An experimental investigation into the behaviour of de-structured chalk under cyclic loading

Abstract

Low-to-medium density chalk can be de-structured to soft putty by high-pressure compression, dynamic impact or large-strain repetitive shearing. These process all occur during pile driving and affect subsequent static and cyclic load-carrying capacities. This paper reports undrained triaxial experiments on de-structured chalk, which shows distinctly time-dependent behaviour as well as highly non-linear stiffness, well-defined phase transformation (PT) and stable ultimate critical states under monotonic loading. Its response to high-level undrained cyclic loading invokes both contractive and dilative phases that lead to pore pressure build-up, leftward effective stress path drift, permanent strain accumulation, cyclic stiffness losses and increasing damping ratios that resemble those of silts. These outcomes are relatively insensitive to consolidation pressures and are distinctly different to those of the parent intact chalk. The maximum number of cycles that can be sustained under given combinations of mean and cyclic stresses are expressed in an interactive stress diagram which also identifies conditions under which cycling has no deleterious effect. Empirical correlations are proposed to predict the number of cycles to failure and mean effective stress drift trends under the most critical cyclic conditions. Specimens that survive long-term cycling present higher post-cyclic stiffnesses and shear strengths than equivalent ‘virgin’ specimens.

Full text

An experimental investigation into the behaviour of destructured
chalk under cyclic loading
TINGFA LIU,REZAAHMADI-NAGHADEH†,KENVINCK‡, RICHARD J. JARDINE
§
,
STAVROULA KONTOE||, RÓISÍN M. BUCKLEY¶ and BYRON W. BYRNE**
Low-to-medium-density chalk can be destructured to soft putty by high-pressure compression,
dynamic impact or large-strain repetitive shearing. These process all occur during pile driving and
affect subsequent static and cyclic load-carrying capacities. This paper reports undrained triaxial
experiments on destructured chalk, which show distinctly time-dependent behaviour as well as highly
non-linear stiffness, well-defined phase transformation and stable ultimate critical states under
monotonic loading. The chalk’s response to high-level undrained cyclic loading invokes both
contractive and dilative phases that lead to pore pressure build-up, leftward effective stress path drift,
permanent strain accumulation, cyclic stiffness losses and increasing damping ratios that resemble
those of silts. These outcomes are relatively insensitive to consolidation pressures and are distinctly
different to those of the parent intact chalk. The maximum number of cycles that can be sustained
under given combinations of mean and cyclic stresses are expressed in an interactive stress diagram
which also identifies conditions under which cycling has no deleterious effect. Empirical correlations
are proposed to predict the number of cycles to failure and mean effective stress drift trends under the
most critical cyclic conditions. Specimens that survive long-term cycling present higher post-cyclic
stiffnesses and shear strengths than equivalent ‘virgin’specimens.
KEYWORDS: chalk putty; cyclic loading; destructuration; triaxial; laboratory testing
INTRODUCTION
Chalk is a very soft biomicrite composed of silt-sized crush-
able calcium carbonate (CaCO
3
) aggregates. Vinck et al.
(2022) demonstrate how low-to-medium-density chalks (with
intact dry densities, IDD ,1·70 Mg/m
3
) develop stiff, brittle
and ultimately dilative behaviour when sheared from in situ
effective stress levels. However, their mechanical properties
degrade markedly under dynamic, cyclic or high-pressure
shearing, with important implications for problems such as
the design of driven piles (Carrington et al., 2011; Diambra
et al., 2014; Carotenuto et al., 2018; Buckley et al., 2020a).
Impact driving creates low-strength, destructured, chalk
putty beneath the piles’advancing tips, which spreads and
further softens around their shafts. Buckley et al. (2018) and
Vinck (2021) identified how destructuration varied with
radial distance from the axes of open steel piles at shallow
depths (above the water table), considering conditions after
driving, and after long-term ageing and load testing. The
thin annuli of putty formed around shafts on driving
provided average driving resistances 20 kPa and reconso-
lidated over time to achieve notably lower watercontents and
significantly greater shear strengths. The response of the
reconsolidated putty to monotonic and cyclic loading, as well
as interface shear, is central to addressing axial capacity and
cyclic loading performance for piles driven in chalk.
This paper explores the cyclic behaviour of reconsolidated
destructured chalk. Stress-controlled cyclic triaxial tests are
reported on material from the ‘axial–lateral pile analysis for
chalk applying multi-scale field and laboratory testing’
(ALPACA) project’s St Nicholas-at-Wade (SNW), UK pile
research site, whose geotechnical profile and chalk properties
are described by Vinck (2021). The destructured chalk’s
response to undrained cycling is interpreted with reference to
those of saturated silts and silty sands, as reported by Carraro
et al. (2003), Mao & Fahey (2003), Hyde et al. (2006), Sanin
& Wijewickreme (2006), Sag
˘lam & Bakır (2014) and Wei &
Yang (2019). Ahmadi-Naghadeh et al. (2022) report parallel
research into the intact chalk’s cyclic response under similar
cycling, identifying behaviour that differs starkly from that of
unbonded soils and compares more closely with that of rocks,
concretes or metals. Bialowas et al. (2018) and
Alvarez-Borges et al. (2018, 2020) report earlier testing on
reconstituted SNW chalk.
CHALK PUTTY FORMED BY DYNAMIC
COMPACTION
Laboratory dynamic compaction, applied at in situ water
content, destructures low-to-medium-density chalk in an
analogous way to pile driving (Doughty et al., 2018) and
provides uniform batches for laboratory testing. Puttified
Department of Civil Engineering, University of Bristol, Bristol,
UK; formerly Department of Civil and Environmental Engineering,
Imperial College London, London, UK
(Orcid:0000-0002-5719-8420).
†Formerly Department of Civil and Environmental Engineering,
Imperial College London, London, UK; now Department of
Construction Engineering and Lighting Science, School of
Engineering, Jönköping University, Jönköping, Sweden
(Orcid:0000-0002-2215-441X).
‡Department of Civil and Environmental Engineering, Imperial
College London, London, UK (Orcid:0000-0002-0990-0895).
§ Department of Civil and Environmental Engineering, Imperial
College London, London, UK (Orcid:0000-0001-7147-5909).
|| Department of Civil and Environmental Engineering, Imperial
College London, London, UK (Orcid:0000-0002-8354-8762).
¶ School of Engineering, University of Glasgow, Glasgow, UK
(Orcid:0000-0001-5152-7759).
** Department of Engineering Science, Oxford University, Oxford,
UK (Orcid:0000-0002-9704-0767).
Manuscript received 14 July 2021; revised manuscript accepted
12 January 2022.
Discussion on this paper is welcomed by the editor.
Published with permission by the ICE under the CC-BY 4.0 license.
(http://creativecommons.org/licenses/by/4.0/)
Liu, T. et al.Géotechnique [https://doi.org/10.1680/jgeot.21.00199]
1
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specimens were formed for this study through compaction
of block samples preserved from 1·4 m depth, whose
unconfined compression strengths (UCS) exceeded 3 MPa,
despite their 29–30% initial natural water contents. Up to
150 blows were applied at 2 s intervals with a 4·5 kg
ram and 300 mm drop height to intact lumps contained
in a 100 mm dia. mould to produce 0·3 litre batches of
chalk putty. Mixing every 50 blows ensured uniformity,
and the process, which took 10 min, involved slight
drying with 1% water contents reductions. Index testing
indicated 9 ± 3 kPa fall-cone undrained shear strengths,
liquid and plastic limits of 30·6% and 24·2%, respectively,
grain specific gravity G
s
= 2·71 and median grain size
D
50
3·0 μm.
Figure 1 presents constant-rate-of-strain (CRS; at 0·6%/h)
oedometer compression curves for intact and destructured
putty chalk samples. Also shown is a test on samples
reconstituted by re-hydrating pulverised dried chalk to 1·4
times the liquid limit. The intact and reconstituted com-
pression (NCL*) oedometer curves of natural clays reflect
their different structures (Burland, 1990). Smith et al. (1992)
employed the ratio of the intact soil’s vertical effective stress
at yield σ′
vy
to that projected onto the reconstituted curve at
the same void ratio as a scalar ‘oedometer sensitivity’
measure of the clay’s structure. Fig. 1 indicates an oedometer
‘sensitivity’of 24 for the natural chalk. The intact chalk
shows S
u
1·2 MPa at this depth (Vinck et al., 2022), which
suggests a higher undrained shear strength sensitivity 130.
