1039
Lateral stress changes and shaft friction for
model displacement piles in sand
Barry M. Lehane and David J. White
Abstract: The paper describes a series of tests performed in a drum centrifuge on instrumented model displacement
piles in normally consolidated sand. These tests examined the influence of the pile installation method, the stress level,
and the pile aspect ratio on the increase in lateral effective stress on the pile shaft during static load testing to failure.
A parallel series of constant normal load and constant normal stiffness (CNS) laboratory interface shear experiments
was performed to assist interpretation of the centrifuge tests. It is shown that although the cycling associated with pile
installation results in a progressive reduction in the stationary horizontal effective stress acting on a pile shaft and
densification of the sand in a shear band close to the pile shaft, this sand dilates strongly during subsequent shearing to
failure in a static load test. The dilation (the amount of which depends on the cyclic history) is constrained by the surrounding soil and therefore leads to large increases in lateral effective stresses and hence to large increases in mobilized shaft friction. The increase in lateral stress is shown to be related to the radial stiffness of the soil mass
constraining dilation of the shear band and to be consistent with measurements made in appropriate CNS interface
shear tests. The paper’s findings assist in the extrapolation of model-scale pile test results to full-scale conditions.
Key words: sand, displacement pile, centrifuge tests, shaft friction.
Résumé : Cet article décrit une série d’essais réalisés dans un centrifuge en forme de tambour sur des modèles de
pieux à déplacement instrumentés placés dans un sable normalement consolidé. Ces essais examinent l’influence de la
méthode d’installation des pieux, du niveau des contraintes et du rapport géométrique du pieu sur l’augmentation de la
contrainte latérale effective sur le fût du pieu durant l’essai de chargement statique à la rupture. On a réalisé en parallèle une série d’expériences de cisaillement à l’interface en laboratoire, à charge et rigidité normales constantes, pour
aider à l’interprétation des essais au centrifuge. Il est montré que, quoique la charge cyclique associée à l’installation
du pieu résulte en une réduction progressive de la contrainte effective stationnaire horizontale agissant sur le fût du
pieu et en une densification du sable dans une bande de cisaillement près du fût du pieu, ce sable se dilate fortement
durant le cisaillement subséquent à la rupture dans un essai de chargement statique. La dilatation dont la quantité dépend de l’histoire des contraintes est confinée par le sol environnant, et en conséquence, conduit à de fortes augmentations des contraintes effectives latérales et de là, à de fortes augmentations du frottement mobilisé au fût. On montre
que l’augmentation en frottement latéral est reliée à la rigidité radiale de la masse de sol contenant la dilatation de la
bande de cisaillement et est cohérente avec les mesures faites dans des essais appropriés de cisaillement CNS sur
l’interface. Les résultats de cet article aident à l’extrapolation des résultats d’essais de pieux, de l’échelle du modèle à
des conditions de pleine échelle.
Mots clés : sable, pieu à déplacement, essais au centrifuge, frottement du fût.
[Traduit par la Rédaction]
Lehane and White
Introduction
Laboratory-scale investigations into pile behaviour remain
popular because of the high cost of field testing and the possibility of achieving specific soil characteristics in a laboratory environment. Model pile tests in sand have been
performed in laboratory test chambers for many years (e.g.,
Kérisel 1964) and, more recently, at elevated g levels in the
centrifuge (e.g., de Nicola 1997; Bruno 1999; Klotz 2000;
Fioravante 2002). Extrapolation of these experimental results
1052
to full-scale conditions is hampered, however, by the uncertainty surrounding scale and size effects. For example, although Klotz and Coop (2001) argued that there is little
evidence for the diameter dependence of the ultimate shaft
shear stress (qs) that can develop on a pile in sand, Foray et
al. (1998) and others showed that qs decreases as the pile diameter (D) increases and as the mean particle size (D50) decreases. Furthermore, as illustrated by Garnier and König
(1998), the displacement required to mobilize ultimate shaft
friction on model piles is often comparable to that required
Received 29 June 2004. Accepted 8 December 2004. Published on the NRC Research Press Web site at http://cgj.nrc.ca on
18 August 2005.
B.M. Lehane.1 School of Civil and Resource Engineering, University of Western Australia, Crawley, Perth, WA 6009, Australia.
D.J. White. University of Cambridge, The Schofield Centre, Cambridge University Engineering Department, Trumpington Street,
Cambridge CB2 1PZ, UK.
1
Corresponding author (e-mail: [email protected]).
