250+ TOP MCQs on Active Earth Pressure of Cohesive Soils and Answers

Foundation Engineering Interview Questions and Answers for Freshers on “Active Earth Pressure of Cohesive Soils”.

1. The principal stress relationship on a failure plane is given by _______
a) σ₁=σ₃ tan² α
b) σ₁=2c tan⁡α-σ₃ tan² α
c) σ₁=2c tan⁡α+σ₃
d) σ₁=2c tan⁡α+σ₃ tan² α
Answer: d
Clarification: The principal stress relationship on a failure plane is given by,
σ₁=2c tan⁡α+σ₃ tan² α,
Where, σ₁=major principal stress
σ₃=minor principal stress
(α=(45°+frac{φ}{2}), )
φ=angle of internal friction
c=cohesion.

2. The Belli equation of lateral pressure of cohesive soil is ____________
a) p_a=γzcot² α-2c cot⁡α
b) p_a=γzcot² α+2c cot⁡α
c) p_a=-2c cot⁡α
d) p_a=γzcot² α/2c cot⁡α
Answer: a
Clarification: Since the principal stress relationship on a failure plane is given by,
σ₁=2c tan⁡α+σ₃ tan² α,
σ₁=γz and σ₃=p_a,
∴ γz=2c tan⁡α+p_a tan² α
∴ p_a=γzcot² α-2c cot⁡α.

3. The Belli equation at the ground surface is given by _________
a) p_a=γzcot² α-2c cot⁡α
b) p_a=γzcot² α+2c cot⁡α
c) p_a=-2c cot⁡α
d) p_a=γzcot² α/2c cot⁡α
Answer: c
Clarification: Since the Belli equation of lateral pressure of cohesive soil is given by,
p_a=γzcot² α-2c cot⁡α,
at the ground surface, z=0,
∴ p_a=-2c cot⁡α.

4. The tension at the top level of retaining wall reduces to zero at a depth ___________
a) (z_0=frac{q-2c cot⁡α}{γ} )
b) (z_0=frac{2c tan⁡α}{γ} )
c) (z_0=frac{2 cot⁡α}{γ} )
d) (z_0=frac{cot⁡α}{γ} )
Answer: b
Clarification: Since the Belli equation of lateral pressure of cohesive soil is given by,
p_a=γzcot² α-2c cot⁡α,
When p_a=0,
∴ (z_0=frac{2c tan⁡α}{γ} )

5. The depth at which the tension is zero for cohesive soils with retaining wall in terms K_a is _____
a) (z_0=frac{2cK_a}{γ} )
b) (z_0=frac{2c}{γ} frac{1}{√K_a } )
c) (z_0=frac{2cK_a}{γ} )
d) (z_0=frac{2c}{γ}(frac{1}{K_a}) )
Answer: b
Clarification: The tension at the top level of retaining wall reduces to zero at a depth,
(z_0=frac{2c tan⁡α}{γ}, )
Since, (K_a=frac{1}{tan^2 (45°+frac{φ}{2})}, )
∴ (z_0=frac{2c}{γ} frac{1}{√K_a}. )

6. The effect of cohesion in the soil is to __________
a) reduce pressure intensity
b) increase pressure intensity by 3
c) double the pressure intensity
d) increase pressure intensity by 4
Answer: a
Clarification: Cohesion is the component of shear strength of a rock or soil that is independent of inter-particle friction. Due to the cohesion, the particles of the soil are in close contact by which they distribute the load evenly.

7. For a cohesive soil, the pressure intensity is reduced by a factor of __________
a) 2c cot⁡α
b) 2c tan⁡α
c) 2c sin⁡α
d) 2c cos⁡α
Answer: a
Clarification: The equation of pressure intensity due to cohesion is given by,
p_a=γzcot² α-2c cot⁡α.
Thus, the effect of cohesion is to reduce the pressure intensity by a factor of ” 2c cot⁡α”.

8. The total net pressure for a cohesive soil is given by ________
a) P_a=(frac{1}{2}) K_a γH² cot² α-2c cot⁡α
b) P_a=γH²-2c cot⁡α
c) P_a=K_a γH²-2c cot⁡α
d) P_a=K_a H²-2c cot⁡α
Answer: a
Clarification: The total net pressure is given by,
(P_a=int_0^H p_a.dz = int_0^H(γzcot^2 α-2c cot⁡α).dz)
∴ P_a=(frac{1}{2}) K_a γH² cot² α-2c cot⁡α.

