On the service behaviour of masonry viaducts

The vast majority of studies of masonry bridges have been based on ultimate load performance. There is an increasing body of observational evidence that behaviour at service load is fundamentally different. Railway viaducts, in particular, are suffering damage under normal traffic that is

• not predicted by available analyses

• not properly diagnosed

• treated without real understanding.

This paper describes a system of behaviour that has become apparent over 30 years of engagement with bridges. Much of this engagement has been at second hand, as users of the Archie masonry arch analysis software family call for help and provide photographs of damaged bridges. In addition, the authors have had the opportunity to directly and closely observe, and indeed measure, movement of a few viaducts.

These observations led first to an increasing sense of unease about the accepted models of behaviour and the assessments and interventions based on them, then eventually to the new model presented in this paper.

This paper first summarises the observed damage, then sets out the new model of behaviour. Measurement of the response of a railway viaduct to normal passenger loads supports the model. Some brief calculations show that collapse is unlikely to be an issue. The response of typical piers is considered. The serious implications of this new understanding are highlighted in the discussion section, and consideration is given to the next steps in turning this new model into a tool for the rational management of masonry arch viaducts.

The most pronounced, and best known, fault in viaducts particularly is the spandrel crack. These occur in single-span bridges but are much more prevalent in viaducts and that, in itself, provides a clue to differences of behaviour. In stone bridges, or those with brick arches and stone edge voussoirs, the crack usually forms vertically through the arch (Figure 1). In brick, the initial damage often takes a corbelling line from course to course, beginning at the inside face of the spandrel wall and stepping outwards half a brick at each course (Figure 2). The sources of this damage have been described in detail by Harvey (2012).

Another behaviour that is well recorded and for which treatments have been developed is the outward movement of parapets. At Enterkin Burn on the Glasgow and South West Railway, a track slab was constructed in the form of a trough to contain the lateral pressure that was assumed to cause this damage, but it seems possible that this is a misdiagnosis and that the symptoms have been treated rather than the root cause.

The problems that concentrated the authors’ attention on this issue were horizontal cracks in spandrel walls on straight, or nearly straight, viaducts (Figure 3). Here, very often, the parapets have not been pushed sideways, so it seems that lateral pressure on bends may well be the cause of the lateral movement, but the horizontal crack at which the movement takes place is unlikely to be created by such pressure.

The authors observed these cracks at Frodingham viaduct, near Scunthorpe in 1986. This is believed to be the most heavily loaded viaduct in the UK. It carries train loads of raw materials into the Scunthorpe iron and steel works and loads of finished product out, some 20 trains per day each with about 70 axles of 25 t. There are horizontal cracks that run for many spans. Some are at the level where the thinner parapet sits on the thicker spandrel wall, some at the level of the arch crown (Figure 3). They can be observed because the viaduct has been embanked to about half way up the semi-circular arches. This embankment seems to have made little difference to behaviour. No measurement of the movement has yet been possible, but loose bricks in some spans amplify it and show it to be mostly vertical: the parapet or top courses of the spandrel wall move up and down relative to the parts below as trains pass.

Observing similar cracks in Marsh Lane viaduct in Leeds was the trigger for further thought and investigation (Figure 4). There is spalling damage at the top crack (at the base of the parapet), which further emphasises the up and down nature of the movement. In some cases, the flexing leads to damage at the edge of the arch (as seen in the following section).

An archive photograph of London Road viaduct in Brighton (Figure 5) after bomb damage adds another element to the story. A large part of the arch has remained firmly attached to the masonry fill or backing within the structure. This is of critical importance to the arguments that follow.

The essence of the argument presented is that the behaviour of viaducts is controlled largely by stiffness. This can be no surprise, for force follows stiffness in every structure, but those working on masonry often lose sight of it because masonry stiffnesses are so high. It is relative stiffness, however, which is of issue.

Consider a pair of arches sitting on a pier (Figure 6), with masonry or concrete fill. The darker-shaded section – including perhaps a third of each arch, the fill and (if present) the walls above – forms a block. This block is extremely stiff and amply strong enough to behave as a unit under most loads. The remaining third of the arch between blocks is more flexible.

The arch behaviour described by Hooke (1676), Castigliano (1879), Heyman (1981) and Harvey and Smith (1991) demands that the arch is a flexible member, as indeed the arch itself will be. Removing this flexibility changes behaviour in a dramatic way because the arch can no longer flex over its full length.

