P a g e |13‐ 1 Chapter 13
Lateral Earth Pressure: At-Rest, Rankine, and Coulomb
1. Which of the following is not a retaining structure?
(a) Retaining wall
(b) Basement wall
(c) Raft
(d) Bulkhead
2. When a retaining structure does not move either to the right or to the left of its initial
position, the ratio of the effective horizontal stress to the effective vertical stress is
generally represented by (a) K (b) K0 (c) Ka (d) Kp 3. For coarse grained-grained soils, the coefficient of earth pressure at rest can be estimated
by using the Jaky’s equation, which is given as (a)
1 sin φ
(b)
1
sin φ
φ
sin φ
(c)
1
(d)
0.44
0.42
%
where all the symbols have their usual meanings.
4. The total force per unit length of the retaining wall of height H when it does not move
either to the right or to the left of its initial position is given as
(a)
γ
(b)
γ
(c)
γ
(d)
γ
where all the symbols have their usual meanings.
5. The magnitude of coefficient of earth pressure at rest in most soils ranges between
(a) 0.0 and 0.5.
(b) 0.0 and 1.0
(c) 0.5 and 1.0.
(d) 0.5 and 2.0.
6. The condition in which every point in a soil mass is on the verge of failure refers to
(a) elastic equilibrium.
(b) plastic equilibrium.
(c) both (a) and (b).
(d) none of the above.
© 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. P a g e |13‐ 2 7. When a retaining structure moves towards the soil backfill, the stress condition within the
soil backfill is called
(a) at rest state.
(b) active state.
(c) passive state.
(d) both (b) and (c).
8. The Rankine’s theory of earth pressure assumes that
(a) the back face of the wall in contact with the soil backfill is smooth.
(b) the wall extends to an infinite depth.
(c) both (a) and (b).
(d) the soil is massless.
9. The coefficient of Rankine’s active earth pressure
(a)
tan 45°
φ
(b)
tan 45°
φ
(c)
tan
45°
φ
(d)
tan
45°
φ
10. The coefficient of Rankine’s passive earth pressure
(a)
tan 45°
φ
(b)
tan 45°
φ
(c)
tan
45°
φ
(d)
tan
45°
φ
11. In the Rankine’s active state, the failure plane within the soil backfill makes an angle with
the horizontal given as
(a) 45°
(b) φ
(c) 45°
φ
(d) 45°
φ
12. In the Rankine’s passive state, the failure plane within the soil backfill makes an angle
with the horizontal given as
(a) 45°
(b) φ
(c) 45°
φ
(d) 45°
φ
© 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. P a g e |13‐ 3 13. For the Rankine’s active state, the active earth pressure from the cohesionless soil backfill
at the bottom of a retaining wall of height H is
(a)
γ
(b)
γ
(c)
γ
(d)
γ
where all the symbols have their usual meanings.
14. For the Rankine’s passive state, the passive earth pressure from the cohesionless soil
backfill at the bottom of a retaining wall of height H is
(a)
γ
(b)
γ
(c)
γ
(d)
γ
where all the symbols have their usual meanings.
15. The total active force per unit length of the retaining wall of height H from the
cohesionless soil backfill is given as
(a)
γ
(b)
γ
(c)
γ
(d)
γ
where all the symbols have their usual meanings.
16. The total passive force per unit length of the retaining wall of height H from the
cohesionless soil backfill is given as
(a)
γ
(b)
γ
(c)
γ
(d)
γ
17. The total active force on the retaining wall of height H from the cohesionless soil backfill
acts above the base of the wall at a height of
(a) /4.
(b) /3.
(c) /2.
(d) 3 /4.
18. The total passive force on the retaining wall of height H from the cohesionless soil
backfill acts above the base of the wall at a height of
(a) /4.
(b) /3.
(c) /2.
(d) 3 /4.
