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A method for the geotechnical design of heat exchanger piles

H. Peron, C. Knellwolf and L. Laloui

Ecole polytechnique fdrale de Lausanne, Laboratory of Soil Mechanics, CH-1015Lausanne, Switzerland; PH (+41) 21 6932315; FAX (+41) 21 6934153; email:

[email protected]

ABSTRACT

There is currently a lack of established calculation method for thegeotechnical design of heat exchanger piles. Thermo-mechanical effects are ignored

and large overall security factors are therefore applied. This paper presents a new

geotechnical numerical design method for heat exchanger piles, based on the loadtransfer approach. The method is validated on the basis of two in situ measurements.

It is shown how the pile design could be adapted and optimized with respect to

concrete resistance and the mobilization of the pile shaft friction during the operation

of the heat exchange system.

INTRODUCTION

This paper considers a new sustainable technology for the intermittent storage

of energy in soils, namely heat exchanger piles. Heat exchanger piles take advantage

of the ground as an energy storage system. The heat exchange system consists of

absorbing and transporting ground thermal energy to buildings via a fluid circulatingin pipes placed within the piles. In the case of a hollow pre-cast pile, the pipes are

placed in the hollow part in contact with the inner wall of the concrete. In the case of

cast-in-place piles, the pipes are fixed to the inner side of the metallic reinforcement.Actually, any kind of foundation can be used as a heat exchanger, such as retaining

walls, slabs, anchors, etc. With this geothermal use of geostructures, buildings can be

economically cooled and heated with a heat pump (Figure 1).The heat exchanger pile technology, although very successful in Europe faces

a lack of rational knowledge of the thermal effects on the behavior of the foundations.

In particular, no design method is yet available to consider the complex interactionsbetween thermal storage and the mechanical behavior of these geostructures.

Therefore, for years, the dimensioning of heat exchanger piles has been based onempirical considerations (Bonnec 2009). In order to err on the safe side, the safetyfactors usually employed for typical piles are considerably increased. This may lead

to considerable extra costs and non-standard construction skills. In situ experience

shows that applying a thermal load induces a significant change in the static behaviorof a foundation pile. In this paper, a new geotechnical design method for heat

exchanger piles is described and validated on the basis of in situ data. Finally,

representative cases for which thermal loads could lead to failure are discussed.

470Geo-Frontiers 2011 ASCE 2011


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Heat exchanger pile

Heat pump

Layer 1

Layer 2

Building

Soil

Figure 1. Representation of a heat exchanger pile system (Laloui et al., 2006)

A NEW GEOTECHNICAL DESIGN METHOD FOR HEAT EXCHANGER

PILES

Origin of thermal stresses in heat exchanger piles

In service conditions, the pile is heated or cooled due to the circulation of theheat exchanger fluid within the pipes cast in the concrete. The temperature generally

lies between +4 C (to avoid freezing of the pile and of the ground) and +30 C.

Please Note that in the UK energy piles are designed to temperatures of -1 C to +35C. However, in some situations (bad operation or even external thermal recharge

from solar panels), increase in the temperature up to +40 or +50 C is conceivable

(SIA 2005, Silvani et al. 2008). Basically, the heating of a pile induces expansion,while the cooling induces contraction. If the pile is unrestrained, the change in

temperature Tinduces a uniform free strain th,f = .T, where is the coefficient

of thermal expansion of the pile. In the general case, a part of the strain th,fis blocked

by the surrounding soil and the structure, so that only the observed strain th,o isfinally produced. The fact that the soil and the structure restrain the pile in its

movements introduces some additional stresses in the pile.

A convenient way to cope with the process and to assess the additionalstresses in the pile is to use the degree of freedom of the pile (denoted n). The

degree of freedom of the pile is defined by the ratio between the free and observed

axial strains th,fand th,o (Bochon 1992, Laloui et al. 2003). The degree of freedom istheoretically 0 when the pile is completely blocked and 1 when the pile is completely

free to move. In the general case, n ranges from 0 to 1 due to the variable shaftfriction mobilization and restraint at the two extremities of the pile. The observed

strain then reads,th o n T =

The blocked strain th,d is the difference between free and observed strain.

