*Article* **The Infrared Radiation Characteristics of Sandstone Fracture Seepage under Coupled Stress-Hydro Effect**

**Ruoyu Cui 1,2, Kewang Cao 1,2,\*, Xinci Li <sup>3</sup> , Rana Muhammad Asad Khan 4,5, Naseer Muhammad Khan <sup>6</sup> , Wei Liu <sup>7</sup> , Qiangqiang Gao <sup>7</sup> , Fagang Wang 7,8,9, Yuanzhong Yang <sup>10</sup>, Jiangbo Quan 8,11 and Saad S. Alarifi <sup>12</sup>**


**Abstract:** Effective monitoring of rock fracture and seepage is an important information means to ensure the safety of geotechnical engineering. Therefore, sandstone samples were subject to uniaxial compression under different hydraulic conditions in the presence of infrared radiation and observation. This study uses the multiple infrared radiation indexes (∆AIRT, IRV, VDIIT) and image data to analyze the influence of coupled stress-hydro effect of infrared radiation change on sandstone surface. The main findings are: (1) The surface temperature of sandstone samples rises in the compaction and linear elastic stages, keeps stable or decreases in the fracture development stage, and rapidly decreases in the post-peak failure stage. (2) The samples with internal water pressure not more than 0.30 MPa, surface temperature and load curve at the compaction and linear elastic stage have a strong power function relationship, which a coefficient of determination is 0.8900. (3) The IRV curve appears as a pulse jump at the time of water seepage. After that, both the fracture development and the post-peak failure stages have stepped up. The VDIIT curve also appears to be a pulse jump at the time of water seepage, and obvious up and down fluctuations exist before water seepage and fracture. (4) Based on the Pauta Criterion, by analyzing the values of VDIIT during the experiment, the early warning threshold of sandstone fracture seepage is determined to be 0.00559. The research finding can provide an experimental and theoretical basis for the early warning of flood accidents in underground rock engineering.

**Keywords:** coupled stress-hydro effect; uniaxial loading; infrared radiation; warning threshold; non-destructive monitoring

### **1. Introduction**

With the rapid development of social construction, many cities worldwide have taken the development and utilization of underground space as an important way to

**Citation:** Cui, R.; Cao, K.; Li, X.; Khan, R.M.A.; Khan, N.M.; Liu, W.; Gao, Q.; Wang, F.; Yang, Y.; Quan, J.; et al. The Infrared Radiation Characteristics of Sandstone Fracture Seepage under Coupled Stress-Hydro Effect. *Sustainability* **2022**, *14*, 16454. https://doi.org/10.3390/ su142416454

Academic Editors: Mahdi Hasanipanah, Danial Jahed Armaghani and Jian Zhou

Received: 22 November 2022 Accepted: 5 December 2022 Published: 8 December 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

solve the population, resource and environmental crises and implement the concept of sustainable development [1–9]. However, the development of underground space and other geotechnical engineering is often restricted by groundwater [10–17]. Because water can cause changes in the physico-chemical properties of rocks, it is generally regarded as one of the most active and direct factors in geotechnical engineering disasters [18–25]. The rock in the engineering site is usually subject to the double action of water pressure and external force. Therefore, it is imperative to explore the dynamic law of rock fracture and seepage under the coupled stress-hydro effect and carry out the prediction research of water damage accidents to reduce the occurrence rate of geotechnical engineering accidents.

It has been found, that when the rock breaks, it usually releases electromagnetic energy [26–31], elastic energy [32–41], thermal energy [42–44], acoustic energy [45–51], and other kinds of energy [52]. Hence, generating a variety of disaster warning methods related to rock mass, such as infrared radiation method [53,54], electromagnetic radiation method [55,56], acoustic emission method [57,58], potential method [51,59] and microseismic method [60,61]. Among these, as a non-contact method, the infrared radiation method has the advantages of high accuracy [62], strong reliability [63], simple operation [64], and visualization [65], etc., which provides a convenient and accurate early warning method for rock fracture seepage monitoring under coupled stress-hydro effect.

