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14.333 GEOTECHNICAL LABORATORYPermeability

BERNOULLI’S EQUATION

Zg

vu hw

2

2

Where:

h = Total Headu = Pressurev = Velocityg = Acceleration due to Gravityw = Unit Weight of Water

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14.333 GEOTECHNICAL LABORATORYPermeability

Zg

vu hw

2

2

Therefore:

Zu hw

v ≈ 0(i.e. velocity of water in soil is negligible).

v ≈ 0

BERNOULLI’S EQUATION IN SOIL

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14.333 GEOTECHNICAL LABORATORYPermeability

Figure 5.1. Das FGE (2005).

CHANGE IN HEADFROM POINTS A

& B (H) BA h hh

B

w

BA

w

A ZuZu h

BA h hh

Lh i

BA h hh

h can be expressed in non-dimensional form

Where:i = Hydraulic GradientL = Length of Flow between

Points A & B

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14.333 GEOTECHNICAL LABORATORYPermeability

Figure 5.2. Das FGE (2005).

VELOCITY (v) VS. HYDRAULIC GRADIENT (i)General relationship shown in Figure 5.2

Three Zones:1. Laminar Flow (I)2. Transition Flow (II)3. Turbulent Flow (III)

For most soils, flow is laminar. Therefore:

v i

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14.333 GEOTECHNICAL LABORATORYPermeability

DARCY’S LAW (1856)

Where:v = Discharge Velocity (i.e. quantity of water in

unit time through unit cross-sectional areaat right angles to the direction of flow)

k = Hydraulic Conductivity (i.e. coefficient ofpermeability)

i = Hydraulic Gradient* Based on observations of flow of water through clean sands

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14.333 GEOTECHNICAL LABORATORYPermeability

after Casagrande and Fadum (1940) and Terzagi et al. (1996).

SOILPERMEABILITY

ANDDRAINAGE

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14.333 GEOTECHNICAL LABORATORYPermeability

From FHWA IF-02-034 Evaluation of Soil and Rock Properties.

Good drainage

10-8 10-910-710-610-510-410-310-210-11.0101102 10-8 10-910-710-610-510-410-310-210-11.0101102

Poor drainage Practically impervious

Clean gravel Clean sands, Clean sand and gravel mixtures

Impervious sections of earth dams and dikes

“Impervious” soils which are modif ied by the effect of vegetation and weathering; f issured, weathered clays; fractured OC clays

Pervious sections of dams and dikes

Very f ine sands, organic and inorganic silts, mixtures of sand, silt, and clay glacial till, stratif ied clay deposits, etc.

“Impervious” soils e.g., homogeneous clays below zone of weathering

Drainage property

Application in earth dams and dikes

Type of soil

Direct determination of coefficient of permeability

Indirect determination of coefficient of permeability

*Due to migration of f ines, channels, and air in voids.

Direct testing of soil in its original position (e.g., well points). If properly conducted, reliable; considerable experience required. (Note: Considerable experience

also required in this range.)

Constant Head Permeameter; little experience required.

Constant head test in triaxial cell; reliable w ith experience and no leaks.

Reliable;Little experiencerequired

Falling Head Permeameter;Range of unstable permeability;* much experience necessary to correct interpretation

Fairly reliable; considerable experience necessary (do in triaxial cell)

Computat ion:From the grain size distribution(e.g., Hazen’s formula). Only applicable to clean, cohesionless sands and gravels

Horizontal Capillarity Test:Very little experience necessary; especially useful for rapid testing of a large number of samples in the f ield w ithout laboratory facilities.

Computat ions:from consolidation tests; expensive laboratory equipment and considerable experience required.

10-8 10-910-710-610-510-410-310-210-11.0101102 10-8 10-910-710-610-510-410-310-210-11.0101102

COEFFICIENT OF PERMEABILITYCM/S (LOG SCALE)

SOIL PERMEABILITY AND DRAINAGE

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14.333 GEOTECHNICAL LABORATORYPermeability

FACTORS AFFECTING PERMEABILITYPermeability is not a fundamental soil property but depends upon a number of factors:

• Particle size distribution• Particle shape and texture• Mineralogical composite

• Void ratio• Degree of saturation• Soil fabric

• Nature of fluid• Type of Flow• Temperature

Invariable for a given soil

Dependent upon placing and treatment of the soil

Relate to the permeabilityTemp. Correction:

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14.333 GEOTECHNICAL LABORATORYPermeability

HYDRAULIC CONDUCTIVITY: LABORATORY TESTINGConstant Head(ASTM D2434)

Falling Head(no ASTM)

Figure 5.4. Das FGE (2005). Figure 5.5. Das FGE (2005).

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14.333 GEOTECHNICAL LABORATORYPermeability

Constant Head(ASTM D2434)

AhtQLk

tkiAAvtQ )(Where:

Q = Quantity of water collectedover time t

t = Duration of water collection

tLhkAQ

Figure 5.4. Das FGE (2005).

LABORATORY TESTING: CONSTANT HEAD

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14.333 GEOTECHNICAL LABORATORYPermeability

LABORATORY TESTING: CONSTANT HEAD

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14.333 GEOTECHNICAL LABORATORYPermeability

Falling Head(No ASTM)

2

110303.2

hhLog

AtaLk

dtdhaA

Lhkq

hdh

AkaLdt

Where:A = Cross-sectional area of Soila = Cross-sectional area of Standpipe

Figure 5.5. Das FGE (2005). 2

1loghhe

AkaLt

Integrate from limits 0 to t

Integrate from limits h1 to h2

after rearranging above equation

after integration

or

LABORATORY TESTING: FALLING HEAD

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14.333 GEOTECHNICAL LABORATORYPermeability

LABORATORY TESTING: FALLING HEAD

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14.333 GEOTECHNICAL LABORATORYPermeability

210sec)/( cDcmk

Uniform Sands - Hazen Formula(Hazen, 1930):

Where:c = Constant between 1 to 1.5D10 = Effective Size (in mm)

eeCk

1

3

1

Sands – Kozeny-Carman(Loudon 1952 andPerloff and Baron 1976):

Where:C = Constant (to be determined)e = Void Ratio

85.024.1 kek

Sands – Casagrande(Unpublished):

Where:e = Void Ratiok0.85 = Hydraulic Conductivity @ e = 0.85

e

eCkn

12

Normally Consolidated Clays(Samarasinghe, Huang, and Drnevich, 1982):

Where:C2 = Constant to be determined experimentallyn = Constant to be determined experimentallye = Void Ratio

HYDRAULIC CONDUCTIVITY: EMPIRICAL RELATIONSHIPS