© 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. P a g e |13‐ 4 19. For the Rankine’s active state, the active earth pressure from the cohesive soil backfill at
the bottom of a retaining wall of height H is
(a)
γ
(b)
γ
(c)
γ
2
(d)
γ
2
where all the symbols have their usual meanings.
20. An application of surcharge at the top of the soil backfill
(a) causes no change in the earth pressure along the depth of the wall.
(b) decreases the earth pressure along the depth of the wall.
(c) increases the earth pressure along the depth of the wall.
(d) increases the earth pressure near the top of the wall only.
21. The presence of cohesion in the soil backfill
(a) causes no effect on the earth pressure along the depth of the wall.
(b) decreases the active earth pressure along the depth of the wall.
(c) increases the passive earth pressure along the depth of the wall.
(d) both (b) and (c).
22. The depth of tension cracks in the cohesive soil backfill under undrained condition is
(a)
(b)
(c)
(d)
23. The development of tensile cracks in the upper part of the cohesive soil backfills
(a) causes no effect on the earth pressure along the depth of the wall.
(b) decreases the active earth pressure along the depth of the wall.
(c) increases the active earth pressure along the depth of the wall.
(d) both (b) and (c).
24. For a retaining wall with a rough vertical back, the total active earth pressure acts
(a) horizontally.
(b) in a direction making an angle greater than 90° with the vertically upward direction.
(c) in a direction making an angle smaller than 90° with the vertically upward direction.
(d) in any direction.
25. For a retaining wall with a rough vertical back, the total passive earth pressure acts
(a) horizontally.
(b) in a direction making an angle greater than 90° with the vertically upward direction.
(c) in a direction making an angle smaller than 90° with the vertically upward direction.
(d) in any direction.
© 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. P a g e |13‐ 5 26. Which of the following earth pressure theories consider the roughness of the back of the
wall?
(a) Rankine’s active earth pressure theory
(b) Rankine’s passive earth pressure theory
(c) Coulomb’s earth pressure theory
(d) All of the above
27. For a continuously sloping backfill behind the retaining wall the total earth pressure is
(a) horizontal.
(b) vertical.
(c) inclined.
(d) inclined but parallel to the sloping backfill.
28. The Coulomb’s active earth pressure coefficient becomes equal to the Rankine’s active
earth pressure for
(a) α = 0 and θ = 0
(b) α = 0 and δ′ = 0
(c) θ = 0 and δ′ = 0
(d) α = 0, θ = 0 and δ′ = 0
where α is the angle made by the top surface of the soil backfill with the horizontal, θ is
the inclination of the back face of the wall to the vertical, and δ′ is the angle of friction
between the soil backfill and the wall.
29. The wall friction results in
(a) reduction in the total active earth pressure.
(b) increase in the total passive earth pressure.
(c) both (a) and (b).
(d) increase in the total earth pressure.
30. When the soil-wall interface friction angle becomes greater than about half of the soil
backfill frictional angle, the Coulombs’ earth pressure theory overestimates the passive
force, which is on
(a) the unsafe side of the design.
(b) the safe side of the design.
(c) both (a) and (b) governed by the site conditions.
(d) none of the above.
31. The total dynamic active force a retaining wall from a granular backfill depends on
(a) horizontal seismic coefficient, kh.
(b) vertical seismic coefficient, kv.
(c) unit weight of soil, and wall geometry.
(d) all of the above.
32. For design of retaining walls in seismic prone areas, the maximum value of kh is typically
taken as
(a) 0.1.
(b) 0.5.
(c) 1.0.
(d) 5.0.
© 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. P a g e |13‐ 6 33. The critical horizontal seismic coefficient kh(cr) is defined in terms of vertical seismic
coefficient kv and effective angle of internal friction φ′ as
(a) k h ( cr ) = (1 − k v ) tan φ ′
(b) k h ( cr ) = (1 + k v ) tan φ ′
(c) k h ( cr ) = (1 − k v ) cos φ ′
(d) k h ( cr ) = k v tan φ ′
34. Shukla et al. (2009)’s procedure for calculating dynamic active earth pressure does not
consider
(a) unit weight of backfill.
