## 1 Introduction  
Solar panels or wind-mills attached to buildings have been widely used to generate renewable energy for electric power supplies [1]. However, renewable energy has a nature of intermittency due to climate and day-and-night diurnal cycles and cannot provide uninterrupted energy supplies [2]. One of the solutions is to store extra renewable energy when it is available for later usage by the compressed air energy storage (CAES) technology [3, 4]. Utilizing the CAES technology, a new pile foundation system is being developed for renewable energy storage through a multi-disciplinary research project [5, 6]. This system uses the CAES technology to store renewable energy inside the reinforced concrete pile foundation configured with hollowed sections, as illustrated in Figure 1.  
The compressed air can result in high air pressure at the inner surface of the pile foundation. Extensive analytical and experimental studies have been conducted for the pile foundation subjected to the high air pressure for different pile construction materials, including regular reinforced concrete [7], fiber reinforced concrete [8], high-performance concrete [9, 10], steel [11], and steel-concrete composites [12]. In these studies, the compressed air is assumed to go through a complete cooling process, where the temperature of the compressed air will drop back to normal room temperature [7]. However, the complete cooling process is somewhat challenging and requires extra cost. Therefore, the temperature of the compressed air might not drop back to room temperature if sufficient cooling is not provided. In such a case, the temperature in the energy storage pile foundation varies during daily air compressing and releasing cycles, which can generate thermal stresses and affect the structural safety of the pile foundation.  
As a first step to investigate the thermal effect, this paper studies temperature distributions inside the concrete section for the pile foundation through non-steady state heat transfer analyses. The temperature change that originated from compressing and releasing air was first calculated following the thermal dynamic processes of the CAES. The heat transfer analysis was then conducted using two-dimensional (2D) plane strain models by applying the temperature change at the inner surface of the pile foundation. Several parameters were considered in the study, including thermal conductivities of the concrete, specific heat capacities of the concrete, and dimensions of the pile foundation. The obtained temperature distribution can be used for investigation of the thermal stress inside the foundation and surrounding soil.  
Extensive research work, including experiments and numerical analyses, have been conducted on the temperature distribution and thermal mechanical behavior for thermo-active pile foundations [13, 14, 15, 16, 17, 18, 19]. However, the thermo-active pile foundation, which uses the pile as a heat absorber, is different from the proposed energy storage pile foundation system, where the pile is used as an energy storage medium through compressed air. Although both foundation systems involve the heat transfer phenomena inside the pile, there are significant differences in protocols, magnitudes, and applied locations of the temperature loading. Therefore, the analytical and experimental results from the thermo-active pile  
Figure 1: Proposed energy storage foundation system (Modified from [5]).  
foundations cannot be applied for the proposed energy storage pile foundation. It is necessary to conduct the heat transfer analysis specifically for the temperature loading conditions in the energy storage pile foundation.