Engineering Questions with Answers - Multiple Choice Questions

# Passive Earth Pressure: Rankine’s Theory

1 - Question

In case of passive state of plastic state of equilibrium, the lateral pressure is the _________
a) minor principal stress
b) major principal stress
c) major principal plane
d) minor principal plane

Explanation: In case of passive state of plastic state of equilibrium, the lateral pressure is the major principal stress while the vertical pressure is the minor principal stress.

2 - Question

The passive earth pressure intensity is given by _______
a) pp=γz cot2 α
b) pp=γz tan2 α
c) pp=γz sin2 α
d) pp=γz cos2 α

Explanation: In case of passive state of plastic state of equilibrium,
pp=σh=σ1, and σ3=σv=γz,
∴ for non-cohesive soils, σ1=σ3 tan2 α,
∴ pp=γz tan2 α.

3 - Question

The passive earth pressure intensity in terms of coefficient of passive earth pressure is _________
a) pp=Kp γH
b) pp=γH
c) pp=Kp H
d) pp=Kp γ

Explanation: The passive earth pressure intensity is given by,
pp=γz tan2 α,
since, Kp= tan2 α,
∴ pp=Kp γH.

4 - Question

The ratio between coefficients of passive and active earth pressure is __________
a) cot2 (45°+φ2)
b) cos2 (45°+φ2)
c) tan4 (45°+φ2)
d) sin2 (45°+φ2)

Explanation: The coefficient of passive earth pressure is Kp= tan2 α and that of the coefficient of active earth pressure is Ka=1tan2(45°+φ2),
∴ KpKa = tan2 α* tan2 α
KpKa=tan4(45°+φ2).

5 - Question

For angle of internal friction of 250, the ratio of coefficient of passive and active earth pressure is __________
a) 2
b) 4
c) 6
d) 8

Explanation: Given,
angle of internal friction φ=250,
∴ KpKa=tan4(45°+φ2)=tan4(45°+252),
Kp/Ka =6.

6 - Question

The relation between Kp and Ka is _____________
a) Kp=Ka
b) Kp=1+Ka
c) Kp=1-Ka
d) Kp=1/Ka

Explanation: The coefficient of passive earth pressure is,
Kp= tan2 α,
the coefficient of active earth pressure is,
Ka=1tan2(45°+φ2),
∴ Kp=1/Ka.

7 - Question

For a cohesion less soil, the total passive pressure Pp at a depth H is ___________
a) Pp=12 Kp γH2
b) Pp=γH2
c) Pp=Kp γH2
d) Pp=Kp H2

Explanation: The pressure intensity pp is given by,
pp=Kp γz,
The total earth pressure P0 at rest per unit length is,
Pp=∫H0Kp γz.dz
∴ Pp=12 Kp γH2.

8 - Question

For a cohesion less soil with surcharge Q, the passive pressure intensity is ___________
a) pp=Kp γz+Kp q
b) pp=Kp γz-Kp q
c) pp=Kp γz*Kp q
d) pp=Kp γz/Kp q

Explanation: 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 Kp q. Hence, lateral pressure at the depth of wall H is pp=Kp γz+Kp q.

9 - Question

For a surcharge angle β, the passive earth pressure is __________
a) pp=γzcos2β−cos2φ√cosβ+cos2β−cos2φ√
b) pp=γzcosβ+cos2β−cos2φ√cosβ−cos2β−cos2φ√
c) pp=γzcosβ−cos2β−cos2φ√cosβ+cos2β−cos2φ√
d) pp=γzcosβcosβ+cos2β−cos2φ√cosβ−cos2β−cos2φ√

Explanation: If the backfill is having its top surface inclined to the horizontal at an angle β, then the passive earth pressure is given by,
pp=γzcosβcosβ+cos2β−cos2φ√cosβ−cos2β−cos2φ√,
where, β= surcharge angle
γ=unit weight of the soil
φ= angle of internal friction.

10 - Question

For a surcharge angle β the coefficient of passive earth pressure is _______
a) Kp=cos2β−cos2φ√cosβ+cos2β−cos2φ√
b) Kp=cosβcosβ+cos2β−cos2φ√cosβ−cos2β−cos2φ√
c) Kp=cosβ−cos2β−cos2φ√cosβ+cos2β−cos2φ√
d) Kp=cosβcosβ−cos2β−cos2φ√cosβ+cos2β−cos2φ√

Explanation: The vertical pressure in case of backfill with surcharge,
σ= γzcosβ,
Therefore, from the assumption of stresses being conjugate,
Kp=cosβcosβ+cos2β−cos2φ√cosβ−cos2β−cos2φ√

11 - Question

When the surcharge angle β is reduced to zero, then the coefficient of passive earth pressure is ______
a) 1
b) 1−sinφ1+sinφ
c) 1+sinφ1−sinφ
d) 0

Explanation: For backfill with sloping surface, the coefficient of passive earth pressure is given by,
Kp=cosβcosβ+cos2β−cos2φ√cosβ−cos2β−cos2φ√,
When the surcharge angle reduces to zero, β=0,
substituting this in the equation, we get,
Ka=1+sinφ1−sinφ.

12 - Question

In case of cohesive backfill, the passive pressure intensity is given by _______
a) pp=γz tan2 α-2c tan⁡α
b) pp=γz tan2 α+2c tan⁡α
c) pp=-2c tan⁡α
d) pp=γz tan2 α/2c tan⁡α

Explanation: Since the principal stress relationship on a failure plane is given by,
σ1=2c tan⁡α+σ3 tan2 α,
σ1=pp and σ3=γz,
∴ pp=2c tan⁡α+γztan2 α
∴ pp=γz tan2 α+2c tan⁡α.

13 - Question

In case of cohesive backfill, the total passive pressure is _________
a) Pp=12 Kp γH2+2cH tanα
b) Pp=γH2+2c tanα
c) Pp=Kp γH2-2c tanα
d) Pp=Kp H2-2c tanα

Explanation: The pressure intensity pp for a cohesive soil is given by,
pp=Kp γz+2c tanα,
The total earth pressure P0 at rest per unit length is,
Pp=∫H0Kp γz+2c tanα.dz
∴ Pp=12 Kp γH2+2cH tanα.

14 - Question

With respect to the flow value, the total passive pressure for cohesive backfill is _______
a) Pp=12 Nφ γH2+2cH √Nφ
b) Pp=γH2+2c √Nφ
c) Pp=Nφ γH2-2c √Nφ
d) Pp=Nφ H2-2c √Nφ

Explanation: The flow value is given by,
Nφ= tan2 α=Kp,
since the the total passive pressure for cohesive backfill is given by,
Pp=12 Kp γH2+2cH tanα,
therefore on substituting the value of Nφ in the equation, we get,
Pp=12 Nφ γH2+2cH √Nφ.

15 - Question

At the ground surface, there will be no passive pressure in the case of cohesive backfill.
a) True
b) False