-
Liu, HY., Zygounas, F., Diambra, A., & Pisano, F. (2018).
Enhancedplasticity modelling of high-cyclic ratcheting and pore
pressureaccumulation in sands. In Numerical Methods in
GeotechnicalEngineering IX: Proceedings of the 9th European
Conference onNumerical Methods in Geotechnical Engineering (NUMGE
2018),June 25-27, 2018, Porto, Portugal CRC Press.
Peer reviewed version
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-
Enhanced plasticity modelling of high-cyclic ratcheting and pore
pressureaccumulation in sands
H.Y. Liu & F. ZygounasSection of Geo-Engineering, Department
of Geoscience and EngineeringDelft University of Technology, Delft,
The Netherlands
A. DiambraDepartment of Civil Engineering, Faculty of
EngineeringUniversity of Bristol, Bristol, UK
F. PisanòSection of Geo-Engineering, Department of Geoscience
and EngineeringSection of Offshore Engineering, Department of
Hydraulic EngineeringDelft University of Technology, Delft, The
Netherlands
ABSTRACT: Predicting accurately the response of sands to cyclic
loads is as relevant as still challengingwhen many loading cycles
are involved, for instance, in relation to offshore or railway
geo-engineering appli-cations. Despite the remarkable achievements
in the field of soil constitutive modelling, most existing modelsdo
not yet capture satisfactorily strain accumulation under
high-cyclic drained loading, nor the the build-up ofpore pressures
under high-cyclic undrained conditions. Recently, bounding surface
plasticity enhanced with theconcept of memory surface has proven
promising to improve sand ratcheting simulations under drained
loadingconditions (Corti et al. 2016). This paper presents a new
model built by combining the memory surface conceptby Corti et al.
(2016) with the well-known SANISAND04 bounding surface formulation
proposed by Dafaliasand Manzari (2004). The outcome is a new sand
model that can reproduce phenomenologically the fabric evo-lution
mechanisms governing strain accumulation under long-lasting loading
histories (here up to 104 loadingcycles). In undrained test
simulations, the model proves capable of correctly capturing the
rate of pore pressureaccumulation, preventing precocious occurrence
of cyclic liquefaction.
1 INTRODUCTION
Predicting accurately the response of sands to cyclicloads is
still challenging when many loading cyclesare involved. More
specifically, cyclic accumulationof permanent strain and pore water
pressure may leadto reduction of capacity, serviceability and
fatigue re-sistance (Andersen 2015). The term ‘ratcheting’
isadopted to denote the gradual accumulation of plas-tic strains
under loading cycles (Houlsby et al. 2017).In engineering practice,
soil ratcheting is often de-scribed by using empirical equations
derived from ex-perimental measurements (Pasten et al. 2013).
Empir-ical formulations of this kind may be found for long-term
strain accumulation phenomena (Sweere 1990,Lekarp and Dawson 1998,
Wichtmann 2005) andshort-term pore pressure build-up during
earthquakesor storms (Seed et al. 1975, Green et al. 2000,
Idrissand Boulanger 2006). Although empirical equations
have proven efficient to use, some limitations standout clearly:
(1) high-cyclic tests for calibrating empir-ical relations are
usually costly and time-consuming;(2) the use of reconstituted sand
specimens goes be-yond the scope of standard soil characterisation.
Analternative approach is to set up a reliable advancedconstitutive
model that can capture satisfactorily sandratcheting and related
strain/pore-water-pressure ac-cumulation trends under different
cyclic loading con-ditions and drainage scenarios.
In this work, the memory surface concept is com-bined with the
structure of the model prosed byDafalias & Manzari (2004)
(SANISAND04 model).The reference SANISAND04 model, which is
buildupon a critical state and bounding surface
plasticityframework, includes a fabric-dilatancy tensor to
re-produce soil fabric effects. The suitability of com-bining
bounding surface theory and memory surfaceconcept has been proven
by the work of Corti et al.
-
(2016). Soil fabric and its evolution are recorded by anewly
introduced memory surface, enclosing a stressregion which the soil
feels to have already experi-enced and thus characterised by high
stiffness.