The intact CRS trace suggests that oedometer sensitivity
declines towards unity as pressures increase post-yield and
the e–σ
v
′trace curves towards the NCL* whose compression
index C
c
*
= 0·18. The fully destructured putty starts at a
lower liquidity index than the reconstituted chalk, but
follows a similar trend once σ
v
′.50 kPa, falling far below
the intact sample’s curve, although exhibiting similar
unloading curves and swelling indices C
s
0·01. The putty
exhibited markedly time-dependent one-dimensional (1D)
compression behaviour in parallel stage loaded oedometer
tests that gave secondary compression coefficients
C
αe
=Δe/Δlog
10
(t) = 0·003 over the 100 ,σ
v
′,400 kPa
range and a C
αe
/C
c
= 0·06 ratio, which is remarkably high
for an inorganic soil (Mesri & Vardhanabhuti, 2006). As
shown later, triaxial specimens prepared from the putty
developed significant volumetric strains under relatively
modest isotropic consolidation stresses and attained specific
volume–mean effective stress (v–p′) states well below (or
‘dryer than’) the destructured chalk followed in its CRS
oedometer test. These findings and related features are
discussed later in relation to the state parameter framework
for sands (Been & Jefferies, 1985).
TRIAXIAL TESTING ON PUTTY SAMPLES
Apparatus and procedures
Cyclic triaxial tests were performed with automated
hydraulic stress-path apparatus. A suction cap and half-ball
connection system helped to align the (initially soft) specimens
with the load cells and minimise tilting and bedding. Layered
latex discs and high-vacuum grease deployed at the specimen
tops and bottoms reduced end constraint. Putty was placed in
5–10 g increments into a split mould, lined with a latex
membrane, pre-set on the triaxial base platen. Care was taken
to eliminate macro-voids and produce uniform 38 mm dia.,
80 mm high, specimens with flat ends, topped with poly
(methyl methacrylate) (PMMA) caps. The soft specimens’
ability to maintain regular shapes and resist disturbance
during mould dismantling and instrumenting was improved
through an ‘in-mould’isotropic consolidation stage
implemented by maintaining a triaxial cell-to-back-pressure
difference of 70 kPa for 15 h under drained conditions, which
led to volume strains of 10%. The resulting, relatively robust,
specimens’dimensions were then measured and sets of linear
variable differential transducer (LVDT) local strain sensors
were mounted, including a radial-strain belt.
The specimens were saturated by applying 300–400 kPa
back-pressure, maintaining p′= 20 kPa until B.0·97, fol-
lowed by isotropic consolidation at 1 kPa/min to reach the
targeted mean effective stresses ( p′
0
), which led to average
C
αe
values (0·0034 and 0·0046) under p′levels of 200 and
400 kPa, respectively. Creep periods of 8–12 days allowed
residual axial straining to diminish to ,0·005%/day, 1000
times lower than the 5%/day applied in subsequent mono-
tonic shearing stages. Samples consolidated to p′
0
= 200 kPa
and 400 kPa had post-creep (pre-shearing) void ratios of
0·63 and 0·59, respectively, corresponding to water contents
(23·3% and 21·8%) that, as noted in the putty zone around
driven pile shafts, fell well below those of the undisturbed
intact chalk and far below the oedometer curves shown in
Fig. 1.
Test programme and code
Five monotonic ‘control’tests characterised the putty’s
response to undrained shearing (at 5% axial strain/day)
after isotropic consolidation to p′
0
= 70, 200 and 400 kPa
followed by drained creep, that aimed to match the medium
to high range of radial effective stresses (10 ,σ′
rf
,500 kPa)
interpreted around the ALPACA pile shafts after full ageing
(Buckley et al., 2020b). Specimen details and testing
conditions are outlined in Table 1.
The subsequent cyclic programme focused mainly on
11 tests at p′
0
= 200 kPa, supplemented by four experi-
ments cycled from p′
0
= 400 kPa with, naturally, lower initial
void ratios. Cell pressures were held constant, while deviator
stresses varied sinusoidally about a fixed q
mean
by the
amplitudes q
cyc
listed in Table 2. Note that q=(σ′
v
–σ′
h
) and
p′=(σ′
v
+2σ′
h
)/3, and that q
mean
and q
cyc
are also shown as
ratios of the putty chalk’sp′
0
and 2S
u
values to aid
interpretation. Relatively long periods of 300 s were
adopted to enable full control, pore-pressure equalisation
and detailed logging of all parameters. Recalling the
material’s time-dependent compression behaviour, the tri-
axial tests may overestimate the degree to which cycling
1·1
1·0
0·9
0·8
0·7
0·6
0·5
0·4
0·3
Void ratio, e
110
De-structured
Reconstituted
Intact
100
σ'
v: kPa
Intact σ'
vy
NCL∗ (Cc
∗ = 0·18)
1000 10 000 100 000
(All specimens from 1·4 m bgl.)
Fig. 1. One-dimensional compression behaviour of destructured
(puttified), reconstituted and intact chalk established from CRS
(constant rate of strain; 0·6%/h) tests
LIU, AHMADI-NAGHADEH, VINCK, JARDINE, KONTOE, BUCKLEYAND BYRNE2
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affects offshore structures under typically shorter (perhaps
10 s) period cyclic loading. Each test’s code is composed as
(a) letter ‘D’denotes destructured chalk
(b) letter ‘M’signifies monotonic and letters ‘Cy’indicate
cyclic loading
(c) group letters A, B, C or D signify the level of maximum
qapplied, in ascending order
(d) a numeral signifies the applied q
cyc
level in the A to D
groups, in ascending order; letter ‘X’represents the
single case where negative q
mean
was applied
(e) letter ‘E’signifies the test series performed at the
elevated p′
0
of 400 kPa.
MONOTONIC TESTS
The putty’s response to undrained triaxial compression
(TXC) and extension (TXE) is displayed in Fig. 2, plotting
zoomed-in q–p′effective stress paths and deviatoric stress
(q)–axial strain (ε
a
) trends over the small to medium strain
range. Specimens exhibited broadly linear elastic behaviour
up to ε
a
limits of 0·002% and 0·003% for the p′
0
= 200 and
400 kPa tests, respectively, corresponding to increments
Δq23·1 and 43·0 kPa with an average Δq/(2S
u
)0·22.
The q–p′effective stress paths rose nearly vertically
upon compression and extension, suggesting that the
re-consolidated (mildly aged) putty’s initial stiffness response
was largely isotropic (Vinck et al., 2022).
The effective stress paths rotated to follow leftward
(contractive) stages after mobilising modest ‘peak’resistances
(after relatively small strains, ε
a
,0·2%) and showed strain
softening as shearing continued up to phase transformation
(PT) points at which their paths rotated abruptly and
climbed towards ultimate (critical state) conditions (see
Table 1). Continued straining led to markedly higher ultimate
strengths as the specimens attempted to dilate from their
states positioned well below the normal compression line
indicated in Fig. 1.
As discussed later, the chalk putty’s resistance to cyclic
loading is dominated by its pre-PT behaviour. The peak
pre-PT q(
PT
) points were taken as indicating the operational
monotonic shear strengths (2S
u
), giving rounded S
u
values of
50 kPa and 100 kPa for the p
0
′= 200 and 400 kPa tests,
respectively, with S
u
/p′
0
= 0·25. Specimens undergoing exten-
sion developed similarly contractive pre-PT responses to
shearing, followed by dilation after reaching PT, giving
broadly similar, yet not fully symmetric stress paths and shear
strengths to the compression tests, despite their different σ
1
directions and b=(σ
2
–σ
3
)/(σ
1
–σ
3
) ratios (or Lode angles θ).
While the isotropically consolidated putty did not manifest
any significant combined effect of anisotropy or bratio
on its pre-PT shearing behaviour, the extension tests’dilative
post-PT stages were truncated prematurely by localised
necking from ε
a
7·5% onwards that obscured any trend
towards stable ultimate critical states.
Table 1 summarises the specimens’linear elastic
(maximum) Young’s moduli (E
max
u
), their PT stress points,
large-strain ultimate (critical state) states and the correspond-
ing strains. The q/p′ratios at PT, critical state (in com-
pression) and ultimate failure in extension in the (inherently
more reliable) higher pressure tests were 1·05, 1·27 and
0·86, respectively. The latter two ratios both correspond to
ϕ′
cs
31°, matching the angle found in high-pressure tests on
intact samples.