Many scholars have recently studied the infrared radiation characteristics of rock failure and instability. Wu et al. [66] believe that there are abnormal changes in the infrared radiation image and temperature curve before rock failure. Lin et al. [67] found that the evolution law of average infrared radiation temperature is closely related to rock porosity, and the process of rock failure can be inferred from this. Huang et al. [68] found that the surface emissivity of loaded rock varies linearly with stress through experiments. Cao et al. [69] proposed a new index, "load-unload response ratio (LURR)" based on the rock failure characteristics under cyclic loading and unloading conditions. Zhang et al. [70] conducted some experiments on preflawed sandstone to investigate the infrared radiation characteristics during failure process and presented a new quantitative model based on Verhulst inverse function.

In addition to the above research on the infrared radiation characteristics of dry rocks, some scholars have conducted relevant experiments with water-bearing rocks. Cao et al. [71] carried out uniaxial loading tests of sandstone with different water content and thus proposed a quantitative analysis index of energy dissipation infrared radiation ratio, which was applied to predict and identify the failure of saturated rock. In addition, his team also found that rock saturation weakened its mechanical properties and amplified the changes in infrared radiation during the bearing process. According to the experimental results, they established a uniaxial loading constitutive model of rock based on infrared radiation [72]. Cai et al. [73] studied the infrared radiation characteristics of sandstone, granite, and marble with different water saturations during loading. They considered that the increment of infrared radiation has a great relationship with rock samples' water content and compressive strength. Shen et al. [74] proved through experiments that the maximum infrared radiation temperature of rock samples presents different characteristics at different stages of loading.

However, because many rock masses in the project site are under the simultaneous and continuous action of water pressure and external force, the above research cannot fully meet the requirement of real engineering application. Therefore, this paper innovatively designed the infrared radiation observation experiment of sandstone failure seepage under the coupled stress-hydro effect and established the quantitative characterization method of sandstone failure seepage through the infrared radiation response indicators, i.e., AIRT, IRV, and VDIIT. After that, the infrared radiation warning threshold of sandstone fracture and seepage was determined. The research results can provide an experimental and theoretical basis for the early warning of flood accidents in geotechnical engineering, e.g., tunnels, mines, and underground reservoirs.

#### **2. Experimental Design 2. Experimental Design** *2.1. Experimental System and Equipment* **2. Experimental Design**

#### *2.1. Experimental System and Equipment* The infrared radiation observation experiment for sandstone fracture and seepage *2.1. Experimental System and Equipment*

*Sustainability* **2022**, *14*, x FOR PEER REVIEW 3 of 23

*Sustainability* **2022**, *14*, x FOR PEER REVIEW 3 of 23

The infrared radiation observation experiment for sandstone fracture and seepage under coupled stress-hydro effect, consists of a pressure control system, a hydraulic loading system, a digital camera system, and an infrared monitoring system. The influence of coupled stress-hydro effect on the infrared parameters of the sandstone surface is analysed through the collection of various parameters during the experiment; the initial position and damage characteristics of sandstone seepage fracture under various conditions are investigated. Figure 1 depicts the experiment system schematic diagram. under coupled stress-hydro effect, consists of a pressure control system, a hydraulic loading system, a digital camera system, and an infrared monitoring system. The influence of coupled stress-hydro effect on the infrared parameters of the sandstone surface is analysed through the collection of various parameters during the experiment; the initial position and damage characteristics of sandstone seepage fracture under various conditions are investigated. Figure 1 depicts the experiment system schematic diagram. The infrared radiation observation experiment for sandstone fracture and seepage under coupled stress-hydro effect, consists of a pressure control system, a hydraulic loading system, a digital camera system, and an infrared monitoring system. The influence of coupled stress-hydro effect on the infrared parameters of the sandstone surface is analysed through the collection of various parameters during the experiment; the initial position and damage characteristics of sandstone seepage fracture under various conditions are investigated. Figure 1 depicts the experiment system schematic diagram.

provide an experimental and theoretical basis for the early warning of flood accidents in

provide an experimental and theoretical basis for the early warning of flood accidents in

geotechnical engineering e.g., tunnels, mines, and underground reservoirs.

geotechnical engineering e.g., tunnels, mines, and underground reservoirs.

**Figure 1.** Experimental system diagram. **Figure 1.** Experimental system diagram. **Figure 1.** Experimental system diagram.

