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Computers and Geotechnics 55 (2014) 378–391
Contents lists available at ScienceDirect
Computers and Geotechnics
journal homepage: www.elsevier .com/ locate/compgeo
A load transfer approach for studying the cyclic behaviorof
thermo-active piles
0266-352X/$ - see front matter � 2013 Elsevier Ltd. All rights
reserved.http://dx.doi.org/10.1016/j.compgeo.2013.09.021
⇑ Corresponding author.E-mail addresses:
[email protected] (M.E. Suryatriyastuti), hussein.
[email protected] (H. Mroueh).
M.E. Suryatriyastuti a, H. Mroueh a,⇑, S. Burlon ba Laboratoire
Génie Civil et géo-Environnement (LGCgE) – Polytech’Lille,
Université Lille1 Sciences et Technologies, Villeneuve d’Ascq
59655, Franceb Institut Français des Sciences et Technologies des
Transports, de l’Aménagement, et des Réseaux (IFSTTAR), Marne la
Vallée 77447, France
a r t i c l e i n f o
Article history:Received 15 April 2013Received in revised form
22 July 2013Accepted 29 September 2013Available online 19 October
2013
Keywords:Thermo-active pilesCyclic thermal loadingSoil–pile
interfacet–z FunctionModjoinFinite difference
methodThree-dimensional modeling
a b s t r a c t
Unsatisfactory understanding of thermally induced axial stress
and mobilized shaft friction in thethermo-active piles has led to a
cautious and conservative design of such piles. Despite the fact
thatthe number of construction works using this type of piles has
been rapidly increasing since the last20 years and none of them
witnessed any structural damage, the question that still remains is
how toovercome the cyclic thermal effects in such piles to optimize
the design method. This paper presents asoil–pile interaction
design method of an axially loaded thermo-active pile based on a
load transferapproach by introducing a proposed t–z cyclic
function. The proposed t–z function comprises a
cyclichardening/softening mechanism which is able to count the
degradation of the soil–pile capacity duringtwo-way cyclic thermal
loading in the thermo-active pile. The proposed t–z function is
then comparedto a constitutive law of soil–pile interface behavior
under cyclic loading, the Modjoin law. Afterwards,numerical
analyses of a thermo-active pile located in cohesionless soil are
conducted using the two cycliclaws in order to comprehend the
response of such pile under combined mechanical and cyclic
thermalloads. The behaviors of the pile resulting from the two laws
show a good agreement in rendering the cyc-lic degradation effects.
At last, the results permit us to estimate the change in axial
stress and shaft fric-tion induced by temperature variations that
should be taken into account in the geotechnical design ofthe
thermo-active pile.
� 2013 Elsevier Ltd. All rights reserved.
1. Introduction
The thermo-active piles have successfully incorporated the
heatexchanger elements to the structural pile foundations. Other
thansupporting the static weight of structure, the thermo-active
pilesare used to provide thermal energy to the overlying building
by cir-culating the heat carrier fluid inside the piles [1,2]. In
consequence,the thermo-active piles are subjected not only to the
mechanicalloading of the overlying structure but also to a two-way
cyclicthermal loading (i.e. seasonal thermal loading) according to
thethermal needs of building. Installation of the thermo-active
pilesin European countries [3–6] showed that the usage of these
pilesis advantageous in increasing the energy performance and in
min-imizing the annual cost [6,7]. But at the same time, this
latter pre-sents high risk on the mechanical resistance of both
foundationsand upper structure [8–10] because the circulating warm
fluid dur-ing summer produces a pile expansion and the circulating
coolfluid during winter produces a pile contraction [11,12].
Besides,no design code that takes into account the thermal
interaction on
the geotechnical capacity of pile foundations is available yet
[13].For years, contractors have done constructions with
thermo-activepiles based on empirical considerations or on a
conservative designmethod by increasing the safety factor [13,14].
As a result, a biggerdimension of pile and a higher piling cost are
required.
Due to the limited knowledge concerning the impact of
thermaloperation on the geotechnical performance, the response of
ther-mo-active piles under combined mechanical and cyclic
thermalloads becomes a major interest for establishing a more
effectivegeotechnical design criterion. Since the ratio of the pile
diameterto the pile length is very small, the temperature
variations injectedin the pile affects mainly the pile axial
response [15]. In situ expe-riences of the new building at Swiss
Federal Institute of Technologyin Lausanne [10] and the Lambeth
College in London [8] have re-marked an important change in
mobilized shaft friction and axialload distribution at the
soil–structure interface by the change oftemperature [16]. These
changes are stated to be dependent onthe degree of axial fixity at
the head and the toe of pile foundation[8,16]. While most reliable
method to determine the response ofthe piles is based on the
results obtained from pile load tests, thismethod can be expensive
and time-consuming [17]. Other alterna-tive means to study the
axially loaded piles is by conducting
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M.E. Suryatriyastuti et al. / Computers and Geotechnics 55
(2014) 378–391 379
numerical modeling with finite element analysis or with
loadtransfer analysis (t–z function). The first approach permits to
mod-el any constitutive soil behavior with non-linearity and
complexsoil–structure interaction, but in fact it does not really
providepractical solutions for piling problems [18]. The second
approachrequires to divide the pile into a number of segments
supportedby discrete springs representing the soil resistance at
each shaftelement [19,20], where the movement of the pile at any
segmentis related to the shaft friction at that segment [20].
