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A new approach for quantifying the two-dimensional joint roughness coefficient (JRC) of rock joints

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Abstract

The joint roughness coefficient (JRC) is the key factor in predicting the peak shear strength of a rock joint. In this paper, we present a new approach for quantitatively calculating the JRC of two-dimensional rock joints. First, the two dimensionless indexes of cumulative relative relief amplitude (CRRA) and weighted average gradient (WAG) are defined to represent the morphology characteristics of a joint profile. Second, the ten standard roughness profiles suggested by Barton and Choubey are digitized, and the values of CRRA and WAG for each profile are calculated. Based on the JRC, CRRA and WAG results of the standard joint profiles, an equation for calculating the JRC, which takes the CRRA and WAG as inputs, is proposed by utilizing the multiple nonlinear fitting method. Finally, the validity of the proposed method is investigated by performing laboratory and numerical direct shear tests of 12 joint profiles with different JRCs. The results show that the established equation can accurately quantify the JRC of a two-dimensional joint. However, the accuracy of the JRC greatly depends on the sampling interval along the joint profile. The recommended length of the sampling interval is no greater than (1/120) L.

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Some or all data, models, or code generated or used during the study are available from the corresponding author by request.

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Acknowledgements

The authors gratefully acknowledge the support of National Science Foundation for Young Scientists of China (No. 51709176), Hebei Province Science Foundation for Yong Scientists (No. E2018210046), Guizhou Province Key Technology R&D Program (No. 2019-2883), Key Foundation of Education Department of Hebei Province (No. ZD2020333) and Key Project of Hebei Natural Science Foundation (No. F2019210243).

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Correspondence to Niu Jiandong.

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Appendix

Appendix

Servo-control mechanism

During all stages of the test, the velocities of the walls are adjusted via a servo-control mechanism to maintain a constant confining stress. The stresses and strains experienced by the sample are determined in a macro fashion by computing the stress acting upon, and relative displacement of, opposite walls.

The force arising from wall displacement is,

$$ \Delta F^{{{\text{wall}}}} = k_{n}^{{{\text{wall}}}} N_{c} \dot{u}^{{{\text{wall}}}} \Delta t, $$
(16)

where \(\Delta F^{{{\text{wall}}}}\) is the resultant force increment on the wall, \(N_{c}\) is the number of contacts on the wall, \(k_{n}^{{{\text{wall}}}}\) is the average stiffness of these contacts, \(\dot{u}^{{{\text{wall}}}}\) is the wall velocity and \(\Delta t\) is the time-step. Hence, the change in mean wall stress is,

$$ \Delta \sigma^{{{\text{wall}}}} = \frac{{k_{n}^{{{\text{wall}}}} N_{c} \dot{u}^{{{\text{wall}}}} \Delta t}}{A}, $$
(17)

where A is the wall area.

For stability, the absolute value of the change in wall stress must be less than the absolute value of the difference between the measured and required stresses. In practice, a relaxation factor is used, such that the stability requirement becomes,

$$ \left| {\Delta \sigma^{{{\text{wall}}}} } \right| < \alpha \left| {\Delta \sigma } \right|, $$
(18)

where \(\alpha\) is relaxation factor.

The wall velocity could be computed as

$$ \dot{u}^{{{\text{wall}}}} = G\Delta \sigma , $$
(19)

where G is the gain factor.

Finally, according to Eqs. (1719), the following inequation is true:

$$ \frac{{k_{n}^{{{\text{wall}}}} N_{c} G\Delta t}}{A} < \alpha , $$
(20)

The gain factor is finally computed as,

$$ G = \frac{\alpha A}{{k_{n}^{{{\text{wall}}}} N_{c} \Delta t}}. $$
(21)

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Wei, Y., Sifan, L., Hanhua, T. et al. A new approach for quantifying the two-dimensional joint roughness coefficient (JRC) of rock joints. Environ Earth Sci 80, 484 (2021). https://doi.org/10.1007/s12665-021-09780-7

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