Can. Geotech. J. 42: 1039–1052 (2005)
doi: 10.1139/T05-023
© 2005 NRC Canada
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Can. Geotech. J. Vol. 42, 2005
for full-scale piles (i.e., 2–10 mm); in model tests, such relative movements may even be greater than those required to
mobilize full base capacity. Scaling laws also seem to vary
with the pile installation method, as shown, for example, by
Al-Mhaidib and Edil (1998), who indicated that qs for “buried” piles was over double that for a driven pile with D =
48 mm, whereas little influence of the method of installation
was inferred for piles with D = 178 mm.
Experimental investigations of pile shaft friction in sand
generally use strain gauges or load cells to measure the axial
pile load distribution, from which the distribution of local
shaft friction can be calculated. A more complete understanding of the mechanisms controlling the shaft friction
may be obtained if the lateral stresses acting on the pile
shaft are also measured, as illustrated, for example, in tests
involving the 100 mm diameter Imperial College London instrumented field pile; see Lehane et al. (1993) and Chow
(1997). Klotz and Coop (2001) were the first to report lateral
stress measurements on (16 mm diameter) centrifuge displacement piles in sand, but they provided no information
concerning lateral stress changes that occur as a pile is
loaded to failure from an at-rest position.
The investigation presented here examines the lateral stress
changes that take place during installation and load testing
of 9 mm square, closed-ended centrifuge model piles installed into sand. Such lateral stress changes were measured
under a variety of testing conditions and are used, together
with data from constant normal load (CNL) and constant
normal stiffness (CNS) direct shear interface tests, to shed
light on factors that can assist in extrapolation from
model-scale to full-scale conditions.
Fig. 1. Analogy between a pile–soil interface and a CNS test.
Model for pile shaft response
Previous model testing has shown that a thin shear zone
exists adjacent to a loaded pile shaft, whereas the more distant soil remains largely undeformed (Robinsky and Morrison 1964; White and Bolton 2004). Therefore, as shown in
Fig. 1, the load transfer behaviour at the pile shaft can be
idealized as the shearing of a thin interface zone surrounded
by a soil mass that undergoes minimal deformation and restrains the shear-induced volume changes in the interface
zone. Changes in lateral stress on the pile shaft arise from
changes in volume of the shear zone and will increase with
increasing levels of confinement provided by the surrounding soil. This behaviour is analogous to that seen in CNS interface shear box tests (e.g., see Airey et al. 1992).
The change in lateral stress, ∆σ h, on a cylindrical pile
shaft of diameter D, due to a change in shear band thickness,
∆t, can be compared with the response in a CNS interface
shear box test by considering elastic cavity expansion
(Boulon and Foray 1986), as follows:
[1]
∆σ h = (4G∆t)/D = kn ∆t
where G is the operational shear modulus of the soil around
the pile; and kn is the spring stiffness in the CNS test.
Lehane and Jardine (1994) verified the form of eq. [1] by using a database of measured or estimated values of ∆σ h adjacent to displacement piles and showing that ∆σ h increased
with sand density and stress level and decreased strongly
with pile diameter. Values for ∆t and G cannot, however,
currently be estimated to provide realistic predictions for
∆σ h. The soil deformation imposed by pile installation influences G, which, even for small ∆t, may differ appreciably
from the in situ very small strain value, G0. The thickness of
and the volumetric strain within the pile–soil interface zone
govern ∆t. Few observations of this zone have been made,
although some insight can be gained from interface tests in
transparent-sided shear boxes (e.g., Uesugi et al. 1988).
Such uncertainty prompted the investigation, described in
the following, of the link between ∆σ h measured in a load
test on a displacement pile in sand with that inferred from a
CNS interface test.
Drum centrifuge experiments
Pile details
The pile experiments were performed in the drum centrifuge at the University of Western Australia (UWA). The ring
channel of this machine has an outer diameter of 1.2 m, an
inner diameter of 0.8 m, and a channel height (⬅ sample
width) of 0.3 m. This centrifuge was selected in preference
to the UWA beam centrifuge, as it offered the possibility of
conducting multiple pile installations within the same sample without the need to halt the centrifuge (and hence cycle
the soil self-weight). The independently rotating central
shaft and tool table can be driven relative to the ring channel
by a hollow stepper motor and brought to a halt, independ© 2005 NRC Canada
Lehane and White
1041
Fig. 2. UWA geotechnical drum centrifuge.
ently of the channel, to allow instruments to be changed. An
actuator is mounted on the tool table, on which the pile is attached and controlled. A full technical description of this
centrifuge is presented by Stewart et al. (1998), and the centrifuge is shown, with the safety cover removed, in Fig. 2.
