The arch faces are the most vulnerable point of a stone arch bridge. The upstream faces in particular are more easily damaged, as they are exposed to impacts from debris.
Why the Facing Stones of the Arch are Vulnerable
The individual arch stones in the arch faces tend to twist out of the arch surprisingly easily. While the stones in the middle of the arch are locked in pretty firmly by the adjoining stones, the face stones have a free end that can be leveraged down and out. Under the right conditions, high-velocity debris can knock stones out of the arch of a bridge.
The Pudden Bridge (Esch’s Spur Bridge) near Dexter in Cowley County, Kansas, is an example. Half of the facing stones have fallen from the upstream surface of the middle arch. Flooding in 2017 started the process, breaking free two or three arch stones. More flooding in May of 2019 seriously worsened matters, causing half of the facing stones of the arch to collapse.

Preventing Damage to the Face of the Arch
A highly effective method of preventing arch stones from being knocked from an arch is to cut the faces flush. Individual arch stones that stick out farther than others are very vulnerable to being broken free. Ideally, even in floods the high-water mark should not reach the arch proper, but this ideal is frequently neglected or even impractical.
The facing stones should also be as long as possible, as the longer stone has more friction holding it in. The friction that holds the arch together should be maximized. Running joints should be avoided. The better the workmanship, the longer the arch will stand.

Pudden Bridge: An Example of Arch Facing Destruction
Pudden Bridge has some features which no doubt played a role in the partial collapse of its middle arch.
The facing stones on Pudden Bridge tend to be quite small, which makes them rather vulnerable to the floods that rage through the archways. The upstream faces of the arches are also not particularly flush. This may be due to the breaking of stones from the floods of over a century.
Finally, Walter Sharp relied extensively on mortar to make the angles of the arch stones. While he kept the face joints fairly tight — though not precision-cut — the inner archwork is heavily dependent on the mortar. As the mortar leaches out with age, the stones become loosened and vulnerable to debris impacts.

Cutting the Facing Stones
For DIY projects, most of the streams being spanned hardly have enough velocity to harm the bridge. Nevertheless, cut the arch faces BEFORE the arch is completed; it can be rather easy to knock stones loose if you attempt to cut them later. Fortunately, arch stones that are knocked free can be replaced back into the arch.