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Review Venetian churches of Lefkada, Greece Construction documentation and seismic behaviour ‘‘Virgin Mary of the Strangers’’ Charis Apostolopoulos a , Panagiotis Sotiropoulos b, * a Laboratory of Technology and Strength of Materials, Department of Mechanical Engineering and Aeronauts, University of Patras, 26500 Patras, Greece b Laboratory of Architectural Technology and Urban Planning, School of Engineering, University of Patras, 26500 Patras, Greece Received 8 December 2005; received in revised form 25 October 2006; accepted 27 October 2006 Available online 2 January 2007 Abstract Lefkada suffers from frequent and strong earthquakes. On August 14, 2003, an earthquake with a magnitude of 6.2 on the Richter scale, one of the strongest ever to occur in the Greek territory, resulted in serious damages of 40 churches. This paper presents certain important morphological features of the Virgin Mary of the Strangers church and the particular structural system of the monument. The peak response of the church during the August 14, 2003 earthquake in Lefkada is studied numerically through the finite elements method using a response spectrum analysis. Moreover, the ground acceleration record of the main earthquake in the centre of the town is con- sidered in the present investigation. The numerical results obtained show very good agreement with the faults exhibited in the structures, and this leads to the determination of the vulnerable areas of the structures affected. Ó 2008 Elsevier Ltd. All rights reserved. Keywords: Venetian churches of Lefkada; Morphological characteristics; Church pathology; Seismic behaviour; Dynamic analysis Contents 1. Introduction ............................................................................... 435 2. Seismic risk in the area........................................................................ 435 3. Monument description ........................................................................ 436 3.1. General information .................................................................... 436 3.2. Church’s structural data ................................................................. 436 4. Monument pathology......................................................................... 437 4.1. Perimeter masonry – wooden bearing structure – roof ............................................ 437 4.2. Humidity – biological action .............................................................. 439 4.3. Church flooring........................................................................ 439 4.4. Foundations .......................................................................... 439 5. Numerical analysis ........................................................................... 440 5.1. Finite element model .................................................................... 440 5.2. Modal analysis ........................................................................ 441 5.3. Dynamic analysis ...................................................................... 441 0950-0618/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.conbuildmat.2006.10.016 * Corresponding author. Tel.: +30 6947007179. E-mail addresses: [email protected] (C. Apostolopoulos), [email protected] (P. Sotiropoulos). www.elsevier.com/locate/conbuildmat Available online at www.sciencedirect.com Construction and Building Materials 22 (2008) 434–443 Construction and Building MATERIALS
Transcript
Page 1: Expertiza Biserica Cu Ansys

Available online at www.sciencedirect.com Construction

www.elsevier.com/locate/conbuildmat

Construction and Building Materials 22 (2008) 434–443

and Building

MATERIALS

Review

Venetian churches of Lefkada, Greece Construction documentationand seismic behaviour ‘‘Virgin Mary of the Strangers’’

Charis Apostolopoulos a, Panagiotis Sotiropoulos b,*

a Laboratory of Technology and Strength of Materials, Department of Mechanical Engineering and Aeronauts, University of Patras, 26500 Patras, Greeceb Laboratory of Architectural Technology and Urban Planning, School of Engineering, University of Patras, 26500 Patras, Greece

Received 8 December 2005; received in revised form 25 October 2006; accepted 27 October 2006Available online 2 January 2007

Abstract

Lefkada suffers from frequent and strong earthquakes. On August 14, 2003, an earthquake with a magnitude of 6.2 on the Richterscale, one of the strongest ever to occur in the Greek territory, resulted in serious damages of 40 churches. This paper presents certainimportant morphological features of the Virgin Mary of the Strangers church and the particular structural system of the monument. Thepeak response of the church during the August 14, 2003 earthquake in Lefkada is studied numerically through the finite elements methodusing a response spectrum analysis. Moreover, the ground acceleration record of the main earthquake in the centre of the town is con-sidered in the present investigation. The numerical results obtained show very good agreement with the faults exhibited in the structures,and this leads to the determination of the vulnerable areas of the structures affected.� 2008 Elsevier Ltd. All rights reserved.

Keywords: Venetian churches of Lefkada; Morphological characteristics; Church pathology; Seismic behaviour; Dynamic analysis

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4352. Seismic risk in the area. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4353. Monument description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 436

0950-0

doi:10.

