** Permeability **is the property of soil mass which permits the flow of water through its interconnected voids.2 methods are used to determine its coefficient.

Table of Contents

## Darcy’s Law for Permeability of soil

A soil mass exerts considerable forces when water flows into it, which affect the stability of the hydraulic structures.

For the effective design of engineering works, the permeability of the soil is the most important property to be considered.

### Darcy’s Law :

The flow of water through soil is governed by Darcy’s Law in 1856.

By conducting experiments, Darcy demonstrated that for laminar flow in a homogeneous soil, the velocity of flow is given by

*V=Ki*

Where K = Coefficient of permeability

i = Hydraulic gradient.

This velocity is also known as the superficial velocity or the discharge velocity.

According to Darcy,the soil mass of cross section A having discharge Q is given by :

Q = KiA

Where, i=Hydraulic gradient ,

A= Total cross section area of soil.

The following are the measuring units of * permeability*.

cm/sec,microns/sec,mm/sec,ft/day.

### Permeable soil

If a soil have continuous voids,then such soil is called permeable soil.

Gravel and sand comes under permeable soil.

### Impermeable soil

For the soil if K<0.000001 cm/sec,then such soil is called impermeable soil.

Stiff clay comes under impermeable soil.

## Limitations of Darcy’s law

The following are the limitations of the Darcy’s law:

- This is law is limited only to laminar flow conditions. In general Clay, salts, fine sands have laminar flow. As long as the Renolds number R<1, then the flow will be laminar.
- The exact range of the validity of Darcy’s law is difficult to predict. Experiments need to be conducted for predicting the relationship between Velocity (V) and hydraulic gradient (i).
- According to this law, The relationship between velocity and hydraulic gradient should be linear.
- For colloidal clay, in which the inter-stiles are very small and velocity is very small, the Darcy law is not valid.

## Coefficient of absolute permeability

Attempts are made to seperate the effect of properties of water from effects of the properties of soil.

So another coefficient was introduced known as the coefficient of absolute permeability. (K absolute).

This coefficient not only depends on the properties of water but also depends on the properties of soil.

## Factors effecting the permeability

The following the main factors :

- Size of the soil particles
- The shape of the soil particles.
- The function of density or Void ratio
- Structure of soil mass
- Properties of peculated fluid or water
- Degree of Saturation
- Adsorbed water

### 1. Particle size of soil

This coefficient (K) of soil is proportional to the square root of the particle size (D).

As compared to fine grained soils,the permeability of coarse grained soils is very large.

For coarse sand the permeability is one million times more than that of clay.

### 2. Shape of the particle

Compared to rounded particles,angular particles have greater surface area.Soils with angular particles are less permeable than those with rounded particles for the same void ratio.

But in natural deposit,the void ratio for a soil with angular ratio have greater than that of rounded particles and the soil with angular particles are more permeable.

### 3. Void ratio of particles

The permeability is more in the case of flocculated structure as compared to that in the dispersed structure for the same void ratio.

### 4. Properties of water

The ease with which a liquid can flow through a soil also depend on the liquid itself.For example a thick viscous oil will move at a slower rate than water.Therefore,the greater the viscosity the lower is the permeability.

### 5. Degree of saturation

For soils which are not fulled saturated contains air pockets,formed due to entrapped air or due to air liberated from percolating water.

Due to the presence of air, the flow will be reduced due to blockage of passage.

### 6. Adsorbed water

In fine grained soils consists of a layer of adsorbed water strongly attached to the surface.In the pores,it causes obstruction to the flow of water and hence reduces the permeability of soils.

## 2 Methods of tests for determining the Coefficient of permeability

This coefficient can be determined by 2 methods of tests:

- Field tests
- Laboratory tests.

## Laboratory test methods

The following are the laboratory methods:

### Direct methods:

- Constant head test
- Falling head test.

### In-direct methods:

- Consolidation test
- Compaction from the grain size
- Horizontal capillary test

#### Constant head Test

This test is more suitable for coarse grained soils.

The given soil sample can be remoulded by compacting the given soil at the given density in the mould. the length (L) and cross-section area (A) is calculated.

From the oven head tank,water is allowed to pass through the soil sample,the head (h) is maintained constantly through out the test period.

A reasonable quality of water (Q) is calculated in a measuring jar in a given time (t) when a steady flow is established through the soil sample.

As per the Darcy’s law,**K = QL/Aht**

#### Falling head Test

This falling head test is used for fine-grained soils which are relatively less permeable.

In this test method,the amount of water entering into the soil sample is measured instead of the amount of water which is flowing out of sample.

In this method ,the soil sample is prepared as same as constant head test.The water is allowed to enter in to the sample and the amount of water entered into the sample in a certain period of time (t) is measured using a burette of certain cross-sectional area (a)

Let h1,h2 are the heads at the time intervels t1,t2 respectiviely.

The coefficient is calculated by **K = aL log (h1/h2)/A(t2-t1)**.

## Field test methods

The following methods are used in field test methods:

- Pumping out test
- Pumping in test

### Pumping out test

This test is more accurate and it is influenced by large area surrounding the well.

### Pumping in tests

The following are the pumping in tests.

- Open end test
- Packer test

These test are mostly used for testing rocks and individual stratum.

### Conclusion:

The property of soils which permits the flow of water through voids is called permeability. The above-mentioned factor affects its movement in the water and the above-mentioned laboratory and field tests are used for determining its coefficient.

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