Soil Mechanics - Permeability of Soil

1. Due to rise of temperature, the viscosity and unit weight of the percolating fluid are reduced to 80% and 98%, respectively. Percentage change in coefficient of permeability(k)
(a) 78.4%
(b) 22.5%
(c) 0 %
(d) none of these

2. Due to rise in temperature, the viscosity and unit weight of percolating fluid are reduced to 70% and 90% respectively. Other things being constant, the change in coefficient of permeability will be
(a) 20.0%
(b) 28.6%
(c) 63.0%
(d) 77.8% (IES 1996)
Hint: Taylor equation k = \frac{r}{\mu }.\frac{{{e^3}}}{{1 + e}}{C_D}^2

3. The coefficient of permeability of a soil is 5 x 10⁻⁵ cm/sec for a certain pore fluid if the viscosity of the pore fluid is reduced to half, the coefficient of permeability will be
(a) 5 x 10⁻⁵ cm/sec
(b) 10 x 10⁻⁵ cm/sec
(c) 2.5 x 10⁻⁵ cm/sec
(d) 1.25 x 10⁻⁵ cm/sec (GATE 1991)

4. For a soil mass, horizontal coefficient of permeability({k_H}) is given by
(a) \frac{1}{{{H^2}}}\left( {{k_1}{H_1}^2 + {k_2}{H_2}^2 + ..{k_n}{H_n}^2} \right)
(b) \frac{1}{{{H^3}}}\left( {{k_1}{H_1}^3 + {k_2}{H_2}^3 + ..{k_n}{H_n}^3} \right)
(c) \frac{1}{H}\left( {{k_1}{H_1} + {k_2}{H_2} + ..{k_n}{H_n}} \right)
(d) \frac{H}{{({H_1}/{k_1}) + ({H_2}/{k_2}) + ..({H_n}/{k_n})}}  

5. For a soil mass, vertical coefficient of permeability({k_V}) is given by
(a) \frac{1}{{{H^2}}}\left( {{k_1}{H_1}^2 + {k_2}{H_2}^2 + ..{k_n}{H_n}^2} \right)
(b) \frac{1}{{{H^3}}}\left( {{k_1}{H_1}^3 + {k_2}{H_2}^3 + ..{k_n}{H_n}^3} \right)
(c) \frac{1}{H}\left( {{k_1}{H_1} + {k_2}{H_2} + ..{k_n}{H_n}} \right)
(d) \frac{H}{{({H_1}/{k_1}) + ({H_2}/{k_2}) + ..({H_n}/{k_n})}}

6. A glacial lake clay deposit is found to have a series of silt partings in it at an average vertical spacing of 2 m. The silt layers are about 3 mm in thickness and have a permeability of 100 times that of clay. The ratio of the horizontal and vertical permeability will be
(a) 0.87
(b) 1
(c) 1.147
(d) none of these

7. A stratum of soil consists of three layers of equal thickness. The permeabilities of top and bottom layers are K = 10⁻⁴ cm/s and that of middle layer is K = 10⁻³ cm/s. Then the value of the horizontal coefficient of permeability {k_H} for the entire soil layers is
(a) 2 x 10⁻³ cm/s
(b) 4 x 10⁻⁴ cm/s
(c) 3 x 10⁻⁴ cm/s
(d) 1.5 x 10⁻⁴ cm/s (IES 1994)

8. A bed of sand consists of three horizontal layers of equal thickness. The value of Darcy’s k for the upper and lowers layers is 1 x 10⁻² cm/sec and that for middle layer is 1 x 10⁻¹ cm/sec. The ratio of the permeability of the bed in the horizontal direction to that in the vertical direction is
(a) 10 to 1
(b) 2.8 to 1
(c) 2 to 1
(d) 1 to 10 (IES 1996)

9. If {k_x} and {k_z} are the permeabilities in x and z direction respectively in a two dimensional flow situation, the effective permeability {k_e} is given by
(a) {k_e} = \sqrt {{k_x}.{k_z}}
(b) {k_e} = \sqrt {{k_x}/{k_z}} 
(c) {k_e} = \sqrt {{k_x} + {k_z}}  
(d) none of these (GATE 1999, AMIE Summer 97)

10. For a given soil mass, the average coefficient of permeability is 10⁻³ cm/sec and coefficient of permeability in horizontal direction is 5 x 10⁻³ cm/sec. The coefficient of permeability in vertical direction is
(a) 1 x 10⁻⁴ cm/sec
(b) 5 x 10⁻⁴ cm/sec
(c) 2 x 10⁻³ cm/sec
(d) 5 x 10⁻³ cm/sec (IES 1992)

Answers

    1. (b)    2. (b)    3. (b)    4. (c)    5. (d)
    6. (c)    7. (b)    8. (b)    9. (a)    10. (a)

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These questions are taken from the book "Objective Questions (Civil Engineering)". The Kindle edition of this book is available at just ₹ 99/- only! 

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