## 1 Introduction  
As a main rock type in hot dry rock reservoirs, granite is an intrusive rock among acidic igneous rocks, and its main minerals are quartz, potassium feldspar, acidic plagioclase, etc., which are thought to be products of the partial melting of middle-lower crustal protololiths, during orogenesis and crustal thickening or thinning (I-type, S-type, A-type, M-type) [1, 2], and it is always characterized by high strength, compactness and low permeability. The temperature of dry hot rock can reach 150-650 \({}^{\circ}\)C [3], and the exploitation technique is mainly based on the enhanced geothermal system. During the production process, the stability of wellbore in a high-temperature reservoir may be affected by the low-temperature drilling fluid [3, 4]. In addition, the hydraulic fracturing process is also influenced by the mechanical properties of dry hot rock cooled by the low-temperature water or other fluids [5, 6, 7, 8, 9, 10, 11]. During the long-term geological disposal of high-level nuclear waste buried in a repository [12, 13, 14], it should also be taken into account that the surrounding rock mass heated by nuclear waste may be cooled by groundwater. Under the geological conditions of high temperature and high pressure, the above-mentioned engineering rock mass is subject to the complex coupling effect of temperature field, seepage field and stress field when in contact with low-temperature fluid. In order to determine the mechanical properties of rock mass under this condition, it is necessary to study certain strength parameters (cohesion and the internal friction angle) and the failure criterion of water-cooled granite under high temperature. This would be helpful for understanding the mechanism of hydraulic fracturing and wellbore stability problems during water injection in hot dry rock reservoirs. In recent years, some experimental studies have been conducted on the physical and mechanical properties of granite samples after high-temperature and water-cooling treatment. The main research results are as follows:  
(1) Physical properties: It has been found that the mass, volume and density of granite samples decrease with an increase in heating temperature [15; 16; 17]. In addition, it has been observed in some studies that the P-wave velocity of granite does not change obviously when the heating temperature is lower than 200 \({}^{\circ}\)C, while it decreases significantly with an increase in temperature from 200 \({}^{\circ}\)C to 800 \({}^{\circ}\)C [15; 16; 17; 18], but some other studies have shown that the P-wave velocity decreases monotonically with increasing temperature [19; 20]. There are also some studies on the porosity and permeability of granite after high-temperature and water-cooling treatment [21], and they find that porosity or permeability does not change significantly when the treatment temperature is lower than a threshold value (400-500 \({}^{\circ}\)C), while it increases obviously when the temperature is higher than this threshold [15; 19; 22; 23]. (2) Mechanical properties: Some studies [19; 24; 25; 26] show that the uniaxial compressive strength and Young's modulus of granite samples decrease monotonously with the treatment temperature. However, some other studies [17; 18; 27] report that the uniaxial compressive strength and Young's modulus generally remain constant or increase slightly when the treatment temperature is lower than a threshold value (200-400 \({}^{\circ}\)C), while they decrease significantly when the temperature is higher than the threshold. In addition, triaxial compressive test results show that the compressive strength of the granite samples increases when the temperature increases from 25 \({}^{\circ}\)C to 300 \({}^{\circ}\)C, and it decreases when the temperature changes from 300 \({}^{\circ}\)C to 900 \({}^{\circ}\)C, and the range of strength variation decreases significantly with the enhancement of confining pressure [15].