The tests used a 9 mm square, 185 mm long, steel,
closed-ended pile, shown in Fig. 3. Lateral soil stresses (σ h)
acting on the pile were measured with four 6 mm diameter
earth pressure sensors, which were located at distances
above the pile base (h) of 9, 27, 54, and 108 mm, that is, at
h/B values of 1, 3, 6, and 12, where B is the pile breadth
(9 mm). Two further sensors were located at the opposite
pile face, at h/B = 1 and 3, to provide a check on the repeatability of lateral stress measurements at these relative tip
depths. The sensors were bonded in slots machined into the
pile face, which were then filled with clear epoxy. The sensor cables passed through a central void in the shaft and
emerged 165 mm above the pile tip, for connection to the
data acquisition system. The model pile design also allowed
for full-length extension pieces to be added to each of the
uninstrumented pile faces so that pile width (W) to breadth
(B) ratios of 2 and 6 could also be tested. The centreline average roughness (Rcla) of the steel pile and extension pieces
was 0.6 ± 0.1 µm.
Test programme
Fine silica sand was used in the experiments. This sand
was deposited in flight (at 20g) by dry pluviation in the
300 mm wide drum channel to the full channel depth of
200 mm. Water was introduced into the sand to induce a
suction pressure that allowed the sample to be levelled to a
uniform full depth of 180 mm after the channel was brought
to a halt. The channel was then accelerated to 50g and remained spinning at either 50g or 150g over the 9 day duration of the pile-testing programme. Cone penetration tests
(CPTs) at 50g were the first tests conducted, and these commenced 24 h after “spin-up”, when no further drainage of
water from the base of the sample was observed. Emptying
of the channel at the end of the test series revealed evidence
of slightly moist sand (with a water content of 2.5 ± 0.5%)
in a 50 mm thick layer adjacent to the sample base, indicating that completely dry conditions had not been achieved.
The testing schedule, which is summarized in Table 1, included 18 separate pile installations in the sand, 14 of which
had a final embedment depth of 120 mm. The investigation
examined the effects of three modes of installation explicitly,
as follows:
(i) Monotonic installation: The piles were pushed into the
sand continuously at a rate of 0.2 mm/s, with a brief
pause at a tip depth of 60 mm to allow a static load test
to be conducted.
(ii) Jacked installation: The piles were installed in a series
of jacking strokes. For each stroke the piles were pushed
at 0.2 mm/s for a distance of 2 mm, followed by extraction at 0.005 mm/s until the pile head load was zero.
Each “jacking stroke” resulted in a net penetration of
between 1 and 1.5 mm (with the lower net penetration
being typical toward the end of installation, because of
the higher rebound on unloading).
(iii) Pseudo-dynamic installation: The piles were installed in
a series of downward jacking increments of 2 mm at
0.2 mm/s, followed by extraction by 1.5 mm at
0.2 mm/s; the extraction component simulated the rebound experienced by driven piles as the reflected tension wave approaches the pile head. Each cycle resulted
in a net penetration of 0.5 mm.
Static compression load tests (performed at 0.005 mm/s)
were conducted at embedded pile lengths of 60 and 120 mm
for the 50g tests and at an embedment of 60 mm for the
150g tests. The maximum embedment (of 120 mm) ensured
© 2005 NRC Canada
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Can. Geotech. J. Vol. 42, 2005
Fig. 3. Schematic drawing and photo of instrumented centrifuge model pile.
that the piles were at least 60 mm (≈7B) above the base of
the drum channel. Tension tests followed the compression
tests on the 120 mm long piles.
It is noteworthy that a preliminary experiment indicated
no difference in penetration resistance when the monotonic
installation rate was varied between 0.005 and 0.2 mm/s. All
pile installations and load tests could therefore be considered
fully drained.
Sand properties
Properties of the sand used in the experiments are summarized in Table 2. This sand is produced commercially
by Imdex Ltd., in Australia, and is a natural, subrounded,
fine–medium silica sand. The interface friction angle (δ) between the sand and the model pile (where tan δ = ratio of
shear to normal effective stress) was of importance to the
test interpretation, and therefore 16 direct shear, CNL interface tests were performed, using a steel interface with the
same roughness as that of the pile (i.e., Rcla ≈ 0.6 µm) for a
range of initial sand relative densities (Dr) and normal effective stresses (σ ′n). Typical plots of mobilized interface friction angle and vertical displacement against horizontal
displacement are shown in Fig. 4a; all peak and constant
volume interface friction angles measured (δ p and δ cv) are
plotted in Fig. 4b.
