Civil Engineering Reference
In-Depth Information
of earth pressure at rest
k
0
0.5. Thus the value of
m
0.67
v
0
. Note in
Eq. (7.5) that the value of
m
must be in terms of pounds per square foot.
After the value of
G
max
has been determined from Eq. (7.5), the value of
eff
(
G
eff
/
G
max
)
can be calculated by using Eq. (7.4). To determine the effective shear strain
eff
of the soil,
Fig. 7.8 is entered with the value of
eff
(
G
eff
/
G
max
) and upon intersecting the appropriate
value of mean principal effective stress (
m
in ton/ft
2
), the effective shear strain
eff
is
obtained from the vertical axis.
2.
Determine the volumetric strain
v
. Figure 7.9 can be used to determine the volu-
metric strain
v
of the soil. This figure was developed for cases involving 15 equivalent uni-
form strain cycles, which is representative of a magnitude 7.5 earthquake. In Fig. 7.9, the
cyclic shear strain
cyc
is equivalent to the effective shear strain
eff
calculated from step 1,
except that the cyclic shear strain
cyc
is expressed as a percentage (%
cyc
100
eff
). To
determine the volumetric strain
v
in percent, either the relative density
D
r
of the in situ soil
or data from the standard penetration test must be known. For Fig. 7.9, assume the
N
1
in the
figure refers to (
N
1
)
60
values from Eq. (5.2).
To use Fig. 7.9, first convert
eff
from step 1 to percent cyclic shear strain (%
cyc
100
eff
). Then enter the horizontal axis with percent
cyc
, and upon intersecting the relative
FIGURE 7.8
eff
for values of
eff
(
G
eff
/
G
max
) from Eq. (7.4) and the mean principal
effective stress
Plot that is used to estimate the effective shear strain
. (
Reproduced from Tokimatsu and Seed 1987, with
permission from the American Society of Civil Engineers.
)
m
