Civil Engineering Reference
In-Depth Information
3.
Rocking:
The increase in shear stress caused by the dynamic loads acting on the foun-
dation must be considered in the analysis. Lightly loaded foundations tend to produce
the smallest dynamic loads, while heavy and tall buildings subject the foundation to
high dynamic loads due to rocking.
Given the many variables as outlined above, it takes considerable experience and judg-
ment in the selection of the undrained shear strength
s
u
to be used in Eq. (8.11).
8.4.3 Example Problem
This example problem illustrates the use of Eq. (8.11). Assume that a site has a subsoil pro-
file shown in Fig. 8.13. Suppose that a tall building will be constructed at the site. In addi-
tion, during the life of the structure, it is anticipated that the building will be subjected to
significant earthquake-induced ground shaking.
Because of the desirability of underground parking, a mat foundation will be con-
structed such that the bottom of the mat is located at a depth of 20 ft (6 m) below ground
surface. Assuming that the mat foundation will be 100 ft long and 100 ft wide (30 m by 30
m), determine the allowable bearing pressure that the mat foundation can exert on the
underlying clay layer. Further assume that the clay below the bottom of the mat will not be
disturbed (i.e., lose shear strength) during construction of the foundation.
Solution.
Based on the sensitivity values
S
t
listed in Fig. 8.13, this clay would be classi-
fied as a quick clay. The analysis has been divided into two parts.
Part A.
To prevent the soil from being squeezed out or deforming laterally from
underneath the foundation due to rocking of the structure during the earthquake, the allow-
able bearing pressure should not exceed the maximum past pressure (also known as the pre-
consolidation stress). Recognizing that the building pressure will decrease with depth, the
critical condition is just below the bottom of the foundation (i.e., depth
20 ft). At a depth
of 20 ft (6 m), the preconsolidation stress is about 1.2 kg/cm
2
(2500 lb/ft
2
), and it increases
with depth. Thus the allowable bearing pressure should not exceed 120 kPa (2500 lb/ft
2
).
Part B.
The next step is to consider a bearing capacity failure. As indicated in Fig. 8.13,
the average undrained shear strength
s
u
from field vane shear tests below a depth of 20 ft (6 m)
is about 0.6 kg/cm
2
(1200 lb/ft
2
). Field vane shear tests tend to overestimate the undrained
shear strength because of the fast strain rate and anisotropy effects, and thus a correction should
be applied. Using Bjerrum's (1972) recommended correction (see Fig. 7.19 of Day 2012), the
correction factor
0.85 for a plasticity index
40 (the plasticity index is from Fig. 8.13,
where the liquid limit
w
l
is about 65 and the plastic limit
w
p
is about 25). Thus the corrected
undrained shear strength is equal to 0.6 kg/cm
2
times 0.85, or
s
u
0.5 kg/cm
2
(50 kPa).
Using Eq. (8.11
b
) gives
q
ult
5.5
s
u
(
1
0.3
B
L
)
7.1
s
u
(7.1) (50 kPa)
350 kPa
__
Using a factor of safety of 5.0 to account for the possibility of a loss of shear strength
during the earthquake yields
q
all
q
ult
FS
350 kPa
___
_______
5.0
70 kPa or 1400 lb/ft
2
