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A Simplified Model for Time-Dependent Deformation of Rock Joints

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Abstract

Understanding the time-dependent deformation behavior of rock joint is important when evaluating long-term stability of structures built on or in jointed rock masses. This study focuses on the time-dependent strength and deformation of unweathered clean rock joints. First, five grain-scale joint models are established based on Barton’s standard joint profiles using the GBM-TtoF creep material model. Barton’s non-linear shear strength criterion is adopted to determine the short-term shear strength of the joints. Second, a series of creep simulations are conducted to investigate major factors (normal stress, shear loading ratio, and joint roughness) that influence the long-term shear strength and the sliding velocity of the joints. The results reveal that normal stress has more influence than joint roughness on resisting creep slipping of the joints. Third, an equation for the prediction of creep sliding velocity is developed by fitting the simulation results and the equation is verified by experimental data. Finally, a creep slipping model for simplified flat joints is proposed, which can be used to model the long-term shear strength and sliding velocity of joints under creep deformation conditions. The creep slipping model, which can be used in both stationary and variable stress conditions, is useful for simulating time-dependent behaviors of jointed rock mass using the distinct element method.

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Abbreviations

\(\tau_{S}\) :

Short-term shear strength

\(\tau_{L}\) :

Long-term shear strength

JCS :

Joint wall compressive strength

\(\phi_{b}\) :

Basic friction angle of macro-joint

JRC :

Joint roughness coefficient

\(\sigma_{n}\) :

Normal stress

UCS :

Uniaxial compressive strength of rock

\(c\) :

Cohesion of rock in the TtoF (time-to-failure) model

\(\phi\) :

Friction angle of rock in the TtoF model

\(\sigma_{t}\) :

Tensile strength of rock in the TtoF model

\(c^{c}\) :

Cohesion of contact element

\(\phi^{c}\) :

Friction angle of contact element

\(\sigma_{t}^{c}\) :

Tensile strength of contact element

\(i\) :

Dilation angle of contact element

\(Jks\) :

Shear stiffness of contact element

\(Jkn\) :

Normal stiffness of contact element

\({\tau \mathord{\left/ {\vphantom {\tau {\tau_{S} }}} \right. \kern-\nulldelimiterspace} {\tau_{S} }}\) :

Shear loading ratio

\(\xi\) :

Long-term shear strength ratio

\(JRC_{mob}\) :

Mobilized joint roughness

\(\phi_{mob}\) :

Mobilized joint friction angle

\(JRC_{c - mob}\) :

Mobilized joint roughness due to creep damage

\(C_{j}\) :

Dimensionless parameter

\(\xi_{0}\) :

Basic long-term shear strength ratio

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Acknowledgements

This work was financially supported by NSERC (Natural Science and Engineering Research Council of Canada, RGPIN-2016-04052), the China Scholarship Council (Grant No. CSC201806370225), and MIRARCO of Laurentian University.

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Authors and Affiliations

  1. Bharti School of Engineering, Laurentian University, Sudbury, ON, Canada

    Mingzheng Wang & Ming Cai

  2. MIRARCO-Mining Innovation, Laurentian University, Sudbury, ON, Canada

    Ming Cai

  3. Key Laboratory of Ministry of Education for Safe Mining of Deep Metal Mines, Northeastern University, Shenyang, China

    Ming Cai

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  1. Mingzheng Wang
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Correspondence to Ming Cai.

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Wang, M., Cai, M. A Simplified Model for Time-Dependent Deformation of Rock Joints. Rock Mech Rock Eng 54, 1779–1797 (2021). https://doi.org/10.1007/s00603-020-02346-2

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