Structural Analysis of Historic Construction – D’Ayala & Fodde (eds)© 2008 Taylor & Francis Group, London, ISBN 978-0-415-46872-5

The Athens Parthenon: Analysis and interpretation of the structuralfailures in the orthostate of the northern wall

E.E.ToumbakariDirectorate for the Conservation of Ancient Monuments, Ministry of Culture, Athens, Greece

ABSTRACT: An investigation on the typology of the failures recorded on the first row (orthostate) of theParthenon northern wall was undertaken. The analysis of the failure causes was based on the simultaneousconsideration of (a) the kinematic constraints of each block, (b) the applied system of deformations/displacementson each block and (c) the applied system of deformations/displacements on the wall itself. Moreover, a numericalanalysis was also undertaken, and characteristic results are also reported. The effect of the marble anisotropy(in terms of the position of the marble soft plane inside the block) was also studied. The main conclusion of thestudy is that the mechanical action of the connectors could explain the observed structural pathology, whereasrust is not a necessary condition for the structural failures to occur.

1 INTRODUCTION

The longitudinal walls of the Parthenon are composedof 19 rows of marble blocks. The first bottom row,called orthostate, is composed of blocks with averagedimensions 1.44 m length, 0.55 m depth and 1.15 mheight. The last row is composed of architrave withaverage dimensions 2.44 m length, 0.5 m depth and1.04 m height. The intermediate 17 rows are built withsmaller marble blocks (length 1.22 m, height 0.52 m).The even-numbered rows are composed of two linesof blocks, disposed with their long axis parallel to theaxis of the wall. Many blocks of the external line, fac-ing north, are conserved, whereas the internal ones,facing south, are lost. In the odd-numbered rows theblocks are placed perpendicular to those of the even-numbered rows (Fig. 1). The blocks are horizontallyconnected with clamps and vertically with dowels(Fig. 2). The main actions that affected the mechan-ical history of the walls of the Parthenon are the fireof 267 A.D. and the explosion of 1678 A.D. during thesiege of Athens by the Venetians. The latter caused thecollapse of the larger part of the walls.

Previous investigators on the state of preservationof the Parthenon (Korres & Bouras 1983) argue thatthe cross section of the connectors is designed soas to have lower strength than the anchorage area.So failure of the connectors and not of the marbleitself is expected to occur. If, however, marble failureoccasionally occurred, it must be preceded by marblecracking due to rust and volume increase of the ironconnectors.

Figure 1. Structure of the walls of the cella (Orlandos 1977).

2 POSITION OF THE PROBLEM

The present work summarizes the main issues of thestudy for the structural restoration of the orthostate ofthe N.Wall, which includes the description and docu-mentation of the condition of the marble blocks, theanalysis & interpretation of their structural pathology(Toumbakari 2006) together with a numerical analysis,

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Figure 2. Connectors at the orthostate level (Orlandos1977). There are also two dowels on the orthostate uppersurface, which are not shown.

Table 1. Location of the marble fractures.

Dowels Dowelsupper bedding

Clamps surface surface Outsidearea of

No E W E W E W connectors

1 n.e. n.e. + + 1st: n.f. + n.f.2nd: +

2 + n.e. + + + + +3 + + + + + + +4 + + + + + + (C)5 + + + + + + n.f.10 + + + + + + +11 + + + + + + n.f.12 + + + + + + +13 + + + + + + n.f.14 + + + + + + + C15 + + + + + + n.f.16 + + + + + + n.f.

Subtotal 11 10 12 12 12 12 5Total 69 5

n.e.: not clear because of detachment of big marble volume.n.f.: no failure C: cracking +: failure.

whose main results are also discussed (Toumbakari2007a; Filippoupolitis 2007).

