You cannot have a stone arch bridge without the bridge abutments. The abutments are the end supports for the arch(es).
Abutments are different from piers. The most obvious difference is that piers are located in the stream, while the abutments are located at the ends of the bridge.
However, bridge abutments do more than piers. While it is possible to design a chain of low, flat arches such that they balance out on thin piers, the abutment actually has to handle the entire thrust of the arch(es) to lock them in place.
The proper size for an abutment is almost entirely determined by the arch it is supporting. Obviously, a larger, longer arch merits a larger abutment. However, the type of arch is a critical determining factor as well.
Resisting the Thrust
A low, flat arch, especially a segmental arch of less than 90-degree arc, exerts substantial horizontal thrust on its abutments. The job of the abutment is to take this horizontal thrust and convert it entirely into downwards thrust for stability.
One possibility to relieve this thrust is to “tie” the ends of the arch together. The famous Luten concrete “tied arches” did this by running a material with a high tensile strength between the abutments under the water.
While this method does work well when dealing with concrete, as well as steel (as in the case of the bowstring trusses of old), it is not very suitable for stone. The discrete blocks of stone would make tying the ends of the arch a challenge, and, besides, the stone masonry tradition predates the tied arch era.
Most stone arch bridges resist the horizontal thrust with massive abutments. These massive abutments provide the arch with essentially a large chunk of laid stone to try to shove. Where possible, setting the ends of an arch into the bedrock underneath the stream itself offers a simple and very reliable solution. The bedrock is not likely to go anywhere, and needs no construction. This is the simplest method of resisting the thrust of an arch, even if it is uncommon.
Abutment Thickness Vs. Arch Design
The thickness of the abutments depends first and foremost on the type of the arch.
A Roman arch needs little thickness to the abutments, save what is strictly required to support the arch.
A segmental arch uses thicker abutments in proportion to the shallowness of the arc. For a given span, the lower the rise, the thicker the abutments must be.
A basket-handle arch is trickier. The basket-handle arch does indeed end flat on the abutments, yet the arch still has significant thrust higher up. To handle this, basket-handle arches are usually thicker towards the bottom than at the top of the arch. This, obviously, means that the abutments must be thicker by default to accommodate the wider arch bottom. Furthermore, room must be left to accommodate more masonry higher up on the arch for stability.
The higher the springing point of the arch, the thicker the abutments need to be. If the arch starts high up in the air, the abutment can actually act as a lever. The end result is that the thrust of the arch can actually topple the abutment if the abutment is too tall relative to its thickness.
Abutment Thickness Vs. Height
Clearly, the longer the span, the thicker the arch must be. Also, the more height the abutment has above the springing of the arch, the thinner it can be.
The taller the abutment is, the more weight it has, which is why if we keep piling up the abutment over the ends of the arch, the more stable the arch will be. The flip side of this is that the height of the abutment is usually defined by the desired road grade.
The end result, then, is that the abutment’s height will be what it will be, so the abutment’s thickness is the adjustable factor.
Arches sprung at the streambed do not need thick abutments. This is because there is more weight over the top of the arch by default.
Abutment Thickness Vs. Span
How do you know how thick the abutment should be for a given span? These days we can use software to determine abutment thickness, but in the previous centuries everything about arch bridge design was empirically determined. The relationship between span and abutment thickness is not linear.
In recent years the Kasese district of Uganda has put forth a superb manual on stone arch bridge building which includes a table of dimensions (including abutments) for Roman arches and 90-degree segmental arches, ranging from spans of one meter up to 20 meters. From this manual, it is interesting to see that for a two-meter-span 90 degree segmental arch the abutment thickness is going to be roughly half the span. A 20 meter-span arch of the same arc shape needs abutments only slightly more than one quarter of the span.
The manual shows that Roman arches use thinner abutments, with a thickness of roughly one third the span being used for a two-meter Roman arch.
DIY Arch Bridge Abutments
So what about advice for the DIY enthusiast? Thicker abutments ensure stability.
Our experiments determined that thick, solid abutments help compensate for weaknesses both in the abutments and in the arch. As a good rule of thumb, we’d recommend building abutments that are at least one half the span in thickness for any arch with a rise of 0.2 times the span and higher. This ensures solidity, and, for most small DIY bridges, should not use excess material.
The abutments need to be safely secured, preferably on bedrock. Hard-packed soil located at least a foot below the streambed level will work for a foundation if the bottom of the abutment is flared to distribute weight.
For the die-hard enthusiast determined to build a LARGE span, if at all possible lock the ends of the arch in bedrock. Bedrock provides an almost foolproof abutment.
Remember: The abutments need to have solid rock at least up to the top of the springing stones for stability.