Civil Engineering Reference
In-Depth Information
4.
(
N
1
)
60
values:
As previously mentioned, the average (
N
1
)
60
value for the sand deposit
was determined to be 9.
5.
G
max
: Equation (7.5) was used to calculate the value of
G
max
. It was assumed that the
mean principal effective stress
m
was equal to 0.65
v
0
. Note that
G
max
is expressed in
terms of kips per square foot (ksf) in Table 7.2.
6.
Equation (7.4):
The value of
eff
(
G
eff
/
G
max
) was calculated by using Eq. (7.4). A peak
ground acceleration
a
max
of 0.45
g
and a value of
r
d
from Eq. (6.7) were used in the
analysis.
7.
Effective shear strain
eff
:
Based on the values of
eff
(
G
eff
/
G
max
) and the mean princi-
in ton/ft
2
), Fig. 7.8 was used to obtain the effective shear strain.
8.
Percent cyclic shear strain
%
cyc
:
pal effective stress (
m
The percent cyclic shear strain was calculated as
eff
times 100.
9.
Volumetric strain
v
:
Entering Fig. 7.9 with the percent cyclic shear strain and using
(
N
1
)
60
9, the percent volumetric strain
v
was obtained from the vertical axis.
10.
Multidirectional shear:
The values of percent volumetric strain
v
from step 9 were
doubled to account for the multidirectional shear.
11.
Earthquake magnitude:
The earthquake magnitude is equal to 6.6. Using Table 7.1,
the volumetric strain ratio is approximately equal to 0.8. To account for the earthquake
magnitude, the percent volumetric strain
v
from step 10 was multiplied by the VSR.
12.
Settlement:
The final step was to multiply the volumetric strain
v
from step 11,
expressed as a decimal, by the layer thickness. The total settlement was calculated as
the sum of the settlement from all six layers (i.e., total settlement
3.5 in.).
Summary of Values.
Based on the two methods, the ground surface settlement of the 50-
ft- (15-m-) thick sand layer is expected to be on the order of 2 to 3
1
⁄
2
in. (5 to 9 cm). As pre-
viously mentioned, the actual settlement as reported by Seed and Silver (1972) was about
2
1
⁄
2
in. (6 cm).
7.4.5 Limitations
The methods for the calculation of volumetric compression as presented in Sec. 7.4 can
only be used for the following cases:
●
Lightweight structures:
Settlement of lightweight structures, such as wood-frame
buildings bearing on shallow foundations
●
Low net bearing stress:
Settlement of any other type of structure that imparts a low net
bearing pressure onto the soil
●
Floating foundation:
Settlement of floating foundations, provided the floating founda-
tion does not impart a significant net stress upon the soil
●
Heavy structures with deep settlement:
Settlement of heavy structures, such as massive
buildings founded on shallow foundations, provided the zone of settlement is deep
enough that the stress increase caused by the structural load is relatively low
●
Differential settlement:
Differential movement between a structure and adjacent appur-
tenances, where the structure contains a deep foundation that is supported by strata below
the zone of volumetric compression
