An interesting feature of many multi-span stone arch bridges is cutwaters — protrusions of stone attached to piers that improve the hydraulic properties of the bridge. Cutwaters not only help to prevent scour, they also prevent the accumulation of debris against the piers.
Benefits of Cutwaters: Debris Prevention
Bridges without cutwaters on the upstream faces of the piers tend to have serious debris-gathering tendencies. Trees floating down the stream hit the pier and get stuck. A cutwater tends to encourage floating objects to slide under the arches rather than smacking into the pier and staying there. In Kansas cutwaters were primarily used for this reason. The Dunkard Mill Bridge on the Walnut River near Arkansas City had cutwaters added after the bridge was completed, as the debris problem was worse than originally anticipated.
Benefits of Cutwaters: Improved Bridge Hydraulics
Blunt piers tend to create enormous vortexes when the water is up. This can undermine the bridge, leading to collapse. A triangular upstream cutwater smoothly slices the water, allowing it to flow under the bridge in a more controlled fashion. Downstream cutwaters are also useful for the same reason — they allow the streams flowing under the arches to rejoin smoothly, rather than forming a whirlpool against the pier. The idea is to keep the water flowing smoothly and gently, minimizing the effect the bridge has on the stream.
Stone arch bridges typically have triangular cutwaters. These triangles slice the water neatly, allowing for smooth flow. However, the tip of the triangular cutwater represents something of a weak point, as it can be chipped by high-velocity debris.
Occasionally stone bridges were constructed with a rectangular cutwater. Quite frankly, a rectangular cutwater probably does not significantly improve the hydraulics of the bridge, though scour will more likely occur away from the bridge proper. However, the cutwaters themselves may get undermined. Rectangular cutwaters downstream of a bridge quite possibly are really there as buttresses, helping to brace the pier against the current.
Circular cutwaters seem to be the best shape, as they deflect debris, allow the water to flow under the bridge fairly smoothly, and yet have no obviously vulnerable surfaces. Most modern highway bridges rest on circular piers that act as cutwaters.