Precursors of Cyclic Loading and Unloading Sandstone Failure Based on “Acoustic-Thermal” Loading–Unloading Response Ratio

Abstract

Coal mining often causes periodic disruption in the rock mass around the stope. The study of the deformation and failure characteristics of cyclic loading and unloading sandstone is very critical for gaining a thorough understanding of the mechanisms of rock damage, degradation, and failure. This kind of investigation is very helpful in determining the precursors of rock failure and the instability of engineering structures. In this research study, the properties of acoustic emission and infrared radiation of cyclic loading and unloading sandstone are explored using a cyclic loading and unloading sandstone experiment. Based on acoustic emission and infrared radiation, the loading–unloading response ratio of rock is established. It is found that the response variables of sandstone during the loading stage based on acoustic emission (AE) counts and the loading–unloading response ratio based on average infrared radiation temperature (AIRT) both rise suddenly in the last cycle, which may be a precursor of “acoustic-thermal” approaching rock failure. On this basis, the quantitative analysis index of infrared radiation of differential infrared energy change rate (DIECR) is proposed, that is, the change of square of ΔAIRT in unit time, and based on AE counts and DIECR, the loading–unloading response ratio of “acoustic-thermal” is defined. It is found that the “acoustic-thermal” loading–unloading response ratio suddenly increases during the penultimate cycle of loading and unloading. This feature can be taken as the initial precursor of rock failure. Together with the “acoustic-thermal” imminent failure precursor of rock, it constitutes the “initial precursor-imminent failure precursor” combined with the internal fracture and surface infrared radiation temperature field during the cyclic loading and unloading process of rock, realizing the hierarchical monitoring and early warning of cyclic loading and unloading rock failure. The research results lay a theoretical and practical foundation for using infrared radiation to monitor engineering disasters caused by rock fracture and failure in mining engineering.

1. Introduction

During the mining of coal resources, the coal rock in front of the working face undergoes a dynamic process characterized by an increase in original rock stress and axial stress, as well as a decrease in confining pressure (unloading), eventually leading to rock failure. Affected by the disturbance of loading and unloading, the mechanical performance of rock mass under cyclic loading is one of the important factors affecting the long-term stability of the projects. The mechanical behavior and catastrophic process of coal and rock under cyclic loading will become extremely complex [1,2,3,4]. Therefore, it is of great significance to analyze the mechanical characteristics of rocks in the process of cyclic loading and unloading and to study and capture the failure precursors of rocks in the process of cyclic loading and unloading for monitoring the stability of rocks in coal mining faces.

Yin et al. [5,6,7,8] put forward the concept of loading–unloading response ratio because of the disturbance characteristics of rock materials during the cyclic loading and unloading process, proving that the loading–unloading response ratio has the same physical mechanism as the accelerated release of energy, and tried to predict the mine earthquake using loading–unloading response ratio theory. Song [9] studied the temporal and spatial evolution characteristics of the loading–unloading response ratio in earthquake prediction and obtained the migration direction and migration rate of the abnormal loading–unloading response ratio before the earthquake. Trotta [10] studied the sensitivity of loading–unloading response ratio theory to specific parameters when predicting certain earthquakes. Liu [11] studied the application of the loading–unloading response ratio to the characteristics of rock failure precursors by using REPA simulation software. Can et al. [12] used a solid lattice model to demonstrate that the loading–unloading response ratio will increase with the increase in load and then rise to the peak. Before the occurrence of the main fracture, the loading–unloading response ratio decreased sharply, and the concept of maximum fault orientation, namely the direction of maximum fault action, was proposed, forming a new method to calculate the loading–unloading response ratio.

