Study on the Grayscale Characteristics of Borehole Images of Progressive Failure of Coal Bodies with Different Moisture Contents

Abstract

The failure process of a coal body around a borehole has progressive characteristics. Image characteristics can visually characterize the stress and failure characteristics of the coal body around a borehole during progressive failure. To investigate the effect of the moisture content on the progressive failure of the coal body around the borehole, an image test system for the deformation and fracture of coal rock was used, and progressive failure tests of coal body specimens with different moisture content conditions around boreholes were performed. We acquired images of the deformation field during the entire process of specimen failure. Based on the grayscale image theory, the variation in the grayscale characteristic parameters of the progressive failure process was analyzed. The results show that throughout the progressive failure of coal bodies with different moisture contents around a borehole, the main specimen failure can be divided into six stages: compression density, elastic deformation, crack initiation and stable extension, crack nonstable extension, post-peak softening, and post-peak failure. With increasing moisture content, the σ_cd/σ_f values of the 20%- and 40%-moisture-content specimens were 5.1% and 11.3% lower than those of the dry specimens, respectively, and the maximum uniaxial compressive strength σ_f was 5.1% and 17.4% lower than those of the dry specimens, respectively. The number of cracks that developed decreased. The grayscale histogram had a reduced grayscale peak at each stage, and the surface distortion diminished. The declining grayscale mean curve indicates a lagging development of stress concentration zones. The declining grayscale entropy curve indicates that macroscopic cracks form. The rising grayscale standard deviation curve indicates the delayed development of strain localization zones and weakening of specimen damage. The study explains the deformation and failure characteristics of the coal body around the borehole and the variation in grayness.

1. Introduction

Gas extraction is a process to remediate gas disasters, and water drilling is widely used in the drilling construction process. Coal bodies around boreholes are affected by different moisture contents and exhibit distinct force characteristics. The crack sprouting, expansion and development processes in each stage are more complex and difficult to observe and characterize, especially regarding their influences on borehole sealing technology and the extraction effect [1,2,3,4,5]. Therefore, it is of great engineering significance to perform research on the image grayscale characteristics of coal bodies around boreholes with different moisture contents. These images can visually analyze the change characteristics of the stress concentration, surface strain, and strain localization zone of the coal body around the borehole at different stages.

Numerical simulation and physical experimental research have shown that the coal body around the borehole displays a progressive failure and a certain pattern of crack development during the failure process [6,7,8]. Some scholars further divided the progressive failure process into five stages according to the stress threshold: compression density, elastic deformation, stable crack expansion, unstable crack expansion, and post-peak failure stages [9,10,11,12,13]. These studies reveal the deformation mechanism of coal bodies around boreholes. Water drilling is widely used in the drilling construction process and around coal bodies. Therefore, scholars have analyzed the process of coal rock crack emergence, expansion, and final failure patterns in different stages of progressive failure of coal rock bodies under different moisture content conditions through experiments [14,15,16]. Moreover, the moisture content affects various mechanical parameters of the coal body, such as the modulus of elasticity, elastic energy, peak uniaxial compressive strength, peak modulus, and internal friction angle [17,18,19]. With the advancement of science and technology, digital cameras and image technology have developed substantially. Many scholars have used imagery techniques to analyze the coal body damage [20,21]. Kou used a CT scan to analyze the deformation of a coal rock body [22], and Zhang used scattered digital image technology to analyze the coal rock fracture, crack development extension, and failure evolution [23]. The former can characterize the change in internal cracks, and the latter can characterize the specimen surface deformation. In addition, during a noncontact study of the specimen loading strain field, Zhang [24] used grayscale images to characterize the specimen deformation and failure. Some scholars introduced grayscale characteristic parameters to quantify the specimen stress concentration, crack development, and strain localization zone characteristics [25,26,27,28,29]. Grayscale images and their characteristic parameters can better characterize the crack extension pattern of coal damage.

In summary, the above studies lack the division of progressive failure stages and analysis of the deformation characteristics of each stage at different pore-bearing coal sample moisture contents. Based on this observation, it was proposed that full-process progressive failure fracturing tests should be performed with porous coal specimens with different moisture contents: dry, 20% and 40%. The stress threshold was used to divide the failure stages, and the image analysis method was used to study the grayscale image characteristics of specimens with different moisture contents at each stage. Image analysis was also used to analyze the impacts of the moisture content on the mechanical characteristics, grayscale images, grayscale histograms, and grayscale characteristic parameters of specimens at each stage, and to reveal the crack expansion, deformation, and grayscale changes of specimens at each stage with different moisture contents. The results of this study can provide theoretical guidance for the analysis of coal failure images in gas extraction boreholes and borehole sealing technology.

