250+ TOP MCQs on Seepage through Anisotropic Soil and Answers

Soil Mechanics Multiple Choice Questions on “Seepage through Anisotropic Soil”.

1. For an anisotropic soil, the permeability in the horizontal and vertical direction are k_x and k_y respectively. What will be the effective permeability of the soil?
a) k_x+k_y
b) k_xk_y
c) √( k_xk_y)
d) k_x/k_y
Answer: c
Clarification: For an anisotropic soil, k_x≠k_y. Therefore, the effective permeability of the soil is given by k’=√( k_xk_y).

2. A soil mass has k_x=8*10^-7cm/s and k_y=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
Answer: c
Clarification: Given,
k_x=8*10^-7cm/s
k_y=4*10^-7cm/s
k’=√( k_xk_y)
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 k_y=4*10^-7cm/s, then k_x is equal to ________
a) 6*10^-7cm/s
b) 7*10^-7cm/s
c) 8*10^-7cm/s
d) 9*10^-7cm/s
Answer: d
Clarification: Given,
k’=6*10^-7cm/s
k_y=4*10^-7cm/s
k’=√( k_xk_y)
6*10^-7 =√(4*10^-7* k_x)
∴ k_x=9*10^-7cm/s.

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
Answer: c
Clarification: 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
Answer: d
Clarification: 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) k_x≠k_y
b) k_x+k_y=0
c) k_x-k_y=0
d) k_x/k_y=1
Answer: a
Clarification: In an isotropic soil k_x=k_y=k. But for anisotropic flow medium is k_x≠k_y. The laplace equation is (k_xfrac{∂^2 h}{∂x^2}+k_yfrac{∂^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_yfrac{∂^2 h}{∂y^2}=0)
d) (frac{k_x}{k_y}frac{∂^2 h}{∂x^2}+frac{∂^2 h}{∂y^2}=0)
Answer: d
Clarification: for anisotropic soil, k_x≠k_y
∴ (k_x frac{∂^2 h}{∂x^2}+k_yfrac{∂^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
Answer: b
Clarification: 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)
Answer: c
Clarification: 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°
Answer: c
Clarification: 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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