Concrete
A flurry of activity produces an oblong pile of sand. Dig a hole in the beach, down where the sand is fine and water seeps in, steadily filling the hole. Grab a double handful of dripping sand, raise it, plop it down on the beach. Quickly, while the last layer is still wet, reach back into the hole, mix the sand around and pick up as much will fit into cupped hands. Lay it down on the growing pile, agitate it, let it flow and settle. Repeat until the pile is big enough to work with.
Water lubricates the sand grains; they float, briefly, in the slurry you mix up and plop onto the beach. Once the handful of sand is stationary, the water starts to flow out the bottom and the sand settles with it. As you agitate, the lubricated grains nestle in next to each other, turning and fitting. This is why a wet-packed pile is more solid than a damp sand pile.
There's a practical limit to the size of this free pile. The taller it is, the faster water settles out from the upper layers. If it gets too dry, the next layer's water will run out too quickly and the sand can't do its nestling. When the pile is carved, it'll split along the horizon. Build the pile up beyond about eighteen inches and you have trouble.
Repeated trips to the beach allowed me to refine the technique. Some of my arches fell before they were finished, sign of learning. Eventually I ran into the size limit, so I worked on adding detail. The last arch I built had a Gothic sort of shape, with inner arches. Then it was time to go back to school, back to dry flat Nebraska. With me went some photographs of these arches, taken by others. I was too busy building to shoot pictures, but the prints aroused lots of curiosity. I showed them to friends and posted one on the school's bulletin board.
Hang a string between two points: the curve it makes is a catenary, the physical response of string to gravity. The shape's signal feature is that all stress is in line with the string. It doesn't matter how much it curves, whether you pull it tight or let it hang deeply, the curve is a balanced catenary. Let the string hang so that the distance across is a little less than the vertical drop. Coat the string with epoxy, let it harden, then invert it. This is a catenary arch. Turn it to sand and you have a structure that balances gravity with compression, equally distributed along the legs. Go to the Exploratorium in San Francisco and you can make an arch out of loose blocks of wood. It stands, balanced, no glue in the joints. Sand stands also, with water's surface tension holding the grains together.
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