1 (a)
Draw the free body diagram of forces for an embankment in c-ϕ soil with circular failure surface and define the notations used. Also determine the factor of safety with respect to cohesion for a submerged embankment 25 m high and having a slope of 40°. The properties of soil are ϕ=10°, c=40 kN/m

^{2}, γ_{sat}=19 kN/m^{3}, Taylor's stability number, S_{n}=0.097.
5 M

1 (b)
An unsupported excavation is to be made in soil having ϕ=12°, c=19 kN/m

^{2}, γ=19 kN/m^{3}. What is the maximum depth of unsupported excavation in soil? And draw the active pressure distribution diagram.
5 M

1 (c)
Considering Coulomb's theory of lateral earth pressure, draw and define the forces acting on the cohesionless backfill at failure under active state behind a retaining wall. Also, why are retaining walls usually designed for active earth pressure?

5 M

1 (d)
Explain the basic difference in the theoretical bearing capacity computation of shallow and deep foundations.

5 M

1 (e)
Define allowable bearing capacity of soil and what is the effect of increase in width and depth of a footing on the bearing capacity and settlement behaviour of footing resting on i) sand and ii) clay?

5 M

1 (f)
In what respect does the design of braced cuts differ from that of a retaining wall and what are apparent earth pressure diagrams used in the design of braced cuts?

5 M

2 (a)
Derive an expression for factor of safety of an infinite slope in a c-ϕ soil when there is a steady seepage parallel to the slope.

7 M

2 (b)
A deep cut of 12 m depth is made soil for the construction of a road. The properties of soil are: cohesion=30 kN/m

^{2}, angle of internal friction =15° and a unit weight=20 kN/m^{3}. The slope angle of the cut is 35°. Consider a trial slip circle of radius 20 m passing through the toe and cutting the top ground surface at a distance 5 m from top edge. Determine the factor of safety with respect to cohesion for the given trial slip circle by friction circle method. Assume factor of safety w.r.t friction as 1.5.
8 M

2 (c)
Critically compare Rankine's theory with the Coulomb'd lateral earth pressure theory.

5 M

3 (a)
Explain Culmann's method for the determination of active earth pressure on retaining wall considering the effect of line load on backfill.

8 M

3 (b)
A 7 , retaining wall with a smooth vertical back face has a stratified back fill and a surcharge load of 10 kpa. The properties of soil are as follows up to 3.5 m height from top: unit weight=15 kN/m

^{3}, angle of shearing resistance =10° and cohesion=10 kpa. Draw the lateral active earth pressure diagram and estimate the resultant thrust on the wall and its position.
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3 (c)
What are the different types of conduits and the factor that affect the load on a conduit?

4 M

4 (a)
For the cantilever sheet pile wall shown in Figure 1, compute the embedment depth below the dredge line.

10 M

4 (b)
Differentiate between general, local and punching shear failure of shallow foundations.

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4 (c)
Describe how the bearing capacity of soil for shadow foundation can be determined from standard penetration test.

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5 (a)
Check the stability of the wall shown in Figure 2. Unit weight of concrete=24 kN/m

Safe bearing capacity = 500 kpa

^{3}. Foundation sail: Y = 19kN/m^{3}, Ï• = 20°, C=40 kpa, &=23°Safe bearing capacity = 500 kpa

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5 (b)
A circular foundation of 2.5 m diameter carries a load of 2500 kN. The soil has following properties :γ=19kN/m

(a) Find the depth at which the foundation should be loaded to provide a factor of safety of 3.

(b) What is the depth of location of foundation if there exists a water table close to the ground surface?

^{3}, Φ =30°, c=4kN/m^{2}, N_{c}=37.2, N_{q}=22.5, N_{γ}=19.7. Using Terzaghi's theory,(a) Find the depth at which the foundation should be loaded to provide a factor of safety of 3.

(b) What is the depth of location of foundation if there exists a water table close to the ground surface?

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6 (a)
Explain the internal stability of mechanically stabilized retaining wall.

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6 (b)
Explain the method of computation of settlement of pile groups in clayey soil.

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6 (c)
A precast concrete pile of diameter 450 mm is driven into stiff clay. The unconfined compressive strength of the clay is 200 kN/m

^{2}. Determine the length of pile required to carry a safe load of 400 kN with factor of safety=2.5. Assume adhesion factor=0.55.
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6 (d)
Following data was obtained in a vertical pile load test on a 300 m diameter pile. Plot the load-settlement curve and determine the allowable load as per IS code.

Load (kN) | 50 | 100 | 200 | 300 | 400 | 500 | 600 |

Settlement (mm) | 2.5 | 4 | 9.5 | 16.5 | 27 | 40.5 | 61 |

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