Table 1. Summary of undrained monotonic triaxial tests: maximum Young’s moduli, stress conditions and the corresponding axial strains (in
brackets) at phase transformation (PT) and ultimate states
Test e*p′
0
:
kPa Eu
max:
MPa
Eu
max
pref

p′
0
pref

05
†
q
(PT)
:kPa
(ε
a
:%) p′
(PT)
:
kPa q
(ult)
:kPa(ε
a
:%) p′
(ult)
:
kPa (q/p′)
ult
ϕ
ult
′:
degrees
DM-C1 0·714 70 643·1 7637·0 42·6 (0·6%) 39·9 309·7 (30·9%) 229·4 1·35 31·6
DM-C2 0·648 200 1195·3 8397·6 106·1 (1·4%) 100·3 606·1 (24·0%) 480·8 1·26
DM-C3 0·606 400 1472·5 7315·1 208·9 (1·2%) 198·3 1618·5 (25·0%) 1273·0 1·27
DM-E1 0·609 200 1114·1 7827·2 132·1 (1·1%) 149·1 207·4 (7·0%) 233·4 0·89 30·1
DM-E2 0·580 400 1393·1 6920·7 256·9 (1·0%) 319·9 364·2 (7·0%) 453·9 0·80
*Void ratio prior to undrained shearing; calculated based on post-test water content measurements.
†p
ref
, reference pressure (101·3 kPa).
Table 2. Summary of cyclic triaxial test conditions and parameters
Test e*q
mean
:kPa q
mean
/(2S
u
)q
cyc
:kPa q
cyc
/(2S
u
)q
max
:kPa q
max
/(2S
u
)q
mean
/p
0
′q
cyc
/p
0
′
DCy-A1 0·644 0 0 30 0·30 30 0·30 0 0·15
DCy-B1 0·607 0 0 45 0·45 45 0·45 0 0·23
DCy-C1 0·615 30 0·30 30 0·30 60 0·60 0·15 0·15
DCy-C2 0·621 15 0·15 45 0·45 60 0·60 0·08 0·23
DCy-C3 0·659 0 0 60 0·60 60 0·60 0 0·30
DCy-CX 0·616 15 0·15 45 0·45 60 0·60 0·08 0·23
DCy-D1 0·621 79 0·79 17 0·17 96 0·96 0·40 0·09
DCy-D2 0·675 57 0·57 30 0·30 87 0·87 0·29 0·15
DCy-D3 0·648 44 0·44 44 0·44 88 0·88 0·22 0·22
DCy-D4 0·621 28 0·28 60 0·60 88 0·88 0·14 0·30
DCy-D5 0·591 0 0 75 0·75 75 0·75 0 0·38
DCy-A1-E 0·620 0 0 60 0·30 60 0·30 0 0·15
DCy-B1-E 0·587 0 0 90 0·45 90 0·45 0 0·23
DCy-C3-E 0·597 0 0 120 0·60 120 0·60 0 0·30
DCy-D5-E 0·575 0 0 150 0·75 150 0·75 0 0·38
*Void ratio prior to undrained monotonic pre-shearing or cyclic shearing; calculated based on post-test water content measurements.
THE BEHAVIOUR OF DESTRUCTURED CHALK UNDER CYCLIC LOADING 3
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CYCLIC TESTING PROCEDURES AND FAILURE
CRITERIA
As listed in Table 2, the cyclic triaxial experiments
investigated a range of one- and two-way q
mean
,q
cyc
and
q
max
conditions, including cycling into extension. The elevated
pressure (p′
0
= 400 kPa) tests concentrated on symmetrical
two-way conditions (with q
mean
= 0). The procedures mirrored
the intact chalk testing by Ahmadi-Naghadeh et al. (2022).
Target q
mean
values were applied by undrained strain-
controlled loading at a rate of 5% axial strain/day, followed
by pauses of 48–72 h in which the specimens sustained their
q
mean
values without drainage until the local axial strain rates
fell below 0·005%/day. These steps were critical for distinguish-
ing the specimens’subsequent cyclic straining from any
creep provoked by applying the q
mean
component. Fig. 3
demonstrates how axial strains developed in DCy-D1 to
DCy-D4 during their: (a) undrained monotonic pre-shearing;
(b) extended creep pauses; and (c) first applied cycle. Also
indicated are the corresponding average maximum Young’s
(E
max
u
) and secant cyclic moduli (E
sec
u,cyc
) developed over
the first peak-to-trough half cycle. The creep strains are sig-
nificant and increased with applied q
mean
to represent a large
fraction of the overall straining. The creep pauses allowed the
specimens to regain stiffness after pre-shearing and the
subsequent cyclic moduli depended primarily on the stress
amplitudes imposed. Doughty et al. (2018) and Vinck (2021)
detail the abrupt stiffness degradation shown by chalk putty
specimens; E
max
u
moduli decay by 40% from initial values
after shearing to 0·01% axial strain. They ascribe the rapid
stiffness degradation to microstructural alteration and brittle
re-cementation.
The testswhich survived to 10 000 cycles extended forseveral
weeks. All ‘surviving’specimens were sheared to undrained
monotonic failure; as shown later, stable cycling improved the
puttified chalk’s monotonic resistance and stiffness.
Undrained cyclic behaviour is often assessed in earth-
quake geotechnics through testing under symmetrical
two-way loading. The failures that define the soils’cyclic
resistance ratios (Ishihara, 1996) are defined as occurring
when specified double-amplitude (DA) axial (or shear) strain
limits are met. Failure under non-symmetrical loading
conditions is defined referring to either peak or accumulated
cyclic strains (Yang & Sze, 2011). Cyclic failure criteria and
strain limits are often tailored to reflect the geo-material’s
cyclic behaviour and the engineering problems addressed
(Wijewickreme & Soysa, 2016).
Noting that stringent deformation tolerances are
specified for offshore wind turbine design (Byrne et al.,
2017), the cyclic strain limits were set lower than is routine in,
for example, liquefaction assessment. Failure was defined by
whichever of two criteria was satisfied first
(a) criterion A: occurrence of 1% double-amplitude
(DA = ε
a, peak
ε
a, trough
) axial strain
(b) criterion B: absolute peak or trough axial strain (|ε
a
|)
exceeding 1%.
The criteria reflect chalk putty’s potentially marked stiffness
degradation under cycling. As demonstrated later, they lead
to outcomes that are compatible with other measures of
cyclic failure, including trends for pore water pressures, shear
strength reductions and damping ratios.
UNDRAINED CYCLIC TEST OUTCOMES
Table 3 summarises key outcomes from the cyclic
experiments: the axial strains and ranges of cyclic stiffness
(E
sec
u,cyc
) and damping ratio (D) experienced up to the number
of cycles (N
f
) at which failure occurred, or the final cycle for
tests that survived 10 000 cycles. Discussion on the mean
effective stress drift trends follows later.
Cycling from p′
0
= 200 kPa
Considering the tests performed from p′
0
= 200 kPa,
Fig. 4 illustrates how N
f
varies with the normalised loading
parameters q
cyc
/(2S
u
)–q
mean
/(2S
u
) and q
cyc
/(p′
0
)–q
mean
/(p′
0
).
The three unfailed cases are annotated as ‘.N
max
’where
800
700
600
500
400
300
200
100
–100
–200
–300
–400
0
q: kPa
q: kPa
0 200 400 600 800 1000 1200
p': kPa
DM-C1
DM-C2
DM-C3
DM-E1
DM-E2
DM-C1
DM-C2
DM-C3
DM-E1
DM-E2
MTE = 0·86
CS
MTC = 1·27
CS
To qult =
1618·5 kPa
qult = 1618·5 kPa
qult = 606·1 kPa
qult = 309·7 kPa
(q/p')PT = 0·05
Necking
commenced
x: Phase transformation point
1000
750
500
250
–250
–500
0
–10·0 –7·5 –5·0 –2·5 0
εa: %
(a)
(b)
2·5 5·0 7·5 10·0
Fig. 2. Triaxial compression and extension behaviour of puttified
chalk: (a) effective stress paths; (b) deviatoric stress–axial strain
response (see also details in Table 1)
120
100
80
60
40
20
–20
–40
–60
–0·01 0·01 0·02
Local axial strain, εa: %
0·03 0·04 0·05 0·06 0·070
0
q: kPa
DCy-D1
DCy-D2
DCy-D3
DCy-D4
Ave Emax : 1·32 GPa
u
Esec : 0·96 GPa
u,cyc
Esec : 1·05 GPa
u,cyc
Esec : 1·16 GPa
u,cyc
Esec : 1·33GPa
u,cyc
Fig. 3. Deviatoric stress–axial strain responses for tests DCy-D1 to
DCy-D4 during monotonic pre-shearing, creep and first cycle, also
indicating average maximum Young’s modulus in pre-shearing and
secant cyclic moduli for the first peak-to-trough half cycle
LIU, AHMADI-NAGHADEH, VINCK, JARDINE, KONTOE, BUCKLEY AND BYRNE4
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N
max
is the number of stress cycles applied. Two nominal
N
f
= 1 contour lines are plotted from (q
mean
,q
cyc
) = (0, 2S
u
)to
(2S
u
, 0) and (q
mean
,q
cyc
) = (0, 2S
u
)to(2S
u
, 0), neglecting
minimal variations in S
u
between compression and extension
(see Fig. 2) and any possible rate dependency of shear
strength between monotonic shearing at 5% per day and that
developed over the final cycle of loading.
