Structural Analysis of Historic Construction – D’Ayala & Fodde (eds)© 2008 Taylor & Francis Group, London, ISBN 978-0-415-46872-5

Assessment and strengthening masonry arch bridges

C.L. BrookesGifford, Southampton, UK

ABSTRACT: This paper describes how during the last 10 years Gifford has been applying a novel numericaltechnique to accurately assess the strength of masonry arch bridges, and for weak bridges, to design repairs andstrengthening. This has involved a major development programme including full-scale laboratory tests, supple-mentary load tests on bridges in the field, monitoring programmes and verification of the arch bridge structuralanalysis which has been based on the Finite/Discrete Element technique. The advantages this technique providesover conventional masonry arch bridge analyses, both mechanism and traditional Finite Element modelling, aredescribed and how through partnering an innovative assessment and strengthening service is being delivered. Therelevance of this approach to emerging serviceability limit state arch bridge assessment, which is seen as beingparticularly important for Railways, is also discussed. Some practical issues relating to bridge strengthening andworking within national codes of practice are also covered.

1 INTRODUCTION

It is likely that there are at least half a million masonryarch bridges in use throughout the world today, princi-pally carrying road and rail. European railways aloneaccount for 200,000 bridges (Orbán 2004). Thesebridges form a vital asset. Their replacement cost isalmost incalculable yet a world wide insatiable appetitefor economic growth is in some cases pushing their useto the limit.

Despite being ancient in form, masonry archesare notoriously difficult to accurately assess. At alllimit states their behaviour is complex, deriving theiroverall behaviour from the interaction of individualparts, blocks, bricks, mortar and fill. Several meth-ods for assessing the strength of arch bridges havebecome well established, but their generalised use islimited and their application for designing strength-ening difficult. Finite Element analysis, which has tobe non-linear to predict strength, has also been suc-cessfully applied but the choice of tensile materialproperties can be problematic as this can artificiallyinfluence the predicted strength.

The Finite/Discrete Element method, whichinvolves the automatic computation of interactingbodies is, therefore, a natural choice for representingmasonry and this type of non-homogenised structure.Like the conventional Finite Element method, beinga generalised approach also means that, subject toverification, any geometric form of masonry can besimulated. Consequently, there are no restrictions to

the arch bridge form, the number of spans, rings andpiers that can be modelled. Also, unlike many simplerstrength assessment methods, there is no adherence topredetermined failure mechanisms, for instance, a setnumber and pattern of hinges.

The application of the Finite/Discrete Elementmethod has marked a step change in the rigour that cannow be applied to the structural analysis of masonryarch bridges. Not only can it be used to accuratelyassess strength but also to determine bridge defor-mation, including all significant non-linear effects,making it possible to assess behaviour at both strengthand serviceability limit states. Also, being a gener-alised approach the behaviour of complex bridgescan be assessed where for example a concrete sad-dle may exist, or the bridge is propped and in thecase of strengthening, retrofitted reinforcement isintroduced.

Through partnering with Cintec International whomanufacture and install a masonry anchor system,Rockfield Software who produce the ELFEN (Rock-field 2003) structural analysis software, Gifford havecompleted over 170 bridge assessments and bridgestrengthening designs, mainly in the UK but also inthe USA, Australia and India. Known as Archtec, thisservice was originally conceived for efficient, eco-nomic and sympathetic strengthening of arches, butthe method of structural analysis can also provideaccurate strength assessment of existing bridges andon many occasions has been used to show that bridgesdo not need to be strengthened.

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2 CONVENTIONAL ASSESSMENT

Methods of strength assessment have been categorised(McKibbins & Melbourne 2006) as semi-empirical,limit analysis and solid mechanics methods.

2.1 Semi-empirical methods

Most semi-empirical methods are based on the MEXE(Military Engineering Experimental Establishment)method which evolved from work undertaken in the1930s for the military to rapidly assess arch bridges.It is often still used as a first pass strength assessmentbut its use is highly subjective and there are many lim-itations. It is of little value for any detailed work suchas the design of strengthening.

