3350
Proceedings of the 18
th
International Conference on Soil Mechanics and Geotechnical Engineering, Paris 2013
3.2
Soil stiffness
In these analyses, the coefficient of thermal expansion in the
soil was held at 1.5E-5°K
-1
, and the soil Young’s modulus was
doubled from 30 MPa to 60 MPa. The predicted response in
terms of change in axial stress and pile-soil interface shear for
this case is also shown in Figs. 4 and 5 (dash-dot line) and can
be compared to the analysis that used a soil Young’s modulus of
30 MPa (solid line).
As the soil Young’s modulus doubled from 30 MPa to
60 MPa, both the change in axial stress and interface shear
stress increased, although the proportionality between the
solutions was slightly less than two, due to relative pile-soil
compressibility effects.
These results show that the operational stiffness in the soil
mass will influence the response seen in the thermally loaded
pile, and also illustrates how a stiffer shear response at the
interface may lead to higher axial stresses in the pile.
4 DISCUSSION
Although a simple elastic model has been used to represent the
pile and soil in the analyses presented here, the results presented
highlight some interesting features.
The first relates to the compatibility of these results with
observations and the simple descriptive models previously
presented. The descriptive model was developed from and in
rder to exp
o
lain the observed mechanisms of response in the
th
here when this
ption was
m
as inl
ith o
tion th
s
i.
ion at pile
terfac
when
compar
the field, and the
theoret
st thermal
deformation. Table 3 provides a comparison of the predicted
(F
either a larger
dif
se of model and test piles.
few TM pile tests that have been reported in the literature and
hus, implicitly assumes that the pile expands/contracts more
t
at the soil.
In the analyses presented
et, the predicted response w
assum
bserva
ine w
s, wi
ome differences due to the assumption of elastic soil response,
e. linear variation of frict
-soil in e.
The predicted changes in axial stress were rather small
ed with the values measured in
ical value for a pile fully restrained again
EA) and observed restraining effect on two test piles, from
Amatya et al. 2012.
This suggests that the pile as modelled in the FEA was
almost completely free to expand and contract (the predicted
deformation between the extremities of the pile confirms this),
even when additional restraint in the form of
ferential in soil-concrete
-values or higher soil stiffness was
considered.
Table 3. Thermal load and axial stress respon
Parameter
FEA
Lambeth EPFL
2
Temperature change,
T (°C)
+30
+29
1
+21
Max. axial stress change as %-
fully restrained value, P
fix
3
10% -
20% 56%
36%
Notes: 1. First heating phase of Lambeth College heat sink pile;
2. First heating phase, Test T-1, EPFL
3. P
fix
=
TA
pile
E
pile
(= 7069 kN for FEA results)
The second point of note relates to the importance and
interdependence of the thermal boundary condition as
demonstrated here by the assumption of either zero heat flow
(perfect insulation) or constant temperature (no change relative
to starting temperature) on the ground surface and the relative
een the soil and the pile.
that the thermal boundary conditions and
eld in the vicinity of the head of the pile was
cru
stant temperature boundary condition
wa
ansion, the pile was still able to expand relative to
the soil mass and thus generate compressive axial stresses.
A
of b
cha
sen
these relationships needs
Cam R.G. and Mitchell J.K. 1968. Influence of temperature
variations on soil behavior. ASCE J. Soil Mech. and Fdtn. Div.,
ASCE,
94
, 709-734
Cekerevac C. and Laloui L. 2004. Experimental study of thermal effects
on the mechanical behaviour of a clay. Int. J. Numer. Anal. Meth.
Geom.
28
, 209–228
Cruz Silva F. 2012. Load-displacement behaviour of thermo-active
piles. MSc Thesis, Instituto Superior Tecnico, Lisboa, Portugal, 105
pages (in Portuguese)
Laloui L. Nuth M. and Vulliet L. 2006. Experimental and numerical
investigations of the behaviour of a heat exchanger pile. Intl J.
Num. and Anal. Meth. in Geom., 30, 763 – 781.
McCartney J.S. and Rosenberg J.E. 2011. Impact of heat exchange on
the axial capacity of thermo-active foundations. ASCE Geo-
Frontiers 2011 : Advances in Geotechnical Engineering, GSP 211,
488-498
Mackay J.C. 2009. Sustainable Energy - without the hot air, UIT
Cambridge Ltd., 383 pages
)
Marques M.E.S. Leroueil S. and Almeida M.S.S. 2004. Viscous
behaviour of St-Roch-de-l’Achigan clay, Quebec. Can. Geot. J.
41
,
25-38
thermal expansion betw
The results suggest
thus the temperature field within the model impart their own
form of restraint in the pile-soil interaction process, in addition
to any mechanical restraint of the pile.
In particular, the cases examined here illustrate that the
temperature fi
cial in determining the form of response obtained from the
analysis, i.e. while heating a pile in a soil with a higher
coefficient of thermal expansion than the pile itself – as was the
case in the Lambeth College test - compressive stresses where
predicted only when a con
s specified at ground surface.
The constant temperature surface boundary condition meant
that the soil near the surface and adjacent to the pile head was
cooler, and despite the soil having a higher coefficient of
thermal exp
5 CONCLUSIONS
linear elastic numerical model has been applied to the
blem of the TM
pro
loading of piled foundations and the results
have been found to generally reproduce observed mechanisms
ehaviour.
The results presented here highlight that there is a complex
interaction between the foundation and soil material’s thermal
racteristics, and the thermal boundary conditions. The
sitivity of the predicted response to
to be investigated further.
Finally, the factors that determine the degree of fixity against
rmal expansion that can be mobilised on the pile shaf
the
t also
require deeper investigation, and future studies will focus on the
pile-soil interface and the impact of thermal boundary
conditions.
6 REFERENCES
Amatya B.L. Soga K. Bourne-Webb P.J. Amis T. and Laloui L. 2012.
Thermo-mechanical behaviour of energy piles, Géotechnique,
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(6), 503-519
Baldi G., Hueckel T. and Pellegrini R. 1988. Thermal volume change of
the mineral-water system in low-porosity clay soils. Can. Geot. J.,
25
, 807-825
Bourne-Webb P.J. Amatya, B. Soga K. Amis, A. Davidson, C. and
Payne P. 2009. Energy pile test at Lambeth College, London:
geotechnical and thermo-dynamic aspects of pile response to heat
cycles, Géotechnique
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(3), 237-248
Bourne-Webb P.J. Amatya B. and Soga K. 2013. A framework for
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)
Brandl H. 2006. Energy foundations and other thermo-active ground
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