The sand that lets a body in and will not let it out

In films, quicksand is a pit that drags its victims down until only a hat remains on the surface. In the world it is a patch of wet ground near a river mouth, a salt lake or a beach, firm-looking until someone steps on it, which then lets them sink to the knees or the waist and holds them there. People do die in it, but not by being swallowed: they are held while a tide comes in, or exhaust themselves trying to pull free. The physics explains both halves of that — why a body sinks a little way and no further, and why getting out is so much harder than getting in — and the two halves come from different properties of the same material.

A solid until it is disturbed #

Natural quicksand is fine sand, a tenth of a millimetre across or less, with water and a little clay, and often salt. Daniel Bonn and his colleagues, who studied samples from a salt lake in Iran in 2005, found the grains held apart at a loose packing — a sand fraction near forty per cent, well below the sixty per cent of sand that has settled under its own weight — by a weak network of clay particles flocculated by the salt. The network gives the material a yield stress, the property the paste that holds up its own hill followed in toothpaste and wet concrete: below a threshold stress it does not flow at all.

The salt matters as much as the clay. Clay particles are thin platelets whose faces carry a negative charge, and in fresh water each is surrounded by a cloud of positive ions that keeps its neighbours at a distance. Salt crowds those clouds in: the screening length, the distance over which a charge’s field survives in an electrolyte, falls from tens of nanometres in fresh water to a nanometre or less in brine, as the long-range force that does not reach found for charges screened by a plasma. With their repulsion screened, the platelets stick where they touch, edge to face, into an open framework like a house of cards — flimsy, but able to hold sand grains apart at a packing they would never keep on their own.

The material at rest is a soft solid with a loose skeleton of grains inside it, a structure that should not exist in loose sand and is held there only by the clay. Disturb it — a footstep, a vibration, the shear of a body pressing down — and the stress locally exceeds the yield stress, the clay network breaks, and the loose skeleton collapses. The grains, no longer held apart, fall into the water around them, and for a moment there is a dense suspension: sand in water, with the water carrying the weight. Its viscosity falls by orders of magnitude, the way the paste that forgets it was stirred found a thixotropic material thinning when its structure is broken, and anything heavy on it begins to sink.

This liquefaction is the same thing that happens to waterlogged loose soils in an earthquake, and to the tailings dams that the angle that does not know the size of the heap mentioned among the worst industrial failures: a loose, saturated granular material whose grains are suddenly unable to carry the load turns it over to the water, which cannot carry shear at all. The ground flows. In quicksand the flow is local, around the disturbed patch, and the material that flows is dense.

Why nothing sinks very far #

The liquid a body sinks into is mostly sand. At a sand fraction of 0.41, with quartz grains of 2.65 times the density of water, it has a density of $1 + 1.65 \times 0.41 = 1.68$ times water’s. A person, with lungs half full, has a mean density of about 1.03. By Archimedes’ principle a floating body displaces its own weight of liquid, so the fraction of the body submerged is the ratio of the densities.

In fresh water a person floats with almost all of their volume under water, held up only by the air in their lungs. In liquefied quicksand only six-tenths of the body need be submerged. Upright, a person sinks to somewhere above the waist and stops; lying back, spreading the body over a larger area, they float with more of themselves clear, as in the Dead Sea but more so. Bonn’s group tested this with beads of the same density as a person, placed on quicksand and shaken: they sank part of the way and no further. A person cannot be swallowed by quicksand, and the films are wrong.

The sinking is also limited in a second way. As a body sinks it pushes the liquefied sand aside and down, and that sand, freed of its clay network, begins to settle. Within minutes the grains near the body have packed together and the material around it is no longer a liquid.

The principle is the one the balloon that floats at a density followed in a stratified liquid: a body settles at the level where it displaces its own weight, and in a liquid much denser than itself that level is shallow. What makes quicksand feel as though it pulls is not the depth but the speed of the first sinking, which is quick while the sand is liquid, and the way it then stops — not because the body has floated, but because the liquid has turned back into a solid around it.

