THE COLOSSEUM: SAFETY EV ALUATION AND PRELIMINARY CRITERIA OF INTERVENTION
G. Croci University of Rome "lA Sapienza"
Via Elldossiana 18
/-00184 Roma, Ita/y
SUMMARY For many years the Colosseum has been the object of interdisciplinary research aimed at assessing its structural behaviour and safety leveI. Studies of the historical documentation, in situ investigation and analytical modelling have allowed us to understand lhe partial collapse causes. In this paper we are too proposed some mathemalical madels, which are carried out to allow lhe safety assessment in present situalian after the restoratian works in the 19th
century. The results are discussed and the weakness of the monument with regard to earthquakes is outlined. The zones requiring strengthening are studied in delail and some preliminary criteria ofintervenlion are praposed.
1. THE HISTORY AND THE STRUCTURAL BEHAVIOUR
I. From 72 a.O. to 443 a.O. - The first centuries
I . I The hi story The Flavius Amphilheatre, whose construction lasted about ten years. was
dedicated and opcned to public in 80 a.O., during lhe reign of Titus (tig. I) . The works presumably started in 72 a.O. with lhe simultaneous construction offour similar portions separated on plan by lhe two principal axes of symmetry; Ihis explains the speed of the reali sation, some structural imperfections, such as lhe insufficient bearing lenglh of lhe blocks in some zones, and lhe prcsumably weak connection of the four portions in correspondence to lhe two principal axcs . The Colosseum was covered with a velarium whose documentation has been completely lost; a possible configuration designed on the basis of st ructural analysis, lha! we have carried out taking into account the characteristic of the hemp ropcs that probably have been used The second peculiarily of the construction, is lhe site Ihat has probably played an important role in the damages and col1apses as we shall see later. The site was originally the lake of lhe Domus Aurea and was then partially filled to create the basis for lhe foundations; the result was hetcrogeneous soil and foundations (partially represented by a concrete bed) and an alteration of the hydrographic settlemenl. In the first centuries ofthe Colosseum's life, il was affected by fires, small earthquakes and floods. In the 217 a. D. a tire, caused by lightening, bumt the timber structures Df the top roof; importam fires also occurred in 250 a.D. and 321 a.O. It is important however 10 observe that . although lhe restoration works following lhe 2 17 tire were recorded as having taken place over tive years, it is unlikely that they substantially affected the stonc elements calcined by lhe tire or lhe masonry damaged by lhe fl ood. However, in spil e of these events, the Colosseum maintained lhe original strength and soundness.
G. CROCI I Thc Colosscurn
Fig. I: Viell' ofColosseum
L \ n r \, r! II 1 r \ ,~ ! .. ,
Fig. 2: lhe Colosselll11 after lhe earlhqllake of }3~9
155
156 STRUCTURAL ANALYSIS OF HISTORICAL CONSTRUCTIONS
1. 1.2 Mathematical models related to lhe dead load In arder to verify the original safety leveIs a first finite element mathematical
medel considered the Colosseum in it s original form o The static analysis has demonstrated tha! lhe original structure performed well , showing lhe sk ill and fo relhought Df lhe ancient designers and builders. The structure appears to be aver dimensioned, reaching a maximum compressive stress of only 24 KN/m2 at lhe base af the travertine picrs. Whilsl the strength is of many hundreds KN/m2
The medel has a1so shown lha! lhe arches inserted in lhe elliptical wall s induce a horizontal thrust with a radial componenl corresponding to each pier, lhal is added to lhe thrust produced by the ambulatory vaults; the corresponding tensile hooping st resses are anyway lesscr Ihan I KN/m2.
