# Soil Mechanics Questions and Answers – Permeability of Stratified Soil Deposits

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This set of Soil Mechanics Questions and Answers for Freshers focuses on “Permeability of Stratified Soil Deposits”.

1. Each layer of stratified soil deposit has its own coefficient of permeability.
a) True
b) False

Explanation: This is true as each layer of the soil in the soil deposit could contain different grain sizes, voids ratio, entrapped and frozen matter, etc.

2. The average coefficient of permeability of whole deposit will depend upon _________
a) direction of flow with respect to bedding plane
b) direction of flow but not with respect to the bedding plane
c) length of the bedding plane
d) width of the bedding plane

Explanation: The average coefficient of permeability does not depend upon the length or the width of the bedding plane but rather depends upon direction of flow with respect to bedding plane.

3. The average permeability parallel to the bedding planes is given by________
a) $$k = \frac{k_1 z_1+k_2 z_2+⋯.+k_n z_n}{z}*\frac{1}{2}$$
b) $$k = \frac{1}{\frac{z_1}{k_1} +\frac{z_2}{k_2} +⋯+\frac{z_n}{k_n}}$$
c) $$k = \frac{z}{\frac{z_1}{k_1} +\frac{z_2}{k_2} +⋯+\frac{z_n}{k_n}}$$
d) $$k = \frac{k_1 z_1+k_2 z_2+⋯.+k_n z_n}{z}$$

Explanation: For flow parallel to the bedding plane,
Total discharge=sum of discharge through the individual layers
q=q1+q2+…+qn
q=kiz=k1 z1+k2 z2+⋯.+kn zn
∴ $$k = \frac{k_1 z_1+k_2 z_2+⋯.+k_n z_n}{z}.$$
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4. The average permeability perpendicular to the bedding planes is given by________
a) $$k = \frac{k_1 z_1+k_2 z_2+⋯.+k_n z_n}{z}*\frac{1}{2}$$
b) $$k = \frac{1}{\frac{z_1}{k_1} +\frac{z_2}{k_2} +⋯+\frac{z_n}{k_n}}$$
c) $$k = \frac{z}{\frac{z_1}{k_1} +\frac{z_2}{k_2} +⋯+\frac{z_n}{k_n}}$$
d) $$k = \frac{k_1 z_1+k_2 z_2+⋯.+k_n z_n}{z}$$

Explanation: For flow perpendicular to the bedding plane,
The head loss through the individual layers is different,
h=h1+h2+….+h3
Since the velocity is given by,
V=ki=kh/L
∴h=vz/k
vz/k=v1z1/k1+ v2z2/k2+….+ vnzn/kn
∴ $$k = \frac{z}{\frac{z_1}{k_1} +\frac{z_2}{k_2} +⋯+\frac{z_n}{k_n}}$$

5. A soil deposit has three layers of soil. The permeability of the second layer is twice that of the first layer and the permeability of the third layer is thrice that of the first layer. The thickness of each layer is 5m. What will be its average permeability parallel to the bedding plane?
a) k
b) 2k
c) 3k
d) 4k

Explanation: Given,
Let the permeability of the three layers be k1, k2, and k3.
K1=k
K2=2k
K3=3k
And z1=z2=z3=5m
For flow parallel to the bedding plane,
$$K_x=\frac{k_1 z_1+k_2 z_2+⋯.+k_n z_n}{z}$$
$$K_x=\frac{5k+10k+15k}{15}$$
∴ Kx=2k.

