A New Criterion for Peak Shear Strength of Rock Joints with a 3D Roughness Parameter

  • Liren Ban
  • Chengzhi QiEmail author
  • Haoxiang Chen
  • Fayuan Yan
  • Chenmeng JiEmail author
Original Paper


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.


Shear strength Rock joints Joint surface Roughness anisotropy Size effect 



Joint roughness coefficient


Brightness area percentage


Projective covering method


A roughness parameter based on the local apparent dip of the asperities


Polylactic acid

2D, 3D

Two-dimensional, Three-dimensional


Charge coupled device


A new roughness parameter proposed by Ban et al. (2018)

AHD(δ), AHD0

The values of AHD with the measurement scale of δ and1 mm


The fractal dimension

m, mc

Aspect ratio, critical aspect ratio


The internal friction angle of an intact rock (°)


Normal stress (MPa)


Cohesion of an intact rock (MPa)


The interval to mesh the joint surface (mm)


The height of the nth asperity

\(h_{n}^{ * }\)

The equivalent height difference


The coordinate data of the jth column of the ith row


The numbers of asperities along and perpendicular to the shearing direction, respectively


The length of the jth column in the shear direction


The ratio of the peak shear strength to normal stress


The initial dilation angle (°)


The peak dilation angle (°)

a, b

Regression coefficients based on experimental data


The basic friction angle (°)


Joint roughness coefficient


The value of JRC for the ith profile


The number of the selected profiles on the joint surface


The cavity percentage of the joint surface


The roughness of the joint surface without cavity


AHD0 for the ith analysis direction

\(\overline{{{\text{AHD}}_{0} }}\)

Average value of AHD0i of all analysis directions


Total number of analysis directions


Roughness anisotropy parameters


The roughness parameter for the ith analysis direction


The average calculation error



This work was supported by the National Key Basic Research Program of China (973) (Project no. 802015CB575) and the National Natural Science Foundation of China (Project nos. 51478027 and 51174012).

Compliance with Ethical Standards

Conflict of Interest

Liren Ban declares that he has no conflict of interest. Chengzhi Qi declares that he has no conflict of interest. Haoxiang Chen declares that he has no conflict of interest. Fayuan Yan declares that he has no conflict of interest. Chenmeng Ji declares that he has no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Civil and Transportation Engineering, Beijing Advanced Innovation Center for Future Urban DesignBeijing University of Civil, Engineering and ArchitectureBeijingChina
  2. 2.School of Mechanics and Civil EngineeringChina University of Mining and Technology (Beijing)BeijingChina
  3. 3.College of Architectural and Civil EngineeringBeijing University of TechnologyBeijingChina

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