The effect of cyclic heating and cooling on mechanical and deformation responses of granites under preset angle shearing

In the process of geothermal energy exploitation, granites undergo cyclic heating and water cooling due to the heat conduction from distant rock mass to the cooled rock. The mechanical response, deformation and acoustic emission (AE) characteristics of granite treated by cyclic heating (150–300 °C) and water cooling (1–15) under the coupling action of compressive and shear stress were analyzed by preset angle shear tests in three preset angles (45°, 55°, 65°) at macroscopic level. Given that the peak strength of granite shows an accelerating downward trend with the increase of heating temperature and cycle times. The cohesion of granite declines, and the internal friction angle increases in general. AE activities are active throughout the loading process, which shows ductile failure characteristics of granite obviously. The accumulative AE events decrease by 69.3% with increasing heating temperature (150–600 °C), and 82.4% with increasing cycle times (1–15). The crack initiation area gradually shifts from the two ends of sample to the middle area with the increasing thermal damage. Shear behaviors inside the granite start earlier and last for a longer period, which results in the complex fracture network distribution of turtle shape and the shearing failure of “Z” shape on the surface of 600-1 sample. Scanning electron microscopy (SEM) was conducted to reveal the microscopic mechanism of thermal damage. Given that the intergranular and transgranular cracks induced by the uneven expansion of particles connect with each other and form a complex crack network as the thermal damage increasing. The continuous heating with high temperature causes minerals to melt and deform, resulting in the decrease of bonding strength between particles. All above results can provide references for the analysis and prediction of rock stability of granite in Enhanced Geothermal Systems (EGS) project.


Introduction
With the continuous consumption of non-renewable energy, the increase of global temperature caused by carbon dioxide is becoming more and more prominent (Duffy et al. 2012). Based on this, the development of new energy which is efficient, green and clean has been paid more attention by scholars (Chu et al. 2012). As a huge heat source, the core temperature of earth is as high as 6000 °C (Anzellini et al. 2013). Under the action of temperature gradient between the core and surface of earth, the heat continuously exports from the interior of earth, which makes the geothermal resources clean, abundant and widely distributed (Jalilinasrabady et al. 2013;Becattini et al. 2017;Pathiranagei et al. 2021). As an important form of geothermal resources, the hot dry rock (HDR) exists in the deep underground of 3-10 km mostly (Huang et al. 2012). Due to the huge earth stress and high temperature, there is no steam inside the HDR and the structure is dense (Zhang et al. 2019).
Enhanced Geothermal Systems (EGS) transfer the heat from high temperature formation to earth surface by water, which generally requires two or more wells to drill into the high temperature formation. The cold water is injected through one of the wells, which passes through the high temperature formation of HDR to absorb heat and discharges from the production well (Asai et al. 2019), as shown in Fig. 1. The cold water entering the geothermal reservoir inevitably leads to a sharp decline in the HDR temperature. The temperature difference between cooled rock and distant rock mass with high temperature induces the heat transfer between them, causing the temperature increase of cooled rock mass. Thus, in this process, the reservoir rock undergoes repeated impacts of water quenching cycles, which results in the uneven expansion of different minerals and the thermal damage to HDR (He et al. 2018;Yin et al. 2021a, b, c). The thermal damages are mainly reflected in the mechanical properties, deformation and failure characteristics of rock mass, which finally affects the rock stability and project efficiency. Therefore, it is of great significance to investigate the effects of cyclic heating and water cooling on the mechanical properties and deformation characteristics of HDR.
At present, the effect of high temperature on granite has been studied by many scholars in different aspects, including the internal porosity (Chaki et al. 2008), permeability evolution (Kožušníková et al. 2011;Yin et al. 2019a, b;Tian et al. 2020), fracture mechanics (Peng et al. 2020;Miao et al. 2021), mechanical properties (Chen et al. 2017;Qin et al. 2020), and ultrasonic response (Nasseri et al. 2007;Fan et al. 2017). Ma et al. (2020) studied the mechanical behavior of rocks under real-time high-temperature heating through true triaxial experiments, and analyzed the effect of real-time high-temperature heating on the shear strength parameters. Huang et al. (2017) conducted uniaxial compression tests on granite samples which contains three reserved holes, and obtained the effect of temperature on the mechanical parameters of granite. Zhao et al. (2017) used the Micro-CT technique to characterize the microstructure of samples under room temperature and 500 °C specifically, and observed the appearance of transgranular cracks when heated to 500 °C. Yin et al. (2021a, b, c) analyzed the shear mechanical responses of sandstone exposed to high temperature through direct shear test, and found that the peak shear strength, residual shear strength and terminal normal stress all display an exponential variation with temperature. However, these studies focus on the properties of heated or heating granites mostly, and the rapid cooling effect of injected water on the HDR in the actual geothermal exploitations is ignored. The effects of cyclic heating and water cooling on the properties of granite need to be studied further. Yin et al. (2019a, b) analyzed the effect of cyclic heating and cooling on the fracture properties of granite by conducting semi-circular bending tests, and found that the fracture toughness of granite gradually decreases with the increase of temperature and cycle times. Zhu et al. (2018) studied the damage evolution of granite under cyclic heating and water cooling through uniaxial compression, Brazilian splitting test and acoustic emission monitoring technology.
