# Thermal Deformation of Granite under Different Temperature and Pressure Pathways

Authors: Peng Zhao; Zi-jun Feng
Journal: Advances in Materials Science and Engineering
 (2019)

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## Abstract

The thermal cracking of rocks is the phenomenon of expansion and deformation of mineral particles inside the rocks. The thermal deformation of the same granite sample under different heating pathways was meticulously analyzed, and the effect of the variation of external stress on the thermal expansion was carefully studied. The thermal deformation threshold temperature was low under triaxial stress, and a larger expansion was produced under uniaxial stress. The thermal deformation of the rock mass was found to be irreversible. Upon heating to the same temperature, the expansion was found to decrease with the increase in the number of thermal cycles. Besides, for each thermal cycle, the amount of deformation caused by cooling was always greater than the amount of deformation caused by temperature rise; this difference in deformation was especially obvious under a change from triaxial stress to uniaxial stress. In the process of elevated temperature which has the same heating rate, the thermal expansion coefficient was greater under uniaxial stress than it was under triaxial stress; under same external stress, the thermal expansion coefficient with a high heating rate was generally greater than the thermal expansion coefficient with a low heating rate.


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## Body

## 1. Introduction

It has become very important to realize the significance of the study of the thermal deformation of granite under high temperature and pressure. The highly radioactive elements under the deep burial of nuclear wastes are expected to increase the temperature of the surrounding rock masses up to 300°C within the next ten years. The penetration of the radiation from the radioactive elements through the surrounding rocks into the biosphere will have a serious consequence on the environment that humans live [1–6]. During the extraction of geothermal energy from high-temperature rock masses, the degree of thermal rupture of granite or other rock foundation directly affects the permeability of rock mass, which in turn affects the extraction efficiency of geothermal energy [7–12]. It is also necessary to initiate extensive research on the deformation behavior of rocks under high temperature and pressure in other fields like oil extracting and underground gasification of coal resources [13, 14]. In the 1980s, Ramana had demonstrated that the thermal expansion coefficient of granite increases with increasing temperature when granite was heated in free state [15]. Homand-Etienne and Houpert had heated different kinds of granite from room temperature to 600°C and visualized the crack densities and size on the surface of granite rocks by scanning electron microscopy (SEM). The SEM images indicated that the intracrystalline crack length was always longer than the intercrystalline ones and that the width of the cracks also increased as the temperature increases [16]. Van der Molen studied the association between the transition temperature of α-β quartz, and the thermal expansion of granite at high pressure and found that the confining pressure impeded the cracks from opening [17]. Heard had heated the quartz feldspar to 300°C at different pressures and concluded that thermal expansion could be suppressed by external stress, with the coefficient of thermal expansion decreasing with increasing stress [18]. According to the studies from Gautam, the microstructure of sandstone would rearrange at temperatures below the melting point [19]. In addition, Xi and Zhao measured the ultrasonic velocity and elastic modulus of a rock sample by studying the mechanical characteristics of granite after cooling it from a high temperature. The results showed that the internal temperature of the high temperature rock changed dramatically during cooling in water. The mechanical properties of the rock mass had been greatly damaged, as indicated by the reduction in the ultrasonic speed, uniaxial compressive strength, tensile strength, and elastic modulus [20]. All these aforementioned studies have played a vital role in understanding the mechanism of the changes in rock mass under high temperature and pressure and have also provided genuine guidance for many engineering projects. However, there are still certain problems in this regard that have not received enough attention.The rock mass is usually under three-dimensional stress under natural conditions. However, during excavation projects and geothermal development, a spatial structure often forms inside the rock mass and it undergoes a transition from a three-dimensional stress to two- (or one-) dimensional stress. The rock mass encounters repeated variation of temperature and stress, owing to which the deformation characteristics of the rock mass become extremely complicated. However, the studies conducted at high temperature in the laboratories are usually based on the application of a single triaxial or uniaxial stress. The outcomes of these experiments ignore the influence of the change of stress on the thermal deformation of the rock mass before and after the excavation. This study focuses on the thermal deformation of the same rock sample under different temperatures and pressure pathways and the effect of the change of external stress on it.


## 2. Methods

### 2.1. Sample Preparation

The rock sample chosen for the study is “Lu gray granite,” which was taken from Pingyi county, Shandong province, China. The process of sample preparation involved the drilling of the rock core with rhinestone as the first step, the interception of the required length with a saw machine as the next step, followed by the polishing of the rock core into a flat and smooth cylinder as the third step. The final granite sample obtained had a height to diameter ratio of 2 : 1 and a size of 50 mm × 100 mm.“Lu gray granite” has a fine-grained dense texture with a high compressive strength. The mineral composition mainly includes feldspar, quartz, and illite, the grain size of feldspar being about 1-2 mm and that of quartz being 0.6-0.7 mm. Moreover, there are some other minerals too, such as calcite and siderite. The cement between the mineral particles contains mostly clay minerals and a small amount of silica.