According to previous research, the physical basis of rock fracture and damage is the ongoing growth of microscopic features such as pores and microcracks. Its essence is the mutual conversion between total strain energy, elastic strain energy, and dissipative strain energy, and the process of releasing energy to the external boundary in the form of electromagnetic radiation, heat energy, and kinetic energy [13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]. This also provides a theoretical basis for the use of acoustic emission and infrared radiation to monitor the damage and fracture process of mining rock. Acoustic emission technology is a common communication method that has the advantages of long transmission distance, strong anti-interference ability, low cost, easy positioning, simple operation, and easy access for ordinary people. At present, the application fields include underwater communication, vehicle communication, security monitoring, wireless capacitor communication, medical equipment, industrial automation, and other different industries and fields. Infrared radiation, as a new monitoring method, has the advantages of non-contact, convenient portability, and high measurement accuracy. The current application areas include thermal imaging, and infrared thermal imaging technology can be used to detect problems such as thermal damage, water pipe leakage, and energy loss in buildings; security monitoring and infrared radiation technology can be used to manufacture night vision devices, surveillance cameras, and other equipment. Infrared radiation technology can also be used for medical diagnoses, such as detecting diseases by detecting changes in body temperature on the surface of the human body. In the automotive industry, infrared radiation technology can be used to detect the engine temperature, tire temperature, etc. of vehicles, improving their performance and safety. In addition, infrared radiation technology is currently applied in the field of mining rock mechanics.

However, the change characteristics of infrared radiation during rock cyclic loading and unloading need to be further studied. Acoustic emission is used to monitor the fracture characteristics inside the rock, while infrared radiation is used to monitor the evolution characteristics of the temperature field on the rock surface. If the rock loading–unloading response ratio can be defined by using acoustic emission and infrared radiation, the internal and external monitoring of engineering rock mass fracture characteristics can be realized, and the stability of engineering rock mass can be better monitored. In this paper, a new index of infrared radiation (differential infrared energy change rate (DIECR)) is proposed. On this basis, the loading–unloading response ratio is defined by combining infrared radiation and acoustic emission to determine the failure precursor of rock. The research results provide an experimental theoretical basis for infrared remote sensing monitoring and early warning of mine disasters and rock engineering disasters in a better way.

2. Experimental Design

2.1. Experimental Equipment

In this study, the uniaxial loading machine was used as a loading machine having model cn.64, and manufactured by MTS Company of the United States. The maximum loading capacity of the loading machine is 1000 kN. The accuracy of load and displacement measurements is lower than 0.5%. The machine can work on different modes of loading, i.e., equal displacement and equal stress loading and cyclic loading and unloading. The FLIRA615 type of infrared camera equipment is used. Its measurement accuracy is not more than 0.02 °C, its maximum data acquisition rate is 50 times per second, its spatial resolution is 640 × 480 pixels, and its infrared radiation collecting wavelength range is 7.5–14 μm. The acoustic emission monitoring system model PCI-2 is used in the experiment, and its main technical parameters are: low noise of the acoustic emission channel, built-in waveform, and HIT processor; bandwidth range of 1 KHz–3 MHz; dynamic range greater than 85 dB; a digital signal processor that has a built-in 10-channel filter may perform real-time analysis on sampling while also being able to fulfill demands for high precision and reliability.

2.2. Rock Samples and Test Methods

In this study, the sandstone samples were collected from a coal mine (work face), Shandong, China. The rectangular representative samples have dimensions 50 nm × 50 nm × 100 mm. To maintain the same integrity and mineralogical composition, representative samples were extracted from the same boulder. After the extraction of representative coring samples, they were subjected to the polishing process with sandpaper to ensure the non-parallelism at both ends of the height and width were less than 0.3 mm and 0.05 mm, respectively. In this paper, five rock samples were processed, numbered A₁, A₂, A₃, A₄, and A₅, respectively. The rock sample was thoroughly treated before being wrapped in plastic film and taken for the experiment. Before experimenting, a layer of plastic film with a thickness of 0.9 mm must be applied to the upper and lower plats end of the testing apparatus. This layer should be made of polyphyllene terephthalate to prevent heat conduction between the rock sample and the end face of the press. This protection avoids the effect on experimental findings of infrared radiation observation. We arranged four acoustic emission probes on the two surfaces of the rock sample, as shown in Figure 1. Place the infrared thermal imager a meter in front of the rock sample, and make sure the infrared radiation, acoustic emission, and press are started simultaneously. Figure 2 illustrates the experimental setup. The data collection frequency of the press and infrared radiation equipment is set to 10 and 25 per second, respectively. Cyclic loading and unloading adopt the method of equal increment to load and unload, with each increment of 20 kN, and then unload to 5 kN; that is, the loading and unloading load path is 0-20 kN-5 kN-40 kN-5 kN-60 kN. The test will stop automatically when the rock is completely damaged. The loading and unloading speeds are 1 kN/s. The bottom area of the rock sample processed in this paper is 0.0025 m², so the loading and unloading stress path is equivalent to 0–8 MPa-2 MPa-16 MPa-2 MPa-24 MPa. According to the loading and unloading stress path, the curve of stress variation with the number of cycles in the process of cyclic loading and unloading of sandstone is drawn as shown in Figure 3. The maximum stress of this cyclic loading and unloading will increase by 8 MPa for every increase in the number of cycles.

