Civil Engineering Department College of Engineering

Course: Soil Mechanics (CE 359)

Lecturer: Dr. Frederick Owusu-Nimo

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What is permeability? A measure of how easily a fluid (e.g., water) can

pass through a porous medium (e.g., soils)

Loose soil

- easy to flow

- high permeability

Dense soil

- difficult to flow

- low permeability

water

Permeability Values

Soil Type Permeability (m/sec)

Clean gravel Coarse Sand Fine Sand Silty Clay Clay

1 – 0.01 0.01 – 10-4

10-4 – 10-5

10-5 – 10-7

< 10-7

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• Permeability varies widely for different soils (1ms-1 for

clean gravels to 10-10 ms-1 for unfissured clay

Factors affecting Permeability

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Permeability values depend on several factors

(fluid and soil properties)

• Fluid viscosity (also dependent on temperature)

• Size and continuity of pore spaces (depends on

size, shape of particles, void ratio, etc)

• Presence of discontinuities

Determination of Permeability

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• Laboratory Methods o Indirect Laboratory Methods

• From Consolidation Tests: 𝑘 = 𝑚𝑣𝑐𝑣𝛾𝑤

• From grading characteristics (Hazen formulae) : 𝑘 = 𝐶𝐷102

o Direct Laboratory Methods

• Constant Head Permeability Test – for coarse grained soils

• Falling Head Permeability Test – coarse and fine grained soils

• Field Methods o Well Pumping Test

o Tracer Tests, etc

Constant Head

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Falling Head

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Example 1 • The permeability of a soil sample is determined in

the lab using the constant head permeability test.

What is the permeability of the soil in m/sec if these

test values were obtained/used

o Length of specimen =45cm

o Area of specimen =23cm2

o Head difference = 71cm

o Amount of water collected in a period of 3min = 354cm3

Example 2 • For a falling head permeability test, the following

values are given:

o Length of specimen = 200mm

o Area of soil specimen = 1000mm2

o Area of standpipe = 40 mm2

o Head difference at time t= 0 is 500mm

o Head difference at time t=180sec is 300mm

Determine the permeability of the soil in cm/sec

Well Pumping Tests o The reliability of laboratory methods depends on the extent

to which the test specimens are representative of the soil

mass as a whole. More reliable results can generally be

obtained by the in-situ field methods

o A well extending the whole thickness of aquifer (water

bearing formation) is sunk

o As water is pumped, a drawdown, maximum at the well

and reducing radially from the well is created

o Observation wells are also sunk at radial distances from the

well to monitor water levels

o When steady state is established, various parameters are

measured, and with the help of Darcy’s law and Dupuits

assumption, the permeability of aquifer is determined

Well Pumping Tests • Dupuit’s assumption- the hydraulic gradient at any

point is constant from the top to the bottom of the

water bearing stratum and it is equal to slope of the

water surface / table

𝑖 =𝑑ℎ

𝑑𝑟

h is the height of water table at radius r from the well

• Aquifer types

o Unconfined aquifer – impervious layer only at bottom

o Confined aquifer – impervious layer at both top and

bottom

Unconfined Aquifer • Consider two boreholes located on a radial line at distances r1 and r2

from the centre of the well

• The respective water levels relative to the bottom of the stratum being

h1 and h2.

• For any distance r, the area through which seepage takes place is

2πrh, where r and h are variables. Then applying Darcy’s law:

Akiq

2 2

1 1

2 222 1

1

2 1

2 2

2 1

d2

d

d2 d

ln ( )

2.3 log( / )

( )

r h

r h

hq rhk

r

rq k h h

r

rq k h h

r

q r rk

h h

Confined Aquifer For a confined stratum of thickness H the area through which seepage

takes place is 2πrH, where r is variable and H is constant.

The drawdown curve must always be above the confining layer

2 2

1 1

22 1

1

2 1

2 1

d2

d

d2 d

ln 2 ( )

2.3 log( / )

2 ( )

r h

r h

hq rHk

r

rq Hk h

r

rq Hk h h

r

q r rk

H h h

Akiq

Assumptions of well pumping formula

• The test well must penetrate the full thickness of the

water bearing formation

• A steady flow condition must exist (i.e. water levels

in test and observation wells become constant)

• The formation is homogenous, isotropic and extends

an infinite distance in all directions

• The Dupuit’s assumption is valid

Note • Pumping tests lower groundwater unevenly and

may cause uneven stresses in soils. Thus pumping

tests near existing structures can cause uneven or

differential settling.