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

Foundation Engineering

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

The document Stability Analysis of Slopes Civil Engineering (CE) Notes | EduRev is a part of the Civil Engineering (CE) Course Foundation Engineering.
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Chapter 11
Stability Analysis of Slopes
:
Factor of safety:
Factor of safety of a slope is defined as the ratio of average shear strength (Ƭf) of a soil to the average shear stress (Ƭd) developed along the potential failure surface.
Stability Analysis of Slopes Civil Engineering (CE) Notes | EduRev
Fs = Factor of safety
Ƭf= average shear strength of the soil
Ƭd= average shear stress developed along the potential surface
Shear Strength:
Shear strength of a soil is given by
Stability Analysis of Slopes Civil Engineering (CE) Notes | EduRev
Where, c = cohesion
Φ= angle of internal friction
σ= Normal stress on the potential failure surface
Similarly, the mobilized shear strength is given by
Stability Analysis of Slopes Civil Engineering (CE) Notes | EduRev
Cd and Φd are the cohesion and angle of internal friction that develop along thepotential failure surface
Stability Analysis of Slopes Civil Engineering (CE) Notes | EduRev
Fs w.r.t cohesion is
Stability Analysis of Slopes Civil Engineering (CE) Notes | EduRev

 SLOPES:
1. Infinite Slope
2. Finite Slope

1. Infinite Slope:- If the slopes represents the boundary surface of infinite soil man & the properties of the soil at similar depth below the ground, it is termed as infinite slope.
-Failure take place due to ‘sliding’ 
-Failure surface is parallel to the ground plane or slope 

2. Finite slope:- 
-Slopes are of finite extent bounded by top and bottom surfaces 
-Failure take place due to rotation. 
-Failure plane is either circular spiral

STABILITY ANALYSIS OF INFINITE SLOPES:
(i) Cohesionless dry soil/dry sand
Stability Analysis of Slopes Civil Engineering (CE) Notes | EduRev
The factor of safety against sliding failure is
Stability Analysis of Slopes Civil Engineering (CE) Notes | EduRev
Under the limiting equilibrium Fs =1
Stability Analysis of Slopes Civil Engineering (CE) Notes | EduRev
“The maximum inclination of an infinite slope in cohesion less soil for stability is equal to the angle of internal friction of the soil”.The limiting angle of inclination for stability of an infinite slope in cohesionless soils as shown below

Stability Analysis of Slopes Civil Engineering (CE) Notes | EduRev
Stability Analysis of Slopes Civil Engineering (CE) Notes | EduRev
(ii) Seepage taking place and water table is parallel to the slope in Cohesionless soil

- Water table at a height h above the the failure plane:
Fs=(1-γw.h/γ.z).tanΦ/tanβ
(iii) If water table is at ground level : i.e. h=z

Fs=γ'tanΦ/γtanβ

(v) Infinite Slope of Purely Cohesive Soil

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

Here H = z = depth of slice/cut.
At critical stage Fc =1

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

where Sh = Stability Number.

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

(vi) C-f soil in Infinite Slope 

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

STABILITY ANALYSIS OF FINITE SLOPES
(i) Fellinious method (For purely Cohesive Soil)

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

where F = Factor of safety
r = Radius of rupture curve
l = length of rupture curve

(b)
 Stability Analysis of Slopes Civil Engineering (CE) Notes | EduRev
Stability Analysis of Slopes Civil Engineering (CE) Notes | EduRev

Factor = Factor of safety it tension cracks has developed.

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

(ii) Swedish Circle Method

 F=(c'L+tanΦ∑W cosα)/∑wsinα
Stability Analysis of Slopes Civil Engineering (CE) Notes | EduRev

where, F = Factor of safety

 (iii) Friction Circle Method

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

(iv) Taylor’s Stability Method (c -f soil)

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

In case of submerged slope g' should be used instead of g and if slope is saturated by capilary  flow then gsat should be used instead of g.

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

where fw = Weight friction angle.

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