buildings

Article Seismic Vulnerability of Masonry Lighthouses: A Study of the Bengut Lighthouse, Dellys, Boumerdès, Algeria

Karima Amari 1, Amina Abdessemed Foufa 1, Mustapha Cheikh Zouaoui 1 and Giuseppina Uva 2,* 1 Environnement et Technologie pour l’Architecture et le Patrimoine, Institut d’architecture et d’urbanisme, Université Saad Dahleb, 0900 Blida, Algeria; [email protected] (K.A.); [email protected] (A.A.F.); [email protected] (M.C.Z.) 2 Department of Civil, Environmental, Land, Construction and Chemistry, Polytechnic University of Bari, 70126 Bari, Italy * Correspondence: [email protected]



Received: 24 October 2020; Accepted: 9 December 2020; Published: 18 December 2020


Abstract: In Algeria, lighthouses are an essential element of the maritime landscape and constitute a substantial part of the local historical and cultural heritage, marked by a great variety of styles, architecture, geometrical forms, and materials. The study presented falls into the general context of pre- and post-seismic conservation of Algerian lighthouses, since all these stone masonry buildings are situated in areas characterized by a medium–high seismic hazard. In the paper, a relevant example has been analyzed: the Bengut Lighthouse, which has been classified as “National Heritage” by the Algerian Ministry of Culture and has been severely damaged by the Boumerdès that occurred on 21 May 2003. After an overview of historical lighthouses in Algeria and their morpho-typological classification, the case study of the lighthouse at Cap Bengut is presented, showing the results of a detailed survey of the geometric and constructive features and of the actual cracking and damage pattern. First, based on the critical analysis of this knowledge framework, a preliminary qualitative evaluation of the seismic vulnerability has been made, analyzing and classifying the set of local and global failure modes coherently with the observed structural pathologies and damages. Then, numerical modeling has been implemented in TreMuri computer code, performing a set of pushover analyses. This allowed the investigation of the criticalities in the response of the building to seismic actions, characterization of the dynamic behavior, and comparison with the actual observed damages, which are discussed, providing an interpretation of the global and local failure modes. Based on the results of the visual assessment and numerical analysis, guidelines for the retrofitting intervention have been proposed, by considering, on the one hand, the objective of effectively mitigating the elements of vulnerability pointed out by the results and, on the other, the main principles of conservation and restoration. The presented study and its results, in perspective, are intended to provide a basis for developing risk and vulnerability analysis of typological classes of historical lighthouses at a large scale.

Keywords: historical lighthouses; masonry; Boumerdès earthquake; Algeria; seismic vulnerability; non-linear static analysis

1. Introduction According to the Italian author C. Bartolomei, lighthouses represent both a historical and cultural source for the architectural maritime heritage of a country, besides being physical markers of the coastal landscape [1]. The practice of maritime signaling by means of maritime lamps was introduced for the