The location of the failures at the orthostate blocksis summarized in Table 1. Failure is defined as marblefracture and detachment. Usually, the detached frag-ment is lost. Among the 74 failures of the orthostateblocks, 69 are located at the area of the connectors andonly 5 (i.e. 7.2%) are located in areas not affected bythe connectors’ action. Moreover, the external (north-ern) orthostate blocks have not been affected by fire.Therefore, their structural pathology can be attributedto a limited set of factors, namely the explosion, therust and eventually earthquakes that have occurredprior to 1687. If however the connectors were designedto fail prior to the marble, then why is the majority ofthe observed failures located at the anchorage area?

3 RECENT OBSERVATIONS and DATA

The extent of damage reasonably permits the assump-tion that, all those failures cannot be solely attributedto rust. The undertaken investigation aimed to findout whether mechanical action of the connectorscould as well generate marble failure, without rust asprerequisite.

Before proceeding to the analysis of the failuremodes and to the numerical analysis, the followingobservations need to be reported:

1. The contours and volume of the detached marblepresents similarities for all blocks. This excludeshuman intervention as a cause for fracture, becausehuman intervention would have produced a varietyof fracture configurations.

2. Failure concerns practically all connections of allthe available blocks. A similar case could be theOpisthodomos (western) area, in which originalclamps and dowels of the architraves were uncov-ered during the 2001–2004 restoration campaign.Our assessment of their preservation, is that theybehaved very well, despite the observation of super-ficial rust (Archives 2007, Toumbakari 2007a).Moreover, marble failure was concentrated in areaswith residual deformations. It is reasonable toassume that the quality of the iron of the orthostateconnectors is similar to the aforementioned. So, ifrust cannot be excluded, it is difficult to argue thatit produced such extended mechanical effects onlyat the orthostate.

3. The analysis (Papadimitriou et al. 2007) of theunique ancient connector recently found in theNorthern Colonnade showed that the clamp andlead were conserved in a good condition, rust hasaffected the external 2 mm of the iron whereasthe anchorage area was in an excellent state ofpreservation (Toumbakari 2007b).

4. In addition, rust usually creates a one-sided detach-ment, which then provides sufficient space for theconnector to expand. Thus, marble detachment onthe other side of the connector is not necessary. Theorthostate clamps’ anchorage areas are practicallyall characterized by detachment on both sides of theconnector.

5. Available experimental results relative to the designof new dowels have shown that failure alwaysoccurs in the marble and not in the connector (Zam-bas 1989). On the contrary, when new clamps (withdimensions close to the ancient ones’) were sub-jected to tension, it was the connector that failed(Zambas 1994). To the best of our knowledge, thereare not available results with clamps subjected toshear.

6. The failure configuration is similar to failure pat-terns, already well-known in the literature (CEB

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1994), attributable to dowel and anchor mechanicalaction.

On the basis of the above, the following hypoth-esis was developed: The concentration of failures atthe area of the connectors could be attributed to themechanical action of the clamps and dowels, whenthe bearing structure (either entablature or wall) wassubjected to strong external (horizontal) actions.

Rust could have, and certainly has, occurred, butit is not considered sufficient for the generation ofsuch large number of failures. Moreover, rust is notthe unique condition for the generation of smallcracks, which will later initiate fracture. Those crackscan also be generated if the marble blocks are sub-jected to tension-inducing actions, such as temperaturechanges, environmental actions and vibrations due todynamic loading. Recent experimental work on mar-ble properties and behaviour (Vardoulakis et al. 2002)established the existence of residual deformations onmarble specimen subjected to tensile load as well asthe non-linear behaviour of the material even at anearly stage of loading. In the study, no explanationas to the origin of those deformations is provided.It can, however, be assumed that they could be theresult of the opening of small cracks at surfaces con-taining argillosilicic veins, as is empirically known topractitioners.These cracks can conceptually be assimi-lated to “notches”, which will facilitate (but, of course,not generate) crack propagation under the mechanicalaction of the connectors.