* CoE-m

3.1. General information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4363.2. Church’s structural data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 436

4. Monument pathology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437

4.1. Perimeter masonry – wooden bearing structure – roof . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4374.2. Humidity – biological action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4394.3. Church flooring. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4394.4. Foundations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439

5. Numerical analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440

5.1. Finite element model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4405.2. Modal analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4415.3. Dynamic analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 441

618/$ - see front matter � 2008 Elsevier Ltd. All rights reserved.

1016/j.conbuildmat.2006.10.016

rresponding author. Tel.: +30 6947007179.ail addresses: [email protected] (C. Apostolopoulos), [email protected] (P. Sotiropoulos).

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TM

a

1

L

V

T

C. Apostolopoulos, P. Sotiropoulos / Construction and Building Materials 22 (2008) 434–443 435

6. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442Acknowledgement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443

1. Introduction

The historical churches on the island of Lefkada cover aperiod of 500 years. The most significant buildings dateback to the times of Venetian rule (1684–1797), and theyhave been classified as historical monuments. They arelocated in the historic centre of the town of Lefkada inNorthwestern Greece, and they represent an importantpart of the Greek cultural heritage.

The town of Lefkada is built on alluvial soil at an alti-tude slightly above the sea level. The town is protectedby the Ionian Sea by a sandy stretch which surrounds thelagoon and plain of Lefkada. In 1300 AD when Lefkadawas under the rule of the Franks and until the end of the17th century [1], the castle of Aghia Mavra at the north-eastern entrance to the town served as the Franks’ head-quarters and became the centre of development for thenorthern most residential centre of the island.

During the 1971 census [2], the churches of Lefkada,along with the Catholic monasteries and the countrysidechapels, numbered approximately 105 [3,4]. These historicmonuments have been renovated, and their current dimen-sions and exterior appearance are the result of such resto-ration works necessitated by either partial damage orcollapse due to earthquakes [5]. The town’s most significantchurches are made of lime conglomerate engraved stones inaccordance with the ashlar system which uses average-sizedstones. These stones are usually rectangular and are verycarefully tooled. Sometimes, untanned lime stones are alsoused. In the earthquake of August 14, 2003, the churches ofthe Venetian period suffered the most serious damageamong medieval and recent monuments. As a result, over40 churches were declared unfit for use [6].

The aim of the present work is to make a short presen-tation of the restoration study of the church dedicated toVirgin Maria of the Strangers. It is the first time that thetypological and morphological characteristics of the monu-ment are recorded and documented, faults are mapped,and analyses are carried out applying the finite elementmethod in order to determine the sensitive areas of thestructure. A dynamic spectral analysis of the structural sys-tem was also carried out in order to verify the response of

able 1aximum ground acceleration, velocity and displacement values (Lefkada’s E

/a Position Code Acceleration (cm/s2)

L* V* T*

. Lefkada LEF10302 333.4 185.6 40

*, Longitudinal component.*, Vertical component.*, Transversal component.

the structure to the seismic loads that developed as a resultof the earthquake. This paper is part of a more comprehen-sive survey of seven important churches of the Venetianperiod. The investigations concerning restoration startedafter the 2003 earthquake aiming both at evaluating alldata that might possibly assist in the morphological andstructural documentation and restoration of significantVenetian churches in Lefkada, and at developing the meth-odology to be used for the analysis of specific monuments.The main idea underlying the present work is to make inte-grated and documented interventions on the historic build-ings and to formulate technical proposals which are worthyof implementation. These should be preceded by a compre-hensive diagnostic procedure [7–9].

2. Seismic risk in the area

One of the strongest earthquakes ever recorded in theGreek territory took place off the west coast of Greeceon August 14, 2003 with k = 20.60�E, u = 38.76�N,and had its epicentre 10 km off the town of Lefkada.The ground acceleration lasted approximately 18 s, andthe peak ground accelerations (PGA) reached the valuesof 0.42 and 0.33 in horizontal directions, respectively.Unfortunately, seismic recordings of the ground move-ment for the vertical component are not available. Theearthquake was caused by a seismogenic fault with con-figuration breaking, which has repeatedly caused strongearthquakes in the greater Ionian Island region [10].The peak values of the ground motion parameters arelisted in Table 1 [6].

