STRUCTURAL ANALYSIS OF HISTORICAL CONSTRUCTIONS P. Roca, J.L. González, A.R. Marí and E. Onate (Eds.)

© CIMNE, Barcelona 1996

THE TESTING, ANALYSIS AND ASSESSMENT OF MASONRY ARCH BRIDGES

T.H. Hughes Cardiff School of Engineering

Queens Buildings, Cardiff Universify of Wales

C"d;ff, CF2 lXH. U.K.

NOTATION

d

f PAL r s w

o: d. o: if. 0"1 ,0"2

ABSTRACT

arch ring thiekness depth of fill over areh crown provisional axle load areh rise arch span loaded length tensile strength of unit

tensile strength of mortar

eompressive strength of unir

compressive strength of mortar

principIe stresses (radial and ei rcumfrential direction)

Masonry areh bridges exist in varying numbers in most eountries in the world. A full understanding of these eomplex struetures is important for two principal reasons, they continue to rorm a significant element of many countries transport infrastructure and because there are a large number of historieally important structures. In general the work in the UK undertaken in Tecent years has been driven by the eeonomic need to maintain the infrastructure. In addition there is a move to construct gravity arch structures using new materiais in an attempt to replicate lhe longevity clearly demonstrated by these, many, aneient structures.

This paper eontains a slate of lhe art report on the work undertaken during the las! decade on masonry arch bridges. The Teview concentrates on the work undertaken in lhe UK since Ihis forms lhe bulk of the Tcsearch buI does include contributions from other parts of the world. The paper contains details of the (a) experimental studies undertaken aI both small and medium model scale as well as on real structures, (b) analysis us ing plastic methods and finite element analysis and (c) some consideralion of lhe use of lhe analysis lools for load assessment.

Keywords Analysis, Arehes, Bridges, Masonry, Mechanism, Finile Element

T. H. HUG HES I Masonry arch bridges 65

1. lNTRODUCT10N

Masonry arch bridges represent the oldest form of crossing still of economic significance. In some, even developed, countries they sti II

"

form the principIe element of 30

the bridge stock . The resu lts of a samp!e sllrvey llndertaken in the UK for lhe Departmenl of Transport [ I ] are presenled in Figure J which shows lhe percentage type of bridge

BAITISH AA, IL wo.TERw.o.yS BOA,F10 GOVEANMENT

_ MASONAY t@Sj ME TAL O AEINFORCED CONCAETE

structures and their ownership Figu re I Distribulion of bridge type and ownership in lhe UK[I] It is apparent that in lhe UK

masonry arches sti!! eonstinlte a significant infraslrllctllre il1veSl lllcnt. The survey also conlained details of lhe dislriblllioll of lhe spans of lhe masonry arches, this infonnalion is conlained in Figure 2. AI the smaller end the difference belween a bridge and a culvert beeomes somewhat academic . T he maximul11 spall in lhe UK is actllally 66 metres.

In addition lO lhe economic arglllllcnl l!lere exists, in the UK, a large number of listed, that is hislorically prolecleel, arch bridges bllild by renowned Engineers inc1uding Smeaton , Rennie, Telford and Brunel, these are in addition to earlier mediaeval examples. Thcse struc tures frequcntly conlinuing to flllfil both the ecollomic alld historie roles .

"

" " \2 .5

SPAN

Figure 2 Di stribulion of m<tsonry arch bridge spans in [l1e UK[ 1]

There is little eurren! distinetion between the cons iderati on given to arches constrllcted of brick and block masonry, both normally being covered by the lerm masonry. The significan! (eatures of lhe traditional arch are shown in Figure 3. Tlle principal elemenlS are lhe ablllments, lhe arch ring , lhe spandrel walls (including lhe parapet walls) and lhe fill material.

The wingwal ls (nol shown) <Ire also significam . Tllere is also frequently additional masonry between lhe arch ring <lnu lhe fill. This can be i n lhe fonn of hallnching above lhe ablltments or additional arch rings of less competent masonry . Oceasionally there are interna! spandrcls, induded both 10 rcduce weight and to provide additional strength. Voicled cylinders are also sometimes included above lhe abutments to

66 STRUCTURAL ANALYSIS OF HISTORICAL CONSTRUCTIONS

reduce weight in certain geometries these may continue through lhe spandrel and thus be visibJe ar lhe ends may be c!oseu by lhe spandrel wall. In addition for muItispan arches lhe piers themselves are significam.

There are tWQ

feCen! books dealing exclusively with masonry arches lhe first contains a significanl elemenl Df lhe international historical background to these stnlcwres[2] and lhe second a recent state Df lhe art review cf currenl UK research and pracli sef3]. In addition a recent

, .

Spandrd Wall

international conference on arch bridges was devoted aI mos! exclusively to masonry bridges[4].

Figure J PrincipIe reatures af a rnasonry arch bridge

2. TESTING PROGRAMMES

The testing programmes can bc convenien tly divided into lhe fuH sca le testing af real arch struClllres and lhe laboratory lllodeHing aI smaUer scalc. The cancept of scale is inlcresting bccause lhe dominance of gravity forces in lhe strength of these arch struclures Illeans Ihat small !1lodels are nOI sl11all scale Illodels of larger structures but are in fael full SC<1le !1lodels 01' sl11{!ll bridges. Some of lhe larger laboralory models have however becn 01' an equivalen! size 10 tlle smaller fllll scale structllres.

2.1 FuI! Scale Site Testing

The UK full scale testing programme was becn organised and financed by the TranspOr! Research Laboratory for lhe Departlllenl of Transport. The prograrnrne starled in 1985 and involved the lesting 10 deslruction af a number of disused bridges. To date 1i masonry arch bridges have been tested incJuding 2 full scale laboratory SlrtlClures.

