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Unformatted text preview: lding. The damping caused by escape of the seismic waves,
which have been transmitted into the building, back
into the ground is called “ Radiation Damping”. 1.2 Radiation Waves
The seismic waves escaping back into the ground are called
radiation waves, and these waves cause radiation damping.
When the building foundation is forced to vibrate vertically,
a stress called “ Contact Earth Pressure” is caused at the
boundary between the bottom surface of the foundation and
The distribution of this
contact earth pressure
over the bottom surface of
the foundation is called
“ the Contact Earth
Three types of distribution
(Rigid, Uniform, and
Parabolic distribution as
shown) are observed. The types of the distribution are altered depending on :
(a) foundation rigidity
(b) soil classification
(c) soil nonlinearity. When a part of the vertical
contact earth pressure is
picked out and applied on
the ground surface, the
vertical displacements of
the ground surface can be
calculated. At a distance of 10 m from the
point where the impulsive force is
applied, the first peak denoted by
P is appeared, and two peaks
denoted by S and R are appeared
following the P.
With increasing distance from the
force application point, these
peaks appear at an increasingly
later time, and it can be seen that
these peaks are propagated at a
Connecting the occurrence times
of these peaks by straight lines
and estimating the propagation
velocity from the inclination of
these lines. It can be found that the propagation velocity for the peak P
is 2450m/sec, that for the S is 1000m/sec, and that for R is
920m/sec. The seismic waves consist of ;(a) P-waves , (b) S-waves
and (c) Rayleigh’s waves called “ Surface Waves”.
These peaks correspond to the P-waves, the S-waves, and
the Rayleigh’s waves. In the case of a homogeneous half space, the relation of
propagation velocity between these waves is decided only
by the Poisson’s ratio of the ground as shown in the Figure.
The Poisson’s ratio
of the ground is
normally in the
range of 0.4 to 0.5.
velocity of the
Rayleigh’s waves is
about 10 % lower
than that of the Swaves. The vibration of energy to the ground is transmitted by Pwaves, S-waves, and Rayleigh’s waves, and in the case of a
homogeneous half space, the contribution ratio of the
energy transmission for the these waves are 7%, 26%, and
67% respectively for P, S, and Rayleigh’s waves.
So, the calculation shows that more than one half of the
energy is transmitted by the Rayleigh’s waves.
The above explanations with regard to the radiation wave...
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- Summer '14