Engineering Questions with Answers - Multiple Choice Questions
Active Earth Pressure: Rankine’s Theory – 2
1 - Question
For a dry backfill with no surcharge, the active earth pressure intensity is _________
a) pa=Ka γH
b) pa=γH
c) pa=Ka H
d) pa=Ka γ
View Answer
Answer: a
Explanation: The active earth pressure intensity is given by,
pa=Ka γH,
where, σ1σ3=σvσh=Ka=1tan2(45°+φ2),
γ=unit weight of the back fill
H= height of the retaining wall.
2 - Question
The resultant active pressure per unit length of wall for dry backfill with no surcharge is _______
a) Pa=12KaγH2
b) Pa=γH2
c) Pa=Ka γH2
d) Pa=Ka H2
View Answer
The resultant active pressure per unit length of wall for dry backfill with no surcharge is _______
a) Pa=12KaγH2
b) Pa=γH2
c) Pa=Ka γH2
d) Pa=Ka H2
3 - Question
Answer: a
Explanation: The pressure intensity p0 is given by,
pa=Ka γz,
The total earth pressure P0 at rest per unit length is,
Pa=∫H0Kaγz.dz
∴ Pa=12KaγH2
View Answer
The resultant active pressure per unit length of wall for dry backfill with no surcharge acting at _________ above the base of wall.
a) H/2
b) H
c) H/6
d) H/3
4 - Question
Answer: d
Explanation: The pressure distribution of the stresses in the retaining wall due to the backfill is triangular one. Since the pressure distribution is triangular, the resultant active pressure per unit length of wall will act at the centroid of the wall, which is at a distance of H/3 from the base of the wall.
View Answer
For a submerged backfill, the active earth pressure is given by _________
a) pa=Kaγ’z
b) pa=Kaγ’z-γwz
c) pa=Kaγ’z+γwz
d) pa=Kaγ’z*γwz
5 - Question
Answer: c
Explanation: For a submerged backfill, the lateral pressure is made up of two components,
lateral pressure due to submerged weight of backfill
lateral pressure due to water
∴ pa=Kaγ’z+γwz.
View Answer
If free water stands on both side of a retaining wall, the lateral earth pressure is given by ____
a) pa=Ka γ’ z
b) pa=Ka γ’ z-γw z
c) pa=Ka γ’ z+γw z
d) pa=Ka γ’ z*γw z
6 - Question
Answer: a
Explanation: When the free water stands on both side of a retaining wall, the water pressure is not considered and the net pressure is given by,
pa=Ka γ’ z.
View Answer
If the angle of internal friction decreases, then Ka ___________
a) decreases
b) increases
c) equal to zero
d) does not change
7 - Question
Answer: b
Explanation: Since the coefficient of earth pressure for active state of plastic equilibrium is given by,
Ka=1−sinφ1+sinφ. Therefore, from the equation it is clear that as the angle of internal friction decreases, then Ka increases.
View Answer
For the same value of φ, the backfill is partly submerged to height H2 and the backfill is moist to a depth H1. Find the lateral pressure intensity at the base of wall.
a) pa=Ka γH1-Ka γ’ H2+γw H2
b) pa=Ka γH1+Ka γ’ H2+γw H2
c) pa=Ka γH1+γw H2
d) pa=Ka γH1+Ka γ’ H2
8 - Question
Answer: b
Explanation: When the backfill is partly submerged to height H2 and the backfill is moist to a depth H1, lateral pressure intensity is due to:
lateral pressure due to moist weight of backfill
lateral pressure due to saturated weight of backfill
lateral pressure due to water
∴ pa=Ka γH1+Ka γ’ H2+γw H2.
View Answer
Answer: b
Explanation: For the different value of φ, the coefficient of active earth pressure is different. Since, the lateral pressure intensity is due to:
lateral pressure due to moist weight of backfill
lateral pressure due to saturated weight of backfill
lateral pressure due to water
∴ pa=Ka2 γH1+Ka2 γ’ H2+γw H2. We have to consider Ka2 over Ka1 as the φ1>φ2.
9 - Question
If the backfill carries a uniform surcharge q, then the lateral pressure at the depth of wall H is ____________
a) pa=Ka γz+Ka q
b) pa=Ka γz-Ka q
c) pa=Ka γz*Ka q
d) pa=Ka γz/Ka q
View Answer
Answer: a
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 Ka q. Hence, lateral pressure at the depth of wall H is pa=Ka γz+Ka q.
10 - Question
The height of fill Ze, equivalent to uniform surcharge intensity is __________
a) q/γ
b) q-γ
c) q+γ
d) q*γ
View Answer
Answer: a
Explanation: The height of fill Ze, equivalent to uniform surcharge intensity is given by,
Ka γze=Ka q,
∴ ze=qγ.
11 - Question
For finding out the active earth pressure for a backfill with sloping surface, the Rankine’s theory makes as additional assumption of ________
a) vertical and lateral stresses are normal to surcharge
b) vertical and lateral stresses are tangential to surcharge
c) vertical and lateral stresses are conjugate
d) vertical and lateral stresses are negligible
View Answer
Answer: c
Explanation: The additional assumption of vertical and lateral stresses are conjugate is made as, it can be shown that stresses on a given plane at a given point is parallel to another plane, the stresses on the latter plane at the same point must be parallel to the first plane.
12 - Question
The vertical and the lateral pressures have the same angle of obliquity β.
a) True
b) False
View Answer
Answer: a
Explanation: In Rankine’s theory, the additional assumption of the vertical and lateral stresses are conjugate is made. Being conjugate, both the vertical and the lateral pressures have the same angle of obliquity β.
13 - Question
The Rankine’s lateral pressure ratio is given by ________
a) K=cos2β−cos2φ√cosβ+cos2β−cos2φ√
b) K=cosβ+cos2β−cos2φ√cosβ−cos2β−cos2φ√
c) K=cosβ−cos2β−cos2φ√cosβ+cos2β−cos2φ√
d) K=cosβcosβ−cos2β−cos2φ√cosβ+cos2β−cos2φ√
View Answer
Answer: c
Explanation: The ratio K is the conjugate ratio or the Rankine’s lateral pressure ratio, which is given by,
K=cosβ−cos2β−cos2φ√cosβ+cos2β−cos2φ√,
where, β=surcharge angle
φ=angle of internal friction.
14 - Question
For backfill with sloping surface, the coefficient of active earth pressure is given by ______
a) Ka=cos2β−cos2φ√cosβ+cos2β−cos2φ√
b) Ka=cosβ+cos2β−cos2φ√cosβ−cos2β−cos2φ√
c) Ka=cosβ−cos2β−cos2φ√cosβ+cos2β−cos2φ√
d) Ka=cosβcosβ−cos2β−cos2φ√cosβ+cos2β−cos2φ√
View Answer
Answer: d
Explanation: The vertical pressure in case of backfill with surcharge,
σ= γzcosβ,
Therefore, from the assumption of stresses being conjugate,
Ka=cosβcosβ−cos2β−cos2φ√cosβ+cos2β−cos2φ√.
15 - Question
When the surcharge angle reduces to zero, the coefficient of active earth pressure is given by
a) Ka=1
b) Ka=1−sinφ1+sinφ
c) Ka=1+sinφ1−sinφ
d) Ka=0
View Answer
Answer: b
Explanation: For backfill with sloping surface, the coefficient of active earth pressure is given by,
Ka=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.