Civil Engineering Reference
In-Depth Information
Solution.
The easiest solution consists of dividing the pile into two sections. The first
section is located above the groundwater table (
z
0 to 3 m) and the second section is that
part of the pile below the groundwater table (
z
3 to 6 m). The average vertical stress will
be at the mid-point of these two sections, or:
v
(at
z
1.5 m)
(1.5 m)(19 kN/m
3
)
29 kPa
v
(at
z
4.5 m)
(3 m)(19 kN/m
3
)
(1.5 m)(9.9 kN/m
3
)
72 kPa
For a concrete pile:
w
3
4
3
4
(30
)
22.5
Substituting values into Eq. (11.11): For
z
0 to 3 m,
L
3 m and therefore
Q
s
equals:
Q
s
(2
rL
)(
v
k
tan
w
)
(2
)(0.15 m)(3 m)(29 kPa)(1)(tan 22.5
)
34 kN
For
z
3 m to 6 m,
L
3 m and therefore
Q
s
equals:
Q
s
(2
rL
)(
v
k
tan
w
)
(2
)(0.15 m)(3 m)(72 kPa)(1)(tan 22.5
)
84 kN
Adding together both values of
Q
s
, the total frictional resistance force
34 kN
84 kN
118 kN. Applying a factor of safety of 3, the allowable frictional capacity of the
pile is approximately equal to 40 kN.
Combined End-Bearing and Friction Pile in Cohesionless Soil.
For piles and piers
subjected to vertical compressive loads and embedded in a deposit of cohesionless soil,
they are usually treated in the design analysis as combined end-bearing and friction piles
or piers. This is because the pile or pier can develop substantial load-carrying capacity
from both end-bearing and frictional resistance. To calculate the ultimate pile or pier
capacity for a condition of combined end-bearing and friction, the value of
Q
p
is added
to the value of
Q
s
.
In the previous example of a 6 m long pile embedded in a silty sand deposit, the allow-
able tip resistance (60 kN) and the allowable frictional capacity (40 kN) are added together
to obtain the allowable combined end-bearing and frictional resistance capacity of the pile
of 100 kN.
Pile Groups in Cohesionless Soil.
The previous discussion has dealt with the load capac-
ity of a single pile in cohesionless soil. Usually pile groups are used to support the founda-
tion elements, such as a group of piles supporting a pile cap or a mat slab. In loose sand
and gravel deposits, the load-carrying capacity of each pile in the group may be greater
than a single pile because of the densification effect due to driving the piles. Because of
this densification effect, the load capacity of the group is often taken as the load capacity
of a single pile times the number of piles in the group. An exception would be a situation
where a weak layer underlies the cohesionless soil. In this case, group action of the piles
could cause them to punch through the cohesionless soil and into the weaker layer or cause
excessive settlement of the weak layer located below the pile tips, such as shown in the
lower left diagram of Fig. 11.14. This condition could also develop when there is a loose
sand layer that liquefies during the earthquake and the group of piles punch downward into
the liquefied soil.
In order to determine the settlement of the strata underlying the pile group, the 2:1
approximation can be used to determine the increase in vertical stress
v
for those soil
layers located below the pile tip. If the piles in the group are principally end-bearing, then
the 2:1 approximation starts at the tip of the piles (
L
length of the pile group,
B
width
of the pile group, and
z
depth below the tip of the piles). If the pile group develops
