Thermal Infrared Precursor Information of Rock Surface during Failure Considering Different Intermediate Principal Stresses

Abstract

Rock failure generally leads to serious consequences, and it is significant to obtain the precursor information prior to failure using associated techniques. Thus, it is essential to acquire and probe the relevant precursor information. In this study, true triaxial tests are performed on red sandstone specimens under varying intermediate principal stress conditions. The thermal infrared image evolution and the temperature-induced change characteristics of rock failure are also analyzed using infrared thermal imaging technology. In addition, with the assistance of a high-speed photography technique, these characteristics during the true triaxial compression and unloading processes are systematically investigated to determine how the intermediate principal impacts on thermal image, temperature, and fracture propagation. Finally, the evolution mechanism of the specimens is summarized, and a non-contact thermal infrared rock failure precursor indicator is proposed, which can give significant advance notice of rock collapse before the abnormal temperature change. The results show that there exist thermal infrared temperature precursors, thermal image precursors, and rapid development of rock macroscopic cracks before rock failure. Abnormal thermal images are prior to the abnormal temperature changes. As the intermediate principal stress increases, thermal abnormalities will change accordingly. Both temperature changes and thermal image anomalous patches can be utilized as precursor information of rock collapse, and the mechanism and specific information of thermal infrared failure precursors can be preliminarily determined in time and space. Our results can function as a significant frame of reference for the analysis and prevention of rock failure due to sudden instability.

1. Introduction

In the process of rock excavation, the sudden unloading induced by external forces often disturbs the internal rock mass and breaks its original mechanical equilibrium, resulting in the energy release in rock mass and possibly the subsequent sudden instability failure [1,2]. For example, in tectonically active regions, a substantial quantity of elastic strain energy accumulates in the highly stressed rock mass. The excavation unloading can result in the sudden release of stored elastic energy, causing instability failure, which is categorized as energy-accumulated-induced rock mass instability failure [3,4,5]. In addition, due to the true triaxial stress conditions (σ₂ > σ₃), hard rock failure and related disaster issues under deep true triaxial stress (σ₂ > σ₃) are extremely complex [6]. Generally, hard and brittle rock masses do not have precursory damage information before instability failure, making it difficult for researchers to predict the occurrence of their instability failure [7] and posing a severe threat to people’s lives and property security. However, the examination of recorded case studies of large-scale rock failures suggests that every instance of rock mass collapse is preceded by a discernible indication of rock mass behavior [8]. Therefore, it is crucial to investigate the precursor information of rock failure to prevent and control the sudden instability failure disasters.

With the rapid advancement of research methods and techniques in the field of rock mechanics, numerous scholars found that thermal infrared imaging could be used to study rock failure-induced damage. In the 1990s, Luong [9] was the first researcher to apply thermal infrared technology to investigate the characteristics of thermal images revealing concrete and rock failure processes and pointed out that thermal infrared radiation signals could be used to monitor the crack penetration process. Gorny et al. [10] and Tronin [11] reported pre-rock-failure anomalies in the thermal infrared image signal in seismically active areas. Additionally, experiments on the rock failure process associated with excavation suggested that thermal infrared temperature can indicate the stress changes of the rock formation at varying depths, and thus thermal imaging can indicate the rock failure process [12,13].

Deng et al. [14] found different characteristics of thermal infrared radiation signal variation at varying stress values. The abrupt signal variation is closely related to both rock properties and loading methods. Based on this and using advanced experimental monitoring instruments, extensive investigations [15,16] regarding the thermal infrared precursor information of rock damage have been conducted, achieving fruitful and satisfying results. With an increasing number of in-depth studies on rock damage, in order to quantitatively analyze the thermal infrared temperature of the rock failure process under pressure, many scholars started to employ the thermal infrared monitoring technique to explore the mechanisms of rocks with different lithologies and proposed some quantitative analysis indexes that reflect the damage characteristics and precursor information of specimens [17,18,19,20,21]. During rock loading, variations in infrared radiation temperature on the surface of the rock correspond to rock stress change and can be periodically classified into five phases: initial, elastic, stress locking, unlocking, and yielding [21]. In recent years, many scholars have combined true triaxial loading tests with thermal infrared monitoring techniques and the thermal infrared information of rock failure under true triaxial stress conditions was more thoroughly explored [22,23,24]. These studies validate that it is more reliable to apply thermal infrared technology to the true triaxial test to monitor rock damage.

Although abundant studies on thermal infrared information during rock damage have been carried out, those regarding the changing law of thermal infrared information and the effect of precursor information are rare, which are urgently necessary. In this paper, we study the temperature change characteristics and failure process of a deep rock mass under varying intermediate principal stress conditions in the true triaxial loading and unloading test. The temperature and fracture precursor information of rock specimens subjected to varying intermediate principal stress conditions are compared by measuring their thermal infrared thermal image evolution process and temperature change. Finally, the damage characteristics and damage precursors of red sandstone under true triaxial stress conditions are studied. It shows that thermal infrared thermal images and temperature anomalies appear before rock failure, which can serve as an indicator for effectively predicting and preventing disasters associated with rock instability failure resulting from excavation and unloading in engineering.