1.2 From 443 to 1703 - The Four Slrong Earthquakes
1.2.1 The history The first important event thal effectively caused some destructions of lhe
Tllonument was the earthquake in 443 a.O., estimalcd of VIII-IX grade Merca11i Scale, with lhe epicentre in lhe roman region. Paol us Oiaconus in hi s "Historia Ro mana" said tha! "tam terribili terremolu Roma concussa est, uI plurimae aedes eius et aedificia co rruerinl ". The Colosseum suffered damages on lhe sitting grades, in lhe arena and podiulll areas and at the attic leveI. 11 look three consulales to be reslored and some of the works can sti11 be secn a! the 10p of lhe externaI wall, where a chaotic cyclopic masonry was seI. After this, news about the building seems to fade: lhe las! ludo mceting is recorded in the year 523 a.D.; lhen, in the year 663 a.O., Constantinus 111 ordered lhe tearing down of lhe bronze plalcs of the atti c. 1I is believed thal in this period lhe locking slirrups amo llg the blocks were also taken Oll" Ihis spoiling callscd lhe ruplu re of many blocks, Ihus 10ca11y modifying the stress stale dist ribulio n. After lhe 5th century the Colosseum was nOI only disllsed and abandoned but also sma11 earthquakes occurred and expanding plant rOOlS opened exist ing cracks and created ncw ones. There was Ihen a IX grade carthquake in May 801. with probable epicentre in the Abbruzzese Appennino . The cyclopic order columns a! lhe attic inner levei fe 11 into the cavea, causing huge damages in the inclined barrei vaults and arena; other less striking structural cracks also accurred . We believe that thi s is lhe dat e a f the loss of continuity at the top of lhe e11iptical wa11s. The next information about the monument is dated at lhe beginning o f lhe 12th century. lt was Ihen inhabited by patrician families (Frangipane and Annibaldi) who fartified the Iwo lower leveis af the south·eastcm side. Unfortunately there is no iconography available of this period, with lhe exception of a commemarative medal ofLudwig the Bavarian (year 1328) lhat shaws the Calosseum behind o lher buildings wilh the upper row sti ll intact; the occasion of lhe representation, lhe cOIllIllcmoration of lhe new emperor, and the small scale of the piclure expIa in the lack af reliabil ity. Minor earthquakes occurred in 1255. 1287, 1300, 1321,1348 Even if lhe pope Innocenzo IV ordered lhe destruclio l1 of lhe fortificat ions, lhis must have been more or less ho w the Colosseum was in 1349 when anather destructive earthquake occurred in Rome \Vith VIII · IX grade. The most famous witness, Petrarca, said "magna clIm partem collapsat" . This carthquakc. the most destructive in central
G. CROClI Thc Colosscunl 157
Italy, with epicentrum in the Umbro-Abbruzzese, produced the complete failure of the two externai cylindrical walls on the Celio si de of lhe Colosseum. Afier lhe earthquake of 1349 the Colosseum, reduced to a ruin, was abandoned and in 1362 the heap of rubble, especially from lhe IWO externai walls, constituted a small hill, named "Coxa Colisei" (fig . 2) . The use of lhe materiais (marble and brick) was a bane of contenlion belween the reman people, the Frangipane family and the represenlatives of Pope Urbano VIII , as il was required for lhe conslruction of some roman palaces and St. Peter's Basilica. It seems, anY'-vay, that the removais were usually from lhe fallen portions; there is no evidence of demolition except for Iimited ones authorised by the popes. Some "spontaneous collapses" are recorded in 1646 and 1689; lhe cause of these phenomena Ihat cannOI be direclly related to particularly events, nor to seismic aCl ions, will be explained later. In 1703 the fourth and last slrong earthquake occurred; lhe origin was once again in the Appennino region and crealed wide destruclions in lhe city af L'Aquila. Although lhe energy characteristics were similar to thase of 1349 earthquake, the damages were much less extensíve, as just one arch is recorded as havíng coll apsed in the outer wall and three arches in lhe second wall ; ít appears therefore to be a reverse in the trend of the increase af damages and failures in the succession of lhe earthquake of 443-80 1-1349. We have nol aI present complete data to explain this differenl behaviour; one possible explanation however can lie in lhe different characterislics of the soil beneath the foundalions: Iherefore, once lhe Slructures on lhe weaker bed have collapsed the remaining have a greater resistance. Deeper analysis and invesligations are presently in progresso
1.2.2 Mathematica l models related to seismic aClions The theoricaJ behaviour ofthe Colosseum under lhe effecl of seismic action has
been analysed slarting with a global elastic linite element model laking into account lhe differenl characteristics oflhe soil To quanlity lhe seismic aClion lo be used in lhe malhematical ana lysis, two ditTcrent melhods. which gave similar resulls, have been considered: a) lhe hislorical data aboul seismic events recorded in the area : il can be seen Ihat an earthquake of VIII 10 IX grade. in M.S. scale, has a return pcriod of abou! 500 hundred years; b) sludies 00 seismic characteristics of lhe area; some studies assessed Ihal a Richler inlensity of 6.68 can be attached lo a period of 400 to 500 yea rs and therefore a ground acceleralion of 0.05 to 0.06g can be deduced. Evaluating lhe amplificalion of the masonry structure up lo 25 to 3 limes, a design value of 0.15g, is obtained. very elose to the value 0. 16 slated in the Italian Seismic Code for lhe 3rd calegory area. this Is the valuc that we have adopled. The models indicate that lhe zone of higher stresses is in the allic wall. and in panicular in lhe zone of the minor axis towards lhe Colle Celio; thi s is the area where lhe firsl breach in lhe wall may have occurred. In fac! il is here Ihal the maximum horizontal stress (up to 8 KglClll 2, figs. 3, 4), due 10 seismic action in lhe x-direclion. is reached. This levei of tension cannot be sustained by the friclion present in lhe horizontal dry joints ofthe blocks because oflhe low vertical Joad. Similar results have been reached with lhe seislllic action in y-direction. A delailed examination of the resulls of the seismie analysis allows us to consider Ihal lhe allic wall could reach a criticai condition near the minor axis (on lhe Celio side) with a large range of possibJe eanhquake direclions as opposed lo lhe small range of earthquake direclions which could afreel lhe wall around lhe major axis.
