# Mechanical and Heterogeneous Properties of Coal and Rock Quantified and Mapped at the Microscale
## 4 Results and Discussions
### Heterogeneity of Coal and Rock  
#### 4.3.1 Profiles of Indents  
Figure 10 shows the profiles of indents on shale, mudstone and coal. Three pictures marked I are the profiles of indents according to the shape of indenter when depth is \(h_{m}\). Pictures marked II are the profiles when depth is \(h_{p}\) after unloading, which correspond to the pictures marked III obtained from the SEM. During the experiments, it was hard to obtain the SEM images of shale after indenting.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multicolumn{3}{c}{**Shale**} & \multicolumn{3}{c}{**Mudstone**} & \multicolumn{3}{c}{**Coal**} \\ \cline{2-10}  & \(H_{IT}\) & \(E_{IT}\) & \(K_{c}\) & \(H_{IT}\) & \(E_{IT}\) & \(K_{c}\) & \(H_{IT}\) & \(E_{IT}\) & \(K_{c}\) \\ \hline
1 & 476.39 & 25.88 & 2.11 & 335.90 & 9.02 & 1.24 & 519.87 & 5.94 & 0.81 \\
2 & / & / & / & 1517.50 & 16.82 & 1.56 & 453.89 & 5.79 & 0.78 \\
3 & 3238.90 & 18.78 & 2.59 & 267.10 & 7.40 & 0.92 & 499.76 & 5.93 & 0.82 \\
4 & 1951.30 & 40.74 & 1.09 & 1527.60 & 18.47 & 1.52 & 417.81 & 5.53 & 0.78 \\
5 & 585.23 & 25.31 & 2.11 & 830.67 & 14.25 & 1.81 & 415.51 & 5.92 & 0.84 \\
6 & 449.20 & 10.12 & 1.11 & 200.62 & 8.01 & 1.10 & 279.26 & 4.54 & 0.73 \\
7 & 761.73 & 31.37 & 2.63 & 573.31 & 13.12 & 1.36 & 391.74 & 5.33 & 0.74 \\
8 & / & / & / & 412.69 & 10.39 & 1.31 & 437.66 & 5.51 & 0.75 \\
9 & 678.59 & 12.34 & 1.40 & 306.61 & 9.39 & 0.98 & 415.99 & 5.61 & 0.78 \\
10 & 809.27 & 11.36 & 1.44 & 664.65 & 13.13 & 1.18 & 399.25 & 4.71 & 0.68 \\
11 & 1580.60 & 13.74 & 1.37 & 179.39 & 6.46 & 0.81 & 434.08 & 5.48 & 0.77 \\
12 & 3089.20 & 19.58 & 1.89 & 1283.30 & 14.21 & 1.57 & 426.79 & 5.34 & 0.75 \\ Mean values & 1362.04 & 20.92 & 1.77 & 674.95 & 11.72 & 1.28 & 424.30 & 5.47 & 0.77 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Micromechanical parameters of shale, mudstone, and coal.  
Figure 10: _Cont._According to Figure 10b, the indent of mudstone-11 has the largest area. The depth during the load-holding is 2804.60 nm, which is the largest depth, being 2112.47 nm after unloading. In contrast, testing shale-3 has the smallest indention area, with the maximum loading depth of 905.99 nm and unloading depth of 139.09 nm.  
Mainly based on picture I in Figure 10a-c, the differences between the no.1 to 12 indents on the surface of shale are greater than the other two samples, which means the heterogeneous properties of shale are more differentiated than mudstone and coal. It is noticeable, however, that the indent areas obtained from the SEM (picture III) are much larger than that got from calculation (picture II). During unloading, elastic recovery causes these impressions to change their initial shape [56]. This phenomenon illustrates that the elastic recovery of the impression is not equal for the whole area, and the tip of indenter is the largest recovery position (Figure 3b), meaning that the stress under an indent varies from high levels in the vicinity of the tip, to vanishingly small values far away from it [57]. Figure 10a-III, b-III, and c-III show no obvious pile-up on the surfaces of rock and coal around the contact impression, even though they are elastic-plastic materials, which guarantees the measurement accuracy of micro hardness, elastic modulus, and fracture toughness [58].