### 2.2. Experimental System

As shown in Figure1, the experimental system utilizes the grating ruler to collect the axial deformation data of the rock sample in real time. Axial pressure is loaded by the servo-controlled rock testing machine at high temperature and pressure; a grating ruler was set on the top of servo-controlled rock testing machine to collect the data of axial displacement; and the confining pressure is indicated by the automatic confining pressure pump. These two pressure parameters are independently controlled. Eight sets of heating rods are scattered around the rock sample to ensure that the sample is heated uniformly during the heating process. One end of the thermocouple is in contact with the sample, and the other end is connected to the temperature control system, so that the heating rate can be controlled according to the feedback data from the thermocouple, as per the requirements of the experiment.Figure 1
(a) Setup photograph and (b) schematic of the experimental device.
(a)
(b)


### 2.3. Experimental Procedure

The same sample was heated to different temperatures with different heating rates. At the beginning of experiment, the specimen was loaded external pressure to target value and heated to preset temperature with corresponding heating rate, holding the preset temperature for about two hours and than cooling down to room temperature. After testing, the sample was cooled down to room temperature at each thermal cyclic, and the value of the axial displacement was recorded in order to get the length of the sample at that particular instant. This length was considered as the original length for the calculation of the axial strain for the next temperature test so that the value of axial strain in each thermal cycle always varied from zero. Numerous studies have shown that 300°C is a very critical temperature point for granite. Before 300°C, the natural cracks inside the sample will be closed due to the expansion of internal mineral components, resulting in the rock becoming dense, the permeability decreasing, and compressive strength increasing. However, when the temperature was elevated from 300°C to 600°C, a large amount of thermal cracking occurs, the permeability of rock will suddenly increase, and the physical mechanical properties such as compressive strength, tensile strength, and elastic modulus of the rock drop sharply [21–23]. Therefore, in this study, the sample was heated to different target temperatures as shown in Table 1, and the law of thermal deformation was observed. The experimental procedure is shown in Figure 2 and all the parameters in experiment are listed in Table 1.Table 1
Parameters during heating experiment.
Thermal cycles
Maximum temperature (°C)
Heating rate (°C/min)
External pressure
1
350
2
σ
a = 8 MPa, σc = 5 MPa
2
640
3
σ
a = 8 MPa, σc = 5 MPa
3
300
3.5
σ
a = 8 MPa, σc = 0 MPa
4
600
5.5
σ
a = 8 MPa, σc = 0 MPa
5
600
3
σ
a = 8 MPa, σc = 0 MPa
Note:σa denotes axial stress and σc denotes confining stress.Figure 2
Experimental procedure. Note: ▵t was for about 2 h.


## 2.1. Sample Preparation

The rock sample chosen for the study is “Lu gray granite,” which was taken from Pingyi county, Shandong province, China. The process of sample preparation involved the drilling of the rock core with rhinestone as the first step, the interception of the required length with a saw machine as the next step, followed by the polishing of the rock core into a flat and smooth cylinder as the third step. The final granite sample obtained had a height to diameter ratio of 2 : 1 and a size of 50 mm × 100 mm.“Lu gray granite” has a fine-grained dense texture with a high compressive strength. The mineral composition mainly includes feldspar, quartz, and illite, the grain size of feldspar being about 1-2 mm and that of quartz being 0.6-0.7 mm. Moreover, there are some other minerals too, such as calcite and siderite. The cement between the mineral particles contains mostly clay minerals and a small amount of silica.


## 2.2. Experimental System

As shown in Figure1, the experimental system utilizes the grating ruler to collect the axial deformation data of the rock sample in real time. Axial pressure is loaded by the servo-controlled rock testing machine at high temperature and pressure; a grating ruler was set on the top of servo-controlled rock testing machine to collect the data of axial displacement; and the confining pressure is indicated by the automatic confining pressure pump. These two pressure parameters are independently controlled. Eight sets of heating rods are scattered around the rock sample to ensure that the sample is heated uniformly during the heating process. One end of the thermocouple is in contact with the sample, and the other end is connected to the temperature control system, so that the heating rate can be controlled according to the feedback data from the thermocouple, as per the requirements of the experiment.Figure 1
(a) Setup photograph and (b) schematic of the experimental device.
(a)
(b)


