# Geotechnical Engineering Questions and Answers – Seepage through Anisotropic Soil

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This set of Soil Mechanics Multiple Choice Questions & Answers (MCQs) focuses on “Seepage through Anisotropic Soil”.

1. 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

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

2. 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

Explanation: 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. 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

Explanation: 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.
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4. 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

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

5. 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

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

6. For an anisotropic soil ________ is true.
a) kx≠ky
b) kx+ky=0
c) kx-ky=0
d) kx/ky=1

Explanation: In an isotropic soil kx=ky=k. But for anisotropic flow medium is kx≠ky. The laplace equation is $$k_x\frac{∂^2 h}{∂x^2}+k_y\frac{∂^2 h}{∂y^2}=0.$$

7. The laplacian form of equation for anisotropic soil is ______
a) $$\frac{∂^2 h}{∂x^2}+\frac{∂^2 h}{∂y^2}=0$$
b) $$k_x \frac{∂^2 h}{∂x^2}+\frac{∂^2 h}{∂y^2}=0$$
c) $$\frac{∂^2 h}{∂x^2}+k_y\frac{∂^2 h}{∂y^2}=0$$
d) $$\frac{k_x}{k_y}\frac{∂^2 h}{∂x^2}+\frac{∂^2 h}{∂y^2}=0$$

Explanation: for anisotropic soil, kx≠ky
∴ $$k_x \frac{∂^2 h}{∂x^2}+k_y\frac{∂^2 h}{∂y^2}=0$$
Rewriting it, $$\frac{k_x}{k_y}\frac{∂^2 h}{∂x^2}+\frac{∂^2 h}{∂y^2}=0.$$

8. The actual flow net for anisotropic soil will have orthogonal set of curves.
a) True
b) False

Explanation: First flow net is drawn for transformed section obtained by reducing the x-axis dimensions by a factor $$\sqrt{\frac{k_x}{k_y}}.$$ The actual flow net is obtained by retransforming the cross section by multiplying by a factor $$\sqrt{\frac{k_x}{k_y}}.$$

9. The deflection of flow lines at interface of dissimilar soils is given by ______
a) $$\frac{k_1}{k_2} =cosθ$$
b) $$\frac{k_1}{k_2} =sinθ$$
c) $$\frac{k_1}{k_2} =\frac{tanθ_1}{tanθ_2}$$
d) $$\frac{k_1}{k_2} =cotθ$$

Explanation: The deflection of flow lines at interface of dissimilar soils is given by the formula, $$\frac{k_1}{k_2} = \frac{tanθ_1}{tanθ_2}.$$
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. 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°

Explanation: Given,
k1=9×10-7 cm/s
k2=4×10-7 cm/s
θ1=30°
since $$\frac{k_1}{k_2} = \frac{tanθ_1}{tanθ_2}$$
$$\frac{9×10^{-7}}{4×10^{-7}} = \frac{tan30}{tanθ_2}$$
∴ θ2=14.39°.

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