## 3 Results and Discussion
### 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 (\(E_{\text{IT}}\)) and hardness (\(H_{\text{IT}}\)) 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 hygothermal coupling. The calculation results are presented in Table 2.  
Figure 11: Changes of \(h_{\text{m}}\) and \(h_{\text{p}}\) of coal samples under different conditions. 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 \(E_{\text{IT}}\) 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 hygothermal coupling. Compared to the initial state, humidification reduced the average \(E_{\text{IT}}\) by 0.66 GPa (a decrease of 17.14%), and hygothermal coupling reduced it by 0.19 GPa (a decrease of 4.94%). In contrast, heating increased the average \(E_{\text{IT}}\) by 0.06 GPa (an increase of 1.56%). \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Number**} & \multicolumn{2}{c}{**N**} & \multicolumn{2}{c}{**N-H**} & \multicolumn{2}{c}{**N-T**} & \multicolumn{2}{c}{**N-H-T**} \\ \cline{2-10}  & \(E_{\text{IT}}\)/GPa & \(H_{\text{IT}}\)/MPa & \(E_{\text{IT}}\)/GPa & \(H_{\text{IT}}\)/MPa & \(E_{\text{IT}}\)/GPa & \(H_{\text{IT}}\)/MPa & \(E_{\text{IT}}\)/GPa & \(H_{\text{IT}}\)/MPa \\ \hline 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 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mechanical parameters of coal samples. Figure 12: Variation trend of elastic modulus and hardness under different conditions. (**a**) Elastic modulus. (**b**) Hardness. (**c,d**) Average elastic modulus and average hardness. The average value of \(H_{\text{TT}}\) 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 \(H_{\text{TT}}\) 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 \(H_{\text{TT}}\) 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 \(H_{\text{IT}}\) and \(E_{\text{IT}}\).