A tentative family of curved N
f
( = 10, 30, 100, 300, 1000,
3000 and 10 000) contours that extends to q
mean
/(2S
u
)=
0·15 is included to illustrate stress interaction patterns in the
one- and two-way cycling regions of the 200 kPa p′
0
tests.
Nominal contours are shown as dashed straight lines over the
unpopulated extension region and link the contours towards a
putative lower q
cyc
/(2S
u
) limit of 0·15. The lower level, high N
f
,
contours show less curvature and tighter spacings than those
representing high-level cycling. The interactive stress diagram
region below the N
f
= 10 000 contour represents the stable
area within which, although strains could accumulate slowly
and effective stresses reduce, cyclic failure did not occur.
As shown in Fig. 4, the contours applying in the one-way
compressive cyclic region (q
mean
q
cyc
) situated above the
N
f
= 10 000 contour, curve downwards rapidly towards the
right-hand corner (q
cyc
/(2S
u
) = 0). The interpreted two-way
contours (where q
mean
q
cyc
) confirm that chalk putty is
more susceptible to compression–extension loading than
one-way compression. Similar interactive failure schemes
were established from axial cyclic loading field tests on piles
driven in chalk by Buckley et al. (2018).
The test outcomes for the 400 kPa p′
0
tests are broadly
compatible with the contours in Fig. 4, although the higher
pressure tests developed excess pore pressures at higher rates
and failed at a significantly earlier stage in DCy-B1-E, as
detailed later. The chalk’s response to high-level cyclic loading
is demonstrated by two unstable tests, DCy-C3 and DCy-D4,
which were pre-sheared to different q
mean
but cycled with
identical q
cyc
. Figs 5 and 6 plot their stress–strain response, the
overall effective stress paths as well as zoomed-in illustrations
of six illustrative cycles prior to and shortlyafter their nominal
failure at N=N
f
. Fig. 7 shows how the secant undrained cyclic
Yo u n g ’smodulus(E
sec
u,cyc
) and damping ratio (D) evolved in
test DCy-D4, showing the following.
(a) Axial strain accumulation accelerates markedly as
cyclic failure develops. Straining tended towards a
positive ε
a
(bulging) pattern in DCy-D4, while negative
ε
a
(and necking) developed in DCy-C3. While DCy-D4
satisfied failure criteria A and B simultaneously
(at N
f
= 47), DCy-C3 met criterion B one cycle after
matching criterion A at N
f
= 65.
(b) Stress–strain curves fall initially in tight bands, fanning
out as failure approached. ‘Kinks’(as termed by
Wijewickreme & Soysa (2016)) were evident in the
post-N
f
stress–strain loops, where strain hardening
occurred and (tangent) stiffnesses increased as deviatoric
stresses cycled towards their peaks and troughs.
(c) Effective stress paths drift leftward invariably as pore
water pressures grow. The paths traversed the PT points
and slopes defined by monotonic loading (see Fig. 2),
as well as the critical state slopes M.
(d) Both contractive and dilative behaviour occurs during
individual cycles, as shown in Fig. 6. Best-fit lines drawn
through the cyclic PT points identified from the
effective stress path loops of two-way cyclic tests with
q
mean
= 0 indicate (q/p′)
PT
cyc
gradients of 0·54 and
0·38 in compression and extension, respectively,
that fall well below the monotonic PT stress ratios.
Mao & Fahey (2003) report similar findings for
calcareous silts as do Porcino et al. (2008) for an
uncemented carbonate sand under cyclic simple shear.
Table 3. Strains, pore pressure changes, stiffness and damping ratio variations during cyclic loading, considering changes from the first cycle up to the N
f
cycle, or final cycle in the unfailed tests
Test q
mean
/(2S
u
)q
cyc
/(2S
u
)q
max
/(2S
u
) Imposed cycles, N
max
N
f
*ε
a
at N
f
:% ε
a
/N
f
:% r
u
:%†Secant cyclic Eu;cyc
sec : MPa Damping ratio, D:%‡
DCy-A1 0 0·30 0·30 10 024 Unfailed 0·078 7·78 10
6
0·10!34·5 903!1166 4·80!3·70
DCy-B1 0 0·45 0·45 717 486
(A)
0·210 4·32 10
4
1·91!85·3 951!14·0 6·51!21·2
DCy-C1 0·30 0·30 0·60 10 058 Unfailed 0·085 8·45 10
6
32·1!54·1 1067!1155 9·53!8·06
DCy-C2 0·15 0·45 0·60 676 645
(B)
0·829 1·29 10
3
20·2!95·7 918!9·3 12·8!26·4
DCy-C3 0 0·60 0·60 181 65
(A)
0·023 3·54 10
4
3·86!77·2 841!23·2 13·0!21·3
DCy-CX 0·15 0·45 0·60 361 357
(A, B)
0·516 1·45 10
3
10·1!80·3 1067!13·9 4·82!19·9
DCy-D1 0·79 0·17 0·96 9600 Unfailed 0·147 1·53 10
5
42·8!67·4 1334!1444 5·56!2·95
DCy-D2 0·57 0·30 0·87 10 614 5528
(B)
0·984 1·78 10
4
40·1!82·7 1160!269·7 6·90!20·1
DCy-D3 0·44 0·44 0·88 240 183
(B)
0·926 5·06 10
3
22·2!92·4 1045!35·6 10·9!25·9
DCy-D4 0·28 0·60 0·88 58 47
(A, B)
0·523 0·011 30·3!90·2 955!21·6 11·1!25·7
DCy-D5 0 0·75 0·75 170 18 0·005 2·78 10
4
6·45!76·9 508·0!46·9 17·9!23·9
DCy-A1-E 0 0·30 0·30 10 085 Unfailed 0·036 3·57 10
6
0·40!64·2 1428!1023 4·51!7·35
DCy-B1-E 0 0·45 0·45 149 142
(A)
0·071 5·0 10
4
1·81!89·0 1236!34·3 8·15!22·1
DCy-C3-E 0 0·60 0·60 57 50
(A)
0·080 1·6 10
3
2·70!82·5 1190!57·3 12·2!24·1
DCy-D5-E 0 0·75 0·75 18 16
(A, B)
0·085 5·31 10
3
6·56!67·3 815·0!80·9 17·0!23·3
*Superscripts (A) and (B) denote the applied cyclic failure criteria. Cycling control of test DCy-D5 deteriorated as specimen softened significantly after 13 cycles.
†r
u
, pore water pressure ratio (%), defined as: r
u
=(p
0
′p′)/p
0
′=Δu/p
0
′.
‡Damping ratio calculated as: D=A
loop
/(4πA
elastic
); A
loop
–area enclosed by a stress–strain (q–ε
a
) loop for a complete sinusoidal stress cycle; A
elastic
–unloading half-cycle elastic triangle areawith height as
q
cyc
(=(q
peak
q
trough
)/2) and width as cyclic strain (= (ε
peak
ε
trough
)/2).
THE BEHAVIOUR OF DESTRUCTURED CHALK UNDER CYCLIC LOADING 5
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(e) There is systematic variation in the damping ratio and
cyclic stiffness trends. Damping ratios show maxima
near failure, followed by marked post-failure reductions
as cyclic strains increase. Doygun & Brandes (2020)
reported similar, although less abrupt, post-peak
decreases for sands.
Equivalent traces are shown in Fig. 8 for two typical
‘stable’(N
f
.10 000) tests, DCy-A1 and DCy-D1, with the
latter being pre-sheared to the highest q
mean
and both being
cycled with the lowest q
cyc
in their sub-group. The specimens
accumulated only small axial strains over 10 000 cycles,
developing ε
a
–Npatterns that can be matched by power-law
functions (ε
a
=aN
b
) with b= 0·502 for both cases. Their
stress–strain loops evolved steadily, with moderately increas-
ing cyclic stiffnesses and decreasing damping ratios, as listed
in Table 3. Applying a large number of such low-level cycles
resulted in a stable, non-linear, but principally reversible
response that enhanced the destructured chalk’s cyclic
resistances. Similar outcomes were reported for silica sands
(by Aghakouchak et al. (2015)) and stiff glacial till (see
Ushev & Jardine (2022)). The pore water pressure ratio r
u
(=(p′
0
p′)/p′
0
=Δu/p′
0
,p′
0
= 200 kPa) tended to stabilise after
2000 cycles and eventually reached 34·5% and 67·4% in
DCy-A1 and DCy-D1, respectively. The specimens’cyclic
stress path orientations correlated directly with their position
relative to the (q/p′)
PT
cyc
lines indicated in Fig. 8.