Concerning the connectors’mechanical action, it isimportant to estimate if the developing pressure isentirely transferred on the marble walls. It is recalledthat the void between the connector and the marble wasoriginally filled with lead, which, in unconfined condi-tions, is an energy-absorbing and deformable material.In the case of ancient connectors, however, lead is ina situation of triaxial confinement. It has to be admit-ted that this confinement might not be perfect due toconstructional imperfections, nevertheless it is certainthat the deformability of the lead is limited, especiallyin a horizontal direction, where the filling of the voidis complete. Thus, doubts are cast about the deforma-bility of the system under confined conditions. Furtherexperimental work is nevertheless necessary to clarifythis issue.

4 METHODOLOGICAL APPROACH

The analysis followed a dual approach, qualitative andquantitative (ICOMOS 2004, Tassios 2006). The qual-itative approach is defined as “an approach basedon the direct observation of the structural pathologyand material deterioration as well as on historic andarchaeological research”. The quantitative approachis based on “the properties of the materials and

structural elements, instrumental (or not) follow up ofthe behaviour of the structure and structural analysis”(ICOMOS 2004).

The direct observation of the structural pathologyfocused on the analysis of the type of action (tension,shear. . .) that could have produced it. It consisted inthe definition of failure modes on the basis of similarand repetitive failure patterns and in the search for asystem of deformations/ displacements at the blocklevel, which could have generated them. This sys-tem had to be compatible to the kinematic constraintsimposed by the connectors as well as to the defor-mations/ displacements that have been applied on thewalls. The latter, subjected to horizontal actions, couldbe described as plates with partial constraints at threeedges and free at the upper edge, because the roof hadalready collapsed before the explosion. Consequently,three criteria for the analysis and interpretation of thestructural pathology were defined: (a) kinematic con-straints applied on the building block, (b) system ofdeformations/displacements applied on the block and(c) system of deformations/displacements applied onthe wall. These criteria had to produce a system offorces, compatible to the observed pathology. Duringthe study, it was observed that the failure configura-tion also depends on the local system of argillosilicicveins as well as on the direction of the marble soft planeinside the block.The first do not affect the failure modebut do affect the precise shape of the failure surfaceand volume of the detached fragment.The latter permitor hinder the development of the one or other failuremode.The qualitative approach permitted the determi-nation of the type of actions that were applied by theclamps and dowels on the anchorage area. It is howevernot sufficient because, if it highlights the mechanismsof failure, it still cannot differentiate between the pri-mary cause of the failures, namely mechanical actionor rust.

A numerical analysis was therefore necessary inorder to investigate if it is possible for the failures tooccur under the connectors’mechanical action. Exper-iments are very important in this respect, and if theyare available in the case of dowels (Zambas 1989),they still need to be completed in the case of clampssubjected to shear. Two 3D models were created withthe use of solid Finite Elements and the Sofistikcode (Toumbakari 2007a, reworked by Filippoupolitis,2007). They represent marble blocks with length andheight equal to 0.6 m and depth equal to 0.5 m (which isthe average depth of the Opisthodomos architraves andorthostate blocks).The choice of these dimensions wasjustified by previous numerical analyses (Toumbakari2007a), in which it was shown that the effect of the con-nectors does not overpass a distance of 0.25–0.30 m.The models are shown in Figures 13 and 14. Theload cases and boundary conditions are described inTables 2 and 3. In what follows, only the analyses of

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Table 2. Load cases and boundary conditions of the con-nectors’ models (s.w. = self weight).

Loadcases Clamp∗

LC 1 s.w. + vert. loads + shear force 1 kNLC 2 s.w. + vert. loads + shear force 15 kNLC 3 s.w. + vert. loads + shear force 29 kNLC 4 s.w. + vert. loads + shear force 1 kN + tens.force

1 kNLC 5 s.w. + vert. loads + shear force 15 kN + tens.force

15 kNLC 6 s.w. + vert. loads + shear force 15 kN + tens.force

30 kNLC 7 s.w. + vert. loads + shear force 29 kN + tens.force

30 kN

∗Boundary conditions at surfaces which are part of the mar-ble block: constraint of displacements & rotations in alldirections.

