## Abstract

An energy pile undertakes the functions of supporting the superstructure and controlling the indoor temperature of the building, and the thermal-mechanical coupling response of an energy pile makes its load transfer mechanism different from that of conventional engineering piles. Moreover, the thermal-mechanical coupling responses of the energy piles in summer and winter conditions are also different and need to be explored separately. Based on a ground source heat pump pile foundation workshop project in Kunshan city, Jiangsu Province, a multiphysics simulation study was carried out. The simulation results of the outlet water temperature and pile settlement are consistent with the real-world measurements, which verifies the reliability of the numerical simulation. The responses of the temperature distribution, axial stress, lateral shear stress, and settlement of the energy pile in summer and winter were analyzed, and the response laws of the energy pile in different seasons were obtained. Compared with the pure conventional load state, under the effect of thermal-mechanical coupling in winter conditions, the maximum compressive stress of the pile body is reduced by about 11.5%, but the settlement of the pile top increases by about 47.66%. Therefore, the winter conditions should be used as the design energy for the normal use of the pile. The control condition of the limit state: compared with the pure conventional load state, the maximum compressive stress of the pile increases by about 12% and the settlement of the pile top decreases by about 7.23% under the thermal-mechanical coupling effect of the summer condition. Therefore, the summer condition is the pile control conditions for the limit state of the body’s carrying capacity.

## 1. Introduction

An energy pile is a building emission reduction technology that uses geothermal energy. The energy it provides can meet most of the heating and cooling needs of buildings and has less impact on the environment. Therefore, this green and low-carbon technology has become the norm in the development of human society. Scholars at home and abroad have launched different studies on energy piles (as shown in Figure 1).

Most of the research performed by domestic and foreign scholars is done with three methods: field in situ tests, indoor physical model tests, and numerical simulations [1–4]. Some scholars have compared and verified the three methods. The research is roughly divided into aspects such as performance evaluation, optimization design, thermal conductivity, and thermal response of energy piles.

The evaluation and optimal design of energy piles is an emerging research direction in recent years. Huang et al. [4] proposed a new type of independent drawable double helix energy pile and evaluated its heat pumping effect by numerical simulation. Alberdi-Pagola et al. [5] verified and optimized an actual energy pile foundation in Denmark through multiple pile g-functions and optimization algorithms, reducing the number of energy piles required by 32.4%. Jelušič and Žlender [6] proposed optimal design suggestions for conventional and geothermal energy piles through a comparative analysis of conventional and geothermal energy piles optimized based on mixed integer and nonlinear programming (MINLP). Some scholars have proposed calculation methods for different numerical model parameters to optimize the accuracy of energy piles in numerical simulations [7, 8]. Han et al. [9] evaluated the energy saving potential and economic and environmental benefits of the energy pile system as a whole and found that the energy saving benefit of the energy pile system was highly dependent on the climate zone.

Compared with the new direction of energy pile optimization and evaluation, scholars are turning their attention more toward the thermal conductivity and thermal response of energy piles. Heat transfer performance is a key factor in considering the working performance of energy piles. There are many research results on the influence of various factors on the heat transfer performance of energy piles and the optimization of the heat transfer performance.

Through laboratory tests and numerical simulation analysis, scholars have verified that soil seepage and groundwater flow have a large impact on the heat transfer and energy exchange efficiency, respectively, of energy piles [10–13]. It has also been shown that many factors, such as the pile-to-well ratio, the distance between the piles, the diameter of the heat exchange pipe, the inlet water temperature, and the thermal conductivity coefficient of the soil layer around the energy pile, will affect the working efficiency of energy piles [14–20]. In terms of the long-term working performance of energy piles, it has been found that when energy piles are thermally cycled, the soil moisture content will decrease, which will affect the thermal conductivity of the soil, make the temperature around the energy piles accumulate, and reduce the energy exchange efficiency of the energy piles [21, 22]. Elkezza et al. [23] started from the material aspect, adding graphene powder to the concrete to improve heat transfer performance of an energy pile. The heat transfer performance of the energy pile affects its working efficiency, and the thermal response of the energy pile is related to its reliability, safety, and superstructure. Compared to traditional pile foundations, results on the thermal response of energy piles have not been consistent, making it an emerging issue.