2. Theoretical and Calculation Method

2.1. Progressive Failure Phase Division Characteristic Stress

Characteristic stress values to divide the progressive failure stage are determined by the crack closure stress σ_ee, initiation stress σ_ci, destruction stress σ_cd, and peak stress σ_f, where σ_ci and σ_cd are determined based on the crack volume strain method [30,31,32,33]. When the specimen itself has many fissures, σ_ci is difficult to determine through the stress–strain curve and must be determined through the fissure volume strain–axial strain curve. The fracture volume strain consists of two parts. One part is the volume change ε_cV for the original fracture closure and budding new fracture expansion, and the coal rock body volume strain can be expressed by the axial strain ε₁ and radial strain ε₂. The other part is the elastic deformation volume strain ε_eV at the same stress level.

$${\epsilon }_v={\epsilon }_{ev}+{\epsilon }_{cV}$$

(1)

$${\epsilon }_{cV}={\epsilon }_1+2{\epsilon }_2-\frac{1-2\nu }{E}({\sigma }_1+{\sigma }_3)$$

(2)

where E is the modulus of elasticity in the elastic phase, ν is Poisson’s ratio, σ₁ is the axial stress, σ₃ is the circumferential pressure, ε₁ is the axial strain, and ε₂ is the radial strain.

According to Equations (1) and (2), it can be obtained the specimen crack volume strain–axial strain curve. When the specimen is in the elastic state, the elastic volume strain is equal to the total volume strain, and the crack volume strain curve is horizontal, which indicates that the crack volume strain remains constant. When the specimen is in the crack extension stage, the internal crack starts to crack and expand, the crack volume starts to expand, and the crack volume strain curve deviates from the horizontal line; these actions make the curve move in the tensile direction, where the critical stress is the specimen crack initiation stress σ_ci. When the load continues to increase, the volume deformation will shift from compression to expansion, and the volume strain–axial strain curve will have an inflection point caused by the continuous crack expansion and slip inside the specimen. This inflection point corresponds to the crack failure stress σ_cd.

2.2. Grayscale Images and Characteristics of the Progressive Failure Process

The grayscale image describes the sensitivity of pixels and reflects the distribution characteristics of the image chromaticity or brightness level [34]. The grayscale can be divided into 0~255 levels; a whiter pixel in the image corresponds to a higher corresponding gray level, and a blacker pixel in the image corresponds to a lower gray level. The acquired images are converted into grayscale images, and the corresponding grayscale histograms are plotted with MATLAB. The grayscale image histogram distributes the image pixels over the entire grayscale interval, and the frequency of each gray-level pixel can be observed from the histogram. The microfracture evolutionary behavior can be identified by the microfracture-generated grayscale changes. The third-order moment μ in the grayscale histogram represents the degree of image distribution asymmetry, i.e., the stress concentration on the specimen surface [24], and is calculated as follows:

$$\mu ={\displaystyle \sum _{k=0}^{255}{(k-m)}^3}{p}_r(k)$$

(3)

where k is the gray level, m is the average gray level, and p_r(k) is the probability of occurrence of the k gray level.

The image grayscale change characteristics and statistical trends throughout progressive destruction are analyzed according to the grayscale image statistics. The fracture evolution characteristics and energy conversion of the specimen surface are reflected, and the quantitative relationship between the change in grayscale characteristic parameters and the fracture expansion characteristics is explored to construct an analytical model that truly reflects the fracture evolution characteristics. In this paper, we implement the gray mean, entropy, and standard deviation parameters to quantitatively describe the grayscale characteristics. The gray mean value m of the grayscale image represents the average image grayscale value, which reflects the specimen surface deformation trend [24]. The entropy value h of the grayscale image represents the degree of disorder of the image grayscale distribution, which reflects the accumulation of energy dissipation inside the specimen during progressive failure [35]. The standard deviation σ_std of the grayscale image is the degree of grayscale image dispersion, which reflects the development of localized deformation bands on the specimen surface [25].

