With the increasing embedding depth of the basement

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Unformatted text preview: s frequency is always lower in comparison with the natural frequency under the fixed-based condition. With the increasing embedding depth of the basement, the resonance frequency of the coupling system increase and the amplitude shows a decreasing tendency. This is caused by both the increased restraint effect and the radiation damping due to the embedding, as previously described. The vibration of the coupling system during an earthquake is considered. The figure shows the behavior of a building with a basement during an earthquake. For simplification, the seismic waves are assumed as sine waves with the frequency f Hz and with displacement only in horizontal direction. They are propagating upward at a right angle to the ground surface. (This type of seismic waves is called SH-waves) As shown, the amplitude of the seismic waves amplifies when the seismic waves approach the ground surface. The seismic input motion into the building through the basement takes place not only through the bottom surface, but also through the side walls. The seismic input motion from the bottom surface becomes smaller, since the amplitude of the ground vibration decreases with increasing depth of the basement. However, the input from the walls increases, since the contact area of the walls to the ground becomes wider. When the basement has a high rigidity in comparison to the ground, this input from the walls becomes the input averaging the deformation of the ground. Next, the input motion that has entered into the building vibrates the building, and the vibration energy escapes from the bottom surface of the basemen and the side walls as radiation waves. The figure shows the resonance curves at the top of the building. The response amplitude Ub at the top of the building is normalized by Ug at the surface of the free field. The free field indicates the ground, which is located so far that the response of the ground is not affected by the existence of the building. The resonance curves shown exhibit the embedding effect described above. Dynamic Soil Structure Interaction END Chapter 1 : Introduction Kenji MIURA, Dr. Eng. Professor Graduate School of Engineering Hiroshima University...
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