Scholars at home and abroad have carried out much research in the related areas of this study [19, 20, 24–28]. Wu et al. [29] started with the stress history of soil and found that compared with overconsolidated clay, normally consolidated clay exhibits higher irreversible pile head settlement and pile end resistance. Through laboratory experiments, Liu et al. [30] found that the moisture content of the sand around the energy pile affects the frictional resistance at the pile-soil interface caused by temperature. Through in situ experimental research, Xiong et al. [31] found that the contribution of the radial effective pressure change of the pile-soil interface to the shaft friction during the heating process cannot be ignored. Moradshahi et al. [32] established and verified a numerical model with measured section temperature and strain. The analysis found that the temperature and thermal stress were the largest at the pile center and decreased with increasing radial distance. Through indoor model tests, Yang et al. [33, 34] found that the thermal cycle of the energy pile will increase the temperature rise of the pile and soil and cause the pile body temperature to rise and the pile body stress and top displacement to accumulate. In addition, numerous studies have revealed that the deformation and stress distribution of the energy pile during temperature cycling are affected by the restraint at the end of the pile [35–38].

Referring to the current research on energy piles, it is believed that the thermal conductivity and thermal response of energy piles are affected not only by the soil layer and material but also by factors such as the season and the form of heat exchange pipes. Based on a plant project in Kunshan, Jiangsu Province, this paper reports the temperature distribution of a single pile and soil around the pile and the thermal response of the pile body after the heat transfer stability of parallel dual U heat exchange pipes in summer and winter conditions.

## 2. Project and Pile Foundation Design Overview

The case study presented in this paper is a plant project in Kunshan, Jiangsu Province. There are two plant buildings (as shown in Figure 2), and the heat pump system is set indoors (as shown in Figure 3).

Among them, the first building is also used as an office, covering an area of 911.83 m^{2}, with three floors and a total height of 15.3 m. The second building covers an area of 2328.72 m^{2}, with one floor above the ground and a height of 9.15 m. The shallow soil of the project construction site is poor; there is no good shallow foundation bearing layer. The design adopts a pile foundation. Combined with the design of the ground source heat pump system, some pile foundations are selected to apply energy pile technology. There are five types of energy piles in the project, which are as follows: series double U precast pile buried pipe (R1), parallel double U precast pile buried pipe (R2), single U precast pile buried pipe (R3), parallel double U cast-in-place pile buried pipe (A1), and parallel double spiral cast-in-place pile buried pipe (F1). The first building adopts a cast-in-place pile foundation, and the plane layout of the pile foundation is shown in Figure 4.

A1 and F1 are cast-in-place piles set at the bottom of the factory building. The form of the buried pipe is shown in Figure 5. The length of pile A1 is 15 m, and the pipe diameter is 0.6 m. The buried pipe form is shown in Figure 6. The specifications of the three different buried pipe forms are the same: the pile length is 15 m, the pile diameter is 0.4 m, and the backfill materials are yellow sand and soil.

According to the drilling exploration data of the site, the experience of the exploration operators, and the results of the indoor geotechnical test, the stratum distribution of the site is judged as reported in Table 1.

## 3. Construction of the Three-Dimensional Numerical Model of the Energy Pile

### 3.1. Numerical Simulation

In this paper, the ANSYS Workbench finite element analysis software is used to conduct thermal and mechanical coupling simulation analysis of energy piles. As a multiphysics and optimization analysis platform, ANSYS Workbench combines the Fluent software that can accurately simulate fluid analysis and provides data coupling between the software, providing users with great convenience.