In general, the reported researches about cyclic heating and water cooling of granite focus on the uniaxial, triaxial compression and Brazilian splitting tests mostly Zhu et al. 2020). Due to the discontinues of rock mass widely distributed and the huge earth stress in deep underground, when there is a certain angle between the principal stress direction and the movement direction of local rock mass, the rock mass will be coupled with the compressive and shear stress and is more prone to fail with shearing (Yin et al. 2016;Du et al. 2021;Meng et al. 2021). However, there are few studies which focus on the mechanical and deformation characteristics of granite under the action of compression and shear, which involves the complex stress condition of HDR in the geothermal exploitation. The evolution of acoustic emission characteristics, deformation and failure characteristics of granite treated by cyclic heating and water cooling under the action of compression and shear are worthy of further exploration.
Based on the shortcomings of the current research, in this study, the granite samples were treated by cyclic heating and water cooling at 4 levels of heating temperature (T = 150, 300, 450, 600 °C) and 4 levels of cycle times (N = 1, 5, 10, 15). In order to avoid the excessive compression caused by small shear angle, the preset angle shear (PAS) tests were carried out with three shear angles (α = 45°, 55°, 65°) for the samples of each T and N. The shear angle α represents the angle between the shear plane and the positive horizontal direction, as shown in Fig. 6. The digital image correlation technology (DIC) and acoustic emission (AE) monitoring system were used to obtain the AE characteristics and deformation characteristics of sample. According to the results, the effect of cyclic heating and water cooling on the mechanical response of granite were analyzed, as well as the transformation of brittleness and ductility and the evolution of AE characteristics. The deformation response and failure mode of granites with different treatment were also analyzed. In addition, the microscopic mechanism of thermal damage to granite was explored by using scanning electron microscope, which provides better explanations for the evolution of mechanical and deformation responses of granite at the macroscopic level.

Sample preparation and testing procedure
The preparation of granite samples The granite used in this test is typical coarse-grained granite from Xuzhou City, Jiangsu Province, which is the most common type of HDR in geothermal projects. The average density of the granite is 2.716 g/cm 3 and there are no visible cracks on surface in the natural state. The matrix is dense and the thermal stability is good. The results of X-ray diffraction (XRD) show that this type of granite is mainly composed of minerals such as quartz, feldspar, hornblende and biotite (Yin et al. 2021a, b, c). The size of the sample is a cube of 50 × 50 × 50 mm. All sides of samples were polished to be smooth, and the parallelism of opposite sides was controlled to be ± 0.02 mm. The adjacent two sides were perpendicular to each other and the deviation was controlled within 0.25° to avoid the local damage caused by uneven surface Luo et al. 2020). The samples were heated to the target temperature by using the MXQ1700 muffle furnace. The maximum heating temperature of this equipment can reach 1700 °C with an accuracy of ± 1 °C, as shown in Fig. 2a. Four temperature levels were set in this test (T = 150, 300, 450, 600 °C), respectively. At each temperature level, each level of cooling cycle (N = 1, 5, 10, 15) was performed, respectively. The specific process of cyclic heating and water cooling is as follows. Firstly, the granite sample was heated to the target temperature at a rate of 5 °C/min using MXQ1700 muffle furnace to avoid thermal shock effects Zhu et al. 2021), and maintained the target temperature for 2 h to ensure the sample being heated overall. Then, the samples were taken out and quickly put into the cool water of 25 °C for 2 h to be cooled completely. After that, the samples were picked up from the water and placed in a cool and dry place for 24 h to dry the surface. Finally, the samples were put into a drying box which maintains 50 °C to be dried for 24 h. In order to ensure that the temperature of each water cooling cycle is 25 °C, the cooling distilled water was updated in real time after each cooling cycle. The schematic diagram of cyclic heating and water cooling process is shown in Fig. 2b.
The samples after cyclic heating and water cooling are shown in Fig. 2c. With the increase of T and N, more visible cracks appear on the sample surface and the openings  of cracks become larger. The number of "150-15-2" means the second sample of T = 150 °C and N = 15. Since the DIC technology was used in this experiment to capture the deformation characteristics of the granite, according to previous studies (Gao et al. 2015;Huang et al. 2020), it is necessary to spray clear and uniform speckles on the surface to meet the needs of the accuracy of the DIC equipment (Fig. 2d).

Testing procedure
The equipment of PAS test is composed of MTS816 rock mechanics test system and shearing dies with adjustable shearing angle (Fig. 3). MTS816 test system is divided into the test system and control system, which provides a maximum axial load of 1459 kN and the maximum stroke of 100 mm. The axial displacement and axial load are automatically recorded by the control microcomputer. The shearing dies which can be adjusted with a shearing angle ranging from 35° to 80° are placed between the press head and the tray of MTS816. The axial load is decomposed by the shearing dies into the normal force perpendicular to the preset shear plane and the shear stress acting on the preset shear plane (Xie et al. 2007). As the axial load increasing, the shear stress at the preset shear plane gradually reaches the shear strength of granite, causing the instability and failure of sample finally.
At the initial stage of loading, the sample was preloaded to the target axial load of 0.25 kN by force control and kept constant. Subsequently, the loading method was changed to displacement control, and the axial loading velocity was set to 0.005 mm/s to ensure the balanced states of samples during the loading process. At the same time, DIC system was used to monitor the evolution of deformation characteristics of samples during the loading process with a recording interval of 0.5 s (Fig. 3). The AE system of PCIE-Q87-i2 model was used to monitor the AE signals during the test with a recording interval of 0.1 s (Fig. 3).

