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Abbreviations
- A :
-
Total area of shear surface
- \(\alpha\) :
-
Joint plane angle
- \(\alpha_{i}\) :
-
Inclination of interface
- β :
-
Slope face angle
- \(c_{a}\) :
-
Jennings’ equivalent cohesion
- \(c_{I}\) :
-
Intact rock cohesion
- \(c_{J}\) :
-
Joint cohesion
- d j (x):
-
Major geological discontinuity function
- \({\mathbf{F}}\) :
-
Column vector of known forces
- \(F_{R}\) :
-
Local loading
- \(F_{s}\) :
-
Factor of safety
- \(\phi_{a}\) :
-
Jennings’ equivalent friction angle
- \(\phi_{I}\) :
-
Intact rock friction angle
- \(\phi_{J}\) :
-
Joint friction angle
- g(x):
-
Ground profile function
- γ :
-
Unit weight
- H :
-
Slope height
- H′:
-
Failure mass height
- k :
-
Seismic coefficient
- K :
-
Discontinuity persistence
- \({\mathbf{K}}_{s}\) :
-
Static coefficient matrix
- \({\mathbf{K}}_{v}\) :
-
Kinematics coefficient matrix
- L :
-
Boundary length
- m :
-
Number of boundaries for the element
- N :
-
Normal force
- N′:
-
Effective normal force
- \({\mathbf{N}}^{\prime }\) :
-
Column vector of unknown effective normal forces and virtual force
- ∑JL:
-
Total length of joint segments
- ∑RBR:
-
Total length of rock bridges
- T :
-
Shear force
- U :
-
Pore water force
- \({\mathbf{V}}\) :
-
Vector of unknown displacements of elements
- \({\hat{\mathbf{V}}}\) :
-
Vector of known displacements on flexible boundary
- W :
-
Weight
- X :
-
Vector of failure surface
- \({\mathbf{X}}^{\prime }\) :
-
Vector of intersections of the ground profile and the interfaces
- x′ i , y′ i :
-
Coordinates of vertex on the ground profile
- x i , y i :
-
Coordinates of vertex on the failure surface
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Acknowledgments
This research is supported by the National Natural Science Foundation of China (Project Nos. 51274249, 51174228), the Scholarship Award for Excellent Doctoral Student granted by Ministry of Education of China, the Doctoral Program Foundation of Higher Education of China (Project No. 20120162110009), and the State Scholarship Fund from the China Scholarship Council (Project No. 201306370135).
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Zhang, K., Cao, P., Ma, G. et al. Stability Analysis of Rock Slope Controlled by Major Geological Discontinuities Based on the Extended Kinematical Element Method. Rock Mech Rock Eng 49, 2967–2975 (2016). https://doi.org/10.1007/s00603-015-0877-9
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DOI: https://doi.org/10.1007/s00603-015-0877-9