This paper presents a numerical study of the seasonal
tempera-ture induced change in mechanical behavior of pile in the
aim tooptimize the geotechnical design capacity of the
thermo-activepiles. The work is based on the concept of
soil–structure interac-tion and thus requires the development of a
constitutive law thattakes into account the cyclic behavior at the
soil–pile interface.Two numerical approaches are proposed: load
transfer analysisin one-dimensional model and finite difference
analysis in three-dimensional model. In the first part, a
development of a nonlineart–z function at soil–pile interface
comprising a cyclic hardening/softening mechanism is presented.
This function is then employedto the load transfer method for the
design of thermo-active piles ina practical engineering approach.
The conceptual background, theworkability, and the performance of
the proposed function com-pared to the results from experimental
tests are discussed. The sec-ond approach used in this work is
based on modeling the soil–pilecontact using the constitutive
interface law Modjoin [21] with fi-nite difference method. This
constitutive law had been developedin the laboratory and has
recently enhanced to control cyclic deg-radation phenomena as
strain ratcheting, strain accommodationand stress relaxation [22].
The study is distinguished into two ex-treme head restraint
conditions: a free head pile and a fully re-strained head pile.
2. Development of t–z function under two-way cyclic loading
The fundamental requirement of load transfer analysis is
theappropriate t–z function used to measure the local shaft
frictionand the relative displacement of soil–pile. A number of t–z
curvesresulted from in situ static loading tests has been
established byCoyle and Reese [23], Coyle and Sulaiman [24], Frank
and Zhao[25], and Reese and O’Neill [26]. These t–z curves were
originallyobtained empirically but may now be obtained more
satisfactorilyvia theoretical relationship with the stiffness of
the surroundingsoil [27,28].
Randolph has developed a theoretical t–z function under axi-ally
cyclic loading and implemented it to RATZ numerical com-putation
program analysis [29,30]. The function consists of alinear elastic
part, a nonlinear parabolic shape function describ-ing the strain
hardening/softening mechanism, and also a func-tion considering
cyclic degradation effects [30,31]. In its recentversion, some
extensions have been included such as thermalstrain in the pile,
but it is limited to a single magnitude of thecyclic thermal
strains for each analysis. Laboratory of soilmechanics in Swiss
Federal Institute of Technology Lausannehas worked on two-way
cyclic thermal loading by adding theunloading curve in the t–z
curve developed by Frank and Zhao[32]. The curve is implemented
into ThermoPile program soft-ware, which is designed specifically
for analyzing the thermo-ac-tive piles behavior [32]. However, the
curve is limited to twolinear elastoplastic branches and a plateau
corresponding tothe ultimate stress value without having a
kinematic hardeningcriterion [13,32].
Authors intend to develop a theoretical nonlinear t–z
functionwhich is able to describe the cyclic hardening/softening
mecha-nism under two-way cyclic loading. This t–z function is
implemented into an algorithm programming language offering
apractical design tool for the geotechnical design of
thermo-activepiles.
2.1. Conceptual background
Generally speaking, the seasonal thermal contraction and
dila-tation in the thermo-active piles can be equated with a
two-waycyclic axial loading. A number of experimental
investigations havebeen carried out to learn the response of piles
under cyclic axialloading. Holmquist and Matlock [33] stated that
two-way cyclicloading results in a dramatic reduction in the pile
load capacitymuch more than that in the case of one-way cyclic
loading. Besides,they pointed out that the reduction in shaft
friction has reached upto 75% in the case of extremely large
displacement amplitudes.Data collected by Bea et al. [34] showed a
remarkable increase inpile head settlement with the number of
cycles, causing a reduc-tion in load capacity. On the other hand,
Bjerrum [35] and Beaet al. [34] indicated that the more rapid the
rate of loading is, thegreater the pile capacity becomes. Desai et
al. [36] and Fakharianand Evgin [37] concluded that in cohesionless
soils, the interfaceresponse gets stiffer as the number of cycles
increases, while therate of stiffening decreases.
Poulos found that under two-way axially cyclic loading,
thereduction in material volume leads to the reduction in
normalstress and consequently to the reduction in shear stress
mobilizedbetween the shaft and the soil [18,38]. According to these
facts,Poulos concluded that the degradation in shaft resistance
dependsnot only on the reduction in shear stress as a function of
absolutecyclic slip displacement, but also on the reduction in
normal effec-tive stress due to volumetric strain during cyclic
shearing [37,39].The former component may become more significant
in less com-pressible soils whereas the latter component may
dominate incompressible soils.
As a summary, modeling the nonlinear relationship betweenthe
shaft friction and the relative displacement at the
soil–pileinterface under two-way cyclic loading should satisfy the
followingconditions:
� Reduction in shaft friction with increasing the number of
cycles[18,33,34].� Degradation in shaft resistance with the
accumulation of abso-
lute tangential displacement [37,39].� Reduction in normal
stress by the volumetric strain with
increasing the number of cycles [39].� Increase in shaft
resistance with a higher loading rate [34,35].� Increase in pile
settlement with increasing the number of cycles
[34].� Hardening and stiffening in interface with increasing the
num-
ber of cycles [36].� Decrease in rate of stiffening with
increasing the number of
cycles [36].
With respect to the hypotheses above, a new formulation
ofnonlinear t–z function is developed. The proposed t–z function
isdivided into two stages of loading: the initial relation under
mono-tonic loading and the extension under cyclic loading.
