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**Chapter 11Stability Analysis of Slopes**:

Factor of safety of a slope is defined as the ratio of average shear strength (Ƭ

F

Ƭ

Ƭ

Shear strength of a soil is given by

Where, c = cohesion

Φ= angle of internal friction

σ= Normal stress on the potential failure surface

Similarly, the mobilized shear strength is given by

C

F

**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

The factor of safety against sliding failure is

Under the limiting equilibrium F_{s} =1

“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

(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:

F_{s}=(1-γ_{w}.h/γ.z).tanΦ/tanβ

(iii) If water table is at ground level : i.e. h=z

F_{s}=γ'tanΦ/γtanβ

(v) Infinite Slope of Purely Cohesive Soil

Here H = z = depth of slice/cut.

At critical stage F_{c} =1

where S_{h} = Stability Number.

(vi) C-f soil in Infinite Slope

**STABILITY ANALYSIS OF FINITE SLOPES**

(i) Fellinious method (For purely Cohesive Soil)

where F = Factor of safety

r = Radius of rupture curve

l = length of rupture curve

(b)

Factor = Factor of safety it tension cracks has developed.

(ii) Swedish Circle Method

F=(c'L+tanΦ∑W cosα)/∑wsinα

where, F = Factor of safety

(iii) Friction Circle Method

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

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

where f_{w} = Weight friction angle.

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