Acoustic Emission and Damage Characteristics of Granite Subjected to High Temperature

Acoustic emission (AE) signals can be detected from rocks under the effect of temperature and loading, which can be used to reflect rock damage evolution process and predict rock fracture. In this paper, uniaxial compression tests of granite at high temperatures from 25°C to 1000°C were carried out, and AE signals were monitored simultaneously. ,e results indicated that AE ring count rate shows the law of “interval burst” and “relatively calm,” which can be explained from the energy point of view. From 25°C to 1000°C, the rock failure mode changes from single splitting failure to multisplitting failure, and then to incomplete shear failure, ideal shear failure, and double shear failure, until complete integral failure. ,ermal damage (DT) defined by the elastic modulus shows logistic increase with the rise of temperature. Mechanical damage (DM) derived by the AE ring count rate can be divided into initial stage, stable stage, accelerated stage, and destructive stage. Total damage (D) increases with the rise of strain, which is corresponding to the stress-strain curve at various temperatures. Using AE data, we can further analyze the mechanism of deformation and fracture of rock, which helps to gather useful data for predicting rock stability at high temperatures.

e related mechanical parameters are the basis for the study of excavation and stability in underground engineerings.
e peak strength is the macroscopic representation of rock, which cannot reflect internal damage evolution.As an important method in acoustic nondestructive testing, rock internal defects and damage evolution process can be accurately monitored by acoustic emission (AE) detection [16][17][18][19].
In recent years, AE detection technology has been used in rock mechanics by many scholars [20][21][22][23][24][25][26][27].For example, Ganne et al. [20] studied the brittleness of rock before peak stress by the AE technique, and four stages of accumulated AE energy were given.Alkan et al. [21] determined the expansion boundaries of rock by studying AE signals of different strain stages in triaxial compression tests.He et al. [22] observed that there were much higher amplitude and lower frequency events near the bursting failure of rock samples, and the accumulated AE energy release increased rapidly from unloading state to rock failure.Gasc et al. [23] studied rock structural transformation and mineral reaction under high temperatures and high pressures by X-ray diffraction and AE detection of serpentine.Chmel et al. [24] studied AE energy release of granite under impact loading.Zhang et al. [25] studied AE properties of halite, glauberite, and gypsum during compression test with different loading styles and saturation conditions.Zhang et al. [26] calculated the correlation fractal dimensions of AE counts at different stress levels, and the value at the failure point showed a polynomial decline with the increase of temperature.Guo et al. [27] carried out comprehensive studies on rockdetected AE characteristics, failure mode, crack initiation stress, damage evolution law, and stress-strain constitutive model after thermal damage.
Since AE monitoring technology has practical application in the determination of ground stress, tunnel, and slope engineerings [28,29], there are few studies on AE characteristics of granite at high temperature.Granite, as an ideal material for storing high radioactive nuclear waste, has a series of advantages such as low permeability, compactness, and high strength.erefore, it is of theoretical and practical value to study AE and damage characteristics of granite at high temperatures.
In this paper, uniaxial compression tests of granite at different temperatures (25

Experimental Methodology
Granite was chosen from Shandong province of China, which is mainly comprised of feldspar, quartz, mica, and so on, based on X-ray diffraction analysis (Figure 1).Due to the internal volume limit of the high temperature environment furnace, according to the International Society of Rock Mechanics (ISRM) standard [30], 25 mm diameter rock specimens with the height-to-diameter ratio of 2 were used in the test.e average density of granite is 2.612 g/cm 3 at room temperature.

Test Equipment.
e test was completed in the State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology.
e main equipment used in this test includes a MTS810 material testing system (Figure 2(a)), a MTS652.02high temperature environment furnace matched with MTS810 (Figure 2(b)), and the PCI-2 all-digital AE monitoring system of American Physical Acoustics Corporation (experimental system) (Figure 2(c)).