Table 3. Load cases and boundary conditions of the con-nectors’ models (s.w. = self weight).

Loadcases Dowel∗

LC 1 s.w. + vert. loads + shear force 1 kN (uniformdistr/tion)

LC 2 s.w. + vert. loads + shear force 5 kN (uniformdistr/tion)

LC 3 s.w. + vert. loads + shear force 14 kN (uniformdist/ion)

LC 4 s.w. + vert. loads + shear force 1 kN (triang.distr/tion)

LC 5 s.w. + vert. loads + shear force 5 kN (triang.distr/tion)

LC 6 s.w. + vert. loads + shear force 14 kN (triang.distr/tion)

∗Boundary conditions at surfaces which are part of the marbleblock: constraint of displacements & rotations in all direc-tions.At bedding surface: constraint for vertical displacementonly.

Failure Modes I and II, which correspond to the afore-mentioned models, will be developed. The remainingthree failure modes will be summarily described inthis work.

5 FAILURE MODES OF THE ORTHOSTATEBLOCKS

5.1 Failure mode I

This failure mode is related to the clamps, which arelocated at the upper surface of the orthostate blocks(Fig. 3). Failure consists in the detachment of marblefragments on both, in most cases, sides of the clamps(Figs 5, 6). In Figure 3 both the initial (in dotted lines)

Figure 3. Initial (dotted lines) and deformed position of theorthostate block, on which the area affected by the clamps’pressure is highlighted.

Figure 4. First detachment due to the clamps’ shear force.

and deformed shape of two adjacent orthostate blocksunder the effect of a horizontal action are presented.The system of clamps and lead (hereafter: clamps)initially resists the applied deformation. The role oflead is crucial in force transfer. Because the clampstend to conserve their shape, they exercise pressure onthe marble with a direction opposite to the externalaction (grey area in Fig. 3). This could lead to a firstdetachment (Fig. 4), if the shear force applied by theconnector is higher than the resistance of the marble.As the clamp is now free from the constraint imposedby the marble wall (which detached), it is obliged tobend, in order to follow the deformation of the wall.Inversely, the wall deformation is possible either if theclamp is able to deform in flexion or if the marblefails. The ensuing clamp flexural deformation resultsin the development of pressure on the remaining mar-ble wall. As in the first step, failure mode I occurs, ifthe applied force is higher than the shear resistance ofthe marble. The configuration of the clamp’s area aftercomplete failure is shown in Figures 5 and 6.

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Figure 5. Typical configuration of Failure Mode I.

1. Position ofclamp2. Missingnorthernfragment3. Detachedand repairedsouthern fragment

Figure 6. Failure of orthostate block 5 with Failure Mode I.

Alternatively, failure mode I can also occur withsimple relative horizontal displacement between themarble blocks without rotation. In this case, a one-sided marble detachment can occur.

Figure 6 illustrates orthostate block No 5 of thenorthern wall, in which failure mode I occured. It canbe seen that, detachment on both sides of the clamphas occurred. The northern fragment is lost, whereasthe southern was found and repaired. The shape of the

Figure 7. Initial position (dotted lines) of one block anddeformed position of two adjacent blocks. The position ofthe southern (rear) dowel is shown on the left block, whereasthe northern (front) dowel is shown on the right block.

latter is clear, as it is not affected by the presence ofother connectors. On the contrary, in the northern side,detachment occured at the whole marble height. Thiscould be explained by the simultaneous occurence oftwo failure modes, I and III, due to the failure of theadjacent (to the clamp) dowel of the upper surface.

5.2 Failure mode II

Typically, the orthostate blocks possess two dowels attheir bedding surface. They are located close to thenorthern (front) and southern (rear) surfaces of theblock. Failure mode II is characterised by detachmentof the marble cover of each dowel either at a limitedheight (Figs 9 , 10) or at the whole height . In this case,failure occurs probably due to the synergistic effect ofthe action of the dowels with the connectors of theupper surface (Failure Modes I and II).