Assuming a linear elastic behavior of the pile, the additional stress th due to thermal

loading is proportional to th,d. Presently, in situ strain and stress measurements along

pile while heated or cooled down are very scarce. Complete set of data are availablein Laloui et al. (2003) and Bourne-Webb et al. (2009).

Basic assumptions of the proposed method

The method relies on the following basic assumptions:

1) The pile displacement calculation is done using a one dimensional finite difference

scheme (only the axial displacements are considered). The radial displacements and



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their mechanical interactions with the soil are neglected (such interactions are

considered small with regards to the effects of the axial displacements).

2) The pile behavior is considered linear and elastic. The properties of the pile,

namely its diameterD, Young modulusEpile and coefficient of thermal expansion ,

remain constant along the pile and do not change with temperature.

3) The relationships between the shaft friction/shaft displacement, head stress/headdisplacement and base stress/base displacement are known.

Upwards movements are taken as positive; downwards movements are

negative. Compression stresses are taken as negative.

Pile displacement calculation

The pile displacement for a mechanical load P is done by the load transfer

method (Coyle and Reese 1966). In this method, the pile is subdivided into severalrigid elements, which are connected by springs representing the pile stiffness. Each

rigid element experiences along its side an elasto-plastic interaction with the

surrounding soil. The pile base element is supported by the reaction of the substrate,the pile/soil interaction being elasto-plastic as well. The relation between the shaft

friction and pile displacements, as well as the relation between the normal stressesand the pile displacements at the base, are described by load transfer functions.

In the following, the load-transfer functions proposed by Frank and Zhao

(1982) are used for the mobilized shaft friction and base reaction, respectively, versuspile displacements. The curves feature two linear parts and a plateau equal to the

ultimate value.Ks andKb are the slopes of the shaft and base load transfer functions

for the first linear branches, respectively. Ks and Kb are related to the Menard

pressuremeter modulusEM. In the present study, an unloading branch has been added,accounting for the irreversible behavior of the soil. The load transfer functions

described above are chosen for convenience. Other forms are indeed possible.The load transfer curves describe the mobilized stress for a givendisplacement. The originality of the present approach is to consider the pile-supported

structure interaction, represented by the spring constantKh.Kh ultimately depends on

many factors, such as the supported structure rigidity, the type of contact between thepile and the foundation raft, the position and the number of heat exchanger piles. On

the basis of the soil-pile interaction laws defined above, the calculation of the thermo-

mechanical response of the heat exchanger pile is made as follows. First, the stressstate and the pile displacements induced by the imposed mechanical loading are

calculated; this state is further referred to as the initialization state and corresponds to

effects due to the weight of the building. Then, from the initialization state, the pile

response due to the thermal loading (heating or cooling occurring during heatexchange) is calculated. Each element i of the pile has a length hi, diameterD and

sectionA.

Thermal loading

When a pile is heated or cooled, it dilates or contracts about a null point(Bourne-Webb et al. 2009). The null point is situated at that depth NP where the sum



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of the mobilized friction along the upper part plus the reaction of the structure is

equal to the sum of the mobilized friction along the lower part plus the reaction at thebase. In order to assess the blocked strain, an iterative procedure is applied following

the method described below.

1) Choice of a starting value for the observed deformation: to compute a first

set of mobilized resistance (mobilized shaft friction and resistance at the extremities),the pile is initially assumed to be totally free to move. The first displacement

calculations are therefore done with th=th,f = T.2) Displacement calculation: the thermal displacement calculation is done

from a non zero initialized displacement and strain state induced by the mechanical

loading. By definition, there is no displacement at the null point. Using the t-z curve,

a first set of mobilized reaction stresses is obtained. The axial stress in the pile th,i

induced by the thermal free displacement of the pile is the sum of all the externalforces divided by the pile section A. In the case of unloading (uplift), the stress path

follows the unloading branch.

3) Calculation of the blocked thermal strain th,b(from the mobilized stress).

4) Calculation of the observed strain (the blocked strain minus the free one).Steps 2 to 4 must be repeated with the new set of observed strains th = th,o. Theobserved strain will converge to the actual values of the blocked and observed strain.

Related parameters, such as pile displacement, internal axial stresses, mobilized shaftfriction and mobilized reaction at the base and head of the pile, are then deduced.