Pressure control system Pressure control system

This test uses the MTS C64.106 electro hydraulic servo universal testing equipment as the pressure control system, as shown in Figure 2. In Figure 1, the press may display the test parameter curve dynamically and record the axial stress, strain, displacement, and load in real-time. The sampling frequency is 1000 Hz, the maximum static load is 1000 kN. The loading, displacement, and deformation accuracy are within 0.5%. This test uses the MTS C64.106 electro hydraulic servo universal testing equipment as the pressure control system, as shown in Figure 2. In Figure 1, the press may display the test parameter curve dynamically and record the axial stress, strain, displacement, and load in real-time. The sampling frequency is 1000 Hz, the maximum static load is 1000 kN.The loading, displacement, and deformation accuracy are within 0.5%. Pressure control system This test uses the MTS C64.106 electro hydraulic servo universal testing equipment as the pressure control system, as shown in Figure 2. In Figure 1, the press may display the test parameter curve dynamically and record the axial stress, strain, displacement, and load in real-time. The sampling frequency is 1000 Hz, the maximum static load is 1000 kN.

The loading, displacement, and deformation accuracy are within 0.5%.

**Figure 2.** MTS electro-hydraulic servo universal testing machine.

Digital camera system TThe Canon 600D SLR camera is used in this experiment to record the images. It has TThe Canon 600D SLR camera is used in this experiment to record the images. It has an 18 million pixel CMOS sensor, a digital 4 image processor, a 3-inch reversible LCD

Digital camera system

Digital camera system

The Canon 600D SLR camera is used in this experiment to record the images. It has an 18 million pixel CMOS sensor, a digital 4 image processor, a 3-inch reversible LCD screen, full HD video recorder. The camera will record the entire experiment and be utilised to watch the sample fracture and water seepage process in the later stages of the experiment. an 18 million pixel CMOS sensor, a digital 4 image processor, a 3-inch reversible LCD screen, full HD video recorder. The camera will record the entire experiment and be utilised to watch the sample fracture and water seepage process in the later stages of the experiment. Hydraulic loading system screen, full HD video recorder. The camera will record the entire experiment and be utilised to watch the sample fracture and water seepage process in the later stages of the experiment. Hydraulic loading system

*Sustainability* **2022**, *14*, x FOR PEER REVIEW 4 of 23

*Sustainability* **2022**, *14*, x FOR PEER REVIEW 4 of 23

**Figure 2.** MTS electro-hydraulic servo universal testing machine.

**Figure 2.** MTS electro-hydraulic servo universal testing machine.

#### Hydraulic loading system PPull a steel pipe out of the drilled sandstone, fill it with water, connect the pressure PPull a steel pipe out of the drilled sandstone, fill it with water, connect the pressure

Pull a steel pipe out of the drilled sandstone, fill it with water, connect the pressure gauge, and link it to the air pump interface, before strong glue using to secure the perforated iron sheet to the top of the sandstone. An air pump compression technique is used to verify that the internal water pressure reaches and maintains a specific value during the test. The primary air compressor (Figure 3) characteristic parameters are listed in Table 1. gauge, and link it to the air pump interface, before strong glue using to secure the perforated iron sheet to the top of the sandstone. An air pump compression technique is used to verify that the internal water pressure reaches and maintains a specific value during the test. The primary air compressor (Figure 3) characteristic parameters are listed in Table 1. gauge, and link it to the air pump interface, before strong glue using to secure the perforated iron sheet to the top of the sandstone. An air pump compression technique is used to verify that the internal water pressure reaches and maintains a specific value during the test. The primary air compressor (Figure 3) characteristic parameters are listed in Table 1.

**Figure 3.** Air compressor. **Figure 3.** Air compressor. **Figure 3.** Air compressor.

**Table 1.** Main characteristic parameters of the air compressor. **Table 1.** Main characteristic parameters of the air compressor. **Table 1.** Main characteristic parameters of the air compressor.


Infrared observation system Infrared observation system

Infrared observation system An infrared thermal imager and its professional control system comprise the infrared radiation observation system, as shown in Figure 4. The infrared thermal imager is an uncooled infrared thermal imager with the type varioCAM HD head 880 from infra Tec, Dresden, Germany. The essential characteristics and performance of the infrared thermal imager are described in Table 2. An infrared thermal imager and its professional control system comprise the infrared radiation observation system, as shown in Figure 4. The infrared thermal imager is an uncooled infrared thermal imager with the type varioCAM HD head 880 from infra Tec, Dresden, Germany. The essential characteristics and performance of the infrared thermal imager are described in Table 2. An infrared thermal imager and its professional control system comprise the infrared radiation observation system, as shown in Figure 4. The infrared thermal imager is an uncooled infrared thermal imager with the type varioCAM HD head 880 from infra Tec, Dresden, Germany. The essential characteristics and performance of the infrared thermal imager are described in Table 2.

