actively becoming involved in a nationwide research ... · advances in computing power and the fe...

Improving masonry bridge assessment using

a non-linear finite element package

P.A. Woolfenden

Civil Engineering Structures Team, British Rail Research,

Derby, UK

Abstract

Bridge assessment requires the determination of the load carrying capacity ofa structure. Evaluating the structural response of a masonry arch to loadingconditions is a complex task and considerable effort has been put intomodelling masonry arch behaviour. This has facilitated the production ofanalytical methods and software tools capable of predicting the collapse loadof masonry arches. A collaboration between British Rail Research (BRR) andNottingham University (NU) has produced comprehensive analytical software,employing the latest Finite Element (FE) techniques. BRR has refined thissoftware to produce a fast, flexible and easy-to-use "Masonry Arch FEAnalysis" system (MAFEA), which has recently been adapted for use as ageneral arch assessment software package.

1 Introduction

For masonry arches in the United Kingdom (UK), the most widely usedassessment methods for structures carrying either road or rail [1,2,3] employderivatives of the modified "MEXE" estimation method. Although thismethod is straightforward in application, many simplifying assumptions aremade and results produced can be both inaccurate and unrepresentative of realarch structural behaviour.

Today, the railways of Britain rely on around 33000 masonry arch spansto support both road and rail infrastructures. Many of these structures are inexcess of 100 years old and require effective assessment procedures as a keypart of an efficient maintenance strategy. This requirement led to BRR

Transactions on the Built Environment vol 6, © 1994 WIT Press, www.witpress.com, ISSN 1743-3509

270 Railway Design and Management

actively becoming involved in a nationwide research program, seeking toovercome the limitations of the MEXE method and provide new assessmentmethods and tools.

2 Modern Analysis Methods

During the last decade, a number of analytical methods and software toolshave been developed by researchers [4,5,6,7]. These have overcome mostof the limitations found in the modified MEXE method and possess varyingcapabilities.

Mechanism methods assume the arch is rigid and locate the position offour hinges to determine the lowest collapse load by a structural mechanism.

Elastic methods are based on Castigliano's minimum strain energy analysisand assume no compressive strength limitation. Arch behaviour prior tocollapse is modelled by effective arch barrel thinning, crack development andhinge formation.

Non-linear Finite Element methods offer the most comprehensive, flexibleand realistic modelling of arch structure and behaviour. By using elastic-plastic analysis, it is possible to provide a detailed structural response of anarch to any level of loading, not just at collapse. Early FE developmentsconcentrated on the use of curved beam elements, with complex analyticalproperties. These proved slow in problem solving, due to numericallyintensive algorithms and limited computing resources.

Recent collaborative work between NU and BRR has resulted in thedevelopment of a powerful suite of FE programs. These have exploited newadvances in computing power and the FE science. Three types of element areemployed; these are spatially and analytically optimised for computationalspeed and efficiency, without compromising the structural modelling of thearch (Figure 1).

The single ring program models single arch barrels with tapered beamelements. These allow rigid body motion and simulate changes in the archcross section (by "thinning" of the barrel). Surrounding fill pressures aremodelled by reactive springs and mass loads.

The multi-ring program models arch spans containing multiple rings ofmasonry with 8-noded quadratic elements. In addition to the single ringcapabilities, effects of ring separation and abutment configuration can beanalysed.

The three dimensional program models a full arch with 8-noded curvedshell elements. These extend the single ring element capabilities to representlateral effects of skew (around 50% of railway arches are skewed), spandrelwalls, twisted abutments and diagonal cracking. Pressure effects of both filland spandrels are modelled by simple one dimensional elements.

All three programs calculate the arch collapse load by a load-driven,incremental and iterative analysis technique. After applying dead load to themodel, increments of live load are distributed onto the barrel through the fill.


Railway Design and Management 271

accumulated load, in terms of deflection and cross-sectional stress changes.

CRACKEDARCH RING

8-NODEDISOPARAMETRICQUADRILATERAL

ELEMENT

Multi-Ringp

CRUSHING

CRACKING

Single Ring

CRUSHING

CRACKING

Three DimensionalP

CURVEDQUADRILATERALSHELLELEMENTS

Figure 1: Finite Element modelling of the masonry arch barrel

This process continues until the load is sufficient to cause a collapsefailure of the barrel, due to extremes of stress and/or deflection.