Buildings 2020, 10, 247; doi:10.3390/buildings10120247 www.mdpi.com/journal/buildings Buildings 2020, 10, 247 2 of 30 Buildings 2020, 10, x FOR PEER REVIEW 2 of 31 offirst the time coastal in the landscape Mediterranean [1]. The basin practice by the of Greeks maritime in the signaling 6th century by means AD [2]. of In maritime fact, the origin lamps of was the introducedFrench word for “phare” the first comes time in from the theMediterranean Greek word ba “pharos”sin by the which Greeks refers in the to the6th namecentury of AD the island[2]. In fact,where the the origin Alexandria of the French Lighthouse, word long “phare” held tocomes be the from first the edifice Greek of itsword kind, “pharos” is situated. which As lightsrefers visibleto the namein the distance,of the island these where lighthouses the Alexan shine,dria during Lighthouse, the night, long over held the Mediterraneanto be the first edifice Sea, to of indicate its kind, their is situated.position toAs sailors lights as visible they navigate in the closedistance, to the these coasts lighthouses of Southern shine, Europe, during North the Africa, night, and over western the MediterraneanMiddle East. Thus, Sea, merchants,to indicate their throughout position the to sailor ages,s have as they been navigate able to close easily to locate the coasts dangerous of Southern zones Europe,and navigate North towards Africa, theand ports western [3]. Middle East. Thus, merchants, throughout the ages, have been able toToday, easily from locate the dangerous Moroccan zones to the and Tunisian navigate border, towards the Algerianthe ports [3]. coast is illuminated by several buildingsToday, used from for the maritime Moroccan signaling to the Tunisian (Figure1 ).border According, the Algerian to the Nationalcoast is illuminated Board of Lighthouse by several buildingsAuthorities used (NBLA), for maritime 25 of them signaling date back (Figure to the 1). French According period to (approximately the National 150Board years of agoLighthouse [4]) and Authoritiesshow architectural (NBLA), elements 25 of them typical date ofback the to 19th the andFrench 20th period centuries (approximately with some typological, 150 years ago structural, [4]) and showand stylistic architectural variations. elements Because typical of theof the relevance 19th an ofd 20th their centuries maritime with function some and typological, architectural structural, value, andmany stylistic associations variations. are involved Because inof thethe protectionrelevance andof their conservation maritime function of this built and heritage, architectural and several value, manyresearch associations studies have are beeninvolved devoted in the to protection the issue: and conservation of this built heritage, and several research studies have been devoted to the issue: Manuals of preservation for the lighthouses drawn up by the International Association of • LighthousesManuals of preservation Authorities (IALA)for the lighthouses and Association drawn Internationale up by the International de Signalisation Association Maritime of (AISM)Lighthouses [5]. Authorities (IALA) and Association Internationale de Signalisation Maritime Project(AISM) “MED-PHARE”,[5]. which focus on the preservation and development of the maritime built • heritageProject “MED-PHARE”, and its beacons [which6–9]. focus on the preservation and development of the maritime built Cataloguesheritage and of its the beacons lighthouses, [6–9]. semaphores, and beacons within the Mediterranean region. • Catalogues of the lighthouses, semaphores, and beacons within the Mediterranean region.

Figure 1. Lighting mapmap ofof thethe Algerian Algerian coast coast showing showing the the network network of of lighthouses lighthouses deployed deployed during during the theFrench French colonial colonial era (1947).era (1947).

The issueissue ofof conservation conservation and and restoration restoration of theseof th historicese historic monumental monumental buildings buildings is closely is closely related relatedto structural to structural safety and safety in particular and in seismic particular safety, seismic since almost safety, all since areas almost along the all Mediterranean areas along Seathe Mediterraneanare characterized Sea by are high characterized seismic hazard. by high From seismic this point hazard. of view, From the this reference point of scientific view, the framework reference scientificis represented framework by vulnerability is represented studies by andvulnerability methods studies of modeling and methods and analysis of modeling of historical and masonryanalysis ofstructures, historical whichmasonry will structures, be briefly which mentioned will be inbriefly Section mentioned2. Regarding in Section lighthouses, 2. Regarding which lighthouses, include whichslender, include high components, slender, high a specificcomponents, reference a specific will be re madeference to thewill research be made devoted to the research to masonry devoted towers, to masonrysince they towers, have important since they peculiarities. have important peculiarities. The aim of the paper is to provide a technical contributioncontribution to the preservation of the historical and cultural heritage that lighthouses represent represent in in the world, first first of all by tracing a protocol of knowledge that includes the survey, inventory, and mapping of recurrent typological, architectural, Buildings 2020, 10, 247 3 of 30 knowledge that includes the survey, inventory, and mapping of recurrent typological, architectural, and constructive features, and then characterizing specific structural aspects, since conservation and restoration of these buildings depends crucially on structural safety, particularly when there are additional risk factors such as seismic hazard. The paper addresses the development of this methodology through a paradigmatic case study, for which a critical historical knowledge path and a vulnerability study are carried out, identifying the main modes of damage, the elements of structural criticality and proposing intervention guidelines for seismic risk mitigation. This case study is the Cap Bengut Lighthouse (Dellys, Algeria), which has been classified as “National Heritage” by the Algerian Ministry of Culture. The objective is not to perform a specific assessment and design of interventions limited to a single building, but rather to exploit modeling and numerical analysis for identifying the general elements that influence vulnerability, selecting the characteristic modes of damage and classes of intervention which are most effective for the risk mitigation. The relevance of the proposed study consists, therefore, in the possibility of extending the approach to a whole morpho-typical class of buildings, with three objectives: (1) define and systematize the methodological operational path; (2) provide a reference basis for the calibration of indirect vulnerability algorithms on the regional scale; (3) develop, in perspective, specific models of typological–mechanical vulnerability for large-scale analyses. After an overview of the architectural heritage of lighthouses in Algeria and the seismic vulnerability of masonry structures, the survey, characterization, and interpretation of crack and damage patterns carried out for the case study will be presented, as well as the numerical modeling, analysis, and related results.