A‘transitional’response, between the above ‘stable’
and ‘unstable’styles, was observed in DCy-D2 under
q
mean
/(2S
u
) = 0·57 and q
cyc
/(2S
u
) = 0·3. Fig. 9 shows how the
specimen’s axial strain accumulated almost linearly up to
N= 4000 and accelerated rapidly up to N7000, followed by
afarslower‘near-stable’trend towards N=10 000, leading to
a large ultimate strain of 5·5%. Strain criterion A was met
when peak axial strain reached 1% at N
f
=5528, while the
strain amplitude remained far below the 1% criterion B limit
throughout. The specimen’s resistance to loading (from q
min
to q
max
) was maintained by its tendency to dilate, which
kept r
u
largely constant at 82% and the effective stress loops
settled to a stable pattern after N.7000.
Cycling from p
0
′= 400 kPa
Cycling from p′
0
= 400 kPa and p′
0
= 200 kPa (with
q
mean
= 0) provoked broadly compatible cyclic patterns.
Although the higher pressure tests developed lower (absolute)
strains and higher cyclic stiffness under similar normalised
loading levels (see Table 3), higher pore water pressure ratios
were observed. The unfailed test DCy-A1-E developed a
final r
u
twice that of its low-pressure equivalent DCy-A1
after 10 000 cycles, while unstable test DCy-B1-E developed
pronouncedly more rapid r
u
growth than DCy-B1 (see
Fig. 10). Cyclic failure was accompanied by marked and
simultaneous changes in axial strains, pore water pressures,
cyclic stiffness and damping (see Fig. 7). Fig. 10 also gives
further details on how the stress path loops evolved in tests
DCy-B1 and DCy-B1-E with reference to the (q/p′)
PT
cyc
lines indicated by the two-way cyclic tests. The cyclic PT
lines appear largely independent of p
0
′level in both triaxial
compression or extension.
Cyclic strain accumulation and stiffness trends
The specimens’(permanent) strain (captured at the end
of each full-stress cycle) accumulation, cyclic stiffness
–0·5 –0·4 –0·3 –0·2 –0·1 0 0·1 0·2 0·3 0·4 0·5
qmean/p'
0
qcyc/(2Su)
q
min
/(2S
u
) = –1
q
max
/(2S
u
) = 1
qcyc/p'
0
1·0
0·9
0·8
0·7
0·6
0·5
0·4
0·3
0·2
0·1
0
0·5
0·4
0·3
0·2
0·1
0
qmean/(2Su)
–1·0 –0·8 –0·6 –0·4 –0·2 0 0·2 0·4 0·6 0·8 1·0
p'
0 = 200 kPa cyclic failure
p'
0 = 200 kPa unfailed
p'
0 = 400 kPa cyclic failure
p'
0 = 400 kPa unfailed
DCy-D1
Nf > 9600
DCy-D2
Nf = 5528
Nf = 10 000
Nf = 3000
Nf = 1000
DCy-D3
Nf = 183
DCy-C1
Nf > 10 058
DCy-A1
Nf > 10 024
DCy-B1-E
Nf = 142
DCy-A1-E
Nf > 10 085
DCy-CX
Nf = 357
DCy-C3-E
Nf = 50
DCy-D5-E
Nf = 16
DCy-D5
Nf = 18
DCy-C3
Nf = 65
DCy-B1
Nf = 486 DCy-C2
Nf = 645
Nf = 300
Nf = 100
Nf = 1
Nf = 10
Nf = 30
DCy-D4
Nf = 47
?
Fig. 4. Cyclic interaction diagram expressed in normalised q
cyc
/(2S
u
)–q
mean
/(2S
u
) and q
cyc
/p
0
′–q
mean
/p
0
′stress space, also indicating the interpreted
contours of number of cycles (N
f
) to failure for p
0
′= 200 kPa and p
0
′= 400 kPa tests series as summarised in Table 3
150
125
100
75
50
25
0
–25
–50
–75
–100–6 –4 –2 0 2
Axial strain, εa: %
4681012
q: kPa
qcyc = 60 kPa
DCy-C3
DCy-D4 Nf = 47 Nf = 49 N = 51 N = 53 N = 55
Fig. 5. Unstable cyclic response in tests DCy-C3 and DCy-D4:
stress–strain behaviour
LIU, AHMADI-NAGHADEH, VINCK, JARDINE, KONTOE, BUCKLEY AND BYRNE6
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degradation and mean effective stress drifting patterns can
be categorised into three broad groups. Accumulated cyclic
strain trends are plotted in Fig. 11(a) for the unstable cyclic
resistance ratio ‘CRR’(q
mean
= 0) group. The specimens
developed minimal (0·025%) straining over their initial
stable stages, before trending abruptly towards negative
(extension), as cyclic failure approached, and peak-to-trough
amplitudes exceeded 1% (criterion A). Most tests developed
positive strains over their initial cycles, followed by a trend
to reverse towards extension failure. Tests DCy-D5 and
DCy-D5-E which cycled with the highest (q
cyc
/(2S
u
)) ratio of
0·75 accumulated negative strains throughout. The overall
straining patterns were consistent between the p′
0
= 200 and
250
200
150
100
50
0
–50
–100
–150
0 50 100 150 200 250
75
50
25
–25
–50
–75
0
75
100
50
25
–25
–50
0
q: kPa
p': kPa
MTXE = 0·86
MTXC = 1·27
(q/p')PT = 1·05
DCy-C3
DCy-D4
DM-C2
DM-E1
0 25 50 75 100 125 150
0 25 50 75 100 125 150
(q/p')cyc
PT
(q/p')cyc
PT
(q/p')cyc
PT
(q/p')cyc
PT
DCy-C3
Cycle start point
DCy-D4
Cycle start point
N = 69 67 65 63 61 59
N = 5149 47 45 43 41
Fig. 6. Stress paths for unstable tests DCy-C3 and DCy-D4 and the identified cyclic PT lines
30
25
20
15
10
5
0
100101
N
102
Damping ratio: %
1500
1250
1000
750
500
250
0
Damping ratio
Eu,sec
cyc
Eu,cyc : MPa
sec
Fig. 7. Damping ratio and cyclic stiffness evolution in unstable test
DCy-D4
0·20
0·15
0·10
0·05
–0·05 0 2000 4000 6000
N
8000 10 000 12 000
0
Axial strain, εa: %
Test DCy-A1
Test DCy-D1
a = 0·00085, b =0·502
a = 0·0015, b =0·502
Fitted trend, εa = aNb
(a in %)
250
200
150
100
50
–50
–100
–150
0
q: kPa
0 50 100 150 200
p': kPa
(a)
(b)
250 300 350 400
(q/p')cyc
(q/p')PT = 1·05
PT
(q/p')cyc
PT
MTXC = 1·27
MTXE = 0·86
DCy-A1
DCy-D1
DM-C2
DM-E1
Fig. 8. Unfailed (N
f
> 10 000) tests DCy-A1 and DCy-D1: (a) axial
strain; (b) effective stress path
THE BEHAVIOUR OF DESTRUCTURED CHALK UNDER CYCLIC LOADING 7
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400 kPa tests, while their cyclic stiffnesses were markedly
dependent on the levels of p′
0
and cyclic stress ratio, as shown
in Fig. 12.
Figures 11(b) and 12 plot the corresponding trends for
the unstable q
mean
=0 group tests. Axial strains accumulated
in the direction of pre-shearing q
mean
and the straining
was generally more abrupt in tests with higher q
cyc
/(2S
u
)
or negative q
mean
(test DCy-CX). Test DCy-D2 developed
‘transitional’cycling behaviour (as discussed previously) with
its stiffness degrading significantly over its initial 6000 cycles
but recovering subsequently. As revealed in Fig. 7, damping
ratios generally increased over the initial cycles with the
applied q
cyc
/(2S
u
) ratio, but reached similar peaks (on average
23·4%, see Table 3) as failure approached.