Axial load-displacement responses of granites
For example, when α = 45°, the axial load displacement curves for various T and N are shown in Fig. 4. As it shows, when the heating temperature T is the same, with the increase of N, the load displacement curve moves downward as a whole. The higher the T, the greater the downward movement, which indicates that the increase of N at lower temperatures has less effect on the thermal damage inside the rock mass. The deterioration effect of cyclic heating and cooling on the granite is greater with the higher heating temperature, and the thermal damage degree of the rock mass is continuously intensified.
The heating temperature T and cycle times N also affect the brittleness and ductility of granite greatly (Fig. 4). When the temperature and cycle times are relatively low (T = 150, 300 °C, N = 1, 5), the axial load of the specimen decreases linearly until the failure after reaching the peak loads, showing obvious brittle failure characteristics. However, at higher temperature and cycle times (T = 450, 600 °C, N = 10, 15), due to the development of thermal induced cracks inside the granite, the load-displacement curves show a stepped or curved downward trend after the peak load, exhibiting obvious ductile failure characteristics.
As shown in Fig. 5, the peak load F peak of samples basically shows an accelerating downward trend with the increase of T and N. In the range of heating temperature lower than 600 °C, the thermal damage of granite experiencing an accelerating upward trend with the increase of heating temperature, which is consistent with the thermal damage constitutive model proposed by previous research (Xu et al.2018). When N = 5, T increases from 150 °C to 600 °C, F peak decreases by 2.86, 6.96, 18.18%, respectively. F peak decreases greatly while T increases from 450 to 600 °C (Fig. 5a), which is mainly due to the phase transition of the quartz in the granite around 573 °C. The larger volume expansion of the minerals and the looser granite result in a rapid decline in mechanical properties ). In addition, the convection heat transfer characteristics and temperature gradient play an important role on the thermal damage degree of granite. On the one hand, with the increase of the heating temperature, the temperature gradient increases during the water cooling process, resulting in a larger gradient stress inside the sample. On the other hand, as the heating temperature increases, more thermally induced micro-cracks generate in the granite samples due to severer uneven expansion of particles. The increasing thermally induced micro-cracks provide more heat convection channels for the heat exchange between rock and cooling water, which also increases the convection heat transfer area between granite matrix and cooling water. The increasing heat transfer area accelerates the convective heat transfer process and results in the severer cyclic thermal shock to the granite.
When T = 450 °C, N increases from 1 to 15, F peak decreases by 5.7, 16.1, and 29.9%, respectively, showing an accelerating downward trend (Fig. 5b). It is worth noting that before T reaches 600 °C, the decreasing rate of F peak increases with the increase of N. When T = 600 °C, N increases from 1 to 15, F peak decreases by 39.7, 50.7, and 60.5%, respectively, showing a decelerating downward trend. That's probably because that the five times of cyclic heating and water cooling with T = 600 °C have caused great thermal damage to the granite, and a large number of thermal induced cracks have developed inside the rock. The effect caused by the increase of N on the damage of granite is limited. Therefore, the decreasing rate of F peak gradually slows down.

Shear strength parameters of granites for various T and N
The stress condition of the sample during the PAS test is shown in Fig. 6. In the PAS test, the sample is subjected to the vertical force F provided by the test machine and the horizontal friction fF exerted by the rollers of shearing dies. Through the decomposition, the shear stress acting on the shearing plane and the normal stress perpendicular to the shearing plane are obtained, as shown in Eqs. (1) and (2).
where τ is the shear stress, F s is the corresponding shear force. σ is the normal stress acting on the shearing plane, and F n is the corresponding normal force. A is the shearing area, calculated as 0.0025 m 2 according to the sample size. ( α is the preset shear angle. f is the rolling friction coefficient which can be almost negligible since the upper and lower rollers of shearing dies are lubricated sufficiently. Finally, according to F peak of each specimen at three shear angles of 45°, 55°, and 65°, the corresponding peak shear stress and normal stress are calculated as Eqs. (1) and (2). According to the Mohr-Coulomb strength theory, there is a relationship between the shear strength and the normal stress, as shown in Eq. (3).
where τ c is the shear strength, and σ n is the corresponding normal stress when τ = τ c . c is the cohesion, and φ is the internal friction angle.
The cohesion c and the internal friction angle φ of the samples can be obtained by linear fitting to τ c and σ n of three angles , as shown in Fig. 7a and Table 1. It can be seen that R 2 in the final fitting results are all greater than 0.9, indicating the obtained shear strength parameters are relatively accurate.
As shown in Fig. 7b, with the increase of T, cohesion c showed a decreasing trend overall, and the decreasing process can be divided into two stages. When T = 150-450 °C, c decreases by 15.9% (N = 1), 24.1% (N = 5), 27.5% (N = 10), 31.3% (N = 15), respectively. When T = 450-600 °C, c decreases greatly and faster, by 57.5% (N = 1), 60.1% (N = 5), 65.6% (N = 10), 72.6% (N = 15), respectively. The decrease of c in the early stage is mainly due to the different thermal expansion coefficients of the minerals in the granite after cyclic heating and water cooling, which results in the uneven expansion of particles inside the granite. The fracture opening between mineral crystals becomes larger and cohesion c declines. When T = 450-600 °C, the phase change of the quartz minerals inside the granite causes the sharp expand of granite volume at 573 °C. Some bonding minerals between particles begin melting due to the higher temperature, resulting in a large loss of cohesion c. In addition, with the increase of N, c also showed a downward trend.
