A laboratoryscale model test is conducted to improve the understanding of the effects of thermal cycles on the mechanical behavior of energy piles. The model pile is composed of cement mortar and dry sand with a relative density of 30% is used for the model ground. After applying the working load to the pile head, the pile is subjected to three thermal cycles with a magnitude of
Energy piles are pile foundations equipped with fluid carrying pipes to exchange heat with the surrounding medium. Owing to the temperature change, the energy pile expands or contracts during the thermal operation. Because of the complex pilesoil interaction under thermomechanical loading, the mechanical behavior of energy piles is quite different from that of conventional piles. The in situ test results reported by Brandl [
It is worth noting that energy piles experience seasonal expansion and contraction throughout the service period. As a result, the surrounding soil is subjected to cyclic loading, which may have an important impact on the mechanical behavior of energy piles. Because in situ tests are expensive and timeconsuming, the performance of energy piles subjected to thermal cycles has typically been studied by physical modeling or numerical simulations. Kalantidou et al. [
The centrifuge method has been used successfully in the geotechnical research field as the stress field of the soil can be reproduced reasonably. Although the scale factor of the heat transfer is not the same as the geometric one, the centrifuge experiment can also provide useful information of the thermomechanical behavior of energy piles [
Loria et al. [
At present, the understanding of the longterm behavior of energy piles remains limited. To obtain insights into the effects of thermal cycles on the settlement and the capacity of energy piles, a laboratoryscale model test is performed. The measured temperature response and mechanical behavior are analyzed and used to validate a finite element model. Then, a series of numerical sensitivity analyses are carried out to investigate the impacts of thermal cycles on the mechanical behavior of energy piles with different soil and pile head restraint conditions. The focus is on the thermally induced displacement, thermally induced axial force, shear stress response at the pilesoil interface, and pile bearing capacity after thermal cycles.
The experimental setup is shown in Figure
Experimental setup.
The soil used in the study was dry Yangzhou sand. The particlesize distribution of the sand is shown in Figure
Particlesize distribution of the sand.
The model ground was prepared by “raining” the dry sand in the model box and by compacting it to achieve a relative density of 30%. A series of triaxial tests were carried out to characterize the sand behavior at the same relative density. After filling the sand to a thickness of 450 mm, the model pile was fixed in the center of the model box using a temporary support. Then, the filling process was conducted to achieve a total sand layer thickness of 1350 mm.
Two tests were performed in the study. In the first test, the pile was vertically loaded to failure. The ultimate pile resistance was determined based on the measured loaddisplacement relationship.
In the second test, the pile was first loaded to a working load of 0.8 kN. After the mechanical loading process, three thermal cycles were applied to the pile. The time duration of each cycle was 24 h. The pile temperature was first increased by 15°C by cycling the hot water in the heat pipe. After 30 min of cycling, the fluid circulation was stopped to allow the pile temperature to decrease naturally to the indoor temperature.
The vertical load on the pile head was applied by rigid steel blocks. Two symmetrically placed dial gauges (D1D2) were used to measure the settlement at the pile head. Six strain gauges (S1–S6) were installed at 150 mm intervals along the pile shaft, beginning at a depth of 150 mm from the pile top. Four temperature sensors (T1–T4) were used to measure the pile temperature. Another nine temperature sensors (T5–13) were installed in the soil at different distances from the center of the pile (Figure
It should be noted that the stress level in the 1 g model test was quite lower than that of the prototype system. As a result, the stressdependent mechanical behavior of the sand is different from the actual case. Hence, the aim of the test is not to predict the behavior of a prototype but to investigate the influences of the cyclic thermal loading on the performance of energy piles and the mechanism involved.
In this study, the numerical analyses of energy piles were performed using ABAQUS software. As the temperature response can be regarded as independent of the stress/deformation field, a sequentially coupled technique was used in the study. First, the temperature was calculated through an uncoupled heat transfer analysis. Then, the position varied and timedependent temperatures were read into the sequence stress analysis as predefined fields. The thermal strain and the effect on the mechanical response were accounted for by including the thermal expansion coefficient in the material property definition.
The numerical analyses were carried out under threedimensional conditions. Considering the symmetry of the problem, only one quarter of the model was included in the computation. Both the vertical and horizontal displacements were fixed on the bottom of the model domain, and only horizontal displacements were constrained on the lateral sides.
The initial stresses due to gravity were calculated by the bulk unit weight and the coefficient of earth pressure at rest,
The initial temperature of the analysis domain was
Measured temperature variation of the pile.
The pile was considered thermoelastic and was modeled as a linear elastic material. The relevant parameters are given in Table
Material parameters of piles.