2. Experimental Set-Up

2.1. Test Preparation

The lithology of the specimen used in this test is red sandstone. Red sandstone is characterized by strong texture, dense structure, and high integrity. The specimens utilized in this study are rectangular-shaped pieces of red sandstone with the dimensions of 100 mm × 100 mm × 200 mm. The error of end flatness is within ±0.05 mm while verticality error is within ±0.25°. The uniaxial compression tests were carried out before triaxial compression tests, and the uniaxial compressive strength (UCS) is about 75 MPa. Therefore, the maximum principal stress was established at 60 MPa (80% UCS) and the minimum principal stress was established at 5 MPa in the true triaxial loading and unloading tests. Four totally different intermediate principal stress cases were set up, and 3 specimens were tested for each load condition. The specimen is as shown in Figure 1b.

The true triaxial test was performed with the new high-pressure servo dynamic true triaxial rigidity tester TAW1-5000/3000, and the FLIRSC305 infrared thermal imaging camera was used to record the temperature and thermal image of the specimen at the free face. In addition, the SVSI high-speed digital camera was utilized to capture the development, expansion, and connection of rock surface fractures.

2.2. Stress Path

The test was divided into 4 groups, each including 3 specimens, making a total of 12 specimens. The real triaxial unloading test scheme is briefly described as follows: firstly, a 0.5 MPa force was applied to the direction of the maximum principal stress σ₁ using the displacement control method and thus the specimen’s end face was touching the transmission column’s surface. Then, the load control mechanism was switched to ensure that the design value of the maximum principal stress is loaded at a rate of 0.2 MPa/s. The maximum principal stress was held steady, and the intermediate principal stress was loaded to the design value in the same way. Likewise, the intermediate principal stress σ₂ was held steady, and the minimum principal stress was loaded to the design value, and the stress state was kept for 10 s. After the initial stress loading was completed, σ₃ on one side was quickly unloaded. Meanwhile, the opposing side was adjusted to displacement control, and then the loading speed was increased by 2 kN/s until the specimen was damaged. The stress state is shown in Figure 2. In this process, the high-speed camera and infrared thermal imaging camera collect data simultaneously. The main true triaxial stress values in this study are as follows: the maximum principal stress (σ₁) is fixed at 60 MPa. The intermediate principal stress (σ₂) is 10 MPa, 20 MPa, 40 MPa, and 60 MPa, respectively, and the minimum principal stress (σ₃) decreases from 5 MPa to zero. The test details are shown in

Table 1. Parameters of the true triaxial loading and unloading test.

Test Group Number	σ1 (MPa)	σ2 (MPa)	σ3 (MPa)	Number of Specimens
A-1	60	10	5→0	3
A-2	60	20	5→0	3
A-3	60	40	5→0	3
A-4	60	60	5→0	3

.

3. Thermal Infrared Image Change Characteristics

Thermal infrared images can illustrate the evolving process of the radiation temperature field at the free face of a rock specimen, and directly express the strength of thermal infrared radiation on the specimen surface. Additionally, the precursors of thermal images before rock damage are captured, and the differences of the precursor information of thermal images under different principal stress conditions are compared.

3.1. Change of Thermal Image

To study the thermal image process of rock specimens during the true triaxial compression failure, the thermal image evolution process during rock loading under different principal stress conditions is shown in Figure 3. In particular, Figure 3a shows the thermal infrared image evolution process on the unloaded specimen free face with an intermediate principal stress of 10 MPa. Thermal abnormalities appear on the upper section of the specimen free face during the entire evolution process. In the initial stage, the thermal images were evenly distributed, and no abnormal patches were seen on the free face. The first thermal image abnormality appeared on the upper section of the free face 5.5 s before the complete damage of the rock specimen, and the area of the abnormal patch was about 2.3 cm². The abnormal patch gradually expanded downward with the rise of axial stress, and the maximum area of the abnormality reached 38cm² before the damage of the rock specimen. It is notable that the temperature increased abruptly when the specimen free face was damaged. The thermal image shows an obviously bright jet-like high-temperature anomaly area, confirming the high temperature inside the formed rupture crater. Subsequently, the temperature on the surface decreased and the thermal image anomaly gradually dissipated.

Figure 3b shows the evolution of the thermal infrared image of the unloading specimen free face with an intermediate principal stress of 20 MPa. The thermal image evolution process is described as follows: in the initial stage of unloading, no abnormal spot has been observed on the free face, and the thermal image abnormality appeared for the first time after about 7 s of the specimen failure, with an abnormal area of 6.5 cm². The abnormal area gradually expanded with the continuous increase of pressure, reaching a maximum of 41 cm², and the instantaneous failure of the specimen subsequently. As a result, the simultaneous energy release led to a sudden temperature increase, and anomalous patches featured by high brightness and temperature appeared on the rupture surface. The thermal image anomalies gradually faded after the specimen rupture.

Figure 3c shows the thermal infrared image evolution process on the unloading specimen free face when the intermediate principal stress is 40 MPa. The thermal image evolution process is as follows: the thermal infrared image of the specimen free face is evenly distributed during unloading, and no abnormal spot has been observed. At 9 s before the specimen failure, two obvious abnormal patches emerged at the uppermost part of the specimen with an area of 2.8 cm². The abnormal patch gradually developed from top to bottom, forming a large abnormal patch, and the abnormal surface developed to the maximum area of 45 cm². Both high- and low-temperature patches were generated as a result of the specimen failure in the thermal image, and then the abnormal bright temperature surface gradually dissipated.

