Civil Engineering Reference
In-Depth Information
TABLE 7.1
Earthquake Magnitude versus Volumetric Strain Ratio for Dry Sands
Number of representative
Earthquake magnitude
cycles at 0.65
max
Volumetric strain ratio
8
1
⁄
2
26
1.25
7
1
⁄
2
15
1.00
6
3
⁄
4
10
0.85
6
5
0.60
5
1
⁄
4
2-3
0.40
Notes:
To account for the earthquake magnitude, multiply the volumetric strain
v
from
Fig. 7.9 by the VSR. Data were obtained from Tokimatsu and Seed (1987).
have 5 percent or less fines. For dry sands (i.e., water content
0 percent), capillary action
does not exist between the soil particles. As the water content of the sand increases, capil-
lary action produces a surface tension that holds together the soil particles and increases
their resistance to earthquake-induced volumetric settlement. As a practical matter, clean
sands typically have low capillarity and thus the method by Tokimatsu and Seed (1987)
could also be performed for damp and moist sands.
For silty soils, R. B. Seed (1991) suggests that the most appropriate adjustment is to
increase the (
N
1
)
60
values by adding the values of
N
corr
indicated in Sec. 7.2.2.
7.4.4 Example Problem
Silver and Seed (1972) investigated a 50-ft- (15-m-) thick deposit of dry sand that experi-
enced about 2
1
⁄
2
in. (6 cm) of volumetric compression caused by the San Fernando earth-
quake of 1971. They indicated that the magnitude 6.6 San Fernando earthquake subjected
the site to a peak ground acceleration
a
max
of 0.45
g.
The sand deposit has a total unit weight
t
95 lb/ft
3
(15 kN/m
3
) and an average (
N
1
)
60
9. Estimate the settlement of this 50-ft-
(15-m-) thick sand deposit using the methods outlined in Secs. 7.4.2 and 7.4.3.
Solution Using Fig. 7.7.
As shown in Fig. 7.7, the volumetric compression rapidly
increases as the (
N
1
)
60
value decreases. Since the peak ground acceleration
a
p
0.45
g,
the
horizontal axis is entered at 0.45. For an (
N
1
)
60
value of 9, the volumetric strain
H
/
H
is
about equal to 0.35 percent. The ground surface settlement is obtained by multiplying the
volumetric strain, expressed as a decimal, by the thickness of the sand layer, or 0.0035
50 ft
0.18 ft or 2.1 in. (5.3 cm).
Solution Using the Tokimatsu and Seed (1987) Method.
Table 7.2 presents the solution
using the Tokimatsu and Seed (1987) method as outlined in Sec. 7.4.3. The steps are as fol-
lows:
1.
Layers:
The soil was divided into six layers.
2.
Thickness of the layers:
The upper two layers are 5.0 ft (1.5 m) thick, and the lower
four layers are 10 ft (3.0 m) thick.
3.
Vertical effective stress:
For dry sand, the pore water pressures are zero and the ver-
tical effective stress
v
0
is equal to the vertical total stress
v
.
This stress was calcu-
lated by multiplying the total unit weight (
t
95 lb/ft
3
) by the depth to the center of
each layer.
