# Irrigation Engineering Questions and Answers – Stability of Earthen Slopes

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This set of Irrigation Engineering Multiple Choice Questions & Answers (MCQs) focuses on “Stability of Earthen Slopes”.

1. Which of the following method is also called as the Slices method?
a) Fellenius method
b) Swedish slip circle method
c) Bishop’s simplified method
d) Spencer’s method

Explanation: Swedish circle method is also called as the method of slices and Fellenius method is a modified version of it. Swedish circle method assumes the condition of plain strain with failure along a cylindrical arc. The location of the center of possible failure arc is assumed and the earth mass is divided into slices.

2. In Fellenius method for small values of angle of internal friction of soil, the critical arc passes ________________
a) through the toe of the slope
b) above the toe of the slope
c) below the toe of the slope
d) anywhere near the toe of the slope

Explanation: The critical arc passes below the toe of the slope for small values of angle of internal friction of the soil (0° to 15°) if the angle of inclination is less than 53°. For large values of internal friction angle, the critical arc passes through the slope.

3. What is the correct expression of equivalent liquid unit weight?
a) ϒeq.tan2 [45 – Φ/2]
b) ϒeq.tan2 [45 + Φ/2]
c) ϒeq.tan [45 – Φ/2]
d) ϒeq.tan [45 + Φ/2]

Explanation: This term is used in the analysis of the stability of the foundation against shear. It is based on the assumption that soil has an equivalent liquid unit weight which would produce the same shear stress as the soil itself.
ϒeq.tan2 [45 – Φ/2]
where ϒeq = the equivalent unit weight of dry soil in foundation and dam and Φ = the equivalent angle of internal friction.

4. Calculate the maximum shear-stress induced if the horizontal average shear stress induced in u/s portion of the dam at the base is 36.45 kN/m2.
a) 43.74 kN/m2
b) 47.38 kN/m2
c) 51.03 kN/m2
d) 54.67 kN/m2

Explanation: By Photoelastic studies, the maximum intensity of shear stress is equal to 1.4 times the average shear intensity at a distance 0.6 B from the heel.
max = 1.4 Ꞇavg = 1.4 x 36.45 = 51.03 kN/m2.

5. Calculate the factor of safety at the point of maximum shear if unit shearing resistance is 97.9 kN/m2 and the maximum shear-stress induced is 55.72 kN/m2. Check whether the dam is safe or unsafe.
a) F.O.S = 1.93 and safe
b) F.O.S = 1.75 and unsafe
c) F.O.S = 0.569 and safe
d) F.O.S = 1.75 and safe

Explanation: F.O.S will be the ratio of the unit shearing resistance to the maximum shear stress developed.
F.O.S = 97.9 / 55.72 = 1.75
this value should be more than unity, hence safe. 