Figure 3d exhibits the evolution of the thermal infrared image on the unloading specimen free face when the intermediate principal stress is 60 MPa. The first thermal abnormality appeared at 13 s before the specimen failure, and the thermal abnormality area was about 2.1 cm², which gradually expanded to a maximum area of about 47 cm² before specimen failure. Then, the specimen collapsed, and bright high-temperature belts appeared. Compared with the bright high-temperature patches that appeared under the previous smaller intermediate principal stress, the patch that appeared at 60 MPa stress is larger and longer, with a broader expansion area.

In general, the pre-failure thermal image abnormality on the free face for each specimen has undergone three development stages. (1) At the initial unloading stage, the thermal image on the specimen surface changes from an evenly distributed state to the appearance of abnormal spots that gradually expand into abnormal patches. (2) Before the complete failure, the above abnormal patches are connected with each other to form a thermal image abnormal surface. (3) The rupture crater then appears at the highest thermal image temperature and instantly penetrates the free face. At this time, the temperature at the rupture area rises abruptly and high-temperature thermal patches are formed. The high temperature gradually dissipates after the failure.

According to the analysis of the above results, during the period from unloading to rock specimen failure, obvious thermal image anomaly evolution can be observed on the free face. These thermal image anomalies appear soon after the immediate failure of the rock specimen, and the damage area is consistent with the area where the thermal image anomaly appears. Unloading-triggered rock failure can result in different conditions of fractures, mainly tension fractures and shear fractures [25]. The thermal infrared images of the two types of fractures are manifested by different forms of thermal image anomalies. For tensile fractures, there is a prominent temperature decrease of the thermal anomaly, while the temperature increases for those in shear fractures. The damage of the specimen free face is entirely collapsed, and there is no more fracture expansion therein. The shear fractures are rarely distributed here and thus the thermal image precursor information before specimen failure is mainly shown as light-colored anomalies. After the specimen free face is ejected, the temperature rises due to the heat due to the friction occurring associated with the dislocation of rupture surface, thus showing a pattern of intertwined high- and low-temperature thermal images.

3.2. Characterization of Thermal Image Precursor Information

Table 2. Evolution of the infrared thermal abnormality.

σ2 (MPa)	Time of First Appearance of the Abnormality (s)	Initial Thermal Abnormality Area (cm2)	Maximum Thermal Abnormality Area (cm2)
10	5.5	2.3	38
20	7	6.5	41
40	9	2.8	45
60	13	2.1	47

shows the vertical analysis of the thermal infrared thermal image precursor information under different intermediate principal stresses under the true triaxial unloading state. It is clear that the size of the intermediate principal stress is responsible for the change of the thermal infrared thermal image precursor information, which is mainly manifested by the time at which the precursor information appears, the abnormal area and the clarity of the images, and the differentiation degree of the abnormal thermal image.

Figure 4 shows the comparative analysis of the first appearance time of the thermal image under different intermediate principal stress conditions, where the horizontal axis represents the change of the intermediate principal stress σ₂ and the vertical axis denotes the first appearance time of thermal image T. The fitted curve is presented in Figure 4, suggesting a reliable linear relationship and excellent fitting effect. The relationship conforms to the following equation:

$$T=0.14{\sigma }_2+3.92$$

(1)

Figure 5 shows the comparative analysis of the thermal image abnormal area under different intermediate principal stress conditions, where the horizontal axis indicates σ₂ and the vertical axis stands for the thermal image area S. It can be seen that the thermal image initial area is not correlated well with the size of intermediate principal stress. The maximum area of thermal abnormality has a better fitting relationship with the intermediate principal stress, obeying the following equation:

$$S=0.18{\sigma }_2+36.97$$

(2)

By comparing and analyzing four groups of thermal image precursor information under different intermediate principal stresses, the following conclusions were preliminarily obtained: (1) the thermal infrared thermal image precursor information appears earlier as the intermediate principal stress increases, which corresponds to the results of the true triaxial loading test. (2) There are no rules of the area of the first thermal image anomaly, but the maximum thermal image anomaly area before the specimen failure increases with the rise of the intermediate principal stress, and the recognition of the precursor information also increases accordingly. (3) The spatial differentiation of thermal abnormalities under low intermediate principal stress is low, and vice versa. The thermal image evolution process is more concentrated. The thermal abnormalities span a larger area during the whole process from the initially small abnormality area to the post-expansion maximum abnormality area. (4) No abnormalities appear in the thermal image of the free face after unloading; instead, they appear only when the axial stress is loaded into a certain value, which indicates that the main factor resulting in the differential change of the thermal image precursor information is the change of intermediate principal stress.

4. Characteristics of Thermal Infrared Temperature-Time Curve Change

In this section, we study the variation characteristics of thermal temperature on the red sandstone specimen free face with time in the true triaxial compression test under different intermediate principal stress conditions. The temperature-time curve is compared with the stress-strain curve for detailed analysis. The temperature-time curve characteristics are further analyzed to capture and compare the temperature-time curve precursor information. The free face is only exposed when the minimum principal stress is unloaded on one side; thus, the temperature-time curves in the figure are captured after unloading.