158 ST RUCTURAL ANALYSIS OF HI STORICAL CONSTRUCTIONS
Fig. 3: Tensile horizOJJfal slresses due lo lhe seismic aclioll in lhe X-direcl ioll correspolldúlg lo lhe 3nd mude
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4 , .' !·l . ... ;
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Fig. 4: Tensile horizonlal slresses due lo lhe seismic aclioll in lhe Y -direcliolJ
G. CROCI I Thc Colosseum 159
Another zone where the model shows a criticai situation is in the first levei of piers in lhe inner elliplical wall, near lhe major axis. Particularly wilh seismic aClion in lhe xdirection some piers' sections are partialised by lhe presence of tensile stresses and reach compression of about 50 KN/m2. The tensile stresses anyway are not high enough to cause lhe visible damages of lhe first levei piers and it is evidenl thal a single eanhquake could nol have caused lhe ruin of a large portion of lhe monument. It is necessary lO inlerprel lhe elastic and postelastic behaviour of lhe Colosseum in its original configuration to understand tht: leal phenomena. Referring to fig o 5, during an earthquake, while lhe vertical axial force "N" remains constant, there is a transfer of effort, from lhe stresses, "Til, which characlerise lhe circurnferenlial behaviour, to lhe bending behaviour "M", in the pillars, This behaviour is schemalically represented in figo 6: in the elastic phase il is lhe circumferenlial tensile st resses in lhe elliplical walls which give the main contribulion; il is only after they reach Iheir peak value linked 10 lhe friclional limil ofthe horizontal joint, lhat larger deformations (qualitatively represenled by õ in the diagram), and relevant bending moments are generated in lhe pillars. In conclusion, we pass progressively fram an "N-T" behaviour to an "N-(T)-M" behaviour, 11 is important to note Ihat, after lhe firsl earthquake, permanenl deformations (and thus permanent bending moments) remain so lhat lhe global behaviour, even for low levei seismic actions, becomes weaker and weaker; fig o 7, show lhe sinusoidal deformations. signs ofthe earthquakes on lhe externai wall oflhe Coli seum. This interpretation of lhe phenomena is in accordance wilh the hislorical documents Ihat indicate Ihat lhe two earthquakes of 443 and 801 caused only a loosening of lhe masonry in lhe allic levei , as well as in lhe horizonlal bands of lhe lower leveis, with consequenl sliding between the blocks, particularly in lhe zçme ofthe minar axis on lhe Celio side. These sliding movemenlS caused incremcnls in lhe annular length and Ihus oul of plumb Moreover this iniliated lhe vert ical cracks which began in lhe attic wall and which were leR. unrepaired after the earthquake of 80 1. Despile lhe small ent il Y of Ihese damages. Ihey comprimised the efficiency of the Iwo-dimensional behaviour of
'lhe attic wall , so Ihal il was more easily damaged during successive minor earthquakes ( 1255, 1287, 1300, 1348), This weakness of lhe attic wall, which extended to lhe lower leveis, explains lhe ruin of lhe large portion of lhe IwO ou ler elliptical walls near the minor axis on the Celio side during lhe earthquake of 1349. An interesting queslion is whether lhe failure of the Celio si de is mostly due to the weaker foundalions. In effect lhe remaining side shows tensions thal surpass lhe limit for lhe iniliation of frictional movement (wilh lhe seismic aClion in y-direclion in lhe malhemalical model) . Thus il is possible Ihat lhe foundation factor was important nOI onl y during seismic aclions (amplifying deformalions and lensions on lhe Celio side as visible in lhe model for aClion in lhe x-direclion), bUI al50 after and belween Ihose cvcnts, wilh diAcrcntial settlement due lo lhe effects of the oUI-of-plumb, especially on lhe Celio side; these aspecls are the subject of deeper invesligations.
