An Experimental Investigation on the Microscopic Damage and Mechanical Properties of Coal Under Hygrothermal Conditions

Abstract

Investigating the microstructural damage and mechanical properties of coal under deep mine hygrothermal conditions is essential for ensuring the safe and efficient extraction of coal resources. In this study, X-ray diffraction (XRD), scanning electron microscopy (SEM), energy-dispersive spectroscopy (EDS), and nanoindentation techniques were employed to examine the surface morphology and microscale mechanical properties of coal samples exposed to four environmental conditions, initial, humidified, heated, and coupled hygrothermal, under a peak indentation load of 70 mN. The results indicate that humidification led to the formation of dissolution pores and localized surface softening, resulting in a 15.9% increase in the peak indentation depth and reductions in the hardness and elastic modulus by 29.53% and 17.14%, respectively. Heating caused localized disintegration and the collapse of the coal surface, accompanied by surface hardening, with a slight 0.4% decrease in the peak indentation depth and increases in hardness and the elastic modulus by 1.32% and 1.56%, respectively. Under the coupled hygrothermal condition, numerous fine dissolution pores and microcracks developed on the coal surface, and the mechanical properties exhibited intermediate values between those observed in the humidified and heated states. Notably, the elevated temperature suppressed the moisture penetration into the coal matrix to some extent in the hygrothermal environment. A positive correlation was found between the hardness and elastic modulus, independent of the coal sample condition. The mineralogical composition significantly influenced the microscale mechanical behavior, with hard quartz minerals corresponding to lower peak indentation depths and a higher hardness, whereas soft kaolinite showed the opposite trend.

1. Introduction

As China’s shallow energy sources are gradually exhausted, coal mining activities are progressively shifting to greater depths. Under the conditions of “three highs and one disturbance,” the gradual increase in the in situ stress, geothermal temperature, rock mass fracturing, and water inrush poses significant challenges for deep coal mining and underground engineering activities [1,2]. The presence of water facilitates the formation of pores and fractures in coal and concurrently reduces its load-bearing capacity. Temperature also contributes to the progression of microstructural defects, including pores and cracks. The macroscopic mechanical properties of coal are strongly correlated with its microscopic damage and the consequent deterioration of mechanical properties [3,4,5].

Currently, the research on the mechanical properties and failure characteristics of coal primarily depends on field core sampling. However, compared to conventional hard rocks, coal in the hygrothermal environments of deep mines displays more extensive internal fracturing and a significantly reduced strength, complicating the acquisition of standard-compliant specimens suitable for conventional tensile, compressive, and shear mechanical testing [5,6]. Therefore, introducing a novel testing method to characterize the mechanical properties of coal under hygrothermal conditions is imperative. Nanoindentation technology was initially proposed and applied by Kalei in Russia in 1968 [7]. Traditional test methods impose stringent requirements on the sample size, geometry, and structural integrity, making sampling and specimen preparation challenging. In contrast, nanoindentation technology offers rapid data acquisition and localized, non-destructive testing capabilities, making it well-suited for structurally complex and compositionally heterogeneous materials such as coal.

In recent years, nanoindentation technology has been extensively adopted by researchers to investigate the strength, deformation characteristics, and creep behavior of coal and rock masses due to its simplicity, efficiency, and non-destructive nature [8,9]. Sun et al. [10] employed nanoindentation tests to quantify the elastic modulus and firmness coefficient of coal, highlighting that nanoindentation technology offers an effective approach for characterizing the mechanical properties of coal at the microscale. Liu and Ma et al. [11,12] demonstrated that nanoindentation technology, beyond measuring conventional mechanical parameters such as the firmness coefficient and elastic modulus, can also be employed to assess fracture toughness and creep characteristics in rock mechanics studies. Chen et al. [13] performed mechanical tests on shale utilizing nanoindentation technology and compared the findings with those obtained from macroscopic testing. Their results demonstrated that nanoindentation can accurately characterize micromechanical properties and effectively predict macroscopic mechanical behavior. Bennet and Eliyahu et al. [14,15] conducted nanoindentation tests on different bedding planes of shale; their results indicated that nanoindentation technology effectively characterizes the mechanical properties of highly anisotropic materials. Dou et al. [16] performed nanoindentation tests on Huanggang granite under both dry and water-saturated conditions. Their results indicated that, compared to dry specimens, water-saturated specimens exhibited a significantly greater maximum indentation depth and plastic deformation, accompanied by marked reductions in nano-hardness and Young’s modulus. Nie et al. [17] combined nanoindentation with small-angle X-ray scattering techniques and demonstrated that the micromechanical properties of soft coal are predominantly influenced by large pores, whereas those of hard coal are chiefly governed by rigid mineral inclusions. Sun et al. [18] employed nanoindentation techniques to measure the hardness, elastic modulus, and fracture toughness of fragmented coal, observing that although the hardness and elastic modulus remained relatively constant with an increasing peak load, the fracture toughness exhibited a pronounced increasing trend. Liu et al. [19] investigated eight types of coal using nanoindentation tests, an XRD analysis, and FESEM-EDS imaging and demonstrated that the nanoscale mechanical properties of coal are strongly correlated with the coal rank, mineral composition, and microstructure. Jia et al. [20] conducted nanoindentation experiments to analyze the variations in the elastic modulus and hardness of coal samples before and after freezing and further investigated the correlation between these two properties. The results indicated that the porosity of the coal samples increased to varying extents after freezing and that the elastic modulus and hardness exhibited a positive correlation. Kossovich et al. [21] conducted depth indentation tests on three different types of coal and found that the mechanical properties of the coal matrix change with the coal grade, whereas the inclusion properties do not change as significantly. Epshtein et al. [22] combined modern nanoindentation technology with transmitted-light microscopy and proposed the use of a classic exponential weight function to describe the relationship between the effective elastic contact modulus of the sample and the indentation depth and verified the effectiveness of this method based on different maximum indentation depths.

