Stability Analysis of Slopes | Civil Engineering SSC JE (Technical) - Civil Engineering (CE) PDF Download

Chapter 11
Stability Analysis of Slopes:
Factor of safety:
Factor of safety of a slope is defined as the ratio of average shear strength (Ƭ_f) of a soil to the average shear stress (Ƭ_d) developed along the potential failure surface.

F_s = Factor of safety
Ƭ_f= average shear strength of the soil
Ƭ_d= average shear stress developed along the potential surface
Shear Strength:
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_d and Φ_d are the cohesion and angle of internal friction that develop along thepotential failure surface

F_s w.r.t cohesion is

 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.