6. What will be its average permeability perpendicular to the bedding plane if a soil deposit has three layers of soil? The permeability of the second layer is twice that of the first layer and the permeability of the third layer is thrice that of the first layer. The thickness of each layer is 5m.
a) 11k
b) 18k
c) $$\frac{11}{18}k$$
d) $$\frac{18}{11}k$$

Explanation: Given,
Let the permeability of the three layers be k1, k2, and k3.
K1=k
K2=2k
K3=3k
And z1=z2=z3=5m
For flow perpendicular to the bedding plane,
$$K_z = \frac{z}{\frac{z_1}{k_1} +\frac{z_2}{k_2} +⋯+\frac{z_n}{k_n}}$$
$$K_z = \frac{15}{\frac{5}{k}+\frac{5}{2k}+\frac{5}{3k}} = \frac{18}{11} k.$$

7. A soil deposit has three layers of soil. The permeability of the second layer is 1/2 that of the first layer and the permeability of the third layer is 1/3 that of the first layer. The thickness of each layer is equal. What will be its average permeability parallel to the bedding plane?
a) 11k
b) 18k
c) $$\frac{11}{18}k$$
d) $$\frac{18}{11}k$$

Explanation: Given,
Let the permeability of the three layers be k1, k2, and k3.
K1=k
K2=1/2k
K3=1/3k
And z1=z2=z3=z
For flow parallel to the bedding plane,
$$K_x=\frac{k_1 z_1+k_2 z_2+⋯.+k_n z_n}{z}$$
$$K_x=\frac{zk+\frac{zk}{2}+\frac{zk}{3}}{3z}$$
∴ Kx=$$\frac{11}{18}k$$.

8. What will be its average permeability perpendicular to the bedding plane if a soil deposit has three layers of soil? The permeability of the second layer is 1/2 that of the first layer and the permeability of the third layer is 1/3 that of the first layer. The thickness of each layer is equal.
a) k
b) 1/2k
c) 1/3k
d) 1/4k

Explanation: Given,
Let the permeability of the three layers be k1, k2, and k3.
K1=k
K2=1/2k
K3=1/3k
And z1=z2=z3=z
For flow perpendicular to the bedding plane,
$$K_z = \frac{z}{\frac{z_1}{k_1} +\frac{z_2}{k_2} +⋯+\frac{z_n}{k_n}}$$
$$K_z = \frac{z}{\frac{z}{k}+\frac{2z}{k}+\frac{3z}{k}}=\frac{1}{2}k.$$

9. The coefficient of permeability of the two soil layers 1 and 2 in soil deposit is 9*10-7 cm/s and 4*10-7 cm/s respectively. The thickness of the layers is equal. The value of average permeability parallel to bedding planes is ________
a) 4.5*10-7 cm/s
b) 5.5*10-7 cm/s
c) 6.5*10-7 cm/s
d) 7.5*10-7 cm/s

Explanation: Given,
K1=9*10-7 cm/s
K2=4*10-7 cm/s
Let the thickness of each layer be z,
Therefore the total thickness is 2z.
For flow parallel to the bedding plane,
$$K_x=\frac{k_1 z_1+k_2 z_2+⋯.+k_n z_n}{z}$$
$$K_x=\frac{z*9*10^{-7}+ z*4*10^{-7}}{2z}$$
∴ Kx=6.5*10-7 cm/s.

10. The coefficient of permeability of the two soil layers 1 and 2 in soil deposit is 9*10-7 cm/s and 4*10-7 cm/s respectively. The thickness of the layers is equal. The value of average permeability perpendicular to bedding planes is ________
a) 4.5*10-7 cm/s
b) 5.5*10-7 cm/s
c) 6.5*10-7 cm/s
d) 7.5*10-7 cm/s

Explanation: Given,
K1=9*10-7 cm/s
K2=4*10-7 cm/s
Let the thickness of each layer be z,
Therefore the total thickness is 2z.
For flow perpendicular to the bedding plane,
$$K_z = \frac{z}{\frac{z_1}{k_1} +\frac{z_2}{k_2} +⋯+\frac{z_n}{k_n}}$$
$$K_z = \frac{2z}{\frac{z}{9*10^{-7}}+\frac{z}{4*10^{-7}}}$$
∴ Kz = 5.5*10-7 cm/s.

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