# Group Pile Effect on Temperature Distributions inside Energy Storage Pile Foundations
## 4 Analytical Results and Discussions
### Temperature Distribution in Soil  
This section discusses the effect of group pile on temperature change and distribution inside the soil layer. Figure 11 demonstrates the temperature profile contours for surrounding soil at the end of selected loading cycles for the \(s=7\) m case. Similar to the concrete section, heat is gradually transferred into the soil from the pile, resulting in a gradual increase in temperature. As seen in Figure 11a-c, before the heat reaches the outer surface of the soil (center line between the two piles), the temperature inside the soil is distributed uniformly along the circumferential direction. As seen in Figure 11d-f, after the heat reaches the outer surface of the soil, the thermal effect of the adjacent pile starts and the temperature distribution along the circumferential direction is not uniform anymore. Therefore, this section will present and discuss temperature distribution along two radial directions: horizontal (\(\theta=0^{\circ}\)) and diagonal (\(\theta=45^{\circ}\)). Figure 12 demonstrates the temperature history within several cycles for \(\theta=0^{\circ}\) at (a) the inner surface of the soil (\(r_{o}\)); (b) the quarter of the soil layer (\(\frac{s}{4}+\frac{r_{o}}{2}\)); and (b) the center between two piles (\(\frac{s}{2}\)). In all cases, the temperature inside the soil gradually increases with the cycles, having a faster change at the earlier cycles. The group pile cases have a similar temperature at the location near the concrete pile in earlier cycles as the isolated pile case does. As the cycle increases, the group pile cases start to show a higher temperature than the isolated pile due to the heat transferred from the adjacent pile. The smaller the pile spacing and the further the location from the concrete section, the earlier this temperature difference starts. However, after a sufficient amount of cycles, the temperature in the soil tends to converge to a similar value (about 110 \({}^{\circ}\)C) for all group pile cases regardless of location. Such a phenomenon is different from the isolated pile case, where the temperature in the soil is stabilized at different values when moving away from the concrete pile. Figure 10: (a) Identification of cycles when group pile starts to affect the temperature (\(N_{G}\)) at the outer surface of the pile section; (b) \(N_{G}\) for each point of pile section. Figure 13 shows temperature distribution along the radial direction in the soil at the end of each cycle for different pile spacings for (a) \(\theta=0^{\circ}\) and (b) \(\theta=45^{\circ}\). As seen, temperature distribution along the radius follows the same trend for both the horizontal and diagonal directions. The group pile effect tends to make the temperature distribution more uniform in the soil with increase of the loading cycle. After a sufficient amount of cycles, the temperature distribution in all group pile cases reaches a similar constant pattern. Figure 11: Temperature profile contour for soil at the end of (**a**) the 1 st loading cycle; (**b**) the 13 th loading cycle; (**c**) the 25 th loading cycle; (**d**) the 400 th loading cycle; (**e**) the 800 th loading cycle; and (**f**) the 1000 th loading cycle. Figure 12: Temperature history within multiple cycles (1 st–3 rd, 8–10 th, 20–30 th, 150–200 th, and 800–1000 th) for \(\theta=0^{\circ}\) at (**a**) the inner surface of the soil; (**b**) the quarter of the soil layer; (**c**) and the center between two piles. As a reference, the temperature distributions at steady-state in the soil for the thermo-active pile from works of literature are shown as blue lines in Figure 13. As seen, the thermo-active pile shows a much lower temperature as compared to the energy storage pile due to the differences in the thermal loading discussed in the Introduction section.