The effects of T and N on the internal friction angle φ are shown in Fig. 7c, which provides that the effect of T on the internal friction angle φ is more significant than that of N. When T increases from 150 to 600 °C, the internal friction angle φ increased by 15.5% (N = 1), 8.8% (N = 5), 12.3% (N = 10) and 12.8% (N = 15), respectively, showing an overall upward trend. The disappearance of the interlayer water and bound water in the granite due to the high temperature heating results in a decrease of the lubricity degree between mineral particles. At the same time, pore structure on the mineral surface induced by the thermal decomposition of some minerals and the rock debris peeled off from the matrix also lead to the increase of friction characteristics on grain surface, accompanied by the increase of φ.

AE characteristics of granite for various T and N
In recent decades, acoustic emission (AE) technology has been widely used to study the crack evolution and failure mechanism of rocks. Since the expansion of micro-cracks have to radiate elastic waves outward, AE events are consistent with the evolution process of cracks inside the rock mass. In this study, the real time and accumulative AE counts during the shearing process were obtained by AE technology to analyze the crack evolution inside the granite sample. As shown in Fig. 8, the results of T = 450 °C and N = 5 were analyzed as examples, and the typical AE evolution process can be roughly divided into five stages: Crack closure stage (I): This stage is the interval between 0 and point cc. The original micro-cracks in the granite and the cracks induced by thermal shock are closed under the action of compression, and the load displacement curve appears nonlinear trend in this stage, presenting a concave obviously. At the same time, AE events do not fluctuate greatly at this stage and always maintains at a low level. Less energy is released in the crack closure stage.
Elastic deformation stage (II): This stage is the interval between point cc and ci. After the crack closure stage, the granite enters the elastic deformation stage, and the load-displacement curve shows a linear trend. As the loading continues, the granite undergoes elastic deformation and accumulates elastic strain energy gradually under the action of stress, along with the friction and dislocation of closed rough fractures. AE event is also gradually developing, but remains at a relative low level. It is worth noting that at the end of the elastic stage, the real-time AE events increase slightly at point ci, which is considered by some scholars to be the starting point of crack initiation (Bruno et al. 2013;Ghasemi et al. 2020).
Crack initiation and stable propagation stage (III): This stage is the interval between point ci and cd, and the point ci is usually regarded as the crack initiation point. In this stage, both of the closed primary cracks of rock and thermal induced cracks begin to expand stably after elastic deformation, and new cracks begin to initiate. The load-displacement curve gradually deviates from the linear state of elastic stage and transforms into a curve form. At the same time, the initiation of new cracks and the expansion of existed cracks cause the limited release of strain energy, and AE activity is more active than that in stages I and II. The real-time AE events showed an increasing trend gradually.
Unstable crack propagation stage (IV): This stage is the interval between point cd and c, the internal cracks expand unstably and further connect with each other. There are obvious shear deformation fracture areas on the sample surface, and the load displacement curve rises slowly, accompanied by several sudden load drops. During this process, the elastic strain energy is further released during this process, along with the loud noise made by samples. AE events increase suddenly and continue to rise.
Failure stage (V): This stage is the interval after point c, and point c is the peak load that the sample can bear. After reaching the peak load, the granite becomes unstable, and the cracks expand and penetrate to form a shear failure band, causing the rapid decrease of bearing capacity of rock mass. At the same time, a large amount of strain energy stored inside the rock is released, accompanied by loud noise and the splashing of granite fragments. AE counts increase sharply at the same time. In addition, heating temperature T and the cycle times N have a great influence on The AE evolution of granite for N = 1 and T = 450 °C is taken as examples to analyze, as shown in Fig. 9a-c. When T = 150, 300 °C, and 450 °C (N = 1), AE events in the crack closure stage maintain at a very low level. However, the AE signal is more active even in the crack closure stage when T = 600 °C (Fig. 9d). A possible reason is that when T comes to 600 °C, the quartz in the granite undergoes a phase transition at 573 °C, which results in a significant increase of micro-cracks and fracture network induced by thermal shock. The closures of these cracks lead to the active of AE events. Therefore, a larger proportion of AE events is monitored at the beginning process of loading relative to the whole loading process. It is worth noting that when T = 150, 300 °C, AE events mostly concentrated in the stage IV and V. The accumulative AE curve is relatively gentle in the early stage, and showed a steep increase in the stage IV and V, which presents obvious brittle failure characteristics. When T = 450 °C, the accumulative AE curve presents a step-like rise as a whole. When T = 600 °C, the AE events are active in the whole loading process, and the accumulative AE curve rises steadily throughout the whole process, showing obvious ductility characteristics compared with the low heating temperature. The main reasons are as follows possibly: firstly, the increase of T induces more thermal cracks in the rock mass, which makes crack closure stage longer. The increase of crack closures leads to a relatively active AE events in the initial loading stage. Secondly, the decrease of mechanical properties of granite results in the local failure at lower stress levels, which cause the early release of strain energy. The strain energy released in stages IV and V reduces, resulting in the decrease of AE events in stages IV and V. Finally, the accumulative AE curve shows a steady upward trend. Figure 9e-h shows the AE response of granite for various cycle times N (T = 450 °C). When N = 1, 5, and 10, the AE events at the initial stage are mainly caused by the closures of primary cracks and thermal damage cracks. A large number of AE events still concentrates on the failure stage. When N = 15, the AE activity is generally active during the entire deformation process, and the accumulative AE curve showed a steady upward trend, instead of a sudden increase at the failure stage. The ductile failure characteristics of granite are enhanced with the increase of cycle times N. Figure 10 depicts the influence of T and N on the accumulative AE events in the whole loading process of granite. When T increases from 150 to 600 °C, accumulative AE events decreased by 33.1, 46.0, and 69.3%, respectively. With the increase of N from 1 to 15, the accumulative AE events decreased by 17.8, 71.6, and 82.4%, respectively. Due to the more thermal shock caused by the increase of T and N, more energy needs to be consumed by the closures of cracks. The friction between particles and more local failures leads to the decrease of strain energy stored in the granite, causing the reduction of accumulative AE events. The failure characteristics of granite change from brittleness to ductility.

