## 3 Stability Analysis of Cavity Interface  
Stability analysis of the horizontal section cavity of the dry hot rock U-shaped well involves sealing the cavity, where the geological heat passes through the metal material of the sealing layer and exchanges heat with the liquid alloy heat transfer medium, without any loss of fluid mass. However, the pressure in the dry hot rock formation and the thermal stress caused by cyclic heat exchange can lead to an imbalance between the rock pressure and heat transfer medium inside the heat exchange channel, potentially causing rock fracturing and instability in the heat exchange channel. To ensure the structural stability of the cavity in the horizontal section of the U-shaped well, the cavity structure must be optimized. The most stable cavity structure is a cylindrical structure with a smaller diameter; however, the horizontal section of the U-shaped well cannot form a cylindrical structure after hydraulic fracturing and acidification. Therefore, the cavity sealed in the horizontal section of the U-shaped well exhibits structural instability, and is especially prone to collapse during changes in formation pressure and thermal stress. This section mainly analyses and studies the stability of the surrounding rock of the cavity sealed in the horizontal section of the U-shaped well. The interface between the metal lining layer and the rock within the cavity sealed in the horizontal section of the U-shaped well exhibits irregularity, as shown in Figure 1. Since the cavity sealed in the horizontal section extends along the length of the wellbore, structural issues crossing the wellbore section are simplified into a plane strain problem, as illustrated in Figure 2. The sealing layer is formed by injecting a high-temperature liquid alloy into the channel of the dry hot rock reservoir after undergoing heat conduction and cooling to solidify. The thickness of the sealing layer is determined by the time controlled by heat conduction between the high-temperature liquid alloy and the dry hot rock. Due to the irregular shape of the dry hot rock formed by small-scale hydraulic fracturing and acidification, the sealing layer also has an irregular shape. However, due to the similar heat conduction properties of the high-temperature liquid alloy, the sealing layer formed in the reservoir has thermal stability. The thickness of the sealing layer formed at the same heat conduction control time should be the same. Heat exchange occurs as the working fluid flows through the channel containing the sealing layer and directly exchanges heat with the inner lining. Since the dry hot rock exchanges heat directly with the sealing layer, the temperature of the sealing layer is higher than that of the heat exchange working fluid. A temperature gradient is formed between the heat exchange working fluid close to the sealing layer and the heat exchange working fluid in the direction of the central axis. The flow rate of the heat exchange working fluid effectively must be controlled effectively to achieve efficient heat exchange. In Figure 2, the stability of the horizontal segment ring storage cavity is divided into the stability of the entire cavity body and the stability of the irregular interface between the cavity body and the rock. The stability of the cavity body is mainly controlled by the equivalent radius of the cavity, where a smaller equivalent radius results in higher stability of the cavity body. However, a smaller equivalent radius of the cavity body leads to a smaller contact area between the cavity rock and the lining of the ring storage alloy, reducing heat transfer efficiency. The stability of the irregular interface between the cavity rock and the rock is mainly controlled by the combined effect of thermal shock-induced thermal stress and the pressure of the heat transfer medium on the rock interface. The high-temperature damage to rock materials under unconstrained heating is mainly controlled by the tensile strength of the rock material at high temperatures.