Non-linear Shear Strength Model for Coal Rocks

  • Jiayi Shen
  • Ling WanEmail author
  • Jianping Zuo
Technical Note


The strength of the intact rock is one of the most important aspects required to build numerical models for many rock engineering projects, such as open pit mining and tunnel excavations. Numerous failure criteria have been proposed for predicting the intact rock strength. A working group (Alejano and Bobet 2012; Chang and Haimson 2012; Da Fontoura 2012; Eberhardt 2012; Labuz and Zang 2012; Priest 2012) of the International Society of Rock Mechanics (ISRM) on ‘Suggested Methods for Failure Criteria’ was established to standardize the various failure criteria used in practice engineering applications.

It is known that the strength envelope of intact coal rock is a non-linear function of the confining stress level (Medhurst and Brown 1998). However, the linear Mohr–Coulomb (MC) strength criterion is still widely used in real engineering applications due to its simplicity and mathematical convenience in the field (Jimenez et al. 2008; Shen et al. 2012; Zhu 2017).

The MC...


Coal rocks Shear strength parameters Uniaxial compressive strength Mohr–Coulomb Confining stress 

List of symbols

c (MPa)


ϕ (°)

Angle of friction

σ1 (MPa)

The maximum principal stress

σ3 (MPa)

The minimum principal stress or confining stress

σ3max (MPa)

Maximum confining stress

σci (MPa)

Uniaxial compressive strength (UCS)

σci_fitted (MPa)

Fitted UCS


Fitting parameter


Fitting parameter


Fitting parameter


Fitting parameter


Intermediate auxiliary parameter


Absolute average relative error percentage


Number of tests


Relative error


Correlation coefficient



This research has been funded by the National Natural Science Foundation of China (nos. 51504218 and 11372363). The authors would like to express their gratitude to anonymous reviewers for their constructive comments on the paper.

Supplementary material

603_2019_1775_MOESM1_ESM.docx (34 kb)
Supplementary material 1 (DOCX 33 KB)


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Copyright information

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

Authors and Affiliations

  1. 1.Institute of Port, Coastal and Offshore EngineeringZhejiang UniversityHangzhouChina
  2. 2.State Key Laboratory of Coal Mine Disaster Dynamics and ControlChongqing UniversityChongqingChina
  3. 3.Chongqing Key Laboratory of Heterogeneous Material MechanicsChongqing UniversityChongqingChina
  4. 4.State Key Laboratory of Coal Resources and Safe MiningChina University of Mining and TechnologyBeijingChina
  5. 5.Institute of Rock Mechanics and Fractals, School of Mechanics and Civil EngineeringChina University of Mining and TechnologyBeijingChina

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