Geotechnical News • March 2012
43
fied by equating the Fluid Mechanics
parameter, hydraulic radius, to the Soil
Mechanics ratio of pore volume to
surface area of all the grains. Once in
the pipe analogy mode it is a simple
matter to determine permeability from
a combination of the Darcy-Weisback
formula and the Colebrook equations
for surface roughness (e/D = 0.05
adopted herein). Flows ranging from
laminar to turbulent are assigned based
on R
e
, or where transient conditions
are sometimes found to be appropriate
for coarse sands.
C.
The programprovides the following
output:
Figure 17 is a plot of three sets of data
points produced by the computer pro-
gram EPWPGRAD. The soil grada-
tion is what I call fully proportionate,
with a grain size ranges from 75mm
down to 0.002mm. What I mean by
fully proportionate is that each size
is equally represented with respect to
dry weight. In other words this is a
perfectly well graded silt and sand and
gravel.
A range of packing densities (e = 0.4,
0.5 and 0.6) was evaluated for the
purpose of illustrating the strong influ-
ence of this parameter. The permeabil-
ity for each of these “specimens” at
20°C was calculated for the appropri-
ate flow type (laminar to turbulent)
using the built-in PERMSOIL subrou-
tine. The Crowding Factor found for
these void ratios (respectively) were in
the ranges: 6.4 to 10.9; 3.6 to 6.7; and,
2.3 to 4.5.
The plot in Figure 17 shows the
theoretical relationship linking rates
of movement between the phases
with the pressure generated in the
water phase as it opposes motion. The
magnitude of pore pressure generation
is shown in terms of gradient, and this
is because it is built up, one particle
after another in sequence, increasing
progressively in the direction of the
relative motion of the solid phase. It
is only the pressure component (F
p
)
which is involved here, since the
viscous component (F
b
) cannot be seen
by pressure sensitive devices.
Figure 18 shows how each of the two
separate hydrodynamic components,
that is, viscosity and pressure, contrib-
ute to the overall resistance. Here it
may be seen that for the range of con-
ditions depicted, pressure is the domi-
nant component, and the contribution
of viscosity becomes less as velocities
increase and void ratios decrease.
Deformation
Up to this point the computations have
been dealing with the type of motion
that is best described as translational
– the case of an intact, and unchang-
ing, arrangement of separate particles
which make up a stable soil-structure
moving as an undisturbed fixture
through water. As seen in Figure 17
void ratio is a sensitive parameter in
this context. And so, to put a number
on the additional contribution made by
soil-structure deformation to pressure
generation, the procedure involves
looking at void ratio changes, which
are an accompaniment of deformation,
as the key to the solution.
From the data plotted in Figure 17 it
can be seen, for any chosen rate of
relative motion, that the pore pressure
increases with decreasing void ratio.
This is what we know as contrac-
tive behaviour. Similarly, it can be
seen that dilation would cause pore
pressure reduction; again, something
which fits well with accepted and
rational ideas. And finally, needless to
say, if there are no void ratio changes
then there is no reason to expect other
than translational pressure changes in
the pore water.
What this suggests therefore is that
in order to evaluate the response of
pore water to deformation we need
to superimpose the effects of void
ratio changes on those associated with
translation of the intact structure as
it moves relative to the fluid phase.
As a consequence of this reasoning,
the methodology I propose for the
evaluation of pore pressure changes
(either positive or negative depending
on whether the soil-structure responds
to the deformation in a contractive or
dilative way) is to first create a trans-
lational plot, and from this, determine
the magnitude and rate of additional
pore pressures contributed by how the
void ratio alters with time.
Hydraulic gradients
The most important fact to bear in
mind about pore water pressure is that
a hydrostatic pressure distribution has
no influence whatever on the behav-
iour of the soil-structure, however
loose and unstable. I’ve been down to
135 feet in open water protected by no
more than swim trunks and experi-
enced no distress whatever because of
the added 58 psi (400 kPa) of water
pressure. And I’m sure enough that
mineral grains of quartz aren’t any
more sensitive.
In still open water there is no hydrau-
lic gradient. A deeply submerged
slope will have very high pore water
pressures, but they are irrelevant if
there is no pressure differential across
the bottom/ground, such as might be
brought about by the passage of storm
waves. Otherwise it is like standing in
still air under atmospheric pressure.
You are not aware of the air pressure -
and, it isn’t until a wind picks up that
you know the air is there at all. So,
being told the pore water pressure at a
single point in the soil is of little use
to us. We need data from at least three
separate points to know the hydrau-
lic gradient magnitude and direction
(vector) before we can have some idea
about what might be going on.
Figure 19 was prepared to illus-
trate the similarities and differences
between seepage forces and forces
generated during two-phase rela-
tive motion. The top sketch shows a
permeameter, which is the laboratory
equivalent of steady state seepage, as
for instance under a dam. The hydrau-
lic gradient is the locus of the pressure
head along the flow direction; it is
parallel to the “energy line” and lies
below it by an amount equal to the
velocity head. There’s nothing new
