Darcy's law

PRESENTATION ON….

Permeability

&

Darcy’s Law &

It’s Validity 

PERMEABILITY

PERMEABILITY

• Permeability is defined as the property of soil which permits flow of water through it.• A soil is highly pervious when water can flow through it easily. E.g. Gravels.• In an impervious soil, the permeability is very low and water cannot easily flow

through it. E.g. Clays.• Rocks are impermeable • Permeability is a very important engineering property of soils. A knowledge of

Permeability is essential for:-

Settlement of building Yield of wells Seepage through and below the earth structures Earth pressure Uplift pressure under hydraulic structure.

FACTORS AFFECTING PERMEABILITY OF SOILS

The following factors affect the permeability of soils:-

1. Particle size

2. Properties of pore fluid.

3. Void ratio of soil.

4. Shape of particles.

5. Structure of soil mass.

6. Degree of saturation.

7. Absorbed water.

8. Impurities in water.

DETERMINATION OF COEFFICIENT OF PERMEABILITY

The various methods to determine coefficient of permeability are as under :-

Methods to determine coefficient of permeability

Laboratory Methods Field Methods Indirect Methods

1) Constant head 1) Pumping out tests 1) Computation from the

Permeability test 2) Pumping in test particle size

2) Falling head 2) Computation from

Permeability test Consolidation test

CONSTANT HEAD PERMEABILITY TEST:-

Object:-

To determine the coefficient of permeability of a soil specimen by constant head method.

Equipments:- Permeability mould, internal diameter = 100mm, effective height = 127.3mm,

capacity = 1000ml, complete with all accessories Constant head tank. Graduated cylinder, stop water, thermo meter. Filter paper, vacuum pump. Weighting balance, 0.1 gm accuracy.

CONSTANT HEAD PERMEABILITY TEST:-

Test Procedure:-

1. Measure internal dimensions of the mould. Apply a little grease on the inside to the mould.

2. Take about 2.5kg of the soil, from a thoroughly mixed wet soil, in the mould. Compact the soil at the required dry density using a suitable compacting device.

3. Remove the collar and base plate. Trim the excess soil level with the top of the mould.

4. Clean the outside of the mould. Find the mass of the soil in the mould. Take a small specimen of the soil in container for the water constant determination.

5. Saturate the porous stones.

6. Place the porous stone (disc) on the drainage base and keep a filter paper on the porous stone.

7. Place the mould with soil on the drainage base.

8. Place a filter paper and a porous stone on the top of specimen.

9. Connect the constant head tank to the drainage cap inlet.

10. Open the stop cock, and allow the water downward so that all the air is removed, then close the stop cock.

11. Now, again open the stop cock and at the same time start the stopwatch. Collect the water flowing out of the base in a measuring flask for some convenient time interval.

12. Measure the difference of head (h) in levels between the constant head tank and the outlet in the base.

 • c/s area of specimen = A = (π/4) x D2 (cm2) • Volume of mould = V = (π/4) x D2 x L (cm3)

• Mass of wet soil in the mould = M = M2 – M1

Where, M1 = mass of empty mould.

M2 = mass of mould + wet soil

• Bulk density of soil, = _____ gm/cm3

• Dry density of soil, = _____ gm/cm3

 Results:- The coefficient of permeability of a given soil sample is …………

cm/sec

FALLING HEAD PERMEABILITY TEST :-

Object:-

To determine the coefficient of permeability of a soil specimen by falling head method.

Equipments:-

All the equipments required for the constant head permeability test.

FALLING HEAD PERMEABILITY TEST :-

Test Procedure:-

1. Prepare the remoulded soil specimen in the permeameter and saturate it.

2. Keep the permeameter mould in the bottom tank and fill the bottom tank with water up to its outlet.

3. Connect the water inlet nozzle of the mould to the stand pipe filled with water. Permit water to flow for some time till steady state of flow is reached.

4. Now open the valve of stand pipe and record the time (t) to fall the head from h1 to h2. Repeat this step at least twice.

Normally, Constant head permeability test is used for more permeable soils like

sand. Falling head permeability test is used for less permeable soils like clay.

DARCY’S LAW & IT’S VALIDITY

WHO WAS DARCY?

Henry Philibert Gaspard Darcy was born June 10, 1803 in Dijon, France. Admitted to the French School of Bridges and Roads in Paris, part of the

Corps of Bridges and Roads. After graduation, he was eventually assigned by the Corps to a position in Dijon.

In 1828, Darcy designed a 12.7 km system of aqueducts to supply the city of Dijon with surface water. The system included 28,000 m of pressurized surface lines and required no pumps or filters.

Made important contributions to flow and friction loss in pipes, created an improved pitot tube design, and was the first to postulate the existance of a boundary layer in fluid flow.

In 1856, carried out experiments while researching sand filters that lead to Darcy’s Law.

Died unexpectedly January 3, 1858 from pneumonia during a trip to Paris.

DARCY’S LEGACY

Place Darcy, Dijon, France.

Henry Philibert Gaspard Darcy (1803–1858)

DARCY’S LAW

 The law of flow of water through soil was first studied by Darcy in 1856.

The Darcy’s law is,

“For laminar flow through saturated soil mass, the discharge per unit time is proportional to the hydraulic gradient”.

q = k.i.A

= k.i = v

v = k.i ……. Darcy’s Law

Where, q = Discharge per unit time (rate of flow)

A = Total c/s area of soil mass

i = Hydraulic gradient = h/L

k = Darcy’s coefficient of Permeability

v = Velocity of flow (discharge velocity)

If a soil sample of length L, and cross- sectional area A, is subjected to differential head of water ( h1 – h2), the hydraulic gradient (i) will be equal to,

i = =

q = k. . A We know that v = k.i If hydraulic gradient (i) is equal to unity,

v = k

ASSUMPTIONS OF DARCY’S LAW :-

The following assumptions are made in Darcy’s law.

The soil is saturated. The flow through soil is laminar. The flow is continuous and steady. The total cross sectional area of soil mass is

considered. The temperature at the time of testing is

270C.

VALIDITY OF DARCY’S LAW

1. Darcy’s law is valid if the flow through soils is laminar : The flow of water through soils depends upon the dimension of particles. In fine grained soils

the dimensions of the interstices (voids) are very small and flow is necessarily laminar. In course- grained soil, the flow is also laminar. However, in very coarse grained soils, such as

gravels, the flow may be turbulent. For flow through soils, the flow is laminar if the Reynolds number is less than unity.

2. As per Allen Hazen, the maximum diameter of the particle for the flow to be laminar is about 0.50 mm.

3. It is valid for flow in clays, slits and fine sands. In coarse sands, gravels and boulders, the flow may be turbulent and Darcy’s law may not be applicable.

4. For Darcy’s law to be valid, the relationship between velocity (v) and hydraulic gradient (i) should be linear.

5. In extremely fine-grained soils, such as collodial clay, the interstices are very small. The velocity is therefore very small. In such soils, the Darcy’s law is not valid.

THANK YOU…..