## 3 Results and Discussion
### Analysis of Micromechanical Properties of Coal Samples
#### 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 (\(l_{\mathrm{m}}\)) and the residual indentation depth after unloading (\(l_{\mathrm{p}}\)) 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 hydrothermal 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 \(l_{\mathrm{m}}\) and \(l_{\mathrm{p}}\) of coal samples under four different conditions. As shown in the figure, under a constant load of 70 mN, the average value of \(l_{\mathrm{m}}\) 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 hygothermal 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 \(l_{\mathrm{m}}\) exhibited an increase of 560.03 nm (15.90%) and 157.03 nm (4.45%) after the humidification and hygothermal treatment, respectively, while it showed a slight decrease of 14.22 nm (0.4%) after heating. In the initial condition, the average value of \(l_{\mathrm{p}}\) was recorded as the lowest, measuring 1406.81 nm. After humidification, it increased to a maximum of 1987.40 nm, whereas following the hygothermal coupled treatment, it declined to an intermediate level of 1632.07 nm. Relative to the initial condition, the average value of \(l_{\mathrm{p}}\) exhibited an increase of 580.59 nm (41.27%) and 225.26 nm (16.01%) after humidification and hygothermal 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  
Figure 10: Indentation characteristics after unloading in different states. mineral, kaolinite, reducing strength. Consequently, both the average values of \(h_{\text{m}}\) and \(h_{\text{p}}\) increased after humidification. Heating induced the evaporation of moisture from the coal surface, resulting in drying and hardening, thereby decreasing the average values of \(h_{\text{m}}\) and \(h_{\text{p}}\) compared to the initial state. Following the hygothermal coupled treatment, both the average \(h_{\text{m}}\) and \(h_{\text{p}}\) 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 hygothermal conditions.