Test: Infinite Slopes - Civil Engineering (CE) MCQ

Earth embankments are commonly required for railways, roadways, earth dams, levees and river training works.

Stability analysis of an infinite slope of cohesive soils
Shear strength of cohesive soils is given by,
S = C + (γ_d H Cos² i) tan ϕ
Shear stress of cohesive soil is given by,
τ = γ_d H cos i sin i
As the normal stress σ depends upon the height H of the slope, an expression for the height can be found by equating the shear stress and shear strength
C + (γ_d H Cos² i) tan ϕ = γ H cos i sin i

This the height at which the slope is just stable and is known as critical height (HC)
Calculation:
Given,
C = 20 kPa, γ_d = 16 kN/m³
i = 40°, H = 5 m

tan ϕ = 0.413
ϕ = 22.44° 

The failure of slopes takes place mainly due to the action of a gravitational force which tends to pull the upper portions of the soil mass downwards to a nearly more level surface.

Taylor's stability number method:
(i) Taylor introduced a dimensional parameter, called taylor's stability number, which is given by

Where, H = Effective height of slope
H_c = Critical height of slope
F = FOS
(ii) In this method, Taylor's stability number is read from taylor's chart in order to analyze the stability of slope for a given values of strength parameters of the soil.
(iii) Taylor's method is suitable for c-ϕ soils and for ϕ = 0 (pue clays)
Calculation:
Given, C = 1 t/m², γ = 2 t/m² and H_c = 5 m

Slopes may be of two types: i) infinite slopes and ii) finite slopes.

An analysis of stability of slopes consist of determining the most severely stressed internal surface and the magnitude of the shearing stress to which it is subjected and determining the shearing stress along the surface.

Given φ = 30° and i = 12°
Formula, F = tan φ /tan i
F = tan 30° / tan 12°
F = 2.72.

In the limiting case of stability, the angle of slope is known as the angle of repose φ.

Slopes extending to infinity do not exist in nature.

If a slope represents the boundary surface of a semi-infinite soil mass, and the soil properties for all identical depths below the surface are constant, it is called an infinite slope.