Foundation Engineering Questions and Answers – Earth Pressure Introduction – 1

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This set of Foundation Engineering Multiple Choice Questions & Answers (MCQs) focuses on “Earth Pressure Introduction – 1”.

1. The plastic state of stress when the failure is imminent was investigated by ___________
a) Rankine
b) Darcy
c) Skempton
d) Terzaghi

Explanation: The plastic state of stress failure of the soil samples was studied by Rankine in the year 1860. Darcy is known for his works in the field of soil permeability.

2. ___________ is used for maintaining the ground surface at different elevations.
a) Floor
b) Retaining wall
c) Ceiling
d) Roof

Explanation: The retaining wall is used to resist the lateral earth pressure due to the backfill soil. It prevents the landslides by maintaining the ground surface at different elevations in hilly regions.

3. The material retained by the retaining wall is known as_________
a) roof
b) slab
c) backfill
d) footing

Explanation: The material retained by the retaining wall is known as backfill. The surface of the backfill can be both horizontal as well as inclined. It should be noted that the angle does not exceed the angle of repose of the soil.
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4. The backfill has its top surface ____________
a) horizontal only
b) inclined only
c) both horizontal and inclined
d) vertical only

Explanation: The backfill can have its top surface as a horizontal surface or as an inclined surface. It should be noted that the angle does not exceed the angle of repose of the soil or else it will fail.

5. The portion of backfill lying above a horizontal plane of wall is called ________
a) surcharge
b) base
c) foot
d) truss

Explanation: The portion of backfill lying above a horizontal plane of wall is called as the surcharge. The surcharge is a load which is imposed upon the surface of the soil close enough to the excavation to cause a lateral pressure to act on the system in addition to the basic earth pressure.

6. Surcharge angle β is ____________
a) inclination of surcharge to the vertical
b) inclination of surcharge to the normal of the wall
c) inclination of surcharge to the horizontal
d) inclination of surcharge to the tangent to the wall

Explanation: The surcharge is a load which is imposed upon the surface of the soil close enough to the excavation to cause a lateral pressure to act on the system in addition to the basic earth pressure. Its inclination to the horizontal is known as Surcharge angle β.

7. A body is said to be in plastic equilibrium, if every point of it is ________
a) in the verge of failure
b) in equilibrium
c) in stable state
d) elastic state

Explanation: A body is said to be in plastic equilibrium, if every point of it is in the verge of failure. The transition from the state of plastic equilibrium to the state of plastic flow represents the failure of the soil mass.

8. The stress condition during plastic equilibrium can be represented by _____________
a) $$\frac{σ_1-σ_3}{2}\frac{σ_1+σ_3}{2} sinφ=cosφ$$
b) $$\frac{σ_1-σ_3}{2}+\frac{σ_1+σ_3}{2} sinφ=c cosφ$$
c) $$\frac{σ_1*σ_3}{2}-\frac{σ_1+σ_3}{2} sinφ=c cosφ$$
d) $$\frac{σ_1-σ_3}{2}-\frac{σ_1+σ_3}{2} sinφ=c cosφ$$

Explanation: The stress condition during plastic equilibrium can be represented by the equation of Mohr-Coulomb,
$$\frac{σ_1-σ_3}{2}-\frac{σ_1+σ_3}{2} sinφ=c cosφ,$$
Where, σ1=major principal stress
σ3=minor principal stress
φ=angle of internal friction.

9. The stress condition during plastic equilibrium in terms of tangent of angle is _______
a) $$σ_1=tan⁡(45°+\frac{φ}{2})+σ_3 tan^2 (45°+\frac{φ}{2})$$
b) $$σ_1=2c+σ_3 tan^2 (45°+\frac{φ}{2})$$
c) $$σ_1=2c \,tan⁡(45°+\frac{φ}{2})+σ_3$$
d) $$σ_1=2c \,tan⁡(45°+\frac{φ}{2})+σ_3 tan^2 (45°+\frac{φ}{2})$$