The programme was intended 10 cover lhe full range of arch materiais, including block concrete, brickwork oI' different numbcrs of rings, dressed stone and random rubble, lhe full range of geolllelric shapes incJueling segmental and elliptical of different spanlrise ratios anel span /deplh mlias, af different crossing orientation including square and skew spans, 01' single anel Illulti-span as well as of different conclition including both badly crackeel anel distorted ZlS weU as brand new structures.

T H_ HUGHES / Masonry arch bridges 67

It is clear that 11 is insufficient for a full parametric study of each parameter but it was felt important to ensure ali features were included in at least one test bridge. Table 1 details the range of the geometric parameler variation tested to date.

Geometric Property Range of Values

rise to span ratio 0.16 < ris < 0.50 ring Ihickness 10 spll.n rat io .034 < d/s < .094 soil to ring thickness ratio 0.28 < fld < 2.15 loaded length 0.3m < ·w < .75m skew O deg < angle < 29 deg Table I Range of geornetnc pararneter values from ful! scale tests

lt is clear from Table 1 that there are is a large range of basic geometric shapes covered by the tests but the fuH range of the real structures is considerably larger. This is important in identifying the principIe structural actions to be considered since these are largely determined by these geometric parameters . For example the tests have shown the significance of the restraining action provided by the fill material in high rise to span ratio arches and for shallow arches failure modes involving elastic snap-through have occurred.

The static load tests involved loading in lhe vicinity of the 1/4 to 1/3 point of the arch span with the load being applied througb a spreader beam of length, usually, 750 mm across the fuH width of the bridge between parapels . The loading beam was used to ensure that there was not a local soil bearing failllre beneath the applied load. The loading system normally reacted against ground anchors previously drilled through the arch. Attempts were made to isolated these anchors from the arch using ducting although Ihere is same evidence of t!lese providing significant longitudinal restraint against the normal sway failllre mode.

The instrumentation included in the tests were primarily remote sensing or surface mounted to avoid undue disturbance of the fill material and the loss of expensive instrumentatian at collapse. In arle case the actlJal thickness of lhe arch ring is questionable becallse af lhe random nature of lhe rubble and its total disintegration at final collapse coupled with this need lO avoid Irial pits prior to loading. For lhe ful! scale "modeI" lests there has been the inclusian of pressure gauges in lhe backfill. These pressure gauges have become mare praminent as lhe recognition af lhe importance of the fiH behaviour has become clearer.

Fuller details of the background \O the tests is contained elsewhere [31 togelher with a full list of references of lhe specific publications covering the individual teslS.

2.2 Small Scale Laboratory Test ing

As identified above the cancept of physical scale modelling af lllasanry arches is problematic. Many madels are referred 10 as scale madels of larger protolype structures whilst lhe structures and models are, in fact, simply geomctrically simi lar. Indeed in some cases 1/4 or 1/2 scale brick units have been used lO maintain the geometric similarity. In trulh many of the real effects identilied, whether the effect 01'

68 STRUCTURAL ANALYSIS OF HISTORICAL CONSTRUCTIONS

backfill or Df lhe crushing strength Df lhe arch ring materia l, are nol properly modelled aI ali , with lhe results only giving qualitative and nol quantitative asscssments Df lhe erfeelS. For this reason these models should be classcd by span ralhe r lhan by scalco

No attempt is made here to detail a11 lhe Jaborato ry tests undertaken. The paramcters investigated in lhe laboratory modelling and the general ou tcomes, where available, and how Ihey may efreel lhe numerical mode!ling, to be considered laleT, are included below. The following erfeels have been identified/i nvestigated using laboratory tests cf between 300mm-6000mm span.

1) Spandrel wall SUPOQrt The action Df spandrel walls has becn shown lO significantly enhance lhe failure load of ncw model arches [5]. Unfortunately for general assessments their contribuiion is rarely considercd bccause of the difficulty in ensuring combined action. In lhe real slructures lhey have both fallen orf at an early loading stage or remained intact wi th lhe arch failing between them. For mult ispan arches thei r contribution is more assured because rotation of the pier requires spandrel movement.

2) Arch nn!! seoarallon Invesligation of lhe condition of, particula rl y, brickwork arches has shown lhat on a number of occasions the individual brickwork courses that form the main arch ring have become separated from each olher. This can oeeur for a number of rcasons and becausc arch brickwork is gcnerally streleher bondcd, Ihat is with no headed eourses eonneeting lhe separale layers, it is surprising lhat it is nOI more eornrnon. The lack of headers, always olherwise included in multi·course walls, may be associaled with historie experienee but is more likely to be simply related to lhe difricully in matehing lhe differcnl courses. 1I is no! uneommon in tunnels for a row of headers lO be provided where lhe eourses gel baek in line. This slructural weakness has becn simulated in laboralory st ruelures by using a sand layer between eourses ralhe r Ihan lhe normal morlar [6}. In these situations lhe results indicate a signi ficant rcduetion in strength when eompared to idcnt ical tests with a monar layer. Recent full scale patch load tests, not to failure, on an arch with severe ring separation where attempts were made to invesligate lhe movcment belween layers, has shown a different result with liule or no discernible difference in the vertical Illovements of the different layers under load. Ring separat ion was also present in the fllll scale leSIS and does not particularly seem 10 have effected lhe nurncrical model prediclions made, none of which have atlemplcd 10 model ring separation.

3) Arch rino crushing There is littlc informat ioll of the effect of varialions in lhe crushing sl renglh of masonry although some early work has been undertaken loading areh rings without backfill [7]. Therc is ll\Jmerical analysis evidence of its effeel buI this is di scllssed laler.

4) Cyclic loading Some reeent work has bcen undertaken investigaling the effecI of repeated cyclic loading [8]. Thcsc loads havc been applicd c\ose to lhe quartcr poim and after some initial damage the archcs appcar to !lave settled into a stable condition. The arches have then becn loaded to failure and have shown little effeet on the ultimate load.

