The most popular idea is that the stream was first diverted, then a mound of dirt was constructed where the arch would be. The stones were placed, and the dirt removed leaving only the stone arch. Only trouble is that some of these bridges don't appear to have a single keystone. And the stones are of different sizes and number on each side of the arch. The bridge had been routinely inspected a few days before its unexpected collapse, and everything seemed OK .
Information is lost from each generation to the next.
These bridges were built by long-gone craftsmen, and they took many of their secrets with them.