Specimens in the unfailed group (N
f
.10 000) accumu-
lated moderate (,0·16%) permanent strains, as demon-
strated in Fig. 11(c). The cyclic stiffness decreased slightly
but gained ultimately by on average 15% in the p′
0
= 200 kPa
tests, as listed in Table 3, while the elevated stress test
(DCy-A1-E) lost 30% stiffness, correlating with its much
greater proportional reduction in p′(see Fig. 14(a) later).
Figure 8 gives examples of how equation (1) power-law
functions match the evolution of permanent cyclic strains
with N. A similar approach was applied to other unfailed
tests, and to the initial stages of unstable tests prior to strain
reversal or significant acceleration. Parameters aand b
were controlled predominantly by q
cyc
and were relatively
insensitive to q
mean
. The empirical curve-fitting equations (2)
and (3) provide a means of estimating permanent strains
60·06
0·05
0·04
0·03
0·02
0·01
–0·01
0
5
4
3
2
1
0
–1 0 2000 4000 6000
N
8000 10 000 12 000
Axial strain, εa: %
Double amplitude, εa: %
εa
Nf = 5528
DA εa
Axial strain
Double amplitude
Fig. 9. Axial strain accumulation and double-amplitude trends for the
‘transitional’test DCy-D2
120
100
80
60
40
20
00 100 200 300 400
N
(a)
500 600 700 800
0 50 100 150 200
p': kPa
(b)
250
75
100
125
50
25
0
–50
–25
–75
–100
–125
q: kPa
MTXC
MTXE
(q/p')cyc
PT
(q/p')cyc
PT
(q/p')PT
Solid symbol: DCy-B1
Open symbol: Dcy-B1-E
N = 484
N = 488
N = 490
N = 138
N = 140
N = 144
Nf = 486
Nf = 486
Nf = 142
Nf = 142
DCy-B1
DCy-B1-E
ru: %
Fig. 10. Tests DCy-B1 ( p
0
′= 200 kPa) and DCy-B1-E
(p
0
′= 400 kPa): (a) pore water pressure ratio; (b) selected stress path
loops near cyclic failure
0·100
0·075
0·050
–0·025
–0·050
–0·075
–0·100
0·5
0·4
0·3
0·2
0·1
–0·1
–0·2
0·20
0·15
0·10
0·05
–0·05
0
0
0·025
0
DCy-B1
DCy-C3
DCy-D5
DCy-B1-E
DCy-C3-E
DCy-D5-E
DCy-C2
DCy-D1
DCy-C1
DCy-A1
DCy-A1-E
DCy-A1
DCy-C1
DCy-D1
DCy-A1-E
DCy-CX
DCy-D2
DCy-D3
DCy-D4
Towards large-strain extension failure
100101102
N
(a)
103
100101102
N
(b)
104
103
100101102
N
(c)
104
103
Accumulated axial strain, εa: %
Accumulated axial strain, εa: %
Accumulated axial strain, εa: %
Fig. 11. Trends for accumulated cyclic strain against number of
cycles: (a) unstable group, q
mean
= 0; (b) unstable group, q
mean
=0;
(c) ‘stable’(unfailed within 10 000 cycles) group
LIU, AHMADI-NAGHADEH, VINCK, JARDINE, KONTOE, BUCKLEY AND BYRNE8
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developed prior to cyclic failure and can be employed when
developing and calibrating analyses of overall pile response
to axial cycling through global or local t–zapproaches, as
described by Jardine (2020).
εa¼aðNÞbð1Þ
a¼00011 ln qcyc
p′
0

00012ðin %Þð2Þ
b¼0265 e½5328ðqcyc=p′
0Þ ð3Þ
Cyclic resistance ratios
Drawing on the symmetrical cycling tests (with q
mean
= 0),
Fig. 13 demonstrates trends for cyclic stress (q
cyc
/(2S
u
)) and
resistance (CRR: q
cyc
/(2p′
0
)) ratios against N
f
or N
max
. The
trends are compatible with those commonly observed for
carbonate sands and silts (Sanin & Wijewickreme, 2006;
Porcino et al., 2008) and can be matched by the function
given as equation (4), which is plotted as a dashed line in
Fig. 13 through both the p′
0
= 200 and 400 kPa test points.
qcyc
ð2SuÞ¼024þ1
132 þ035 ½log10 ðNfÞ25ð4Þ
The q
cyc
/(2p′
0
)–N
f
trend can be derived by noting the
correlation of 2S
u
triaxial compression (q)
PT
p′
0
/2 found
in the monotonic tests. The function implies a q
cyc
/(2S
u
)
ratio of 0·32 at N
f
= 10 000 and a lower limit of 0·24 below
which regular symmetric two-way loading can be applied
indefinitely. The q
cyc
/(2S
u
) limit of 0·24 is lower than in
tests DCy-A1 and DCy-A1-E, which did not show fully
stable trends for mean effective stress (discussed below).
The lower limit exceeds the linear elastic (Y
1
) threshold
with Δq/(2S
u
)0·22 developed under monotonic loading
(as discussed previously) and could be regarded as the limit
to the outer kinematic Y
2
surface within which specimens
develop hysteretic closed stress–strain loops with non-linear
yet recoverable straining (Smith et al., 1992; Kuwano &
Jardine, 2007; Ushev & Jardine, 2022).
MEAN EFFECTIVE STRESS DRIFTS
The tests’detailed, cycle-by-cycle measurements enable
further interpretation and application in the laboratory
test-based predictive framework for axial cyclic pile loading
assessment described by Jardine et al. (2012), Rattley et al.
(2017) and Jardine (2020). Figs 14(a)–14(c) plot the ratios of
mean effective stress changes (Δp′=p′
N=i
p′
N=1
) for all tests
by reference to specimens’pre-shearing p′
0
of 200 or 400 kPa,
in ascending q
cyc
/p′
0
sequences. The following observations
apply.
(a) All tests showed Δp′/p′
0
decreasing continuously against
N. It is possible that cycling at lower levels would
identify conditions under which no reduction occurred.
(b) Steeper rates of Δp′/p′
0
drift were observed in specimens
cycled from higher pressures ( p′
0
= 400 kPa) under
q
cyc
/p′
0
ratios ,0·3 than in equivalent p′
0
= 200 kPa
experiments, but the influence became less discernible at
higher q
cyc
/p′
0
.
(c) The rates of Δp′/p′
0
degradation depended principally on
the cyclic stress ratio (q
cyc
/p′
0
). The influence of q
mean
/p
0
′
was modest over the central portion of the interactive
stress diagram and became more significant as
(q
cyc
+q
mean
)/p′
0
exceeded 0·4 in the p′
0
= 200 kPa tests,
causing the N
f
contours to curve down markedly (see
Fig. 4).
Tests on dense sands and stiff clays show that pre-cycling
with relatively high stress ratios (as occurs during pile
driving) reduces and, at low q
cyc
/p′
0
can even reverse, the
Δp′/p′
0
drift rates observed on renewed cycling at lowerq
cyc
/p′
0
levels (Aghakouchak, 2015; Aghakouchak et al., 2015;
Rattley et al., 2017). It remains to be established whether
such trends apply to destructured chalk. The above authors
demonstrated how the Δp′/p′
0
–N(or Δσ′
z
/σ′
z0
–N) relationships
from cyclic triaxial, hollow cylinder apparatus or simple
shear tests could be expressed by the power-law form in
1500
1250
1000
750
500
250
0
Eu,cyc
secsec : MPaEu,cyc : MPa
100101102
N
(a)
103
1500
1250
1000
750
500
250
0
100101102
N
(b)
104
103
DCy-B1
DCy-C3
DCy-C2
DCy-CX
DCy-D2
DCy-D3
DCy-D4
DCy-D5
DCy-B1-E
DCy-C3-E
DCy-D5-E
LVDT malfunction
over N:150–600
Fig. 12. Cyclic stiffness degradation trends for unstable tests:
(a) q
mean
= 0; (b) q
mean
=0
1·0
0·8
0·6
0·4
0·2
0
qcyc/(2Su)
qcyc
CRR: qcyc/(2p'
0)
qmean/(2Su) = 0 (p'
0 = 200 kPa)
qmean/(2Su) = 0 (p'
0 = 400 kPa)
110100
Number of cycles to 1% DA axial strain
1000 10 000
0·25
0·20
0·15
0·10
0·05
0
(2Su) 1·32 + 0·35 × [log10 (Nf)]2·5
= 0·24 + 1
Fig. 13. Trends for cyclic stress ratio (q
cyc
/(2S
u
)) and cyclic resistance
ratio (CRR: q
cyc
/(2p
0
′)) against number of cycles to failure (N
f
)
THE BEHAVIOUR OF DESTRUCTURED CHALK UNDER CYCLIC LOADING 9
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equation (5) and applied to generate shaft capacity degra-
dation trends that match trends from cyclic pile tests (Jardine
& Standing, 2012).
