MEASUREMENT OF PERMEABILITY
BY FALLING-HEAD PERMEAMETER
A specimen of soil is placed in a falling-head permeameter. The specimen has a cross-
sectional area of 66 cm^2 and a height of 8 cm; the standpipe has a cross-sectional area of
0.48 cm^2. The head on the specimen drops from 62 to 40 cm in 1 h 18 mm. Determine the
coefficient of permeability of the soil, in centimeters per minute.
Calculation Procedure:
- Using literal values, equate the instantaneous discharge
in the specimen to that in the standpipe
The velocity at which water flows through a soil is a function of the coefficient of perme-
ability, or hydraulic conductivity, of the soil. By Darcy's law of laminar flow,
v = ki (2)where / = hydraulic gradient, k = coefficient of permeability, v = velocity.
In a falling-head permeameter, water is allowed to flow vertically from a standpipe
through a soil specimen. Since the water is not replenished, the water level in the stand-
pipe drops as flow continues, and the velocity is therefore variable. Let A = cross-section-
al area of soil specimen; a = cross-sectional area of standpipe; h = head on specimen at
given instant; H 1 and H 2 = head at beginning and end, respectively, of time interval T; L =
height of soil specimen; Q = discharge at a given instant.
Using literal values, we have Q = Aki = -a dhfdt.
- Evaluate k
Since the head h is dissipated in flow through the soil, i = h/L. By substituting and rear-
ranging, (AkIL)dT= - a dhlh\ integrating gives AkTIL = a In (H 1 Ih 7 ), where In denotes the
natural logarithm. Then
aL hl
k=
^l
«Y 2(3)
Substituting gives k = (0.48 x 8/66 x 78) In (62/40) = 0.000326 cm/in.
CONSTRUCTION OF FLOW NET
State the Laplace equation as applied to two-dimensional flow of moisture through a soil
mass, and list three methods of constructing a flow net that are based on this equation.
Calculation Procedure:
- Plot flow lines and equipotential lines
The path traversed by a water particle flowing through a soil mass is termed a flow line,
stream-line, or path of percolation. A line that connects points in the soil mass at which
the head on the water has some assigned value is termed an equipotential line. A diagram
consisting of flow lines and equipotential lines is called a flow net.