2.2 Limit analysis methods

Most conventional bridge assessments are now carriedout using computerised versions of limit analysis alsoknown as mechanism analysis. In its simplest formthese methods consider a 2D arch comprising a seriesof blocks of infinite compressive strength, which can-not slide against each other and cannot carry tension.A routine is used to establish the locations of hinges inthe span followed by calculations of reaction and thenvector algebra to position the resultant line of thrust.The method produces a lower bound solution. In otherwords, if a load path can be found that lays entirelywithin the masonry then the modelled arch is capableof sustaining that load even if it is not the true load path.

Limit analysis techniques have proved to be excel-lent tools for first phase strength assessments butseveral restrictions exist that are important in thedesign of strengthening. The most important of theseis the inability to calculate strain and displacement.Consequently, it is not possible to determine the distri-bution of stress at operational load levels, it is difficultto assess the serviceability of bridges and in the caseof strengthening, it is not possible to determine theshare of load between the existing bridge and thestrengthening.

2.3 Solid mechanics methods

The established technique used to model continuumbased phenomena in solid mechanics such as deforma-bility is the Finite Element Method (FEM). Not sur-prisingly this has also become the most popular solidmechanics method used for arch bridge analysis, andthere are numerous well developed industry qualitycomputer programs available.

Like limit analysis most work is carried out using2D representations, generally plane strain, but 3D shelland solid models are used for special assessments.

Although these techniques can be good fordetermining displacements, strains and stresses at

operational load levels they quite often become dif-ficult to use to predict ultimate strength and damage.This is generally because of the type of solver thatis used, normally an implicit solver, and the effortrequired to ensure internal forces are in equilib-rium with external loads, as brittle materials such asmasonry soften and redistribute load. The solution tothe equilibrium problem is normally to use a hypothet-ical masonry tensile strength but choosing a suitablevalue, large enough to achieve equilibrium conditionsare met but small enough not to influence the result,can be a challenge.

3 THE FINITE/DISCRETE ELEMENT METHOD

3.1 Description

Numerical techniques have been devised to representdiscontinua where body or particle interaction definesoverall behaviour (Cundall 1971). Perhaps, the mostadvanced technique that describes this behaviour is theDiscrete Element Method (DEM). The relatively newFinite/Discrete Element Method (FDEM) (Munjiza2004) is a combination of FEM and DEM and pro-vides a more natural approach to the simulation ofmany materials and structures. It has been applied toa diverse range of engineering and scientific prob-lems from food processing to rock blasting. Throughautomated adaptive modelling, even the transitionfrom continua to discontinua and the fracturing andfragmentation process can be represented.

FDEM is aimed at problems involving transientdynamic systems comprising large numbers ofdeformable bodies that interact with each other. Mod-els involve typically thousands, but in extreme casesmillions, of separate Finite Element meshes auto-matically interacting with each other using DEMcontact algorithms. The solution of the continuumequations associated with FEM is well established, thealgorithms within DEM less so.

Contact detection and contact interaction lay at theheart of DEM. Contact detection is aimed at iden-tifying discrete elements that can potentially comeinto contact with each other and eliminating thosefar away from subsequent contact interaction algo-rithms. Different algorithms have been developed fordifferent packing densities for example, sparse andmoving or dense and static. The chief aim here is toreduce computing effort. Contact interaction appliedto the surfaces of discrete elements coupled throughthe detection process is where interface behaviour iscalculated. Here interface laws are applied accordingto the surface characteristics of the contacting discreteelements for example, frictionless no-tension contact.During the solution of transient dynamic problems ofeven quite modest size millions of contacts will bedetected and resolved.

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Another key aspect of FDEM is that the analysisinvolves all equations of motion, is therefore dynamicand uses an explicit central difference solution scheme(Owen 1980). This involves a time stepping procedurethat is conditionally stable, but unlike many conven-tional FE solvers that use an implicit solution scheme,does not involve computationally intensive matrix fac-torisation. Solutions are achieved only through the useof very small time steps. The critical time step sizebelow which steps must remain for stability and accu-racy is given by the time taken for a stress wave to travelacross the smallest finite element. The efficiency ofDEM contact detection and the avoidance of equilib-rium calculations allows FDEM simulations to predictfailure, collapse and post-failure kinematic behaviour.

3.2 Application to masonry arch bridges

Masonry is a non-homogenised material, can beregarded as a discontinuum and as such is ideallysuited to FDEM. Simply, masonry arch bridges are aspecial form of masonry structure, which is an impor-tant consideration when faced with complex bridgearrangements.