4.1. Temperature-Time Curve Characteristics

Figure 6 displays the temperature-time curves and stress-strain curves of rock specimens under different intermediate principal stresses, respectively. Specifically, Figure 6a shows the characteristic analysis of the change of temperature-time curve at the free face with an unloading stress of 10 MPa. In this section, the temperature-time curve can be classified into five stages (i.e., I stable stage; II abnormal turning stage; III pre- steep increase stage; IV steep increase stage; V decrease stage). Under the stress of 10 MPa, the first stage is 164–225 s. The temperature fluctuation in this stage is small and lasts for a long time. The second stage is 226–276 s, during which the curve turns and presents a “U” shape. Notably, point L is the initial temperature drop point, point P is the lowest point, and point K is the point where the temperature rises again. Stage III is 277–300 s, after point K, the turning trend ceases, and the temperature curve returns to a stable state. When the curve reaches point M, the temperature rises drastically, and the curve enters stage IV (301–314 s). At this time, the specimen free face is broken. The surface temperature rises suddenly, and the destruction process time is short. The V stage is 315–348 s; the temperature rises abruptly and then falls back, followed by gradual decrease. The valley point P is about 38s from the moment of specimen damage, the peak temperature of the free face at the time of damage is 21.05 °C, and the peak stress is 100.25 MPa. Significantly, there is no relationship between the five stages of temperature and deformation stage. The change of temperature results from the crack propagation (tensile crack and shear crack). However, the deformation stage of the specimen is related to the specimen volume and crack propagation rate. In addition, it is obvious that the time of each temperature stage is not consistent with the time of deformation stage.

Figure 6b shows the characteristic analysis of the change of temperature-time curve of the unloaded free face at 20 MPa. It is obvious that the precursor information appears 56 s before the specimen is damaged. The temperature of the free face at the time of specimen failure is 21.06 °C, and the peak stress is 134.58 MPa. The first stage of the temperature-time curve is 161–378 s, which remains generally stable. The second stage, in which an obvious turning change appears, is 379–401 s. The duration of change is short, exhibiting a deep “V-shape” pattern. The third stage is 402–443 s, which is a general stable stage before the sudden temperature increase. Stage IV is 444–458 s, where the curve suddenly rises and then falls back. Stage V is 459–508 s, where the curve falls back to a low temperature level, followed by the subsequent gradual temperature decrease. During the test under 20 MPa intermediate principal stress, the duration of the turning change process of the temperature-time curve is short and the value of the temperature drop is large.

Figure 6c shows the characteristic analysis of the temperature change of on the free face at 40 MPa. From the curve change pattern, it can be seen that with the increase of the intermediate principal stress, the magnitude change of the temperature curve in the stable stage becomes larger, and the turning change P point is 75 s from the specimen failure moment. The maximum temperature on the free face at the failure moment is 21.08 °C, and the peak stress reaches 152.86 MPa. The time period from stage I to stage V are: 204–425 s, 426–453 s, 454–502 s, 503–548 s, and 549–600 s, respectively. The changing process is described as follows: during stage I, the temperature changes within the range of 20.76 °C~20.88 °C, and the maximum difference value reaches 0.12 °C. During stage II, the temperature characteristic points L, P, and K are 20.87 °C, 20.71 °C, and 20.96 °C, respectively, with a downward fluctuation of 0.16 °C and an upward fluctuation of 0.25 °C. Meanwhile, temperature change with a turning trend and the precursor information is obvious. The temperature change within stage III is still characterized by an intense fluctuation, reaching 0.13 °C. The temperature rises significantly in stage IV, with a temperature value of 21.08 °C. The high temperature maintains for 45 s before falling back.

Figure 6d shows the characteristics of the temperature-time curve at the free face at 60 MPa. The overall characteristics of the curve are similar to those in Figure 6a, with a high fluctuation intensity and range. The precursor information appears at 98 s after the specimen failure. The maximum temperature reaches 21.10 °C and the peak stress is 165.75 MPa. The five stages of the temperature-time curve are 226–433 s, 434–475 s, 476–548 s, 549–558 s, and 559–627 s, respectively. The upper and lower temperature limits in stage I are 20.93 °C and 20.77 °C, respectively, with a temperature difference of 0.16 °C. The temperature curve in stage II still shows a “V”-shaped turning change pattern. The temperature curve drops suddenly but then increases slowly. In stage III, the temperature change has a maximum fluctuation of 0.1 °C, and there is another drop before the sudden temperature increase, that is, the K point to M point. In stage IV, the temperature jumps and maintains a high level. The whole process lasts 9 s, and then the temperature curve falls back, indicating that the temperature of the free face gradually decreases.

The overall variation of the temperature-time curve can be summarized as follows: low fluctuation in the early stage; turning change before specimen failure; resumption of slight fluctuation; sudden increase; decrease. In particular, the temperature-time curve shows a turning change in stage II, which is considered the precursor information of specimen failure. After comparison, it is clear that the temperature-time curves possess earlier turning changes than those yielded in the stress-strain curves, and the sudden increase in temperature corresponds to the significant decrease in stress. Furthermore, the temperature-time curves correspond well with the stress-strain curves. The precursor information of specimen failure is also earlier than that in the stress-strain curves.