If the pier top block is effectively rigid, it can only move up and down or rotate. It is held longitudinally by the arches and supported on the pier. It will therefore rotate about a point where the vertical through the pier and the horizontal through the crowns meet (Figure 7). The pier can offer no significant resistance to this rotation, and will accommodate it by rotating at the foundation as shown. There is some room for variation of the centre of rotation because the reaction at the pier will move towards the load and the thrust in the unloaded span will move towards the intrados.

This rotation is imposed within the width of the bridge by the vehicle loads, but is resisted more effectively by the combination of spandrel wall and parapet, which can be regarded (until a crack forms) as a unit. The resistance to rotation at the edges leads to very high stresses at various points and it is impossible to predict which point will prove weakest in a particular bridge. Horizontal cracks may develop in the spandrel wall (Figure 8) or vertical cracks in the arch itself under the inside edge of the spandrel wall (Figure 1). Indeed, it may well be that a horizontal crack forms first but does not produce a sufficient release and the stresses at the edge of the arch are enough for a crack to form there too.

It has recently been possible to measure movement in a rail viaduct in such a way that the behaviour described can be identified. The viaduct has four spans of 9·14 m with rise of 2·24 m and ring thickness 0·58 m. With piers 1·35 m thick, the viaduct has a total length between abutments of 40·61 m.

Vertical deflections at the quarter points were measured using newly developed lightweight deflection poles. Deflection at the pier was recording by tracking movement of a printed target in video, with cameras positioned well away from the viaduct to avoid the influence of ground movement adjacent to the pier. Movement under normal traffic was recorded.

Deflection pole measurements are made with linear potentiometers sampled at high resolution. Taking various error sources into account, the accuracy is better than 0·01 mm. Measurements from video are of lower quality, with noise and quantisation error in the output producing a resolution of about 0·1 mm.

Figure 9 shows a summary of the results at one pier. The left-hand measurement is at the quarter point of the span from which the train is approaching, the central point at the left-hand face of the pier and the right at the quarter point of the second span.

Plotting the position of these points relative to ‘at rest’ at various times through the transit, the lines remain straight. The block is rocking but not bending.

If this view of behaviour is correct, the ‘pier block’ can be treated as a free body in isolation so far as live load is concerned. Figure 10 shows this block and the various forces acting on it (extracted from Figure 7).

The pier offers no significant resistance to horizontal movement at the base of the block. Setting aside the influence of the spandrel walls and parapets for a moment, there is similarly little resistance to vertical movement at the left and right edges of the block.

The weight on top of the pier will be the total from arch crown to crown.

The critical loading will be with the maximum eccentricity, which may be with a group of four axles straddling the crown, but that will only be critical if the next group is more than a span behind. That is, if the vehicle length is greater than span plus pier thickness. The critical vehicle is the longest available and that is probably (in the UK) an HTA. The axle spacings of an HTA vehicle are shown in Figure 7 in relation to a span of 9·14 m or 30 ft.

If a 2 m pier is considered to be the biggest to be expected, then the span at which the concentrated effect begins to dissipate is 14·5 m or 47 ft. 50 ft (15·24 m)spans are not uncommon but Frodingham is 30 ft (9·14 m), as is Marsh Lane. The smallest spans may be the most critical because the mass increases with the square of the dimension while the destabilising effect of the live load depends only on the lever arm.

It is therefore of value to consider the effect of a railway HTA vehicle axle group on a 30 ft (9·14 m) span. It seems sensible also to consider the 4:1 span rise ratio that is a reflection of Marsh Lane.

In calculating the results presented here the following assumptions have been made.

• (a)

  The whole of any load in the half span acts on the appropriate pier.

• (b)

  There is no stabilising effect from the arch or spandrel walls.

• (c)

  There is no dynamic effect on the loads (this partially compensates for the error in (a)).

• (d)

  The worst case is four axles straddling the arch crown, when the next bogies each side will be directly over the piers.

The load system and resulting reactions are illustrated in Figure 10.

The maximum tilt measured is 2·2 mm over a 7·5 m length. Under a fully loaded freight train, the load will be nearly doubled, so one might expect a differential deflection of 4 mm. The ring is 0·58 m deep. This rotation will produce a wedging action. If the rotation does not cause a crack at the crown, the effective depth at which the resultant acts will be much less than the ring thickness, perhaps closer to 300 mm. This creates a change of horizontal length 0·3/7·5 × 4 or 0·16 mm (Figure 10). The minimum length over which this displacement might become strain is of the order of 7·5 m. (In practice, the ends of the section are not rigid, so the strain will be rather less). This produces 21 microstrain. The elastic modulus of Victorian brick masonry is highly variable, but taking a value of 5 GPa as plausible, the resulting change in stress at the centre of force is 106 kPa. The average over the stress block of 140 mm is 2/3 of that or 70 kPa and the corresponding force is 119 kN in the 4 m half-width of the viaduct. The restoring moment is then 119 × 0·3 = 36 kNm to support the train, which is negligible in the context of the disturbing moments.