The approach that has been developed for archbridges, applied using the implementation withinthe Finite Element computer program ELFEN, usessmeared masonry compressive properties and explicitmortar shear and tensile properties. Each brick or blockunit is modelled with a separate finite element meshand each unit becomes a single discrete element. Ithas been found that units can also be grouped together(Brookes 1998), a blocky arrangement of four or fivebricks glued together, to improve computational effi-ciency without any loss of accuracy. The masonry archis then assembled using blocky arrangements in hun-dreds, possibly thousands of discrete elements. Otherbridge parts for example, fill, surfacing and backingare similarly represented although the material modelsare different.

FDEM arch bridge models will develop failuremechanisms consistent with limit analysis results ifthese are critical as well as providing displacements,stresses and strains consistent with solid mechanics.

Another key aspect to the use of FDEM andthe adopted modelling approach is that representingmasonry at a fundamental scale requires only com-monly available and basic material parameters to beused in order to accurately characterise bridge struc-tural behaviour. Non-linear material models are usedto define the deformable behaviour of the masonry incompression and the fill in tension. A perfectly plas-tic Von Mises yield criterion is generally used to capcompressive strength, and a Rankine yield criterionused to give a simple no-tension soil model.

The behaviour of mortar, as well as other contactingsurfaces such as masonry to fill, is included by usinginterface material models. Interface models give the

Figure 1. Part of a modelled masonry arch barrel showingFE mesh (left) and DE mesh (right).

Figure 2. Historic masonry ovens, FDEM simulation usedto assess residual strength of an unusual arrangement ofarches. Dark contours show areas of highest compression.

surface of discrete elements appropriate mechanicalproperties. Mortar is represented differently depend-ing on the type of construction. Historic constructioninvolving lime mortar joints is represented using a no-tension Mohr-Coulomb friction relationship. Modernmasonry with cement mortar produces masonry withsome tensile strength. In these instances good pre-dictions of masonry behaviour can only be made byincluding mortar tensile strength and a fracture energyformulation to model the development of cracking.Generally, masonry arches are historic constructionsand do not include cement mortar.

For most types of masonry the generic materialcharacteristics, compressive strength, Young’s modu-lus, mortar friction and mortar cohesion, necessaryfor FDEM simulations are readily available (Hendry1990, BD 21/01 2001, BS 5628-1 2002). They areno more demanding to obtain than those parametersrequired for conventional limit state analyses. An esti-mate for Young’s modulus for different types of fill incompression is similarly available.

There are no limitations to the geometric arrange-ments of arches that can be represented withFDEM other than those associated with computationalresource. However, models are kept as simpleas possible to reflect the confidence in materialparameters, geometric arrangement and to be reason-ably compatible with the codes of practice through

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Figure 3. A sequence of snap shots showing a typical FDEMlive load assessment process and this instance failing. Darkcontours show areas of highest compression.

which all design and assessment work has to be under-taken. Hence, the large majority of simulations are 2Dand plane strain.

In assessment and design, live load is generallyapplied by explicit representation of axle loads usingdiscrete elements. Weight is applied to these elementsand the axles moved across the span with a pre-scribed velocity. As transient dynamic solutions areobtained, regard has to be given to acceleration arisingfrom sudden movement and inertia effects. Conse-quently, loads are applied smoothly and slowly toensure static responses are obtained. Permanent loadsare introduced through construction sequences, whichdepending on the barrel shape, may necessitate theuse of modelled temporary false work; a process thatis always required with real arch bridges.

Although the time required to develop FDEMbridge models exceeds that of comparable limit anal-ysis representations, these models can still be assem-bled in several hours. Also solution times, which are

Figure 4. FDEM simulation showing use of temporaryformwork to support the barrel whist dead load is applied.

Figure 5. A typical arrangement of reinforcement which inthis instance is shown installed from above.

continuously tumbling as ever faster computersbecome available, are modest compared with similarFEM representations with strength analysis completedin around 4 hours for a typical bridge on a 3.6 GHz PC.This includes the calculation of permanent loads andthe traverse of a single vehicle. To complete an assess-ment or design, several axle arrangements have to beconsidered to be sure the critical case is identified, sothis could take several days.With relatively small prob-lem sizes, around 5,000–10,000 degrees of freedom,mass scaling techniques to accelerate the solution pro-cess are never used to obtain solutions, but are usefulto quickly check the simulation process.

