Stability of Slopes Notes | EduRev

Soil Mechanics

Civil Engineering (CE) : Stability of Slopes Notes | EduRev

The document Stability of Slopes Notes | EduRev is a part of the Civil Engineering (CE) Course Soil Mechanics.
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Stability Analysis of Slopes

The quantitative determination of the stability of slopes is necessary in a number of engineering activities, such as:

  1. the design of earth dams and embankments,
  2. the analysis of stability of natural slopes,
  3. analysis of the stability of excavated slopes,
  4. analysis of the deepseated failure of foundations and retaining walls.

Quite a number of techniques are available for these analyses

Stability of Slopes Notes | EduRev

Factor of Safety

The factor of safety is commonly thought of as the ratio of the maximum load or stress that a soil can sustain to the actual load or stress that is applied. Referring to Fig. given below the factor of safety F, with respect to strength, may be expressed as follows:

Stability of Slopes Notes | EduRev

where τff is the maximum shear stress that the soil can sustain at the value of normal stress of σn, τ is the actual shear stress applied to the soil.
Above equation may be expressed in a slightly different form as follows:
Stability of Slopes Notes | EduRev
Two other factors of safety which are occasionally used are the factor of safety with respect to cohesion, Fc, and the factor of safety with respect to friction, Fφ.
The factor of safety with respect to cohesion may be defined as the ratio between the actual cohesion and the cohesion required for stability when the frictional component of strength is fully mobilised. This may be expressed as follows:
Stability of Slopes Notes | EduRev
The factor of safety with respect to friction, Fφ, may be defined as the ratio of the tangent of the angle of shearing resistance of the soil to the tangent of the mobilised angle of shearing resistance of the soil when the cohesive component of strength is fully mobilised.
Stability of Slopes Notes | EduRev
A further factor of safety which is sometimes used is FH, the factor of safety with respect to height. This is defined as the ratio between the maximum height of a slope to the actual height of a slope and may be expressed as follows:
Stability of Slopes Notes | EduRev
Stability of Slopes Notes | EduRev
where, Cm = Mobilized Cohesion
m = Mobilized Friction Angle
Cm = C / Fs and tan∅m = tan∅ / Fs
Factor of Safety w.r.t. Cohesion (fc)
and Fc = C / Cm
where, Hc = Critical depth
H = Actual depth
Stability of Slopes Notes | EduRev

Stability Analysis of Infinite Slopes
  1. Cohesionless dry soil/dry sand
    W = yz cosβ
    Stability of Slopes Notes | EduRevStability of Slopes Notes | EduRevwhere,
    τ = Developed shear stress or mobilized shear stress
    σn = Normal stress.
    Stability of Slopes Notes | EduRev
    where,
    Fs = Factor of safety against sliding
    Stability of Slopes Notes | EduRev 
    For safety of Slopes
    β < φ

    Fs > 1Stability of Slopes Notes | EduRev
  2. Seepage taking place and the water table is parallel to the slope in Cohesionless SoilStability of Slopes Notes | EduRevh = Height of water table above the failure surface.
    Stability of Slopes Notes | EduRev
    φ’ is effective friction angle
    γ-avg. total unit weight of soil above the slip surface upto ground level.
    Stability of Slopes Notes | EduRev
  3. If water table is at ground level: i.e.,
    h = z
    Stability of Slopes Notes | EduRev
  4. Infinite Slope of Purely Cohesive Soil
    Stability of Slopes Notes | EduRev
    Fc = Hc/H
    Here H = z = depth of slice/cut.
    At Critical Stage Fc = 1
    Stability of Slopes Notes | EduRev
    where, Sη = Stability Number.
  5. C-∅ Soil in Infinite Slope
    Stability of Slopes Notes | EduRev
  6. Taylor's stability no.
    Stability of Slopes Notes | EduRev
    (for cohesive soil)
    Max. theoretical value of stability no. = 0.5
    Max. practical value is = 0.261
    Sη = [tanβ - tan∅]cos2β (for C-∅ soils)
Stability Analysis of Finite Slopes
  1. Fellinious Method
    (For Purely Cohesive Soil)
    (i) (F = Cr2θ / we) where, F = Factor of safety
    r = Radius of rupture curve
    I = Length of rupture curveStability of Slopes Notes | EduRev(ii) F = Cr2θ1/ weStability of Slopes Notes | EduRevF = Factor of safety it tension cracks has developed.
    zc = 2C / γ
  2. Swedish Circle Method
    Stability of Slopes Notes | EduRev
    where, F = Factor of safetyStability of Slopes Notes | EduRev
  3. Friction Circle Method
    Fc = C / Cm
    Stability of Slopes Notes | EduRevStability of Slopes Notes | EduRev
  4. Taylor's Stability Method (C-∅ soil)
    Stability of Slopes Notes | EduRev
    In case of submerged slope γ should be used instead of γ and if slope is saturated by capillary flow they γsat should be used instead of γ.
    Stability of Slopes Notes | EduRev
    where ∅w = weight friction angle. 
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