2.2. Proposed t–z function under monotonic loading
2.2.1. Basic principleUnder monotonic loading, the formulation
of the proposed t–z
function is based on the Frank & Zhao t–z law [25] with
respectto the French design standard for the deep foundations
design[40]. The shaft friction mobilized at the soil–pile interface
qs re-lated to the tangential displacement ut is given by:
-
Fig. 1. Parametric study of a.
Fig. 2. Comparison of the proposed t–z function and the t–z law
of Frank & Zhao[17].
Fig. 3. Parametric study of b.
Fig. 4. Parametric study of c.
380 M.E. Suryatriyastuti et al. / Computers and Geotechnics 55
(2014) 378–391
qs ¼ qs0 1� e�uta
� �ð1Þ
where qs0 (kPa) and a (m) denote the ultimate mobilized
frictionand the rate of mobilized friction under monotonic loading,
respec-tively. A parametric study of the influence of parameter a
on theevolution of shaft friction qs is given in Fig. 1. It shows
that thesmaller the value of a, the smaller displacement is needed
for mobi-lizing friction at the pile shaft, which leads increasing
the stiffnessof interface. The gradient of the function represents
the slope ofthe curve and can be equated to the coefficient kt in
the Frank &Zhao law. Therefore, the choice of parameters qs0
and a is done byan approximation to the Frank & Zhao
coefficient [25], or, it canbe taken from the Menard’s pressure
meter modulus EM and Me-nard’s pressure limit pLM [41] according to
the French national codefor deep foundation [40].
Fig. 2 shows the comparison of the proposed t–z function to
theFrank & Zhao law under monotonic loading, both for fine
soils andgranular soils. By setting the parameter a in accordance
with kt, thet–z curves resulting from the proposed function are
very close tothe curves of Frank & Zhao law. When the value of
a is equal tothe imposed relative displacement ut, the mobilized
friction ob-tained using Eq. (1) is equal to 63% of the ultimate
mobilized fric-tion. At this state of displacement, the difference
between themobilized frictions obtaining from the proposed t–z
function andthe Frank & Zhao law is below 5 kPa.
2.2.2. Strain hardening/softening parametersStrain
hardening/softening phenomenon in materials depends
on the void ratio in granular soils and on the Atterberg limits
in
fine soils. In order to consider the nonlinear behavior of
strainhardening/softening, the proposed t–z function introduces
threeother parameters b, d, and c in following equation:
qs ¼ qs0 1� e�uta
� �þ budt e
� utcð Þd ð2Þ
where b (kPa) and c (m) indicate the amplitude of strain
hardening/softening and the rate of strain hardening/softening
under mono-tonic loading. d is an unitless parameter which controls
the timeloading rate.
The first part of the equation defines the relation of shaft
resis-tance and tangential displacement with the control of
ultimateshaft resistance, whereas the second part of the equation
de-scribes the peak of shaft resistance related to the loading rate
thatmay be attained in parabolic function. The peak of shaft
resis-tance may occur only in dense soil with a high loading rate,
forexample in over consolidated clay or in dense sand. The
greaterthe parameter b is, the higher the peak of parabolic curve
is ob-tained, which corresponds eventually to the denser soil (Fig.
3).For a same given value of b, parameter c controls the radius
ofparabolic curve expressing the velocity of strain
hardening/soft-ening mechanism (Fig. 4).
The parametric study of d has successfully described
thehypothesis of Bjerrum [35] and Bea et al. [34] who showed that
amore rapid loading rate contributes to an increase in pile
capacity.Thus, a greater parameter d reveals to a higher peak of
shaft resis-tance (Fig. 5).
-
Fig. 5. Parametric study of d.
M.E. Suryatriyastuti et al. / Computers and Geotechnics 55
(2014) 378–391 381
2.3. Proposed t–z function under two-way cyclic loading
In analyzing the behavior of piles subjected to cyclic
loading,three aspects of soil response should be considered: the
degrada-tion of soil–pile resistance and/or soil modulus, the
loading rate ef-fects, and the accumulation of permanent
displacements [18]. Theproposed t–z function under two-way cyclic
loading comprising ofthose aspects is given in following
equation:qs ¼ qsi
þAð�1Þnþ1 qs0þDqsð1�e�utse Þ
� �1�e�Rj
ut�utia j
� �þbe�
utse jut�utijde�
ut�uticð Þ
2� �
ð3Þ
where n denotes the number of inversion loading during
two-waycyclic loads. qsi (kPa), uti (m), and uts (m) indicate the
initial calcu-lated friction at each inversion loading cycle (qsi =
0 for n = 1), theinitial displacement obtained at each inversion
loading cycle(uti = 0 for n = 1), and the cumulative displacements
during two-way cyclic loads (uts ¼
Pjutij).
The degradation of interface resistance is controlled by
theparameters Dqs (kPa) and e (m) which express the amplitude
ofcyclic strain hardening/softening and the rate of cyclic strain
hard-ening/softening.
The function R in Eq. (4) controls the stiffness hardening
ofinterface at each inversion loading cycle, ranging between 1
andq. Inside the function R, parameters q and n allow controlling
cyclicfatigue effects in interface behavior, such as stress
relaxation orstrain ratcheting, where q indicates the amplitude of
cyclic degra-dation and n is the rate of degradation.
Factor A in Eq. (5) is the interface stiffness hardening
factorwhich is dependent on the level of stress obtained. A takes
into ac-count the distance between the actual stress state qsi and
the max-imum cyclic stress state qs0 + Dqs which may vary with the
cycles.If an inversion of loading cycle occurs at high level of
stress, a high-er value of A is produced and thus the interface
becomes stiffer inthe next cycle. This factor varies between 1.0
and 2.0.