T. H. HUGHES I Ma<;onry arch bridges 69

5) Fundamental freguencies The application of a small impulse load. via a hammer, to produce a vibration response, at various stages of applied load, is eurrently being used in an attempt to quantify the effeet of "damage" on lhe natural frequencies of arehes. This work in volves medium span models and full scale monitoring [9].

6) Ablltment movement Most nllmerieal analysis assume a rigid ablltment. Reeent moves to develop new construetiol1 teehniques for masonry arehes together with the need for suffieient headroom has identified flat arehes on synthetiea1iy reinforeed soil foundatians as being econamically viable. 011 shallow arehes lhe effee! af ablltment movemenl is considered crucial and some limited testing has been undertaken [lOJ.

7) Serviceability Experimentation on serviceability has only properly been considered via the cyelie loading referred to above (4). As a result of the load deflection curves from a large number of tests it has been assllmed, for the UK standards, that the limit for serviceability approximately corresponds to one hal f of the ultimate load [lI]. This is considered to eorrespand approximately with the limit of the elast ie response and with the visual and audib!e onset of damage. This is a very subjective view as seve ra1 arches have shown almost no evidence of damage up to the maximum load and have then demonstrated significan! softening to failure.

8) StrengthcninO" There are a range of strengthening techniques used in the UK under experimental investigation incl lld ing increasing the ring th ickness by saddling [1 2] or by spraying the int rados (13], bath witil minima l concrete reinfarcement. 80th have demonstratcd significant increases in strength over both lhe damaged slate and the new original state. In addition madel tests using both retrofit reinforcernent [14J alld spandrcl wall tics have bcen undertaken.

9) rvlulti-snan Limited labaratory studies of the effeels of adjaeent spans on the strength of arch bridges have been undertaken [15]. The lests undertaken on three span arches have shown a signifieant decrease in strength, when compared to lhe identical single span equivalen t, the intcrmediate supporting piers were however quite slender.

To date little of lhe results 01' Ihis model1ing work has found its way inte the current UK assesSlllent practise [11] but it has helped identify effects and Illllch af it is still vcry rcccnt and ongoing.

2.:1 Acceler;lIed Gravity Laboratory TestinO"

To date ali the model tests have been undertaken aI unit gravity althOllgh work is just slarting in lhe UK on lhe testing aI accelerated gravily using a geotechnicaJ centrifuge [16] . The dominance of gravity, both in the stability af the structllres and the slresses within both lhe fil1 and arch ring, means that in practise few, if any, of the smalJ scale models have identified masonry material failure (crushing) or

70 STRUCTURAL ANALYSIS OF HI$TOR1CAL CONSTRUCTIONS

attcmplcd to propcrly model lhe intcraction betwten lhe fi l! and arch ring which is strcss dependent.

Ooe of lhe known advantages of small scale tcsting is lhe accurate definition of lhe boundary conditions and lhe accu rate repcatability of lhe tesls . Since much tcsting work is unde rtaken lo prov ide benchmarks against whicb numerical analysis can be comparcd and because both of these goals have becn difficult to ach ieve wit h large modcl scale work this is secn as a major advantage. The large physical size of lhe large laboratory slruc lurcs together wilh lhe appl ication of large loads has causcd sevcre problcms of rcpcatabi l ity and lhe poor dcfinition of boundary conditions.

Prcv ious unil gravity work on masonry has becn undCrlaken thal proves lhe viabilily of scalc modclling of l~lason ry and Ihis is being cxtended in lhis ncw work to include cllrvcd masonry slruclurcs and the soillstructure intcraction. This work is cllrrenllyal 1/6111 scale bul wi ll cvcntually inclllde 1I18th scale models.

2.4 Pailu re modes idenlificd in leSIS

Thcrc are Ihrce main failurc modes Ihal have becn idcnlificd for masonry archcs which are shown, diagramll1atic,1l1y, in Figure 4.

i) Thc formalion of a mcchanislll, bere joinl opcning gradllally progresses throllgh lhe ring ai, aI lcast fOllr locations, lhe joinls Ihcn

!-linge llingc

I'ossiblc S11ap Throllgh

Figure 4 Simp[ificd failure modes of masonry arch bridges

rolate and lhe Slructure gradual1y collapscs.

ii) Elaslic snap-Ihrough prior 10 lhe full forlllation of hinges. Hcre lhe joint opening can cause significanl secliolls of vcry tlcxiblc ring carrying large Ihrusls. The progress of mechanism failure is pre-emplcd by a rapid snap Ihrougll.

iii) Material failllrc whcre significanl parts of lhe ring crush.

Clcar[y cOlllbinalions, of lhe above, are also possiblc. Tablc 2 shows lhe basic rcsu[ls of nine of lhe TRL IcSIS anel givcs a briel" descriplion of lhe actual failure modcs observed in cach casc.

Whcn a [oad <lpplicd, aI or near Ihc quartcr span of an arch, is increased four cracks or hinge points will gradually formo Thesc hinges nOflnally occur one at cilhcr abuIIIK'lll. ÚIlC under lhe load poinl <lI onc approximaleJy half way bClwccn lhe load poinl anel lhe f:)f abutment. This failun; mode bccomcs more complicalcd by lhe

T H_ HUGHES I Masonry areh bridges 7 1

Name Sp"n Failure Failure Mode (m) Load (kN)

Prestwood 6.55 228 FOLlr Pins Bridgemill 18.30 3100 Snap Ihrough Bolton 6.00 1170 Four Pins Shinafoot 6.16 2500 Four Pins complicated by random brick

conslruclion Torksev 4.90 I080 Snao Ihrough Baroower 10.36 5600 Crushing bclow load

Preston 5.18 2100 Crushing bcJow load Strathmashie 9.43 1325 Not we ll defined with material falling out of

existing cracks

Barlae 9.87 2900 Heavily skewed. Snap through followed by shcar failure in spandrel wall

1'able 2 Failure modes of ful1 sizc test bridges

introduet ion of spandrcl walls and fill material. and also becomcs Icss clear whcn the arch ring is constructcd Df wL'aker and lcss homogcncolls materiaIs, for cxample random rubble or 510nc.

