Civil Engineering Reference
In-Depth Information
Above the centre of rotation, passive pressures will develop in front of the pile, while
below the centre of rotation, passive pressures will develop behind the pile. For longer
piles, a plastic hinge will develop at some depth down the pile, and only the upper
part of the pile will undergo significant displacement (Figure 4.35(b)). Although the
soil will be subjected to loading below the plastic hinge, calculation of the failure load
will only require knowledge of the limiting pressures acting over the upper part of the
pile, above the plastic hinge.
Where a pile is embedded in a pile cap which is restrained from rotation, three
different collapse modes are possible, as shown in Figure 4.36. Short piles will translate
as a rigid body with the pile cap, while progressively longer piles will first form a plastic
hinge at the level of the pile cap, and then a plastic hinge at some distance down the
pile. In practice, the majority of piles encountered behave as long piles as regards
lateral capacity. Failure will thus be by the mode shown in Figure 4.36(c).
In calculating failure loads, it is customary to treat the soil as a rigid plastic mate-
rial, idealizing the profiles of limiting pressure as shown in Figure 4.35, with sharp
transitions from full limiting pressure acting in front of the pile just above the hinge
point, down to zero at the hinge point and, for short piles, full limiting pressure acting
behind the pile just below the hinge point. The relevant equivalent forces,
P
, and their
appropriate lever arms,
l
, are shown in Figure 4.35 for an unrestrained pile. For short
piles, the moment at point
B
is
P
bc
(
l
bc
−
h
), where
h
is the depth of the hinge point, and
this must be less than the plastic moment for the pile section. Horizontal equilibrium
then gives
H
f
=
P
ab
−
P
bc
(4.56)
while moment equilibrium entails that
H
f
(
e
+
h
)
=
P
ab
(
h
−
l
ab
)
+
P
bc
(
l
bc
−
h
)
(4.57)
For a given profile of limiting pressure acting on the pile,
P
ab
and
P
bc
may be evaluated
and these two equations solved to find
H
f
.
If the pile fails by forming a plastic hinge, this will occur at the point of maximum
bending moment, and thus of zero shear force. In Figure 4.35(b), the moment at
B
Figure 4.36
Failure modes for laterally loaded piles.
