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# Seepage through Anisotropic Soil

1 - Question

For an anisotropic soil, the permeability in the horizontal and vertical direction are kx and ky respectively. What will be the effective permeability of the soil?

a) kx+ky

b) kxky

c) √( kxky)

d) kx/ky

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Answer: cExplanation: For an anisotropic soil, kx≠ky. Therefore, the effective permeability of the soil is given by k’=√( kxky).

2 - Question

A soil mass has kx=8*10-7cm/s and ky=4*10-7cm/s. The effective permeability of the soil is ______

a) 4.6*10-7cm/s

b) 6.6*10-7cm/s

c) 5.6*10-7cm/s

d) 7.6*10-7cm/s

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Answer: cExplanation: Given, kx=8*10-7cm/s ky=4*10-7cm/s k’=√( kxky) k’=√(8*10-7 *4*10-7) k’=5.6*10-7cm/s.

3 - Question

If the effective permeability k’ is 6*10-7cm/s and ky=4*10-7cm/s, then kx is equal to ________

a) 6*10-7cm/s

b) 7*10-7cm/s

c) 8*10-7cm/s

d) 9*10-7cm/s

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Answer: dExplanation: Given, k’=6*10-7cm/s ky=4*10-7cm/s k’=√( kxky) 6*10-7 =√(4*10-7* kx) ∴ kx=9*10-7cm/s.

4 - Question

If a fully saturated soil mass has a water content of 100%, then its void ratio is _________

a) less than the specific gravity

b) greater than the specific gravity

c) equal to specific gravity

d) does not depend on specific gravity

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Answer: cExplanation: Given, Degree of saturation S=1 water content w=100% void ratio e=wG/s ∴ e=1G/1 ∴ e=G.

5 - Question

The coefficient of permeability is 6*10-7cm/s for a soil with a certain liquid. If the viscosity is reduced to half, then the coefficient of permeability is __________

a) 6*10-7cm/s

b) 17*10-7cm/s

c) 8*10-7cm/s

d) 12*10-7cm/s

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Answer: dExplanation: Given, k=6*10-7cm/s if the viscosity is reduced to half, the coefficient of permeability doubles. ∴k=12*10-7cm/s.

6 - Question

For an anisotropic soil ________ is true.

a) kx≠ky

b) kx+ky=0

c) kx-ky=0

d) kx/ky=1

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Answer: aExplanation: In an isotropic soil kx=ky=k. But for anisotropic flow medium is kx≠ky. The laplace equation is kx∂2h∂x2+ky∂2h∂y2=0.

7 - Question

The laplacian form of equation for anisotropic soil is ______

a) ∂2h∂x2+∂2h∂y2=0

b) kx∂2h∂x2+∂2h∂y2=0

c) ∂2h∂x2+ky∂2h∂y2=0

d) kxky∂2h∂x2+∂2h∂y2=0

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Answer: dExplanation: for anisotropic soil, kx≠ky ∴ kx∂2h∂x2+ky∂2h∂y2=0 Rewriting it, kxky∂2h∂x2+∂2h∂y2=0.

8 - Question

The actual flow net for anisotropic soil will have orthogonal set of curves.

a) True

b) False

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Answer: bExplanation: First flow net is drawn for transformed section obtained by reducing the x-axis dimensions by a factor kxky−−√. The actual flow net is obtained by retransforming the cross section by multiplying by a factor kxky−−√.

9 - Question

The deflection of flow lines at interface of dissimilar soils is given by ______

a) k1k2=cosθ

b) k1k2=sinθ

c) k1k2=tanθ1tanθ2

d) k1k2=cotθ

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Answer: cExplanation: The deflection of flow lines at interface of dissimilar soils is given by the formula, k1k2=tanθ1tanθ2. Where, θ1 and θ2 are angles made by flow line with the normal at the interface before and after the deflection respectively. K1 and k2 are the coefficients of permeability of soils 1 and 2 respectively.

10 - Question

If at interface of dissimilar soils, k1=9×10-7 cm/s and k2=4×10-7 cm/s. The deflection of flow lines at interface has θ1=30°, then θ2 will be _______

a) 12.39°

b) 13.39°

c) 14.39°

d) 15.39°

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Answer: cExplanation: Given, k1=9×10-7 cm/s k2=4×10-7 cm/s θ1=30° since k1k2=tanθ1tanθ2 9×10−74×10−7=tan30tanθ2 ∴ θ2=14.39°.