No systematic variation of δ with σ ′n was observed for the
investigated σ ′n range of 50–150 kPa. The mean measured δ p
values (for Dr > 0.5) and δ cv values of 16° and 12.5°, respectively, are comparable to δ p and δ cv values of 18.4° and 11°,
respectively, reported by Frost et al. (2002) in similar experiments with dense, but coarser, sand (D50 = 0.72 mm). De-
spite the relatively smooth interface, all samples with Dr >
0.5 dilated during shear and attained a maximum dilation of
5–10 µm before reaching constant volume conditions. This
small measured change in sample height is over 10 times the
Rcla value and cannot therefore be associated with the soil
particles lifting as a rigid body out of the troughs on the
steel surface. Peak interface friction angles were developed
at horizontal shear box displacements of <0.2 mm; constant
volume shearing and the mobilization of δ cv required a
greater displacement of 2–3 mm.
The CPT end resistance (qc) profiles measured at 50g and
150g, using a 6 mm diameter 60° cone, are plotted in Fig. 5a.
Comparison of these profiles indicates that qc varies in proportion to (σ ′v)0.8±0.05, assuming that suction pressures within
the sand were zero and that, hence, total and effective vertical stresses were equivalent. Application of the relationship
proposed by Lunne and Christoffersen (1983) for normally
consolidated sands, which assumes that qc varies with
(σ ′v)0.7, suggests that the relative density (Dr) increases with
depth, from ≈20% near the sample surface to ≈80% at a
depth of 60 mm and to ≈90% at 120 mm (see Fig. 5b). This
distribution of Dr may be attributed to the fixed height of the
feed nozzle above the channel and hence to the progressive
reduction in the fall height of the sand during deposition.
In addition to the CPT qc data showing compatibility between the 50g and 150g levels, the fact that the CPT qc values were found not to vary with time over the complete test
series (which lasted 9 days) provides further evidence of the
absence within the sand of any significant suction pressures
arising from the sample formation process (described previously).
© 2005 NRC Canada
1043
150
1
J
Yes
No
No
Centrifuge results
50
1
P-D
Yes
Yes
Yes
50
1
P-D
Yes
Yes
Yes
50
1
M
Yes
Yes
Yes
50
1
J
Yes
Yes
Yes
50
1
P-D
Yes
Yes
Yes
50
1
J
Yes
No
No
50
2
J
Yes
Yes
Yes
50
6
J
Yes
Yes
Yes
150
6
J
Yes
No
No
150
2
J
Yes
No
No
Lateral stresses during installation (␴hc and ␴hm)
Lateral stresses recorded when the piles were stationary
(σ hc) and maximum values recorded when piles were moving (σ hm) during each stage of the jacked and pseudo-dynamic
installation are summarized in Fig. 6. The plotted stresses
are mean values derived from four separate pile installations
(e.g., tests T1, T4, T5, and T10 for monotonic installation;
see Table 1). The reliability of all σ h measurements was investigated in statistical analyses performed by Ong (2003),
who found the coefficient of variation (COV) of stresses recorded at any specific depth and h/B value for a given pile
installation method to be ≈0.12; the stresses measured by
different sensors at the same h/B value (i.e., those at h/B = 1
and 3; see Fig. 3) showed a similar COV.
The values of σ hc are clearly dependent on the mode of
pile installation and on the relative depth of the pile tip (h).
The lowest σ hc values were recorded during the two-way cycling imposed by pseudo-dynamic installation and at large h
values (where the sand adjacent to the pile shaft was subjected to a large number of shearing cycles during the installation process). Despite the low σ hc values, the stresses
increased significantly during installation increments to
reach σ hm values that were often more than 10 times larger
than the stationary values. The stress changes (∆σ hi = σ hm –
σ hc) increased with depth and reflected the CPT qc profile.
Note: M, monotonic installation; J, jacked installation; P-D, pseudo-dynamic installation.
50
1
M
Yes
Yes
Yes
g level
Pile aspect ratio (W/B)
Installation method
Compression test at L = 60 mm
Compression test at L = 120 mm
Tension test at L = 120 mm
50
1
J
Yes
Yes
Yes
50
1
P-D
Yes
Yes
Yes
50
1
M
Yes
Yes
Yes
50
1
M
Yes
Yes
Yes
50
1
J
Yes
Yes
Yes
50
1
J
Yes
Yes
Yes
T9
T2
T1
Test No.
