Geotechnical News March 2011
63
GEO-INTEREST
ers. And I suppose, as the grains come
to rest again, for an instant at least, the
weight could even increase a bit.
How the Prediction was Made
Despite the fact that apparatus
resonance and boundary conditions
obscured what would otherwise have
been a clearer picture, I was quite
happy with the comparison between
the history of load cell output and the
prediction.
The prediction was made on the
simple assumption that the weight
shown on the scales would be equal to
the resistance offered by the water to
the falling ball.
In Fluid Mechanics a hydrodynamic
force is known to act in resistance to
solids moving through fluids. Our sis-
ter technology tells us how to deter-
mine the magnitude of that Drag Force
[ F
D
] for any relative velocity between
the two phases (solid and liquid). This
force is calculated using their equation:
F
D
= C
D
ρ
A v
2
/2
where:
C
D
Coefficient of Drag
ρ
mass density of fluid (water)
A equatorial area of the solid
(ball)
v relative velocity of fluid and
solid.
Of these four variables “
ρ
” is virtu-
ally a constant (1000 N/m
3
) over the
range of temperatures we’re interested
in. We pick the value of “A”, or rather,
the diameter of the sphere we want to
look at. The relative velocity is the in-
dependent variable we want to track.
For the moment I’ll not show you
the standard Fluid Mechanics way of
presenting the range of values for C
D
,
and I’m withholding it for two reasons.
First, it is such an ugly looking log-log
plot related to that rather obscure hy-
draulic leveller, the Reynolds Number,
that I’m afraid any interest the normal
geotechnical reader might have in this
idea would evaporate on the spot. Sec-
ondly, in the next article I will propose
what I believe to be a better, more in-
tuitively acceptable, way for us to view
C
D
. This “geotechnical” version of the
Hunter Rouse relationship, while giv-
ing the same values as the original for
the spherical solids I’m dealing with
here, also opens a door to important in-
sights into other hydrodynamic aspects
of Soil Mechanics.
Using the above
equation I wrote
a simple computer program (“BALL-
FALL.exe”) to determine the position
of the ball, and the force acting on it at
any time I wanted during its progress
from stationary to Terminal Velocity.
That’s where the data for the red curve
comes from. This program is freely
available from Geotechnical News for
anyone who wants it.
The conclusion I draw from the rea-
sonable correspondence between the
test readings and the calculated values
is that the water in front of the moving
solid carries a compressive force which
is just about equal to the drag resis-
tance offered by the water to the mov-
ing particle. Furthermore, I believe this
reveals the actual physical mechanism
of pore water generation within satu-
rated soils experiencing deformation.
Pore pressure generation is simply
a matter of hydrodynamics. And when
you think about it, how could it be oth-
erwise ?
What this Approach says about
Liquefaction
The program BALLFALL does the
calculations needed to construct the
curve in Figure 6. This relationship
is for a spherical particle of specific
gravity 2.65 falling through 20° C
water. The x-axis covers the range of
diameters of interest to us. The y-axis
gives the amount of fall required to
transfer 99% of the particle’s weight to
the water; for convenience this value is
shown in terms of the ratio of the fall
distance to the particle diameter.
The ratio 0.29 is highlighted because
it is theoretically a readily achievable
amount of fall. This is the amount of
free drop which is available when the
idealized loose packing of spheres con-
tracts to the stable dense packing, in-
volving a void ratio change from 0.91
to 0.35. And this geometric fact imme-
diately suggests an interesting proposi-
tion: If this same density change were
suddenly brought about in a saturated
fine rounded sand by some triggering
event, then the condition necessary for
liquefaction of the mass would exist
during the transformation.
Although I intend to limit myself
to dealing with manageable geometric
shapes I should say here that I think
the more angular shapes of natural
grains make them more vulnerable to
this effect, and this is because of the
larger voids that can exist between less
rounded particles. So on this basis I
don’t have difficulty in thinking very
loose sand-sized deposits, for instance,
pro-glacial sands, or some dredged
fills, could very easily liquefy once the
saturated soil-structure gets a serious
jolt, or more to the point, as I discuss
in a later article, is exposed to a surface
wave.
Looking further along the x-axis of
Figure 6 to the coarse sand and gravel
size range you can see that the ratio of
fall-to-diameter is above 10. This im-
plies that a gravel, of say 1 inch size,
would need to find an open space of
about 10 inches depth beneath it to
fully shed its weight, and thereby, its
frictional capacity. It is very difficult
for me to imagine any geotechnical
circumstances, whether natural or ar-
tificial, where almost a foot of open
space could exist in a gravel deposit.
This tells me that the idea of gravel
size deposits liquefying is unreason-
able. Of course in the case of a debris
flow, that’s quite another matter, and
one which I hope to return to later in
this series.
Along the same line of reasoning,
how a well graded deposit of any type
could liquefy I find quite unimagi-
nable. Even if the finer particles found
room to lose their weight these would
entail only a small loss of the general
frictional capacity, the loss being pro-
portional to the relative volume they
contributed to the overall soil mass.
Within such an aggregate there is just
nowhere the larger particles could drop
unhindered.
Summary of Practical
Implication
What the foregoing hydrodynamic
line of reasoning says to me about
liquefaction is that:
