86
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
2 PILE FOUNDATIONS
2.1
Axial shaft friction
Arguably the most important aspect of pile design, estimation of
the profile of limiting shaft friction, has proved resistant to
analytical treatment, although understanding of the processes
involved has gradually developed. This has allowed appropriate
non-dimensional quantities on which the limiting shaft friction
depends to be identified. A full discussion of the current design
recommendations for shaft friction was provided recently by
Jeanjean (2012), and so the remarks below are limited to
relatively high level principles underlying the guidelines.
In clays and other fine-grained soils, where installation of
driven piles occurs over a shorter time scale than dissipation of
excess pore pressures, the main quantities to be considered are
the undrained shear strength, s
u
, of the sediments, the vertical
effective stress,
'
v0
, and pile geometry: diameter, D, and
embedment length, L. It may also be necessary to consider the
distance, h, of the element in question from the pile tip. With
these parameters as input, empirical correlations have then been
used to establish guidelines for the limiting shaft friction,
f
,
normalised by s
u
or
'
v0
, as a function of s
u
/
'
v0
, L/D and h/D.
Other quantities such as the internal angle of friction, and in situ
stress ratio, K
0
, are captured to some extent by the strength
ratio, s
u
/
'
v0
, at least within the accuracy of the empirical
database. In some clays it may also be necessary to consider the
extent to which shaft friction may be limited by a low interface
friction angle between pile and soil, or immediately adjacent to
the pile, due to the formation of residual surfaces in the clay.
For sands, the cone resistance, q
c
(more strictly the net
resistance, q
net
) essentially replaces the undrained shear strength
in terms of providing a normalising quantity for
f
and
'
v0
. The
interface friction angle must also be considered, although
spanning a relatively small range for typical pile surfaces.
The area ratio of open-ended driven piles, relating the cross-
sectional area of steel to the gross cross-sectional area of the
pile, affects the external soil displacement and hence the stress
changes in the soil around the pile. For fine-grained soils this
will influence the extent of the excess pore pressure field
generated during pile installation, and hence the time scale of
excess pore pressure dissipation and increase in shaft friction
(Randolph 2003), as discussed further below.
It has always been intriguing that the database of pile load
tests in clay does not show discernible differences in shaft
capacity depending on whether the pile was open-ended or
closed-ended (including solid), even though the external stress
changes during installation must be affected to some degree.
However, cavity expansion analysis shows that, for typical wall
thickness ratios (or ratios of D
eq
/D), the expansion stress is not
significantly less (perhaps 15 to 20 %) than for a solid pile, and
also some proportion of the total stress increase is lost during
the consolidation process, moderating the difference. By
contrast, suction caissons have much higher D/t ratios, and even
more so when allowance is made for some of the soil displaced
by the tip entering the caisson. Hence the final shaft friction will
be lower than for a driven pile in similar soil (Randolph 2003).
For sands, the area ratio, A
r
(or more precisely the effective
area ratio, Lehane et al. 2005) influences the magnitude of the
radial stresses established in the soil as the pile tip passes, and
which subsequently decrease as the pile is driven deeper. A
subtle difference among the different cone-based design
methods is the manner in which the area ratio is implemented in
the estimation of shaft friction (Schneider et al. 2008). In the
Imperial College method (Jardine et al. 2005), the shaft friction
is taken to degrade from its initial value as a function of the
distance, h, normalised by the equivalent diameter, D
eq
, (where
D
eq
2
= A
r
D
2
). By contrast, in the UWA approach (Lehane et al.
2005), while the area ratio is used to modify the ratio of radial
stress (close to the pile tip) to q
c
, the subsequent decay in radial
stress is expressed as a function of h/D. These two approaches
result in quite similar forms of expression for the shaft friction,
but the underlying conceptual models differ. Friction
degradation according to h/D, rather than h/D
eq
seems more
logical, since the soil at depths shallower than the pile tip no
longer has any knowledge of (or influence from) the area ratio
in respect of subsequent densification within the shearing zone
adjacent to the pile. The influence of the area ratio on the initial
radial stress is also supported by analysis (White et al. 2005).
It is acknowledged that the use of the distance, h, to quantify
friction degradation is really a surrogate for the number of shear
stress cycles to which the soil is exposed, since it is the cyclic
shearing that provides the underlying mechanism (White and
Lehane 2004). Normalisation by D pre-supposes that piles of
different diameter are subjected to broadly similar numbers of
hammer blows per diameter advance. Relatively easy or hard
driving will affect the rate of friction degradation with h/D.
Indeed, ad hoc experimental evidence suggests that hard
driving, with limited advance per blow, can cause greater harm
due to friction degradation than any benefit obtained by
advancing the pile tip further.
A missing element from current friction degradation models
is any quantified minimum value of shaft friction, below which
degradation ceases, because the density of the sand at the pile-
soil interface has reached its maximum value for the particular
effective stress level. This type of stabilisation has been
explored through constant normal stiffness (CNS) shear box
testing, and the framework of a predictive model proposed,
based on concepts of critical state soil mechanics (DeJong et al.
2006). The secondary influence on the rate of degradation of the
cavity stiffness, which is proportional to G
max
/D, would
probably be too elusive to extract from the database of pile load
tests, but offers a suitable basis with which to refine predictive
approaches.
2.2
Post-installation consolidation
The increase in pile shaft capacity following installation is
amenable to analysis, since it corresponds to dissipation of
excess pore pressure through (primarily) radial consolidation.
Analytical solutions for radial consolidation, following insertion
of a solid object such as a pile or piezocone, give the normalised
excess pore pressure, U =
u/
u
initial
, as a function of a non-
dimensional time T = c
v
t/D
2
, where c
v
is the consolidation
coefficient (Randolph and Wroth 1979). The solution depends
on the rigidity index, G/s
u
, associated with cavity expansion
(i.e. the penetration phase). For G/s
u
~ 100, the relationship
between U and T may be approximated by
75.0
50
T/T1
1
U
(1)
where T
50
is the time for 50 % dissipation and is about 0.6. The
corresponding value of T
90
is about 12.
The consolidation coefficient is that associated with radial
consolidation and, just as for piezocone dissipation, is biased
more towards conditions of swelling, which occurs in the mid to
far field, rather than the compression and loss of water content
that occurs close to the pile. For an open-ended pile or caisson,
the outer diameter, D, should be replaced by the equivalent
diameter, D
eq
, so that T is defined as (Randolph 2003)
2
r
v
2
eq
v
DA
tc
D
tc
T
(2)
There is very limited field data with which to compare the
solution for excess pore pressure dissipation, although some
recent studies have reported increases in pile driving resistance
