# Design of RC Structures Questions and Answers – Retaining Walls – Stress Analysis of Soils

This set of Design of RC Structures Multiple Choice Questions & Answers (MCQs) focuses on “Retaining Walls – Stress Analysis of Soils”.

1. Which of the following is incorrect assumption for Rankine pressure theory?
a) Soil mass is semi – infinite
b) Soil mass is homogeneous
c) Soil mass is cohesion less
d) Soil mass is wet

Explanation: The Assumptions of Rankine theory involves soil mass that is semi – infinite, homogeneous, dry, cohesion less. Ground surface is plane that is horizontal or inclined. Here back of the wall is vertical and smooth. Wall yields about the base, satisfying the deformation conditions for plastic equilibrium.

2. What is the value of total active earth pressure (Pa) or the resultant pressure per unit length of the retaining wall?
a) 1 / 2 (Ka.γ.H)
b) 1 / 2 (Ka.γ.H2)
c) 1 / 3 (Ka.γ.H2)
d) 1 / 4 (Ka.γ.H2)

Explanation: The total active earth pressure (Pa) or the resultant pressure per unit length of the wall is given by:
1 / 2 (Ka.γ.H2)
Here (H) is the height of retaining wall,
(γ) is unit weight of soil and
(Ka) is coefficient of active earth pressure.
The pressure acts at a height of (H / 3) above the base of retaining wall.

3. What is the equation to find coefficient of active earth pressure (Ka) for retaining walls having dry back fill with no surcharge?
a) (1 – sinΦ) / (1 + sinΦ)
b) (1 – sinΦ) / (sinΦ – 1)
c) (1 + sinΦ) + (1 + sinΦ)
d) (1 + sinΦ) / (1 – sinΦ)

Explanation: The coefficient of active earth pressure is denoted by (Ka). Its value is:
(1 – sinΦ) / (1 + sinΦ)
Here (Φ) is the angle of internal friction, for the backfill.
This should be used while determining the active earth pressure for dry or moist backfill with no surcharge.

4. In case of submerged back fill the sand fill behind the retaining wall is saturated with water. The lateral pressure is divided into two components.
a) False
b) True

Explanation: In the case of submerged backfill the sand behind the retaining wall is saturated with water. The lateral pressure is made up of two components. The first is lateral pressure due to submerged (γ’) of soil. Second is lateral pressure due to water.

5. What is the equation for lateral earth pressure at a depth of (h) below the surface for submerged backfill?
a) pa = Kaγ’ + γw.h
b) pa = Kaγ’h + γw
c) pa = Kaγwh + γ’.h
d) pa = Kaγ’h + γw.h

Explanation: The equation for lateral earth pressure at a depth of (h) below the surface for submerged backfill is:
pa = Kaγ’h + γw.h
Here (Ka) is the coefficient of the active earth pressure,
(γ’) is submerged weight of soil and
w) is unit weight of water.

6. What is the value of lateral earth pressure at the base of the retaining wall for submerged backfill?
a) pa = Kaγ’H + γw.H
b) pa = Kaγ’H + γw
c) pa = Kaγ’ + γw.H
d) pa = Ka.H + γw.H

Explanation: The value of lateral earth pressure at the base of retaining wall for submerged backfill is given by:
pa = Kaγ’H + γw.H
Here (H) is the height of retaining wall,
(Ka) is the coefficient of lateral earth pressure,
(γ’) is the submerged unit weight of soil and
w) is unit weight of water.

7. If the free water stands on the both sides of the wall for submerged backfill the water pressure is considered.
a) True
b) False

Explanation: When free water stands on both the sides of the wall the water pressure is not considered. The net lateral pressure in that case is given by:
pa = Kaγ’H
Here (H) is the height of retaining wall,
(Ka) is the coefficient of lateral earth pressure and
(γ’) is the submerged unit weight of soil.