According to a geological map issued by the HellenicInstitute of Geological and Mineralogical Explorations(IGME) [11], the town area is built on recent alluvial soil.In accordance with the Greek Seismic Code (EAK 2000)[12], the subsoil of the town of Lefkada is classified undercategory C, whereas in accordance with Eurocode 8(CEN/TC250/SC8/N317, 2002), it is classified under cate-gory C or E. It can be said that the town’s soil, togetherwith its surface geology, topography and mechanical–dynamic properties, played a significant role during theearthquake of August 14, 2003 [13]. The concomitant

arthquake, of August 14th, 2003.)

Velocity (cm/s) Displacement (cm)

L V T L V T

8.6 29.7 9.9 31.7 4.30 2.30 4.60

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436 C. Apostolopoulos, P. Sotiropoulos / Construction and Building Materials 22 (2008) 434–443

appearance of faults was attributed to the case-by-case dif-ferent roles of the soil. The earthquakes of 1704, 1769,1825, 1869, 1914, 1948, 1953 and 1973 should also be con-sidered [14]. Following the destructive earthquake in 1948with a magnitude of 6.5 on the Richter scale, severalchurches were repaired. The subject church, however, wasin use until August 14, 2003.

3. Monument description

3.1. General information

The church is a typical single-nave, single-space IonianIsland basilica located in the north-western part of thetown. The original structure was built in 1718 by Kon-stantinos Varvarigos as a private church, with the permis-sion of the Venetian Government. In 1723, the churchbecame collegial. The initial structure consisted ofuncoursed stone masonry walls, lacking external decora-tion and embellishment. During the 1769 earthquake,the church suffered serious damages, but it was subse-quently reconstructed in 1785 from the ground up withthe help of individual contributions. The western facadewas restored in 1839 according to the commemorativeinscription in the key of the facade niche. The nave struc-ture was crowned with a wooden saddle-shaped roof. Asshown in (Fig. 1), the northern and western facades arebetter preserved. The various baroque stone reliefs onthe door frames and the lintels are also noteworthy.The wooden iconostasis shown in (Fig. 2a) is believedto be the first work of Efstathios Proselantis [2], whilethe interior of the church (Fig. 2b) is the work of Lefk-ada icon painters.

Fig. 1. Virgin Mary of the Strangers. T

3.2. Church’s structural data

The churches of the Venetian period are made of stonemasonry along the perimeter and have a rectangular floorplan and wooden roofs. The external load bearing wallshave a single structure, which on the northern and wes-tern sides includes sand and limestone masonry, and cera-mic fragments embedded in the joint mortar. They end upon the exterior at an ashlar structural system of conglom-erate engraved stones. On the other facades, the sand andlimestone masonry is plastered in the same structuralmanner, since it does not have an ashlar structure. Themasonry of this church has a 65 cm cross-section alongthe perimeter and is approximately 5.10 m high. In mostchurches, the altar niche has an opening roughly equiva-lent to the opening of the western entrance, which givesthe ground plan an almost absolute symmetry, thusreducing the development of yawing and, consequently,of faults. Lime mortar has been used as the joining mate-rial in the masonry.

Porus stone is the main structural decorative materialof the external walls. The interior of the church alongits longitudinal sides (this is common in many churches)has been covered with wooden panelling which ismounted on wooden struts at a distance of approximately5–10 cm from the internal face of the bare perimetermasonry (Fig. 3a). The roof and wooden canopy loadsare directly transferred to the above mentioned 15 · 15wooden trusses (Fig. 3c), through the horizontal perime-ter wooden beam.

The main structural element, the upper perimeter cor-nicing of the church is made of reinforced concrete whichresults in the strong influence of the structure’s seismic

he present condition of the facades.

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Fig. 2. (a) Wooden iconostasis. (b) View of the canopy and the wooden iconostasis (detail).

C. Apostolopoulos, P. Sotiropoulos / Construction and Building Materials 22 (2008) 434–443 437

response. The continuous horizontal cornices reinforce theoff-field bending function of the masonry. This is due to thefact that they receive horizontal seismic loads vertically andparallel to the wall, resulting in the transmission of loads tothe transversal bearing walls. A concrete tie beam was builtat the western and eastern gables during previous interven-tions in 1948 and 1953. In addition to the gables, the revet-ment of the roof, the flooring, and the exterior plaster seemto have undergone reparations as well.