Material failurc of lhe arch ring undcr lhe cxccssive loading is causcd by lhe strcss resulting from joint opening. Tlle collapse cOIHlllcncing without the l'lIll l'ormation of ali lhe hinges. Thi5 local l'ailure can, in thcory, occur aI any of lhe incip icnt hingcs but whcn it initiatcs fail urc it usually occurs in the extrados under lhe load point. Thc loading conditions at this locat ion are extremely complcx and there is a clear lack of knowledge cOllcerning the mechanism of failure by crushing. Thc curvcd nature of the ring , togcl her with morlar-block intcracl ion , lhe presence of the large laleral applicd load. ali occurring ai lhe extreme edge oI' the Illasonry ullil, will producc lII1LJsual conditio115 beyond currcnt masonry modcls. Back analysis, 011 arches that showed no signs of such a failurc. has 11O\Vevcr indicatcd lhat the material su rvives I11l1cll longer Ihan that delermined from traditiona! masonry wall eri[('ria. 1'11is typc of crushing fai lure is mosl COlllmon in archcs constructcd oI' lhe wcakcr materiaI s, for exalllple s!one rubble archcs.

Thcrc is also lhe possibilily oI' lhe local ised failure oI' 1l1:tsonry bridges, in cases whl're high in[cnsily 10:lds and poor or inadcquale ll10rtar cause sec lions of lhe arch ring lo fali oul by punching sllear.

2.5 Sitc data for bricl!!c mo(]elling

The COSI of collecting good site data, espccia lly for bridges wh ich carry vchiclIlar traffie, can frcqucntly excced the cost of lhe analysis . For oruinary bridge load aSSCSSlllents it is lI s11:111y lIecessary to start wilh the sil1lple basic geollletric data. Th is includcs span (s), centre span ri se (r). ring lhickncss (d) anel soil dCplh (I) togcLh cr with lhe bridge width. lhe mosl criticai dilllcnsion is lhe rin,!; lhickncss and sincc Ihis CdnnOI bc I1lcasu rcd propcrl y wilhou l a Irial pit il C:ln, slIbjcc l la a sil1lil:l r

72 STRUCTURAL AN ALYSlS OF HISTORICAL CONSTR UCT10NS

experience with similar bridges in lhe locality, be based on lhe visible edge af ring beneath the spandrel walls. In lhe authors experience the actual thickness is rarely significantly less than tha! visible. In addition the initial site visit should identify the arch material, the position af any cracks ar distortion af the masonry ar other defects, and other faetar likely to be relevant, for example rutting af the road etc. A preliminary assessment can then be undertaken.

Ir lhe assessment is in any way marginal it will be necessary to gather more site data . Ir trial pits are possible then these can i) confirm lhe assumed ring thickness, ii) allow the type ofbackfill material to be assessed and if possible iii) determine the extend of any haunching above the abutments. It is difficuh to determine this infarmation from cored bo reholes since there is frequently a merging af masonry into the fil! particularly in stone ralher that brick arch bridges. Additional information on waterproofing, previous attempts to graut the til! or saddle the arch, and services can also be ascertained.

It is unusual to abtain samples from lhe masonry for laboratory tesling. This is because of j) the inherent difficulty in obtaining decen! samples, jj) the damage to lhe structure jji) the large variabilily in results requiring a number of samples and iv) lhe value of lhe data in lhe analysis is ofien less important than frequently imagined This las! poinl resuhs from the important distinction bclwcen masonry units, ie bricks, blacks stones, etc. and masonry, and because lensile strength is more important in analysis than compressive strength.

The development of flatjacks for lhe determination af lhe insitu slress SI ale, modulus of elasticity and even material strength values, to be discussed later, has an importan! role in lhe future development af masanry arch bridge material testing.

3. ARCH ANAL YSIS

The analysis of masonry arches has been used to perform a range of fllnctions. · ]n the UK bridge assessment has beeo the major concern, associated with the need lo assess load capacity of bridges for the 40 tonne and eventually 44 lonne vehicles. The current analyses can be conveniently divided into a number of groups.

1) Empírical equations and ideali sed c10sed form sollltions used solely for the purpose af bridge assessment.

2) Simple numerical analysi s , using rcadily availablc engineering general elasti c analysis software, again used solely for the purpose of bridge assessmcnt.

3) Simple mechanism analysis tailored for application to arch bridges , developed to directly include fill passivc rcstraint and simple arch ring crusl1ing . Developed both as a researcl1 tool and for exploitation as commercial masonry arch assessment software.

4) More sopl1isticated rigid block kinematic models, including sliding, crushing and multileaf analysis. Only used, to date, as research too ls.

5) Discretised cracking elastic analysis.

T. H. HUGHES / Masonry :m:h bridges 73

3.1 Advanced analysis methods

The analysis covered by group 5) is considered in more detail in the eurrent paper. It ean be eonveniently divided into l-D models, which are now regularly used in the UK as analysis and assessment tools, and the more eomplex 2-D and 3-D models whieh are still under development and are generally only used for research purposes.

The earliest work into the use of non-linear models in the analysis of masonry arches was carried out in the early 1980's. The initial applications showed that not only was there potential in using ~hese methods in predicting tbe ultimate load carrying eapacity, but they would also be useful in determining lhe areas that would crack under abnormal loads. These non-linear methods have some obvious advantages over lhe other analytical solutions, as they can provide information on the extent of cracking, lhe stress and strain leveis wilhin lhe arch and lhe deOections at ali positions under any load situation.

In both the l-D and 2-D rnodcls it is usual to assume a I melre strip load. The limited experimental data suggests that the load is rapidly laterally distributed once il hits the arch ring beeause of membrane action, this would suggest that the bridge load should be assessed rather than the loaded lane but it is still common in lhe UK to use a lane based analysis.