The main purpose of the paper is to provide a re-liable
constitutive model to: (1) complement/replacedemanding laboratory
sand testing as input to dis-placement/rotation accumulation
procedures; (2) en-hance the real time-domain simulation during
shortercyclic loading histories. The proposed model is vali-dated
by simulating results of experimental tests per-formed on a quartz
sand and the Karlsruhe sand un-der cyclic loading conditions. The
experimental dataregard both drained (Wichtmann 2005) and
undrained(Wichtmann and Triantafyllidis 2016) triaxial tests
in-vestigating the influence of varying the mean confin-ing
pressure, cyclic stress amplitude and void ratio.
2 MODEL FORMULATION
2.1 General modelling strategy
The proposed model improves the cyclic performanceof SANISAND04
by introducing a memory surfaceto keep track of relevant fabric
effects and to simu-late realistic sand cyclic behaviour under both
drainedand undrained loading conditions. The selected back-bone
bounding surface model (SANISAND04 model)was developed by Dafalias
& Manzari (2004), witha fabric-dilatancy tensor defined to take
into accountthe effects of increased dilation following cyclic
con-tractive behaviour. In SANISAND04, soil stiffnessis determined
by the distance between current stressstate and its conjugate point
on the bounding surface.However, the fabric-dilatancy tensor, which
only ac-tivates if the stress path crosses the phase
transfor-mation line (PTL), is not sufficient to fully describethe
influence of soil fabric especially when the soil isresponding
within its contractive regime. Therefore,SANISAND04 is less
suitable for simulating soil pro-gressive stiffening during cyclic
loading, since it willoverpredict strain accumulation and the rate
of porepressure build-up. The proposed model introduces
acircular-shape memory surface as a third model sur-face in the
normalised π plane, as illustrated in Fig-ure 1. The memory surface
evolves during the loadingprocess following three main rules: (1)
changes sizeand position with plastic strains to simulate
gradualevolution of the soil fabric; (2) always encloses thecurrent
stress state and (3) always enclose the yieldsurface. The bounding,
critical and dilatancy surfacesare defined using an Argyris-type
shape to capture theresponse of the soil at varying load angle. The
adop-tion of state parameter Ψ (Been and Jefferies 1985),defined as
the difference between the current voidratio and the critical void
ratio (Ψ = e − ec) at thesame mean stress level, allows to
reproduce the influ-ence of the void ratio over the whole
loose-to-denserange. For the critical state line, a power
relationship
is adopted as suggested by (Li and Wang 1998). Thecomplete model
formulation is presented in the workof Liu et al. (2018), following
the previous develop-ments by Corti et al. (2016).
Figure 1: Visualisation in the π-plane of the three-surface
modelformulation
2.2 Implementation of the memory surface
Introduction of the memory surface is linked to amodification of
the hardening coefficient h, see Equa-tion 1:
h =b0
(r− rin) : nexp
µ0
(
p
patm
)0.5(
bM
bref
)2
(1)
Here, bM = (rM − r) : n denotes the distance betweencurrent
stress ratio point r and its image point onmemory surface rM ,
projecting along the direction ofunit normal to the surface n. The
dependency of hon the current pressure p through the term
(p/patm)
0.5
is introduced to improve the original formulation ofCorti et al.
(2016) and follows some findings fromCorti et al. (2017).
Definitions for b0 and rin are thesame as in Dafalias & Manzari
(2004). patm is the at-mospheric pressure. bref , which is adopted
for nor-malisation, is the reference distance indicates the sizeof
bounding locus along the current load angle.
Thememory-surface-related parameter µ0 quantifies theinfluence of
fabric effects on soil stiffness, especiallyin the transition from
ratcheting to shakedown be-haviour. In this case, soil stiffness
depends not onlyon the relative distance between current stress
state(r) and its image point on bounding surface (rb), butalso on
the distance between r and its image point onmemory surface (rM ).
This is reflected in the expres-sion of the hardening modulus Kp in
Equation 2.
Kp =2
3ph(rb − r) : n (2)
The evolution of memory surface center αααM is as-sumed to be
along the direction rb − rM - see Equa-tion 3:
dαααM =2
3〈L〉hM(rrrb − rrrM) (3)
-
A
(a) memory surface expansion (b) memory surface shrinkage
Figure 2: Evolution of the memory surface size: (a) memory
surface expansion during virgin loading conditions; (b) memory
surfaceshrinkage during dilative straining.
