Arch Bridges: History, Analysis, Assessment, Maintenance and Repair [1 ed.] 9058090124, 9789058090126

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ARCH BRIDGES

PROCEEDINGS OF THE SECOND INTERNATIONAL ARCH BRIDGE CONFERENCE VENICE/ITALY/6-90CTOBER 1998

Areh Bridges History, analysis, assessment, maintenance and repair Editedby

Anna Sinopoli Istituto Universitario di Architettura, Venice, Italy

@

T aylor & Francis

...", Taylor & Francis Group

LONDON AND NEW YORK

The texts 01 the various papers in this volurne were set individually by typists under the supervision 01 each 01 the authors concerned.

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Published by Taylor & Francis 2 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN 52 Vanderbilt Avenue, New York NY 10017 Transferred to Digital Printing 2007 ISBN 90 5809 012 4 © 1998 Taylor & Francis Publisher's Note The publisher has gone to great lengths to ensure the quality of this reprint but points out that some imperfections in the original may be apparent

Arch Bridges, Sinopoli (ed.)© 1998 Taylor & Francis, ISBN 90 5809 012 4

Table of contents

Preface

IX

History 0/ structural mechanics 1850-1880: Bridge-building and modem structural mechanics E.Benvenuto

3

The relationship between the Gothic model and the conception of bridges ACoste

15

Empirical methods for the construction of masonry arch bridges in the 19th century MCorradi

25

Arch and vault from 1800 to 1864 K.-E. Kurrer & A Kahlow

37

History 0/ construction Conceptional design of Renaissance arch bridges H.Falter &ABögle

45

Brick bridges and historical transportation systems MChalana

53

Construction knowledge between the 18th and the 19th century applied to arched masonry systems in Venice G.Riva & P.Valle

57

M. Uvy versus lde La Gournerie: A debate about skew bridges ABecchi

65

The masonry bridges and viaducts of the first Piedmontese railway, 1845-1853 LRe

73

The experimental approach in the evolution of construction systems: The contribution of the Porcheddu company of Thrin to the refinement of the Hennebique system for the construction of arch bridges AM Sassi Perino & G. Faraggiana

81

v

Equilibrium and limit analysis The assessment of strength of masonry arches

95

1 Heyman Lower and upper bound theorems for masonry arches as rigid systems with unilateral contacts ASinopoli, MCorradi & F.Foce

99

On the analysis of multi-ring brickwork arch bridges MGilbert

109

On the definition of the geometrical safety factor of masonry arches ADe Rubeis

119

The mechanism model in the seismic check of stone arches P'Clemente &ARaithel

123

Theoretical models and analysis Minimum and maximum thrust states in Statics of ancient masonry bridges MComo

133

An upper bound analysis for the strength assessment of masonry arch bridges AF.Ashour & .s:W.Garrity

139

A contact mechanical approach to the theory of the elastic voussoir arch

147

H. Parland & A Miettinen Hardening and shakedown of masonry arch joints B.T.Rosson & T.E.Boothby

155

On the use of Somigliana dislocations applied to masonry arches

163

L Feletti & M Rapallini

Numerical methods Jor strength assessment Finite/ discrete element models for assessment and repair of masonry structures D.R.1Owen, D.Peric, N.Petrinic, CLBrookes & P.1James

173

Distinct element analysis of stone arches G. Mirabella Roberti & F. Calvetti

181

FE modelling of the dynamic response of Kimbolton Butts bridge ABensalem, H.Ali-Ahmed, CA Fairfield & ASibbald

187

Numerical simulation of experiments in arch bridges P.Roca, CMolins, T.G.Hughes & CSicilia

195

Interactive assessment of masonry arch bridges AKumar

205

Load capacity of multi-arch masonry bridges CMolins & P.Roca

213

VI

Safety evaluation and retrofitting of an arch r.c. bridge CModena &D.Sonda

223

An approach to the structural model for masomy arch bridges: Pont Saint Martin as a case study G.Frunzio & MMonaco

231

Non-destructive testing Tomography for NOT applied to masomy structures: Sonic and/or EM methods S.Valle, LZanzi, LBinda, ASaisi & G.Lenzi

243

Radar testing of masomy arch bridges with soil backfill CColla, D.MMcCann & MCForde

253

The behaviour of open spandrei brickwork arch bridges CMelbourne & HTao

263

NOT as a tool for detection of gradual safety factor deterioration in loaded arches A Bensalem, HAli-Ahmed, CA Fairfield & A Sibbald

271

Dynamics and experimental testing Effects of vehicle impact loading on masomy arch parapets B.Hobbs, MGilbert & T.Molyneaux

281

The collapse behaviour of a multi-span skewed brickwork arch bridge CMelbourne

289

Oynamic testing of masomy arch bridges J.W.Bintrim,J.ALaman & T.E.Boothby

295

Restoration of a two arches masomy bridge: Experimental testing and mechanical behaviour ASalvatori

305

Special problems and new design Some notes on system behaviour in arch bridges W.J.Harvey, F.W.Smith & R.Barthel

315

The influence of soil and masomy type on the strength of masomy arch bridges T.G.Hughes, MCR.Davies & P.R.Taunton

321

Mass concrete arches CMelbourne & S.K.Njumbe

331

Conservation and maintenance A Roman viaduct-bridge in Campania: History, structure and maintenance A Baratta & T. Colletta

343

Construction conception and structural conservation of masomy arch bridges MBellomo & S.D'Agostino

353

VII

Damages of existing stone bridges in Greeee MKaraveziroglou-Weber, E.Karayianni & E.Stavrakakis

361

The Veniee-Mestre masonry road bridge: Checking durability of maintenanee operations G. Riva & F. Russo

369

Stone bridges and historie Ameriean landscapes C1Rusnak & T.E.Boothby

377

Repair and strengthening Widening and strengthening of London' s Kingston Bridge T.N.Healey & 1H.W.Counsell

389

Set up of restoration methodologies for cast iron bridges in Veniee F.Bonollo, CModena,ATiziani &MR.Valluzzi

399

Repair and strengthening of five full seale masonry areh bridges S.KSumon

407

Strengthening masonry arch bridges through bacldill replacement by eonerete G. FauchotlX & CAbdunur

417

Repair of the old stone bridge of Krania in Greeee M Karaveziroglou-Weber, E. Stavrakakis, E. Belissari, MEftaxia & C Panousi

423

Supplement Thermal effeets on a masonry areh bridge investigated using ABAQUS 11 Robinson, D.1 Prentice & D. Ponniah

431

Author index

439

VIII

Arch Bridges, Sinopoli (ed.) © 1998 Taylar & Francis, ISBN 90 5809 012 4

Preface

Eighteenth century researchers often used the image of a labyrinth to represent their own bewilder­ ment about the contradictory concepts on statics of vaulted masonry structures. The historical development of the arch theory is marked by the search for an Ariadne 's thread able to direct the application of static principles without losing sight of the experimental evidence and the empirical data related to materials and building techniques. The end of the XIX century marks the conclusion of that development: The concepts typical of the Resistance des corps solides moved from the original field of application of en charpente structures to that of en ma~onnerie constructions, and strongly supported the interpretation of the masonry arch as a 'systeme imparfaitement elastique' as intended by Castigliano in 1879. That was the period in which structural engineering was beginning to acquire its modem connotation: Castigliano expounded his theorems on the work of deformation; Winkler prepared his famous Lehre von der Elasticität und Festigkeit, and following the line indicated by the contribu­ tions of Maxwell and Clebsch with the 'forces method' and the 'displacements method', a mature synthesis of structural applications was reached by Müller-Breslau, with the method of equations of compatibility for hyperstatic systems. Modem structural engineering was to evolve from these new theoretical bases by designing daring arch bridges, thanks also to the use of new materials such as steel and concrete, and the adoption and invention of new technologies. From then on the elastic properties of materials, the degree of hardening of mortar, and the variable thicknesses of hewn stones and joints became the elements on which to base knowledge of the exact position of the thrust line in masonry arches. This methodology was the one adopted by the avant garde of European structural engineers at the end of the nineteenth century, and new experimental research also took place on the elastic properties of stone materials and masonry structures. In spite of all that, some scientists were still perplexed regarding this approach, because of the uncertain deformative properties of the masonry, that did not make it possible to find the unique solution of a statically indeterminated structure. What makes the position of the modem structural engineer very embarassing is the change in attitude necessary to approach masonry constructions: No longer as a daring planner of innovative projects, but as a respectful conserver of ancient monuments. The operator should find a methodolo­ gical foothold that will provide guidelines for strength assessment, and thus allow a plausible restoration procedure. A century later, the debate has been reopened among scientists; and paradoxically, this phase of critical rethinking has coincided with the rediscovery of the mechanical tradition that the affirmation of the elastic approach had contributed to make people forget. In fact, in those cases where the 'deterministic' approach that is characteristic of elastic method cannot be applied, one can only IX

accept the logic underlying limit analysis and design, which had already been applied to testing of steel structures, but, which is also conveniently adaptable to stone ones, using the plausible hypothesis of no tension material and infinite compressive strength. The papers in this volume were presented at the Second International Arch Bridge Conference held in Venice in October 1998. They record the breadth of research, knowledge and debate about arch bridge history, analysis, design, assessment, maintenance and repair; they bring together the experiences of academic, technical and professional worlds from many countries. Anna Sinopoli

x

History of structural mechanics

Arch Bridges, Sinopoli (ed.)© 1998 Taylor & Francis, ISBN 90 5809 012 4

1850-1880: Bridge-building and modem structural mechanies Edoardo Benvenuto lstituto di Costruzioni, Universita di Genova, ltaly

ABSTRACT:The present rather rhapsodic introduction to the more specific papers concemed with the history of structural mechanics does not deserve any interest for the readers that are acquainted with this subject. The scientific events belonging to the thirty years between 1850 and 1880 that will be here shortly recalled and discussed are weil known to historians. They have been studied by the author in some of his previous works (e.g., An Introduction to the History 0/ Structural Mechanics, Springer, New York, 1991, vol. 2) and find nearly exhaustive treatment in numerous excellent essays, from Timoshenko's (1953) to Charlton's (1982) etc. The aim of this historical outline of those thirty years is confined to emphasize the explicit or concealed reasons that connected the rapid ripening of modem structural mechanics with the contemporary construction of important and famous bridges (continuous tubolar bridges, but also framed or masonry arch bridges), and, more generally, with the "spirit" of that period which gave rise to challenging new routes in different fields of culture, scientific thought, technology, industrial production and architectural taste. see in the following pages. At last, during those years, the first great linguistic revolution took place in mechanics, which renewed and unified statics and every branch of structural science under the new light cast by Staudt's Geometrie der Lage according to a grand project that encompassed Maxwell' s highly refined geometrical and topological intuitions (1864) , the solid construction of Culmann's Graphische Statik (1864-65) and Cremona's projective investigations (1872). We may weil say that the thirty years between 1850 and 1880 seem to have nursed a sort of miracle, as if a long process started centuries before and spread along heterogeneous paths had suddenly matured, marshalling its fruits within a harmonious system of connections, confirming formal symmetries and providing promising analogies. A perfect synthesis that deserves the same opinion Timoshenko gave on Castigliano's major work: very little more was said about structural mechanics from that time to date, if not by particular developments and along heterogeneous paths once again. The scientific events briefly mentioned above might give the opportunity to teil an exciting tale made consistent by the intrinsic concatenation of ideas ruling the development of theoretical expressions. However, in this instance, such an approach would not allow us to understand the real meaning of the story I am going to tell. As a matter of fact, it is a complex story in which several

1 THIRTY YEARS DECISIVE TO STRUC­ TURAL MECHANICS The years from 1850 to 1880 were crucial to the creation of modem structural mechanics. Its fundamental works appeared du ring that period. Contributions so important as to be still used today, whose author is sometimes unknown or not even mentioned, scientific discoveries that have made their author highly thought of, just because they have acquired a life of their own as common and anonymous heritage of technical knowledge. In those years, the mathematical theory of elasticity, though already ideally outlined by its greatest founders (Navier, Cauchy and Poisson) during the third decade of the century, acquired the status of organic discipline, strict and admirably simple, thanks to Lame, who first expounded it in full (1852), and to Saint-Venant and his epoch-making memoirs on torsion and flexure of prisms (1855-56), and later to Clebsch and his famous treatise (1862). And finally, it was Saint-Venant who made a powerful integration of the general theory of elasticity and the strength of materials in his Notes and Appendices that enriched the third edition of Navier's Resume des Le~ons. In those same years, the theory of beam systems and statically indeterminate frameworks was outlined and then perfectly formed according to different but converging approaches, as we shall 3

2 TRAINS UPSET THE OLD WORLD

possible "plots" intertwine, each one following its own logieal evolution even though from distinct and partial viewpoints, making determining contributions to the whole configuration. Naturally, the development of concepts within the field of theoretical and applied mechanics plays a decisive role, as we shall see. But also other reasons of a practical, political, social and cultural nature have as much weight as that. There is the role played by the new Weltanschauung generated by the industrial revolution that introduced new materials, new building techniques, new working practices and new relationships between social classes, and the enonnous problems brought about by urbanisation. There is also the separation between architectural taste, bound to the historicist codes of eclecticism, and the engineering of the most daring constructions, in which the iron construction technique itself embodied a new intentional aesthetic value. This intertwining of düferent paths makes it hard to sketch out a historical outline of our thirty-year period. The hierarchy of events is often quite uncertain, and sometimes misleading. The boundaries between disciplines are not clear cut and what belongs to each of them cannot be foreseen from the beginning. "Only the chronicler who lists the events without telling the small ones from the big ones does consider the fact that history does not neglect anything of what has happened", wrote W. Benjamin in some of his notes on philosophy of history. A century earlier, such a thought had been expressed by V. Hugo at the end of his rieh description of the meaningless episodes that all together shaped the year 1817: "History nearly always neglects these small details, and could not do otherwise lest it would waste its time on trifles. However (he continued) these episodes wrongly said small - for there are no small events in man's history, nor smallleaves in the woods - are useful. The way each year is shaped makes out the shape of a century". WeIl, in writing down this paper, I feIt Victor Hugo's words and especially his matchless example very close. If the historian wants to report all richness of the events faithfully and accurately, and convey something of what he has understood by getting to know the great masters, getting close to their views of the world, participating in their exploits, learning to love them as for a longstanding habit, he has to venture on a wider horizon so as to breathe a climate and be testimony to a community of feelings. His tale should sound like a rhapsody encompassing fragments and memories around the main thread of the narration; like the flowers of the field Bernanos talked ab out, each of those fragments, each of those quotations seem to have no scent but all together make the air smell beautifully.

I mentioned Victor Hugo. There is one of the letters he sent to his wife that may perhaps help us get familiar with the climate of that time. Actually, the letter dates back to some years earlier than the period we are talking about, but at the beginning of our story the common feeling must have been not much different. For the first time the novelist had travelled by train from Antwerp to Brussels. "In the evening, on my way back, the night was falling. I was in the first coach. The locomotive was blazing and roaring before me; huge reddish rays, that tinged the trees and the hills all around, turned together with the wheels. The train going to Brussels has met ours. There is nothing more frightening than these two speeds that dart side by side, multiplying each other in the passengers' eyes. No one could see anything between the two trains: no coach, nor man, nor woman could be seen go by, just whitish or dark shapes in a whirl. From that whirl shouts and howls were coming out... One has to try hard not to think that the iron horse is areal beast. One can hear its breath when it rests, its moan when it sets off, its howl when it runs: it sweats, quivers, whistles, whinnies, slows down, drags; enonnous bundles of yellow sparks sprinkle at each turn of the wheel or from its hooves, and its breath goes high above us as clouds of white smoke, then tom by the trees lining the road". In those years, from 1850 to1880, train is a great protagonist. It becomes part of the landscape but has an important place in the symbolic universe, too. It carries men and goods, weaving a new communication network, and gives direction, on ideal tracks, also to thoughts. Around 1850, in Europe the railway network spread for about 33,000 km and in the USA for 32,000 km. Around 1880, the European network was about 200,000 km long and the American one 250,000. 3 THE BRIDGE, A GREAT PROTAGONIST One can easily realise the impact that such a powerful development had on the second half of the 19th century engineering. The bridges that "decorate" the railway and its tunnels somehow look like the big domes that in the past centuries crowned churches and monumental buildings. The construction might as weIl be characterised by different criteria aimed at meeting venustas and utilitas requirements; a great number of craftsmen might be busy getting work done autonomously according to their own skills; but when the dome was to be erected, the work could no longer scatter in hundred streams, and had to be concentrated in its creator's mind and hands. Structural design, know­ how, static consistency came out in full sight. In 4

name. While Walter's dome is as boring as a clicht\ Röbling's bridge looks like the sign of a new adventure. This is what the imaginative engraver feIt when, representing the bridge from an impossible viewpoint as standing out above the crowded skyline of the neighbourhood, tumed it into a sort of rainbow that, from high up, links the two shores of the sea. Bridge history numbers happy and sad dates: around the '50s, adverse fortune fell on several suspension bridges, too agile and daring. Some time later, an American statistic recorded a frightening datum: from January 1st to December 31st 1877, as many as 251 American and Canadian bridges collapsed because of structural defects and not only because of exceptional circumstances such as floods and lightning. In 1879, the Scottish Christmas holidays were distressed by a tremendous disaster: thirteen bays of the Tay bridge, built by Thomas Bouch between 1872 and 1876, were gulped down by the river during a hurricane just while a train coming from Edinburg was running on it at 7.30 on the evening of December 28th. Three hundred passengers disappeared under the waves, and of the iron structure stood up only some stumps around the piers, as a moon half-hidden behind the clouds let the rescue squad see. "There have been a lot of suppositions going on - wrote Mr. Walker, the railway manager, in his report - to explain how come thirteen massive bays were fully uprooted so as to leave no trace at all. The most plausible explanation is that the side pressure caused by the wind while the weight of the train was producing a vertical one generated vibrations increased by the simultaneous action of the hurricane ... ". Whatever it was, it ended up with Thomas Bouch facing the consequences: for seven years he had yeamed for the commission to build the Firth oj Forth bridge, and he was about to get it, but the Tay disaster made English M.P. 's change their mind. The commission was given to engineers Harrison, Fowler and Baker whose mighty project ensured that the new bridge would be hurricane-proof. Much luckier than Bouch was, in those years, Gustav Eiffel. His practise became an intemationally renowned firm, areal might. The Szegedin bridge, object of a competition which all European builders had taken part in, was one of his first works; then, in 1875, it came the Mississippi bridge in St. Louis with a bay 158.5 m long; and again, in 1877-78, the "Maria Pia" bridge on Douro with "the biggest in the world" framed arch for a span of 160 m; a quite similar framed arch was to be inserted in the well-known Garabit viaduct, 122 m high above the valley, whose construction lasted up to 1884. However, the idea of a viaduct crossing the valley at such a height must be assigned to Uon Boyer, a young engineer, who nobody remembers; we have to give credit to hirn for the bridge concept

them there was all the evocative strength of forms; beauty was reached in one act in which science, technique, imagination, poetry, memory interpenetrated. Similarly, the 19th century bridge entices the greatest energies, the best of constructive art and science. It was a benchmark test for structural theory and, at the same time, the most effective demonstration. It was the most favourable opportunity to use new building materials, especially iron, and was also the freest place where to test new forms, leaving aside the expressive constraints descending from architectural tradition. In addition, a bridge, just as such, houses symbolic values still hidden. It is not made to draw anybody's attention nor be the object of the passer-by's aesthetic pleasure but is a go-between, a means to be left behind, a subdued piece of architecture to get a glimpse of. That integration of "channel" and "message" that some mass communications system scholars of our century have indicated as the main feature of industrial society crossed by the mass media network (see Mc Luhan) can be found somehow anticipated in the 19th century care taken in bridgebuilding. It can be said that, as the Middle Ages found the joining of its peculiar ideal regions in erecting cathedrals, and the Renaissance and Baroque set that crossroad of cultural co-ordinates in erecting temples and palaces as emerging architectural types strongly characterising the city image, the 19th century gave its best in bridgebuilding, especially railway bridges. This is where the most articulate disputes of the wise crowded; this is where the technicians' most daring inventions took their origin; this is where new industrial energies and economic plans gathered; this is where the power of the most advanced countries shone and developing countries started integration. It was in functional connections, often unrelated to the city image, in a subdued architecture to get a glimpse of swiftly, with no particular symbol involved in it, that the 19th century retrospectively recognised its own symbol. When T. Walter was commissioned the construction of the Capitol' s immense dome in Washington, the need was explicit, nothing else could be done: the structural framework employed by the architect disappears, hidden behind a form fully set down to the smallest detail, tradition assailed and discouraged resulting in an abstraction of itself. Instead the Brooklin Bridge commissioned to Röbling is something else altogether. I am not just referring to constructive efforts (for instance, the pneumatic caissons used to secure the two piers were more than 50 m long and 30 m wide and employed about 600 workers) but also to the impressive image of the work. It is not by chance that, still today, present advertising prefers to use that image to advertise a New York-based brand5

domes concerned typical problems of construction practice, but they actually took place in decentred places, among mathematicians and academicians unacquainted of building sites and knowing nothing at all about architecture. Their goal was knowledge for knowledge's sake, there was no interest in the technical application of the results achieved. Only in the 19th century did a synthesis occur; those results were translated and submitted to engineers' requirements; real constructions became occasion and reason for deep investigations. At that moment, then, technical indications were based on correct scientific knowledge, no longer only on general tradition. Construction techniques were perfected but became subject to being verified or falsified. From that time to date, building has acquired the rank of science but has had to pay for it by changing its epistemological statute, making structural firmitas, rather than the assumption, the goal and object of renewed inventions and discoveries.

and its economic testing, while to another young engineer, Maurice Koechlin, we must credit the perfect calculation of this admirable structure. 4 BUlLDINGCRAFf TAKES THE SCIENCE ROAD The eventful course of bridges matches a change in construction history which characterised the 19th century, especially the period we have been talking about here. While up to that century building techniques came in use and then were perfected before a mathematical theory could provide ground to them or change them according to its own principles and calculations, from now on what happens is almost the contrary. The relationship between scientific elaboration and construction becomes closer and closer: technique seems more and more applied science and foIlows the same evolutionary logic based - as Popper and Bachelard upheld - on a trial and error dialectic, on the fruitful, continuous clash of conjectures an d refutations. The construction errors of the first constructions - tragically documented by a set of disasters - became frequent occasions for theoretical investigations, and raised inflamed debates between scientists and technicians who, searching for causes, widened any possible conjectures, investigated aspects at first considered of minor importance or simply not taken into account, removed deep-rooted beliefs, suggested new procedures or new structural forms. This is how buildingcraft took the science road. Up to then, the codes of workmanlike construction­ whether secretly handed down among the members of guilds and schools or mentioned by writers of architecture treatises or found in the first works on "Science of Engineers" and "Resistance of materials" that in the 18th century summed up the pre-industrial revolution knowledge - were of a different nature altogether. The technical code, like the aesthetic one of the architectural "orders", has little in common with a "falsifiable conjecture": it is never abstractly formulated and is not to be verified or denied against experimental data, for it shapes and builds its own experienced material, bringing it onto manufactured articles predictable as to use and configuration according to a tradition weIl tested through the years. As a matter of fact, what rules it is the intersection of compounded reasons that cannot be all referred to rational grounds, for they also refer to external aspects that fit into a theory with difficulty and cannot be investigated through a strictly scientific logic. If it is true that Galileo's studies on the cantilever beam, the experimental investigations carried out from Hooke's time on, the 18th century discussions on flexible and elastic curves, the static analyses on masonry vaults and

5 TUBOLAR BRIDGES AND THE THEORY OF CONTINUOUS BEAMS So it happened that some 19th century bridges played a leading role, they became really epoch­ making. Especially two of them deserve particular attention: the Conway and Britannia tubolar bridges. I will not describe their construction aspects, for I will just mention the great debate raised inside and outside England. Starting from W. Fairbairn's report of 1849, several scientific memoirs were issued on those admirable examples of new structures. They were dealt with by E. Clark, R. Stephenson, E. Hodgkinson, W. Pole, T. Tate, J.M. Rieppel, D.J. Jourawski, B.P.E. Clapeyron. The dangers deriving from the instability of compressed frame members came to light, checking techniques based on models were dealt with in a deeper way, wind and uneven insolation effects were taken into account. Britannia's statical scheme raised interest and allowed Clapeyron to refer his famous work on continuous beams to an update topic. In presenting his work to the Academie, Clapeyron seems to show off his engineer experience: unlike many of his academic colleagues devoted to mere speculation, he was able to show the theory effectiveness in detail and with some superiority as an expert does: "The huge amount of money invested in railways ­ he opened his speech - have boosted construction theory, causing engineers to have to solve difficult problems before which, only few years ago, they would give up. None of the new solutions ( ... ) stand out for its originality and greatness more than Robert Stephenson's bridge buHt on the straits of Menay. The bridge is a straight-line beam supported by four bearings ( ... ). Here like anywhere else practise has overcome theory: nonetheless the latter 6

the carpet thickness is made infinitesimal or null. No answer was so given to the question about the real nature of Euler' s principium: was it a particular hypothesis related to elasticity, or was it a statics equation still unknown? That question raised a deep debate that ended exactly a hundred years later. The decisive results then included in the general structural theory still applied today generated just from the ups and downs of that debate. Those who backed up the thesis that a new law of statics should be still worked out based their opinion on sound philosophical reasons (how is it possible that Nature loses its deterrninism when one recognises the existence of a rigid body as plausible?). But then they had to make uncertain hypotheses easily confutable by clever counter-exarnples. Those who backed up the other party - the strictest ones from a physical-mathematical viewpoint - managed to get excellent solutions for the elastic case but were forced to put aside the uncomfortable shade of indeterrninism by supporting the thesis - not much plausible according to empirical intuitions - that in Nature no rigid body may exist. The discussion had been joined by the major European scientists, from d' Alembert and Fourier, since the late 18th century. The querelle became quite inflamed in Italy in the Memorie di Mate­ matica e Fisica of the Societa ltaliana (the current Accademia Nazionale delle Scienze detta dei IL) The basic idea our scientists vaguely pursued may be summed up as follows: the cardinal equations of statics are not sufficient for they only govern the equilibrium effective causes (external forces and constraint reactions) and do not explain the final causes, that is, they cannot say anything about that great "principle of economy" which is never contradicted by Nature and always chooses the simplest and straightest way from all those possible, as if Nature took care in not wasting her resources sine necessitate, choosing the more convenient way to meet all different needs making the lesser "strain". By assuming such a principle it comes that a certain expression of constraint reactions must have a minimum value in connection with the solution sought. That is enough to identify the only true distribution of reactions within the range of the statically adrnissible solutions. The recent English analytical philosophy is keen on repeating that metaphysic does good to science as the scouts do good to the arrny the day before the battle. As to say that the roads of science are often traced by uncertain but promising metaphysical images. In my opinion this interpretation is not all right, nor I will dare tire on so subtle and many­ sided epistemological subjects. However, when it comes to redundant constraint reactions, the analytical philosophy schematism may be useful. That unsuccessful search for a principium generale led construction theory to a powerful method

has to intervene to answer for the facts and set rules where our predecessors were only guided by vague intuitions" . Clapeyron's memoir, published by the Comptes rendus in 1857, clearly expounds the solving technique of a continuous beam on more bearings that leads to the well-known equation of three moments. In effect, the same result had been published two years before by Bertot for the M~moires of the Societ~ des Ing~nieurs Civils de France. However, it is likely that Clapeyron had already worked out the equation of three moments and announced it without publishing it. This was typical of hirn: when he found the fundamental theorem on elastic potential energy narned after hirn, he inforrned only his friend Lam~ who, later on, included it in his '52 treatise, frankly stating authorship. On the other hand, it is difficult to establish a precise chronology of the discoveries related with the problem of continuous beams. In those years a small crowd of engineers and scientists gave more or less noteworthy contributions to this subject: from Lamarle (1855) to Köpke (1856), Scheffler (1857, 1858), Belanger (1858, 1862), Heppel (1858), Bresse (1859), Wink1er (1862), Mohr (1860, 1862, 1868), etc. 6 METAPHYSICAL ROOTS OF MODERN STRUCTURAL MECHANICS ? The solution to the continuous beam problem is not only the answer to a technical need - as Clapeyron presented it - but it is also an important step ahead in an age-old theoretical - or rather, metaphysical ­ discussion that sums up the evolution of modern structural mechanics in the 19th century. This old story originated from a 1773 study by Euler in which the renowned, and by then elderly, geometry scholar studied the pressure of a rigid body on its supporting rigid plane. What can we say when the number of supporting points exceeds that strictly necessary to ensure equilibrium? The cardinal equations of statics are not sufficient, they leave room to a paradoxical indeterminacy, as if adding one or more redundant bearings made it impossible to identify the right solution arnong all those statically admissible. Euler removed the problem by proposing a new principium generale (general principle), that is, the reactions exerted by the plane be proportional to segments taken from the supporting points whose second ends belong all to a unique plane. That principle comprised an irreducible ambiguity: on one hand, it could easily be demonstrated by assuming that the (rigid) supporting plane is covered with a thin elastic carpet; on the other, it showed itself as a law valid also in the case of a rigid plane, that is, even when 7

capable of analysing elastic structures; credit for passing from metaphysical half-light to scientific clarity must be given to several authors who independently came to analogous outcomes, sometimes without one knowing about the other and often at the cost of demonstration defects or illegitimate hypotheses. I will mention in order the nearly perfect contribution of French philosopher Augustin Carnot (1827), the one still indefinite of captain Vene (1828), the strict one yet stilllimited of G.M. Pagani della Torre (1838) and, though for a problem unrelated to bearings, the proposal - a little bit high-sounding - of Rev. H. Mosely who introduced a "new Principle in Statics, called the Principle of Least Press ure" (1833) which influenced the British area to a fairly large extent and was finally lucidly interpreted and expounded by James H. Cotterill, who may rightly be said its true discoverer (1865).

network of points and lines was so able to represent a physical model for any solid (according to the molecular theory of elasticity), but, on the other hand, its direct reference to the problem of framework was equally clear. All at once there were achieved universality of the object studied by the elasticity theory and consistency with engineering application. Even the principle, that is, Dorna's new equation, changed: no longer an anonymous quadratic expression of constraint reactions but the elastic strain energy made its protagonist. After retuming the problem and its solution to the high position it deserved, Menabrea was then able to take the risk and work out a new general principio on stress distribution in an elastic system, the "principio di elasticita" (principle of elasticity). According to Menabrea's words it states: "When an elastic system is in equilibrium under the action of external forces, the work developed by the tensions and compressions of the bonds linking the different points of the system is aminimum". A principle is worth as long as it can co-ordinate phenomena and, because of its nature, it needs no demonstration. But the principle at issue called for some sort of demonstration. Instead of considering the internal work minimum condition as the means to connote and perhaps define elastic systems, it seemed more reasonable to turn the principle into a theorem relating it to the well-known mechanics laws and to the ordinary phenomenological description of elasticity. Menabrea was long taken up by that, often unsuccessfully, rejecting criticism from colleagues and inferiors, relying on rhetorical emphasis when exactness was lacking, reaffirming what stated through examples, calling upon the most distinguished scientists as witnesses, who had been supporting hirn against lieutenant Emilio Sabbia's quarrels. It was the undertaking of his life. One of these people to whom Menabrea had referred to when defending his principle, the great J.Bertrand of the Academie Fran~aise, hit the mark in a very respectfulletter (1870) he sent to the by then famous Piedmontese general. But our Menabrea did not show he had understood. He kept to the same attitude even later. When he came to know the decisive works carried out by young engineer Alberto Castigliano, he only mentioned them as further confirm of his principle. Besides, who has ever seen a notable, academician, professor, general, marquis of the val Dora for war merits, senator, several times minister and also prime minister submits to the degree dissertation of a penniless student who makes a living out of giving tuition in mathematics to Turin middle-classes' sons trying to get a qualification to soften his young wife's hard life and find a job with the railway engineers? Who may be amazed if the concise and inattentive quotation Menabrea deigns to make

7 TOWARDS THE GENERAL THEORY OF ELASTIC SYSTEMS In Italy, the search for a teleological principle (though by then clearly limited to elastic systems) had a remarkable extent becoming a real italienische Nationalsfrage . In 1857, professor Alessandro Dorna from Turin, because of the good offices of Luigi Federico Menabrea, a much more influential colleague, was given satisfaction to have a long memoir published among the Proceedings of the Academy of Turin. Once again, his work dealt with the problem of supports, and once again he obtained a quadratic expression of reactions whose minimum led to the solution. The demonstrative argument upheld by Dorna was still obscure and misleading on the whole but the result achieved seemed be good in applications. This lack of consistency was surely realised by colonel Menabrea, but he did not bother very much. There was no doubt that Dorna's solution was true, then it could not be left there among the proceedings of an uninfluential Academy. It deserved to be taken before the most distinguished scientists who at that time were competing with one another on the Comptes Rendus of Paris. The politician' s talent just lies in being able to seize the opportunity on the spur of the moment. And Menabrea had such talent. In reality, he added very little to Dorna's demonstration still full of gaps but extended its interpretation so that it became a general method for thoroughly describing the elastic behaviour in energy terms. To this end, he changed the reference model: no longer a body resting on a plane but the "elastic system" made up of material points interconnected by elastically deformable linear elements. The 8

strain energy and the so called "complementary energy", having the former a physical meaning, being the latter formally defined by Euler­ Legendre's transformation. If Crotti's works had properly been spread and adequately understood the painful dispute on the Italian method versus the "Germ an" method based on the principle of virtual work that divided several Austrian-German scientists for a few years after 1883 would have not occurred. In addition, it must be said that on that occasion Castigliano' s outcomes found an experienced and influential supporter in Müller­ Breslau and so were accepted by the late-century technical world. Their main opponent was Otto Mohr on account of the improper attribution of the expression "strain work" to the complementary energy. From this viewpoint, it was a reasonable opposition even though it did not consider Crotti's explanation. However such a violent dispute hid a little bit of personal grudge, at least in Mohr, who had been annoyed by the enthusiasm Müller-Breslau had shown when defending Castigliano in his Wochenblatt für Architekten und Ingenieure. Mohr was sure he hirnself had first said everything was needed, and perfectly. He was not wrong at all: his Beiträge included in Zeitschrift des Architekten und Ingenieure Vereins of Hannover "made" the modem construction theory - quoting one of those works (1874) in the famous Abhandlungen of 1913 he was rightly entitled to be proud of having introduced, for the first time, the principle of virtual work to solve structural problems, achieving the double goal of generality and pertinence. However, as the historian must be faithful to the course of events, such priority statement has to be corrected. And not on account on the Italian competition, feared and fought by Mohr, but because of the other much more pressing anticipation of Mohr' s outcomes made by great English scientist James Clerk Maxwell in one of his short essays of 1864 published (or rather, "hidden") among the pages of the Philosophical Magazine. As it was a peculiar review not much read by technicians, Maxwell's work had not been known for over a decade, allowing a good number of scientists to re-disco ver some bits of it over again and claim their authorship. Perhaps it was right that things went like that for the sudden arrangement of structural mechanics occurred in the '70s of last century is the convergence of different lines, the sum of particular contributions, a harmonious complex and not a single intuition prevailing on the others.

(1875) even alters Castigliano's name, making it a less common Castiglione? Sometimes history does justice, taking time and rather roughly, that is troe, but it does. Castigliano happened to find two great supporters who took care of his work and preserved his memory, as if they had been assigned the task to make amends for the cruel fate that fell on the young engineer from Asti who died in 1884 when he was only 37. The first one of these supporters was undoubtedly paid back, becoming aleader of the European technical world. His name is still very popular to any student of engineering wrestling with construction theory: it is Heinrich Franz B. Müller-Breslau. The other one, instead, did not get much out of that; most people do not even know his name, and his decisive, lucid works are scattered in little-read, little-circulated reviews: it is Francesco Crotti. It is just to hirn we owe the thorough clearing up of the question. Castigliano, then, had managed to turn the "principio di elasticita" (principle of elasticity) into a rigorous theorem at first referred to trosses only and then extended to elastic beams in general. The basic concepts were already evident in his dissertation for his finals (1873) and in the following short essays published in the proceedings of the Accademia of Turin (1875) that summed up the main points and added further investigations and developments. However Castigliano made the real break-through when he wrote his fundamental treatise in French: Theorie de l' equilibre des systemes elastique et ses applications published in Turin in 1879 by worthy publisher Negro. That treatise marked the transition from theoretica1 investigation to applicative synthesis, from the general aims of a theorem to the actual treatment of the technica1 problems crucial to structural engineering according to an unvarying method. The different cases that, up to then, had separately been investigated, each being a special case, became easy exercises multipliable and variable at leisure. The first theorems on "strain work derivatives" made possible to tackle the who1e solution; the attached theorem on the extremum of the same work fitted any statically indeterminate problem unitarily even when its statement had to be corrected to take into account any possible se1f­ straining. The extent of the synthesis, like a reductio ad unum of the technical possibilities, is the greatest value of the Theorie. Instead, Castigliano ' s mathematica1 language was not so straightforward as James Henry Cotterill's who had inferred the theorems on the strain work derivatives as simple applications of variational calculus (1865). On the other hand, as to the deepening of the conceptual interpretation Castigliano cannot compete with his colleague and friend Francesco Crotti either. It was in fact Crotti who made clear the difference between

8 A PARALLEL STORY: THE MASONRY ARCHBRIDGE One of the remarkable applications developed by 9

elastic model did not fully agree with the real behaviour of masonry structure but was sure that, within assigned limits and for small strains, the approximate results obtained through the (linear) elasticity methods were practically more than acceptable. This was to be a point greatly investigated theoretically and experimentally around the late 19th and early 20th century. I will not mention anything about it as it does not fall within the period at issue in this lecture.