In summary, although numerous studies have utilized nanoindentation and related experimental techniques to investigate the micromechanical properties of rocks such as shale, sandstone, and coal, research specifically targeting the surface damage and mechanical behavior of coal under the hygrothermal conditions typical of deep mining environments remains relatively scarce. Therefore, conducting an in-depth investigation into the evolution of microscopic damage and the mechanical response of coal under hygrothermal conditions holds substantial theoretical and engineering value for elucidating the deterioration mechanisms of coal’s mechanical properties in complex deep mining environments.

2. Materials and Methods

2.1. Sample Collection and Preparation

The coal samples were obtained from the 2-2 Upper Coal Seam of the Shilawusu Coal Mine in Ordos, China, at a depth of 698 m. The samples consisted of freshly dislodged coal directly collected from the underground working face. To minimize environmental contamination and mechanical damage during transportation, the samples were immediately wrapped in plastic film and transported to the laboratory. The fresh coal blocks were ground and sieved to pass through a 200-mesh screen to produce coal powder for X-ray diffraction (XRD) analysis. Additionally, the coal blocks were cut into four rectangular specimens with dimensions of 10 mm × 10 mm × 5 mm, labeled as N1, N2, N3, and N4.

The upper and lower surfaces of the specimens were ground to achieve parallelism. Considering the high surface smoothness required for nanoindentation, the specimens underwent a rigorous grinding and polishing protocol to ensure measurement accuracy. Sandpapers with grit sizes of 400, 800, 1500, 2000, 2500, and 3000 were sequentially applied during the grinding process. Subsequently, polishing was performed using diamond suspensions with particle sizes of 0.5, 0.25, and 0.1 μm. After polishing, the specimen surfaces were cleaned with anhydrous ethanol to meet experimental cleanliness standards. Finally, each specimen was sealed in plastic wrap to prevent contamination and surface degradation. The specimen preparation and testing procedure is schematically illustrated in Figure 1.

2.2. Test Process

2.2.1. XRD Test

The coal powder samples were analyzed using X-ray diffraction (XRD) for both qualitative and quantitative phase identification. The corresponding diffraction patterns are presented in Figure 2.

As shown in

Table 1. Proportion of mineral components in coal samples.

Mineral Composition	Amorphous	Kaolinite	Quartz	Carbonate
Mass fraction/%	84.28	10.44	4.12	1.16

, the coal sample is primarily composed of amorphous organic matter, accounting for 84.28%. In addition, kaolinite (Al₂(Si₂O₅)(OH)₄), quartz (SiO₂), and carbonate minerals (FeCO₃, CaCO₃) are also present, accounting for 10.44%, 4.12%, and 1.16%, respectively. Notably, the clay mineral kaolinite constitutes a relatively high proportion. Based on the mineral composition, the coal sample can be classified as a typical heterogeneous material.

2.2.2. Coal Sample Condition Control

The sample isolated from air immediately after preparation was designated as the initial state (N1), and the RHP120 constant temperature and humidity chamber was used to control the environmental conditions. Prior to implementing different environmental conditions, the chamber’s temperature and humidity were pre-adjusted to meet the required test settings. Three polished samples were selected for different environmental conditioning treatments: (1) Sample N2-H-12h was subjected to a humidity level of 95%; (2) Sample N3-T-12h was subjected to a temperature of 55 °C; and (3) Sample N4-HT-12h was subjected to coupled hygrothermal conditions (95% humidity and 55 °C temperature). Each treatment lasted for 12 h.

