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CIVE 2004: Permeability

This document discusses permeability and Darcy's law. It defines permeability as the ease with which a fluid, such as water, flows through a porous medium like soil. Darcy found that the rate of water flow through soil is proportional to the head difference and cross-sectional area, and inversely proportional to the length of the soil sample. This relationship is known as Darcy's law. The document also describes how permeability is determined through laboratory constant head and falling head tests.

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Akshay Bundhoo
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46 views15 pages

CIVE 2004: Permeability

This document discusses permeability and Darcy's law. It defines permeability as the ease with which a fluid, such as water, flows through a porous medium like soil. Darcy found that the rate of water flow through soil is proportional to the head difference and cross-sectional area, and inversely proportional to the length of the soil sample. This relationship is known as Darcy's law. The document also describes how permeability is determined through laboratory constant head and falling head tests.

Uploaded by

Akshay Bundhoo
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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CIVE 2004

Permeability
Flow of water through soils

• The ease with which a fluid flows through a porous


medium is an engineering property known as
permeability

• In soil mechanics, the fluid is water and the porous


medium is the soil mass

• In soils, the voids are interconnected and form


continuous paths for the movement of water
Flow of water through soils
It is important to assess the permeability of a soil mass:

• Evaluate the amount of water that will enter a pit


during construction, or the amount of stored water that
may be lost by percolation through or beneath a dam

• Evaluate the uplift or seepage forces beneath


hydraulic structures for stability analyses

• Provide control of seepage velocities so that fine-


grained soils are not eroded from the soil mass
Flow of water through soils
There are two issues:

• Quantity of flow

• Porewater pressures
Types of flow

•Laminar flow: each particle of water flows along a


definite path which never intersects the path of another
particle

•Turbulent flow: paths taken by water particles are


irregular and twisting

The flow velocity in soils is generally low so that the flow


is laminar
Bernoulli equation
The Bernoulli equation is commonly used in pipe flow
but is also applicable to flow of water through a soil
mass:
Bernoulli equation
Bernoulli equation:

• Total head causing flow = Elevation head + Pressure


head + Velocity head

• Since velocity of flow in soils is small, the velocity


head is usually ignored

• Flow takes place between 2 points, if and only if there


is a difference in total heads between the 2 points
Darcy’s law
Darcy found that the rate of flow, q, was:

• Proportional to the head difference h

• Proportional to the cross sectional area A

• Inversely proportional to the length L of the soil


sample

h
qk A
L
Darcy’s law

q  kiA
k = Coefficient of permeability (m/s)

i = Hydraulic gradient

A = Cross-sectional area
Discharge (or flow) and seepage velocity
The discharge velocity, v = ki.

v is a superficial velocity which is determined relative


to the soil total cross-section area, A.

The flow velocity through the voids is higher and is


termed seepage velocity, vs.

Rate of flow = q = Av = Av vs
where Av is the cross-section area of voids.
Av
Porosity, n
A
Discharge (or flow) and seepage velocity

v ki
vs  
n n
Determination of k
Laboratory methods:
• Coarse-grained soils – constant head test
• Fine-grained soils – falling (or variable) head test
Determination of k (m/s)
Constant head test
Determination of k (m/s)
Falling (or variable) head test
Determination of k (m/s)

Falling (or variable) head test

al  ho 
k  ln 
A(t1  to)  h1 

al  ho 
k  log 10 
A(t1  to)  h1 

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