J.1.1 Dne Dimensional Models

The tirst work was carried out on the development a tinite element program used beam elements, with a no tension formulation and a parabolic stress strain reJationship in compression [17]. The unorthodox formulation was limited by its lack of inclusion of a soil model and the possible effeets of moving abutments. However , this inilial application showed the advantages to be gaincd by lhe use of the tinite elcment method when considering the serviceability of masonry arches.

A more conventional program was developed using curved ring elements and using a smeared continuum to establish the extent of lhe cracked zone [18,19]. Eight Gaussian integration points were used through the depth of the element to establish the extent of the tension zone and thus the craeked area. AS with earlier work use was made of a simple tension cut off model, where lhe masonry was not allowed to develop any tensile forces, prior to cracking. However, the later models developed allowed for a tension softening zone on unloading, but still most of the analyses undertaken limited the tension to zero. Tbe eompression models used were general!y elasto-plastic rclationships with a limiting stress levei and a strain cut off, after which it was assumed that the material was cornpletely crushed. As the software was developed it was realised that lhe soil models were becoming increasingly important; initially sai 1 was taken as dead Joad only. Later work showed that these effects were very signifieant, 50 horizontal one dimensional spring elements were incorporated into the models to include for the efreels of lhe tills passive resistance. The models

74 STRUCTURAL ANALY$I$ QF !-I 1$TOR1 CAL CONSTRUCTION$

included geometric non linearity and, by using deflection control, were able to simulate post peak load behaviour.

A cracking elastic analysis was developed. based on the early elastic work cf Castigliano, which incorporated joint opening by reduction Df ri ng thickness [20]. The basic simple model was extended to include geometric non-linearity and the 50il model detailed Ja ler . As with lhe finite element analysis lhe incípicnt hinges emerge frem the ana1ysis and do nOl always conform to lhe usual assumed positions. Figure 5 shows lhe application cf this method to Presto" arch. This is a semi elliptical arch which produced crushing under lhe load, lhe l-D analysis show lhe position af hinge formatian with hinges forming at the springings, this method assumes no shear failure at the tight curvature near the springings. It is

l N: '.0.0.0

Figure 5 Predictcd hinge positions for Prestoo arch.

likely that such a geometry would in fact have haunching and as a flat arch would then likely fail with an element of crushing. This l-O numerical model has becn used to investigate the influence of the various material parameters on the predicted (ailure load [21] and a parametric study , in probability space, has been undertaken that suggests that these l-O type moclels provide more robust load assessments than the simple elastic analysis that fo rms the basis of lhe current UK masonry arch assessment standard [22]. In addition the use of these advanccd anaIyscs have identitied the need to determine lhe initial stress state cf these highly redundant structures if normal serviceability parameters are to be considered.

Furthcr work on 1-0 tinite elements used tapered straight bcam elements [23,24]. The mcthod allowed for the alteration of the effective depth if cracking, crushing or both occllrred during the itcrative processo This method of tapering allowcd for the inclusion of the sections of the arch ring which were in compression, excluding zones which had developed tensile stresscs. The formulation allowed (oor a compressive yidd stress levei after which lhe material was assumed to be crushed. The soil model used was inc1uded as a number of horizontal one dimensional spring elements conncctcd to the arch ring. However, these were only activated when the arch ring movcd in to the till, providing only passive resistance. Tbe tapers were based on a linear variation of section inertia along the element thus considerably simplifying lhe element matrix formulationo

The l -O elastice cracking models have providcd a valuable insight ioto lhe behaviour of masonry arch bridges. AI lhe limit if lhe soil model and the geometric non lioearity is removed then the results should tcnd towards lhe mcchanism sohJlions and this provides a good test on the numcrical procedures. Since the analysis wiJl fai!

T. H. HUG HES I Masonry arch bridges 75

and this provides a good test on the numerical procedures. Since the analysis will fail if lhe elements become too thin the mechanism represents and upper bound.

The inc1usion of the geometric non linearity a1ways reduces lhe predicted collapse load. Some argue that masonry arches are too thick lO suffer geomelric

",~(P:':',,':"~' _ _ _______ _______ ---,

o .•

o .•

effecls but as lhe 0 .4

arches lhus

crack 'thin'

and lhe

effective sections reduce and lhe line af thrust straightens, which ali contributes to lhe effecl.

0 .2

oL---~~--~----~----~----~ o 0.5 1.5 2.5

tE I Em

Figure 6 Variation of predicled test bridge failure loads with elastic modulus [25]

Parametric stlldies have been undertaken, using l-O cracking models, on lhe effect of variations in lhe governing material properties [25]. Figure 6 shows lhe variation in the predicted failure load, for the bridges detailed in Table 2, with variations in the assumed elasticity. The results indicate a factor af 2, increase or decrease, in the assumed value generales only a 10-15% change in lhe predicted load.

More important is the varialion resu lting fram changes in lhe principie sai l para meter , lhe angle of internai fríclion, this variation is shown in Figure 7. The soil parameler produces a more sensitive response with a 10% change producing a 0- 10 % change in the resulting failure load.

'" r"-"-".::"'-' ----------- - - ----,

~ o .•

o .•

o .•

0 .2

oL-----~ ______ ~ ______ ~ ____ ~ o .• o .• , ,.,

I~ I ~n)

Figure 7 Varialian of predicted lest bridge failure loads with soil friclion angle (25)

The effect af variations in the compressive stress, shown in Figure 8, produces a much less sensitive response, in fact in same ardes there is no visible effecl. This early work l-O has been confirmed by lhe results of recen! 2-D analysis and poses sevcre questions abou t assessmen! methods based solely on compressive strength.