The parallel double U-shaped buried pipe pile (No. A1) is selected for simulation analysis, and the energy pile model is established by the Autodesk Revit software. The model includes three parts: the heat exchange pipe, pile, and soil surrounding the pile. The model file was imported into ANSYS, and the setting of the heat exchange fluid was completed through the fill function. The length of the pile is 15 m, and the diameter is 0.4 m. The depth of the double U-shaped heat exchange pipe buried in the pile foundation is 14.5 m. The inner diameter of the heat exchange pipe is 20 mm, and the outer diameter is 25 mm. The model is 6.6 m in diameter and 18 m deep. A schematic diagram of the model is shown in Figure 7:

### 3.2. Meshing Model

The energy pile model includes four parts: water, pipe, pile, and soil. For the thermal-fluid-structure coupling analysis, the meshing of the flow field and the structural field is involved. Therefore, the structural mesh needs to be refined to capture the temperature, displacement, strain energy, and stress energy gradients at the site of interest; meanwhile, the fluid mesh needs to be refined to capture the velocity, pressure, and temperature gradients at the site of interest. In this paper, the default meshing method of Workbench is used, and both the fluid and the structure are divided into components. The fluid grid is divided according to the following: water, pipe, and pile adopt an expansion layer, where the thickness of the first layer is 0.75 mm, and the number of layers is 5. The grid size of water is defined as 2 mm, the grid size of pile is 20 mm, and the size of soil is 300 mm. Automatic grid division is selected for pile and soil, that is, switching back and forth between tetrahedron and sweeping grid. Unlike a hexahedron grid, a tetrahedron grid cannot be automatically generated by sweeping. The pipe surface grid is divided into 6 layers. The mesh is refined near the U-shaped pipe bend, and the contact between the nozzle and the pile is locally refined. The model fluid meshing is shown in Figure 8. The size of the structural mesh is the same as that of the fluid, and it is divided according to the default method of the system. The overall mesh parameter settings of the fluid and structure are shown in Table 2.

### 3.3. Parameter Setting

The setting of model material parameters mainly involves thermal conductivity, specific heat capacity, density, elastic modulus, Poisson’s ratio, and internal friction angle. The material assignment objects include four parts: pile, soil, pipe, and water. Among them, the parameters of water can be directly found in the Fluent material database, while the thermal properties of soil can be obtained through field tests, and the parameters of pile foundation and pipes can be obtained through table look-up. The specific parameter settings are shown in Table 3.

The test piles are comprehensively evaluated by combining the thermal response test of the thermal energy of the pile foundation with the pile foundation load test. The test platform consists of two parts: one part is used for the thermal response test, the other part is used for the static load test of the piles, and the two parts are used in combination during the test. The construction area of the plant is between 1000 and 5000 m^{2}. It can be seen from the specifications that the design grade of thermal energy utilization of the pile base is medium, and the thermal physical properties of the soil are obtained by the in situ thermal response test method.

The initial soil temperature was measured to be 18.74°C, the comprehensive thermal conductivity of the soil was 1.877 W/(m·k), and the specific heat capacity was $1.644\xd7106$ J/(kg·k).

## 4. Controlling Equation of the Thermal-Mechanical Response of the Energy Pile

### 4.1. Turbulence Model

In Fluent, as default constants, $C1\epsilon =1.44$, $C2\epsilon =1.92$, and $C\mu =0.09$, the turbulent Prandtl numbers of turbulent kinetic energy $k$ and dissipation rate $\epsilon $ are $\sigma k=1.0$ and $\sigma \epsilon =1.3$, respectively.

### 4.2. Heat Transfer Governing Equation

The heat exchange liquid in the parallel double U-shaped buried pipe of the pile foundation exchanges heat with the pipe wall mainly by heat convection, while the heat transfer between the pipe, the pile foundation, and the rock and soil is mainly carried out by heat conduction.

^{2}) is the heat flow per unit area, $keq$ (w/(m

^{2}·°C)) is the equivalent heat transfer coefficient of the contact surface, and $Tf$ and $Tpipe$ are the temperatures of the fluid and the pipe wall, respectively. Since the flow velocity of the liquid in the pipe has a great influence on the heat transfer of the pipe wall, the Dittus-Boelter formula takes into account the radial heat transfer capacity of the pipe wall material.

^{3}) is density; $Cp$ (J/(kg·°C)) is specific heat capacity; $T$ (°C) is temperature; $K$ (w/(m·°C)) is the thermal conductivity; $Q$ (w/m

^{3}) is the heat source intensity; $\u2207$ is the Hamiltonian symbol.