2.2.3. SEM and EDS Test

Prior to the nanoindentation tests, to further investigate the microscopic damage characteristics of coal under hygrothermal conditions, a Zeiss-G300 (Zeiss, Oberkochen, Germany) scanning electron microscope was employed to observe the surface micromorphology of coal samples under different conditions, including particle morphology, cracks, pores, and matrix features. Additionally, the distribution of key elements was analyzed using energy-dispersive X-ray spectroscopy (EDS) with an Oxford Xplore30 spectrometer (Oxford Instruments, Abingdon, UK), thereby identifying the presence of specific minerals. Given the differing specimen size and environmental requirements between SEM/EDS and nanoindentation tests, four additional specimens were prepared and subjected to humidification and heating treatments under the same hygrothermal conditions as described previously for samples N1 through N4.

2.2.4. Nanoindentation Test

(1)

Test Principle

Nanoindentation testing is capable of evaluating mechanical properties such as hardness, creep behavior, elastic modulus, and load–depth responses at the nanoscale. A standard test procedure typically involves three stages: loading, holding at peak load, and unloading. The Berkovich indenter, featuring a regular three-sided pyramidal geometry, is the most widely used tip in nanoindentation testing. When the indenter penetrates the surface of the specimen, the surrounding material first experiences elastic deformation. As the load continues to increase, plastic deformation progressively develops, eventually forming an indentation profile that mirrors the geometry of the indenter [23]. The indentation profile is shown in Figure 3a, where $h_{\mathrm{p}}$ is the residual indentation depth after unloading, $h_{\mathrm{m}}$ is the peak indentation depth, $h_{\mathrm{s}}$ is the sinking depth of the specimen surface, $h_{\mathrm{c}}$ is the contact depth under the peak load, and $h_{\mathrm{k}}$ is the creep depth generated during the load retention process. After unloading the load, the typical load–depth curve is shown in Figure 3b, where $F_{\mathrm{n}}$ is the peak load, $h_{\mathrm{r}}$ is the tangential depth of the unloading curve, and the slope S of the initial stage of the unloading curve is the tangential stiffness at the indentation position [18,24,25].

Nanoindentation tests were performed using the German Bruker Hysitron TI Premier system, which offers a maximum indentation depth of 5 μm, an effective load resolution of 50 nN, and a loading range of 0–150 mN. The instrument employs an electrostatic drive mechanism and features excellent temperature drift control, rapid data acquisition, and high measurement accuracy, fully satisfying the experimental requirements. The classic Oliver–Pharr method was employed to determine the hardness and elastic modulus of the specimens. As this method does not account for the load-holding stage, a holding period of 10 s was applied to ensure stable unloading data [18,24]. The specific calculation process is as follows:

$$F_{\mathrm{n}}=m{(h-h_{\mathrm{p}})}^n$$

(1)

where $F_n$ is the load, mN; constants m and n are determined by fitting the unloading curve.

According to the definition of contact stiffness, it can be obtained by deriving the power function fitting formula of the unloading curve at the peak load or peak depth position [18].

$$S={\left({\displaystyle \frac{\mathrm{d}{F}_{\mathrm{n}}}{\mathrm{d}h}}\right)}_{h=h_{\max }}=mn{(h_{\mathrm{m}}-h_{\mathrm{p}})}^{n-1}$$

(2)

As shown in Figure 3b, the contact depth can be calculated according to Formula (3).

$$h_{\mathrm{c}}=h_{\mathrm{m}}-\eta (h_{\mathrm{m}}-h_{\mathrm{r}})$$

(3)

where $\eta$ is a constant related to the geometry of the indenter. For the Berkovich indenter, $\eta$ = 0.7268.

For the Berkovich indenter used in this paper, the relationship between the contact projection area ($A_{\mathrm{c}}$) and the contact depth can be expressed by Formula (4).

$$A_{\mathrm{c}}=24.5{h_c}^2$$

(4)

Nanoindentation hardness ($H_{\mathrm{IT}}$) and reduced modulus ($E_{\mathrm{IT}}$) are calculated by Formulas (5) and (6):

$$H_{\mathrm{IT}}=F_{\mathrm{m}}/A_c$$

(5)

$$E_{\mathrm{r}}=S\sqrt{\pi }/(2\alpha \sqrt{A_c})$$

(6)

where $\alpha$ is a constant related to the shape of the indenter. For the Berkovich indenter,$\alpha$ = 1.034.

