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

Seismic behaviour of barrel vault systems

A. Marini & G. GiardinaUniversity of Brescia, Italy

P. RivaUniversity of Bergamo, Italy

E. GiurianiUniversity of Brescia, Italy

ABSTRACT: In this paper, the experimental study on the rocking behaviour of a full scale barrel vaultedstructure undergo cyclic horizontal loading is discussed. The study is the first part of an ongoing experimentaland theoretical research program, developed by the University of Brescia, concerning the seismic behaviour ofmasonry buildings.

The scope of the paper is to provide some evidence of the rocking mechanism experienced by barrel vaultedstructures undergo horizontal loading. Understanding of the behaviour of such structural systems is fundamentalfor their seismic vulnerability assessment, as well as for the correct design of possible strengthening techniques.

The structural behaviour is also investigated by means of non linear finite element analyses. Numerical resultsare validated through comparison with experimental results. After validation, the FE model can be applied todifferent case studies.

1 INTRODUCTION

Earthquake hazard reduction is progressively becom-ing one of the most important issues in the structuralrehabilitation discipline. The assessment of the seis-mic vulnerability of historical constructions and thedesign of successful strengthening techniques are dif-ficult tasks, mainly because the structural behaviourdepends on too many parameters of uncertain defini-tion, but also because of the little knowledge abouttraditional construction techniques, historic materialproperties and constraints (D’Ayala & Speranza 2002,Binda 1999).

However, important lessons have been learned fromthe analysis of the damage induced to historic con-structions by recent earthquakes, lessons on the realstructural behaviour of engineered and non engi-neered constructions (Lagomarsino et al. 2004), aswell as lessons on how to improve structural perfor-mance (Borri et al. 2002, Modena et al. 2000). Recentearthquakes also provided an opportunity to evalu-ate previous structural interventions, based on actualperformance during a real ground motion (Guerrieri1999).

The earthquake behaviour of masonry structureshas been widely studied experimentally, analytically

and numerically. Although the knowledge of the struc-tural behaviour of masonry structures has greatlyenhanced in the last decades, little is still knownabout the structural behaviour of vaulted structuresundergoing seismic action.

The survey of damaged vaulted structures showsthat seismic action induces bending of the vault ring,as well as rocking of the abutments at the base.

The rocking of vaulted structures and transversediaphragm arches has been studied mainly analyticallyand numerically by different authors, whereas fewerexperimental results are available.

Utilizing the principle of virtual work, focus hasbeen paid to the onset of failure mechanisms and totheir evolution in the large displacement field, to thedefinition of structure capacity curves (Abruzzese &Lanni 1999, Housner 1963, Lagomarsino et al. 2004),and to the out-of-phase rocking of the abutments(Como et al. 1991).

Furthermore, a simplified analytical method, basedon limit analysis, was proposed by Giuriani et al.(2007) to assess the seismic vulnerability of trans-verse arches undergoing rocking of the abutments.The discussion focused on the different behaviour oftransverse arch systems subjected either to rest orrocking conditions and highlighted the physics and

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the phenomena involved in the mechanisms. It wasshown that in the at-rest condition, the arch lateralthrust can be largely or entirely resisted by the buttressaction of the abutments, depending on their geome-try and massiveness, thus possible ties must confineonly the part of the arch thrust exceeding the buttressaction (Giuriani & Gubana 1993, 1995). Conversely,as rocking modifies the resisting mechanism of theabutments, increasing the arch thrust and consider-ably diminishing the confining buttress action, the archthrust must be entirely confined by the existing ties(Giuriani et al. 2007). A significant increase in thetie tensile force is expected during rocking. The sameconclusion was drawn by Lagomarsino et al. (2004)by analysing the kinematics of the problem using theprinciple of virtual work.

In this work, focus is paid to the experimental rock-ing behaviour of a barrel vaulted structure undergoingexternal lateral loading. The effect of seismic actionon the vault crown is beyond the scope of this paperand will be studied in the future research.

The scope of the paper is to provide evidence ofthe rocking mechanism experienced by barrel vaultedstructures undergoing horizontal loading, which iscritical for their seismic vulnerability assessment, aswell as for the correct design of possible strengtheningtechniques.

Focus is made on the modelling of the experimen-tal test, on the choice of the geometry of the vault,the technical and technological aspects concerning itsconstruction, as well as on the bench set up, the loadapplication system, and the instrument set up.

