Geotechnical Engineering

DHARM

SEEPAGE AND FLOW NETS 199

SUMMARY OF MAIN POINTS

1. Flow of water through soil under a hydraulic gradient is called ‘‘Seepage’’.


2. A flow net is a system of squares or rectangles formed by flow lines intersecting equipotential
   lines.


3. The rate of flow is given by q = k. H. s, where s, the shape factor (= nf /nd), is provided by the flow
   net.


4. The basic equation for seepage is Laplace’s equation: ∂
   ∂

∂

∂

2

2

2

2

h

x

h

z

+ = 0 (for isotropic soil). A flow

net is simply a solution of this equation for a given set of boundary conditions.

5. Functions which satisfy Laplace’s equation are called ‘Conjugate harmonic functions’.


6. From a flow net one can obtain (a) rate of flow, (b) pore pressure, and (c) gradient.


7. In anisotropic soil, the section must be transformed, using XT = kkzx/. x; the effective perme-
   ability, ke, is then given by kkxz.


8. The flow through an earth dam is bounded by a top flow line or phreatic line, which is deter-
   mined first. The location depends upon the drainage conditions at the downstream toe and the
   inclination of the discharge face. The phreatic line mostly follows the base parabola of Kozeny,
   with slight modifications at the beginning and the end, as given by A. Casagrande.


9. The flow around a circular well constitutes a radial flow net.


10. Graphical method of sketching by trial and error and analogy methods are important among the
    methods of obtaining flow nets.


11. ‘‘Quick’’ refers to a condition wherein a cohesionless soil loses its strength because the upward
    flow of water makes the effective stress zero; the hydraulic gradient at which this condition is

imminent is called the critical one, and is given by ic =

()

()

G

e

−

+

1

1

12. The seepage force per unit volume of the soil is i. γw and (for isotropic soil) acts in the direction
    of flow.

References

1. A. Casagrande: Seepage through Dams, JI. New England Water Works Association, June, 1937.
   Reprinted by Boston Society of Civil Engineers, Contributions of Soil Mechanics, 1925 to 1940.


2. P. Forchheimer: Hydraulik, 3rd ed., Leipzig, Teubner, 1930.


3. G. Gilboy: Hydraulic Fill Dams, Proc. Int. Comm. on Large Dams, World Power Conference,
   Stockholm, 1933.


4. M.E. Harr: Ground Water and Seepage, McGraw Hill, 1962.


5. A.R. Jumikis: Soil Mechanics, D. Van Nostrand Co., Princeton, NJ, 1962.


6. K.S. Kozeny: Grundwasser bewegung bei freiem Spiegel, Fluss und Kanalversicherung, Wasserkraft
   und Wasserwirtschaft, No. 3, 1931.


7. T.W. Lambe and R.V. Whitman: Soil Mechanics, John Wiley & Sons, Inc., NY, 1969.


8. D.F. McCarthy: Essentials of Soil Mechanics and Foundations, Reston Publishing Company,
   Reston, Va, USA, 1977.