The evolution of memory surface size is shownmathematically with
Equation 4. From experimentalobservations, contractive soil
behaviour (positive vol-umetric strain by geotechnical convention)
leads tomore stable soil fabric configuration and therefore,stiffer
soil behaviour. Thus, it is reasonable to link itwith an expansion
of the memory surface. The expan-sion of the memory surface mainly
take places duringvirgin loading (see Figure 2(a)), which is
defined asthe state when the yield and memory surfaces are
tan-gential to each other at the current stress point. Thesize of
the memory surface is linked to the variablemM and its expansion is
linked to the evolution ofmemory surface center, as shown in the
first term of
the Equation 4 (i.e.,√
2/3dαααM : nnn):
dmM =
√
3
2dαααM :nnn−
mM
ζ
(
1−x1 + x2
x3
)
〈−dεpv〉(4)
Here, x3 = (rM − rC) : nM , x1+x2 = (r
M − rD) : nM
(see Figure 2(b)). The unit tensor nM represents thedirection of
rM − r. During virgin loading conditions,soil stiffness is governed
only by the distance betweenthe current stress and its image on the
bounding sur-face. Under non-virgin conditions (for example
afterload reversal), the memory surface acts as an addi-tional
bounding surface. Soil stiffness is increased bythe non-zero
distance bM (see Equation 1) betweenyield surface (f ) and memory
surface (fM ). Stiffersoil behaviour is captured in this
manner.
By contrast, dilative soil behaviour leads to aweaker granular
arrangement (also known as ‘fab-ric damage’), and the soil loses
part of its stiffness.This situation can therefore be linked to the
shrinkageof the memory surface size. In the model, the mem-ory
surface contraction mechanism, or fabric dam-age mechanism, only
activates when negative plas-tic volumetric strains are generated.
As presented bythe second term of Equation 4, if positive
volumetric
strains are generated, 〈−dεεεpv〉= 0 because of the Mac-Cauley
brackets. The reduction in memory surfacesize, which is
schematically described in Figure 2(b),happens on the opposite side
of rM , along the direc-tion (rMrC). To guarantee that the yield
surface al-ways lies inside the memory surface, the size reduc-tion
ends if the memory surface and the yield sur-face become tangential
to each other at the contractionpoint (in other words, when 1− (x1
+ x2)/x3 = 0),even if the soil is still experiencing negative
volumet-ric strain. The reduction rate of memory surface sizeis
controlled by the parameter ζ .
2.3 Enhanced dilatancy coefficient
In SANISAND04, a fabric-dilatancy tensor is intro-duced into the
flow rule, or to be more specific, intothe dilatancy coefficient D.
The feature is introducedto reproduce the experimental observation
that whenstress path crosses the PTL and load increment rever-sal
is imposed, there is an obvious increase in porewater pressure
build-up with respect to the number ofcycles under undrained cyclic
loading conditions. Theunderlying mechanism is the change of fabric
orien-tation. Instead of using a single tensor, the proposedmodel
accounts for fabric effects through the relativeposition and
distance between the memory surfaceand the dilatancy surface,
according to Equation 5:
D = Ad(rrrd − rrr) : nnn Ad = A0 exp
β
〈
b̃Md〉
bref
(5)
In this work, whether the sand is more prone to di-
lation or contraction is determined by the term b̃Md =(r̃d −
r̃M) : n, which basically modulates the mag-nitude of D (not the
sign) depending on the occur-rence of previous dilation or
contraction. The graph-ical representation of this mechanism is
provided in
-
Figure 3: Illustration of image points for modifying current
dila-tancy coefficient.
Figure 3. If b̃Md > 0, the soil has experienced di-lation
during the previous loading process, imply-ing a sort of
‘contraction bias’ under subsequent un-loading. The dilatancy D is
enlarged because of alarger dilation coefficient Ad by noticing
that the term
exp(
β〈
b̃Md〉
/bref)
> 1 in this situation. In this way,
the model can simulate more significant pore wa-ter pressure
build-up under undrained loading. Con-
versely, if b̃Md < 0 , soil fabric orientation is biased
toward dilation, exp(
β〈
b̃Md〉
/bref)
= 1. It should be
noted that the dilatancy coefficient in Equation 5 sub-stitutes
the fabric-tensor concept used by Dafalias andManzari (2004), and
the two associated constitutiveparameters.