Furthermore, the experimental results are used tovalidate a FE model.Validation of the FE model allowswidening the field of its application to different casestudies.

The study is the first part of an ongoing researchprogram developed by the University of Brescia, whichis focused on the role of vaults in the seismic behaviourof masonry vaulted structures, the assessment of theeffectiveness of some retrofitting techniques, and onthe proposal of simplified analytical methods.

2 EXPERIMENTAL TEST

2.1 Modeling of the experimental specimen

In this paper the behaviour of a barrel vaulted structureundergoing rocking is analysed. As a reference, a realtwo storey building having a barrel vault at the groundfloor is considered (Fig. 1a).

Barrel vaults are 3D structures having a complexthree-dimensional stress distribution (O’Dwyer 1999).However, in the frequent case of long barrel vaultslacking the connections to the head walls, an esti-mate of the structural behaviour can be obtained by

A

I II

(a) (b) (c)

Figure 1. Definition of the experimental model geometry:(a) reference structure, (b) unit stripe, (c) experimental model.

10°

10°

51°

0.25

2.00

1.40

0.38 2.50 0.380.

991.

610.

12

3.40

0.12

2.60

0.10

Figure 2. Geometry of the experimental model.

modelling the barrel vault as a series of adjoiningarches of unit width (Giuriani E. et al. 1999). In thisscenario, according to this simplified analytical model,a unit stripe A was selected and analysed (Fig.1 a,b).

As a second step in the definition of the experimen-tal model, the upper masonry wall were removed andtheir weight was introduced in the model by addingpoint loads at top edges of the abutments. (Fig. 1c).The geometry of the experimental model is detailedand shown in Figures 2–3, respectively.

As for the construction technique, the wall layoutand the layer by layer brick arrangement were derivedby historic construction treatises (Carbonara 1996,2004, Giardina et al. 2007a; Fig. 4a). The resultingwall cross section is a single leave three head wall.

The thickness of the vault crown varies along thespan: the vault ring is 0.12 m thick at the key and 0.25 mat the springing (Fig. 4b).

The structure is built on two reinforced concretesupport; each abutment is fixed to the support withvertical rebars which allow rotations at the base,

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Figure 3. Full scale model of the barrel vaulted structure.

Figure 4. (a)Abutment brick arrangement; (b) change in thecrown thickness; (c) specimen constraint at the base; (d) detailof the backfill; (e) Plexiglas plate constraint to the masonry.

reproducing the real structural constraints, but inhibit-ing any shearing sliding (Fig. 4c).

An intrados tie rod confines the arch horizontalthrust at the springing. The 12 mm tie rod, having aninitial pretension of 7 kN (equal to 75% of the vaultlateral thrust) is anchored to the abutments using steelplates.

The backfill consists of fine sand, laterally con-tained by means of Plexiglas plates bolted to themasonry structure (Fig. 4d). Bolt-hole clearanceavoids any participation of the Plexiglas to the resist-ing mechanism (Fig. 4e). Thin layers of chalk are

Figure 5. Vertical load application system: (a) side view ofthe loading apparatus, (b) load distribution at the wall topedge, (c) cup-springs at the base reducing the vertical barstiffness.

inserted in the backfill to emphasise the vault crowndeformation during loading and unloading cycles(Fig. 4d).

Four 7 kN point loads are applied at the top edgesof the abutment to simulate the first floor masonryweight. Transverse steel profiles spread the load alongthe crown (fig. 5a,b). The load is applied trough ver-tical rebars tightened to the concrete supports. Fourpacks of cup-springs are interposed at the rebar bases,as shown in Figures 5a–c, to reduce the stiffness of therebars. This was done to prevent an increase in verticalload due to rebar elongation induced by increasing theapplied lateral displacement.

The total dead load of the specimen, including theadditional load of the vertical rebars is W = 90.7 kN.

2.2 Testing bench and lateral load applicationsystem

The experimental test aims at investigating thebehaviour of vaulted structures undergoing earthquake-induced rocking of the abutments. Further studies willfocus on the bending moment induced in the vaultcrown by seismic action.

The seismic action is simulated by introducing hor-izontal loads at the vault springing. Horizontal pointloads are applied by means of an electro-mechanic jackfixed to a steel frame, as shown in Figure 6. The hori-zontal loading system was designed in order to imposethe same force (instead of the same displacement) toeach abutment (Fig. 6). The load is equally dividedbetween the abutments through the pulley and ropesystem shown in Figure 6. The point load is uniformlyspread at the vault springings by means of transverseloading beams.

