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© 2005 Nature Publishing Group
Vol 437|29 September 2005
635
Liquefaction of quicksand under stress
A person trapped in salt-lake quicksand is not in any danger of being sucked under completely.
People or animals caught in quicksand find it
very hard to escape
1
. Here we show that quick-
sand acts as a trap because it becomes unstable
when it is forced to move — first it liquefies,
and then it collapses. But a simple sinking test
demonstrates that it is impossible for a human
to be drawn into quicksand altogether.
The natural quicksand that we study here
consists of fine sand, clay and salt water. Rheo-
metrical tests (Fig. 1a, b) reveal its extreme
sensitivity to very small variations in stress.
At rest, its viscosity slowly increases with time
— a behaviour characteristic of clays
2,3
. This
reflects the formation of a fragile colloidal
gel that has a random, delicately balanced
structure. At higher stress, a spectacular lique-
faction of the material takes place: the steady-
state viscosity changes by several orders of
magnitude for a variation in stress of less than
1%. The higher the stress, the more liquid
the quicksand becomes, so movement by a
trapped body causes it to sink in deeply.
Why is it that, once sunk in quicksand, it is
so difficult to escape? Because the apparent
viscosity of quicksand increases after the initial
stress-induced liquefaction, unlike that of clay
or sand alone
3,4
. After liquefaction, the quick-
sand is seen to segregate into a water-rich phase
and a sand-rich one. The apparent viscosity
increase is therefore due to the formation of
sand sediment, which has a very high volume
fraction (
0.8) and viscosity. It is the diffi-
culty of moving this densely packed, wet sand
that leads to trapping. Water must be intro-
duced into the compacted sand to liquefy it,
which requires huge forces: to introduce water
at a speed of 1cms
1
, say, a pressure of 10
6
pas-
cals (Pa) is needed
1
, assuming a typical sand-
pore size of 10 m. To pull out a foot at this
speed, a force of some 10
4
newtons is required
— about that needed to lift a medium-sized car.
By mixing sand and clay in salt water, a
laboratory quicksand can be
created with a structure that
reproduces the behaviour of
natural quicksand. It is just
strong enough to support the
weight of an adult person
1
at a
very low volume fraction of
sand (
0.4): the correspond-
ing stress of about 510
4
Pa is
similar to the measured elastic
modulus of quicksand (Fig. 1c).
This very loosely packed sand
does not collapse under its own
weight owing to the yield-
stress of the colloidal clay gel.
However, if the delicately bal-
anced structure is perturbed,
the gel will liquefy, rendering
the packing of the sand unsta-
ble and leading to collapse
5
.
Salt is an essential ingredient
for the collapse in laboratory
and natural quicksand —the
latter originates from salt lakes
whose salinity is close to that of
the Dead Sea. The salt destabi-
lizes the colloidal gels, causing
the colloids to flocculate
2
,
which subsequently destroys
the granular network.
We also simulated someone
moving in quicksand to see
whether — once partially sub-
merged — the victim would
sink helplessly beneath the surface. A sinking
test
6
was used in which the speed at which
an aluminium bead (radius r2 mm) sinks
into quicksand is measured. At rest, the
bead remains on the surface, although it has
a higher density (
) than the quicksand
(2.7 g ml
1
compared with 2 g ml
1
). If the
whole system is mechanically shaken to mimic
movement in the quicksand, the results agree
with the rheological findings (Fig. 1a, b). At
small amplitudes (acceleration a3.16 m s
2
),
the bead stays afloat; however, liquefaction
occurs at larger amplitudes and the resulting
low viscosity causes the bead to fall to the bot-
tom of the container (Fig. 1d). Liquefaction is
so rapid in this case that sedimentation does
not have time to occur.
Viscosity values differed for the rheology and
sinking experiments as the initial states were
different: in the sinking test, the sample had
been allowed to age to enable it to support the
bead. However, the critical acceleration does
give roughly the same critical stress (exerted by
the bead) for liquefaction as the rheology mea-
surement of 1.3 Pa:
ra/3 was about 1.5 Pa.
The most important conclusion from the
sinking experiment is that it is impossible to
sink beads with a density of 1 g ml
1
: they con-
tinue to ‘float’. As this is typically the average
density of humans and animals, any unfortu-
nate victim should sink halfway into the
quicksand, but could then take solace from the
knowledge that there would be no risk of being
sucked beneath the surface.
A. Khaldoun*, E. Eiser†, G. H. Wegdam*,
Daniel Bonn*‡
*Van der Waals-Zeeman Institute and †HIMS,
University of Amsterdam, 1018 XE Amsterdam,
The Netherlands
e-mail : bonn@science.uva.nl
‡Laboratoire de Physique Statistique de l'Ecole
Normale Supérieure, 75231 Paris Cedex 5, France
1. Lambe, T. W. & Whitman, R. V. Soil Mechanics (Wiley, New
York, 1969).
2. Van Olphen, H. J. An Introduction to Clay Colloid Chemistry
(Wiley, New York, 1977).
3. Coussot, P., Nguyen, Q. D., Huynh, H. T. & Bonn, D.
Phys. Rev. Lett. 88, 175501 (2002).
4. Huang, N. et al. Phys. Rev. Lett. 94, 028301 (2005).
5. Lohse, D., Rauhé, R., Bergmann, R. & van der Meer, D.
Nature 432, 689–690 (2004).
6. Ferroir, T., Huynh, H. T., Chateau, X. & Coussot, P.
Phys. Fluids 16, 594–601 (2004).
7. Batchelor, G. K. An Introduction to Fluid Dynamics
(Cambridge Univ. Press, Cambridge, 1967).
Competing financial interests: declared none.
doi:10.1038/437635a
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–2
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51015202530354045 1 2 3 4 5
Distance (cm)
6789
Volume of quicksand (%)
400 600 800 0 200 400 800
3 10
Viscosity (Pa s)
a
c
Elastic modulus (Pa)
Viscosity (Pa s)
d
b
200
Time (s)
600
Figure 1 | Rheological and mechanical determination of quicksand
properties. a, Liquefaction under shear of natural quicksand
from a salt lake near Qom, Iran. Viscosity is plotted against time
for quicksand (water content, 50% by weight (wt%); grain size,
50–200 m; clays, about 7 wt%, mostly montmorrilonites; salinity,
0.1 M) for the imposed stress levels indicated in the figure.
b, As a,
but with laboratory quicksand (90 wt% sand, 10 wt% bentonite in
salt water; total water, 50 wt%). Salinity higher than 0.02 M is
necessary for collapse, which is visible as a viscosity increase after
liquefaction.
c, Shear elastic modulus, G, of natural and of
laboratory quicksand for different volume fractions of water,
measured with a rheometer (frequency, 1 Hz; deformation, 0.1%).
d, Sinking experiment, showing viscosity as a function of depth of
sinking in a quicksand column (50% water) for different amplitudes
of shaking. For comparison with results in
a, b, we converted the
falling speed into an effective viscosity by using Stokes law
7
.
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