A three span stone masonry bridge dating back to the middle of the 19th century, still in the roadway network, is assessed to prevent its demolition. Its industrial heritage value and ecological concerns were the principal reasons for the assessment. The carbon footprint of the stone arch replacement would be approximately 200 t CO2 emission owing to 430 m3 reinforced concrete in the new structure. Besides the cultural monument, considerable energy, CO2 emissions and natural resources can be saved in accordance with the sustainable development goals. Standards, guides and commercial software do not provide an adequate support for the assessment of masonry arch bridges, therefore an innovative two phase application of a commercial linear sttructural analysis code and an original in-house code was developed for the purpose. Thousands of stone ach bridges still in service worlwide give the case study more general importance

Davis, Lucy

Fajman, Petr

Řeřicha, Petr

English

CTU Open Journal Systems (Czech Technical University, Prague / České vysoké učení technické v Praze)

https://doi.org/10.14311/APP.2022.38.0630Acta Polytechnica CTU Proceedings 38:630–634, 2022 © 2022 The Author(s). Licensed under a CC-BY 4.0 licencePublished by the Czech Technical University in PragueRESCUE OF A STONE BRIDGE WITH RESPECT TO CURRENTCONDITION AND STANDARDSPetr Řeřichaa,∗, Petr Fajmana, Lucy Davisba Czech Technical University in Prague, Faculty of Civil Engineering, Department of Mechanics, Thákurova 22,166 29 Praha, Czech Republicb McGill University, Faculty of Engineering, 45 Sherbrooke Street West, Montreal, Canada∗ corresponding author: petr.rericha@fsv.cvut.czAbstract. A three span stone masonry bridge dating back to the middle of the 19th century,still in the roadway network, is assessed to prevent its demolition. Its industrial heritage value andecological concerns were the principal reasons for the assessment. The carbon footprint of the stonearch replacement would be approximately 200 t CO2 emission owing to 430 m3 reinforced concrete inthe new structure. Besides the cultural monument, considerable energy, CO2 emissions and naturalresources can be saved in accordance with the sustainable development goals. Standards, guides andcommercial software do not provide an adequate support for the assessment of masonry arch bridges,therefore an innovative two phase application of a commercial linear sttructural analysis code and anoriginal in-house code was developed for the purpose. Thousands of stone ach bridges still in serviceworlwide give the case study more general importance.Keywords: Natural resources preservation, sandstone, bridge, arch, stress, displacement.1. IntroductionThe three-span sandstone arch bridge was built in 1857and remains an important part of the second-classroadway network, see Figure 1. It was considered fora reconstruction with total demolition of the arches.The owner planned to remove the arches and topparts of the piers and replace them with a reinforcedconcrete structure that would be a reminder of thearches of the stone bridge.In order to prevent an irrecoverable loss of theindustrial heritage, an extensive load capacity as-sessment was conducted for the bridge with the re-placement of the pavement. Standard assessmentsdetermine load rating based on the limit states anal-ysis. The load models used for the purpose differin various countries substantially, for instance ei-ther the ultimate (in Europe) or serviceability limitstates (in the US) are preferred. Instead, the checkof the available building standard’s criteria is usedherein. The conditions of the EN 1990 Part 2 TrafficLoads on Bridges have been checked to testify thatthe bridge with its valuable stone arches can remaina part of the roadway network without limitations.A number of clauses of the EN 1996-1-1 could be ap-plied even though the standard is not designed forbridges.“There is a multitude of assessment methods avail-able for masonry arch bridges, yet there is no widelyaccepted framework for their application”, this quo-tation from [1] is a sad fact. Tens of papers reporton sophisticated methods based on advanced materialand structural models. None of them are acceptablefor the design practice for two principal reasons,Figure 1. Front view of the sandstone bridge atPonikla.(a) the application requires specific high competen-cies of the designer and specialized software(b) the input material and structure data are notavailable for the models.The present approach is simple: the assessmentmethod can use only the data available in a com-mon design environment and with reasonable cost.This admits relatively simple material models. The fi-nite element technology is preferred since it can modelthe components of the bridge and their interactions ina way that other methods and codes (modified MEXE,plasticity theorems like Ring [2], Castiligliano theoremlike CTAP code [3] and others) cannot. At the sametime it is widely available. The absence of designstandards or other “widely accepted framework” givesthe load rating of an important bridge the character630vol. 38/2022 Rescue of a stone bridge with respect to current condition and