R ¼ e�ðn�1Þn þ qð1� e�ðn�1ÞnÞ ð4Þ
A ¼qsi � ð�1Þ
nþ1 qs0 þ Dqs 1� e�utse
� �� �
qs0 þ Dqs 1� e�utse
� �������
������ ð5Þ
Fig. 6. (a) Stress relaxation when q and n = 1 (b) no relaxation
when q and n = 3.
2.4. Performance of the proposed t–z function
To study the performance of the proposed t–z function,
severaltests are conducted in two different modes:
strain-controlled and
stress-controlled. If the deformation is maintained constant
withthe increment of cycles, the stress will gradually decrease due
tocyclic fatigue in interface. This phenomenon is known as
stressrelaxation [42–44]. Otherwise, if the stress is sustained
along thecycles, a progressive accumulation of plastic strain
during cyclesoccurs, known as strain ratcheting phenomenon
[42–44].
Figs. 6 and 7 show the parametric study of cyclic
degradationparameters q and n at strain-controlled and
stress-controlled con-ditions. When the values of q and n are set
at 1.0, the phenomenaof stress relaxation and strain ratcheting are
important. The higherthe values of q and n are, the stiffer the
interface behaves undercyclic loading. Accordingly, there is lower
variation of the decreasein shaft resistance per cycle (Fig. 6b)
and the accumulation of plas-tic strain becomes slower and smaller
(Fig. 7b).
A direct shear test under cyclic loading in strain-controlled
wasconducted at Centre d’Etudes et Techniques de l’Equipement
(CETE)Nord Picardie. Due to cyclic softening, the results showed
thatthe friction mobilized became lower with increasing the
numberof cycles, but the interface stiffness increased at each load
cycle.Fig. 8 shows a comparison of the results from direct shear
testand from modeling the interface behavior with the proposed
t–zfunction. By setting the parameters in the proposed function
inaccordance with the material properties used in the direct
sheartest, the proposed t–z function can successfully describe
similarphenomena in interface.
-
Fig. 7. (a) Strain ratcheting when q and n = 1 (b) no ratcheting
when q and n = 3.
Fig. 8. Comparison of the results from direct shear test and the
proposed t–zfunction.
Fig. 9. Comparison of the Modjoin law and the proposed t–z
function (a) stressrelaxation phenomenon (b) strain ratcheting
phenomenon.
382 M.E. Suryatriyastuti et al. / Computers and Geotechnics 55
(2014) 378–391
3. A constitutive law of the soil–pile interface under
cyclicloading: Modjoin
Modjoin is a constitutive law of interface behavior under
cyclicloading in the framework of elastoplasticity based on the
conceptof bounding surface [21]. The elastic part is defined by two
param-
eters: normal stiffness kn and shear stiffness kt, which relate
thenormal stress r to the normal displacement un and the shear
stresss to the tangential displacement ut. Modjoin incorporates
soil non-homogeneity, non-linearity, cyclic degradation, post-peak
soften-ing–hardening, and interface contraction–dilatation.
The limit resistance of the interface is defined by the
boundarysurface. The boundary surface fl with the associated
isotropic hard-ening function Rmax are governed in following
equations:
fl ¼ jsj þ rnRmax ð6Þ
Rmax ¼ tan /þ DR 1� eADRup
tr
� �ð7Þ
where Rmax depends on friction angle u and cumulative plastic
tan-gential displacement uptr . DR and ADR are the control
parameterswhich indicate respectively the amplitude and the rate of
isotropichardening.
The kinematic surface fc encloses the domain of yielding,
whichis controlled by the associated kinematic hardening function
Rc. fcand Rc are given in Eqs. (8) and (9) and are governed by the
param-eters cc, bc, and k as follows:
fc ¼ js� rnRcj ð8Þ
dRc ¼ k ccjRmax � Rcjbc
� �ð9Þ
where cc and bc express the amplitude and the rate of
kinematichardening and k denotes plastic multiplier.
Finally, the flow rule to reproduce the contracting phase
fol-lowed by dilating phase is given in Eqs. (10) and (11). This
rule de-
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M.E. Suryatriyastuti et al. / Computers and Geotechnics 55
(2014) 378–391 383
pends on the actual plastic tangential displacement uptc, the
dilationangle wc and the velocity of phase change ac.
@g@rn¼ tan wc �
s� rnRcrn
��������
� �e�ac u
ptc ð10Þ
@g@s ¼
sjsj ð11Þ
This constitutive law is capable of drawing cyclic
degradationphenomena of the soil–pile interface, such as mean
stressrelaxation, hardening/softening stress, strain ratcheting,
and strainaccommodation [22]. Fig. 9 shows the comparison of the
Modjoinlaw and the proposed t–z function in rendering stress
relaxationphenomena under a strain-controlled test and strain
ratchetingphenomena under a stress-controlled test.
4. Study of a thermo-active pile under two-way cyclic
thermalloading
The response of thermo-active piles under two-way cyclic
ther-mal loading during their seasonal operation time becomes
onemajor interest to optimize their geotechnical capacity.