Castigliano's Theorie with particular accuracy deals with bridges, especially arch bridges. As a matter of fact, the subject had been addressed by Castigliano in 1876 in two practise-based memoirs, and in a book in which his name did not appear for it was published by the Railway Works and Maintenance Department of North ltaly in 1878. It is noteworthy the fact that Castigliano focused his attention not only on iron arch bridges (Mohr, to~, dealt with them in the same years) but also on masonry arch bridges, explicitly aiming at extending the general elastic analysis methods to them (see Etude du pont avec mafonnerie en briques construit sur l'Oglio pour La ligne directe du chemin de Jer de Milan a Venise; and especially Etude du pont en pierre de taille construit sur Le Doire aTurin, par l'lngenieur eh. Mosca). In the 19th century, the story of the mechanical theories on masonry arch bridges is parallel to that of the theories on statically indeterminate systems that I have briefly outlined above. It can be said that between 1850 and 1880 the thorny question was clarified, though masonry was included in the treatment of elasticity. Similarly, the discussion between those who insisted on searching a new "staticaL principLe" apt to get rid of stress in the rigid body to which masonry was assimilated, and those who considered that indeterminacy unavoidable unless one could make hypotheses a suitable stress-strain relation for masonry. The first party included several authors of the thirty-year period at issue such as Scheffler (1857) who resumed Moseley's idea, Drouets (1865) and his "principle of maximum stability", Clericetti (1873) and his "principle of equality of maximum pressures", Salemi-Pace (1879) who referred back to the experimental research on symmetrical arches carried out by Boistard in the 18th century. The second party included more theoretical scholars, starting from Winkler who was able to re-formulate and demonstrate the principle of least pressure intuited by Moseley when dealing with the elasticity theory (1867; 1879), and from Perrodil who since 1872 had suggested that the formulas on the strength of materials be extended to masonry vaults describing the new view in aseries of subsequent papers (1876, 1879, 1880). In 1875, Francesco Crotti, disagreeing with Clericetti' s ideas, asserted that the search for the pressure curve "must be conducted according to the methods inferred from the theory of elasticity, based on yielding and displacement in wedges". From the same year, the Memoirs of the Academy of Turin started publishing a thorough work by Giovanni Curioni who studied vaults starting from the formulas worked out for the elastic strain in curvilinear beam. Within such context we find Castigliano's works mentioned above and dealing with masonry arch bridges. He knew weIl that the

9 BUILDINGCRAFT ON THE LANGUAGE ROAD In those years the positivist spirit, the project for a new view of the world under the light cast by an objective science, the progress of peoples who feel they have no frontiers and develops in the grand works of industry and intercontinental communications seem to keep to their promises. "Human thinking, get rid of your constrictions" wrote Italian poet Carducci, fervent and naive interpreter of those triumphs; and the poet's mind went back to the protagonist of the imminent liberation, to the new god of iron and fire; in its sparks and grape-shot he saw "the power of the reason": "A monster, handsome and frightful, frees itself from irons, runs the oceans, runs the earth, as twinkling and smoky as a volcano, climbs the mountains, eats up the plain ( ... ) its breathe like a whirl, he goes, Satan the great". Less ambitious but more productive, Mr. Limousin confined hirnself to praising the comfortable travelling conditions that the Pacific lines' customers would enjoy: "You are free to go from a coach to the other and can also go out onto the platform to enjoy the lovely sight. A man and a boy keep on walking the aisle between the seats and seIl books, newspapers, fruit and food. The guard will never disturb you to check tickets provided you place your ticket under the ribbon of your hat". Other means, less material and more incisive, though, were assigned the task to free thought and practice from persistent biases, binding traditions, systematic sub divisions of reality that up to that time had been accepted as an unrenounceable heritage. It is what happened in the field of architectural research, and on the symbolically meaningful horizon of aesthetics. Freeing of culture from the strict classicist precepts meant a renewed encounter with the Gothic-like forms of legendary Middle Ages expressing their deep rooting in history without embracing the rule of perfection - in relationships, orders, elements as if they had been Nature' s law - to promote imaginative re­ constructions instead. The same years in which baron Haussmann spent two million Francs to cancel old medieval Paris's traces and turn her into 10

the ville lurniere spread along her wide boulevards, Viollet le Duc spent as much money as hirn to re­ build the magical Pierrefonds castle from scratch on the foundations of some ruins: from a fortress well­ equipped to held out mob of soldiers and knights disappeared from ages to a charming, romantic castle such as one of those fairy-tales and Dore's engravings are full of. From New-Gothic forms it came easy to re-discover any other historical form which the late 19th century middle-class took up softly, as if leafing through a pattern-book of styles reproducible at will according to tastes. What at one time had been matter and spirit of an age gradually became a linguistic envelope, a mere covering left to the skills of architects well-experienced in fac;:ades. History was got rid of not by denying it but by putting its veneer on, 1ike a fancy-dress worn on the stage. There is nothing to wonder about if architectural eclecticism eventually merged in more and more arbitrary inventions, mixing with art nouveau experiments and making way to the new movement that would break the ties with the past. Reference to the past was its more evident and symbolic aspect, changeable and surmountable more easily. A good example was the memorable banquet held on July 4th, 1884 joined by Monsieur Bartholdi and others. When M. de Lesseps presented the huge statue of liberty standing out among Parisian blocks to Uvy Morton, the USA minister, they were all pleased to mention similar outstanding works of the past: the Thebes Osymandias, Phidias' Athena, the Taranto Apollo, the legendary Colossus of Rhodes, the Palatine Apollo in Rome, Nero's Mercury that cost more than 40 million sesterzii, Arona St. Charles. Past splendour had been defeated, thanks to the powerful iron framework Eiffel managed to hide behind the statue's drapery. Science and technology progresses were unmatchable; the competition with history, turned into aseries of records, delivered the palm of victory into Bartholdi's hands. 10

storm our century. The great protagonists of that time did not know that their names would become legendary. Their lives and works were not in the spotlight of history, indistinct among the many who nobody then would remember. Here are a few dates and some events, in jumbled confusion and with no claim to their being a thorough historical outline. In the course of the '50s, while theory of elasticity and structural mechanics were making or were about to make the great achievements briefly mentioned above, other syntheses matured. Rudolph Clausius, through a step-by-step process, discovered the second principle of thermodynamics and, together with William Thompson, worked out the law which all physical processes comply with. August Krönig and Clausius laid the foundations of the kinetic theory for gasses that cleverly combined the molecular and macroscopic descriptions following more successfully the way opened by Navier, Cauchy and French elasticity scholars for solid mechanics. In the Journal de Crelle, Karl Weierstrass set the new fundamentals of modem calculus. At Erlangen, G.Staudt created a new language for "situation geometry": an unusual way of linking sentences made up of connections and syntactic symmetries replaced formulas and figures. The most ancient and influential mathematical science, that is, geometry that since time immemorial had been considered the model of universal and necessary truth was disrupted by the new non-Euclidean views opened up by Bernard Riemann. Even statics, having much (perhaps everything?) in common with geometry, would be remarkably affected. Augustus De Morgan and George Boole gave a mathematical language to logic, changing its features and unifying thought laws within the same algebraic formalism. Some many things over a decade! At the beginning of the '60s creativity seemed to burst as a deadline immediately due. The inventions of technique overrun any field. Bessemer became rich with his converter; Perkin investigated the benefits of aniline; De Lesseps started the works for the Suez Canal; de Cristoforis build astrange "igneous­ pneumatic machine" which nobody knew how it would end up; some attention was given to Antonio Pacinotti for another curio he had discovered on a rotating ring within a magnetic field; Lenoir had the first internal combustion engine work; Leschot, a Swiss watchmaker, got busy with a diamond rock drill to be employed for the great tunnels in the Alps that were being built; Solvay expected to make a lot of money with soda. Scientists were taken up by other thoughts: back from his fundamental works on elasticity, Kirchhoff devoted hirnself to spectrography. Cannizzaro and his students triumphed at the chemical Conference in Karlsruhe telling atoms from molecules at last; Maxwell worked hard at the London King College where his

TOWARDS GREAT SYNTHESES

Those years were not marked only by that sort of victories, surely striking yet superficial. The true great victories, those that start a new course and make the future bright, are never celebrated in banquets; they go unnoticed by the crowds and do not raise any interest in the powerful. They enter history quietly, like walking on tiptoe, along the most secluded paths. Between 1850 and 1880, during our thirty-year period of structural accounts, the structure of science had changed entirely. Technique made unhoped-for achievements taking the same road we are still moving along; art and culture foreshadowed a deep transformation, advancing the consuming deep crisis that would 11

Cremona, recogmsmg his merits and declaring hirnself a careful reader of his works as well as a beneficiary of Cremona's investigations in new projective geometry. Cremona, too, did not disparage applications: the examples included in his famous 1872 treatise on reciprocal figures concern meaningful applications to the framed arch and to bridge frameworks. However the core of his work was somewhere else, that is, in the first pages, rather obsolete by now, in which the author seems to make fun of technical concreteness to transform trusses into mere geometrical figures. If even for Maxwell, to whom we owe the first start of the theory, the definition of frame reads "system of lines connecting a number of points", for Cremona the definition sounds quite peculiar: after wandering around lines, points and faces in an abstract space, the truss, seemingly forgotten, suddenly reappears in the most unexpected form as the diagram reciprocal to another diagram, namely the well-known diagram named after Cremona.

extraordinary power of synthesis kept hirn gripped to working out the theory of fields; but he spared some time to tackle structural problems and showed two lines of research that were to be the main points of the scientific debate during the following years. 11 THEORETICAL POWER OF A LAN­ GUAGE REVOLUTION: GRAPHICAL STATICS

I have already said something about one of the following works published in 1864 whose title is "On the calculation of the equilibrium and stiffness of frames". It anticipated everything Italians and Germans would manage to say about calculation of elastic frames. The other work, that deals with statics and the determination of tension in frames, is entitled "On reciprocal figures and diagrams of forces" and anticipated everything Germans and Italians would manage to say about graphical statics. The most important author is Karl Culmann, born in Palatinate, highly skilled in engineering and fond of geometry (especially the new geometry of situation), a professor in Zurich. His work was epoch-making: it worked out a new language, it rearranged the concepts and terms of the wh oie structural subject, it disrupted every previous synthesis to find a new one so simple and evocative to be later adopted as an unchangeable outcome by his successors - whether knowing it or not - nearly up to date. His Graphische Statik of 1864-65 became the unmatchable model of an endless series of reductions, adaptations, hand-books, graphic manuals for intermediate technicians, exercise­ books ad so on. Culmann, on his part, was not happy at all with the incredible success and the reductive use his scientific message was having. The practical applications had to be certainly an important outcome of his graphical statics (see e.g. his elegant and nearly surprising solution to the problem of elastic arches, that represents perhaps the best application of his new approach to the theory of elasticity - Chapter III and IV of the 4th Section of the treatise), but, please, in moderation! The real aim was another: it was the construction of a perfect, all-inclusi ve language, usable spontaneously. It was the fascination of a synthesis and the formal harmony that in the mathematician's eyes appeared a convincing, self-validating criterion, not just the complex tangle of funicular polygons and polygons of forces that suitably linked together filled the working day at the drawing table of the young trainees at the engineers' ateliers. The teachers at the polytechnic schools had different ideas, though, all of them except one, perhaps: an Italian, Luigi Cremona. Culmann, who did not restraint hirnself from criticising his colleagues, greatly respected

12 THE LANGUAGE ROAD: A DESTINY OF STRUCTURAL MECHANICS? This is one of the cases, often happening in science history, in which the formallanguage achieves such a high level of accuracy to be mixed up with the described reality, becoming one with it and eventually swallowing it up. The matter would deserve to be looked into epistemologically, similarly to wh at other fields have gone through. Unlike strictly empirical sciences, mechanics has a compounded statute: undoubtedly it looks at facts but the way it interprets them makes it close to deductive system, it makes it look like a mathematics matter, according to Lagrange ' s program. When it comes to mathematics, it is not always easy to tellianguage from concept and even less easy is to understand which of the two terms comes first. I have been dealing with history of structural mechanics for several years. As my studies developed, I feIt I had to find out whether the following epistemological hypothesis was verified by the events: that the development of structural mechanics was realised in its gradually improved syntheses, its changing interpretations, its harmonious connections more by language changing rather than by the empirical base extending. The same fact, as found in different languages, changes its look, in short it changes its conceptual identity, differently relating to the other facts and the period syntactic rules that on the whole connote the theory. This is why the history of our mechanics is above all the history of language revolutions, each tending to include the whole discipline field, re-defining its components, the 12

mathematical references, the mutual relationships between elements. From Culmann's time to today we have seen several metamorphoses. There has been the season of vector algorithms ended with the absolute or autonomous calculus worked out by Burali-Forti and Marcolongo. There has been the Ionger and more successful season in wh ich the entire corpus of continuum mechanics has been translated in terms of the tensor calculus introduced by Ricci and Levi-Civita. There has been the season of reflection and clarification according to recent functional analysis outcomes. There has been, and it is still blooming, the metamorphosis brought about by computers. Wh at amazes us is how radical such language changes have been. Leafing through any treatise on finite elements or on the matrix analysis of structures one has the feeling that many modern authors believe they have invented everything, as if structural mechanies had been born in their brains and some of their colleagues', having taken from the past only a few embryonic fragments, associated to farnous names, and waiting to be at last arranged within an organic, comprehensive context. I may perhaps end this lecture by regretting the present-day ignorance of history and the misuse and overuse of technicality that is driven to face only the short-lived, everyday world and follow its fashions, biases, jargon by a sort of misleading productive nagging thought. Instead, the truth is that even this new fashion aimed at re-founding the whole discipline according to a new language apt to include it is an old story gloriously rooted in the past. Among all its records there undoubtedly stands out the excellent re-foundation of statics in the language of the "geometry of situation" to which Culmann and Cremona pursued during the thirty years from 1850 to 1880 - that are dealt by this paper.

13

Arch Bridges, Sinopoli (ed.)© 1998 Taylor & Francis, ISBN 90 5809 012 4

The relationship between the Gothic model and the conception of bridges AnneCoste

School 0/ Architecture, Saint-Etienne, France

ABSTRACT: The main objective ofthis paper is to show the particularity and the role ofthe Gothic model in the history of the building of the bridges. So, we will explain how the principles of the Gothic reference have influenced the conception of the arch bridges constructed in stone, metal and concrete for three centuries. During the 18 th century, the new ambition of the building of bridges required efficient methods of calculation that the science of the Strength of Materials was to bring. In France, the work of Jean-Rodolphe Perronet is a tuming point. Through this question replaced in the general history ofthe architecture, we can observe that the wish to calculate the great structures coincides with the survey of the Gothic structural model at this time. The underlying idea ofthe words we formulate here about the Gothic model is that the engineers and the architects who study the ancient monuments or the ancient arch bridges have to establish a coherence between the model they use and the object they study. We use the history as an interesting tool in order to show the particularity of every building model in architecture and we think that the modelisation is a good place for the integration of the archeological and historical viewpoints. It is necessary to understand how these different models are used in the process of creation in order to elaborate an approach of modeling for ancient monuments which takes their building principles and their historical specificities into account. I THE ORIGIN OF THE RELATIONS HIP BETWEEN THE STRENGTH OF MATERIALS AND THE GOTHIC BUILDING MODEL

constructive qualities by the 18th and the 19th centuries' builders on the projects of arch bridges at this time until nowadays. Before this, we want to point out two hypotheses. Our first hypothesis throws light on the existence of reciprocal links between the different interpretations of the Gothic architecture and the state of the scientific knowledge at the time of their formulation. If we precisely look at the way Gothic architecture was understood during the 18 th century, we can notice that the architects used the tools developed in the field of mechanics. We can also observe that the discovery of the building performance of the Gothic architecture influenced the development of the method of calculation for the structures : on the occasion of the Sainte-Genevieve church building by Soufflot, notably. During the 19th century, the approach of the architects differed from the engineers', but the Gothic model exerted a great influence on the metallic building and on the rationalist notion of triangulated structure. The functionalist interpretation of Gothic architecture owes its formulation to the development of the

In France, since the time of Jean-Rodolphe Perronet, the preoccupations of the engineers have differed from those of the architects : the split with architects precisely occured when the Gothic buildings became an interesting reference. We want to show what characterizes the transition period of the 18 th century, regarding the calculation. At this time, after Deswarte and Lemoine (1997), "a concem for an order, a logic and an output which arouses through a modelisation of the shapes, a systematization of the methods of composition and making, and an optimization of the quantities of matter and costs thanks to the tool of calculation" has emerged. 1.1 Two preliminary ideas

The objective of this paper is to show the influence of the discovery of the Gothic architecture's

15

an inventory of the different models used in order to represent the behaviour of the arches. We will exarnine how the models were transfered from the field of monuments to the field of bridges, considering some relevant objects produced during the period studied : from Perronet's bridges to Maillard's. There are different ways to simulate the mechanical behaviour ofthe structures ofthe ancient monuments : we can use physical models, graphic models or mathematical models. The Strength of Materials provides us with various models but, before this, simplistic ways offered a representation of mechanical phenomena. The first one is what we call the "human model" : it was used by Villard-de­ Honnecourt in his Album. We can see two figures simulating the behaviour of an arch. This kind of representation is used later with real persons in order to simulate the principles of the high bridge on the Firth ofForth. At the beginning of the 20 th century, the weil known work of the Catalan architect Antonio Gaudi

Strength of Materials. At the beginning of the 20th century, the question of medieval rationalism has been revisited with the method of elasticity. Nowadays, the objective is not to develop new tools: various methods exist (F.EM., D.E.M., ... ) and the challenge for the architects and engineers is to adapt them to the specific problems ofthe ancient monuments in order to elaborate an efficient process ofmodelling (Coste 1997a). The second hypothesis of this paper underlines the possible use of a theoretical model -elaborated following a complex reality- in order to conceive a new production. So we can observe how the theoretical model of Gothic architecture influenced the creation during the 19th century -notably, the architecture of metal- and the 20 th century. We are going to see that, from the 18 th century, the Gothic building model has influenced the French authors of architectural monuments and bridges. On the other hand, the progresses of the mechanics and its methods have modified the theoretical interpretation of the Gothic model during the same period. So the question of the theory of Gothic architecture concems the history of arch bridges on account of both the methods of analyse which are used and the reference it constitutes for the creation. 1.2 The nation 0/ model First, we want to point out the ambiguity ofthis term used in the field of architecture : between a theoretical notion and a generic term which gathers the mathematical models together (Coste 1997b). The notion of model conceming architecture is old, marked by the idea of mimesis, i.e. the imitation of nature or of an object which is identified as exemplary and which the architect uses in his proj ect. This notion also belongs to the scientific field and it is conveyed by the vocabulary of the computers : in this case it is the notion of a schematic idea elaborated in order to approach the complex reality of a phenomenon or of a process. It is sometimes an object of reference endowed with ideal qualities and which is !iable to be copied, and sometimes it is a theoretical object provided with the whole properties of the empirical reality it represents. Therefore, the notion of model is paradoxical in the field of architecture: situated between "paradigm" and "representation", it is both an exercice of abstraction of a physical rea!ity and the materialization of an idea. Nevertheless architects have always used the models in order to devise and also to understand a situation. We propose to make

Fig 1. A drawing ofVillard-de-Honnecourt

Fig 2. A model of the bridge on the Firth of Forth (1890), given by its author

16

to the geometrical and mathematical models used since the 18th century. We are not going to develop the nwnerous contributions to the elaboration of the sciences of the balance and of the dimensioning but we can refer to various publications (Radelet-de­ Grave and benvenuto 1995). Nevertheless, let us mention that Belidor, in the Science 0/ the Engineers (1729), noticed the absence of available tools and announced the new will to scientifically work out the shape and the thickness of the vault and their piedroits and the arches of the bridges and their piers. That inaugurated a century, the Age of Enlightenment, animated by the most virulent and fruitful debates on that question. We will look at the models ofunderstanding used during this time and the role of the Gothic reference in this activity of research. In order to understand it, let us visit the work of two important actors of the discussion about the building of the French Pantheon: Jacques-Germain Souftlot and Emiland­ Marie Gauthey. For a long time before Laugier who recommended to umtate the Gothic architects regarding the building rather than the decoration, Soufflot already pointed out the constructive value of the cathedrals and he asked : "Couldn't we, without committing a crime, measure these so daring monwnents and consider the whole or some parts of them ?" (Soufflot 1741). In fact, Soufflot achieved this wish later, on the occasion of the Sainte­ Genevieve church project: he has been quite inspired by that experience. We know that the building of the Sainte­ Genevieve church's dome by Soufflot is an important chapter in the history of construction. From 1769, when the pillars, only, were implemented, until the beginning of the 19th century after the completion of the superstructure, the Soufflot's project has been continually criticized. Pierre Patte first opened a discussion about the section of the pillars (Patte 1770). We will put these events in relation with the focus laid on the Gothic architecture and then throw light on its role during this epic of which constructive stakes are considerable. In fact, it was not only an architectural or a building quarrel, the major problem concemed the tools of evaluation of the project. Gauthey wrote (in 1771): "I firstly observe that the theory of the Academician De la Rire which we have followed until now to calculate the thickness of the piedroits of the vaults is wrong. He assumed that the breaking occurred at 45 degrees, which seldom takes place, within a large range of several types of structures (...). The breaking actually occurred in the most

used the analogy between the catenary and the thin vault in order to conceive the shape of the arches and the vaults of its churches. This theory has been expressed by Hooke at the 17th century and developed after that by nwnerous researchers (pesciullesi-Rapallini 1995). The thread constitutes both a model of intelligibility and a model of creation. We are going to briefly study the great stages of the modelisation of the arches' mechanical behaviour with graphical and mathematical models through the question of the interpretation of Gothic architecture.

1.3 The interpretation 0/ the Gothic architecture from the IB'h century to nowadays Abrief survey over the various interpretations of the Gothic architecture shows some of the notions of models used by architects from the methodological angle. We can see how they have cultivated an history always revived according to the development and the elaboration of these very models. We can easily recount the history of the interpretations of the Gothic architecture according

Fig 3. A model for the conception ofthe shape ofthe arches of a church, by A. Gaudi

17

unfavourable cases at the height of 45 degrees for the barrel vaults and the semi-circular vaults ; but it occurred in a very different way for spherical vaults : it is much lower" . He gave his version of the calculations demonstrating that Souftlot's predictions were right. In the Traite de la construction des ponts he wrote later on and that has been published after his death by Navier (Navier 1809-1816), Gauthey developed his own theory i.e. a breaking in four blocks with rotation of the blocks some in relation to the others. Gauthey belonged to the group of the most convinced innovators (Coste et al 1993). His 1771 work begins with this remark: "Among the Arts which seem the most liable to be guided by sciences, Architecture is one of those on which the mathematical principles and the rules of engineering can be applied with the most numerous advantages" (Gauthey 1771). But when the quarreion Sainte­ Genevieve broke, the infInitesimal calculation was not maste red by the main actors of what was then at stake. The disruption it engendered was soon to emerge as the step was in fact crossed with the creation of the Ecole Polytechnique (1794) after the French revolution. The new generations of students of the school of civil engineering, from then on recruited at Polytechnique, were provided with the necessary mathematical knowledge to face the new applications of analyses and of engineering (Picon 1992). Although Gauthey did not have this mathematical stock of knowledge at his disposal, he nonetheless worked hard to allow architecture to take advantage of the progress regarding mechanics and calculation. He undoubtedly favoured their efficient application as early as the following generation (Benvenuto-Corradi 1993). As far back as 1771, Gauthey showed the possible application of what he called the mathematical sciences to the art of building. He thus concluded his report: "If we endeavoured to reason this way on the buildings and to appreciate the projects before realizing them, it would be the best means to reach the perfection of this art". To reach the following stage, the science of the dimensioning with the calculation was to substitute itself for the harmonic laws of the classical model codifIed according to the rules ofthe good taste. This was the aim of the various experiments undertook on the "weakness ofthe materials". The theoretical tools were not yet mastered but the idea of a right dimensioning of the structures was on the other hand not new. According to Carlo Lodoli (1690-1761), architecture had to depend entirely on the nature of the materials and of the laws of static. The influence of the Scottish

engineers James Gregory and James Stirling -who were then developing their works at Padova- was obvious. The publications of their disciples Francesco Aigarotti and Andrea Memmo were parts ofthis very ambition, no matter their scientifIc. In France Pierre Patte also considered that : "The great art in architecture consists in giving as much thickness needed for the solidity". He deplored the lack of knowledge of his contemporary designers in this matter and, on that occasion, acknowledged the lessons ofthe Gothic architecture : "We always carry out airnlessly and we multiply the useless objects, putting more than less : the Goths were known to know more than us in this matter". So, if the Gothic architecture became a model of economy for numerous builders, the question remained : how then determining what is necessary from what is sufficient ? In the age of Gauthey, the experimental processes were in full expansion. A real enthusiasm for the experiments of the behaviour of materials aroused this movement. An extract of Souftlot's discourse -told at the Royal Academy of architecture on the Monday 20 th November 1775, for the opening of its new rooms- illustrates this : "We will see machines ready to demonstrate the strength of metals, the resistance of the woods and of different materials under a load. The experiments will reassure us in practice against the ideas as adapted as they are badly founded which ask for dimensions much more above than those necessary concerning the metals and materials and which lead, because of those who engage in improper use and in shallow fears, to harmful excess loads and to spendings which could be applied more usefully" (Souffiot 1775). As for Jean-Rodolphe Perronet, he worked with the mathematician Prony in order to calculate and to achieve his audacious projects of arch bridges inspired by the Gothic model. During the 18th century, the French engineers, have turned to the Gothic architecture as a reference for the new solutions of frame they invented and they chose the useful tools to model and to calculate the stability and the solidity of their works. Little by little, the tools of the building science have been used also in order to analyse the mechanical behaviour of the frame of the great cathedrals and to found an architectural theory of the Gothic model. So, it is difficult to distinguish which one has more influenced the other in that processus : did the Gothic model influenced the conception of the high structures or did the building sciences used for their conception influenced the architectural theory ? The 19th century saw the development of the elasticity, notably with the work of Navier.

18

Nevertheless, the graphic tools were favoured by the architects : the method of Mery (1840) was very used at this time. If the engineers then controleci the methods of caiculation, the architects keep a preference for the graphic methods until nowadays. Viollet-Ie-Duc logically used this kind of method in order to demonstrate the "rationalism" of the Gothic building ; although, badly assimilated notions of elasticity influenced its interpretation too. At the begining of the 20th century, an architect (Pol Abraham) and an engineer (Victor Sabouret) called into question the ancient theories of Viollet­ le-Duc and Choisy but the historians of architecture didn't modify their viewpoint. Later, Robert Mark has studied the same question with the methods ofthe photoelasticy. Therefore, nowadays, the Gothic theory is always influenced by Viollet-Ie-Duc studies. Nevertheless, we can examine this question with the present tools of modeling and caiculation and bring new answers.

A

Fig 4. An example of a model used by Duc (1 854)

1

Fig 4. An example of a model used by (1840)

favoured

~ .._,,-_.. _

_.r~

"""'~-

......

-

.....

Fig 8. A D.E.M. model (MJean & J.-J. Moreau)

E.Violle~-le­

2 THE GOTHIC REFERENCE FOR BUILDING OF THE ARCH BRIDGES

THE

The Gothic model is based on an ideal of lightness and elevation achieved through the constructive performance which is staged as a spectacle. The two great characteristics of the Gothic architecture are the notion of balance and the concept of frame, for which the rules of the economy are very important: economy of materials, economy of production, economy of building. The Gothic cathedrals belong to the family of the high structures for which the question of the placing is crucial: the notions of repetetive modules and cambers of bearing are developed at this occasion. The Gothic architecture is thought in order to live and to evolve, not as a

Fig 5. A photoelastic model used by R.Mark (1982)

19

building of this kind of bridge requires simultaneous removal of the whole centering. Beyond the vocabulary (vault, arch, abutrnent, ... ), the constructive concept is comparable to the cathedral. We think that Jean-Rodolphe Perronet has made the transition between the architecture of the Age of Enlightenment and the industrial era. These crucial changes are very interesting because they have aroused a polemic which is comparable to the quarrel of Sainte-Genevieve church. For a long time, the bridges have been thought as the addition of autostable arches which took the stress thanks to their massivity. With Perronet, the bridge is become a real frame : the balance of each part is substituted for a general balance. Perronet has pursued this logic very far. His first projects have been classical but he was to surpass Soufflot in daring. Perronet clearly abandonned the classical model and he has changed the way to conceive an arch bridge (Perronet 1771). The conception of an arch bridge arouses the same two great technical questions than the cathedrals: the bearing distance -which is directly linked to the problem ofthe reversal ofthe supports­ and the strength to water stress (strength to external stresses in the case of a cathedral - wind for example-). Since the classical concept has been abandoned, the bearing distance between the piers have increased and the rise of the arches has decreased. For the conception of a bridge, as for a Gothic cathedral, the engineer has to resolve the problem of balance and the placing. About the Louis XVI bridge (1787-1791) Perronet has refered to the Gothic model (Perronet 1792). He has released the lessons of Gothic architecture in his projects of arch bridges: legibility, constructive daring, logic of dynamical balance, relationship between the parts and the whole, etc. Perronet claimed this reference. The economy of matter, the piers' profile, the arches' tension, the covored distances : we find in Perronet's bridges the structural and constructive qualities he discribed about the Gothic cathedrals. Above all, Perronet has broken off the "law of continuity" governing the stereotomy science, as Antoine Picon analysed it (1987). The break between the various parts of the structure, brought in by Perronet, has carried out a crucial change of reference model. He has abandoned the three-centred curve shape which ensured a transition between the pier and the arches and the continuity of the line for a broken system. On the other hand the continuity of the conception and production process was made up : the questions of building and placing have been integrated in the project. "An other feature ofthe building model thus emerges. The architectural structure as conceived by

fixed image like a classical temple. The constructive problems which are raised by the building of the arch bridges are comparable: the span, the arch pressure, the balance and the placing, etc. We are going to see how these concepts directly or undirectly have influenced die builders of arch bridges for three centuries.

2.1 The arch bridges constructed in stone Two great French engineers contributed to the elaboration of the theory and to the practical achievement of numerous bridges: Emiland-Marie­ Gauthey and Jean-Rodolphe Perronet. Wehave seen the role of Gauthey during the French Pantheon polemic and we know through the Memoire sur les regles de l'architecture (Gauthey undated) that he had made a clever analysis of the Gothic reference, notably about the notion of effect that the medieval builder had developed (Coste & Boulon 1997). In his bridges however, we don't find the daring which characterizes the system of cupola imagined by Gauthey for the Givry church. The change occurred with Perronet, in the last part of his work, with the transfer of the Gothic concepts in the fielf of bridges. Therefore, in France, we can say that the "revolution" in the field of arch bridges took place with J.-R. Perronet. He has explicitly refered to the building model of the Gothic cathedrals too : we know that thanks to a letter he had sent to Soufflot on the occasion of the French Pantheon polemic (Picon 1987). In fact, even if the majority of his projects were classical, the last bridges he has devised, like the bridge Louis XVI started in 1787 in particular, responded to a completely different logic : the piers were as thin as possible and the bridge floor was supported by tight arches, balanced with massive abutments. In the way of a cathedral's span, such bridge must be balanced globally. The

Fig 9-10. E.-M.Gauthey : the similarity between the cupola of Givry church and the bridge Echavannes, Chalon-sur-Saone.

20

has shawn that "a bridge can take very big stresses using not so much cast iron than the one of South Wark... Hollow cast iron arches ensuring the lightness, the solidity and the economy of the structure as his 1839 report shaw it" (Coronio 1997). The metallic architecture fmally embodies the rationalist ideal which was attributed to the Gothic model by the theories of the 19th century. The metallic structures literally make material the mechanical behaviours pointed out with the graphic models of combined vectors into a balanced system. The sections used in the metallic frames allow a direct visual relationship. They illustrate the ideal which was attributed to the Gothic builders : to give at each component only the necessary thickness. The steel structures are the privileged field for the application of the Strength of Materials, and thanks to its homogeneity, the steel produces "Gothic" shapes, in the meaning of the 19 th century. The Swiss school, until Maillard and more recently Santiago Calatrava, was to train the heirs of that leanings in the field of the reinforced concrete. Kar! Culmarm (1821 -1881), professor at the Polytechnicum of Zurich, was the inventor of the graphie static (followed by Cremona, Mohr, etc.). For htis tendency, the shape of the bridge must cOÜlcide with the optimal ca1culated stress, the structure is the direct transposition of the graphic method (Pieon 1997).

Fig I!. J.-R.Perronet, the bridge "Louis XVI", Paris Patte is based on the hypothesis of a continuity between causes and consequences v/hich contrasts with the division of the mode of production. On the contrary, the building model relies on a continuous process from the conception to the concrete placing" (Picon 1987).

2.2 The arch bridges constructed in metal The structure may resist to dynamic stresses by its balance and lightness rather than its mass. This idea, so cleverly exploited in the cathedrals of the 13 th century (thanks to the use of the iron pieces), is really used in the field of the arch bridges only since the 19th century, notably with the metallic building. Viollet-Ie-Duc widely contributed to the development of this concept. He has built an ideal model in order to understand the Gothic architecture which was unrecognized at this time. lt was a tool, it was a theoretical model, not the reality. During the 19th century, the conjonction of different factors (new materials, development of the Srength of Materials, ... ) gave the possibility to imagine new structures. At this moment of the building history, the references had an very important role : the theoretical building models were necessary to exploit these new ways. So the observation of the Gothic model and the theory which was producted with it (right or not) had a fundamental task of operator in the process of project. We find again the philosophy of the Gothic model during the 19th century with Antoine Remy Polonceau. He wrote that "the elasticity as uniform as possible and the lightness of the components" were better than then "heavy and rigid solutions". With the structure ofthe Carrousel (1831-1834), he

Fig 12. S.Calatrava : a bridge on the Nervion, Bilbao (Spain)

2.3 The arch bridges constructed in reinforced concrete With the arch bridges constructed in reinforced concrete we again fmd two aspects of the Gothic building model: the logie of relationship between the shape of the structure and the laws of the Strength of Materials and, on the other hand, the intelligence ofthe plaeing.

21

dynamical vision of the structure in Calatrava's work. Thinking of Maillard's arch bridges, we have studied the cupola ofthe church of Givry, in order to understand the building thought of Gauthey : our hypothesis was that he wanted to lighten the structure removing some needless matter in delicate area (Coste-Boulon 1997). From the time of the Gothic builders to nowadays, from Gauthey to Maillard, we can follow the play of the influences and the transposition ofthe models. The evolution of the sciences and the techniques give us new models

About this last point. we can notice that the construction in reintorced concrete. which was much developed in the field of arch bridges after the bombing of the First World War, generates very different problems from the steel building construction. This solution is cheaper because of the manpower : however it requires the placing of concrete forms on arches. These arches for the centring have to be as repetitive as possible in order to reduce the cost. We can see that the economical criterion has direct repercussions on the shape of bridge, exactly as in the Gothic model. Maillard's work takes place in the movement of [he School of Zurich. He underlined the working of the stresses. the recess of the parts of the structures which are needless, the concept of the frame directly produced by the study of the pulls that it takes. The Gothic architecture has been understood like that during the 19th century. Nevertheless the Gothic structure was coupled with its own representation : in this way, a system of extreme lightness was superposed on the structure itself. We can find this

1,""''''1IU(ll I':T 'Io'O""" .... ~1QI. "U 1'O! at the joint of rupture (which in the technicalliterature is generally equal to q> =60° starting from the vertical crown joint), one obtains e. = 1.4e. Tavemier (1907) suggested taking the thickness of the arch at the springer equal to e. = 1.4e. If the springer is inclined at 60° with respect to horizontal, Tavemier's rule corresponds to the following ratio

Circular (or segmental) arches: rise:span

s

X )i

Ys

road

k2

k.

railway

k2

k.

0.15 0.15 0.20 0.17 0.15 0.14 0.20 0.16 0.15 0.13 0.20 0.15

YtO 0.15 0.12 0.20 0.14 Yt2 0.15 0.12 0.20 0.13 At the same time, study began on skew arches (biaises) and as a consequence rules were formulated to determine crown joint and haunch thicknesses. Skew arches were usually given the same thickness as support arches with the same profile as the oblique head section. However, given that skew arches in practice are never built according to the rules on which the various brickworks were theoretically formed, nor, in his opinion, did they satisfy all the conditions required for good arch structures, Resal 'recommended' using an even greater thickness. If we indicate a as the acute angle of the skew and e' as the keystone

e. = ~ which differs from Dejardin's in -Vcosq> quantity ...jcosq> instead of cosq> at the denominator of the fraction. The following limitation is often found in technical manuals for circular arches: the estrados must be a circular arch with radius R included in the following two quantities: 1.1 25(p + e) ~ R ~ 1. 25(p + e) . This gives intermediate results between the two formulas mentioned above (Dejardin e Tavemier). In this case, too, the Croizette-Desnoyers rule was often used and was applicable to semi-circular arches and semi-elliptical arches. According to Croizette-Desnoyers, the joint of rupture at the haunches is identified in correspondence to the span passing through the semi-rise (for full semi-circular arches), and in correspondence to the springers for circular arches with a width equal to or less than that of a semi-rise.

thickness, one can say: e' = ~ that for -ysena

a =45°(skew critical angle) provides e' =1.4e.

3.2

Arch thickness at the springers

The first author to suggest varying the thickness of the keystone arches towards the springer was Dejardin (1845), Figure 3.

ele

The values given below refer to the ratio for circular, depressed semi-elliptical arches with ratio rise:span s =L, in which 2a identifies the width of 2a the arch: ratio s semi-circular and semi-elliptical arches 2.00

O'

,

,

...... >,........f9:v::!.. ; ;

, B

=_e_.

b

surmounted arches

2.00

o Figura 3. Segmental arcb witb varying tbickness.

circular and depressed elliptical arches

He recommended keeping constant (from the crown joint towards the springer) the vertical projection (Mm) of any of the joints of the arch,

rise:span s )i YtO Yt2 1.40 1.25 1.15 1.10 circular 1.80 elliptical 1.80 1.60 1.40

YJ X Ys

31

Ys

3.3

proposed in the "Manuale dell'Ingegnere" (Colombo), which for backing values of h 1 < 1.50 is:

Abutments and piers thickness

Abutments thickness. The second important theme taken into account by the treatiser on masonry bridges, was the measurement of the abutments and the piers. This also give rise to a large number of technical formulas. Withfindicating the rise of the arch, L its width, S, the thickness of the abutments, e the thickness of the crown joint, h the distance from the springing line to the foundation base, h 1 the height of the backing. The quantity H is equal to: H=h+.f+e+0.60 for h 1 0.60. The most widely used formulas can be summed up as follows in accordance with the type of intrados curve. Semi-circular arches:

Les guillier

S,

S, = ..JL(0.42 + 0.17L + O. 44h) 2f+e while for values of h 1 ;?: 1.50 with H =(h + f + e) is:

0.17L ) +0.0185H..,jh; S, =..JL( 0.42+--+0.44h 2f+e In the "Hütte's Manual", on the other hand, the following equation is to be found:

S =!=..(3L-f)+100+!!.. , 8 f+L 6

which for semi-circular arches becomes:

=(0.60+0.04h)..JL

5

German-Russian Engrs. S,

After making a precise comparison of the thicknesses used in numerous bridges, Castigliano decided that the best formulas were L'EveilIe's. His only objection was with regard to abutment thicknesses, which, in his opinion, were insufficient for very low values of h. In effect, L'Eveille's equation for segmental arches and h = 0 would give S, =0 . It has to be pointed out, however, that Croizette­ Desnoyer gives a slight different formula where with h = 0 one would have S, = O. 33[ m]. According to Croizeue-Desnoyer the correct equation is as follows:

=O. 305 + ~ L + !!.. + !!J.. 24

6

12

Segmental arches: Lesguillier

S, = [0.60+ 110(7 - 2)+ 0.04h ]..JL

/ .

(

L'Evellle

S, = 0.33+0.212L

)OC Vii(j+e)

Formula used by German engineers S =0.305+0.125L(3L-f)+ 2h+h 1 , L +f 12

oc

Formula used by Italian civil engineers S,

S, =0.33+0.212LVH (f+e) '

=0.05h+0.20L+(107~5L)(7)

Equation applied for the execution of the Udine­ Venzone (Italy) railway brickworks:

Semi-elliptical or semi-oval arches: Lesguillier

S,

=[0.60 + 0.05(7 - 2) + O. 04h]..JL

S, = 0.20 + 0.030(p + 2e)+ O.lOh

L'Eveille

where p is the curvature radius of the arch. The meaning of the other symbols is already known.

S = (0.43+0.154L) l(h+0.54f )( 0.84L ) 'H O. 65.f + e ,

Piers thickness. The piers must fulfil the following two conditions: support fixed and moving loads; resist differences in thrust produced by two consecutive arches. The first condition imposes that the piers must be the same thickness as the abutments. The second condition implies that the thickness must be equal to at least twice that of crown joint thickness.

