Civil Engineering Reference
In-Depth Information
Figure 3.5.
Principle of site effects associated to the alluvial cover: the incident waves are
trapped therein and their vertical reflections (figure on the left) cause a resonance
phenomenon characterized by amplification peaks at certain frequencies (fundamental and
harmonic). The curves on the right illustrate the variability of the amplification according to
damping (full line:
]
= 2.5%,
T
= 0°; dotted line:
]
= 0.5%,
T
= 0°) and the angle of
incidence (dashes: z = 2.5%,
T
= 60°)
3.4.3.2.3. Spectral signature
Within the frequency field, trapping effects are expressed through the strong
frequency dependency of surface amplification (or “transfer function” H(f), and the
relationship of the surface Fourier spectrum As(f) with that of the depth incident
motion A(f). These transfer functions can be calculated with exact methods for a
limited number of configurations (1D stratified media, “canonical” valleys or basins
perfectly semicircular, elliptical or spherical geometrically speaking). Here we only
give results for a simple model with only one sediment layer (medium 1) resting on
a rocky substratum (medium 2) by means of a horizontal interface.
In this case, the complex transfer function for vertically incident S waves is
given by the relationship:
H(f) = 2 C/
ª
C cos 2ʌ f h/ȕ isin2ʌ f h/ȕ
º
¬
¼
1
1
where
h
is the depth of the layer,
f
the frequency
, C
the mechanical impedance
contrast
UE UE U
the density of medium i and
E
L
the S wave speed of
medium i.
/
,
22
11
i
This general formula gives access to resonance frequencies
f
n
and to the
corresponding amplifications (Figure 3.5 right):
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