# Permeability of Soil

The ability of soil to allow flow of water through it is called as permeability of soil. It is very important factor for the structures which are in contact with water. Flow of water in soil takes place through void spaces, which are interconnected. Water does not flow in a straight line, but in a winding path. However in soil mechanics flow is considered to be in a straight line at an effective velocity. The velocity of flow depends on size of pores.

## Importance of Permeability of Soil

• Permeability influences the rate of settlement of a saturated soil under load.
• The stability of slopes and retaining structures can be greatly affected by the permeability involved.
• The design of earth dams is very much based upon the permeability of soil used.
• Filters made of soils are designed based upon their permeability.

## Properties of Permeability of Soil

• Solving problems involving pumping seepage water from construction excavation.
• Estimating the quantity of underground seepage.
• Stability analysis of earth structures and earth retaining walls subjected to seepage forces.

## Factors Affecting Permeability of Soil

• Grain size or Particle size

$K=CD_{10}^{2}$

The above equation is given by Alan Hazen. Permeability depends on shape and soil of soil particles.Permeability varies with square of particle size diameter.

• Void Ratio

If the presence of voids is more then the permeability is also more.

$K=\frac{e^{3}}{1+3}$

• Composition

For gravels, sand and silts presence of mica can decrease the permeability of soil. For clay, water attracted between clay particles reduces the permeability.

• Structural Arrangement

Remolding of natural soil reduces permeability. If soil contains more rounded particles, the permeability is more.

• Stratification

When flow of water is parallel to strata, permeability will be more when compared with flow perpendicular to strata.

• Presence of foreign particles and entrapped air

This affects the permeability as it reduces void space and it blocks the inter-connectivity between the pores.

• Degree of saturation

If the soil is dry or partly saturated the permeability of soil is always less.

## Permeability Range of Different Soil Mass

• Gravel  –  $10^{0}$  cm/s
• Sand     –  $10^{0}$ – $10^{-2}$  cm/s
• Silt         –  $10^{-2}$ – $10^{-4}$  cm/s
• Clay      –  $10^{-4}$ – $10^{-6}$  cm/s

## Darcy’s Law

In 1856, french hydraulic engineer Henry Darcy published a report on the water supply of the city of Dijon in France. In that report, Darcy described the result of an experiment designed to study the flow of water through a porous medium. Darcy’s experiment resulted in the formulation of mathematical law that describes fluid motion in porous media. Darcy’s law states that the rate of fluid flow through porous medium is proportional to the potential energy gradient within that fluid. The constant of proportionality is the Darcy’s permeability of soil. Darcy’s permeability is a property of both porous medium and the fluid moving through the porous medium. In fact, Darcy’s law is the empirical equivalent of the Navier-Strokes equation. Darcy’s flow velocity for laminar flow is defined as the quantity of fluid flow along the hydraulic gradient per unit cross sectional area. Velocity of flow through a porous media is directly proportional to the hydraulic gradient responsible for flow.

$V=Ki=K\frac{\Delta h}{L}$

Here,

• V = discharge velocity or superficial velocity
• k = coefficient of permeability or hydraulic conductivity
• $\Delta h$ = fall in total head
• L = length of soil specimen

## Assumptions of Darcy’s Law

• Soil is fully saturated.
• Temperature during testing is 27°C.
• Flow through soil is laminar
• Entire cross sectional area is available for flow
• Flow is continuous and steady.

## Validity of Darcy’s Law

Darcy’s law is valid only for slow and viscous flow, fortunately most groundwater flow cases fall in this category. Typically any flow with a Reynolds number less than 1 is clearly laminar and it would be valid to apply Darcy’s law. Experimental tests have shown that flow regimes with values of Reynolds number upto 10 may still be Darcine.

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