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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

Downloaded by [] on [19/04/22]. Published with permission by the ICE under the CC-BY license

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

Δq23·1 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

05

†

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

=aN

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 N7000, 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).

εa¼aðNÞbð1Þ

a¼00011 ln qcyc

p′

0

00012ðin %Þð2Þ

b¼0265 e½5328ðqcyc=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

ð2SuÞ¼024þ1

132 þ035 ½log10 ðNfÞ25ð4Þ

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

¼ABþðqcyc =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.

C¼348 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

=1sin(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=ee

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

05*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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