Formula used by German engineers S,

h

S =-L+l00+­ , 24 6

L'Eveille S = (0.60+0.162L) /0.865L(h+0.25L) , 1 H(0.25L + e)

=0.05h+0.20L+(107~5L)(7)

Other very widely-used formulas, which were also widespread because they were published in civil engineering manuals, are, for example, those

32

Moreover, if they are situated in the bed of a water course, the piers must also be able to withstand pressures produced by the movement of the water. If the pier is supporting two arches and it is admissible to believe that the two thrusts are equal (as they are produced by arches of the same width resting on the same pier and with the same loads and overloads), the following ratio can be applied:

E=

Si 'fm V l;e

that its normal at the intrados curve forms a 45° angle with the vertical. To avoid making very long calculations, he advised substituting this type of arch with elliptical arches, with a variable ratio between deflection and span of 0.50 and 0.80. L'Eveille's were, however, the most common formulas and are summed up as folIows: circular arches

(4)

where h represents the height from the foundation springing line to the haunch joints of rupture; H is the distance between the foundation line and the bridge's road line; e is the crown joint thickness;fis the distance between the crown joint extrados and the haunch joint of rupture; d is the horizontal distance between the haunch joints of rupture; P is the weight of the section of arch up to the joint of rupture; (J) is the specific weight of the material used to build the bridge; k is a safety coefficient which is to be established according to experience. Semi-circular arches: experience, research and identification of the thrust line (usually carried out by using Mery' s graphic construction), the calculations to evaluate the mechanism of collapse of the arch, carried out with the help of Petit's tables (1835), and therefore the position of the joints of rupture, all these factors suggested to the majority of scholars that a sufficiently reliable choice was the haunch joint of rupture, for parallel extrados arches, at two-thirds of the semi-circumference, Le. with a 60° incline with respect to the vertical passing through the crown joint. Circular arches: experience, calculations and evaluation of thrusts using graphical statics instruments, show that if the direct bearings of the circular arch meet the intrados below the joint of rupture, the arch rupture will continue to appear at this point; viceversa, the rupture will appear at the joint that is closest to the springer. In the technical literature, therefore, the following indication is often found. To correctly evaluate the thickness that is to be assigned to bridge piers, the following modifications should be made to the equation (4): if Dis the width of the arch and h, fand d are indicated by h = h + o. 25D, f = o. 25D, d = o. 865D, depending on the type of intrados curve, a suitable formula can be established for the measurement of pier thickness, as shown below. Anses de panier arches: Mery (1840) established that the joint of rupture is positioned in such a way

E = (0.33 + O. 212D)

p,fSi f+e D

semi-circular arches

1h+~25D E = (0.60 + 0.162D)ro:25D + e 0.865D

anses de panier arches

1h+0.54D E=(0.42+0.154D) ~ 0.465D+e 0.84D Sejourne (1913-16) suggested using the following formulas as an alternative the above: E> YsL, and in any case E = 0.4 + 0.15L or E = 0.8+ O.IL, applicable to road bridges with depressed arches of any type. It must be remembered, though, that pier shape and size do not depend solelyon the stability of the contruction; they are often over-sized to meet certain aesthetic tastes. Other 'rules' were expressed by numerous authors. Some of the most interesting are mentioned here. Perronet suggested using the equation: E = 2.25e. Castigliano advised giving the piers a thickness equal to roughly half that of the abutments. Colombo established three ratios from which the one that gave the largest dimensions was to be chosen:

E=0.20h'+0.6,

E=%,

E=7{O

in which h' indicates pier height from the foundation line to the arch springer. Other widely-used formulas were: 1) E =0.292+2e, generally applicable whatever the width of the arches; 2) other authors preferred to adapt the values of E as a function of arch width, therefore the following indications are often found: for span arches L $ 10m E=2.50e for span arches L > 10 m E=3.50e

33

On the other hand, by taking into account the coefficient k, Resal stated that: a) for arches of the same thickness and width, the least depressed arch is the most stable; b) for arches with the same value of p and e, the most depressed arch is the least stable. Resal believed then that he could identify a "coefficient 0/ boldness" (A) in a bridge in the

1 1 more frequently adopted was - L > E > - L . 5 10 However, all authors advised assuming a minimum value of E equa1 to the sum of all the thicknesses at the springer of two adjacent arches sharing the same pier and which have a horizontal springer. In the case of inclined springers, E will be equal to the sum of the horizontal projections of the two thicknesses of the springing lines of the two adjacent arches sharing the same pier. 4 MAXIMUM ARCH SPAN The maximum span of a masonry bridge was established in the PIauen bridge (or Federico Augusto bridge), at Dresden, which measured an impressive 89.90 m, with an arch rise of 18.80 m and a ratio s = Resal (1896), noting that in a masonry bridge the majority of the load is represented by its se1f­ weight, suggested bearing in mind the following indications: 1) two similar arches, i.e. built with the same materials, but having different widths, even with the same ratio sand crown joint thicknesses and with haunches of the same proportions, have similar line of thrust, and at the corresponding cross sections the maximum values of stresses have the same ratio as arch width; 2) if the thickness of an arch is reduced without altering its longitudinal axis, the maximum stresses increase, despite the reduction in total weight. Calling e the initial thickness and e' the reduced thickness, Resal established that the ratio of the

Ys.

stresses in the two arches was equal to

5 CONCLUSIONS As we can deduce from the above, the attention of bridge builders basically concentrated on the search for practical measurement formulas that would facilitate the determination of the size of the various parts of structures. The verification calculations that would ensure the stability of the construction were referred to a subsequent stage. In effect, and following on from early attempts by 18th century authors (de La Hire, Belidor, Couplet, Bossut, Bouguer), the development of arch and vault statics was greatly stimulated in the 19th century by the definition of complex calculation codes, and the setting out by Coulomb and Mascheroni of a rigorous theory regarding the rupture behaviour of the arch. We do not want to go into this important chapter in the his tory of construction, which has already been summarized in the historical synthesis in the note (Poncelet 1852, Benvenuto et al. 1988), but we will give abrief outline of the principal calculation methods that were 'recommended' in 19th century studies on bridges and refer to the historical synthesis mentioned for an in-depth study of the subject. The methods suggested for the verification of arch stability can be classified in the following groups: - Hypothetical thrust fine methods: Moseley, Mery, Scheffler (minimum strength method), Drouets (maximum stability method), Dupuit, Kleitz,

~

1 therefore for the value e '= - e the stresses should 2

increase by approximately 25%. If L is the width or span of the arch, the ratio increases in proportion to Land similarly the pressure values will increase. Therefore, according to Resal, the previous rule can not be applied with sufficient reliability; 3) if the thrust at crown joint ( SH) has an expression

Ye

like SH = ke L

2

8r

= Lp

assuming for p the average 2 value of the various radii of the arch's intrados curve. Some examples of "coefficient 0/ boldness" are given in the following table: A e L / 439 2,60 33,80 Fouchard bridge 26 25 625 25 Nogent bridge 50 639 49,2 17,73 25,96 Tournon bridge 690 15,90 27,60 Antoinette bridge 50 931 61,50 27,50 30,95 Lavaur bridge 7,60 1066 44,80 5,60 Mosca bridge ll50 7,40 46 50 Cloris bridge 12,81 42,90 1308 61 Chester bridge 17,60 40,70 1363 Cabin John bridge 67 1517 72,25 20,70 42 Trezzo bridge 1667 2,13 88 37,89 Souppes arch

quantity of A

in which / is the rise and k is a

coefficient dependent on the profile of the limit thrust line and on the specific weight of the . -U.1S, reasonabl y approx1mate . 1y masonry, th e ratio

8r

equal to the length of the middle radius (p) of the intrados curve (especially in segmental arches), therefore the thrust is proportional to quantity pe.

34

Boston, UK, on 3-6 September 1995, lead us to hope for the greater integration between Mechanics and Architecture with the common aim of making further contributions to developing awareness of the science of construction field.

Clericetti, Gerstner, Knochenhauer, Schubert, Hagen, Weisbach, Barlow; - Methods based on research into the theoretical profile most advantageous for stability: Villarceau, Saint-Guilhem, Carvallo, Hagen, Weisbach­ Hermann, Denfert-Rochereau, Tourtay, Legay; - Area of stability methods: Durand-Clay, Cinq, Gilliot, Peaucellier, Gobert; - Methods dependent on the theory of elasticity: Castigliano, Lavoinne, Tourtay, Resal, the "elasticity ellipse method". (Benvenuto et al. 1988). A useful summary of the methods used for verifying the stability of masonry bridges can be found in Chaix (1890) and Campanella (1928). It is important to remember that of all the authors mentioned previously, and of all the solutions they suggested, only a few received any significant recognition, despite the interesting proposals that were formulated by all the authors. In fact those who had greater luck were the ones who were able to pro pose answers, instruments and elementary methods, even if they were not rigorous or equal to the problem under examination. Proof of this can be found in Mery's method. His graphic construction for the laying out of the thrust line in an arch became the best-known and most widely used instrument. During the 19th century other authors received adequate recognition, especially Durand-Clay, Villarceau, Dupuit, even if the solutions they suggested are subject to criticism and objections. It is only during this century, firstly through the work of Heyman (1966, 1969, 1982) and subsequently, taking his same line of thought, through other authors that we have seen an interesting "rediscovery" of the disused paths of research which best represent a possible interpretation of the collapse behavior of the arch in terms of Plastic Theorems, and in the same spirit as 18th century theories (Sinopoli et al. 1997). However, even though developments in the subject had defined what were to become the two main lines of research, 'Elastic' and 'Plastic' methods, as far back as the first few years of this century, 'Empirical' methods received animated attention, as witnessed by their widespread publication in technical manuals. This is one of the reasons to repropose a little-known chapter of the science of construction, even though the construction of masonry bridges has by now been relegated to the area of construction systems that are no longer used, in favor of reinforced concrete and steel for the construction of bridges. Active interest in understanding the statics behavior of arches and vaults, witnessed by recent studies in numerous international magazines and at recent conferences on the theme of construction, including this one, which intends to repeat the success of the First International Conference on Arch Bridges held at

REFERENCES Albenga, G. 1953. I ponti. Torino: UTET. Alberti, L.B. 1483. De re aedijicatoria. A eura di G. Orlandi. Milano: Il polifilo (1966). Aragon, E . 1909. Ponts et ouvrages en ma~onnerie. Paris: Dunod & Pinat. Aurie, M.A. 1911. Ponts en ma~onnerie. Paris. Bauemfeind. C.M. 1872. VorltJgebltJuer zur BrUckenbaukunde mit erlautendem Texte . SlUUgart. Benvenuto, E. 1981. La scienza delle costruzioni e il suo sviluppo storico, ebap. 9: 322-392. Firenze: Sansoni. Benvenuto, E. 1991. An Introduction to the History 01 Structural Mechanics, Part 11: Vaulted Struetures and Elastie Systems: 309-437. New York: Springer-Verlag. Benvenuto, E., M. Corradi & F. Foce 1988. "Sintesi storiea sulla statiea di arebi, volte e eupole nel XIX seeolo", Palladio, nuova serie, 2: 51-68. Roma: Ist. Poligrafieo e Zecca dello Stato. Bonneau, L. 1908. Etude sur les voutes et viaducs. Paris: Dunod & Pinon. Brizzi, E. 1951. "AtlUalitA, statiea e geometria c1assiea deI ponte a Santa Trinita", Panorami della Nova Citta . CampaneIla, G. 1928. Trattato generale teorico pratico

deli 'Arte dell'lngegnere civile, industriale ed architetto, "Ponti in Muratura". Milano: Vallardi. Castigliano, A. 1876. ''Formule razionali ed esempi numerici per il ealeolo pratieo degli arebi metallici e delle volte a botte murali", L'Ingegneria Civile e le Arti Industriali, 9: 129-135; 10: 145-153. Cbaix, J. & E. Cbambaret (1890). Traite des ponts. I partie: "Ponts en ma~nnerie". Paris: Facbon & Artus. Colombo, G. 1923 . Manuale dell'lngegnere, 47a-50a Edizione. Milano: Hoepli. Corsetti, M. 1944. Teoria e pratica delle Costruzioni. Vol. 11. Torino: Paravia. Cosyn, L. 1901-02. "Etude theorique sur la resistanee des voutes", Nouvelles Annales de la construction , Septembre, Oetobre, Novembre, Decembre 1901; Janvier, Fevrier & Mars 1902: 1-80 (off-print). Paris: Beranger. Croizette-Desnoyers, Pb. 1885. Cours de construction des ponts, 2 vol. Paris: Dunod. Debauve, 1873. Manuel de l'ingenieur, Ponts en ma~onnerie . Paris. Degrand, E. & J. Resal 1887. Stabiliti des voutes, t. I, "Ponts en ~onnerie". Paris: Baudry. Dejardin, 1845. Routine de l'Etablissement des voutes ou

Recueil de lormules prariques et de tables determinant a priori et d'une maniere elementaire le trace, les dimensions d'equilibre et le metrage des voutes d'une espece quelconque. Paris: Carilian-Greury & Dalmont.

35

et en metal pour routes, canaux et chemins de fer . Paris: Dunod. Nicodemi, R. 1913. Voltometria. Napoli: Pironti. Palladio, A. 1570. I Quattro Libri dell'Architettura di Andrea Palladio, Libro In. Venezia: Domenico de' Franceschi. Petit, 1835. "Memoire sur le calcul des voGtes circulaires" , Memorial de l'ojficier du Genie, 12: 73-159. Paris: Impr. Royale. Perronet, J.-R. 1777. Memoire sur la reduction de l'epaisseur des Piles, et sur la courbure qu'il convient de donner aux Voutes, lu a I'Academie des Sciences, le 12 novembre 1777. Perronet, J.-R. 1782-83 . Description des projets et de la construction du pont de Neuilly, de Mantes, d'OrIeans, de Louis XY/, ecc., Paris: Impr. Royale. Poncelet, J.V. 1852. "Examen critique et historique des principales theories ou solutions concemant I'equilibre des voGtes", Comptes Rendus, XXXV, n. 15: 494-502; n. 16: 531-540; n. 17: 577-587. Rankine, WJ. Macquom 1863. Manual of Civil Engineering. London: Griffin. Resal, J. 1896. Cours de ponts. Paris. Rota, A. 1867. Della costruzione dei Ponti di struttura murale, Dissertazione. Napoli: Stamperia di F. Ferrante. Ruddock, T., 1979. Arch Bridges and their Builders 1735­ 1835. Cambridge: Cambridge University Press. Schlömitch, O. 1904. Uebungsbuch zur Studium der höhere Analysis, Leipzig. Schroot, P.A. 1898. "Note sur le trace des joints dans les voGtes elliptiques executees en briques", Nouvelles AnnaLes de la construction, Decembre 1898 (off-print). Paris: Baudry. Sejourne, 1914. Grandes Voutes, 6 tomes in 3 vols. Bourges: Tardy-Pigelet. Serlio, S. 1537-1575. Sette libri deU'Architettura di Sebastiano Serlio. Sevin, E. 1952. Cours de Ponts en Maronnerie. Paris: Eyrolles. Sinopoli, A.. M. Corradi & F. Foce 1997. "Modern Formulation for Preelastic Theories on Masonry Arches", Journal of Engineering Mechanics, Vol. 123(3), March 1997: 204-213. Strassner, A. 1927. Neuere Methoden zur Statik der Rahmentragwerke und der elastischen Bogentrager, chap. 2: Der Bogen und das Brückengewölbe. Berlin. Tavemier, H. 1907. "Pont a arcs de pierre de taille articules a la def et aux naissances avec joints coules en zinc", Annales deI ponts et chaussees, s. VIII: 6-43. Tourtay, C. 1903. "Methode de caIcul rapide des voGtes et de leurs culees", estratto da Nouvelles AnnaLes de La construction, Septembre, Octobre & Novembre 1902: 1-34 (off-print). Paris: Beranger. Tolkmitt, 1912. Leitfaden [Ur das Entwerfen und Berechnung gewölbter Brücken. Berlin. Vallette, R. 1947. Construction des ponts. Paris: Dunod. Weale, J. 1843 . The Architecture ofBridges, 5 vols. London. Wiebeking, C.F. 1810. Traite contenant une partie essentielle de la seience de construire les ponts. Munich.

Dubosque, J. (1896). Etudes theoriques et pratiques sur les murs de soutenement et les ponts et viaducs en maronnerie. Paris: Baudry . Dupuit, J. 1870. Traite de l'equilibre des voutes et de la construction des ponts en maronnerie, 2 vol. Paris: Dunod. Espitallier, G. (1897). Cours de construction. Ponts et viaducs. Ponts en maronnerie, Ponts en bois, Ponts metalliques. Paris: Charles-Lavanzelle. Ferrieu, R. & P. Lorton 1923-24. Cours de ponts en maronnerie. Paris: Ecole Sp&:ia1e des Travaux publics. Ferroni, P. 1808. "Della vera curva degli archi dei ponte a Santa Trinita", Memorie della Societii Italiana delle Scienze, Tomo XN (1809) . Verona. Gauthey, E.-M. 1809-1816. Traite de la construction des ponts, 3 vols. Paris: Didot. Gautier, J. 1714. Traite des ponts et Chaussees. Paris. Gautier, H. 1755. «Dissertation sur I'epaisseur des culees des ponts C..)>>: 335-412. Traite des ponts OU il est parIe de ceux des Romains et de ceux des modernes, 4e ed. Paris: V.ve Ducbesne. Herbst, C. 1910. "Die ästhetische Kreisbogenkurve", Zeitschrift[Ur Mathematik und Physik, 58: 72-89. Heyman, J. 1966. "The stone skeleton", Int. J. Solids and Struct., 2(2): 249-279. Heyman, J. 1969. "The safety of masonry arches", Int. J. Mech. Sei., 11(4): 363-385. Heyman, J. 1982. The Masonry Arch. Chichester: Ellis Horwood. Jorini, A.F. 1927. Teoria e pratica della Costruzione dei Ponti (5th ed.). Milano: Hoepli Jouret, A. 1946. "Paul Sejourne (1851-1939)", Technica, 4: 1­ 28 (off-print). Lyon: Impr. reunise. Legay, 1900. "Memoire sur le trace et le caIcul des voGtes en ma~nnerie", estratto da Annales des ponts et chaussees, 4e trimestre 1900: 1-96 (off-print). Paris: Dunod. L 'Eveille, 1854. "Note Sur les Ponts en Ma\ionnerie: De I'epaisseur a donner a la def et aux culees des ponts en ma~nnerie", Bulletin de la Societe d'Agriculture, Seiences et Arts de la Sarthe, 2e serie. T. III (11): 73-89. Le Mans: Monnoyer. Ligowski, W. 1854. Die Bestimmung der Form und Starke gewölbter Bogen mit Hilf der hyperbolischen Funktionen. Berlin. Loria, G. 1930. Curve piane speciali, algebriche e trascendenti. Milano: Hoepli. Marchat, 1878. Traite de la resistance des materiaux appliqee ii la construction des ponts. Mascheroni, L. 1785. Nuove ricerche sull'equilibrio delle volte. Bergamo. Maurel, Ch. 1894. "Note sur les detormations des voGtes surbaissees", Nouvelles Annales de la construction (2 tevrier 1894). Paris: Boudry. Mery, E. 1840. "Memoire sur l'equilibre des voGtes en berceau", Annales des ponts et chaussees, s. I, le trim., t. XIX: 50-70. Mesqui, J. 1986. Le pont en France avant le temps des Ingenieurs . Paris: Picard. Morandiere, R. Bricheteau (de la), 1874-1888. Traite de la Construction des Ponts et Viaducs en pierre, en charpente

36

Arch Bridges, Sinopoli (ed.)© 1998 Taylor & Francis, ISBN 90 5809 012 4

Arch and vault from 1800 to 1864 Karl-Eugen Kurrer Verlag Ernst und Sohn, BerUn, Gemumy

Andreas Kahlow Fachhochschule Potsdam, Germany

ABSTRACT: The incursion of the paradigm of elasticity theory into the mechanical modelling of vaults has its origins in the history of construction as well as in the his tory of theory. The process of abandoning the thrust line theory and of reinterpreting the vault into an elastic curved bar took place in the 19th century against the background of the rise of wrought iron girder construction. An initial culmination of this development was the introduction of wrought iron into the construction of bridges and halls, starting in the mid-1800s. The transition in practice from cast to wrought iron made it easier to accept elasticity theory in practical design. The lag in experimental research became evident. German development in the l860s was influenced considerably by the work of Navier, Bresse and others. Thus Bendei and Winkler after hirn applied the theory of elastic arches to the static analysis of the bridge over the Rhine at Koblenz. This paper analyses the formation of a practical theory of curved bars and its interaction with the practice of design. compressive strength of cast iron was with structures that were working like arches. Bridges and roof-structures with beam-shaped forms and flat segmental arches were avoided. This was very different in timber-construction, where it was obvious that the flexural rigidity was the crucial advantage of the material. There are many examples of timber bridges of suspension structure and trussed beam in Switzerland and in addition there are the early arch-bridges like the one of the Grubenmann brothers in Schaffhausen. At the end of the 18th century experiments of loadbearing capacity were carried out on models. In 1776, Leonhard Euler developed his definition of the modulus of elasticity as weIl as the buckling theory from experiments on a model of the lattice girder-arch bridge in St. Petersburg. At the beginning of the 19th century the Bavarian engineer, Car1 Friedrich Wiebeking, developed on his so called "Wasserbauhof' systematic material tests for timber and stone on a large sca1e. One aim was to study the construction of flat, arch-shaped bridges, which were built with minimal effort from about the beginning of 1810 (Hilz 1993). The green timber was precambered in order to achieve a maximum rise which resulted in an improved loadbearing capacity. The mathematician J.G. Späth analysed the Wiebeking bridges in a book from l8ll. He starts an analysis of deformations, something which was applied to steel-structures only 30 years later. In a

1 MATERIAL AND CONSTRUCTION Two paradigms existed around 1800: there are elastic materials like wood and there are non elastic materials like stone and wrought iron. The reason for this distinction is not only a consequence of the different types of construction, which developed historically but also in the theoretical approach to the crack-behaviour. Since Galilei fibrous materials have been seen as tension or compression members with elastic properties, whereas shear properties were associated with earth, brick or stone. Without doubt Galilei's model of the fibrous and elastic muscular system played a certain part in this approach. In 1798 Girard wrote: «Besides the materials made out of elastic fibres, ex ist many more which consist from parts which are glued together side by side, for example stones and generally all types of metal. It is easy to see that the laws of resistance of solid structures, at which we have been looking so far, have to be different in a similar way as their organisation differs from the one of the fibrous substances». It is surprising that it was taken for gran ted that iron was a non elastic material, although since the construction of the Coalbrookdale-bridge 1779 iron buildings were existing, which would have been big enough to draw the attention to elastic deformations. The reason why these deformations were not realised lies probably in the chosen form of construction. The only way to make use of the high 37

simple way he showed in tables the relationship between load, deformation and compressive force in the imposts, which were gained from experiments. The measured values were then summarized in "logistic" formulae. The consideration of lateral compression already took into account that the differential moment between two bending states has to be proportional to the difference in lateral shear between these two arched forms. The possibility of a vault effect, on which the iron-construction are based, was not considered in Späths analysis (Späth 1811). Nevertheless, at the beginning of the 19th century there was a strong desire to invent new principles of construction or to try forms of construction with untypical materials. The question of saving material was getting more important. Especially the roof-constructions were bringing forth innovations: Hübsch with his suspension-roofs in Baden and Bohemia and Gilly with his p1ank-girders in Prussia. Roof constructions made of boarded girders were occasionally considered to be timber-vaults and thus the reference to the material was abandoned. Gilly reported in his magazine: "Sammlung Nützlicher Aufsätze" ("Collection of useful essays") from 1798 that short pieces of timber are used «so that they press against each other like stones in a vault». The same method was be used in France for bridges, to~, and the shape was to be chosen by hanging out a chain (Gilly 1798). The intention to construct a thrust line cannot be described any better. It is obvious that the practitioners like Gilly were less strict about the fact whether their constructions were theoretically correct or not. In a lot of cases developments were anticipated in this way, which could not have been proven mathematically yet, but which were innovative in terms of constructions. Around 1830 Ardant systematically examined plank-girders and measured the horizontal shear concluding that boarded p1ank-girders were neither materialsaving nor especially stiff. In the end he will dismiss them more or less. The boarded girders did have advantages which were utilised later as grid­ constructions which are known as Zollinger-roofs. The innovative power of the practitioners, who neglected the "logic" of the material in favour of the real experiment, seemed to have played an important role also in the transition of the theory of elastics from the area of timber towards cast iron. In the 1840s this transition took place in view of the railway services, when the question of the effective stresses became important for cast iron bridges. Around 1800 and for a long time afterwards measurements of the elastic deformation of cast iron were rare. Thomas Young who connected the theory of elasticity to the undulatory optics suddenly made this topic interesting for physicists. He gave a good

overview over the early experiments in his "Natural philosophy" of 1807. In the year 1847 the report of an English govemment commission which had examined the use of cast iron in railway installations, Was discussed all over Europe. In the evaluation of the results dynamic loads, which led to vibrations, were distinguished as the reason for a lot of failures. A series of examinations of deflections of existing bridges started around 1850. In the year 1855 a report in the "Annales des Ponts et Chaussies" concems itself with measurements under differential temperatures which were carried out on the Southwark-Bridge (Busche 1855). In the year 1852 Pirel is reporting about the deflection of the cast iron Lormant-Bridge under load of a passing train. This experiment is recorded on paper with a mechanic writer (probably for the first time) and the influence of the temperature is also measured (Pirel 1855). Considering these facts one can see that the further development of the theory of the elastic arch in the beginning of the 1850s was a logical progression. Navier's theory, which he developed on the model of the timber arch, included the axial force resulting from the elastic change of the curvature, but the influence of temperature was not considered. This problem occurred only on railway­ bridges with big spans. The work of Bresse was also during this time. Not only did they temperature influences to the theory of elastic arches, they also opened up a completely new view of steel as a linear elastic material. The practical construction, which was again far ahead for example Fairbain's bent plate crane made of wrought iron, became the paradigm of a new generation of structures. 2 THEORY OF ARCHES - STEELBRIDGE CONSTRUCTION - TIMBER CONSTRUCTION Navier wanted his structural theory also to be applied to structural arch bridges made of timber and steel. He even specified the function of the influence of the horizontal shear to statically indetermined two hinged arches under a moving verticalload. However, his theory of arches was to be used by P. Ardant only one and a half decades after the first publication of Navier's book "Mechanics 0/ the art 0/ construction" (Navier 1826). The moduli of elasticity which are necessary for the analysis of wooden and iron arches, Navier calculated indirectly by comparing the deflection measured on loaded single span girders and cantilever beams with the formulas he deduced for this special case from the linearized differential equation for the deflection.

38

_ .!~"!. -

fii!l=:

__ ~ __ __ __

__.~.

____.._____ __._ /J

J~ ·l i"

-- - -­

(,1'''9,1

Figure l. Pont Arcoie, Paris 1854-55.

2.1 French steel bridge construction 1845 to 1855

published his work: "Etudes theoriques et experimentales sur etablissement des charpentes a grande portee" in the year of 1840. 1847 the complete translation was printed in the "Magazine for the practical art of construction" under the title "Studies based on theory and experience about the installation 0/ timber constructions under high tension". Ardant was professor for architecture and construction of buildings at the Ecole d' Applications de l'artillerie et du genie de Metz. There - in the frame of a construction-c1ass - he summarised all important formulas of Navier's theory of arches for arch-constructions of timber, which inc1uded the flexural rigidity EI and the modulus of elasticity of the structure.

To determine the modulus of elasticity of the wrought ir on arches of the viaducts c10se to Terascon M.M. Collet-Meygret returned to the method of Navier. He measured the crown­ deflection of two parabola shaped model-arches for different states ofloading, put the values in Navier's differential equation of bending for elastic members and obtained the moduli of elasticity for different loads. The maximal deviation from the average was about 10% (Baum garten 1855). 1854/55 Oudry built the Pont d' Arcole - later called Pont de l'hotel de ville - over a lateral branch of the Seine in Paris (Figure 1): he created a bridge which became the reference for all future arch bridges made from wrought iron. The bridge spans over 80 meters with a rise of only f =6.12 m. With the ratio of rise to span of / = Oudry doubled the ratios of the most daring vault bridges made from stone. The cross-sectional depth of the wrought · iron arch of the pont d' Arcole was 1.4 meters in the abutment and was reducing to 0.38 meters at the crown. Oudry couldn't analyse the arch made out of rolled iron profiles and wrought iron plates with Navier's theory of arches, because Navier had not taken into account the important impact of the elastic rigidity of extension to the structural behaviour of flat arches. Probably Oudry may have returned to Mery's theory of vaults. Thus the theory of arches had to step back in favour of the theory of vaults. With a small thickness at crown Oudry tried to avoid the negative influence of temperature changes to the internal forces and the deformation of the arch. The arch can be statically modelled as an arch elastically fixed at both ends and a joint at the crown with moderate rotation-capacity.

ll3

~

o

2.2 Ardant's experiments with timber plank-girders At the request of the French ministry of war Ardant

r.:,."

_D~IL=

o

Figure 2. Experimental device of Anlant at Metz in the 1830s.

39

«Constant figures have to be included into these formulae, which describe the specific elasticity of the timber pieces and it is necessary to verify these for arches of different pieces of timber with experiments» (Ardant 1847). These experiments Ardant made on the expenses of the department of war in Metz. To the 1"'Ecole" in Metz and to the department of war by which it was supervised belonged halls for horseriding and manoeuvres, carparks and other hall-like buildings with large spans. Ardant measured the horizontal shear and the deformations of 15 circular shaped timber constructions with spans around 12 meters and symmetrically arranged single loads. On both ends of the arch cast iron cylinders were moving on steel­ tracks. Just above the cylinders two ropes were fasted, which carry weights (Figure 2). In order that the span is not changing the weights are corresponding with the horizontal shear resulting from the loading of the arch. This way the arch­ structures examined by Ardant are once statically indetermined two-hinged arches, in which forces and deformations are linked. From Navier's Theory of Arches Ardant derived the common formula for the crown-deflection of circular shaped, slightly bent arches with a circular or rectangular cross-section.

_.!.(KV )lh EI

Y- 2

behaviour of timber-arches and from the relevant structural system of a two hinged arch (equation 3) is maximal different by a factor of 10 for the same type of timber (pine wood). It is from: O.060E:5: E m :5: O.6E

Eis the modulus of elasticity which results from the

measurement of the deformation of a timber-beam on two supports and the evaluation of the corresponding equation of the theory of beams. The modulus of elasticity of the examined arches is weaker, when the battens that they are made of are thinner. And it is weaker when fewer bolts and iron rings are connecting them (Ardant 1847). This remark could be a hint that the moment of inertia of the cross-section of arches consisting of battens was clearly smaller than the one of the solid cross section put in the equations (1) and (3). This should have been the case especially under big deformations caused by the relative displacement of the batten surfaces! The second reason may have been that the shear rigidity GA q (the product of the shear modulus G and the shear section A q is approaching infinity GA q ~ 00) which Navier didn 't consider could have caused a significant part of the crown­ deflection Y because the effective shear area was significantly reduced by the relative displacement of the plank surfaces. The attempt of Navier and Ardant to develop a concept to find a material­ constant by considering the structural behaviour of constructions with identical material, which they had developed for beams and then transferred to arches failed for different reasons. The insufficient experimental conditions (insufficient connection of the battens) were making the comparison between the real structure and the structural model impossible. But even when the test-conditions would have been adapted better to the structural model of a two hinged girder, Navier' s theory of arches would have limited this concept by assuming infinite stiffness of longitudinal elastic rigidity, which is essential for arches. His theory is based on an elastic stiff arch (EA ~ 00). This way Ardant was able to discuss Navier' s theory of arches in detail and to add a few cases of application. But this method remained similar to Navier's analysis of beams.

(1)

2

where Y =crown-deflection, I = span, h = rise, V = total of the vertical loads, EI = flexural rigidity, K = constant factor depending on the distribution of the verticalloads. Whereas Ardant was able to calculate the factor K for every single case of loading with the theory of arches, he derived the modulus of elasticity from his large scale experiments. For every load case "j" with the total load Vi he measured the resulting crown-deflection Yi and calculated the arithmetical average of the ratio

(4')

Fig. 4 gives a sketch of the relation (4'). It is interesting to notice that it represents aquasi - linear correlation between 'Ymech and 'Ygeom· This results reinforces the simple definition of the geometrical safety factor that gains a clearer mechanical meaning.

- 0 .6

- 0. 4

- 0 .2

0 .2

0. 4

0.6

The collapse F for xb = 0.9 Ri, varying the position

of F and the thickness t of the arch

Fig.6a

121

07

l"'Iecc

0.6

0.5 O.

03 0.2

-0 . 6

-0 . 4

0.2

-0 . 2

O .•

geoM 5

0.6

The coJlapse F for Xb = 0.8 Ri, varying the position

of F and the thickness t of the arch

Fig.6b

The function Ymech = F(\eom> for Xb = 0.8 Ri

Fig.7b

0.12

l"'Iecc

0.1 0.08 0.06 0.0,

1.2 '0 . 04

1.'

The function Ymech -0 . 4

0.2

O••

The coJlapse F for Xb = 0.7 Ri, varying the position

of F and the thickness t of the arch

Fig. 6c

2 .'

=F(\eom> for Xb =0.7 Ri

Fig. 7c

REFERENCES Couplet, P. 1729. De la poussee des voutes, Histoire de /'Aeademie Roya/e des seienees, p. 79 and 1730 p. 117. Heyman, 1. 1969. The safety ofmasonry arches.lnt. J. Meeh. Sei ., Pergamon Press, 11:363-385. Heyman, J. Dec. 1980. The estimation of the strength of masonry arches. Proe. Instn . eie. Engnrs, Part 2, 69:921-937. Corno, M. 1992. On the equilibrium and CoJlapse of Masonry structures.Meeeaniea, 27, Netherland Kluwer Ac. Pub!. Lucchesi, M. and Padovani 1997. On the coJlapse of masonry arches. Meeeanica, 32.

6b and 6c give the coJlapse point loads F = F(xp, t) for different values of the arch thickness and for the above defmed values of the arch embrace. The corresponding curves of Figures 7a, 7b and 7c represent the corresponding functions Ymech = F(\oonJ. The observed quasi-linear dependence of of Ymech on Ygoom is confmned also in these more general cases.

0.8

Mecc 06

O'

geol'l 5

The function Ymech

2.2

2 .0

geoM

.02

-0 . 2

1.8

= F(\eom) for Xb = 0.9 Ri

Fig.7a

122

Arch Bridges, Sinopo/i (ed.)© 1998 Tay/or & Francis,/SBN 90 5809 012 4

The mechanism model in the seismic check of stone arches P'Clemente ENEA, Centro Ricerche Casaccia, Roma, Italy

A.Raithel Dipartimento di Analisi e Progettazione Strutturale, Universita Federico II, Napoli, Italy

ABSTRACT: The safety check of a stone arch, made up of voussoir laid dry, under seismic actions is a static matter, considering that the structure behaves as a rigid body. From a technical point of view it is important to avoid that the structure turns into a mechanism, even though also in this case the safety is possible. In fact, after some oscillations, the arch may return to its natural configuration. As well-known the safety of stone arches require the loads thrust line to be anywhere within the arch profile. Being verticalloads fixed, the goal is to define a horizontal load factor such to turn the structure into a mechanism. In this paper the results of a comprehensive numerical investigation, carried out using an iterative method to find the collapse mechanism and the corresponding horizontal load factor, are shown. 1. INTRODUCTION The behavior of arch made up of rigid voussoir laid dry (Heyman 1966) is very different from that of an elastic structure, especially when subject to seismic actions. In fact, the vulnerability of an elastic structure under seismic loading is essentially related to the frequency content of the seismic input. If the Fourier spectrum of this shows significant content at the main structural resonance frequencies, the structure is sensitive to it and may present high values of the amplification factor from the basement to the top. Vice versa if the frequencies of the structure are not in the interval in which the seismic input spectrum shows important amplitudes, the earthquake will have not important effects on the structure. The study of an arch of rigid voussoir must be performed in a very different way. Because of its infinite rigidity, a stone arch does not show any relative motion with respect to its base, until the amplitude of the external load is that to turn the structure into a mechanism. From this consideration we deduce that the safety check of stone arches can be studied as a static problem (Clemente 1998). In this paper the safety of stone voussoir arches under seismic loading is analyzed. The mechanism in which the structure can be turned and the relative horizontal acceleration value are found using an

iteration procedure by means of a purposely written computer code. 2. STRUCTURAL MODEL The static analysis of stone arches was developed by Heyman (1966 and 1969), who applied the ideas of plastic theory to masonry. He proposed the model of arch made up of voussoir laid dry, for which the assumption that stone has no tensile strength is almost exactly true: although stone itself may have some tensile strength, the joints will not, therefore no tensile forces can be transmitted from one voussoir to another. Besides, stresses are low enough to not allow crushing of the material. This observation is equivalent to the assumption that stone has an infinite compressive strength. He also assumed that friction between voussoirs is high enough to suppose that sliding failure cannot occur. With this assumptions the limit behavior of such cross-section is completely described by the limit domain in the plane M-N (bending moment - axial force) made of two straight lines starting from the origin (see also Occhiuzzi & C1emente 1992):

M

=

s being the arch thickness.

123

± N sl 2

(1)

Figure 1 Structural model of a stone arch und er seismic motion Failure of the arch occurs when sufficient hinges form to turn the structure into a mechanism. In other words if a line of thrust lying wholly within the masonry which represents an equilibrium state for the structure under the action of the external loads and which allows the formation of sufficient hinges to transform the structure into a mechanism can be found, then the arch is on the point of collapse. The uniqueness theorem may be stated for masonry as folIows: if the variable loads are specified as ratios of one of their number and they have been increased from their working values to the collapse values by a load factor, while the dead load does not change, the value of that load factor on the point of collapse is unique. The safe theorem states that a structure is safe if a line of thrust in equilibrium with the external loads and lying wholly within the masonry can be found . It is important to point out two considerations. First of all the thrust line of the safe theorem need not be the actual thrust line: every thrust line in equilibrium with external loads, lying within the arch profile, if any, can be chosen to check the structure. Moreover we do not know the actual stresses in the structure. In fact, we did not make any assumption about the material constitutive relationship, but the fact that the thrust line lies within the masonry ensures that there are only compressive actions, which can be transmitted from each voussoir to the next. Heyman's ideas were applied to study the limit behavior and to find out the collapse mechanisms of stone arches under dead - plus - vertical live loads and to investigate the influence of the various parameters on the collapse mechanism and on the structural safety (Clemente et al. 1995). Let us consider the voussoir arch in Figure 1 and suppose that one thrust line in equilibrium with the dead loads exists which lies wholly within the

124

masonry. The base of the arch is subjected to a negative horizontal acceleration - xg . In this condition the arch is subjected to the vertical loads and to the horizontal inertial forces due to the acceleration. According to the safe theorem the structure is safe if a line of thrust in equilibrium with the external loads and lying wholly within the masonry can be found. In this case the horizontal loads play the role of the live loads, whereas the vertical ones are fixed. The uniqueness theorem is still valid. When the seismic loads are put in action and are increased from zero to the collapse value, the line of thrust changes and at least four hinges form. At the point of collapse the thrust line must pass through the hinge points. If the hinge is at an internal section the line of thrust must be tangential to the arch profile. Collapse mechanism and load factor can be found by using the same iteration procedure shown in the case of the vertical travelling load (Clemente et al. 1995). This can be started giving a first mechanism and the corresponding diagrams of the velocity components (Fig 2a). The equilibrium equation can be written:

Pv+)"Ph=O

(2)

where Pv and Ph are the virtual powers due to vertical and horizontal loads respectively (Occhiuzzi & Clemente 1992):

P" = Ph =

r

i

0ZL

qv ·11 dz (3) qh · ~ dz

In (3) qv(z) is the vertical dead load and qh(Z) the horizontal load, ll(z) and ~(z) are the vertical and horizontal components of the velocity, respectively.

Yt

'.' ~

7

.

zs : .

.......

····

.'

"

:b

.. ·.

c .

®

:

,

L

Z2

ZB

:4

•

.,

~' "

A

...... ;:.': ..... ···· 1·· ,

.

'

..-.

..

~ ,

.

~

."

th

Y2 \

c

,

f

'

I

,

..

.' ~4

6:;0.: ®

H . ~"

ih r

Y2

. ". : -. ...

;

1\

f

i • .~ ZeB

Ta

\

: Zc

j~ Y

,

Z2

Z'c

\

,

~

Figure 2 Thrust line in the generic iteration (a) and actualline ofthrust (b) As we can see the vertical loads have, in that case, a stabilizing effect. In fact, because in (2) there are no terms with the internal forces acting at the hinges, which are still unknown, the equilibrium on the point of collapse is guaranteed by P v which must be negative. From (2) the kinematically admissible load factor can be deduced:

Jc =- Pv/ Ph

funicular polygon and the arch profile (Fig. 2b). In the present investigation a high number of voussoirs has been considered . So the obtained load factors are certainly not less than the actual ones, related to the actual size ofthe voussoirs. 3. SEISMIC ACTIONS MODELLING

(4)

If the arch is subject to the self-weight only, the horizontal forces are equal to the product between the mass of each voussoir and the horizontal acceleration xg and are applied at the center gravity

and so the load intensity associated with the assumed mechanism. The load being known, it is possible to find out the reactions and then the funicular polygon passing through the assumed hinges. The value given by (4) is the collapse load factor only if the funicular polygon, passing through the hypothesized hinges, is elsewhere within the masonry; if it is not, in the next step we must move the hinges to the sections where there are the maximum distances between the

of each voussoir, i.e. at the same point of the vertical loads. The structure is subjected to a parallel forces system, whose direction is determined by the ratio xg / g between the horizontal ground acceleration and the gravity acceleration. It is as the springing of

125

a)

b)

c)

d) Figure 3. Seismic action models

the arch were not at the same height, and the structure was fixed on a inc\ined plane. If the back-fill is acting on the structure the problem is quite complex. Consider a voussoir arch subject to a horizontal negative acceleration -x g . Each voussoir is subjected to the inertial force due to its own mass, acting at the center point of the voussoir. Four models (Fig. 3) are assumed to simulate the structure - back-fill interaction: MI (Fig. 3a): each voussoir on the left is subjected to the inertial force due to an horizontal strip of the back-fill, and acting at its center point. The length ofthis strip is assumed to be equal to the distance between the arch center line and the vertical line passing through the left springing ofthe arch. The

back-fill on the right tends to separate trom the arch, because of its inertial forces. As a result the right half structure is subject to vertical loads and own inertial forces due to its own mass only. M2 (Fig. 3b): the left half arch is loaded as in the model MI. The back-fill on the right is supposed to be attached to the structure. As a result the voussoir of the right half arch are subjected to the inertial forces due to an horizontal strip of the back-fill and acting at its center point. The length ofthis strip is assumed to be equal to the distance between the center line and the vertical line passing through the right springing. M3 (Fig. 3c): each voussoir is subjected to an horizontal force equal to the vertical loads acting onit. 126

/0/

3.0

C

~--------- - --

t:;j 0.5

--MI

Parabolic arch flL = 0.2 y= 0.5

- - - M2

Parabolic Arch sIL = 0.035

y=O.5

- - - - M3

-

2.0

h=O

----M4

,-< 1.0

B

.......::-:.:..

.----

o1

A

- -- -.: :"_-:_'- :.--- - --~ 0.01

i

0.04

0.01

0.07

0.1

0.1

sIL

I-~i

0.2

~

3.0

"i'D

Circular arch fIL = 0.2 y= 0.5

:1­

Circular Arch sIL = 0.035 Y= 0.5

----M3

2.0

t:;j 05

1

- - M2

0.5

0.4

h=O

----M4

.-
O,{t(n),L\(n)öu} ~ 0, ~

.L

....!.