76 STRUCTURA L ANALYSIS OF HISTOR ICAL CONSTRUCTIONS

Ali the above work suffers from lhe consideration of masonry as a single material and lhe therefore required average or smcarcd material properties, and their simplification of the compressive state of

U ~tP:é/-'P~"),---_______ _______ -----,

• • o .•

o .•

o .•

o.,

the ring. For oL-----~----~----~----~--~ u u u u U

(d I a'ç) example mosl modern masonry

Figure 8 Variation of predicted tesl bridge failure loads with compressive strength [25]

theory suggests lhat lhe failure in compression involves the tensile splitting of lhe units caused by lhe poisson ratio effect generated in lhe softer mortar, thi s is often attributed to a different poisson ratio when in fact it is a result of lhe difference in the unit and mortar stiffness. The concept of "crushing" of masonry as a global material failure is lhus suspect especially when this is occurring in the extreme fibres of an eccentrically loaded arch ring. Similarly the models require lhe masonry elastic modulus al lhough lhis smearing is nol considered to cause significant errors. In a l-D analysis the lack of any tensile strength in lhe mortar joint is relatively easy to consider since lhe joint is always at righl angles lO lhe ring. Some methods update lhe geometry and effective ring thickness whereas others incorporate lhe effect via smearing in the numerical integration to determine the beam stiffness.

The are a number of drawbacks in considering arches using these I-D models {hese are listed in comparison wi th 2-D modelling.

1 ) The soi! can only be treated as a vertical load plus, at best, a non-linear hori zontal spring. The besl soi! model assumes initially an , at rest, lateral earth pressure at dead load and allows deflection dependant increases in lateral pressure as lhe arch moved into the soi l

c . ~Uu l u • • • S"b~,.d.

A • •• " ••

----,---" Kaa, I

-6 o

SoU Prusure O .

.r---r-

Kpo,

6-HorizontalOeUection

Figure 9 Soil spring model used in l-D analysis

mass and similar decreases as the arch moved away from lhe soi!. These changes in the soi! pressures are lhen limiled by the relevam aclive and passive coefficient cut-offs, this is shown diagrammatically in Figure 9 . There can be no allempt to properly model either the lrue restraining effec t of lhe soi! or lhe possibility of lhe soil actualJy arching in its own right. Similarly lhe loading

T. H. HUG HES I Masonry arch bridges 77

has to applied to lhe arch ring, invariably using some distribution law, ralher than the true distribution obtained as lhe soi! deforms under load.

2) The treatment of the abutments is simplistic, either assumed as rigid or at best acting as some son of spring.

3) The proper modelling of cracking and phenomena such as ring separation is impossible.

4) Many arches are sufticiently thick and curved such lhat some l-D simplifications are reaJly invalid.

3 I 2 Two Dimensional Madels

To date ali the models developed treat masonry as a single material and are undertaken at 'macro ' levei, the treatment of an arch as a 'micro' moclel with the individual masonry units and the mortar joint separately modelled by eJements with different material properties is realistically outside lhe scope of present hardware.

Al! 2-D models have been based on a plane strain consideration of a section through lhe arch. The first 2-D simulations [19] maintained the use of 1-0 ring elemenls but incorporaled 2-D elements to moclel soi l behaviour. These models nol onJy improved lhe soil modelling but also overcame lhe problem, in the I-D model, of distributing the live load through lhe sail to the ring. This had previously been based on a specified load di striburion angle.

lt became apparent that lhe simple I-D models would be of limited use in lhe modeIling of arch ring behaviour. This led to lhe development of two dimensional models in which the fill could be modelled directly using standard FEM soil s models and lhe arch ring could be moclelled using more Ihan one element through ils thickness.

The 2-D model developed by Choo et ai [26] used traditional eight noded isoparametric elements to medel lhe arch and, ralher surprisingly, horizontal elements l-O elements as the fil!. These fill elements only provided resistance when the arch ring moved into lhe fil!. To enable cracks to form when tcnsion forces develop the rather cumbersome method of the discrete disconnecting and reconnecting of nodes was incorporated. This method could mede I cracking in both the radial and tangential directions, as would occur in the case of ring separat ion. A1though lhe disconnecling of nodes is not ideal i( is more useful in masonry modelling lhan concrele modelling because the failure planes do coincide w'i lh either lhe bed course or the mortar layer between adjacent rings. Since the easiest way of generating finile elemenl I1lcshes is to use equal radial and circumfrential element boundaries these naturally coincide with the directions of these weakjoints.

The two dimensional finite element· program developed by Loo and Yang [27] used a linear elastic tension-tension zone with a tension cut-off, lhis was followed by a signi ficant linear slrain softening region , between 5 and 10 times lhe strain at peak

78 STRUCTURAL ANALYSIS OF HISTORICAL CONSTRUCTIONS

stress, and a quadratic compressive stress strain relationship with an equally large linear strain softening zone. Failure in lhe compressionfcompression zone was via a Von Mises plasticity mode!. The soil model developed by Loo ct ai was in lhe form Df a separate tinite element program with vertical fill elerncnts, each held in position at the base by hinges in line with lhe arch extrados. This enabled lhe vertical and horizontal forces to be detcrmined at these hinge points due to the soilloading.

Neither cf Choo's Cf Loo's analyses included lhe soil as a 2· D media. Ali Df lhe above models also surfer from their consideration Df masonry as a homogenous isotropic material, indeed the governing failure properties in Loo 's modcl are the masonry compressive st rength and the masonry tensi le strength neither of which has any real meaning.

Recem work has been undertaken using a modified concrete model at micro scale to model the behaviour of brickwork loaded in the manner of arch brick rings [28]. The results of a series of analyses with differing compressive and tensile stresses applied normal to the main material axis has been used to develop an anisoptropic masonry model where the failu re surface is governed by the mortar compressive and tensile st rength and the masonry unit compressive and tensile strength as shown in Figure 10. Whereas in traditional masonry modelling it has been necessary to develop a 3-D failure surface, by rotating the direction of the principie stresses to the material axis, to properly model the brick mortar interaction, this was not considered necessary as lhe principie stress directions in the arch ring of a masonry arch bridge coincide c10sely with lhe material axes, That is, the principie stresses are essentially ci rcumfrential and radial. In addition when the angle between these stresses and the material axis are aI their largest these generally correspond to regions of lhe arch whcre lhe stresses are low and still wilhin the elastic region.