3. Experimental Results

The average infrared radiation temperature (AIRT) is a type of infrared radiation index. This reflects the overall infrared radiation intensity of the loaded and unloaded rock surfaces. It can be calculated by using Equation (1) [28]:

$$AIR{T}_p=\frac{1}{M}\frac{1}{N}{\displaystyle \sum _{y=1}^N{\displaystyle \sum _{x=1}^M{f}_p(x,y)}}$$

(1)

where f_p is the temperature value at a certain point on the rock surface, and f_p is a matrix. p is the number of frames of infrared radiation data, and x and y are the number of rows and columns of infrared radiation two-dimensional matrix data, respectively.

During the cyclic loading and unloading of sandstone, the dissipative strain energy promotes the initiation, development, expansion, and coalescence of its internal primary pores and microcracks. This ultimately causes the failure of sandstone. At the same time, the expansion and development of pores and microcracks in sandstone will cause the response of acoustic emission and infrared radiation signals on the surface. AE counts reflect the number and degree of micro-fractures in the rock and are used to calibrate the damage fracture of loaded rock. Figure 4 shows the load–displacement curve during the loading and unloading of the rock cycle. As shown in Figure 4, the peak loads of samples A₁–A₄ are 310 kN, 239 kN, 215 kN, and 219 kN, respectively, with corresponding displacement values of 2.58 mm, 2.69 mm, 2.77 mm, and 2.15 mm. It should be noted that both rock samples A₁ and A₂ failed during the loading stage. The theoretical peak load of rock sample A₁ during the last cyclic loading was 320 kN. When loaded to 310 kN, due to insufficient bearing capacity to support the pressure of the press, a brief stress drop occurred, and rock burst failure occurred. Rock sample A₂ formed a large hysteresis loop during the penultimate cycle of loading and unloading, which produced large dissipative strain energy during this cycle of loading and unloading, promoted the rapid development of pores and microcracks in the rock, and reduced the bearing capacity of the rock, leading to rock burst failure after the last cycle loading did not reach the peak value of the last cycle loading, and a short stress drop occurred at 214 kN. Figure 5 shows the change curve of rock stress, AIRT, and AE counts with time under loading and unloading. As shown in Figure 5, the AE counts in the first three cycles of loading and unloading of sandstone are slightly higher than those in the subsequent cycles of loading and unloading. This is because irreversible pore fissure compaction occurred in the initial stage of the cyclic loading and unloading of sandstone; although the deformation of rock in the subsequent cycles of loading and unloading is mainly elastic. When rock sample A₁ is loaded and unloaded in the penultimate cycle, the AE counts start to show a large mutation, which indicates the beginning of a large-scale internal fracture of rock; that is, the rock will be damaged. During the loading and unloading process of sandstone, the variation trend of the AIRT curve and stress curve has a good consistency. The AIRT curve shows an upward trend during the loading phase and a downward trend during unloading. As the AIRT decline during unloading is greater than the AIRT rise during loading, the AIRT overall shows a downward trend during the cyclic loading and unloading process of sandstone. Based on their investigation of this phenomenon, the authors suggest that the thermal mechanism of sandstone during cyclic loading and unloading is primarily the thermoelastic effect, that is, the temperature rise produced by elastic deformation. When the sandstone reaches the stress unloading condition, the elastic deformation, i.e., the heat absorption phenomenon, will return. The temperature is currently dropping. As a result, when the sandstone is loaded, the temperature rises, and when it is unloaded, the temperature drops. Furthermore, heat generated by elastic deformation during loading may be absorbed when the sandstone is unloaded. Microfracture will occur during the cyclic loading and unloading of rock. A previous study has shown that when a tensile microfracture occurs, the temperature reduces, and when a shear microfracture occurs, the temperature rises [29]. AIRT displays a negative trend in the process of rock cyclic loading and unloading, indicating that the number of tensile microcracks during cyclic loading and unloading is larger than the number of shear microcracks. Furthermore, heat will be generated by the friction between particles induced by irreversible deformation during rock cyclic loading and unloading. In conclusion, the thermoelastic effect causes the temperature to rise during the loading process, while the elastic deformation recovery phenomenon causes the temperature to drop during the unloading process. The shear microfracture and friction heat phenomenon cause the temperature to rise, and the tension microfracture causes the temperature to drop. A minor amount of heat dissipation may occur during rock loading and unloading, resulting in an overall decrease in AIRT.