**Figure 4.** Infrared thermal imager.


**Table 2.** Main Characteristic Parameters of Infrared Thermal Imager System.

#### *2.2. Sample Preparation*

The rock samples used by the authors were taken from the coal mine site and made by cutting a whole rock. First, the authors preliminarily screened the processed rock samples and eliminated the rock samples with surface cracks. Next, the authors used the U510 non-metallic ultrasonic detector to accurately measure the wave velocity of the sample. During the process, the probe should be kept in direct contact, and the probe should be in close contact with the sample through the couplant. At the same time, the authors eliminated the samples whose wave velocity deviated by more than 10% to ensure the maximum elimination of the dispersion of rock samples. The representative samples of cubic shape had dimensions 100 mm × 100 mm × 100 mm. To provide a space for water injection in the sandstone, drill a sandstone cylinder with a diameter of 50 mm and a depth of 65mm, at the centre of the sample surface with a drilling machine (see Figure 5a). After that, a steel pipe with an exterior diameter of 20 mm, an inner diameter of 18 mm, and a length of 200 mm (see Figure 5b) and an iron square piece of specification 80 mm, shall be used (see Figure 5c). Keep the drilled sandstone, steel pipe, and perforated iron sheet in a ventilated area for 24 h to allow the strong adhesive to set completely. Simultaneously, the small space at the three-part junction must be filled with strong glue and sealed to guarantee that the processed sample does not leak (see Figure 5d). *Sustainability* **2022**, *14*, x FOR PEER REVIEW 6 of 23

**Figure 5.** Sample manufacturing process. (**a**) Borehole sandstones; (**b**) Steel pipes; (**c**) Perforated iron plates; (**d**) Finished samples. **Figure 5.** Sample manufacturing process. (**a**) Borehole sandstones; (**b**) Steel pipes; (**c**) Perforated iron plates; (**d**) Finished samples.

**Sample Number**

0.15–1

**Water Pressure**

0.3 MPa

0–3 0.15–3 0.30–3 0.45–3

Figure 1 depicts the pressure control system, water pressure loading system, digital camera system, and infrared observation system. The infrared observation instrument and digital camera are placed 1 m in front of the sample to enable observation and recording. The steel pipe is used to fill the interior chamber of the loaded sample with water sample, and the steel pipe is connected to the air compressor via the rubber pipe to assist later pressurisation. Place the loaded specimen on the presser pressure plate. Given the poor bearing capacity of the rock sample's cavity, a specification of 100 mm (length) × 35 mm (width) × 30 mm (height) metal cushion block is placed on the solid part of the rock sample and its center is aligned with the loading center, as illustrated in Figure 6. Simultaneously, the reference sample used for noise reduction must be put and kept on the loaded sample's side, and its height must be consistent with that of the loaded sample.

**Sample Number**

0.30–1

**Water Pressure**

0.45 MPa

**Sample Number**

0.45–1

**Water Pressure**

0.15 MPa

**Table 3.** Experimental grouping.

**Sample Number**

0–1

*2.3. Experimental Process*

**Water Pressure**

0 MPa

To ensure the accuracy of the experimental monitoring data, the flatness parameters of the rock sample surface are set as follows: the roughness of the rock sample surface is less than 0.1 mm, and there is no bulge and depression. The side of the rock sample shall be perpendicular to the upper and lower end faces, with a deviation of less than 0.05◦ . Rock samples are natural samples without special treatment such as drying or soaking. The rock sample shall be put into the laboratory one day before the experiment to ensure that the temperature of the rock sample is consistent with the temperature of the experimental environment. That is to prevent the accuracy of the infrared radiation response information from being disturbed by the heat transfer during the experiment.

The test is divided into 4 groups, with 3 samples in each group, 12 in total. Four different water pressures of 0 MPa, 0.15 MPa, 0.3 MPa and 0.45 MPa are, respectively, used to pressurize. The experimental samples grouping details are given in Table 3.