2. Seismic Vulnerability of Masonry Buildings: A Brief Overview Modern Mediterranean towns consist of many UnReinforced Masonry (URM) buildings that are more than 100 years old and were generally designed and built to withstand only vertical, static loads, whereas the inertial seismic loads were not explicitly considered. Moreover, several pathologies such as degradation and aging of materials, or invasive interventions during renovation projects, have considerably increased their general vulnerability. The combination of the high vulnerability of these masonry buildings and the seismic hazard of the Mediterranean region determine an overall severe level of seismic risk [10–12]. The structural behavior of masonry structures is particularly complex and depends on several factors, including the geometry of the structure, the quality of the materials used, and the actual conditions of the building. Anyway, some common features can be recognized: high self-weight; anisotropic and history-dependent structural behavior; good compressive and shear strength and negligible tensile strength [13–15]. The peculiar seismic response also depends on the following characteristics [13]:

Quality of walls and texture: the overall in-plane and out-of-plane behavior is strictly related • to the properties and arrangement of the different constituents, which are extremely variable, especially in ancient constructions. Slenderness of walls (which should be limited to ensure their stability and prevent out-of-plane • mechanisms): post-earthquake observations have shown that out-of-plane mechanism is the type of damage most frequently observed in ancient URM buildings [16,17]. Proper structural organization, to enhance the spatial behavior and allow the distribution of actions • among all supporting elements: this is mainly related to the presence of effective connections between orthogonal walls, and between masonry walls and horizontal diaphragms to ensure the “box-like” behavior during an earthquake. Rigidity and resistance of floor diaphragms for effectively guaranteeing the redistribution of • seismic actions, reducing out-of-plane vibrations of walls and increasing structural redundancy. Buildings 2020, 10, 247 4 of 30

Although in the past the “conceptual” rules for the appraisal of seismic vulnerability have proved to be generally satisfactory as a basis for the construction and conservation of masonry buildings, presently new tools and concepts for the structural analysis of masonry are available. Several recent studies have pointed out the importance of analyzing the non-linear response of masonry by properly modeling the constitutive response, and in particular the low tensile strength, the progressive development of damage with stiffness and strength degradation. Among the different typologies of existing masonry structures, towers have a particularly severe seismic vulnerability for several reasons. Gravity loads combined with slenderness typically induce a high compressive stress, often close to the limit value. The additional flexural loads under seismic events, in the long term, could induce damage or even global collapse [18,19]. In the recent scientific literature, there are many research studies devoted to the development and validation of specific tools for the seismic analysis of masonry towers, especially focusing on non-linear approaches, both static and dynamic [20–22], which are for existing masonry structures a recommended alternative to linear ones for the detailed safety assessment of individual buildings. When dealing with large building assets, considering that economic and human resources available are often limited, it is not possible to proceed with detailed investigations and safety assessments on each building. The use of preliminary large-scale vulnerability analyses becomes therefore a fundamental step and, in fact, for the widespread residential building stock, this is a widely adopted approach that allows the preliminary screening, identification of critical issues and priorities based on general data easy to collect. These are 1st level approaches based on indirect semeiotic, typological algorithms, and calibrated on the observation of real damage detected after earthquakes [10–12,23,24]. With reference to some specific typologies of monumental and historical buildings, there are well-acknowledged algorithms developed by the scientific community [25–27]. The aim of the paper is to develop this path for the case of lighthouses, for which a specific framework does not exist yet. However, it becomes fundamental to make numerical calibrations with appropriate non-linear models and methods on representative cases for which post-seismic observations are available, such as the one proposed here. The future objective, however, is broader. The first perspective is the development of semeiotic typological models, as usually done with indirect vulnerability methods. A more advanced future target, then, is the proposal of typological–mechanical approaches, in which the seismic fragility assessment derives from the multi-variate numerical analysis of samples generated from representative models [28].

