Civil Engineering Reference
In-Depth Information
Table 1.9
Shear wave velocities for foundation materials (in m/s).
Material (type)
Depth,
H
(m)
1 <
H
< 6
7 <
H
< 1 5
H
≥ 15
Loose saturated sand
60
-
-
Sandy clay
100
250
-
Fine saturated sand
110
-
-
Clay/sand mix
140
-
-
Dense sand
160
-
-
Gravel with stone
180
-
-
Medium gravel
200
-
-
Clayey sand with gravel
-
330
-
Medium gravel
-
-
780
Hard sandstone
-
-
1,200
effect'. Resonance is a frequency-dependent phenomenon. The site period
T
S
for uniform single soil
layer on bedrock can be estimated from the relationship:
4
H
v
T
=
(1.24.1)
S
S
where
T
S
is in seconds.
H
and
v
S
are the depth of soil layer (in metres) and soil shear wave velocity
(in m/s), respectively. The shear wave velocity
v
S
of the soil layer is a function of the soil type and the
depth of the deposit. The average values given in Table 1.9 may be used with equation (1.24.1) ; the
latter equation provides the natural period of vibration of a single homogeneous soil layer. Periods
associated with higher modes can be determined as follows:
1
4
H
v
T
=
(1.24.2)
S,
n
2
n
−
1
S
in which
n
represents the
n
th mode of vibration (
n
> 1).
In alluvial surface layers, vibrations are amplifi ed due to multi-refl ection effects. The ratio of the
amplitude
a
g
at the ground surface to the amplitude at the lower boundary layer (bedrock)
a
b
is given
by (Okamoto, 1984 ):
1
2
−
a
a
ω
H
v
ω
H
v
⎛
⎜
⎞
⎟
g
b
2
2
2
=
cos
+
α
sin
(1.24.3)
s
s
in which
ω
is the natural circular frequency of the soil layer and
α
is the wave- propagation impedance
given by:
ρ
ρ
v
v
ss
bb
(1.24.4)
α
=
where
and
v
are the density and velocity of the surface layer (subscript s) and lower layer (subscript
b), respectively.
ρ