From the above Formulas (1)–(6), it can be seen that if the load is not maintained after the peak value to eliminate the creep effect, the deformation of the sample will continue to increase during the unloading stage, causing $h_{\mathrm{p}}$ to be close to or equal to $h_{\mathrm{m}}$, and the calculated parameters will seriously deviate from the actual values.

When the non-rigidity of the indenter is neglected, the elastic modulus of the coal sample can be represented by $E_{\mathrm{r}}$. Otherwise, the elastic modulus should be calculated using Formula (7).

$$E_{IT}={\displaystyle \frac{1-{v^2}_{IT}}{\frac{1}{E_r}-\frac{1-{v^2}_i}{E_i}}}$$

(7)

where $v_{IT}$ is the Poisson’s ratio of the sample, and Poisson’s ratio has almost no effect on the calculation results. In this paper, $v_{IT}$ = 0.3 is taken, and $E_i$ and $v_i$ are the elastic modulus and Poisson’s ratio of the indenter material, respectively. In this paper, $E_i$ = 1141 GPa and $v_i$ = 0.07.

(2)

Test scheme

Test areas with surface flatness meeting the requirements were selected under four conditions: initial, humidification, heating, and coupled hygrothermal. The peak load for each indentation was set to 70 mN, with a constant loading and unloading rate of 0.5 mN/s. After reaching the peak load, a holding time of 10 s was applied to minimize creep effects. To reduce randomness in the test results and avoid interference between different phases, a grid indentation technique was employed [9]. Within each test area, a 200 μm × 200 μm region was selected, with a spacing of 100 μm between adjacent indentation points. Nine indentation points were arranged in each area, resulting in a total of thirty-six indentation points across the four conditions. The indentation points numbered one to nine are shown in Figure 4.

3. Results and Discussion

3.1. Analysis of Microscopic Morphology Characteristics of Coal Samples

SEM and EDS Results Analysis

Bulleted lists look like this:

Coal samples under four conditions—initial, post-humidification, post-heating, and after the coupled hygrothermal treatment—were observed using a Zeiss G300 scanning electron microscope (SEM). All sample surfaces were initially at the same baseline condition before their exposure to the respective environments. As shown in Figure 5, under the initial conditions, numerous debris-like particles are observed on the surface of the coal sample, possibly due to natural cracks within the coal matrix or the peeling of weakly bonded mineral surfaces, leading to a certain degree of surface roughness. The overall structure appears relatively dense, indicating that the microstructure of the coal body is largely intact before the exposure to hygrothermal environments. Although minor undulations, small pores, and a limited number of microcracks are present in localized regions, these defects are distributed in isolation, suggesting that the structural integrity of the coal body remains high in the initial state, reflecting a low level of structural damage.

As illustrated in Figure 6, humidified conditions led to discernible changes in the coal’s surface microstructure as a result of elevated moisture levels. Compared to the initial state, particle edges appeared blurred, likely resulting from water infiltration, which softened the intergranular boundaries. This blurring effect suggests a weakened interparticle cohesion and slight swelling of mineral phases. Additionally, microcracks developed along structurally weakened zones, while dissolution pits were observed in specific regions due to water-induced erosion and mineral leaching. Furthermore, the moisture exposure resulted in a partial disintegration of clay minerals, leading to localized pore expansion and more gradual transitions between particles and the surrounding matrix, collectively indicating a degradation of microstructural integrity.

As illustrated in Figure 7, compared to the humidification treatment, heating markedly decreases the inherent moisture content of the coal sample via a dehydration process that gradually advances from the exterior to the interior, leading to a notable increase in the localized surface roughness. Certain particle surfaces exhibited signs of exfoliation and spalling, attributable to the thermal stress-induced weakening of interparticle bonds and microstructural disruption. Moreover, prominent fragmented structures were observed in localized areas, suggesting the partial disintegration and collapse of weaker zones within the coal matrix. The microcrack density notably increased under heating, with multiple cracks propagating deeply within the sample, indicating the progressive evolution of thermally induced damage and mechanical degradation.

As illustrated in Figure 8, the combined effects of humidification and heating resulted in pronounced alterations in the surface morphology of the coal samples, which differed substantially from those induced by humidification or heating alone. The surface roughness increased compared to the humidified condition, likely due to thermal stresses intensifying the weakening effects caused by moisture, but remained less pronounced than the roughness observed under heating alone. Following the coupled hygrothermal treatment, a significant increase in fine dissolution pits was observed on the coal surface, indicating enhanced mineral leaching driven by the synergistic action of the moisture and heat. This was accompanied by the continued development and eventual coalescence of microcracks, reflecting the progressive deterioration and cumulative damage of the microstructure under the coupled hygrothermal environment.