Model pile  Concrete pile  

Density, 
2000  2500 
Thermal conductivity, 
0.9  2.0 
Specific heat, 
1050  970 
Linear thermal expansion coefficient, 
24.5  10 
Elastic modulus, 
4  30 
Poisson’s ratio, 
0.2  0.18 
The thermal characteristics of the dry sands considered in this study were evaluated considering the volumetric fractions of the solid soil particles and the pore air. The adopted thermal constants listed in Table
Material parameters of the sands.
Yangzhou sand (test sand)  Loose Sacramento River sand  Dense Sacramento River sand  

Thermal parameters  Dry density, 
1490  1450  1670 
Thermal conductivity of soil particle, 
2.4  2.4  2.4  
Specific heat of soil particle, 
930  930  930  
Linear thermal expansion coefficient of soil particle, 
10.0  10.0  10.0  


MC model  Elastic modulus, 
3.34  —  — 
Poisson’s ratio, 
0.3  —  —  
Cohesion, 
0  —  —  
Friction angle, 
30.6  —  —  
Dilation angle, 
0.0  —  —  


BS model  Initial void ratio, 
0.78  0.87  0.61 
Elastic swelling modulus, 
0.01  0.01  0.0075  
Poisson’s ratio, 
0.3  0.2  0.2  
Critical void ratio at 100 kPa, 
0.60  0.97  0.84  
Slope of the critical state line, 
0.12  0.076  0.076  
Ellipse aspect ratio, 
2.0  2.2  1.65  
Residual friction angle in compression, 
30.6  34.6  36.2  
Residual friction angle in tension, 
30.6  34.6  36.2  
Peak friction angle, 
32.0  35.7  43.8  
Plastic modulus, 
1.0  2.0  2.0  
Elastic modulus at 100 kPa, 
12.0  18.7  21.5 
To model the stressstrain relationship of the sand, both the MohrCoulomb (MC) model and the bounding surface (BS) model developed by Bardet [
In ABAQUS, the yield surface of the MC model is expressed as
Inside the yield surface, the strain increment is elastic and is related to Young’s modulus,
Although the MC model can capture the soil failure behavior reasonably, it has a limited capacity to simulate the soil deformation behavior, especially in cases where the magnitude and direction of the load change significantly.
To simulate the accumulation of irreversible strain during cyclic loadings, the BS model was implemented in ABAQUS and used in the analysis. In the BS model, the elastic strain increment is calculated using a nonlinear bulk modulus,
The direction of the plastic strain increment is the same as that of the image stress on the bounding surface. The bounding surface is expressed as
The hardening of the bounding surface is controlled by the plastic volumetric strain:
The plastic modulus,
The soil parameters are summarized in Table
The soilpile interface was modeled as a layer of thin elements, and the constitutive parameters were taken as the same as those for the surrounding sand.
The computed and measured loadsettlement relationships are compared in Figure
Loadsettlement relationship.
One possible reason for the deviation between the predicted and measured results is that the model tests were conducted under the 1 g condition, and thus the soil stresses due to gravity were relatively small. At such low confining stress levels, the sand is expected to be dilative. During the loading process of the pile, the soil expansion due to shear was constrained by the rigid pile body. As a result, the horizontal stress at the pile shaft and the corresponding shaft resistance increased with loading until the critical state was reached. In the analysis with the MC model, the dilation angle was taken as zero to avoid the unrealistic volume dilatancy when shear failure occurs. Hence, the ultimate pile resistance was underestimated. In the analysis with the BS model, the statedependent dilatancy can be simulated using the elliptic plastic potential. However, the parameters used in the analyses were obtained from the tests conducted at relatively high stresses, and thus the soil dilatancy behavior at low stress levels may not be represented very accurately.
The measured temperature responses of the pile and soil are shown in Figure
Temperature variation. (a) Measured. (b) Computed.
The measured and computed temperature profiles at the end of the first heating phase are compared in Figure
Temperature profiles.
The measured thermally induced displacement at the pile head is shown in Figure
Thermally induced displacement at the pile head.
It can be seen from Figure
To further investigate the displacement pattern of the energy pile, two additional analyses (with the MC and BS models) were performed at the ultimate load predicted by each model. The predicted thermal displacements are shown in Figure
Predicted thermal displacement under the ultimate load.
The distributions of the thermal strain at the end of the
Thermal strain profile.
It is observed that the thermal strains at the middle portions of the pile are slightly smaller than those at the lower and upper portions. This distribution pattern of thermal strain is consistent with that reported by Amatya et al. [
Although there are some differences between the simulation and observation results, the main characteristics of energy piles subjected to thermal cycles can be captured reasonably by the proposed numerical approach. Therefore, it can be used to obtain a deeper insight into the longterm performance of energy piles.