4 ARCHTEC

4.1 Description

Archtec strengthening has been described as ‘KeyHole Surgery’ for bridges because of the absence ofany major intervention to the arch barrel. Generallyconstruction comprises retrofitting stainless steel rein-forcement around the circumference of the arch barrel.The reinforcement is grouted in to holes drilled in tothe bridge with a coring rig from the road surface or,alternatively in the case of multi-span structures, frombelow.

Arches conventionally fail by the development offour hinges leading to a mechanism. The design basisfor the strengthening is to locate the reinforcement so

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Figure 6. Installation from below in a multi-span bridgeusing precisely aligned diamond drilling coring equipment.

as to provide bending strength at the critical locationsthereby resisting the development of the hinges. Byproviding bending resistance the arch barrel is able toresist the critical loading conditions more efficientlyand the peak compressive stresses in the masonryare reduced. A similar procedure is applied to morecomplex arrangements including multi-span archesalthough failure mechanisms and anchor positioningrequires anchors to be placed in different positions.

4.2 Benefits

Compared with conventional arch bridge strengthen-ing such as concrete saddling and lining, the Archtecservice has several practical benefits:

1 Through the use of FDEM a good assessment ofexisting strength and bridge behaviour is obtained.This allows accurate matching of strengthening tothe loading requirements if the bridge is understrength, thus minimising any intervention. Alter-natively, strengthening may be avoided.

2 Strengthening is invisible which is particularlyimportant for historic and heritage bridges.

3 Construction is small scale and fast to implement.4 Disruption to bridge users during strengthening is

much less than saddling.5 A more sustainable solution with lower envi-

ronmental impact, embodied energy and carbonemissions.

6 Because displacement and strain is predictableassessments and strengthening designs can bebased on limits states other than purely ultimatestrength.

7 Each anchor installation provides a core of infor-mation that can be used to confirm the materialsand internal arrangement of the bridge.

8 In many instances all these factors equate toreduced cost.

4.3 Working with codes of practice

Archtec services have to be provided within a frame-work which embraces as far as possible national codes

of practice. Unfortunately, outside of the UK, thereare few rules to help Engineers assess arch bridges.For example live loading is almost always developedfor beam arrangements of bridges where load supportis primarily through bending, masonry strength assess-ment is often permissible stress based, and bridgespecific earthquake rules are geared towards steel andconcrete construction. In India the railways have a codeof practice for masonry arch bridges which imposealmost arbitrary performance limits on deflection.

The use of FDEM to simulate arch bridges isa performance based method, useful for limit stateassessment and design, but cannot be directly used forrules that have been developed for linear, often inac-curate, working stress approaches. In these instancesto satisfy bridge technical authorities hybrid analysesare run along side the more realistic and reliable limitstate work. The results allow additional checks to bemade with local codes of practice.

5 VERIFICATION

The process which has been undertaken to verify theFDEM analytical methods employed by Archtec haveincluded a number of key strands and evaluations asfollows:

1 Against conventional methods of arch assessment.2 Against published data from full-scale tests of

unstrengthened arches carried out by others.3 Against full-scale tests by TRL of bridges strength-

ened by the Archtec method which were specif-ically commissioned as part of the verificationprocess.

4 Against the results obtained by monitoring bridgesin the field including before and after strengtheningcomparisons.

Additionally, a philosophy of fixing material param-eters for whole series of tests where similar masonryconstruction has been employed (compressive strengthof bricks, mortar type etc.) has been adopted. Thismakes it impossible to adjust an individual arch anal-ysis to gain better correlation with tests within a serieswithout influencing all others. Similarly, the analysisof Archtec strengthening follows on from verified andfixed unstrengthened analyses.

A selection of the verification work (Brookes 2003)and recent field trials illustrating the accuracy andflexibility of FDEM arch simulation follows.

6 FULL-SCALE ARCH TESTS

6.1 Strengthened arches

In order to test the practical implementation ofArchtec, to validate the FDEM method of structuralanalysis, to help quantify key strength parameters and

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Figure 7. First Archtec full-scale test arrangement.

to illustrate the degree of strengthening that could bearchived, two full-scale tests of Archtec strengtheningwere carried out at TRL. Both tests used partially ringseparated brick forms to be representative of archesthat would warrant strengthening, and were also simi-lar to unstrengthened bridges tested in an earlier seriesso that experimentally derived comparisons could beeasily made.

