How much weight can a stone arch bridge carry? The answer to this deceptively simple question depends on several factors.
How the Bridge is Loaded
Before we discuss factors of the bridge geometry itself, there is another factor worth considering: How the stone arch bridge is loaded makes a difference. A point load is the worst loading method for a stone arch bridge, while a distributed load placed over the arch is considerably easier to handle. And this holds even if we are not considering loads distributed over the width of the bridge, but also loads distributed over the length of the span.
The Thrust Line
Arch bridges rarely fail due to breaking of the stones; rather they fail when the thrust line escapes the width of the arch. The thrust line is far more likely to be shifted out of the arch with a heavy point load; this heavy load upsets the balance of the arch. The arch can, of course, still carry some point load; the arch is always built thick enough to accommodate a range of variations in the thrust line caused by loads. A distributed load helps keep a balance within the arch, resulting in much greater carrying capacity, for now the thrust line is shifted much less under load. With an evenly distributed load, the arch is put under more compression rather than seeing a drastic change in the thrust line that results in more compression in some areas and less compression in others.
Better Distributed Loads
This shifting of the thrust line under point loads is why stone bridges are sometimes rated with various weight ratings for differently sized vehicles. Vehicles with more wheels distribute the load better than their smaller counterparts, hence why a stone bridge can conveniently carry heavier loads the larger the vehicle. On a related note, a stone bridge can be strengthened by the addition of a reinforced concrete slab on top.
The slab helps distributes the loads; and a bridge reinforced this way can possibly carry over three times the weight it could before the slab was added.
Bridge Geometry: Fill Depth
If a bridge has enough fill on top, it can carry more weight than an identical structure with little more than a fine coating of gravel or pavement over the crown of the arch. Not only does the extra weight of the fill help put the arch under more compression, thereby dampening the change in thrust caused by heavy point loads, but the fill helps distribute loads better as described above.
Bridge Geometry: Arch Thickness
Arch thickness, naturally, is the single biggest factor in determining how much weight the bridge can carry. The reason is simply that the thicker arch can accommodate greater variations in the thrust line under loading. Thus, there is more of a “buffer” available in the arch’s geometry, allowing a greater variety of loading scenarios.
Arch Shape
Obviously the shape of the arch is important. Generally, lower-rise arches can carry less weight than more rounded arches. This is because the lower-rise arches have less tolerance for imbalanced loads. Usually, the worst loading scenario is at the haunches of the arch. This is why a low-rise segmental arch may be incredibly strong under loads placed on the top of the arch yet be unable to carry a heavy vehicle. A Roman arch, due to the shape, is much more tolerant of loading at the haunches than a segmental arch, even if the Roman arch shape tends to not be as suited for heavy loads at the top. Thus, it will be seen that, under a moving load, the Roman arch provides a better overall carrying capacity than a segmental arch; though the crown of the Roman arch is weaker, the haunches, which is usually the limiting factor in the strength of a stone bridge, are stronger. Thus, a Roman arch is generally recognized as stronger than a segmental arch.
Other Factors: Walls
Generally, the retaining walls for the fill over the bridge such as the spandrel walls are not given much attention when analyzing a bridge. However, it is possible, should the walls have been built thin, for these retaining walls to be a limiting factor in the strength of the bridge. And the reason is quite simple. If we have loose fill and thin walls, it is possible for a heavy load, especially if the load is located near the edge of the bridge, to cause enough pressure in the fill to collapse the walls. Obviously, the failure of these walls would cause a loss of roadway, which could potentially result in the heavy load plummeting off the bridge, regardless of how strong the arch proper is.
Other Factors: Abutments
The abutments are often assumed to be impervious to sliding when load rating a stone bridge. For a Roman arch the abutments are not too important, but for a segmental arch, if these abutments are not thick enough, a heavy load can theoretically cause the arch to collapse due to spreading of the abutments. In practice, the abutments are usually overdesigned on a stone bridge, and the weight of the fill over them helps to hold them firmly in place.
Stone Arch Bridges 