The abutment foundations we built for that first bridge in Port Hope are not the only kind we've used. The foundations described below have also worked well and in a couple of other cases I've discovered a combination of stone and concrete has been quite a suitable solution for small dry stone footbridges of this type. Below is a description of two other ways it can be done if the situation allows for it.
Here at the public bridge in Russell Ontario, ten foot wide, four foot deep holes were dug by machine and U shaped forms were assembled of plywood and then concrete poured to make the abutments. Less concrete was needed because of the clever U shape design. Clear gravel was used to fill up the four feet of depth around the abutments and tapered back to eventually be the support the tails of the bridge.
Stones were embedded in the fresh concrete to be a resistance to any sheering action across the top of the flat surface of the abutment. Re-bar or long bolts can be used here instead.
In Wellington Ontario we used concrete forms again but created six inch high steps in combination with embedded re-bar to act as resistance to the lateral push of the arch.
At Bruce's bridge we dug precise 8x8 by 8 foot deep holes in the hard subsoil and then added clear sharp 3/4 gravel to within 12 inches of the surface. After compacting it thoroughly we built our bridge on top of this dense gravel foundation. Lateral movement of the bridge was avoided by bedding the first larger foundation stones below grade into the gravel.
The bridge is 8 years old and has showed no sign of movement or slumping.