The characteristic parameters of the gray mean m, entropy h, and standard deviation σ_std are calculated as follows:

$$\{\begin{array}{l}m={\displaystyle \sum _{k=0}^{255}{p}_r(k)}\\ h=-{\displaystyle \sum _{k=0}^{255}{p}_r(k)}{\log }_2{p}_r(k)\\ {\sigma }_{std}=\sqrt{{\displaystyle \sum _{k=0}^{255}{(k-m)}^3}{p}_r(k)}\end{array}$$

(4)

3. Experiments

3.1. Specimen Preparation

Specimen preparation was divided into two processes: original sample forming and water treatment. The original sample was formed by mixing gypsum and water with a mass ratio of 7:3 to make pulp [36,37]. When configured, the specimen slurry was filled into a 70 mm × 70 mm × 70 mm square specimen box, a prefabricated drilling device was placed inside the box, and the processing error was checked to ensure that it satisfied the international standards for rock mechanics specimens. The specimen was treated, and air bubbles in the slurry were expelled by vibration. The mold was removed after 24 h for maintenance, placed in a cool and ventilated place for 30 d, and polished after solidification. The prefabricated scattered spots of black matte paint on the specimen surface, which were applied on a uniformly sprayed white matte primer, dried after being sprayed to create a random pattern. The average moisture content of a saturated specimen is 40% [38]. Therefore, a YED/HS-150-type constant-temperature and -humidity test chamber was used for drying and water retention [39]. The specimens were divided into three groups—dry, 20% moisture content and 40% saturated moisture content—with five specimens in each group. Each sample was named according to “sample type–moisture content–serial number”. For example, HS-40%-1 represents the No. 1 saturated specimen, HS-20%-1 represents the No. 1 control specimen, and HS-0%-1 represents the No. 1 dry specimen. During sample maintenance, the coal samples were weighed every 24 h until the sample weight m1 was constant, and then the samples were removed.

To reduce the influences of nonhomogeneous specimen dispersion on the experimental results, the following tasks were performed during the test: (1) Test the mechanical properties of complete specimens with the same loading rate and choose specimens with high overlapping of the stress–strain curves, which have less mechanical parameter variability and good homogeneity. (2) Use three sets of coal specimens with no surface cracks and identical longitudinal wave speeds for the wave speed test.

3.2. Test Process

The tests were conducted with the DNS200 loading system and VIC-3D^® noncontact full-field strain observation system, as shown in Figure 1. The loading system adopts the displacement loading method, and the loading rate is 0.05 mm/min. The VIC-3D^® noncontact full-field strain observation system consists of a digital image correlation (DIC) processing software, a binocular CCD camera, a data acquisition-and-storage system, and illumination equipment. The dynamic microscopic specimen scatter images during the loading process are acquired by the binocular CCD camera with a 1-Hz acquisition frequency, the specimen surface displacement and strain are calculated and analyzed by the DIC software, and the grayscale histogram of the specimen surface strain is calculated with the MATLAB algorithm.

4. Progressive Failure Phase Grayscale Analysis

4.1. Progressive Failure Stage Division

Dry, 20% and 40% moisture content specimens with obvious surface deformation characteristics and uniform texture were selected according to the DNS200 loading system results, and the stress–strain curves were plotted, as shown in Figure 2 and Figure 3.

The characteristic stress threshold values can be obtained from Figure 2 and Figure 3, as shown in

Table 1. Typical specimen characteristic stress threshold values.

Specimen	σee/MPa	σci/MPa	σcd/MPa	σf/MPa	σee/σf	σci/σf	σcd/σf
HS-0%	2.70	5.34	8.79	12.93	0.209	0.413	0.680
HS-20%	2.49	4.87	7.96	12.27	0.203	0.397	0.649
HS-40%	2.07	4.22	6.42	10.68	0.194	0.395	0.601

.

As shown in Figure 2 and Figure 3, the dry and moisture-bearing specimens show identical progressive failure trends. Table 1 shows that the failure process can be divided into six stages:

① Stage I—pressure density stage. In the specimen internal primary crack pressure-dense closure, there are no significant changes in surface deformation, and the stage ends at the crack closure stress σ_ee. With increasing moisture content, the specimen σ_ee/σ_f ratio decreases by 4.2~7.5%. A comparison with the literature [40] shows that the ratio reduction rate is small. This paper uses porous coal specimens with larger porosity and stronger permeability than red sandstone, and the water has a greater effect on the coal body internal microcrack filling.