Test Procedure and Method.
e process of whole test is divided into two parts.(1) Firstly, rock samples were heated to the preset temperatures of 200 °C, 400 °C, 600 °C, 800 °C, and 1000 °C at a heating rate of 50 °C/min in MTS 652.02.e high temperature was kept for 20 minutes to ensure that the rock samples were heated evenly.
ere are three samples at each temperature point.(2) Secondly, the uniaxial compression test was carried out by MTS810 using displacement control, at the loading rate of 0.005 mm/s at high temperatures.Considering the effect of reducing ambient noise and improving signal acquisition reliability, the AE threshold was set to 45 dB and the amplifier was set to 40 dB.
e operating frequency of the NANO-30 sensor is 100∼400 kHz, the lower limit of the filter parameters was set to 100 kHz, the upper limit was set to 400 kHz, a total of 1024 data were collected in every incident event, and the acquisition rate was 1 MHz.At the beginning of the compression test, the AE signal was monitored and recorded at the same time.

Test Results and Discussions
3.1.Mechanical Properties.Typical stress-strain curves are selected under uniaxial compressive tests for each group of temperature, as shown in Figure 3. e stress-strain curves show similar shape in general and can be divided into four stages of compaction, elasticity, yield, and failure; this result is the same as that of most of the researches [1][2][3][4][5][6][7].
Since there are three rock samples at the same temperature, Figure 4 gives the average value of peak stress and peak strain with temperature (the phase transition line is at 573 °C, when the quartz changes from α phase to β phase), and two kinds of curves can be divided into four stages.
(1) e first stage is from 25 °C to 400 °C.At   However, the peak strain increases to 1.29% of 800 °C, increased 21.28% compared to 600 °C.(4) e fourth stage is from 800 °C to 1000 °C.Quartz changes from β-to β-squamous quartz at 870 °C [33], causing peak stress decreased to 24.82 MPa at 1000 °C, 21.51% compared to 800 °C.e peak strain increases rapidly to 1.99% of 1000 °C, with an increase of 54.11% compared to 800 °C.e rise of temperature causes the enhancement of rock molecules' thermal motion and leads to the weakness of rock cohesion, and then the grain surface is more likely to slip, and the plasticity is more obvious at high temperature.

AE Characteristics.
AE signal is directly related to the evolution of rock damage.e internal cracks in the rock are evolved and damaged during uniaxial compression tests; the energy contained in the rock will be released in the form of elastic waves, and these weak signals can be monitored and recorded by AE sensors.So, the AE technology has become an important way to study rock damage mechanism and predict rock failure.According to the experimental data, the stress-strain curve, the AE ring count rate, and the accumulated AE ring counts subjected to the temperature of 25 °C to 1200 °C are shown in Figure 5.

Advances in Materials Science and Engineering
It can be seen that the AE ring count rate is corresponding to rock stress-strain curves at various temperatures.Firstly, the AE signal is very small at the rock compaction stage and then increases slightly at elastic deformation stage due to the germination of microcracks.With the increase of loading, the AE signal increases obviously because of the expansion of rock internal cracks and reaches the maximum value at rock peak stress, and then it decreases gradually until the sample is completely damaged.
Figure 6 shows that the change of accumulated AE counts with temperature is consistent with the change of peak stress but the variation range is inconsistent.From 25 °C to 600 °C, the accumulated AE counts decrease from 22.91 ×10 5 to 1.35 × 10 5 , with a decrease of 94.10%, and the peak stress decreases by 62.03%.From 600 °C to 800 °C, the accumulated AE counts increase rapidly and reach the maximum value of 25.34 × 10 5 of 800 °C, this may be due to a large number of microscopic cracks that extend to macroscopic cracks at high temperatures, and rock plasticity is signi cantly enhanced.
ere is no obvious variation in peak stress at this stage; the reason has been explained in Section 3.1.From 800 °C to 1000 °C, the accumulated AE counts have a decline of 57.58% and peak stress decreases by 21.51% compared to 800 °C.
3.3.Failure Mode.Not only rock strength, but also the failure mode was a ected by high temperature.Granite is composed of various mineral crystals, with regional, noncontinuous, heterogeneous, and other physical properties.After subjected to di erent high temperatures, the change of rock internal grain structure will lead to di erent failure modes.
Figure 7 shows di erent rock failure modes under uniaxial compression tests.From 25 °C to 200 °C, rock failure transforms from single splitting surface to multisplitting surface, which is mainly caused by tensile cracks at this stage, and the failure surface is parallel to axial stress.At 400 °C, there is an incomplete penetrating shear crack after rock failure, rock surface is stripped, and the grain is loose.is is because rock failure is caused by the common role of tension and shear.When temperature reaches 573 °C, the rock sample undergoes phase transition, the cohesion between the particles becomes weak, and the shear crack propagates and converges.erefore, there are more cracks and the rock shows the ideal shear failure type at 600 °C; then, the rock failure type changes from double shear rupture at 800 °C to completely integral rupture at 1000 °C.

