# Thermo-Mechanical Performance of a Phase Change Energy Pile in Saturated Sand

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## Abstract

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## Featured Application

**Phase change energy pile can be used to utilize shallow geothermal energy efficiently.**

## Abstract

## 1. Introduction

## 2. Brief Description of Experiments

#### 2.1. PC Pile Development and Experiment Conditions

#### 2.2. Loading Condition

^{3}/h for 16 h, followed by cooling to initial room temperature (18.5 °C) with circulating water at the same flow rate for 8.5 h. Three continuous heating–cooling cycles were performed in the experiments. The temperature in pile and soil, pore pressure of the soil, and strain along the pile were measured during the thermal cycle. The layout of the position of measuring points of the temperature and soil pressure is shown in Figure 2a. Thermocouples and strain gauges were fixed onto a steel reinforcement inside the pile to measure the temperatures and thermal strain (Figure 2b).

## 3. Numerical Models

#### 3.1. Basic Assumptions

- Since the vertical static load imposed on the pile head was small and the rigidity of the pile itself was relatively large, the load on pile head would not cause plastic damage, so an ideal linear elastic material was used to approximately model the pile.
- As the temperature change range was not large, the change of material parameters, such as the thermal conductivity, specific heat, and elastic modulus of the pile and soil, were not considered during the thermal cycles and loading.
- During the heat transfer process of the energy pile, the temperature change in the longitudinal direction was much smaller than the temperature change in the radial direction. Therefore, the heat transfer of the energy pile in the longitudinal direction was negligible.

#### 3.2. Governing Equations

#### 3.2.1. The Governing Equation of Heat Conduction

#### 3.2.2. The Governing Equation of Heat Convection

#### 3.3. Constitutive Models

#### 3.3.1. Thermo-Elastic Model of the Pile

#### 3.3.2. Mohr–Coulomb Model of Soil

#### 3.4. Finite Element Model

#### 3.5. Mechanical Model

- (1)
- The elastic modulus of the pile (E = 3.25 × 10
^{4}MPa) and Poisson’s ratio of soil ($\upsilon =0.35$), and the friction angle of the soil were input into the material properties module. In addition, the permeability coefficient of saturated soil was input as $k=6\times {10}^{-3}$ cm/s, whereas the specific gravity of the interstitial fluid was set to 10 kN/m^{3}. - (2)
- The heat exchange tube model and the pile body model were set as binding constraints, the interface between the energy pile and soil were simulated as a frictional contact in the tangential direction. The coefficient of friction (μ) between soil and concrete pile was considered as tanϕ, where ϕ is the internal friction angle of the sand used in the experiments.
- (3)
- The pile and soil were first subject to gravity force, and then a static load of 6.5 kN was applied to the pile head. The surrounding and bottom of the soil were set as a completely fixed boundary, and the top surface was a free boundary with a pore pressure set to 0 in the predefined field, which means that the top surface was the drainage boundary. Finally, the calculation results of the temperature model were substituted into the stress model for the thermal and mechanical coupling.

