Shear properties of two-order morphology of rock joints

The surface morphology of rock joints is composed of two-order morphology, including macroscopic undulation components (first-order) and asperities of joint surfaces (second-order), and different morphologic components contribute differently to the shear characteristics during the shearing process. 3D laser scanning, 3D printing technology and similar materials are adopted to produce different model joints in batches, and direct shear tests are carried out under different normal stress conditions. The test results show that under the same normal stress, the second-order morphology shear wear is close to the overall morphology and greater than the first-order morphology. Under different normal stresses, the average variation rate of the two-order roughness parameters gradually increases with the increase of the normal stress before and after shearing. The average variation rate of the first-order roughness parameters ${\eta _{\rm I}}$ is 1.99%~4.03%, and that of the second-order roughness parameters ${\eta _{\rm{ \mathsf{ π} }} }$ is 5.97%~8.16%. The cosine angle is calculated based on the principle of "cosine similarity" to evaluate the similarity of the joints before and after shearing. The cosine angle of the second-order morphology fluctuates most, the cosine angle of the first-order morphology is close to the overall morphology, and the shear wear characteristics of the second-order morphology and the shear dilatancy characteristics of the first-order morphology are verified. The above results are of reference significance for the evaluation of the shear strength of joints.