# Foundation Engineering Questions and Answers – Earth Pressure Introduction – 2

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This set of Foundation Engineering Interview Questions and Answers focuses on “Earth Pressure Introduction – 2”.

1. In active state, the minor principal stress σ3 is _________
a) horizontal direction
b) vertical direction
c) can be both vertical and horizontal direction
d) in no direction

Explanation: In active state, the minor principal stress denoted by σ3 is in horizontal direction. While in the passive state, the minor principal stress σ3 is in vertical direction.

2. In passive state, the major principal stress σ1 ____________
a) horizontal direction
b) vertical direction
c) can be both vertical and horizontal direction
d) in no direction

Explanation: In passive state, the minor principal stress denoted by σ3 is in vertical direction. While in the passive state, the major principal stress σ1 is in horizontal direction.

3. In passive state, the minor principal stress σ3 is _________
a) horizontal direction
b) vertical direction
c) can be both vertical and horizontal direction
d) in no direction

Explanation: In active state, the minor principal stress denoted by σ3 is in horizontal direction. While in the passive state, the minor principal stress σ3 is in vertical direction.

4. For cohesion-less soil, the ratio of major to minor principal stress is __________
a) $$\frac{σ_1}{σ_3} = cos^2 (45°+\frac{φ}{2})$$
b) $$\frac{σ_1}{σ_3} = sin^2 (45°+\frac{φ}{2})$$
c) $$\frac{σ_1}{σ_3} = tan^2 (45°+\frac{φ}{2})$$
d) $$\frac{σ_1}{σ_3} = tan^2 (45°-\frac{φ}{2})$$

Explanation: The stress condition during plastic equilibrium is given by,
$$σ_1=2c \,tan⁡(45°+\frac{φ}{2})+σ_3 tan^2 (45°+\frac{φ}{2}),$$ and for cohesion-less soil, c=0,
∴ $$\frac{σ_1}{{σ_3}} = tan^2 (45°+\frac{φ}{2}).$$

5. The ratio of horizontal stress σh to vertical stress σv is _______
a) coefficient of earth pressure
b) coefficient of volume change
c) coefficient of compressibility
d) coefficient of consolidation

Explanation: The coefficient of earth pressure is defined as the ratio of The ratio of horizontal stress σh to vertical stress σv.
∴ $$K=\frac{σ_h}{σ_v}.$$ Where, K = coefficient of earth pressure.

6. The coefficient of earth pressure for active state of plastic equilibrium is given by ___________
a) $$K_a=\frac{1}{tan^2 (45°+\frac{φ}{2})}$$
b) $$K_a=tan^2 (45°+\frac{φ}{2})$$
c) $$K_a=sin^2 (45°+\frac{φ}{2})$$
d) $$K_a=\frac{1}{cot^2 (45°+\frac{φ}{2})}$$

Explanation: For the case of active state, the major principal stress denoted by σ1 is in vertical direction and the minor principal stress σ3 is in horizontal direction.
∴ $$\frac{σ_1}{σ_3} =\frac{σ_v}{σ_h} =K_a=\frac{1}{tan^2 (45°+\frac{φ}{2})}.$$

7. The coefficient of earth pressure for passive state of plastic equilibrium is given by ________
a) $$K_p=\frac{1}{tan^2 (45°+\frac{φ}{2})}$$
b) $$K_p=tan^2 (45°+\frac{φ}{2})$$
c) $$K_p=sin^2 (45°+\frac{φ}{2})$$
d) $$K_p=\frac{1}{cot^2 (45°+\frac{φ}{2})}$$

Explanation: For the case of passive state, the major principal stress denoted by σ1 is in horizontal direction and the minor principal stress σ3 is in vertical direction.
∴ $$\frac{σ_1}{σ_3} =\frac{σ_h}{σ_v} =K_p=tan^2 (45°+\frac{φ}{2}).$$

8. The coefficient of earth pressure for active state of plastic equilibrium in terms of sine function is _______
a) $$K_a=1-sinφ$$
b) $$K_a=\frac{1-sinφ}{1+sinφ}$$
c) $$K_a=\frac{1+sinφ}{1-sinφ}$$
d) Ka=1+sinφ

Explanation: The coefficient of earth pressure for active state of plastic equilibrium is,
$$K_a=\frac{1}{tan^2 (45°+\frac{φ}{2})},$$
∴ therefore in terms of sine function,
$$K_a=\frac{1}{tan^2 (45°+\frac{φ}{2})}=\frac{1-sinφ}{1+sinφ}.$$

9. The coefficient of earth pressure for passive state of plastic equilibrium in terms of sine function is _______
a) $$K_a=1-sinφ$$
b) $$K_a=\frac{1-sinφ}{1+sinφ}$$
c) $$K_a=\frac{1+sinφ}{1-sinφ}$$
d) Ka=1+sinφ

Explanation: The coefficient of earth pressure for active state of plastic equilibrium is,
$$K_p=tan^2 (45°+\frac{φ}{2}),$$
∴ therefore in terms of sine function,
$$K_p=tan^2 (45°+\frac{φ}{2})=\frac{1+sinφ}{1-sinφ}.$$

10. During the active state of plastic equilibrium, the retaining wall moves _______
a) towards the fill
b) away from the fill
c) does not change its position
d) remains in equilibrium

Explanation: During the active state of plastic equilibrium, the major principal stress denoted by σ1 is in vertical direction and the minor principal stress σ3 is in horizontal direction. Therefore, the movement of the wall will be away from the back fill.

11. During the passive state of plastic equilibrium, the retaining wall moves _______
a) towards the fill
b) away from the fill
c) does not change its position
d) remains in equilibrium

Explanation: During the passive state of plastic equilibrium, the major principal stress denoted by σ1 is in horizontal direction and the minor principal stress σ3 is in vertical direction. Therefore, the movement of the wall will be towards the back fill.

12. In active state of plastic equilibrium, the earth pressure on the wall ________
a) increases
b) decreases
c) is zero
d) is constant

Explanation: When the wall moves away from the backfill, mobilization of the internal resistance of the soil takes place in the direction away from the wall. Hence the earth pressure on the wall decreases.

13. In passive state of plastic equilibrium, the earth pressure on the wall ________
a) increases
b) decreases
c) is zero
d) is constant

Explanation: In passive state of plastic equilibrium, when the wall moves towards the fill, the earth pressure increases because the shearing resistance builds up in the direction of the wall.

14. In active state, the failure wedge shows ____________
a) downward movement
b) upward movement
c) left side movement
d) right side movement

Explanation: In the active state of plastic equilibrium, the wall moves away from the fill because of the mobilization of the internal resistance of the soil taking place in the direction away from the wall. Due to this the failure wedge shows downward movement.

15. In passive state, the failure wedge shows ____________
a) downward movement
b) upward movement
c) left side movement
d) right side movement