3. Lighthouses in Algeria Like in many regions along the Mediterranean Sea, lighthouses in Algeria have existed for a long time, but their number increased during the French colonial era. The vast territory of the African inland was rich in agricultural and mineral products that could be conveniently exploited to sustain foreign trades, and this fostered the growth of the maritime navigation between Algeria and Europe, opening a direct major trading route [29]. Maritime signaling was much developed through the construction of several important lighthouses along the Algerian coastline, which stretches almost in a straight line from W.10◦ S to E.10◦ N for 1600 km (Figure1) and sees presently the presence of a rich maritime organization and buildings. The lighthouses are generally spaced out in such a way that when sailing close to the land, even in thick fog at least one signal can be seen [30]. Algerian lighthouses bear witness to a long period of history and crystallize diversified architectural assets according to the period and place in which they were built. Consequently, a wide typological variability can be recognized, in relation to several geometrical criteria: form, height, and position of the towers. Table1 shows a morpho-typological survey of the lighthouses present along the Algerian coast in which the following elements have been classified: geometry in plan; maximum height; position of the Buildings 2020, 10, 247 5 of 30 tower in relationBuildingsBuildingsBuildings to2020 2020 2020 the, 10, ,,10 building. 10x, FOR,x x FOR FOR PEER PEER PEER AREVIEW REVIEW totalREVIEW number of 24 buildings has been surveyed. For each category,5 of55 of 31of 3131 the number ofBuildings lighthouses 2020, 10, x showing FOR PEER REVIEW that feature is reported in round brackets. 5 of 31 TableTableTable 1. 1.Morpho-typological1. Morpho-typologicalMorpho-typological classification classificationclassification of ofofAlgerian AlgerianAlgerian lighthouses lighthouseslighthouses according accordingaccording to totoform, form,form, height, height,height, and andand BuildingsBuildingsBuildingsBuildings 2020 2020 2020 2020, ,10 10, 10,, 10,x ,x FORx, , FOR x xFOR FORFOR PEER PEER PEER PEERPEER REVIEW REVIEW REVIEW REVIEWREVIEW 55 of5 of5 of31 of31 31 31 positionpositionposition of oftheof the the tower. tower. tower. Table 1. Morpho-typologicalTable 1. Morpho-typological classification classification of Algerian of Algerian lighthouses lighthouses according according to to form, form, height,height, and TableTableTableTable 1.1. 1. Morpho-typological1.Morpho-typological Morpho-typological Morpho-typological classificationclassification classification classification ofof of ofAlgerianAlgerian Algerian Algerian lighthouseslighthouses lighthouses lighthouses accordingaccording according according toto to toform,form, form, form, height,height, height, height, andand and and and position ofposition the tower. of theQuadrangular tower.QuadrangularQuadrangular (11) (11) (11) Circular Circular Circular (08) (08) (08) Octagonal Octagonal Octagonal (05) (05) (05) positionpositionpositionposition of of of the ofthe the the tower. tower. tower. tower. Quadrangular (11) Circular (08) Octagonal (05) QuadrangularQuadrangularQuadrangularQuadrangularQuadrangular (11) (11) (11) (11) Circular Circular Circular Circular Circular (08) (08) (08) (08) Octagonal Octagonal Octagonal Octagonal Octagonal (05) (05) (05)(05) (05)