## 2.3. Experimental Procedure

The same sample was heated to different temperatures with different heating rates. At the beginning of experiment, the specimen was loaded external pressure to target value and heated to preset temperature with corresponding heating rate, holding the preset temperature for about two hours and than cooling down to room temperature. After testing, the sample was cooled down to room temperature at each thermal cyclic, and the value of the axial displacement was recorded in order to get the length of the sample at that particular instant. This length was considered as the original length for the calculation of the axial strain for the next temperature test so that the value of axial strain in each thermal cycle always varied from zero. Numerous studies have shown that 300°C is a very critical temperature point for granite. Before 300°C, the natural cracks inside the sample will be closed due to the expansion of internal mineral components, resulting in the rock becoming dense, the permeability decreasing, and compressive strength increasing. However, when the temperature was elevated from 300°C to 600°C, a large amount of thermal cracking occurs, the permeability of rock will suddenly increase, and the physical mechanical properties such as compressive strength, tensile strength, and elastic modulus of the rock drop sharply [21–23]. Therefore, in this study, the sample was heated to different target temperatures as shown in Table 1, and the law of thermal deformation was observed. The experimental procedure is shown in Figure 2 and all the parameters in experiment are listed in Table 1.Table 1
Parameters during heating experiment.
Thermal cycles
Maximum temperature (°C)
Heating rate (°C/min)
External pressure
1
350
2
σ
a = 8 MPa, σc = 5 MPa
2
640
3
σ
a = 8 MPa, σc = 5 MPa
3
300
3.5
σ
a = 8 MPa, σc = 0 MPa
4
600
5.5
σ
a = 8 MPa, σc = 0 MPa
5
600
3
σ
a = 8 MPa, σc = 0 MPa
Note:σa denotes axial stress and σc denotes confining stress.Figure 2
Experimental procedure. Note: ▵t was for about 2 h.


## 3. Results

### 3.1. Results and Analysis of Axial Strain

The thermal deformation of rock is mainly caused by the thermal expansion of mineral particles inside the rock. The deformation characteristics are related to the intrinsic properties of rock such as the mineral composition, particle size, degree of pore and crack development, and the integrity of its internal structure. It is also affected by the presence of the external stress and temperature. The force generated in the various parts of the rock that is not capable of expanding freely when the temperature changes is called thermal stress. According to the mechanism of thermal stress generation, it is known that easier the rock mineral particles are subjected to constraints, easier will be the generation of thermal stress, and greater the constraints in mineral particles, larger will be the generation of thermal stress. When the thermal stress is greater than the yield stress between the mineral particles, microcracks appear inside the rock. The phenomenon of the breaking of rocks by heat stress, caused by the uneven expansion of the mineral particles, is called thermal rupture. During the process of elevating the temperature from RT to 500°C, microcracks generated by thermal cracking begin to appear at 200°C, connected each other at 300°C to form a large crack, and at 500°C, most already connected cracks have formed the closed irregular polygons that surrounded the granite grains [24]. The heating of the rock causes its expansion, thereby resulting in an increase in the volume. The enlarged volume is mainly composed of two parts—one is the volume in which the internal mineral particles expand and the other is the volume of the pores and cracks formed by thermal cracking. Neither of the two can be ignored easily. In fact, Wu analyzed the influence of the thermal cracking of rocks and found that the porosity of some rocks increases nearly by ten times after the process of heat treatment [25]. According to the research of G Simmons, the volume of the newly generated crack is exponentially related to the highest temperature of rock sample that can be reached, and the rock which has lowest initial crack porosity always change in greatest rate of increase [26]. The expansion of mineral particles almost occurs throughout the heating process, while the thermal cracking occurs only in a certain stage of the heating process. The cracks are generated at the peak of the heating process, leading to expansion and hence an increase in the volume of the rock. Therefore, the rock is expected to exhibit obvious thermal deformation when thermal cracking occurs to a large extent. For the convenience in analysis, the temperature at which the sample begins to show significant thermal deformation during the heating process is called the thermal deformation temperature threshold.Shown in Figure3 is the axial strain changes versus temperature under different confining pressures. It can be seen from the figure that the axial strain changes earlier with the confining pressure, and the axial strain is significantly smaller in the absence of confining pressure.Figure 3
Axial strain change versus temperature under triaxial and uniaxial stress.Under the action of confining pressure, the rock is compressed inwards, the inner mineral particles are squeezed closer to each other, and the thermal expansion is more restricted. Therefore, as the temperature increases, a small temperature gradient can generate a large thermal stress between the mineral crystal particles [27], so that the yield limit between the mineral crystal particles is reached quicker and the thermal rupture occurs sooner. It is because of this that the axial deformation of the rock sample begins to change first in the presence of confining pressure. As the temperature continues to rise after the thermal deformation starts to occur, the cracks in the rock expand, develop, and connect to reach up to a certain size until they are destroyed by the confining pressure, which is also accompanied by a decrease in the opening degree. At the same time, when the inner mineral particles expand, they are forced to fill the gaps of the internal cracks first before they can continue to deform the outer portion of the rock. As a result, the external deformation is partially offset by the internal fissure space, so that the overall change in the axial strain under a confining pressure is relatively flat. Nevertheless, for the heating process under the uniaxial stress, the expansion of the sample is not limited by the confining pressure, because of which the limit of the outward expansion is relatively smaller. As a result, heating up to the same temperature can produce a larger deformation. In summary, the thermal deformation of the rock corresponds to a lower thermal deformation temperature threshold under the triaxial stress and can generate a larger expansion under uniaxial stress.The sample experienced a temperature of 300°C for five times during the entire thermal cycle. The respective strains when the temperature was raised to 300°C are demonstrated in Figure4. It can be observed that the axial deformation was different for every cycle of the samples being heated to the same temperature under the same external pressure. For instance, the axial strain was 0.02 when the temperature was raised to 300°C for the first time, while it increased to nearly three times during the second cycle. Overall, the axial strain at 300°C gradually decreased with the increase in the number of thermal cycles.Figure 4
Change of axial strain at 300°C versus the number of heating cycles.Every thermal cycle experienced by the rocks leads to the generation of new cracks until a steady state is reached after 2–5 times [25]. In this work, the sample is heated to 350°C only during the first heating cycle since the thermal rupture is not sufficient enough. The internal structure is relatively complete, and there is still a lot of room for deformation. Therefore, the axial strain during the second cycle as the temperature is raised to 300°C is greater than the axial strain experienced in the first cycle. In fact, under the repeated action of thermal stress and external load, the structural skeleton constructed by the harder mineral particles is continuously damaged. More and more internal cracks are developed, and the internal integrity of the rock samples deteriorate. As a result, a larger volume needs to be filled by mineral particles during expansion every time the temperature is raised, so that the axial strain created is smaller each time the same temperature is reached. In general, for the cases where the external loading does not change, the deformation should be smaller in the process of heating up the sample to the same temperature. In other words, an increasing number of energies was required to produce the same deformation as the number of thermal cycles increase.