,-Itll

~1tJ- I ,- o o o o o o o : Íl '-." " ." .!IO ., , ;

1 .... 01 \ · 1) .. ",, _ SI ....... O •

.. _._-_ ... -" o

.\

---.--_. Figure 10 Failure surface for curved masonr model [28]

T. H. HUGHES I M:lSonry arch bridges 79

3 1 3 Three Dimensional Models

To date little work has been undertaken 00 masonry arches in three dimensions.

Some initial work has been undertaken using plate elements of variable lhickness coupled to soil springs in ao auempt to model the effeets of spandrel walls and to provide some indication of lhe effeet of diagonal eracks [29]. This later work was necessary to assist in the determination of so called condition factors for load assessment. These studies use the same basie approach as the l-D analysis where the region of lhe arch where teosioo is initially delermined are effectively removed from consideration by reassigning lhe plale thickness ai lhat location.

More advanced work on lhe 3-D analysis of masonry arehes has recently been published using lhe so-ealled homogenisation technique [30]. Homogenisation is a process whereby a staeked series of bricks and the mortar between are initially considered and it is assumed that under a uniform load there is eOlllpatibility of lateral and transverse st rain between the units and mortar. This together with consideration of force equilibrium allows lhe overall response of lhe staek lO be modelled by an anisolropic layered analysis where lhe elastic components are funetions af the brick and mortar elastic properties and of the geometry of the brick and mortar joinl. The seeand stage homogenisation involves assuming that a series of these staeks are formed with mortar layers between. The homogenisation process is lhen repeated. Finallya the fuH set of elastic constants for a three dimensional analysis are obtained again dependant on lhe separate unit and mortar properties and lhe unit and mortar dimensions. Following an anisotropie homogenous analysis the average masonry stresses and strains are detennined and this can then be di saggregated into scparate briek aod mortar stresses. In the receot work eraeking was included aod lhe homogenisalion of the eracked elements undertaken and applied lo masonry arch .b ridges (31]. The work has yet lo be exlended lO include lhe soil modelling. This form of analysis is considered appropriale for modelling in plane loads in walls and has becn used in laterally loaded walls but lhe laek of through wall bond in arehes coupled to lhe limited number of rings suggests that a modifieation to this process is required for masonry arehes.

3 2 Modellino lhe Initia! Stale

Ali lhe above sophisticated analysis require an assumplion of lhe initial state of lhe strueture. This is importanl becallse lhe masoory areh is a high!y redundant structure and its response to loading depends critieally on its inilial statc. This important inOuence has, in fact, becn ignored in almost ali lhe above analysts.

The initial state of an areh, thal is the eurrent dead load state, depends 00 a number of faetors, the constrllction teehniqlle specifieaHy including when the formwork was st ruek, the consolidation of lhe fiH material and specifieally the al resl pressure it provides to the arch ring, lhe historieal movements of lhe abulments dnd lhe creep wilhin lhe masonry. It has been shown Ihat arehes ean remain stable under

80 STRUCTURA L A NALYSIS OF !-IISTORICAL CONSTRUCT10NS

a wide range of initial states and that at working loads the deflections, stresses and craeking are dominated by the assumed initial state condition [32].

The importance of the initial state has lead to recent rescarch into the use of flatjacks in lhe areh ring masonry to determine both the insitu elastic properties of the masonry and lhe initial stress. These flatjacks operate using lhe gauged stress relief of a slot within lhe mortar which is then relurned to its original stressed state using lhe flatjacks. The work to date suggesls lhat masonry tends to be a very forgiving material and that the extremes of initial stable states do not prevail with the measured dead load stresses being associated with more uniform stress distributions within the ring [33,34]. The work has recently been extended to determine lhe live load stress within arches by mimieking lhe tive load ring strain behaviour using a computer eontrolled pressure within the natjaek.

3 3 Future model1ing developments

The use of l-O and 2-0 non linear elastics analyses has produeed a large amount of useful information on lhe load earrying characteristics of masonry arehes at, and prior to, collapse. There are however a number of unresolved matters that need lO be addressed in future work and eonsideration of lhe above progress to date ean perhaps provide some pointers.

The l-O models appear to have a Iimited future in providing any further insight into single span masonry arch behaviour. If lhe effeet of lhe spandrel wall stiffening of multispan piers can be neglecled they eould yel be expanded to model multispan arches.

To date geometric non-linearity has been included in a number of 1· 0 models, it has, however, nol yet been used in 2·0. This needs to be addressed if the 2·0 models are intended to be used for a more advanced consideration of ultimate load , this is particularly important if work on lhe developmenl of new shall arches progresses.

The relative merits of using 2-0 soils models with 1-0 arch ring models or }. D soils models with 2·D areh ring models needs to be addressed. There is general aeeeptance of the need and value of soi l models but 10 date no overall acccpted direction for 2·D work exists. If lhe approach adopted for lhe 2-D work is a plane strain analysis whcrc more sophisticated arch e1ements are develupcd lhen there seems little rcason to use l -D soi ls models. The general plastieity models that will form part of the arch ring model could be used, with appropriate parameter values, to better model the soi! behaviouT.

To lhe aulhors knowledge ali the areh bridge models current1y used both in 1· D and 2-D modelling, with one exception [31], use a composite model of masonry behaviour, these use either a smeared or tapered masonry model. Many of the problems associated with modelling masonry arches are exceptionally severe when compared to those found in normal masonry walled slructures. For example lhe crushing under the point load, previously discussed, also the interaetion between the

T. H. HUGHES I Masonry arch bridgl!s 81

arch ring and both internal and externaI spandrel walls. In addition to moving to general 2-D models it may also be necessary to use some of the more advanced masonry models.

