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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
The figure shows the
behavior of a building
with a basement during
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.
amplitude Ub at the
top of the building is
normalized by Ug at
the surface of the
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.
Graduate School of Engineering
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- Summer '14