Explanation: The stress condition during plastic equilibrium can be represented by the equation of Mohr-Coulomb,
$$\frac{σ_1-σ_3}{2}-\frac{σ_1+σ_3}{2} sinφ=c cosφ,$$
since tan⁡φ=sinφ/cosφ
∴ $$σ_1=2c \,tan⁡(45°+\frac{φ}{2})+σ_3 tan^2 (45°+\frac{φ}{2}).$$

10. The flow value is given by ______
a) $$N_φ=cot^2 (45°+\frac{φ}{2})$$
b) $$N_φ=cos^2 (45°+\frac{φ}{2})$$
c) $$N_φ=tan^2 (45°+\frac{φ}{2})$$
d) $$N_φ=sin^2 (45°+\frac{φ}{2})$$

Explanation: The flow value is given by,
$$N_φ= tan^2 (45°+\frac{φ}{2}),$$
where, Nφ=flow value
φ=angle of internal friction.

11. The plastic equilibrium stress equation in terms of flow valve is _____
a) σ1=2c∛Nφ3 Nφ
b) σ1=2c√Nφ3 Nφ
c) σ1=2cNφ3 Nφ
d) σ1=Nφ3 Nφ

Explanation: The stress condition during plastic equilibrium is given by,
$$σ_1=2c \,tan⁡(45°+\frac{φ}{2})+σ_3 tan^2 (45°+\frac{φ}{2}),$$
since, $$N_φ= tan^2 (45°+\frac{φ}{2}),$$
∴ σ1=2c√Nφ3 Nφ.

12. The Mohr Coulomb equation in terms of stress components in x-z plane is ______________
a) $$\sqrt{((\frac{σ_z-σ_x}{2})^2+τ_{xz}^2))} -\frac{σ_z+σ_x}{2} sinφ=c cosφ$$
b) $$\sqrt{((\frac{σ_z-σ_x}{2})^2+τ_{xz}^2))} \frac{σ_z+σ_x}{2} sinφ=c cosφ$$
c) $$\sqrt{((\frac{σ_z-σ_x}{2})^2+τ_{xz}^2))} = c cosφ$$
d) $$\sqrt{((\frac{σ_z-σ_x}{2})^2+τ_{xz}^2))} -\frac{σ_z+σ_x}{2} sinφ=cosφ$$

Explanation: The Mohr Coulomb equation is given by,
$$\frac{σ_1-σ_3}{2}-\frac{σ_1+σ_3}{2} sinφ=c cosφ,$$
Where, σ_1=major principal stress and σ3=minor principal stress.
∴ in terms of stress components in x-z plane it is,
$$\sqrt{((\frac{σ_z-σ_x}{2})^2+τ_{xz}^2))} -\frac{σ_z+σ_x}{2} sinφ=c cosφ,$$
where, σz=stress in z-direction
σx= stress in x-direction.

13. Combing the three equations, $$\sqrt{((\frac{σ_z-σ_x}{2})^2+τ_{xz}^2))} -\frac{σ_z+σ_x}{2} sinφ=c cosφ$$, $$\frac{∂σ_x}{∂x}+\frac{∂τ_{xz}}{∂z}=0$$, and $$\frac{∂τ_{xz}}{∂x}+\frac{∂σ_x}{∂z}+γ=0$$, lead to the equation called ___________
a) Kolter’s equation
b) Terzaghi’s equation
c) Darcy’s equation
d) Skempton’s equation

Explanation: The material just in the verge of flowing plastically is still in static equilibrium and will satisfy the equations of, $$\frac{∂σ_x}{∂x}+\frac{∂τ_{xz}}{∂z}=0, \,and\, \frac{∂τ_{xz}}{∂x}+\frac{∂σ_x}{∂z}+γ=0.$$ These equations with the Mohr Coulomb equation give the Kolter’s equation.

14. The solution of Kolter’s equation gives ____________
a) permeability of soil
b) orientation of slip lines
c) specific gravity of grains
d) seepage pressure

Explanation: The solution of Kolter’s equation for a given boundary condition gives the orientation of slip planes together with the stress at each point at the failure zone.

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

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

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