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The area ratio content of the asperities with different apparent dip angles is studied based on Grasselli’s apparent dip angle distribution function. An approximate expression of the minimum dip angle of the asperities in contact is further obtained according to the contact theory. For regular joints, the peak dilation angle is the average dip angle of all asperities on the contact part. Extending the above idea to the peak dilation angle of rough joints, the peak dilation angle model is derived based on the apparent dip angle distribution of the real contact asperities. In the derivation process, the peak dilation angle of an arbitrary stress state is directly obtained, instead of obtaining the initial dilation angle first and then defining the relation between the peak dilation angle and the initial dilation angle. The more important innovation is that all the parameters in the new model are of physical significance and easy to obtain; furthermore, they are not obtained by fitting test results. Based on 89 sets of test data, the predicted values of the new model are compared with those of the other 4 existing models. The results show that the prediction accuracy of the new model is the best. Besides, the mesh scales of rock joint are discussed, and the size range of the triangle mesh is obtained. It is proposed to remove the isolated points with a large apparent dip angle when processing test data. The shear mechanism of rough joints is further clarified in this study: the dilation is regarded as the average apparent dip angle of the asperities in contact at a certain stress level. This view is easy to understand and follow. It is as simple and beautiful as many natural principles.

The peak shear displacement (PSD) of artificial joints was studied by the shear test of cement mortar duplicate joints under constant normal load. First, the splitting rock joints were produced by the Brazilian splitting method, and the high-precision point cloud of joint surface morphology was acquired by three-dimensional (3D) scanning method. The polylactic acid (PLA) base mold was produced by 3D printing technology. The duplicate joints with the same joint surface as the splitting rock joints were obtained by pouring cement mortar on the PLA base mold. Then, shear tests of 20 cement mortar specimens with 5 groups of joint surface morphologies under 4 different normal loads were carried out, and the joint shear stress-displacement curves were obtained. The influencing factors of the PSD were studied. The results indicate that the PSD is inversely related to the joint roughness and positively related to the normal stress (NS). The limitation of Barton’s empirical formula is that it cannot predict (fit) the PSD of the joints with JRC = 0 and reflect the effect of NS on the PSD. To quantitatively study the PSD of joints, an empirical formula that can comprehensively consider the influence of surface roughness and NS is introduced based on the test results. The modified model overcomes the limitation of Barton’s empirical formula which ignored the NS and can well reflect the sensitivity of joint roughness coefficient (JRC) to PSD. The acquisition of PSD can provide a basis for the numerical simulation of rock engineering and provide quantitative research methods for the analysis of stick-slip events.

Rock is a material that is affected by wear, and the curvature of the asperities on a rock joint surface increases with the degree of wear after shearing. Based on the Greenwood and Williamson (GW) model, a new model considering the change of asperity curvature is proposed to explain the wear behaviour of rock joints. First, the shear stiffness formula for a joint surface is derived when the asperity curvature is constant, which shows that the shear stiffness increases with increase of asperity curvature. According to the Mohr–Coulomb criterion, the yield position of a single asperity under normal force and tangential friction force is discussed. Then, the critical normal force for a single asperity at a specific friction coefficient is obtained, which shows that the normal force corresponds to the curvature radius of the asperity. A rough surface model with multi-level curvature radius is proposed. With increase of normal force, the higher-order asperities gradually fail and the curvature radius become larger. A specific pressure value excites a specific radius of curvature, and the larger the pressure, the larger the radius of curvature. The relation between the normal force and the curvature radius is proposed and a shear stiffness formula considering the change of curvature radius of the asperity is derived. The proposed model is verified on the basis of the published experimental results. The calculation results of the proposed model can reflect the test results well: for a given joint surface, with increase in normal force the joint surface gradually becomes smooth; for different joint surfaces, with increase in roughness, the joint surface is more easily smoothed.

With the help of 3D printing and 3D laser scanning techniques, cement mortar joint samples with a certain surface morphology were prepared. Shear tests of 20 sets of matching joint samples and 8 sets of joint samples with different percentages of cavity area were performed under constant normal load and uniform shear displacement. The results show that the distribution characteristics of the equivalent height difference based on the new roughness description were in accordance with the distribution of the wearing area after shearing, and the effect of cavities on the peak shear strength is essentially due to the influence of the cavities on the roughness of the joint surface. The relationships between the peak shear strength and the two roughness parameters were discussed, and a new criterion for predicting the peak shear strength of rock joints was proposed. It was noted that the roughness parameter system adopted in this paper, which can describe the peak shear strength, was reasonable. The roughness anisotropy of the five joint surfaces was discussed, and a corresponding quantification parameter AAHD accounting for the roughness anisotropy was proposed. The roughness of the joint surface has a positive size effect, a negative size effect and no size effect in a certain direction. However, no matter the direction, the roughness parameters will gradually stabilize as the research scale increases. A similar relationship between the roughness anisotropy parameters and research scales was also observed. To check the applicability of the proposed criterion for estimating the peak shear strength of natural rock joints, 12 sets of rock joints with the same surface morphology were produced based on a numerically controlled engraving technique. Under the same loading conditions as those in the shear tests of the cement mortar replication joints, the peak shear strengths of the rock joints were tested, and the results indicated that the new criterion was also applicable to predict the peak shear strength of natural rock joints.