### 3.2. Results and Analysis of Axial Displacement

Figure5 shows the axial displacement of the sample after cooling it to room temperature every time the temperature was raised. It can be found that the value of the axial displacement after cooling to room temperature is not constant but kept on increasing with an increase in the number of heating cycles. The increase is obvious, especially after the removal of the confining pressure.Figure 5
Axial displacement after each heating varies with the number of thermal cycles.The opening of the cracks due to a rise in the temperature and the closure of the cracks under an external stress occur almost simultaneously. When the temperature is raised, the sample is thermally expanded and the volume is increased. As a result, cracks are generated, expanded, and connected. When the temperature is lowered, the thermal stress gradually disappears. The mineral particles after the thermal expansion at high temperature decrease in volume when cooled. The other mineral particles occupy the reduced volume during the process of adjusting the position, and thus the degree of opening of the crack is reduced and is sometimes compressed enough to even close. The internal structure of the rock changes when subjected to high temperature, and the solid skeleton constructed by the harder mineral particles gets damaged, thus reducing the bearing capacity of the rock significantly. Zhao et al. employed the computerized tomography (CT) to observe thermal cracking in the Lu gray granite, and the results are shown in Figure6 clearly indicates that the thermal cracking occurred and developed with increasing temperature [28]. During the cooling process, the axial displacement of the rock sample which is compressed to the length before heating, will not stop the deformation but will continue to get compressed under the axial pressure. Therefore, the amplitude of compression of the sample during every cooling step is always greater than the amplitude of expansion when the temperature is increased in this heating experiment.Figure 6
Effect of high temperature on the mesostructure of Lu gray granite (Zhao et al.).The lateral expansion of the rock sample under constant confining pressure is restricted during the temperature rise. The interactions generated in this process prevent the axial deformation from generating a component in the lateral direction to some extent, thereby impeding the changes in the axial deformation itself. Under a three-dimensional pressure, the sudden removal of the confining pressure of the rock promotes the surge of acoustic emission [29], indicating that the structural frame that primarily bears the external force is getting destroyed rapidly. When the triaxial stress on the rock sample changes to the uniaxial stress, the deviatoric stress in the axial direction suddenly increases and the sample experience a process equivalent to uniaxial compressing. In a case where the internal structure of the sample is damaged severely, a very large scale of compression is bound to occur. Therefore, the axial deformation upon cooling to room temperature in the third cycle has a large jump as compared to the second cycle. The most striking conclusion is that the changes in the external pressure are pretty significant for the deformation of the rock mass, especially for the rock which is already subjected to high temperature in advance.


