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Slide 1 of 14Revised 03/2013
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
Slide 2 of 14Revised 03/2013
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
Slide 3 of 14Revised 03/2013
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
Slide 4 of 14Revised 03/2013
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
Slide 5 of 14Revised 03/2013
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
Slide 6 of 14Revised 03/2013
14.333 GEOTECHNICAL LABORATORYPermeability
after Casagrande and Fadum (1940) and Terzagi et al. (1996).
SOILPERMEABILITY
ANDDRAINAGE
Slide 7 of 14Revised 03/2013
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
Slide 8 of 14Revised 03/2013
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:
Slide 9 of 14Revised 03/2013
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).
Slide 10 of 14Revised 03/2013
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
Slide 11 of 14Revised 03/2013
14.333 GEOTECHNICAL LABORATORYPermeability
LABORATORY TESTING: CONSTANT HEAD
Slide 12 of 14Revised 03/2013
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
Slide 13 of 14Revised 03/2013
14.333 GEOTECHNICAL LABORATORYPermeability
LABORATORY TESTING: FALLING HEAD
Slide 14 of 14Revised 03/2013
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
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