## 5. Research on the Response Law of Single Pile under Thermal-Mechanical Coupling Load

The single pile model established in Revit is imported into the fluent module of Workbench. The energy equation is opened, the turbulence model is set, the boundary condition is defined, and the flow velocity value in the heat transfer pipe and the fluid temperature value at the inlet of the pipe are set. The temperature distribution of the pipeline fluid is calculated by Fluent, so as to simulate the temperature difference of water at the inlet and outlet of the pipeline. The temperature distribution of the pipeline fluid is calculated by fluent, so as to simulate the temperature difference of water at the inlet and outlet of the pipeline.

The flow rate of the water is 0.6 m/s, and the temperature at the inlet of the pipeline is 45°C. When the operating temperature of the parallel double U-shaped pile foundation buried pipe energy pile is 45°C, the water temperature at the outlet of the pipe is 42.2°C, and the fluid temperature decreases by 2.8°C.

The fluid temperature at the inlet of the pipe was set to 5°C, and the fluid temperature variation in the pipe after stable heat transfer in winter was simulated in Fluent. In winter, the temperature of the hydrothermal solution is lower than that of the underground environment, and the heat is transmitted from the soil to piles, pipes, and water. After running for about 36 h, the heat exchange is stable, and the temperature at the outlet is 6.28°C, which is 1.28°C higher than that at the inlet.

The temperature result of the model during the simulated summer condition is cut along the symmetry plane of the $Z$ axis to obtain the vertical temperature distribution plot shown in Figure 9. It can be clearly seen from the figure that the vertical temperature distribution shape during summer conditions is approximately elliptical, and there is thermal interference between the branches of the parallel double U-pipe.

The temperature results under two working conditions calculated by Fluent are imported into the static structural module in ANSYS Workbench, as shown in Figures 10 and 11.

When the water temperature is higher than the ambient temperature (45°C), the water flowing in the pipe transfers heat via convection to the place where the water contacts the pipe wall, and then, the heat diffuses in the pipe, pile foundation, rock, and soil in a thermally conductive manner. When the water temperature is lower than the ambient temperature (5°C), heat is collected from the soil, pile foundation, and pipe to the wall in a thermally conductive manner, and then, heat is exchanged with the low-temperature fluid in a thermal convection manner. The temperature diagram of the structure shows that the maximum temperature of the pipe wall is 44.914°C in summer and 5.0468°C in winter. The temperature is not equal to the water temperature under the two conditions, which fully demonstrates the existence of thermal radiation between water, pile, and soil.

### 5.1. Simulation Analysis of the Axial Stress of a Single Pile

In the analysis, the axial stress of the pile is positive in tension and negative in pressure. The distribution curve of axial stress along the pile length under thermal-mechanical coupling load is given in Figures 12 and 13, and the calculation results under a pure mechanical load $P=1600$ kN and pure thermal load are also given. Figure 11 shows that the axial compressive stress of the pile body under the pure mechanical load $P=1600$ kN is linearly distributed. The maximum value is at the top of the pile, which is 3.183 MPa, and the minimum value is at the bottom of the pile, which is 0.326 MPa. The thermal load transferred by circulating water at 45°C causes additional axial compressive stress, which is large in the middle of the pile and smaller at both ends. The top of the pile is considered as an unconstrained free surface. Under the action of temperature, the pile end releases temperature work by deformation. The maximum value is approximately 0.65 MPa at 7.5 m below the pile top. The stress distribution from 12 m to the bottom of the pile is linear because the depth of the heat exchange pipe is 12 m, which has little effect on the stress of the bottom of the pile. Figure 13 shows that the circulating water at 5°C will cause a large axial tensile stress in the middle, but a small stress at the ends, with a maximum value of approximately 0.6 MPa at 7.8 m below the pile top. The maximum additional axial stress caused by temperature changes occurs below the middle of the pile, which is caused by the constraints of the pile end foundation soil.