② Stage II—elastic deformation stage. All stress–strain curves show a linear growth trend, and the stage ends at the crack initiation stress σ_ci. No significant changes occur on the surface of either dry or moisture-bearing specimens. With increasing moisture content, the specimen σ_ee/σ_f ratio decreases by 3.5~4.2%, which indicates that water has less influence on the deformation at this stage.

③ Stage III—crack initiation and stable expansion stage. This phase begins and ends at the crack failure stress σ_cd. The stress–strain curve of the dry specimen rapidly increases with the development of more internal stress concentration areas and the formation of more microcracks from Stage II. The rising trend of the moisture-containing specimen curve is slower, the surface strain is larger, and the stress is smaller than those of Stage II. With increasing moisture content, the specimen ratio σ_cd/σ_f obviously decreases by 5.1~11.3%, which indicates that water affects the crack initiation and stable expansion stage of the specimen and results in hysteresis in the specimen deformation behavior.

④ Stage IV—crack nonstable extension stage. This stage starts and ends at the peak stress σ_f. Macroscopic main cracks appear on the surface of the dry specimen, the curve has a tendency of elastic–plastic deformation, and the surface deformation is obvious. No moisture-bearing specimens show macroscopic main cracks on the surface, and the curve tends to slowly rise. The uniaxial compressive strength significantly decreases with increasing moisture content (dry specimen >20% moisture content specimen >40% saturated moisture content specimen). There is a 5.1% higher uniaxial compressive strength at the peak point of the dry specimen (σ_f = 12.93 MPa, ε = 0.01) than that at the peak point of the 20% moisture content specimen (σ_f = 12.27 MPa, ε = 0.012). There is a 17.4% higher uniaxial compressive strength at the peak point of the dry specimen than that at the peak point of the 40% full moisture specimen (σ_f = 10.68 MPa, ε = 0.014). With increasing moisture content, the surface strain increases and specimen deformation hysteresis occurs, which indicates that water has a softening effect on the specimen.

⑤ Stage V—post-peak softening stage. After the specimen reaches the maximum compressive strength, the specimen stress–strain curve is decreased while the axial deformation is still rapidly increasing; the rock is further softened after the peak, and the phase stops at 90% of the peak strength after the peak σ_RS1. Macro cracks appear on the surface of the moisture content specimens, and the surface deformation is obvious. With increasing moisture content, there are fewer surface cracks.

⑥ Stage VI—post-peak destruction stage. The specimen has been completely destroyed inside the macroscopic main crack, and other secondary cracks accelerate the development of mutual penetration to form a macroscopic fracture surface and a broken area; these observations are accompanied by a sharp rock specimen expansion. With increasing moisture content, specimens tend to develop ductile failure.

4.2. Grayscale Image of Progressive Failure Cracks

According to the specimen size, a 48 pixel × 48 pixel area centered on the borehole was selected to draw grayscale images of each stage and to analyze the deformation and failure characteristics of each progressive failure stage, as shown in Figure 4.

As shown in Figure 4, the drying and moisture content specimens show different surface deformation characteristics at each stage, and the trends are as follows:

① Dry specimen. In Stage II (σ_ci = 5.34 MPa, ε = 0.0061), the dry specimens show obvious tensile and compressive strain zones inside and around the borehole, and internal microcracks are developed. In Stage III (σ_cd = 8.79 MPa, ε = 0.0076), the tensile strain zone in the upper part of the specimen expands, an obvious localization zone appears on the left side [41], and macroscopic cracks almost appear. In Stage IV (σ_f = 12.93 MPa, ε = 0.01), the primary cracks are fully developed through the surface of the specimen, secondary cracks are developed and extended, and the number of cracks is high. In Stage V (90% σ_f = 11.64 MPa, ε = 0.0104) and Stage VI (80% σ_f = 10.34 MPa, ε = 0.0129), the specimen strain localization zone increases, and the specimen failure is accelerated.

