# Roughness Evolution of Granite Flat Fracture Surfaces during Sliding Processes
## 1 Introduction  
Shear is a common mechanical process in nature, such as various friction processes in life, and landslides and earthquakes in the geology field are also related to shear [1, 2]. There are many factors affecting the shear process, of which roughness is a more important one. During shear sliding, abrasive wear is constantly occurring and the geometry of the sliding surface, i.e., the roughness, is constantly changing, while the roughness also affects the sliding process in turn. In a large number of shear-related studies, the morphology of the fracture surfaces before and after shearing is observed and recorded using electron microscopes [3, 4] or scanners [5, 6] in order to analyze the relationship between roughness and the shearing process. For example, [PERSON] and [PERSON] [6] recorded the morphology of granite fractures before and after fluid injection tests under triaxial conditions, and the results showed that after shearing, both saw-cut and natural fractures experienced roughness wear, and the natural fracture faces showed more wear. Meanwhile saw-cut fractures showed more seismic behavior. [PERSON] et al. [4, 5] compared the morphology of sandstone fracture surfaces before and after triaxial tests and found the relationship between confining pressure and roughness from the analysis. In addition, materials such as casted specimens [7], salt rock [8] and homalite [9] have been employed in studies related to the roughness. [PERSON], [PERSON] [10] and [PERSON] [11] studied the evolution of roughness with slip by conducting shear tests on rough fracture surfaces using limestone. And the most direct effect of roughness on the shear process is to change the shear strength and slip stability. Generally, the rougher the sliding surface, the higher the peak shear strength [12]. Specifically, however, attention is also paid to the strength of the material itself and the different failure modes [13, 14, 15, 16]that occur during shear. Asperities with higher material strengths are less likely to be cut off and therefore produce higher shear strengths. Conversely, rougher bodies are sheared at lower strengths and are therefore relatively more stable, similar to the distinction between cut-off along the serration root and shear dilation that has been suggested in some studies [14; 15; 16]. Rough sliding surfaces also provide better stability [17], whereas smooth faults tend to produce larger stress drops, leading to larger earthquakes. In addition, it has been demonstrated that roughness has a significant effect on the pattern and length of seismic nucleation [18; 19; 20; 21]. For smaller roughness, the roughness amplitude is significantly positively correlated with the length of nucleation. While for larger values of roughness amplitude, the discontinuity surface mainly exhibits aseismic slip. The above studies give the correlation between roughness and strength, stability, and the effect of roughness on various behaviors in the friction process, which deeply reflects the important role played by roughness in the shear process. But the change rule of roughness itself is rarely studied. On the one hand, there exist a variety of indicators to measure roughness [22], and most of them are one sided. On the other hand, the change in friction surface morphology during shear is also random, and a large number of samples are needed to investigate the evolution process. However, the above laboratory tests usually only record the morphology of the fracture surface at the beginning and end of the test, and most of the tests were limited by the equipment, and the slip distances were only approximately ten millimeters, which resulted in very limited changes in roughness. Statistical data on a number of fault profiles by [PERSON] and [PERSON] [23] show that the faults with small slips are rougher than those with large slips. In these results, field investigations of in situ faults, although more realistic, make it difficult to observe the evolution of roughness.