Deformation responses of specimens for various T and N
In order to obtain the evolution of deformation characteristics of granite under the action of compression and shear, DIC technology was used in this test to monitor the deformation evolution process of granite surface. The speckle deformation image was recorded by a high-speed CCD camera,   and the evolution of principal strain field was obtained by processing the photos using the Gom Correlate software. Figure 11 shows the nephogramat of principal strain at the critical points of five stages of samples when T = 300, 600 °C, N = 1, α = 65°. In the crack closure stage, the primary cracks and thermal induced cracks are closed under the combined action of compression and shear. The strain distribution of sample surface is relatively uniform, and there is no obvious local large strain area.
After the crack closure stage, the sample enters the elastic deformation stage. The point ci is the point where elastic stage ends and stable propagation stage of cracks starts. The cracks initiate and then expand after elastic deformation. From the nephogramat of principal strain, it can be seen that there is obvious local large strain area on the sample surface, which indicates the initiation of cracks.
As the loading continues, the sample enters the stable propagation stage of cracks, and the point cd is the end point of this stage. A strip shaped local large deformation area is formed near the preset shear plane, and the shear band is basically formed. The granite surface is caved partially, and the disappearance of the speckle leads to a white blank area in the nephogramat of principal strain. However, at this time, the crack has not penetrated completely,  and the mineral grains are still in a state of interlocking. The granite sample still has a certain bearing capacity. In the stage of unstable crack propagation, the primary and secondary cracks further expand and connect with each other, causing the increase of local large strain area and a wider shear band. After the granite reaches the peak load, with the decrease of the axial load, the cracks on the shear band penetrate completely. Finally, the granite loses the bearing capacity and is sheared into two pieces.
In order to figure out the evolution process of shear cracks inside the 300-1 and 600-1 sample throughout the whole loading in Fig. 11, the micro-cracking mode is judged by comparing RA and AF which are calculated by the following equations (Rodríguez and Celestino al. 2019).
The tensile cracks usually propagate accompanied by the energy release in the form of longitudinal waves, while shear cracks in the form of shear waves. The difference of transmission speed of the waves causes that shear cracks propagate with higher RA, tensile cracks propagate with low RA value, as exhibited in Fig. 12a. The evolution process of RA and AF characteristics of samples which corresponds to 300-1 and 600-1 in the Fig. 11 is shown in Fig. 12b and c. With the time rising, both temperature samples have undergone the transformation process of "high AF-high RA-high AF". At the initial stage of loading process, the AF level of both temperature samples remains higher than RA, which indicates the shear events are not active. When T = 300 °C, high levels of RA are mainly concentrated in the severe damage stage, accompanied by the rapid propagation of shear cracks between point cd and c in Fig. 11a. After the peak point, RA decreases rapidly and changes to be lower than AF, which indicates the tensile events induced by the large shear become active in this period. Compared to the sample of 300 °C, the high RA level of the 600 °C sample starts at an earlier point accompanied by the appearance of large strain area at stable propagation stage between point ci and cd in the middle position of the sample (Fig. 11b), and then maintains for a longer period. Due to the severer damage caused by the heating and cooling, the increase of thermally induced micro-cracks, the increase of crystal gap and the decrease of cohesive lead to the deterioration of rock mechanical properties. From the perspective of fracture mechanics, under a low load level, the stress concentration at the crack tip exceeds the bearing capacity of the matrix, and the shear cracks are more prone to develop and expand. Based on this, the shear events of severer thermally damaged samples appear earlier and last for a longer period in the loading process. The more active shearing events eventually leads to an increase in the degree of specimen shear failure, as showed in Fig. 11b. Figure 13a shows the principal strain nephogramat at the critical points of each stage when N = 1. At the point ci, when T = 150 °C, the lower end is the origin point of strain distribution and strain areas radiate to the upper region in the form of radioactivity. The crack damages first appear at the upper and lower ends of the sample when T = 300 °C, and local large strain area shows a trend of extending from the ends to the middle of sample surface. However, when T = 600 °C, the large strain area appeared in the middle of sample surface firstly, and showed a tendency to expand to both ends. To sum up, the crack initiation area of the granite shifts from the ends of sample surface to the middle area gradually with the increase of T. The increase of T leads to the increasing temperature gradient inside the sample, and results in the larger expansion of the primary cracks and more thermally induced micro-cracks. These micro-cracks interconnect and form a complex three dimensional crack network, which failed firstly during the loading process. Ultimately, the cracks initiate at the middle area of sample surface firstly.
