(3) sample 0.30–2 ΔAIRT(℃)

 ΔAIRT Load

Ⅰ

0.10

0.12

0.14

0.16

Figure 10 depicts the ∆AIRT-load curve for sample (0.30–2). The initial value of ∆AIRT was −0.671 ◦C. In the compaction stage (0 s~193.05 s), the load rises to 51 kN and ∆AIRT rises to −0.646 ◦C. In the linear elastic stage (193.05 s~524.76 s), the load curve and ∆AIRT showed a nearly linear rising trend, in which the load increased to 210.04 kN, ∆AIRT rose to −0.601 ◦C. During the whole fracture development stage (524.76 s~637.80 s), the load increased from 210.04 kN to 253.37 kN, which is also the peak load. During this period, the ∆AIRT was stable, and only slightly increased by 0.011 ◦C. After the peak of the load curve, the ∆AIRT and the load have a sudden drop trend, wherein ∆AIRT dropped to −0.773 ◦C, which overall decreased by 0.183 ◦C. 0 200 400 600 800 1000 1200 0.04 0.06 0.08 Time(s) Ⅳ 0 50 **Figure 9.** Experimental data of sample 0−3.

100

150

Load(kN)

200

250

Ⅲ

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Ⅱ

**Figure 10. Figure 10.**  Experimental data of 0.30–2 sample. Experimental data of 0.30−2 sample.

Figure 11 shows the ∆AIRT's difference of the three samples at each stage. It revealed that in the compaction stage, the water body is confined to the interior of the rock sample. Its control effect on the ∆AIRT has not yet appeared, so the temperature change trend of the rock sample surface is dominated by the temperature rise caused by loading. In the linear elastic stage, the original fracture in the rock sample is gradually closed in the previous stage, the internal water body is difficult to seep out, so the surface temperature of the rock sample is still rising. In the fracture development stage, the internal cracks of the rock sample begin to grow, and gradually develop into macroscopic cracks, which is visible to the naked eye. The cracks begin to meet and penetrate, and the sample volume expands. In this stage, as the water begins to seep out along the developed fracture, its cooling effect on the rock sample surface begins to appear, in which 0–1 sample is cooled by 0.013 ◦C and 0–3 sample is cooled by 0.067 ◦C. Although the 0.30–2 sample still has a small temperature rise of 0.011 ◦C, the temperature rise trend has been significantly suppressed. In the post-peak failure stage, the load curve has decreased significantly since the macro fracture surface was formed. The water in the rock sample flows out in large quantities, resulting in a significant cooling effect. Among them, 0–1 sample is cooled by 0.003 ◦C, 0–3 sample is cooled by 0.118 ◦C, and 0.30–2 sample is cooled by 0.183 ◦C.

*3.2. The Functional Relationship between ΔAIRT and Load before Sandstone Seepage* By plotting the ΔAIRT-load curve of each rock sample, it can be found that when the internal water pressure is not more than 0.30 MPa, the load and ΔAIRT show a certain positive relationship in the compaction stage and the linear elastic stage, that is ΔAIRT In this experiment, when the internal water pressure is not more than 0.30 MPa, the water seeps out after the crack is developed, thus causing the cooling phenomenon. When the water pressure is 0.45 MPa, the internal water body seeps out in the linear elastic stage, thus, the ∆AIRT value changes from up to down. For rock samples with a water pressure of 0.45 MPa, the analysis of ∆AIRT changes will be given in combination with IRV and VDIIT.