4. Loading–Unloading Response Ratio

4.1. Loading–Unloading Response Ratio Based on Acoustic Emission

The loading–unloading response ratio theory is a nonlinear theory derived from earthquake prediction research that has been partially studied and applied in earthquake prediction as well as disaster prediction such as landslides, rock bursts, reservoir earthquakes, and engineering health detection.

The theory of loading–unloading response ratio is proposed according to the stress–strain constitutive curve of materials. Its starting point is based on the difference between the ratio of the loading stage response and the unloading stage response of the system under stable and unstable conditions. It can be used to study the characteristics of system instability precursors and predict system instability [1]. The main idea is that for a system, the load P (which can be input parameters such as stress) and the response variable R (which can be output parameters such as strain) are considered to have a small change ΔP in P and a change ΔR in R, defined as the response quantity X. When the system is stable, X is near a constant, but when the system tends to become unstable, its value significantly increases. Let X+ and X− be the response quantities when loading ΔP > 0 and unloading ΔP < 0, respectively. The dimensionless number is defined as the loading–unloading response ratio. To quantitatively characterize the difference between loading response and unloading response, the following two basic quantities are defined: the first is the response quantity X, which is defined as [30]:

$$X=\frac{\Delta R}{\Delta P}$$

(2)

Among them, ΔP and ΔR represent the increments of load P and response variable R. The other is the loading–unloading response ratio, which is defined as:

$$Y=\frac{X_{+}}{X_{-}}$$

(3)

where Y is the loading–unloading response ratio.

Yang et al. [31] showed that the following relationship exists between damage variable D and acoustic emission ringing frequency N:

$$D=\frac{N_{}}{N_{\mathrm{m}}}$$

(4)

where N is the acoustic emission count after the material has sustained internal damage from the load, and N_m is the cumulative acoustic emission count after the material has been completely damaged.

The change rate of damage variable D during the loading and unloading of sandstone is $\Delta D_{+}$ and $\Delta D_{-}$, respectively. The acoustic emission counts are generated during loading and unloading. Which can be used for D calculation in the loading and unloading process. It can be calculated by using Equations (3) and (4):

$$D_{+}=\frac{N_{+}}{N_{\mathrm{m}}}$$

(5)

$$D_{-}=\frac{N_{-}}{N_{\mathrm{m}}}$$

(6)

$$\frac{\Delta D_{+}}{\Delta D_{-}}=\frac{N_{+}}{N_{-}}$$

(7)

The relationship between AE counts and loading–unloading response ratio can be defined as:

$$Y=\frac{\Delta D_{+}}{\Delta D_{-}}=\frac{N_{+}}{N_{-}}$$

(8)

By processing the AE counts in the above formula, the loading–unloading response ratio represented by the AE counts can be calculated, as shown in Figure 6. This shows that the response variable of the rock sample in the loading stage presents a changing trend of “rapid decline—constant—rapid rise”. The response variable of rock sample A₁ in the unloading stage presents a changing trend of “rapid decline—constant—rapid rise”, while rock sample A₂ presents a stable change trend as a whole. The loading–unloading response ratio curve of rock sample A₁ fluctuates as a whole, with a sudden increase in the last cycle, while the loading–unloading response ratio curve of rock sample A₂ decreases first and then changes gently as a whole. The response variable of rock sample A₁ in the loading stage during the penultimate cycle loading and unloading is 477.6 MPa⁻¹, and the last cycle loading and unloading has a significant sudden increase. The value after the sudden increase is 3838.5 MPa⁻¹, which is 8.04 times the former. The response variable of rock sample A₂ in the loading stage during the penultimate cycle loading and unloading is 1591.3 MPa⁻¹, and the last cycle loading and unloading has a significant sudden increase. The value after the sudden increase is 6295.0 MPa⁻¹, which is 3.96 times the former. The response variables of rock samples A₃ and A₄ during the loading stage also undergo a sudden change during the last cycle of loading and unloading. The last sudden increase in response variable in the loading stage of a rock sample can be used as a precursor of rock failure.