Duringwinter operation, a cooler fluid is injected in the pile to
extractthe heat energy from the soil, thus the pile contracts. The
temper-ature of the injected fluid must be above 0 �C to
avoidfreezing–thawing of the surrounding soil [7]. During summer
oper-ation, the cooled down soil is recharged by circulating
awarmer fluid along the pile, thus the pile expands. The
cycliccontraction–dilatation of thermo-active piles during the
period ofoperation induces change in axial load and shaft friction
that leadsto the degradation in the soil and interface resistances
[8–10,16]. Inorder to analyze the cyclic behavior of the
thermo-active pile,numerical simulations are performed using the
two cyclic laws:the proposed t–z function with load transfer method
in 1D modeland the Modjoin law with finite difference method in 3D
model.Since the behavior of the thermo-active pile is dependent on
theaxial fixity at the head and the toe of the pile [8,16], this
presentstudy conducts two extreme cases of the pile head axial
fixity.The first case concerns the free head pile with constant
thermalhead load over the cycles (i.e. zero head axial fixity) and
the secondcase concerns the restrained head pile with constant
thermal headdisplacement over the cycles (i.e. infinite head axial
fixity). Thestudy focuses on observing four aspects that are
influenced and de-graded during cyclic thermal loading: pile head
settlement, headload capacity, axial load distribution, and local
shaft friction.
4.1. Numerical model
A single thermo-active pile with a square section of widthB = 60
cm and length H = 15 m is founded on very loose sandy soils.The
pile is initially subjected to incremental monotonic loading
Table 1Properties of materials and of Modjoin interfaces.
Properties Notation Soil
Density of material qm 195Young’s modulus E 10 MThermal
conductivity kT 1.5Specific heat extraction c 800Coefficient of
thermal expansion aT 5 �Normal stiffness kn –Shear stiffness kt
–Friction angle u –Dilation angle w –
corresponding to the permanent load of building during the
con-struction phase. According to the French design standard for
thedeep foundations, the mechanical working load applied to the
pileQmec is fixed at 33% of the ultimate monotonic load QULT when
thepile head settlement is equal to 1/10 B [40,45]. This stage of
loadingoccurs at n = 0 with an index ‘‘mec’’.
In addition to the mechanical working load, the pile is also
sub-jected to the temperature variations during the seasonal
energyextraction, with a temperature gradient ±10 �C from the
groundtemperature. The temperature gradient in the pile is assumed
tobe uniform over the entire pile, and, accordingly, the addition
ofthermal loading is applied in terms of a uniform thermal
deforma-tion eth by multiplying the temperature gradient DT with
the con-crete thermal expansion coefficient aT. Thermal loading
cycles areperformed during 12 year of thermo-active pile operation,
com-prising of 24 seasonal cooling and heating cycles. Each cycle
corre-sponds to 1 season of temperature loading (i.e. 6 months)
inneglecting the daily temperature variation in the pile. Fig. 10
illus-trates the schematic of loading sequences in the
thermo-activepile. Since the ratio of the pile diameter to the pile
length is verysmall, radial movements of the pile induced by
temperature varia-tions can be neglected in comparison with
thermally induced axialmovements of the pile [15]. Hence, for each
cycle of loading, thetemperature variation induces change in axial
deformation of thepile as follows:
en ¼ emec � eth ¼ emec � ðaTDTÞ ð12Þ
Both pile and soil are assumed to behave in linear
thermo-elas-tic conditions, with the Young’s modulus E of soil is
equal to10 MPa and that of pile is 20 GPa. The coefficients of
thermalexpansion aT are taken as 5 � 10�6/�C for soil and 1.25 �
10�5/�Cfor pile. The properties of soil are taken from CETE Nord
Picardiedata for very loose sand.
In the one-dimensional model, the analysis is performedusing
load transfer method by applying the proposed t–z func-tion
presented in Section 2.3. The pile is divided into a numberof
segments supported by discrete springs that represent themobilized
resistance along the shaft qs and at the base of pileqp (Fig. 11).
The method consists of back-calculating the bound-ary condition at
the pile head by imposing an assumed pile tipmovement for each load
cycle. Each pile segment must satisfythe vertical equilibrium for
each load cycle. The load transfermethod is implemented into a
computer program that has beendeveloped to analyze the axially
loaded thermo-active pile. Aflowchart of iterative programming
language is given in Fig. 12while the detail equations used to
solve the equilibrium are pre-sented in Appendixes A and B.
The three-dimensional analysis is carried out using an
explicitfinite difference program FLAC3D. Due to the symmetric
condition,only one-fourth of the complete domain is modeled (Fig.
13). Thesoil is refined around the pile in order to increase the
precisionin the areas of high strain gradient. After a parametric
analysis,
Pile Modjoin interface
0 kN/m3 2500 kN/m3 –Pa 20 GPa –
W/m2 1.8 W/m2 –J/kg �C 880 J/kg �C –10–6/�C 1.25 � 10–5/�C –
– 22 MN/m– 8.33 MN/m– 30�– 1�
-
Fig. 10. Schema of cyclic thermal loadings.
Fig. 11. 1D model with load transfer t–z method.
384 M.E. Suryatriyastuti et al. / Computers and Geotechnics 55
(2014) 378–391
the mesh was fixed with the soil lateral extension is set at 15
m(25B) and the height of soil mass at 30 m (2H). Interface
elementsare introduced at the vertical zone of contact between the
soil andpile. The interfaces employ the constitutive Modjoin law in
nonlin-ear elastoplastic behavior, presented in Section 3. The
interface
normal stiffness kn and shear stiffness ks are chosen in
accordancewith the interfaces theory and background of FLAC3D code
[46]. Ta-ble 1 summarizes the elastic and thermal properties of
soil, pile,and Modjoin interfaces. These properties are assumed not
tochange with temperature variation.
