Permeability

It is the property of the soil which allows passage of fluid through it

Permeable soil: When a soil has continuous voids.

Example: Gravel , sand 

• A soil is said to be highly permeable when K> 10-1 cm/sec.
• Soil is said to be impermeable when K< 10-7 cm/sec.
• Example: stiff clay

Darcy’s law: For flow through soils

V=ki or Q=k.i.A.

Where

• V = discharge velocity of flow = Q/A = Discharge /Area
• i = hydraulic gradient = AhIL = loss of head per seepage length
• A = perpendicular cross sectional area
• “V” is called discharge velocity or superficial or fictitious velocity
• k = Coefficient of permeability--cm/sec or mm/sec
• When i= 1 ,V=k
• :. k is velocity of flow under unit hydraulic gradient

Validity of Darcy’s law:

• For laminar flow conditions only
• Generally, laminar flow will prevail in clays, silts and fine sands.
• Flow will be laminar as long as Reynolds number <1, when Re is calculated considering characteristic length as the average particle diameter.

Seepage velocity(V) or actual or true velocity:

• Vs = Discharge/Area of voids
• Vs = V/n = Discharge velocity/porosity
• Vs is always greater than V.

Coefficient of percolation(kp):

• Vs ∝ i ∴  Vs =k.i
• kp= coefficient of percolation = k/n
• ∴ kp >k

Where 

• Ds = effective grain size  = D10
• yw= unit weight of percolating liquid
• e = void ratio 
• C = shape constant depends upon type of soil, shape of soil particle and packing. 
• u= viscosity of percolating fluid “

Factors affecting k:

1. Size of particle : k  ∝  D102.
2. Shape of particle : For same void ratio, the soils with angular particle are less permeable than those with rounded particles, k is inversely proportional to specific surface area
3. Void ratio: k ∝ e3/1+ e                                                                                        >>Paradoxically, the soils with largest void ratio (clays) have less permeability.
4. Properties of percolating fluid: k = y
   w/
    u
                                                                                                                        
   Viscosity changes drastically with 
   temperature                                                                                                     
   k is reported at standard temperature of 
   27°C as per Indian Standards.                                                           
   

• kt = permeability at temperature of t°C when viscosity is ut
• k27 = permeability at temperature 27°C when viscosity is u27 permeability increases with an increase in temperature due to reduction of the viscosity.

Degree of saturation : Permeability of partially saturated soil is considerably smaller than that of a fully saturated soil dueto presence of air.

>>Adsorbed water: Adsorbed water or diffuse double layer decreases permeability

Determination of permeability : by using permeameter.

Constant head test:

• Suitable for coarse grained soils like Gravel, sand with k> 10-1 cm/sec
• head is kept constant and the discharge is measured, knowing the head causing flow, the hydraulic gradient ìs calculated. The “k” is determined using the formula,

Q=k.i.A.

Variable head test:

• For fine sands and silts with k = 10-2 to 10-4 cm/sec.
• Discharge is not required to be measured.
• k is calculated using the formula 
  

Where, a = area of stand pipe

L = length of soil specimen

a = cross sectional area of soil specimen

t2-t1 = time interval in which head drops from h1 to h2.

Consolidation test data: Suitable for clays with k < 10-6 cm/sec

Capillary-permeability test:

• Suitable to find k of partially saturated soil.
• Capillarity and permeability both can be found.

Pumping out test:

• Most accurate among all tests, since large area surrounding the well is influenced.
• Used for large engineering projects.
• It is expensive

Pumping ¡n test:

• Commonly used for testing rocks and individual stratum.
• Example: Open-end test, Packer test(for rocks)

Permeability of stratified soil deposits:

(a) Flow parallel to planes of stratification

• Loss of head or hydraulic gradient is same for all layers.
• Total discharge, Q = q1 + q2 + q3
  

(b) Average permeability for perpendicular to flow, kv.

kh is always greater than kv