Abstract
In this paper, an analytical model for the stability analysis of rock slope subjected to block toppling pertaining to different hydraulic forms has been developed. In the traditional analytical model, ground water pressure is considered to be varied hydrostatically. To better reflect the physical situation, three different hydraulics forms have been considered in developing a stability model for a rock slope susceptible to block toppling. It is well known fact that presence of ground water causes the instability in a rock slope. The present study observes that hydraulic distribution forms also significantly influence the stability of the rock slope. Ground water pressure markedly increases the toppling forces on the blocks and reduces the normal and shear force at the base of block along failure plane, thereby causing instability. The increase in toppling force and reduction in the factor of safety on the blocks are more prominent when the flow slit is blocked, indicating a condition of permanent or seasonal frozen strata. The study highlights that adopting the traditional hydraulic form to analyse block toppling stability, considering presence of ground water would not be suitable for all field conditions. This necessitates the selection of an appropriate hydraulic distribution form based on the encountered field conditions.
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Abbreviations
- a 1 :
-
Height difference at the top of adjacent blocks below the crest
- a 2 :
-
Height difference at the top of adjacent blocks above the crest
- b :
-
The height difference at the base of adjacent blocks
- H :
-
Slope Height
- L n :
-
Distance from the base of the block to the point of application of Pn−1
- M n :
-
Distance from the base of the block to the point of application of Pn
- N :
-
Total number of blocks
- n :
-
Number of block (numbered from toe to uppermost block)
- P n :
-
The normal force of n + 1th block to nth block
- P n−1 :
-
The normal force of n − 1th block to nth block
- Q n :
-
Shear force between n + 1th and nth block
- Qn−1:
-
Shear force between n − 1th and nth block
- R n :
-
Normal force at the base of nth block
- S n :
-
Shear force along the base of nth block
- V 1, V 3 :
-
Ground water forces along the sides of block
- V 2 :
-
Ground water forces along the base of block
- W n :
-
Weight of nth block
- y n :
-
Height of nth block
- y w, z w :
-
Depth of the water along the sides of block
- α a :
-
Dip direction of discontinuity along base
- α b :
-
Dip direction of discontinuity along width
- αs :
-
Dip direction of discontinuity along face
- Δ x :
-
Width of block
- γ r :
-
Unit weight of rock
- γ w :
-
Unit weight of water
- ϕ b :
-
Overall dip of failure plane along base
- ϕ d :
-
Friction angle along the side of the block
- ν p :
-
Friction angle along the base of the block
- ψ d :
-
Dip of the orthogonal plans forming the sides of the blocks
- ψ f :
-
Slope angle below the crest
- ψ p :
-
Dip of plane forming base of the block
- ψ s :
-
Slope angle above the crest
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Chaudhary, N., Metya, S. & Sharma, K.K. Influence of Hydraulic Distribution Pattern on the Rock Slope Stability under Block Toppling Failure. KSCE J Civ Eng 28, 1253–1266 (2024). https://doi.org/10.1007/s12205-024-1309-8
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DOI: https://doi.org/10.1007/s12205-024-1309-8