② A 20%-moisture-content specimen. In Stage III (σ_ci = 5.34 MPa, ε = 0.0061), the specimens are locally deformed, and a more obvious stress concentration phenomenon appears. In Stage IV (σ_f = 12.27 MPa, ε = 0.0117), macroscopic cracks appear on the left side of the specimen and around the borehole, and specimen failure begins. In Stage V (90% σ_f = 11.04 MPa, ε = 0.0131) and Stage VI (80% σ_f = 9.82 MPa, ε = 0.0141), the surface strain localization zone is fully developed, the number of cracks increases, and the specimens are severely damaged.

③ A 40%-moisture-content specimen. The surface change of the specimen is not obvious until Stage IV. In Stage IV (σ_f = 10.68 MPa, ε = 0.014), a significant stress concentration appears around the borehole of the specimen through its surface. In Stage V (90% σ_f = 9.61 MPa, ε = 0.0154), macroscopic cracks appear on the surface of the specimen but have not penetrated the surface. In Stage VI (80% σf = 8.54 MPa, ε = 0.0164), the surface strain localization zone is fully developed, the macroscopic primary crack penetrates the surface, the number of secondary cracks increases, and the specimen is severely damaged.

Longitudinal observation shows that the moisture content has the following effects on each failure stage: (1) In Stage I, no significant changes occur on the surfaces of both dry and moisture-bearing specimens. (2) In subsequent stages, with the increase in moisture content, the stress concentration phenomenon on the specimen surface appears to lag, the macroscopic crack development of the specimen appears to lag, the degree of specimen deformation is weakened, the number of cracks is reduced, and the development of the localized zone of surface strain is delayed.

4.3. Progressively Corrupted Image Grayscale Histogram

Based on the grayscale images of the surfaces of the dry and moisture-containing specimens [42], the grayscale histogram at each stage is drawn, as shown in Figure 5. The grayscale peaks in each stage first increase and subsequently decrease, the grayscale distribution changes from “low and wide” to “high and narrow”, and the grayscale values move to low grayscale. The calculated grayscale histogram results are consistent with the experimental results of the literature [38].

As shown in Figure 5, at Stage IV, the peak increase in grayness significantly changes with the change in moisture content, and the grayness histogram has the following trends when the failure of the specimen is analyzed with Stage IV as the axis:

① Before the stress is loaded to σ_cd, the peak grayness of the dry specimen rises faster than it does, the grayness distribution changes to “high and narrow” faster, and the third-order moment μ arc is larger, which indicates that the strain field on the specimen surface is unevenly distributed. The surface deformation localization zone is more developed, mainly due to the dry specimens in the nonstable crack extension stages. The peak grayness of the specimen containing moisture more slowly rises, and the third-order moment μ arc is smaller. By combining these results with those of Figure 4, the strain field inside the specimen is uniformly distributed, and water plays a role in filling the microcracks inside the specimen at the early stage of compression density, while no obvious stress concentration phenomenon occurs at the nonstable crack expansion stage.

② When the stress is between σ_cd and σ_f, the peak grayness values of the HS-0%, HS-20%, and HS-40% specimens are 15.04 × 10⁴, 11.81 × 10⁴, and 14.72 × 10³, respectively. When the moisture content increases, the peak grayness corresponding to the peak stress point significantly decrease; the peak grayness of the moisture-bearing specimen rapidly increases, the grayness distribution rapidly changes to “high and narrow”, the third-order moment μ arc increases, and the internal strain field is not uniformly distributed. These phenomena occur because the moisture-bearing specimens have a certain energy storage period before the stable crack extension stage when energy is released, stress concentration zones appear, and microscopic cracks are formed [25].

③ After the stress is loaded to σ_f, the peak grayness of the dry specimen more rapidly decreases, the grayness distribution shifts to “low and narrow”, the third-order moment μ arc decreases, and the grayness distribution remains in the (40,110) interval. The failure is severe, mainly due to the macroscopic main crack of the specimen running through the surface, which results in stress failure at the crack and a reduced load-bearing capacity. The peak grayness of the 20%-moisture-content specimen linearly decreases, which indicates that the macroscopic main crack appears and has not yet penetrated, and more residual stress in the specimen is causing further failure to the specimen. The grayness peak of the 40% moisture content specimen slowly decreases and subsequently stays within the (40,110) interval, which indicates that the maximum uniaxial compressive strength of the specimen is small after the macroscopic cracks appear on the surface of the 40% moisture content specimen, the residual stress after the peak is small, and the specimen slowly experiences failure and shows a ductile failure trend.

