Laboratory determination of the coefficient of permeability

There are 2 general types of permeability test methods that we can perform in the laboratory.

1) Constant head permeability test. ( for high K soils)
2) Falling head permeability test. ( for low K soils)

1). Constant head permeability test 

In this test method our water levels are constant. Basically this test is used to determine the coefficient of permeability for sandy soils which means soils with high coefficient of permeability. It is possible to perform this test both disturb and undisturbed samples.

Allow the system to reach the equilibrium (steady) state condition. Once the equilibrium state reach, collect water to a graduate flask within a time "t". change the head "h" and repeat the procedure to get few more readings.

Calculations

We can calculate the coefficient of permeability by using this equation,

K = QL/Aht

where,
K = coefficient of permeability
L = length of the specimen
t = time for discharge
Q = volume of discharge
A = cross section area
h = hydraulic head difference
 
2). Falling head permeability test 

In this test method the water level should be constant during the test. Basically this test is used to determine the coefficient of permeability for clayey soils which means soils with low coefficient of permeability.Porous stones are use to supply uniform pressure to the sample. We need to setup the equipments and keep few days to saturate the sample and to expect the steady state.

Calculations 

Assume within time dt water level drop dh,

H = p/gamma w + z

H1 = (h+X-L)*gamma w/gamma w + L
H1 = h + X

H2 = X*gamma w/ gamma w + 0
H2 = X

therefore head difference (delta h) =  H1 - H2
                                                        =  -X + (h+X)
                                                        =  h
using darcy's law,
V = K i
V = K h/L

and
Q = VA


therefore,
Q = Kh/L * A

but
Q = a dh/dt

we measure head up-word from datum but Q measure down-word,
therefore,
Q = - a dh/dt
- a dh/dt = K A h/L ( because Q = Kh/L * A)
dt = - aL/AK (dh/h)

this is a equation of a straight line Y = mx + c 

by the gradient of this graph we can easily find the K.




m = tan (theeta)
tan (theeta) = a*L / A*K
K = a * L / A tan (theeta)