Test: Analysis of Infinite Slopes - Civil Engineering (CE) MCQ

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

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.

Explanation:

Stability analysis of Finite Slope:

(i) If the slope is of finite extend bounded by top and bottom surfaces, then it is termed as finite slope.

(ii) Failure of finite slope takes places due to rotation and failure plane is either circular or spiral.

(iii) Finite slope may have any of the following mode of shear failure.

• Slope failure
• Base failure

Slope failure:

• Face Failure: Failure surface passes through slope above the toe. This type of failure takes places in case of steep slope, soil mass near the toe is rigid or stringer in comparison to soil mass above the toe.
• Toe Failure: It is the most common mode of failure of finite slope in which failure surface passes through the toe. This failure also occur in steel slope when soil mass is homogenous above and below the toe.

Base Failure: 

• Failure surface passes below the toe.
• This type of failure takes place when soil mass below the toe is soft and weak in comparison to soil mass above the toe.

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.

Since the factor of safety FC with respect to cohesion, also represent the factor of safety with respect to height
FC = C / Cm = HC / H
Where, Cm is the mobilized cohesion at a depth H.

The factor of safety against sliding is given by equation:
F = τf /τ = tan φ / tan i.