4.4. Progressive Failure Grayscale Characteristic Parameters

Considering the experimental variability, the gray mean, entropy, and standard deviation of the three grayscale characteristic parameters of the HS-0%, HS-20%, and HS-40% grayscale images during loading are separately calculated. To suppress the influence of directional components on the calculated results of the specimens, the results are normalized, where the horizontal coordinates of the curve are the stress levels, the negative values are the residual stresses after the peak of the stress–strain curve, and the vertical coordinates are the normalized values of the grayscale characteristic parameters.

The grayscale mean refers to the overall trend of the grayscale variation, and the curve is shown in Figure 6. A smaller mean value corresponds to a more obvious stress concentration phenomenon. The mean grayness curves of all dry and moisture-bearing specimens show a decreasing trend, and the changes in the second, fourth, and fifth stages have the following obvious trends:

① In Stage II, the mean grayness curve of the dry specimen decreases faster, which indicates that there is a more obvious stress concentration on the surface of the dry specimen at this stage. The specimens with 20% and 40% moisture contents show an obvious rapid decline phase in the grayscale mean curve at Stage IV, which indicates that the stress concentration zone on the surface of the specimens appears for the first time with a hysteresis effect when the moisture content increases.

② In Stage IV, a sudden drop in the mean grayness curve of the dry specimen indicates the emergence of macroscopic cracks on the dry specimen surface of the dry specimen, and full development of the localized surface stress zone at this stage. The 20%-moisture-content specimen shows a sudden drop at the peak point, while the 40% moisture content specimen has not appeared, which indicates a hysteresis in the surface macroscopic cracking with increasing moisture content.

③ In Stage V, the mean grayness curve of the dry specimen shows a decreasing trend, which indicates that the secondary cracks on the surface of the dry specimen increase at this stage, and the surface strain field is larger. The 20% specimens and 40% specimens fall more gradually, and the specimens retain a certain load-bearing capacity with a tendency toward ductile failure.

The grayscale entropy value refers to the degree of grayscale confusion, and the curve is shown in Figure 7. The grayscale entropy value indicates the change in energy during specimen deformation and failure. The falling curve indicates the energy dissipation of the specimen, and the rising curve indicates the energy accumulation. All ash entropy curves of the dry and moisture-bearing specimens show a decreasing trend with obvious changes in the first, third, and fourth stages that abide by the following trends:

① In Stage I, there is a chaotic and ordered fluctuation state of the dry specimen grayscale entropy curve. The accumulation and dissipation of microcrack pressure density energy inside the specimen is stable at this stage, and the total energy inside the specimen remains stable. The 20%- and 40%-moisture-content specimens at this stage of the gray entropy curve experience a short fluctuation after a rapid rise in the specimen internal water-filled microcrack. Additionally, the compression density process is short, and the energy accumulation leads to a rapid rise in the curve [23].

② In Stage III, the ash entropy curves of both dry and moisture-bearing specimens show a decreasing trend, which indicates that the specimen begins to deform at this stage, the strain field increases, the dissipated energy increases, and the internal energy decreases.

③ In Phase IV, the grayscale entropy curve of the dry specimen shows a fast decreasing trend, which indicates the emergence of macroscopic cracks in the specimen and intensification of dissipation energy. The grayscale entropy curves of the 20%- and 40%-moisture-content specimens show a fast-decreasing trend lag, which indicates that with increasing moisture content, the macroscopic cracks appear to lag, and the dissipation energy intensifies the delay.

The grayscale standard deviation is the grayscale image dispersion degree, and the curve is shown in Figure 8. Reflecting the localized deformation of the specimen surface, the falling curve indicates the formation of a localized deformation zone. The standard deviation curves of the dry and moisture content specimens show a decreasing trend, and the changes are obvious in the first, fourth, fifth, and sixth stages with the following trends:

① In Stage I, the standard deviation curve of the dry specimen grayness has a chaotic and ordered fluctuation state. The internal microcrack densification process leads to curve fluctuation changes and a shorter fluctuation time for moisture-containing specimens, which indicates that water has a filling effect on the internal pore structure of the specimen at the early stage of loading, which results in shorter densification fluctuation times.