3 MODEL CALIBRATION
The model parameters can be divided into two sets.The first set
can be entirely derived from monotonictests, although they
influence the cyclic performanceas well (from G0 to n
d in Table 1 and Table 2).Their calibration rely on drained
and/or undrainedmonotonic triaxial tests (Dafalias and Manzari
2004,Taiebat and Dafalias 2008). The second set containsthe memory
surface related parameters i.e., µ0, ζ andβ in the Table 1, which
can be estimated by fittingprocedures (Liu et al. 2018).
Calibration of µ0 canbe more easily achieved through cyclic tests
wherethe soil is experiencing contractive behaviour. In
thiscondition, ζ and β, have no influence on the modelprediction
because of the absence of dilative soil be-haviour. Conversely,
calibration of ζ and β requirestests with (at least part of)
loading paths crossingthe PTL. In particular, the parameter β
controls thereduction rate of the mean effective stress
duringundrained loading after stages of dilative deformation(after
which more pronounced effective stress reduc-tion is observed
experimentally).
In Table 1, model parameters for a quartz sand arecalibrated
based on the experimental work conductedby Wichtmann (2005). Six
sets of drained monotonictriaxial tests are used for calibrating
the monotonic
parameters, while memory surface-related parametersare
calibrated based on the strain accumulation curvewith loading
cycles up to 104. Table 2 lists modelparameters for the Karlsruhe
fine sand-experimentaldata published by Wichtmann and
Triantafyllidis(2016). In total, 10 sets of drained and
undrainedmonotonic triaxial tests are simulated to identify
themonotonic parameters. For the memory surface pa-rameters, the
calibration relies on isotropic cyclic tri-axial undrained tests,
using the observed trends of ac-cumulated pore water pressure ratio
against numberof cycles.
4 MODEL VALIDATION
4.1 Drained tests
For the drained case, model parameters are calibratedagainst
experimental results from Wichtmann (2005)on a quartz sand, as
listed in Table 1. For memorysurface-related parameters, the
calibration procedurerelies on the drained cyclic test with ein =
0.674, withother load conditions the same as described in Fig-ure
4. Performance of the proposed model is vali-dated through the
comparison between triaxial ex-perimental results and simulation
results under cyclicloading conditions, with focus on different
initialvoid ratio and different cyclic stress amplitude
qampl.Wichtmann’s experiments concern one-way asym-metric cyclic
loading performed in two stages: afterthe initial isotropic
consolidation up to p = pin, p-constant shearing is first performed
to reach the tar-get average stress ratio ηave = qave/pin; then,
cyclicaxial loading at constant radial stress is applied to ob-tain
cyclic variations in deviatoric stress q about theaverage value
qave, i.e. q = qave ± qampl. High-cyclicsand parameters are tuned
to match the evolution dur-ing regular cycles of the accumulated
strain norm εacc
defined through the accumulated axial strain εacca
andaccumulated radial strain εaccr , as:
εacc =√
(εacca )2 + 2(εaccr )
2 (6)
4.1.1 Influence of initial void ratioThe influence of the soil
initial void ratio on soildrained cyclic behaviour is studied by
performingdrained triaxial tests on soil samples with initial
voidratios ein = 0.803, 0.674 and 0.580. Other loading pa-rameters
are kept unaltered: pin = 200 kPa, η
ave =0.75 and qampl = 60 kPa. Comparison between ex-perimental
results and model simulations are pre-sented in Figure 4. Based on
the experimental ob-servations, denser sand specimens accumulate
lessstrains. The model seems to capture quantitativelywell all
relevant trends. The model also accuratelypredicts the accumulated
strain for the cases of ein =0.803 and 0.674, the loose and medium
dense sand.However, for the dense sample ein = 0.580, the
modelslightly overestimates the accumulated strain.
