Engineering Questions with Answers - Multiple Choice Questions

# Active Earth Pressure of Cohesive Soils

1 - Question

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

Explanation: 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°+φ2),
φ=angle of internal friction
c=cohesion.

2 - Question

The Belli equation of lateral pressure of cohesive soil is ____________
a) pa=γzcot2 α-2c cot⁡α
b) pa=γzcot2 α+2c cot⁡α
c) pa=-2c cot⁡α
d) pa=γzcot2 α/2c cot⁡α

Explanation: Since the principal stress relationship on a failure plane is given by,
σ1=2c tan⁡α+σ3 tan2 α,
σ1=γz and σ3=pa,
∴ γz=2c tan⁡α+pa tan2 α
∴ pa=γzcot2 α-2c cot⁡α.

3 - Question

The Belli equation at the ground surface is given by _________
a) pa=γzcot2 α-2c cot⁡α
b) pa=γzcot2 α+2c cot⁡α
c) pa=-2c cot⁡α
d) pa=γzcot2 α/2c cot⁡α

Explanation: Since the Belli equation of lateral pressure of cohesive soil is given by,
pa=γzcot2 α-2c cot⁡α,
at the ground surface, z=0,
∴ pa=-2c cot⁡α.

4 - Question

The tension at the top level of retaining wall reduces to zero at a depth ___________
a) z0=q−2ccotαγ
b) z0=2ctanαγ
c) z0=2cotαγ
d) z0=cotαγ

Explanation: Since the Belli equation of lateral pressure of cohesive soil is given by,
pa=γzcot2 α-2c cot⁡α,
When pa=0,
∴ z0=2ctanαγ

5 - Question

The depth at which the tension is zero for cohesive soils with retaining wall in terms Ka is _____
a) z0=2cKaγ
b) z0=2cγ1√Ka
c) z0=2cKaγ
d) z0=2cγ(1Ka)

Explanation: The tension at the top level of retaining wall reduces to zero at a depth,
z0=2ctanαγ,
Since, Ka=1tan2(45°+φ2),
∴ z0=2cγ1√Ka.

6 - Question

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

Explanation: 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 - Question

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

Explanation: The equation of pressure intensity due to cohesion is given by,
pa=γzcot2 α-2c cot⁡α.
Thus, the effect of cohesion is to reduce the pressure intensity by a factor of ” 2c cot⁡α”.

8 - Question

The total net pressure for a cohesive soil is given by ________
a) Pa=12 Ka γH2 cot2 α-2c cot⁡α
b) Pa=γH2-2c cot⁡α
c) Pa=Ka γH2-2c cot⁡α
d) Pa=Ka H2-2c cot⁡α

Explanation: The total net pressure is given by,
Pa=∫H0pa.dz=∫H0(γzcot2α−2ccotα).dz
∴ Pa=12 Ka γH2 cot2 α-2c cot⁡α.

9 - Question

If a tension crack is developed at the top of wall to a depth Zo in cohesive soils, then the total net pressure is zero for a depth of _________
a) 2Zo
b) 3Zo
c) 4Zo
d) 5Zo

Explanation: A negative pressure develops and because of it, a crack is developed in the soil upto a depth Zo. The sum of negative pressure and the positive pressure will be compensated at a depth of 2Zo. Hence, the total net pressure is zero for a depth of 2Zo.

10 - Question

The critical height for an unsupported vertical cut in cohesive soil is given by _____________
a) Hc=q−2ccotαγ
b) Hc=4ctanαγ
c) Hc=4cotαγ
d) Hc=cotαγ

Explanation: If a tension crack is developed at the top of wall to a depth Zo in cohesive soils, then the total net pressure is zero for a depth of 2Zo. This means that the soil will be able to stand with a vertical face up to a depth of 2Zo.
∴ The critical height Hc=4ctanαγ.

11 - Question

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=P21+W2−−−−−−−−√
c) P=(P1+W)2
d) P=P1-W

Explanation: 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=P21+W2−−−−−−−−√,
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 - Question

When the top tension portion of the wall in cohesive soil is neglected, the total lateral thrust is given by __________
a) Pa=12Ka γH2 cot2 α-2c cot⁡α
b) Pa=12Ka γH2 cot2 α-2c cot⁡α+2c2γ
c) Pa=12Ka γH2 cot2 α-2c cot⁡α-2c2γ
d) Pa=Ka H2-2c cot⁡α

Explanation: When the negative tensile portion is neglected, the total lateral thrust is given by,
Pa=∫Hz0pa.dz=∫Hz0(γzcot2α−2ccotα).dz
substituting for z0=2ctanαγ,
∴ Pa=12Ka γH2 cot2 α-2c cot⁡α+2c2γ.

13 - Question

If the cohesive backfill carries a surcharge of q per unit area, then the lateral pressure is increased by _________
a) Ka q
b) q
c) Ka
d) Ka/q

Explanation: 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 Ka q.

14 - Question

The lateral pressure for cohesive backfill with surcharge q is ___________
a) pa=γzcot2 α-2c cot⁡α+qcot2 α
b) pa=γzcot2 α+2c cot⁡α+cot2α
c) pa=-2c cot⁡α-cot2 α
d) pa=γzcot2 α/2c cot⁡α

Explanation: When the cohesive backfill carries a surcharge of q per unit area, then the lateral pressure is increased by Ka q. Since, Ka=cot2α,
∴ pa=γzcot2 α-2c cot⁡α+qcot2 α.

15 - Question

For a cohesive backfill with surcharge q, when at depth z0, pa=0, then the depth z0 is ___________
a) z0=q−2ccotαγ
b) z0=2ctanαγ−qγ
c) z0=2cotαγ+qγ
d) z0=cotαγ−qγ