More details can be found in Knellwolf et al. (2010).

Numerical implementation

The above numerical method has been coded in the Java language and

validated against an analytical calculation of the pile deformations for a mechanical

loading. Several soil layers can be considered, each of them with differentparameters. For each layer, specific soil proprieties can be defined. The bearing

capacity can either be calculated by the code from analytical expressions or setdirectly by the user. In order to set the load transfer function proposed by Frank and

Zhao (1982), one can enter the Menard pressuremeter modulus, the ultimate shear

stress and bearing capacity at the base. The interaction between the pile and the

supported structure is modeled by an elastic law, the stiffness of which is directlydefined by the user. Pile geometry as well as material parameters (Young modulusand thermal expansion coefficient) are set to be constant with depth. The weight of

the building (i.e., the mechanical load) and the change in temperature with respect to

pile depth (i.e., the thermal load) are both defined by the user. The verification of the

static behavior of the pile is further done by comparing the total axial stress to theresistance of the concrete pile on the one hand, and the total mobilized bearing forces

to the ultimate bearing capacity on the other hand.

VALIDATION OF THE METHOD

In order to validate the above method, experimental data on the stresses andstrains experienced by a heat exchanger pile are required. The validation is



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undertaken using the results of two comprehensive full scale in situ tests: one carried

out at the EPFL in Lausanne, Switzerland (Laloui et al. 2003, 2006) and another oneundertaken at Lambeth College in London, UK (Bourne-Webb et al 2009).

In-situ energy pile at EPFL (Switzerland)

A 25 m long heat exchanger pile that was part of a pile raft supporting a four

storey building was equipped with load cells, extensometers and temperature sensors

(Laloui et al. 2003, 2006). This pile was subjected to a thermal load, generated by aheat carrying fluid circulating in polyethylene pipes embedded in the concrete pile.

The Young modulus of the pile was estimated from laboratory tests and cross-hole

ultrasonic transmission tests, yielding the value Epile = 29.2 GPa. The pile crossesfour layers of sandy and silty gravels (layers A1, A2, B and C) while the bottom of

the pile rests on a stiff layer (molasse, layer D). The soil geotechnical parameters

were obtained on the basis of geotechnical investigations and two static pile loadingtests. The groundwater table was found to be very close to the ground surface.

The behavior of the pile was measured for seven successive constructionstages. Test 1 was done before the construction of the building. The strains were

therefore only due to the thermal load. In Test 7, the whole building was built andwas acting on the pile. Varying changes in temperature were applied (up to 21.8 C in

Test 1 and 14.3 C for Test 7). The complete set of soil parameters used for the

validation of the modeling approach is listed in Table 1.

Table 1. Soil parameters used for modeling the EPFL pile.

Soil Layer A1 A2 B C D

Ks [MPa/m] 16.7 10.8 18.2 121.4 -

qs [kPa] 102 70 74 160 -

Kb [MPa/m] - - - - 6681335qb [kPa] - - - - 11000

The pile section is considered to be constant. Both experimental and modeled

pile axial strains for Test 1 are shown in Figure 2, for one average temperature

increments. As mentioned above, Test 1 was done before the construction of thebuilding; the mechanical load and pile head-structure contact stiffness Kh are

therefore set to zero. For Test 7, the experimental and numerical results are shown in

the form of the degree of freedom. The soil parameters are the same as in Test 1.Because the building is completely constructed (representing a mechanical load ofP

= 1000 kN), a stiffness Kh = 1.5 GPa/m is further imposed at the contact pile head-

structure.Kh, as the only parameter for which no information is available, is chosen inorder to match the measured degree of freedom. The excellent fitting of the method

results with the experimental data (see Figure 2) shows that the new approach is able

to reproduce the observed behavior, either in the case of thermal loading alone or in

the case of both thermal and mechanical loads.



