Permeability MCQ Quiz in मराठी - Objective Question with Answer for Permeability - मोफत PDF डाउनलोड करा

Concept:

Transmissibility:

• It is also known as transmissivity.
• It is the product of the coefficient of permeability and thickness of the aquifer.

T = k × b

Here,

T - Transmissivity (m²/day)

k - Coefficient of permeability (m/day)

b - Thickness of aquifer (m)

Calculation:

Given,

It is given the aquifer is confined at top and bottom by impermeable layers so, the Flow-through aquifer occurs parallel to the bed of the aquifer.

∴ Equivalent permeability of the aquifer is given by

\({{\rm{k}}_{{\rm{parallel}}}} = \frac{{{{\rm{k}}_1} \times {{\rm{H}}_1} + {{\rm{k}}_2} \times {{\rm{H}}_2} + {{\rm{k}}_3} \times {{\rm{H}}_3}}}{{{{\rm{H}}_1} + {{\rm{H}}_2} + {{\rm{H}}_3}}}\)

Putting values of k and H

\({{\rm{k}}_{{\rm{parallel}}}} = \frac{{30 \times 4 + 10 \times 2 + 20 \times 6}}{{4 + 2 + 6}}\)

⇒ k_eq = 21.67 m/day

∴ From (1)

T = 21.67 × 12 = 260m²/day

Concept:

Permeability is defined as the property of a porous material that permits the passage or seepage of water (or other fluids) through its interconnecting voids.

Factors affecting the permeability of soil are

1. Grain size

2. Properties of the pore fluid.

3. Voids ratio of the soil.

4. The structural arrangement of the soil particles.

5. Entrapped air and foreign-matter

6. Adsorbed water in clayey soils

The structural arrangement of the particle may vary, at the same voids ratio, depending upon the method of deposition or compacting the soil mass. The structure may be entirely different for a disturbed sample as compared to an undisturbed sample which may process stratification. The effect of structural disturbance on permeability is much pronounced in fine-grained soils.

A sample of clay and a sample of sand has the same specific gravity and void ratio. Their permeabilities would differ because the size ranges of their voids would be different.

Concept:

Coefficient of permeability for coarse grained soil is determined by means of Constant-head permeability test. The degree of saturation of soil should be 100%.

By Darcy’s Law,

Q = k i A

Where "i" is the hydraulic gradient 

⇒ i = H/L

\(Q = k\frac{h}{L}A\)

\(k = \frac{{QL}}{{Ah}}\)

where,

q = Discharge collected in time ‘t’, L = Distance between manometer taping points

A = Cross-sectional area of the sample., H = Difference in manometer levels i.e the head loss.

Calculation:

Given,

 L = 6 cm, A = 50 cm², H = 40 cm,

→ i = h/L = 40/6 = 6.66 

∴ Hydraulic gradient of the soil sample 6.66

Explanation:

Permeability of Stratified soil:

• Natural soil deposits generally are not homogeneous, but consist of a number of layers. The thickness and the coefficient of permeability of the layers may vary to a large extent. In such cases, it is required to compute the equivalent coefficient of permeability of the entire soil deposit.

• When a soil deposit consists of a number of horizontal layers having different permeabilities, the average value of permeability can be obtained separately for both vertical flow and horizontal flow, as k_V and k_H respectively.

Consider a stratified soil having horizontal layers of thickness H₁, H₂, H₃, etc. with coefficients of permeability k₁, k₂, k₃, etc.

For vertical flow:

The flow rate q through each layer per unit area is the same.

q = q₁ = q₂ = q₃ = .....

For Horizontal flow:

When the flow is horizontal, the hydraulic gradient is the same in each layer, but the quantity of flow is different in each layer.

i = i₁ = i₂ = i₃ =....

So, from the above relation, In a layered soil, the average coefficient of permeability in the horizontal direction is greater than the average coefficient of permeability in the vertical direction.

Concept:

Permeability in stratified soil:

Case 1 : When the flow is along the bedding plane i.e. Horizontal flow

Equivalent permeability, \({{\rm{K}}_{{\rm{eq}}}} = \frac{{{{\rm{K}}_1}{{\rm{H}}_1} + {{\rm{K}}_2}{{\rm{H}}_2} + {{\rm{K}}_3}{{\rm{H}}_3}}}{{{{\rm{H}}_1} + {{\rm{H}}_2} + {{\rm{H}}_3}}}\)

Case 2 : When flow is perpendicular to the bedding plane i.e. Vertical flow

Equivalent permeability, \({{\rm{K}}_{{\rm{eq}}}} = \frac{{{{\rm{H}}_1} + {{\rm{H}}_2} + {{\rm{H}}_3}}}{{\frac{{{{\rm{H}}_1}}}{{{{\rm{K}}_1}}} + \frac{{{{\rm{H}}_2}}}{{{{\rm{K}}_2}}} + \frac{{{{\rm{H}}_3}}}{{{{\rm{K}}_3}}}}}\)