The mechanism of failure could be described asfollows: with the application of a horizontal force(or displacement) towards the north, rotation betweenadjacent blocks with or without relative displacementtakes place (Fig. 7). Both dowels of an orthostateblock develop resistance to this movement. The dowellocated close to the southern marble surface fails eas-ily because it has a small cover against the direction ofthe applied force or displacement (Fig. 8). The failureof the dowels closer to the northern marble surface ismore difficult to interpret because it is not compatible(it is actually opposite) to the direction of the reactionforce of the dowel.

It can, however, be assumed that the kinematicconstraints (imposed by the rear dowel of the block)are already released, following the mechanism previ-ously described. The constraints of the block now are:(a) on the one side still an active clamp but not dowel,whereas, (b) on the other side, both a clamp and adowel still active (Fig. 8, right block). To permit fur-ther displacement, it is necessary that the cover of the

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Figure 8. Detachment of the cover of the southern (rear)dowel.

Figure 9. Failure of the cover of the southern (rear) dowelof orthostate block 12.

clamp, which is located at the side of the rear dowel(not shown in Figure 8), has failed following Mode I.The release of both constraints on the one side of theblock result in rotation of the block around the axis ofthe still active clamp and dowel of the other side. If,failure of both clamps occurs, then rotation can occuraround the remaining dowel. In both cases rotationcould result in marble detachment towards the north(Figure 10).

5.3 Failure mode III

Failure mode III is observed with the two dowelsof the upper surface of the orthostate. It consists inthe detachment of a marble cone towards the north(i.e. towards the direction of the applied force ordisplacement) (Fig. 11).

For this failure to occur, it is necessary that a rel-ative displacement and rotation takes place between

Figure 10. Failure of the northern (front) dowel.

dowel

Figure 11. Failure mode III of the northern dowel of theupper surface of orthostate block 10.

the orthostate and the corresponding block of the rowabove. This requirement is compatible with the defor-mation of the whole wall as a plate. Its analysis willbe presented in another work.

5.4 Failure mode IV

This failure mode is characterized by fracture of theblock and separation in two fragments. This frac-ture theoretically occurs in areas not influenced bythe connectors and is attributed to out- of-plane bend-ing of the block. The position of the marble soft plane

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upper surface

northern (front) elevation

Figure 12. Section of the orthostate soft plane with thenorthern elevation. Left: block 3 (vertical), right: block 4(horizontal).

Table 4. Position of marble soft plane and failure modes ofthe orthostate of the Parthenon northern wall

Direction of soft plane Failure mode

SectionIn relation withto bedding northern

No surface elevation I II III IV

1 vert/incl1 horizontal yes yes yes no2

2 vert/incl vertical yes yes yes yes3 vert/incl vertical yes yes yes yes4 vert/incl vertical yes yes yes no3

5 vert/incl horizontal yes yes yes no10 vert/incl vertical yes yes yes yes11 vert/incl horizontal yes yes yes no12 vert/incl horizontal yes yes yes yes13 vert/incl horizontal yes yes yes no14 vert/incl vertical yes yes yes yes4

15 vert/incl horizontal yes yes yes no16 vert/incl horizontal yes yes yes no

1 inclined (less than approx. 30◦) in relation to a verticalplane.2 in conjunction to the eastern wall of the cella.3 not fracture but cracking has occurred.4 in conjunction to the middle wall of the cella).

inside the block is of fundamental importance. Indeed,failure mode IV was observed only in cases, wherethe soft plane direction crossed vertically with thenorthern elevation, as it will be developed hereafter.(Table 4, Fig. 12). It occurs either when not all con-nectors have failed or if there are additional kinematicconstraints, such as the presence of transverse walls. Inpractice, even this failure mode is not always indepen-dent to the connectors.With the exception of orthostateblock 2 (Table 4), on the other blocks, in which thisfailure mode occurred (blocks 3, 10, possibly 14), itseems that the presence of weak planes close to theconnector area resulted in fracture which might initi-ate from the connector area but clearly continues insidethe block. This failure cannot therefore be classifiedunder modes I, II or III.