A masonry arch that suffers a small spreading

between its abutments

Fig.2

Both examined cases are a11 examples of masonry settled structures. We want to inquire into stress and strain changes occurring in masonry structures when slighty uneven settlements occur in their foundations. First, let us consider the masonry structure before the settlement, at a given admissible equilibrium state under the action of the loads q. The structure will transmit forces to its foundation.

°'v'öuE1'1(2)

Condi tions (I) and (2) are necessary and sufficient to the admissible equilibrium state.

134

Let us consider also the part of the foundation structure that will suffer the settlement: for instance, the central pier of the bridge of Fig. 1 or the abutment of the arch of Fig.2. Let Ilr be the reaction transferred f rom this part of foundation to the overstructure. According to the previous definition, Il is the reaction load factor, an useful parameter to discuss equilibrium of the system. To put in evidence the action of this reaction upon the structure, we can remove the constraint whose reaction is just Ilr. Arelease has been thus allowed at the foundation of the structure. The released structuraI system will be loaded by the loads q and the reaction Ilr, this last acting along the release direction.The remaining part of the foundation reactions, that don't work along the release, is indicated as R . The released system is at an admissible cquilibrium state under the extemal forces q and Ilr. This state will be caIled "state /.l ". Consequently, it Joes exist in the structure an internal compatible stress state 0, i.e. without tensile stresses, in cquilibrium with the given loads. Putting in evidence the dependence of the reaction factor Il with the staticaIly admissible stress rleld, we call "statically admissible" the so defined reactionfactor Il = Il(O), that is a suitable function of the corresponding staticaIly admissible stress state o. For instance, with reference to the arch of Fig. 2, ünce that apressure curve 0, internal to the arch and runicolar of the loads q, has been given, the thrust acting at the abutments is completely defined. Thus, at the state /.l we have:

Equilibrium: The virtual work equation (1) holds. Thus, putting in evidence the virtual work of the reaction Ilr, we have, < ={t·>,~ öu}+ Il + + < q,öu >

(3)

. Compatibility: lnequalities (2) applied to the stress state 0 give 5 0, {t,~ÖU}+ ~ 0, of the reaction r is not" apriori" defined. By graduaIly changing stresses inside the structure assigning corresponding lower values to Il, we gradually change the reaction Ilr transmitted by the roundation to the structure. At least for a first stage, the admissible equilibrium will be saved. By gradually reducing the reaction factor Il, a

\'a1ue Ils of Il is met at which the structure settles and the settlement mechanism state [(Corno, 1995,1996) will be attained. The corresponding statically compatible stresses will be now Os. The structure will begin to displace along the settlement mechanism Vs with "frozen" stresses Os. Let us analyse now the settlement state of the structure. At this peculiar mechanism state, all the three conditions of equilibrium, compatibility and mechanism will be satisfied. We have:

- Equilibrium: = {t~n>,~öu}+ Ils+ + < q,öu >

(5)

- Compatibility: 5 0, {t~n>,~ÖU};:::

°

(6)

- Mechanism: Along the mechanism v s we have = 0,

0, thesettlementreactionfactor IAs(os, vs) is the unique reaction factor satisfying conditions of equilibrium, compatibility and settlement mechanism. We concIude that the settlement reaction factor Ils(os, vs) is the maximum among all the kinematicallyadmissible reaction factors !1(v) and

(15)

expressing equality between the active work of the loads q and the resisting work lA(v) of the reaction lA(v)r along the settlement v . From equilibrium and compatibility conditions at the settlement state ms, we get - {~),Li (n)öu} - = lAs + < q,ÖU >

(17)

Thus, according to the assumption (9) and therefore with the thrust r resi sting against the loads q , i.e.with < 0 , we get

(12)

°

!1(V) + < q,v> =

°

Subtraction of equality (15) from inequality (17) gives

Subtracting from this inequality the settlement mechanism equality (8) gives (IA(0) - IAs)

:S

The settlement reaction factor IAs(os, vs) cannot be

(11)

IA(O)+

lAs + < q,v>

= lA(o)

+

o~

Thus, with öu = v, taking into account eq.( 15) at the state ms gives

Statically and kinematically admissible settlement

reaction factors

Fig.3

(16) 136

minImum arnong all the statically admissible reaction /actors 1-1-(0) (Fig.3).

This value represents the vertical reaction of the loundation of the settled central pier of the bridge.

An example

REFERENCES

Fig. 4 gives a sketch of a two spans rnasonry bridge. The width of the piers is a and the span length is 4a. The load, which we assurne to be uniforrnly distributed along the spans, is equal to q. The weight of the single pier is qa and the total weight of the bridge is 14qa. We assurne that the central pier undergoes a vertical settlement. A settlement mechanism with a generic position of the span hinge, defined by the unknown abscissa x, is sketched in Fig. 4 . Here x is the distance between the absolute rotation center of the span and the span hinge (0 ~ x ~ 3 a ). Other mechanisms, with the internal hinge in the pier in place of the hinge located at the intrados of the seetion connecting the pier with the span, are not significant. [p))) ))))

Corno, M. 1992. On the equilibrium and collapse of masonry structures. Meccanica 27 Netherland: Kluwer Acad. Publ. Corno, M.1995. Mechanism states in Masonry Bodies, in Meccanica delle Strutture Murarie, A.I.A.S ., Quademo n.2. Corno, M. 1996. On the role played by Settlements in the Statics of Masonry Monuments, atti dei Convegno "Geotechnical Engineering for the Preservation of Monuments and Historie Sites" Napoli, 3-4 Oet. 1996, ed. Balkema. Corno, M. 1996. Multiparameter Loading and Settlments in Statics of Masonry Structures, in ..Atti dei Convegno" Meccanica delle Murature tra teoriaeprogetto ", Messina 18-20 Sept. 1996, ed. Pitagora, Bologna. Coulomb, C.A. 1821. Essai sur une application des regles ... " Memoires de Mathematique & de Physique, presentes a I 'Acadernie Royale des Sciences, vol.7, 1773, pp.343-382, Paris (1776», reprinted in Theorie des machines simples., Paris. Couplet, P. 1729. De la poussee des voutes, Histoire de l'Acad. Royale des Seiences, Paris. Heyman, J. 1966. The stone skeleton. Int. Journ. Solids and Struct., 2. Heyrnan, J. 1982. The safety of masonry arches, Int.J.Mech. Sei., Pergamon Press, Vol.l1. Heyrnan,1. 1982. The masonry arch, Ellis Horwood Limited, Chichester, England. Hooke, R. 1931. A description 0/ helioscopes And some other instruments, London, 1675, See Gunther, R.T., Early Science in Oxford, vol.8. Kooharian, A. 1953. Limit Analysis of voussoir (segmental) and concrete arches, Proc. Am. Concrete Inst. 89. La Hire, P. De 1712. Sur la construction des voutes dans les edifices, Memoires de l'Academie des Seiences, Paris. Prager, W. 1959. An introduction to Plasticity, Addison- Wesley, Reading, Mass.

/ I r l l l l l ll"lm..

~~I:

.. g

g

Z

"4-1

9

10

4

A

V I.

AG'\]

A two spans rnasonry bridge that settles

at its centraJ pier

Fig.4

To obtain the vertical reaction of the settled central pier, we can use the kinematical approach by cvaluating flr, by means (18), as the maximum reaction among the kinematically admissible ones. According to the assurned mechanism, with q the span rotation angle, we have = q (-3a 2 - x 2

+ 8ax), fl(v) < r, v >

=- I-' r xq

and ~1(V) r = q(- 3a 2 /x - x

+ 8a).

By varying x in the interval (0,3 a 1the maximum of ~l r is attained where d (I-' r )/ dx = o.

Thus we get x = a./3 and (~r)s

=(~r)max = 2qa (4 -

'/3) '" 4,54 qa. 137

Arch Bridges, Sinopo/i (ed.)© 1998 Tay/or & Francis,/SBN 90 5809 012 4

An upper bound analysis for the strength assessment of masonry arch bridges A.EAshour& s.WGarrity Department ofCivil and Environmental Engineering, University ofBradford, UK

ABSTRACT: A numerical method of estimating the strength of masonry arches is presented. The method is based on a mechanism analysis of the arch at collapse with the failure mode idealised as an assemblage of rigid blocks separated by zones of displacement discontinuity; the masonry is assumed to be rigid-perfectly plastic. The shape and position of the fracture lines and the displacement of the rigid blocks of masonry are the variables in the energy equation. Minimisation of the predicted collapse load produces the optimum shape and position of the fracture lines. Comparisons of the predicted collapse loads and crack patterns at failure show good agreement with the results obtained from model tests in the laboratory. 1 INTRODUCTION The brick or stone masonry arch was used by many ancient civilisations as a structural form and, by the Middle Ages, the requisite construction techniques and experience had spread to many countries. Since then, many thousands of masonry arches have been built. In particular, numerous bridges and viaducts were constructed to aid the development of strategically important settlements and communities into what have become the towns and cities of the modem world. By the early part of this century, the use of brick and stone masonry for bridge construction declined in favour of reinforced concrete, cast iron, wrought iron and steel construction. In spite of this decline, there are still many thousands of brick or stone masonry arch bridges, tunnel linings and viaducts to be found throughout Europe. In the UK alone, it is estimated that there are in the order of 70,000 masonry arch spans alm ost all of which are at least 100 years old. Furthermore, many of these structures are still in use and form the heart of the nation's transportation infrastructure as weIl as being an important part ofthe UK's industrial heritage. 1.1 Strength Assessment and Strengthening 01 Masonry Arch Bridges

As is the case in many other countries, most rail, highway and canal bridges in the UK are subjected to regular visual inspections and more thorough principal inspections as part of a bridge management

strategy. Although many masonry arch bridges have been found to be in extremely good condition, given their age, it is not surprising that a variety of defects have been identified. These include:- arch ring separation; diagonal cracking and hinging of the arch ring; cracks in the abutments and piers; leaning and bulging wingwalls and spandrei walls; spandrei wall separation; dropped voussoirs; leached mortar joints and frost damage of the masonry units (Sowden 1990, Page et al. 1991, Page 1993). To complicate matters further, many arch bridges have been widened or strengthened using materials or forms of construction that are different from those used in the original construction. At present, standard public highway live loading in the UK comprises a maximum axle loading of 38 tonnes. As part of the gradual harmonisation of the European Union member states, a European directive has been issued to increase the maximum public highway live loading to 40 tonnes. There is a possibility that this upper limit may be increased to 44 tonnes in the future. As a result, in recent years, many engineers in the UK have been engaged in a major programme of bridge strength assessment and repair. As part of this work, a number of strength assessment methods have been developed and used for masonry arch bridges; these are considered in more detail, later. In addition, a variety of repair methods has been used including grouting, pressure pointing, partial reconstruction, retro-reinforcement, saddling, lining ofthe intrados or soffit, stitching and the use of spandrei wall ties (Sowden 1990, Welch 1995, Garrity 1995a).

139

1.2 Design 0/ New Masonry Arch Bridges

that will not only be costly but might also impair the long term performance of the bridge (MeIbourne 1991). Worse still, a very conservative method of strength assessment that yields a considerable underestimate of the strength of a bridge, could lead to the specification of very substantial, unsightly repairs or even demolition. When designing new masonry arch bridges, the use of a very conservative method of analysis could result in the specification of forms of construction that would be prohibitively expensive to build. Consequently, it is very unlikely that many engineers will choose to design new masonry arch bridges even though the high initial costs of construction will be offset in the long-term by low maintenance costs.

A critical review of existing highway structures in the UK (Garrity 1995b) indicated that clay brick masonry has considerable potential as a durable material for new highway structures including short span arch bridges. This view is gaining support from an increasing number of bridge engineers in the UK, particularly those engaged in the management of the nation's bridge stock who have found that the maintenance costs of stone and brick masonry arch bridges are, in general, significantly less than modem steel and concrete alternatives (Halsall et al 1994). This experience led, in part, to the construction in 1993 of Kimbolton Butts Bridge which is thought to be the first all-new clay brick arch bridge built in the UK since the turn ofthe century (Garrity et al 1995). The growing interest in the use of masonry arches for new bridge construction is reflected in the commissioning of a new design guide and advice note for the design of new unreinforced masonry or concrete arch bridges by the UK Department of Transport (Mair 1995) and the publication of design guidance by the UK Brick Development Association (Cox et al 1996).

2.2 Review 0/ Methods

2 METHODS OF ANALYSIS OF MASONRY

ARCHES

2.1 Basic Requirements

Numerous tests on model and full-scale arches in the laboratory (Royles et al 1991, Melbourne et al 1995, to name a few) and redundant arches in the field (Page 1993) have contributed a great deal to the understanding of the behaviour of masonry arch bridges. A number of different modes of failure have been identified. Of these, the 4-hinge collapse mechanism and snap-through failures are the most common. In addition, it is now weil documented that the load carrying capacity of a masonry arch bridge is influenced by the degree of continuity between the spandreI walls and the arch ring; the restraining effect of wingwalls; the interaction between the arch ring, the spandreI walls and the fill material and the structural integrity of the arch ring. Consequently, it is evident that defects such as spandreI wall separation, ring separation and cracking of the arch ring, are also likely to influence the strength of an arch bridge. Hence, for maximum economy, the methods of analysis used for strength assessment or for the design of a new arch bridge or the repairs for an existing structure, should take into account any likely interaction between the different elements of construction and, where appropriate, any defects. Failure to model the behaviour with sufficient realism could, in some cases, lead to repair works

0/ Analysis

A number of different methods of analysis have been developed for masonry arch bridges (Hughes et al 1997). Of these, the "cracking-elastic" and the "mechanism" methods (Heyman 1982, Gilbert et al. 1994, Boothby 1995) are the most versatile. Consider the cracking-elastic method first; this is generally based on a finite element approach. Experience shows that the method becomes computationally very complex and expensive if attempting to model anything other than just the undamaged arch ring and the fill material of a single span bridge. It is, however, likely to be useful for modelling the in­ service behaviour of a structure up to the onset of first cracking provided that a realistic constitutive model is used. The mechanism or rigid-block method of analysis is likely to be the better of the two methods of analysis for strength assessment as it offers greater versatility with less computational complexity and expense. In particular, it has been used to model arch ring separation (MeIbourne et al. 1995) and it should also be possible to model multi-span construction, the effects of spandreI walls and wingwalls, a range of defects and different forms of repair. This paper introduces a numerical technique for assessing the strength of a single-span masonry arch based on a rigid-block method of analysis.

140

3 MATERIAL MODELLING The narrow failure zones of masonry arches can reasonably be modelIed to be in astate of plane stress. Modified Coulomb failure criteria (May et al. 1986) with tension cut-off, as shown in Fig. 1, is considered as the failure criteria for masonry.

(1,

and

(12

=Principal stresses

E,

and

E:2

=Principal Strains

(13

r

(12

=0 rl

(1,

E, (1pc

,

...

(1pt

E2

(E,. E2) \...

(1pc

_\

Figure 1. Assumed failure surface for masonry (May et al. 1986)

The behaviour of masonry is characterised by strain softening not by the yield plateau that would normally be required to apply the plastic theory. To account for this behaviour, the masonry strength is reduced by applying an effectiveness factor. Hence, the effective plastic compressive strength apo is given by:

(J'pc = vmfc

4 PROPOSED METHOD OF ANALYSIS 4.1 Mechanism ofFailure

(1)

where!c is the brickwork compressive strength and Vm is the effectiveness factor for compression strength. Similarly, the plastic tensile strength apt of masonry is given by:­

a pt = Pmf,

quantitative predictions. In practice, the effectiveness factor is calculated for a structure by calibrating the theoretical calculated capacity against experimental results.

(2)

where}; is the tensile strength of masonry (20 {O.O­ 0.1} !c) and Pm is the effectiveness factor for tensile strength. As the ductility of masonry in tension is very limited, Pm will be very smalI. The reason for introducing these factors is to account for the Iimited ductility of masonry and to obtain reasonable

141

The experimental tests referred to earlier show that, at collapse, the arch ring will generally fail in a hinged mode as shown in Fig. 2. This mode may be idealised as an assemblage of five rigid blocks separated by four yield Iines. Rigid blocks I and V, representing the abutments of a single span bridge, are fixed. The other three rigid blocks, II, III and IV, rotate about instantaneous centres. Although, this paper is based on the aforementioned 4-hinge collapse mechanism, the technique described can also be used to modelother forms of failure such as snap-through failures as weil as a variety of defects that could markedly reduce the load carrying capacity of a masonry arch bridge.

Rigid Block III II

Rigid Block IV

,P

~\dLi~

Figure 2. Four hinge collapse mechanism

4.2 1nternal Energy Dissipation

At collapse, a "yield" line or plastic hinge will form between each two rigid blocks. In the general case, all the deformations are located in the yield line, that is, an idealisation of a narrow discontinuity zone with many criss-crossing cracks and crushing zones. The shape of the yield line and thedisplacements of the rigid blocks are the unknowns and will be obtained by minimising the collapse load of the arch ring predicted from the energy equation. The numerical technique presented in this paper is based on that developed to predict the load capacity of reinforced concrete deep beams (Ashour et al. 1994) with modifications to accommodate the material properties ofmasonry. The internal energy dissipated by masonry along a yield line I separating the two rigid blocks 1 and 11, as shown in Fig. 3(a), is to be ca1culated. The displacement components of rigid block 1 referred to the origin 0 of the global axes are UI (horizontal), VI (vertical) and q (rotational). Similarly, the corresponding displacement components of rigid block II are Uff, Vff and .aff . The relative displacements across the yield line I referred to the origin 0 are:­ u, =Uff-UI V, = Vff -VI

(3)

7],=n ff -n l

The position ofthe instantaneous centre ofrelative rotation 0' is given by:­ v/ x/=­ 7]/

y/

=--:;;; u/

The yield line I is divided into N segments as shown in Fig. 3(a). The radial co-ordinates of different stations along the yield line are fixed, and the angular co-ordinates Bi of different stations are varied and will be obtained after minimising the collapse load predicted by the energy equation of the arch ring. The relative displacement 6; ofthe segment "i" is :­

8 i = r,7]i

(5)

where ri is the distance between the instantaneous centre of relative rotation 0' and the midpoint of the segment "i" as shown in Fig. 3(b). If the local co-ordinate system shown in Fig. 4(a) is considered, the corresponding plastic strain rates are:­

.

8

n

~

c' = --1. cos y

c; =0

(6)

.

8.

nl

2~

c' = - ' siny

where ~ is the width of the narrow yielded zone between the two rigid blocks 1 and 11 and y is the angle between the relative displacement 6; and the yield line normal n as shown in Fig. 4(b). The principal strains are:­

8 c;. =2~ - ' (l+cosy) .

8

(7)

c~ = - 2~ (l-cosy)

(4)

The energy dissipation W per unit volume is given by:­ 142

Rigid. Block I

I..

oL

cb

v '

I

-Id

xl

6.t

I"

n

a). Yield line between adjacent rigid blocks

b). Segment "j" of the yield line

Figure 3. Details oftypical yield or fracture line W = O",sj + 0"2si

(8)

(11)

WJ =Wili

and the dissipation Wi per unit length measured in the direction ofthe t-axis along the yield line is:­

W,=MW

where ti is the length of the segment i. The total energy dissipated w" in the masonry over the entire length ofthe yield line is:­

w" = LW; N

= ßb(O"IS; + 0" 2S~)

(9)

where b is the dimension perpendicular to the (n-t) plane. The significant possible position of stresses on the yield surface is at the corner A, see Fig. 1. For point A, substituting crj=crpt and cr2=crpc' the dissipation is given by:­

M

M

2ß

2ß

(12)

Ifthe number ofyield lines is m, then the total energy dissipated W/ is:­ m

W/ = L~

W, = 0" p t - ' (1 +cosy)+ O"pc-' (l-cosy) = M· 2~ [ O"pt(J+cosY}+O"pc(J-cosy} ]

;=1

= F(Oi , UmYm"(}m}

(13)

1=1

4.3 Externat Work Done

(10)

The external work done by the external loads is calculated from:­

The above equation (10) for energy dissipation is valid for both shear-tension (-1CI2~y~1CI2) and shear­ compression (1CI2~y~31C12) states. The energy dissipated W~ by the masonry in segment j of the yield line is given by:­

143

WE

= A,

NB NPL L

L (PjvVmj + PjuUmj)

(14)

m=1 j=1

where Pp, and Pi. are the vertical and horizontal components of the plane external load at joint j, Vmj

"I

"" 0 and K> 0, then the load {AP, AP2 ... AP m } induces the same Sn and a mechanism with the same hinges with displacements {KU, KU 2 •.• KU m } where A and K are arbitrary positive constants. It may be shown that if a load {P"} induces an admissible state {P", N", M"} then for any mechanism, with corresponding load displacements {U'}, the virtual work is non-positive LP;U~ ::; O.

cr, = N(s) + M(s)y A I

E, =Eo(S)+W(s)y;

(3)

The equilibrium of the arch is determined by three redundants, the horizontal thrust H, the shear force Z and moment X which act at the elastic centroid of the arch (Fig. 2a). These determine together with the non-redundant N°, MO the normal force N and momentM

N(s)=N"-HcoslJ-ZsinlJ;

f crdA M = f crydA.

N=

A

M(s)=Mo-Hz-Zx+X ;

(4)

A

The elastic energy W can be expressed as stress energy W cr by astate of admissible equilibrium AE< or as strain energy W E by an admissible kinematic state AKe of the monolithic arch. Overlooking the effects of trans verse stresses cry and shear stresses "t we obtain from (4)

(2)

Equality holds only for the mechamsm induced by the collapse load {pn}, i.e. if {U'} = {Un} . Formula (2) can be interpreted geometrically, introducing the load space R m and the dual load displacement space R m,. Condition (2) and the multiplicity rule then imply that the set of loads P, to which corresponds admissible equilibrium, constitutes the convex cone E(P) of stability [6]. The stable loads constitute the interior EO(P) of E(P) and the generatrices p n of the lateral surface of E(P) are orthogonal to the set of load displacements U n of the collapse mechanism. These Un in turn constitute the generatrices of the convex cone :='(U) of detachment. As an antithesis

W =.!.(fN2dS+fM2dSJ

a 2l EA EI

W, =

±f(EAe~

(5)

+ EIri"l ~s

W cr is, because of (5), a positive definite quadratic form of the loads P and redundants. According to Castigliano's role the redundants can be determined by the partial derivatives aw = v . xe' aH

to the cone EO(P) of stable loads, the interior :=.0 (U) of :='(U) constitutes the cone of disintegration (Fig. 2c).

aWa = az

V

. zo'

aW a = ax co,

(6)

where v xe , Vze and co., are the mutual horizontal and vertical translations and rotation of the abutments, respectively. Since V xe = V ze = co., = 0 the above derivatives are zero, which implies that W cr attains a minimum. This minimum is a qudratic form, and it satisfies Clapeyron' s work equality. Therefore

2. THE MONOLITHIC CLAMPED ELASTIC ARCH The voussoir arch is transformed into a monolithic elastic arch if we retain conditions a) of section 1. and drop all restrictions concerning tensile stresses. The displacements are continuous and differentiable. We base the analyses of the arch on the technical theory of elastic eccentrically loaded straight beams and on Navier's assumption that every cross-section of the arch remains plane. This implies that the longitudinal strain e and the normal stress cr can be expressed by

W=.!."" a 2w pp 2LLapap , J ,

1

W=-"PU 2L ' ,

J

a2 w

aPjap = K jj

(7)

j

(1')

The mInImum property of W can be given a geometrical interpretation by the concept of the stiffness D. This we define as the ratio of the load

148

plane r i bisects the gap, represented by the dilatation vector Yn. The state of stress and strain {O", u} induced by some load {P} can be decomposed

intensity 1P 1(for instance norm of loads Pi in Rm) to the load displacement U p = (LPiUi)/1 P I. According to Clapeyron' s equation

[p[

[p[2

[p[2

D=-=--=U p I,PiU i 2W

(8)

where {O"e, ue} corresponds to a monolithic elastic arch and {O"h, Uh} is astate of eigenstress induced by the edge effect of the opening gaps of the joints. In addition to conditions (i-iv) most of the characteristics of the monolithic structure rernain valid with some modifications [4]. The stress energy W" is not a quadratic form, but a homogeneous function of second degree of loads and redundants. Castigliano's rule and MaxweIl's rule expressed by the derivatives of W (eqn. 6), Clapeyrons equation (7') and the expressions conceming the stiffness (9), (10) remain valid. At given loads {P} the stress energy W" can be expressed as the surn of two orthogonal parts

Hence, D can be expressed either by 1pI and W"" corresponding to a equilibrium state {P, o""}, or by W' E corresponding to a displacement state {u' ,c' } and U'p

~~

Da = 2W;

D' E

2W'

= (U~;2

(9)

For the actual stiffness D of the solution of the elastic problem we get the bounds [4] D:

:0;

(10)

D:O; D:

The stiffness vector {Li! Li2 ... Li m }T is then defined by

Li i

p.!.

= [~[ D2;

.!.

[Li[ = D 2

(11)

Substituting Pi = 1P kVD!12 and LPiUi = 1P 12 I D into (7) we obtain the stiffness surface F(Li) F(Li)

a-2 w =I , -aPiaP L i L i -1 = 0 , J j

(12)

Because the second partial derivatives of the quadratic form W are constant elements K ij of a matrix, F(Li) represents in R m an ellipsoid EM, called the stiffness ellipsoid.

(13)

{O", u}= {O"e, u.}+ {O"h' u h }

W(a)

=W,(aJ + Wh(a h)

(14)

because {O"h} is astate of eigenstress and solei y {O"e} balances the load. The multiplicity rule of section I applies also to the voussoir arch: If the load {P} induces astate {O", u}, then the load {AP}, where A > 0, induces astate {AO", AU} with unchanged contact interfaces at the joints. In order to adapt the treatment of the voussoir arch to that of the monolithic arch, we consider an assembly of two adjacent voussoir halves (Fig. tal. The elongation Liu(y) of the assembly is, because of condition (iv), expressed by Liu, (y)

=u

y

-

u Y_ 1

= V + roy

(15)

where v is the extension of the centroid axis and ro denotes the mutual rotation of the end faces AY.I and A v•

3. CONTACT MECHANICS OF THE ELASTIC VOUSSOIR ARCH

We apply the principle of virtual work to the kinematic part {u, c, y} of {O", u} and states {O"' e, c' e} and (0""" c",) induced by a constant force N' = 1 and constant M" = 1 respectively. According to equation (3) there applies

Webase the analysis of the arch on sections 1,2 but we modify Navier's assumption. Thus i) No contact slidings occur at the joint, y, = 0; Yn ~ 0 ii) The joints don't transfer tensile stresses O"s :0; 0, but the voussoirs have infinite strength. iii) The shear force Q(s) is small compared with N(s): 1Q I« 1N 1 iv) The middle section of the voussoir and the contact area r i at the joint remain plane. This contact

0":. = A;

, Y. 0" sc =-, I

149

,

CSC

. c' =-~

= EA '

ye

EA

,,"=.1...; c~Ye = -vy ­ sc EI EI

Co

(16)

a)

, "

"

............

/'

,

I

I I I

I

I

I

v-1

V2

...........\

v

V2

,,

~~

.............

...

"

\ \\

~~

Q

"

\

\

\

\

\

I

\

\

\ \ \

I

~

..................

..............................

"

ly

b)

y.

Wh

YP km

= Ir (km) I

r=Vh+(OhY

kph

o+----Ly 0; Yh cU h Ph = - = - - ; k k11h

I Nie

1 OOh U h =-:;-­

(19)

20m

y, k

11h uh

p, = - - = ­

H -7I

C/

IflmlS!

then

0h,1)h,Uh

(3 + r(2 -Im I) Im I)Oh 1-(lm l-2)2

Iuhl==

(4 -Iml+ r(2 -lml»Oh

1-(l m l-2)2

(21)

I

=0

and

if

kl then 0h' Th ,Iu h1-7 00. In order to extract

W

the edge effects Vh, Olt" Wh and Yh, y. for a voussoir with variable N, M we resort to the field {u, €, y} of symmetrically loaded (Q = 0) straight voussoirs where at the joints ~, = O. Applying Clapeyrons rule to the eccentric load PV • 1 = Pv = lNi land corresponding state {Uh} with ~U(Yp)h = Wh i ,we get

1 1 L(N 2 M 2 } (N i )2d i (22) =-f - + - s+- I--o (m ,A) ° 2 EA EI 2 i EA h 0

The solution with respect to the redundants may be obtained either, by minimizing W n, the system is eonsituted by m+n linear equations with m+n unknown quantities. The disloeations (.1} are quantities similar to the extemal fore es in the theory of struetures. Di Pasquale (1996) raised this questions: "Poiehe le solleeitazioni {X} dipendono da (F) e da {.1}, e possibile assegnare le eomponenti di .1 in modo ehe le eomponenti di {X} verifiehino partieolari eondizioni?" Colonnetti already answered to this question with his proposition (§ 2 ). ln the system of linear equations whieh represents the problem, it is known that the elasto-kinematie equations may be substituted with a minimum eondition, for example the minimum of the strain energy funetional, so modifying the solving system:

l

Figure I. The truss structure analyzed.

The fietitious strain energy in presenee of disloeations imparted on the trusses 1,2,3 is: C= ±K(X I2 +X 22 +X 32 +xi +X S2 )

(4)

-X I.1 I -X 2 .1 2 -X3.13 where KI=K2=K3=K4=Ks=K, i.e. in the hypothesis of trusses with equal geometrie and meehanie eharaeteristics. The eondition of stationariness of the funeional leads to:

X _

}-

X2 X

(2)

sub [A]{X}+{F}=O

165

- 11.1} + 3-fi.1 2 - 4.13 - 3-fiFK 2lK

=_ --fiL1} -

_ 3­

5.1 2 + -fiL1 3 + 2FK 7K

-4L1} + 3-fiL1 2 -11.1 3 + 3-fiFK

(5a)

X4

=

-Li l (3.J6 -7..fi) - Li 2 6..J3

--'-----~'-------=----

42K

+

-Li 3 (7..fi + 3.J6) - 6..J3FK

+ ----''-'-------'---­ 42K

Xs =

-Li I (-7..fi +3.J6)-6..J3Li 2 _ - ' - -_ _-C......_ _ +

(5b)

42K

considering the structure made up only with the two active trusses. Therefore the problem is solved in the hypothesis that the trusses may res ist only against tensile stresses. Finally we might evaluate the displacements: it may be noticed that the horizontal one is indeterrninate (for the considerations about this problem see Di Pasquale (1996».

Li 3 (7..fi - 3.J6) - 6..J3FK

+ ---''---------''----­ 42K

which express the stresses in the trusses of the structure deriving by the simultaneous application of external forces and dislocations. This result allows us to modify "ad arte" the stress state to change where oported to respond to stated requirements: for example to reduce the maximum sagitta of a beam or to elirninate those zones subjected to a stress state not adrnissible with the mechanical charateristic of the employed material. 3.1 Unilateral constraints If we form the hypothesis that the truss structure of the Fig.l is made by unilateral material, for example a material unable to resist against compressive stresses, i.e. a thread structure, we may try to find out which are the dislocations generating in the compresses trusses an adrnissible stress state, that is Xi2::0. The stresses in the trusses subjected only to extemal forces, are: Xl =X 3 =-0.202F X2

X 4 = X s = 0.247F

= -Q.286F

(6)

We may observe that trusses 1, 2, 3 are subjected to compressive stresses and so to neutralize the not adrnissible stresses we introduce in the three trusses three dislocations Li\,Li 2 ,Li 3 which give Xi 2::0 (i=I ,...,3). So the problem to solve becomes: {

Xl =X3 =0 X 2 =0

4 SOMIGLIANA DISLOCATIONS FOR THE CALCULATION OF MASONRY STRUCTURES Di Pasquale (1997) introduces the extension of the use of the Somigliana dislocations to render the fractured zones in a masonry arch caused by the no tensile stress resistance. Under the hypothesis of the validity of the conservation of plane sections, he demonstrates the possibility insert in a N.T.M. arch a constraint able to neutralize the inadmissible stresses. The change in the shape of the voussoir may be thought generated by the insertion of three elementary dislocations corresponding to the necessary volumetric variation: Lin the lenght variation caused by the normal stress, Lit and Lim shape variation caused by the sliding due to shear force and by the rotation due to the bending moment. These parameters define entirely the dislocation. It is important to underline that if the structure in which we insert the wedge is statically deterrninated, the constraint obtained acts only on the material confined between the two sides of the voussoir. On the contrary if the structure is statically indeterrninated the relative displacements of the sides of the voussoir generate a further stress state which causes also elastic deformations. The conditions on the neutralizing of tensile stresses let us to obtaine the parameters of the dislocation which doesn't cross the whole section:

f = h-3u

1 = Li 3 = -..fiFK 3

2 Li 2 = -FK 3

(8)

The wedge necessary to neutralize the positive stress coincides with the crack which the arch made up with no-tension resistant material would show.

corresponding to following the stress in the structure

X l =X 2 =X 3 =0

X 4 = X s = 0,5773

(10)

Es

which leads to: Li l

2N h h-3u A (3uf

= -s - - ­

(7)

s

4.1 Beam with straight axis Let's consider a beam with straight axis fixed at its ends, of lenght four times its height and subjected to a concentrate load condition Papplied in the middle. In this case where only bending moment and shear force are present, in order to obtain the crack

(9)

It is worth to underline that this solutions coincides with the one that we rnight obtain 166

parameters we need to introduce a Volterra dislocation such to generate compressive stress in the structure. The initial state is the following, obtained with the insertion of a Volterra dislocation of value wl = 2,5Ph/EA.

A.

c''''

_

,...'"'

,,"eC")

I

/!,

K

~

w

-_;::.'~:' ,

.. ....

~

u = {(u. -"-2)' n n 0

.

....-:.~~..~?~~I,;-

Figure 2.(a). Controlled demolition of a chimney.

for for

(u. - "-2)' n > 0 (u, -"-2) . n:s; 0

(1)

is applied in order to define which parts of the surfaces are in contact as weil as to determine the intensity of tractions arising from contact. Two contacting bodies in motion can also experience some relative tangential displacement which can be expressed as follows

=(u. -"-2).t

U,

(2)

where t is the vector in the plane previously defined by its normal n, while UI and U2 represent the displacements of the points PI and P 2 respectively (Figure 3).

r;

.---

.-­ -~

=­

.:

~I

Figure 2.(b). Silo flow.

Figure 3. Contact between two bodies .

....

The decomposition of the total relative displacement between the two points on interacting boundaries determines a convenient decomposition of the total contact traction t C as follows

2.3 Contact models

t

The numerical techniques for simulating both frictional sliding and fracturing result from the latest developments in continuum based computational plasticity [6,9,19] . Trus paper concentrates on a solution method for coupling of polygonal and

C

= tC·n+tc · t= t:(un)+t~(u,)

In view of the finite element method applied to describe the behaviour of material, the resultant force transmitted surface to another through the area of 175

(3)

which is the solid from one contact is

obtained by integrating the contact tractions as follows

P(u)=

I~e) (u)= e

I[ f e

N1

2.00

Figure 9: Pointed arch geometry

The situation is the opposite if the quarter span load (E2 conditions) is considered: in this case, the limit load is the 16% and the 24% of the self weight for the pointed arch and the reference geometry, respectively. The results corresponding to the E3 and E4 conditions can be interpreted in a similar way: in fact, when the arch supports are moved outwards the horizontal support reaction reduces by the 11 % and the 7% of the "at rest" value, for the pointed and the reference arches respectively . On the contrary, when the arch supports are moved inwards, the support reaction can be increased by the 17% for the reference arch and only by the 10% for the pointed one.

iCJ'Vd

Bae kfil/ finit e elem ents

63 kN 114 kN

113 kN 115kN 32 kN m

32kN m

N/ 297 kN I

,,

!/

----,

6.9 m Nod e num ber

M Mom ent

N Thru st

@

6.m/

Ag .6 Res u/ts of Ela stic

ana lys is.

N

.308 kN

200

60 M kNm 40

ji

7_

M kNm

A

100

"­

23 20

-"

.

V,

\ 975

800

r--

1000

200

N kN

Fig .7 Arc h mo me nt- thru st rela tion shi p.

!

j

:30, 8

! 977

400 600 800 N kN

Fig . 8 Pie r mo me nt - thru st re/a tion shi p.

.,

47 kNm

SiL1i Fig .9 Res u/ts of ana / Yes : with p/astic hing

i

N M 7. at Nodes 1,6 and 107 kNm < 115

1000

: 307 kN

210

(!J

Plas tie hing e

one at the bottom of the pier). However, if a fourth hinge forms in one of the arch spans prior to the formation ofall the necessary hinges, then a single span collapse of the arch would occur which mayaIso lead to the progressive collapse ofthe adjoining spans. Thus a multi-span arch bridge could collapse due to any number ofhinges between 4 and 7 depending on where they are located. The analyses and insertion of hinges should be continued until just prior to be insertion of the 'last' hinge which would cause the formation of a collapse mechanism (at which the solution matrix would become singular or nearly singular) for the bridge. During this process, if the vehicular loads applied at the 'critical' positions can be equilibrated by the internal forces, then the bridge would be deemed to have passed its assessment for that loading. 6

approached and can also be applied to multi-span arch bridges. In view of these advantages, the increased computational time due to manual interventions in assessing such structures should be considered a good investment particularly as this leads to a beUer understanding of their behaviour. REFERENCES I. Department ofTransport: Departmental Standard BD 21/93: The Assessment of Highway Bridges and Structures, 1993. 2. Department ofTransport: Departmental Advice Note BA 16/93: The Assessment ofHighway Bridges and Structures, 1993. 3. Department ofTransport: Departmental Standard BD 21184: The Assessment of Highway Bridges and Structures, 1984. 4. Department ofTransport : Departmental Advice Note BA 16/84: The Assessment ofHighway Bridges and Structures, 1984. 5. Pippard A J S: The Approximate Estimation of Safe Loads on Masonry Bridges, Civil Engineer in War, Institution of Civil Engineer, 1948. 6. Military Engineering Experimental Establishment: Classification (of Civil Bridges) by the Reconnaissance and Correlation Methods, Christchurch (MEXE), May 1963 . 7. STAAD III: Structural Analysis and Design Suite, Version 18, Research Engineers (Europe) Limited, Bristol, 1994.

EXAMPLE

The concepts described earlier were used in the interactive assessment of an old two span arch bridge in Richmond, Surrey shown in Figure 5. The equivalent factored axle loads of 63 and 114 kN per metre, corresponding to the 40 Tonnes vehicular loadings on the road are applied at the critical positions. Figure 6 indicates the elastic moment and thrust distributions and Figures 7 and 8 indicate the moment-thrust interaction capacities for arch and pier sections respectively. The moments of 62, 32 and 32 kNm at Nodes 1, 6 and 7, weil exceeded the 47, 23 and 23 kNm moment capacities indicated by Figure 7. If limitation of 'elastic' stress in the arch had been the criteria, the live load capacity ofthe bridge would have had to be restricted to the 7.5 Tonnes vehicular loadings only. Figure 9 indicates the results following the insertion of plastic hinges of 47, 23 and 23 kNm capacities at the Nodes I, 6 and 7 respectively. This confirms the capacity of the bridge to be adequate for the 40 Tonnes vehicles and justifies its present unrestricted use by all vehicles. Ifaxle loads had been even heavier, the next hinge would have formed at the foot of the pier, followed by the possibility of another hinge forming in the first span itself. 7

CONCLUSIONS

An interactive approach of masonry arch bridge

assessment, applying the classical plastic hinge and

development of collapse mechanisms concepts, is

presented here. This utilises the usual elastic analysis

programs for equations solving, incorporates non­

linearity by manually applying 'first principles' of

mechanism formation and allows control on the

'assumptions', 'criteria' and 'workings' ofthe solution

process. The approach reflects the significantly

increased arch capacities as mechanism conditions are

211

Arch Bridges, Sinopoli (ed.)© 1998 Taylor & Francis,lSBN 90 5809 012 4

Load capacity of multi-arch masonry bridges Climent Molins & Pere Roca Universitat Politecnica de Catalunya, Barcelona, Spain

ABSTRACT: This paper presents the application of a numerieal model specifically developed for the non­ linear analysis of masonry constructions to simulate the serviee and the ultimate response of multi-arch masonry bridges. The model allows to determine the ultimate load of the bridge taking into account most of the phenomena involved in the strength capacity of the structure, such as cracking in tension, yielding and crushing in compression and second order equilibrium. To illustrate the capacity of the model, two real examples of application are described, showing different failure modes with partial or complete development of hinges at the arches or at the piers. 1 INTRODUCTION

curved members with variable cross section, to simulate the service and the ultimate response of multi-arch masonry bridges. The model allows to simulate the response of bridges throughout a11 the loading process up to failure taking into account most of the phenomena involved in the strength capacity of the structure, such as cracking in tension, yielding and crushing in compression and second order equilibrium. The validation of the numerical model was made through the comparison of the experimental results of several tested single arch bridges with the analytieal results. Two real examples of application have been selected to be described in this paper. Both bridges are representative of a large amount of similar multi-arch masonry bridges nowadays in service in Spain. The first one, the Magarola bridge, located near Barcelona, is composed of five brick masonry barrel vaults having a span 20 meters long. The second example is the San Rafael bridge over the Gaudalquivir river in Cordoba, Spain. It is composed of eight mass concrete flat arches with span of 17 m. Both examples illustrate the ability of the model to deterrnine the load the capacity of multi-arch masonry structures through the simulation of failure modes whieh inc\ude the development of hinges at the arches or at the piers. Moreover, failures due to the crushing of the fabric previous to the complete generation of the theoretieal ultimate mechanisms are also accounted for.