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Thereg. of ofThere Thereof of masonrymasonry masonry masonryis is anis an an important buildingsimportant buildingsimportant buildings buildings ancient (stone (stone ancientancient(stone (stone and/orbuiltand/or and/or built and/orbuilt envi brick)envi envibrick) brick) brick)ronmentronmentronment datingdating dating dating in fromin from inthefrom fromthe the coastal the the coastalcoastalthe the colonialcolonial colonial colonialtowns towns towns period period ofperiod periodof ofthe the the North, [35],[35], [35],North, North,[35], amongamong among mainlyamong mainly mainly previous zones(PGA) is, respectively: in each of the Z previous II a: PGA zones= 0.25 is, respectively: g; Z II b: PGA Z II= a:0.3 PGA g and= 0.25 Z g; II: Z PGA II b: =PGA0.4 = g. 0.3 There g and is Z II: consistingconsistingconsistingwhichPGAwhichwhichwhich = several 0.4several ofseveral several of ofg.masonry masonryTheremasonry lighthouses lighthouses lighthouses lighthouses is buildings an buildingsbuildings important that that that that severely severely (stoneseverely severely (stone(stone ancient and/orsuffered, suffered, and/orsuffered, and/orsuffered, built brick) brick)thenvi brick)th th roughoutthroughoutroughout roughoutronmentdating datingdating the fromthe the in fromthefrom ages, ages,the ages, ages,the coastalthe thethe the colonialthe the colonialeffects colonialeffects effects effectstowns periodof of ofperiod period ofseismic ofseismic seismic seismicthe [35], North, [35], [35],shocks. shocks. shocks. shocks.among amongamong mainly an important ancient built environment in the coastal towns of the North, mainly consisting of masonry whichwhichwhichconsisting several severalseveral oflighthouses lighthouseslighthousesmasonry thatbuildings thatthat severely severelyseverely (stone suffered, suffered,suffered, and/or th brick) throughoutthroughoutroughout dating the thethe fromages, ages,ages, the thethe effectscolonial effectseffects of periodof ofseismic seismicseismic [35], shocks. shocks.shocks. among buildings (stone and/or brick) dating from the colonial period [35], among which several lighthouses which several lighthouses that severely suffered, throughout the ages, the effects of seismic shocks. that severely suffered, throughout the ages, the effects of seismic shocks. A notable example of the Buildings 2020, 10, 247 6 of 30 post-earthquake behavior of masonry towers in Algeria is given by the structural damage of Bengut LighthouseBuildings after 2020, 10 the, x FOR May PEER 2003 REVIEW Boumerd ès Earthquake. 6 of 31 Historical lighthouses are extremely vulnerable because of the following reasons: A notable example of the post-earthquake behavior of masonry towers in Algeria is given by the Geometrystructural damage of towers: of Bengut as already Lighthouse mentioned, after the the May tower 2003 Boumerdès generally hasEarthquake. high compressive vertical • stressesHistorical due to lighthouses gravity loads. are Underextremely seismic vulner loading,able because the slendernessof the following can reasons: cause significant flexural loads• Geometry and lateral of towers: drifts, as easily already leading mentioned, to local the damagetower generally or global has collapses.high compressive The presencevertical of adjoiningstresses structures due to gravity can also loads. influence Under the seismic tower loading, seismic the vulnerability: slenderness can the possiblecause significant interaction reducesflexural the slenderness loads and lateral of the drifts, tower easily but, leading at the to same local time,damage provides or global stress collapses. concentrations The presence at the contactof adjoining zone between structures tower can and also theinfluence confining the tower structures seismic [ 36vulnerability:]. the possible interaction reduces the slenderness of the tower but, at the same time, provides stress concentrations at the Geographical position: they are in zones of medium–strong seismicity (Figure2). • contact zone between tower and the confining structures [36]. Degradation• due to age: the lighthouses dating from the French colonial era are sometimes more • Geographical position: they are in zones of medium–strong seismicity (Figure 2). than• 150Degradation years old due (the to age: first the one lighthouses was built dating in 1861, from the the last French one incolonial 1954 [era37]). are sometimes more than 150 years old (the first one was built in 1861, the last one in 1954 [37]).

FigureFigure 2. Geographical 2. Geographical location location of of the the lighthouses lighthouses in the the seismic seismic map map of ofAlgeria, Algeria, CGS. CGS.