Δp′
p′
0
¼ABþðqcyc =p′
0Þ

NCð5Þ
where A,Band Care parameters defining the rate of p′
degradation and the maximum cyclic stress ratio that
could lead to beneficial, null, or deleterious cycling effects.
The p′
0
= 200 kPa tests with (q
cyc
+q
mean
)/p′
0
,0·4 indicate
A=0·05 and B=0·12, regardless of the applied q
cyc
/p′
0
ratio, with the following best-fitting linear correlation for
parameter C.
C¼348 qcyc
p′
0
ð6Þ
The chalk putty tests indicated a far wider 0·3 ,C,1·3
range than reported for dense sands or stiff clays. Fig. 14(d)
demonstrates how the above correlations and parameters
provide generally good matches (shown as dashed lines)
with the (mainly p′
0
= 200 kPa) experiments. Note that fully
stable responses are expected when q
cyc
/p′
0
,|B| = 0·12 (or
q
cyc
/(2S
u
) = 0·24), in keeping with the q
cyc
/(2S
u
) lower limit
implicit in equation (4).
POST-CYCLIC MONOTONIC SHEAR AND CRITICAL
STATE BEHAVIOUR
Table 4 summarises key outcomes of post-cyclic mono-
tonic undrained shearing stages conducted after the five tests
that sustained 10 000 cycles, listing the initial stress con-
ditions and pore pressure ratios (r
u
) along with the initial
maximum and normalised Young’s moduli (E
max
u
) and the
ultimate stresses and strains attained. When sheared mono-
tonically from initial conditions with an average r
u
= 62%, the
pre-cycled specimens exhibited maximum Young’s moduli
that were broadly comparable to those of ‘virgin’specimens
sheared from r
u
= 0 (see Table 1). More pronounced changes
were found in the putty’s normalised stiffness ratios,
(E
max
u
/p
ref
)/(p′
0
/p
ref
)
0·5
, where p
ref
= 101·3 kPa, which were
on average 58% higher than for the monotonic tests
conducted without pre-cycling. Long-term (35 days)
undrained low-amplitude stress cycling enhanced stiffness
and led to slightly higher shear strengths. The pre-cycled
specimens manifested principally dilative responses and
trended towards ultimate shear strengths with ultimate
stress ratios M=(q/p′)
ult
rising moderately from 1·27 to 1·34.
Figure 15 considers the state paths followed in the
v–log(p′) plane by the destructured chalk during undrained
triaxial compression tests from p
0
′of 70, 200 and 400 kPa.
This treatment enables further interpretation and modelling
of chalk’s mechanical response and destructuration behav-
iour with critical-based approaches, such as the Lagioia &
Nova (1995) framework.
As noted earlier, the pre-shearing states achieved by the
destructured specimens after their initial ‘in-mould’and later
isotropic consolidation and creep stages fell (unexpectedly)
well below the CRS 1D compression path, when projected
assuming K
0
=1sin(ϕ′
cs
) = 0·48 from Fig. 1. The tests’PT
points are shown and a critical state relationship is drawn
through the tests’ultimate shearing points, which fall, as
DCy-D1 (qcyc/p'
0 = 0·09, qmean/p'
0 = 0·40)
DCy-A1 (qcyc/p'
0 = 0·15, qmean/p'
0 = 0)
DCy-C1 (qcyc/p'
0 = 0·15, qmean/p'
0 = 0·15)
DCy-D2 (qcyc/p'
0 = 0·15, qmean/p'
0 = 0·29)
DCy-A1-E (qcyc/p'
0 = 0·15, qmean/p'
0 = 0)
DCy-CX (qcyc/p'
0 = 0·23, qmean/p'
0 = 0·08)
DCy-B1 (qcyc/p'
0 = 0·23, qmean/p'
0 = 0)
DCy-C2 (qcyc/p'
0 = 0·23, qmean/p'
0 = 0·08)
DCy-D3 (qcyc/p'
0 = 0·22, qmean/p'
0 = 0·22)
DCy-B1-E (qcyc/p'
0 = 0·23, qmean/p'
0 = 0)
DCy-C3 (qcyc/p'
0 = 0·30, qmean/p'
0 = 0)
DCy-D4 (qcyc/p'
0 = 0·30, qmean/p'
0 = 0·14)
DCy-C3-E (qcyc/p'
0 = 0·30, qmean/p'
0 = 0)
DCy-D5 (qcyc/p'
0 = 0·38, qmean/p'
0 = 0)
DCy-D5-E (qcyc/p'
0 = 0·38, qmean/p'
0 = 0)
qcyc/p'
0 = 0·30,
(DCy-A1, C1)
qcyc/p'
0 = 0·23,
(DCy-CX, B1, C2)
qcyc/p'
0 = 0·30,
(DCy-C3, D4)
qcyc/p'
0 = 0·38,
(DCy-D5)
0·2
0
–0·2
–0·4
–0·6
–0·8
–1·0
Δp'/p'
0
0·2
0
–0·2
–0·4
–0·6
–0·8
–1·0
Δp'/p'
0
0·2
0
–0·2
–0·4
–0·6
–0·8
–1·0
Δp'/p'
0
0·2
0
–0·2
–0·4
–0·6
–0·8
–1·0
Δp'/p'
0
DCy-C1
DCy-D1
DCy-A1
DCy-D2
DCy-A1-E
100101102
N
(a)
103100101102
N
(b)
103
N
(c)
100101102103100101102
N
(d)
103104
104
Fig. 14. Drifting trends for mean effective stress during cycling: (a) q
cyc
/p
0
′0·15; (b) q
cyc
/p
0
′0·23; (c) q
cyc
/p
0
′0·30; (d) fitted trends for tests
with p
0
′= 200 kPa and mostly (q
cyc
+q
mean
)/p
0
′< 0·4
LIU, AHMADI-NAGHADEH, VINCK, JARDINE, KONTOE, BUCKLEY AND BYRNE10
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expected, below the 1D compression curve, but also below
the critical state relationship established for intact chalk
through high-pressure triaxial tests. It is interesting to
speculate whether the intact and destructured critical state
line (CSL) relationships would fall closer if it had been
possible to compress beyond the 30% maximum axial
strain that can be imposed in triaxial tests.
The destructured samples’tendency to dilate significantly
post-PT is compatible with their ‘dry’position relative to
their CSL. In terms of the Been & Jefferies (1985) frame-
work, the specimen’s state parameters (ψ=ee
cs
) decrease
systematically as p
0
′grows, a trend that is reflected in the
high-pressure tests’tendency to produce higher cyclic excess
pore pressures.
COMPARISON OF INTACT AND DESTRUCTURED
CHALK
As noted in the introduction, the cyclic response of
piles driven in chalk is affected by both the putty zone
around the shaft and the surrounding intact mass. It is
therefore interesting to contrast the undrained cyclic triaxial
behaviour of chalk in both conditions, drawing on represen-
tative paired tests that applied identical mean and cyclic
stresses. Fig. 16 offers such a comparison for tests with
q
cyc
/(2S
u
)=q
mean
/(2S
u
)0·44. Cyclic failure in the putty
involves pore pressure build-up, leftward drifting of the
effective stress path, cyclic stiffness loss and growing
damping ratios (see also Figs 5–7 and 10–12). In contrast,
the intact chalk shows a very stiff cyclic response, with little
or no sign of pore pressure change or impending instability.
The cyclic effective stress paths remain within a tight band
beforehand and until shortly before abrupt brittle failure,
which leads to markedly dilative pore pressure trends.
Ahmadi-Naghadeh et al. (2022) conclude that the intact
response is closer to that of harder rocks and solids, such as
concretes and metals, whose cyclic or fatigue failure is
dominated by their inherent microstructures and triggered
by local stress concentrations that promote progressive wear
and shearing.
SUMMARY AND CONCLUSIONS
Heavily destructured soft putty forms in the field under
intense compression or large-strain, repetitive shearing.
Understanding the putty’s behaviour after reconsolidation
is crucial to advancing driven pile design in chalk. This paper
reports 20 high-resolution triaxial experiments and other
tests on putty formed by dynamic compaction followed by
re-consolidation and explores their responses to both mono-
tonic and one- and two-way sinusoidal deviatoric undrained
loading. The experiments, which ran in parallel alongside
an intact chalk programme, led to the following main
conclusions.
(a) Chalk that is destructured by dynamic compaction
manifests distinctly time-dependent behaviour.