The surface mapping of coal samples under different conditions was performed using energy-dispersive X-ray spectroscopy (EDS) with the Oxford Xplore 30 energy spectrometer. Elemental distribution maps for carbon (C), oxygen (O), aluminum (Al), silicon (Si), potassium (K), calcium (Ca), and iron (Fe) were generated. According to the XRD analysis of the coal samples, aluminum is identified as the characteristic element of kaolinite (Al₂(Si₂O₅)(OH)₄); thus, areas exhibiting the highest aluminum enrichment correspond to kaolinite distribution zones. Silicon is present in both kaolinite and quartz (SiO₂); however, regions with silicon enrichment but a minimal aluminum content indicate quartz-rich zones. Iron and calcium are characteristic elements of carbonate minerals, specifically siderite (FeCO₃) and calcite (CaCO₃), respectively. Accordingly, regions exhibiting the highest concentrations of iron and calcium correspond to the distribution zones of carbonate minerals.

3.2. Analysis of Micromechanical Properties of Coal Samples

3.2.1. Load–Depth Curve Characteristics

The SEM imaging and EDS elemental analysis can only provide qualitative or semi-quantitative insights into the presence of microstructural surface damage in coal samples under various conditions. Therefore, it is essential to further investigate the mechanical properties and deformation behavior of coal at the microscale. Figure 9 presents the load–displacement curves obtained from nanoindentation tests conducted under different conditions. The curves labeled 1 to 9 in the legend correspond directly to the load–depth responses of indentation Points 1 through 9 within the designated test area.

The SEM imaging and EDS elemental analysis are limited to providing qualitative or semi-quantitative assessments of microstructural surface damage in coal samples under various conditions. Therefore, it is necessary to conduct a more in-depth investigation into the mechanical properties and deformation behavior of coal at the microscale. Figure 9 presents the load–depth curves derived from nanoindentation tests performed under varying environmental conditions. The curves labeled 1 to 9 in the legend represent the load–depth responses at indentation Points 1 through 9 within the specified testing region.

The test results of the indentation depth (h) and load (F) change curves are more consistent with the typical load–depth curve characteristics. As a representative heterogeneous material, coal exhibits variations in its mineral composition even within a single test region, resulting in a noticeable dispersion among the load–depth curves of different indentation points. In the loading stage, before the load reaches the peak, the indentation depth increases rapidly, and then the growth rate slows down. In the load-holding stage, the load remains constant, creep deformation occurs on the surface of the coal sample, and the indentation depth continues to increase. In the unloading stage, the elastic deformation of the coal sample is partially restored, but there is still irreversible plastic deformation.

The measured indentation load–depth curves are generally consistent with the typical characteristics of load–depth responses in nanoindentation tests. As a representative heterogeneous material, coal exhibits significant variability in its mineral composition even within a single testing region, leading to the noticeable dispersion among the load–depth curves of different indentation points. During the loading phase, the indentation depth increases rapidly at first, and then the growth rate gradually slows as the load approaches its peak. In the holding phase, the applied load remains constant while creep deformation occurs on the coal surface, resulting in a continued increase in the indentation depth. During unloading, a partial recovery of the elastic deformation is observed, but irreversible plastic deformation remains.

As shown in Figure 9, marked variations are evident in the load–depth curves among different indentation points under the same treatment condition. Based on the SEM analysis, Figure 9a illustrates that under the initial condition, the curves at Points 2 and 5 exhibit pronounced deviations from the rest. Point 2 shows a notably higher peak indentation depth, whereas Point 5 presents a significantly lower depth. Figure 9b indicates that after humidification, the coal surface undergoes softening, accompanied by an increase in dissolution pores, which leads to higher peak indentation depths at some locations. Figure 9c reveals that relative to humidification, heating results in the surface hardening of the coal; however, the concurrent development of pores and cracks leads to increased indentation depths at specific locations. Figure 9d demonstrates that following the hygrothermal coupled treatment, the dispersion of load–depth curves among measurement points falls between the dispersions observed under humidified and thermally treated conditions.

3.2.2. Indentation Depth Characteristics

Under identical testing conditions, if the mineral components within the indentation area possess greater strength or hardness, both the peak indentation depth ($h_{\mathrm{m}}$) and the residual indentation depth after unloading ($h_{\mathrm{p}}$) are generally reduced. Conversely, when the mineral phases have a lower hardness or when the area contains more microcracks, both tend to increase correspondingly. As shown in Figure 10, indentation morphologies under different treatment conditions were recorded using the integrated imaging system of the Hysitron TI Premier nanoindenter. The results show that, despite identical loading conditions, the projected areas of residual indentations exhibited a significant variability across different test locations, underscoring the pronounced effect of the coal’s microscale heterogeneity. Specifically, compared with the initial state, the indentation contour became more pronounced after humidification, less pronounced after heating, and displayed intermediate characteristics under the coupled hygrothermal treatment.