8. What will be the equation for lateral earth pressure intensity when backfill is partly submerged?
a) pa = KaγH1 + KaH2 + γw.H2
b) pa = KaγH1 + Kaγ’H1 + γw.H2
c) pa = KaγH1 + Kaγ’H2 + γw.H2
d) pa = KaγH + Kaγ’H + γw.H

Explanation: If the backfill is partly submerged or moist to a depth of (H1) below the ground level then it’s submerged. The lateral pressure intensity at the base of the wall is:
pa = KaγH1 + Kaγ’H2 + γw.H2
Here (Ka) is active earth pressure coefficient.
This value is correct when (Φ) is same for moist and submerged soil.

9. What is the Value of lateral earth pressure at the base of the wall when backfill is with a sloping surface?
a) Pa = (1 / 2)γHKa
b) Pa = γHKa
c) Pa = γKa
d) Pa = HKa

Explanation: If the surface behind the wall is sloping then the angle of inclination of surface is (β) with the horizontal. The intensity of lateral earth pressure at the base of the wall is given by:
Pa = γHKa
Here Ka = (cosβ) [cosβ – √(cos2β – cos2Φ) / cosβ + √(cos2β – cos2Φ)].
The pressure acts parallel to the sloping surface of the surcharge.

10. Passive earth pressure is exerted on a wall when it can move towards the backfill.
a) False
b) True

Explanation: Passive earth pressure is exerted on a wall when it can move towards the backfill. This condition occurs when the retaining wall supports an arch, subjected to arch thrust moving it towards the fill.

11. What is the value of coefficient of passive earth pressure (Kp) for retaining walls according to Rankine’s theory?
a) (1 – sinΦ) / (1 + sinΦ)
b) (1 + sinΦ) / (1 – sinΦ)
c) (1 – sinΦ) / (sinΦ)
d) (sinΦ) / (1 + sinΦ)

Explanation: The intensity of passive pressure at height of (h) is given by:
pp = Kp.γ.h.
(Kp) is the coefficient of passive earth pressure. It is given by:
(1 + sinΦ) / (1 – sinΦ)
Coefficient (Kp) is the inverse of active earth pressure (Ka).

12. What is the value of (Kp) when backfill having the top surface inclined at an angle (β)?
a) (cosβ) [cosβ – √(cos2β – cos2Φ) / cosβ + √(cos2β – cos2Φ)]
b) (cosβ) [cosβ + √(cos2β – cos2Φ) / cosβ – √(cos2β – cos2Φ)]
c) (cosβ) [cosβ – √(cos2β – cos2Φ) / √(cos2β + cos2Φ)]
d) (cosβ) [√(cos2β – cos2Φ) / cosβ + √(cos2β – cos2Φ)]

Explanation: When the top surface of the backfill is inclined at an angle (β) the intensity of passive pressure is:
pp = Kp.γ.h
The coefficient of passive pressure given by:
(Kp) = (cosβ) [cosβ + √(cos2β – cos2Φ) / cosβ – √(cos2β – cos2Φ)].

13. Which of the following is not a mode of failure of a retaining wall?
a) Overturning
b) Bearing failure
c) Excessive pressure or tension at heel
d) Sliding

Explanation: The retaining wall can fail in various modes. Modes of failure include overturning about the toe, sliding, and failure of soil due to excessive pressure at toe or tension at heel. It can also fail by bending of stem or base of slab or heel slab.

14. What is the value of minimum factor of safety for used for overturning failure of retaining walls?
a) 2
b) 3
c) 4
d) 6

Explanation: Overturning is the most hazardous mode of failure of retaining wall. It is due to the unbalanced moments. The factor of safety due to overturning (F1) is given by:
(MR / MO)
Minimum factor of safety is taken equal to 2.

15. What is the expression to determine factor of safety (F2) due to sliding failure for retaining walls?
a) (2μ∑W / H)
b) (μ∑W / 2H)
c) (μ∑W / H)
d) (∑W / H)

Explanation: When horizontal force (Pa) tends to slide the wall away from the fill. The factor of safety doe to sliding is given by:
(F2) = (μ∑W / H).
Here (μ∑W) is the force of resistance (F),
(μ) is coefficient of friction,
(∑W) is sum of vertical forces and
H = Pa.

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