### 3.3. Behavior of the Thermal Expansion Coefficient

Thermal cracking of rock is a continuous process for energy accumulation and release [30]. When the degree of microcrack opening is large, the coefficient of thermal expansion upon thermal cracking is large. On the other hand, when the crack opening is suppressed, such as that under a triaxial stress, the measured coefficient of thermal expansion is relatively small [31]. In general, as the temperature increases, the coefficient of thermal expansion of the rock becomes larger than the average of the thermal expansion coefficients of the minerals that make up the rock. The “extra” expansion can attribute to the new cracks caused by the different expansion rates of the mineral particles [32]. The coefficient of thermal expansion is defined by the change in the magnitude of the length caused by a unit change in temperature. This parameter basically reflects the rate of deformation of the sample as a function of temperature. The thermal expansion coefficient is mainly influenced by the presence of an external stress and the rate of heating.Figure7 shows the influence of confining pressure on the thermal expansion coefficient of rocks. It can be seen that the peak height of the coefficient of thermal expansion under confining pressure is lower than that under uniaxial pressure. That is to say, the coefficient of thermal expansion measured in the process of thermal deformation with a larger confining pressure is smaller. When the mineral particles in the rock sample expand, the restraint caused by the confining pressure will hinder the mineral particles from expanding outwards. The large pore structure developed by the crack plays a role in counteracting the deformation. The fractures are filled by other mineral particles, which not only offsets the external deformation of the rock to some extent but also leads to the reduction of the space that is used for accommodating expansion of the mineral particles. Thus, the thermal deformation of the sample is comprehensively limited. Therefore, after the thermal cracking starts occurring, its suppression by the confining pressure allows the sample to not only have a smaller extent of expansion, but also a slower rate for the same.Figure 7
Thermal expansion coefficient (α) change versus temperature under different confining pressures.Another significant factor affecting the coefficient of thermal expansion is the rate of increase of the temperature. Figure8 shows the effect of the different heating rates on the coefficient of thermal expansion of the sample. The temperature threshold of thermal expansion coefficient was found to vary with the rate of heating. For instance, the temperature threshold of thermal expansion coefficient is lower when the heating rate is 5.5°C/min than when it is 3°C/min. The peak maxima were also different for different heating rates.Figure 8
Thermal expansion coefficient (α) change versus temperature under different heating rates.It can also be seen from the figure that, in a certain temperature range during the heating process, the thermal expansion coefficient at a low heating rate is higher than that at a high heating rate. This shows that the value of the thermal expansion coefficient at a higher heating rate is not completely above its value at a lower heating rate. One of the reasons is that the magnitude of the difference of the heating rate is not large enough to have any visible difference in the severity of the thermal deformation. The other reason may be attributed to the characteristics of the thermal deformation itself. The thermal rupture of rocks occurs intermittently and periodically with increasing temperature [33]. Because of the intermittent thermal rupture and the uncertainty of the position of thermal cracking inside the rock sample, the thermal expansion coefficient is less likely to exhibit the absolute same curve even under the same conditions of external pressure and heating rate. At a particular temperature range, the sample may either be undergoing an intense thermal deformation or it may be in the energy saving phase between two thermal deformations. Both the situations may appear exclusively at the same temperature range in two different sets of the heating experiments. Therefore, the coefficient of thermal expansion with a low heating rate may also be greater than the coefficient of thermal expansion with a high heating rate.However, the intermittent, multiperiod characteristics of the heat deformation behavior do not affect the severity of the thermal deformation or the maximum value of the thermal expansion coefficient that can be achieved. Higher heating rates accelerate the accumulation of energy inside the rock, causing the thermal stress between the mineral particles in the rock to exceed its yield limit more quickly. When the heating rate is high, the formation speed, development speed, and connectivity of the microcracks cause the sample to produce rapid, significant expansion, so that the thermal expansion coefficient with a higher heating rate starts to change earlier. Moreover, a higher heating rate will cause the mineral particles inside the rock to accumulate higher thermoelastic strain energy in a short time, as a result of which the thermal deformation will be more intense in the energy release phase, where in the thermal stress it does a positive work. This justifies the reason for the peak value of the coefficient of thermal expansion to be larger at a heating rate of 5.5°C/min than at 3°C/min.