The overturning moment is thus approximately 1400 kNm. The weight on the pier is about 1700 kN so the eccentricity will be 0·81 m, placing the load 100 mm from the face of the pier.

To provide a broader picture of behaviour, a range of standard structures was considered. In each case, the ring thickness was calculated using Rankine's rule (ring thickness = sqrt(36·6 × radius) in mm). The pier thickness was taken as span/7·5. Backing was assumed to reach the level of the crown intrados. The results are presented in Figure 11. The non-linearity of these lines is a function of various non-linearities in the structural model.

There are, of course, many factors that have potential to modify these results. As the issue here is the rotation demanded of the block, the elastic performance of the pier under eccentric load becomes significant. The possibility of impact loading must be considered, although the inertia of the system is so high and impact loads so short it is unlikely that they would have a dramatic effect. Any voids in the structure would reduce the dead weight, with a corresponding reduction in stability. Figure 11 also shows the effect of a 10% reduction in weight, which is typical for a voided structure.

These calculations are simplistic. This is a three-dimensional problem and there are many potential modes of failure, each leading to a different distribution of load. For example, if the upper section of the wall sits on the rising end of the backing block, the stabilising effect is substantial. However, if a spandrel crack develops through the ring, part of the stabilising force is potentially lost.

If the thrust remains within the middle third of the pier throughout transit, the tilt of the pier block will depend largely on the flexure of the pier. On rock, the base will not rotate; so the thrust in the pier will be inclined such that the pier bends into an ‘S’. The degree of eccentricity at top and bottom will be controlled by the pier flexibility. On any other foundation, rotation will occur so that a parallel-sided pier will bend into a single curve, although the curvature is likely to be very small. For example, the rotation in Figure 7 is about 1·2 min of arc.

The corresponding differential of displacement of 2·2 mm between the quarter points is enough, if restrained, to put considerable tensile stress on the mortar beds of the spandrel and parapet near the descending point.

There may be resistance to believing that long-established perceptions of viaduct behaviour are invalid. In a different context, Feynman (1999, p. 169) said ‘For a successful technology, reality must take precedence over public relations for nature cannot be fooled.’ The evidence of damage is there to be seen and no desk or lab work can argue against it. The load paths are definitely not what have been previously assumed, although it is far from certain that the path proposed is the correct one. It is unlikely to be the whole truth.

The implications of this are serious and immediate. Any load that can concentrate around 50 t on half a viaduct span is likely to lead to problems. Sooner or later, two such loads will coincide and the effect will be dramatically increased. Once a crack is formed, much smaller loads will open and close it, doing progressive damage that may not be rapid but will be inexorable.

The biggest danger economically is in bridges where new traffic is to be applied. Existing analyses will allow the comfortable impression that there is no danger, but damage is likely to become evident shortly after the new traffic begins. With contracts already in place with hauliers, load or speed restrictions are likely to lead to compensation payments.

Traditional forms of bridge strengthening (saddles and track slabs) add negligibly to the stiffness of the system. A troughed slab may reduce or even stop the transverse movement of parapets but will not prevent the rocking motion that will continue to do other damage.

The biggest concern is that damage will accumulate in unexpected ways, potentially leading to falling masonry long before the structure becomes inadequate for traffic (Figure 6).

The arguments and evidence presented appear to the authors to be compelling, but the detail of the described behaviour remains to be established. More field measurement is needed, coupled to both detailed and simplified analysis to enable boundaries to be put on behaviour. Only then will it be possible to develop assessment tools that are properly validated.

It will also be necessary to reconsider treatment of damage, and strengthening of damaged and undamaged viaducts.

It is essential that the new processes are fully reversible because existing techniques do not deliver the required outcomes and any new ones will be untried.

Current analyses of viaducts fail to identify the potential for damage that occurs in practice. A model is proposed that explains the damage that occurs.

Simple calculations show that the structures retain adequate capacity but will deteriorate through mechanical damage. Repairs and strengthening that do not take this behaviour into account are likely to do more harm than good.

The total economic cost of ignoring true behaviour can be very high, involving compensation payments to hauliers whose operations are actually damaging the bridges. Repairing damaged bridges, even if it is possible, can be very costly.

When altering masonry structures, the risk of doing damage is high because understanding is poor. Any intervention should be reversible.