**Table 3.** Experimental grouping.

#### *2.3. Experimental Process*

Figure 1 depicts the pressure control system, water pressure loading system, digital camera system, and infrared observation system. The infrared observation instrument and digital camera are placed 1 m in front of the sample to enable observation and recording. The steel pipe is used to fill the interior chamber of the loaded sample with water sample, and the steel pipe is connected to the air compressor via the rubber pipe to assist later pressurisation. Place the loaded specimen on the presser pressure plate. Given the poor bearing capacity of the rock sample's cavity, a specification of 100 mm (length) × 35 mm (width) × 30 mm (height) metal cushion block is placed on the solid part of the rock sample and its center is aligned with the loading center, as illustrated in Figure 6. Simultaneously, the reference sample used for noise reduction must be put and kept on the loaded sample's side, and its height must be consistent with that of the loaded sample. *Sustainability* **2022**, *14*, x FOR PEER REVIEW 7 of 23

**Figure 6.** Details of samples. **Figure 6.** Details of samples.

infrared thermal imager.

continue the experiment.

*2.4. Experimental Data Processing Method*

sample must be extracted again in a small range.

dimensional matrix with the following expression:

After arranging the necessary equipment and samples, each experimenter is responsible for configuring the storage directory and other basic settings for the press, infrared thermal imager, and other equipment, with a 0.2 mm/min loading rate. After that, the air compressor increases the water pressure to the desired value, and the valve is closed to guarantee that the internal water pressure of the rock sample remains constant. After arranging the necessary equipment and samples, each experimenter is responsible for configuring the storage directory and other basic settings for the press, infrared thermal imager, and other equipment, with a 0.2 mm/min loading rate. After that, the air compressor increases the water pressure to the desired value, and the valve is closed to guarantee that the internal water pressure of the rock sample remains constant. After

After setup, the infrared thermal imager, digital camera, press, and other equipment will begin to operate in unison under the unified password. It is prohibited for laboratory staff

After the test, all equipment shall stop working at the same time, and the test personnel shall properly save the data of all equipment, and take photos of the fracture morphology of the rock sample. After cleaning the test bench, place the next sample to

In the infrared radiation information collection system, the infrared thermal imager maps the rock samples' physical and structural changes during the experimental procedure to the infrared radiation temperature field. It shows in the form of infrared thermal images. When the difference between the background temperature and the temperature of the rock sample is large, the abnormal features of the infrared thermal picture are not visible (as shown in Figure 7), so the infrared radiation data of the rock

A rectangular area (as illustrated in Figure 7) is constructed along the whole sample section in the infrared radiation acquisition system, and the infrared radiation response information of the rectangle area is then retrieved and preserved in the form of a series of two-dimensional matrices. The resampled infrared radiation data of frame P is a twosetup, the infrared thermal imager, digital camera, press, and other equipment will begin to operate in unison under the unified password. It is prohibited for laboratory staff to move around and close the laboratory windows, curtains, and all lighting sources that may create radiation interference during the information gathering procedure of the infrared thermal imager.

After the test, all equipment shall stop working at the same time, and the test personnel shall properly save the data of all equipment, and take photos of the fracture morphology of the rock sample. After cleaning the test bench, place the next sample to continue the experiment.

### *2.4. Experimental Data Processing Method*

In the infrared radiation information collection system, the infrared thermal imager maps the rock samples' physical and structural changes during the experimental procedure to the infrared radiation temperature field. It shows in the form of infrared thermal images. When the difference between the background temperature and the temperature of the rock sample is large, the abnormal features of the infrared thermal picture are not visible (as shown in Figure 7), so the infrared radiation data of the rock sample must be extracted again in a small range. *Sustainability* **2022**, *14*, x FOR PEER REVIEW 8 of 23

**Figure 7.** Infrared thermal image of rock sample. **Figure 7.** Infrared thermal image of rock sample.

respectively.

calculated:

