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Non-linear Shear Strength Criterion for a Rock Joint with Consideration of Friction Variation

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Abstract

Under shearing, joint asperities get sheared off and damaged. Moreover, shearing and sliding and the interaction between normal and shear stresses occur simultaneously. The nonlinearity of the shear strength envelope is closely related to the joint material, normal stress level, and morphological characteristics. This study analyzed the correlation of the friction angle with the normal stress level to overcome overestimation or underestimation at relatively low or high normal stress levels in the JRC–JCS empirical model. A hyperbolic function was adopted to describe the degradation of friction for different normal stress levels, and the modified non-linear shear criterion \(\tau = \sigma_{\text{n}} \tan (\phi_{\text{r}} + \Delta \phi /(1 + a\sigma_{\text{n}} /{\text{JCS}}))\) was proposed. Furthermore, the proposed model avoids direct connection to the surface morphology, which is convenient for practical use. Statistical analysis of the experimental data and comparison with the JRC–JCS model verified the validity of the proposed model and present an excellent method for characterizing the non-linearity of the failure envelope for the rock joint.

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Fig. 1

(data from Tang and Wong 2016)

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Fig. 3

(Reproduced with permission from Maksimović 1996)

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(from Maksimović 1996)

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Abbreviations

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

Normal stress

\(\phi\) :

Friction angle

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

Tensile strength

\(\sigma_{\text{T}}\) :

Transition stress in Patton model

\(\phi_{\text{P}}\) :

Friction angle of peak shear strength

\(\phi_{\text{b}}\) :

Basic friction angle

\(d_{\text{n}}\) :

Peak dilation angle

\(s_{\text{n}}\) :

Contribution of asperities degradation in friction angle

\(\phi_{\text{r}}\) :

Residual friction angle

\(\tau\) :

Peak shear strength

JRC:

Joint roughness coefficient

JCS:

Joint compressive strength

\(P_{\text{N}}\) :

Median angle pressure in Maksimović model

\(c_{\text{T}}\) :

Apparent cohesion in Maksimović model

\(\phi_{\text{MAX}}\) :

Friction angle of the initial surface roughness of the discontinuity

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

Uniaxial compressive of intact rock

\(\Delta \phi\) :

Difference between \(\phi_{\text{MAX}}\) and \(\phi_{\text{r}}\)

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Acknowledgements

This paper gets its funding from project (51474249, 51774322, 41562016) supported by National Natural Science Foundation of China; Project (2016CX019) supported by Innovation-driven Plan in Central South University; Project (2017zzts534) supported by the Fundamental Research Funds for the Central Universities of Central South University. The authors wish to acknowledge these supports.

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  1. School of Resources and Safety Engineering, Central South University, Changsha, 410083, Hunan, China

    Hu Wang & Hang Lin

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  1. Hu Wang
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  2. Hang Lin
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Correspondence to Hang Lin.

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Wang, H., Lin, H. Non-linear Shear Strength Criterion for a Rock Joint with Consideration of Friction Variation. Geotech Geol Eng 36, 3731–3741 (2018). https://doi.org/10.1007/s10706-018-0567-y

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