Calculation methods based on the uItimate mechanism have shown their capability and practieal applicability to analyse single arch bridges. Particularly, some extended versions of the ultimate mechanism afford to approach complex effects such as the strength contribution of spandrei walls and infill, or to consider a limited compressive strength (Crisfield and Packham, 1989). However, their application to multi-arch and open spandrei bridges encounters important difficulties which often lead to the acceptance of some drastic simplifications, such as reducing the analysis to a single arch and thus ignoring the possible effects induced between the different arches. All these simplifications are required because of the difficulty to foresee the position of the line of thrust (or the collapsing mechanism) in the case of complex structures inc\uding a set of arches and piers. On the other hand, F.E. Method applied to multi-arch bridges requires a large amount of computer resources making its practical use difficult, specially in combination with appropriate constitutive equations to model masonry as fragile material. This paper presents the application of a numerical model specifieally developed for the nonlinear geometrie and material structural analysis of masonry constructions, consisting of

213

2 NUMERICAL METHOD All calculations presented in this paper were developed using a Generalised Matrix Formulation (GMF) for the study of spatial structures composed of curved, spatial members with variable cross section, specifically developed for the nonlinear geometrie and material analysis of skeletal masonry constructions. Nonlinear material behaviour is inc\uded by means of elastoplastie constitutive equations under shear and compressive stresses, while a linear-elastic perfectly brittle behaviour is assumed in tension. Nonlinear geometric effects caused by the imposition of the equilibrium condition upon the deformed configuration of the structure are considered, but assuming that the increments of both displacements and sectional rotations are moderately smalI. In order to account for the resisting contribution of the infill in arch bridges, an approach based on its discretisation into a system of equivalent linear elements is adopoted. This equivalent system is composed of aseries of tapered members -fill elements- with their axes parallel to the bridge platform, and another series of joint elements used to link the former to the extrados of the arch. An introduction to the method and its validation is presented in Roca et al. (1998). More details of the formulation of the numerieal model can be found in Molins & Roca (1998) and Molins (1996).

carried out a programme of tests on three large­ scale multi-span (each one of 3.00 m) briekwork arch bridges inc\uding slender piers. All tested models failed by generating hinged mechanisms involving the entire the bridge. In all cases, ultimate failure loads were lower than those recorded for single span bridges. They also observed that the critical loading point was not at quarter span, but c\oser to the crown and that the spandrei walls had a significant influence on the behaviour and strength of such bridges. In order to achieve a better understanding of the resisting response of multi-arch bridges, & Ponniah (1994) performed Prentiee experimental tests on aseries of double span arch models constructed using timber blocks to represent the voussoirs with stocky piers. In their analysis they found that collapse occurred through local failure of the loaded span only, with no hinges in the adjacent span. According to their experiments, lowest failure loads occurred around mid-span of the loaded arch and its value was 20% lower than a proportioned single span. Recently, the same team of the University of Edinburg tested a 2 m double span briek arch (Robinson et al. , 1997). An analytieal research on the pier adequacy to use a single span assessment for two-span arch bridge was done by Hughes (1995). This work was based on the mentioned experiments carried out by Melbourne et al. (1995). 4 EXAMPLES

3 PRECEDING WORKS ON MULTI-SPAN MASONRY ARCH BRIDGES

4.1 General remarks

Harvey and Smith (1991) studied the mode of failure of multi-span arch bridges using a mechanism based analysis. Their analyses provided lower bound solutions for the load capacity and the associated modes of failure. They conc\uded that failure resulted from the development of agiobai mechanism at lower loads than those observed for equivalent single span bridges. They also distinguished two main categories of multi-span bridge failure: those in whieh only the loaded arch failed and those in whieh the failure involved more arches, depending mainly on the relative stiffness of the piers. One of the firsts experiments carried out to study the load capacity of multi-arch bridges is due to Melbourne et al. (1995). These researchers

The main objective of the studies carried out were: first, to estimate the deterministic load factor of the structures subjected to trafik loads using standard axle loads and , second, evaluate the security of the structures by means of reliability techniques, inc\uding a large amount of numerical simulations. The latter work is now being carried out and will deserve further publications. Some common hypothesis used in both examples are that: (I) the axles distribute the load uniformly in the cross section, (2) the favourable effect of the longitudinal distribution of the load through the infill can be neg\ected, and (3) abutments are considered absolutely rigid. The second hypothesis is reasonable when working with vehic\es of various axles whieh, in fact, produce a more distributed load pattern.

214

26.50

f ·9

ARCH 1

t

20.00

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~.9°i

20.00

ARCH 3

AReH 2

20.00

ri

AR CH 4

ARCH 5

FRONT ELEVATION 22.50

" .00

"4.50"1"'1 1.00

t50~ 1.00

2.70

VI

V2

V3

V4

,U' 501

7.00

I

'.00

f

PLAN

MAGAROLA BRIDGE

Figure 1.- Plan and front view of Magarola bridge. cores to be tested in the laboratory. Some of the tested cores, which incIuded brick and mortar joints, gave valuable information about the masonry 's strength. Horizontal boreholes detected concrete backing on the four piers.

4.2 Magarola bridge 4.2.1 Description

Magarola bridge is located in Esparreguera (Province of Barcelona) in the road N-II, PK 582,000. This bridge is in good condition despite the enlargement of its platform with a concrete slab made in 1990. All the data used in the study was obtained during the geometrie and mechanic characterisation of the bridge carried out in april 1997. This bridge (Fig. 1) is composed of five brick masonry barrel vaults spanning twenty meters. The overalllength of the structure is 160 m and its maximum height is 25 m. The section of the piers is variable and measures 7x3 m at the abutments of the arches. The piers are built of rubble stone masonry reinforced with ashlars in their corners. The bridge was begun to build at the last decade of the past century, and was completed during the twenties. The main geometrie parameters of the arches and the mechanical properties of the materials are shown in the Tables land 2 respectivelly. The shape of the arches was defined by obtaining the coordinates of twenty one (21) points. It allowed to prove the exactitude of the semicircunference they describe. Six vertical boreholes of 2.10 m to 2.25 m and four horizontal ones of 1.5 to 3.17 m (Fig. 1) allowed to recognise the inside geometry of the bridge and its composition, and to obtain several

Table 1.- Bridge of Magarola. Main geometrie and material nature eharaeteristies. Arch shape Semicircular (barrel) Free span 20.00 m 1.05 m Arch thickness Arch width 7.00 m 10.00 m Rise at midspan Depth of fill at crown 1.15 m Arch ring material Brick masonry Infill material Gravelly sandlbrown cIay Backing Plain concrete Table 2.- Magarola Bridge: Average material properties derived from the eharacterisation works or used in the analyses. Arch ring (MPa) (experiment) 15.0 Compres. Strength (MPa) (assumed) Elastic modulus 3000 (MPa) (assumed) 0.01 Tensile strength (Kglm J ) (experiment) 1800 Density FilZ (MPa) (assumed) 1.0 Compres. Strength 30 (MPa) (assumed) Elastic modulus (Kg/m J) (experiment) 2300 Density

215

Figure 2.- Stress state of Magarola bridge under dead loads.

Figure 3.- Stress state of Magarola bridge at failure .

section. Connections between the upper node of the piers and the springing node of the arches are modelIed by rigid links. The whole model contains 131 elements, incIuding the joint ones. In all the analysis perforrned, dead load is first applied in one step. Successive increments of live load are then applied until reaching failure. Two different types of vehicIes are considered: first, one composed of three axles of 80 kN, 100 kN and 80 kN separated 1.33 and 5 m between them, and, second, another composed of five axles

4.2.2 Structural model and analyses performed

Realistically evaluating the load capacity of barrel vaults bridges, as Magarola, requires to take into account the horizontal action of the infill, in addition to its dead load. Using the referred technique of modelling (Roca et al., 1998), each arch ring is discretised by eight elements, and eight infill elements were connected to the ring ones by joint elements. Piers are modelIed using one element of variable cross216

4.2.3 Results 75

•

70

65

•

60

~ 55

• •

~ 50

45

•

,

40

35

:

30 5.55

Position (m)

11.1

16.65

22.2

Figure 4.- Load factor vs. position for Magarola bridge. of, from the back one, 66 kN, 66 kN, 70 kN, 135 kN and 74 kN separated 1.25 m, 1.26 m, 5.41 m and 3.95 m. All studies are carried out using the non­ linear material analysis (NLM). It was previously observed, through some tentative analyses, that the effect of the second order equilibrium were negligible, as commonly occurs in barrel vaults including in-fill.

Non-linear analysis of the structure under dead loads showed that the arch rings are quite uniformly compressed excepted a short zone at the extrados of the springings (Fig. 2). In all figures showing stress states, white colour means cracking and grey scale is used in compression. The first step in the calculations was to determine the most unfavourable type of vehicle and its most unfavourable position over the structure. It was difficult to define apriori which one of the vehicles would be worst because the back boggie of the three axle vehicle concentrates more load than the boggie of the five axle one (three axles in the bogie) that is the heaviest. The analyses showed that the five axle vehicle acting very c10sed to mid span of the second arch was the most unfavourable for this bridge. However, the differences between applying the load on the second arch or on the third are slight. Figure 4 shows the evolution of the load factor for five axle vehicle along the second arch. This factor refers the multiplier of the vehicle loads which produces numerical prediction of failure . In

Figure 5.- Deformed shape at failure of the arch 2, Magarola bridge.

Figure 6.- Deformed shape at failure of Magarola bridge. 217

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Figure.7.-San Rafael bridge in Cordova

SAN RAFAEL BRIDGE

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all posItIOns failure is due to crushing in compression at the crown of the second arch. That crushing occurs for a quasi collapsing mechanism involving the formation of three hinges in the arch, one in each pier (not completed), three in the first arch of the bridge and two (not completed) in the third arch (adjacent to the second). Figures 3, 5 and 6 show the stress state 0 and the deformed shape of the bridge at failure. As can be observed in Figures 5 and 6, the boundary conditions induced by the flexibility of the piers and the adjacent arches increases the flexibility of the loaded arch. They also allow to deteet a huge rotation experimented by the seetions around the erown of the seeond arch. In fact, the eomparison of these results with those obtained supposing rigid supports at the springings of the arch shows that the loss of load capacity induced by the aetual support eondition is 50%. 4.3 San Rafael bridge 4.3.1 Description

San Rafael bridge over the Guadalquivir river is

loeated in Cordova in the road N-IY. This is an urban bridge in very good eondition. All the data used in the study belong to the original design and the geometrie and mechanic charaeterisation works earried out in October 1997. This bridge (Fig. 7) is eomposed of eight plain eonerete flat arehes spanning almost twenty four meters. The overall length of the structure is 240 m and its maximum height is 16 m. The seetion of the piers is variable and measures 24x4 m at the abutments of the arehes. The piers are also built of conerete with faces simulating stone masonry. The ereetion of this bridge was eompleted in 1940. The main geometrie parameters of the arehes and the meehanieal properties of the materials are shown in the Tables 3 and 4 respeetively. In the geometrie eharaeterisation works the shape of the arehes was defined by obtaining the co-ordinates of eleven (11) points. It allowed to prove that, as the drawings indieate, the bridge consisted of a flat eireular arch instead of a parabolic one. Nine vertieal boreholes of 3.0 m to 5.0 m (Fig. 8) allowed to confirm the inside geometry of the bridge as the same found in the drawings. Nine eonerete cores were tested in

Figure 8.- Deformed shape of the arches 2, 3 and 4 at failure, San Rafael bridge.

I ~wo

1_ . UC4 1 __ 11 &4

I _.:w u

I

Figure 9.- Hinges at failure in the loaded areh, San Rafael bridge. 219

Table 3.- Bridge of San Rafael. Main geometrie and material nature eharaeteristies. Arch shape Flat circular Free span 23 .72 m Arch thickness 1.00 to 1.20 m Arch width 19.00 m Rise at mid-span 4.95 m 17.50 m Radius Depth of fill at crown 1.15 m Arch ring material Plain concrete In-fill material Gravel Table 4.- San Rafael bridge: Average properties Arch ring (MPa) (experiment) Compres. Strength Elastic modulus (MPa) (experiment) (MPa) (experiment) Tensile strength (assumed) (Kg/m 3) (experiment) Density

material 24.0 24000 3.50 0.01 2600

Fill Compres. Strength Elastic modulus Density

(MPa) (assumed) 1.0 (MPa) (assumed) 30 (Kg/m3) (experiment) 2200

compression (in two of them was also measured the deformation modulus) and two in tension (Brazilian).

4.3.2 Structural model and analyses performed When dealing with flat arches, the contribution of the spandreI' s in-fill in the strength can be often neglected without sensitive underestimation of the load capacity of the arch. However, it is known that in very slender flat arches, that contribution should be taken into account in order to not underestimate their actual capacity. In this case, some tests were done to determine the difference between including or not the second order effects in a numerical model showed that the difference was always less than ten percent. Using the technique of modelling already presented, each arch ring was discretised by eight elements and the piers by one element, having all of them variable cross-section. Connections between the upper node of the piers and the springing node of the arches were modelled by rigid links. The entire model contains 71 elements. Areduction of the total width of the platform to 12 m was used in the calculations.

Figure 10.- Deformed shape at failure for a load on the crown, San Rafael bridge.

•

1 .15 dm1

The probability density of the X variable is thus defined, updated by means of the sampIe of x observations "a posteriori". The procedure has been applied to concrete, defining its characteristics "a priori" on the basis of indications provided in the design documentation and of considerations concerning the characteristics of the materials utilised at the time of construction. The concrete compressive strength, defined "a posteriori", shows an increment in the maximum value and a decrement in the variance [fig.l 0].

Displafc1.\\ents 0 .05021

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between

0-10

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2,65

2,48

I

The use of Bayesian inference techniques, coupled with a method of estimating failure probability based on FORM-type procedures (First-Order Reliability Method), allows for direct updating of failure probability as compared with the initial one. Utilising level 11 probabilistic procedures the measurement of structural safety is carried out by means of the safety index ß, which is directly linked to the failure probability through the relation: Pt -

HAX [5

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Fig.1 0 Distribution of S12 on the arch

235

SAP90

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Fig.13 Distribution ofMmax on the arch

237

SAP90

Table I. Results of the parametrie analysis

E = 1500 N\mm2

Young modulus Poisson's ratio

v =0.1

v = 0.2

v =0.3

E = 2000 N\mm2 v =O.1

v=0.2

v =O.3

E = 2500 N\mm2 v =O.1

v =0.2

v =0.3

M 11 (KNm)

min max

-123 216

-123 219

-123 224

-123 216

-123 219

-123 224

-123 216

-123 219

-123 224

M 22 (KNm)

min max

-112 216

-176 438

-23 7 672

-112 216

-176 438

-237 672

-112 216

-176 438

-237 672

M min(KNm)

min max

-123 216

-123 438

-123 672

-123 216

-123 438

-123 672

-123 216

-123 438

-123 672

Mmax(KNm)

min max

-112 216

-176 219

-237 224

-112 216

-176 21 9

-237 224

-112 216

-176 219

-237 224

SII (KN)

min max

- 664 - 381

- 717 - 372

-777 - 362

- 664 - 381

- 717 - 372

-777 - 362

- 664 - 381

-717 - 372

-777 - 362

S22 (KN)

min max

- 664 063

- 143 108

- 233 184

- 664 063

- 143 108

- 233 184

- 664 063

- 143 108

- 233 184

S min (KN)

min max

- 669 - 381

- 741 - 372

- 833 - 362

- 669 - 381

-741 - 372

- 833 - 362

- 669 - 381

-741 - 372

- 833 - 362

Smax (KN)

min max

- 612 63

- 120 120

- 180 216

- 612 63

- 120 120

- 180 216

- 612 63

- 120 120

- 180 216

---

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238

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Fig. 15 Distribution of normal stresses according the arch wideness direction in the non-linear analysis

4 CONCLUSIONS

AKNOWLEDGEMENTS

In a widely compressed structure like an arch, because of the limited but significant tensile strength of masonry, the cross section can be taken as totally reacting. The assumption about a linear behaviour seems reasonably good, so that a simple linear F.E.M: analysis can be perfonned. It has been shown that a linear F.E.M. analysis can provide a satisfactory qualitative stress distribution, whereas a non linear analysis is somewhat superfluous. On the contrary, the value of the safety degree based on the comparison between the masonry strength and the stress evaluated by means of a F.E.M. analysis, whatever would be the accuracy of the numerical analysis, seems too distant from the realone. The safety degree evaluated by means of a c1assical limit analysis, though higher of the real one, seems to approach it better. Moreover, the results of a F.E.M. analysis are too depedent on the exactness of mechanical parameters detennination, which often are difficult to evaluate by experimental analyses. Nevertheless they can be useful, in case of restoration of a masonry arch, by giving a qualitative map ofthe "intervention areas".

The support of the Itahan Ministry of University and Scientific Research (M.U.R.S.T.) is gratefully aknowledged.

239

REFERENCES Aboudi, 1., 1991. Mechanics of composite materials - An unified micromechanical approach, Elsevier, Amsterdam-Oxford-New York-Tokyo. Ansys user's manual, Swanson Analysis Systems. Broomhead, S.F., Choo, B.S. 1992, The British rail masonry arch bridge assessment program, Proceedings of the 6th Canadian Masonry Symposium, Saskatoon, Saskatchewan, Canada. Das, P.C. 1993. Examination of masonry arch assessment methods, Proceedings of IABSE Syposium on "Structural Preservation of the Architectural Heritage", Rome. Frunzio, G., Gesualdo, A., Monaco, M. 1998. Structural modelling of a stone masonry arch

bridge, Proceedings of the 8th Canadian Masonry Symposium, Jasper, Alberta, Canada.

Franciosi, V. 1986. L'arco murario, Restauro nn. 87­ 88. Hendry, A.W. 1995. Masonry arch design at the end 0/ the 19th century, Proceedings of the 4 th International Masonry Symposium, London, u.K. Heyman, J. 1966.The stone skeleton, Intenational Journal 0/ Solids and Structures, vol. 2. Heyman, J. 1969. The safety of masonry arches, International Journal 0/ Mechanical Sciences, vol. 1. Heyman, J. 1982. The masonry arch, Ellis HOlwood Limited, Chichester, U.K. Romano, G., Sacco, E. 1984, Materiali non resistenti a trazione: equazioni costitutive e metodi di calcolo, Atti Istituto di Scienza delle Costruzioni, Universita degli Studi di Napoli, n. 350. Wilson, E., Habibullah, A., 1990. SAP90, a computer program /or finite element analysis 0/ structures.

240

Non-destructive testing

Arch Bridges, Sinopo/i (ed.)© 1998 Tay/or & Francis,/SBN 90 5809 012 4

Tomography for NDT applied to masonry structures: Sonic and/or EM methods S.Valle & L.Zanzi Department ofElectronics and Information, Politecnico ofMilan, ltaly

L.Binda & A.Saisi Department ofStructural Engineering, Politecnico ofMilan , Italy

G.Lenzi ISMES SPA, Seriate, Italy

ABSTRACT: The research developed by the authors concerns the calibration and the application of the tomographie procedures (sonie and radar tomography) to qualify the internat morphology of structural elements in masonry. The paper outlines the differences, the advantages and the drawbacks in the use of sonic and eiectromagnetic (Ground Penetrating Radar) systems referred also to on site applications. The paper shows the first results of the in-situ tests carried out on ancient masonry piers.

I.INTRODUCTION The experience of these last decades consequent to several seismic events shows how difficult it is to choose preventive or repair techniques to be applied to historie stone masonry buildings. Their load bearing structure consist of walls which are made with highly inhomogeneous material composed in multiple leaves. The extemal leaves are usually made with shaped or more or less regular stones while the inside leaf is usually made with rubble masonry. This type of construction is also frequently found in defence massive walls of castles, in walls of bell or defence towers, but also in large piers as the ones bearing bridges or vaults and arches in churches. Sometimes these walls only consist of two leaves badly connected by an irregular continuous joint. They usually badly suffer during the earthquake both under in plane or out of plane forces. The second ones are frequently cause of partial or total collapses. Physical or analytical modelling of these walls cannot apply homogeneization if the real technique of construction of the wall is not known. Furthermore the knowledge of the wall prospect is not enough to have information on how the inside is made (Hendry, 1994). Inside the wall there might be also cracks and voids and damages which make it weaker (Binda et al., 1994.)

243

In order to qualify the state of preservation of stone or brick masonry walls and piers, the internat defects, the presence of multiple leaves and their type of connection a knowledge of the inside is important. Two possible ways can be followed to reach this knowledge: (i) destructive survey through coring or local demolition, (ii) non destructive survey carried out by NDT (non destructive techniques) as thermography, sonic and EM or X-ray tests. Sonic and radar tests seem to be very promising being widely used also in other fields like medicine or geotechnique were a diagnosis has to be done on the state of damage present in unhomogeneous. Applications have already been done in large structures such as masonry dams and bridges. These applications allow to collect a great amount of data whose interpretation is very difficult, when a detailed information is requested. Nevertheless these procedures are continuously applied even if doubtful results are obtained; there is therefore a need for calibration of methods and procedures in laboratory and on site. The authors are applying sonic and radar tests since a rather long time (Binda et al. 1994, Binda et al. 1997, Schuller et al. 1995, Valle & Zanzi, 1996a,b, Valle et al., 1997). The paper outlines the differences, the advantages and the drawbacks in the use of sonic and

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real applications to stone and brick masonry piers inspections.

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2.PROBLEM DESCRIPTION

a)

b)

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Figure 1. Echo radar section of a multiple 1eaf wall section(c) before (a) and after the data processing (b) .

Figure 2. Example ofwall section. electromagnetic (Ground Penetrating Radar, GPR) systems referred also to on site applications. The discussion is extended to a wide range of algorithms for tomographic reconstruction including traveltime, amplitude, migration and diffraction methods. The discussion of all the aspects will be documented by showing laboratory tests and some 244

One of the most difficult application for sonic and EM tests concerns the detection of leaves and of their characteristics (connections, voids, etc.) in a multiple leaf wall or pier. Sonic or radar measurement by transparency or echo are sei dom successful due to the fact that: (i) the leaves are parallel to the surface where the antenna is applied (Fig. 1), (ii) the rubble and mortars used for the internalleaf are usually made with the same material as the externaiones (Fig. 2) (Binda et al. 1997). Among the ND applications the tomographic technique is quite attractive for the high resolution that can be obtained (Schuller et al. 1995, Valle & Zanzi, 1996b). Because of the cost of a tomographic survey ( acquisition time and processing complexity) needs good a understanding of which results can be achieved and how. In fact, the accuracy of tomography depends on many parameters: the source (sonic or electromagnetic), the number and the position of measurements, the equipment settings, the reconstruction algorithms. Both sonic and radar systems are suitable for traveltime tomography (TI). Usually, materials present complementary behaviours with respect to sonic and EM velocity (i.e., slow sonic materials are generally fast materials for EM waves and vice­ versa). This indicates that one method may be more appropriate than the other depending on the material nature. In some cases, where it is not possible to apply the radar method (large presence of metals or water), the sonic can be the only solution; vice-versa when the sonic fails fully (large presence of voids or chaotic inhomogeneities) the radar can detect the main elements of the object section. A score to sonic tomography is that elastic parameters are expected to be more correlated with the sonic velocity rather than with EM velocity. On the other hand, radar systems, provided the antennas are calibrated, are much more indicated than sonic for the application of other powerful reconstruction techniques such as amplitude tomography, migration and diffraction tomography. Both the sonic and the radar systems suffer the difficulty of the source signature extraction. Finally, cost considerations are also important and with respect to these it should be pointed out that the

GPR equipment is much more expensive but the acquisition times for radar data may be an order of magnitude below the correspondent sonic acquisition times. 3 SONIC AND RADAR TOMOGRAPHY 3.1 Tomography principles and resolution

Tomography, from Greek "tomos" (slice), reproduces the internal structure of an object from measurements collected on its external surface. Tomography's principle is the Fourier Slice theorem (Kak & Slaney, 1984), thas shows how a complete slice of an object can be extracted from a proper set of measurements. It is essential to stress that the resolution capabilities of tomography can be evaluated only taking in account the measurements locations (i.e., the angular distribution of the observations and their spatial sampling) by means of the above theorem. Furthermore the physical limits related to the wavelength should be considered. In fact sonic and EM sources produce difrraction phenomena that limit the resolution. Thus, when the measurements are properly carried out (i.e., the angular coverage and the spatial sampling honour the Fourier Slice Theorem), the resolution has a physical limit strictly related to the wavelength involved in the survey. On the contrary, when the measurements do not satisfy the above conditions because of the environment or because of the structure geometry (i.e., in a wall survey), the resolution limits could even more unfavorable. All these concept are developed in (V alle and Zanzi, 1996b). The result of the tomographic inversion is a map of a property of the materials. In case of traveltime tomography (TI) the measured quantity is the traveltime of the signal and the map is the distribution of the propagation velocity within the object. In case of amplitude tomography (AT) the measured quantity is the amplitude of the signal and the map is related to the distribution of the absorption coefficient. 3.2 Acquisition

A special care should be devoted to: (i) choice of location of measurements, (ii) accuracy in their topographic location, (iii) choice of optimal transducers/antennas (operating frequency), (iv) availability of auxiliary tools for a faster and easier

245

acquisition procedure, (v) settings of the acquisition electronic equipment (time range, filters, gains, time sampling, number ofbits for AID conversion). All of those items must contribute to get a reasonable number of good sonic/radar signals: the object section will be uniformly illuminated from any direction (provided that is possible) and each single trace will contain clear information of its crossed path; hence the signals will be clean with low noise, not clipped and long enough. In such way it will be easier to extract from the signal all the needed characteristics for inversion. The (iii) point will be accomplished by a spectral analysis of the received signal; in fact, the choice of operating frequency as higher as possible suffers the limitation of absorption that is proportional to frequency and to object size. Hence the trade-off between resolution (that requires high frequency) and penetration depth is a critical aspect in the design of a tomographic survey. The determination of the absolute time scale is an ther important item. Usually the zero time do not corresponds with the first sampIe of a trace. It can be obtained in different ways: by coupling the antennas and measuring the cable and electronics delay, or acquiring a sequential set of traces with antennas located at different distances. In this second case the regression of arrival times versus distance allows to compute the zero time. The specific characteristics of commercial radar equipment allow to use some different tools and procedures to make the radar tomography faster and easier than the sonic one. 3.3 Processing and inversion

TI and AT do not require huge pre-processing of the signals. The most critical step in TI is first arrival picking. In addition AT (only for GPR) needs the knowledge of the antenna directivity pattern for a correct interpretation of amplitudes. Data inversion is a simple optimisation problem that can be solved by applying standard methods such as the Singular Value Decomposition or the Conjugate Gradient algorithrn. TI is implemented according to geometrical optic approximations (i.e., thin rays, honouring Snell law) and assurnes that dispersion and scattering effects are negligible. The above assumptions are also used for the AT implementation. Specifically the no scattering assumption means that all the amplitude variations are interpreted as absorption effects once the data have been compensated for geometrical spreading

and antenna pattern. Again we have to stress that this is a rough approximation and results will show that scattering can actually be more remarkable than absorption. Traveltime extraction can be done automatically when SNR is fltvourable. Otherwise, picking is manually performed with the help of an interactive software. The amplitude is the peak-to-peak excursion or the square root of the signal energy measured on the first break wavelet after the corrections for geometrical spreading and antenna pattern. The difficulties in the extraction of the radar signature when the antenna is coupled to the interface, suggest the use of an arbitrary reference amplitude. As a consequence, AT will be used only for producing qualitative images that may help the interpretation of the slice. The inversion algorithm is based on the SVD. Resolution improvement can be achieved by using irregular grids (V alle & Zanzi, 1996). The design of the irregular grid can be fully automatic or interactive; in any case, it should be guided by any available a-priori information, by the coverage map that indicates the areas with a low rate of observations and by the previous reconstructions that help the user to localise the areas of main interest where higher resolution is desirable. 4. APPLICATIONS AND COMPARlSON OF THE RESULTS Radar surveys were carried out with a GSSI equipment (SIR2 with 900 or 1000 MHz antennas). A mechanical pulse velocity equipment was used to acquire sonic data at the Castle of Malpaga. The input signal was generated with an hammer instrumented with a small accelerometer. The transmitted pulse was received by and accelerometer mounted on the masonry surface. Signals (both input and output) were acquired and stored by a waveform analyzer intefaced with a computer. The sonic source in the second application is an electro-mechanical pulser designed by ISMES. 4.1 Description 0/ the sites

The village of Malpaga is situated between Bergamo and Brescia in the north western part of Italy. The Castle (Fig. 3) was built in the XIVth century. The interior was very simple since its function was essentially defense. Originally the height ofthe walls was one floor less than the present. In 1456 Bartolomeo Colleoni a famous noble from Bergamo

246

Figure 3. View ofthe Castle ofMalpaga.

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Figure 4. Example of a masonry texture at Malpaga Castle. and Captain under the Venice Republic, restored and rebuilt some parts of the Castle, which was preserved since then in fairly good conditions. The walls of rooms and courtyards are covered with wonderful frescoes and temperas. The morphology of the stone-masonry wall sections is still practically unknow, being the stone walls of the castle built in different times and with different building technology. The masonry texture is shown in Figure 4. In order to detect the state of the beautiful masonry structure a pier was chosen. The pier is at the bottom of the highest tower of the castle. The application of radar and sonic tomography was attempted in order to verify the connection between the pier and the attached wall and to detect the presence of defects (voids, inelusions ...). The second example is the church of S.Egidio at Fontanella, elose to Bergamo (Fig. 5). The church was probably built around the XIth cent. It has 3

Figure 6. Particular view ofthe bell-tower ofFontanelle

Figure 5. View ofthe Church. naves and in the aisle four piers support the bell tower. This tower has a square plan and it is very massive. The stonework is rather regular with large blocks made of a local sandstone (stone ofMapello). The Church was subjected to many repair works along the centuries. At the beginning of this century the bell-tower showed many structural problems. The piers were badly cracked and were subject to differentials displacements. The bell tower was repaired with ties and cement grouting (Fig. 6). Despite these works, the piers and the bell tower continue to show structural problems.

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Figure 7 shows the Power Spectral Density of both radar and sonic signals; they are both affected by the absorption that decreases the frequency peak. Figure 8 shows the geometry of a pier of Malpaga castle near Bergamo (ltaly). Figure 9a shows a quite evident fast anomaly located at the center of one side of the pier. This may be due to a local separation of the wall from the pier. The south side ofthe pier also shows a high velocity zone that has been interpreted as an artifact produced by the low data coverage in that area. Figure 9b shows the AT result using the

247

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Figure 9 (a). TI result; 870 data had been acquired with a measure step 10cm by using 900MHz antenna. (b) AT result.

same data: the anomaly is present in the same position. The grid a1lows an accuracy of about 20 cm that is the sizing and positioning ofthe anomaly.

248

Figure 10 shows the results of the sonic test processed with MIGRATOM (Jackson & Tweeton, 1994). The general result is similar to the radar ones, enhancing a low velocity area. The sonic test in this case shows a very important limit. Due to the wall structure and to the presence of a thick pIaster (with fresco) the high frequency components are filtered. The output signals have a rather low frequency content. Figure 7b shows the power spectral density of a group of signals. Since the wavelength is equal to the ratio between wave velocity and frequency, this effect led to an output signal contains only very long wavelengths. The sonic test in this case does not have a resolution able to detect in detail the pier morphology but it gives an overall description ofthe position of low velocity points. The echo profile along the south side of the pier confirms the presence of the anomaly (Fig. 11). The events indicated by the arrows correspond to the reflection from the front and the back sides of the anomaly. Further echo profiles acquired at different heights did not show this anomaly; as result it can be then considered as confined. The second application is a survey carried out on a stone pier of an old church. The power spectral density of both radar and sonic signals are shown in Figure 12; absorption is less evident than in the Malpaga application, since the pier has compact facing stones. Figure 13 shows an homogeneous section with an anomaly in the centered low part that could have been produced by the shortage of measurements in that zone due to the roughness of the external surface. The internal part of the section shows a slightly higher velocity for EM TI (Fig. 13a) and lower for sonic TI (Fig. 13c) indicating a

low quality material inside the pier. AT result matches both with EM and sonic TT ones (Fig. 13b). In figure l3c the grid used for the inversion is shown. Since the texture of the external stones was visible, the gridding had been done following the positions and size of the external stones allowing a reduction of the unknowns without arbitrary

constraints. The shorter sides of the pier reveals better quality material (faster for sonic and absorbing for EM AT). A comparison of the three sections gives a preliminary mapping of the different materials of the pier on the basis of this principle: two or more zones presenting the same sonic and EM behavior can be considered same material; on

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Figure 12. (a) power spectral density of GPR 1000 MHz antenna signals acquired on the stone pier survey (frequency peak at 600 MHz). (b) power spectral density of sonic signals acquired on the same pier (frequency peak at 1500 Hz). 249

Figure 13. Stone pier (160 x88 cm). (a) TI result with 1000 MHz antenna (734 data with 10cm measure spacing). (b) AT result. (c) sonic result (637 measurements, 10 cm spacing) ( for the meaning of letters see paragraph) (d) Grid used in the tomographic inversion: external pixels follow the stone texture.

the contrary when zones present a similar behavior only for sonic (EM) then their materials are different. An example of this evaluation is shown in figure 13c: zone A is fast for sonic and slow for EM as B, so materials are likely the same; zone C is slow as A for EM but is slow also for sonic, so materials should be different. This shows a further use of the complementary behavior of sonic and EM survey. 5. MIGRATION To improve the resolution is necessary to comply with the actual behaviour of EM waves. Diffraction phenomena carry a great deal of information on the rapidly varying features of an object function. Provided they are taken into account they allow the detection of edges and small scatterers that TI and AT are unable to see. This result can be accomplished by migration. Thanks to the full-wave approach MIG uses both amplitude and phase so that the potentials of TI and AT are joined together. MIG is an imaging technique strictly related to DT. In our implementation, radar signals are kinematically migrated over constant velocity diffraction ellipses. No amplitude corrections are applied to compensate for geometrical spreading or source patterns (Valle et al., 1998). The simplicity of the algorithm is very much favoured by the assumption of an homogenous medium where scattering anomalies are embedded in. All the radar traces are used and good results can be achieved without any data preprocessing. Preliminary tests were performed on a laboratory model simulating a brick covered pier with two polystyrene anomalies embedded in a concrete core (the geometry is superimposed to the results). By including the a-priori information about the external brick perimeter and after a few preliminary reconstructions that guided the design of a proper irregular grid, an interesting result with AT (Figure 14a) was obtained. The geometry of the vertical anomaly is fairly accurate whereas the horizontal anomaly is overestimated. However, the result indicates that the no-scattering assumption is inappropriate; the amplitude variations associated with scattering produced by the polystyrene bodies are interpreted as absorption losses so that low-loss materials such as polystyrene or bricks seem more attenuating than a homogeneous high-loss medium such as the concrete core. In this case, diffraction phenomena affect amplitudes more than absorption. The MIG result (Figure 14b) is quite better in

250

spite of the complexity of the model (the homogeneous background is a very rough approximation because of the large velocity contrast between bricks and concrete): both anomalies are detected with the right position and the actual size. The MIG result of the Malpaga Castle's pier is shown in Figure 15: energy is focused where the anomaly is located, but a strong smearing of it reduces the quality of the reconstruction. This result is not satisfactory as the laboratory one but several factors explain the partial failure of MIG: the spatial sampling of measurements is good for TI and AT

(a)

(b) Figure 14. (a) AT result ofa 500MHz experiment on a laboratory model (100xIOOcm) The geometry the ofbrick covering and the two polystyrene anomalies embedded in theconcrete core are superimposed. 600 records were collected ensuring a complete angular coverage (source and receiver were placed either on opposite sides or on adjacent sides) with a measure step of 10 cm. The dark gray indicates high 10ss material. (b) MIG results on the same data.

• Radar is less time consuming then sonic due to the facility of antenna moving, especially when continuous acquisition is feasible. • Migration is a promising technique for his resolution capabilities, but requires further developments. Figure 16 shows the wavelength versus frequency involved in sonic and radar survey of masonry structures; each curve refers to a constant velocity material. In the future the survey design will be guided by the wavelength evaluation in order to optimise the choice of the source and of the other parameters of acquisition.

150

100

50

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ACKNOWLEDGEMENTS

Figure 15. MIG result on the Malpaga pier. but not enough for MIG; TI and AT are more robust when the profile of the section is irregular; the homogeneous background assumption is not satisfied. 6. CONCLUSIONSAND FUR1HERDEVELOPEMENTS

The authors wish to thank Prof. F.Rocca for his theoretical support, the technicians M.Cucchi and L.Gerosa, the students L.Cattaneo, S.D'Ascola, D.Finazzi, M.Sgheiz for their cooperation in the experimental work in situ and data processing. REFERENCES Abbaneo S., M. Berra & L. Binda 1996. Pulse velocity test to qualify existing masonry walls: usefullness of waveform analyses, 3rd Conf Nondestrnctive Evaluation 0/ Civil Strnctures and Materials, Boulder, CO, USA ; pp. 81-95,.

The research points out some important aspects concerning the use of radar and sonic techniques. Some comments are given in the following: sar1c

• Before using sonic andlor radar tests it is important to verify the applicabi1ity of the test

itself.

• Only low frequency sonic pulses are allowed for

investigation of old masonry because of their 'E' -, 1=:""'1 ----= 1 1 :::::::r- -I 0.41 1 \ " 1" .. greater energy content and lower attenuation in 02 the presence of multiple cracks. The axxl 2500 300l 3500 disadvantage is that the 10ng wavelength limits ~~ the resolution in the detection of the masonry morphology. 0.8 • The resolution and the choice of the frequency :E: 0.6 both tor sonic and radar should be calibrated and controlled directly on site, before testing, by a 0.4 frequency analysis of the recorded input and 02 output signals. 4 8 10 14 12 • In the case histories presented, sonic freQJerx:y (Hz) x 10' tomographic imaging was able to indicate the overall condition, while the GPR, thanks to Figure 16. Wavelength versus frequency for smaller wavelengths revealed more details. different velocity media (a) sonic, (b) Ground Penetrating Radar (dimensions are respective1y [mls] and [cmJns]).

1,~cxi>'l"""

t

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251

Mt[

Abbaneo S., M. Berra, L. Binda & A. Fatticcioni 1994. Non destructive evaluation of bricks­ masonry structures: calibration of sonic wave propagation procedures, Int. Symposium Non­ Destruetive Testing in Civil Engineering (NDT­ CE), Berlino, Vol. 1, pp. 253-260, 1995 Abbaneo S., Schuller M., Binda L., Atkinson R. & Berra M., Acoustic tomography application to the study of a full-scale model of a masonry building, Conv. 7NAMC, Notre Dame, USA, Vol. 1, pp. 533-546, 1996. Binda, L., Colla, C. & Forde, M.C. "Identification of moisture capillarity in masonry using digital impulse radar" , J Construetion & Building Materials, 8, No. 2, 101-107. Binda L., A. Fontana & G. Mirabella 1994. Mechanical behaviour and stress distribution in multiple-Ieaf walls, 10th Int. BriekiBloek Masonry Cont, Calgary, Vol. 1, pp. 51-59, Binda, L., G. Lenzi, & A. Saisi. 1997. NDE of masonry structures: Use of radar test for the characterisation of stone masonries, Proe. VII Int. Conf. Struetural Faults and Repair -'97, Assembly Room, Edinburgh, 8-10 July 1997, Engineering Technics Press, vol. 3, 505-514 Binda L., A. Saisi, L. Gerosa & G. Lenzi. 1997. GPR application to multiple leaf stone masonries, International Colloquium "Inspeetion and Monitoring ofthe Arehiteetural Heritage", 15-16 May 1997, pp. 215-222 Colla, C., P.C. Das, D. McCann & M.C. Forde 1997. impulse radar Sonic, electromagnetic & investigation of stone masonry bridges, J. Non­ destruetive testing and evaluation International, vol. 30, No. 4, pp. 249-254. Colla, C., D.M. McCann, M.C. Forde, P.C. Das, & A.J. Batchelor 1997. Radar tomography of masonry arch bridges, Proe. VII Int. Cont Struetural Faults and Repair -'97, Assembly Room, Edinburgh, 8-10 July 1997, Engineering Technics Press, vol. 1, 143-153. Hendry A.W. 1994, Aspects of stability and strength of stone masonry structures, Third Internatinal Masonry Conferenee, Proeeedings of the British Masonry Society, N. 6 Kak, A.C., & M. Slaney 1984, Principles of Computerized Tomographic Imaging, IEEE Press,. Schuller M.P., M. Berra, R. Atkinson & L. Binda 1995. Acoustic Tomography for Evaluation of Unreinforced Masonry, 6th Conf. on Struetural Faults & Repair, Vo1.3, pp. 195-200.

