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Geotechnical News March 2011
GEO-INTEREST
is seen as the cyclical waveforms su-
perimposed on the record of the ap-
paratus weight. Anyway, looking past
the superimposed waves, it can be seen
clearly enough that within a short time
the weight of the system comes climb-
ing back towards its pre-release weight.
The excitement at the end of the trace is
the crash when the ball runs into a sand
buffer at the bottom of the cylinder.
The waveforms due to system reso-
nance are a bit of a nuisance and are
a result of using a ball too big for the
overall mass of the system. Basically,
in hindsight, the cylinder was too small
for the size of the ball. And also, apart
from vibrations, I should think it likely
there are boundary interference effects
involved which contaminate the data.
So what is being done at the moment to
remove these undesirable attributes is
to build a much longer and wider cyl-
inder where the water pressure ahead
of the ball is measured with an array
of pressure transducers distributed
about the base. Here, David Woeller of
ConeTec has come to my aid by con-
tracting Ron Dolling of Adara Systems
to build this new apparatus, and most
generously, donating it to this effort. So
more and better data is on its way.
In any event, I believe there is al-
ready enough confirmation from the
UBC results to answer the Three Bea-
ker question, and to keep moving for-
ward with this idea.
Interpretation of UBC Results
As the load cell was set to read zero
after all the objects contributing to the
mass of the experimental setup were in
place, any weight change subsequently
showing up from this initial static
condition would need to be explained
in terms of a force arising out of the
dynamic activity within the system.
So as I see it, what went on inside the
cylinder to explain the recorded trace
may be understood as follows.
The instant the ball is released by
the electromagnet its buoyant mass
is set free in
the gravitational field. In
consequence, being instantaneously
exposed only to gravitational attraction
it begins to accelerate at a rate of “g”
towards the centre of the earth. There-
fore, since the ball is at this first instant
in absolute free-fall there is no net ac-
celeration acting on the mass to give it
weight. This situation can be expressed
as
Weight = m ( g – g ) = 0
This is why the load cell suddenly
loses awareness, or fails to perceive,
the ball’s existence at the instant the
electromagnet drops it. The next thing
that happens – really it begins to hap-
pen simultaneously with the ball being
set free - is that the ball starts to move
downwards in response to gravity.
Once relative motion is initiated
between the two phases, the water be-
comes aware of the ball’s presence and
tries to obstruct its further intrusion.
This is because, as a viscous fluid,
the water opposes the cavity expan-
sion imposed on it by the progress of
the ball through its domain. This op-
posing force we call hydraulic drag.
Now, and this is the essential point:
In order to support these drag forces it
is then necessary that the water below
the ball provide an equal and opposite
reaction. It is this drag force reaction
which shows up as increased weight on
the load cell. The only way the water
can convey this load is by compressive
pressure. And I believe this is a clear
example of the very same mechanism
which accounts for excess pore water
pressure in saturated soils.
If there is enough open water be-
low the falling ball it then becomes a
competition between gravity and drag,
the one trying to increase the speed of
fall, the other trying to slow it down.
And the drag force, being proportional
to the square of the ball’s velocity, is
bound to win in the end. With enough
fall distance they come to a standoff
when the speed of the ball reaches the
point where the increasing drag forces
rise to become equal to the buoyant
weight of the ball. This familiar con-
dition we know as Terminal Velocity
[v
T
].
Terminal Velocity &
Liquefaction
In our line of business at present, we
come across the concept of Terminal
Velocity in the hydrometer test where
Stokes’ Law provides the relationship
between small spheres and their v
T
values, thereby allowing us to calculate
the size distribution of silts. But
now perhaps there is another more
interesting use for it. And that is as a
criterion for liquefaction.
I think that attaining relative veloci-
ties of v
T
for particular sized particles is
a necessary condition for saturated soils
composed of those particles to liquefy.
This is simply because at v
T
the entire
buoyant weight of the particle has been
transferred to the water, thus rendering
it effectively weightless. Weightless
particles can have no frictional capac-
ity because there is no normal force to
impart to neighbouring particles. In es-
sence, they have become dominated by
the enveloping water, and functionally
a part of the fluid. In a word, liquefied.
A consequence of this line of rea-
soning is that it is only uniformly grad-
ed soils that are prone to liquefaction.
This seems to be so because if different
sizes were involved in the mix it is hard
to imagine how they all could attain v
T
at the same time without moving past
one another.
For some time past I’ve been hop-
ing to establish an axiom of saturated
soil behaviour that says: Increasing
pore water pressure is not the
cause
of failure – it is the
result
of failure.
In the particular case of the liquefac-
tion-type failure discussed above that
seems to be true. This is because the
triggering event in the sequence is the
failure of the soil-structure to prevent
a particle from falling. It is only after
the fall that water pressure begins to in-
crease. Whether that argument can be
sustained in the more general case of
non-catastrophic soil-structure defor-
mations I’ll have to try and sort out as
we go along.
Answer to the Three Beaker
Question
This UBC lab test was designed to
replicate the essential situation in the
Three Beaker question, and that is,
what weight would show up on the
scales during collapse of the soil-
structure?
After this effort it seems the answer
is that at the moment of collapse the
weight drops. It then gradually recov-
