Site Response Characteristics Of Seismic Waves At Arbitrary Angles

More and more studies have shown that seismic waves are usually transmitted to the near field in oblique incidence,not in the vertical direction.When seismic waves are transmitted from the bedrock to the ground at different angles of incidence,they have different effects on the construction site and the ground buildings.At present,the research on seismic SV waves is mostly limited to the incident angle less than the critical angle.In order to extend the incident angle of seismic SV waves to greater than the critical angle range,the site response analysis of seismic waves at any angle is realized.Based on the principle of seismology,the reflection and transmission coefficients of the seismic wave obliquely incident to the elastic interface and the free surface are derived,and the reflection coefficient of the SV wave incident on the free surface at any angle is derived.Then apply the superposition principle to obtain the elastic half space calculation method,and compile the corresponding MATLAB calculation program.Based on the model examples,the site response characteristics of seismic waves at arbitrary angles are studied,and the influence of incident angle on seismic response of the site is analyzed.Research indicates:(1)In the case of P wave incidence,as the incident angle increases,the vertical amplitude gradually decreases,and the horizontal amplitude first increases and then decreases.When the angle of incidence is equal to 40°,the horizontal amplitude is approximately equal to the vertical amplitude and reaches a maximum at 65°.(2)The seismic response under the action of SV waves is closely related to the relationship between the angle of incidence and the critical angle.When the incident angle is smaller than the critical angle,as the incident angle increases,the horizontal amplitude gradually decreases,and the vertical amplitude gradually increases.When the angle of incidence is equal to the critical angle,the horizontal amplitude reaches a maximum and the vertical amplitude reaches a minimum.When the incident angle is larger than the critical angle,the horizontal amplitude rapidly decreases sharply,and decreases to zero at 45°,and then changes parabolically,and the vertex is located near 70°,and its value is about 0.5.(3)When the incident angle of the SV wave is larger than the critical angle,the reflection coefficient is a complex number,and the horizontal vibration and the vertical vibration caused thereby are also complex numbers,and the phase difference between the two is exactly 0.57i.It shows that the horizontal vibration and the vertical vibration are orthogonal under the action of simple harmonics.(4)The seismic field response is not only related to the incident angle,but also related to the frequency of the seismic wave.The overall performance is that the vibration is weakened with the increase of the frequency,but different types of incident waves have different effects on the horizontal displacement and the vertical displacement.When the P wave is incident at a small angle or the SV wave is incident at a large angle,the frequency change has a great influence on the vertical displacement.When the P wave is incident at a large angle or the SV wave is incident at a small angle,the frequency change has a great influence on the horizontal displacement.When the incident angle of the SV wave is equal to the critical angle,the frequency change has a greater influence on the horizontal displacement and less on the vertical displacement.(5)When the SV wave is incident,the seismic response of the site at different depths is related to the wavelength of the seismic wave.The overall performance is that the vibration first weakens and then increases with the increase of the depth.If the depth is less than a quarter of a wavelength,when the incident angle of the SV wave is equal to the critical angle or away from the critical angle,the depth change has a greater influence on the horizontal displacement and less on the vertical displacement.If the depth of the formation is greater than a quarter of a wavelength less than one-half of the wavelength,when the incident angle of the SV wave is less than 50°,the depth variation has a greater influence on the horizontal position and the vertical displacement;when the incident angle is greater than 50°,the depth variation has less effect on the horizontal displacement and the vertical displacement.