Considering the variability of measured parameters among different points under identical conditions, box plots were utilized to visually represent the central tendency and dispersion of the indentation data. The plots display the upper whisker, upper quartile, mean, median, lower quartile, and lower whisker of the indentation depths across all measurement points.

Figure 11 presents the variations $h_{\mathrm{m}}$ and $h_{\mathrm{p}}$ of coal samples under four different conditions. As shown in the figure, under a constant load of 70 mN, the average value of $h_{\mathrm{m}}$ in the initial condition was recorded as 3529.51 nm. After heating, it decreased to a minimum of 3515.29 nm; after humidification, it increased to a maximum of 4090.54 nm; and, subsequently, following the hygrothermal coupled treatment, it settled at 3686.54 nm, which was the value between those observed under humidified and thermally treated conditions. Relative to the initial condition, the average value of $h_{\mathrm{m}}$ exhibited an increase of 560.03 nm (15.90%) and 157.03 nm (4.45%) after the humidification and hygrothermal treatment, respectively, while it showed a slight decrease of 14.22 nm (0.4%) after heating.

In the initial condition, the average value of $h_{\mathrm{p}}$ was recorded as the lowest, measuring 1406.81 nm. After humidification, it increased to a maximum of 1987.40 nm, whereas following the hygrothermal coupled treatment, it declined to an intermediate level of 1632.07 nm. Relative to the initial condition, the average value of $h_{\mathrm{p}}$ exhibited an increase of 580.59 nm (41.27%) and 225.26 nm (16.01%) after humidification and hygrothermal treatments, respectively. In contrast, the thermal treatment led to a slight reduction of 16.11 nm (1.15%).

Under the constant peak load, the indentation depth of samples under the same condition is typically regarded as stable. According to previous XRD results, the coal samples contain minerals such as kaolinite, quartz, and carbonates. Compared to the initial state, humidification softens the coal surface and promotes the hydration of the surface clay mineral, kaolinite, reducing strength. Consequently, both the average values of $h_{\mathrm{m}}$ and $h_{\mathrm{p}}$ increased after humidification. Heating induced the evaporation of moisture from the coal surface, resulting in drying and hardening, thereby decreasing the average values of $h_{\mathrm{m}}$ and $h_{\mathrm{p}}$ compared to the initial state. Following the hygrothermal coupled treatment, both the average $h_{\mathrm{m}}$ and $h_{\mathrm{p}}$ increased relative to the initial state, with magnitudes intermediate between those observed following humidification and heating treatments. These results indicate that the elevated temperature partially inhibits the moisture ingress into the coal matrix under hygrothermal conditions.

3.3. Analysis of Hardness and Elastic Modulus Results

3.3.1. Comparative Analysis of Hardness and Elastic Modulus Under Different Treatments

According to Formulas (1) through (7), the elastic modulus ($E_{\mathrm{IT}}$) and hardness ($H_{\mathrm{IT}}$) at each measurement point of the test coal sample under four different conditions were calculated. Here, N represents the initial state, N-H represents the state after humidification, N-T represents the state after heating, and N-H-T represents the state after hygrothermal coupling. The calculation results are presented in

Table 2. Mechanical parameters of coal samples.

Number	N		N-H		N-T		N-H-T
	EIT/GPa	HIT/MPa	EIT/GPa	HIT/MPa	EIT/GPa	HIT/MPa	EIT/GPa	HIT/MPa
N-1	3.631	273.642	3.504	264.762	3.723	361.57	3.316	247.273
N-2	2.983	163.812	3.274	203.468	3.615	306.747	3.660	268.625
N-3	4.045	302.211	3.706	320.786	4.176	286.536	4.135	315.138
N-4	4.073	287.213	3.236	196.081	4.312	322.364	3.516	237.975
N-5	4.591	366.602	3.117	170.684	3.515	218.072	3.259	182.788
N-6	4.076	290.772	3.109	169.848	3.996	290.677	3.640	233.024
N-7	3.739	369.306	3.052	187.673	3.579	205.483	3.581	251.219
N-8	3.813	269.595	3.272	184.892	4.011	298.376	4.208	322.248
N-9	3.721	289.314	2.430	142.743	4.223	357.081	3.662	228.935

.