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Figure 6. (a) Load application system; (b) perspective viewof the testing bench and the pulley system.

Figure 7. (a) Instrument layout, (b) detail of LVDT Cyand Ey.

2.3 Instrument set up

During the loading and unloading steps, vertical andhorizontal displacement were recorded at some keypoints of the structure by means of linear variabledisplacement transducers (LVDT).

The drift of the abutments at different heights wasmonitored by LVDT Ax, Bx, Fx, Gx, whereas LVDTCxy, Dy, Exy were located to detect any flexuraldisplacement along the vault ring (see Fig. 7a).

The vertical component of the displacements at thevault springing and keystone were measured usingLVDT Cy, Dy and Ey. These instruments were fixedto the vault intrados trough spherical hinges slidingon horizontal supports (Fig. 7b), in order to reduceinterference with the global lateral displacement.

The applied load is measured by means of a loadcell placed between the jack and the transverse beam.

Figure 8. Applied horizontal force versus abutment tophorizontal displacement curve (LVDT Bx, Fx).

The tension in the vertical rebars and the tie rod werealso monitored during the test.

2.4 Loading modalities

Load-controlled cyclic tests were carried out with aloading rate of 600 N/min. The specimen was initiallysubjected to loading and unloading cycles, in the samedirection. The horizontal point load was increased by2 kN (corresponding to 2.2% of the total vertical load)from cycle to cycle, until the vault developed a fourhinge mechanism. Later, two fully reversed cycle wereapplied by repositioning the steel frame. The maxi-mum applied load was equal to 11 kN (equal to 12%of the total vertical load W).

It is worth noting that as a result of the increasein the horizontal displacement, a small increase of theaxial force in the rebars occurred, changing the verticalconfinement of the specimen, despite the use of thecup-spring systems.

Details on the experimental study can be found inGiardina et al. (2007b).

3 EXPERIMENTAL RESULTS ANDDISCUSSION

Figure 8 shows the structural response in terms ofapplied horizontal force versus abutment top horizon-tal displacement (LVDT Bx, Fx). Figure 9a and 9bshow the detail of the curve for positive and nega-tive applied horizontal loads. The structural responseremains basically linear elastic until 6–7 kN (equal to6.6% of the total vertical load) for both directions ofapplied displacement.

As for the cyclic behaviour, damage is accumulatedafter a few load cycles, and the global stiffness slightlydecreases.

Figure 8 shows that the structure is relatively ductilewith little dissipation capacity and a pronounced self-centering behaviour (see the flag-type curve). Inelasticdeformations are almost negligible compared to themaximum experienced displacements.

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Figure 9. Details of the (a) positive and (b) negative appliedhorizontal force versus abutment top horizontal displacementcurve (LVDT Bx, Fx).

The test was interrupted during the negativeload application (10 kN = 10%W, top displacement of47 mm corresponding to a 1.5% drift) after a fur-ther vertical crack opened from excessive compressivestrength on the four hinge mechanism.

For increasing applied lateral forces, cracks subse-quently formed at the vault springing, where the vaultcrown thickness abruptly halves, and at the abutmentbases. As a result, the global stiffness of the structureprogressively decreases (Fig. 8) and the envelope curveshows a piecewise linear behaviour. Figure 10 showsthe evolution of the structure toward the 4 hinge mech-anism; numbers refer to the crack onset chronology,and to the value of the applied load triggering the crack.It is worth noting that the mechanisms change for dif-ferent directions of the applied loads (Fig. 10a,b). Thisis evidenced by the higher position of the crack inthe left abutment base (Fig. 10b), which results in adifferent rocking behaviour of the two abutments.

All cracks perfectly closed upon the first loadreversals, whereas in the final stages, for increasingdrifts, the non-cohesive backfill material poured intothe larger crack at the vault crown extrados (n.2 inFig.10b), thus preventing its closing.

Figure 11 shows the structural response in termsof applied horizontal force versus horizontal displace-ment at the vault springings (LVDT Ax, Gx). Whenpositive horizontal forces are applied, a maximumpositive differential displacement of 0.04 mm wasrecorded, which corresponds to the lengthening of the

Figure 10. Crack pattern for: (a) positive and (b) nega-tive applied lateral loads; (c) detail of the cracks in crackpattern (b).

