The stone arch bridge is a rather novel structure in the line of bridges. At a glance, it seems almost impossible that an arch, made of many discrete stones, could possibly stand, let alone support weight, yet that they do is entirely undeniable.
One more picturesque explanation of why an arch stands is that two columns of falling stones are “falling” into each other and hence can’t fall all the way. A more scientific explanation of the reason why arches not only stand, but hold weight, is that all of the forces in the bridge are in compression; all the forces push together instead of pulling apart. Hence, the arch stands because all the stones are busily pushing together.
As each individual stone acts as a wedge, gravity pulling down on the mass collectively in effect forces the stones tightly together. For the arch to stand, the line of thrust must be contained within the stones; otherwise, at the point where the line of thrust escapes the arch, there is sufficient pressure to actually squeeze the stones up and out of the arch.
Furthermore, the thrust should be kept within the middle third of the arch. If the thrust leaves the middle third of the arch, the structure can flex and become highly unstable. For illustration, try squeezing a small stack of toy blocks tightly at one edge — they will suddenly snap out dramatically. If you squeeze them in the center, they are stable. This is the principle behind the “middle third” rule.
The natural line of thrust for a freestanding arch is parabolic; however, the weight of the fill, which is usually much greater on the “haunches” (sides) of the arch than the top, tends to distort this parabolic shape.
The arch must pass its own weight and the weight of any and all loads on the top to the ground somehow. The weight is taken by large abutments. With a Roman arch, all of the weight is more or less straight down; however, for a segment of a circle — a flatter arch — more weight is transferred horizontally. Because a flat arch has a large amount of horizontal thrust and, therefore, a tendency to slide out at the ends, it is necessary to transfer this thrust into more of a downward direction. This is accomplished by making the abutments heavy. The downward weight of the abutments tends to shove the line of thrust downwards as well.
The amount of weight an arch can handle is directly related to how much weight is required to make the line of force escape the middle third of the arch at any point. This failure point doesn’t have to be on top of the arch; in fact, it is often on the haunches where this worse-case scenario is encountered.
Interestingly, the more static load (fill) that is placed on top of the arch, the greater the weight-handling ability of the bridge. After all, not only does the even weight of the fill tend to press all of the arch stones more tightly together, but the fill distributes the weight of any vehicles across a larger area.
On flatter arches, an often overlooked point to remember is that how much weight the bridge can handle can sometimes be limited by how much weight it takes to cause the arch to start sliding because the abutments are not massive enough to handle the force. But when the bridge is not overweighted, the line of individual stones in the arch routes the load around the arc of the arch, to the abutments, and from there into the ground, resulting in a stable, strong structure made out of the same material as the earth itself, and which can stand the test of time.