At the point c, the local large strain area of strip shape near the shear plane is relatively narrow and smooth when T is under 600 °C, indicating the brittle failure characteristics of granite at low temperature. When T increases to 600 °C, the width of large strain area increases greatly, along with the staggered connection of cracks at sample surface. The large strain area extends to the both sides of shear band and form a larger damaged area at sample surface, showing the obvious ductile failure characteristics. At the point cp, the specimen reaches the ultimate strength, and the cracks penetrate to form the final failure state. When T = 150, 300 °C, the damage degree in the middle area of the sample is relatively low, and the damaged area concentrated at both ends of the sample. When T = 450, 600 °C, the severe damaged area of the sample is concentrated in the middle area. It is worth noting that the final distribution of failure cracks presents an "Z" shape when T = 600 °C. According to the shear strength parameters of granites for various T and N, the internal friction angle of granite increases with the increasing T. The treatment of cyclic heating and water cooling increases the roughness of particle surface, and the uneven expansions of particles also make the whole sample looser. When the specimen is finally destroyed by shear, both the left and right blocks shear and dislocate reciprocally. The increase of particle surface 150-1-cc (0.12F peak ) 150-1-ci (0.34F peak ) 150-1-cd (0.67F peak ) 150-1-c (F peak ) 150-1-cp (0.81F peak ) 300-1-cc (0.14F peak ) 300-1-ci (0.38F peak ) 300-1-cd (0.71F peak ) 300-1-c (F peak ) 300-1-cp (0.90F peak ) 450-1-cc (0.15F peak ) 450-1-ci (0.41F peak ) 450-1-cd (0.78F peak ) 450-1-c (F peak ) 450-1-cp (0.89F peak ) 600-1-cc (0.23F peak ) 600-1-ci (0.51F peak ) 600-1-cd (0.85F peak ) 600-1-c (F peak ) 600-1-cp (0.95F peak ) (a) The nephograms of principal strain of specimens at key points ( N = 1) (b) The distribution of cracks on ultimate failure modes of the samples for various T T=150℃ T=300℃ T=450℃ T=600℃ Fig. 13 The deformation characteristics of five stages of samples for N = 1 roughness and looseness of granite result in the local stress concentration and cause the secondary cracks to expand rapidly, which forms the cracks of "Z" type finally. Figure 14a is the principal strain nephogramat at critical points of each stage of granites for various N when T = 450 °C. With the increase of cycle times N, the crack network thermally induced expanded massively and extends from the center to the edge of specimens, resulting in the widespread distribution of cracks on sample surface. These micro-cracks expand and connect with 450-1-cc (0.15F peak ) 450-1-ci (0.41F peak ) 450-1-cd (0.78F peak ) 450-1-c (F peak ) 450-1-cp (0.89F peak ) 450-5-cc (0.20F peak ) 450-5-ci (0.38F peak ) 450-5-cd (0.65F peak ) 450-5-c (F peak ) 450-5-cp (0.96F peak ) 450-10-cc (0.21F peak ) 450-10-ci (0.37F peak ) 450-10-cd (0.64F peak ) 450-10-c (F peak ) 450-10-cp (0. 29 Page 16 of 21 each other at lower stress level, resulting in a large local strain area which connects the end and the edge of sample, as shown at point ci of N = 5, 15. It is worth noting that under the combined action of compression and shear, the tensile failure cracks appeared firstly at the sample surface when N = 5, 15. Then, the shear failure cracks extend from the tensile cracks secondly near the preset shear plane. Tensile cracks appear significantly earlier than shear cracks, it is mainly because the shear strength is mainly composed of friction and bonding force between particles, while the tensile strength is mainly composed of bonding force between particles. The treatment of cyclic heating and cooling causes a large distribution of internal three-dimensional crack network, which connects the ends and edges of granite sample and results in the decrease of cohesion and the tensile strength. So, the tensile cracks appear earlier than the shear cracks. Figures 13b and 14b show the final failure modes of samples when N = 1 and T = 450 °C, the damaged area expands gradually with the increase of T and N. When T and N is relatively small, most of the cracks focused on the preset shear plane, and the development degree of secondary cracks is relatively low, showing obvious brittle failure characteristics. When T = 600 °C and N = 15, due to the increase of micro-cracks induced by cyclic heating and water cooling, the distribution of failure cracks on the sample surface is more extensive. The secondary cracks basically develop from the shear band to the sample edges. Intensive damage appears in the middle area and form a dense and complex crack network of turtle shape, showing strong ductile failure characteristics. In order to quantify the degree of aggregation of failure cracks on the sample surface, the concept of crack density is established, which can be calculated as shown in Eq. (6).
where ρ c is the crack density, N c is the total number of cracks on the sample surface, and A is the area of surface.