Figure 11. Details of the (a) positive and (b) negativeapplied horizontal force versus abutment displacement at thevault springings (LVDT Ax, Gx).

vault span (Fig. 11a). Conversely, when negative hor-izontal displacement was applied, 4 mm of relativedisplacement was surveyed, resulting in the shorteningof the vault span (Fig. 11b).

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Figure 12. Vertical displacement at the vault intradosspringing and key sections (LVDT Cy, Ey, and Dy) in case ofpositive applied lateral loads (see Fig. 9a).

Figure 13. Sand backfill cracks due to internal tensionforce.

The horizontal displacements of the abutmentsinduced the bending of the vault crown. The verticaldisplacements at the intrados of the vault springing andkey, recorded by transducers Cy, Ey and Dy are shownin Figure 12 for positive lateral load cycles. The maxi-mum uplift displacement of the vault intrados is equalto 5.6 mm at the right springing, corresponding to 1/3of the abutment top lateral displacement; whereas a2.5 mm maximum downward displacement, equal to1/8 of the abutment top displacement, was recordedat the left springing. The vault key also rose 1.9 mm.Vault flexural deformations were emphasized by thecrack extending into backfill (Fig.13).

The tie tensile force significantly changed forincreasing applied lateral loads (Fig. 14).

When positive maximum displacements wereapplied and the mechanism was that correspondingto the crack pattern of Figure 10a, the tie tensile forceincreased to 12% of its initial value (�F = 0.82 kN,Fig.14a). Note that the test was stopped in this directionwell before the cracks had completely penetratedthe element cross sections. Thus, for increasing lat-eral displacement, a further significant incrementin the tie tension should be expected. Furthermore,the abutments underwent a positive relative dis-placement of �L = 0.04 mm (Fig. 11a) at the vaultspringings, which only partially explains the incre-ment in the tie force. As a matter of fact, given

Figure 14. Tie traction force for a few cycles of: (a) positiveand (b) negative applied horizontal forces.

the tie length L = 3260 mm, the axial strain is equalto ε = �L/L = 1.23 × 10−5, thus the increment inthe axial force is �F = εESAT = 0.29 kN (whereES = 210000 MPa, AT = 113 mm2). The further tieincrement indicates that following the development ofthe crack pattern, the ideal arch increases its span andthe buttress action significantly reduces (Giuriani E.et al. 2007).

When negative maximum displacements wereapplied, the mechanism changed, as shown inFigure 10b. The crack pattern showed two wide cracksat the abutment bases located at different heights, thusresulting in a negative relative displacement of theabutments at the vault impost. In this case, the tie ten-sile force reduced to approximately 50% of its initialvalue (Fig. 14b).

Finally, the vertical tension in the rebars increasedduring the test, as the lateral load and displacementincreased, despite the positioning of the cup-springpacks at the bar bases. However, the maximum incre-ment was at most equal to 15% of the initial value.

4 NUMERIC ANALYSES

Numeric analyses were carried out prior and after theexperimental tests. Pilot analyses provided some use-ful information to guide the modelling and designof the experimental test. On the other hand, uponcompletion of the experimental test, the experimentalresults were used to validate the numeric model.

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Figure 15. Mesh B. Contact elements are located aside eachwhite element along the vault crown and the abutments,and along the vault-to-backfill and backfill-to-abutmentinterfaces.

The model validation is necessary, in order toextend the application of the numeric model to dif-ferent case studies, geometries and load layouts. Thisway, the FE analyses can help practicing engineersin defining retrofitting strategies, and in testing theireffectiveness.

Different numeric models were implemented. First,a pilot linear elastic analysis was performed for thegeneral understanding of the structural behaviour(Mesh A). Once the governing mechanisms were iden-tified, the model was further refined both in termsof modelling assumptions and material behaviour. Asecond model was developed by adopting contact ele-ments to simulate and allow the onset and developmentof cracks in the structure (Mesh B) Finally, in a thirdmodel, non linear constitutive laws for masonry wereadopted (Mesh C). Mesh B showed the best fitting ofthe numeric results and is discussed in the following.The complete discussion concerning the numeric studycan be found in Giardina et al. (2007c).

Geometry as well as loading conditions are derivedfrom the experimental tests.Therefore, the loads actingon the model are:

– dead load– vertical point loads at the abutment top edges– horizontal point loads applied at the springing.

The analyses is performed by incrementing the hori-zontal points loads.

Mesh A was used to identify the zones of weaknesswhere tensile stresses concentrate, i.e. where cracksmight develop. The results highlighted that higher ten-sile stresses occur along the vault ring, at the abutmentbase and, when horizontal loads are applied, at the vaultspringing.