4.2. Characteristics of the Precursor Information in Temperature-Time Curves

Based on the true triaxial loading test, the characteristics of the temperature changes on the specimen free face during the true triaxial compression test under different intermediate principal stresses are analyzed. In addition, the precursor information shown in the temperature-time curve is captured to reveal the different characteristics under different intermediate principal stresses, respectively.

Figure 7 shows the comparative analysis of the appearance time of temperature precursors under different intermediate principal stress conditions. The horizontal axis represents ${\mathsf{\sigma }}_2$, and the vertical axis represents the appearance time of temperature precursors. The fitted information in the figure indicates that the size of the intermediate principal stress and the time of early appearance of the pre-failure turning process are linearly correlated, and the fitting effect is good. Additionally, the temperature precursor information appears earlier with the rise of principal stress, and conforms to the following equation:

$$T=1.15{\mathsf{\sigma }}_2+29.24$$

(3)

Table 3. Characteristic analysis of thermal infrared precursory information under different intermediate principal stresses during the unloading test.

σ2 (MPa)	Thermal Infrared Imaging	Time Duration to Damage Moment (s)	Thermal Abnormality Characteristics	Thermal Image Migration Process and Area	Thermal Imaging Scale
10	Initial abnormality and its extension	5.5 s before the damage, the first abnormality appears. Then, it expands until it disappears.	The initial abnormality patch gradually expands and forms irregular patterns, and the temperature distribution is uneven.	The anomaly is concentrated in the upper end. The initial anomaly area is 2.3 cm2, and the maximum area is 38 cm2.
20	Initial thermal abnormality and its extension	7 s before the damage, the abnormality appears. 1 s before the damage, it disperses and then disappears.	Triangular abnormality patch appears at the upper part first. Then, it develops into an anomalous trapezoidal pattern. The temperature distribution is high in the middle and low peripheral areas.	Thermal abnormality expands. The initial abnormal area is 6.5 cm2, and the maximum area reaches 41 cm2.
40	Initial thermal abnormality and its extensions	9 s before the damage, the first abnormality appears at the upper end. 7.5 s before the damage, it extends to the middle part.	The abnormality is dotted at first, distributed on both sides of the upper end. The abnormality expands to the middle part, showing stripes.	The initial thermal abnormality area is 2.8 cm2. As it expands to the middle, its maximum area reaches 45 cm2.
60	Initial thermal abnormality and its extension	13 s before the damage, the abnormality appears in the middle and upper part, and it presents an opposite cone at the ejection moment.	The initial anomaly is manifested as a small bright temperature point, which expands into two anomalous conical patterns. The top of the conical pattern is the source of rupture.	The initial thermal abnormality area is 2.1 cm2, and the maximum reaches as high as 47 cm2. The abnormality extends to the upper end.

shows the vertical comparative analysis table of the precursor information characteristics under different intermediate principal stresses. According to the test results, the differences in four aspects (i.e., the manifestation form, appearance time, duration, and the temperature fluctuation amount) of the precursor information on the curve are mainly compared and analyzed, and three main conclusions are obtained: (1) the turning change of the temperature-time curve is mainly in “U” and “V” patterns. Specifically, the “U” pattern is dominant when ${\sigma }_2$ is low, and the temperature decreases and rises slowly. As ${\mathsf{\sigma }}_2$ increases, the turning change is dominated by a “V” pattern. Then, the pattern sharply changes to deep “V” when ${\mathsf{\sigma }}_2$ increases to 40 MPa and 60 MPa. (2) The precursor information on the temperature-time curve appears earlier with the increase of ${\mathsf{\sigma }}_2$. (3) The duration of the turning change process is longer and the difference of temperature fluctuation is smaller under low ${\mathsf{\sigma }}_2$, while the process is relatively shorter and the temperature fluctuation is larger under high ${\mathsf{\sigma }}_2$. Thus, it is easier to identify the precursor information under high principal stress.

Table 4. Characteristics of temperature-time curve precursor information under different intermediate principal stresses.

σ2 (MPa)	Precursor Pattern	Advance Time	Temperature Change Value	Duration
10		38 s	0.1 °C↓ 0.11 °C↑	50 s
20		56 s	0.1 °C↓ 0.12 °C↑	22 s
40		75 s	0.16 °C↓ 0.25 °C↑	27 s
60		98 s	0.11 °C↓ 0.09 °C↑	41 s

shows that the magnitude of the abnormal turning change is significantly higher than the maximum fluctuation within the stable stage, indicating that it is reliable to use this phenomenon as the precursor information. With the increase of the intermediate principal stress, there is not much difference between the fluctuation magnitude of the stable stage and the anomalous turning change, but their overall temperature values gradually increase. Such a phenomenon may be caused by the increasingly intense destruction of the free face associated with the stress increase, which leads to more heat released by friction and hence increases the temperature.

The characteristics of the precursor information on the temperature-time curve vary with ${\mathsf{\sigma }}_2$; the reasons are akin to those corresponding to the true triaxial loading tests. In this subsection, on the basis of the true triaxial loading test, the temperature characteristics of the precursor information on the specimen free face under the true triaxial paths are discussed, and the corresponding characteristics of the thermal infrared precursor information on the free face of red sandstone are investigated.