-
Fig. 12. Flowchart diagram of calculation.
M.E. Suryatriyastuti et al. / Computers and Geotechnics 55
(2014) 378–391 385
According to the type of soil, the value of parameter b in
theproposed t–z function is set at zero and thus no intervention of
thisparameter takes place in the second part of Eqs. (2) and (3).
Thematerials are considered to undergo cyclic fatigue effects with
a
cyclic softening tendency. Hence, the cyclic degradation
parame-ters q and n in the proposed t–z function are set at 1.0.
This condi-tion is also translated into the parameters used in the
Modjoinmodel with DR and ADR are set at �0.05 referring to cyclic
soften-
-
Fig. 13. 3D model with the Modjoin interfaces.
(a) Ratio to the head settlement at the mechanical loading
(b) Ratio to the head settlement at the first cooling/heating
cycles
Fig. 14. Temperature-induced change in head settlement in the
free head pile.
386 M.E. Suryatriyastuti et al. / Computers and Geotechnics 55
(2014) 378–391
ing behavior. Since the analysis in the one-dimensional model
doesnot model the surrounding soil mass, the bearing stress qp is
notallowed to have a negative value in order to limit the
degradationin the base resistance. A comparable assumption is
applied in thethree-dimensional model; the interface Modjoin at the
pile baseis perfectly bonded to the soil and is not allowed to have
separa-tion. The choice of cyclic hardening parameters in the
proposedt–z function is adjusted to the Modjoin model.
For the sake of clarity, downward movements of w are
takenpositive while upward movements are negative.
Compressivestresses and forces are taken positive while tensile
stresses andforces are negative according to the convention in soil
mechanics.The response of the thermo-active pile over the cycles
will be de-tailed in the following section, for both the free head
pile and therestrained head pile. The behavior resulting from 1D
analysis usingthe proposed t–z function is compared to that of
resulting from 3Danalysis using the Modjoin law.
4.2. Response of a free head thermo-active pile
In both models, the head settlement induced by the tempera-ture
variations varies below 30% of the mechanical head settle-ment
(Fig. 14a). High variation of settlement occurs in the
firstcooling–heating cycles when the pile undergoes the first
thermalcontraction and dilatation. After the second cooling–heating
cycles,the relative variation of pile head settlement during cyclic
loads in-creases smoothly up to 20% of its value at the first
cooling–heatingcycles (Fig. 14b). Fig. 14b shows clearly that
cyclic settlement ofboth models started with the same initial
slopes but the t–z modelhas a higher cyclic strain softening.
Fig. 15 shows the distribution of axial force along the pile in
thebeginning of the cooling–heating cycles and in the final
cooling–heating cycles as well. A decrease in axial force is found
in the firstcooling cycle due to the pile shortening. Afterwards,
the variationin axial force in the pile increases with the number
of cycles, withthe values of variation in cooling are smaller than
those in heating.The increase in axial force is caused by the
degradation of interfaceand soil properties during cyclic loading.
However, the highest va-lue of axial force variation at the final
cycle is 9% for 1D model and16% for 3D model (Fig. 15).
In the case of free head pile, the distribution of shaft
frictionshows an opposite response at the upper part and the lower
partof pile. When the pile is cooled, the bearing stress decreases
whilethe shaft friction increases due to the pile contraction. On
the con-trary, when the pile is heated, an increase in bearing
stress and adecrease in shaft friction are occurred owing to the
expansion ofpile.
The variation of local friction vs. local tangential
displacementpoints out the cyclic fatigue phenomenon at the
soil–pile interfacefor both models. Because of the choice of cyclic
hardening/soften-ing parameters in the models, a phenomenon of
strain ratchetingappears (Fig. 16). However, at the lower-half of
the pile(Fig. 16b), the degradation in interface capacity is
smaller due tothe presence of soil surrounding the pile which
resists the stressmobilized for the case of 3D model. For the case
of 1D model, thefriction of interface tends to increase at the
lower-half of the piledue to the boundary condition of the 1D model
which limits thedegradation in the bearing stress.
-
Fig. 15. Change in axial force induced by temperature variations
in the free head pile (a) Model t–z and (b) Model Modjoin.
(a) at depth z = ¼ H
(b) at depth z = ¾ H
Fig. 16. Change in the soil–pile interface response at different
depths in the free head pile.
M.E. Suryatriyastuti et al. / Computers and Geotechnics 55
(2014) 378–391 387
4.3. Response of a restrained head thermo-active pile
It is shown that under constant head displacement, the
ther-mo-active pile undergoes a decrease in head axial force
relativeto the force at the mechanical loading stage up to �60%
(for thet–z model) and �20% (for the Modjoin model) (Fig. 17a).
Thisindicates a relaxation phenomenon due to the degradation
ofsoil–pile resistance which is affected by the choice of
parame-ters. For the same parameters used, the cyclic behavior of
thefully-restrained head pile does not show a similar
behaviorbetween the t–z and the Modjoin model, unlike the
responseof the free head pile (Section 4.2). Fig. 17b shows that
the 1Dt–z model brings out a high diminution in pile head
capacitythat is possibly due to the absence of soil mass
surrounding thepile. Besides, for the same displacements obtained,
the forcesrepartition between the 1D and the 3D models are
obviouslydifferent.