-
Table 1: Model parameters for the quartz sand for drained cyclic
simulationsElasticity Critical state Yield surface Plastic modulus
Dilatancy Memory surface
G0 ν M c λc e0 ξ m h0 ch nb A0 n
d µ0 ζ β
130 0.05 1.25 0.702 0.015 0.81 0.7 0.01 5.05 1.05 2.25 1.06 1
270 0.0005 0.2
Table 2: Model parameters for the Karlsruhe fine sand for
undrained cyclic simulationsElasticity Critical state Yield surface
Plastic modulus Dilatancy Memory surface
G0 ν M c λc e0 ξ m h0 ch nb A0 n
d µ0 ζ β
95 0.05 1.35 0.85 0.056 1.038 0.28 0.01 7.6 1.015 1.2 0.56 2.15
85 0.0001 6
100
101
102
103
104
0
1
2
3
4
number of cycles N
acc
um
ula
ted
to
tal s
tra
in ε
acc [
%]
ein=0.803
ein=0.674
ein=0.580
(a) Experimental results
100
101
102
103
104
0
1
2
3
4
number of cycles N
ein=0.803
ein=0.674
ein=0.580
acc
um
ula
ted
to
tal s
tra
in ε
acc [
%]
(b) Simulation results
Figure 4: Influence of soil density on strain accumulation under
drained conditions (a) experimental results; (b) simulation
results.Confining pressure pin = 200 kPa, stress obliquity η
ave= 0.75, stress amplitude qampl = 60 kPa.
4.1.2 Influence of cyclic stress amplitude
The impact of the cyclic stress amplitude on the ac-cumulated
permanent stain under drained cyclic con-ditions is studied by
performing three different stressamplitudes (qampl = 80 kPa, 60 kPa
and 31 kPa)on three soil samples. In the tests, confining
pressurepin = 200 kPa, stress obliquity η
ave = 0.75, initialvoid ratio ein = 0.702 are considered.
Comparison be-tween experimental results and model simulations
arepresented in Figure 5. The experimental results showthat
increasing cyclic stress amplitude leads to largeraccumulated
strain, corroborating findings of otherexperimental works
(Escribano et al. 2018). This issuccessfully predicted by the
model, see Figure 5.
4.2 Undrained tests
The undrained perfromance of the model is validatedby comparing
model simulations with five sets of ex-perimental results by
Wichtmann and Triantafyllidis(2016) on Karlsruhe fine sand. Model
parameters arelisted in Table 2. The results are presented in
termsof accumulated pore water pressure ratio (ru, whichrepresents
the accumulated pore water pressure uacc
normalised by the initial effective confining pressure,i.e. ru =
u
acc/p′in ). Parameters µ0, ζ and β are cal-ibrated by fitting
the experimental data presented inFigure 6(b).
4.2.1 Influence of initial effective confiningpressure and void
ratio
In Figure 6, three sets of results are presented withsimulation
results from both the new model and theoriginal SANISAND04 model.
For all three sets ofresults, the simulation of the SANISAND04
modelshow clear liquefaction with accurate ultimate rulevel.
However, the predicted number of cycles to liq-uefaction is in all
instances too low. In other words,SANISAND04 underestimates
significantly the resis-tance to liquefaction, especially as the
void ratio de-viates from emax.
The impact of the initial void ratio is studied bycombing the
test results on medium dense sand (Fig-ure 6(a), the initial void
ratio ein = 0.825) with thedense sand results (Figure 6(b), the
initial void ra-tio ein = 0.759). For both tests, the initial
effectivepressure p′in = 100 kPa, the cyclic stress ratio ς ,
de-fined as ς = qampl/p′in, equals to 0.3. A slower increas-ing of
ru is observed compared to that of for densersand. It indicates
that under the same loading condi-tion, the resistance to
liquefaction for dense sands ishigher than for loose sands. The new
model predictsthe ultimate ru level and number of loading cycles
ina reasonable accurate magnitude with a single set ofparameters,
especially for the dense sand.
The influence of the initial effective confining pres-sure p′in
is shown in Figure 6(a) and Figure 6(c). Forboth tests, ς = 0.3. In
Figure 6(b), the initial effec-tive confining pressure p′in = 100
kPa and the num-ber of cycles N to liquefaction is 54. For Figure
6(c),p′in = 300 kPa and N = 269. Overall, the new model
-
100
101
102
103
104
0
0.5
1
1.5
2
Number of cycles N
Accu
mu
late
d s
tra
in [
%]
qampl
=80 kPa
qampl
=60 kPa
qampl
=31 kPa
(a) Experimental results
100
101
102
103
104
0
0.5
1
1.5
2
number of cycles N
qampl
=80 kPa
qampl
=60 kPa
qampl
=31 kPa
acc
um
ula
ted
to
tal s
tra
in ε
acc [
%]
(b) Simulation results
Figure 5: Influence of cyclic stress amplitude on strain
accumulation under drained conditions (a) experimental results; (b)
simulationresults. Confining pressure pin = 200 kPa, stress
obliquity η
ave= 0.75, initial void ratio ein = 0.702.