252

Valle, S. & L. Zanzi 1996a. Radar Tomography for Cavities Detection, SAGEEP'96 April 28-May 1, Keystone, Colorado. Valle, S. & L. Zanzi 1996b. Resolution in radar tomography for wall or pillar inspection, 6th international Conferenee on Ground Penetrating Radar, September 30-0etober 3, Sendai, Japan. Valle, S., L. Zanzi, G. Lenzi & G. Bettolo, 1997. Structure inspection with radar tomography, Int. Coll. lnspeetion and monitoring of the eultural heritage, IABSE-ISMES, May 15-161997, Seriate, Italy. Valle, S., L. Zanzi, & F. Rocca 1998, Toward high resolution radar tomography, 7th Int. Cont on Ground Penetrating Radar (GPR '98), May 27-30, Lawrence, Kansas, USA. Valle, S. & L. Zanzi 1998, Traveltime radar tomography for NDT on masonry and concrete structures, European Journal of Environmental and Engineering Geophysies. (appearing on) Jackson, M.1. & D.R. Tweeton 1994. MIGRATOM. Geophysical tomography using wavefronts migration and fuzzy constraints, R.I. 9497, bureau ofMines, USA, Deparement ofInterior

Arch Bridges, Sinopo/i (ed.)© 1998 Tay/or & Francis,/SBN 90 5809 012 4

Radar testing of masonry arch bridges with soil backfill C.Colla Formerly: Civil and Environmental Engineering Department, Edinburgh University, UK

D. M. McCann & M.C. Forde Civil and Environmental Engineering Department, Edinburgh University, UK

ABSTRACT: This paper focuses on the use of single and 2-channel digital radar systems to investigate masonry arch bridges with soi! backfill using antennae in monostatic, bistatic and transmission mode, also for tomographic inversion. From a laboratory study it has been demonstrated that even small concentrations of sodium chloride salt can cause substantial attenuation ofthe signal. Thus routine de-icing using salt can cause significant problems for the use of radar for the investigation of masonry arch bridges. In addition, bridges having a higher moisture content will also be subject to substantial signal attenuation. Fields studies are given on two bridges in Scotland to illustrate the applicability of the various radar techniques using a multi channel digital radar system. I INTRODUCTION

springers for the arch. Other key factors include knowledge of whether the bridge is an arch backfilied with soi! thus giving load dispersion, or whether the bridge has a cellular hollow construction (Jervoise 1936, Ruddock 1979, Anon 1864). If the bridge is soil filled, knowledge of the condition ofthe soi!- wet or dry, compact or loose ­ is also relevant. It is against this background that the research reported in this paper was carried out. The specific Non Destructive Testing method herein discussed is Subsurface Impulse Radar and its performance in conductive environments.

Masonry arch bridges comprise up to 40% of the UK bridge stock (Page 1989) and represent a significant portion of the bridge stock in continental Europe (Binet 1996, Yanez & Alonso 1996). Most ofthese bridges are in excess of 100 years old, were designed for horse drawn trafiic and yet are subject to ever increasing axle loads due to EU Regulations and increased traffic volume. They have generally been considered to be "maintenance free" and often neglected in this context. With growing concern about their safety, mathematical analyses have been undertaken which have demonstrated that the load carrying capacity of a bridge may not coincide with modern requirements. UK policy has moved to the situation that if a bridge fai!s a theoretical mathematical analysis ofload carrying capacity, and yet looks to be in good conditions visually, then rather than weight restriet the structure further ­ monitoring is undertaken. This monitoring may take the form of ongoing NDT investigations and also NDT integrity investigations to assess whether there are unknown features within the structure which would permit a more realistic assessment of the load carrying capacity (Das et al. 1995). In order to undertake effective finite element work, which is being correlated with scale model work, there must be a clear and unambiguous knowledge of the internal construction of the masonry arch bridge. For example the size and shape of the arch is a critical factor as is the size and shape of the

2 OBJECTIVES OF RESEARCH Subsurface radar for structure investigation produces short pulses of high frequency electromagnetic energy (tipically in the range 100­ 1500 MHz) which are transmitted into the structure. The propagation of the radar signal depends on the electrical properties (dielectric and conductive) of the materials encountered, and it is described by its velocity and attenuation. These properties also determine the signal power that is retlected at boundaries where the electrical properties vary (Topp et al. 1980, Smith-Rose 1934, Greaves et al. 1996). Thus, the effective application of the radar for the high-resolution definition of features (masonry stratigraphy, voids, defects) is a function of the antenna frequency used, whilst the

253

propagation of the radar signal depends on the electromagnetic response of the materials investigated. Work has been carried out both in the laboratory and on site to identify the effectiveness of the Radar technique when the signal is propagating through conductive materials (saline solutions, c1ayey and wet materials). The effects of the signal attenuation on the penetration of the wave, and their implications on the operating mode (reflection, transmission and tomographic survey) of the radar system have been studied. The implications of the use of varying antenna frequencies on the signal velocity and on the resolution of inner geometrical dimensions of the structure (voids, thickness of walls and arch) have also been investigated. Figure I . 8ide view of masonry test rig with wooden gate in the foreground.

3 LABORATORY WORK

3.1 Experimental test rig A 2.4 m long x I m wide x 1.5 m high test rig was built in the laboratory. Its main part consists of a 3­ sided masonry box with the fourth side equipped with a wooden gate to gain easy access to the inside of the test rig and to facilitate any loading and unloading of fill material (Fig. I). The masonry brickwall was built of Class A Engineering solid bricks and mortar in the proportion I: 14:3 of cement, lime, sand. The wall is one header thick and its foundations are secured into a slot cut out of a plywood base which also constitutes the base of the rig. In this phase of the experimental work, the masonry rig was lined with a PVC sheet to create a watertight container for the water which constituted the fill material and to maintain the brickwall in a dry condition. The rig was filled with water up to 1.3 m level and sodium chloride was dissolved into the water to create brine solution in different concentrations: 0.05 %, 0.1 % and 0.25 % by weight of salt to the water. Rebars (0 3.5 cm) were immersed in the water and maintained vertical by suspending them from a timber frame which was also built around the rig. The metal rods were located at 10, 40 and 70 cm away from the brickwall along which the radar antenna was dragged for data collection (Fig. 2).

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and smooth picture of the radar targets. Twenty centimetre marks along the direction of movement of the antenna were recorded at the top of the plots. Reflections from the masonry walls and the metal re-bars were picked up. The survey was repeated for the different salt concentrations in the water, while brine conductivity and temperature were monitored, (Tab. I). Table I. Values of brine temperature, concentration and conductivity measured during the experiment arlne temperature lS'alt concentration Conductivity

3.2 Radar survey Aradar antenna with nominal centre frequency of 900 MHz was used to collect reflection data within a time ranges of 60 ns. The antenna was moved along one side of the masonry rig, scanning in the horizontal direction, to plot horizontal cross sections of the structure. The antenna had a survey wheel attached to record a constant number of scans per unit distance travelled and to obtain a more accurate 254

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0•05% , •••• 0.10% ' _ _ _ 0.25%

_(n..c)

where 0 = 0 dc + (0 &" & 0 combines both d.c. conductivity and dielectric losses. And &' is the real part of the dielectric constant. Expression (1) is approximate and requires that 0/(0&'&0 be much less than 1. The signal waveforms were analysed in the time domain to quantify the reduction of signal power due to the increasing conductivity values with increasing salt concentrations. The decrease in energy was calculated in relative terms, measuring the amplitude of the corresponding peaks which show up in the form of sinusoids between 7 and 10 ns on the time axis. From Figure 4 it is evident how an increase in conductivity of only 0.4 mS.m-l , causes a reduction of 34% in the amplitude of the signal, when passing from 0.05% to 0.1 % salt content in the water: one third of the power of the signal is lost. When the salt content increases to 0.25%, the signal amplitude decreases a further 17%, reaching only 50% of the power of the signal registered at 0.05% salt content. Note that even though the sodium chloride content doubles from 0.05 to 0.1 %, and increases five times to reach 0.25%, the salt concentrations considered in the experiment are low values compared to sea water (3-3.5% on average) or to localised high concentrations of salt as could be encountered in masonry arch bridges and other historical and modern structures due to de-icing salt capillary suction from ground through foundations and other environmental factors (Baronio & Binda 1989). The outcome from the amplitude analysis study is an exponential reduction in signal amplitude as the conductivity of the material increases due, in this case, to increasing sodium chloride content. From the above discussion and equation (1) it follows that conductivity affects the attenuation of the signal, which in turn governs the penetration capability of the signal. To verify and confirm whether the phenomena observed were to be attributed primarily to a variation of the real part of the dielectric constant or to the increased conductivity of the material, a calculation of the dielectric constant of salt water was conducted. First, the veJocity of the eJectromagnetic wave through brine was calculated

Figure 3. The relationship between salt content at di fferent concentrations in water, and amplitude of the reflected signal from the Mt re-bar.

I

• Ig n a 1 a tte n u a tlo n

• ",s

ii. E e

....

100 to .0 70 60 50 .0 30 20 10









0 .05%

0 . 10%

0 . 25%

aalt concentratlon

Figure 4. The relationship between salt concentration in water and the relative decreased amplitude of the signal, caIculated from the experimental data.

.

ELECTROMAGNETIC WAVE VELOC ITY IN

FUNCTION OF CHLORIDE CONTENT IN WATER

~I

_

,

'0

3>

:

.s

30 25

~

20 15

:;:;

10

.­ o.t

0.2

0.3

0.4

0.'

position of reflectors (m)

i

255

OJ~

0.7

-+-0.05%

....... 0.10%

0.25% .

"----'

Figure 5. Representation of the electromagnetic wave velocity measurements calculated by time domain analysis.

for the three chloride concentrations considered. From the known geometrical position of the retlectors in brine and the 2-way travel times from each retlector measured from the radargrams, the pulse veJocity was calculated by time domain analysis and found to be constant throughout (Fig. 5)

From the velocity values obtained and the expression for radar signal velocities at higher frequencies in low-Ioss materials (Equation (2», (padaratz & Forde 1995) the real part of the dielectric constant of brine at the salt concentrations used in the experiment was ca1culated and found to be in the narrow range between 80 and 81 which covers the dielectric constant values of sea water and fresh water. V=

c

G " C'

the bridge (Colla et al, 1997). The transmitter, on the downstream east wing wall was moved horizontally, whilst the receiver was stationary, at the same level, on the upstream wing wall. The survey was repeated a number of times with the same movement procedure for the transmitter, whilst the receiver moved along in 0.5m steps to obtain an adequate coverage ofthe bridge section (Fig. 6b). The radar plots obtained are of the kind shown in Figures 7,8 where the first arrival trave1 times are recorded at the receiver location (upstream). The first finding from this radar survey is a generally low velocity of the EM signal which indicates the values of dielectric constant within the bridge to be significantly different from the values expected for construction or fill materials. The average value for the die1ectric constant Er for the composite bridge construction [masonry/soil fill!masonry] was computed to be approximately 56. This value is weIl above reference values published in literature and could be explained by a high moisture content in the fill, due to possible moisture-drainage problems in the bridge. Previous studies of the same structure and in particular a conductivity survey conducted on the abutment and wing walls (Colla et al, 1995), highlighted such problems as high water content in the bridge materials. Conductivity values obtained were in a very high range indicating soil filling behind the abutment and wing walls comprising materials with high conductivity (argillites, wet c1ays or alluvium and sand), or high moisture contentlsalinity. In this context, both dielectric constant and conductivity increase with increasing water content. The presence of salts in pore water - from routine winter road maintenance - will increase the conductivity even further, without affecting proportionally the dielectric constant. Consider now Figure 7 and the position of the receiver Rx in relation to the transmitter on the downstream side: the shortest EM wave ray paths and corresponding shortest travel times are to be expected when the transmitter reaches the position just opposite the receiver Rx - assuming that the material within the bridge is homogeneous. Similarly the received signal would show the maximum amplitude at this location (its attenuation being mirumum there) whilst at longer transmitter/receiver distances the signal would show greater attenuation. In Figure 7 this is true for the received signals to the right of the Rx position, but not to its left hand side. In Figure 8 the situation is even more complex: at a transmitter position between 0 and 1 m on the downstream side and a receiver position of 3.5 m on the upstream wall, the shortest trave1 time registered on the scan, is actually the longest distance travelled. Also, the attenuation

(2)

where c = 3 x 10 8 m/s, the propagation ve10city of electromagnetic waves in free space. The calculation, while agreeing with values published in literature regarding the die1ectric constant of salt water (Kraus 1988, Von Hippel 1954, Nat. Bureau of Standards 1958), confirms the initial hypothesis of constant real part of dielectric constant at the increase of salt content. In other words, the permittivity controls the speed of the E.M. pulse, whilst increasing conductivity reduces the depth of penetration. 4 SITECASES 4.1 Middleton Bridge

North Middleton Bridge, is a twin arch stone masonry bridge (Fig. 6a)in Scotland on which radar antennae in the range from 100 MHz to 1 GHz centre frequency were used with different objectives and in different system configurations. In general high frequency antennae give good spatial resolution but give only shallow penetration as the signal becomes rapidly attenuated and may suffer from c1utter (Padaratz & Forde 1995). In this project, higher frequency antennae were used for the identification of masonry wall thickness and near­ surface voids /defects. Lower frequency antennae are better suited to penetrate deeper into the abutment as they emit more powernd signals, but their long wave length is a detriment to spatial resolution. Also, targets of "small dimensions" or "small thicknesses" can be missed. In the case of this structure, its significant width ­ over 8 metres - and the die1ectric properties of the filling materials did not permit the use of even the lowest frequency antenna in a retlection mode, to scan the whole bridge horizontal section from upstream to downstream side. Operating the equipment in this mode, the radar signal has to trave1 twice the distance from the antenna to the target. In view of the above, radar time sections for tomographic inversions were collected by using two 100 MHz antennae positioned on opposite sides of

256

of the signal is greater, compared with the case of Figure 7. If the simplified equation for velocity (Equation (2» is assumed valid, then it can be postulated that the phenomena can be attributed to uneven dielectric constant values cross the bridge section, with materials characterised by lower dielectric constants between 0 and 2.5 m on the wingwall than between 2.5 and 5 m. The attenuation of the received signal seems to follow the same trend seen for the velocity. Since it is particularly noticeable when the receiver is at location 3.5 m, it can be deduced that materials on the right hand side of the wingwall are characterised by higher dielectric constants and also by higher conductivity values. This assumption need to be reconsidered if the general equation for EM wave velocity is used (Equation (3): v=

c

[&; [Jl+mh +lllY,

. .~ ';;'. ;:~\_ ~" ~3~ ' .'. :_~ :':::~ ::: : : : · · "='~:: -3

-4

l



0.2 0.15

~__H _ I 2

4

0.1 0.05

6

o

Time (sec)

a) Velocity W. Vertical D334-6.

in l

i 1

~

Hz.

-l

o r---+--~--~----r-~ o 25 50 75 100 125 I

1--_.

Time (sec)

~

Hz.

d) Frequency Spectrum W. Horizontal. D334-6.

!

0.2 T

t

2 +

-4

I

125

0.05

4 T

§. 0 ~ -1 .2" -2 :!! -3

100

0.1

c) Velocity W. Horizontal D334-6.

~

75

0.2

r~i

E

50

0.15

; 0 !~------~--------+_------~

~ -1 Q 2 4 6

0- 3

25

b) Frequency Spectrum W. Vertical D334-6.

4

-4

p..

o

2

4

­

0.15 0.1 0.05

ob o

6

Time (sec)

e) Velocity E. Vertical D334-6.

I

T~=): -~I g) Velocity E. Horizontal D334-6.

25

50

Hz.

75

100

125

f) Frequency Spectrum E. Vertical D334-6.

!

0.25 0.2

T

0.15 0.1 0.05

o

o

25

50

Hz.

75

100

125

.1

h) Frequency Spectrum E. Horizontal D334-6.

Figure 7. Velocity and Frequency Spectrum for Calibration Truck.

300

U GI Je

E

0.2

4 3 2

0.15 0.1

E.

0

~ -1 @

~ -2 ~ -3

2

-4

Time (sec)

1

3

4

a) Velocity W. Vertical D334-20.

U GI Je

E

E.

~ u .2 ~

4 3 2 1 0

-1 @

-2 -3 -4

E.

2

1

3

4

2

0tL---LI!h~/""'...~ . =-----!---­ . . .

Vi 1

2

-2

3

4

o ro

100

125

Time (sec)

PlI l

25

50

Hz.

75

100

125

0.5 0.4 0.3

02~ 0.1

o

-0.1

25

I

I

I

I

50

75

100

125

Hz.

f) Frequency Spectrum E. Vertical D334-20. 0.6 0.5 0.4 0.3 0.2 0.1

u

I

0

75

d) Frequency Spectrum W. Horizontal D334-20.

3

-5

Hz.

0.05

Time (sec)

e) Velocity E. Vertical D334-20.

~

50

0.1

~ : ±

.2

0 25

0.15

~ -1

g

o

0.2

4

= E

o

b) Frequency Spectrum W. Vertical D334-20.

c) Velocity W. Horizontal D334-20.

U

0.05

2

3

Time (sec)

g) Velocity E. Horizontal D334-20.

4

O +---~---+----~--+_--~

o

25

50

Hz.

75

100

125

h) Frequency Spectrum E. Horizontal D334-20.

Figure 8. Velocity and Frequency Spectrum for Drop-Weight Device.

301

Table 2. Vibration Assessment Criteria. Bridge or Instrument Stony Brook

Zellars Power

Vibrars

all

VeIocity (mm/sec) 1.50

Freq. Hz. 10

R Value 2.35

Truck Truck Truck Truck Drop-Weight Drop-Weight Drop-Weight Drop-Weight Drop-Weight Drop-Weight Drop-Weight Drop-Weight

a11 all all a11 P#2 P#2 P#2 P#2 P#4 P#4 P#4 P#4

7.00 0.75 0.00 1.00 42.0 7.00 0.50 0.50 30.0 4.00 1.00 1.00

27 27 27 27 50 27 27 27 50 27 27 27

.995 .995 .995 .995 1.84 .995 .995 .995 1.84 .995 .995 .995

52,200 599 0.00 1,065 3,480,000 52,200 266 266 1,780,000 17,050 1,065 1,065

37.1 17.7 0.00 20.2 55.4 37.1 14.2 14.2 52.5 32.3 20.3 20.3

Truck Truck Truck Truck Drop-Weight Drop-Weight Drop-Weight Drop-Weight Drop-Weight Drop-Weight Drop-Weight Drop-Weight

a11 a11 a11 all P#4 P#4 P#4 P#4 P#5 P#5 P#5 P#5

2.00 3.00 7.00 2.00 0.50 1.00 40.0 1.25 1.00 0.75 25.0 1.00

25 25 25 25 25 25 75 25 25 25 75 25

.487 .487 .487 .487 .487 .487 1.46 .487 .487 .487 1.46 .487

3,950 8,882 48,400 3,950 247 987 4,740,000 1,520 987 555 1,850,000 987

25.9 29.4 36.8 25.9 13.9 19.9 56.8 21.8 19.9 17.4 52.7 19.9

Loading

Position

Truck

888

19.5

D-334 E.Horiz E. Vertical W. Horiz. W. Vertical E. Horiz E. Vertical W. Horiz. W. Vertical E. Horiz E. Vertical W. Horiz. W. Vertical D-441

E. Horiz E. Vertical W. Horiz. W. Vertical E. Horiz E. Vertical W. Horiz. W. Vertical E.Horiz E. Vertical W. Horiz. W. Vertical

device impacted the bridge at the same spandrel wall as the large response. The Stony Brook testing indicates reservations in the use of vibration testing alone to detect damage. The large longitudinal cracks present in the arch barrel (Figure 10) did not appear to have influenced the vibration records. Although the R-value for Stony Brook indicated general damage, the application ofDIN 4150 to the truck records reached a different result. The peak to peak velo city and the calculation ofvibrars both indicate minimal damage. The Hunterdon tests indicate that the global response ofthe bridges are good, while individual instrument locations indicate damage. This is shown through the large velocities found with the East horizontal seismometer at D-334 and the West Horizontal seismometer at D-441.

The different criteria used to evaluate the structures in table 2 indicate different states of subsequent damage. There is good correlation between the peak-to-peak velocities and the vibrars limits. Both criteria indicate localized damage in the two Hunterdon County bridges. The R-value found using truck tests has poor correlation with the rest ofthe criteria. The frequency ofvibration lends interesting inforrnation about these structures. The frequency appears to be higher in the areas of damaged structural components, almost doubling in the areas ofhigh velocity observations. In these areas, the high frequency vibrations are quickly damped out by the structure with a maximum response duration of a tenth of a second.

302

Figure 9. Longitudinal Craek at Crown ofNorth Span

Figure 10. Drop-Weight Device.

Conclusions

for the structure. The doser the drop-weight moved to the loeation of the large response, the more defined that response became.

This study involving dynamie testing arrived at the following condusions. The use of dynamie testing proeedures is relatively simple to implement. The amount oftime neeessary to instrument and test the bridges is reduced in comparison with deflection measurements. The large velocities present in only one instrument indicate that there is some promise that vibrations can determine the position of localized damage. The two Hunterdon bridges both had large responses in one horizontal seismometer during both the drop-weight and truck tests. Vibration studies are not the quick answer to masonry arch assessment. The Stony Brook Bridge tests gave no indication ofthe large crack shown in figure 10. The testing did not indicate damage in any ofthe eriteria except the R-value which only indicated minimal damage. The drop-weight device was a useful tool in condition assessment. The drop-weight device tests produced better frequency spectra than the truck tests, because the response was fee ofthe biases present in truck loading. The frequency spectra showed dear peaks at the free vibration frequencies ofthe bridges. Also, the ease in changing the load location enabled the tests to develop a better global and local response function

References

Boothby T. E., Laman 1. A. and Bintrim 1. W. "Field Testing ofthe Stony Brook Bridge," Final Report, Pennsylvania Transportation Institute, The Pennsylvania State University Research Office Building, Report Number PTI 9813, January 1998. Brown G., Pretlove A.J., Ellick 1.C.A., Hogg V., and Choo B.S., "Changes in the Dynamic Characteristics of a Masonry Arch Bridge Subjected to Monotonie Loading to Failure," Proceedings 0/ the First International Conference on Arch Bridges, Bolton, UK, September 1995, pp. 375-383 . Ellick J.C.A. (1995). "Vibration Characteristics of Masonry Arch Bridges," Ph.D. Thesis, The University ofReading, 1995. German Standard DIN 4150 Part 3: Structural Vibrations in Buildings, 1986. 303

Arch Bridges, Sinopo/i (ed.)© 1998 Tay/or & Francis,/SBN 90 5809 012 4

Restoration of a two arches masonry bridge: Experimental testing and mechanical behaviour Antonello Salvatori Dipartimento di /ngegneria delle Strutture, delle Acque edel Terreno, University ofL'Aquila,/taly

ABSTRACT: The various geotechnical, chemical-physical and structural behaviours of an historical brick masonry bridge located in the middle Adriatic coastal region ofItaly, are analyzed. The considered monument is the ancient masonry bridge on the Rio river (along state road 81), near Teramo, in the coastal north Adriatic belt of the Abruzzo region, about 20 km far from the Adriatic sea. In order to correlate the structural behaviour and the damage assessment together with the material properties of the brick masonry, a lot of investigation have been performed, involving both chemical-physical and mechanical testing on the bricks and the relevant mortars, completed by a F.E. computational analysis, in order to understand some causes of existing damage, and to evaluate the correct dynamical behaviour of the analyzed structures by comparison with in situ testing. The results deriving from the performed analyses are compared each other, obtaining a clear picture of the material properties, and achieving a satisfactory explanation of the damage assessment of the monument, related both to the dynarnical behaviour produced by heavy traffic condition, and to the relevant seismic history. By this way, accurate repair techniques have been employed for the bridge structures, with particular reference to the pile foundation and to the masonry arches, so that further restoration and maintenance works on similar masonry bridges belonging to the same area can benefit themselves of the scientific knowledge of this masonry bridge behaviour. I INTRODUCTION The chemical-physical and structural behaviour of an ancient brick masonry bridge, located in the middle Adriatic coastal region of Italy, are analyzed in relationship with hydrogeological and geotechnical situation in the considered area. The examined monument is the historical masonry bridge on the Rio river (along state road 81), near Teramo (Fig. 1). The area located near Teramo is a homogeneous one as for soil properties and for material monumental building characteristics. The bridge is composed by a two arches masonry structure, each spanning over 15 m, based upon a central pile, composed by a rectangular part with circular edges, 6.50 m long and 2.5 m thick, and upon two lateral twin shoulders. The deck is 5.60 m wide, and before restoration supported heavy traffic with some difficulties. The pile and the shoulders, 6.50 m high, are direct1y superposed upon the soil, without any enlargement in the foundation structure. The soil characteristics are typical of the gray clays in that area, namely known as "Laga mountain formation" .

It is worth noticing that this kind of direct foundation involves some problem with the hydrogeological properties of the area, because of the conformation of the Rio river valley in its final section before its c\osure in the Vornano river. Also the deck width plays arelevant röle in the damage occurring to the main bridge structure, because of the presence of fatigue stresses located along two well defined longitudinal lines. In fact, due to its strictness, heavy traffic (especially trucks and line buses) passed always along the same longitudinal trails, causing some displacement in the road pavement. In order to correlate the structural behaviour and the damage assessment together with the geological characteristics of the site and the geotechnical properties of the foundation soil, according to the mechanical properties of the brick masonry, deep analyses have been performed, involving hydrogeological studies, geotechnical inquiry about soil properties, chemical-physical and mechanical testing on the bricks and the mortars. All these analyses have been correlated with computational ones by modeling the bridge structural components

305

Figure 1. Rio river bridge before restoration (south view). c)

by F.E. technique, with the aim to have a better evaluation ofthe causes ofthe actual damage, and an accurate evaluation of the dynamical behaviour of the analyzed structures before and after the restoration. Because of heavy trafiic conditions seem to playa relevant röle in some longitudinal cracks along the brick arch, and due to the prevision of increased trafiic loads during next bridge life, this particular kind of monumental structure is analyzed to fully evidence the behaviour of the structural system, and of the relevant materials, under severe stress, fatigue, hydrogeological and atmospheric conditions, along with its various material behaviour: brick and concrete for the arch structure, sandstone and mortar for the piles. The whole work has the aim to improve the restoration techniques for these monuments through a deep knowledge off hydrogeological and geotechnical site conditions, material and structural dynamie behaviour. In a previous work (Salvatori et al. 1994), the chemical-physical and the structural behaviour (also under heavy trafik dynamical forcing) of the temple of S.Maria dei Tricalle in Chieti were analyzed, to correlate the chemieal properties of the bricks with the dynamical behaviour ofthe temple structure. This structure is strictly correlated with the present work because of the similitude of the brick masonry in the two (however different as for function as for devising) monuments. Many interesting results were obtained, in particular the complete agreement between the chemical-physical properties of the masonry and the static and dynamic behaviour of the church. Furtherrnore, experimental dynamical testing carried on the church had shown the main modal shapes of the church structure, exactly compared with the analytical ones, both for the shape and for the frequencies. In fact, the study regarded the complete knowledge of the constitutive materials,

d)

e) Figure 2. Rio river bridge: before restoration: a)

longitudinal cross section; b) lateral north view;

c, d) transversal cross sections;

after restoration: e) longitudinal cross section.

and their behaviour under severe conditions; sampies of bricks were taken from different parts of the monument, allowing the correlation between the material properties and the structural behaviour. This kind of analysis revealed itself very useful in order to get parametric values to test material and structural properties decay in time. In fact, the repetition of the experimental modal testing (by seismometrie analysis) during time can show how great the variation of mechanical and chemical properties is, and consequently, by the decrease of the modal experimental frequencies, the decay of the brick quality. The same analysis is needed for the old masonry bridge on the Rio river,. These structures have been compared because of their particular structural situation: while for the temple of S.Maria dei Tricalle trafflc condition seemed to be the cause of some cracks and fatigue phenomena of the bricks and relevant mortar, for the Rio river bridge heavy trafiic conditions seems to playa relevant röle in the observed longitudinal cracks along the brick arch. So this different kind of monumental structure is analyzed to fully evidence the behaviour of such a structural system, and of the relevant materials, with

306

the aim to achieve precious indications about the brick property decay along with time, by dynamical testing ofthe whole structure. 2 CHEMICAL-PHYSICAL ANALYSIS The analyses of the brick masonry structure have been performed to achieve the data necessary to characterize the materials (mortars and bricks) both from a chemical-physical point ofview and from the mechanical one. Sampies of bricks and mortars were taken from different part of the bridge (deck, lateral walls, pile, shoulders), (Fig. 3) and experimental investigations have been carried out in order to correlate the chemical and physical properties to the decay forms. These were also assessed by visual inspection. Further analyses have been performed to compare the material with the structural behaviour; for this aim, laboratory tests have been made on the bricks to determine the mechanical properties. The sampling were taken according to different state of conservation and differentiation in the materials (see CNR-ICR 1980). The following analyses have been performed on all the specimens: X-ray diffraction (XRD), light and scanning electron microscopy (SEM) (mineralogical­ petrographical analyses) (see CNR-ICR 1980, 1981), mercury porosimetry (P) (see CNR-ICR 1982), helium pycnometer (YR, y) water absorption by total immersion and capillarity (CiV, IS) (see CNR-ICR 1983) (physical testing), ionic chromatography (see CNR-ICR 1983) and X-ray energy dispersive analysis, loss on ignition (L.O.I.) at 950°C (chemical aspect). In order to define the computational model, some compression test have been made both on cubic (60x60x60 or 100xlOOxlOO mm) and cylindrical (83x150 mm) sized brick sampies; by this way, the compressive strength and the other mechanical properties were respectively determined. Besides, samplings were collected by using püwder and core drilling, in order to get information on the decayed masonry as weil as on the mechanical features. The descriptions of bricks and mortars (see CNR­ ICR 1985, 1988), together with the relevant chemical-physical-mechanical properties and the type of damage (Van Baien et al. 1996) are shown in Tables 1- 4. In particular, in tables 1 and 2 the brick and mortar physical characteristics are shown, to fully evidence the various types of bricks and mortars contemporaneously existing in the bridge structure, while in tables 3 and 4 chemical and mechanical results are evidenced, to show how chemical properties can influence the overall mechanical behaviour of the bridge structure (both under static and under dynamic condition):

Figure 3. Core drilling of brick sampie from the East shoulder

Table 1. Description and features of the collected bricks. Rio river bridf{e brick properties

Size (mm) 60xl00x250 -;- 300x400x500

Colour dark and light red! yellow

Type heterogeneous

Type 0/ encrostation

damage spalling, loss of adhesion

deformation, efflorescence

Soluble salts chloride-nitrate

Mineralogical Quartz K-feldspar,

composition plagioclase, Calcite

Pyroxenes, ghelenite

amorphous phase

Pore radii 40Jlm-20mm

Table 2. Description and characteristics of the collected mortars. Rio river bridf{e mortar properties

Gray

Colour Type 0/ Efflorescence

damage biological degradation

encrostation

loss of cohesion

Substrate.cohesion Tough

Binder lime

Aggregate river sand and calcite

Distribution Medium

round sand

Sphericity Aggregate d> 0.4. On the other hand the incIusion depth has a profound effect on the strain distribution. With increasing incIusion depth, the measured axial strains increase within the orifice and decrease at the perimeters. There is a marked increase in compressive stresses within the orifice when bJb ratio is less than 0.4. Figure 7 shows the strain distribution ratio Sr; ratio of strains at orifice (at PI) to those in the vicinity of the incIusion (at P2) for the various prisms with increasing load. Since the bulk of stress flow occurs within the concrete in the core of the section, any reduction in its volume will increase the magnitude of load intensity transmitted through this region. In other words the effective width of the section is reduced. These plots also provide valuable information on the behaviour of the section with loading history. While the incIusions help 'deflect' load towards the centre of section, an attempt is made for the load to spread towards the perimeters as failure is approached. This was also evident from the axial stress contours near failure in the finite element model. One should bare in mind the need for a

N 10 E ..§ 8

b '"'" ~ Q)

'" ] 1;) .~

]

Q)

J

-:1:- t~ = 6mm~ l -b=9mm

~

6

\

4

-

2 0

o

0.2

0.4

0.6

t--­

0.8

belb

Figure 8. Effects of orifice diameter on the stresses within the orifice. 5.1. 2

Effects 0/ inclusion properties.

From the results of the interface study, it is cIear that the type of incIusion material almost entirely determines the stress1strain distribution within the prism and effectively how much load is transmitted through the inclusion. In order to determine the effect different inclusion materials have on the stress1strain distribution and hence the nature of load transfer within the prism, a range of material

336

Table 2. Inclusion material properties. Arbitrary inclusion number 1 2 3 4 5 6 7 8 9 10 11

12 13

14 15 16 17 18 19 20

k

10

e M

Elastic Poisson modulus Ei ratio (N/mm2) Vi 2500 500 30000 0.1 70000 200000 2500 5000 30000 0.2 70000 200000 2500 5000 30000 0.3 70000 200000 2500 5000 30000 0.4 70000 200000

~

"§ :;;

!

N~

~

6

:1, 4

-2

2

0

4

(a)

6

/"

M

ci

-h

4

N

0­

:;;

]

e ~

...,.

.L>

V ~

0 -2

o

2

4

8

6

mT

elastic properties, modulus of elasticity and poisson ratio are selected, table 2.

(b) 6

Other properties such as coefficient of friction and density are kept constant in a linear elastic analysis. It should nonetheless be born in mind that the interaction of all these properties including durability should be taken into account in adopting optimum inclusion material type. A modulus of 30kN/mm2 and a poisson ratio of 0.2 are used for the concrete. The results are expressed In modular ratio, mT; ratio of inclusion modulus to concrete modulus, and shown in figure 9. With very low modular ratios, the bulk of the load is transmitted through the concrete. This was noted with the experimental prism sampies which had a modular ratio of about 0.12. For high modular ratio configuration, much of the load is directed towards the inclusion but at a very decreasing rate beyond mT > 1 This appears to suggest that there is no benefit in increasing the stiffness of the inclusion beyond that necessary to provide adequate strength. A seetion plot across the width of both the prism with a low modulus inclusion (LMI) and one with a high modulus inclusion (HMI) explains the nature of load transfer

6

mT

/'"

~

M

ci

~

11

11

~

.5 :;;

Ni

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--0-

.§

e :(l

0

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~

~ -2

o

2

6 mT

(c)

Figure 9. Effect of inclusion modulus on stresses in (a) orifice, (b) inclusion vicinity at peripheries and (c) within the inclusion in the prism. clearly. It can be observed that the load is 'diverted' towards the peripheries of the section in comparison to the case in the LMI. As for the poisson ratio of the inclusion material, only strains within the inclusion and in

337

particularly transverse strains are significantly affected. There is minimal effect on the stress distribution within the entire composite prism. The poisson ratio effect is shown in figure 11 Despite the effective width reduction evident in the prisms with the LMI, the state of stress within the orifice (compression compression; see Fig 9 (a) ) is such that this loss is compensated by enhanced concrete performance.

500

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tl

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100

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0.1

0.2

-

0.3

-

-x-mr = 6.67

0.4

Poisson ratio of inclusion material

--------­

(a)

I··----HMI LMI I

o

1\

/

50

_\\

...........

~ 200

0

...----..

--

r--.

·s

400

t3 200

>-­

\

100

c

-50

.~

-o-mr = 0.08 -Q-mr=0.17

.~ -100

ISO 200 250

e

Distance along width of prism (mm) [section x3 - x3]

"~

-ISO

~

-200

~

Figure 10. FE section plot across the width of the prism

-mr=1 -mr=2.33 -x-mr=6.67

-250

o 5.2

Eccentric Load

The neutral axis of the monolithic concrete prism can be calculated from elastic theory and is in line with experimental results. However, width the other specimens the precise location is difficult to measure, but from the finite element results, it is 'shifted' towards the compressive fibre. This would be expected since the effective section width is reduced. However there is not a linear plot from compressive fibre to tension fibre because the tensile strains or stresses are virtually eliminated Figure 12 and 13 shows the plots of measured strains at both the compressive fibre (C) and tension fibre (T). Also shown on figure 14 is a plot of strain distribution across the section for typical finite element model and measured strains on the various prisms plotted on the graph. The effect of the inclusion acts to change the slope of the curve. It can be seen from the measured strains that the tensile strains on the tensile fibres are reduced by as much as between eight to fifteen times as a result of the introduction of the inclusion. The introduction of inclusions significantly reduced the axial tensile strains that would occur in a similar

0.1

0.2

0.3

0.4

Poisson ratio of inclusion material

(b) Figure 11 . Inclusion poisson ratio effect on the strains within the inclusion: (a) axial; (b) transverse

monolithic concrete prism. This will significantly reduce or eliminate the occurrence of surface and/or micro cracks and therefore improve durability The reduction in stiffness or rigidity, which helps relieve the tensile stresses, is believed to result mainly from the expansion of the inclusion and a rigid movement ofthe surrounding concrete. The prism models have provided considerable insight on the behaviour of an inclusion - concrete composite unit at its most fundamental form. They showed the significant role played by the orifice in load transmission, especially with concentric loads. The eccentrically loaded prisms showed a significant reduction of tensile strains in the vicinity of the inclusion. In an arch, the eccentricity of the thrust line causes regions of tensile strain, the magnitude of which can be locally reduced significantly by the presence of inclusions. This 338

300

~ 200

• There was no benefit in terms of performance of the resulting structure in using inclusions with relatively higher stiffnesses. UPVC was therefore chosen for its durability, low stiffness stress relaxation, and of course it is a relatively cheap plastic.

~

l=!:J

-g ..9 100

o

o

-200

200

400

600

• The inclusions acted as local stress relievers and therefore encouraged the stress to flow through the orifice, effectively reducing the width to that of the orifice with concentric loading. With eccentric loads, the axial tensile strains that would occur in a similar monolithic concrete prism were significantly reduced.

800

micro strain

Figure 12 . Axial strains on both compression and tension fibres of section (position P3) in (SO) 300

• The depth of the inclusion was found to have a significant effect on the stress/strain distribution and values within the specimens. The thickness ofthe inclusion on the other hand had a minimal effect on the strain distribution.

~ 200

~

-g

~ -T

..9 100

o

o

-200

200

400

600

• Knowledge of the ratio of stress within the orifice to the perimeter (stress distribution ratio) would be useful in design applications especially in elastic analysis.

800

micro strain

Figure 13. Axial strains on both compression and tension fibres of section (S9).

Acknowledgement

The authors wish to acknowledge the support and collaboration of Lancashire County Council (Bridges section), TRL, and the University of Salford.

400

-,

'§

200

-

1;;

e ~

J .~

1_ FEM(S9)

----__ --

---.(I

0

~

A

-

IA

J

so

REFERENCES Jackson, N 1986. Civil Engineering materials, Macmillan Education Ltd, London, UK. Melbourne, C 1987. A new arch construction technique, Proc. Int. Conference on the design and construction of non-conventional structures, Civil Comp. Press, UK. Melbourne, C 1988. A new arch construction technique", Struct. Eng. Review, UK. Melbourne, C & Irvine, B 1994. Mass concrete arches, Bridge assessment management and design, Elsevier, UK. Melbourne, C. Weeks, L 1995. Mass concrete arches, Proc. First Int. Conference on arch bridges, Bolton, UK, Sept 1995 Melbourne, C Field study - Cunningham Brook Bridge Widening, SERC report, GRlD55009

-200

o

50

100

150

200

250

distance along section (mm)

Figure 14 . Strain profiles across section showing position of neutral axis. behaviour has been observed in the preliminary arch models tested. 6 CONCLUSIONS Based on the experimental and FE results, the following conclusions can be made.

339

Melbourne, C 1993. Structural monitoring 01 Monk New Bridge on A59, Lancashire, TRL, Contract N02050, London, UK. Neville, A. M. 1981. Properties olconcrete, Longman Scientific & TechnicaI, UK. Ogorkiewick, R.M. 1977. The Engineering properties 01 plastics, Oxford University Press for the Design Council, The British Standards, Oxford, UK. Wilde, B Concrete Bob 's railway viaduct, Concrete International, Vol. 118, No 7, ACI, Detroit, USA, July 1996. Williarns, E.O 1927. The philosophy olmasonry arches, lust Civil Eng selected engineering papers, No 56, ICE UK. Williarns, 0 & Williarns, O.T 1960 Luton­ Dunchurch: design and execution, Proc. ICE, No 6435, UK. Wilson, W. S 1906-1907. Some concrete

viaducts on the West Highland Railway, Min Proc ICE, Vol. 170, pp. 304­ 307 UK, 1906-1907. Wood-Hill, A & . Pain, E.D 1904. On the

construction 01 a concrete railway-viaduct, Proc ICE, Vol. CLX, No 3502, UK.