#### increases with the increase of load. The 0–2 sample, 0–3 sample and 0.30–2 sample with typical experimental results are selected for analysis. *3.2. The Functional Relationship between* ∆*AIRT and Load before Sandstone Seepage*

To further explore the functional relationship between ΔAIRT and load in this process, the ΔAIRT and load data of these rock samples in the compaction and linear elastic stages can be extracted. The function fitting can be performed according to the time parameters as shown in Figure 12. After several fitting times of, it was found that the trend By plotting the ∆AIRT-load curve of each rock sample, it can be found that when the internal water pressure is not more than 0.30 MPa, the load and ∆AIRT show a certain positive relationship in the compaction stage and the linear elastic stage, that is ∆AIRT increases with the increase of load. The 0–2 sample, 0–3 sample and 0.30–2 sample with typical experimental results are selected for analysis.

of the power function model is consistent with the corresponding relationship point. The functional expression of ΔAIRT and load (L) is: AIRT *<sup>b</sup>* ∆ = *aL* (6) where, ΔAIRT is the average infrared radiation temperature difference (°C), *L* is the axial load (kN), *a* and *b* are coefficients. To further explore the functional relationship between ∆AIRT and load in this process, the ∆AIRT and load data of these rock samples in the compaction and linear elastic stages can be extracted. The function fitting can be performed according to the time parameters as shown in Figure 12. After several fitting times of, it was found that the trend of the power function model is consistent with the corresponding relationship point. The functional expression of ∆AIRT and load (L) is:

$$
\Delta \text{AIRT} = \text{aL}^{\text{b}} \tag{6}
$$

where, ∆AIRT is the average infrared radiation temperature difference (◦C), L is the axial load (kN), a and b are coefficients.

**Figure 12.** Data of each sample in the compaction and elastic stages. (**a**) 0−2 sample; (**b**) 0−3 sample; (**c**) 0.30−2 sample. **Figure 12.** Data of each sample in the compaction and elastic stages. (**a**) 0–2 sample; (**b**) 0–3 sample; (**c**) 0.30–2 sample.

Figure 13 depicts a fitting curve of ΔAIRT-load of each sample. The maximum standard deviation of the fit curve for each sample is only 0.06429, and the minimum value of the function correlation coefficient is 0.8924, which indicates that the model selection and fit effect are ideal. The details about each sample are given in Table 4. Figure 13 depicts a fitting curve of ∆AIRT-load of each sample. The maximum standard deviation of the fit curve for each sample is only 0.06429, and the minimum value of the function correlation coefficient is 0.8924, which indicates that the model selection and fit effect are ideal. The details about each sample are given in Table 4. *Sustainability* **2022**, *14*, x FOR PEER REVIEW 14 of 23

**Figure 13.** Fitting curve of each sample. (**a**) 0−2 sample; (**b**) 0−3 sample; (**c**) 0.30−2 sample. **Figure 13.** Fitting curve of each sample. (**a**) 0–2 sample; (**b**) 0–3 sample; (**c**) 0.30–2 sample.

0–2 0.9063 −0.36895 −0.09505 6.429% 0–3 0.9623 0.06149 0.15406 2.705% 0.30–2 0.8924 −0.70989 −0.02894 2.517%

Figure 14 depicts the ΔAIRT-load-IRV curve of 0.45–2 sample. It revealed that in the compaction stage (0 s−217.15 s), the ΔAIRT of 0.45–2 sample shows an upward trend, rising from −0.013 °C to 0.057 °C, increasing by 0.070 °C, and the corresponding load curve bends upward to 36.98 kN. As the water body inside the rock sample has not yet seeped out, the control effect on the surface temperature of the rock sample has not yet appeared. The temperature change trend is mainly dominated by the temperature rise caused by

**Deviation**

uniaxial loading, and the IRV has been stable between 0.013 and 0.016.