The anchor arrangements were configured for a sta-tionary point load test and, therefore, were arrangedasymmetrically with respect to the span. In prac-tice, with moving axle loads, anchor arrangementsare arranged symmetrically to reflect critical loadingpositions on both sides of the span.

Comparing the load versus displacement resultsobtained by FDEM simulation with those obtainedfrom the strengthened test shows strength predictionsto be within 2% of test results. There is also verygood stiffness correlation, displacements remainingwithin approximately 5% of test values, throughoutthe loading stage.

Making comparisons between the two tests,strengthened versus unstrengthened, show the failureload of the strengthened arch barrel has been increasedby a factor of approximately 2, the anchors delayed theformation of hinges and added considerable strengthto the arch barrel, and the arch failed in a gradualand a ductile manner. In practice the characteristics ofthe arch barrels are improved sufficiently for intendedloading.

Figure 8. Comparison of load versa deflection charac-teristics between the first Archtec test results and FDEMpredictions. Deflection is measured in the barrel at the spanposition of the load.

Figure 9. Comparison of strengthened and unstrengthenedtest results.

6.2 Observations relating to serviceability

No clear definition of serviceability exists for masonryarches. Deflections and cracking behaviour is nor-mally used to define a serviceability limit state. How-ever, in arches these quantities are generally small andvery difficult to detect under expected service loadsand they cannot be calculated by conventional struc-tural analysis. However, results from monotonic andcyclic load tests have been used to derive masonrystress limits in terms of a limiting factor of the ulti-mate capacity below which permanent damage doesnot occur from repeated loading.

Based on work done by TRL in the 1980’s, theHighways Agency assessment standards for archesare based on serviceability being maintained providedapplied loads do not exceed half the ultimate capacity.

Cyclic loading on bridge piers has been investigatedby British Rail Research and some progress madein linking fatigue of brickwork with a serviceabilitylimit state. It was concluded that, for dry brickwork, ifapplied loads do not exceed half the ultimate capacityan infinite number of load cycles could be sustained.However, for saturated brickwork lower load levels arerequired.

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Figure 10. Comparison of maximum predicted compressivestresses between strengthened and unstrengthened bondedrings.

Both observations of monotonic loading and cyclicloading have led to the recommendation of a 50% ruleand are in effect stress limit based.The currentArchtecdesign method, which uses load factors based on theUK Highways Agency standards, embraces the ser-viceability limit state implicitly within the load andmaterial factors used at the ultimate limit state. Whilstthis method is consistent with current practice, FDEManalysis used in the design of Archtec strengtheningenables the behaviour of the arch under serviceabil-ity loading to be investigated in ways never beforepossible.

Comparison of results from the unstrengthenedand Archtec tests show that under identical loads,displacements are very similar. Corresponding struc-tural analysis of the test arches predicts compressivestresses in theArchtec strengthened arch that are lowerthan the unstrengthened arch under the same load-ing. For example, using the bridge proportions of theArchtec tests and UK highway 40/44 tonne vehicleaxle loading, under the maximum service load themaximum compressive stress in the masonry barrelwas reduced by approximately 15%. The reduction instress is due to the fact that the strengthening intro-duces bending capacity into the arch barrel, which cantherefore resist the applied loading at the critical pointsmore effectively. Hence, on the basis that serviceabil-ity can be defined by a stress limit, the reduction ofstress levels in the masonry in Archtec strengthenedbridges has a beneficial effect on serviceability.

Other aspects of bridge serviceability might be con-cerned with specific deteriorated conditions in archbarrels, such as loose bricks and ring separation. Therisk here is that debris falling from a bridge wouldrepresent an unacceptable hazard. An example of anarch barrel in a weakened condition that could developloose bricks as a result of partial ring separation hasbeen tested and used in comparison with Archtec.Displacement results show that Archtec strengthen-ing significantly increases the stiffness of the ring

separated barrel restoring it to that of the fully bondedcase (as-built condition).The implication is that strainsin the intrados have been reduced and the risk ofbricks loosening is thereby also reduced. Provided anarch is maintained in reasonable condition the risk ofbricks loosening should be reduced compared to anunstrengthened arch. There is also no reason to doubtthat similar trends in behaviour will occur if the innerring itself is in a deteriorated condition.

