# Roughness Evolution of Granite Flat Fracture Surfaces during Sliding Processes
## 4 Results  
### Summary of Amplitude Parameters  
During the loading process, most of specimens that were under high normal force or low speed loading conditions experienced end shattering or side spalling at the first shear due to localized high stress at the end or side, as depicted in Figure 7. Therefore, these specimens were excluded from the roughness evolution analysis. The results of the remaining specimens were analyzed. Since the position of both the scanner and the specimen cannot be kept absolutely fixed during scanning, the coordinate system of the friction surfaces from each scan is not consistent. Therefore, prior to calculating the amplitude parameters, the coordinate systems of all point clouds need to be unified. Then, a baseline of the profile line extracted from the unsheared specimen is calculated. This baseline is utilized as a reference to obtain the baseline of the profile lines in each scan of this specimen by fitting. Subsequently, these baselines are subtracted to derive the amount of wear on the friction surface of the specimen for each scan. The value of the desired magnitude parameter is calculated from Equations (1) and (2) finally. For each specimen, the roughness parameter value following each shearing operation is derived through the averaging of computational values obtained from multiple profile lines. And prior to calculating the mean, outliers are eliminated using the whisker range of the box plot to ensure the reliability of the data. For samples numbered 14 and 20, where the shear time is less than four, extrapolation methods are employed to supplement the partial data. Figure 6: Schematic diagram of data processing flow. (**a**) Scanning. (**b**) Point cloud processing. (**c**) Extracting profile line. (**d**) Calculating all indicators. As shown in Figure 8, the two plots show the results of the two variables, arithmetic mean value and root mean square of the roughness profile line for various normal force conditions (No. 2 represents specimen numbered 2). The data for each variable are further differentiated between the upper and lower specimens and different directions. Overall, the arithmetic mean and the root mean square of the roughness profile tend to increase as the shear slip increases. These phenomena indicate that the roughness profile is being continuously abraded and the morphology of the whole profile is continuously downward concave; on top of that, the continuous shearing also makes the complexity of the profile line increasing. Due to the inconsistency of the specimen lengths, the short specimens are always in friction. As can be seen from the comparison in the graphs, the mean and RMS values of the shorter specimens are generally larger, which further suggests that the slip results in the roughness of the flat fracture surfaces to become larger. Moreover, this phenomenon seems to have a certain correlation with normal force, particularly in the H direction. The greater the normal force, the more significant the changes in \(Ra\) and \(Rq\). Next, taking the arithmetic mean as an example, a two-way repeated measures analysis of variance (ANOVA) is conducted. Here, the two factors refer to normal force and shear times. Prior to that, a normality test is performed on the data to ensure that the observed variables satisfy (approximately) the normal distribution, and a test of homogeneity of variances is also conducted. Finally, the ANOVA is completed in the \"Data Analysis\" module of Excel, and the results are presented in Figure 9, corresponding to the data in Figure 8a. As can be seen from Figure 9, regardless of the direction, the \(p\)-values corresponding to normal force and shear times are both less than 0.05. Therefore, it can be concluded that at a significance level of 0.05, normal force and shear times both have significant effects on roughness.