Question
When I assess the Permissible Limit State (PLS) of a masonry arch bridge in RING using the CS 454 approach, the PLS adequacy factor is always lower than the Ultimate Limit State (ULS) adequacy factor. When I use the CIRIA C800 approach, the PLS adequacy factor is usually lower than the ULS value, but for some bridges it comes out higher. Why does this happen? Is the result still valid, and should I be doing anything differently when I see it?
Summary
When the Permissible Limit State (PLS) is assessed using the CIRIA C800 approach, RING can occasionally report a PLS adequacy factor that is higher than the corresponding Ultimate Limit State (ULS) adequacy factor. This is a known characteristic of the CIRIA C800 PLS methodology rather than an error in the analysis. It is most likely to occur in arches with a low span to rise ratio. Where it happens, the pragmatic course of action is usually to use the CS 454 approach to PLS instead.
Two different routes to a PLS result
RING supports two approaches to PLS assessment, and they behave quite differently.
CS 454. The PLS result is obtained by factoring down the ULS result (by Cmin). Because the PLS value is derived directly from the ULS value, the PLS adequacy factor will always be lower than the ULS adequacy factor.
CIRIA C800. The PLS and ULS results are obtained using different theoretical approaches. The PLS result is not derived from the ULS result, so there is nothing in the method that guarantees the PLS adequacy factor will be the lower of the two. In most cases it is, but not always.
Why the CIRIA C800 PLS result can exceed the ULS result
The CIRIA C800 PLS methodology uses a simplified representation of the backfill, essentially treating it as acting like a dense fluid. For arches with a low span to rise ratio, this assumption has a greater influence on the calculated response, and the resulting PLS value may not be consistent with the ULS value. In some cases this leads to a PLS adequacy factor that is higher than the ULS adequacy factor.
Should a PLS result higher than the ULS result be accepted?
In general, no. The PLS is intended to identify a load level below which repeated loading will not cause irreversible degradation of the bridge. A PLS adequacy factor higher than the ULS adequacy factor would imply that collapse occurs at a lower load than the onset of irreversible behaviour, which is not physically consistent.
So although the CIRIA C800 analysis itself may have been carried out correctly, a PLS value that exceeds the ULS value should not be relied upon.
What to do
Where the CIRIA C800 approach gives a PLS adequacy factor higher than the ULS adequacy factor, and CS 454 is an available option for the assessment, we recommend reverting to the CS 454 approach for the PLS. This is a valid alternative and can normally be justified on the grounds described above. We recognise that this is not an ideal solution, but it is a pragmatic one until the guidance is updated.