4.3. Study on the Thermal Infrared Warning Indicator

This part attempts to propose the precursor warning indicators of rock failure by considering the temperature anomalies. On the basis of the characteristics of the stochastic distribution of microelements in rocks, we assume that the temperature and failure variables of each microelement obey the two-parameter Weibull distribution and their deformation obeys Hooke’s law in the pre-failure stage. Finally, the damage probability equation of a rock subjected to external load can be established as follows:

$$f\left(x\right)=\frac{k}{\mathsf{\lambda }}{\left(\frac{x}{\mathsf{\lambda }}\right)}^{k-1}exp\left[-{\left(\frac{x}{\mathsf{\lambda }}\right)}^k\right]$$

(4)

where x is the standard deviation of the temperature of the rock surface at a given moment, λ is the average temperature on the surface, and k is the rock non-uniformity index.

x and λ can be obtained by the following equations:

$$x=\sqrt{\frac{1}{n-1}{\displaystyle \sum }_{i=2}^n{\left(T_i-\overline{T}\right)}^2}$$

(5)

$$\mathsf{\lambda }={\displaystyle \sum }_{i=1}^n\left(T_i/n\right)$$

(6)

where $T_i$ is the temperature at any point of the rock surface at time t, and $\overline{T}$ is the average temperature of the rock surface in the period from 0 to t.

The probability density function of the thermal infrared temperature-based micro-element damage variables of the rock with respect to the micro-element temperature variables can be calculated by the following equation:

$$\frac{dD}{dx}=f\left(x\right)$$

(7)

where D is the micro-element damage variable of the rock based on thermal infrared temperature, which can be calculated by the following equation:

$$D=\frac{\left|A_T-A_{T_i}\right|}{A_T}$$

(8)

where $A_{T_i}$ is the temperature value at any point of the rock surface, and $A_T$ is the overall average temperature value of the rock surface.

By substituting Equation (4) into Equation (7), the following equation can be obtained:

$$k=\frac{\ln \left(\frac{x}{\mathsf{\lambda }}\right)}{\ln \left|\ln \left(1-D\right)\right|}$$

(9)

Figure 8a shows the comparison characteristics of the average temperature curve and k-value index of the specimen under a 10 MPa intermediate principal stress condition. The change process of the k-value index can be divided into three stages. The first stage is the part prior to the abrupt change point, which corresponds to the part before 235 s. This part is a stable stage compared with the part after the abrupt change, and the range of k-value fluctuation is basically unchanged in this stage. The second stage includes the period when the k-value shows an abrupt change, corresponding to 235–319 s. In this stage, the k-value fluctuates obviously in the range of 1.0–2.7. Since the moment when the k-value starts to fluctuate, the monitored surface of the rock specimen starts to be damaged. The damage of the rock specimen will continue to increase until the rock failure. The rock specimen completely collapses after 64 s of the abrupt change of the k-value, and the corresponding precursor information time appears 26 s earlier than the thermal infrared precursor information. The third stage is the period when the k-value returns to the stable stage. In this stage, the rock specimen is completely collapsed, accompanied by the rebounded compressor, and the damage of the proximal monitoring surface of the rock sample is no longer changed.

Figure 8b shows the average temperature-time curve and time series comparison of the k-value under a 20 MPa intermediate principal stress condition. The first stage is the part in front of the k-value abrupt change point, corresponding to the time before 326 s. It is prominent that this stage is stable and is manifested as a horizontal straight line. The second stage is the period when the abrupt change of the k-value occurs, corresponding to the time of 326–463 s. In this stage, the k-value fluctuates dramatically, and the k-value suddenly rises at 326 s. The fluctuation range is between 0.2 and 3.1, which is relatively large, indicating that the instantaneous damage of the rock free face is large. The rock specimen completely collapses after 139 s after the abrupt change, and the precursor information appears 53 s earlier than that of the average temperature curve. The third stage is in the period after 463 s, and the k value returns to the stable stage.

Figure 8c shows the comparative characteristics of the average temperature curve and k-value index under a 40 MPa intermediate principal stress condition, which can also be classified by three stages. The first stage is the area in front of the initial abrupt change point of the k-value index, corresponding to the time before 399 s. The second stage is the initial abrupt change stage of the k-value index, corresponding to the time period of 399–546 s, and the initial fluctuation of k-value in this stage is obvious. There are 117 s before the complete failure after the k-value starts to change, which is 42 s earlier than the appearance time of the thermal infrared precursor. In addition, the fluctuation range after the beginning of fluctuation is larger (1.0–2.9). This period starts from the beginning of the obvious fluctuation of the k value, indicating that the damage of the rock specimen-monitored surface lasts until the third stage, during which the k value returns to the stable stage.

Figure 8d shows the comparison of the average temperature curve and time series under a 60 MPa principal stress condition. Similarly, the curve is also divided into three stages. The first stage (i.e., the stable stage) is the part in front of the abrupt change point of the k-value indicator, corresponding to the time before 406 s. The overall fluctuation range of the k-value curve is small. The second stage includes the abrupt change of the k-value and corresponds to the time from 406–542 s. The fluctuation range is large (0.9–2.3), which proves that the persistent damage is larger in this stage. The complete specimen failure occurs after 136 s of the abrupt change of the k-value, and the precursor information appears 38s earlier than the average temperature. In the last stage, the k-value returns to be stable.