*3.3. IRV Response Characteristics of Sandstone Seepage*

**Table 4.** Function fitting parameters of ΔAIRT and load of some samples.


**Table 4.** Function fitting parameters of ∆AIRT and load of some samples.

#### *3.3. IRV Response Characteristics of Sandstone Seepage*

Figure 14 depicts the ∆AIRT-load-IRV curve of 0.45–2 sample. It revealed that in the compaction stage (0 s−217.15 s), the ∆AIRT of 0.45–2 sample shows an upward trend, rising from −0.013 ◦C to 0.057 ◦C, increasing by 0.070 ◦C, and the corresponding load curve bends upward to 36.98 kN. As the water body inside the rock sample has not yet seeped out, the control effect on the surface temperature of the rock sample has not yet appeared. The temperature change trend is mainly dominated by the temperature rise caused by uniaxial loading, and the IRV has been stable between 0.013 and 0.016. *Sustainability* **2022**, *14*, x FOR PEER REVIEW 15 of 23

**Figure 14.** IRV of 0.45−2 sample and other related data. **Figure 14.** IRV of 0.45–2 sample and other related data.

samples.

Under 0.45 MPa water pressure, the water in the rock sample escapes and seeps through the original fissures in the rock and the micro pores between the particles around 340 s (see Figure 15). At the same time, the load value reached 80.41 kN, and remained in a linear rising state, while the AIRT and IRV curves exhibited significant changes. For example, at 339.47 s, the AIRT curve attained a peak value of 0.089 °C before beginning to fall. At 338.81 s, the IRV remained stable at 0.016, but at 342.78 s, the IRV pulse jumped at 0.060 before returning to 0.015 at 343.44 s. It can be seen that when the water pressure is strong (enough to cause a water seepage point and form a water seepage surface in a short time), the inflection point of ΔAIRT from rising to falling and the pulse type jump peak of IRV can be used as an early warning signal for water seepage (water inrush) of rock Under 0.45 MPa water pressure, the water in the rock sample escapes and seeps through the original fissures in the rock and the micro pores between the particles around 340 s (see Figure 15). At the same time, the load value reached 80.41 kN, and remained in a linear rising state, while the AIRT and IRV curves exhibited significant changes. For example, at 339.47 s, the AIRT curve attained a peak value of 0.089 ◦C before beginning to fall. At 338.81 s, the IRV remained stable at 0.016, but at 342.78 s, the IRV pulse jumped at 0.060 before returning to 0.015 at 343.44 s. It can be seen that when the water pressure is strong (enough to cause a water seepage point and form a water seepage surface in a short time), the inflection point of ∆AIRT from rising to falling and the pulse type jump peak of IRV can be used as an early warning signal for water seepage (water inrush) of rock samples.

**Figure 15.** Water seepage diagram of 0.45–2 sample before and after 340 s. **Figure 15.** Water seepage diagram of 0.45–2 sample before and after 340 s.

After water seepage (water inrush) of rock samples, the ΔAIRT value drops rapidly. During the period from 339.47 s to 560.24 s, the ΔAIRT decreased from the peak value of 0.089 °C to −0.039 °C, and the cooling range was as high as 0.128 °C. While the IRV also increased from 0.015 to about 0.034 and maintained stable instability. During this period, After water seepage (water inrush) of rock samples, the ∆AIRT value drops rapidly. During the period from 339.47 s to 560.24 s, the ∆AIRT decreased from the peak value of 0.089 ◦C to −0.039 ◦C, and the cooling range was as high as 0.128 ◦C. While the IRV also increased from 0.015 to about 0.034 and maintained stable instability. During this period, the load curve has been in a linear rising state, reaching 179.46 kN at the end of the stage.

the load curve has been in a linear rising state, reaching 179.46 kN at the end of the stage. In the fracture development stage (560.24 s–638.80 s), IRV appears a step-type jump compared with the previous stage. In the later stage of the last linear elastic stage, IRV was once stable at around 0.034. Though the appearance of first peak of the load curve, the IRV curve rises rapidly, and remains constant at about 0.045 at this stage. This can be understood that the IRV response characteristics of the rock samples entering the fracture development stage. During this period, the load curve decreased from 179.46 kN to about In the fracture development stage (560.24 s–638.80 s), IRV appears a step-type jump compared with the previous stage. In the later stage of the last linear elastic stage, IRV was once stable at around 0.034. Though the appearance of first peak of the load curve, the IRV curve rises rapidly, and remains constant at about 0.045 at this stage. This can be understood that the IRV response characteristics of the rock samples entering the fracture development stage. During this period, the load curve decreased from 179.46 kN to about 165.42 kN, and ∆AIRT was still in a downward trend.