340

Conservation and maintenance

Arch Bridges, Sinopoli (ed.)© 1998 Taylor & Francis,lSBN 90 5809 012 4

A Roman viaduct-bridge in Campania: History, structure and maintenance Alessandro Baratta

Department 0/ 'Scienza delle Costruzioni', University 0/ Naples 'Federico II', Italy

Teresa Colletta

Department 0/ 'Conservazione dei beni Culturali e Architettonici', University 0/ Naples 'Federico II', Italy

ABSTRACT: Research focused on a Roman bridge-viaduct in Campania proves to be a convergence crux of a number of problems of difficult critical-historic solution: from the interpretation of the fabric in the context of Roman bridge architecture to the role of the viaduct in the urban and territorial history and in the old regional topography, up to the formulation ofthe best operational actions for the future asset ofthe work. The matter is then a problem of urban historiography as weil as of restoration. The object of the research is the "Ponte degli Aurunct', named Ronaco bridge, a multi-span roman viaduct, made by 21 arcades for a totallength of 187 ml., near the town of Sessa Aurunca, crossing an old affluent of the Garigliano river and a branch of the old consular Appia road. The fabric is discussed in its more important features, and a maintenance strategy is outlined following basic principles of structural reliability. THE RONACO BRIDGE IN THE "AGER SUESSANUS" Approximately 2 kilometres from the town of Sessa Aurunca, in the north Campanian hinterland, lies the grandiose Roman bridge called "Aurunco" or "of the Aurunci", also known as Ponte Ronaco by the local inhabitants (Fig. I). The bridge is harmoniously set in an unspoilt, wild natural environment and spans a deep depression created by the ancient Travata torrent, a now dry bed that shows the rutting of large

amounts of surface water which flowed here in the past. Ronaco Bridge was a key element in the road system for connecting the ancient town of Suessa to the sea and from there, via the Appian Way, to Rome. Based on the characteristics of the construction materials employed, it is dated to the first half of the second century AD (Colletta 1989a), in full agreement with the dating proposed by Galliazzo (Galliazzo 1989) and based on placing the morphological and construction characteristics of the bridge within a broader classification of Roman bridge building also put forward by Galliazzo (Galliazzo 1988). In modem-day terms, the bridge should really be called a viaduct since, quoting from R. Carafa's writings on the subject (Carafa 1989), "it does not only carry out the function of spanning the water-course, but unites two high points facing each other across a valley". The bridge is made up of 21 round arches of almost the same spans of around 5/6 metres, and was built in opus latericium for a totallength of approximately 176 metres. The shape of the bridge (Fig. 2) follows the gradient of the valley, descending first gradually and then increasingly steeply from the ends towards the centre to then sharply deepen in the central part of the valley, where water erosion had dug deeper into the bed of the ancient torrent. Hence, the height of the piers remains practically unchanged (around

343

regards restoration issues - in view of the many "problems of consolidation present after the irruption of the new technologies and new materials" (Marconi 1982) - and in relation to the territorial history the structure is placed in. Conservation research carried out on a Roman bridge in Campania turned out to be a focus for a series of problems difficult to solve at the historical­ critical level: from the interpretation of Roman bridge architecture to the role of the manufact in the particular urban and territorial history, and in the ancient topography of the region, up to the formulation of operational decisions suitable for the future disposition of the manufact (Colletta 1989a). Therefore, a problem of architcctural historiography as weil as restoration in which achieving the objective involves both the analytical history of the monument and the operations necessary for its protection, also involving future methodological decisions and the common aim of conservation. There is thus the need to give credence to Roberto Pane' s well-known assertions (Pane 1975), and not to overlook - "so as not to be accused of cultural irresponsibility" - theoretical reflection and a commitment to a historical-critical understanding, proceeding to the practice of restoration that is not scientifically intended, in the urgency of bureaucratic, professional and daily problems. Today, everybody realises the appropriateness of a cross-disciplinary relation in the field of restoring ancient monuments and not only at a theoretical and propagandistic level, but in areal effort to overcome the limits of one' s own disciplinary competence (Mansuelli 1982). Issues relating to that part of restoration work of archaeological manufacts that does not only deal with 'excavations', but with the conservation of ancient architectural complexes,

5-6 metres) for most ofthe longitudinal development of the bridge except for the three centre arches, where height with respect to ground level reaches 15 metres. The formal analogy of the viaduct-bridge with the structural types of Roman aqueducts is evident both as regards bridge length and the type of arches and also for certain construction techniques such as that of compensating for falls in gradient of the ground level with - in Galliazzo' s words (Galliazzo 1989) - "high rectangular bases relatively much wider than the piers resting on them and increasingly taller depending on the depth of the water-course or on the valley slope, so that - through the layout of its piers - the viaduct-bridge almost seems to ignore the deep furrowing created by the Rio Travata", without having to excessively increase the height of piers which would have made them too thin and statically less efficient. The bridge extrados thus slopes down from the abutments towards the centre, creating the classic slack rope profile which, apart from the functional reasons of construction already mentioned, constitutes a significant aesthetic element set into the surrounding landscape. Moreover, it must be noted that the characteristics mentioned of the shape of the bridge have certainly required particular attention in constructing the springer of the arches on the piers, which are vertically staggered, accompanied and emphasised aesthetically by a Z-shape moulding representing one ofthe many peculiarities ofthis bridge. 2. CONSERVATION RESEARCH ON RONACO BRIDGE AT SESSA AURUNCA

THE

The special spatial structure of bridge architecture stresses the need for certain considerations both as

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Fig. 2 View ofRonaco Bridge

344

~

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must include inexorable contacts with the urban and territorial history of ancient cities as weil as the history of architecture. Restoration work carried out on these manufacts involves the so-called architectural restoration with all the theoretical and methodological implications this posits: above all, a correct definition of the theory of conservation (De Fusco 1980). The connotation "cultural asset", originally linked to individual cases of recognised worth, has quickly been extended - as is weil known - to include broader issues in a long series of particular aspects that take on an overall value in a territory and thus are of acknowledged interest. Hence, also the attention for a territory as a "complex cultural asset" in its unitary structural organisation, that is, as a historicised structure (Arnpolio 1980). Conservation research thus moves in the direction of more suitable investigation instruments, not being limited to the sole manufact isolated from the environmental context, but going into greater depth on the urbanistic reasons. Moreover, it also makes up for any lapses of information from "classic" sources of traditional historiography, written documentation and literary sources, together with iconographic and cartographic sources, and with an accurate architectural survey of the "assets" to be known and preserved. Restoring ancient architectural manufacts is essentially a question of reading and interpretation having, as a strong assumption, an in-depth philological and historical study aimed at the architectural monument which, having been built to serve a certain purpose, also underwent modifications, interventions, changes of purpose and so on even during its ancient history (Colletta 1987). All this constitutes arecord of a process in a diachronic sense that does not end if not in re­ inserting the manufact into another phase of the transformation process, the restoration phase, which places the monument back into a context of environmental relations, mainly of the urban kind, with all the difficulties that the situation involves (Mansuelli 1982). This is even more the case for an architectural work whose urban function is prevalent with respect to others, as in the case ofbridges. The conservation of archaeological assets, which is included in a more general picture of conservation and safeguard of historical and artistic heritage, as weil as the architectural and urban planning one, is acquiring the new themes of integrated conservation. In this way, conservation lifts archaeological work from a kind of research purely aimed at the excavation and contemplation of a monument to lead

it on to its "real aim that is essentially a cultural and historical research aim, without overlooking a proper use of these monuments to make them known to the general public" (Bianchi Bandinelli 1974, 1976); i.e. a form of safeguard that takes into account the aims of using the monument in a modern context, in which there must be an awareness of the importance these assets have even from an economic and tourist standpoint (Colletta 1978, 1993). In this perspective of returning a part of archaeological work to the architect-historian­ preserver, must be placed the conservation problem of an exceptional and unique monument that is the Aurunco Bridge - commonly called Ronaco Bridge, which is one of the most important and significant examples of this construction typology and perhaps the only example of this size from Roman Italy still to be found in situ. (Fig. 3).

Fig. 3: Views ofthe Ronaco bridge at present

The bridge, as a transportation link from the ancient Appia road to the Latina road to the Sessa town from Sinuessa (Colletta 1987, 1989a), enhances with its imposing mass the importance that roman people attributed even to regional road works, as the ones crossing the productive Campania country, aiming at closer and closer connections with imperial Rome (Lepore 1982). A conservation operation of this kind must be treated with an awareness of being in the presence of a 345

taking into account the new important archeological findings, facing - with a historical methodology - the entire territorial and urban stratification of the Sessa area, both as regards collecting systematic data on the ancient topography and also as regards comparing the most recent explanatory hypothesis. The historical and topographical picture of the territory shows the system of colonization and centuriation used by the Romans in ager suessanus with respect to nearby colonies, as weil as the network of ancient roads to Suessa, in order to find the urbanistic reasons for building such an imposing architectural structure and abandoning it later on. The overall road network of this area in the Roman period has been analyzed together with a first cartographic reconstruction, on a present basis, of the ancient itineraries to Sessa Aurunca and to Ronaco bridge, and it has been compared in its subsequent stratification, from the "Royal roads" of the viceroy age to the transformations in the 16-17th century, using the few existing cartographic sources (Colletta 1989a). After having emphasised the urbanistic character of the ancient viaduct-bridge near Sessa Aurunca, to arrive at its chronological position, which is non based on an exhaustive cartographic and iconographic documentation, nor on a specific historiography, many analytic surveys on the intrinsic value of this ancient masonry engineering have been carried out, and it has been compared with other contemporary works. We can understand why the loss af a curriculum, the peculiarity of the construction phase, and its origin have been discovered by a "elose" observation of the work made possible by the scaffolding of the restoration worksite, a methodical tachymetric survey of the work in its general development and a manual "archaeological" survey. Aware ofthe limits ofthese studies, the innovating and precise building technique and the great rigour of the specic local building method have been studied, confirming the idea acccording to which the work had been assigned at the beginning of the second century BC. Besides, the precise analysis of the bridge static system through electronic processing of the data presents, with the accurate dimensional research, the implications of modem structural analysis techniques of Roman bridges, that together with the positive comparison with methods used for building bridges in the nineteenth century leads to a confirmation of the planning system. In this framework, very important is the comparative analysis of the particular type of the Sessa viaduct­ bridge with other contemporary bridges, not only in

unigue manufact - the only Roman bridge of such size in Campania that has come down to us practically intact with its mass of 21 arches. Any analysis cannot, therefore, be limited to technical data because - before proposing any hypothesis for conservation work - there is the need to privilege the role of knowledge of the ancient imposing masonry structure, which strikes the occasional visitor as much as the attentive scholar, for the scale of the construction and also for the still virgin surrounding natural environment in which it is located. So, while examining such a rhythmically organized monument as this bridge, we must immediately face the problematic terms ofthe historical issue. In fact, it is impossible to disregard the fact that, in a work not standing out for its architectural value as a "monumental bridge" - where this means a building particularly solemn and celebrating a person or a quest - where the aesthetic values are opposed by a solid plainness, where the resistance is aimed at satisfying a need thought as long-lasting and in lack of sure stylistic elues as weil as certain mastery, it is necessary to investigate the technical data, as weil as, and especially, those related to the linking system organization. To conduct an exhaustive analysis, as Pietro Gazzola remarkably wrote in his excellent contribution to the study of Roman bridge architecture (Gazzola 1963), we must consider that building a bridge obeys only partially to an imperative ofparticular solemnity, but of essentially unrestrainable usefulness, since it maintains continuity of a pass necessary to urban everyday life. The value of a bridge must be seen not only, and not so much, in terms of adefinite architecture, but as part of a road network of the area in which it is placed, in the urban area, as the Pietra Bridge in Verona (Gazzola 1963) or the bridges in Rome (Anderson 1927, Ashby 1935), or in a wider territory, along consular roads or more internal roads, like Aurunci bridge in Campania. Therefore, the historical-architectural analysis of a bridge is completed, following Gazzola's indications, only if it is conducted in parallel with the survey of the road system which has determined the need for creating this structure in a particular place agreed for its foundation. In this elose link to the territory, the specific interest of the town and country planning historian for roman bridge structures, with reference to the urban and territorial history of ancient Campania, is elear. The survey of Ronaco Bridge is based upon the analysis of the complex urban and road system of northern Roman Campania, where the city of Sessa was, not from an archeological perspective, but

346

Campania, but in the whole Roman Empire where the dissemination of these building on such a wide territory is linked to a social implication. Galliazzo has recorded 931 bridges (Galliazzo 1988), and, according to the author, the Sessa viaduct-bridge represents an innovative type among all viaduct­ bridges and brickwork bridges. Moreover, its typical Campanian construction logic confirms its dating and underlines its importance among Roman brickwork architecture. The results of sectorial surveys aimed at a knowledge of the ancient structure of the Sessa territory in which the bridge is located, the worksite experience and the interpretation of the materials used and of the building techniques, as weil as the deepening of the original static idea and of the obsolete structural logic emerging from the masonry style, have offered new data for a history of Roman bridge architecture in Campania and, through monument history to the general history of Sessa Aurunca's ancient territory, specifically binding human aspects in a chronological dimension. If Mansuelli is right, as he actually is, that "restoration work meant as a means of historical research may be a correct assessment for conservation research applied to an archeological monument, in a documentary concept of the asset" (Mansuelli 1971), the restoring operation is first of all, a peculiar and unrepeatable cognitive moment of the asset itself and it later realises into active preservation. While operational conditions are easier for a mobile art object, they are more complex for an architectural structure such as a viaduct-bridge where a reintegrating intervention is proposed, not considering the Ronaco Bridge asset as belonging to the category of "ruins", but as structurally whole ­ albeit degraded - and in use in its naturallandscape (Colletta 1987). As weil as recovering its image, this kind of intervention effectively implies a will to allow the construction to continue to carry out it role of road connection in its surrounding area and, thus, for its practical utilization, presupposes a consolidation of the masonry, the filling of any gaps and reconstruction of the carriageway side walling. Moreover, preserving the ancient Roman route in which the bridge was an element, in the intricate road network of the Sessa Aurunca area of the Roman era, extends the issue from architectural­ archaeological restoration work to urban and territorial restoration work involving the Falemo area and new themes of archaeological town and country planning (Di Stefano 1983). The urbanistic structure of the bridge must see its resoration, as an analysis of its historical process, in

a whole that is materially undivisable from the reclaiming of the ancient Roman road network present, otherwise the bridge could not be interpreted in its real light. Thus, far from being delivered to the general public as it was originally, and especially because it is not a ruin in the classic sense, the bridge must undergo a recomposition process for its ancient constituent materials and then be represented to public use (something it has never really lost) as a means of bridging a course of water and as a roadway connection - but not for motor vehicles, obviously. To the original function, its use as a means of transit, may be added that of a reclaimed structure for use as a pedestrian stopping or meeting place, even using several levels, according to concepts that are widely used today for urban bridges, in a differentiation ofthe two possible ways of interpreting the bridge in its natural environment: a bridge as connector and as receptor. 3. DIMENSIONING OF THE BRIDGE AND ITS STRUCTURAL "MODERNITY" 3.1 Wall structure and dimensional analysis

The wall structure of the bridge, as regards the arches and piers, is composed of sack masonry with bipedal facing-work bricks with wdge anchorage, and the main wall structure in opus latericium. The piers rest on large stonework bases (opus incertum) . The constitution of the manufact thus appears to have somewhat uniform characteristics. The smaller size composition of the opus latericium would suggest that the behaviour of the material could respond - at least on a macroscopic level - to needs of isotropy and homogeneity. On the other hand, the excellent qualities of resistance of Roman opus latericium, as also seen in analyses of other Roman structures of the imperial period, shows capabilities of considerably withstanding. tensile stress. In this light, the results of certain tests on mechanical resistance carried out on opus latericium sampIes, taken in situ during recent restoration work there, are very significant (Carafa 1980). Not making any distinction between opus latericium sampIes taken from the piers and arches, the test results showed a mean value for compression resistance of about 39 Kg/sq.cm, with a standard deviation of ± 10 Kg/sq.cm. These values, still valid today, relate to the opus latericium in its present state and thus without any consolidation work carried out on it. Therefore, these mechanical resistance values compare favourably with modem concrete mixes of

347

sand, gravel and ordinary limestone cement. Results of tests of resistance to cutting and/or tensile stress are unavailable. However, on the basis of certain tests of resistance to flexure carried out on opus latericium sampies treated with acrylic latexes (the Peter-Cox treatment ofimpregnation under vacuum), it would seem reasonable to foresee a resistance to tensile stress for opus latericium in the region of 10­ II Kg/sq.cm. From the point of view of bridge structure dimensioning, and save for the checks in para. 3.4 below, it is intersting to note the relation between the dimensional characteristics of the bridge and some formulae for arch and pier dimensioning in vogue in 19 century bridge-building which reflect the designing experience of the main builders of the time.

S2

C 20+ C C s= 0.20+-+--- (m) 40 1000 f

S3

s = 0.25 +

(1)

(2)

= m. 0.57

Croizette-Desnoyers' formula instead proposes s = a + 2bR

(meters)

= m. 0.39

(6)

Another rather widespread relation for dimensioning the key thickness of a bridge arch was Kaven's formula

perhaps the simplest, gives the following value for an average bridge arch span of 5.50 metres: SI

(5)

hence

Following the lines set forth by A. Giuffre (see i.e. Giuffre 1995) it is worthwhile to compare the dimensioning of a masonry fabric with the rule 0/ the art of past builders and designers. Nineteenth century builders considered that, since the load was permanently very great in comparison with overloads in walled arches, arch thicknesses depended mainly on the span "C", the rise "f' and on the materials used. Thus, empirical formulae allowing calculation of thickness as a function exclusively of these parameters, or of parameters correlated with them, were considered to be very efficient. Lesguillier's formula (meters)

(4)

The Italian institute of civil engineers proposes the following formula for round arches in bridges

3.2 Arch thickness

s=0.10+0.20C

= m. 0.50

(3)

where R is the intrados radius (for circular arches; for non circular arches, R represents the radius of the circle passing through the springers and the keystone) while a and b represent a pair of coefficients that depend on the lowering and appropriately tabled. For a round arch, the tables supplied with (3) give a=0.15, b=0.15, whence

c( 0.025 + 0.00333 7) (m)

from which S4

= m. 0.42

(8)

Assuming as valid the average of the values given by the preceeding relations, we would obtain s= m. 0.47

(9)

3.3 Dimensioning o/the piers As regards thickness S of the piers, it must be noted that nineteenth century bridge-building tended to somewhat increase the dimensions of piers of many-arched bridges, following the criterion - still shared today - of trying to avoid the possibility that the collapse of one arch would, by not maintaining that element of support necessary between arches, bring down the whole bridge. The result was that of creating actual abutment-piers able by themselves to sustain the stresses released when one of the arches collapsed; even if the piers would do this in a temporary and very precarious way. The more appealing correlation is the one which expresses pier thickness as a function of arch keystone thickness. An overall indication is to be found in early 20th century technicalliterature, which indicates an optimum dimension of 1/5 of the span ofthe arch. Perronet suggested the following relation for a bridge pier S = 2.0s (m)

348

(7)

(10)

u .~~:~ ~_ .

Fig. 4: Finite Elements Model and Results

where s is the arch keystone thickness; in our case, s 0.47 metres

evaluation of the instrinsic static capacities of the bridge, despite all the evident limits of the dimensioning formulae mentioned (e.g. consider the independence - according to the above-mentioned relations - of pier thickness from pier height). It is possible to conclude that, where bridge structure was integral, then this does not present intrinsic conception or dimensioning faults. This justifies the opening of a second study phase for the construction and processing of a mechanical calculus model in order to arrive at a second level of more detailIed and more complete analysis able to provide evaluation criteria in line with modem criteria of structural analysis.

=

S, = 0.94m

(11)

Other empirical formulae were ofthe following type: S=0.29+2s

(m)

(12)

from which S2 =m. 1.23

(13)

or S = 2.5s

(m)

from which

S3 =m. 1.18

3.4 Static behaviour in the linear elastic field

(14)

(15)

It must be noted that, in applying (10), Perronet used to increase the result by 25%, thus practically obtaining the same result as (15). From analyses of the available surveys and essays, it is possible to evaluate the arch keystone thickness in the region of 60 cm, while pier thickness is around 1.60-1 .80 metres (including facing-work). Considering the good performance observed with the opus latericium, it is possible to deduce that nineteenth century technical practice would have considered Ronaco Bridge to be not unsimilar to the state of the art for wall constructions of the time. This is undoubtedly a positive aspect in the

Having ascertained the dimensional conformity of the bridge according to the criteria illustrated in the previous section, there is the need to examine ­ approximately - the static behaviour of the bridge in the longitudinal direction, in order to judge the regularity of stress distribution and to evaluate the intensity of the operational stress compared with the capacity of resistance of the material. Reference has thus been made to an ordinary model of two-dimensional calculus, supposing that the bridge is made of linearly elastic material. In the absence of more exact data, a value of 1000 Kglsq.cm has been assumed for the elastic module of the walling, and a value of 0.1 for Poisson's transverse contraction coefficient. The whole structure has been analysed for half its length (counting on a practical near-symrnetry of the bridge), and for calculus purposes this half has been discretized according to a mesh of finite elements ­

349

defined as the ratio of the investment necessary to restore the initial state to the rebuilding cost. The ftmction D(t) is established as a monotonically decreasing ftmction of the instantaneous bridge reliability R(t)

5468 elements for 3055 nodes (Fig. 4). Figure 5a shows, as an example, the deformation of an arcade (no.3) with amplified shifts in the ratio 100:I with respect to the geometric dimensions, from which the behaviour of the structure on a cinematic level may be qualitatively deduced, with the lateral arcades tending to shift towards the centre of the viaduct, where this tendency is then countered by the same forces of the other half of the bridge. Figures 5b and 5c respectively show the trend of the isostatic tensile stress lines and compression from which the absolute regularity of the stress flows may be seen. Finally, the maximum value calculated for tensile stress is about 1 Kg/sq.cm, here too in sufficient safety conditions where the opus latericium may be considered to be whole and the experimental results ofthe previous section confirmed by further studies.

D(t):R(t) E[O,I]~ D(t) E[O,I]

(16)

If one has not significant data, one can assume the above ftmction as O(t)=I-R(t) with O'(t)=-R'(t)=q(t) (17) where q(t) is the probability density ftmction of the failure time of the construction. Assume that the surveillance of the fabrics is effected by some periodical action (e.g. an inspection or an interrogation to monitoring devices), and that this action has a resolving power I/O b with 0 1 defined as the smallest damage level that can be detected by the tools and methods employed in the inspection. The problem is how frequently should this action be carried out? To answer the question, consider that an inspection at time "T" has given negative result (i.e. no damage has been detected). This means that the actual damage O(T) was less than 0 1 at time "T". The time to to next inspection should be taken in way that in the interval OT, from "T" to the next inspection (at "T+OT"), the damage should not grow much more than Ob which would make restoration of the bridge cumbersome and expensive. The behaviour of the structure in the time OT starting from T (the mission time of the device) can be inferred from the conditional reliability ftmction C(tIT), conditioned upon the fact that at time "T" the damage was less than the threshold OI.The growing of damage starting from time "T" can be expressed as the probability that the structure suffers a damage in (T, T+t) assumed the structure itself is integer at time "T", that means a ftmction of C(tIT), as follows

4 RELIABILITY AND MAINTENANCE POLICY OF THE BRIDGE In a previous paper (Baratta 1997) a rationale has been set up for establishing an optimal maintenance and surveillance strategy of a bridge. The approach is based on the instantaneous damage factor D(t)

T+t

fq(x)dx

F( tlT) = I-qtlT}

T

Iq(x)dx

R(T)-R(T+t)

R(T)

(18)

T

where it is implied that any damage less than 0 1 at time "T" is conventionally assumed to be null. As explained in the paper quoted in above, if the reliability ftmction is constrained to obey the IFR (Increasing Failure Rate) property, the influence of its particular ftmctional form may be rather

Fig. 5: Deformation and Stress in arcade n.3

350

uneffective; therefore in the sequel q(t) will be assumed to be a Gaussian density, unIess weil founded reasons exist to give it a different expression

(t_,)2] q(t)=-R'(t)= ka.J2;exp-~ 1

[

['::::;::::"'1-000 -~T-I OO .......... 1-200 ~T-JOO .......... T..OO

400 r--,---r--~--r--.---.--~-,--~

ti

co

T

T

JR'(x)dx = D. JR'(x)dx

300

1

200

1

.00

1// 1

1 7""""- 1 A C

1

(19)

The a-priori expected lifetime "," is expressive of the time one expects the system can survive without maintenance. A possible estimate for the ratio ofthe variance parameter "a" to "," can be set to a / , = 40%. The time ~T between two inspections can be identified by the equation F(T+~TIT) = D., i.e. T+~T

I

V>T

/~

I ""'*"

1/ ' 1

:6-4

1

1 :::>~T

O +I--~~--~~--~--~~--~~

0.5%

.,5%

2.5%

3,5%

4,5%

Fig. 6: Time between inspeclions (li, yrs) vs. tbe minimum deleclable damage 0. (tbe resolving power ofinspeclions)

(20) value of D. = 5%, one can program aperiod of ",350 years for subsequent inspections, that means a very economical surveillance (poor inspections and very rare), but this leads to a maintenance policy very expensive, in that the cost for restoring the structure is not less than 5% every 350 years with a yearly rate of 0.05/350 = 0,014%. By contrast, if accurate inspections are prograrnmed, say D. = 0.5%, the time between inspections is 90 years, the cost of restoration is 0.5% as weil and the yearly cost of maintenance is 0.005/90 = 0.0056%, i.e. less than one half of the previous one. Note that if one assumes a larger value for D. (i.e. poor surveillance) the policy chosen is to wait for conditions to proceed to full rehabilitation of the bridge. On the contrary, if one plans accurate surveillance, the conservation policy is to perform a good maintenance and to keep the bridge permanently in an acceptable condition. In the case of a robust, ancient manufact, surveillance and maintenance can be relaxed with respect to modem works; the result of the above considerations is that a good maintenance timed at a frequency of some tenth years, with interventions probably limited to protection from water and dampness and to clear the fabric from self­ vegetation, that are in most cases the main deterioration and ageing factors, should be a good policy for conservation of the bridge, apart from unexpected events.

that can be solved with respect to DT. Note that this equation implies that the inspection frequency should increase with the age "T". With the previous assumptions, the surveillance sequence for the Ronaco bridge can be assessed. First D., the inverse of the resolving power of inspections, has to be assessed. Weil organised inspections, made by qualified technicians, can be attributed a higher resolving power (i.e. a smaller D.) than more economical surveillance. On the other side, D. cannot be so large that the recovery of the structure, apart from exceptional events, requires an investment of the same order as the reconstruction cost. Reasonable values for D. can be assumed in the interval 0.5% .;- 5%. Secondly, couples of parameters "," and "a" for the fabric under examination should be dimensioned. For the Ronaco bridge, a very old fabric that has survived without maintenance so long, one can assume , = 1000 yrs. Consequently, the previous estimated ratio yields a = 400 yrs. If one agrees that, starting after the initial restoration work to be undertaken as a condition for the application of the present theory, at every maintenance action the fabric is perseveringly brought to the original integral state as soon as a slight disease is detected, ageing prior to the last inspection can be neglected, and the significant solution of eq. (20) becomes the one corresponding to the line T=O in the Figure 6. From the same plot (line: T = 0), one can see for instance that if inspections are calibrated with a 351

REFERENCES Adam, J.P. 1984. La eonstruetion romaine: materiaux et teehniques. Grands manuels Picard: Paris: Picard Albenga, C. 1958. I ponti: UTET. Torino. Ampolio C. (ed) 1980. La eitta antiea. Bari Anderson, W.J. & al. 1927. The arehiteeture 01 aneient Rome. London-New York. Ashby, T. 1935. The aqueduets 01 aneient Rome. Oxford. Baratta, A & al. 1981. Calcolo di archi in materiale non resistente a trazione mediante il principio dei minimo lavoro complementare. Proe. 1st Nat. Conf ASS.IR. C. CO. Verona. Baratta A & Voiello, G. 1987. Modelli matematici per l' analisi delle strutture murarie. Restauro. 87/88: 81-125 Baratta, A 1986. Ponti a struttura muraria. Restauro. 86:27-59 Baratta, A & Colletta, T. 1988. La sicurezza sismica nella protezione dei patrimonio monumentale: Un problema di metodo. Proe. 3rd Nat. Conf. ASS. IR.C.CO. Catania. Baratta, A 1997. Renewal policy for historical bridges. 3rd Int. CIS Symposium "Intelligent Renewal ". Capri. In press. Benvenuto, E. 1981. La Scienza delle Costruzioni e il suo sbviluppo storieo. Firenze: Sansoni. Bianchi Bandinelli, R. 1974. Italia storieo-artisliea allo sbaraglio. Bari Bianchi Bandinelli, R. 1976. Introduzione all , areheologia classiea eome storia delI ' arte antiea.. Bari Carafa, R. & Colletta, T. 1980. Restauro deI Ponte Ronaeo a Sessa Aurunea. Relazione al progetto di massima, Soprintendenza Archeologica delle Province di Napoli e Caserta. Napoli. Carafa, R. 1989. Il Ponte Ronaco. Lettura ravvicinata" dei monumento nel primo intervento di restauro. In T. Colletta (ed), La struttura anliea deI territorio di Sessa Aurunea. 11 Ponte Ronaeo e Ie Vie per Suessa: 95-106. Naples: ESI. Carbonara, G. 1978. Questioni di principio e di metodo nel restauro d' architettura. Restauro. 36:710. Colletta, T. 1978. La conservazione dei beni architettonici e d' ambiente in una politica di segno nuovo. In U. Leone (ed), Risorse ambientali e sviluppon eeonomieo deI Salento.:220-229. Colletta, T. 1987. Considerazioni preliminari alla ricerca conservativa sul ponte Ronaco a Sessa Aurunca. In G. Spagnesi (ed), Esperienze di Storia deU' Arehitettura e Restauro vol. 11:489-499. Roma.

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Colletta, T. (ed) 1989a. La struttura antiea deI territorio di Sessa Aurunea. Il Ponte Ronaeo e Ie Vie per Suessa. Naples: ESI. Colletta, T. 1989b. Inquadramento storico­ topografico dei territorio sessano in epoca romana. In T. Colletta (ed), La struttura antiea deI territorio di Sessa Aurunea. Il Ponte Ronaeo e Ie Vie per Suessa: 15-34. Naples: ESI Colletta, T. 1993. Recherche conservative urbaine et tourisme culturel dans I' Italie du Sud. Un moyen pour la diffusion de la connaissance. Proe. 01 the Int. Symp. "CuIturaI Tourism ": 20-42. Colombo, Sri Lanka. De Fusco, R. 1980. Il restauro architettonico: ricchi apparati e povere idee. «Op. Cit.». 49:5-16. Di Pasquale, S. 1984. Questioni concementi la meccanica dei ezzi non reagenti a trazione. Proc VII Nat. Conf. AIMETA Trieste. Di Stefano, R. 1983. Il caso di Napoli. In Atti deI

Convegno "Areheologia urbana e eentro antieo di

Napoli ": 101-110. Napoli.

Franciosi, V. 1982. Il procedimento delle tensioni

ammissibili nella verifica degli archi e delle volte in

muratura in zona sismica. Autostrade.9.

Galliazzo, V. 1988. 1 Ponti Romani. 2 voll. Treviso.

Italy:

Galliazzo, V. 1989. Ponti-viadotti e ponti di laterizio

in eta romana. Tipi e confronti. In T. Colletta (ed),

La struttura antiea deI territorio di Sessa Aurunea. 11 Ponte Ronaeo e Ie vie per Suessa: 123-138. Naples: ESI.

Gazzola, P. 1963.1 ponti romani. 2 voll. Firenze.

Giuffre, A 1995. L' intervento strutturale quale atto

conclusivo di un approccio multidisciplinare.

Quaderni ARCo. Restauro, Storia e Teeniea: 5-16.

Heyman,1. 1969. The safety ofMasonry Arches. Int.

Journ. 01 Meehanieal Seienee:363-384.

Lepore, E. 1982. La Campania antica. In AAVV .,

Campania oltre il terremoto: 14-24. Napoli

Mansuelli, G.A 1971. Il restauro come mezzo di

ricerca storica. In AA.VV. Il monumento per I '

uomo: 752-53. Roma.

Mansuelli, G.A 1982. Esempi di restauro

monumentale. In C. Pietramellara & L. Marino

Contributi al restauro areheologico: 60-70. Firenze.

Marconi, P. 1982. Editoriale. Rieerehe di Storia delI '

Aehitettura. 16: 4-5.

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Restauro. 21-22: 5-8.

Arch Bridges, Sinopoli (ed.)© 1998 Taylor & Francis,lSBN 90 5809 012 4

Construction conception and structural conservation of masonry arch bridges M. Bellomo & s. D'Agostino

Interdepartmental Centre ofEngineering ofCultural Heritage, University ofNaples 'Federico Ir ,Italy

ABSTRACT: The research aims at underlining the role of masonry arch bridges in the constructed environment. Masonry bridges always have played an important role in the organisation networks, becoming fundamental works for the complex management ofthe territory. In the last century, with the advent ofmodern scientific culture and the innovative materials, masonry bridges, like all historical constructions, have become - with respect to new structural engineering - archaeological constructions: they can be considered as arecord of the material history. In this light it seems appropriate to document them. For this reason the Interdepartmental Centre of Engineering for Heritage of the University of Naples "Federico 11" aims to draw up a special form for cataloguing masonry bridges, that can be spread by internet. Moreover it is important to re-employ masonry bridges, changing them according to real needs that do not alter the message handed down by their material history. 1 INTRODUCTION

solidly based on a mechanical design conception. De Saint Venant's mechanical-analytical model for solids and the resulting development of the technical theory of beams, allow a spatial conception of structural design based on posts and lintels. This conception spread rapidly from Le Corbusier's Villa Savoye to the non-descript reinforced concrete constructions of modem buildings and the bold structural frames of the great skyscrapers. Historical constructions go outside the structural conceptions of this century's architects and engineers who, proud of the new forms of structural engineering and new materials, view historical buildings as artificial obsolete forms to be reinterpreted according to the analytical models and static plans of the new theory and to be restored through the use of more or less calculated extension and consolidation work which alters the ancient construction conception of these buildings for the sake of guaranteeing an undefined and perhaps presumptious degree of safety. It is by observing the progress of modem structural engineering that the whole wealth of historical constructions may be viewed as archaeological constructions (Bellomo & D'Agostino 1997), an unrepeatable construction form through which various civilisations gave their more concrete and consistent form of expression and which today constitutes mankind's largest record of material history.