The crack density of the granite for N = 1 and T = 450 °C is calculated, as shown in Fig. 15. The crack density rises up with the increase of T and N. When T increased from 450 to 600 °C, the increase of crack density is the largest, reaching 61.5%. It's mainly because the quartz undergoes a phase change at 573 °C, the volume of particle expands greatly. A larger number of thermal shock micro-cracks appear inside the sample and connect with each other during the loading process, resulting in an increase of the crack density. When N increases from 10 to 15, the crack density increases by 81.8%, which is the largest increase of crack density with various N. It's mainly because that the cyclic heating and cooling leads to the development of (6) c = N c A thermal induced cracks and the increase of granite looseness. Finally, the failure cracks density increase and the ductile failure characteristics of granite are enhanced.
In order to further figure out the differences between shear and tensile behavior of granite after cyclic heating and cooling treatment, four typical modes of tensile and shear crack distribution on sample surfaces under different cyclic heating and cooling treatment are analyzed, as shown in Table 2. T represents tensile crack, PT represents primary tensile crack, ST represents secondary tensile cracks, PS represents primary shear crack, TS represents mixed tensileshear cracks, Ss stands for the surface spalling area, and P stands for the principal load stress direction.
When the heating temperature and cycle times are relatively low, the failure of granite sample under compression and shear is dominated by primary tensile crack (PT) and  Table 2. Due to the tensile stress concentration at the end tip of the die, the primary tensile crack usually initials at the end of sample, and propagates along the direction of load principal stress (P direction), which is consistent with previous research (Chai et al. 2011). The edge of PT is relatively smooth when the thermal damage is low (150-1). With the increase of thermal damage to the sample (450-5, 450-15), more secondary tensile cracks perpendicular to the shearing direction are derived from the edge of the primary tensile crack, which are mainly developed from the thermally induced tensile microcracks generated by the treatment of cyclic heating and water cooling. The tensile crack density increases significantly. However, shear cracks always propagate along the preset shear plane, and shear cracks density do not experience great fluctuation with the thermal damage increasing. It is worth noting that the direction of PT is deflected and connected with PS on the surface of 600-15 sample, PT gradually evolves into the mixed tensile-shear crack (TS) with the increase of thermal damage in Model-IV. Due to the rapid increase of thermally induced micro-cracks, the large strain appears firstly at the middle area of sample surface, as depicted in "Deformation responses of specimens for variousTandN". These large strain area induces the deviation of PT direction and the development of TS gradually. More thermally induced tensile micro-cracks develop and connect with each other under the action of compression and shear, and finally form a large number of closed fracture networks on sample surface. The tensile crack density increases significantly, and the tensile crack direction is no longer regular. The shear crack density did not experience a great fluctuate, and the shear crack still along the preset shear plane. The surface spalling and distribution area are larger than other three models.

Microscopic thermal damage mechanism of granites
In this study, Quanta 250 scanning electron microscope was used to study the thermal damage mechanism of granite after the treatment of cyclic heating and water cooling from the microscopic level. The magnification varies from 1000 to 4000 times. SEM results of granite for various T and N are shown in Fig. 16. With the increase of T, the evolution of thermal shock damage in granite can be roughly divided into three stages: initial damage stage I, T = 150 °C; stable damage stage II, T = 300, 450 °C; severe damage stage III, T = 600 °C.
Initial damage stage (I): When T = 25 °C, the granite surface is relatively smooth, no obvious cracks are observed, and only a small amount of debris distributes on the particle surface. The granite matrix is relatively intact (Fig. 16a). When T = 150 °C and N = 1, the thermal decomposition of clay minerals leads to the appearance of micro-pores on particle surface, which provides the basis for the germination of thermal induced cracks. When N = 5, intergranular cracks appear with small aperture thickness and low degree of development (Fig. 16c). When N increases to 10, the primary micro-cracks of mineral particles expand under the action of cyclic gradient stress induced by cyclic heating and cooling, causing the appearance of layered textures and transgranular cracks on the matrix surface (Fig. 16d) thermal shock is mainly the initial propagation of intergranular cracks and initiation of transgranular cracks. Stable damage stage (II): When T = 300 °C, N = 1, 5, the intergranular cracks with larger opening are filled with a large number of rock debris. The layered texture also develops along the bedding plane and evolves into strip fracture groups under the continuous influence of thermal shock (Fig. 16f, g). As N increases to 10, the spacing between each layer increases further, resulting in an increase in the number of transgranular cracks. At N = 15 and T = 450 °C, the transgranular cracks propagate further, along with the appearance of secondary cracks in different directions, causing the further increase of rock debris. The edges of secondary cracks are smooth and the aperture thickness is small (Fig. 16i, j). With the increase of N, Transgranular and intergranular cracks expand to connect with each other and gradually evolve into fracture network, as shown in Fig. 16l, m. The stable damage stage of granite is the formation process of fracture network which is caused by the connection of transgranular and intergranular cracks.
Severe damage stage (III): When T comes to 600 °C, the decomposition, melting and phase transformation of some minerals lead to a significant increase in the roughness of particle surface, and the rock debris distributes in a large range, resulting in the significant increase of internal friction angle φ of granite at 600 °C (Fig. 16n). When N = 5, the closed crack networks cause blocky matrix to peel off from the primary crystal, which results in severe breakage of granite matrix and further enhances the ductility failure characteristics of granite (Fig. 16o). The continuous high temperature causes some minerals to melt and deform, and the bonding strength between mineral particles decreases rapidly, resulting in the sharp decline of cohesion c which represents the macro strength of granite (Fig. 16p). When N reaches 15, a large number of transgranular cracks develop and expand greatly, leading to the fibrosis of mineral crystal and the increase of granite looseness. The mechanical properties of granite decline significantly finally (Fig. 16q).