4.2. Loading–Unloading Response Ratio Based on Infrared Radiation

The elastic deformation and plastic deformation in the process of cyclic loading and unloading of rock cause thermoelastic and frictional heat effects, respectively. These lead to a change in infrared radiation temperature on the rock surface. Previous study findings indicate that the control effect of stress on infrared radiation is universal, simultaneous, and significant [20]. Based on this, the authors propose to use the infrared radiation index to define the loading–unloading response ratio of rock. The AIRT is the most common index for studying the temperature characteristics of the rock surface. This can represent the overall intensity of infrared radiation on the rock surface. The load is the core variable of this experiment, and various other physical and mechanical parameters are affected by it. Usually, the change in stress is selected as the denominator of the response variable to measure the response during the loading or unloading stage. The authors try to establish the loading–unloading response ratio formula based on the AIRT and take the stress and AIRT as the load variable and response variable, respectively. This can be calculated by using Equation (7):

$$X=\frac{\Delta R}{\Delta P}=\frac{\Delta AIRT}{\Delta \sigma }$$

(9)

where X is the response quantity, ΔR is the change in response, ΔP is the change in load, and $\Delta AIRT$ is the change in AIRT.

To modify Equation (7) for the loading and unloading process, the AIRT-based loading–unloading response ratio formula based on the AIRT is defined as:

$$Y=\frac{X_{+}}{X_{-}}=\frac{\Delta AIR{T}_{+}}{\Delta {\sigma }_{+}}/\frac{\Delta AIR{T}_{-}}{\Delta {\sigma }_{-}}$$

(10)

where + and − represent the loading and unloading stages, respectively.

Figure 7 shows the response quantity based on AIRT loading stage, unloading stage, and loading–unloading response ratio in the rock cyclic loading and unloading process. This depicts that the AIRT response of rock sample A₁ in the loading stage fluctuates with the increase in unloading stress, rising from 0.506 °C/MPa at the unloading stress of 40 MPa to 0.811 °C/MPa at the unloading stress of 120 MPa. The AIRT response of rock sample A₂ in the loading stage shows a “W”-shaped change trend with the increase in unloading stress. The AIRT response in the loading stage is 0.858 °C/MPa when the unloading stress is 24 MPa and 0.987 °C/MPa when the unloading stress is 96 MPa.

The AIRT response of rock samples A₁ and A₂ in the unloading stage shows an overall decreasing trend. For example, for sample A₁, at the unloading stress of 40 MPa, the AIRT response is 1.310 °C/MPa; at the unloading stress of 120 MPa, the AIRT response is 0.861 °C/MPa; and the overall decrease in the AIRT response is 0.449 °C. Whereas, for the rock sample A₂, at the unloading stress of 24 MPa, the AIRT response is 1.605 °C/MPa; at the unloading stress of 96 MPa, the AIRT response is 0.726 °C/MPa; and the overall decrease in the AIRT response is 0.879 °C. The AIRT loading–unloading response ratio curve of rock samples A₁ and A₂ shows an overall upward trend with the increase in unloading stress. The AIRT loading–unloading response ratio of rock sample A₁ increases from 0.388 °C/MPa at the unloading stress of 40 MPa to 0.942 °C/MPa at the unloading stress of 120 MPa, and rock sample A₂ increases from 0.534 at the unloading stress of 24 MPa to 1.360 at the unloading stress of 96 MPa. In addition, the AIRT loading–unloading response ratio curves of rock samples A₁–A₄ showed a sharp increase in the last cycle of loading and unloading. The authors proposed that the mutation of the AIRT-based loading–unloading response ratio in the last cycle of loading and unloading be taken as a precursor of rock failure. As for the cause of the sudden change, the authors believe that the microcracks in the rock rapidly developed during the last cyclic loading, generating a large number of microcracks (this view can also be verified from the acoustic emission counting curve in Figure 5). The rapid increase in microcracks led to an increase in AIRT changes, which led to an increase in AIRT response during the loading phase. The deformation in the loading phase is mainly irreversible plastic deformation, which will affect the size of the AIRT change in the unloading phase. Therefore, the AIRT response in the unloading phase decreases in the last cycle of loading and unloading, resulting in a sudden increase in the AIRT-based loading and unloading response ratio.