Table 1. Drum centrifuge pile test programme.
T3
T4
T5
T6
T7
T8
T10
T11
T12
T13
T14
T15
T16
T17
T18
Lehane and White
Lateral stress changes during installation (⌬␴hi)
The lateral stress increases measured for each 2 mm penetration increment used during jacked and pseudo-dynamic
installation (∆σ hi) are compared in Fig. 7, in a format that
allows examination of the effects of pile aspect ratio, pile installation method, and stress level. The following is evident:
(i) The ∆σ hi values measured at a given sensor location
(denoted by h/B) generally decrease as the aspect ratio
(W/B) of the pile increases (Fig. 7a). This trend is consistent with the geometric dependence of the lateral
stiffness constraining dilation at the interface, which is
significantly higher for a square pile than for a wall; the
term 4G/D governs the confinement around a cylindrical
pile in an elastic medium (eq. [1]), whereas the confinement as the pile widens toward the case of a plane strain
strip tends to zero (Davis and Selvadurai 1996).
(ii) For piles (with W/B = 1) installed in the
pseudo-dynamic mode, ∆σ hi values are lower than for
jacked piles for sensors at h/B < 6 (Fig. 7b). This may
be because, over the early stages of cycling (i.e., when
h/B is low), the more severe (two-way) cycling imposed
by pseudo-dynamic installation leads to lower dilation
at the interface (for the imposed pile displacement of
2 mm).
(iii) The ∆σ hi values recorded at 150g are typically 1.5–2.0
times those measured at 50g (Fig. 7c). Such ratios
would be expected when the degree of dilation at the interface is not strongly dependent on the stress level and
is relatively low, as for these cases, the lateral soil stiffness constraining dilation will vary with the stress level
raised to a power of less than unity. For example, if the
operational stiffness is a fixed fraction of G0, the normalization for G0 employed in Table 2 suggests that the
© 2005 NRC Canada
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Can. Geotech. J. Vol. 42, 2005
Table 2. Properties of sand used in drum centrifuge experiments.
Mean effective particle size, D50 (mm)
Uniformity coefficient, D60 /D10
Maximum void ratio, emax
Minimum void ratio, emin
Constant volume friction angle, φ ′cv , measured under triaxial conditions (°)
Peak triaxial compression friction angle, φ ′p , at Dr = 90% (°)
Maximum shear stiffness, G0 /( p′ × patm)0.5 at Dr = 90% at mean effective stress of p′
0.18
2.0
0.76
0.49
34
44
1100
Note: Values reported by O’Loughlin and Lehane (2003); patm = atmospheric pressure = 100 kPa.
Fig. 4. CNL interface shear box tests: (a) typical variations measured in three tests; (b) summary of δ angles measured as a function
of sample Dr.
ratio between ∆σ hi values at 150g and ∆σ hi values at
50g would be (150/50)0.5 = 1.73; this value is in agreement with the ratios plotted in Fig. 7c.
Lateral stresses during static load tests
Static compression and tension tests were conducted on a
number of piles after installation to a final penetration depth
of 120 mm. Typical variations of lateral stress (σ h) with pile
head displacement (wp) recorded in the tension tests, for
each of the three modes of installation, are shown in Fig. 8.
It is apparent that peak σ h values are not attained at 2 mm
movement, implying that the installation σ hm and ∆σ hi values (plotted in Figs. 6 and 7) do not represent fully mobilized maximum stresses. The marked influence of the
installation method on the variation of σ h with wp is apparent. Greater overall increases in σ h were observed following
pseudo-dynamic installation than following monotonic installation. This response suggests that the cyclic installation
© 2005 NRC Canada
Lehane and White
1045
Fig. 5. (a) CPT soundings in drum sample; (b) Dr assessment for drum sample.
methods create either greater dilation during loading of the
pile or stiffer confinement as a result of densification of the
surrounding soil. These measurements of lateral stress are
consistent with the head load measurements, which show the
pullout capacity of the monotonically installed pile to be
only 60% of that of the other piles.
