Geotechnical News December 2011
51
GEO - INTEREST
the Water in the Soil - Part 5
Bill Hodge
In the earlier articles of this series
the talk was mainly about idealized
particles, and it wasn’t until Part 4 that
real soils (sands) entered the argument.
As a practicing Geotechnical Engineer,
idealization is of passing interest: If it
can’t be used in the field [practice] it’s
really irrelevant. And, so saying, it’s
now time to move from contemplating
single solid spheres and advance into
the confusing realm of natural soils.
The key to making that move is what
I’ve called the Crowding Factor, with
the label “K”. The reason for giving it
this name is that its function is to ac-
count for all the hydrodynamic differ-
ences between the magnitude of drag
forces exerted on a single solid particle
moving against free/open water, and
the same particle interacting with the
much restricted pore water within the
confines of a soil-structure void space.
What the Crowding Factor needs to
do is to make it possible to take what
we can learn from Fluid Mechanics and
be able to use it to our benefit in Soil
Mechanics.
Possible Ways of Evaluating
“Crowding”
My initially thoughts on how to
go about assigning values to this
parameter “K” ranged from theoretical
to empirical.
To start with, it seems pretty clear
that what most changes in the imme-
diate hydraulic environment of a par-
ticle, between its state as a single mass
moving through boundless water, and
its radically more confined state within
a soil-structure, is the velocity of the
water interacting with it. In the soil the
water is speeded up while the particle’s
own velocity is not.
This suggests that for any approach
to find justifiable values for the Crowd-
ing Factor the obvious target for ma-
nipulation is velocity. Here, it may be
recalled, that both the Bearing [F
B
] and
Pressure [F
P
] components of drag are
functions of velocity, in the latter case,
to the second power. Apart from the
fairly fixed physical attributes of water,
the only other significant variable in
these components is particle size.
The first thing that came to mind
was how we normally convert open
water flow, the approach velocity [v
A
],
to the equivalent constricted pore space
flow, the void velocity [v
V
]. And that is
simply to take it that for any given rate
of flow the velocities are inversely pro-
portional to the cross-sectional areas
available to them. So where the void
ratio of the soil mass is “e”, we get the
average void velocity by multiplying
the approach velocity by (1+e)/e. For
instance, if we were to apply this rule
to the loosest (e=0.91) array of uniform
spheres we would get a void velocity
2.1 times faster than the approach ve-
locity; and, for the densest (e=0.35)
packing that ratio would equal 3.9.
This simple calculation would sug-
gest that in the loosest packing the
crowding effect would increase the
value of the Pressure component (F
P
),
by a factor of 4.4. This component, you
may recall, is the one I associate with
pore pressure generation, and which is
proportional to the square of the veloc-
ity. The equivalent multiplier for the
densest packing would be 14.9.
If it were not for the fact that the di-
ameter “D” is also part of the F
B
term I
might have been tempted to just leave
it there, that is, go on to assume void
space was the only consideration. So,
where to look next ?
The ConeTec cylinder was available
to me and as it had the capability of
recording the water pressures in front
of an object as it fell through a water
column, the opportunity was there to
measure the comparative effects of
dropping an array of spheres rather
than a single ball. The thought was to
drop arrays of ball bearings while re-
cording the pressure front as the comß-
posite mass approached the transducers
implanted in the base of the cylinder.
By running a series of tests, where
the results of various array geometries
and spherical sizes could be compared
with the theoretical drag forces for that
particular particle size, the Crowding
Factor would be known for that case.
It is obvious that a great deal of testing
might be required to produce useful an-
swers, and these data would for practi-
cal reasons cover only manageable siz-
es such as fine to coarse gravels. Silts
and sands would be out of the question
because of the minute size of the indi-
vidual elements of the array. Another
practical difficulty in this research ven-
ture would have been the unavoidable
effect the housing (containing the ar-
ray) would have on the data, and then,
how on earth could a means be found to
abstract that influence.
