Geotechnical Engineering Questions and Answers – Seepage through Anisotropic Soil

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
View Answer

Answer: c
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
View Answer

Answer: c
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
View Answer

Answer: d
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
View Answer

Answer: c
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
View Answer

Answer: d
Explanation: Given,
k=6*10-7cm/s
if the viscosity is reduced to half, the coefficient of permeability doubles.
∴k=12*10-7cm/s.
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6. For an anisotropic soil ________ is true.
a) kx≠ky
b) kx+ky=0
c) kx-ky=0
d) kx/ky=1
View Answer

Answer: a
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) \(\frac{k_x}{k_y}\frac{∂^2 h}{∂x^2}+\frac{∂^2 h}{∂y^2}=0\)
View Answer

Answer: d
Explanation: for anisotropic soil, kx≠ky
∴ \(k_x \frac{∂^2 h}{∂x^2}+k_y\frac{∂^2 h}{∂y^2}=0 \)
Rewriting it, \(\frac{k_x}{k_y}\frac{∂^2 h}{∂x^2}+\frac{∂^2 h}{∂y^2}=0. \)
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8. The actual flow net for anisotropic soil will have orthogonal set of curves.
a) True
b) False
View Answer

Answer: b
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) \(\frac{k_1}{k_2} =cotθ\)
View Answer

Answer: c
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.
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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°
View Answer

Answer: c
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°.

Sanfoundry Global Education & Learning Series – Soil Mechanics.

To practice all areas of Soil Mechanics, here is complete set of 1000+ Multiple Choice Questions and Answers.

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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He lives in Bangalore, and focuses on development of Linux Kernel, SAN Technologies, Advanced C, Data Structures & Alogrithms. Stay connected with him at LinkedIn.

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