Dry sand can do what wet quicksand cannot. Detlef Lohse and his colleagues showed in 2004 that very fine sand, made extremely loose by blowing air up through it and then letting it settle, swallows a heavy ball completely: the ball’s impact collapses the loose packing, and with only air in the pores there is no buoyancy to stop it, so it sinks until it reaches sand packed enough to bear it, throwing up a jet of sand behind. Dry quicksand of that kind may occur naturally in a few desert settings. It is the absence of a dense liquid, not the presence of one, that lets it swallow things.

A bed that packs down tighter than before #

The grains in a liquefied suspension fall through the water at their settling speed — Stokes’s speed for a sphere, slowed by the crowd of other grains around it. Hindered settling at a sand fraction of 0.41 is about twelve times slower than a single grain’s fall, and the grains collect at the bottom in a bed packed at the sixty per cent of settled sand, with clear water rising above.

A metre of liquefied quicksand settles into 0.68 metres of packed sand with 0.32 metres of water above it, and the time it takes depends on the square of the grain size: two minutes for coarse sand, half an hour for the finest. In real quicksand the settling is local, around the body that disturbed it, and faster, because the volume involved is small. The result is the same: a leg that sank into a liquid is now embedded in sand packed more densely than it was before anyone stepped on it, and the water that let it in has been squeezed upward and out.

Packed sand is strong. Its grains are in contact, locked against one another, and to move them apart requires either breaking those contacts or letting water in between them. The heap that becomes a solid followed how a granular material passes from flowing to jammed as its packing rises, and the change from forty per cent to sixty per cent crosses that threshold decisively.

The suction that holds a foot #

To pull a foot upward out of packed sand, something must fill the space the foot leaves behind. The sand above the foot cannot fall in — it is packed and jammed — so the space must be filled by water drawn in through the pores of the sand around it. Water flowing through a porous material obeys Darcy’s law: the flow rate is proportional to the pressure difference driving it and to the material’s permeability, and inversely to the water’s viscosity and the distance it must travel. Pulling the foot at a speed $v$ demands a flow of $v$ times the foot’s area; the pressure needed to drive it is a suction under the foot, of order $\mu vL/k$ for a foot of size $L$ in sand of permeability $k$.

The permeability of sand is set by its grain size and packing, and the Kozeny–Carman relation, $k = d^2\varepsilon^3/180(1-\varepsilon)^2$ for grains of size $d$ and porosity $\varepsilon$, gives it: about $6\times10^{-12}$ square metres for packed 0.1 mm sand, which is to say that water seeps through it very slowly.

The force is proportional to the speed. That is the defining property of viscous resistance, and it is what makes quicksand feel as it does: a slow pull meets little resistance, a fast one a great deal, and a panicked, jerking attempt to free a leg is exactly the wrong thing. From clean, packed sand of 0.1 mm grains, pulling at a centimetre a second takes four times a person’s weight, and a pull equal to their own weight extracts the foot at under three millimetres a second. The grain size matters through its square: the same pull through sand half as coarse is four times slower.

Natural quicksand is worse than clean sand, because its clay fills the pores. Clayey sands have permeabilities a thousand times lower than clean sands of the same grain size, and the suction at a given speed is a thousand times higher. A pull equal to a person’s weight then frees a foot at a few micrometres a second. That is why estimates of the force needed to pull someone out of quicksand quickly run to many times the weight of a car, and why being trapped is real even though sinking is limited.

Sideways movement meets a second resistance. Packed sand cannot be sheared without expanding, because grains locked against their neighbours must ride up over them to move — the dilatancy that Osborne Reynolds described in the 1880s, and the reason a footprint on a wet beach goes pale and dry for a moment as the sand around it expands and sucks water in from the surface. A leg pushed sideways through packed quicksand makes the sand around it dilate, and the expanding sand draws water into its own pores rather than into the gap beside the leg, adding to the suction. Struggling sideways, in other words, tightens the grip.

Time, not force #

The same arithmetic, turned round, gives the time it takes.