I 3 From 1703 10 1979· From the Ruin lo lhe Restoration Works AR.er the 1703 earthquake lhe Colosseum remained abandoned and consequently
suffered progressive deterioration. The 19th cenlury is lhe century of lhe biggest work evcr carried oul on the Colosseulll. Attenlion was inilially focused on lhe laleral borders of lhe surviving façade, where lhe lack of continuity and Ihus lhe disappearance of circumferenlial stres5es, created lhe mos! unfavourab le situation, \Vorsened by lhe dynamic actions Ihat affected lhe existing boundary of the collapsed zones
160 STRUCTURAL ANALYSIS OF HISTORICA L CONSTRUCTIONS
Fig. 5: Maill slresses aClillg 011 lhe Colossf!um
Fig. 6: EVO/Ufio" of lhe main -"tresses afta b/ock !ric/ioll overlake
G. CRQCI I Thc Colosscurn 161
Fig. 7: SiKIIS of earlhq/lakes (sill/lsmdal deformarioll) visihles 011 lhe exlemal wall
162 ST RUCTURAL ANALYSIS OF HISTORICAL CONSTR UCTIONS
The abutments of Slern (1805-1807) and Valadier (1822-1826) stopped lhe deterioratian pracess and generated a new, adequate static situation (fig. 8); the same cannal be said for lhe dynamic behaviaur as we shall di scuss later. From 1831 to 1846 important works were carried out by Sal vi with lhe reconstruction of the interior circunferencial wall on lhe Celio side and lhe installalion of a system of radial tie-bars in the alignments around the imperial entrance. Ahhough Ihese works were reali sed, and a1though no slrong earthquake has occurred since 1703, a dangerous situation, very elose to collapse, occurred in 1979 when we were asked by the Archaeological Superintendent of Rome to check some piers in lhe inncr circumferential wall , ncar the Stern abutmenl. A decp proccss of eracking (fig. 9) , was immediate1y evident, so that urgent shorage and intcrvention were requ ired. This event , which iniliated lhe study summari sed here, gave us lhe opportunity to highlighl the facl Ihal lhe earthquake produccd not only direcl co ll apses, but also started a process of deterioration related to lhe high stress leveis rcached, which created cracks and micro cracks sensit ive 10 thermo-hygronometric conditions, and particular1y to lhe effects of frost provoking an íncremenl of internai st resses in lhe outer layer ofthe blocks, Ihus facilitating spall ing. This phenomenon justifies lhe numerous "spontancous collapses" that have contributed to the large quantity of material that has becn losl during lhe ccnturies; lhe facl tha! only lhe collapscs corresponding lo lhe earthquakes and few olher situations are recorded by historians is nOI a surpri se: for centuries the Colosseum has been an abandoned ruin, no one being interested in whal happened to it . Fig. lO shows fram a qualitative point af view the evolution af the collapses and the weakening of the structure.
2. THE PRESENT SITUATlON AND THE SAFETY EVALUATION On the basis of what has been shown ir is possible now to give a judgement of
the prescnl safely levei by a criticai interconncction of the information by means of three different processes: the direcl observation, lhe mathemalical analysis, the hislorical survey. I - The direcl observation - A carefully observation of the Colosseum highlights the main alterations Ihal can be summarised as follows : - the materiais: dcteriorations are present in many parts ofthe Monument , linked to the fire, weathering and to the effects of almospheric attack, frost, etc .... : high stresses and cracks have accelerated the related phenomena; - lhe geometry: alterations are particularly cvident in the "earthquake signs", such as lhe frequent separations between the elliptical and radial walls (fig. 11), lhe sliding of lhe blocks in the walls in lhe vaults and lhe arches, the oul-of-plumb of walls and pillars, lhe deformations of the facade (fig. 7) . This last aspect is of particular interest as the circumfcrential si nusoidal deformation, nol always in phase from a levei to another has also praduce relative rotations about their own vertical axes and twisting effects in some pil1ars. - the previous works: the collapses have deeply changed lhe original constmction whose most evident aspects are the Stern and Valadier abutmenls, the works of Salvi , the st rengthening of some elements (arches, pillars, ... ) and lhe insertion of metal chains, (fig. 12) related to lhe out-of-plumb which pragressively increased over time; 11 - The Malhematica! Models - Different modcls were made to take into account differenl hypothesis on the structural behaviour of the monument , due to different hypothetical efficiency of lhe slructural elemcnts. The malhemat ical analysis indicates Ihal lhe surviving façade, belween lhe Stern and Valadier abutmenls as wcll as lhe abutments lhemselves, reach tensil e stresses, initially
G. CROC! / The Colosseulll 163
Fig. 9: Cracks and crushillg discol'(!red ill 1979 in some pillars
lHE EVOLUTlON OF OAMAGES DUE TO EARTHOUAKES ANO OTHER REDUCT10NS IN STRUCTURAL RES1STANCE OVER TIME.