(, ) = ⎣ ⎢ ⎢ ⎢ <sup>⎡</sup> (1,1) (1,2) ⋯ �1, � (2,1) (2,2) ⋯ �2, � ⋮ ⋮ ⋱ ⋮ (, 1) (, 2) ⋯ �, �⎦ ⎥ ⎥ ⎥ ⎤ (1) A rectangular area (as illustrated in Figure 7) is constructed along the whole sample section in the infrared radiation acquisition system, and the infrared radiation response information of the rectangle area is then retrieved and preserved in the form of a series of two-dimensional matrices. The resampled infrared radiation data of frame P is a twodimensional matrix with the following expression:

$$f\_p(\mathbf{x}, y) = \begin{bmatrix} f\_p(1, 1) & f\_p(1, 2) & \dots & f\_p(1, L\_g) \\ f\_p(2, 1) & f\_p(2, 2) & \dots & f\_p(2, L\_g) \\ \vdots & \vdots & \ddots & \vdots \\ f\_p(L\_\mathbf{x}, 1) & f\_p(L\_\mathbf{x}, 2) & \dots & f\_p(L\_\mathbf{x}, L\_g) \end{bmatrix} \tag{1}$$

temperature (ΔAIRT) AIRT can directly reflect the bearing rock surface's overall infrared radiation field where *x* represents the row number of the matrix *fp*(*x*, *y*) and *y* represents the column number; *L<sup>x</sup>* and *L<sup>y</sup>* are the maximum number of rows and columns of *x* and *y*, respectively. According to the obtained temperature matrix, the following parameters can be calculated:

temperature. The average infrared radiation temperature (AIRT (*p*)) of the *p*th frame in the original infrared radiation thermal image sequence is expressed as: (1) Average infrared radiation temperature (AIRT) and ∆Average infrared radiation temperature (∆AIRT)

1 �  

=1

Since the radiation interference of the loaded sample and the reference sample is almost synchronous in time and space, the AIRT of the loaded sample can be subtracted from the AIRT of the reference sample to obtain the denoised ΔAIRT. This can be

The physical meaning of IRV is the changing trend of the dispersion degree of the temperature field in the original infrared radiation thermal image sequence diagram. The variance (IRV (*p*)) of the original infrared radiation thermal image sequence of the *p*th

�  

(, ) (2)

<sup>2</sup> (4)

=1

1 

IRV () =

1 

(3) Variance of differential infrared image temperature (VDIIT)

1 �   

=1

�   

�(, ) − AIRT ()�

=1

The physical meaning of VDIIT is the variation trend of the dispersion degree of the temperature field in the differential infrared radiation thermal image sequence diagram.

calculated by using Equation (3):

frame is expressed as:

(2) Infrared radiation variance (IRV)

AIRT () =

AIRT can directly reflect the bearing rock surface's overall infrared radiation field temperature. The average infrared radiation temperature (AIRT (*p*)) of the *p*th frame in the original infrared radiation thermal image sequence is expressed as:

$$\text{AIRT}(p) = \frac{1}{L\_{\text{x}}} \frac{1}{L\_{\text{y}}} \sum\_{x=1}^{L\_{\text{x}}} \sum\_{y=1}^{L\_{\text{y}}} f\_p(x, y) \tag{2}$$

Since the radiation interference of the loaded sample and the reference sample is almost synchronous in time and space, the AIRT of the loaded sample can be subtracted from the AIRT of the reference sample to obtain the denoised ∆AIRT. This can be calculated by using Equation (3):

$$
\Delta \text{AIRT}(p) = \text{AIRT}(p) - \text{AIRT}'(p) \tag{3}
$$

#### (2) Infrared radiation variance (IRV)

The physical meaning of IRV is the changing trend of the dispersion degree of the temperature field in the original infrared radiation thermal image sequence diagram. The variance (IRV (*p*)) of the original infrared radiation thermal image sequence of the *p*th frame is expressed as:

$$\text{IRV}(p) = \frac{1}{L\_x} \frac{1}{L\_y} \sum\_{y=1}^{L\_x} \sum\_{x=1}^{L\_y} \left[ f\_p(x, y) - \text{AIRT}(p) \right]^2 \tag{4}$$

#### (3) Variance of differential infrared image temperature (VDIIT)

The physical meaning of VDIIT is the variation trend of the dispersion degree of the temperature field in the differential infrared radiation thermal image sequence diagram. The variance (VDIIT (P)) of the differential infrared radiation thermal image sequence of the *p*th frame is expressed as:

$$\text{VDIIT}(p) = \frac{1}{L\_x} \frac{1}{L\_y} \sum\_{y=1}^{L\_x} \sum\_{x=1}^{L\_y} \left[ \varphi\_p(\mathbf{x}, y) - \text{AIRT}(p) \right]^2 \tag{5}$$

where *ϕp*(*x*, *y*) = *fp*+1(*x*, *y*) − *fp*(*x*, *y*).