0 20 40 60 80 100−40
−20
0
20
40
Effective mean pressure p’ [kPa]
De
via
toric s
tre
ss q
[kP
a]
Experimental
0 20 40 60 80 100−40
−20
0
20
40
Effective mean pressure p’ [kPa]De
via
toric s
tre
ss q
[kP
a]
New model
0 20 40 60 80 100−40
−20
0
20
40
Effective mean pressure p’ [kPa]De
via
toric s
tre
ss q
[kP
a]
SANISAND04
5 10 15 200
0.5
1
Number of cycles N
r u=
ua
cc/p
’ in
Exp
New model
SANISAND04
(a) p′in = 100 kPa, ein = 0.825
0 20 40 60 80 100−40
−20
0
20
40
Effective mean pressure p’ [kPa]De
via
toric s
tre
ss q
[kP
a]
New model
0 20 40 60 80 100−40
−20
0
20
40
Effective mean pressure p’ [kPa]De
via
toric s
tre
ss q
[kP
a]
SANISAND04
20 40 600
0.5
1
Number of cycles N
r u=
ua
cc/p
’ in
Exp
New modelSANISAND04
(b) p′in = 100 kPa, ein = 0.759
0 100 200 300−100
−50
0
50
100
Effective mean pressure p’ [kPa]De
via
toric s
tre
ss q
[kP
a]
New model
0 100 200 300−100
−50
0
50
100
Effective mean pressure p’ [kPa]De
via
toric s
tre
ss q
[kP
a]
SANISAND04
100 200 3000
0.5
1
Number of cycles N
r u=
ua
cc/p
’ in
Exp
New model
SANISAND04
(c) p′in = 300 kPa, ein = 0.744
Figure 6: Influence of initial effective confining pressure p′in
and initial void ratio ein on soil undrained cyclic behaviour, with
a drainedcycle be applied prior to the undrained cycles. (a) p′in =
100 kPa, ein = 0.825; (b) p
′
in = 100 kPa, ein = 0.759; (c) p′
in = 300 kPa,ein = 0.744. All tests with ς = 0.3.
predicts satisfactory the undrained behaviour at bothqualitative
and quantitative levels.
4.2.2 Influence of cyclic stress ratio
Cyclic triaxial tests are conducted on two soil samplesat ς =
0.2 and ς = 0.25, respectively. For both tests,the effective
confining pressure is p′in = 200 kPa. Theresults are shown in
Figure 7. The experimental re-sults in Figure 7(a) indicate that
for the soil samplewith ein = 0.842 and ς = 0.2, liquefaction
occurs af-
ter 146 loading cycles. The other soil sample, withein = 0.813
and ς = 0.25, undergoes 77 loading cy-cles before liquefaction
under the same loading con-ditions, see Figure 7(b). It indicates
that the loosersample subjected to smaller cyclic stress
amplituderesists more to liquefaction compared with the
densersample under larger cyclic stress amplitude. Again,SANISAND04
predicts higher pore water pressuregeneration for each cycle, while
the new model per-forms substantially better.
-
0 50 100 150 200−50
0
50
Effective mean pressure p’ [kPa]De
via
toric s
tre
ss q
[kP
a]
New model
0 50 100 150 200−50
0
50
Effective mean pressure p’ [kPa]De
via
toric s
tre
ss q
[kP
a]
SANISAND04
50 100 1500
0.5
1
Number of cycles N
r u=
ua
cc/p
’ in
Exp
New model
SANISAND04
(a) ein = 0.842, ς = 0.2
0 50 100 150 200
−50
0
50
Effective mean pressure p’ [kPa]
De
via
toric s
tre
ss q
[kP
a]
Experimental
0 50 100 150 200
−50
0
50
Effective mean pressure p’ [kPa]De
via
toric s
tre
ss q
[kP
a]
New model
0 50 100 150 200
−50
0
50
Effective mean pressure p’ [kPa]De
via
toric s
tre
ss q
[kP
a]
SANISAND04
20 40 60 80 1000
0.5
1
Number of cycles N
r u=
ua
cc/p
’ in
Exp
New model
SANISAND04
(b) ein = 0.813, ς = 0.25
Figure 7: Influence of cyclic stress ratio ς on soil undrained
cyclic behaviour, with a drained cycle be applied prior to the
undrainedcycles. Effective confining pressure p′in = 200 kPa, (a)
ein = 0.842, ς = 0.2; (b) ein = 0.813, ς = 0.25.