standardsFigure 2. New design of the bridge.of a research task. An assessment method was devel-oped in the course of the solution of the bridge. Theobjective of the contribution is to outline the princi-pal steps of the method and its application to similarbridges. The method is tailored to masonry bridgesmanagement practice and demostrates its application.The sample solution documents the potential of themethod for sustainable infrastructure managementand ecological impact.2. The original restorationconcept, ecological impactScheduled for reconstruction, the owner planned toremove the arches and top parts of the piers and re-place them with a reinforced concrete structure thatwould remind the arches of the stone bridge, see Fig-ure 2. However, considerable economical savings andbenefits for the environment can be achieved whenthe arches are preserved. The construction of the newreinforced concrete structure would require the de-struction and deposition of 230 m3 high quality stonemasonry built with craftsmanship which would be lostforever. Removal and deposition of 400 m3 backfillwould cost money and ecological load. The carbonfootprint would be left owing to 430 m3 reinforcedconcrete with approximately 200 t of CO2 emission.The most important offense against sustainablebuilding would probably be the life span of the new re-inforced concrete structure. The stone arches are 170years old and still in service in spite of the neglectedmaintenance in the last decades. With adequate pro-tection against water leaks they can serve for 150 moreyears. The service life of the proposed reinforced con-crete structure willl certainly be substantially shorter,as in particular the struts above the piers with notchhinges are susceptible to early deterioration. Theecological aspects of the reconstruction speak for thepreservation of the stone arches.3. Load capacity of stone archbridges3.1. Material modelsThe dominant material failures and limit states in thestone arch bridges are(a) the tension cracking in the bed joints,(b) the compression failure in the bed joints.The former occurs already at the service load lev-els and may result in gradual development of virtualhinges and stability loss of the arch with the grow-ing live load. It must be represented in the materialmodel in order to assess the redistribution of the in-ternal forces. The trouble with this limit state is thatthere are no generally accepted quantitative criteriaworldwide. Recently the Czech Guide TP199 of theMinistry of Transport of the Czech Republic intro-duced an admissible relative depth of the cracks in thebed joints. The other trouble is that the predestinedorientation of the cracks makes the no-tension mod-els in general purpose codes almost unusable. Thisfailure mode can effectively be included only in beamelements of the 2D models or shell elements of the 3Dmodels where the kinematic assumptions and domi-nant cross-section normal stresses facilitate the specificno-tension model. The thick shell and beam finiteelements with the no-tension property are derivedin [4].The latter limit state is a kind of a brittle failure,partially contained in case of the arch bridge with fill.The failure criterion for this limit state is the com-pression strength of the masonry. This property is theonly one that can be determined in a diagnostic sur-vey with acceptable cost and reliability. EN 1996-1-1provides support for determining the masonry com-pression strength from the compression tests of thecore bored specimens of the stones and by nondestruc-tive boring tests of the mortar (PZZ 01 device). Thetests were performed for the Ponikla bridge masonryarches and the compression design strength was deter-mined fd = 2 MPa. The value is rather conservativesince the sandstone ashlars of the vault are in goodcondition.The backfill and pavement are linear elastic. Inorder to eliminate extensive backfill failures, theDrucker/Prager criterion is checked in the fill elementsand indicated by asterisks in the graphic output.The elastic properties used in the FEM models aresummarized in Table 1. They are deliberately conser-vative for the backfill. A review of the backfill proper-ties was conducted in the published literature [5] andthese are the values at the low end. During the methoddevelopment, a parametric study showed that softerfill always implies worse stresses in the vault drawing631P. Řeřicha, P. Fajman, L. Davis Acta Polytechnica CTU ProceedingsFigure 3. The minimum stresses [kPa] and crack depths in the Ponikla central span arch. The displacements are1000 times scaled up.E [GPa] G [GPa] ν ρ [t/m3]Arch 10 5 0.25 2.0Backfill 0.1 0.043 0.15 1.8Pavement 31 12.917 0.2 2.5Spandrel 0.1 0.04 0.25 2.2Piers/Abutments 10 4 0.25 1.8Table 1. Elastic properties considered in this case study.an important conclusion. The fill material constantsfrom the table are on the safe side and can be usedin bridge assessment when nothing is known aboutthe fill quality. The value 0.4 GPa is recommendedwhen at least a compacted cohesionless material canbe assumed. Selection of the Young moduli of thearch parts is facilitated by a convenient property ofthe FEM model, see the next section [6].The