Experimental and Theoretical Study of Shear Instability of Rock Joints in the Direct Shear Test
Publication: International Journal of Geomechanics
Volume 21, Issue 3
Abstract
The stability of a rock joint was often dominated by one or more major asperities along the slip surface with a large bearing capacity to resist instability. In this study, direct shear tests were performed on artificial split rock joints. The shear failure mechanism of major asperities was revealed and a physical model was developed to describe the shear instability of the rock joint, by coupling a strain-softening constitutive model (based on the Weibull distribution) with a friction model (based on the piecewise function). The effects of constant normal load (CNL) and asperities on cutting-tooth behavior and shear instability characteristics of a rock joint (e.g., sudden jump values Δu1 of shear displacement, elastic energy release ΔU1, and shear instability proneness K2) were studied. The results showed that the shear instability of the rock joint was mainly affected by the CNL and major asperities. The physical model fits well with the shear stress–shear displacement curves of the rock joint. The necessary condition of shear instability (which is K2 ≤ 1) and predicted sudden jump values Δu1 of shear displacement were derived by using cusp catastrophe theory. The cutting-tooth effect of major asperity becomes more obvious with the increase of CNL. Here, Δu1, ΔU1, and K2 all decrease with the increasing CNL. The proposed physical model and the shear instability analysis may improve the understanding of the unstable shear failure behavior of rock joint both in the laboratory and in nature.
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Data Availability Statement
All data, models, and code generated or used during the study appear in the published article.
Acknowledgments
This work is funded by the National Key Research and Development Program of China (Grant No. 2016YFC0801607), National Science Foundation of China (Grant Nos. 51525402, 51874069, 51761135102, and 51904057), Fundamental Research Funds for the Central Universities of China (Grant Nos. N170108028, N170106003, and N180106003) and Postdoctoral Science Foundation of China (Grant No. 2018M641706). In addition, the authors would like to express their sincere thanks to Yuhan Li from Beijing Foreign Studies University, who helps to polish the language of this article.
Notation
The following symbols are used in this paper:
- A
- area of rock joint surface;
- a and b
- nondimensional parameters of RSF law;
- c
- cohesion of rock specimen;
- CNL
- constant normal load;
- D
- failure probability of REVs;
- Dc
- critical slip distance of RSF law;
- d
- peak shear displacement of tooth-shaped rock joint;
- E
- elastic module of rock specimen;
- FN
- normal load applied on rock joint;
- f
- shear strength of tooth-shaped rock joint;
- fA(u) and fB(u)
- shear force of A-part and B-part;
- total shear force of A-part and B-part;
- h
- material coefficient;
- i
- climbing angle of tooth-shaped rock joint;
- ia
- dihedral angle;
- JCS
- joint compression strength;
- JRC
- joint roughness coefficient;
- K0, K1, and K2
- stiffness ratio;
- k
- friction stiffness of tooth-shaped rock joint;
- kf
- friction stiffness of kf1, kf2, and kf3;
- kf1, kf2, kf3
- friction stiffness of phase I, II, and III;
- absolute value of the slope at turning point ut;
- km
- stiffness of testing machine;
- kr
- shear stiffness of gap zone;
- initial shear stiffness of the major asperity;
- ks
- series stiffness of P2 and P3;
- L
- length of specimen;
- m
- Weibull modulus (or shape parameter);
- n
- correction factor;
- p
- control variables of cusp catastrophe model;
- q
- control variables of cusp catastrophe model;
- R
- shear load applied on rock joint;
- Rs
- area ratio of S1 and S2;
- S1
- original area;
- S2
- projective area;
- UCS
- uniaxial compressive strength;
- u
- shear displacement of rock joint;
- u0
- measured average peak shear displacement;
- uR
- loading displacement of test machine;
- uj
- shear displacement values of critical points;
- up
- predicted peak shear displacement;
- upm
- measured peak shear displacement;
- ur
- predicted initial point of residual shear displacement;
- us
- shear displacement values of critical points;
- ut
- predicted shear displacement of turning point;
- V and V0
- steady slip velocity at different times;
- Vp
- wave velocity of rock specimen;
- V(x)
- potential function of cusp catastrophe model;
- W(u)
- potential function of the specimen-machine system;
- x
- state variable of cusp catastrophe model;
- β
- inclined angle (or average climbing angle) of major asperity;
- θ
- state variable of RSF law;
- λ1, λ2, λ3, λ4, and λ5
- regression coefficients;
- μ
- steady state friction coefficient;
- μ0
- reference steady state friction coefficient;
- ν
- Poisson ratio;
- ξ1 and ξ2
- dimensionless parameters;
- σn
- constant normal stress;
- σt
- tensile strength of rock specimen;
- τp
- predicted peak shear strength of rock joint;
- φ
- internal friction angle of rock specimen;
- φ(u)
- strength distribution function of REVs;
- φb
- basic friction angle;
- φr
- residual friction angle;
- ω
- reduction factor;
- Δf
- sudden jump value of shear force;
- ΔU1
- elastic energy release;
- Δu1
- predicted jump value of shear displacement; and
- ΔW1
- dimensionless elastic energy release.
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Published In
International Journal of Geomechanics
Volume 21 • Issue 3 • March 2021
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Mar 11, 2020
Accepted: Oct 11, 2020
Published online: Jan 7, 2021
Published in print: Mar 1, 2021
Discussion open until: Jun 7, 2021
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