**Question 1. **

A pipe is laid along one proposed footing (1^{st}) boundary with a depth of 5m. A uniform loading (100kPa) is given by 1^{st} footing. 2^{nd} proposed footing is near to the 1^{st} footing with a distance of 2m. 2^{nd} footing give a uniform loading, 80kPa. Calculate vertical stress increment (Δσ_{v}) due to these two footings for A, B C, D and E on the pipe.

**Question 2. **

H_{1} = 2.5m, e = 0.5, G_{s} = 2.65

H_{2} = 2 m, e = 0.65, G_{s} = 2.68

H_{3} = 3m, e = 0.81, G_{s} = 2.71

Plot variation with depth from the top to Point C for σ'_{v} and σ_{h} when the soil is at rest.

**Question 3. **

A pipe line project uses the natural stability of soil (short-term). A strip area was excavated. After the completion of the project, soil backfill will be applied. To design the slope, a saturated sample of clay is found to have a water content (w) of 60 %. Atterberg Limits were wL = 80 and wP = 30.

1. Estimate the undrained shear strength (c_{u}) of clay. (Assume the shear strengths to be 200 kPa and 2 kPa at Liquidity Index (IL) values of 0 and 1, respectively).

2. If β = 60°, is the slope safe?

3. Based on your judgement, what is the appropriate factor of safety for this slope?

4. What should be the value of β, in order to achieve your appropriate factor of safety?

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