Q : volumetric water flow rate (volume/time units)
k : coefficient of permeability (or hydraulic conductivity) (length/time units)
h1: total hydraulic head in the entrance of the cylinder (length units)
h2: total hydraulic head in the exit of the cylinder (length units)
L: length of the cylinder (length units)
Α: cross sectional area of the flow [(length)² units]
i = (h1-h2) / L : the hydraulic gradient
h1-h2: hydraulic head difference (length units)
The total hydraulic head has two components: a) the elevation head, he, is the height of a point from a random reference level and b) the piezometric head, hp, is the water pressure at this point divided by the unit weight of water
Flow velocity :
Infiltration rate :
i) Flow vertical to bedding planes
ii) Flow parallel to bedding planes
1) Constant Head Permeameter
2) Falling Head Permeameter
ho: initial hydraulic head
h: hydraulic head after t time
ln: natural logarithm
As the water flows through the voids, it creates forces that are applied on the soil particles in the direction of its motion.
j: seepage force per unit volume
i: hydraulic gradient of the flow
γw: unit weight of water
When the water flows through soil, seepage forces must be taken into account for the calculation of the effective stresses.
When water flows upwards in soil, there is a critical hydraulic gradient value where the weight of the soil particles is counteracted by the seepage force. In that case, soil behaves like a viscous liquid and this phenomenon is called quicksand. The critical hydraulic gradient is given by the equation:
γαν: unit weight of buoyancy
γw: unit weight of water
K20℃= permeability factor at temperature of 20℃
KT℃ = permeability factor at temperature of T℃
n20℃ = water viscosity at temperature of 20℃
nT℃ = water viscosity at temperature of T℃
The diagrams below show the values of the fraction nT℃ / n20℃ as a function of temperature that varies from T=12℃ to T=30℃
1) For loose, clean (without fines) sand (Hazen,1930):
k (cm/sec) = c * D210
c = a constant that varies from 1.0 to 1.5
D10= effective grain size in mm
2) For fine to medium, clean sand (Casagrande, 1967)
k = 1.4 * e2 * k0.85
k = permeability factor for e void ratio
k0.85 = permeability factor for e void ratio equal to 0.85
3) The Kozeny-Carman equation for sandy soils:
c1 = a constant
It has been found that: C1 = C2 * D2.3210 * Cu0.6
D10 = effective grain size
Cu = uniformity coefficient
C2 = a constant
4) For normally consolidated clays (1982):
where C3, n = constants
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