For soils having a constant modulus:(6.50)For soils having a linearly increasing modulus:
(6.51)The relationships 6.50 and 6.51 are only approximate, but Davisson and Robinson state that
they are valid for structural design purposes provided that lmax, which is equal to L/R, is
greater than 4 for soils having a constant modulus and provided that zmax, which is equal to
L/T, is greater than 4 for soils having a linearly-increasing modulus. From the above equa-
tions the equivalent length Leof the fixed-base pile (or column) is equal to ezfand the crit-
ical load for buckling is
(6.52)
and
(6.53)
6.4 Lateral loads on raking piles
The most effective way of arranging piles to resist lateral loads is to have pairs of piles
raking in opposite directions as shown in Figure 6.5. The simple graphical method of
Pcr(^2) EI
(ezf)^2
for fixed- (and translating- ) headed conditions
Pcr
(^2) EI
4(ezf)^2
for free- headed conditions
zf 1.8T
Depth to point of fixity zf 1.4R
352 Piles to resist uplift and lateral loading
M M
H
H
P P
e
L
zf
e
e
L
y
x
(a) (b)
Fixed base
Figure 6.37Bending of pile carrying vertical and horizontal loads at head (a) Partly embedded
pile (b) Equivalent fixed base pile or column.