165.42 kN, and ΔAIRT was still in a downward trend. In the post-peak failure stage (638.80 s–711.71 s), IRV continued to rise in stages. IRV, which was previously stable at 0.045 in the fracture development stage, rose rapidly to 0.055 and maintained a stable fluctuation trend. During this period, the load curve In the post-peak failure stage (638.80 s–711.71 s), IRV continued to rise in stages. IRV, which was previously stable at 0.045 in the fracture development stage, rose rapidly to 0.055 and maintained a stable fluctuation trend. During this period, the load curve reached the peak of 168.61 kN and began to drop, while the ∆AIRT value was stable at −0.079 ◦C.

reached the peak of 168.61 kN and began to drop, while the ΔAIRT value was stable at −0.079 °C. Figure 15 is an image recording of water seepage of the 0.45–2 sample before and after 340 s. The rock sample's observation surface is dry at 338 s, and a wet water point appears at the upper part of the rock sample, that is, the water seepage point. The seepage point is the starting point of the seepage process. After the water seepage, the wet area centered on the water seepage point began to expand. With time, it mainly expanded to Figure 15 is an image recording of water seepage of the 0.45–2 sample before and after 340 s. The rock sample's observation surface is dry at 338 s, and a wet water point appears at the upper part of the rock sample, that is, the water seepage point. The seepage point is the starting point of the seepage process. After the water seepage, the wet area centered on the water seepage point began to expand. With time, it mainly expanded to the lower part of the rock sample and rapidly formed water droplets to slide down, which also affected the changes in ∆AIRT curve and IRV curve.

#### the lower part of the rock sample and rapidly formed water droplets to slide down, which *3.4. VDIIT Response Characteristics of Sandstone Seepage*

also affected the changes in ΔAIRT curve and IRV curve. *3.4. VDIIT Response Characteristics of Sandstone Seepage* Figure 16 is the ΔAIRT-load-VDIIT curve of the 0.45–2 sample. Figure 16 revealed the VDIIT of this rock sample is always around 0.0040 in the early stage of the experiment. However, between 250.20 s and 252.28 s, VDIIT jumped from 0.0040 to 0.0062, and then Figure 16 is the ∆AIRT-load-VDIIT curve of the 0.45–2 sample. Figure 16 revealed the VDIIT of this rock sample is always around 0.0040 in the early stage of the experiment. However, between 250.20 s and 252.28 s, VDIIT jumped from 0.0040 to 0.0062, and then rapidly decreased to 0.0016. This point can be used as a precursor of water seepage of rock samples. After a development period, VDIIT suddenly increased to 0.0130 at 340.13 s, then

in Figure 17.

jumped to 0.0408 at 342.78 s. This time point also corresponds to the inflection point of AIRT from rising to falling and the water seepage phenomenon, as shown in Figure 15. the left of the center upper part. Over time (555 s–560 s), the two seepage zones developed, expanded, and penetrated each other, forming a Y-shaped macro fracture. During this period, the ΔAIRT also rapidly decreased to 0.013 °C. in Figure 17. Figure 17 shows the macro crack development and fracture in the water seepage process of 0.45–2 sample before and after 552 s. At 551 s, longitudinal cracks appeared in

rapidly decreased to 0.0016. This point can be used as a precursor of water seepage of rock samples. After a development period, VDIIT suddenly increased to 0.0130 at 340.13 s, then jumped to 0.0408 at 342.78 s. This time point also corresponds to the inflection point of AIRT from rising to falling and the water seepage phenomenon, as shown in Figure 15.

rapidly decreased to 0.0016. This point can be used as a precursor of water seepage of rock samples. After a development period, VDIIT suddenly increased to 0.0130 at 340.13 s, then jumped to 0.0408 at 342.78 s. This time point also corresponds to the inflection point of AIRT from rising to falling and the water seepage phenomenon, as shown in Figure 15.