Based on the previously provided nanoindentation load–depth curves and the calculated results in Table 2, an analysis was conducted on the mechanical properties of coal samples under different treatment conditions. Figure 12 illustrates the trends in the elastic modulus and hardness of the coal samples subjected to various treatments. As shown in Figure 12, the average $E_{\mathrm{IT}}$ under a peak load of 70 mN was 3.85 GPa in the initial state, 3.19 GPa after humidification, 3.91 GPa after heating, and 3.66 GPa following hygrothermal coupling. Compared to the initial state, humidification reduced the average $E_{\mathrm{IT}}$ by 0.66 GPa (a decrease of 17.14%), and hygrothermal coupling reduced it by 0.19 GPa (a decrease of 4.94%). In contrast, heating increased the average $E_{\mathrm{IT}}$ by 0.06 GPa (an increase of 1.56%).

The average value of $H_{\mathrm{IT}}$ for the coal samples in the initial state, after humidification, after heating, and following hygrothermal coupling was 290.27 MPa, 204.55 MPa, 294.10 MPa, and 254.14 MPa, respectively. Compared to the initial state, humidification reduced the average $H_{\mathrm{IT}}$ by 85.72 MPa (a decrease of 29.53%), while hygrothermal coupling resulted in a reduction of 36.13 MPa (a decrease of 12.45%). In contrast, heating increased the average $H_{\mathrm{IT}}$ by 3.83 MPa (an increase of 1.32%).

In combination with the SEM observations and the characteristics of the indentation depth, it can be inferred that the coal surface inherently contains varying degrees of pores and cracks, which become more pronounced under humidification, heating, and hygrothermal coupling. Compared to the initial state, humidification softens the coal surface, resulting in reductions in both the average values of parameters $H_{\mathrm{IT}}$ and $E_{\mathrm{IT}}$. Heating leads to moisture loss on the sample surface, resulting in hardening and subsequent increases in the average values of $H_{\mathrm{IT}}$ and $E_{\mathrm{IT}}$. Under identical controlled conditions, moisture exerts a more pronounced effect on the coal damage than temperature. After the hygrothermal coupled treatment, the degree of damage falls between that observed under humidification and heating alone, suggesting that the elevated temperature may partially offset moisture-induced damage.

The results of the nanoindentation test show that the increase in the water content significantly reduces the hardness and elastic modulus of the coal sample surface. This trend is highly consistent with the research results of Yao et al. [26] on the reduction in the macroscopic compressive strength and elastic modulus of coal–rock composites under different water content conditions. Although this study mainly focused on overall mechanical properties, the current experiment provides direct evidence at the microscale, revealing the water-induced softening effect and its structural response at the mineral level. The above results not only verify the mechanical changes at the macroscopic level but also show that microstructural degradation can serve as a precursor to the weakening of the mechanical properties of the coal body.

3.3.2. Relationship Between Hardness and Elastic Modulus

According to Formulas (1) through (7) and the dimensional analysis, and assuming that the compliance of the diamond indenter does not affect the elastic modulus, the relationship between the hardness and elastic modulus can be analyzed. By combining Formulas (5), (6), and (8), it can be derived that the hardness and elastic modulus satisfy the relationship expressed in Formula (9).

$$E_{\mathrm{IT}}/(1-{v^2}_{\mathrm{IT}})=E_r$$

(8)

$$H_{\mathrm{IT}}=\lambda E_{\mathrm{IT}}$$

(9)

where $\lambda$ is the slope of the linear relationship between the hardness and elastic modulus.

Formula (9) is employed to model the relationship between the hardness and elastic modulus for coal samples subjected to various treatment conditions, with the fitting results presented in Figure 13 and the corresponding parameters listed in

Table 3. Hardness and elastic modulus fitting parameters.

Coal Sample Status	Slope (λ)	Goodness of Fit (R2)
initial	0.07571	0.9837
humidification	0.06488	0.9720
heating	0.07291	0.9877
Humidification–heating	0.06971	0.9914
summary	0.07140	0.9820

.

Figure 13a illustrates the fitted relationships between the hardness and elastic modulus of coal samples under different treatment conditions. Combined with the fitting parameters listed in Table 3, the experimental results demonstrate a strong linear correlation between the two mechanical properties. The goodness-of-fit (R²) values under the initial, humidification, heating, and hygrothermal coupled treatment conditions were 0.9837, 0.9720, 0.9877, and 0.9914, respectively, indicating that the linear model constrained to pass through the origin provides an excellent fit across all cases. Figure 13b further integrates the test data from all conditions, yielding an overall R² of 0.9820. According to Equation (9), the hardness and elastic modulus are positively correlated under all treatment conditions, indicating that this relationship is independent of the coal’s physical state.