Bridge owners and experts in the field recognise thedesirability of further research with respect to the ser-viceability limit state and phenomena such as masonryfatigue. However, at the current time no specific guid-ance or criteria exist with respect to explicit evaluationof the serviceability state in arches.

To provide increased confidence that the service-ability of a bridge is being improved by Archtecstrengthening additional checks have been introducedinto the design process. As a precautionary measurein the absence of other guidance, the following addi-tional serviceability criteria are included in the designprocess:

1 Either check that stresses under the required liveloading do not exceed those in the unstrengthenedbridge under existing live loading, or alternativelycheck that stresses in the strengthened bridge arebelow an agreed serviceability limit state value.

2 To be sure that existing defects are not made worse,or for that matter introduced into arch barrels byArchtec strengthening, strains along the intradosunder the required live loading are checked toensure they do not exceed those in the unstrength-ened bridge under existing live loading. Strains arecalculated over a reasonable length so that an esti-mate of radial joint cracking, critical to looseningof bricks, is included.

These criteria are considered very conservative andstresses and strains beyond these limits may be quitesafe and have no adverse serviceability effects. How-ever, further fundamental research is required toestablish appropriate limiting criteria.

7 FIELD MONITORING

Several bridge monitoring programmes have beenundertaken during the last decade to help verify FDEMarch simulations, and for strengthened bridges, tomake before-and-after behaviour comparisons. Themost recent of these was for Indian Railways with thefirst part of the programme completed in 2007 andwhich involved two unstrengthened multi-span brickarch bridges.

The principal aims of the programme were tocompare measured barrel vertical displacements andintrados circumferential strains with those predictedusing FDEM simulations. Load tests were carried out

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Figure 11. Eight span Indian Railway arch bridge, one oftwo monitored. Bottom – FDEM model.

Figure 12. Typical measured and predicted static verticaldisplacements for four train positions. FDEM results arecurves.

Figure 13. Typical measured and predicted dynamic (trainspeed 10 km/h) vertical displacements at the crown of span 4.

using a 1000 tonne freight train. Wagon loads wererecorded at a ministry weigh station and axle loadswere recorded using calibrated arrays of strain gaugesspot welded to the tracks in several places at eachbridge. A series of static tests were carried out withaxles in designated positions. Dynamic tests were alsocarried out with the train running at constant speeds of

10, 40 and 65 km/h. During the dynamic tests verticalaccelerations were also recorded.

Vertical displacement results were found to besensitive to the stiffness of the foundations, which isessentially unknown, and also to the transverse distri-bution of the live loading. A process involving linearregression was used to take account of these effects.Overall, measured and predicted results compared wellfor all static load cases considered.

Vertical displacements measured during thedynamic tests were compared with predictions andgood correlation obtained. For predictions, the engineand two wagons traversed the bridge. Good correlationwas obtained for the first eight axles of the train.

8 CONCLUDING REMARKS

FDEM has now been used successfully for a decadeon over 170 arch bridge assessments and strengtheningprojects as part of theArchtec engineering partnership,and is now recognised as special assessment tool. Dur-ing this period, verification of this technique has beencarried out by making comparisons with the resultsof full-scale tests, with data published by others onarch tests, with the results obtained by conventionalarch bridge assessment methods and with the resultsobtained from monitoring programmes in the field.In all instances good comparisons of strength andstiffness have been made.

Recognising that arch bridge displacement, strainand damage can also be predicted, and that these fac-tors are important to bridge serviceability, further workhas been carried out to investigate in-service bridgebehaviour. This has including predicting responsesunder static and dynamic live load and making compar-isons with monitored results. However, until limitingcriteria is developed, whether strain, stress, crack orfatigue based, and until the serviceability behaviour ofmasonry arch bridges is better understood, a methodhas been developed that ensures stress and strain con-ditions when strengthening for larger loads do notexceed those in existing arch barrels under existingloading.

By representing the constituents of masonry archbridges in a natural and non-homogenised way FDEMcan provide realistic simulation of structural behaviourfor use in both special assessment and strengtheningdesign.

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