The VDIIT also shows abnormal fluctuation when the rock sample breaks and water seep. At 551.27 s, VDIIT jumps from 0.0043 of the previous frame to 0.0063, then drops to 0.0017 at 552.60 s. It can be seen from the image records that this time point corresponds to the macro crack development and fracture water seepage process of the rock, as shown

Figure 17 shows the macro crack development and fracture in the water seepage process of 0.45–2 sample before and after 552 s. At 551 s, longitudinal cracks appeared in the middle of the rock sample observation surface, and water flowed out at the lower part. At 552 s, a VDIIT fluctuated when longitudinal water seepage growth also appeared, at

The VDIIT also shows abnormal fluctuation when the rock sample breaks and water seep. At 551.27 s, VDIIT jumps from 0.0043 of the previous frame to 0.0063, then drops to 0.0017 at 552.60 s. It can be seen from the image records that this time point corresponds to the macro crack development and fracture water seepage process of the rock, as shown

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**Figure 16.** VDIIT of 0.45−2 sample and other related data. **Figure 16.** VDIIT of 0.45–2 sample and other related data. -0.08 0

The VDIIT also shows abnormal fluctuation when the rock sample breaks and water seep. At 551.27 s, VDIIT jumps from 0.0043 of the previous frame to 0.0063, then drops to 0.0017 at 552.60 s. It can be seen from the image records that this time point corresponds to the macro crack development and fracture water seepage process of the rock, as shown in Figure 17. 0 100 200 300 400 500 600 700 800 -0.10 Time(s) -0.01 -20 **Figure 16.** VDIIT of 0.45−2 sample and other related data.

**Water Seepage Precursor**

**Figure 17.** Macro crack development and fracture water seepage process of 0.45–2 sample before and after 552 s. The red circle represents the location of fracture development. **Figure 17.** Macro crack development and fracture water seepage process of 0.45–2 sample before and after 552 s. The red circle represents the location of fracture development.

Figure 17 shows the macro crack development and fracture in the water seepage process of 0.45–2 sample before and after 552 s. At 551 s, longitudinal cracks appeared in the middle of the rock sample observation surface, and water flowed out at the lower part. At 552 s, a VDIIT fluctuated when longitudinal water seepage growth also appeared, at the left of the center upper part. Over time (555 s–560 s), the two seepage zones developed, expanded, and penetrated each other, forming a Y-shaped macro fracture. During this period, the ∆AIRT also rapidly decreased to 0.013 ◦C.

In order to reflect the mutation characteristics of VDIIT of the sample, the mutation threshold of VDIIT is determined based on the Pauta Criterion, and the discrimination criteria can be calculated using Equation (7).

$$|\varepsilon - \mu| > \Im \sigma \tag{7}$$

where: *ε* is the VDIIT value, *µ* is the average value of VDIIT, *σ* is the standard deviation of VDIIT. The infrared radiation threshold is *µ* ± 3*σ*.

For example, the Sandstone sample 0.45–2 mutation threshold of VDIIT of the sandstone sample based on Pauta Criterion is 0.00798. It can be seen from Figure 16 that the VDIIT index based on the Pauta Criterion can effectively identify the VDIIT mutation in the process of water seepage (water inrush), which can be used as an early warning of disasters. Table 5 shows the mutation threshold statistics of all sandstone samples. The average value of the upper threshold of the mutation threshold is 0.00627, the maximum value is 0.00798, and the minimum value is 0.00559. When water seepage (water inrush) occurs in the rock, the difference in the infrared radiation temperature matrix increases, which makes VDIIT suddenly increase. Therefore, when identifying VDIIT mutations, it is only necessary to consider the upper threshold. In the application process, the minimum value of mutation threshold 0.00559 should be taken as the early warning threshold to ensure the accuracy of early warning.