The analysis above indicates that the thermal damage of granite caused by cyclic heating and water cooling is firstly reflected in the propagation of intergranular cracks and the initiation of transgranular cracks. With the increase of T and N, the transgranular cracks increases significantly and then branch into secondary cracks which interconnect with other cracks, causing the generation of the fracture networks finally. When T reaches 600 °C, the roughness of particle surface increases greatly, and the closed fracture network causes the blocky matrix to be detached from the crystal. The melting and deformation of some minerals result in a significant decrease in the bonding strength between grains, accompanied by the increase of granite looseness.
In addition, the heat transfer characteristics of rough cracks may have a great influence on the thermal shock effect on granite in the water cooling process. With the increase of T, the differences of heat transfer coefficient between cracks with different roughness become larger, and rougher cracks provide larger heat transfer coefficient and better heat transfer effect (Zhan et al. 2021). According to the results of SEM in Fig. 16, with the increase of T and N, the thermal decomposition of some mineral particles leads to the appearance of fine pores on the granite crystal surface. These fine pores increase the surface roughness of crystal particles and thermally induced micro-cracks to a certain extent, which leads to the increase of heat transfer coefficient of cracks. The crystal gap and thermally induced micro-cracks are the main channels of fluid in the water cooling process of granite, the increase of the heat transfer coefficient of cracks will inevitably leads to the increase of heat transfer efficiency of the whole granite during the water cooling process. Finally, the increase of heat transfer efficiency further enhances the thermal shock effect on granite in cyclic heating and water cooling treatment.
The treatment of cyclic heating and cooling finally causes a great damage to the mechanical properties and enhances ductility failure characteristics of granite.

Conclusion
In this study, granite samples were treated with cyclic heating and water cooling to simulate the cyclic heating and cooling process of granite in the geothermal exploitation. The preset angle shear (PAS) tests were carried out on the treated samples to obtain the mechanical response of granite with various T and N in the whole loading process. The evolution law of shear strength parameters as cohesion c and internal friction angle φ of granite is revealed. At the same time, through the acoustic emission (AE) and digital image correlation (DIC) technologies, the internal crack evolution and deformation response of the granite sample during the loading process were obtained. The brittle-ductile transformation mechanism of granite treated by cyclic heating and cooling was also analyzed. Finally, SEM images of the granite with various T and N were obtained by scanning electron microscopy, and the thermal damage mechanism of granite treated by cyclic heating and water cooling was analyzed from the microscopic level. The following conclusions are drawn: (1) The treatment of cyclic heating and water cooling will cause great damage to the mechanical properties of granite. With the increase of heating temperature T and cycle times N, the thermal damage degree of granite increases, and the peak strength shows an accelerated decreasing trend. The load displacement curve in post peak stage changes from sudden drops to stepped drops, showing the obvious ductile failure characteristics of granite. In addition, with the increase of T and N, the cohesion c of granite showed a downward trend, but the internal friction angle φ gradually increased. When T increases from 150 to 600 °C, the internal friction angle φ increased by 15.5% (N = 1), 8.8% (N = 5), 12.3% (N = 10) and 12.8% (N = 15), respectively. (2) According to the evolution process of AE events, the treatment of cyclic heating and cooling has great influence on the crack evolution characteristics of granite.
With the increase of T and N, the proportion of AE events in the failure stage decreases comparing to the whole loading process, and AE activities are active throughout the whole loading process. The increasing rate of accumulative AE curve gradually decreases, and the ductile failure characteristic of granite is enhanced. The increase of energy dissipated by the closure of thermal induced cracks and friction between particles results in a decrease of the stored elastic energy, which ultimately leads to a decrease of accumulative AE events. When N = 1, T increases from 150 to 600 °C, the accumulative AE events decrease by 69.3%; when T = 450 °C, N increases from 1 to 15, the accumulative AE events decrease by 82.4%.
(3) The deformation responses of granite are greatly affected by T and N. At a lower temperature (T = 150, 300 °C), the cracks start from the ends of sample, and then propagate the middle area of sample surface. With the increase of T, the crack initiation area gradually shifts from the ends to the middle area of sample. When T = 600 °C, the crack initiation area is located in the center of the sample, and gradually expands to both ends as the loading continues. At the same time, the increase of thermal damage leads to the increase of granite looseness, surface roughness of mineral particles and micro-thermal induced cracks. The failure cracks of granite samples with higher T and N (T = 600 °C, N = 15) finally show a complex fracture network distribution of turtle shape and a shear failure mode of "Z" type. The failure crack density on the surface also increases, and the granite shows strong ductility characteristics. (4) At the micro-level, the thermal damage of granite caused by cyclic heating and water cooling is mainly reflected in the formation of crack network, the decrease of the bonding strength between particles and the increase of the particle surface roughness. With the increase of T and N, transgranular and intergranular cracks interconnect with each other and evolve to form a crack network. The closed crack network causes the blocky matrix to peel off from the matrix, causing the granite to be loose and broken.