K_eq for the horizontal direction is always greater than K_eq for the vertical direction

Calculation:

Equivalent permeability is given by,

\(\therefore {{\rm{K}}_{{\rm{eq}}}} = \frac{{{\rm{H}} + {\rm{H}} + {\rm{H}}}}{{\frac{{\rm{H}}}{{{{10}^{ - 4}}}} + \frac{{\rm{H}}}{{2 \times {{10}^{ - 4}}}} + \frac{{\rm{H}}}{{{1.5 \times{10}^{ - 4}}}}}} = 1.384 \times {10^{ - 4}}{\rm{\;cm}}/{\rm{sec}}\)

Concept:

\(\rm{Seepage\;Velocity\;(V_s) = \frac{Discharge\;Velocity\;(V)}{Porosity\;(n)}}\)

\(\rm{Porosity\;(n)=\frac{e}{1+e}}\)

Where, e = Void Ratio

Given:

Void ratio, e = 0.8, and Discharge velocity = 20 × 10-3 m/s

Calculation:

Porosity, \(\rm{n= \frac{{\rm{e}}}{{1 + {\rm{e}}}} = \frac{{0.8}}{{1 + 0.8}} = 0.444}\) 

Seepage velocity, \(Vs = \frac{V}{n} = \frac{{20\times {{10}^{ - 3}}}}{{0.444}} = 45 \times {10^{ - 3}}m/s\)

Explanation:

Direct Methods:

Direct methods to determine the permeability of the soil in the lab:

1. Constant head permeability method (suitable for coarse-grained soil)
2. Falling head permeability method (suitable for fine-grained soil)

Constant head permeability test:

The constant head permeability test is a common laboratory testing method used to determine the permeability of granular soils like sands and gravels containing little or no silt. This testing method is made for testing reconstituted or disturbed granular soil samples.

By Darcy's law-

Q = k i A

\(Q = k\frac{h}{L}*A\)

\(k = \frac{QL}{Ah}\)

k = permeability of soil

Q = discharge passing through soil sample

L = length of soil sample

A = area of sample

Falling head permeability test:

The falling head permeability test is used to find the permeability of relatively less permeable soil (fine-grained soils) where discharge is small.

Permeability \(k = 2.303 \frac{aL}{At}ln\frac{h1}{h2}\)

Direct methods to determine the permeability of the soil in the field:

1. Pumping out test
2. Pumping in test

The consolidation test can be treated as an indirect method to determine the permeability of soils as it releases the fluid present in the voids of soil. While the compaction test is the phenomenon to expel the air present in the soil.

Explanation

Permeability depends on both soil properties and Fluid properties

The kozney – Carman equation is quite useful, it reflects the effect of factors that affect permeability

\(k = \frac{{{\gamma _w}}}{\mu } \times \frac{{{e^3}}}{{1 + e}} \times D_{10}^2\)

Where,

D10 is effective grain size

e is the void ratio

μ is viscosity , γ w is unit weight of water

a) Grain size: The coefficient of permeability includes D102, where D10 is a measure of grain size

If the void ratio is the same then permeability is more in coarse soil than in the fine soil

b) Void ratio: From the equation, it is clear that k ∝ e2

If the particle size is the same, then loose soils are more permeable than dense soils

c) Degree of saturation: Permeability is directly proportional to the degree of saturation

d) Particle shape:

It is expressed in terms of specific surface area and permeability relates to specific surface area as ‘k ∝ 1/S2 ‘

e) Adsorbed Water

Adsorbed water is the water layer formed around the soil particle especially in the case of fine-grained soils. This reduces the size of the void space by about 10%. Hence, permeability reduces.

Concept:

According to Darcy law, Q = K.i.A

where Q = discharge , K = permeability, i = hydraulic gradient, A = area of cross-section

given, Q = \({150 ml\over120sec }= {150cm^3\over120sec } = 1.25cm^3/s\)

i = 2, A = 12.5 cm²

1.25 cm³/s = K x 2 x 12.5 cm²

K = 0.05cm/s = 0.5 mm/s

Concept:

Allen Hazen:

Allen Hazen(1892) concluded that linear dependency of the velocity and hydraulic gradient existed if the effective size of soil did not exceed 3 mm.

Allen Hazen's formula:

The coefficient of permeability of a soil is proportional to the square of representative particle size.

K = C × D102

Here  K = Coefficient of permeability

C = A constant, which is taken as 100

D10 = Particle size in cm (it is expressed such that 10% particles are finer than this size)

Calculation:

Given data;

D10 = 0.2 cm

C = 100

Allen Hazen's formula:

K = C × D102

K = 100 × (0.2)²

K = 4 cm/s