The thermally induced axial force decreases greater
duringcooling than that of during heating (Fig. 18). For the 1D
t–zmodel, the axial force decreases uniformly over the entire
lengthof the pile. For the 3D Modjoin model, the axial force
decreasesalong the depth until reaching a stiffer base resistance
at thepile base due to the bonded interface with the soil.
Therefore,the maximum degradation in axial force at the final
cooling islower at the 3D model (�25%) than that of the 1D t–z
model(�65%).
In the restrained head pile, shaft friction decreases
graduallyalong the depth of pile. It is noted that the degradation
of ther-mally-induced friction is higher during cooling than that
of dur-ing heating. This is due to the decrease in the base
resistancewhen the pile base lifts up during contraction.
Relaxation phe-nomenon also appears in the response of the
soil–pile interface.Fig. 19 points out a gradual diminution in
shaft friction duringthermal cycles. The variation of tangential
displacement is con-stant during cycles in the 1D model because the
mobilized stressis supported only by the elastic pile. Different
response of inter-face is observed in the 3D model. The Modjoin
interfaces devel-op cyclic degradation phenomenon while the
surrounding soilremains elastic with no cyclic degradation and thus
causes anaccumulation of tangential displacement at the
soil–pileinterface.
-
(a) Ratio to the head force at the mechanical loading
(b) Ratio to the head force at the first cooling–heating
cycles
Fig. 17. Temperature-induced change in head axial force in the
restrained headpile.
Fig. 18. Change in axial force induced by temperature variations
in the restrained head pile (a) Model t–z and (b) Model
Modjoin.
(a) at depth z = ¼ H
(b) at depth z = ¾ H
Fig. 19. Change in soil–pile interface response at different
depths in the restrainedhead pile.
388 M.E. Suryatriyastuti et al. / Computers and Geotechnics 55
(2014) 378–391
-
M.E. Suryatriyastuti et al. / Computers and Geotechnics 55
(2014) 378–391 389
5. Conclusion
A development of a theoretical t–z function for the
soil–pileinterface under two-way cyclic loading is being
established in thispaper. The function is based on a series of
results and hypothesesof the previous field and laboratory
investigations. The proposedfunction is able to describe the cyclic
strain hardening/softeningmechanism and the degradation phenomenon
during cyclicloading, comprising the fatigue effects such as stress
relaxationand strain ratcheting. The function consists of nine
parameters:
� qs0 and a which describe the mobilization of friction
undermonotonic loading.� b, d, and c which control the strain
hardening/softening under
monotonic loading.� Dqs, e, q, and n which take into account the
cyclic strain harden-
ing/softening.
This proposed t–z function is then employed to the load
transfermethod by developing a numerical program in the intention
to of-fer a practical engineering tool for the design and analysis
of thethermo-active pile behavior.
Afterwards, 1D analysis of a single thermo-active pile under
axialmechanical and cyclic thermal loads is conducted by using the
loadtransfer method with the proposed t–z function. A comparison
mod-el using three-dimensional finite difference analysis with the
consti-tutive Modjoin interfaces law is also conducted. The
responses of athermo-active pile resulting from 1D and 3D analyses
are comparedin order to study the cyclic degradation effects
induced by seasonaltemperature variations. While the 1D load
transfer method permitsto have a simplified and practical
calculation with high time effi-ciency, the 3D model using the
Modjoin law with finite differencecode proposes a complete
interaction analysis with higher numeri-cal time consumption. The
global response of the thermo-active pilein this study performs a
good concordance in both models. The pres-ence of the elastic soil
surrounding the pile in the 3D model leads to adifferent local
response at the soil–pile interface between the twomodels. This
numerical study points out the capability of the twolaws of
soil–pile interface behavior to render the cyclic
degradationeffects in the thermo-active pile.
According to the axial fixity at the pile head, the degradation
ofsoil–pile resistance during cycles generates increase in pile
headsettlement for the free head pile or decrease in pile head
capacityfor the restrained head pile. The free head pile tends to
have differ-ent behavior at the upper and the lower part of pile.
In the re-strained head pile, axial force and shaft friction
distributions areuniform over the pile length. The parameters
chosen in this numer-ical study lead to the emergence of cyclic
fatigue effects: strain rat-cheting and stress relaxation
phenomena. An ongoing project ofin situ loading tests of full-scale
thermo-active piles will providereal data and thus help to
calibrate the cyclic parameters used inthe numerical model.
At the end, the numerical results obtained in terms of
dis-placements, axial forces and local shaft friction could be
usedto justify rationally the design of thermo-active piles and
thusestablish a secure basis design method instead of doubling
thesecurity factor. To begin with, the values of the pile head
dis-placement during thermal cycles could be used to verify the
ser-viceability limit states. Afterwards, the distribution of axial
stressin the pile permits to control the compression and/or the
tensilestate in concrete. Finally, the evolution of local friction
along theshaft allows calculating the mobilized shaft resistance
and themobilized base resistance and thereby estimating the
requiredsecurity factor.
Acknowledgements
The work described in this paper forms part of a research
pro-ject ‘‘GECKO’’ (geo-structures and hybrid solar panel coupling
for opti-mized energy storage) which is supported by a grant from
theFrench National Research Agency (ANR). It is an industrial
project,involving four public companies and two research
laboratories incivil and energy engineering sector: ECOME, BRGM,
IFSTTAR, CETENord Picardie, LGCgE–Polytech’Lille and LEMTA–INPL.
The authorswould like to express their gratitude to their partners
for their con-tinuous support in this and ongoing project.
