Civil Engineering Reference
In-Depth Information
where
s
u
undrained shear strength of cohesive soil (total stress analysis), lb/ft
2
or kPa. As
discussed in Sec. 5.5.1, often undrained shear strength is obtained from uncon-
fined compression tests or vane shear tests.
c,
undrained shear strength parameters (total stress analysis). As discussed in
Sec. 5.5.1, these undrained shear strength parameters are often obtained from
triaxial tests, such as unconsolidated undrained triaxial compression test
(ASTM D 2850) or consolidated undrained triaxial compression tests
(ASTM D 4767).
h
horizontal total stress, lb/ft
2
or kPa. Since vertical shear surfaces are assumed
(see Fig. 8.7), normal stress acting on shear surfaces will be the horizontal total
stress. For cohesive soil,
h
is often assumed to be equal to
1
2
v
2.
For an unliquefiable soil layer consisting of cohesionless soil (e.g., sands), use an
effective stress analysis:
f
h
tan
k
0
v
0
tan
(8.2
c
)
where
h
horizontal effective stress, lb/ft
2
or kPa. Since vertical shear surfaces are
assumed (see Fig. 8.7), the normal stress acting on the shear surface will be the
horizontal effective stress. The horizontal effective stress
h
is equal to the
coefficient of earth pressure at rest
k
0
times the vertical effective stress
v
0
, or
h
k
0
v
0
.
effective friction angle of cohesionless soil (effective stress analysis).
Effective friction angle could be determined from drained direct shear tests or
from empirical correlations such as shown in Figs. 5.12 and 5.14.
Example Problems.
The following example problems illustrate the use of Eqs. (8.1)
and (8.2).
Example Problem for Cohesive Surface Layer (Total Stress Analysis).
Use the data
from Prob. 6.15, which deals with the subsurface conditions shown in Fig. 6.15 (i.e., the
sewage disposal site). Based on the standard penetration test data, the zone of liquefaction
extends from a depth of 1.2 to 6.7 m below ground surface. Assume the surface soil (upper
1.2 m) shown in Fig. 6.15 consists of an unliquefiable cohesive soil and during construc-
tion, an additional 1.8-m-thick layer of cohesive soil will be placed at ground surface. Use
a peak ground acceleration
a
max
of 0.20
g.
Assume that after the 1.8-m-thick layer is placed at ground surface, it is proposed to
construct a sewage disposal plant. The structural engineer would like to use shallow strip
footings to support exterior walls and interior spread footings to support isolated columns.
It is proposed that the bottom of the footings be at a depth of 0.5 m below ground surface.
The structural engineer has also indicated that the maximum total loads (including the
weight of the footing and the dynamic loads) are 50 kN/m for the strip footings and 500 kN
for the spread footings. It is desirable to use 1-m-wide strip footings and square spread foot-
ings that are 2 m wide.
For both the existing 1.2-m-thick unliquefiable cohesive soil layer and the pro-
posed additional 1.8-m-thick fill layer, assume that the undrained shear strength
s
u
of the soil is equal to 50 kPa. Calculate the factor of safety of the footings, using
Eq. (8.1).
Solution.
The first step is to check the two requirements in Table 8.3. Since the foot-
ings will be located within the upper unliquefiable cohesive soil, the first requirement is
met. As indicated in the example problem in Sec. 7.3.3, the surface unliquefiable soil layer
must be at least 3 m thick to prevent liquefaction-induced ground damage. Since a fill layer
equal to 1.8 m is proposed for the site, the final thickness of the unliquefiable soil will be
equal to 3 m. Thus the second requirement is met.
