Permeability
Permeability of Soil
The permeability of soil is a property that describes quantitatively, the ease with which water flows through that soil.
Darcy's Law: Darcy established that the flow occurring per unit time is directly proportional to the head causing flow and the area of cross-section of the soil sample but is inversely proportional to the length of the sample.
(i) Rate of flow (q)
Where, q = rate of flow in m3/sec.
K = Coefficient of permeability in m/s
I = Hydraulic gradient
A = Area of cross-section of sample
where, HL = Head loss = (H1 – H2)
(ii) Seepage velocity
where, Vs = Seepage velocity (m/sec)
n = Porosity & V = discharge velocity (m/s)
(iii) Coefficiency of percolation
where, KP = coefficiency of percolation and n = Porosity.
Constant Head Permeability Test
where, Q = Volume of water collected in time t in m3.
Constant Head Permeability test is useful for coarse grain soil and it is a laboratory method.
Falling Head Permeability Test or Variable Head Permeability Test
a = Area of tube in m2
A = Area of sample in m2
t = time in 'sec'
L = length in 'm'
h1 = level of upstream edge at t = 0
h2 = level of upstream edge after 't'.
Konzey-Karman Equation
Where, C = Shape coefficient, ∼5mm for spherical particle
S = Specific surface area =
For spherical particle.
R = Radius of spherical particle.
When particles are not spherical and of variable size. If these particles passes through sieve of size 'a' and retain on sieve of size 'n'.
e = void ratio
μ = dynamic viscosity, in (N-s/m2)
= unit weight of water in kN/m3
Allen Hazen Equation
Where, D10 = Effective size in cm. k is in cm/s C = 100 to 150
Lioudens Equation
Where, S = Specific surface area
n = Porosity.
a and b are constant.
Consolidation equation
Where, Cv = Coefficient of consolidation in cm2/sec
mv = Coefficient of volume Compressibility in cm2/N
Capillary Permeability Test
where, S = Degree of saturation
K = Coefficient of permeability of partially saturated soil.
where hc = remains constant (but not known as depends upon soil)
= head under first set of observation,
n = porosity, hc = capillary height
Another set of data gives,
= head under second set of observation
- For S = 100%, K = maximum. Also, ku ∝ S.
Permeability of a stratified soil
(i) Average permeability of the soil in which flow is parallel to bedding plane,
(ii) Average permeability of soil in which flow is perpendicular to bedding plane.
(iii) For 2-D flow in x and z direction
(iv) For 3-D flow in x, y and z direction
Coefficient of absolute permeability (k0)
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