# Group Pile Effect on Temperature Distributions inside Energy Storage Pile Foundations
## 4 Analytical Results and Discussions  
### Temperature Distribution in Concrete  
This section discusses the effect of the group piles on temperature change and distribution inside the concrete section. Figure 6 illustrates the temperature distribution contours inside the concrete section at the end of several loading cycles for the \(s\) = 7 m case. Although the temperature at the inner surface comes back to 20 \({}^{\circ}\)C at the end of each cycle due to the imposed thermal loading cycle of the CAES (refer to Figure 4b), the heat penetrates the concrete section gradually and the temperature inside the concrete section increases with the cycles. The temperature is distributed uniformly along the circumferential direction because of symmetrical geometries and loading conditions. Therefore, the results in this section are presented and discussed along the radial direction at \(\theta\) = 0\({}^{\circ}\)  
Figure 6: Temperature profile contour for concrete at the end of (**a**) the 1 st loading cycle; (**b**) the 5 th loading cycle; (**c**) the 50 th loading cycle; (**d**) the 200 th loading cycle; (**e**) the 400 th loading cycle; and (**f**) the 1000 th loading cycle. Figure 7 represents the temperature history within several cycles for different pile spacing at (a) the one-third location (\(r=\frac{2r_{i}+r_{o}}{3}\)); (b) the two-thirds location (\(r=\frac{r_{i}+2r_{o}}{3}\)); and (c) the outer surface (\(r=r_{o}\)). Generally, the temperature change shows a cumulative effect and gradually increases with cycles. The increase in temperature is more rapid in early loading cycles than in the later ones. The group pile effect results in a temperature increase inside the concrete section due to the heat transferred from the adjacent piles. This effect was negligible in the earlier cycles since the heat from the adjacent pile was not reached yet. As the pile spacing becomes smaller, the effect of the adjacent pile starts to act earlier, resulting in a more rapid temperature increase. However, at the last loading cycle (1000), the temperatures in all group pile cases, regardless of the pile spacing, converge at a similar temperature, which is higher than the isolated pile case. In addition, comparing Figure 7a-c, it is noticeable that, moving away from the interior surface of the concrete section to the soil layer, the temperature fluctuation within each cycle becomes smaller. Figure 8 shows the distribution of temperature along the concrete section for selected cycles at (a) the middle of a cycle (19:00) and (b) the end of a cycle (7:00). With the increase of loading cycles, the group pile effect tends to increase the temperature away from the inner surface. This trend results in a more uniform temperature distribution at 19:00 but a larger variation along the radial direction at 7:00. The group pile effect starts earlier for the cases with smaller pile spacing, but the temperature distribution in the last cycle converges to a similar distribution regardless of pile spacing. Figure 7: Temperature history within multiple loading cycles (1 st–3 rd, 8–10 th, 23 rd–25 th, 198–200 th, and 998–1000 th) for different \(s\) at (**a**) the one-third location; (**b**) the two-thirds location; and (**c**) the outer surface. As a reference, the temperature distributions at steady state in the concrete section for the thermo-active pile from works of literature are shown as blue lines in Figure 8. As seen, the thermo-active pile shows a much lower temperature and a more uniform distribution as compared to the energy storage pile foundation due to differences in the thermal loading discussed in the Introduction section. Figure 9 presents the highest temperature ever reached in each cycle for various pile spacing at (a) the one-third location (\(\frac{2r_{i}+r_{o}}{3}\)); (b) the middle location (\(\frac{r_{i}+r_{o}}{2}\)); (c) the two-thirds location (\(\frac{r_{i}+2r_{o}}{3}\)); and (d) the outer surface (\(r_{o}\)) of the concrete section. For all these cases, the maximum temperature increases as the loading cycle increases.