S,F , I
r-= .. ~--;-, 1-- ..,--1--_-___ _
r --
, I
. '~:1:·.:.~r,,="'t.:r":,r:r.~ - ... ...... u .. "
Fig. 10: Qualita/h1f! evolllfloll of failureé1· al1d loss of material
164 STRUCTURA L ANALYSIS OF HISTORICAL CONSTRUCTIONS
Fig. 11 .' Separa/íon helweell circlIIII!erellfial anti radial walls
Fig. / 2: ('hoin.\' plm:t'd in lhe 191h c.:enlllly
G. CROCl I Thc C010SSCIIIll !65
in the eireumferential direetion, whieh overtake the frietion between the bloeks; this means thal sliding between the travertine blocks ean be produeed, and as a eonsequence ofthe increased bending moment in lhe pillars, there is a reduction in lhe effeetive section of the pillars Ihemselves that can lead to criticaI situations. The mathematical models also show that lhe current situation is weaker than the original situation due to the loss of cireumferential eontinuity. 111 . The histarieal survey strong earthquakes (VIII and IX degrees on the Merealli scale) dacumented in Rome every )·5 eenturies, have always produccd damagc and collapses; besides they have initiated deterioration processes which have brought about collapses ar dangerous situations decades ar eenturies after the event itself. To interpret the lesson from history regarding the present situation we have to take into account lhree aspects : · the increasing weakness of the structure aftcr each earthquake in relation 10 lhe sliding belween the blocks, the deformations, lhe out·of.plumb and lhe increasing stresses in the columns; from this poinl of view lhe present situation is worse than the situation in lhe pasl. · the role of lhe soil and foundations; lhe zone \Vhere lhe characteristics are \Vorse corresponds to lhe most damaged part of the monument; from this point of view the capacity of the surviving structures, especia11y lhe tàçade, appear better as they probably bear onto efl'icient foundations; • the different geometry and the configuratian afthe aetual struClure, and in particular the façade including lhe Stern and Valadier abutments; this situalion has never been tested by strong earthquakes so no specific information can be extracted from hislory
3. PRELlMINARY CRITERIA OF INTERVENTION The interaction bet\Veen lhe different information mentioned above and Iheir
critica! analysis, makes it possible to have a reliable piclure of lhe situation and allows us to express some concern, especially \Vith the prospect of the nexl slrong earthquake. The exceptional value ofthe monument requires however prudence in lhe judgements deeper analysis and more sophistieated mathematical madels are going to be developed, and we expecl in few years to !lave acquired elements la reduce lhe uncertainties: il will be possible therefore 10 ensure an adequate margin of safety and durability, minimizing any alteration corresponding to lhe interventions. The preliminary indications on lhe possible strategies for interventions on the façade can be synthesi sed as fo11o\'ls : • to conneCI the externaI \Vall to the ambulatory vaults and lhe radial walls (after cheeking lhe effectiveness ofthe chains placed in lhe Ilineteenth century) • to improve the circumferential resistance which is currently only provided by lhe frietian between the blocks: · to improve lhe transverse flexural resistance af the abutments where the circumferenlial collaboration is missing. Some cables (steel or synthetic fibres), passibly prestressed should be useful for these purposes; as previaus mentioned, howcver, these are JUS! preliminaT)' ideas la be verified and detaiJed on lhe basis of the new data that will be acquired , taking inta account thal. due to the dynamic nature af the problem, any possibilily lo dissipate part ofthe energy must be favoured .