5. Discussion

The fracture expansion of the rock specimen during loading is closely related to the loading method used. Li et al. [26] found that the triaxial failure of rock is caused by the propagation of microcracks. Based on this, we infer that the magnitude of the intermediate principal stress will also affect the crack extension. Plenty of scholars have conducted research on crack extension and morphology of rock failure [27,28,29]. However, the application of thermal infrared techniques to investigate rock crack extension is scarce. In this section, the relationship between thermal infrared information and rock fracture is probed for the purpose of enhancing the reliability of the thermal infrared precursor information on rocks.

Based on the true triaxial test results, we found that there is a certain correspondence between the rupture process of rock specimens and the change of thermal image anomalies. Moreover, we further study the correspondence between specimen failure and the change of thermal image anomalies during the test.

(1)

Relationship between thermal image abnormalities and fracture extension when ${\sigma }_2$ = 10 MPa

Microscopic and macroscopic thermal cracking occurs during the loading process [30]. Figure 9 shows the correspondence between rock failure and thermal image abnormality under the 10 MPa intermediate principal stress. It can be seen that during the period from the initial thermal image to the first appearance of the thermal abnormality phenomenon, there is no fracture development on the free face, and as the area of the thermal image abnormality expands, the spalling of rock debris occurs for the first time in area B of the free face. Subsequently, a small fracture develops at the spalling site. At this moment, the abnormal surface of the corresponding area develops into an abnormal patch, followed by the specimen failure. The rock fragments pop out from the free face, and a high-temperature thermal image appears.

(2)

Relationship between thermal abnormalities and fracture extension when ${\sigma }_2$ = 20 MPa

Figure 10 shows the correspondence between rock fractures and thermal anomalies under the 20 MPa intermediate principal stress. The first abnormality still appears before the appearance of microcracks in area D. Then, local fragmentation is observed therein, and the high-temperature abnormal surface appears in the thermal image at the corresponding position. The abnormal surface expands continuously and finally forms two extremely high bright temperature strips. At this moment, the specimen collapses, and the temperature strips correspond to two main penetrated fractures on the free face. The thermal abnormalities in the crater formed after the specimen failure show a pattern of high temperature alternating with low temperature. Specifically, the high- and low-temperature regions are associated with shear and tensile fractures, respectively [25]. These differential characteristics of thermal images can be used to infer the properties of fractures.

(3)

Relationship between thermal abnormalities and fracture extension when ${\mathsf{\sigma }}_2$ = 40 MPa

Figure 11 shows the correspondence between rock fractures and thermal anomalies under the 40 MPa intermediate principal stress. When the thermal anomaly expands into a bright temperature strip, fractures start to appear in areas H and D of the free face and then penetrate the rock specimen rapidly. After that, the free face collapses, and the temperature at the failure site increases significantly due to the intense friction. The thermal image shows an extremely high bright temperature point. The secondary damage is mainly generated by rock ejection. The occurrence of secondary cracks means that the microcracking and failure of rock materials increase [31]. The strain energy released by the rock mass during violent stress-driven failure is largely converted into kinetic energy of ejection [32]. Therefore, we can infer that the occurrence of secondary damage means more serious damage to the rock specimen, and the temperature of the thermal image in the ejection zone is high. After the specimen entirely collapses, the temperature inside the free face gradually decreases and the thermal image dissipates abnormally.

(4)

Relationship between thermal abnormalities and fracture extension when ${\mathsf{\sigma }}_2$ = 60 MPa

Figure 12 shows the correspondence between rock fractures and thermal anomalies under the 60 MPa intermediate principal stress. According to the information in the figure, it can be seen that when the first anomaly appears on the thermal image, the specimen free face remains intact, and no fractures appear. Later, when the thermal anomaly surface expands into a triangle, rock fragments splash in area D of the free face and form a fracture that penetrates the upper end surface. Meanwhile, the thermal image shows a bright anomaly. When the specimen is damaged to a great extent, the entire free face collapses. The abnormal distribution of thermal images in the rupture surface is uneven, with the thermal images showing high temperature in the deeper part and low temperature in the shallow part. Under this stress path, with loading in the direction of σ₁ and unloading in the direction of σ₃, the rupture face of the specimen is rough and parallel to the directions of σ₁ and σ₂, and the specimen failure of the specimen is severe [33]. These observations are consistent with the results of our test.

In the whole test process, thermal abnormalities on the free face all appear before fracture appearance, and their locations are consistent with the future fracture locations. In other words, the thermal abnormalities temporally warn of the damage of the specimen and spatially predict the fracture location of the specimen. In the process of rock specimen failure, the thermal abnormality features on the free face can be used to distinguish the property of rock fractures. The high-temperature thermal image corresponds to shear frictional fractures, while the low-temperature thermal image corresponds to tensile fractures [34].

Under the condition of true triaxial stress (σ₂ > σ₃), the specimen fractures are not randomly distributed; instead, they show directional alignment and regular distribution characteristics [6].

Table 5. Characterization of damage patterns of rock specimens in true triaxial loading and unloading tests.