In order to explore the factors impacting on the roughness of natural rock joints, a new roughness parameter AHD (the average equivalent height difference) is proposed based on study of joint surface by using the 3D laser scanning technology. The new parameter AHD cannot only reflect the roughness anisotropy of joint surface, but the sampling interval effect and the size effect on roughness. To quantitatively characterize the roughness anisotropy of joint surface, a new anisotropy parameter AAHD is established based on the new roughness parameter AHD. The new parameter AAHD is more comprehensive and reasonable than the anisotropy parameter Ka obtained by Belem because of its consideration on surface morphology in all shear directions, while Ka only considers the largest and the smallest values of roughness parameter. Based on the new parameter AAHD, the sampling interval effect and the size effect on the roughness anisotropy are further studied. The obtained results show that the roughness of joint surface is determined by shear directions, sampling intervals, and research sizes (which refers to window sampling size). It is found that the size effect on roughness depends on shear directions and stabilizes when research size increases to a certain value, while the roughness anisotropy is determined by sampling intervals and research size as well.

A new three-dimensional shear-strength criterion (3DSSC) considering the three-dimensional (3D) roughness of rock joints and the internal friction angle of rock masses is discussed. Two methods for transforming the parameters of the 3DSSC into the linear Mohr–Coulomb failure criterion parameters are proposed. The calculation method of the anti-sliding safety coefficient of a rock slope controlled by a single anchored rock joint is derived, and anchoring parameter analysis is carried out. Compared with the equivalent linear fitting method and tangent equivalent method for obtaining the Mohr–Coulomb shear-strength parameters, the 3DSSC can be directly applied to calculate the rock slope stability controlled by a single rock joint. The change in the characteristics of the anti-sliding safety coefficient of the slope with the changes in the 3D roughness parameters, shear rate, and internal friction angle are discussed. The sensitivity of these factors to the slope stability is analyzed. It is suggested that for rock slopes with high roughness and a small internal friction angle, the weakening effect of the anchoring force angle on the anti-sliding stability of the slope should be taken into account.

Determination of the configuration and size of fracture process zone (FPZ) at dynamic crack tip is still a problem unsolved completely at present. In this paper, based on elastic dynamic theory and stress functions, a method for evaluating the configuration and the size of FPZ is proposed and the feasibility of the method is demonstrated. The configuration and size of the FPZ near the crack tip in dependence on crack propagation velocity are determined by using the Von Mises and Tresca criteria, respectively. Numerical results show that FPZ at mode II and mode III dynamic crack tip is distributed symmetrically with respect to crack plane and increases with the crack propagation velocity. FPZ changes more rapidly when the Rayleigh wave velocity is approached. The effects of Poisson’s ratio on FPZ are discussed. Analysis reveals an intricate dependence on Poisson’s ratio in plane strain condition.

To clearly portray the mechanical behavior of the shear process and to relate three-dimensional surface morphology to the shear strength of rock joints, we propose a new method, the equivalent height difference system, which can reflect that different geometric parameters of the asperities contribute differently to shear strength. A roughness parameter, the average equivalent height difference (AHD), is obtained by averaging the equivalent height difference in the shear direction, which can reflect the fluctuation and directivity of the joint surface morphology. The values of AHD at different sampling intervals were studied. The relationship between AHD values and sampling intervals is power law. Another roughness parameter, fractal dimension (DAHD), was proposed based on the fractal component, which characterizes the relationship of roughness at different scales and describes the roughness comprehensively from the point of view of scale. We used these two newly proposed roughness parameters to characterize the roughness of five joint surfaces. The results show that the new method can well reflect the three-dimensional morphology of the joint and describe the anisotropy of roughness, and it can also overcome the influence of the sampling interval.

Based on the index, the root mean square of the first derivative of the profile (Z2), the contribution of the asperities with different geometric characteristics to the peak shear strength (PSS) is considered, and an improved roughness index (Z2)ds is proposed. (Z2)ds is reasonably related to the PSS and can reflect the directionality of the PSS. The direct shear tests of 60 joints under different normal stress are carried out. Test results show that the PSS is related to normal stress, surface morphology and shear direction. The joint equivalent dip angles and the abrasion zone of joints after shearing share a similar distribution. There is a clear linear relationship between (Z2)ds and the joint PSS. Accordingly, a new relationship between the roughness index (Z2)ds and PSS is proposed. The new relationship can eliminate the influence of sampling intervals. The proposed index (Z2)ds establishes a reasonable relationship between the surface roughness and shear mechanical properties of rock joints. This is helpful to study the shear behavior of rock masses in a specific direction in engineering geology.

The surface morphology of a rock joint is closely related to its mechanical properties. To reasonably characterize a rock surface, two new roughness parameters were proposed in this paper. One is related to the average slope angle of asperities that contribute to the shear strength, and the other reflects the frictional behavior of asperities that is defined as the maximum possible contact area in the shear direction. Taking the standard joint roughness coefficient profiles as example, these two roughness parameters can be applied to describe the directional characteristics of shear strength. Based on their relationships with initial dilation angles, the proposed roughness parameters were incorporated into a peak shear strength criterion. It is shown that the predicted peak shear strength is consistent with experimental data, and there is a power–law relationship. The application range of new roughness parameters was determined, which may facilitate a measurement process.