### 5.2. Simulation Analysis of Side Shear Stress of Single Pile

Figures 14 and 15 show the shear stress distribution curves of the pile side under pure mechanical load $P=1600$ kN, under cyclic hydrothermal load (additional shear stress) and under thermal-mechanical coupling load. In the simulation of the pile foundation, the shear stress between pile and soil is considered friction. In this analysis, the pile is taken as the active body, the shear stress on the lateral side of the pile is called positive friction, and the shear stress under the lateral side of the pile is called negative friction. Affected by the heat exchange pipe, the pile will inevitably produce zero displacement somewhere along the pile due to the counteracting processes of thermal expansion and contraction; the friction resistance at this point is zero, which is called the neutral point. Figures 13 and 14 show that the neutral point appears at 5.51 m below the pile top in summer and 6.42 m below the pile top in winter. Figure 14 shows that under the condition of 45°C, the pile heating causes additional negative friction on the upper part of the pile and additional positive friction on the lower part of the pile; the frictional resistance at the pile head and bottom varies greatly, while the middle part does not change significantly, which is an approximately linear distribution. This is due to the expansion and elongation of the pile caused by the temperature rise, which leads to a larger frictional resistance in the middle and smaller at the ends. The negative friction caused by the thermal load reduces the positive friction caused by mechanical load P and increases the positive friction of the pile bottom. Figure 14 shows that at 5°C, the pile is cooled and contracted, resulting in additional positive friction on the upper part of the pile and additional negative friction on the lower part of the pile. The additional positive friction at the upper part of the pile is superimposed with the positive friction caused by the mechanical load, and the total friction at the top of the pile increases. The additional negative friction at the lower part of the pile is superimposed with the additional positive friction caused by the mechanical load, and the total friction at the bottom of the pile is reduced.

### 5.3. Single Pile Settlement Simulation Analysis

From Figures 16–18, it can be seen that under pure mechanical loading (1600 kN), the top displacement (downward) of the energy pile is 2.45 mm, and the bottom displacement (downward) of the pile is 0.07 mm. Under the cyclic hydrothermal load at 45°C, the displacement of the pile top (upward) is 0.05 mm, and the displacement of the pile bottom (downward) is 0.11 mm. Under the thermal-mechanical coupling load, the displacement of the pile top (downward) is 0.18 mm, and the displacement of the pile bottom (downward) is 2.4 mm. The temperature of circulating water at 45°C is higher than that of the underground environment, and the temperature rise causes pile expansion. The additional axial displacement caused by the pile expansion makes the pile head bulge, which leads to a decrease in pile top settlement. At the same time, the additional axial displacement increases the settlement of the pile bottom.

Figures 19 and 20 show that under the cyclic hydrothermal load of 5°C, the displacement of the pile top (downward) is 0.78042 mm, and the displacement of the pile bottom (upward) is 0.22368 mm. Under the thermal-mechanical coupling load, the displacement of the pile top (downward) is 3.2371 mm, and the displacement of the pile bottom (upward) is 0.17077 mm. The temperature of circulating water under the condition of 5°C is lower than that of the underground environment temperature. The cooling causes the shrinkage of the pile and the additional axial displacement of the pile, which leads to an increase in the displacement of the pile top and a decrease in the displacement of the pile bottom.

## 6. Comparison and Validation of Site Survey and Numerical Simulation Results

The measured data of the project site temperature tester are compared with the software simulation results, and the results are shown in Table 4.

From the table data, it can be seen that under winter conditions, the measured and simulated increase in temperature of the single energy pile pipe outlet water were 1.23°C and 1.28°C, respectively, a difference of 0.05°C. Under the summer conditions, the measured outlet water temperature of the single-pile heat exchange pipe with an energy pile decreases by 3.49°C, while the simulated value decreases by 2.80°C, a difference of 0.69°C. The reasons for the deviation between the simulation and the measured results are as follows: ① the influence of groundwater on the heat transfer of energy piles is ignored in the numerical analysis; ② the actual soil around the pile is composed of various soil layers with different thermal properties, so there is an error between the simulated TRT thermal response test value and the actual value;③ the ground temperature set in the simulation is constant, but the actual ground temperature fluctuates within a certain range.

