Civil Engineering Reference
In-Depth Information
vertical and horizontal deformations may be written in terms of a flexibility matrix,
F
,
and the applied load as
⎡
⎤
⎡
⎤
⎡
⎤
w
u
θ
F
wP
0
0
P
H
M
⎣
⎦
=
⎣
⎦
⎣
⎦
0
F
uH
F
uM
(4.92)
0
F
F
θ
H
θ
M
For a pile battered at an angle
ψ
to the vertical, the matrix
F
must be replaced by a
transformed matrix,
F
, where
F
=
T
T
FT
(4.93)
and
⎡
⎤
cos
ψ
−
sin
ψ
0
⎣
⎦
T
=
sin
ψ
cos
ψ
0
(4.94)
0
0
1
One aspect of the effect of lateral loading on axial capacity that deserves particular
attention is the possibility of a gap opening up around the pile near ground level-aso-
called 'post-holing' effect. Piles subjected to axial loading together with cyclic lateral
loading generally fail at a point where the lateral component of load is zero, and the
pile is then close to its neutral position. In the design of piles for offshore structures,
it is generally recognized that load transfer into the soil close to the sea-floor (under
axial loading) should be ignored because of the risk of post-holing. The question is:
to what depth will such post-holing occur?
Some estimate of the extent of any gap forming around the pile (particularly in
fine-grained soils) may be made by considering the lateral deflection at which yield in
the soil close to the pile will occur. Baguelin
et al
. (1977) have considered the case of
a circular disc moving sideways through elastic, perfectly plastic material, with shear
modulus,
G
, and shear strength,
c
u
. They showed that the lateral movement is related
to the normal stress change,
σ
n
, in front of and behind the disc, by
u
/
d
∼
σ
n
/
G
(4.95)
The load deflection curve for the disc was essentially linear up to a normal stress
change of about 2
c
u
. This would indicate that non-linear effects, and the possibility
of gapping around the pile, would start to occur at a normalized deflection of
u
/
d
∼
2
c
u
/
c
u
of 100, this would be about 2%of the pile diameter.
Thus, in assessing the extent of any post-holing, and loss of shaft friction, it is
necessary to estimate the depth down the pile at which the cyclic lateral movements
are less than about 2% of the pile diameter. Above this level, it would be imprudent
to rely on significant shaft friction under axial loading.
G
. For a typical value of
G
/
4.5 Piles in deforming soil
There are many situations in which loads are induced in a pile by virtue of the defor-
mation of the surrounding soil. The most common example is where piles are installed