Profiles of ultimate lateral stress (␴hf)
Typical profiles of stationary and ultimate lateral stresses
(σ hc and σ hf) recorded in tension and compression tests are
shown in Fig. 9. The ultimate values of lateral stress, σ hf,
were mobilized at a pile head displacement of between about
5 and 8 mm. It is seen that despite the higher initial lateral
stresses acting on the monotonically installed pile, the values
of σ hf for the jacked and pseudo-dynamically installed piles
are slightly higher. When the piles’ tension capacities were
combined with best-fit (linear) σ hf profiles derived from the
four σ hf measurement levels, it was found that the ultimate
interface friction angle mobilized in tension was 18° for the
monotonically installed pile and 16.5° for the jacked and
pseudo-dynamically installed piles. These δ angles are
higher than those recorded in interface shear box tests
(where δ p = 17° and δ cv = 12.5°), suggesting that the recorded lateral stresses may be under-registered as a result of
cell action. Higher δ values of between 16° and 18° were
measured at maximum shear stress in CNS interface shear
tests (discussed below), indicating that the degree of
under-registration is not likely to be significant.
The maximum lateral stress (σ hf) profiles measured at ultimate conditions in the compression tests (Fig. 9a) show
trends broadly similar to those observed in tension tests with
maximum values measured at some distance above the pile
tip; this profile was also observed in centrifuge tests on
monotonically installed piles reported by Klotz and Coop
(2001). The σ hf values in the compression tests are greater at
a depth of 66 mm and lower at a depth of 93 mm than the
corresponding values recorded in the tension tests.
Insights from CNS interface shear tests
As discussed with reference to Fig. 1, dilation of the sand
at the pile interface, combined with the restraint provided by
the surrounding sand mass, may explain the large lateral
stress increases observed during pile loading in the centrifuge tests. A number of interface shear tests were performed
under CNS conditions to examine the dominant role of such
stress changes on shaft friction mobilized in the centrifuge
tests.
The CNS value, kn, relevant to shaft loading conditions is
given by eq. [1]. The equivalent pile diameter (D) in terms
of area for the centrifuge pile is ≈10.1 mm, and if the dilation is low, kn may be evaluated using the very small strain
value (G0). However, for the ∆t value of 10 µm seen under
CNL conditions in Fig. 4, the cavity strain, ∆t/D, is ≈0.1%,
and the operational G value may be expected to be about
0.4G0 (Fahey et al. 2003). This is a simplification that ignores the stress and strain changes imparted by pile installa© 2005 NRC Canada
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Can. Geotech. J. Vol. 42, 2005
Fig. 6. Lateral stresses recorded during (a) jacked pile installation; (b) pseudo-dynamic installation. Note that these are average values
derived from four separate installations.
tion. On this basis and adopting the expression in Table 2
for the undisturbed G0 value, one can estimate the values of
kn for the centrifuge piles; these estimates were in the region
of 3000–4000 kPa/mm below a depth of 60 mm in the 50g
tests. The latter kn value was used in the CNS tests discussed
here.
The CNS tests used smooth steel interfaces with the same
roughness and texture as the centrifuge piles had. The response of two dry sand samples with Dr = 0.7 and an initial
normal stress (σ ′n) of 400 kPa during monotonic shearing to
failure is shown in Fig. 10. Sample 1 was sheared directly to
failure and showed a behaviour similar to that of the samples
tested under CNL conditions (see Fig. 4), except for the perhaps surprising trend of the initially dense sample to contract under shear, with a consequent reduction in normal
stress; such contraction may be a result of the high initial
normal stress level. To simulate the centrifuge pile installation prior to monotonic shearing to failure, sample 2 was
first subjected to 50 two-way shearing cycles with a displacement amplitude of 0.2 mm. The sample experienced a
net contraction during each cycle, the magnitude of which
reduced as the number of cycles increased.2 After 50 cycles,
the normal stress had reduced to 175 kPa from the initial
value of 400 kPa, as a result of a net sample contraction of
56 µm. This reduction in σ n is consistent with the trend evident in Fig. 6 of stationary lateral pile stresses (σ hc) reducing with increasing distance above the pile tip (h). For
example, at a depth of 90 mm during (two-way)
pseudo-dynamic installation, σ hc reduced from 29.5 kPa at
h/B = 1, where the sand had already been subjected to 18 cycles, to 9 kPa at h/B = 3, where the sand had undergone 81
cycles. White and Lehane (2004) showed that cycling with
2
consequent contraction at the interface is the primary mechanism leading to the reduction of σ hc with h.