**Table 5.** Water seepage (water inrush) threshold of sandstone samples.


#### **4. Discussion**

The rock, before uniaxial loading, contains a certain amount of pores, air and water. In the process of uniaxial loading, the internal stress of rock mass will increase, accompanied by pore compression, crack development, fracture and water seepage.The coupling effect of water pressure and stress leads to rock mass fracture, and the crack development will promote the seepage of water in the rock. The change of energy (∆E) on the rock surface under coupled stress-hydro effect mainly includes the following five parts:

$$
\Delta \mathbf{E} = \Delta \mathbf{E}\_1 + \Delta \mathbf{E}\_2 + \Delta \mathbf{E}\_3 + \Delta \mathbf{E}\_4 + \Delta \mathbf{E}\_5 \tag{8}
$$

∆E<sup>1</sup> is energy that the gas escape process carries in the primary pore. It has been confirmed through laser Raman spectroscopy analysis technology that CH4, CO2, O<sup>2</sup> and other gases are in most rocks' pores [75]. Before the pores are damaged, the internal gas exists in the interior or surface of the pores in a free or adsorbed state. Under the action of external load, the pores are compressed or even destroyed, resulting in the escape of internal gas. In the process of gas escape, some energy will be taken away. Therefore, generally, ∆E<sup>1</sup> < 0.

∆E<sup>2</sup> is the energy generated by friction heat generation. In the rock's interior, the friction behavior will occur between the pores, fractures, joints and rock particles developed in all directions. Two factors affect the friction heat generation process: the positive pressure on the contact surface and the friction coefficient. When the friction coefficient is constant, the greater the normal stress on the contact surface, the greater the friction force, and the more work is done to overcome the friction force in the process of crack and particle sliding, thus causing the temperature of the contact surface to rise, so ∆E<sup>2</sup> > 0.

∆E<sup>3</sup> is the energy generated by the thermoelastic effect. The change of temperature rise of the loaded sample is in direct proportion to the change of stress, and the expression is:

$$
\Delta \mathbf{T}/\mathbf{T} = \mathbf{K}\_0 \Delta \sigma \tag{9}
$$

where: T is the absolute temperature of the solid unit; ∆T is the temperature change; ∆σ is the variation of the principal stress sum, and K<sup>0</sup> is the thermal elastic coefficient.

In the process of uniaxial loading, the principal stress increases with loading, so the sample temperature rises, ∆E<sup>3</sup> > 0.

∆E<sup>4</sup> is the heat generated by the expansion of original pores, fractures, and joints in the rock and the development of new fractures. With the increase of external load, internal pores and joints will shrink and close. With further loading, the pores will collapse, and the original fractures and joints will further expand, penetrate and merge, accompanied by new fractures. The increase of heat accompanies this process, so ∆E<sup>4</sup> > 0.

∆E<sup>5</sup> is the energy loss caused by the water body escaping. With the development, expansion, and penetration of rock fracture, the water in the sample begins to seep out. Water's specific heat capacity and thermal inertia are larger than rock's. The water has an evaporation effect, the temperature of water under the same conditions is lower than that of surrounding objects, and the water seepage part shows an obvious low-temperature area in the thermal image. With the increase of water seepage, the temperature of rock sample decreases continuously, so ∆E<sup>5</sup> < 0.

The whole process of the experiment, includes the above five energy changes. With the difference in stress state, damage degree and other conditions of rock samples, the five changes work together to cause the rise and fall of rock sample temperature.

In the process of fracture and water seepage caused by rock mass compression, the seepage of water in the rock mass will lead to a decrease in infrared radiation temperature, while the thermal elastic effect, friction thermal effect, and crack propagation thermal effect will lead to the increase of infrared radiation temperature in the rock mass. Because the temperature drop of water seepage is higher than the temperature rise of rock fracture, the infrared radiation temperature of the rock will drop rapidly when the rock is near the fracture seepage. Infrared radiation has a strong sensitivity to water, which also provides the feasibility for monitoring the rock water seepage (water inrush) of underground engineering with infrared radiation.