## 4. Results and Discussions

#### 4.1. Validation of Numerical Model

#### 4.1.1. Temperature Change in Soil

#### 4.1.2. Strain Change in the Pile

#### 4.1.3. Pile Displacement

#### 4.1.4. Soil Pressure around Pile

#### 4.2. Comparison between PC pile and Ordinary Pile

#### 4.2.1. Temperature Change of Pile

#### 4.2.2. Strain in Pile

#### 4.2.3. The Displacement of Pile

#### 4.2.4. Soil Pressure around Pile

#### 4.3. Influence of Thermal Loads on PC Piles

#### 4.3.1. Temperature Change

#### 4.3.2. Strain Change in PC Pile

#### 4.3.3. Displacement on Pile Head

## 5. Conclusions

- (1)
- Phase change materials can be used in energy piles to reduce the temperature change of the pile to a certain extent. At the end of heating, the temperature of the PC pile was 0.6 °C lower than that of ordinary energy pile without phase change materials. When the temperature dropped below 22.5 °C, the temperature decreased more slowly than the ordinary pile due to the exothermic phase change of paraffin, and the range of soil temperature change around the pile reduced by 0.03 m compared to the ordinary pile.
- (2)
- At the end of heating, the strain at the measuring point of the phase change energy pile was 2% smaller than that of the ordinary energy pile, and the displacement was reduced by 6%, which shows that the addition of phase change materials can reduce the thermal response of the energy pile compared with ordinary pile. Moreover, the stress distribution in the pile can be reduced and consequently the durability of the pile can be improved. After the thermal cycles, the residual deformation was basically the same.
- (3)
- The difference in the soil pressure change around the PC pile at the end of heating was small, indicating that the addition of phase change materials has little effect on the soil pressure around the pile.
- (4)
- When the thermal load increased from 10 °C to 30 °C, the exchange range between pile and soil increased from 0.2 m to 0.45 m, and the growth rate decreased with the increase in thermal loading. The pile strain showed a nonlinear increasing trend with the increase of thermal loading. Meanwhile, the observed strain and axial stress of the pile increased with the increase of the depth.
- (5)
- In the heating stage, the increment of the displacement at the head of the PC pile increased with the increase of the thermal loading. After the cooling stage, the residual strain and plastic displacement also increased with the increase of the thermal loading. At the loading condition of $\Delta T$ = 10 °C, the phase change material had the greatest influence on the displacement and residual strain of the pile. With the increase of the thermal loading, its influence became less and less obvious. Therefore, in the design of phase change energy piles, full consideration should be given to the compatibility of the thermal loads and the phase-change temperature of the material. While phase-change material is of great potential for use in controlling the thermal response of energy piles, more attention should be paid to balance the heat transfer rate and the thermal response of the pile.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Experiment setup. (

**a**) Symmetrical configuration of PC pile test in horizontal direction (unit: mm); (

**b**) heat exchange tubes in the pile.

**Figure 2.**Layout of measuring points. (

**a**) Arrangement of thermocouples (unit: mm); (

**b**) location of strain gauges and thermocouples within the pile body.

**Figure 4.**Comparison of experimental and simulated results of soil temperature around the pile. (

**a**) Temperature change at TS11; (

**b**) Temperature change at TS13.

**Figure 5.**Experimental and simulated results of strain change in the pile. (

**a**) Time history of strain change; (

**b**) strain distribution at the end of the first heating.

**Figure 6.**Comparison of pile displacement in the static loading stage and heating stage. (

**a**) Displacement of the pile in the static loading stage; (

**b**) displacement of the pile during thermal cycles.

**Figure 10.**Comparison of strain in different piles. (

**a**) Time history of strain change; (

**b**) distribution of strain along the depth.

**Figure 13.**Temperature distribution after heating for 16 h under different thermal loads. (

**a**) ΔT = 10 °C; (

**b**) ΔT = 20 °C; (

**c**) ΔT = 30 °C.

**Figure 15.**Axial strain and stress of the PC pile under different thermal loadings. (

**a**) Axial strain; (

**b**) Axial stress.

Sample Material | Thermal Conductivity W/(m·K) | Specific Heat Capacity J/(kg °C) | Coefficient of Thermal Expansion (/°C) | Relative Density |
---|---|---|---|---|

saturated sand | 2.7 | 1155 | 1.46 × 10^{−6} | 42% |

ordinary concrete | 1.89 | 963 | 0.98 × 10^{−5} | -- |

phase change concrete | 1.65 | 1080 | 0.9 × 10^{−5} | -- |

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**MDPI and ACS Style**

Du, T.; Li, Y.; Bao, X.; Tang, W.; Cui, H.
Thermo-Mechanical Performance of a Phase Change Energy Pile in Saturated Sand. *Symmetry* **2020**, *12*, 1781.
https://doi.org/10.3390/sym12111781

**AMA Style**

Du T, Li Y, Bao X, Tang W, Cui H.
Thermo-Mechanical Performance of a Phase Change Energy Pile in Saturated Sand. *Symmetry*. 2020; 12(11):1781.
https://doi.org/10.3390/sym12111781

**Chicago/Turabian Style**

Du, Ting, Yubo Li, Xiaohua Bao, Waiching Tang, and Hongzhi Cui.
2020. "Thermo-Mechanical Performance of a Phase Change Energy Pile in Saturated Sand" *Symmetry* 12, no. 11: 1781.
https://doi.org/10.3390/sym12111781