Civil Engineering Reference
In-Depth Information
where
0. At the level of the pile base, the deformation field due
to the base load may be approximated by (Randolph and Wroth, 1979)
ζ
=
ln(
r
m
/
r
0
) and
α
s
≥
d
b
π
w
=
w
b
(5.11)
r
giving rise to a base interaction factor,
α
b
, for a pile at spacing
s
,of
d
b
π
α
b
≈
(5.12)
s
For groups of piles symmetrically placed around a pitch circle, where each pile responds
identically, the load settlement response of the
i
th pile may now be estimated directly
from equation (4.43), but with the factor
ζ
∗
given by (Randolph, 1979)
ζ
replaced by
n
α
s
ij
ζ
∗
=
ζ
(5.13)
j
=
1
where (
α
s
)
ii
is taken as unity, and the factor
η
replaced by
n
α
b
ij
η
∗
=
η/
(5.14)
j
=
1
Interaction of the deformation fields around the pile shafts is much greater than
around the pile bases, because of the logarithmic decay with pile spacing (compared
with 1
s
for the pile base). This results in a greater proportion of the applied load
being transmitted to the base of piles in a group than for single piles, as confirmed by
model pile tests (Ghosh, 1975).
For pile groups where the piles are not all subjected to the same load, for example
under a stiff pile cap, the above approach must be modified by evaluating an overall
interaction factor for each pair of piles in the group. The interaction factor must allow
not only for the deformation field around the pile shaft, for example the logarithmic
decay around the pile shaft given by equation (5.10), but also the stiffening effect of
the neighbouring pile.
Mylonakis and Gazetas (1998) have shown that the interaction factor in respect of
the pile head response may be expressed as the product of two terms representing the
logarithmic decay and a 'diffraction factor',
/
ξ
, giving
ln
r
m
/
s
α
=
ξ
(5.15)
ζ
For homogeneous soil conditions, ignoring the (relatively minor) interaction at the
level of the pile bases, the diffraction factor,
ξ
, may be expressed in terms of the
non-dimensional quantities
and
μ
L
(see equations (4.49)), as
sinh
2
L
+
2
sinh
2
L
−
L
+
cosh
2
L
−
1
2
l
L
+
l
l
2
l
2
l
2 sinh
2
L
+
2
sinh
2
L
+
cosh
2
L
ξ
=
(5.16)
l
2
l
4
l