Figures 15 and 17 show the whole process of sandstone before (fracture and water seepage) and after macro fracture development and water seepage, respectively. The microcracks on the surface of rock samples under uniaxial loading are mainly tensile cracks. For example, the microcracks on the surface of rock 0.45–2 sample first appear in the middle and late stages of loading, and gradually expand with the increase of stress, eventually forming large-scale fracture and water seepage. The authors believe this is related to the fact that the sandstone selected in this test is hard brittle sandstone. Hard rock has no obvious post-peak stage than soft rock samples such as mudstone. It is generally destroyed immediately after the peak strength, accompanied by sound. The hard rock stress-strain curves show a rapid decline after the peak stress. This type of rock strength is higher than soft rock. Most rock samples are axially split; the failure surface is nearly parallel to the axial tension failure. The specimen will not be damaged immediately after axial splitting, but also has a certain bearing capacity until a through tensile failure crack is formed in the rock. However, the water seepage in the rock sample impacts the rock's failure form; that is, a small number of rock samples appear shear microcracks on the surface in the

middle and late stages of loading, and then the water seeps out along the shear microcracks. This is because the water seepage in the rock sample has a lubricating effect on the rock particles, reduces the friction force of particle crystals for friction sliding, and thus promotes the growth of primary cracks and the generation of new cracks (tensile cracks and shear cracks). The propagation of primary cracks can induce the generation of new cracks, and local damage is easy to occur, eventually leading to shear microcracks in a few rock samples. However, the seepage effect of water in the rock mass is affected by the rock mass microstructure. The rock microstructure in different areas of underground engineering is different, even in different regions of the same rock. In future research, the authors will further study the seepage effect of water in the rock mass and the corresponding infrared radiation characteristics, in combination with the microstructure characteristics of the rock mass to finally realize the monitoring and early warning of water seepage (water inrush) in underground engineering.

#### **5. Conclusions**

To explore the infrared radiation changes in the process of sandstone fracture and water seepage and determine the corresponding infrared radiation warning threshold, this study designed the infrared radiation observation experiment of sandstone failure seepage under the coupled stress-hydro effect and evaluated the corresponding relationship among load, AIRT, IRV, and VDIIT during the experiment. The following conclusions were drawn:


**Author Contributions:** R.C.—Conceptualization, writing-original draft and experiments; K.C.— Conceptualization, supervision and project administration; X.L.—Software and data curation; R.M.A.K.— Methodology; N.M.K.—Visulization; W.L.—Writing review&editing; Q.G.—Investigation and Data curation; F.W.—Experiments; Y.Y.—Investigation; J.Q.—Writing-review&editing; S.S.A.—Writing-review& editing. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the major university level scientific research project of Anhui University of Finance and Economics, "Research on the Connotative Characteristics and New Era Inheritance and Innovation of Northern Anhui Culture under the Yangtze River Delta Integration Strategy",(ACKYA20003). Also this research was supported by Researchers Supporting Project number (RSP2022R496), King Saud University, Riyadh, Saudi Arabia.

**Data Availability Statement:** The data that supports the findings of this study is available from the corresponding author upon reasonable request.

**Acknowledgments:** This research was funded by the major university level scientific research project of Anhui University of Finance and Economics, "Research on the Connotative Characteristics and New Era Inheritance and Innovation of Northern Anhui Culture under the Yangtze River Delta Integration Strategy",(ACKYA20003). Also this research was supported by Researchers Supporting Project number (RSP2022R496), King Saud University, Riyadh, Saudi Arabia. Meanwhile, the authors gratefully acknowledge Yangyang Wang and Jiangtao Zhai for helpful suggestions.

**Conflicts of Interest:** The authors declare no conflict of interest.

### **References**