The measured data of pile settlement in the project site are compared with the software simulation results and are shown in Table 5.

According to the data in the table, the pile shrinks in the cold winter conditions. The measured shrinkage value of the pile is 1.12 mm, and the simulated shrinkage value is 0.79 mm. Under the summer conditions, the pile is heated and expanded. The measured pile elongation is 0.17 mm, and the simulated pile elongation is 0.04 mm. The reasons for the differences between the simulated values and the measured values are as follows: ① the soil around the pile is composed of soil layers with different mechanical properties and formation conditions, which cannot be incorporated into the model; ② the influence of groundwater on the mechanical properties of the soil around the pile is ignored in the simulation.

## 7. Conclusion

In this paper, the temperature distribution of a single energy pile and the soil around the pile is studied, in addition to the thermal response of the pile after stable heat exchange of the parallel double U heat exchange pipe, and the following conclusions are obtained:

- (1)
After the heat transfer is stable, in the summer conditions, the temperature in the rock and soil increases first along the vertical direction, then reaches stability, and finally decreases. The winter condition is the opposite. The farther away from the pile center, the smaller the soil temperature fluctuation along the vertical direction

- (2)
With the addition of a load at the top, the stress, which is compressive, of the pile is linearly distributed. Under the summer conditions, the temperature of the pile rises, the temperature stress generated is nonlinearly distributed and it is a compressive stress at both ends. Therefore, under the thermal-mechanical coupling effect of the summer working condition, compared with the conventional load, the stress load of the pile increases by about 12%. Under the winter conditions, the temperature of the pile decreases, and the temperature stress distribution is similar to that under the summer conditions. It is still a nonlinear distribution, with higher stress at the two ends and lower stress at the middle; this is slightly different from that under the summer conditions, where the temperature stress is tensile. Therefore, under the condition of thermal coupling in winter, compared with the conventional load, the stress load of the pile is reduced by about 11.5%, and the safety of the pile is improved. In conclusion, the design of an energy pile should be based on the value of thermal-mechanical coupling in summer

- (3)
With the load placed at the top, the shear stress distribution of the pile side is large in the middle and small at both ends, and the direction is upward. Under the temperature load of summer conditions, the shear stress distribution of the pile side is large at both ends and small in the middle, and the change is linear. The point where the lateral shear stress is zero is at 1/3 of the pile depth. The direction of the lateral shear stress above zero is downward, and the direction of the lateral shear stress below zero is upward. Under the temperature load of winter conditions, the size distribution and zero position of the lateral shear stress of the pile are similar to those of summer conditions, but the direction of the lateral shear stress is opposite. The lateral shear stress above zero is upward, and the lateral shear stress below zero is downward. Therefore, under the condition of thermal coupling in summer, the maximum shear stress of the pile side is near the bottom of the pile, and the direction is upward. Under the condition of thermal coupling in winter, the maximum shear stress of the pile side is near the top of the pile, and the direction is upward

- (4)
Under the load, the settlement of the energy pile top is the largest, and the settlement of the bottom is the smallest. Due to the effect of temperature in summer conditions, the pile top displays upward displacement, while the pile bottom still undergoes downward displacement. With thermal coupling in the summer, the pile top still settles, but the displacement is lower about 7.23% than that under the pure load. Due to the effects of temperature in winter, the pile top settles, while upward displacement occurs at the pile bottom. Due to thermal coupling in winter, the settling of the pile top is greater about 47.66% than that under the pure load. Therefore, the settlement of the energy pile foundation in winter is the control condition that should be considered in structural design

## Data Availability

The datasets and materials used and/or analyzed during the current study are available from the corresponding author on reasonable request.

## Conflicts of Interest

The authors declare that they have no conflicts of interest.

## Acknowledgments

This study was financially supported by the National Natural Science Foundation of China (Grant No. 42177167) and the Natural Science Foundation of Shandong Province (Grant No. ZR2019QEE008). We would like to thank our friends and colleagues for their invaluable advice, assistance, and supports during geological body modeling and data acquisition.