4. The4. LighthouseThe Lighthouse at Cap at Cap Bengut Bengut The BengutThe Bengut Lighthouse, Lighthouse, situated situated in the in eastthe east of Algeria, of Algeria, in the in the town town of Dellys,of Dellys, also also known known as “Bordjas Fnar”,“Bordj was builtFnar”, during was built the during 19thcentury, the 19th century, more precisely more precisely in 1881, in at1881, a time at a time when when the townthe town of Dellysof flourishedDellys (Figure flourished3). (Figure In fact, 3). it In was fact, of it greatwas of importancegreat importance for thefor the maritime maritime navigation navigation [38]. [ 38]. After After a centurya century of service, of service, it was putit was out put of serviceout of service due to du a lighte to a non-structural light non-structural damage damage caused caused by a by terrorist a bombterrorist in 1994, bomb first, andin 1994, to the first, destruction and to the (cracks, destructio bothn (cracks, deep and both superficial, deep and superficial, along the outsidealong the walls) and partialoutside collapse walls) and of partial the ceilings collapse caused of the byceilings the Boumerd caused byè thes Earthquake Boumerdès inEa 2003,rthquake later. in 2003, later. Today, the lighthouse is in a severe state of degradation due to lack of maintenance which lasted for more than 12 years. Despite the on-going restoration project that was launched in 2016, after the site was officially classified as “National Heritage” by the Algerian Ministry of Culture, at the present time only the buttresses of the vault ceilings have been installed. The in-plan configuration of the lighthouse approximately consists of an elongated rectangle 29.6 m long and 6.35 m wide. It has two stories and is attached to a quadrangular tower, 33.1 m high, with base dimensions 7.40 m by 7.10 m. Additional information regarding the typology of the walls and their thickness, the mortar used, and floors is shown in Table2. Buildings 2020, 10, x FOR PEER REVIEW 7 of 31 Buildings 2020, 10, x FOR PEER REVIEW 7 of 32

Buildings 2020, 10, 247 7 of 30 Buildings 2020, 10, x FOR PEER REVIEW 7 of 31

Figure 3. 3D drawings of the Bengut Lighthouse. Figure 3. 3D drawings of the Bengut Lighthouse. Today, the lighthouse is in a severe state of degradation due to lack of maintenance which lasted Today, the lighthouse is in a severe state of degradation due to lack of maintenance which lasted for more than 12 years. Despite the on-going restoration project that was launched in 2016, after the for more than 12 years. Despite the on-going restoration project that was launched in 2016, after the site was officially classified as “National Heritage” by the Algerian Ministry of Culture, at the present site was officially classified as “National Heritage” by the Algerian Ministry of Culture, at the present time only the buttresses of the vault ceilings have been installed. time only the buttresses of the vault ceilings have been installed. The in-plan configuration of the lighthouse approximately consists of an elongated rectangle The in-plan configuration of the lighthouse approximately consists of an elongated rectangle 29.6 m long and 6.35 m wide. It has two stories and is attached to a quadrangular tower, 33.1 m high, 29.6 m long and 6.35 m wide. It has two stories and is attached to a quadrangular tower, 33.1 m high, with base dimensionsFigureFigure 7.40 m 3. 3.by 3D 3D7.10 drawings drawings m. Additional of of the the information Bengut Bengut Lighthouse. Lighthouse. regarding the typology of the walls with base dimensions 7.40 m by 7.10 m. Additional information regarding the typology of the walls and their thickness, the mortar used, and floors is shown in Table 2. and their thickness, the mortar used, and floors is shown in Table 2. Today, the lighthouse is in a severe state of degradation due to lack of maintenance which lasted Table 2.TableConstructive 2. Constructive techniques techniques of walls walls and and floors. floors. for more than 12 years. Despite the Tableon-going 2. Constructive restoration techniques project of walls that and wasfloors. launched in 2016, after the Structural site wasStructural officially Element Structuralclassified as “National Geometrical Heritage”Geometrical Scheme Schemeby the Algerian Ministry of Culture, Description Description at the present Element Geometrical Scheme Description time only the buttressesElement of the vault ceilings have been installed. The in-plan configuration of the lighthouse approximately consists of an elongated rectangle WallsWalls made made of rubble of rubble stone. stone. 29.6 m long and 6.35 m wide. It has two stories and is attached to a quadrangularThicknessThicknessWalls made of tower,exterior of of exterior rubble walls: 33.1 stone. walls: m high, WallsWalls of the of the Thickness of exterior walls: Walls of the 5050 cm, cm, chaining chaining at angles. at angles. with basemain dimensions buildingmain building 7.40 m by 7.10 m. Additional information regarding the50 cm, typology chaining at angles. of the walls main building ThicknessThickness of interior of interior walls: and their thickness, the mortar used, and floors is shown in Table 2. 40 cm.Thickness of interior walls: walls:40 cm. 40 cm.

