while the sudden drop of the vertical ground motion is close to zero,which is called the near critical field effect.The particle vibration trajectory is a closed curve and the ground motion shows nonlinear rotational surface wave vibration characteristics.(4)When the total reflection of the seismic SV wave occurs,the reflected P-wave sliding along the ground surface will be generated.Although the shape of the sliding wave will have a large distortion,its displacement value is relatively small,and its influence on the site response can be almost ignored.In this case,the site response can be simplified as the superposition of incident and reflected SV waves.