## 3.1. Results and Analysis of Axial Strain

The thermal deformation of rock is mainly caused by the thermal expansion of mineral particles inside the rock. The deformation characteristics are related to the intrinsic properties of rock such as the mineral composition, particle size, degree of pore and crack development, and the integrity of its internal structure. It is also affected by the presence of the external stress and temperature. The force generated in the various parts of the rock that is not capable of expanding freely when the temperature changes is called thermal stress. According to the mechanism of thermal stress generation, it is known that easier the rock mineral particles are subjected to constraints, easier will be the generation of thermal stress, and greater the constraints in mineral particles, larger will be the generation of thermal stress. When the thermal stress is greater than the yield stress between the mineral particles, microcracks appear inside the rock. The phenomenon of the breaking of rocks by heat stress, caused by the uneven expansion of the mineral particles, is called thermal rupture. During the process of elevating the temperature from RT to 500°C, microcracks generated by thermal cracking begin to appear at 200°C, connected each other at 300°C to form a large crack, and at 500°C, most already connected cracks have formed the closed irregular polygons that surrounded the granite grains [24]. The heating of the rock causes its expansion, thereby resulting in an increase in the volume. The enlarged volume is mainly composed of two parts—one is the volume in which the internal mineral particles expand and the other is the volume of the pores and cracks formed by thermal cracking. Neither of the two can be ignored easily. In fact, Wu analyzed the influence of the thermal cracking of rocks and found that the porosity of some rocks increases nearly by ten times after the process of heat treatment [25]. According to the research of G Simmons, the volume of the newly generated crack is exponentially related to the highest temperature of rock sample that can be reached, and the rock which has lowest initial crack porosity always change in greatest rate of increase [26]. The expansion of mineral particles almost occurs throughout the heating process, while the thermal cracking occurs only in a certain stage of the heating process. The cracks are generated at the peak of the heating process, leading to expansion and hence an increase in the volume of the rock. Therefore, the rock is expected to exhibit obvious thermal deformation when thermal cracking occurs to a large extent. For the convenience in analysis, the temperature at which the sample begins to show significant thermal deformation during the heating process is called the thermal deformation temperature threshold.Shown in Figure3 is the axial strain changes versus temperature under different confining pressures. It can be seen from the figure that the axial strain changes earlier with the confining pressure, and the axial strain is significantly smaller in the absence of confining pressure.Figure 3
Axial strain change versus temperature under triaxial and uniaxial stress.Under the action of confining pressure, the rock is compressed inwards, the inner mineral particles are squeezed closer to each other, and the thermal expansion is more restricted. Therefore, as the temperature increases, a small temperature gradient can generate a large thermal stress between the mineral crystal particles [27], so that the yield limit between the mineral crystal particles is reached quicker and the thermal rupture occurs sooner. It is because of this that the axial deformation of the rock sample begins to change first in the presence of confining pressure. As the temperature continues to rise after the thermal deformation starts to occur, the cracks in the rock expand, develop, and connect to reach up to a certain size until they are destroyed by the confining pressure, which is also accompanied by a decrease in the opening degree. At the same time, when the inner mineral particles expand, they are forced to fill the gaps of the internal cracks first before they can continue to deform the outer portion of the rock. As a result, the external deformation is partially offset by the internal fissure space, so that the overall change in the axial strain under a confining pressure is relatively flat. Nevertheless, for the heating process under the uniaxial stress, the expansion of the sample is not limited by the confining pressure, because of which the limit of the outward expansion is relatively smaller. As a result, heating up to the same temperature can produce a larger deformation. In summary, the thermal deformation of the rock corresponds to a lower thermal deformation temperature threshold under the triaxial stress and can generate a larger expansion under uniaxial stress.The sample experienced a temperature of 300°C for five times during the entire thermal cycle. The respective strains when the temperature was raised to 300°C are demonstrated in Figure4. It can be observed that the axial deformation was different for every cycle of the samples being heated to the same temperature under the same external pressure. For instance, the axial strain was 0.02 when the temperature was raised to 300°C for the first time, while it increased to nearly three times during the second cycle. Overall, the axial strain at 300°C gradually decreased with the increase in the number of thermal cycles.Figure 4
Change of axial strain at 300°C versus the number of heating cycles.Every thermal cycle experienced by the rocks leads to the generation of new cracks until a steady state is reached after 2–5 times [25]. In this work, the sample is heated to 350°C only during the first heating cycle since the thermal rupture is not sufficient enough. The internal structure is relatively complete, and there is still a lot of room for deformation. Therefore, the axial strain during the second cycle as the temperature is raised to 300°C is greater than the axial strain experienced in the first cycle. In fact, under the repeated action of thermal stress and external load, the structural skeleton constructed by the harder mineral particles is continuously damaged. More and more internal cracks are developed, and the internal integrity of the rock samples deteriorate. As a result, a larger volume needs to be filled by mineral particles during expansion every time the temperature is raised, so that the axial strain created is smaller each time the same temperature is reached. In general, for the cases where the external loading does not change, the deformation should be smaller in the process of heating up the sample to the same temperature. In other words, an increasing number of energies was required to produce the same deformation as the number of thermal cycles increase.