short summary of the material models andproperties exposes the uncertainties involved whichinevitably imply low reliability of the analytical mod-els of the masonry arch bridges. On the other hand,most of them were built in the 19th century accordingto empiric rules with ample reserve of load capacity.Decades of their service testify to their robustnessand reliability. These aspects compensate the lowreliability of the analytical models, asserts Boothbyin [7].3.2. Finite element bridge modelsIt is difficult to account in a single complex model forthe interaction of the spans and piers, the transverseasymmetry of the load and structure and non-lineararch behavior. The assessment method therefore usesdifferent FEM models for the tasks.The checks required by the standards are performedin a non-linear 2D (plane strain condition) modelof a single span featuring the no-tension materialspecified above. The simplest Timoshenko beam el-ements [4] are used for the stone arch so that thenormal stresses in the cross-section planes are used inthe above failure conditions. The backfill is meshedby standard CST triangles and the pavement by linearTimoshenko beam elements. The meshing is shown inFigure 3. Clamped arch springings are assumed. Theresults are slightly non-conservative owing to the planestrain 2D idealization which neglects all transverseeffects. Correction factors are used to make up forthe error, see the next paragraph. The linear elasticno-tension material model secures robust convergenceof the equilibrium iterations so that unskilled userscan use the model and code. The model also impliesthat stresses and crack depths do not change whenthe Young moduli of all materials are multiplied bya common factor. A non-commercial code was de-veloped for the purpose and will be available as anOctave/Matlab script when a minimum user interfaceis completed.The other two models are a 3D linear model of onespan with the same boundary conditions as in thenon-linear model and a 3D model of the whole bridgeincluding piers and abutments. They are primarilyused to assess the differences between the 2D and 3Dmodels and the interaction of the arches, piers andabutments.The differences between the 2D and 3Dmodels are expressed in terms of correction factorsfor the 2D solutions. The factors are then used tocorrect the results of the non-linear model. This isnot quite consistent but the bed joints cracking islocalized to relatively small volumes of the vault andthe imperfection is thus accepted.A front view of the bridge and its 3D FEM modelare shown in Figures 1 and 4. The spans are all ap-proximately 11.4 m and the full width of the bridgeis 7.6 m. The single span 3D model is an extractionof the full bridge separated by adjacent pier’s symme-try planes. On the planes, the symmetry boundaryconditions are applied (zero normal and free in-plane632vol. 38/2022 Rescue of a stone bridge with respect to current condition and standardsFigure 4. Full 3D bridge model with two tandem axle forces.displacements). The elements are based on isopara-metric bricks/quadrilaterals enriched by rotationaldegrees of freedom at all nodes. The commercialpackage RFEM from Dlubal Software [8] was usedin the sample solution. Any other package can beused with an adequate modeler. The model’s builditself is rather easy since details of the sructure canbe omitted. Extraction and processing of the relevantstresses and other data may be more demanding anddepends largely on the available software.The other purpose of the full 3D model is to assesthe interaction of the spans, piers and abutments. Thedominant effect of the interaction is the widening ofthe arch subject to the local live load, see Section 3.3for the live load model. The vertical displacementsand rotations of the arch springings owing to the inter-action are neglected in the method. The arch wideningis obtained as the difference of the averaged horizontaldisplacements of the right and left springings. It isthen used in the non-linear 2D model as an imposeddisplacement (kinematic load).3.3. Load modelThe load model LM1 of the EN 1991-1-1 is used. It isknown to be critical for bridges with these space pa-rameters. The same position of the two axle tandemsis considered in all calculations, as shown in Figure 1.The position above the quarter span is generally ac-knowledged to be the most adverse for the arch. Theuniform continuous live loads of LM1 are not shownin Figure 4 but applied on the loaded half of the spanin the calculations. It is worth mentioning that LM4class 1800 kN of the EN standard gives approximatelythe same total load on the half span but is almostuniformly distributed. The dead load is included viamass densities of the bridge components materials.The load factors of the ultimate limit state are usedaccording to the EN and National Application Docu-ment. Loading in the 2D model is taken as the averageover the bridge width of the 3D model loads.3.4. Results for the design load of thePonikla central spanThe solution of the Ponikla bridge for the designloads of the EN 1991-2 is shown in Figure 3 with axletandems of the LM1 allocated at a quarter span ofthe arch. The dead load of the