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# Permeability of Stratified Soil Deposits

1 - Question

Each layer of stratified soil deposit has its own coefficient of permeability.

a) True

b) False

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Answer: aExplanation: 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 - Question

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

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Answer: aExplanation: 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 - Question

The average permeability parallel to the bedding planes is given by________

a) k=k1z1+k2z2+⋯.+knznz∗12

b) k=1z1k1+z2k2+⋯+znkn

c) k=zz1k1+z2k2+⋯+znkn

d) k=k1z1+k2z2+⋯.+knznz

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Answer: dExplanation: 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=k1z1+k2z2+⋯.+knznz.

4 - Question

The average permeability perpendicular to the bedding planes is given by________

a) k=k1z1+k2z2+⋯.+knznz∗12

b) k=1z1k1+z2k2+⋯+znkn

c) k=zz1k1+z2k2+⋯+znkn

d) k=k1z1+k2z2+⋯.+knznz

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Answer: cExplanation: 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=zz1k1+z2k2+⋯+znkn

5 - Question

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

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Answer: bExplanation: 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, Kx=k1z1+k2z2+⋯.+knznz Kx=5k+10k+15k15 ∴ Kx=2k.

6 - Question

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) 1118k

d) 1811k

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Answer: dExplanation: 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, Kz=zz1k1+z2k2+⋯+znkn Kz=155k+52k+53k=1811k.

7 - Question

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) 1118k

d) 1811k

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Answer: cExplanation: 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, Kx=k1z1+k2z2+⋯.+knznz Kx=zk+zk2+zk33z ∴ Kx=1118k.

8 - Question

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

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Answer: bExplanation: 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, Kz=zz1k1+z2k2+⋯+znkn Kz=zzk+2zk+3zk=12k.

9 - Question

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

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Answer: cExplanation: 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, Kx=k1z1+k2z2+⋯.+knznz Kx=z∗9∗10−7+z∗4∗10−72z ∴ Kx=6.5*10-7 cm/s.

10 - Question

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

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Answer: bExplanation: 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, Kz=zz1k1+z2k2+⋯+znkn Kz=2zz9∗10−7+z4∗10−7 ∴ Kz = 5.5*10-7 cm/s.