# Group Pile Effect on Temperature Distributions inside Energy Storage Pile Foundations
## 1 Introduction  
A common method for utilizing renewable energy is to immediately generate electric power for operation of the building via solar panels that are directly attached to residential or commercial buildings [1]. This method eliminates energy loss due to long-distance transportation and maximizes power efficiency for usage. However, the energy generated by these alternative sources has an intermittent nature: they are dependent on climate and daily cycles [2]. Thus, an efficient storage for renewable energy is needed to accommodate the fluctuation of energy supply and to meet customer demand.  
Reinforced concrete pile foundations have been proposed for renewable energy storage by utilizing compressed air energy storage (CAES) technology [3, 4]. The pile foundation is designed with a hollow section, inside which renewable energy can be stored as compressed air and can be released to meet the customer demand. Since high pressure and temperature changes can originate from the compressed air during compressing and releasing processes, it can induce mechanical and thermal stresses, challenging the safety of the foundation. The structural responses of the foundation subjected to high pressure have been studied extensively [5, 6]. The temperature distribution inside the pile foundation for isolated piles has also been investigated [7]. On top of these research results,this paper presents a study on the temperature changes and distributions for the group pile construction since it is a common construction practice. Non-steady-state dynamic thermal transfer simulations were conducted for the group pile under cyclic temperature loadings generated by the compressed air. The magnitudes of the cyclic temperature loading were estimated based on the thermodynamic processes of the CAES. To carry out the heat transfer analysis, a two-dimensional (2D) plane strain model with concrete and soil layers was constructed. During the simulations, this model was subjected to fluctuating temperature inputs applied to the inner surface of the concrete pile. Pile spacing was considered a primary study parameter to evaluate the group pile effect on the temperature distribution inside the concrete section and the surrounding soil.  
Similar thermal transfer analyses and temperature distribution studies were conducted extensively for thermo-active pile foundations [8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19]. In these studies, the pile was treated as a heat absorber for heat exchange between the ground surface and underground regions since the temperature at the ground surface fluctuates seasonally while the underground temperate remains constant. However, the thermal behavior for the energy storage pile discussed in this paper is different from that of the thermo-active pile foundation. These differences originated from the following:  
1. Different heat sources. The thermo-active pile is typically heated up or cooled down by the liquid circulating inside the pile, while the energy storage pile is subjected to temperature changes from the compressed air.
2. Different locations of the thermal loading. The thermo-active pile is typically heated up or cooled down inside the pile section, while the energy storage pile is heated at the inner surface by the compressed air.
3. Different magnitudes of the thermal loading. The thermo-active pile has a temperature change in the range of 10 to 20 \({}^{\circ}\)C for typical applications and can be as high as 30 \({}^{\circ}\)C for extreme heat exchanges [12]. On the other hand, the energy storage pile can result in a temperature increase up to more than 100 \({}^{\circ}\)C.  
Because of these differences, it is not suitable to directly use the research results from the thermo-active pile foundations for the design of the energy storage foundation. Instead, the temperature changes and distributions from the thermo-active pile in current literature will be used as a reference to compare the results obtained in this paper.