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Figure 2. Modeled strains versus measured ones for successive changes in

temperature, Test 1: left, T =17.4 C, right, modeled degree of freedom of thepile versus measured one, Test 7, T= 14.3C (experimental data from Laloui etal, 2003). Kb(X) stands for Kb of Layer X

In-situ energy pile at Lambeth College (UK)

A full scale test was undertaken on a pile located in a construction site

(Lambeth College) in London by Bourne-Webb et al. (2009). Most of the pile is

installed in the London Clay formation, which extends well below the toe level of the

pile. The mechanical load was applied on the pile head with a loading frame. Thestrains were measured with vibrating-wire strain gauges (VWSG) and with fiber-optic

sensors (OFS). The test stages of interest were as follows: an initial mechanical

loading stage (two loading-unloading cycles at 1200 and 1800 kN, respectively), a

cooling stage (with a 1200 kN mechanical load and T= -19 C) and a heating stage

(maintaining the 1200 kN mechanical load, while T= +10 C). The test data showed

significant strain variations in the upper part of the pile, partly due to bending effects,suggesting that little resistance was mobilized in this zone (Bourne-Webb et al 2009).Hence, the shear resistance of the upper 6.5 m is not considered.

The Young modulus Epile is equal to 40 GPa. For the numerical validation

exercise made in the following, typical London Clay geotechnical parameters areused (Marsland and Randolph 1977). In compression, the rigidity on the pile head Kh

is taken equal to 10 GPa/m (based on estimates of the beam profile of the loading

frame and span values). In tension Kh is set to 0.1 GPa/m: this case is experienced

during cooling, and thus the beam rigidity should not interfere. The complete set ofsoil parameters are listed in Table 2 (four layers are distinguished).

Table 2 - Soil parameters used for modeling the Lambeth College pileLayer 1 2 3 4

Depth [m] 0-6.5 6.5-10.5 10.5-16.5 16.5-22.5

EM[MPa] 0 45 45 45

qs [kPa] 0 60 70 80

qb [kPa] - - - 460



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The comparison of the measured and modeled strain profiles of the Lambeth

College pile demonstrates that the method is able to quantitatively reproduce theeffects of mechanical and thermal loadings. The occurrence of tensile axial strain

(and axial stress) during the cooling phase in the bottom part of the pile is well

predicted (see Figure 3). In particular, the decrease of shaft friction in the bottom part

of the pile and increase in the upper part are accurately reproduced. In addition (notrepresented here), the noticeable additional compressive axial strain and stress

increase observed during the heating phase within the whole pile is well assessed. In

the case of heating, the increase in shaft friction mobilization is well reproducedbelow six meters in depth.

Figure 3. Modeled strains versus measured ones for thermal test at the end of

cooling (left), and modeled and measured profiles of mobilized shear stress

during pile cooling (experimental data from Bourne-Webb et al, 2009)

STUDY OF REPRESENTATIVE CASES

In this section, critical situations are examined using the above model, forwhich the temperature changes in the pile lead to structural failure of the pile element

or to serviceability limit state failure as well as ultimate bearing resistance failure. A

pile with a given geometry is considered, which is 10 m in length and 0.5 m in

diameter. The coefficient of thermal expansion of the pile is = 1x10-5 C-1 and theYoungs modulus is Epile = 30 GPa. The soil is homogenous (1 layer). The othermodel parameters are adapted for each case.

Case 1: Floating pile

A floating pile is such that almost the entire weight of the building is

transferred to the ground through friction along the pile shaft; no or little weight is

supported by the base of the pile. If the initial mechanical load (building weight) ischosen such that the mobilized friction is already near the ultimate value, the model

shows that the heating is likely to increase the mobilized shear stress, initiated by the

weight of the building, up to the bearing capacity. In the same time, the additionalcompression in the pile depends on the friction resistance qs. If qs is small, the



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expansion of the pile is slightly constrains, stresses remain well below the structural

resistance. The pile response would actually be different (with more significantcompressive stresses but less chance to reach soil bearing capacity) in the case when

a soil with a larger friction resistance is considered.

When the pile is cooled, the results show negative shear stress can be

experienced, depending on the soil parameters. This situation is favorable in terms ofbearing capacity, but it may generate tension stresses in the pile. The pile therefore

needs to be designed to resist tension. The cooling reduces the mobilized bearing

forces, down to values less than the building weight. The difference is transmitted viathe raft (if any) to adjacent piles. In the case of increased cooling, the tension could

act up to the head of the pile; this would mean the pile pulls on the building.