4.2.3 Best-fit simulations
For all undrained tests above, only one single setof parameters
has been adopted, including an aver-age value of µ0 equal to 85.
The model performswell in (both qualitatively and quantitatively)
cap-turing the undrained cyclic behaviour under differentloading
conditions and relative densities. This demon-strates that the
strategy of combining memory surfaceconcept with bounding surface
hardening theory issuitable to analyse the influence of fabric
effects incyclic loading problems. However, better
simulationresults are possible if different values of memory
sur-face parameters are adopted for different tests. In Fig-ure 8,
five different µ0 values are adopted to simulatethe aforementioned
five undrained cyclic triaxial tests(Wichtmann and Triantafyllidis
2016). Simulation re-sults are presented in terms of ur −N .
Simulation re-sults with different µ0 values fit the experimental
re-sults better than that of the simulation results obtainedusing
µ0 = 85 for all tests. This indicates that even ifthe modelling
strategy is suitable, better memory sur-face evolution law and more
suitable flow rule can stillbe devised.
5 CONCLUSIONS
In this work, a new model was proposed by intro-ducing the
memory surface hardening theory intoSANISAND04 model to properly
simulate sandratcheting and pore pressure accumulation
underhigh-cyclic loading. The memory surface, whichis allowed to
evolve both in size and position inthis model, represents
phenomenologically the evo-lution of sand fabric during repeated
loading. Themodel predictions agrees well with both drained
andundrained cyclic triaxial experimental results underdifferent
loading conditions and different soil densi-ties. The validation of
the model allowed to checkits accuracy with respect to the
following aspects: (1)progressive soil stiffening at increasing
number of cy-cles; (2) larger accumulated strain for looser soil
sam-ples under drained loading conditions at given cycles;(3)
larger accumulated strain for larger stress ampli-tude under
drained loading conditions at given num-ber of cycles; (4)
prediction of pore water pressure ac-cumulation under different
undrained cyclic loadingconditions and soil densities. Overall, the
model haspromising potential to complement costly
high-cycliclaboratory tests, as well as to be employed in
time-domain simulations of cyclic/dynamic soil-structureinteraction
problems.
-
5 10 15 200
0.5
1
Number of cycles N
r u
=u
acc
/p’ in
Exp
µ 0=67
µ 0=85
(a) test settings: p′in = 100 kPa,ein = 0.825, ς = 0.3, best fit
µ0 = 67
50 100 1500
0.5
1
Number of cycles N
r u=
ua
cc/p
’ in
Exp
µ 0 =94 µ
0=85
(b) test settings: p′in = 200 kPa,ein = 0.842, ς = 0.2, best fit
µ0 = 94
0 20 40 60 80 1000
0.5
1
Number of cycles N
r u=
ua
cc/p
’ in
Exp
µ 0 =80
µ 0=85
(c) test settings: p′in = 200 kPa,ein = 0.813, ς = 0.25, best
fit µ0 = 80
20 40 600
0.5
1
Number of cycles N
r u=
ua
cc/p
’ in Exp
µ 0 =87 µ 0=85
(d) test settings: p′in = 100 kPa,ein = 0.759, ς = 0.3, best fit
µ0 = 87
100 200 3000
0.5
1
Number of cycles N
r u=
ua
cc/p
’ in
Exp
µ 0 =82
µ 0=85
(e) test settings: p′in = 300 kPa,ein = 0.744, ς = 0.3, best fit
µ0 = 82
Figure 8: Illustration of memory surface parameter µ0 on pore
water pressure pressure accumulation ratio under undrained
conditions.Experimental results compared with new-model simulation
results with average µ0 = 85 for all five sets and with simulation
resultswith best-fit µ0 value for each set.
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