# Thermomechanical Behavior of Parallel Multi-U-Shaped Energy Piles Under the Summer Condition
## 4 Experimental Results and Numerical Validation of the Parallel Multi-U-Shaped Energy Pile
### Thermomechanical Behavior of the Parallel Multi-U-Shaped Energy Pile  
#### 4.2.1 Analysis of the Energy Pile Stress-Strain  
An energy pile's condition of force and deformation during heating without loading at the top is influenced by the temperature load as well as the impact of soil restrictions surrounding the pile. Without an external load or soil limitation around the pile, the axial free strain \(\varepsilon_{T-Free}\) of the pile body is  
\[\varepsilon_{T-Free}=\alpha_{c}\Delta T \tag{15}\]  
In Equation (15), \(\alpha_{c}\) is the coefficient of thermal expansion of concrete, and \(\Delta T\) is the temperature difference.  
The axial observed strain \(\varepsilon_{T-Obs}\) is calculated as the average axial observed strain at the same section, and Figure 8 displays the measured strain and free strain distribution curve of the pile body along the depth direction. It is evident that the findings of the field tests and the numerical simulation are reasonably compatible. Because of the soil limitation around the energy pile, the measured strain fluctuation during operation is less than the free thermal strain. Since there is no load on top of the pile, it may move upwards freely; the only thing that stresses and strains the pile body is the heat load. Friction at the pile-soil contact also affects the pile body, resulting in non-uniform vertical stresses when heated; curves show a distribution pattern of small in the middle and big on both sides. When the soil around the pile, the pile top, and the pile end constrain the pile body, the axial restrained strain \(\varepsilon_{T-Rstr}\) is as follows:  
\[\varepsilon_{T-Rstr}=\varepsilon_{T-Free}-\varepsilon_{T-Obs} \tag{16}\]  
Calculate the thermally induced restraining stresses in the pile body during the axial restraint stress \(\sigma_{T}\) according to Equation (17).  
\[\sigma_{T}=-E(\alpha_{c}\Delta T-\varepsilon_{T-Obs}) \tag{17}\]  
Figure 7: Temperature clouds of energy piles with different buried pipe forms.  
In Equation (17), \(E\) is the elastic modulus of concrete (kPa).  
Along the section of the deep portion of the pile, the variation rule of the confining stress and temperature change of the energy pile may be calculated. The actual thermal strain produced is less than the free strain because of the restraining influence of pile soil. The maximum confining stress of the energy pile in the chosen field test section occurs at a depth of 10 m of the pile body at 168 h, as shown in Figure 9 and the numerical simulation results at this time. The figure compares the data of energy piles from [PERSON] et al. [33], which were field-tested in Xinyang, Henan Province, which had similar field conditions to this test, with the top of the piles unconstrained and a spiral-type buried pipe. Similar to the test findings, the test data indicated that the greatest extra compressive stress was around 1600 kPa and manifested in the center of the pile. The above experimental results show that when the temperature rise of the pile body under summer working conditions is within 10 \({}^{\circ}\)C, the maximum additional stress of the pile body under the temperature load may reach around 1600 kPa. Therefore, we cannot neglect the effect of temperature change on the bearing capacity of the pile body at the design stage of the grouted energy piles under summer working conditions, and the neglect of this load will cause certain risks for the use of the building structure.  
Figure 8: Observed strain and free strain distribution curve along the depth direction of the pile.  
Figure 9: Curves of pile axial restraint stress with temperature difference, [PERSON] et al. [33].