## 3 Shear Behaviors  
### Effect of Normal Stiffness  
Figure 4 demonstrates the shear actions of the joint at diverse normal stiffness. As displayed in Figure 4a, for the CNL condition (\(k_{\mathrm{n}}=0\)), the curves of shear stress versus displacement can be split into three stages. In stage I, the shear stress rapidly increases with a linear concern with the shear displacement up till it achieves the peak. In stage II, the curve displays stress-softening conduct, characterized by a rapid decrease in shear stress. Finally, the variation of shear stress tends to be stable at approximately 5 mm of shear displacement, indicating the residual stage has reached. Under a low level of normal stiffness (\(k_{\mathrm{n}}<\) 3 MPa/mm), the shear behavior shows stress-softening behavior. When the normal stiffness progresses (\(k_{\mathrm{n}}>\) 3 MPa/mm), the shear stress shows stress-hardening behavior, during which the shear stress increases with an increase in shear displacement. Figure 4b shows the normal displacement versus shear displacement curves. The normal displacement decreases to negative values at initial shearing; after the minimum normal displacement is reached, shear dilation occurs until the shear displacement reaches 10 mm. The dilation was decreased by increasing normal stiffness. This is because the increase of normal stress induced by normal stiffness restrains the increment of dilation. The bows of normal stress against shear displacement are shown in Figure 4c. For CNL conditions, the normal stress remains unchanged during shear, while the variations in normal stress are proportional to the case of normal shift at the CNS status. According to the throwing distance and throwing height, the initial velocities of the broken blocks in different throwing distances were calculated by combining the equations of the flat throwing motion, see Table 3.  
Figure 4: Shear actions of joints under various normal stiffness statuses. (**a**) Shear stress versus shear displacement of joints. (**b**) Normal displacement versus shear displacement of joints. (**c**) Normal stress versus shear displacement of joints. Although the shear stress shows a clear peak value for joints under a low normal stiffness, there are no distinct peak values for joints under a high normal stiffness. To better understand the shear strength of plaster joints under higher normal stiffness, the curves of the surface resistance index (SRI) are used to analyze the relative shearing resistance [38]. The SRI is defined as the ratio of shear stress to normal stress. The variations in SRI against shear displacement are plotted in Figure 5a. The normal stiffness has little influence on joint SRI. The five SRI curves have little difference and almost coincide in the III stage, while there is a separation between the shear stress peak and the II stage, but the maximum difference is only 0.2. This is due to the reality that the shear stress addition of the joint is comparable to the normal stress increment in the shear process under CNS border conditions [38]. Figure 5b displays the peak shear stress and final shear stress of joints under various normal stiffness statuses. With the rise of normal stiffness, the peak shear stress of the joint declines slightly. This is because the normal displacement of the joint is negative in the initial shear stage, which leads to a decrease in the normal stress on the joint. The final shear stress rises linearly with the rise of normal stiffness. After shearing, the failure modes of joints under various normal stiffness are shown in Figure 6. The white part in the figure is the rough body that was nibbled or destroyed by friction in the shearing process. In this paper, image recognition technology is used to extract the damaged part and mark it with a red line. It can also be found that in addition to the rough body failure, many local cracks will occur on the joint surface, which are marked by blue lines in the figure.