#### **3. Experimental Results and Analysis**

### *3.1. AIRT Response Characteristics of Sandstone Seepage*

The loaded specimen ∆AIRT value has prominent change characteristics, mainly showing an upward-downward trend. According to the inflection point (breakpoint) of the corresponding load curve, the whole process can be divided into four stages: (I) compaction stage, (II) linear elastic stage, (III) fracture development stage, and (IV) post peak failure stage.

(1) sample 0–1

Figure 8 depicts the ∆AIRT-load curve for sample (0–1). At 0 s, the ∆AIRT was −0.147 ◦C. In the compaction stage, it showed a fluctuating upward trend. The sample enters the linear elastic stage at 340.17 s, at which the corresponding load is 54.27 kN, the ∆AIRT is −0.100 ◦C, which is 0.047 ◦C higher than that at the beginning. In the elastic stage, the ∆AIRT also showed an upward trend, and the temperature rise rate was almost the same as in the previous stage. Before and after 697 s, the load curve fluctuated, decreasing from 233.32 kN to 215.96 kN. At this time, the corresponding ∆AIRT was −0.043 ◦C, which indicates that the sample was at the end of the linear elastic stage, and the temperature increased by 0.057 ◦C compared with the initial stage. In the next fracture development stage, with the increase of the load curve, the ∆AIRT begins to decrease. At 796.19 s, the load curve has a peak value. After that, it rapidly decreases, which means the beginning of the post-peak failure stage. At this time, the corresponding ∆AIRT is −0.056 ◦C. At 802.80 s, the end of the experiment, the load decreased to 215.86 kN, and the ∆AIRT fell to −0.059 ◦C.

this period, the ΔAIRT was stable, and only slightly increased by 0.011 °C. After the peak of the load curve, the ΔAIRT and the load have a sudden drop trend, wherein ΔAIRT

Figure 11 shows the ΔAIRT'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 ΔAIRT 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.

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 ΔAIRT value changes from up to down. For rock samples with a water pressure of 0.45 MPa, the analysis of ΔAIRT changes will be given in combination with IRV and

dropped to −0.773 °C, which overall decreased by 0.183 °C.

**Figure 8.** Experimental data of sample 0−1. **Figure 8.** Experimental data of sample 0–1.

### (2) sample 0–3

VDIIT.

Figure 9 depicts the ∆AIRT-load curve for sample (0–3). The ∆AIRT at 0 s is 0.056 ◦C, it rises slowly at the compaction stage. In the range of 100.48 s to 120.35 s, ∆AIRT jumps from 0.063 ◦C to 0.081 ◦C, increasing by 0.018 ◦C. During this period, the load has not exceeded 2 kN, and the heat generation is caused by friction of particles in the rock sample. At 454.41 s, the bearing rock sample enters the linear elastic stage. At this time, ∆AIRT was 0.109 ◦C, which is 0.053 ◦C higher than the initial stage. In the linear elastic stage, ∆AIRT continued to rise. At 758 s, the load curve suddenly drops, and the drop amplitude reaches 13 kN. The ∆AIRT value was 0.134 ◦C, and the whole stage increased by 0.025 ◦C. The loaded rock sample thus enters the fracture development stage. In this stage, the load curve drops again at about 836 s, with a magnitude of 9 kN. At 919.91 s, the load curve reached the peak of 202.46 kN, followed by a sudden drop, which is a sign of the beginning of the post-peak failure stage. So far, the temperature drop of the whole fracture development stage is 0.057 ◦C. At the post-peak stage, the load curve and ∆AIRT both decreased rapidly, and the ∆AIRT fell to −0.041 ◦C. *Sustainability* **2022**, *14*, x FOR PEER REVIEW 11 of 23

**Figure 9.** Experimental data of sample 0−3. **Figure 9.** Experimental data of sample 0–3.

 ΔAIRT Load

Ⅰ




ΔAIRT(℃)




Ⅲ

Ⅳ

0

50

100

150

Load(kN)

200

250

300

0 100 200 300 400 500 600 700 800

Time(s)

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