Geotechnical Engineering

DHARM

SOIL MOISTURE–PERMEABILITY AND CAPILLARITY 119

75. According to Scheidegger, the probable reason that porous media do not exhibit a definite
    critical Reynold’s number is because soil can be no means be accurately represented as a bun-
    dle of straight tubes. He further discussed several reasons why flow through very small open-
    ings may not follow Darcy’s law.
    There is overwhelming evidence which shows that Darcy’s law holds in silts as well as
    medium sands and also for a steady state flow through clays. For soils more pervious than
    medium sand, the actual relationship between the hydraulic gradient and velocity should be
    obtained only through experiments for the particular soil and void ratio under study.

5.4.3 Superficial Velocity and Seepage Velocity

Darcy’s law represents the macroscopic equivalent of Navier-Stokes’ equations of motion for

viscous flow.

Equation 5.11 can be rewritten as :

q

A

= k.i. = v ...(Eq. 5.12)

Since A is the total area of cross-section of the soil, same as the
open area of the tube above the soil, v is the average velocity of down-
ward movement of a drop of water. This velocity is numerically equal
to ki ; therefore k can be interpreted as the ‘approach velocity’ or ‘su-
perficial velocity’ for unit hydraulic gradient. A drop of water flows at
a faster rate through the soil than this approach velocity because the
average area of flow channel through the soil is reduced owing to the
presence of soil grains. This reduced flow channel may be schematically
represented as shown in Fig. 5.3.

By the principle of continuity, the velocity of approach, v, may
be related to the seepage velocity or average effective velocity of flow,
vs, as follow :

q = A. v = Av. vs

where Av = area of cross-section of voids

∴ vs = v A

A

v AL

AL

v V

V

v

vv vn

.. .===

vs = v/n = ki/n ...(Eq. 5.13)

where n = porosity (expressed as a fraction).

Thus, seepage velocity is the superficial velocity divided by the porosity. This gives the
average velocity of a drop of water as it passes through the soil in the direction of flow ; this is
the straight dimension of the soil in the direction of flow divided by the time required for the
drop to flow through this distance. As pointed out earlier, a drop of water flowing through the
soil takes a winding path with varying velocities ; therefore, vs is a fictitious velocity obtained
by assuming that the drop of water moves in a straight line at a constant velocity through the
soil.
Even though the superficial velocity and the seepage velocity are both fictitious quanti-
ties, they can be used to compute the time required for water to move through a given distance
in soil.

v

vss

v

GrainGrain GrainGrain

PorePore

Fig. 5.3 Flow channel