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 (Ƭf) of a soil to the average shear stress (Ƭd) developed along the potential failure surface.
Stability Analysis of Slopes | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)
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 SSC JE (Technical) - Civil Engineering (CE)
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 SSC JE (Technical) - Civil Engineering (CE)
Cd and Φd are the cohesion and angle of internal friction that develop along thepotential failure surface
Stability Analysis of Slopes | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)
Fs w.r.t cohesion is
Stability Analysis of Slopes | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

 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 SSC JE (Technical) - Civil Engineering (CE)
The factor of safety against sliding failure is
Stability Analysis of Slopes | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)
Under the limiting equilibrium Fs =1
Stability Analysis of Slopes | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)
“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 SSC JE (Technical) - Civil Engineering (CE)
Stability Analysis of Slopes | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)
(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 SSC JE (Technical) - Civil Engineering (CE)

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

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

where Sh = Stability Number.

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

(vi) C-f soil in Infinite Slope 

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

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

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

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

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

Factor = Factor of safety it tension cracks has developed.

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

(ii) Swedish Circle Method

 F=(c'L+tanΦ∑W cosα)/∑wsinα
Stability Analysis of Slopes | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

where, F = Factor of safety

 (iii) Friction Circle Method

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

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

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

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 SSC JE (Technical) - Civil Engineering (CE)

where fw = Weight friction angle.

The document Stability Analysis of Slopes | Civil Engineering SSC JE (Technical) - Civil Engineering (CE) is a part of the Civil Engineering (CE) Course Civil Engineering SSC JE (Technical).
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FAQs on Stability Analysis of Slopes - Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

1. What is stability analysis of slopes?
Ans. Stability analysis of slopes refers to the assessment and evaluation of the stability of natural or man-made slopes, such as hillsides, embankments, or cut slopes. It involves analyzing the factors that contribute to slope failures, such as soil properties, groundwater conditions, slope geometry, and external forces, to determine the potential for slope instability and the need for appropriate slope stabilization measures.
2. Why is stability analysis important for slopes?
Ans. Stability analysis is important for slopes because it helps in identifying and mitigating the risks associated with slope failures. By assessing the stability of slopes, engineers and geologists can determine the potential for landslides or slope movements, which can pose significant threats to infrastructure, property, and human lives. Stability analysis guides the design of effective slope stabilization measures and helps in making informed decisions regarding slope development or construction projects.
3. What are the methods used for stability analysis of slopes?
Ans. There are several methods used for stability analysis of slopes, including: 1. Limit Equilibrium Analysis: This method assumes that the slope fails along a potential failure surface and evaluates the stability based on the equilibrium conditions. 2. Finite Element Analysis: It is a numerical method that breaks down the slope into small elements and analyzes their behavior under different loading and boundary conditions. 3. Bishop's Method: This method combines the principles of limit equilibrium analysis and Mohr-Coulomb failure criteria to assess slope stability. 4. Simplified Methods: These methods, such as the Swedish method or the Spencer's method, provide simplified approaches to estimate slope stability by considering key parameters and factors.
4. What factors influence slope stability?
Ans. Several factors influence the stability of slopes, including: 1. Soil Properties: Soil characteristics, such as shear strength, cohesion, and internal friction angle, play a crucial role in determining slope stability. Weaker soils with lower shear strength are more prone to slope failures. 2. Groundwater Conditions: The presence and movement of groundwater can significantly affect slope stability. Increased pore water pressure reduces the effective stress and can trigger slope failures. 3. Slope Geometry: The slope angle and shape influence the stability of slopes. Steeper slopes are generally more prone to failures, while slopes with appropriate angles and geometry provide better stability. 4. External Forces: External forces, such as seismic activity, rainfall, or human activities like excavation or construction, can exert additional stresses on slopes, affecting their stability.
5. What are the common slope stabilization measures?
Ans. Common slope stabilization measures include: 1. Slope Grading: Modifying the slope geometry by cutting or filling to achieve a stable slope angle. 2. Drainage Improvement: Enhancing the drainage system to reduce the build-up of excess pore water pressure and improve the stability of the slope. 3. Retaining Walls: Constructing retaining walls to support the slope and prevent soil movement. 4. Slope Reinforcement: Using techniques like soil nails, ground anchors, or geosynthetics to reinforce the slope and increase its stability. 5. Vegetation and Erosion Control: Planting vegetation and implementing erosion control measures to stabilize the slope's surface and reduce erosion-induced instability.
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