Analysis of Damage Characteristics
4.1.Mechanical Damage (D M ) Caused by Loading.Since the evolution of rock microcracks under loading is a random process, the microintensity can be described using the Weibull statistical distribution, which is expressed as [34] where ϕ(ε) is the probability of rock microscopic element damage m and α are the Weibull distribution parameters.A large number of research results show that the accumulated AE ring count is corresponding to the slip of dislocations, the initiation of microscopic cracks, and the expansion of macroscopic cracks in rock materials.In essence, the AE activity is a statistical law, so it must be consistent with the statistical distribution of rock internal aws.If the accumulated AE ring count is Ω m when the rock specimen is completely damaged, then the accumulated AE ring count when the strain increased to ε is Substituting ( 1) into (2), we get Comparing ( 3) and ( 4), D M can be expressed as According to (5), the rock mechanical damage evolution curve under uniaxial compression test at room temperature is shown in Figure 8.
e process of rock mechanical damage under uniaxial compression can be divided into four stages.(1) Initial damage stage I. D M is very small.At this stage, the rock sample is in the microcrack enclosed phase and the initial microcracks and ssures do not start to expand and the AE ring count is few.( 2 e original and new cracks are continuously expanding and merging through the rock, and nally forming macroscopic cracks. e release of elastic strain energy increases dramatically, manifesting as unusually active AE activities, which corresponds to rock unsteady expansion.(4) Destructive stage IV.D M in this stage tends to be gentle and gradually increases to 1 with the increase of strain.e formation of main rupture surface causes a sudden release of stress, resulting in a rapid decline in rock strength.It can be seen that D M de ned by the accumulated AE ring counts can well re ect the whole progressive failure of the rock.
Figure 9 shows that the rock mechanical damage evolution slows down as the temperature increases, indicating that temperature has already caused thermal damage in rock samples.

ermal Damage (D T ) Caused by
Temperature.Many researchers found that rock elastic modulus is the function of temperature [35], so it may be de ned as D T to describe the temperature e ect on rock mechanical performances.Assuming D T is zero at 25 °C and then at the temperature of T, D T can be de ned as follows: where E 0 is the elastic modulus of granite at 25 °C and E T is the elastic modulus at the temperature of T. Table 1 gives the  Advances in Materials Science and Engineering average values of elastic modulus and D T at di erent temperatures.e average elastic modulus shows logistic decline with the rise of temperature (Figure 10), and the tting function is y 0.506 + 7.325 1 +(x478.700) 2.536 , R 2 0.996.
While the average thermal damage shows logistic increase with the rise of temperature (Figure 11), the tting function is e high temperature leads to the increase of rock molecules thermal motion, and the thermal expansion of various minerals across the grain boundary is not coordinated, resulting in a large number of microcracks.With the increase of temperature, these microcracks are expanded and penetrated, leading to the deterioration of rock mechanical properties.