Appendix A
The procedure described below is used for the load transfer
cal-culation of a pile under monotonic loading. The pile is divided
intok segments as shown in Fig. 11, where segment no. 1 indicates
thesegment at the top of the pile and segment no. k indicates the
seg-ment at the bottom of the pile.
1. Assume an initial value of the tip movement wp at the
bottomsegment k.
2. Search the value of the end-bearing stress qp at the pile
basewith the imposed wp by using Eq. (2) of the proposed
t–zfunction.
3. Calculate the end-bearing resistance.
Qp ¼ qp14pB2
� �ðA:1Þ
4. Calculate the elastic deformation at the lower half of
segment k.
eep ¼Q p
14 pB
2EMðA:2Þ
5. Calculate the midpoint movement at segment k.
wk ¼ wp þ12
hkeep ðA:3Þ
6. By applying the estimated midpoint movement at segment
k,search the value of shaft friction at segment k qsk using Eq.(2)
of the proposed t–z function.
7. Calculate the axial load at the midpoint of segment k.
Qk ¼ Q p þ pB12
hkqsk ðA:4Þ
8. Calculate the elastic deformation at the upper half of
segment kand at the lower half of segment k � 1.
eek ¼Qk
14 pB
2EMðA:5Þ
9. Calculate the midpoint movement at segment k � 1.
wk�1 ¼ wk þ12ðhk þ hk�1Þeek ðA:6Þ
10. Search the value of shaft friction at segment k � 1
qsk�1using Eq. (2) of the proposed t–z function.
11. Calculate the axial load at the midpoint of segment k �
1.
Qk�1 ¼ Q k þ pB12ðhk þ hk�1Þqsk�1 ðA:7Þ
12. Do the iteration from the lower half of segment k � 2
untilthe midpoint of top segment by repeating step 8–11.
13. For the upper half of segment 1, calculate the response of
thepile head.
wh ¼ w1 þ12
h1ee1 ðA:8Þ
-
390 M.E. Suryatriyastuti et al. / Computers and Geotechnics 55
(2014) 378–391
Q h ¼ Q 1 þ pB12
h1qs1 ðA:9Þ
Appendix B
The following calculation procedure is done during cyclicthermal
loading in this present study for the free head pileand the
restrained head pile. The procedure is repeated for eachload
cycle.
1. Boundary conditions of the model treated in this study.a.
Qh;n ffi Qh;mec for the free head pile under constant load.b. wh;n
ffi wh;mec for the restrained head pile under constant
displacement.2. Delta temperature ±10 �C from the ground
temperature is
applied uniformly along the pile. Calculate the thermal
defor-mation obtained due to this temperature variation.
eth;n ¼ aTDTn ðB:1Þ
3. Assume an initial value of the tip movement wp,n at the
bottomsegment k.
4. Search the value of the end-bearing stress qp,n at the pile
basewith the imposed wp,n by using Eq. (3) of the proposed
t�zfunction.
5. Calculate the end-bearing resistance.
Q p;n ¼ qp;n14pB2
� �ðB:2Þ
6. Calculate the elastic deformation at the lower half of
segment k.
eep;n ¼Qp;n
14 pB
2EMþ eth;n ðB:3Þ
7. Calculate the midpoint movement at segment k.
wk;n ¼ wp;n þ12
hkeep;n ðB:4Þ
8. By applying the estimated midpoint movement at segment
k,search the value of shaft friction qsk,n using Eq. (3) of the
pro-posed t�z function.
9. Calculate the axial load at the midpoint of segment k.
Q k;n ¼ Q p;n þ pB12
hkqsk;n ðB:5Þ
10. Calculate the elastic deformation at the upper half of
seg-ment k and at the lower half of segment k � 1 with the
addi-tional thermal deformation included.
eek;n ¼Q k;n
14 pB
2EMþ eth;n ðB:6Þ
11. Calculate the midpoint movement at segment k � 1.
wk�1;n ¼ wk;n þ12ðhk þ hk�1Þeek;n ðB:7Þ
12. Search the value of shaft friction at segment k � 1 qsk�1,n
byusing Eq. (3) of the proposed t–z function.
13. Calculate the axial load at the midpoint of segment k �
1.
Q k�1;n ¼ Q k;n þ pB12ðhk þ hk�1Þqsk�1;n ðB:8Þ
14. Do the iteration from the lower half of segment k � 2
untilthe midpoint of top segment by repeating step 10–13.
15. For the upper half of segment 1, calculate the response of
thepile head.
wh;n ¼ w1;n þ12
h1ee1;n ðB:9Þ
Qh;n ¼ Q1;n þ pB12
h1qs1;n ðB:10Þ
16. Repeat step 3–15 until the boundary conditions are
satisfied.
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A load transfer approach for studying the cyclic behavior of
thermo-active piles1 Introduction2 Development of t–z function
under two-way cyclic loading2.1 Conceptual background2.2 Proposed
t–z function under monotonic loading2.2.1 Basic principle2.2.2
Strain hardening/softening parameters
2.3 Proposed t–z function under two-way cyclic loading2.4
Performance of the proposed t–z function
3 A constitutive law of the soil–pile interface under cyclic
loading: Modjoin4 Study of a thermo-active pile under two-way
cyclic thermal loading4.1 Numerical model4.2 Response of a free
head thermo-active pile4.3 Response of a restrained head
thermo-active pile
5 ConclusionAcknowledgementsAppendix AAppendix BReferences