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INDIAN INSTITUTE OF TECHNOLOGY MADRAS, CHENNAI Department of Civil Engineering

CE 3350 Geotechnical Engineering

4. The section of a cantilever retaining wall is shown in Fig. 1. The backfill has the following properties: c' = 0, ϕ' = 41° ; γ = 16 kN/m3. Water table is at a considerable depth below ground surface. Angle of internal friction δ' between the base of the wall and the soil can be taken as 2ϕ/3. The backfill carries a uniform surcharge load of 35 kN/m2. Check the stability of the retaining wall. Safe bearing capacity of the soil below the base is 200 kN/m2.

Tutorial # 3: Lateral Earth Pressure and Retaining Walls Note: Make suitable assumptions wherever necessary.

1. A retaining wall with a smooth vertical back retains sand backfill for a depth of 6 m. The backfill

has a horizontal surface and has the following properties: c' = 0, ϕ' = 28° ; γ = 16 kN/m3 ; γsat = 20 kN/m3. Calculate the magnitude of the total thrust against the wall for the conditions given below: (a) Backfill fully drained but the top of the wall is restrained against yielding, (b) backfill fully drained and the wall is free to yield, and (c) wall free to yield, water table at 3 m depth and there is no drainage. Determine the point of application of the resultant thrust for case (c).

2. A retaining wall, 8 m high, with a smooth vertical back, retains a clay backfill with c' = 15 kN/m2, ϕ' = 15° and γ = 18 kN/m3. Calculate the total active thrust on the wall assuming that tension cracks may develop to the full theoretical depth.

3. A retaining wall 6 m high, with a smooth vertical back is pushed against a soil mass having c' = 40 kN/m2 and ϕ' = 15°; γ = 19 kN/m3. What is the total Rankine passive pressure, if the horizontal soil surface carries a uniform load of 50 kN/m2? What is the point of application of the resultant thrust?

Fig. 1 5. A retaining wall with a vertical back, 8 m high, supports a sand soil with c' = 0 and ϕ' = 34°.

Neglecting wall friction, calculate the total active thrust on the wall, if (a) the water table is below the base of the wall (γ = 16 kN/m3), (b) the water table rises upto a height of 4 m above the base of the wall (γsat = 20.5 kN/m3), and (c) the water table rises upto the ground surface. If the wall is restrained against yielding, what is the magnitude of the lateral thrust for condition at (a)?

6. A smooth vertical wall, 4 m high, retains a soil with c' = 25 kPa and γ = 18 kN/m3. The horizontal backfill surface carries a uniform surcharge load of 50 kN/m2. If the retaining wall is caused to move towards the soil sufficiently to mobilize the passive resistance, draw the pressure distribution diagram. Determine the magnitude and the point of application of the total passive pressure.

7. The section of a cantilever retaining wall along with other relevant details are shown in Fig. 2. Determine the maximum and minimum base pressures of the wall, the factor of safety against overturning and the factor of safety against sliding.

8. (a) Calculate the total active thrust on a vertical wall 5 m high retaining a sand of γ = 17 kN/m3 for

which ϕ' = 35°: the surface of the sand is horizontal and the water table is below the bottom of the wall, (b) Determine the thrust on the wall if the water table rises to a level 2 m below the surface of the sand. The γsat of the sand is 20 kN/m3.

Fig. 2

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9. The soil conditions adjacent to a sheet pile wall are given in Fig. 3. Plot the distributions of active pressure behind the wall and passive pressure in front of the wall.

10. A vertical wall 6 m high, above the water table, retains a 20° soil slope, the retained soil having γ =

18 kN/m3; c' = 0 and ϕ' = 40°. Determine the total active thrust on the wall and the directions of the two sets of failure planes relative to the horizontal.

11. The backfill behind a retaining wall, located above the water table, consists of a sand of unit weight 17 kN/m3. The height of the wall is 6 m and the surface of the backfill is horizontal. Determine the total active thrust on the wall according to the Rankine theory if c' = 0 and ϕ' = 37°. If the wall is prevented from yielding, what is the approximate value of the thrust on the wall.

12. Details of a reinforced concrete cantilever retaining wall are shown in Fig. 4. The angle of friction between the base of the wall and the foundation soil is 25°. The backfill carries a uniform surcharge load of 10 kN/m2. Determine the maximum and minimum pressures under the base. Evaluate the factor of safety against sliding and overturning.

13. A vertical frictionless retaining wall is 6 m high with a horizontal granular backfill. Given: ϕ' =

30° ; γ = 16 kN/m3. For the translation mode of the wall , calculate the active pressure at depths z = 1.5 m, 3 m, 4.5 m and 6 m.

14. For the cantilever retaining wall shown in Fig. 5, calculate the factor of safety with respect to overturning, sliding and bearing capacity.

15. A gravity retaining wall is shown in Fig. 6. Calculate the factor of safety with respect to overturning and sliding. Use the Rankine active earth pressure in your calculation.

16. A gravity retaining wall is shown in Fig. 6. Calculate the factor of safety with respect to

overturning and sliding. Use the Coulomb's active earth pressure in your calculation and take δ' = 2/3 ϕ1'.

Fig. 3

Fig. 4

Fig. 5 Fig. 6

0.96 m

0.8 m