4. Monument pathology

4.1. Perimeter masonry – wooden bearing structure – roof

The damages to the churches of Lefkada caused by the1973 earthquake were aggravated by the earthquake ofAugust 14, 2003, and the width and the length of the exist-ing cracks were increased. This earthquake resulted in thecollapse of the internal and external decorative non-bear-

ing elements of the churches, and in the development ofsevere cracks (Figs. 1 and 4).

The bearing elements of the subject monument appearto have suffered serious damage due to seismic activity,the natural fatigue of the building materials, physicochem-ical and biological factors, creeping deformations, andman-induced factors. It is certain that these deteriorationmechanisms mentioned have acted synergistically ratherthan individually. Following restorative work under thesupervision of the first Antiquities Board [15], the cracksin the masonry were filled both in the altar area (east)and in the loft (west), and new mortar was applied. How-ever, following the earthquake of August 14, 2003, thecracks reappeared at the same or neighbouring positions.

The two longitudinal walls to the north and to the southbear diagonal cracks starting at the windows’ edges andextending towards all directions. Several of these cracksstart at the base of the church, particularly at the door open-ings. Intense diagonal cracks were mainly recorded on the

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Fig. 3. The church’s interior covered by wooden panelling which is supported by wooden struts: (a) section A-A 0, (b) section A-A 0 (detail) and (c) woodenrebband.

438 C. Apostolopoulos, P. Sotiropoulos / Construction and Building Materials 22 (2008) 434–443

western facade but less so in the eastern part, specifically inplaces where the altar niche shell is adjacent to the eastern

Fig. 4. Cracks sustained, in the northern masonry, due to Lefkada’searthquake of August 14, 2003.

gable. At the same locations on the internal surface of themasonry, the stone structure has become loose. Structuraldiscontinuity and unevenness in the height of the horizontalcornice appeared on the crown where the junction of thelongitudinal and of the transversal walls is located.

The original church plans called for the roof to bemainly supported by the wooden struts of the internal woo-den panelling along the perimeter. However, on the insideof the church, the strut bases of the interior wooden panel-ling show increased localised rotting and decay. Therefore,the load carried by the roof and the canopy is transferredto the perimeter walls that are already stressed because ofadditional loads which they are not designed to support.This resulted in the appearance of diagonal cracks and inthe deviation of the masonries from the vertical plane.The deviations of the crown of the longitudinal masonriesoutwards (8 cm at the south-eastern corner) and the swell-ing (by 3–4 cm) of the ashlar engraved stones are typicalfeatures of the current status.

The bearing structure of the roof displays significantdeterioration of certain wooden parts, although the sinking

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C. Apostolopoulos, P. Sotiropoulos / Construction and Building Materials 22 (2008) 434–443 439

of the wooden truss is not obvious at first sight. Severalconnectors have become loose and need to be replaced.In several areas, the connectors are supported on points.These factors play an important role in the seismic behav-iour of the monument.

4.2. Humidity – biological action

The presence of efflorescence on the masonry surface isindicative of physical, mechanical and chemical fatigueprocesses as a result of the reaction of three components:building materials, water, and contaminated compoundspresent in atmospheric water micro organisms may con-tribute as a fourth component). Soluble salts may addition-ally be formed as a result of the interaction of these threecomponents. The presence of efflorescence on the monu-ment is manifested through extensive grey-black flakingon the ashlar elements of engraved stone. The physico-chemical and biological mapping of the church has shownthat the phenomenon is mainly due to the rising dumpfrom the ground and the unrestrained draining of rainwa-ter off the roof. The situation is further aggravated by theaccumulation of rainwater in the surrounding area.

Improper interventions using strong cement mortarswere made on several areas of the perimeter bearingmasonry. The incompatibility of the mortars used is dueto their differences in microstructure and mechanical behav-iour, as well as their increased content of sulphate salts.

Moreover, the formation of biological crust, besides theaesthetic problem, has also caused the decay in theengraved stones and the water erosion of their components.The presence of micro organisms is the result of highhumidity levels in the stone masonry. The composition ofstone materials further favour the development of biologi-cal activity.

4.3. Church flooring

The current flooring of the church was laid after the1973 earthquake and is therefore more recent. The marblepieces used were symmetrically placed in plain patternsaccording to the geometry of the church. The marbleflooring is placed over a 13 cm thick reinforced concreteslab. From the in situ observation carried out and theinformation given by the church board, it appears thatthe concrete extends over the entire interior surface ofthe church and is naturally under the support of the inte-rior wooden panelling struts. This resulted in decay accel-eration of the perimeter pillars, and overall or localizeddisplacement.

