Rock Mechanics and Rock Engineering

, Volume 51, Issue 7, pp 2115–2133 | Cite as

Updates to Grasselli’s Peak Shear Strength Model

  • Yongchao Tian
  • Quansheng Liu
  • Dongfeng Liu
  • Yongshui Kang
  • Penghai Deng
  • Fan He
Original Paper


The morphological characteristics of rock joints have a significant impact on the peak shear strength of a rock mass. In this study, three-dimensional scanning tests have been conducted on 39 joint specimens. Based on the scanning data, the morphological parameter \( C^\prime \) has been developed to describe the joint roughness. With an explicit physical meaning, this index is negatively correlated with the joint roughness and can reflect the anisotropy of surface morphology. Using a newly developed derivation method, the morphological parameter \( C^\prime \) of each joint from the earlier studies has been determined. The scanning test results in this study have been used to confirm the feasibility of this new derivation method. By applying the least square fitting method to the Grasselli’s (Shear strength of rock joints based on quantified surface description. Dissertation, Swiss Federal Institute of Technology, 2001) test results, a new peak shear strength model has been developed. Finally, a comparison of the peak shear strength of rock joint predicted by the new model and other classic models shows that the new model, characterized by simplicity, relatively higher precision, and a definite physical meaning, is feasible to predict the peak shear strength of rock joints.


Joint roughness Morphological characteristics Peak shear strength 

List of symbols

\( \tau_{\text{p}} \)

Peak shear strength (MPa)

\( \sigma_{\text{t}} \)

Tensile strength (MPa)

\( \sigma_{\text{c}} \)

Uniaxial compressive strength (MPa)

\( \varphi_{\text{b}} \)

Basic friction angle (°)

\( \sigma_{\text{n}} \)

Normal stress (MPa)

\( i_{\text{p}} \)

Peak dilatancy angle (°)

\( i_{0} \)

Initial dilatancy angle (°)


Outward normal vector of the triangle unit


The projection vector of n


Outward normal vector of the shear plane


The shear vector

\( \alpha \)

The angle between n 1 and S (°)

\( \theta \)

Dip angle of the triangle unit (°)


Total area (mm2)


The potential contact area (mm2)

\( A_{{\theta^{ * } }} \)

Contact area ratio

\( A_{0} \)

Maximum contact area ratio

\( \theta^{ * } \)

Apparent dip angle (°)

\( \theta_{\text{cr}}^{ * } \)

Critical apparent dip angle

\( \theta_{\rm{max} }^{ * } \)

Maximum apparent dip angle (°)


Distribution parameter defined by Grasselli (2001)

\( C^{\prime} \)

Newly defined distribution parameter

\( \delta \)

Relative error


Joint roughness coefficient


Joint matching coefficient


Joint wall compressive strength (MPa)

\( \beta \)

Angle between schistosity plane and plane normal to the joint (°)

\( y_{\text{calculated}} \)

Calculated results

\( y_{\text{measured}} \)

Measured results



The authors would like to acknowledge the support of the National Basic Research Program of China (973 Program) (Grant No. 2014CB046904) and the National Natural Science Foundation of China (Grant No. 51774267).


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  • Yongchao Tian
    • 1
  • Quansheng Liu
    • 1
  • Dongfeng Liu
    • 1
  • Yongshui Kang
    • 2
  • Penghai Deng
    • 1
  • Fan He
    • 1
  1. 1.The Key Laboratory of Safety for Geotechnical and Structural Engineering of Hubei Province, School of Civil EngineeringWuhan UniversityWuhanChina
  2. 2.State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil MechanicsChinese Academy of SciencesWuhanChina

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