Total Damage (D) Caused by ermomechanical
Coupling.Under the action of temperature and loading, the rock shows di erent damage characteristics.e total damage of the loaded rock at high temperature conditions can be derived from Lemaitre's strain equivalence principle [36], and the total damage D can be calculated by the following equation [37]: According to (9), the curves of rock total damage with axial strain and axial stress at various temperatures are shown in Figures 12 and 13. e initial D is the corresponding With the rise of temperature, the growth trend of rock total damage slows down.At the same damage value, the corresponding strain becomes larger.It means that the rise of temperature causes the intensi cation of Advances in Materials Science and Engineering dislocation movement between rock particles, leading to the weakness of rock strain recovery ability, and thus, the plasticity is enhanced.Figure 13 indicates that D is not only related to the stress state, but also related to the temperature.
By di erentiating (9) to axial strain, the damage evolution rate of rock can be obtained, and the curves are shown in Figure 14.
As the accumulated AE counts, the curve of the rock damage evolution rate also has a good correspondence with stress-strain curves.
e area surrounded by the damage evolution rate curve is just the value of rock mechanical damage.
e maximum damage evolution rate of rock shows logistic decline with the rise of temperature (Figures 15 and  16); the logistic tting function is y −3969.859+ 15428.98 1 +(x0.0611) 0.104 , R 2 0.875.(10) It needs to be emphasized here that the rock AE events during uniaxial loading are not increased monotonically but show the law of "interval burst" and "relatively calm," that is, after each burst of AE events, the AE number is minimal for the next period of time, and this phenomenon is not just before peak stress but in the whole compression test.e "interval burst" and "relatively calm" phenomena can be explained from the energy point of view.When the rock is subjected to external loading, the energy inside the rock will be released, resulting the number of AE events to rise sharply; then the rock will be in the state of "pressure relief" after energy release, and AE events will drop down and show "calm."With the increase of loading, the internal energy will transfer from the "pressure relief" state to the "balanced" state.When loading is further increased, the rock in the "balanced" state will once again release energy, leading to the number of AE ring counts to increase dramatically.It should be noted that the AE "calm" state explained here is not an absolute sense of zero AE event, but a relative concept.

Conclusions
rough the uniaxial compression AE test of granite at di erent high temperatures (25 °C, 200 °C, 400 °C, 600 °C, 800 °C, and 1000 °C), the rock mechanical properties, AE characteristics, failure modes, and damage evolution curves were all analyzed.e thermal damage is de ned by the elastic modulus, the mechanical damage is obtained by AE ring count rate, and the total damage is derived by Lemaitre's strain equivalence principle.e law of rock damage evolution is corresponding to experimental phenomena at di erent temperatures, which veri es that it is reasonable and feasible to establish a rock damage model by using AE technology.e conclusions are as follows: (1) e rock stress-strain curve can be divided into four stages of compaction, elasticity, yield, and failure.e rise of temperature leads to the weakness of rock brittleness and the enhancement of rock plasticity.
(2) e AE ring count rate of rock shows the law of "interval burst" and "relatively calm," which can be explained from the energy point of view.Advances in Materials Science and Engineering microcracks compaction, initiation, expansion, and destruction.With the rise of temperature, the growth trend of total damage slows down and the maximum damage evolution rate shows logistic decline.
) Stable development stage II.D M increases steadily with the increase of strain.e rock crack begins to expand, releasing stable AE signals, which corresponds to the elastic phase of stress-strain curve.(3) Accelerated development stage III.D M increases dramatically.

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°C, 200 °C, 400 °C, 600 °C, 800 °C, and 1000 °C) are carried out, and AE signals in the deformation and failure process are monitored simultaneously.Rock mechanical properties, AE characteristics, failure modes, and damage evolution laws are analyzed.e results can provide useful references to predict rock failure at high temperatures.

Table 1 :
Mechanical and damage values of granite at di erent temperatures.