4. CONVENTIONAL ARCH STRENGTH ASSESSMENT METHODS

4.1 Overview

The ELFEN Finite/Discrete Element analysis employed at the heart of Archtec forms one of several computer based arch assessment methods each of which is appropriate in different circumstances. Generally more approximate non-computer based approaches to strength assessment, such as the modified MEXE (Military Load Classification (of Civil Bridges) by the Reconnaissance and Correlation Methods) method, have not been included in any comparisons.

The principal, conventional, methods of assessment are reviewed in the following sections.

Comparison of the results of these methods with both ELFEN and tests are included in later sections.

4.2 ARCHIE and ARCHIE-M

Archie(2) originally developed at the University of Dundee in 1983 is perhaps the most popular method of strength assessment for masonry arches after the modified MEXE hand calculation method. The latter, whilst often being fit for purpose for approximate assessments, is somewhat subjective. Running under DOS this computer program implements an improved version of the mechanism analysis first published by Heyman(3) in 1980. The chief improvement was the inclusion of horizontal soil pressures in the formulation. In the past, much work has been under taken to verify this program and it is listed in BA 16(4).

Archie is used to undertake strength assessments by entering idealised bridge geometry along with basic material properties for the component parts of the bridge, namely the barrel, fill and surfacing. Dead loads are automatically generated from the bridge geometry and live load arrangements are user defined including how load is distributed transversely. Generally transverse load distribution is based on BD 21(5).

The solution process uses a modified mechanism method to calculate a line of thrust in the arch under dead and live loads. A routine first establishes the locations of four hinges in the span followed by calculation of reactions and then vector algebra is used to position the resultant line of thrust. The method produces a lower bound solution. In other words, if a load path can be found that lays entirely within the masonry then the modelled arch is capable of sustaining that load even if it is not the true load path.

Although Archie is an excellent tool for first visit strength assessments it has several restrictions that can be important as follows.

1. Displacements cannot be calculated as the solution is derived from force equilibrium calculations alone.
    
2. The arch barrel is assumed to be monolithic and, therefore, the behaviour of multiring arch barrels cannot be represented if shearing between rings occurs or rings are separated.
    
3. Failure is based on four hinges developing. Other types of failure cannot be identified.
    
4. True multi-span behaviour cannot be easily assessed. Subject to the same limitations for single arch analysis the program Multi has been developed to provide multi-span assessments where further hinges develop. However, considerable skill and experience of the software is required to obtain reasonable solutions.
    
5. The influence of concrete saddles, arch ribs, internal spandrel walls, reinforcement, complex boundaries and settlement cannot be investigated.
    
6. The use of a passive soil pressure participation factor is subjective, however useful for bounding solutions. This factor determines the maximum proportion of horizontal passive pressure that is applied to the ring at the position of maximum possible movement. The authors suggest that a value no greater than 0.3 should be used, as the soil displacements necessary to achieve a higher factor would also have resulted in a failure of the arch.

Archie-M(6) by Obvis Ltd was first produced in 1999, is written for PC Window environments and uses essentially the same principles in the analysis as the original version. However, the treatment of soil passive pressure and longitudinal distribution of live load as summarised below is slightly different. Consequently, the assessed arch strength is likely to be slightly different from solutions obtained with Archie.

When applied, Archie-M determines the proportion of passive pressure that would be needed to bring the thrust just into the arch at the springing and applies that. In the analysis a new hinge is generated at the springing. If the thrust is outside the arch at a higher point, then the hinge is moved upwards incrementally increasing the passive pressure applied above and removing that applied below until a position is reached where passive pressure is consistently distributed. Clearly, full passive pressure requires a large movement in the fill to mobilize its full shear strength and, therefore, it is recommend by the authors not to exceed half full passive pressure in assessment work. Above half full passive pressure it is likely that the geometry of the bridge would have to change appreciably, a condition that occurs beyond peak strength capacity, before this level of pressure could be realised.

Apart from the alteration in the treatment of passive pressure, the longitudinal live load distribution through the fill has been somewhat rationalised since Archie was first written and has been smoothed to remove step changes in load pressure implied in BD 21 that cannot occur in reality. In this respect Archie-M is perhaps more realistic than Archie.

4.3 RING

RING(7) is the product of more than 10 years of development at the Bolton Institute and the University of Sheffield. The version used in this verification is a PC Windows based program and represents the most comprehensive implementation of the mechanism method of all commercially available programs based on this technique.

Potentially, RING provides several advantages over Archie and could be used to provide the next stage in an assessment program. However, it is not yet widely used in the industry and nor is it listed in BA 16(4). The chief advantages over Archie are the ability to represent multi-ring behaviour and flag potential shear failures but some similar restrictions exist as follows:

1. Using a similar but more complex implementation of mechanism analysis, displacements cannot be calculated as the solution is derived from force equilibrium calculations alone.
    
2. Because of i) strains and damage cannot be calculated. Hence, although solutions are useful for ultimate limit state assessments, which is current practice, serviceability limit states cannot be meaningfully investigated.
    
3. Failure associated with buckling where the non-linear effects of relatively large displacements are critical cannot be considered. Buckling behaviour is important for slender and flat arch barrels.
    
4. The influence of concrete saddles, arch ribs, internal spandrel walls, reinforcement, complex boundaries and settlement cannot be easily investigated.
    
5. As with Archie the use of passive soil pressure participation remains somewhat subjective, but again useful for bounding solutions. Options include uniform horizontal pressure or classical passive pressure, varying with depth.