## 4 Results
However, in enclosed hot dry rock formations without direct contact between gas, liquid, and rock, the maximum temperature gradient is smaller than that of natural cooling. Temperature gradients of 2000 \({}^{\circ}\)C/m, 2200 \({}^{\circ}\)C/m, 2400 \({}^{\circ}\)C/m, 2600 \({}^{\circ}\)C/m, 2800 \({}^{\circ}\)C/m, and 3000 \({}^{\circ}\)C/m are considered for thermal conduction in enclosed hot dry rock formations. The relationship between temperature gradient and stress can be calculated using Formula (1), as shown in the following Figure. Figure 3 illustrates a linear relationship between temperature gradient and stress. As the temperature gradient increases, thermal stress also rises, especially in the vicinity of the heat exchange medium and the rock contact surface, where localized high thermal stress is directly generated in high-temperature environments. Dry hot rocks generate thermal stresses at temperature gradients of 2000 \({}^{\circ}\)C/m, 2200 \({}^{\circ}\)C/m, 2400 \({}^{\circ}\)C/m, 2600 \({}^{\circ}\)C/m, 2800 \({}^{\circ}\)C/m, and 3000 \({}^{\circ}\)C/m are 266.2 MPa, 293.8 MPa, 319.5 MPa, 346.09 MPa, 372.7 MPa, and 399.3 MPa, respectively. As the temperature gradient changes from 2000 \({}^{\circ}\)C/m to 3000 \({}^{\circ}\)C/m, the thermal stress increases by 133.1 MPa. In the horizontal segment cavities of dry hot rock formations at depths of 3000 m, the pressure of the heat exchange medium in the annular storage chamber is mainly determined by gravity and the pressure difference between the two vertical wells. The pressure caused by the gravitational force of liquid alloy metals can be calculated as 255 MPa using Formula (2), while the pressure caused by the gravitational force of water as the heat exchange medium is 30 MPa. Since both the injection and production wells in the U-shaped wells contain heat exchange media, fluid flow is not driven by the formation pressure but by the injection pressure \(\Delta\)p at the injection wellhead. The pressure is highest at one end of the horizontal segment near the injection well, as calculated by Formula (2). Assuming an injection wellhead driving pressure of 20 MPa, the pressures on the rock interface caused by liquid alloy technology and water as heat exchange media, calculated using Formula (2), are 275 MPa and 20 MPa, respectively. The tensile strength of rock can be obtained through experiments or empirical formulas derived from data analysis. In this study, the tensile strength of rock was measured as one-tenth of its compressive strength, which is \(p_{cri}=19.35\) MPa [22]. At a heating rate of 2000 \({}^{\circ}\)C/m, the criteria for dry hot rock tensile failure can be observed. \[p_{T}-p_{a}=266.2-275=-8.8<0 \tag{5}\]  
In a dry hot rock formation at a depth of 3000 m, the rock temperature gradient is 2000 \({}^{\circ}\)C/m. The interface rock will not be damaged by thermal stress generated by heat shock because rocks in deep formations have higher compressive strength and lower tensile strength, thus maintaining stability under certain conditions. In a dry hot rock formation at a depth of 3000 m with a temperature gradient of 2200 \({}^{\circ}\)C/m, the pressure at the interface of the stored rock is 293.8 MPa. \[p_{T}-p_{a}=293.8-275=18.8>0 \tag{6}\]  
In a dry hot rock formation at a depth of 3000 m, the temperature gradient of the rock is 2200 \({}^{\circ}\)C/m. The stored interface rock will experience damage due to thermal stress caused by heat shock. Therefore, at higher temperature gradients, dry hot rock formations at a depth of 3000 m will lose stability due to thermal shock-induced damage.