The loft flooring consists of wooden planks nailed ontostrong wooden beams which are approximately 1 m apartand have a cross-section of approximately 20/25 cm.Beneath this floor, there is a ‘‘ceiling’’ which is also nailedon the lower part of the wooden beams. The loft flooring istilted from west to east because of the way the bearingbeams were positioned on the vertical bearing masonry ele-

ments to the west and east, as well as on the two inner col-umns. The achieved rigidity was not as high as expectedmainly because of the loose connection. An additionalcause was the partial wood decay.

It is an established fact that the floor diaphragm is asignificant stiff element which influences the results of thestatic dynamic analysis of the structure’s bearing. Themain characteristics of the loft flooring and the roofabove the loft have decisively-influenced the behaviourof the monument, primarily with respect to horizontaland, to a lesser degree, to vertical seismic loads. How-ever, the alteration of the dual structural system hasresulted in the homogenization of the static function ofthe wooden diaphragms (loft flooring and canopy), andthis has adversely affected the seismic behaviour of themonument.

4.4. Foundations

Poor soil quality, along with the high undergroundwater level, was a significant technical problem, faced dur-ing the erection of the churches, since water was found at adepth of 30–35 cm during the exploratory investigation ofthe excavation sections.

The implementation of the investigative excavation ofthe two sections, one outside (T1) and one inside thechurch (T2), aimed at verifying (a) the conditions of themonument’s foundations and the underlying subsoil,and (b) the possibility of the presence of a wooden grat-ing under the foundations. Data relating to such struc-tures is available for younger stone buildings, butunfortunately, data pertinent to the Venetian churchesis missing [16].

The interesting technical solution employed to tacklethe poor soil quality used in certain constructions maybe described as follows. A three-layer wooden gratingis placed under the foundation of the ground floor stonemasonries. The grating which is made of horizontalwooden beams is suitably processed in order to preventwater corrosion [17]. The foundations consist of roughor processed stones, fine sand, and pozzolana. In theevent of an earthquake, the entire foundation couldmove uniformly under the superstructure, thus minimiz-ing the risk for unforeseen behaviour. Buildings of thisstructural type are noteworthy because through tradi-tional building techniques, they integrate the philosophyof the existence of a number of anti-seismic defencealternatives. Sections T1 and T2 revealed findings ofwooden beams measuring 10 · 10 cm · cm (Fig. 5).However, the presence of a complete bearing systemwas not established, and the relevant works shall con-tinue with new sections.

Similar bearing systems were used in the past by theVenetians and the English in different areas. Similar foun-dation bearing systems using wood were also found inancient Greek monuments, mainly temples, while it isknown that a similar system consisting of vertically

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Table 2Properties of the church materials used in the finite element model

Material Property Value

Stone masonry Density 2000 kg/m3

Young’s modulus (longitudinal) 2.75 GPaPoisson’s ratio 0.20

Solid brick masonry Density 1800 kg/m3

Young’s modulus (longitudinal) 3.00 GPaPoisson’s ratio 0.20

Wood Density 900 kg/m3

Young’s modulus (longitudinal) 8.50 GPaYoung’s modulus (transversal) 0.30 GPaPoisson’s ratio 0.30

Fig. 6. Finite element model. In the present view a section of the church isshowed as this appears from entrance to the altar to the western door ofthe church including the mixed perimetric masonry, the internal woodenpaneling, the roof, the perimetric cornice and the loft bearing structure.

Fig. 5. Wooden beams findings: (a) Sectional plan, the location of theinvestigative sections T1 and T2, (b) outer investigative section T1. (b1)conglomerate engraved stone, (b2) wooden beam, (b3) water and (c) detailof a wooden beam.

440 C. Apostolopoulos, P. Sotiropoulos / Construction and Building Materials 22 (2008) 434–443

crossing carved stones was used for soil regeneration or forlaying foundations on rocky surfaces [18].