3 Producing the Masonry Arch Finite Element Analysis System (MAFEA)

After receiving the FE software from NU, BRR realised that all threeprograms required complex data and expert knowledge to operate. Thisproblem has been overcome for the single ring program, by the incorporationof a highly graphical, interactive and versatile user interface. This user-friendly, menu driven program ("MAFEA"), has addressed the issues of datainterpretation/entry, analysis configuration and optimisation for speed ofanalysis and results interpretation. MAFEA is controlled by a series ofpulldown menus and contains three functional components.

The first module allows the user to create and manipulate files of inputdata. The information is organised into categories comprising arch geometry,barrel and fill material properties, load traffic configuration and analysiscontrol. Data selection and entry is made through textual and graphicalmenus (Figure 2).

The second module provides a selection of five modes of arch analysis.Mode 1 analyses arch behaviour under its own self-weight. Mode 2 analysesthe collapse load produced from an axle pattern placed at a single position onthe fill surface. Mode 3 moves the axle pattern to several positions across the



NODAL DATAMODE : 9IHTRADOS X - 1185.8IHTRADOS VTHICKNESSFAULTS

w&m \Select entry to alter Node's THICKNESS REDUCTION.<flKKOWS>-Stth(;i hNIHV, <hNl hH>- <hSC>-UUlf, <H >-HM.PFigure 2: A typical MAFEA data entry screen (geometry)

arch to determine the position producing the lowest collapse load. Mode 4determines the arch response to an actual vehicle running across the arch,in terms of crack development and barrel deflection. Mode 5 determines thecritical vehicle from traffic, by performing a mode 3 analysis for each vehicleand calculating a factor of safety for each vehicle to cross the bridge. In allanalysis modes, graphical menus display the arch model, X-Y graphs ofdeflection/stress and loadcase data throughout the loading process. Onanalysis completion, a formatted results data file is produced.

The third module provides post-processing facilities to view and printresults obtained from analyses, in the form of X-Y graphs and results filecontents.

The work establishing the integrity of MAFEA as an effective analysis toolhas been documented in a series of seven BRR reports. These collectivelyform the program documentation and cover the use of the program,parametric studies and comparisons with both full scale physical arch collapsetests [8] and other analysis methods.MAFEA was released to the British mainline railway assessment offices

in 1992 to complement existing assessment methods. Ensuing feedback fromusers has been positive and has identified the need to provide an assessmentframework incorporating a suitably adapted version of the program.

4 Adapting MAFEA for Masonry Bridge Assessments

In establishing a MAFEA assessment procedure, consideration has been givento the provisions of current assessment standards, applicable features of theMAFEA program and the physical resources available to the assessmentengineer. A detailed flowchart of the procedure is given in Figure 3.



ment Flowchart

Figure 3: The MAFEA assessment procedure

The sequence of assessment activities is divided into three phases:-

DataThe first activity requires the input of arch geometry. If a new structure isbeing assessed, then it may be necessary to conduct a site survey to obtain therelevant data. Following this, material physical properties are required. If



the material properties have been tested, specific material data files can becreated; otherwise MAFEA material data files are used. Vehicle loading datais then required, both individually and grouped in traffic files. It should onlybe necessary to create test vehicle data, as MAFEA supplies most rail androad vehicle configurations required for standard assessments.

AnalysisThis begins with modelling of the arch abutments. If they can be assumed tobe rigid, the assessment progresses to the load investigation analysis. If oneor both abutments are flexible, a deflection monitoring analysis (MAFEAmode 4) is performed, using either known or default abutment stiffness data.If the predicted deflections are unsatisfactory, then measured arch deflectionscan be obtained and used to refine the assumed arch property data. Thisprocess is continued until the barrel deflections are modelled correctly.

