90
Proceedings of the 18
th
International Conference on Soil Mechanics and Geotechnical Engineering, Paris 2013
Proceedings of the 18
th
International Conference on Soil Mechanics and Geotechnical Engineering, Paris 2013
from the wedge mechanism to the flow mechanism (Klar and
Randolph 2008).
Although the Murff and Hamilton upper bound solution
treats the conical wedge mechanism as a whole, to provide an
overall lateral resistance for that section of the pile, they
explored suitable variations of N
p
with depth, z, that fitted the
overall upper bound resistance for piles of different embedment.
This led to proposed factors of
D/z
2 1 p
eNN N
(14)
with
adjusted for different strength profiles idealised as
s
u
= s
um
+
z, according to
55.0 ,
D
s
05.0 25.0Min
um
(15)
The value of N
p
therefore increases from a surface value of
N
1
– N
2
, to a limiting value at depth of N
1
(corresponding to
Equation (13)). Assuming a double sided mechanism (with
negative excess pore pressures behind the pile causing the soil
to move with the pile) the Murff and Hamilton mechanism leads
to an almost constant value of 5 for N
2
. Thus the surface value
of N
p
increases approximately linearly with
from about 4 for a
smooth pile (
= 0) to 7 for a rough pile (
= 1).
Jeanjean (2009) has recommended adoption of N
1
= 12 and
N
2
= 4, without consideration of the friction ratio,
. Even for
fully rough conditions this is slightly optimistic in respect of the
surface value of N
p
(8 instead of the upper bound value of 7).
Also, as commented by Murff and Hamilton (1993), the
additional resistance provided by a fully rough pile compared
with a smooth pile “
would seem to be particularly susceptible to
degradation due to cyclic loading, and thus it may not be
prudent to count on it for design
”. A compensating factor to this
(intuitive) consideration is the gradual hardening that occurs due
to consolidation between periods of cyclic perturbation (Zhang
et al. 2011). The net effect of this is that the post-cyclic
monotonic pile responses showed slight increases in resistance
for a given pile displacement. Similar hardening was observed
in centrifuge model tests simulating the interaction of steel
catenary risers with the seabed (Hodder et al. 2013).
Equally important for lateral pile design is the mobilisation
of lateral resistance with displacement. Variations in the
stiffness at small displacements for elements at some depth
down the pile can have a significant effect on the pile head
response. The current API and ISO guidelines for load transfer
curves appear too soft at moderate displacements (Jeanjean
2009), although the initial data point, with P/P
u
= 0.23 for a
displacement of y = 0.1y
c
= 0.25
50
D, implies a rather high
stiffness. Here
50
is defined as the strain in a (triaxial)
compression test at half the failure deviator stress, which is
equivalent to s
u
/3G
50
. Hence for P
u
= 9s
u
D, the initial gradient is
P/y = 9×0.23×3G
50
/0.25 = 25G
50
.
Theoretical solutions for the load transfer response, either
based on an analogy with cavity expansion or closed form
solutions (Baguelin et al. 1977), lead to a gradient of k
py
~ 4G,
and hence a maximum gradient of 4G
0
. Applying this as a limit
at small displacements to the hyperbolic tangent function
suggested by Jeanjean (2009) leads to
y
P
G4
,
D
y
s
G
01.0 tanh Min
P
P
u
0
u
0
u
(16)
For P
u
= 12s
u
D, the transition point occurs at y/D = 0.0009, so
P/P
u
= 0.0003G
0
/s
u
or 0.12 for G
0
/s
u
= 400.
Although Jeanjean’s study was for soft clays, in principle the
same general approach should be applicable to stiff clays but
with some caveats:
Where stiff clays occur at the seabed surface, a gap is much
more likely to develop than for soft clays (since higher
s
u
/
'D, and much greater suctions required to be sustained in
order to prevent a gap forming). As such, the surface factor
(N
1
- N
2
) should be halved, while retaining the same
limiting (plane strain) value of N
p
.
A lower friction ratio,
, is likely to be appropriate, just as
for axial shaft friction.
2.6
Lateral pile resistance – sand
For sand, design recommendations for limiting lateral resistance
still rely on a limit equilibrium calculation for a putative passive
wedge of soil failing ahead of the pile. There is also an
overriding maximum limiting resistance, proportional to depth,
although this is extremely high (such that, in practice, it would
not be reached shallower than depths exceeding 15 pile
diameters). The resulting profiles of limiting resistance are not
consistent with results from numerical modelling, or even with
empirical data that appear to follow a linear trend, below a
depth of about 1 diameter, that is broadly proportional to the
square of the passive earth pressure coefficient, K
p
.
However, any design approach requiring what is ultimately a
bearing resistance, but is couched in terms of friction angle,
',
suffers from the problems of (a) how to ‘measure’
', and
(b) the need to adjust
' according to the resulting implied
effective stress level. Typically values of
' must be deduced
from the results of cone penetration tests. It is therefore far more
logical to link the lateral pile resistance directly to the cone
resistance, following the path taken for axial pile capacity.
Empirically based approaches that express the lateral pile
resistance as a function of the cone resistance have been
proposed for carbonate sands (Wesselink et al. 1988, Novello
1999, Dyson and Randolph 2001). Recently, a numerical study
has been undertaken by Suryasentana and Lehane (2013) to
provide a more theoretical link between lateral pile resistance
and cone resistance, the latter being simulated as spherical
cavity expansion. Material properties were based on those for a
typical silica sand.
Systematic dimensional analysis, with a parametric study
covering a wide range of the various dimensionless groups,
allowed relationships to be developed between normalised
values of pile resistance, cone resistance, depth and lateral
displacement. The eventual relationship incorporated an
exponential term to give a true limiting lateral resistance at large
displacement. The lateral resistance was then expressed as
(Suryasentana and Lehane 2013):
94.0
1.1
61.0
68.0
0v
c
0v
D
y
D
z 9.8 exp 1
D
z
q
2
D
P
(17)
This study represents an important step towards a more rational
approach to the estimation of load transfer responses for lateral
pile design in sand. The rather gradual development of the
ultimate resistance (the terms outside the square bracket in
Equation (17)) is in stark contrast to the hyperbolic tangent
relationship in the current design guidelines, which leads to the
ultimate resistance being mobilised at displacements of 1 or 2 %
of the pile diameter.
3 SHALLOW FOUNDATIONS
Design guidelines for shallow foundations that are provided in
the main geotechnical guides (ISO 2003, API 2011) have
developed from guidance for temporary mudmat foundations to
support steel jacket structures, prior to pile installation. Large
