## 6 Results and Analysis of Numerical Simulation
### Dilation Law of Discontinuities Possessing Different Joint Wall Strengths  
The numerical dilation data of discontinuities possessing different joint wall compressive strengths were derived, and curves of normal displacement vs. shear displacement were plotted, as shown in Figure 14.  
The dilation displacement of discontinuities increased with the increase in shear displacement. In the initial stage of the numerical test, the dilation displacement increased rapidly. However, there was a turning point of increasing rate when the peak shear displacement was reached, the increasing rate of dilation displacement decreased and the dilation curve tended to be gentle. Dilation displacement eventually reached a stable value with the continuous increasing of shear displacement. This was because asperities of discontinuities were cut off in quantities after the shear stress reached the peak value. The dilation effect was significantly weakened until asperities entered the grinding and migration stage, and the dilation displacement then tended to be stable. In conclusion,  
Figure 13: Shear stress contours of discontinuities possessing different joint wall strengths with shear displacement of 5 mm. (**a**) GCR1; (**b**) GCR2; (**c**) GCR3; (**d**) SCR1; (**e**) SCR2; and (**f**) SCR3.  
the dilation displacement of discontinuities was concerned with normal stress. With the gradual increase in normal stress, the cutting effect between asperities of discontinuities was significantly enhanced, thus weakening the climbing dilation effect between asperities and decreasing the dilation displacement gradually. In addition, the increasing rate of dilation displacement also gradually decreased. Dilation values (mm) of discontinuities possessing different joint wall strengths with different morphologies are listed in Table 3.  
Figure 14: Shear dilation curves of discontinuities possessing different joint wall strengths. (**a**) GCR1; (**b**) SCR1; (**c**) GCR2; (**d**) SCR2; (**e**) GCR3; and (**f**) SCR3.  
It is visible from Table 3 that under the effect of the same normal stress, the dilation displacement of discontinuities with JRC of 10.8 was the maximum, the dilation displacement of discontinuities with JRC of 18.7 was second, while the dilation displacement of discontinuities with JRC of 2.8 was the minimum. The reason is that the undulation of discontinuities with JRC of 10.8 was the largest; thus, the climbing effect was the most significant correspondingly. As for discontinuities with JRC of 2.8, the number of rough construction was the least, which is why the dilation effect was basically weakened and the dilation displacement was the minimum. Comparing two types of discontinuities possessing different joint wall compressive strengths with the same roughness, asperities of granite had more obvious embedding effects on mortar due to the compressive strength of granite being approximately three times that of sandstone. Therefore, the damage degree of granite-mortar discontinuities during the shearing process was more severe as a result of the meshing and shearing effects of asperities being greatly enhanced, which weakened the climbing dilation effect correspondingly. Eventually, the dilation value of granite-mortar discontinuities was smaller than that of sandstone-mortar discontinuities.