The load investigation analysis (MAFEA mode 2) is run to determine atypical collapse load prediction for a vehicle with an intense loadconfiguration (usually a single axle), placed at the suspected weakest position.The modelled structural behaviour is observed and the predicted arch capacityis compared with the vehicle load to establish the integrity of the model. Ifthe model behaviour is unsatisfactory, the geometry may need to be adjustedto account for hidden construction (e.g. haunching), or material propertiesaltered to provide more realistic structural condition. In either case, furthersite investigation will be needed, to provide more accurate data. If theanalysis itself is inadequate, the analysis control parameters are refined for theloadcase under consideration. The process of analysis and data refinement isrepeated until the model performs satisfactorily.

AssessmentThe final phase of assessment activity requires the running of a trafficclearance assessment analysis for the validated arch model (MAFEA mode 5).Following selections of relevant input data files, a set of strength adjustmentfactors for partial safety, material condition and analysis limitation aredisplayed. Factor default values are taken from various assessment standards,but can be altered if necessary. Following this, a vehicle progress menu isdisplayed and the analysis commences. Two modes of analyses areperformed, to account for the possibilities of the arch failing due to instabilityor crushing. Each vehicle's progress across the arch is updated by filling aprogress bar on the assessment menu, displaying the lowest possible weightsupported by the arch and its associated "compliance factor". This factor isbased on the ratio of the highest supportable weight that can cross the archand the actual vehicle weight. A compliance value greater than unity updatesthe vehicle data in green, to indicate a "pass" condition; a value less thenunity displays the data in red to indicate a "failure" condition. Figure 4shows a progress menu for an assessment of four railway vehicles, oncompletion of an arch stability analysis. In this example, all four vehicles



have failed to cross the arch and the allowable vehicle loads are determinedby multiplying the failed weights by the compliance factor.

TRAFFIC CLEARANCE ASSESSMENT: Proqr*** Hwiu

t HOHF.i 1*8

lift Offi *0Hasonrjf t POOR

Uatue: '

Figure 4: A MAFEA rail bridge assessment for 4 vehicles

5 Future Developments

In addition to a programme of improvement of the MAFEA assessment

Figure 5: A completed masonry brick prism test

system, work is in progress to convert the other two arch FE programs intoa MAFEA form.Development of a multi-span version of the single ringprogram is in progress at NU and on completion will be incorporated into



MAFEA.A major programme of work is now underway at BRR and NU to

establish serviceability criteria for masonry arches. At BRR, the effects ofenvironmental condition on the compression fatigue life of masonry brickworkhas been investigated, using destructive testing techniques. A series of dryand saturated masonry prisms have been subjected to static and cyclic loadingto establish fatigue life curves. Figure 5 shows a completed test on a drysample. At NU, a series of half scale arch model tests are being conductedto observe the effects of cyclic loading on the condition of the arch barrel.The scale models are being constructed with bricks similar to the ones usedfor the masonry prism tests.

It is intended that the results obtained from both activities will beincorporated into MAFEA as the serviceability limit states which will be usedas the arch assessment criteria.

Acknowledgements

The author wishes to thank the Managing Director of British Rail Researchfor permission to publish this paper and Dr B.S. Choo, Dr M.G. Coutie andDr N.G. Gong of the Civil Engineering Department at the University ofNottingham, for their contributions in developing the methods of analysis.

References

1. The assessment of highway bridges and structures, departmentalstandard BD 21/93, Department of Transport.

2. The assessment of highway bridges and structures, advice note BA-16/93, Department of Transport.

3. British Railways Board. Assessment of the live load carrying capacityof underbridges, Chief Civil Engineer, June 1983.

4. CRISFIELD M.A. and PACKHAM, A.J. A mechanism program forcomputing the strength of masonry arches, TRRL research report 124,1987.

5. BRIDLE R.J. and HUGHES T.G. An energy method for arch bridgeanalysis, Proceedings from the Institution of Civil Engineers, part 2,Sept. 1990, pp. 375-85.

6. CRISFIELD M.A. A finite element computer program for theanalysis of masonry arches, TRRL laboratory report 1115, 1984

7. GONG N.G. Finite Element analysis of masonry arch bridges, PhDthesis, Department of Civil Engineering, University of Nottingham,September 1992.

8. MELBOURNE C The assessment of masonry arch bridges - theeffects of defects, Proceedings from the 1st International Conferenceon Bridge Management, March 1990, pp. 523-531


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