## 3 Shear Behaviors
### Effect of Shear Rate  
The stress and displacement curves of joint shear under diverse shear rates are displayed in Figure 8. With the rise of the shear rate, the shear stress bend of joints gradually moves downward, indicating that the larger the shear rate is, the shear strength of joints gradually decreases. This is mainly due to the joint surface roughness deformation failure and the different contact forces caused by it. When the shear rate is small, there are more time transfer forces in the shear process of the joint, which can fully mobilize the shear performance of the joint. However, when the shear rate is large, the shear process time is short, and the force is mainly concentrated on the part of the rough body that fails to transfer in time. The shear stress curve under different rates has the same trend of change, which is also divided into three stages, that is, within a small shear displacement (0.372-0.74 mm), the shear stress rapidly rises to the peak, after the peak, the shear stress decreases slightly, and then rises steadily. However, the corresponding shear displacement range of each stage of the shear stress curve is different with different shear rates. With the rise of the shear rate, the range of stage I is smaller; that is, the corresponding peak shear displacement is smaller. This is mainly caused by the decrease of joint peak strength and shear stiffness with the rise of shear rate [39]. In the II stage, the smaller the shear rate is the slower the shear stress curve of the joint drops, which indicates that the smaller the shear rate is in this stage, the less the surface roughness failure of the same shear displacement. Then, under the action of constant normal stiffness, the shear stress gradually rises, and when the shear displacement is greater than 7 mm, the slope of the five shear stress curves under different shear rates is similar, but when the shear displacement is greater than 7 mm,  
Figure 6: Failure modes of joints under diverse normal stiffness status. (**a**) For \(k_{\text{n}}=0\); (**b**) For \(k_{\text{n}}=1\) MPa/mm; (**c**) For \(k_{\text{n}}=3\) MPa/mm; (**d**) For \(k_{\text{n}}=5\) MPa/mm; (**e**) For \(k_{\text{n}}=7\) MPa/mm. Figure 7: Damaged surface area and weight of damaged asperity of the joint surface under different normal stiffness conditions. the shear stress curves with shear rates of 5.0, 10.0 and 20.0 mm/min gradually flatten out. The shear stress of joints basically no longer rises, while the shear stress curves continue to rise when the shear rate is 0.5 and 2.5 mm/min, which again confirms the view that the greater the shear rate, the more serious the roughness failure of the surface. Figure 8b shows the curves of normal joint displacements and shear displacements under different shear rates. The shear rate is roughly inversely proportional to the joint dilatancy value; that is, the joint dilatancy gradually decreases with the increase of shear rate, but the influence is limited, and the maximum difference is less than 0.1 mm. Figure 8c displays the normal stress-shear displacement curves of joints at different shear rates. It can be seen from the figure that the influence law of shear rate on the normal stress of joints is consistent with that of joint dilatancy. This is because, under the status of CNS, the normal stress of the joint is mainly caused by the joint dilatancy control, as shown in reference [22]. The peak shear stress and final shear stress of joints under different shear rates were counted in Figure 9. The peak shear stress, final shear stress, and shear rate of the joint are obviously power functions (the exponent is negative). When the shear rate is between 0.5 mm/min and 5 mm/min, the peak shear stress and final shear stress falling rate of the joint are much higher than those when the shear rate is between 5 mm/min. This result is consistent with that of [PERSON] et al. [31], [PERSON] et al. [32], and [PERSON] et al. [33].