Table 5. Failure modes of the blocks of the even-numberedrows of the Parthenon northern wall.

Failure modeRow Surveyednumber blocks I II III IV

2nd 9 17/17 5/11 3/9 1/94th 7 14/14 4/9 1/7 0/76th 6 7/12 2/6 0/6 0/68th 10 19(?)/20 1/8 0/10 0/1010th 10 19/19 4/10 1/10 1/1012η 11 18/18 2/7 0/11 2/1114th 10 20/20 0/7 0/10 0/1016th 11 20/21 1/8 0/9 3/11

Total 74 134/141 19/66 5/72 7/74blocks

18th (archi- 4 7/7 not sur- 6/8∗ 1/4trave) veyed.

Total 78 141/148 19/66 11/80 8/78

∗The two dowel areas that did not fail, show extendedcracking.

5.5 Failure mode V

This failure mode is characterized by local loss ofmaterial, roughly with triangular cross-section, at thefront side of some orthostate bedding surfaces. It isattributed to shear, as it occurred to blocks which eitherrotated strongly or collapsed. It is observed only inthe well-carved front (northern) side of the orthostateblocks and not on the rear (southern) side, which ismore roughly carved.

6 ON THE EFFECT OF THE POSITION OF THEMARBLE SOFT PLANE

Two ways of dressing the orthostate soft plane insidethe orthostate blocks were recorded and are describedinTable 4 and Figure 12.The investigation of the effectof the position of the marble soft plane on the structuralpathology was carried out through the comparison ofthe failures recorded on the orthostate (whose softplane is roughly perpendicular to the bedding sur-face, usually with inclination) (Table 3) and the marbleblocks of the even-numbered rows whose soft plane isroughly parallel to the bedding surface, usually withinclination) (Table 5).

On the basis of the comparison between Tables 3and 5, the following conclusions may be drawn:

1. The effect of the direction of the soft plane appearsclearly in failure mode III. It was observed in mostdowel areas of the orthostate and architrave beams.On the contrary, only 5 (out of 72) failures wererecorded on the blocks of the intermediate 17 rows.

2. Similar observations are valid for failure mode II.If it appears practically in all orthostate dowels

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(a survey of the wall architraves was not possibleat the time of the study), it concerns roughly onlythe 1/3 of the intermediate blocks.

3. Failure mode IV is rare in all cases. In the orthostate,it was attributed to a specific direction of the mar-ble weak plane inside the block (Table 4). It wouldbe of interest to analyze under which conditions itappeared in the wall intermediate blocks.

4. Finally, the effect of the weak plane direction doesnot only affect the possibility (or not) of generationof a specific failure mode but its configuration aswell. Indeed, if failure mode I is recorded in prac-tically all areas of the clamps of the orthostate,architrave and intermediate blocks, the height ofthe detached fragment is significantly reduced inthe last case (the intermediate blocks).

7 RESULTS OF THE NUMERICALANALYSIS

Aims of the numerical analysis were (a) the study offailure modes I and II and (b) the determination of themaximum compressive, tensile and shear stresses thatdevelop under the actions described in Tables 2 and 3.The models are shown in Figures 13 & 14. The clamptensile strength was chosen equal to 55 MPa, the clampshear strength 29 MPa and the dowel shear strength14 MPa (Zambas 1994, Vardoulakis et al. 2002). Inthe case of the dowel analysis, two force distributionson the marble (applied as surface distributed loads andautomatically converted to loads on the correspondingnodes) were selected, namely uniform and triangular.The latter results in higher corresponding stresses σxand σy.

In the case of the clamps, in accordance to the con-clusions of the failure modes’ analysis, mainly shear(and not tensile) forces were considered. It is howeverrecognized that, in rather extreme situations (such asthe explosion), significant tension can also developparallel to shear, therefore some more complex stresssituations were also considered.

