## 1 Introduction  
Currently, there is a diversity of approaches to geothermal energy development [1, 2]. Inside buried pipe energy pile (IBP-EP) has become an important method of extracting geothermal energy from the ground source side [3, 4]. The pile foundation is used as a heat exchange well, which is connected to the heat pump system through a collector pipe, and the heat pump unit extracts the ground-side thermal energy, which is difficult to utilize directly using geotechnical methods, to supply heat or cold to buildings and other infrastructures [5, 6]. At present, the research on IBP-EP tends to be limited, and more scholars focus on energy pile improvement technology. Many energy pile improvement techniques have been proposed, with a focus on improving the energy pile body material [7, 8, 9, 10, 11, 12], the pile structure [13, 14, 15, 16, 17] and the construction process [18, 19, 20, 21]. The deeply buried pipe energy pile (DBP-EP) technology [22] requires the heat exchanger pipe to extend out of the pile into a deep well at the bottom of the pile, with the upper part of the heat exchanger pipe wrapped in pile concrete and the lower part wrapped in backfill. The DBP-EP can be designed with different depths of the pile bottom well to meet different heat transfer needs, making the structure form more flexible. Compared with IBP-EP,DBP-EP is divided into a pile foundation portion and a deep well portion along the depth direction, and the heat transfer mechanism along the depth direction is variable along the cross-section and along the heat transfer medium, as shown in Figure 1. DBP-EP can obtain deeper geothermal energy and can independently satisfy the energy demand of the upper structure. The DBP-EP construction process is flexible, and the construction of the pile foundation casting and the drilling of the heat exchanger pipe can be operated separately, so compared with the construction process for pre-buried IBP-EP heat exchanger pipes, the process for the DBP-EP pipes has a broader application prospect. However, relatively few studies have been conducted on DBP-EP, and only the heat transfer performance of DBP-EP has been analyzed under hot and cold cycles [23; 24; 25], seepage conditions [26; 27], and intermittent operation [28]. The effects of different temperature loads and mechanical loads on the thermomechanical behavior of DBP-EP during the heating process are not known. In recent years, the thermomechanical behavior of energy piles has become a major research focus, with numerous thermomechanical response tests being conducted by scholars, both domestically and internationally. These studies have shown that the additional thermal stress and strain caused by the thermal expansion of the pile body during operation cannot be ignored [16; 29]. The heat exchanger tube within the energy pile facilitates heat exchange, leading to uneven temperature stress distribution throughout the pile, a phenomenon confirmed by the thermomechanical response tests conducted by [PERSON] et al. [30] and [PERSON] et al. [13]. [PERSON] et al. [31] introduced the thermal stress concentration factor to evaluate the inhomogeneity of thermal stresses within energy piles and analyzed the relative impact of various factors contributing to this inhomogeneity. [PERSON] et al. [32] found that assuming a uniform temperature distribution within the pile results in expansion or contraction near the \"zero point\" of the pile. Model tests, including centrifugal and indoor model tests, have become a popular method among scholars for studying the thermomechanical response of energy piles. [PERSON] et al. [33] and [PERSON] et al. [34] used centrifugal modeling tests to investigate these responses, confirming the feasibility of such tests and highlighting the significant impact of the end restraints on the stress-strain behavior of piles. The research team of [PERSON] et al. [9; 35; 36] conducted extensive thermomechanical response tests using indoor modeling and numerical simulations.