## 3.2. Results and Analysis of Axial Displacement

Figure5 shows the axial displacement of the sample after cooling it to room temperature every time the temperature was raised. It can be found that the value of the axial displacement after cooling to room temperature is not constant but kept on increasing with an increase in the number of heating cycles. The increase is obvious, especially after the removal of the confining pressure.Figure 5
Axial displacement after each heating varies with the number of thermal cycles.The opening of the cracks due to a rise in the temperature and the closure of the cracks under an external stress occur almost simultaneously. When the temperature is raised, the sample is thermally expanded and the volume is increased. As a result, cracks are generated, expanded, and connected. When the temperature is lowered, the thermal stress gradually disappears. The mineral particles after the thermal expansion at high temperature decrease in volume when cooled. The other mineral particles occupy the reduced volume during the process of adjusting the position, and thus the degree of opening of the crack is reduced and is sometimes compressed enough to even close. The internal structure of the rock changes when subjected to high temperature, and the solid skeleton constructed by the harder mineral particles gets damaged, thus reducing the bearing capacity of the rock significantly. Zhao et al. employed the computerized tomography (CT) to observe thermal cracking in the Lu gray granite, and the results are shown in Figure6 clearly indicates that the thermal cracking occurred and developed with increasing temperature [28]. During the cooling process, the axial displacement of the rock sample which is compressed to the length before heating, will not stop the deformation but will continue to get compressed under the axial pressure. Therefore, the amplitude of compression of the sample during every cooling step is always greater than the amplitude of expansion when the temperature is increased in this heating experiment.Figure 6
Effect of high temperature on the mesostructure of Lu gray granite (Zhao et al.).The lateral expansion of the rock sample under constant confining pressure is restricted during the temperature rise. The interactions generated in this process prevent the axial deformation from generating a component in the lateral direction to some extent, thereby impeding the changes in the axial deformation itself. Under a three-dimensional pressure, the sudden removal of the confining pressure of the rock promotes the surge of acoustic emission [29], indicating that the structural frame that primarily bears the external force is getting destroyed rapidly. When the triaxial stress on the rock sample changes to the uniaxial stress, the deviatoric stress in the axial direction suddenly increases and the sample experience a process equivalent to uniaxial compressing. In a case where the internal structure of the sample is damaged severely, a very large scale of compression is bound to occur. Therefore, the axial deformation upon cooling to room temperature in the third cycle has a large jump as compared to the second cycle. The most striking conclusion is that the changes in the external pressure are pretty significant for the deformation of the rock mass, especially for the rock which is already subjected to high temperature in advance.