The time is inversely proportional to the force, so tripling the pull saves only a factor of three, and pulling hard enough to free a foot in seconds would need forces that injure the person being pulled. Rescuers instead attack the permeability. Working water down around the trapped leg with a probe or a hose re-liquefies the packed sand around it: the grains are pushed apart, the clay network and the jammed skeleton are both broken, and the sand flows back into the space behind the foot instead of having to let water seep in. The suction disappears at its source. The trapped person can help in the same way, by working the leg gently back and forth to let water down beside it, which builds a thin, water-rich sleeve along the leg — a layer of liquid next to the wall like the depleted layer the viscosity that belongs to the tube found along the wall of a narrow pipe, through which the leg can then slide — and by lying back to spread their weight, which both raises them in the liquid and reduces the pressure that keeps the sand around the legs packed.

The danger is therefore not drowning by sinking but being held in place by something else that is coming. On tidal flats such as Morecambe Bay in England and the bay of Mont-Saint-Michel in France, the soft sands that trap walkers lie in the paths of tides that come in faster than a person can walk, and a trapped person can be reached by the water long before they can free themselves. Cold and exhaustion do the rest. The physics of a trapped foot sets the time scale of a rescue: tens of minutes to hours, against a tide measured in the same units.

A material that changes as it is used #

Quicksand belongs among the materials in this sequence that do not have a single set of properties but change them in response to what is done to them. The fluid that answers back opened the sequence with liquids whose resistance depends on how they are deformed; the suspension that seizes when pushed hard found a dense suspension of cornflour that becomes solid when struck, because the grains are forced into contact faster than the liquid can lubricate them. Quicksand does nearly the reverse twice over: struck, its fragile structure fails and it becomes liquid; left alone, it settles into something more solid than it was. Neither state is its “real” one, and which it presents depends on its recent history — a gel, a liquid and a packed solid in the space of a few minutes.

It also shows the general point that a granular material saturated with water is two materials sharing a load. While the grains touch, they carry the load and the water is a spectator; when the grains are pushed apart, the water carries it, and water carries no shear. The transfer of load from grains to water is liquefaction, and the reverse transfer, as water drains, is consolidation — the slow settling of buildings on clay, which takes years because clay’s permeability is so low. Quicksand performs the whole cycle in minutes, around one person’s legs.

What the drawings leave out #

The figures use representative numbers rather than measurements of any particular quicksand: a yield stress of thirty pascals, sand fractions of 0.41 and 0.6, a foot of 250 square centimetres, and clean quartz grains whose permeability follows the Kozeny–Carman relation. Natural quicksands vary enormously in grain size, clay content and salinity, and the clay case — permeability reduced a thousandfold — is a round figure for clayey sands rather than a property of a specific sample. The suction model treats the foot as a rigid piston drawing water through a uniform packed bed, and ignores the extra resistance of the sand’s own friction against the leg, which adds to the force, and the dilation of packed sand as it is sheared, which can draw in water and add to the suction further. The settling model treats a uniform metre of suspension in one dimension. The domain of the drawings is fine sand from 0.03 to 1 mm, liquefied at a fraction of 0.41 and packed at 0.6.

Still open: what holds the loose skeleton up #

The fragility of natural quicksand depends on the clay network holding a loose packing of sand in place, and why some sands form such networks and others do not — which combinations of clay mineral, salinity and grain size produce a material that liquefies at a footstep — is understood only in outline. The same question matters far beyond beaches. Soils that liquefy in earthquakes, mine tailings that flow when a dam gives way, and the sediments of the sea floor that slump into underwater landslides all owe their danger to a loose granular structure held in a metastable state, and predicting which ones will fail and under what disturbance is one of the hard open problems of soil mechanics.

The physics of a trapped foot is not open. Quicksand is a loose sand skeleton held by a clay gel with a yield stress; a disturbance breaks the gel and the sand liquefies into a suspension 1.7 times as dense as water, in which a person floats with only 0.61 of their volume submerged; the sand then packs down around them in minutes, and a foot can rise only as fast as water seeps through the packed grains to fill the space — 2.7 mm/s for a pull of the body’s weight in clean sand, a thousand times slower with clay in the pores. Quicksand does not pull anyone down. It simply lets them in and then takes its time about letting them go.