# Study on Damage Behavior and Its Energy Distribution of Deep Granite at High-Temperature Conditions

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## Abstract

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## 1. Introduction

## 2. Acoustic Emission Test of Fractured Rock under Triaxial Loading

#### 2.1. Instrument and Control Method

- (1)
- PCI-II acoustic emission test system: In order to reduce the interference of environmental noise during the test, the preamplifier gain and trigger threshold value were set to 40 dB, and the sampling frequency was 0.5 MHz. For the uniaxial compression test, an acoustic emission sensor (Micro 30) was placed in the middle of the rock sample, and vaseline was coated between the rock sample and the sensor to provide good acoustic coupling.
- (2)
- For the tubular high-temperature furnace, we used the programmable high-temperature furnace from the Metallurgical Laboratory of University of Science and Technology Beijing, as shown in Figure 1. The highest heating temperature of the high-temperature furnace is 1000 °C. Temperature control precision is less than 2 °C. The display precision is 1 °C, and the heating rate is controllable at 1 °C/min.
- (3)
- The pressure chamber can apply a radial force of 200 MPa, and can monitor the compression deformation of samples in real time. The maximum pressure of the high-precision oil pressure control system is 200 MPa, precision is 0.01 MPa, directly connected with the high-pressure chamber; the three-way valve system is mainly for loading and unloading of oil inlet valve and oil return valve control, control precision is 0.05 MPa; the ultra-high pressure hand pump can apply the maximum pressure is 200 MPa. Three kinds of confining pressures (0 MPa, 10 MPa, and 20 MPa) are designed. The loading was similar to the conventional triaxial test, and the axial pressure and confining pressure were loaded alternately with a gradient of 5 MPa each time. When it reached the design value, the axial loading rate was 0.02 mm/min to failure.

#### 2.2. High-Temperature Damage Test and Analysis of Rock

^{3}.

_{s}) after high-temperature heating treatment. According to the preparation method of saturated sample suggested by ISRM, the sample was saturated and weighed (M

_{sat}). The effective porosity of the sample (hereinafter referred to as porosity) n can be calculated,

## 3. Acoustic Emission Test Results and Analysis of Fractured Rock under Triaxial Loading

#### 3.1. Total Stress–Strain Curve and Failure Mode

#### 3.2. Effect Analysis of Equivalent Damage Factors on Rock Energy Evolution

^{d}conversion rate. Figure 9 and Figure 10 show the variation curves of dissipated energy conversion rate of samples under different confining pressures, which are used to reflect the damage rate of rock samples during deformation. Figure 9 and Figure 10 show the change curves of dissipated energy conversion rate of samples at 10 MPa and 20 MPa, respectively. It can be seen from Figure 9 and Figure 10 that the dissipation energy conversion rate is small in the pre-peak stage, while the dissipation energy conversion rate reaches the maximum at the point of maximum stress drop.

## 4. Discussion

- (1)
- In the research of rock mass engineering, the primary task is to obtain the distribution characteristics of anisotropic crack in rock mass by using ultrasonic borehole television technology. Using borehole TV, the crack dip angle in the scanning area is segmented statistics, so as to obtain the distribution law of crack occurrence. Secondly, by analyzing the relationship between crack tendency and crack depth, the statistical data of the dominant crack surface are obtained. Then, the number of fracture surfaces within each unit distance is counted to obtain the density distribution characteristics of the fracture surface. These steps are the basis for the study of fractured surrounding rock.
- (2)
- Because the failure of the granite specimens is sudden, the damage is gradual in the specimen before the failure. When the fissure degree in the rock develops to a certain extent, the fissure changes from a stable expansion to an unstable expansion, and then the fissure quickly passes through the rock, causing damage. Therefore, for brittle hard rock, if the support can be carried out before the fissure instability expansion, the development of fissure can be effectively controlled. For example, Wei et al. [41] has carried out 3D network simulation based on deep rock joint of borehole TV, hoping to achieve the purpose of evaluating the stability of surrounding rock by simulating and exploring the distribution law of fracture space. Therefore, the fissure degree corresponding to the inflection point of maximum dissipated energy is finally adopted in this paper as the target factor to measure the support time.
- (3)
- In the study of fractured rocks, the current research is more inclined to simplify fractures into one, two, or more visible artificial fractures [26,27,28,37,38,39], and then analyze the influence of the number of artificial fractures on rock mass deformation and failure, which can reflect the influence of fractures to a certain extent on the macro level. However, this simplified process completely ignores the influence of the interaction between disordered fractures on the evolution of rock deformation energy. Therefore, this paper adopts thermal damage to create this disordered fracture, and replaces the traditional fracture number with the crack degree. The results show that there is an inflection point of maximum dissipated energy change at the fissure degree D = (0.4~0.5). Before the inflection point, the maximum dissipated energy gradually increases, but the variation amplitude is small. This is because the consumption of plastic deformation energy at the crack tip increases during the deformation process, and the fracture development can reduce the brittleness of the sample and make the fracture in the rock more fully developed. After the inflection point, the maximum dissipated energy decreases rapidly, which is due to the development of fractures in the rock mass, which reduces the bearing capacity of the internal structure damage. Figure 12 shows the schematic diagram of the internal fracture degree of rock mass with surrounding rock deformation. Therefore, in engineering support, when the internal fracture degree of rock mass D = (0.4~0.5), the support can be used as the basis for the identification of critical support for key parts.

