It's not caused by erosion. Instead, the rock, itself, forms the arch and the erosion just washes away everything else around it.
…the scientists took samples into the lab, cut them into small cubes, and used pressure plates to simulate the weight of overlying material. They then subjected the cubes to simulated rain or other erosive forces.
What they found, as report today in Nature Geoscience1, is that when subjected to such pressures, even these otherwise crumbly materials quickly eroded into arches, alcoves and pillars that then became extremely resistant to further erosion. Subsequent experiments with more firmly consolidated sandstones from the North American Southwest produced the same result (see video below).
What happens, Mayo says, is that as erosion undercuts the material in ways that would normally cause it to collapse, pressure mounts along the remaining rock where the greatest amount of material has been removed. Eventually, a critical pressure is reached at which the sand grains lock together and become "incredibly stable", he says.