Page 170 - Civil Engineering Formulas

PILES AND PILING FORMULAS 107

of the pile head on y and M can be evaluated by substituting the value of M t
from the preceding equation into the earlier y and M equations. Note that, for
the fixed-head case,

P t T 3 A B y
y f y (4.7)
A
EI B

TOE CAPACITY LOAD

For piles installed in cohesive soils, the ultimate tip load may be computed from
(4.8)
Q bu A b q A b N c c u
2
2
where A end-bearing area of pile, ft (m )
b
2
q bearing capacity of soil, tons/ft (MPa)
N bearing-capacity factor
t
c undrained shear strength of soil within zone 1 pile diameter above
u
and 2 diameters below pile tip, psi (MPa)
Although theoretical conditions suggest that N may vary between about 8 and
c
12, N is usually taken as 9.
c
For cohesionless soils, the toe resistance stress, q, is conventionally
expressed by Eq. (4.1) in terms of a bearing-capacity factor N and the effective
q
overburden pressure at the pile tip vo
(4.9)
q N q vo q l
Some research indicates that, for piles in sands, q, like f s , reaches a quasi-
constant value, q , after penetrations of the bearing stratum in the range of 10 to
l
20 pile diameters. Approximately
q l 0.5N q tan (4.10)
where is the friction angle of the bearing soils below the critical depth. Val-
ues of N applicable to piles are given in Fig. 4.1. Empirical correlations of soil
q
test data with q and q have also been applied to predict successfully end-bearing
l
capacity of piles in sand.
GROUPS OF PILES

A pile group may consist of a cluster of piles or several piles in a row. The
group behavior is dictated by the group geometry and the direction and location
of the load, as well as by subsurface conditions.
Ultimate-load considerations are usually expressed in terms of a group
efficiency factor, which is used to reduce the capacity of each pile in the