Report

Rock Slope Stability Analysis: Limit Equilibrium Method •Plane failure analysis •Wedge failure analysis •Toppling failure analysis Planar Failure Analysis The block is considered to undergoes slippage along the plane for the value of ratio < 1, else it is stable A block is rest on a slope having angle θ Plane failure analysis along a discontinuity B Unstable Block blockW H W θ α A Geometry of a slope for plane failure C Plane failure analysis along a discontinuity Planar Failure Analysis • the plane on which sliding occurs must strike parallel or nearly parallel approximately + 200 ) to the slope face (within • 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 Plane failure analysis along a discontinuity Block A R ShearStren gth Factor of safety = ShearStres s Factor of safety = s w sin( ) A w cos( ) A c Factor of safety = w cos t an A w sin A W cosθ W c tan Normal Stress; Shear Stress , W sinθ = cA w cos tan w sin Water is filled in discontinuities The effective normal stress due to present of water in the joint, is given as ' 1 gh 2 4 Tension crack present in the upper slope surface Tension crack in upper surface of slope and in the face b The depth of critical tension crack, zc and its B C z location, bc behind the crest can be calculated by the D following equations: W bc (cot cot ) cot H plane failure with tension crack Length of discontinuities; AD H CD Sin The weight of the block; Factor of safety = cA w cos tan w sin Tension crack present in the slope surface B z ( H cot b)(tan tan ) C Length of discontinuities; AD D H CD Sin W The weight of the block = Factor of safety = cA w cos tan w sin plane failure with tension crack c Compound slope with water 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 angle Compound slope with a positive upper slope angle Geometry of slope with tension crack in upper slope angle Depth of tension crack, Z H b tan c (b H cot ) tan Weight of unstable block, W 1 H 2 cot X bHX bZ ) 2 X (1 tan cot ) or Area of failure surface, A ( H cot b) sec Driving water force, V 1 w Z w2 2 Uplift water force, U 1 w Z w A 2 Factor of safety = cA ( w cos U V sin ) tan W sin V cos Effect of rock bolts Geometry of slope with tension crack in upper slope and its interaction with rock bolt FOS = cA ( w cos U V sin T cos ) tan W sin V cos T sin Wedge Failure Analysis Geometric conditions of wedge failure: (a) pictorial view of wedge failure; (b) stereoplot showing the orientation of the line of intersection Analysis 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 β and α, and reactions on sliding Plane RA and RB, (b) stereonet showing measurement of angles β and α, (c) crosssection of wedge showing resolution of wedge weight W. Plane failure analysis along a discontinuity Analysis of wedge failure with cohesion and friction angle Pictorial View of wedge showing the numbering of intersection lines and planes Analysis of wedge failure with cohesion and friction angle FS 3 (Ca X CbY ) ( A w X ) tana ( B w Y ) tanb rH 2 r 2 r X sin 24 sin 45 cos na 2 A cos a cos b cos na.nb sin i sin 2 na.nb Y sin 13 sin 35 cos na1 B cos b cos a cos na.nb sin i sin 2 na.nb Analysis of wedge failure with cohesion and friction angle Where, Ca and Cb are the cohesive strength of plane a and b, фa and фb 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, Ψa and Ψb are the dips of planes a and b, whereas, Ψi 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: FS 3 (Ca X CbY ) A tana B tanb rH Toppling Failure Analysis Kinematics of block toppling failure Case 1: Case 2: Case 3: Case 4: Inter-layer slip test If is the dip of slope face and α is the dip of the planes forming the sides of the blocks, then the condition for interlayer slip is given by: (180 − − α) ≥ (90 − ф) or α≥ (90 − ) + ф Block alignment test The dip direction of the planes forming sides of the blocks, αd is within about 100 of the dip direction of the slope face αf, i.e. |(αf− αd)| <10◦ Limit equilibrium analysis for toppling failure The factor of safety can be calculated as the ratio of resisting moments to driving moments Limit equilibrium analysis for toppling failure Model for limiting equilibrium analysis of toppling on a stepped base (Goodman and Bray, 1976). Forces acting on the nth column sitting on a stepped base Figure 17: Limiting equilibrium conditions for toppling and sliding of nth block: (a) forces acting on nth block; (b) toppling of nth block;