LimitState:RING 4.0 beta used to study a complex masonry structure
As part of a wider study by Arcadis (France) for a global methodology for assessment of the loading capacity of complex masonry arch bridges, a special version of LimitState:RING was developed and used to analyse a particularly interesting structure – Masléon Bridge. This note briefly outlines the history of the bridge and the LimitState:RING assessment undertaken.
The full study, including the proposed methodology for the assessment method for complex masonry arch structures, will be available in due course.
Masléon Bridge [Figure 1] was constructed between 1865 and 1868. It is a complex structure totalling 69m in length and supporting a 7m wide highway. The geometry comprises a 15m span main arch and seven smaller, internal vaults (ranging in span from 3.8 to 9.8m). On both sides of the main arch are sub-surface concrete structures that transfer the loads directly to the internal vaults.
Figure 1 - Historic drawing of Masléon Bridge
The bridge is located in the centre of France, near Limoges. During WWII, the Limoges side of the bridge was damaged by the French resistance in an attempt to stop the progress of the German army. Following the cessation of fighting, in 1946, the structure was repaired using a reinforced concrete slab lying transversally across the original masonry spandrel walls.
In the 1980s, on the Masléon side of the bridge, remediation work was undertaken to lighten the weight of the structure. The backfill over the vaults was completely removed and, to carry the road, a concrete slab was constructed that rested atop the spandrel walls and the piers of the vaulting.
It is the presence of the internal vaults, along with the repair and remediation measures undertaken, that make Masléon Bridge such an interesting structure. However, it is these features that also make it difficult to analyse.
Since the time of construction of Masléon bridge, vehicle weights and the load capacity expected from historic structures across France, have increased. This is particularly evident in the Limoges area, where logging activities mean that the expected vehicle weights are particularly high (up to 57 tonnes). This naturally requires reassessment of all bridges in order to provide an assurance of their safety.
The currently available version of LimitState:RING facilitates the assessment of multi-span, multi-ring masonry arch structures but does not model rigid block elements outside of the main arch and pier locations. Therefore, LimitState:RING 4.0 (beta) was developed to incorporate this capability, allowing the concrete elements and complex vaulting structure of Masléon bridge to be represented. This permitted a more accurate estimation of the bridge capacity, and likely failure mechanisms to be identified.
A CAD drawing of the elevation of the bridge was developed and imported into LimitState:RING 4.0 beta as the basis for the model.
The arch barrels were ascertained to be approximately twice as thick at the springing than they are at the crown. For the lower vaults, no extrados arch profile was provided in the drawings, so a conservative uniform thickness (0.63m) was assumed in all cases, this being the minimum thickness of the other internal arches at the crown.
The number of blocks in each arch barrel was also unavailable. It was assumed that the internal vault barrels contained 20 (or fewer) blocks per span and that the main arch contained 40 blocks. This was deemed to provide a solution that was sufficiently accurate.
An individual model of each span was generated and incorporated into the main file. These were then checked against the intrados and extrados profiles of the original arch drawings, to ensure that they matched as closely as possible.
No evidence of backing, mortar loss or arch barrel cracking was found. These features were, therefore, not taken into consideration during the analyses.
The arrangement of the masonry blocks forming the internal vaults was also unknown. A semi-random configuration was therefore assumed. In areas where failure of the masonry was not anticipated, larger blocks were specified. At the points where the vaults meet one another, a vertical line of contacts was applied such that the different vault sections could act (semi) independently of each other if required.
The bridge contains a number of large, concrete load spreading structures.
To the Limoges side (left) is a large ‘beam’ which rests on three supports. These transfer applied load directly to the upper level of masonry vaulting. To the Masléon side (right) is a piled slab structure that rests at one end over the right quarterspan of the main arch.
Both concrete structures were modelled in LimitState:RING as rigid bodies. On the right, the piles were removed from beneath the slab. The backfill was effectively disregarded in this area, so some support was required in order to prevent the slab from ‘sinking’ under its own self-weight. Therefore a small support block was added under the right end. This allowed the slab to slide and rotate, but not move downwards without a large force being applied (a crushing strength of 100N/mm2 was assigned). This was considered to be an acceptable representation of the real life arrangement.
Backfill / Surface Fill
The effects of fill unit weight and horizontal passive restraint provided by the backfill and surface fill were not taken into account during the analyses. However, live load distribution through the fill was considered and assumed to be the same as the software defaults, i.e. Boussinesq with a 30 degree cutoff angle longitudinally and linear with a 1:2 horizontal to vertical slope in the transverse direction.
Ignoring unit weight and passive restraint is a conservative measure and is likely to reduce the critical adequacy factor calculated by the software by a considerable amount.
A number of load vehicles were considered:
- Design convoys (wains and carts – to ascertain likely factor of safety on design loading).
- Regulatory convoys (to ascertain the performance at current vehicle load limits).
- Wood convoys (to ascertain the performance under increased vehicle load limits up to 57 tonnes – see Figure 2).
Each vehicle was moved across the bridge, in both directions, and the critical mechanism and adequacy factor determined at regular intervals.
Figure 2 - Axle loads and spacing for 48 and 57 tonne wood carrying vehicles
Effective Bridge Width
The road over the bridge is 8m wide, consisting of 2x3.50m carriageways and 0.5 m of footpath to either side. The effective bridge width was calculated for each case in accordance with the guidelines set out in BD21/01, conservatively assuming no fill depth and a 2.0m axle width for each vehicle.
Table 1 outlines the results for each load vehicle. The vehicle position is measured horizontally from the springing point of the left pier of the main arch.
Table 1 – Results from the analyses
Given the nature of the structure, it was not surprising to discover that, depending upon the position of the load, the bridge may exhibit one of a number of complex failure modes:
Left Zone - Internal Vault Failure
With load positioned over the left side of the model, it was found that the 16 tonne, double axle regulatory load (Bt) is the critical vehicle when located at -1.86m. This corresponds to loading directly above the smallest internal vault, at the top left of the main arch [Figure 3].
Figure 3 – Critical failure mechanism with loading over left side of bridge
The adequacy factor was found to be 3.89, which is greater than the required value of 3.0 prescribed by French codes of practice. It was therefore concluded that the left part of Masléon Bridge has a sufficient capacity.
Right Zone - Main Span Failure
With load positioned over the right side of the model, it was found that the 57 tonne wood convoy is the critical vehicle when located at 19.29m. This corresponds to loading directly above both the right quarterpan of the main arch and the left side of the concrete slab, which also spreads the load down to the right quarterspan [Figure 4].
Despite this rather concentrated loading, the calculated adequacy factor for this case was found to be 4.77 – again surpassing the required value.
Figure 4 – Critical failure mechanism with loading over right side of bridge
As part of a study on the assessment of complex masonry arch bridge sructures, Masléon Bridge was modelled using LimitState:RING 4.0 beta, software that was capable of considering rigid blocks in complicated arrangements. Various loading conditions were examined, including a number dealing with large wood-carrying vehicles weighing up to 57 tonnes. It was found that the factor of safety on loading in all cases was above 3.0 (the value required by French codes of practice). Additionally, the associated failure mechanisms were seen to be considerably more complex than could have been considered using other versions of the software.
Thanks to Thomas Stablon and Carine Mellier of Arcadis (France) for contributing the majority of the material used to prepare this feature.