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MPSC AE CE Mains 2017 Official (Paper 2)

Option 3 : 2·0

__ Concept__:

As the canal is running in full condition, the soil will be under the water level or submerged in water. Hence the **submerged density** will be used.

Taylor's stability No. (S_{n}) = \(\frac{c}{\gamma _{sub}\times H \times F}\)

Where,

c = cohesion, γ_{sub} = submerged unit weight, H = height of canal, F = Factor of safety

__ Calculation__:

**Given**:

S_{n} = 0.1

c = 0.2 kg/cm^{2} = 200 g/cm^{2}

H = 10 m = 1000 cm, G = 2.5, e = 0.5

So, now we need to determine γ_{sub}

We know,

γ_{sub} = \(\frac{G-1}{1+e}\times γ_w\) = \(\frac{2.5-1}{1+0.5}\times 1\) = 1 g/cm^{3}

Now, putting the values in (Sn) = \(\frac{c}{\gamma _{sub}\times H \times F}\) we get,

0.1 = \(\frac{200}{1 \times 1000 \times F}\)

F = 0.2/0.1

**F = 2**