Backing

Document history

• 2023-03-28 First version

What is backing?

The vast majority of masonry bridges are not arch rings sitting on abutments, covered by fill. Such structures may not have survived when live loads began to increase through the late 19th century and into the 20th. Rather, over the abutments (or piers), outside the arch barrel, they have some for of masonry backing.

Backing is unlikely to be high quality masonry. It is often rubble concrete - broken stone or brick, with sparse and probably low quality mortar. But this does not stop it performing its function, which is to provide a stiff path for thrust.

More complex forms of backing exist, including voided backing or internal spandrel walls. Voids may be true voids or filled, and may be capped with jack arches or slabs. On under-line rail bridges, walls would typically be under each rail, but re-alignment can disrupt this.

What was backing for?

Providing the required horizontal resistance to arch thrust using fill only is difficult or impossible. Achievable levels of compaction would allow substantial movements at decentring. Over time, creep might then allow further movement. The issue of placing and compacting fill would be particularly acute over viaduct piers, in the narrow valley between adjacent arch barrels.

Backing provides a stiff block of masonry, capable of carrying thrust from the moment of decentring, and that will not creep significantly over time.

What does backing do?

This is a different question. At the time most masonry bridges were built, live loads were of no great consequence. All considerations of bridge stability had to do with dead load only. 

Now, live loads are much larger relative to the mass of masonry structures. Backing plays a critical role in conveying thrust from the arch barrel into the abutment or soil. In particular, you are likely to find that a heavy load at the quarter point will result in the line of thrust escaping the arch ring at the opposite abutment.

In viaducts, backing over piers profoundly changes the behaviour of the structure, an issue with which all engineers assessing viaducts should be familiar.

How do we know whether backing is present?

We see many models with no backing. On questioning, the engineer will tell us that, as no investigations have been made, it is necessary to assume that no backing is present.

It is not generally reasonable, especially for railway era bridges, to assume no backing. 

Generally, the most robust evidence for backing is to be found by pulling trial trench back from about the quarter point towards the springing. This will allow level and slope of backing top to be established.

There is often good evidence of backing externally visible, however. Where drainage exists, this will indicate a low point in backing. This is particularly common on viaducts. Even where there is no drainage, the indirect effects of backing can often be seen on the elevation or soffit.

In extremis, coring (from the intrados or from above) can be used to test for backing. It is very easy to get misleading information from such coring exercises. Always start with an idea of likely backing forms, and consider the possibility of voided backing, before designing the coring exercise to test for possible forms. Coring "willy nilly" is likely to cause harm while delivering no useful information.

Backing in Archie-M

When a bridge model is created in Archie-M it defaults to having no backing. Backing is added using the "Structure -> Modify Backing ..." menu option or by right clicking on an abutment or pier and choosing "Add backing ..."

Either of these will open the backing dialog, which allows backing details to be set. When backing is already present, it can be modified by double clicking on a backing area or using the right click context menu to "Edit backing ...".\

On opening, for a two span structure, the backing dialog looks like this:

The "Position" column, as above, may not be wide enough by default to show the full content. It can be expanded. Backing is set for each side of each span. The rows will always run from left to right.

Notice the check box at the top. If this is set, then modifying one row in the table will update all rows to match. This is frequently useful, but in structures with varying span geometry it may be necessary to turn it off.

Backing type is a drop-down, you can select from None, Flat-top, and Tangential.

The numerical values can be edited by clicking on them.

The meaning of the parameters varies between the backing types. The table below summarises, and examples follow. Note that backing material strength is not used in Archie-M version 2.5.1. 

If we look at the Torksey sample model, and open backing dialog, we see this:

This is relatively low backing. A common pattern is flat top backing at crown intrados level:

Notice how the top of backing extends from the back of the abutment to the point of contact with the arch. 

It is possible to limit the project past the springing point using the "Width" parameter. Setting that to 0 produces this result:

That arrangement is very unlikely indeed, it is presented to explain the parameter only. A value of 800 is perhaps more likely:

Note how the backing stops short of the intersection. In general, if you set the width equal to about half the span, you will ensure that backing runs to contact with the arch whatever height you set. The refinement of backing stopping short could only become significant if thrust was running very close to the backing top, in which case it is likely that uncertainty around the exact backing level may be more important.

Tangential backing is fixed by the height over the intrados springing (ie at the abutment face). It meets the arch extrados at the tangent point:

The width parameter is ignored for tangential backing. 

Notice how with backing in place, the blue ticks on the arch extrados are vertical. These are the "force vectors", they show the resultant of the forces applied to the extrados of each segment. Fill applies horizontal as well as vertical pressure, so the force vectors slope. Backing does not. Close inspection of the screenshots immediately above and below will reveal that the thrust curves more in the no backing case. This is a result of the horizontal pressure from fill.

Thrust in backing

It has long been a question, whether it is acceptable for thrust to exit the arch ring into backing. BD21 provided no guidance on the matter. 

CS454 clause 7.10 contains the following:

This is in a section on equilibrium-based analysis. There is a separate section before this on mechanism-based analysis, and references there might tend to imply that Archie-M is "mechanism based". This is misleading. The fact that thinking about mechanism plays a part in understanding Archie-M results (and masonry bridge behaviour) does not make this a mechanism analysis. 

Indeed there is no clear definition of the terms "mechanism-based" and "equilibrium-based" analysis. Plastic theory deals with three criteria: equilibrium, yield, and mechanism. If a mechanism is found that satisfies yield, the loads applied are an upper bound on collapse loads. In contrast, if a state of stress can be found that satisfies equilibrium and yield while supporting imposed loads, the loads imposed are a lower bound on collapse loads. 

Archie-M thrust lines satisfy equilibrium. If the zone of thrust remains within masonry, and a mechanism does not form, then the equilibrium and yield criteria of plastic theory are satisfied. The applied load is then, by the "safe theorem", a lower bound on the collapse load for the model structure. 

To the extent that the model does not represent the real structure, it is necessary for the engineer to consider whether those differences fundamentally change the behaviour, or merely add alternative load paths. Spandrel walls, for example, provide alternative load paths, and cannot reduce the collapse load. Backing over piers in a viaduct changes the behaviour, and requires more consideration.

Returning to the Torksey model discussed above, if we apply an onerous load, with no backing, the picture might look like this:

Note that the thrust is escaping from the arch ring into the fill. This is a clear fail, and will be reported as such in auto-run. If this were a realistic representation of the bridge and load, a fourth hinge would form where the thrust exits the ring, leading to collapse.

With flat top backing at crown intrados level, we see this:

Now, thrust runs from arch ring into backing far below top of backing. A hinge cannot form. The backing provides a stiff path for the thrust, and we would expect the ring, backing and abutment to act as a unit. 

If the backing only came to the top of the second segment, we once again have four hinges forming, creating a mechanism:

This is a borderline mechanism under heavily factored loads. In such cases the application of engineering judgement becomes essential.