Table 2. Constructive techniques of walls and floors.

Structural Geometrical Scheme Description Element Walls of the Walls build of cut stone Walls build of cut Walls of thetowerWalls tower of the masonry.Walls build of cut stone tower stonemasonry. masonry. Walls made of rubble stone. Buildings 2020, 10, x FOR PEER REVIEW Thickness of exterior8 of 32 walls: Walls of the 50 cm, chaining at angles. main building Thickness of interior walls: 40 cm. VaultedVaulted ceilings. ceilings. FloorsFloors FlatFlat formed formed arches arches made made from from cut cut stone. stone.

Walls of the In Figure 4, the main morphological features and irregularities of this buildingWalls build can beof cutclearly stone towerIn Figure observed:4, the main morphological features and irregularities of thismasonry. building can be clearly observed: • Geometric irregularity in plan (Figure 4a): the square tower is contiguous to a rectangular building. Geometric irregularity in plan (Figure4a): the square tower is contiguous to a rectangular building. • • Volumetric imbalance in elevation (Figure 4b): the total height of the tower equals three times Volumetric imbalance in elevation (Figure4b): the total height of the tower equals three times the • the building height, with no seismic joints between them. building• height,Bad connection with no between seismic external joints walls between in the corn them.ers, because of the poor effectiveness between Bad connectionchaining between stone and external walls. walls in the corners, because of the poor effectiveness between • chaining stone and walls.

Figure 4. Drawings of the Bengut Lighthouse: (a) plan view; (b) main façade with indication of the damage distribution; (c) lateral views with indication of the damage distribution.

5. Seismic Vulnerability Analysis of the Bengut Lighthouse The case of the Bengut Lighthouse has been developed by tracing a methodological approach for the vulnerability assessment and performing numerical modeling and analysis based on the non- linear static approach, using the computer code TreMuri (educational version, S.T.A. Data, Turin, Italy) [39], a specific tool for the analysis of URM buildings, in which the seismic assessment is performed by the non-linear static method, according to the Italian seismic code [40], by determining the different capacity curves and limit states.

5.1. Identification of Collapse Mechanisms First, the survey of the cracking and damage patterns presented in Section 4 has been analyzed and interpreted, to provide a systematic classification of the post-seismic situation and incipient collapse mechanisms. In Table 3, to facilitate the interpretation of the different collapse mechanisms of the lighthouse, the general categories are presented and explained through a description of the observed damage. In view of the restoration works and a possible conversion of the lighthouse into Buildings 2020, 10, x FOR PEER REVIEW 8 of 31

Vaulted ceilings. Floors Flat formed arches made from cut stone.

In Figure 4, the main morphological features and irregularities of this building can be clearly observed:

• Geometric irregularity in plan (Figure 4a): the square tower is contiguous to a rectangular building. • Volumetric imbalance in elevation (Figure 4b): the total height of the tower equals three times the building height, with no seismic joints between them. Buildings 2020, 10, 247 8 of 30 • Bad connection between external walls in the corners, because of the poor effectiveness between chaining stone and walls.

FigureFigure 4. 4.Drawings Drawings of of the the Bengut Bengut Lighthouse:Lighthouse: (a) plan view; view; ( (bb)) main main façade façade with with indication indication of of the the damagedamage distribution; distribution; (c ()c lateral) lateral views views with with indicationindication ofof thethe damage distribution. distribution.

5.5. Seismic Seismic Vulnerability Vulnerability Analysis Analysis of of the the BengutBengut LighthouseLighthouse TheThe case case of of the the Bengut Bengut Lighthouse Lighthouse has has been been developed developed by by tracing tracing a methodologicala methodological approach approach for thefor vulnerability the vulnerability assessment assessment and performing and performing numerical numerical modeling modeling and analysisand analysis based based on the on non-linearthe non- staticlinear approach, static approach, using the using computer the computer code TreMuri code TreMuri (educational (educational version, version, S.T.A. Data, S.T.A. Turin, Data, Italy) Turin, [39 ], a specificItaly) [39], tool a forspecific the analysis tool for ofthe URM analysis buildings, of URM in buildings, which the in seismic which assessment the seismic is assessment performed is by theperformed non-linear by static the non-linear method, accordingstatic method, to the according Italian seismicto the Italian code seismic [40], by co determiningde [40], by determining the different capacitythe different curves capacity and limit curves states. and limit states.