In terms of resistances, it is well-known that mar-ble tensile strength values available in the literaturepresent important scattering, attributable to differ-ent test procedures as well as to marble anisotropy(Vardoulakis et al. 2002). The values provided byVardoulakis et al. (2002) were used. Precisely, thetensile strength in the two strong marble directionswas found equal to 9.5 and 10.8 MPa respectively,whereas the tensile strength of the marble soft planewas found equal to 5.3 MPa. Consequently, tensilestresses around 5 MPa were considered sufficient togenerate cracks inside the marble mass.

The main results of the analysis of the connectors(Toumbakari 2007a, Filippoupolitis 2007) are summa-rized in Tables 6 & 7. In the case of the clamp, theapplication of a shear force equal to 15 kN (LC2) at

Figure 13. Model of the.

Figure 14. Model of the.

Table 6. Main results of the clamp analysis.

σx [MPa] σy [Mpa] τxy [Mpa]

LC σc,max σt,max σc,max σt,max σc,max σt,max

1 −0.15 0.37 −0.10 0.35 −0.02 0.062 −2.28 4.79 −0.37 1.75 −0.17 0.853 −4.41 9.22 −0.74 3.37 −0.32 1.644 −0.15 0.43 −0.17 0.36 −0.04 0.075 −2.29 5.73 −2.56 3.29 −0.69 1.116 −2.29 6.66 −5.14 6.66 −1.56 1.867 −4.42 11.08 −5.13 6.60 −1.38 2.18

Table 7. Main results of the dowel analysis.

σx [MPa] σy [Mpa] τxy [Mpa]

LC σc,max σt,max σc,max σt,max σc,max σt,max

1 −0.21 0.37 −0.05 0.20 −0.03 0.132 −1.02 1.84 −0.27 0.99 −0.13 0.683 −2.87 5.14 −0.77 2.76 −0.37 1.904 −0.33 0.50 −0.05 0.23 −0.02 0.125 −1.66 2.51 −0.23 1.18 −0.09 0.616 −4.66 7.03 −0.64 3.30 −0.27 1.71

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the x-direction already results in the development of atensile stress equal to 4.79 MPa, which is consideredsufficient to initiate cracking. A shear force equal tothe clamp shear resistance (LC3) generates a tensilestress equal to 9.22 MPa, which is similar to the mar-ble tensile strength in the second strong direction. Themore complex situations considered in LC5 through 7result in the development of tensile stresses from 5 to11 MPa in both x- and y-directions, which show thatcrack generation is possible. In a similar way, in limitstate situations (LC3, LC6) the developing stresses atthe dowel area are sufficiently high to produce crack-ing (5.14 and 7.03 MPa). These numerical results arecompatible to available experimental results on dow-els (Zambas 1994), which have shown failure of thedowel anchorage area and not the dowel itself.

8 CONCLUSIONS

On the basis of the analysis of the structural failuresin the orthostate of the Parthenon northern wall, thefollowing conclusions were drawn:

1. A methodology for the analysis and interpretationof the structural damages was proposed, based onthe compatibility between (a) kinematic constraintsapplied on the building block, (b) system of defor-mations/displacements applied on the block and(c) system of deformations/displacements appliedon the wall.

2. Five failure modes were recognized: (I) clamp areafailure attributable to shear, (II) dowel area failureattributable to tension and shear, (III) dowel areafailure attributable to tension, (IV) block separationattributable to out-of-plane bending and (V) massdetachment at the base of the blocks, attributable toshear with, occasionnaly, local crushing.

3. The configuration of the failure of the area of theclamps shows that the latter work mainly in shearand not in tension.

4. The position of the marble soft plane inside theblock was found to significantly affect the genera-tion of the failure modes.

5. The mechanical action of the connectors couldexplain the observed structural pathology. Rust isnot a necessary condition for the structural failuresto occur.

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