5. Numerical analysis

5.1. Finite element model

The ANSYS finite element software [19] was used tomodel and analyze the church under consideration. Inmodelling the simulacrum, the symmetry was taken intoaccount without considering the deviations from the verti-cal plane of the church. The properties of the materialsused in the finite element model are presented in Table 2.The Modulus of elasticity for the wood has been consid-ered according to [20,21]. The adhesion at the interface ofthe church’s perimeter masonry walls is low and the pres-ence of external conglomerate stone masonry furtherreduces its modulus of elasticity [22,23], also this type of

masonry is used only in the gables. It is a recently con-structed solid brick masonry with strong bonding mortar.Gables are reinforced by a perimeter tier.

The geometrical complexity of the structure required theuse of 6554 surfaces and 1498 volumes. The stone and themixed masonry were modelled by eight node solid elements(BRICK 45) with three degrees of freedom (DOF) pernode. Two node beam elements (BEAM 4) with six DOFper node were chosen to model the wooden roof beams,the supports, and the vertical struts for the interior woodenrevetment (Fig. 3c). Finally, the interior wooden panellingof the church and the roof coating were modelled by fournode shell elements (SHELL63) with six DOF per node.The final model developed consisted of 11,290 nodes and10,863 elements.

The cross section of the church as seen from the altartowards the western door obtained with the full finite ele-ment model is presented in (Fig. 6). The model presentedincludes the perimeter of the walls marked black in the gra-phic, the inner wooden coated, colored in dark grey, thefrieze in light grey and finally the women’s prayer compart-ment in white.

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C. Apostolopoulos, P. Sotiropoulos / Construction and Building Materials 22 (2008) 434–443 441

5.2. Modal analysis

The intrinsic behaviour of stone structures is known tobe strongly non-linear. However, a linear analysis wasattempted in order to obtain qualitative information onthe possible modal shapes and the corresponding eigenfre-quencies. The first modal shapes appeared in the woodenroof, and the fact that the roof tiles of most churches felloff during the August 14, 2003 earthquake confirmed thisobservation. The main structural mass consists of the firsttwo modal shapes of the church’s stone masonry shownin Fig. 7a and b.

12

14

5.3. Dynamic analysis

The dynamic analysis was carried out in order to checkthe peak response of the structure during the earthquake ofAugust 14, 2003 [24].

The spectral analysis method was applied to calculatethe seismic response. This method includes a full modalanalysis of the structure, peak seismic response calculationsfor each modal shape, and a square sequence of peakmodal shape responses. The modal analysis proceduresand the eigen-frequencies calculated were presented in aprevious section (Modal analysis).

The sequence of peak modal shape responses was gener-ated using the following equation:

Fig. 7. (a and b) The first two modal shapes of the stone walls.

exA ¼ �ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiX

i

Xj

ðeij � Ai � AjÞs

ð1Þ

This rule is known as the CQC-rule (Complete QuadraticCombination). In this equation, Aj are the natural formvalues of A, and eij is the correlation coefficient for thetwo natural forms i and j.

The forces exerted on the structure result from seismicaction and the mass inertia of the structures. Seismic exci-tation at the base of the structure consists of two horizontaland one vertical component. The directions of the two hor-izontal components coincide with the longitudinal andtransversal direction of the seismic waves, respectively,spreading from the earthquake epicentre towards the townof Lefkada. Uniform distribution of seismic action alongthe height of the structure was assumed. It is assumed thatall points of the church make the same movement. Fig. 8aand b show the longitudinal and the traverse earthquakecomponents, respectively, as a function of the period T.For the vertical component, no data is available. It is cal-culated according to the Greek Seismic Code EAK 2000[12] from the following equation:

(b)

(a)

0

2

4

6

8

10

12

14

16

18

0 0.5 1 1.5 2 2.5 3Period (sec)

Acc

eler

atio

n

0

2

4

6

8

10

0 0.5 1 2.51.5 32Period (sec)

Acc

eler

atio

n

Fig. 8. Earthquake design spectrum: (a) horizontal components (longitu-dinal – traversal) and (b) vertical component.

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Fig. 9. Characteristic results of the performed dynamic analysis: (a) normal stresses, (b) shear stresses in the longitudinal plane, (c) shear stresses thetransversal plane and (d) Equivalent Von Mises stresses.