## 3.3. Behavior of the Thermal Expansion Coefficient

Thermal cracking of rock is a continuous process for energy accumulation and release [30]. When the degree of microcrack opening is large, the coefficient of thermal expansion upon thermal cracking is large. On the other hand, when the crack opening is suppressed, such as that under a triaxial stress, the measured coefficient of thermal expansion is relatively small [31]. In general, as the temperature increases, the coefficient of thermal expansion of the rock becomes larger than the average of the thermal expansion coefficients of the minerals that make up the rock. The “extra” expansion can attribute to the new cracks caused by the different expansion rates of the mineral particles [32]. The coefficient of thermal expansion is defined by the change in the magnitude of the length caused by a unit change in temperature. This parameter basically reflects the rate of deformation of the sample as a function of temperature. The thermal expansion coefficient is mainly influenced by the presence of an external stress and the rate of heating.Figure7 shows the influence of confining pressure on the thermal expansion coefficient of rocks. It can be seen that the peak height of the coefficient of thermal expansion under confining pressure is lower than that under uniaxial pressure. That is to say, the coefficient of thermal expansion measured in the process of thermal deformation with a larger confining pressure is smaller. When the mineral particles in the rock sample expand, the restraint caused by the confining pressure will hinder the mineral particles from expanding outwards. The large pore structure developed by the crack plays a role in counteracting the deformation. The fractures are filled by other mineral particles, which not only offsets the external deformation of the rock to some extent but also leads to the reduction of the space that is used for accommodating expansion of the mineral particles. Thus, the thermal deformation of the sample is comprehensively limited. Therefore, after the thermal cracking starts occurring, its suppression by the confining pressure allows the sample to not only have a smaller extent of expansion, but also a slower rate for the same.Figure 7
Thermal expansion coefficient (α) change versus temperature under different confining pressures.Another significant factor affecting the coefficient of thermal expansion is the rate of increase of the temperature. Figure8 shows the effect of the different heating rates on the coefficient of thermal expansion of the sample. The temperature threshold of thermal expansion coefficient was found to vary with the rate of heating. For instance, the temperature threshold of thermal expansion coefficient is lower when the heating rate is 5.5°C/min than when it is 3°C/min. The peak maxima were also different for different heating rates.Figure 8
Thermal expansion coefficient (α) change versus temperature under different heating rates.It can also be seen from the figure that, in a certain temperature range during the heating process, the thermal expansion coefficient at a low heating rate is higher than that at a high heating rate. This shows that the value of the thermal expansion coefficient at a higher heating rate is not completely above its value at a lower heating rate. One of the reasons is that the magnitude of the difference of the heating rate is not large enough to have any visible difference in the severity of the thermal deformation. The other reason may be attributed to the characteristics of the thermal deformation itself. The thermal rupture of rocks occurs intermittently and periodically with increasing temperature [33]. Because of the intermittent thermal rupture and the uncertainty of the position of thermal cracking inside the rock sample, the thermal expansion coefficient is less likely to exhibit the absolute same curve even under the same conditions of external pressure and heating rate. At a particular temperature range, the sample may either be undergoing an intense thermal deformation or it may be in the energy saving phase between two thermal deformations. Both the situations may appear exclusively at the same temperature range in two different sets of the heating experiments. Therefore, the coefficient of thermal expansion with a low heating rate may also be greater than the coefficient of thermal expansion with a high heating rate.However, the intermittent, multiperiod characteristics of the heat deformation behavior do not affect the severity of the thermal deformation or the maximum value of the thermal expansion coefficient that can be achieved. Higher heating rates accelerate the accumulation of energy inside the rock, causing the thermal stress between the mineral particles in the rock to exceed its yield limit more quickly. When the heating rate is high, the formation speed, development speed, and connectivity of the microcracks cause the sample to produce rapid, significant expansion, so that the thermal expansion coefficient with a higher heating rate starts to change earlier. Moreover, a higher heating rate will cause the mineral particles inside the rock to accumulate higher thermoelastic strain energy in a short time, as a result of which the thermal deformation will be more intense in the energy release phase, where in the thermal stress it does a positive work. This justifies the reason for the peak value of the coefficient of thermal expansion to be larger at a heating rate of 5.5°C/min than at 3°C/min.


## 4. Conclusions

Using the servo-controlled rock testing machine with high temperature and high pressure, independently developed by Taiyuan University of Technology, the thermal deformation characteristics of a standard granite sample with 50 mm × 100 mm were studied in details upon repeatedly subjecting it to high temperature and high stress. The analysis leads to the following conclusions:(a)
Thermal deformation of rocks exhibits different behaviors under triaxial and uniaxial stress. Thermal deformation has a lower thermal deformation threshold temperature under triaxial stress and can produce a larger expansion under uniaxial stress.(b)
The thermal deformation of rock mass is irreversible. With an increase in the number of thermal cycles, the expansion becomes smaller when the sample is heated to the same temperature. Besides, for each thermal cycle, the amount of deformation caused by cooling was always greater than the amount of deformation caused by temperature rise especially the external pressure changes from triaxial stress to uniaxial stress. Hence, in the construction of artificial reservoirs in the real geothermal mining system, if it was possible to orientation drop the temperature between the injection well and the production well in a short time in the fracturing zone, the deformation effect is beneficial to the penetration of cracks between two wells, which is significant in improving the extraction efficiency of thermal energy.(c)
In the process of elevated temperature which has the same heating rate, the thermal expansion coefficient was greater under uniaxial stress than it was under triaxial stress; in the process of elevated temperature which has the same external stress, the thermal expansion coefficient with a high heating rate is generally greater than the thermal expansion coefficient with a low heating rate.



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*Source: 7869804-2019-01-08.xml*