9. If a tension crack is developed at the top of wall to a depth Z_o in cohesive soils, then the total net pressure is zero for a depth of _________
a) 2Z_o
b) 3Z_o
c) 4Z_o
d) 5Z_o
Answer: a
Clarification: A negative pressure develops and because of it, a crack is developed in the soil upto a depth Z_o. The sum of negative pressure and the positive pressure will be compensated at a depth of 2Z_o. Hence, the total net pressure is zero for a depth of 2Z_o.

10. The critical height for an unsupported vertical cut in cohesive soil is given by _____________
a) (H_c=frac{q-2c cot⁡α}{γ} )
b) (H_c=frac{4c tan⁡α}{γ} )
c) (H_c=frac{4 cot⁡α}{γ} )
d) (H_c=frac{cot⁡α}{γ} )
Answer: b
Clarification: If a tension crack is developed at the top of wall to a depth Z_o in cohesive soils, then the total net pressure is zero for a depth of 2Z_o. This means that the soil will be able to stand with a vertical face up to a depth of 2Z_o.
∴ The critical height (H_c=frac{4c tan⁡α}{γ}. )

11. For an inclined back and surcharge, if P1, is horizontal pressure and W is weight of soil wedge, then the total pressure is given by __________
a) P=P₁+W
b) (P=sqrt{P_1^2+W^2})
c) P=(P₁+W)²
d) P=P₁-W
Answer: b
Clarification: For an inclined back and surcharge, if P1, is horizontal pressure and W is weight of soil wedge, then the total pressure is given by,
(P=sqrt{P_1^2+W^2},)
This is due to the fact that the total pressure P is the resultant of the horizontal pressure and the weight of the wedge.

12. When the top tension portion of the wall in cohesive soil is neglected, the total lateral thrust is given by __________
a) P_a=(frac{1}{2})K_a γH² cot² α-2c cot⁡α
b) P_a=(frac{1}{2})K_a γH² cot² α-2c cot⁡α+(frac{2c^2}{γ})
c) P_a=(frac{1}{2})K_a γH² cot² α-2c cot⁡α-(frac{2c^2}{γ})
d) P_a=K_a H²-2c cot⁡α
Answer: b
Clarification: When the negative tensile portion is neglected, the total lateral thrust is given by,
(P_a=int_{z_0}^H p_a.dz = int_{z_0}^H(γzcot^2 α-2c cot⁡α).dz)
substituting for (z_0=frac{2c tan⁡α}{γ},)
∴ P_a=(frac{1}{2})K_a γH² cot² α-2c cot⁡α+(frac{2c^2}{γ}.)

13. If the cohesive backfill carries a surcharge of q per unit area, then the lateral pressure is increased by _________
a) K_a q
b) q
c) K_a
d) K_a/q
Answer: a
Clarification: Since the surcharge is the additional load, when the backfill is horizontal and carries a surcharge q, then the vertical pressure increment will be by q. Due to this, the lateral pressure will increase by K_a q.

14. The lateral pressure for cohesive backfill with surcharge q is ___________
a) p_a=γzcot² α-2c cot⁡α+qcot² α
b) p_a=γzcot² α+2c cot⁡α+cot²α
c) p_a=-2c cot⁡α-cot² α
d) p_a=γzcot² α/2c cot⁡α
Answer: a
Clarification: When the cohesive backfill carries a surcharge of q per unit area, then the lateral pressure is increased by K_a q. Since, K_a=cot²α,
∴ p_a=γzcot² α-2c cot⁡α+qcot² α.

15. For a cohesive backfill with surcharge q, when at depth z₀, p_a=0, then the depth z₀ is ___________
a) (z_0=frac{q-2c cot⁡α}{γ} )
b) (z_0=frac{2c tan⁡α}{γ}-frac{q}{γ} )
c) (z_0=frac{2 cot⁡α}{γ}+frac{q}{γ} )
d) (z_0=frac{cot⁡α}{γ}-frac{q}{γ} )
Answer: b
Clarification: Since the lateral pressure for cohesive backfill with surcharge q is given by,
p_a=γzcot² α-2c cot⁡α+qcot² α,
when p_a=0,
∴ (z=z_0=frac{2c tan⁡α}{γ}-frac{q}{γ}. )

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