Incorporating maintained-stress creep stages is
essential to distinguishing the separate impacts of
initial monotonic shearing from subsequent cyclic
loading.
(b) Chalk putty’s response to undrained monotonic
loading resembles that of silts and silty sands,
2·1
2·0
1·9
1·8
1·7
1·6
1·5
1·4
1·3
Intact
De-structured
De-structured
TXC
Drained shearing ultimate
CRS oedometer
End of consolidation and creep
Undrained shearing PT
Undrained shearing ultimate
1 10 100
p': kPa
1000 10 000 100 000
End of
consolidation and creep
Specific volume, v
Intact CSL
(Γ = 2·74, λ = 0·134)
De-structured CSL∗
(Γ = 2·155, λ = 0·08)
Fig. 15. Critical state relationships established for destructured and
intact chalk
2·0
1·6
1·2
0·8
0·4
00 0·4 0·8 1·2 1·6 2·0
Intact (ICy-D4)
(p'
0 = 42 kPa, Su = 1200 kPa)
Puttified (DCy-D3)
(p'
0 = 200 kPa, Su = 50 kPa)
q/(2Su)
p'/(2Su)
ICy-D4 DCy-D3
No tension line
Puttified chalk
M = 1·27
Fig. 16. Effective stress path of intact (Ahmadi-Naghadeh et al.,
2022) and destructured chalk (samples with q
cyc
/(2S
u
)=
q
mean
/(2S
u
)0·44; plotted up to N
f
+ 3 cycles)
Table 4. Summary of maximum undrained Young’s moduli (Eu
max), pore water pressure ratio, ultimate stress states and the corresponding axial
strains (in brackets) of the post-cyclic monotonic tests
Test p′:kPa q:kPa r
u0
:% Eu
max:MPa Eu
max
pref

p0
′
pref

05*q
(ult)
:kPa(ε
a
:%) p′
(ult)
:kPa (q/p′)
ult
ϕ′
ult
: degrees
DCy-A1 120·2 0 39·9 1265·8 11 471 837·1 (31·5%) 640·4 1·31 33·2
DCy-C1 103·6 30 52·7 1159·4 11 319 1002 (27·8%) 744·9 1·35
DCy-D1 94·8 77·3 65·3 1110·4 11 330 919·5 (22·3%) 705·3 1·30
DCy-D2 47·6 67·2 87·4 936·0 13 483 645·2 (19·5%) 465·9 1·38
DCy-A1-E 143·4 0 64·2 1492·4 12 384 1205·3 (18·8%) 881·0 1·37
*p
ref
, reference pressure (101·3 kPa).
THE BEHAVIOUR OF DESTRUCTURED CHALK UNDER CYCLIC LOADING 11
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developing well-defined PT and critical states over
medium to large strains.
(c) Reconsolidated putty’s response to undrained
high-level cyclic loading involves both contractant
and dilative stages, with an overall trend for
positive pore pressure build-up, leftward effective
stress path drift, permanent strain accumulation,
gradual cyclic stiffness losses and increasing damping
ratios.
(d) Experiments on isotropically consolidated samples
identify cyclic PT that occurs at lower q/p′ratios than
under monotonic loading and appears largely
independent of p′
0
level, mean and cyclic stress ratio,
as well as loading direction. The cyclic stress paths were
not bounded by the critical state stress ratios identified
from monotonic tests.
(e) The maximum number of cycles that the reconsolidated
putty can sustain under given normalised
mean and cyclic stresses can be expressed in
interactive stress diagrams that delineate the
stress conditions under which cyclic loading
leads to either failure in given numbers of cycles
or causes no deleterious effect. Puttified chalk is
particularly susceptible to high-level two-way
loading that involves stress reversals between
compression and extension.
(f) Empirical correlations provide predictions for
the number of cycles to failure (N
f
) when
cycling at fixed cyclic stress ratios (q
cyc
/(2S
u
))
under the most critical q
mean
= 0 two-way loading
conditions.
(g) Samples consolidated to different pressure levels
manifest broadly similar overall cyclic loading
responses, although raising the pressures increases the
reconsolidated putty’s susceptibility to cyclic loading
of lower amplitude.
(h) Degradation trends for mean effective stress
(Δp′/p′
0
–N) were found to be affected most
strongly by cyclic stress ratio and well correlated
by power laws. The calibrated Δp′/p′
0
–Ncorrelation
provides important inputs for laboratory-based
global cyclic stability analysis of axially loaded
driven piles in chalk.
(i) Application of large numbers of low-level cycles
invokes a principally reversible, although non-linear,
response. Specimens that survive long-term undrained
cycling offer greater post-cyclic stiffness and shear
strength than ‘virgin’specimens.
(j) The re-consolidated putty’s response to undrained
monotonic and cyclic loading differs markedly
from that of intact chalk. The putty responds
as a fine granular material, whereas the
intact chalk manifests fatigue failure mechanisms
that resemble those of harder rocks and solid materials.
Overall, the interactive cyclic triaxial stress diagrams,
effective stress drift, permanent displacement and stiffness
trends provide key information to aid both the interpretation
of the ALPACA field tests and the cyclic design of piles
driven in other comparable chalks.
ACKNOWLEDGEMENTS
The experimental study was undertaken as part of
the ALPACA and ALPACA Plus Projects funded by the
Engineering and Physical Science Research Council
(EPSRC) grant EP/P033091/1, Royal Society Newton
Advanced Fellowship NA160438 and Supergen ORE Hub
2018 (EPSRC EP/S000747/1). Byrne is supported by the
Royal Academy of Engineering under the Research Chairs
and Senior Research Fellowships scheme. The authors
acknowledge the provision of additional financial and
technical support by steering committee members and
partners: Atkins, Cathie Associates, Equinor, Fugro,
Geotechnical Consulting Group (GCG), Iberdrola, Innogy,
LEMS, Ørsted, Parkwind, Siemens, TATA Steel and
Vattenfall. Imperial College EPSRC Centre for Doctoral
Training (CDT) in Sustainable Civil Engineering and the
DEME Group (Belgium) are acknowledged for supporting
the doctoral study of Ken Vinck. Invaluable technical
support was provided by Steve Ackerley, Graham Keefe,
Prash Hirani, Stef Karapanagiotidis at the Department of
Civil and Environmental Engineering of Imperial College
London is acknowledged gratefully.
NOTATION
A, B, C fitting parameters for mean effective stress degradation
A
elastic
unloading half-cycle elastic triangle area with height
as q
cyc
(=(q
peak
q
trough
)/2) and width as cyclic strain
(=(ε
peak
ε
trough
)/2)
A
loop
area enclosed by a stress–strain (q–ε
a
) loop for a complete
sinusoidal stress cycle
a, b fitting parameters for permanent cyclic strain
C
c
compression index of intact specimen
C
c
*
compression index of reconstituted specimen
C
s
swelling index of intact specimen
C
αe
rate of secondary compression of intact specimen
c′soil cohesion
Ddamping ratio ( = A
loop
/(4πA
elastic
))
D
50
mean particle diameter
Eu
max maximum undrained Young’s modulus
Eu
sec undrained secant vertical Young’s modulus
Eu;cyc
sec cyclic undrained secant vertical Young’s modulus
e
0
specimen initial void ratio
G
s
specific gravity
K
0
earth pressure coefficient at rest
Mcritical state q/p′stress ratio
Nnumber of cycles
N
f
number of cycles to failure
p′mean effective stress
p
0
′initial mean effective stress
qdeviatoric stress
q
cyc
cyclic deviatoric stress amplitude ( = (q
peak
q
trough
)/2)
q
f
deviatoric stress at failure
q
max
maximum qapplied in stress cycle ( = q
mean
+q
cyc
)
q
mean
mean qapplied in stress cycle
q
PT
deviatoric stress at the phase transformation state
q
peak
peak qapplied in stress cycle ( = q
max
)
q
trough
minimum qapplied in stress cycle ( = q
mean
q
cyc
)
r
u
pore water pressure ratio ( = ( p′
0
p′)/p′
0
=Δu/p
0
′)
S
r
saturation degree
S
u
undrained shear strength
Δuexcess pore water pressure
ε
a
axial (vertical) strain
ε
peak
axial strain at q
peak
ε
r
radial (horizontal) strain
ε
s
shear strain ( = ε
a
for undrained triaxial condition)
ε
trough
axial strain at q
trough
ϕ′
cs
critical state shear resistance angle
ϕ′
peak
shear resistance angle at peak
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THE BEHAVIOUR OF DESTRUCTURED CHALK UNDER CYCLIC LOADING 13
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