Question
I've modelled a barrel as "Multi-ring (debonded)" and the adequacy factor is very low. Why is this? Can I do anything about it?
Answer
A "Multi-ring (debonded)" arch model in LimitState:RING conservatively assumes that there is complete delamination between each ring in the barrel and this can give lower than expected adequacy factor values.
Ring separation is a difficult phenomenon to predict; it is quasi-brittle in nature and, as such, the onset can be rather sudden and without many visible cues. For this reason it is prudent to exercise caution when assessing structures that may be susceptible to separation.
However, one may wish to get a better idea of the potential resistance of the structure when full debonding is not in effect. Generally, we would look for some mechanical interlocking between arch rings as signs of bonding. That may be e.g. in the form of brick ‘headers’ showing in the soffit of the barrel, or evidence of repair such as stitching through the layers using metal dowel rods. If the mortar between rings is of good quality and condition, then you may also wish to consider the possibility that the bridge acts as bonded.
Gluing Blocks
As part of our “Advanced Modelling Features of LimitState:RING” webinar, we describe how to ‘glue’ arch blocks together in order to undertake a ‘what if’ analysis on a multi-ring arch. This can be seen at the link below:
Gluing blocks is a relatively straightforward process of selecting contact surfaces and turning off sliding and hinging failure through the Property Editor. Caution must be exercised, however, for spans where there are differing numbers of blocks in the rings and / or the profile is significantly undulating. Here it is easy to inadvertently select smaller circumferential contacts that connect more than two blocks together. Gluing too many of these can cause the arch to act as a monolith and increase the adequacy factor beyond credible levels.
Shear Bond Strength (Adhesion)
Another method of introducing strength to the contacts in a multi-ring model is to provide a shear bond strength. This is the strength developed when contacts are subject to a shear load; i.e. a measure of adhesion along (parallel to) the contacts. This is separate to the friction measure and does not introduce tensile adhesion normal to the contacts. The inclusion of the ability to model shear bond helps users explore ‘what-if’ situations and inform on the capacity of structures; especially when considering bridges with multi-ring spans.
However, the shear bond functionality needs to be employed with care: In LimitState:RING it is assumed that the shear bond will fail in a ductile manner, which is not representative of the quasi-brittle mode of failure observed in practice. Thus it is recommended that a suitably low ‘effective’ value of shear-bond strength is used in the analysis to compensate for this.
This approach has parallels with the treatment of e.g. punching shear in concrete, where an effectiveness factor may be employed. By default, zero shear bond strength is assumed to ensure a conservative solution is obtained. The magnitude of shear bond strength may be determined practically or found in literature. For example, Hendry (Section 8) discusses the range of shear bond strengths likely to be encountered in masonry (0.15N/mm2 to 0.35N/mm2 for the cases discussed therein) and readers may wish to refer to their national guidelines and codes of practice where additional guidance is required.
For more information, refer to the LimitState:RING User Manual (Section 5.6).
Ultimately, the decision is down to the engineer as to the degree of separation that might be present and how this can affect the bridge. LimitState:RING can be used to give a better idea of the likely mode(s) of response, but should be used with the above in mind.
Reference
Hendry, A. (1990), ‘Masonry properties for assessing arch bridges’, Transport and Road Research
Laboratory Contractor Report 244 .