4.3. Loading–Unloading Response Ratio Based on Differential Infrared Energy Change Rate (DIECR)

The AIRT is a commonly used indicator to characterize the infrared temperature field on the rock surface. However, the AIRT has an upward and downward trend during the uniaxial loading and cyclic loading and unloading process of rocks. To reflect the change rate characteristics of the infrared radiation temperature field on the rock surface in real time, this paper defines a new index of DIECR, which can be calculated by using Equation (9):

$$DIECR=\frac{{(\Delta AIRT)}_{i+1}^2{}_{}-{(\Delta AIRT)}_i^2}{T_{i+1}-T_i}$$

(11)

where DIECR is the change rate of differential infrared radiation energy, ${(\Delta AIRT)}_{i+1}^2$ and ${(\Delta AIRT)}_i^2$ are the infrared radiation energy at the $T_{i+1}$ and $T_i$ time, respectively.

DIECR illustrates the trend of infrared radiation energy change over time. In comparison to the infrared radiation energy index, the DIECR can more clearly express the change and adjustment of the infrared radiation energy of rocks, as well as remove the cumulative heat (thermal-mechanical coupling) impact in the loading and unloading of rocks. Figure 8 depicts the stress and DIECR curve of rock during cyclic loading and unloading. The DIECR curve exhibits a consistent fluctuation trend as cyclic loading and unloading occurs, and the fluctuation amplitude rises as unloading stress increases. It is simpler to represent the internal link between stress and infrared radiation during rock cyclic loading and unloading using the DIECR index as a loading and unloading response variable. The loading–unloading response ratio formula is established based on DIECR, which can be calculated by using Equation (10):

$$X=\frac{\Delta R}{\Delta P}=\frac{\Sigma \left|DIECR\right|}{\Delta \sigma }$$

(12)

Then the expression of the loading–unloading response ratio is:

$$Y=\frac{X_{+}}{X_{-}}=\frac{\Sigma |DIECR{|}_{+}}{\Delta {\sigma }_{+}}/\frac{\Sigma |DIECR{|}_{-}}{\Delta {\sigma }_{-}}$$

(13)

Figure 9 shows the loading, unloading response, and loading–unloading response ratio based on DIECR in the process of rock cyclic loading and unloading. This shows that the DIECR response and loading–unloading response ratio in the loading stage of rock samples generally rise and change in a nearly straight line with the increase in unloading stress. The unloading response of rock sample A₁ shows a stable change trend with the increase in unloading stress, while the unloading response of rock samples A₂, A₃, and A₄ shows a slow increase trend and slightly decreases at the last cycle of loading and unloading.

4.4. Loading–Unloading Response Ratio Based on “Acoustic-Thermal”

There are changes in infrared radiation and acoustic emission signal in the process of rock fracture. The acoustic emission mainly monitors the internal microfracture signal in the process of rock loading fracture, and infrared radiation is the surface response signal of the internal microfracture signal. By analyzing the apparent correlation between acoustic emission and infrared radiation, we can lay the foundation for revealing the infrared radiation response mechanism and building a loaded rock constitutive model based on infrared radiation. In this paper, acoustic emission and infrared radiation are used to construct the response variable and loading–unloading response ratio of sandstone during cyclic loading and unloading. The loading and unloading response variables are defined as:

$$X=\frac{\Delta R}{\Delta P}=\frac{\Sigma \left|DIECR\right|}{\Sigma (\Delta AE)}$$

(14)

Then the loading–unloading response ratio formula is:

$$Y=\frac{X_{+}}{X_{-}}=\frac{\Sigma |DIECR{|}_{+}}{\Sigma {(\Delta AE)}_{+}}/\frac{\Sigma |DIECR{|}_{-}}{\Sigma {(\Delta AE)}_{-}}$$

(15)

In the formula, $\Sigma (\Delta AE)$ is the accumulation of AE counts during the cyclic loading and unloading of sandstone.