② In Stage IV, the grayscale standard deviation curve increases, the strain field inside the specimen increases, and the strain localization zone develops. Fast-growing segments first appear in the dry specimens, followed by the full development of strain localization zones and the appearance of macroscopic cracks. With increasing moisture content, the fast-growing section exhibits hysteresis, macroscopic cracks appear delayed, and the strain localization zone development slows.

③ In Stages V and VI, the grayscale standard deviation curve shows a smooth trend, which indicates the formation of secondary cracks in the deformation localization zone of the specimen and a decrease in frequency of the deformation localization zone.

In summary, there is a correspondence between the three grayscale characteristic parameters and the characteristic stress levels at each stage. With increasing moisture content, the grayscale parameter has the following trends: (1) The mean grayscale curve shows a decreasing trend with obvious changes in Stages II, IV, and V. Hysteresis occurs in the descending section of the curve where the surface of the specimen is damaged, with delayed surface macrocracking and deformation failure. (2) The grayscale entropy curve has a decreasing trend with significant changes in Stages I, III, and IV. The slope of the falling curve increases, and the specimen crack sprouting and significant crack expansion processes exhibit a hysteresis response. (3) The overall grayscale standard deviation curve shows an upward trend with significant changes in Stages I, IV, V, and VI. The slope of the rising curve increases, and the localized deformation zone on the specimen surface appears hysteretic and weakly developed.

5. Conclusions

(1) The characteristic stress values were obtained from the progressive failure tests and stress–strain curves of the specimens containing boreholes with different moisture contents. The progressive failure process was classified into the compression-density, elastic deformation, crack initiation and stable expansion, crack unstable expansion, post-peak softening, and post-peak failure stages. With increasing moisture content, the σ_cd/σ_f ratio of the dry and moisture-containing specimens significantly decreased by 5.1~11.3%; the maximum uniaxial compressive strength of the specimens significantly changed, and the moisture-containing specimens had 5.1~17.4% smaller strength values than the dry specimens.

(2) Strain grayscale images can visualize the crack development around the borehole. When the moisture content increased, the failure to the coal rock body around the borehole weakened, the number of cracks on the surface of the specimen decreased, and the stress concentration phenomenon exhibited hysteresis.

(3) The grayscale distribution and grayscale peak increments in the grayscale histogram showed a regular variation. During the destruction process, the grayness distribution moved from high grayness to low grayness and transformed from “low and wide” to “high and narrow”. The peak grayness increment decreased with increasing moisture content, but it significantly increased with increasing moisture content in Stage IV.

(4) The surface deformation failure characteristics of progressive failure specimens were characterized by gray characteristic parameters. With increasing moisture content, the internal structure of the sample softened, the degree of compression resistance decreased, and the brittleness weakened. As a result, the brightness and darkness, confusion, and discreteness of grayscale images decreased. The changes in mean gray value, gray entropy value, and gray standard deviation tend to be flat. The characteristic segments of the curve are hysteretic, which results in a tendency for the specimen to exhibit ductile failure.

This study shows that the grayscale images of the strain fields of the specimens and their characteristic parameters can better characterize the evolution of crack development and expansion at each stage of progressive failure. Thus, this research presents new ideas for the analysis of coal failure images and the guidance of borehole sealing technology.

6. Declarations

The research study was successfully performed with contributions from all authors, and all authors approved the publication of the paper. The data to support the findings of this study are available from the corresponding author upon request. The authors declare that there are no conflicts of interest regarding the publication of this paper. This work was supported by the National Natural Science Foundations of China, Study on permeability enhancement mechanism and parameter optimization of CO₂ deep hole presplitting blasting in coal seam (Grant No. 51874234); the mechanism of gas induced by the fracture expansion in the “U-shaped zone” of the double-prevention drillhole (Grant No. 52104216); subcritical expansion mechanism of cracks around the gas drainage borehole with the stress corrosion (Grant No. 2020M683680XB). The main research idea and manuscript preparation were contributed by Hongyu Pan; Bing Ji contributed to the manuscript preparation and performed the correlative experiment. Xiang Ji gave several suggestions from the industrial perspectives. Lei Zhang, Kang Wang, Haotian Wang, and Tianjun Zhang assisted in finalizing the research work and manuscript. Finally, thanks to the test platform provided by the Key Laboratory of Western Mine Exploitation and Hazard Prevention of the Ministry of Education, the test was successfully completed, and data were obtained.