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Abbreviations
- β :
-
Inclination angle between planes of weakness and the major principal stress
- V R :
-
Volume of layered rock
- V m :
-
Volume of matrix
- V f :
-
Volume of weakness planes
- \( c_{{{\text{R}}\left( \beta \right)}} \), \( \phi_{{{\text{R}}\left( \beta \right)}} \) :
-
Cohesion and internal friction angle of layered rock at angle β
- \( c_{\text{m}} \), \( \phi_{\text{m}} \) :
-
Cohesion and friction angle of matrix
- \( c_{f} \), \( \phi_{f} \) :
-
Cohesion and friction angle of weakness plane
- \( \mu_{{{\text{R}}\left( \beta \right)}} \) :
-
Friction coefficient (\( \tan \phi_{\text{R}} \)) of layered rock at angle β
- \( r_{f\left( \beta \right)} \) :
-
Strength reduction coefficient of anisotropic planes at angle β
- \( \sigma_{{{\text{c}}\left( \beta \right)}} \) :
-
Uniaxial compressive strength of layered rock at angle β
- ρ :
-
Inclination angle of minimum shear strength
- γ, δ :
-
Inclination angle of minimum cohesion and friction angle
- R c :
-
Degree of anisotropy
- a, b, c 1,2, ϕ 1,2, b’s, d’s, \( \hat{c} \), \( \hat{\mu } \) :
-
Constants
- R 2 :
-
Regression R-squared value
- \( \eta_{R}^{\exp } \), \( \eta_{R}^{{p{\text{red}}}} \) :
-
Experimental and predicted values of anisotropic strength
- \( \sigma_{1,\exp } \), \( \sigma_{{1,{\text{pred}}}} \) :
-
Experimental and predicted values of major principal stress at failure
- \( \eta_{R}^{\text{av}} \) :
-
Average of the experimental results
- N :
-
Total number of experimental data points
- AAREP:
-
Average absolute relative error percentage
- \( n_{i} \) and \( n_{j} \) :
-
Unit normals
- \( \varOmega_{ij}^{c} \), \( \varOmega_{ij}^{\mu } \) :
-
Symmetric second-order traceless tensors
- \( V_{\text{p}} \) :
-
P-wave velocity
- α :
-
P-wave velocity propagating perpendicular to the weakness plane
- ζ :
-
Fifth Thomsen parameter
- β 0 :
-
Shift angle
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Acknowledgments
This work was financially supported by the Youth Foundation of National Natural Science Foundation of China (No. 51504208) and the Scientific Fund of Sichuan Provincial Education Department (No. 14ZB0060).
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Shi, X., Yang, X., Meng, Y. et al. An Anisotropic Strength Model for Layered Rocks Considering Planes of Weakness. Rock Mech Rock Eng 49, 3783–3792 (2016). https://doi.org/10.1007/s00603-016-0985-1
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DOI: https://doi.org/10.1007/s00603-016-0985-1