σ2 (MPa)	Front Side (Unloading Face)	Right Side	Left Side	Back Side	General Fracture Characteristics of Rock Specimens
10					The crater is formed by crumbling. Broken “V”-shaped shear displacement zones are seen on both sides. More crushing fractures appear on the back of the specimen. Specimens are dominated by shear damage.
20					The upper A-E zones are the rupture surface. A shear zone runs through the surface along the diagonal. A secondary fracture is developed in the middle part. Feather fractures are seen at the intersection of the main fracture and the secondary fractures.
40					The crumbling damage occurs in the upper part. Both sides show “V”-shaped shear displacement zones. The back of the specimen is intact. The specimen is damaged in three parts but remains intact.
60					Free face is ejected entirely. Both sides form a “V”-shaped shear displacement zone. The upper end shows multiple splitting fractures. The back of the specimen is intact, with many rock fragments.

shows the analysis of the damage pattern of the rock in the real triaxial unloading test. The damage of the rock specimen’s free face is severe in the upper part. The rupture area of the free face increases with the increase of the intermediate principal stress. When it is 60 MPa, the free face is ejected entirely, forming a rupture surface with the same area as the free face. When unloading in one direction, the load in one direction increases, and the load in the other direction is stable, the process of hard rock failure includes four stages: stable stage; small fragment ejection, rock flake ejection, overall collapse [35]. The phenomena in these stages are consistent with the observations in this study. The shear rupture zone on both sides of the specimens generally shows a “V”-shaped pattern, with feather fractures on the shear zone along the diagonal. These are secondary fractures caused by extrusive friction in the shear zone. After specimen failure, the specimen back has a relatively good integrity.

The failure pattern of rock specimens under different intermediate principal stress conditions varies. After in-depth analysis, we suggest that the difference in intermediate principal stress generating these differential changes can be attributed to two main reasons: (1) as the intermediate principal stress rises, the energy accumulated inside the specimen increases. Driven by this energy, the free face gradually collapses. The greater the energy, the greater the damage. The release of energy leads to the reduction of strength, damage, and deformation of rocks [36]. When the intermediate principal stress reaches 60 MPa, the entire free face is completely ejected. (2) The left and right sides of the specimen are surrounded by the intermediate principal stress. The main fractures of the specimen are shear fractures. The increase of the intermediate principal stress will lead to the increase of the compressive stress in the shear zone, resulting in the feather fractures on the shear zone, which results in more serious fragmentation of surrounding rocks. Under a high-confined pressure condition, the specimen fails due to the feather-like shear fractures and secondary fractures are extensively developed [37].

A large number of investigations have explored the precursory information of hard rock failure using different methods and indicators, such as acoustic emissions (AE), microseismic (MS), electric potential (EP), infrasonic energy, etc. [8,34,38,39,40,41]. However, the thermal infrared precursor has its advantages of intuitive thermal image and temperature change, which is easy to be captured. According to the above analyses, it can be seen that the thermal image anomaly appears before rock fragment spalling. Then, the thermal anomalies expand continuously in the crack development area and form a prominent thermal anomaly strip. The area where the thermal image anomalies appear is consistent with the future fracture locations. In addition, the thermal abnormalities can temporally warn of the damage of the specimen. During the gradual damage process of the specimen, the thermal anomaly evolution corresponds well with the fracture expansion, and the thermal anomaly features can indicate the source of the rupture zone and its properties. To be specific, the high bright temperature point of the thermal anomalies is the source of rupture. The high-temperature thermal image corresponds to shear friction rupture, while the low-temperature thermal image corresponds to tension rupture. The fracture properties in the rupture surface can be inferred from the differences of these thermal images.

6. Conclusions

In this study, true triaxial unloading tests are performed by using red sandstone specimens under different intermediate principal stresses. Failure precursors and failure characteristics of the specimens are explored. The following conclusions are obtained:

(1)

Hard brittle rocks do not have clear precursor information on their surface before instability failure, making it difficult to predict the failure occurrence. The change of the intermediate principal stress in the true triaxial test can cause the change of the thermal infrared precursor information of rock failure, which can be used for rock failure prediction, but accurate three-dimensional crack propagation modes cannot be presented and studied through thermal infrared images.

(2)

Before rock failure, anomalous thermal patches appear on the free face. The location of the patches is consistent with the future fractures. The area of the abnormal patches increases with the increase of the intermediate principal stress, and the time of its first appearance is also earlier with the increase of the intermediate principal stress. The thermal abnormalities appear only when the axial stress is loaded to a certain value after unloading, demonstrating that the main factor leading to the differential change of precursor information is the change of the intermediate principal stress.

(3)

Before the failure of the rock specimen, the temperature on the free face will show a turning change. The corresponding curve pattern is a sudden drop followed by an increase, and the time of the anomalous curve occurs earlier with the increase of the intermediate principal stress. Both temperature turning change and thermal anomalous patches can be used as precursor information for rock failure. Additionally, the turning change appears slightly earlier than the thermal image anomaly.

(4)

The failure patterns of the rock specimens under different intermediate principal stress magnitudes are different. The thermal infrared image anomaly region coincides with the rock failure region, and the area of failure region increases with the intermediate principal stress magnitude.