As seen in Fig. 10, the response of sample 2 while being
sheared to failure after cycling is strongly dilatant and in
sharp contrast to the response of sample 1. Although the mobilized interface friction angles are similar, the relative displacement to reach peak shear stress for sample 2 is far
greater than that for sample 1. The dilation of sample 2
reaches a value of 15 µm at a relative displacement of 6 mm,
by which point σ n has increased to 240 kPa and the maximum shear stress is about 82 kPa, only 10kPa less than the
ultimate shear resistance of sample 1. The increased
dilatancy of sample 2 after cycling is almost sufficient to
compensate for the reduced normal stress prior to shearing
to failure. A third sample (sample 3) was prepared and
tested under the same conditions as sample 2, except in this
case the sample was subjected to 200 cycles prior to
monotonic shearing to failure. This cyclic history caused a
rate of reduction in normal stress comparable to that of sample 2, with σ n reducing from 400 kPa to 110 kPa after 200
cycles. However, the maximum shear stress recovered at
6 mm relative displacement under monotonic shearing was
≈17 kPa lower than that for sample 2; this sample also experienced a lower maximum dilation of 10 µm.
The overall behaviour of the samples in the CNS interface
tests is summarized in Fig. 11 on axes of sample contraction
against normal stress. The test paths follow diagonal lines on
these axes, as enforced by the CNS condition. During the
low-amplitude cycles applied to samples 2 and 3, the samples contracted within the shear band adjacent to the interface. The rate of contraction decreased with increasing cycles,
as evidenced by the 18 µm contraction of sample 1 when
The contraction and shear resistance observed over the first half cycle were identical to those seen in the monotonic test on sample 1, indicating that both samples had the same initial density.
© 2005 NRC Canada
Lehane and White
1047
Fig. 7. Ratios of lateral stress increases measured during installation.
sheared directly to failure, compared with the 56 µm over 50
cycles for sample 2 and a further 17 µm of contraction accumulated by sample 3 over the additional 150 cycles. This
sample contraction is not fully recoverable, although samples 2
and 3 do dilate significantly when sheared to failure.
Discussion
CNS interface tests and pile tests
The behaviour observed in CNS interface shear tests displays strong parallels with the lateral stress measurements
recorded in the centrifuge pile experiments. In particular, it
is apparent that
(i) cycling leads to a reduction in normal stress (e.g., compare Fig. 11 with Fig. 6, noting that an increased h
value equates to a higher number of loading cycles during jacked and pseudo-dynamic installation);
(ii) the magnitude of the increases in normal stress during
monotonic shearing to failure increases with the number
of preceding cycles (see Figs. 9 and 11); and
(iii) larger relative displacements are required to mobilize
maximum shear stresses following cycling (see Figs. 8
and 10).
These observations support the analogy depicted in Fig. 1
and are consistent with the form of eq. [1]. The lateral stress
changes and their dependence on the direction of axial loading (tension or compression) are not explained by Poisson’s
effect (as modelled by de Nicola and Randolph 1993), arising as a result of an increase in pile radius during compression loading and a reduction in pile radius under tension
loading. Calculations indicate that the maximum applied pile
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Can. Geotech. J. Vol. 42, 2005
Fig. 8. Lateral stress variations during static tension load tests after monotonic, jacked, and pseudo-dynamic installation of piles.
© 2005 NRC Canada
Lehane and White
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Fig. 9. Lateral stress profiles before and at ultimate capacity in static load tests.
Fig. 10. Response indicated by samples 1 and 2 in CNS interface tests.
head loads in the experiments led to an increase in the centrifuge pile equivalent radius of about 0.1 µm in compression and a radius reduction of just 0.01 µm in tension tests.
If this mechanism was the only one contributing to lateral
stress changes, one would expect reductions in ∆σ h in tension tests and increases in compression tests with magnitudes that were 10 times larger than the reductions in tension
tests; such trends differ considerably from those indicated in
the centrifuge tests.
Although the centrifuge tests showed that the stiffness of
the sand mass and the pile geometry control the lateral stress
changes on the pile shafts, the tests also indicated that this
stiffness value is unlikely to be constant as in the case of a
CNS test. For example, the nonlinear nature of the σ h versus
wp relationships plotted in Fig. 8, particularly at large wp
values, indicates that if the dilation rate is roughly constant
during shearing, the lateral stiffness is not constant and decreases with the increasing cavity strain imposed by dilation.
In addition, ultimate lateral stresses (σ hf), such as those plotted in Fig. 9a, do not show a strong dependence on the pile
installation mode, suggesting that the lateral stiffness at
large pile displacements is also relatively independent of the
installation mode. A schematic representation of the
stress–strain history of sand elements close to the pile shaft,
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Fig. 11. Summary of normal stress–volume paths during CNS
tests.