## 5. Conclusions and Future Work

- (1)
- With the increase in confining pressure, the peak stress and corresponding strain of rock samples with similar equivalent damage factors increase. However, compared with the same confining pressure rock specimens of different initial thermal damage found that when the confining pressure is the same, the greater the confining pressure, the difference in peak stress of different initial thermally damaged samples becomes smaller and smaller, when the confining pressure is 0 MPa, the maximum difference of peak stress is 6 MPa, but when the confining pressure is 10 MPa and 20 MPa, the peak stress is almost identical, and the difference of corresponding peak strain does not decrease with the increase in confining pressure, and is always stable between 0.006 and 0.007. The results show that the peak stress is sensitive to confining pressure and the peak strain is sensitive to the equivalent fracture damage factor.
- (2)
- For rocks with similar equivalent damage factors, the greater the confining pressure, the less the influence of equivalent damage factors inside the rock mass on the failure mode. The evolution of dissipated energy ratio of specimens with different initial thermal damage is similar in the compression deformation failure process under different confining pressures, and all specimens experience four stages, rapid increase → rapid decline → steady at a certain value → rapid rise. In addition, the proportion of dissipated energy of samples with equivalent damage factor D = 0.89 is significantly higher than that of other damaged samples, indicating that the development of internal cracks in granite samples is mutational, and the internal cracks in rock develop rapidly when the thermal stress reaches the threshold value of crack propagation.
- (3)
- Under the same fracture degree, the maximum energy dissipation changes greatly with the increase in confining pressure. Under the same confining pressure, the maximum energy dissipated during rock failure increases slowly first and then decreases rapidly with the increase in fracture degree. Taking 20 MPa as an example, the maximum dissipated energy density remains stable at 3.5–3.6 MJ∙m-3 at D = (0.4~0.5). Before this, the dissipated energy density increases monotonically, and then slowly decreases. Therefore, there is a maximum inflection point at the fissure D = (0.4~0.5). So, when the internal fracture degree of rock mass D = (0.4~0.5), it can be used as the discriminant basis for critical support in engineering support.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Tubular high-temperature heating furnace and mechanical test system: (

**a**) high temperature Muffle furnace; (

**b**) MTS 815 press; (

**c**) load the local magnification picture of the specimen.

**Figure 2.**Relationship between granite porosity and p-wave velocity with temperature: (

**a**) the porosity variation of samples treated at different temperatures; (

**b**) variation of longitudinal p-wave velocity of samples.

**Figure 3.**Stress–strain curves under different confining pressures: (

**a**) D = 0.16; (

**b**) D = 0.36; (

**c**) D = 0.51; and (

**d**) D = 0.89.

**Figure 4.**Variation of characteristic mechanical parameters of rock with fractures under different confining pressures:(

**a**) peak strain; (

**b**) peak stress; and (

**c**) modulus of elasticity.

**Figure 5.**Energy evolution of the sample under 10 MPa: (

**a**) D = 0.16; (

**b**) D = 0.36; (

**c**) D = 0.51; and (

**d**) D = 0.89.

**Figure 6.**Energy evolution of the sample under 20 MPa: (

**a**) D = 0.16; (

**b**) D = 0.36; (

**c**) D = 0.51; and (

**d**) D = 0.89.

**Figure 8.**Relationship between dissipation ratio and strain of samples under different confining pressures:(

**a**) Confining pressure: 10 MPa; (

**b**) Confining pressure: 20 MPa.

**Figure 9.**Dissipation energy conversion rate of the sample under 10 MPa: (

**a**) D = 0.16; (

**b**) D = 0.36; (

**c**) D = 0.51; and (

**d**) D = 0.89.

**Figure 10.**Dissipation energy conversion rate of the sample under 20 MPa: (

**a**) D = 0.16; (

**b**) D = 0.36; (

**c**) D = 0.51; and (

**d**) D = 0.89.

**Figure 11.**The relationship between the maximum dissipation energy conversion rate of each sample and confining pressure.

**Figure 12.**The schematic diagram of the internal fracture degree of rock mass with surrounding rock deformation.

Confining Pressure/MPa | Equivalent Damage Factor (D) | |||
---|---|---|---|---|

D = 0.16 | D = 0.36 | D = 0.51 | D = 0.89 | |

0 MPa | ||||

10 MPa | ||||

20 MPa |

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**MDPI and ACS Style**

Zhou, M.; Qiao, L.; Li, Q.; Yang, J.
Study on Damage Behavior and Its Energy Distribution of Deep Granite at High-Temperature Conditions. *Appl. Sci.* **2023**, *13*, 6498.
https://doi.org/10.3390/app13116498

**AMA Style**

Zhou M, Qiao L, Li Q, Yang J.
Study on Damage Behavior and Its Energy Distribution of Deep Granite at High-Temperature Conditions. *Applied Sciences*. 2023; 13(11):6498.
https://doi.org/10.3390/app13116498

**Chicago/Turabian Style**

Zhou, Ming, Lan Qiao, Qingwen Li, and Jianming Yang.
2023. "Study on Damage Behavior and Its Energy Distribution of Deep Granite at High-Temperature Conditions" *Applied Sciences* 13, no. 11: 6498.
https://doi.org/10.3390/app13116498