Figure 10 shows the variation trend of AE counts and DIECR loading–unloading response ratio with unloading stress during the rock cyclic loading and loading process. As shown in Figure 10, during the cyclic loading and unloading of rocks, the “acoustic-thermal” response of loading and unloading shows a trend of increasing first and then decreasing. The authors believe that this is due to the small number of microfracture events in the early and middle stages of cyclic loading and unloading of sandstone, and the small value of AE counts. With the continuous increase in unloading stress, the change in DIECR increases continuously. A small number of microcracking events will result in a small change in the DIECR caused by friction heat generation. At this time, the thermoelastic effect is the main mechanism of the change in the DIECR. With the increase in unloading stress, the elastic deformation continues to increase, leading to a continuous increase in the DIECR. Therefore, the “acoustic-thermal” response in the loading and unloading stages shows a first rising trend. In the later period of cyclic loading and unloading of sandstone, the pores and microcracks in the rock develop rapidly, the deformation of sandstone enters the stage of unstable crack growth, and acoustic emission microcracks increase rapidly. A large number of microcracking events will increase the change in DIECR caused by friction heat generation, but the elastic deformation will decrease, and the increase in DIECR caused by the thermoelastic effect will decrease. At this time, the friction heat effect and crack growth heat effect are the main mechanisms of DIECR. That is to say, the change of sandstone DIECR in the later period of cyclic loading and unloading shows a steadily increasing trend, but the AE counts show a rapid increase trend, which leads to a downward trend in the “acoustic-thermal” response of loading and unloading during cyclic loading and unloading of rocks. The “acoustic-thermal” response of rock samples A₁ and A₂ in the loading stage reaches its maximum at the unloading stress of 88 MPa and 72 MPa, respectively, and the “acoustic-thermal” response in the unloading stage reaches its maximum at the unloading stress of 64 MPa and 72 MPa, respectively.

As shown in Figure 8, the “acoustic-thermal” loading–unloading response ratio curve of rock samples rises slowly at first, increases suddenly in the penultimate cycle of loading and unloading, and decreases suddenly in the last cycle of loading and unloading. The value of the loading–unloading response ratio of rock sample A₁ before the sudden increase is 0.953, and the value when the sudden increase occurs is 14.91 (the penultimate cycle loading and unloading), 15.6 times that before the sudden increase, and it drops to 0.778 at the last cycle loading and unloading. The value of the loading–unloading response ratio of rock sample A₂ before the sudden increase is 0.486, and the value when the sudden increase occurs is 2.823 (the penultimate cycle of loading and unloading), 5.81 times that before the sudden increase, and it drops to 1.072 when the last cycle of loading and unloading occurs. In addition, the loading–unloading response ratio curves of rock samples A₃ and A₄ showed a sudden increase during the second-to-last cycle of loading and unloading and a decrease during the last cycle of loading and unloading. The authors believe that the sudden increase in the “acoustic-thermal” loading–unloading response ratio curve during the penultimate cycle of loading and unloading is due to the unstable propagation of cracks in the rock at this time, the sharp change of AE counts, and the development of the internal fracture failure of the rock from order to disorder, leading to the sudden increase in the “acoustic-thermal” loading–unloading response ratio. The authors regard the sudden change in the “acoustic-thermal” loading–unloading response ratio during the penultimate cycle of loading and unloading as the initial precursor of rock failure.