Can. Geotech. J. Vol. 42, 2005
Fig. 12. Postulated stress–strain paths followed by sand elements
close to a displacement pile.
Fig. 13. Comparison of lateral stresses measured in the centrifuge and with those obtained in field tests at Dunkirk.
consistent with these observed trends, is shown in Fig. 12. It
can be inferred that cyclic push-in pressuremeter tests may
provide the best means of assessing lateral stresses on displacement piles.
Comparison with field behaviour
Equation [1] predicts that the magnitude of the lateral
stress increases due to dilation under shear varies inversely
with the pile diameter. Although the centrifuge model pile
tests did not specifically examine the effect of pile diameter,
some insights into the diameter effect may be obtained by
comparing the σ h data for jacked piles installed at 50g with
results obtained by Chow (1997) using the 100 mm diameter
Imperial College pile (ICP) in the dense medium sand at
Dunkirk, France. The equivalent prototype pile length and
the depth to lateral stress sensors of the centrifuge pile were
virtually the same as those used in Dunkirk. As shown in
Fig. 13, the CPT qc values below a depth of 3 m for both
pile experiments were also in reasonable agreement.
The stationary and ultimate lateral effective stresses (σ ′hc
and σ ′hf ) recorded in the experiments are plotted in Fig. 13
(assuming, in the centrifuge, that suction pressures in the
© 2005 NRC Canada
Lehane and White
sand are negligible and hence that the effective and total
stresses are equivalent). It may be seen that the two sets of
lateral stress measurements differ significantly, despite the
similarity between the experiments. The σ ′hc stresses for the
centrifuge pile are significantly lower than those measured
at Dunkirk. This is thought to be primarily because the number of jacking cycles imposed on the centrifuge piles was
more than 10 times the number imposed at Dunkirk; some
under-registration of lateral stresses in the centrifuge piles
due to cell action may also contribute to the discrepancy. Although the σ ′hc values are lower, the σ ′hf values for the centrifuge piles are generally much larger than the field-scale
measurements. The result is that the centrifuge-scale ∆σ ′h
values (σ ′hf – σ ′hc ) are 10 times those measured at field scale
at depths of 4.7 and 5.6 m and 4 times those measured at
3.3 m depth. This factor of 10 corresponds to the ratio of the
piles’ (equivalent) diameters and supports the general form
of eq. [1] and the inference that lateral stress increases vary
inversely with pile diameter. Some deviation from this factor
of 10 may be caused by other factors: (i) the higher lateral
stiffness surrounding the ICP, as a result of the lower cavity
strains induced by dilation; (ii) the higher dilation adjacent
to the Dunkirk pile shaft, a result of the greater surface
roughness of the ICP (≈10 µm centreline average roughness); and (iii) the more dilatant response following the
higher level of cycling imposed in the centrifuge tests.
It is of interest to note that the pile displacement required
to develop maximum shaft capacity was ≈3 mm for both the
centrifuge and the Dunkirk piles. Such insensitivity of the
required relative displacement between the pile and sand to
the absolute pile diameter, which is consistent with the existence of a narrow shear band at the pile–sand interface, is a
further characteristic to be accounted for when one is extrapolating to full-scale conditions from laboratory-scale test piles.
Conclusions
The lateral stress changes that take place during pile loading have a dominating influence on the shaft friction that can
develop on small-scale piles in sand. The measured stress
changes are shown to be controlled by the radial stiffness of
the sand mass and the dilation of a shear band at the
pile–sand interface. Useful insights into the variations of lateral stresses can be obtained in CNS interface shear tests, as
the boundary conditions imposed in these tests approximate
those at a pile–sand interface. Reasonable estimations of lateral stress variations require that the CNS tests use an appropriate radial stiffness for the sand mass surrounding the pile
shaft and that a cyclic displacement history be applied that
is compatible with that imposed during displacement pile
installation. Extrapolation to full-scale conditions from
laboratory-scale piles also needs to account for the relatively
weak dependence of the displacement to attain peak shaft
capacity on the pile diameter.
Acknowledgements
The authors would like to acknowledge the centrifuge
staff at UWA, and in particular, the contribution of Danny
(Ongko Sriono) Ong to both the centrifuge test programme
1051
and the subsequent data processing. This research has been
supported by the Australian Research Council.
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