The great revolution in the construction field which took place in the early twentieth century and which then developed on a world scale in the latter half of the century has brought a fundamental change in construction art that sees structure as a specific component of construction science. Construction is the result of a building conception using natural materials and architectures that develop in an organic and complex way. On the other hand, structure is an independent skeleton carried out with industrially produced materials that are purposely defined as structural. The resulting construction is nearly always independent of the morphological and distributive characteristics of the building. This irreversible change has also brought a culture oriented to design that privileges this aspect over that of the building site and which has created a strong binomial between architecture and structure, each designed according to independent criteria, methods and regulations Iinked to different conceptual fields. Over a short time scale, those traditional materials and techniques which had been the basis of man's construction conception for thousands of years have become obsolete and all the ancient culture of construction materials, with its craft rules handed down and enriched over the centuries, has disappeared from architectural culture and even more from that of structural engineering that is now

353

This new cuItural awareness encounters some difficulty fOT the literary views of architecture historians and the technicist concepts of structural engineering. In the complex scenario of historical constructions a very singular typology is represented by masonry bridges normally of the arch kind. These constructions constitute a great weaIth as regards the history of materials they represent and the following notes intend to pose the overall problem of their conservation - highlighting issues connected to their documentation and practical use - so that this rich and complex testimony of man is not lost for ever. 2 THE SPECIFIC NATURE OF MASONRY BRIDGES: THE BRIDGE AS EMBLEM A bridge, conceived as a connecting element between two places, already was an emblematic construction typology in ancient times and remains a tangible expression of the stable control of a territory and its land communication routes. Heidegger's description of the specific nature of bridges is very interesting. He writes «A bridge is something that projects itself "light and powerful" above a river. It not only connects two already existing banks: above all, the connection established by a bridge makes the two riverbanks appear to be riverbanks.(... ) Bridges can be conducive in several ways. A city bridge links the castle quarter to the square of the cathedral, while a bridge at a town gate connects carriages and carts to the surrounding villages. The old non-descript stone bridge spanning a stream grants passage to the cart laden with crops from the fields to the village and allows a timber consignment to access the main road from a country track. A motorway bridge is a link in the great traffic flow network, established by calculus and the principle of maximum speed. In each of these cases, and in increasingly different ways, a bridge facilitates people's calm or hurried passage, allowing them to always reach other banks and, finally, to pass - as mortals - to the other side» Masonry bridges, almost always of the arch type, represent an architectural form in which function and structuraI conception cIearly come together. Indeed, the bridge is perhaps the only type of structure in which we may find cIear continuity from the ancient construction art to modem structural engineering. The technical language itself, which divides the component elements of bridges into piers, abutments, vauIts, haunches and so on, remains regardless of modem changes, and it is the arch bridge itself which cIearly highlights the thrusts and counterthrusts that come into play in incontrovertible harmony. Still today, stone bridges

thousands of years old appear to challenge - with their foundations - the impetuous and varied nature of river courses and torrents. Their conception has been possible through profound knowledge of natural phenomena and their construction has represented the overcoming of considerable difficulties involving the conception and emplacement of timber centerings which by themselves constituted bold temporary structures. Thus, very often, bridges become an emblematic point of reference fOT the territory and in the most prestigious historic town centres. Just to name but a few examples in Italy, it would be unthinkable to visit Venice without seeing the bridge of RiaIto or Florence without taking astroll across the Ponte Vecchio. The centre ofRome has the famous ancient bridges such as the Milvian Bridge and Sant'Angelo bridge, OT the Pons Fabricius and Pons Cestius linking the Tiberine Island to both banks of the Tiber. Finally, the reconstruction of a bridge has also very often taken on symbolic significance as a sign of rebirth OT peace. Examples of this in more recent times incIude the reconstruction of the Santa Trinita bridge in Florence, which had been destroyed during World War II and was immediately rebuilt in masonry like Ammannati's vision, and the work being carried out today on the glorious bridge of Mostar. 3 THE DEVELOPMENT BRIDGES

OF

MASONRY

The Romans may certainly be considered as the greatest bridge builders in the ancient world. They fully realised the inherent capacity of bridges for controlling territories. The timber bridge built on the Rhine by Julius Caesar's legionaries in 55 BC is still an incredible feat of engineering; the bridge was 430 metres long and had 56 spans each of 7.70 metres and was buiIt in a few days. In 104 AD Trajan spanned the Danube with a bridge over one thousand metres long with timber superstructures resting on masonry piers forty metres high (Deli i 1992). Besides these exemplary cases the Roman builders were and remain famous for their masonry work, and bridges certainly constitute an exemplary typology ranging from the more prestigious examples in Rome itself to the great many types throughout the empire - from Europe to Asia and Africa. The deep-rooted conviction of the importance of bridges gave their builders a certain sacred aura such that a "Collegium Pontificorum" was specially founded for these "pontifices" which became the jealous custodian of the rules of their art and of their construction techniques. The fundamental innovation of Roman construction was 354

the ability to build piers and vauIts; this construction technology led to the great honorary arches, amphitheatres, bridges and aqueducts. The harmonious arches of the Pont du Garde, built in 15 AD, still amaze us and it is possible to see traces for the bold construction oftheir centres (Adam 1990). Roman construction techniques spread throughout the empire and the building of bridges and aqueducts became a significant aspect of the construction art as certain emblematic examples show, such as the great Roman bridge of Salamanca, today for pedestrian traffic. This bridge has twenty­ six spans of which fifteen are the original ones and eleven rebuiIt in the seventeenth century. Other examples are the small bridges built along the tortuous routes in the Alps, such as Pont S. Martin and the aqueduct bridge of Pondel in the Val d'Aosta, and one of the last bridges using these construction techniques buiIt at the end of the eighteenth century - the stupendous Carolino aqueduct, conceived by Luigi Vanvitelli for the scenographic requirements of the Bourbon royal palace at Caserta. The decline of Roman civilisation led to reduced communications and connections between places and areas belonging to new territorial domains of much smaller scale compared to those ofthe Empire. As a resuIt, bridge building also adapted to more limited specific needs. This is the case for Medieval bridges, which were often designed to cater for castles and citadels, such as the Ponte delle Torri of Spoleto in Italy: a great ten-arch construction 230 metres long and over 70 metres high buiIt between the twelfth and fourteenth centuries. In the Modern Age, bridges take on their greater characterisations as connectors of opposite banks of rivers that flow through the historic centres of cities. Examples of these are the bridges of Florence such as the Ponte Vecchio, built in the mid fourteenth century, and the Ponte Santa Trinita built by Ammannati, with its three beautiful polycentric arches, and also the Venetian Rialto bridge that was rebuiIt in the present form at the end of the sixteenth century and until the nineteenth century was the only way to get across the Canal Grande. Scientific development and the industrial production of iron and steel, and later of reinforced and prestressed concrete, profoundly changed the conception of bridges leading to greater numbers and varieties being built. A significant example summarising bridge development may be seen in the thirty-seven bridges in Paris ranging from the early seventeenth century Pont Neuf to the innovative aerodynamic shape of the very recent Pont CharIes De Gaulle. However, it is possible to say that - at the same time - the history of arched masonry bridges is a long and glorious one. It intensified with the

development of Construction Science from the closing decades of the eighteenth century and the early twentieth century (Foce & Sinopoli 1996, Di Pasquale 1996) and involved great builders such as Perronet and scientists of the calibre of Alberto Castigliano. Thus, throughout the twentieth century ­ particularly in the latter half - with the widespread results of the Industrial Revolution in Europe and a renewed culture of communications, the development of public works such as roads and railways continued to feature the masonry bridge as an exemplary construction. Masonry bridges were built on the great arteries of communication as weil as along the most tortuous mountain roads and were a constant feature on all the great railway Iines. The last great masonry bridges were buiIt in Europe and in the USA in the first decade of the twentieth century, with arch spans ofbetween 80 and 100 metres. The end of World War 11 and the start of the post war era brought the demise of masonry bridges and this kind of construction type is today considered as something of the past. 4 THE STATIC CONCEPTION: RULES OF THE ART AND GRAPHIC STATICS Mention has already been made of how the innovative Roman construction techniques saw their expression in the use of piers and vaults ranging from those in opus quadrata to those using cement. This typology, which apart from certain exceptional cases was to be found all over the empire, was necessarily based on a clear and simple conception Iinked to a material culture whose founding principles and construction rules were to be part of every master builder's knowledge. Thus, with reference to barrel vaults, essential data were the arch span and the curve of the intrados, the height of the piers, the weight to be supported and the type of masonry to be used for constructing the vault. The thickness of the keystone depended on this data and this thickness was meant to be greater towards the imposts or the imposts themselves had to be strengthened by suitable abutrnents. Certainly, in this conception the considerable amount of masonry of the construction was fundamental since it in effect constituted a stabilising factor and with respect to which the size and distribution ofthe loads became a marginal aspect. The intrados curve in Roman bridges was almost always of the round arch variety and the proportions showed the application of well­ consolidated rules gained through long arduous experience. Obviously, the quality of materials used and the skill with which they were employed was crucially important. The most delicate aspect was

355

always the efficiency of the foundations since the presence of water made it difficult to reach deep foundation plane. Roman technique tried to get around this by widening the base of piers, which often have rather superficial foundations. Certainly, geometric clarity of the bridge typology and the essential aspect of its function always spurred the builders into finding simple principles in the definition of fundamental geometric criteria such as the thickness of keystones and imposts. This approach was founded on an understanding of manufacts and their history , in the quality of materials used and their correct laying in the worksite, and always encouraged builders towards the definition of so-called empirical principles, traces of wruch can be found in the forrnulas used in French and Gerrnan railway manuals of this century for the construction of more modest arch bridges and viaducts. Starting from the eighteenth century the New Science was addressed to the study of constructions which became a kind of artificial nature to be interpreted and reinvented in a mechanical view of the world. This idea, together with the spreading use of industrial materials whose mechanical characteristics were experimentally deterrninable, encouraged the forrnulation of coherent theories allowing the technical design of the construction to be carried out. Thus, structural engineering was born and this science brought with it a new way of conceiving construction based above all on the development of the technical theory of the beam, which was to express all its innovative impetus in the establishment and spreading of rational architecture based on the idea of the construction becoming an autonomous structure. This new view dramatically changed the old concepts changing the relationship between own weight and accidental load so that, while the ancient construction was conceived to sustain its own weight and was fairly indifferent to the action of accidental loads, the new streamlined reinforced or prestressed concrete - or even steel - structures were designed to bear accidental loads with a relatively modest own weight which was in any case still strongly conditioned by the function of the manufact the structure was a part of The advent of modem scientific culture in the last century gave rise to a process of technological innovation which led to an overall change influencing twentieth century culture. In such a rapid continuous process of change, historical constructions have become - with respect to new structural engineering - archaeological constructions that have lost both their conception and their ancient material culture. In a world where the speed of communications becomes essential, the old road network and the railway network itself conceived in the first half of the twentieth century become obsolete. Masonry bridges are thus destined

to become extinct. However, before leaving technological innovation altogether, masonry bridges were among those manufacts that the New Science focused itself on most in order to develop the last prototypes of the beginning of this century to levels never seen before. This was possible by the birth of a science of materials and a conception of mechanic models allowing the forrnulation of coherent models for the design of bridge structures and especially bridge arches. While the principles of the art were based on a physical geometric conception of nature in which the principle of experimental knowledge dominated (Conforto & D'Agostino 1995), the new theories referred to rational assumptions of mechanics and tended to construct general models albeit approximate ones. A notable example is the resistance to traction of stone materials and mortars. Resistance to traction, assessed by Rondelet (1802,1817) as being one eighth of the one relative to compression, was still accepted by Resal (1887) who nevertheless reduced it to one twentieth of the resistance to compression. Castigliano, also an arch bridge designer, preferred not to consider it at all in favour of a clearer and more rational model of mechanical behaviour which assumed masonry as a homogeneous material not resistant to traction. This assumption was implicit in Mery's famous method (1840), which allowed the designing of masonry vaults that enabled the pressure curve not to lead to traction stresses on the materials. Trus method was very successful and was a simple application of graphic statics which from the early nineteenth century to the early twentieth century was an unparalleled calculus instrument. All this allowed the designing of masonry bridges with arch spans of up to 100 metres as weil as a wealth of rninor works through which the mobility of people and goods became assured, leading to the globalisation of civilisation that is characterising the present day and for which works of quite a different conception are required. 5 RESTRUCTURING AND ADAPTATION With the spreading of the new structural conception and the establishing of design coherently based on the theory of the beam and on new materials, the ancient construction conception, the principles and skills that had been consolidated over many centuries disappeared from academia and from the professional sphere to quickly become so obsolete that they were effectively unknown. Over a few decades, marked by a deep cultural break caused by World War 1I, the material culture of rustorical constructions, which had until then been the

356

common domain of architects, archaeologists and engineers, was replaced by the new structural mechanics able to fully independently design its own static plans. At the same time, geotechnic engineering developed with a knowledge of terrains that was much more scientifically based; moreover, the method of foundations on piers and on micropiers developed rapidly and enabled the distribution of loads from bridge abutments and piers much deeper into the ground. The micropier technique then continued to develop moving into the masonry tissue, which was "consolidated" via cement injections and reinforced jointing works without basing these interventions on coherent structural calculus as is normally the case for calculus of steel structures or those made of reinforced or prestressed concrete. Historical constructions are thus seen as something altogether different from the standpoint of the new structural conception; the methods, techniques and materials that had been the very heart and soul of construction were excIuded from technological innovation and from an important awareness of the intrinsic value of material history of historical culture of arehitecture and its conservation. From a rooted cultural conception for which image represents the essence of the historical message, while the material identity is effectively a marginal accessory, technicians have been called upon by the official cuIture to "consolidate" ancient manufacts reinterpreting them in the conception of the static plans pertaining to the new structural view. This has even happened in cases where bridges still kept their traditional use such as the pedestrian bridges of Veniee. This intrusive kind of intervention that pays littIe attention to the fundamental criteria of structural conservation may be emblematically illustrated by the Cannaregio Bridge (Lizzi 1981), which was restructured using bearing piles and reinforced jointing works. What is strongly urged for all historical constructions is that the structural field should acquire a sense of its own history as consider historical heritage as arecord of the material history of construction that should be preserved in full respect of its conceptual and material identity. Yet, until the early decades ofthis century there was still a unitary cuItural vision of historical wealth and construction science. Moreover, in 1910, Guidi 's treatise applied the modem theories of elasticity to the Antoinette Bridge, having a span of approximately 47 metres, built in masonry in 1884. This culture found it difficult to take up the old path hindered by not very far-sighted entrepreneurial views of building technology and of the subordination of technical and professional culture to these views. There is certainly no lack of an alternative cultural strategy that has tried to

concretely define intervention methods (D' Agostino 1997), nor are studies aimed at promoting respect for the ancient construction conception lacking (Calabresi & D'Agostino 1996, D'Agostino 1997), and it is in this eulture that speeific attention to masonry bridges has been focussed. 6 THE DIFFICULT FUTURE OF MASONRY BRIDGES Within the realm of historical constructions, masonry bridges certainly have a very difficult future. While religious buildings have continued to fulfil a never-ending human need over the centuries, and while palaces and castIes bear witness to the events of many historie town centres, only a few great ancient bridges often at the centre of a bustIing city of art still preserve their function and indeed become a significant emblem. On the other hand, most small and large masonry bridges are part of rapidly changing road or railway networks, and current historical culture does not attribute any real importance to them as regards material history. Hence, they tend to be removed or very often abandoned so that they represent a cumbersome dangerous ruin in a natural suggestive landscape and time will finally cancel all their remains. In fact, even if many countries - particularly Italy - century­ old constructions are protected by law which in theory obliges some form of conservation, this is difficuIt to conceive in a good which can no longer be utilised and which is not inserted in a cultural economic circuit. Therefore, there is the need to determine possible functions that enable the ancient manufact to preserve a functional character in a different context. In effect, many masonry bridges, particularly railway bridges, are to be found in scenographic albeit unusual landscapes that - in a society which longs for the requalification of natural features - could be revisited as significant stops on country walks. On other occasions it may be that the valley path is particularly suggestive, and the bridge could then be a focal point from which to have a grand view from on high. Finally, reuse of the bridge structure could suggest new design configurations to service its surrounding area. By building simple understructures composed of appropriate horizontal frames and panels, certain bridges could be turned into warehouses or offices to service a particular area, or turned into culture or music eentres. What counts is developing a cultural awareness allowing local communities to recIaim manufacts that are so important for the history of construction science and of the territory itself, changing them according to real needs that do not alter the message handed down by their material history. 357

NaturaIly, not all bridges can become significant monuments Iike the Pont du Gard, nor can they be as lucky as the mutilated St. Bem:zet Bridge - better known as the Pont d ' Avignon. Nor may all bridges constitute a suggestive setting for famous walks as in Rome or Salamanca, but a more pondered cultural commitment which counters the present tlat superficial handling of the territory could still allow the conservation of many masonry bridges that bear testimony to a rational as weil as industrious human commitment. 7 DOCUMENTATION, CONSERVATION AND UTILIZATION The brief notes above have tried to highlight the specific nature of masonry bridges together with their great dignity in the complex configuration of historical constructions. Here, to conclude, certain points will be made to outline the strategy to be pursued for maintaining bridges as a historical record of material history . Firstly, the aim is to obtain a kind of documentation that is as widespread as it is homogeneous allowing the stratification of a general catalogue of masonry bridges. In order to promote the compilation of such a catalogue, the Interdepartmental Centre of Engineering for Heritage of the University of Naples "Federico 11" aims to contribute to draw up a special form for cataloguing masonry bridges, that can be spread by internet. This initiative can become a contribute for a constant updating of knowledge of masonry bridges, the environment in which they were built and the reasons leading to their construction, utilisation, possible changes and - unhoped for ­ demolition. Naturally, even routine and special maintenance work for bridge conservation will be documented as much as possible, interventions which will hopefully be planned in full compliance with the fundamental principles of static restoration work that obliges an understanding of and respect for the structural conception, the original static plans, documentation on materials and ancient techniques and, finally, provides for lasting interventions using materials and techniques that are compatible with the principles illustrated. The catalogue will also allow the dissemination of design proposals for integrating ancient bridges into a utilisation system compatible with present needs for territorial management. If the initiative has the widespread consensus of institutions, administrations and technical people, then the foundations will be laid for an effective and particular contribution to the material history of historical constructions.

8 CONCLUSIONS Bridges represent works in which there is c1earest evidence of the structural construction concept and trough which it is possible to study the use of materials, construction techniques and traditional worksite organisation. As regards modem structural engineering, masonry bridges can be considered as archaeological manufacts for their unrepeatable nature, thus constituting a historic record of the material employed. The clear construction concept of masonry bridges makes them an ideal laboratory for the conservation of masonry structures. Every action of conservation work must be carried out fully respecting the existing structure, its construction concept and material integrity, without altering its static plan or physical-mechanical behaviour of its materials - especially trough the use of technologies that pertain to new materials. Moreover it is important, on the one hand, to consider re-employing bridges no longer in use; on the other hand it is appropriate to document them in order to create a databank which in time could have a specific role in the documentation of a millenary construction concept. In this light the Interdepartmental Centre of Engineering for Heritage of the University of Naples "Federico 11" aims to contribute to draw up a special form for cataloguing masonry bridges, that can be spread by internet. REFERENCES Adam, J.P. 1990. L'arle di coslruire presso i Romani. Milano: Longanesi e C. Bellomo, M. & D'Agostino, S. 1997. Ingegneria strutturaIe e costruito storico come costruito archeologico Proc. 4th Inler. Symp. on the Conservation qf Monuments in the Medilerranean. Rhodes. 6-11 May 1997: 483. Atene: National Technical University. Calabresi, G. & D'Agostino, S. 1997. General Report on Intervention Techniques. In C. Viggiani (ed) Geotechnieal Engineering jor Ihe Preservation oj Monuments and Historie Si/es. 409-425. Rotterdam: Balkema. Conforto. M.L. & D'Agostino, S. 1995. Sulla concezione strutturale dell'architettura antica, un caso emblematico: la Sostruzione romana. In Meeeaniea delle slruthlre - AI/i XII Congresso Nazionale AlMETA. Napoli. 3-60tlobre 1995: 101-106. Napoli : Ed. Giannini. Conforto, M.L. & D'Agostino, S. 1997. Resistenza meccanica e comportamento strutturale di alcuni prototipi costruttivi dell'area mediterranea, Proc. 4th Inter. Symp. on the Conservation ojMOllUmenls in the Mediterranean. Rhodes 6-11 May 1997, 561-570. Atene: National Technical University. D'Agostino, S. 1997 Tecnologie di intervento per il restauro statico deI patrimonio monumentale. II metodo di lavoro e I'avanzamento tecnico-culturale offerto dalla linea di

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ricerca. In La prolezione deI palrimonio cullurale. La questione sismica - II seminario Nazjonale di Sludio, Roma, 9-10 aprile 1997: 109-114. Roma: Gangemi Ed. D'Agostino, S. 1997. La reintegrazione nel restauro dell'antico: conservazione strutturale tra tradizione costruttiva e innovazione tecnologica. In M. M. Segar Lagunes (ed), La

Reinlegrazione nel Reslauro dell'Antico. La Prolezione deI Palrimonio dal Rischio Sismico - At/i deI Seminario di studi ARCO, Paestum 11-12 aprile 1997: 23-32. Roma: Gangemi Ed. D'Agostino, S. 1997 La resistenza a trazione dei material i lapidei e delle malte nelle antiehe tipologie costruttive. In

Meccanica generale. Meccanica dei fluidi - At/i del XlII Congresso Nazionale AlMETA , Siena, 29 set/embre-3 o/tobre 1997: 173-176. Pisa: ETS ed. Delli, S. 1992. I ponli di Roma. Roma: New Compton Ed. Di Pasquale, S. 1996. L'arie deI coslruire. Tra conoscenza e scienza, Venezia: Marsilio Ed. Foce, F. & Sinopoli, A. 1996. Le svolte di pensiero sulla ritlessione scientifica sulla statica degli archi in muratura.

Coslruire in Lalerizio, 52/53 Guidi, C. 1910. Scienzadelle costruzioni. Torino. Heidegger, M. 1976. Saggi e discorsi, Milano: Mursia. Lizzi, F. 1981. Reslauro slatico dei monumenti. Genova: Sagep Editrice. Mery, E. 1840 Sur /'equilibre des votites en berceau. Ann Ponts et Chaussees. Resal, I. 1887. Ponts en Maf01l11eire, Paris. Rondelet, 1.B. 1802-1817. Traite Theorique et pratique de ['art de Batir, Paris.

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Arch Bridges. Sinopo/i (ed.)© 1998 Tay/or & Francis./SBN 90 5809 012 4

Damages of existing stone bridges in Greece M.Karaveziroglou-Weber & E.Stavrakakis Department ofCivil Engineering. Aristotle University ofThessaloniki. Greece

E. Karayianni Ministry ofPublic Works . Trikala . Greece

ABSTRACT: Three hundred stone bridges are approximately registered in Central Greece. Some of them have deteriorated due to the effects of earthquakes, weathering and trafflc: some of the traffk they were required to carry was much heavier than the one envisaged when they were built. A limited number was blown up during the second world war or sank in water dams. The survived till today historical bridges still stand in fortunate areas bypassed by floods, earthquakes and wars of old and modern times. All of these are of considerable age (over two hundred years) and many are masterpieces of the Greek bridge engineering in the past centuries. Unfortunately, the most ofthese structures suffer from lack ofmaintenance. The research and studies that will be discussed in this paper report on the common damages of arched stone bridges in Central Greece. I INTRODUCTION

In many cases the span ofthe arches is over 30.0m, while their height often is about 20.0m. The width of the bearing structure ranges from 2.3m up to 4.0m. The paved way used by those crossing the stone bridge is usually quite narrow. The stones on the road surface of the old stone bridges form low steps so that the bridge could be ridden by horses in the past (Ph.l).

Natural stone bridges, few of which survived till today, were scattered all over the mainland of Greece but more especially in Western Thessaly and Epirus, the most mountainous part of Greece with the heaviest rainfaJls in the whole country. Because of the large number of rivers and mountain torrents with constant flow of water, it has been imperative from early times that these aqueous obstructions should be surmounted to allow the inhabitants to move freely from place to place. There had been a large variety among the architectural styles of the bridges (Fig.I), the mean difference of which lies in the number and shape of the arches (which sometimes were semi - circular or slightly pointed). In many bridges there are openings, smaJler than the main arches-called relieving arches. Their function was twofold: on the one hand they helped at times of flooding and on the other they gave a Iightness to the superstructure. One arch bridges were built at the point where the river narrowed and could be spanned by a single even wide arch, thus avoiding great and expensive constructions. Sometimes in mountainous areas there were stone bridges with two or more arches constructed at points where the conditions of the surrounding made the building of bridges necessary even in cases where the river-bed was wide. Some stone bridges with a main arch span over 10.Om in Central Greece are given in Table 1 (Galeridis et al 1995, Mantas 1984).

2 DESCRIPTION OF DAMAGES

2. I Common Damages The main damages in the masonry of old stone bridges are as folIows : - Deterioration of mortar in the bed-joints The absence of piaster on the masonry walls, which are built of stones, as weil as on the joints where lime mortar was used, left the stone bridges in easy prey to atmospheric agents; which acted immediatelyon the masonry surface. The main factors that cause natural ageing and weathering are rain, snow (freezing-thawing cycIes), temperature variation and eolic action. The temperature variation, especially in Central Greece, is severe and can arise from -10°C to +40°C during a five month period. There is no doubt that this vast change as weil as the frequent short rains in the region affect the stone masonry surface.

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Arta

Kalogerou

Papastathis

Kaberaga

Zerma Milou

Tsipiani

Fig. 1 Architectural forms of some stone bridges in Epirus (Mantas 1984)

Problems created by air-traffk pollution cannot appear because the most of the bridges are located in rural district and not in industrial areas. Deck surface weathering and water percolating through the arch ring lead to deterioration of the mortar which causes the falling of stones in the arches, especially in the central part ofthem (Ph. 2). - Cracks in stone masonry Longitudinal cracking can be seen on the intrados of the bridge arches (Ph. 3). The reason is foundation settlement or increment of the superstructure loading (Enipeas bridge at Farsala, Porta bridge). - Growth of plants and algae between stones

362

The growth of plants and algae in joints between stone blocks increases the rate of masonry dete­ rioration causing cracks or splitting of joints (Ph. 2). The growth of plants can almost be seen in all of the old stone bridges. In some bridges, because of the abandoning the superstructure is overwhelmed by plants, while roots of trees at the abutments threaten their stability (Paparizena bridge). - Moisture effects Moisture effects on the stones as weil as on the mortar joints can be easily recognised as they change the hue ofthem (dark spots on the bridge surface). - Scour of foundation

Table 1: List of some stone bridges in Central Greece a/a

Bridge

Number Date of Construction of arches

1 Arta 4 3rd c.BC-17th century 2 Placa I 1866 3 Konitsa I 1870 4 Papastath is 4 1746 5 Omolion 4 18th century 6 Kalogerou or Placida 3 1814 7 Noutsou or Cokkorou 1 1750 8 Missiou 2 1748 9 Milou 1748 2 10 Pitsoni 1 1830 11 Palioyefyro 1 12 Chatsiou 1 1804 13 Kontodemos or Lagaridis I 1753 14 Kaberaga I 15 Tsipiani I 1875 16 Vovoussa 1 1748 17 Farsala 7 18th century 18 Kledoniavista or Voidomatis I 1853 19 Mesoyefyra 3 20 Aghion 4 21 Zerma 2 22 Mano1is I 1659 23 Paparizena 1 24 Trizololl I 13th c. 25 Mezilo I 26 Porta or Agh. Vissarion 1 1519 27 Spanou 5 28 Elassona 1 29 Neraidochori 1 1750 30 Sarakina 3 1520 31 Anthousa-M ichou 2 1799 32 Krania I 19th century 33 Palaiokaria I 34 Psiras 2 18th century 35 Moukosi-Pefki I 18th century 36 Keramidi 13th century 3 37 Itea 2 18th century 38 Moscholouriou 12th century 3 39 Tirologoll I 16th centllry 40 Stefaniotiko I 16th century 41 Koplesiou I 18th century

Many bridges suffer from foundation underscouring on the abutments and the lower part of the piers (multi-arch bridges). Loss of fines and erosion of the stone bridge foundation (Ph. 4) occur generally as result of changes in the river regime (river-bed and water flow). 2.2 Wrong interventions The wrong repairing of so me bridges by using concrete must be added, according to the opinion of 363

River Arachos

Arachos

Aöos

Arachos

Penios

Vickos

Vickos

Vickos

Bayotico

Bayotico

Vicackis

Vicackis

Vicackis

Zagoriticko

Vardas

Aöos

Enipeas

Voidomatis

Aöos

Gormos

Sarandaporos

Agraphiotis

Penios

Trizoliotiko

Liascovitik0

Portiatis

Veneticos

Elassonitis

Aspropotamos

Penios

Aspropotamos

Aspropotamos

Portaikos

Mikanis

Malakasiotis

Enipeas

Enipeas

Sofaditis

Petriliotis

Petriliotis

Petriliotis

the authors, to the damages of these structures when

it is carried out without respect of the bridges

historical value.

The following are some examples of wrong repai­

ring:

-Psiras bridge

The use of concrete for coating the deck and the top of the parapets (Ph. 5) caused an aesthetic distortion to the elegant form of this bridge (Karaveziroglou­ Weber et al 1997). As mentioned above (Ph. 1), the stones on the road

Ph. I The road surface ofthe Kalogeros bridge (A. Galeridis' photo archives)

Ph. 2 Damages in the arch ofthe Porta bridge (arch span 28.0m) surface of the old stones form low steps (Karave­ ziroglou et al 1997). Unfortunately, the stone steps of Psiras bridge were covered by a reinforced concrete overlay in the last decade. Ten years after its con­ struction, the reinforced concrete slab on the deck of

364

the bridge, which nowadays is used for pedestrian crossing only, is partially damaged. It has, as a result, a reduce of the damages, which will be caused by removing the concrete coating from the deck and the parapets.

-Stefaniotiko bridge Some 18th- and 19th-century stone bridges have been under continuous service for carrying traffic. The deck enlargement has been done by using reinforced concrete. The parapets in the case of such an intervention have been constructed with steel or reinforced concrete. The Stefaniotiko stone bridge (Fig. 2) with an arch width of 4.0m, located at the rocky Argithea, has a concrete deck of 5.2m and concrete parapets. Concrete was used in order to increase the load capacity of the structure (crossing by vehicles not over 5.0 t). -Tyrologos bridge This one semicircular arch stone bridge, constructed during the Turkish occupation, is overall coated with reinforced concrete except its intrados. So, it is very difficult even to recognise this bridge. This intervention has damaged the natural stone old structure.

-Kopiesion bridge In the case of this bridge, built in the 18th-century, with an arch span of 16.0m and total length of 29.0m, two arched bearing walls of reinforced concrete with a thickness of l.Om have been built on both sides of the old stone masonry in order to bear the heavy traffic loads. This intervention meet the current standards for traffic loading capacity and provide adequate seismic safety but led to the irreparable loss of the historical character of the old structure.

Ph. 3 Cracks on the intrados of the Enipeas bridge at Farsala

Ph. 4 Foundation problems in the Gikas bridge

3 CONCLUSIONS The main conclusions about the condition of the studied arched stone bridges (dating from the 12th century through to the 19th century) and the necessary works for their preservation are the following.

365

Ph. 5 Use of concrete on the parapets top ofthe Psiras bridge ELEVATION

CROSS - SECTION

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reinforced concrete

T

I 1,50

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Fig. 2 Geometrical data of Stefaniotiko bridge Most of these bridges require extensive repair of their stone masonry (refilling the bed-joints, replacement of damaged stones as weil as grouting of cracks), strengthening of the abutments, reconstruction of the road parapets, removing of vegetation growing on the stone structure as weil as of concrete which has been applied in some cases without respect of the historical value of these structures. The abandoning of many bridges since the last fifty years, approximately, when the majority of

366

1

inhabitants of mountain area moved towards the cities, and many of the villages were abandoned, with the influence of the c1imate conditions (windstorms, strong rainfalls and frequent snowfalls during winter) as weil, contributed to the aggravation of the state of these structures. Obviously, the bridges of the last two studies were lost for ever but we hope that such kind of repair and strengthening will never be applied in the future. The modem considerations for preservation of historie bridges make sure that any intervention

must preserve the distinguish original quality of the old structure and respect the integrity of the original designer's structural concept as far as possible. ACKNOWLEDGEMENTS The authors wish to thank the civil engineer A. Galeridis and the Technical Chamber of Greece, Division of Central and Western Thessaly (Trikala), for their help in the photographie documentation of this paper. REFERENCES Galeridis, A. ,Spanos, K. , Makris, K. , Pyrgiotis, J. , Papageorgiou, V. and Kalfa, V. 1995, Stone Bridges of Thessaly, Greece: Technical Chamber ofGreece Karaveziroglou, M. , Poupi, P. and Karajianni, E. 1997, The old stone bridge of Porta (Greece), Proceedings of the International conference on Studies in Ancient Structures, Istanbul: 439-446. Karaveziroglou-Weber, M., Alexopoulos, K. and Andronikos, D. 1998, Repair of an old stone bridge, Structural Studies, Repairs and Maintenance of Historical Buildings, 1997, Southampton, UK and Boston, USA: Computational Mechanics Publications, 607-616. Mantas, S. 1984, The bridges of Epirus (in Greek), Greece: Technical Publications A. E.

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Arch Bridges, Sinopo/i (ed.)© 1998 Tay/or & Francis, /SBN 90 5809 012 4

The Venice-Mestre masonry road bridge: Checking durability of maintenance operations G.Riva Dipartimento di Costruzione dell' Architettura, Istituto Universitario di Architettura, Venice, Italy

ERusso ANAS (National Highway Authority), Venice District, Italy

ABSTRACT: The road and rail bridges that run parallel to one another, joining Venice to the mainland, have a total length of over three and a half kilometres and are composed of more than two hundred and twenty masonry vaults with flat arches. They offer an almost unique opportunity for studying the durability of arched masonry structures exposed simultaneously to the effects of heavy vehicle and rail traffic and a very severe microclimate. This paper makes a systematic study ofthe road bridge from the point ofview ofthe durability performance up to the present day, with regard to the various maintenance jobs carried out. The most delicate problem involving the durability of the structure seems to be maintaining the efficiency of the surface impermeability layers, as it is particularly complex to guarantee the efficient behaviour of this functional layer over a long period especially - as in this case - in the presence of a high volume of heavy traffk 1. HISTORIC INTRODUCTION The question of building a second bridge connecting Venice and the mainland, running parallel to the existing railway bridge, which could facilitate the provision of supplies to the town and increase the efficiency of trade, developed after political unification with the annexation ofthe Veneto region to Italy in 1877, when Manfrin c1early set forth the problem, which also contemplated the entire rearrangement oftransit within the town. Discussions went on for more than half a century, but the decisive moment came with the realisation of the industrial port at Marghera, which covered an area of about 20 square kilometres, and the need to provide a means of communication with this port and the port of Venice so as to develop an intermodal pole that could manage the gradual shift of goods traffic from rail to motor vehicles. These reasons, together with the development of tourism, led to the building of the new bridge in the years 1931-33. The bridge, made in two stages at a distance of about 90 years, consist of two separate structures, made with similar, traditional construction techniques, based on experience according to which long-Iasting behaviour of the work could be

expected. One of the two, built more than 150 years ago and recently enlarged with a new reinforced concrete structure, is for rail traffic while the other, which has been operative for over 60 years, is for automobile and heavy road traffic to and from Venice and its commercial area (Figure 1). 2. THE CHOICE OF CONSTRUCTION WITH RELATION TO DURABILITY The decision of the designing engineer Miozzi (Miozzi 1934) to build the bridge across the lagoon with a masonry bearing structure, in accordance with an old Venetian building tradition, was dictated by assessments of the durability of masonry materials in comparison with reinforced concrete, considering especially the particular micro-environmental conditions in the Venetian Lagoon and the presence, nearby, of the Marghera industrial estate. But this decision was also to prove suitable for the fatigue stress to which it was to be subjected and which Miozzi was probably unable to foresee when the bridge was built in 1933. His choice was no doubt influenced by the positive example of the railway bridge which had already been in operation for 90 years, when the new bridge was in the planning

369

Figure 1.View ofthe Venice-Mestre rnasonry road bridge !forn the island ofTronchetto

stage, and by the long, well-tested tradition of building masonry bridges in the historie centre of Venice. The bridge, which was opened to traffic in 1933, has a length of over 3620 m with 228 vaults spread over 5 embankments contained by supporting walls, of which one at eilher end. The structure are therefore composed of brick vaults about 20.0 m wide, with an average thickness of 53.0 cm and a net span of 10.63 m (between the axes of the piers there is a span of 12.13 m). The bridge runs parallel to the pre-existing railway bridge at a distance of 2.20 m (measured between the bare tympanums) and is connected to it by a reinforced concrete slab, intended as a cycle track but currently used as a footpath, resting on the shoulder of the Istria stone cornice. Since it was built up against the pre-existing structure, the road bridge is exposed to sunlight and to the flushing action ofmeteoric waters only on the side facing south-west, whereas it is completely sheltered from these actions on the opposite side. The materials and the construction methods adopted for the bridge structure echo those chosen for the construction of the railway bridge in its original form, before it was enlarged with a reinforced concrete truss due to the increase in the

number oftracks. One variation that Miozzi made to the shape of the piers was to build them with three pointed openings to facilitate water circulation and to reduce to a minimum the disturbing effect of the structure on the lagoon. The vaults were also strengthened lengthwise by means of four ribs of reinforced concrete in order to share the loads exerted by the carriageway on the continuous masonry area in the piers. The paving of the carriageway in macadam with a penetrating bitumen surface on a sub-base of trachyte from the Euganean Hills and Istria limestone and ungraded road aggregates, was laid on top of the retaining wall made of poor concrete and on the sand filling between the tympanums above the vaults. 3. FIRST PHASE OF THE INVESTIGATION The road paving was reinforced in 1947, with the laying of a binder course and of a wearing course in asphalt mix. Afterwards, maintenance work was carried out at roughly five-year intervals with the laying of thin wearing courses (tapisable). In 1981 the ANAS (National Highway Authority) for the Venice District, in collaboration with the University Institute of Architecture in Venice, the University of 370

Venice and the University of Padua, followed up directly by the authors, launched an articulated programme for experimental checking of the bridge efficiency, conceming the vaulted structure and the piers as weil as the functionallayers ofthe paving. This decision followed the appearance of cracks in the paving and slight phenomena of local sinking and corrugation in the area of the piers where there was a thicker layer of sand in the sub-base. Direct observation revealed that the static condition of the piers was good and exeluded the need for further investigation. The experimental campaign therefore concentrated on checking the static conditions and the durability of the vaults, by making tests on the masonry and its components both on-site and in the laboratory and on the functional layers of the paving (Rinelli & Russo 1982). On the parallel railway bridge, at that time repair works were being completed on the superstructure, which had presented problems due to the percolation of meteoric waters, similar to those which were later found on the road bridge (Fracasso 1980). As regards the masonry vaults of the two bridges, a different attitude was taken: while consolidation work was carried out on the railway bridge, nothing was done on the vauIts of the road bridge, so that the· experimental campaign carried out on site and in the laboratory would allow checking of the conditions of structural reliability. This paper sums up all the phases of diagnostic investigation carried out in the past and examines the procedures adopted with relation to the possible solutions to restore the functionality of the bridge structure.

we consider the structural behaviour of the type of work (Figure 2 and Figure 3). 3.2 Laboratory tests on bricks and masonry

The tests made it possible to determine the characteristics of compressive strength and the deforrning behaviour of the masonry in the vault and to express the stretching measured with strain gauges in terms of stress (Zago & Riva 1981/82). Two undisturbed sampIes were taken on the site, one from a vault and one from the respective parapet. In particular compressive strength and elastic modulus values, measured on the undisturbed masonry sampIe taken from the vauIt number 75, equal respectively to 8.2 and 2500 N/mm 2 , allowed a safety coefficient higher than 4.4 to be obtained for the load conditions tested, a coefficient which is certainly acceptable. 3.3 On-site inspection

The intrados of the vauIts presented a widespread, but not homogeneous, state of decay; they were mostly soaked with water, with persistent signs of dripping even several days after rainfall. The study of the physical and chemical properties of the masonry materials in the vaults - bricks and mortar ­ showed that the cause of the damage was the permeability of the road superstructure, through which the meteoric waters percolated without being conveyed by effective disposal devices, and then filtered through the connections, impoverishing and scouring the mortar. On the intrados of the vaults, in the areas elose to the ends of the vaults, at heights localized between the quarters and the stringers, the bricks showed widespread mechanical disaggregation ofthe surface, extending even over an area of 2.0-3.0 m2 , with a flaking process parallel to the surface that reached a depth of 10.0-20.0 mm. Stalagmite formations could be seen due to the solidification of the salts carried and deposited by the percolating waters. Physical and chemical analyses substantially blamed the action of the percolating meteoric waters, infiltrated through layers that were no longer able to provide waterproofing and not disposed of on account of the inefficiency of the existing drainage facilities, and the salts carried in these waters, for the decay of the bricks due to cyclic overlapping of the effects of salt crystallisation and the phenomenon of

3.1 On-site checking olthe masonry

One of the vaults which showed the most decay was considered and subjected to a load composed of three articulated trucks, each with a weight of 55-60 t, with a load heavier than that contemplated by the regulations in force, but adapted to allow for the heavy traffic conditions due to port activity. Readings were taken of the rise and of strain on the span itself and on the adjacent spans to check the effect of continuity ofthe longitudinal ribs. In the most unfavourable load conditions (springer, quarters and keystone of the vault), the results of these tests provided maximum stress and rise amounting on average to 50-60% of the theoretical values, which are certainly acceptable if

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freezing and thawing, for the formation of calcium carbonate deposits in the form of stalagmites, and for the decay and loss of mortar in the connections. The contribution made to decay by wave surge and the rising of water by capillary action from the area ofthe base due to priming caused by high tides and the rising of the water level above the expected

original level, protected for this reason by the stone covering, must be considered of secondary importance, since the phenomena found are present with equal intensity even in the vaults located at a higher level on the area of the final access ramp to Venice (Piazzale Roma), which are never affected by soaking due to rising capillary action.

372

3.4 Physical and chemical testing ofthe bricks

The analyses carried out revealed the presence of soluble salts in the bricks; these salts are blamed for conspicuous signs of decay found with the typical phenomenon of exfoliation. The analysis of the situation found led the investigators to attribute the principal phenomena of decay to the percolation of meteoric waters and therefore, in the long run, to the lack of routine maintenance over the years. 3.5 Checking (he paving

In order to assess the bearing capacity of the foundation, load tests were carried out on a plate in three distinct areas, corresponding to the keystone, the quarters and the piers, of three vaults. The results of the tests provided a compressibility modulus value higher than the value required by ANAS specifications and CNR standards. On the other hand, for the layers of asphalt mix, both direct observation and checking with semi-empirical methods revealed an insufficient bearing capacity, seen in the appearance of deteriorated areas with relation to the tensive stress due to overloads. Since the tests carried out on the sub-base of the paving had also given positive indications, the ample investigation showed the need for intervention on the road pavings with asphalt blankets to make them suitable for long-term resistance to tensile stress caused by traffic and to provide etfective protection against the infiltration of rainwater both for the vaults still in good conditions and for the sub-bases, which were also in a good state of repair. 4. PREPARATION OF THE RESTORATION PROJECT Considering the diagnostic tests carried out on the work, we had to choose the most suitable type of intervention to restore the structure to the highest possible degree of efficiency. In the end this meant protecting the bearing structures against percolating meteoric waters, which seeped through the paving to reach the masonry work, and improving the wearing course whose layers, with the passing of time, had gradually decayed due to the continuous infiltration of meteoric waters and to their own insufficient thickness.

In addition to these purely technical needs, it was imperative to guarantee the fitness of the bridge for use while the works were being carried out, since it is, even today, the only access for motor vehicles to the city ofVenice. The preliminary studies enabled us to consider the following possible solutions: 1. The first hypothesis consisted of injecting cement into the foundation layer composed of coarse aggregate. An experimental intervention was carried out on two sections of the bridge, injecting it to a depth of 0.7 m with 50 kglm 2 of cement. The injection points were arranged in an established square mesh so as to cover an area of 8x4 m. However, the check of the new bearing capacity, carried out by testing on a plate, gave unsatisfactory results, so the application was excluded. 2. The second hypothesis considered the use of jet grouting: this hypothesis was discarded due to the fact that the strong injection pressures cannot be supported without excessive deformation of the layers of the road superstructure. 3. The third possibility of intervention consisted of removing the existing superstructure and remaking the layers, replacing the bearing layer in macadam - of dubious efficiency when subjected to moving heavy loads and even more so when, as at the piers, it rests on large layers of sand . with a layer of stabilized mix or cement mix. This hypothesis too is abandoned because the thickness of the layer of stabilized mix needed to support the loads would have been too high with relation to the imposed height of the road surface and, besides, the nature of the material would not have guaranteed sufficient waterproofing. On the other hand the use of cement mixture, while respecting the heights, would not have allowed immediate use of the road, due to the long curing times; moreover, in the event of cracking, it would not have guaranteed impermeability of the road foundation. 4. The fourth hypotheses, which was the one chosen by the designers, was to replace the old road foundation with a new structure in proportion to the high volume of traffic using the bridge and which would guarantee a high degree of impermeability. On the basis of previous procedures successfully experimented by ANAS, a catalysed mix was chosen as the material that could guarantee these functions. Thanks to the peculiar characteristics of

373

ORIGINAL PAVING

catalysed mix, it was also possible to allow immediate use of the road, reducing inconvenience to road users to aminimum. After investigation on the local availability of aggregate, the following blend of catalysed mix was decided: basic aggregate (sand) 54% correcting aggregate (sand) 35% Trieste slag 10% set activating catalyst 1% The diagram in Figure 4 shows an example of the typical granulometric analysis of the components of the mix. The mix thus made up provides the following mechanical parameters at 180 days: indirect tensile strength (Brazilian test) 0.6 N/mm2 static flexural strength 1.2 N/mm 2 secant elastic modulus (90% of crack) 8000 N/mm2 permeability coefficient 10-6 + 10-7 crnls Finally, in order to guarantee a high bearing capacity of the entire superstructure, together with a high degree of impermeability, a packet of various layers of asphalt mix was laid on top of the catalysed mix, with a waterproofing asphalt mantle in between. In short, the new road superstructure is composed as folIows, as illustrated in Figure 5: Draining and noise deadening course 4cm Binder course 4cm Asphalt coat 1 cm Base layer 8cm Bearing course in catalysed mix 32cm

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