(b) friction and adhesion between the back face of the wall and the backfill.
(c) effect of tensile crack in the backfill.
(d) both (b) and (c).
35. The retaining walls provide a permanent lateral support to
(a) vertical slopes of soil.
(b) near-vertical slopes of soil.
(c) both (a) and (b).
(d) slopes of soil.
36. Which of the following walls depends mainly on its own weight for stability? (a) Gravity retaining wall (b) Cantilever retaining wall (c) Counterfort retaining wall (d) All of the above 37. Which of the following walls is not economical for supporting high vertical slopes of soil? (a) Gravity retaining wall (b) Cantilever retaining wall (c) Counterfort retaining wall (d) both (b) and (c) 38. Cantilever retaining walls are made of (a) plain cement concrete. (b) reinforced cement concrete. (c) stone masonry. (d) brick masonry. 39. Counterfort retaining walls are similar to (a) gravity retaining walls. (b) cantilever retaining walls. (c) both (b) and (c). (d) none of the above. 40. Which of the following walls consists of a thin stem and a base slab? (a) Gravity retaining wall (b) Cantilever retaining wall (c) Counterfort retaining wall (d) Both (b) and (c) © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. P a g e |13‐ 7 41. At regular intervals, the thin vertical concrete slabs called counterforts that tie the stem
and the base slab together in the counterfort retaining wall reduce (a) shear force. (b) bending moment. (c) both (a) and (b). (d) height of the wall. 42. The main components of a mechanically stabilised earth retaining wall are
(a) cohesive backfill and reinforcing strips.
(b) cohesionless backfill and reinforcing strips.
(c) cohesive backfill, reinforcing strips and a cover on the front face of the wall.
(d) cohesionless backfill, reinforcing strips and a cover on the front face of the wall.
43. Which of the following materials are used as the soil reinforcing element?
(a) Galvanised metallic strips
(b) Galvanised metallic strips and geogrids
(c) Geotextiles and geogrids
(d) Geotextiles, geogrids and galvanised metallic strips
© 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. P a g e |13‐ 8 Answers, Hints and Discussion
1. (c)
2. (b)
Discussion: K0, Ka and Kp are called coefficient of earth pressure at rest, coefficient of active
earth pressure, and coefficient of passive earth pressure, respectively.
3. (b)
Hint and Discussion: See Eq. (13.5). (c) is correct for overconsolidated coarse-grained soils,
see Eq. (13.7), and (d) is correct for fine-grained, normally consolidated soils.
4. (d)
Hint: See Eq. (13.10).
5. (c)
6. (b)
7. (c)
8. (c)
9. (c)
10. (d)
11. (d)
12. (c)
13. (b)
14. (b)
15. (d)
16. (d)
17. (b)
18. (b)
19. (c)
Hint: See Fig. 13.14(d).
20. (c)
Hint: See Eq. (13.38) and Eq. (13.39).
21. (d)
Hint: See Eq. (13.42) and Eq. (13.48).
22. (b)
Hint: See Eq. (13.41).
23. (c)
24. (b)
Hint: See Fig. 13.19.
25. (c)
Hint: See Fig. 13.23.
26. (d)
© 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. P a g e |13‐ 9 27. (c)
28. (d)
Hint: Compare Eq. (13.19) and Eq. (13.54).
29. (c)
30. (a)
31. (d)
Hint: See Eq. (13.59).
32. (b)
33. (a)
Hint: See Eq. (13.75).
34. (d)
35. (c)
36. (a)
37. (a)
38. (b)
Discussion: (a), (c) and (d) are correct for the gravity retaining walls.
39. (b)
40. (d)
41. (c)
42. (d)
43. (d)
© 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.