5. Discussion

In rock engineering, natural rock is not homogenous but rather inhomogeneous, discontinuous, and generally has a large anisotropic layered structure. The study of the anisotropic geomechanical characteristics of rock has always been the key to such rock engineering’s long-term stability. Numerous rock engineering studies have shown that rock is not in a stable stress state but rather is prone to complicated stress disturbance circumstances such as excavation unloading, fatigue loading, explosive cracking, vibration, and so on. The fracture behavior of rock will become complicated as a result of the disturbance effect. As a result, revealing the fracture evolution law of rock under disturbance settings, particularly fatigue and unloading conditions, and conducting associated rock failure research are critical to ensuring the long-term stability of rock structures. The key reasons that create varied deformation and failure characteristics of rock are the rock’s microstructure and the accompanying microfracture mode, which further leads to differences in acoustic emission and infrared radiation characteristics during rock cyclic loading and unloading. The rock mass is a complicated fracture geological material with numerous randomly dispersed flaws such as joints and fractures. From a macro viewpoint, this research solely examines and analyzes the interaction between acoustic emission, infrared radiation evolution, and cyclic loading–unloading of sandstone microfractures. In the future, we should integrate CT scanning to investigate the interaction between microstructure, microfracture mode, and infrared radiation characteristics of the rock surface, as well as expose the rock’s infrared radiation evolution process from a micro viewpoint.

When the stress level is low, the sandstone develops a limited number of small-sized microcracks and microdamages during cyclic loading and unloading, and their positions are disordered and randomly distributed. When there is a lot of stress, the microcracks within the sandstone accumulate and go through to produce enormous fissures. Clusters form when the percentage of large-sized fractures rises. Continued growth will result in the formation of a fracture surface. Crack spatial distribution will evolve from chaos to order. Microcracks are accumulating and becoming big fractures or even massive fracture surfaces. During the last cycle of loading and unloading, the loading stage response quantity based on AE counts and the loading–unloading response ratio based on AIRT had a large sudden change (compared to the previous cycle of loading and unloading), and the authors regard this sudden change as the “acoustic-thermal” imminent failure precursor of rock cycle loading and unloading. In the process of rock cyclic loading and unloading, the “initial precursor-imminent failure precursor” is created when the initial failure precursor is combined with the imminent failure precursor. The analysis of diverse physical quantity information may enhance the reliability of rock fracture precursor identification due to numerous physical effects during rock fracture, such as anomalous changes in temperature, acoustic emission, infrared radiation, stress, and other physical qualities. The “acoustic-thermal” loading–unloading response ratio defined in this paper can overcome the shortcomings of a single factor in predicting rock failure. Its inclusiveness enables it to select multiple responses for simultaneous prediction. The simultaneous warning of multiple physical parameters greatly improves the accuracy of rock failure prediction. In addition, the loading–unloading response ratio defined in this paper realizes the hierarchical early warning of multiple parameters and is not disturbed by the engineering environment. Whether underground engineering tunnels or surface tunnels, high and low geostress or not, as long as the loading and unloading stage can be distinguished and the response quantity can be selected, it can serve as a reminder for the protection of rock engineering instability. In fact, dissipative strain energy is the essence of rock fracture failure during driving cycle loading and unloading. In the future, the failure mechanism of loaded rock should be analyzed from the perspective of micromechanics by integrating the dissipative strain energy, acoustic emission, and infrared radiation, and a multi-physical field model of rock fracture failure should be built to ultimately achieve an accurate prediction of engineering rock stability.

6. Conclusions

The following conclusions were drawn from the research study:

(1)

The response variable at the loading stage based on AE counts shows a changing trend of “rapid decline—constant—rapid rise“, and suddenly increases at the last cycle of loading and unloading, which can be used as a precursor of the imminent failure of rock.

(2)

The loading–unloading response ratio based on AIRT shows a rising trend as a whole and suddenly increases at the last cycle of loading and unloading. This sudden change, together with the mutation of response variables at the loading stage based on AE counts, can establish the “acoustic-thermal” imminent failure precursor of rock.

(3)

The quantitative analysis index of differential infrared energy change rate, namely the change in ΔAIRT square in unit time, is proposed. This new index reflects the mutation characteristics of rock infrared radiation more intuitively than the AIRT index.

(4)

The loading–unloading response ratio based on “acoustic-thermal” suddenly increases during the penultimate cycle of loading and unloading. This feature can be taken as the initial precursor of rock failure, and together with the “acoustic-thermal” imminent failure precursor of rock, it constitutes the “initial precursor-imminent failure precursor” in the process of rock cyclic loading and unloading.

(5)

In this paper, a new infrared radiation index is proposed, and the loading–unloading response ratio is defined based on acoustic emission and infrared radiation. The analysis method of loading–unloading response ratio is innovated, and hierarchical monitoring and early warning of cyclic loading and unloading rock failure are realized.