Originally published 2 July 1990
Independence Day. The sand-castle season begins.
There is in all of us a bit of the architect who wishes to build castles, cathedrals, walled towns, and aqueducts. And what more pleasurable way to indulge these fantasies than by playing in the wet sand, with warm sun on our backs and the sparkling sea lapping our abutments and battlements.
Like many sand-castle devotees, I have worked my way through the genres of our art. One season it’s all Mont-Saint-Michel; the next, the Great Wall of China; the next, King Arthur’s castle. This year I’ve been warming up with the Pyramids of Giza.
A sand pyramid is quick to construct (although to get the slopes just right is not as easy as one might think). A solitary pyramid is not terribly impressive, but a complex of half-a-dozen, in different sizes, with a Sphinx thrown in, makes a display of beach architecture that would dazzle Tutankhamun.
But wait. This is supposed to be a science column. So for all you sand-castle buffs, here’s the Science Riddle of the Sphinx.
Why is wet sand firm?
Dry sand is useless for building; it doesn’t stick together. If sand is too wet, it slumps and oozes. But when the degree of moisture is just right—voila! Towering towers, soaring arches, buttresses that fly.
Something to do with tension?
The firmness of moist sand cannot be the result of a chemical reaction, such as makes a sand-mortar mixture set; when the sand dries out the castle reverts to dust. Nor can the firmness be due to friction, because water acts as a lubricant.
So what’s the answer? One guess might be the firmness might have something to do with surface tension in films of water between the sand grains. Most of us have seen the trick of carefully floating a steel needle on the surface of a bowl of water: The surface tension of the water supports the weight of the needle. Perhaps that same force keeps sand grains from slipping past each other.
Wrong! As every bubble-maker knows, adding glycerine to soapy water increases surface tension and helps make bigger, stronger bubbles. But add glycerine to wet sand and it becomes less firm. So presumably surface tension is not the answer.
For the correct answer to the Sphinx’s riddle I am indebted to an article by Jearl Walker in the January 1982 issue of Scientific American. The answer is both simple and complex.
The simple answer is: Electricity.
The complicated answer is: No theory is entirely satisfactory.
In a few words, here is what probably happens: The surface of a wet sand grain becomes ionized; that is, electricity charged. The charge causes a shift in the average position of hydrogen nuclei in the adjacent water molecules. This polarization of the water reduces its ability to flow. Wet sand is firm because the increased viscosity of the water hinders one grain from sliding over another.
But — some clever reader will say — remember the glycerine! Isn’t it surprising that adding a viscous fluid (glycerine) to a viscous mixture (wet sand) makes the sand less firm?
Uh, hmmmm well, like I said, the simple answer is electricity.
Let’s get back to pyramids. One can make a halfway decent pyramid even with dry sand — and forget all that stuff about ionization and viscosity. But then one must rely on dry friction to keep the sand from slipping. There is a maximum slope that a dry granular material can maintain without slippage, called “the angle of repose” (a lovely phrase, evocative of restful afternoons on sun-drenched beaches). The sand on my beach has an angle of repose of 33 degrees, not steep enough to make a realistic tomb for King Tut. The pyramids at Giza in Egypt rise at an angle of 52 degrees, and to achieve that one needs wet sand.
But now another question arises: Aren’t the real pyramids of Egypt just big piles of dry rocks? What keeps them from collapsing to the angle of repose?
The answer: The pyramids at Giza are built of limestone blocks cut true and square. The weight of the blocks is evenly distributed straight downwards onto blocks of the lower layers — a perfectly stable arrangement.
The great pyramid of Memphis
But stability may have been a lesson the Egyptians learned at great cost. One of their earliest endeavors, the pyramid at Meidum, was apparently built with badly squared blocks, more like sand grains in shape. Part-way through construction the outer layers of the pyramid crumbled and collapsed into a heap. Some considerable re-engineering was required before the pharaohs were able to successfully exceed the angle of repose in their places of ultimate repose.
Meanwhile, down in Memphis, Tennessee, the townsfolk are building a pyramid worthy of their city’s Egyptian namesake, a two-thirds scale replica of the Great Pyramid of Cheops. The pyramid, which will serve as a sports-entertainment arena, is constructed of structural steel with stainless steel cladding. This mode of construction reflects a revolution in building that occurred in the 19th century with the appearance of cheap and plentiful iron and steel.
The steel in the Tennessee structure will weigh 2,550 tons, compared to about 5,000,000 tons of stone in the Great Pyramid of Cheops. The Tennessee builders have their problems, but not with angles of repose. In that respect, sand-castle enthusiasts have more in common with ancient Egyptians than with 20th century architects and engineers.