Case 2: Semi-floating pile

A semi-floating pile is understood as a pile that supports the weight of thebuilding both at its base and through friction along its lateral surface. This situation is

encountered in most practical cases. In the present case, conditions such that thestructural resistance in compression is reached are examined. For this purpose, a stiff

soil is considered, with a relatively high strength (qs = 250 kPa and qb = 38.2 MPa);moreover, both large mechanical and thermal loads are applied. In particular, the

applied temperature variation (T= 50C) is beyond the usual functioning range.The results of this simulation are shown in Figure 4. A noticeable increase in

mobilized shear stress is observed after heating. More importantly, the displacement

of the pile being significantly restrained, an additional compression develops withinthe pile. In Figure 4 (left) the axial compression exceeds a typical pile resistance offcd

= 20 MPa. Due to the high end-bearing resistance, the ultimate bearing capacity is not

problematic. In the same situation, and for the same soil characteristics, hollow

precast piles would be much more likely to experience structural failure than cast-in-place concrete piles because the same axial load would be applied on a smallersection. In the case of cooling, the pile head-structure interaction and the rigid soil-

pile shaft interaction completely constrain the displacements in the upper 5 m (n = 0).

The behavior is in this case close to the one of a floating pile.

25 20 15 10 510

8

6

4

2

0

Axial stress [MPa]

Depth[m]

After Heating

Building Weight

Resistance

Semi-floating pile

0 5000 10000 1500010

8

6

4

2

0

Forces [kN]

Depth[m]

Building Weight

After Heating

Semi-floating pile

Bearing Capacity

Figure 4. Changes in axial stresses (left) and forces (right) within the pile for a

semi-floating heat exchanger pile (T=50 C)



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Below the depth of 5 m, when the pile starts to move, Figure 5 shows that the

unloading of shear stresses is observed first, and the direction of shear stresses isreversed in the lowest part of the pile as well. The development of negative shear

stresses is supplemented with tensile axial stresses. Here, the same phenomena of the

reduced bearing forces, already discussed for the floating pile example, are observed.

Case 3: End-bearing pile

In this case, the load transfer is done via axial stress down to the base. Thedegree of freedom and thus the strain and axial stress due to the thermal loading are

constant in depth and only depend on the stiffness of the bedrock and the upper

structure. This third example yields the following comment: for the design of aconventional pile resting on a hard substrate at its base, neglecting the shaft friction is

conservative. However, if a heat exchanger pile is designed, doing so can be

problematic. The axial stresses due to thermal loading directly depend on the frictionresistance. There is the risk that pile structural failure will be reached due to the

contribution of ignored shear stresses (in particular tensile stresses).

20 15 10 5 0 510

8

6

4

2

0

Axial stress [MPa]

Depth[m]

After Cooling

Building Weight

Semi-floating pile

0 5000 10000 1500010

8

6

4

2

0

Forces [kN]

Depth[m]

Semi-floating pile

Building Weigth

After Cooling

Bearing Capacity

Figure 5. Changes in a) axial stresses and b) forces within the pile for a semi-

floating heat exchanger (T=-50 C)

CONCLUSION

In spite of the existence of hundreds of heat exchanger pile installations, no

design method is available to consider the complex interactions between thermalstorage and the mechanical behavior of geostructures. This paper presents a new

geotechnical design method, which assesses the main effects of thermal loading on

heat exchanger pile stress and strain response. The proposed method is based on theload transfer method and considers the shear resistance of the surrounding soil and

the tip resistance of the soil at the bottom of the pile. The interaction between the pile

and the supported structure, decisive in the case of thermal loading, is also taken into

account. A simplified scheme can be drawn: the heating of the pile induces additionalcompression in the pile and increases the mobilized shear stress. The cooling can

induce a release of mobilized shear stress, possibly leading to the reversal of shear

stress sign and the development of tensile stress in the pile.



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There is interplay between the changes in friction mobilization on the one

hand and the additional efforts within the pile on the other hand, caused by thechanges in temperature and the prevailing soil-pile-supported structure interactions.

This deserves a careful analysis in each case. The proposed method is believed to

furnish adequate analyses for user-defined problems.

ACKNOWLEDGMENTS

This work was partly funded by swisselectric research.

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Coyle, H. M. and Reese, L. C. 1966. Load transfer for axially loaded piles in clay.

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049 thermo pile

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