In Mesh B masonry and backfill were modelledby means of 3–4 node plain strain elements (Fig. 15).The non linear behaviour of the structure was modelled

Table 1. Mechanical properties in Mesh B.

Masonry Backfill

Density 1900 kg/m3 1900 kg/m3

Young’s Modulus 4500 MPa 45 MPaPoisson’s coefficient 0.15 0.15

Contact elements Friction coefficient 0.4

Figure 16. Numeric and experimental capacity curves:(a) applied lateral load vs top displacement of the abut-ments; (b) applied lateral load vs vault intrados verticaldisplacement.

through contact elements, which were located betweenadjoining vault ring voussoirs, along the vault-to-backfill and backfill-to-abutments interfaces, and atthe abutment bases, according to the result of Mesh A.Contact elements allow transferring the axial load onlywhen the surfaces are in contact, whereas shear trans-mission is governed by friction. Mechanical propertiesare summarized in Table 1.

Numeric results are shown in Figure 16a in terms oflateral applied load versus left abutment top displace-ment. The numerical curve shape compares well withthe shape of the experimental curve. The greater stiff-ness and ultimate load are probably due to the selectedmaterial properties. Like the experimental curve, thenumerical curve shows abrupt changes in the slopeat any crack opening (i.e. contact opening). Contact

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Figure 17. Mesh B deformed shape at failure (Magnifica-tion factor of 20).

opening is observed at the same locations where cracksopened in the experimental test. It is worth noting thatthe chronological order of crack development is alsothe same.

Further numeric analyses showed that the crackopening location is a function of the geometry and ofthe applied vertical loads. When large vertical load isapplied to the structure (i.e. in the case of two or morestorey buildings), besides the crack at the abutmentbases, two further cracks form in the vault ring closeto the springing where the thickness of the sectionabruptly decreases. On the other hand, for decreasingvertical loads, these two cracks form in the abutments,close to the vault springings, rather than in the vaultcrown.

Numeric and experimental results also comparewell in terms of vertical displacements along the vaultcrown (Fig.16b), and tensile tie force.

The deformed shape at failure is shown in Figure17.The crack locations correspond to the experimentalmechanism surveyed during the experimental test.

5 CONCLUSIONS

In this paper, the transverse rocking mechanism ofa barrel vaulted structure was investigated by meansof a full scale experimental tests and a non-linear FEanalyses.

The most significant results of the experimentalstudy can be summarized as follows:

• The structure is relatively ductile in terms ofdisplacements. However, little energy dissipationcapacity and a pronounced self centering behaviourare observed. Failure is reached with a four hingemechanism. Any possible retrofitting techniqueshould be respectful of this structural behaviour,by strengthening the structure without reducing itscapacity to meet to displacement demand;

• The tie tension significantly changes during rock-ing. The small abutment relative displacementsinduced by rocking is not sufficient to explain thisincrease in tie tension. The tension is likely toincrease following the loss of the abutment buttress

action and the increase of the ideal arch span.This result should be carefully taken into accountin seismic vulnerability assessment, as tie rodsmight experience excess in tension during an earth-quake, thus requiring additional strengthening. Onthe other hand, depending on the triggered mech-anism, tie tension might also decrease if rockinginduced displacements shorten the vault span.

The numerical study also confirmed that the crackopening locations are a function of the geometry andof the applied vertical loads. When large vertical loadsare applied, two cracks form in the vault ring closeto the springing where the thickness of the sectionabruptly halves. On the other hand, for decreasing ver-tical loads, two cracks form in the abutments, close tothe vault imposts, rather than in the vault crown.

Further experimental tests will be performed onunreinforced and reinforced masonry vaults, to eval-uate the efficacy of some strengthening techniques,such as: extrados spandrel walls, thin slab of claymortar, and FRP. Numerical and analytical modelswill be improved to simulate cyclic behaviour of thestructures.

ACKNOWLEDGEMENTS

The authors gratefully acknowledge R. Squicciarinifor his contribution in carrying out the experimentaltest and L. Martinelli for his technical support. Thiswork was developed within the research project DPC-ReLUIS 2005–2008, Research line n. 1: “Vulnerabilityassessment and antiseismic strengthening of masonrybuildings”. The experimental specimen was built bythe students of the Scuola Edile Bresciana, within ajoined research agreement. Their work, as well as thework of their supervisors, is gratefully acknowledged.

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