In the tanger term there is also the possibility of developing fuH 3-D models so that the fuI! stiffening contributions of the spandrel walls as well as proper consideration lhe fill could be incJuded jnto the analysis. This type of 3-D modelJing will Iikely prove too expensive to be used as anything other than as a research tool. The models could however provide valuable information for use in determining more appropriale 2-D models for general use.

4.0 ARCH ASSESSMENT

The assessmenl of lhe load capacity of existing structures creates significantly more difficulties than the design of new structures. The strength parameters and even lhe geometry are often unknown. There is however evidence of the condition of the structure and even its existence, in the current loading regime, says something about its load capacity. In the UK the MEXE [li] melhod has been used since the 50's and is based on an empirical equation of unknown origino The equation provides a provisional axle load based, PAL, which is then modified by a large number of factors lO take into consideration the joint material and width , the arch material, backfill material. arch shape, arch condition etc.

PAL = 740 (d + I) , s "

Despite lhe considerable investment into the research of masonry arch bridges, alluded to in this paper, over lhe last 10 years the new standard published in 1993 [IIJ retains the MEXE equation as the primary method.

As an alternative an elastic two pinned anaIysis of lhe arch ring is permitted with lhe soil aCling as dead weight only and lhe compressive strength on the arch material being lhe load determining parameter. The development of tensile stresses is conveniently ignored. The results of the application of this method wcre compared by its originators with lhe other mechanism

~'M=='~='=" ="=L'=.=, ~,,~,"~"~ .. ~) ____________________ -, 700 i I 0-... _ 1

.00 + '''cll. "

'00 lP-p l n ... "

o ""'cll. 2

.00 , c. ... ~ 2

300

,"O

'00

• .00

•

+ 5

200 300 .00 500

Experimental load (Tonnes)

o

'00 '00

Figure 11 Variation of the theoretical loads for five assessment techniques compared to the experimental loads

[I I]

and l-O crack.ing elastic methods discussed above, the results suggested indicated a

82 STRUCTUIlAL ANALYS IS OF HISTORICAL CONSTRUCTlONS

wide scaUer. These resulls are presented in Figure 11 which shows a comparison between lhe theorctical toad, determine using lWQ mechanism, tWQ 1-0 elastic cracking and the recommcnded 2-pinncd analysis, and lhe experimental load for lhe 10 full scale bridge tests to failure. Although lhe figure does 001 identify a clear "winner" it is argued by many that there are too many additional effects presen! in lhe fuH scale teS1S that are nOl in any way included in lhe analyses for 5uch an exercise to be uscful. Thc rcsults are 3150 prone to large variations dcpending 00 lhe choice of material parameters adopled by the methods proponcnts. Previous work [22) suggests that lhe result obtained from 5uch a tWQ pinned analysis is dominantly dependent on the assumed eompressive strength which is notoriously diffieult to aceess. Figure 12 shows the variation of a the assessment load , dimensionised

non with

respeel to lhe median

F:allur. LO.d R.tlo .. , x Plnn." EI.Ulc

• , 'hchul ...

• C.ac;k lng EI .. uc , ,

o .• 'gP» XXXX X

,..-x

o .•

""""" o .• o o.,

XXX XX

o .•

x""" .-x

xxxX --xxxxx

o .• o .•

Figure 12 Variation of lhe predieted tes! bridge failure loads wilh ellmulalive probabilit [22]

value, against the variation in lhe material properties for the two pinncd elastie , meehanism and l-D elastie craeking analyses . The olher methods are more reliant on lhe geomelry and weight which are betler determined and conform more to lraditional views on lhe origin of the strength of tltese Slructurcs.

In the authors view lhe mechanism methods, and empirical equations developed from lhem, should form lhe basis for lhe simplesl assessment tools. They have a fundamenlal base in the actual fa ilure modes of the struclUres and with the addilion af passive fill pressure and, much less importantly, malerial c rushing Ihey provide very useful assessment lools. A number of these models are available commercially and a number of engineering consu!tancies have developed similar software in-house.

The l -D elastic c racking models are much more complicated and only lwo are currently available commercially. They provide lhe assessing engineer Wilh significant additional infonnalion which must be treated with an appropriate degree of scepticism. They provide useful information al serviceabilily and can mode! slow moving loads. There is a significan! increased investment in lhe Iraining associated with these pieces of software.

The "is no published work on lhe use of 2-D analysis for regular bridge assessmellt, most of their work has been either for research purposes or for bridges lhat posed particular problems. The economic realities of lhe number of bridges requiring assessment suggests that these types of models with remain relatively

T. H. HUGHES I Masonry arch bridges 83

uncommon in general use. The investment associated with the growth of new masonry arches may change this.

5.0 CONCLUSIONS

There are a number of general conc1usions that can be drawn from lhe work detailed in this paper.

i) Ma,onry arche' continue to play an important role in the tran 'port infrastructure.

ii) There has been a very significant investment into the research of these structures. The experimental work has been significant and has been used to aid the development of numerical tools and to validate assessment methods.

iii) The inveslment into the development of numerical analyses has been less well co-ordinatcd and has resultcd in a number of differenl approaches. Whilsl lhe analyses have provided additional insight into lhe structures behaviour there has unfortunately been little take up of the more advanced nurnerieal tools by industry.

iv) The experimental and some analytical researeh work is moving more towards serviceabilily.

v) Development of better masonry models for use in areh struetures is continuing.

ACKNOWLEDGEMENT

This paper eontains referenees lO the work of many mueh other researehers. The work of my researeh student Martin Baker and researeh assistants Robyn Pritchard and Paul Taunton under contracts [rom lhe Engineering and Physical Sciences Research Council contraclS GR/K04262 and GR/K76296 i, gratefully acknowledged.

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84 STRUCTURAL ANALYSIS OF HISTORICAL CONSTRUCTIONS

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T H. HUG HES I Masonry arch bridges 85

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