A sensitivity analysis was conducted to investigate the longterm performance of a typical concrete energy pile. The pile was 1.0 m in diameter and 20.0 m in length. Two ground conditions, i.e., loose sand and dense sand, were considered.
For each ground condition, three sets of analyses were carried out. In the first set of analyses, the pile was statically loaded to failure at a constant temperature. The ultimate pile resistance was determined based on the predicted loadsettlement relationship.
For the second set of analyses, thermal cycles were applied at the working load level (with a factor of safety of 2.5). Two types of pile head fixities, i.e., a free head pile and a restrained head pile, were considered. The restrained pile considered in this study was an approximation of the single energy pile within a pile group consisting of energy and conventional piles. In this situation, the thermally induced displacement at the pile head is constrained by the raft and can be regarded as zero.
To evaluate the influence of the thermal cycles on the ultimate pile resistance, the pile was reloaded to failure in the third set of analyses.
The pile was modeled using a linear elastic model, and the relevant parameters of which are given in Table
The coefficient of earth pressure at rest,
The initial temperature of the pile and ground was
Temperature variation of the pile in one cycle.
The variations in pile head displacement with the number of thermal cycles are shown in Figure
Variations in pile head displacement for the free head pile.
Variations in the reaction force for the restrained head pile.
Distribution of the shear stress at the pilesoil interface for the free head pile.
Development of shear stress at pilesoil interface for the free head pile. (a) Pile in loose sand. (b) Pile in dense sand.
It is observed that there are different tendencies in shear stress changes for the soils at different depths. After the thermal cycles, the shear stresses between the depths of 12 and 18 m increased, while the shear stresses at other depths decreased. This occurrence can be attributed to the specific relative pilesoil displacement mode at these locations. As shown in Figure
Location of the null point for the free head pile.
Below the null point, the heating induced expansion pushed the pile down and led to an increase in the shear stress. For the upper part of the pile, the upward expansive deformation decreased the relative pilesoil displacement and the shear stress. During the process of cooling, an opposite variation in shear stress occurred. As expected, the shear stresses at these locations changed cyclically. Owing to the accumulation of plastic strains in each cycle, the shear stress at
Because the null point of cooling was deeper than that of heating, the shear deformation of the soil between these two points always increases during the heating/cooling cycles. Hence, the soil at
Distribution of shear stress at the pilesoil interface for the restrained head pile.
Development of shear stress at pilesoil interface for the restrained head pile. (a) Pile in loose sand. (b) Pile in dense sand.
Comparison of load settlement curves of piles with and without thermal cycles. (a) Pile in loose sand. (b) Pile in dense sand.
For the free head in loose sand, referring to Figure
For the free head pile in dense sand, the ultimate shear stress mobilized at
It should be noted that owing to the degradation effect at the pilesoil interface and the change in the soil state, the pile displacement required to mobilize the ultimate resistance increased after thermal cycles. The overall stiffness of the pilesoil system decreased slightly after thermal cycles. Taking into account the accumulated settlement during the thermal operation, the longterm performance of the energy pile seems to be controlled predominantly by the settlement rather than the capacity.
In this study, a laboratoryscale model test was carried out to investigate the behavior of energy piles subjected to thermal cycles. The experimental results were analyzed and used to validate the finite element model. Then, numerical sensitivity analyses were performed to gain deeper insight into the longterm performance of energy piles with different soil and pile head restraint conditions. The main conclusions are as follows:
The experimental result of a free head pile subjected to thermal cycles suggests that the cyclic temperature variation induces irreversible pile settlements. The axial force of the pile increased slightly with the number of thermal cycles.
The proposed sequentially coupled numerical approach can reasonably capture the main characteristics of energy piles subjected to thermal cycles. A suitable model to describe the cyclic behavior of the soil is essential.
The results of the numerical sensitivity analyses showed that the null point of the cooling phase for the free head pile was deeper than that of the heating phase. The shear stress trapped between these two points increased almost monotonically, while the skin forces at other depths decreased gradually with the number of thermal cycles. For the restrained head pile, the skin forces along the entire length of the pile varied simultaneously as the null point was fixed at the pile head. After each thermal cycle, a reduction in skin forces was observed.
The ultimate pile resistance after thermal cycles did not decrease significantly. The longterm performance of the energy pile seems to be controlled predominantly by the settlement rather than the capacity. The presented results are specific to the simulated cases. This should be considered when designing energy piles in other conditions.
The data used to support the findings of this study are included within the article.
The authors declare that they have no conflicts of interest.
This work was supported by the National Natural Science Foundation of China (grant number 51778557) and the Qing Lan Project (grant number 20160512) of the Jiangsu Province Government.