442 C. Apostolopoulos, P. Sotiropoulos / Construction and Building Materials 22 (2008) 434–443

UdðT Þ ¼ c1Av 1þ TT 1

ghb0

qv� 1

� �h i0 6 T 6 T 1

UdðT Þ ¼ c1Avghb0

qvT 1 6 T 6 T 2

UdðT Þ ¼ c1Avghb0

qv

T 2

T

� �2=3T 2 6 T

ð2Þ

where Ud – design value of spectral acceleration, T1, T2 –characteristic values of periods, T1 = 0.20 s, T2 = 0.80 s,b0 – spectral amplification factor 2.50, a – seismic risk zone0.36, A = a*g – maximum ground acceleration 0.36*g, Av –maximum vertical ground acceleration 0.252*g, g – damp-ing correction factor 1.00, c1 – importance factor 1.30, qv –behavior factor 1.50 and h – foundation factor 1.00.

For reasons of brevity, Fig. 9a–d present a selectionof graphical representations of certain typical results ofthis dynamic analysis. More specifically, the plot of nor-mal stress of the stone masonry in the vertical directionis shown in Fig. 9a. Fig. 9b and c show the shear stressesof the stone masonry in the longitudinal and in thetransverse direction, respectively. Finally, the equivalentstresses determined by Von Mises are presented inFig. 9d.

The calculations showed that the peak displacements ofthe analyzed structure resulting from the concurrent actionof the two horizontal earthquake components are quitelimited. Intense localized oscillations of the walls both intheir in-plane and out-of-plane directions appeared in mostmodal shapes. Fig. 9b and c show the shear stresses distri-

bution, as a result of the dynamic analysis on both longitu-dinal and transversal masonry walls of the church. Therespective maximum shear stresses 0.45 MPa and0.2 MPa on masonry walls are recorded in places and areaswhere diagonal cracks were developed. Fig. 9a and d showthe distribution of both normal stresses and the equivalentVon Mises stresses. Similarly, the maximum stresses1.8 MPa and 1.6 MPa are found in lower levels at churchside entrances, where horizontal longitudinal cracks wereactually recorded.

The dynamic analysis results (Fig. 9a–d), in combinationwith the graphical representation of the fractures on thebearing walls (Fig. 1a–d) and taking into considerationthe relative photographic documentation of the damages(Fig. 4), provide a retrospective picture of the present situ-ation allowing for the identification of the susceptible areasof the monument.

6. Conclusion

The greater Lefkada region has the highest seismic activ-ity levels in Europe, and the August 14, 2003 earthquakewas potentially a full-scale experiment, the results of whichmay provide valuable information on earthquakes andtheir respective impact on the specific structural systemsof churches.

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C. Apostolopoulos, P. Sotiropoulos / Construction and Building Materials 22 (2008) 434–443 443

The dual structural system of Lefkada has been inter-nationally recognized as one of the most efficient tradi-tional anti-seismic systems in Europe. The churcheswere designed so that both individual structural systemsreceive loads. Even in cases of masonry collapse, the sys-tem of the wooden pillar struts behind the perimeterwalls inside the perimeter wooden panelling is activated,receiving and supporting all loads from the wooden roofand canopy.

The cracks in the church investigated were mainlylocated in the perimeter walls and at the transversal walls’corners. In many instances, increased earthquake accelera-tion has caused telltale crossed cracks due to the cutting-tensile failure of piers. Thanks to the superior quality ofthe building, though, the masonries were not disorganized,although they suffered cracks and deviated from the verti-cal plane. Hence, restoration is still possible.

The elastic analysis of the bearing structure using finiteelements justifies the cracks’ positioning, since it has beenestablished that cracking occurs where the greatest tensionsare applied.

A large number of faults may be attributed to pre-exist-ing poor conditions due to lack of maintenance, and to nonnormative church restoration and reinforcement worksamong other factors. Finally, particular attention wasgiven to exploring the mechanisms that caused the faults.Thus, less evident conditions affecting the static adequacyand the aesthetic value of the structure were equallyidentified.

Churches exposed to strong seismic action over severalcenturies have undergone a form of natural selection, andonly those better designed and built have survived. For thisreason, particular attention and diligence must be paid tostrengthen the initial structural system of the Virgin Maryof the Strangers church by suitably reinforcing the monu-ment’s vulnerable areas.

Acknowledgement

The technical study, supervision and stabilization of‘‘Virgin Mary of the Strangers’’ Church was assigned tous by the following decision of the Holy Metropolis ofLefkada (Decree No. 815/11.9.2003). The survey wasapproved by the Directorate for Musea and TechnicalServices of the Hellenic Ministry of Culture (Decree No862/8.7.2004).

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