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# Active Earth Pressure of Cohesive Soils

The principal stress relationship on a failure plane is given by _______

a) σ1=σ3 tan2 α

b) σ1=2c tanα-σ3 tan2 α

c) σ1=2c tanα+σ3

d) σ1=2c tanα+σ3 tan2 α

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Answer: d

Explanation: The principal stress relationship on a failure plane is given by,

σ1=2c tanα+σ3 tan2 α,

Where, σ1=major principal stress

σ3=minor principal stress

α=(45°+φ2),

φ=angle of internal friction

c=cohesion.

The Belli equation of lateral pressure of cohesive soil is ____________

a) pa=γzcot2 α-2c cotα

b) pa=γzcot2 α+2c cotα

c) pa=-2c cotα

d) pa=γzcot2 α/2c cotα

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Answer: a

Explanation: Since the principal stress relationship on a failure plane is given by,

σ1=2c tanα+σ3 tan2 α,

σ1=γz and σ3=pa,

∴ γz=2c tanα+pa tan2 α

∴ pa=γzcot2 α-2c cotα.

The Belli equation at the ground surface is given by _________

a) pa=γzcot2 α-2c cotα

b) pa=γzcot2 α+2c cotα

c) pa=-2c cotα

d) pa=γzcot2 α/2c cotα

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Answer: c

Explanation: Since the Belli equation of lateral pressure of cohesive soil is given by,

pa=γzcot2 α-2c cotα,

at the ground surface, z=0,

∴ pa=-2c cotα.

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

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Answer: b

Explanation: Since the Belli equation of lateral pressure of cohesive soil is given by,

pa=γzcot2 α-2c cotα,

When pa=0,

∴ z0=2ctanαγ

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)

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Answer: b

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.

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

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Answer: a

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.

For a cohesive soil, the pressure intensity is reduced by a factor of __________

a) 2c cotα

b) 2c tanα

c) 2c sinα

d) 2c cosα

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Answer: a

Explanation: The equation of pressure intensity due to cohesion is given by,

pa=γzcot2 α-2c cotα.

Thus, the effect of cohesion is to reduce the pressure intensity by a factor of ” 2c cotα”.

The total net pressure for a cohesive soil is given by ________

a) Pa=12 Ka γH2 cot2 α-2c cotα

b) Pa=γH2-2c cotα

c) Pa=Ka γH2-2c cotα

d) Pa=Ka H2-2c cotα

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Answer: a

Explanation: The total net pressure is given by,

Pa=∫H0pa.dz=∫H0(γzcot2α−2ccotα).dz

∴ Pa=12 Ka γH2 cot2 α-2c cotα.

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

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Answer: a

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.

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

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Answer: b

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.

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

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Answer: b

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.

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 cotα

b) Pa=12Ka γH2 cot2 α-2c cotα+2c2γ

c) Pa=12Ka γH2 cot2 α-2c cotα-2c2γ

d) Pa=Ka H2-2c cotα

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Answer: b

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 cotα+2c2γ.

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

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Answer: a

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.

The lateral pressure for cohesive backfill with surcharge q is ___________

a) pa=γzcot2 α-2c cotα+qcot2 α

b) pa=γzcot2 α+2c cotα+cot2α

c) pa=-2c cotα-cot2 α

d) pa=γzcot2 α/2c cotα

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Answer: a

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 cotα+qcot2 α.

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

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Answer: b

Explanation: Since the lateral pressure for cohesive backfill with surcharge q is given by,

pa=γzcot2 α-2c cotα+qcot2 α,

when pa=0,

∴ z=z0=2ctanαγ−qγ.