Geotechnical News June 2011
47
GEO - INTEREST
the Water in the Soil – Part 3
Bill Hodge
While working on this approach to
try and figure out where pore water
pressure comes from, and how it might
be calculated, the realization that
hydrodynamics is a necessary part of
Soil Mechanics became increasingly
obvious. In hindsight I’m surprised it
took me so long to come to appreciate
how crucial a partner Fluid Mechanics
is of Soil Mechanics, especially when
it should have been clear from the start
that deformation of a saturated soil-
structure is basically a matter of water
moving around obstructions.
In the last article I used the Coeffi-
cient of Drag [C
D
] to calculate the forc-
es acting on a solid as it moved through
water. This is of course a term bor-
rowed from our hydraulic colleagues.
Now in this article I want to transform
that term into our own language and
rules of behaviour.
But first, in order to be able to work
effectively with hydrodynamics it is
necessary to become reacquainted
with another of their key terms without
which it would be all but impossible to
advance.
a Word about the Reynolds
Number
I’ve tried to keep away from this
parameter which for most practicing
geotechs will be all but a silent echo
from student days. But the Reynolds
Number [R
e
] is too useful to be
done without. And there is no good
substitute to replace it. Once I found
the need to invoke the ideas and tools
of hydrodynamics I knew I had to learn
to live with the Reynolds Number too.
Back in 1938 Hunter Rouse pub-
lished a curve relating C
D
values for
rough spheres to R
e
. His curve is re-
produced here as the grey line in Figure
7. Fortunately, it covers the full range
of practical interest to us.
Conveniently too, as it turns out, for
geotechnical purposes the value of R
e
is given to an accuracy of two decimal
places by the simple multiple:
R
e
= D v
provided the diameter “D” is in
millimetres, the relative velocity “v” is
in millimetres per second, and the water
temperature is about 20° C. These
conditions result in the combination
of the other hydraulic parameters
becoming equal to unity.
the Problem with Drag
The idea of simply adopting C
D
wholesale made me a bit nervous.
Nervous, mainly, because I had no feel
for it. It’s not something I’d ever used
in the field, like cohesion or friction - a
parameter I could pull out of my head
for a back-of-the-envelope estimate on
the run. At liquefaction velocities this
parameter can vary from 3,000,000 for
fine silt, to less than 0.4 for gravel - and
for no good reason intuitively apparent
to me.
I felt the need to find some way of
relating to the basic physics behind this
widely (I might say wildly) varying
parameter. And preferably, if it were
ever to be confidently adopted in prac-
tice, then in a geotechnically analogous
way. As it turned out, there are two
geotechnical mechanisms with which
we are all familiar and which can be
used to get quite close to replicating
this very useful, but rather intimidating
parameter. The two geotechnical anal-
ogies I found that fitted the bill were
bearing capacity of foundations, and
standpipe piezometers.
Bearing Capacity
Anyone who dived into the water from
a bit too high up doesn’t need to be
told that water resists penetration. It’s
all a matter of speed of entry. This is
because water is viscous and therefore
its resistance to penetration increases
with the rate at which it has to deform.
So the thought arose that the interaction
of a particle moving in water might
be equivalent to steady state bearing
capacity displacement, where the
strength of the “foundation” was
proportional to the rate of straining.
So lets consider that the Drag Force
on a sphere, or maybe just some sig-
nificant fraction of it which I’ll call
the Bearing component [F
B
], is simply
equal to the ultimate bearing capacity
[q
ult
] of a circular footing of the same
size. In normal terminology this is:
F
B
= q
ult
A = c N
c
A
where: c shear strength
N
c
bearing capacity factor
A equatorial area of sphere.
To make this work two shear
strength terms need to be related across
the disciplines: How could soil shear
strength “c” be expressed in terms of
water viscosity “μ” ? Both these terms
are defined as resistance to shearing
force, it is only that the latter is also
directly dependent on the rate of strain-
ing, and consequently has stress-time