arch, fill and pavementis accounted for. The third load component is theimposed horizontal displacement 0.13 mm of the rightarch springing, fill boundary and pavement end. Itequals the arch widening obtained in the full 3D linearmodel, see the last paragraph of Section 3.2.The absolute values of the minimum stresses inthe arch elements are inserted at the arch face wherethey occur (the maximum stresses are always non-negative).The same quantities are inserted at the lower andupper faces of the pavement although they are irrele-vant with respect to the arch assessment. The 0.2 mthick reinforced concrete pavement is considered linearelastic in the model. The bending “waves” character-istic for beams on an elastic layer can be observed inthe figure, note the alternating faces of the minimumstresses in the pavement elements.The crack depths in the arch elements are indi-cated by the inserted line segments. The crack mouthwidths in the bed joints can be computed from thecrack depths, the voussoir lengths and the minimumstrains in the elements when the Timoshenko kine-matic assumption is employed. The arch model is a 1Dcontinuous beam, where the arch elements lengths de-pend on the chosen mesh density. The voussoirs areapproximately 0.4 m long whereas the elements justabout 0.33 m.The load intensities and material properties usedin the non-linear plane strain 2D model are averages633P. Řeřicha, P. Fajman, L. Davis Acta Polytechnica CTU ProceedingsCross-section locations 0 0.25 0.5Extrados stress correction factor 1.18 1.08 1.1Intrados stress correction factor 1.05 - 0.94Table 2. The 3D/2D correction factors for the compressive stresses at three cross-section locations.across the vault width 7.6 m. However, the load modelLM1 for two lanes is not symmetric with respect tothe longitudinal symmetry plane of the bridge. Theasymmetry effect is evaluated through comparisonof the 3D model solutions for the true LM1 loaddistribution with the solution for the average uniformdistribution in the transverse direction. The ratiosof the two stress’ sets are used as 3D/2D correctionfactors and are summarized in Table 2 for the fourcross-section locations along the arch span. Onlycompressive stresses are considered.The stress values from Figure 3 are multiplied bythe correction factors from Table 2 in the last stepof the method. The assessment of the bridge usingthe method determined its safety in the ultimate limitstate as defined in EN 1991-1.4. ConclusionA method for the assessment and load rating of thestone masonry arch bridges is presented. It is designedfor application in bridge management. A single mate-rial property, the vault masonry compression strength,is necessary. Users need no special skills beyond ad-equate experience with the application of the FEMcodes. The safety assessment of the Ponikla bridgeusing available standards together with activities ofother institutions and individuals in the cultural her-itage protection helped to avert the demolition of thebridge’s arches. The simple material model and thededicated finite element can be used to check the com-plex structure against available standards conditions.An extension of the concept to 3D shells is currentlyunder way and then the parallel linear 3D model willnot be necessary for the application of the method.Preservation of the Ponikla bridge represents a contri-bution to the responsible consumption and productiongoal of the sustainable development policy.AcknowledgementsThe authors acknowledge the support of the project NAKIDG20P02OVV001 (Tools for the preservation of historicalvalues and functions of arch and vaulted bridges) providedby the Ministry of Culture of the Czech Republic.References[1] N. Gibbons, P. J. Fanning. Ten stone masonry archbridges and five different assessment approaches. InARCH’10 6th International Conference on Arch Bridges,pp. 482–489. Fuzhou, 2010.[2] M. Gilbert. Ring: a 2D rigid block analysis programfor masonry arch bridges. In Proceedings of theARCH01: 3rd International Arch Bridges Conference,pp. 459–464. Paris, 2001.[3] R. J. Bridle, T. G. Hughes. CTAP theory. JournalInst Highways Transp 36:21–22, 1989.[4] P. Řeřicha. A Mindlin shell finite element for stonemasonry bridges with backfill. Acta Polytechnica62(2):293–302, 2022.https://doi.org/10.14311/AP.2022.62.0293[5] L. J. Davis. Load Rating of a Masonry Arch Bridge:Comparison of 2D and 3D Finite Element Models.Master’s thesis, Czech Technical University in Prague,Faculty of Civil Engineering, 2021.[6] P.-O. Persson, G. Strang. A simple mesh generator inMATLAB. SIAM Review 46(2):329–345, 2004.https://doi.org/10.1137/S0036144503429121[7] T. E. Boothby. Empirical design of masonry archbridges. Journal of Architectural Engineering26(1):02519002, 2020. https://doi.org/10.1061/(ASCE)AE.1943-5568.0000388[8] RFEM 6, FEM structural analysis software. [2021-04-16]. https://www.dlubal.com/en/products/rfem-fea-software/what-is-rfem634

Rescue of a stone bridge with respect to current condition and standards

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Rescue of a stone bridge with respect to current condition and standards

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