3.4. Effect of Mineral Composition on Micromechanical Properties

According to the previous XRD quantitative analysis, the coal samples mainly consist of amorphous organic matter and contain accessory minerals, including quartz, kaolinite, calcium carbonate, and iron carbonate. To investigate the influence of different mineral compositions on the mechanical behavior of coal, indentation responses under both the initial and hygrothermal coupled treatment conditions were examined.

As shown in Figure 14a,c, under the initial condition, the indentation at Point 6 is located entirely within the organic matrix of the coal. In contrast, the indentation tip at Point 2 penetrates a dark-gray crystalline mineral, while the indentations at Points 5 and 7 penetrate light-gray crystalline minerals. Compared to Point 6, the projected indentation area at Point 2 is larger, whereas those at Points 5 and 7 are smaller. The peak indentation depth at Point 6 is 3434.58 nm, while that at Point 2 is 4392.87 nm, indicating a significantly lower hardness at this location. In contrast, the peak indentation depths at Points 5 and 7 are 3129.61 nm and 3289.04 nm, respectively, suggesting these regions are mechanically harder than the organic matrix. Additionally, the hardness at Point 6 is 290.77 MPa; at Point 2, it is substantially lower at 163.81 MPa; and at Points 5 and 7, it is markedly higher, at 366.60 MPa and 369.31 MPa, respectively. It can be inferred that Point 2 most likely corresponds to kaolinite, a mineral characterized by a relatively low strength, whereas Points 5 and 7 are likely associated with quartz, which has a comparatively high strength.

As shown in Figure 14b,d, under hygrothermal coupling conditions, the indentation at Point 1 is evenly distributed within the organic matrix of the coal sample. The indentation tip at Point 5 extends into a dark-gray crystalline mineral, while the tips at Points 3 and 8 are embedded in light-gray crystalline minerals. Relative to Point 1, the projected indentation area at Point 5 is larger, whereas the areas at Points 3 and 8 are smaller. The peak indentation depth at Point 1 is 3762.64 nm, while the depth at Point 5 reaches 4161.67 nm, indicating a significantly deeper penetration. In contrast, the depths at Points 3 and 8 are 3357.19 nm and 3306.39 nm, respectively, both notably shallower than at Point 1. Furthermore, the hardness at Point 1 is 247.27 MPa, while that at Point 5 is 182.79 MPa, indicating a significantly lower hardness. The hardness values at Points 3 and 8 are 315.14 MPa and 322.25 MPa, respectively, both significantly higher than at Point 1. These findings suggest that Point 5 is most likely associated with a lower-strength kaolinite mineral, whereas Points 3 and 8 are most likely associated with higher-strength quartz minerals.

4. Conclusions

(1)

Under initial conditions, the coal surface is relatively dense and intact, exhibiting fewer cracks and pores. After humidification, dissolution pores appear in certain surface regions, resulting in a smoother transition between particles and the matrix. Following heating, the surface roughness of certain areas on the coal sample increased, accompanied by a localized disintegration and collapse. After the hygrothermal coupled treatment, the number of fine dissolution pores and microcracks on the coal surface increased markedly.

(2)

Compared with the initial state, humidification leads to the softening of the coal surface, with average values of $h_{\mathrm{m}}$ and $h_{\mathrm{p}}$ increasing by 15.9% and 41.27%, respectively, while values of $E_{\mathrm{IT}}$ and $H_{\mathrm{IT}}$ decrease by 17.14% and 29.53%. Heating induces surface hardening, leading to slight decreases in $h_{\mathrm{m}}$ and $h_{\mathrm{p}}$, by 0.4% and 1.15%, and corresponding increases in $E_{\mathrm{IT}}$ and $H_{\mathrm{IT}}$, by 1.56% and 1.32%. Under coupled hygrothermal conditions, $h_{\mathrm{m}}$ and $h_{\mathrm{p}}$ increase by 4.45% and 16.01%, respectively, while $E_{\mathrm{IT}}$ and $H_{\mathrm{IT}}$ decrease by 4.94% and 12.45%. The extent of the surface damage under hygrothermal coupling falls between that observed under humidification and heating alone.

(3)

A linear model passing through the origin provides an excellent fit for the relationship between the hardness and elastic modulus under different conditions. The hardness of coal exhibits a positive correlation with its elastic modulus, and this relationship is independent of the coal’s condition.

(4)

The mineral composition on the coal surface has a significant influence on its micromechanical properties. Hard minerals such as quartz tend to result in lower peak indentation depths and higher hardness values, whereas softer minerals like kaolinite lead to higher peak indentation depths and lower hardness values.