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Rock Slope Stability Analysis: Limit Equilibrium Method Plane failure analysis

Wedge failure analysis

Toppling failure analysis 1Planar Failure Analysis A block is rest on a slope having angle

The block is considered to undergoes slippage along the plane for the value of ratio < 1, else it is stable2Plane failure analysis along a discontinuity

ABCHUnstable Block blockWWGeometry of a slope for plane failure3Plane failure analysis along a discontinuity

Planar Failure Analysis the plane on which sliding occurs must strike parallel or nearly parallel (within approximately + 200 ) to the slope face

the failure must daylight in the slope face. This means that its dip must be smaller than the dip of the slope face

the dip of the failure plane must be greater than the angle of internal friction angle of this plane

4Plane failure analysis along a discontinuity

W cosW W sinRBlock A

Factor of safety =

Factor of safety =

Factor of safety = =

Normal Stress;

Shear Stress ,

5Water is filled in discontinuities

The effective normal stress due to present of water in the joint, is given as

6Tension crack present in the upper slope surface

Tension crack in upper surface of slope and in the face7

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9Tension crack present in the slope surface

10Compound slope with water in upper slope angle

Compound slope with a positive upper slope angle

Geometry of slope with tension crack in upper slope angle

Compound slopes have appreciable angle with the horizontal. High slope formation has in generally a positive upper slope angle while the shorter slope has a negative slope angle11

12Effect of rock bolts

Geometry of slope with tension crack in upper slope and its interaction with rock bolt13

14Wedge Failure Analysis

Geometric conditions of wedge failure: (a) pictorial view of wedge failure; (b) stereoplot showing the orientation of the line of intersection15Analysis of wedge failure considering only frictional resistance

Resolution of forces to calculate factor of safety of wedge: (a) view of wedge looking at face showing definition of angles and , and reactions on sliding Plane RA and RB, (b) stereonet showing measurement of angles and , (c) cross-section of wedge showing resolution of wedge weight W.16Plane failure analysis along a discontinuity

17Analysis of wedge failure with cohesion and friction anglePictorial View of wedge showing the numbering of intersection lines and planes

18Analysis of wedge failure with cohesion and friction angle

19Analysis of wedge failure with cohesion and friction angle

20Toppling Failure Analysis

21Kinematics of block toppling failure

22Inter-layer slip test

23Block alignment test

24Limit equilibrium analysis for toppling failure

25Limit equilibrium analysis for toppling failure

Model for limiting equilibrium analysis of toppling on a stepped base (Goodman and Bray, 1976).26

Forces acting on the nth column sitting on a stepped base27

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CbzWDB plane failure with tension crackThe depth of critical tension crack, zc and its location, bc behind the crest can be calculated by the following equations:

Length of discontinuities; The weight of the block;

Factor of safety =

BCDWplane failure with tension crack

Length of discontinuities; The weight of the block =

Factor of safety =

Depth of tension crack,

Weight of unstable block,

or

Area of failure surface,

Driving water force,

Uplift water force,

Factor of safety =

FOS =

Where, Ca and Cb are the cohesive strength of plane a and b, a and b are the angle of friction along plane a and b, is the unit weight of the rock, and H is the total height of the wedge. X, Y, A and B are dimensionless factors, which depend upon the geometry of the wedge, a and b are the dips of planes a and b, whereas, i is the plunge of the line of their intersection.

Under fully drained slope condition, the water pressure is zero. Therefore, factor of safety of the wedge against failure is given by:

Case 1: Case 2: Case 3: Case 4: If is the dip of slope face and is the dip of the planes forming the sides of the blocks, then the condition for interlayer slip is given by:(180 ) (90 ) or (90 ) + The dip direction of the planes forming sides of the blocks, d is within about 100 of the dip direction of the slope face f, i.e.

|(f d)|