Civil Engineering Reference
In-Depth Information
Cohesionless Soil.
For an end-bearing pile or pier, the Terzaghi bearing capacity
equation can be used to determine the ultimate bearing capacity
q
ult
. Assuming a pile
that has a square cross section (i.e.,
B
L
) and for cohesionless soil (
c
0), Eq. (8.4)
reduces to:
q
ult
Q
p
___
B
2
0.4
t
B N
t
D
f
N
q
(11.7)
In comparing the second and third term in Eq. (11.7), the value of
B
(width of pile) is
much less than the embedment depth
D
f
of the pile. Therefore, the first term in Eq. (11.7)
can be neglected.
The value of
t
D
f
in Eq. (11.7) is equivalent to the total vertical stress
v
at the pile
tip. For cohesionless soil and using an effective stress analysis, the groundwater table must be
included and hence the vertical effective stress
v
can be substituted for
v
. Equation (11.7)
reduces to:
For end-bearing piles having a square cross section in cohesionless soil:
q
ult
Q
p
___
B
2
v
N
q
(11.8)
For end-bearing piles or piers having a circular cross section in cohesionless soil:
q
ult
Q
p
___
r
2
v
N
q
(11.9)
where
q
ult
ultimate bearing capacity of the end-bearing pile or pier (psf or kPa)
p
ultimate point resistance force (lb or kN)
B
width of the piles having a square cross section (ft or m)
r
radius of the piles or piers having a round cross section (ft or m)
v
vertical effective stress at the pile tip (psf or kPa)
q
bearing capacity factor (dimensionless)
For drilled piers or piles placed in pre-drilled holes, the value of
N
q
can be obtained
from Fig. 8.11 based on the friction angle
of the cohesionless soil located at the pile tip.
However, for driven displacement piles, the
N
q
values from Fig. 8.11 are generally too
conservative.
Figure 11.13 presents values of
N
q
reported in the literature (Vesi c 1967). For
30
,
N
q
varies from about 30 to 150 while for
40
,
N
q
varies from about 100 to 1000. This
is a tremendous variation in
N
q
values and is related to the different approaches used by the
various researchers, where in some cases the
N
q
values are theoretical, while in other cases
the relationship is based on analysis of field data such as pile load tests.
There is a general belief that the bearing capacity factor
N
q
is higher for driven displace-
ment piles than for shallow foundations. One reason for a higher
N
q
value is the effect of
driving the pile, which displaces and densifies the cohesionless soil at the bottom of the
pile. The densification could be due to both the physical process of displacing the soil
and the driving vibrations. These actions would tend to increase the friction angle of the
cohesionless soil in the vicinity of the driven pile. High displacement piles, such as large
diameter solid piles, would tend to displace and densify more soil than low displacement
piles, such as hollow piles that do not form a soil plug.
Example Problem.
Assume a pile having a diameter of 0.3 m and a length of 6 m
will be driven into a nonplastic silty sand deposit having shear strength properties of
c
. Assume that the location of the groundwater table is located 3 m below
the ground surface, the total unit weight above the groundwater table is 19 kN/m
3
, and
the buoyant unit weight
0 and
30
b
below the groundwater table is 9.9 kN/m
3
. Using the Terzaghi
