## 6 Conclusions  
In conclusion, by combining the detailed results of our calculations and our analyses of data from four samples, we derive the following findings:  
(1) The roughness correction coefficients of the samples consisting of shear-type rock exhibit slight fluctuations as the scale varies, while the same values for the tensile rock samples experience significant fluctuations. Nonetheless, the roughness correction coefficients of all the rock samples are affected by the scale of the fracture samples, thereby indicating that scale has an effect on roughness. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Sample**} & \multicolumn{8}{c}{**Cut Frame Size (Percentage)/\%**} \\  & **10** & **20** & **30** & **40** & **50** & **60** & **70** & **80** & **90** & **100** \\ \hline S1-AP & 2.1552 & 2.2319 & 2.3103 & 2.3594 & 2.3945 & 2.4137 & 2.4375 & 2.4416 & 2.4592 & 2.4759 \\ S1-Sur & 2.0949 & 2.1315 & 2.1057 & 2.0985 & 2.1143 & 2.1114 & 2.1003 & 2.0985 & 2.0908 & 2.2086 \\ S2-AP & 2.1919 & 2.2632 & 2.287 & 2.3206 & 2.3223 & 2.3458 & 2.3647 & 2.3818 & 2.4056 & 2.4222 \\ S2-Sur & 2.0864 & 2.0748 & 2.0926 & 2.1026 & 2.0762 & 2.0632 & 2.0602 & 2.06 & 2.0532 & 2.0515 \\ S3-AP & 2.2115 & 2.3295 & 2.3651 & 2.3832 & 2.3988 & 2.4132 & 2.4175 & 2.4239 & 2.4327 & 2.4157 \\ S3-Sur & 2.1055 & 2.1005 & 2.1138 & 2.0697 & 2.0762 & 2.0664 & 2.0683 & 2.0627 & 2.0681 & 2.0862 \\ S4-AP & 2.2344 & 2.3521 & 2.23 & 2.2741 & 2.2747 & 2.2343 & 2.2412 & 2.2043 & 2.2032 & 2.201 \\ S4-Sur & 2.1524 & 2.1358 & 2.1112 & 2.1299 & 2.1693 & 2.1643 & 2.1714 & 2.1899 & 2.184 & 2.2084 \\ S5-AP & 2.2739 & 2.322 & 2.3264 & 2.3644 & 2.3517 & 2.3373 & 2.3075 & 2.3200 & 2.3256 & 2.3333 \\ S5-Sur & 2.1074 & 2.0665 & 2.0978 & 2.1478 & 2.1307 & 2.1429 & 2.1524 & 2.1477 & 2.163 & 2.1537 \\ \hline \hline \end{tabular} Note: S1-AP represents the fracture width of sample S1, S1-Sur represents the surface of sample S1, and the same principles apply to the notation for the other samples and their fracture widths and surfaces.  
\end{table} 
Table 10: Results of calculating the fractal dimension based on the roughness correction coefficient. Figure 7: Results of calculations for fractured surfaces of three types of rock. The fractal dimensions are non-integer values greater than 2 and lower than 3. The fractal dimension gradually stabilizes with an increasing intercept box size. The fractal dimensions of different faces of the same rock samples are also different. (2) Different formulas for calculating the roughness correction coefficient produce distinct results and exhibit varying sensitivity to size. However, in general, these coefficients undergo some degree of change as the scale of the fracture sampling changes, providing further evidence that scale affects the roughness of fracture surfaces. The roughness of rock fracture surfaces also demonstrates anisotropy, which signifies its directional characteristics. (3) The roughness correction coefficient in a polar coordinate system can be fit to an elliptical shape, suggesting that the anisotropy of the coefficient can be represented using a tensor form. (4) One reason why the effect of scale is more pronounced in the tensile rock samples compared to the shear-type rock samples is the substantial disparity in the fissure range and the distance between the local top and bottom surfaces, with less variation in the fissures in the shear-type rock samples. Conceptualization, G.C., L.M., H.G. and Y.L. ; methodology, G.C. ; software, Q.M. and G.C. ; validation, Q.M. and Y.L. ; formal analysis, Q.M. ; investigation, Q.M. and Y.L. ; data curation, Q.M. and Y.L. ; writing--original draft preparation, Q.M. ; writing--review and editing, G.C., L.M., H.G. and Y.L. ; visualization, Q.M. and G.C. ; supervision, L.M. and H.G. ; project administration, L.M. and H.G. ; funding acquisition, G.C. All authors have read and agreed to the published version of the manuscript.