5.1.5.1. Identification Identification of of Collapse Collapse Mechanisms Mechanisms First,First, the the survey survey of of the the cracking cracking and and damage damage patterns patterns presented presented in in Section Section4 has 4 has been been analyzed analyzed and interpreted,and interpreted, to provide to provide a systematic a systematic classification classific ofation the post-seismicof the post-seismic situation situation and incipient and incipient collapse collapse mechanisms. In Table 3, to facilitate the interpretation of the different collapse mechanisms mechanisms.Buildings 2020 In, 10 Table, x FOR3, PEER to facilitate REVIEW the interpretation of the di fferent collapse mechanisms of the9 of 32 lighthouse,of the lighthouse, the general the categoriesgeneral categories are presented are pres andented explained and explained through through a description a description of the observed of the observed damage. In view of the restoration works and a possible conversion of the lighthouse into damage.a marine In view museum, of the emergency restoration wooden works and supports a possible have conversionbeen placed of inside the lighthouse the building, into just a marine below the museum,ceilings, emergency to prevent wooden their collapse, supports and have steel been stay-rods placed insidehave been the building, fixed inside just the below tower, the ceilings,from top to to preventbottom. their collapse, and steel stay-rods have been fixed inside the tower, from top to bottom.

TableTable 3. Classification 3. Classification of collapse of collapse mechanisms. mechanisms.

DamageDamage Abacus Abacus Illustration Illustration Description Description

SeparationSeparation of of the the north-west north-west façade façade from the fromlateral the walls lateral in proximity walls in of proximity the corner, of GlobalGlobal overturning overturning of of thebecause corner, of the because insufficient of the connection insufficient between thethe façade façade connectionorthogonal walls between and between orthogonal walls walls and andfloors. between walls and floors.

Vertical overturning of the north-east façade, with corner expulsion. This out-of-plane Partial overturning mechanism, with provides local failures of the with diagonal rotation upper part of the walls and collapse, is due to axis the stress concentrations that occur at the intersection of transverse walls and to the presence of large openings.

Cracks in the façades: • X-shaped shear cracks Shear mechanism in • Central vertical crack or arched the façade plane cracks near the corner • Diagonal cracks (single and crossed) in masonry panels.

Buildings 2020, 10, x FOR PEER REVIEW 9 of 32 Buildings 2020, 10, x FOR PEER REVIEW 9 of 32 a marine museum, emergency wooden supports have been placed inside the building, just below the ceilings,a marine to museum, prevent theiremergency collapse, wooden and steel supports stay-rods have have been beenplaced fixed inside inside the building,the tower, just from below top theto bottom.ceilings, to prevent their collapse, and steel stay-rods have been fixed inside the tower, from top to bottom. Table 3. Classification of collapse mechanisms. Table 3. Classification of collapse mechanisms. Damage Abacus Illustration Description Damage Abacus Illustration Description

Separation of the north-west façade from the lateralSeparation walls ofin theproximity north-west of the façade corner, from the Global overturning of becauselateral wallsof the in insufficient proximity connectionof the corner, between Globalthe overturning façade of Buildings 2020, 10, 247 orthogonalbecause of wallsthe insufficient and between connection walls and between9 of 30 the façade floors.orthogonal walls and between walls and floors.

Table 3. Cont.

DamageBuildings Abacus 2020, 10, x FOR PEER REVIEW Illustration Description 10 of 32 VerticalVertical overturning overturning of the of thenorth-east north-east façade, Buildings 2020, 10, x FOR PEER REVIEW withfaçade,Vertical corner withoverturning expulsion. corner of expulsion.This the out-of-planenorth-east10 of 32façade, Partial overturning mechanism,Thiswith out-of-planecorner with expulsion. provides mechanism, This local out-of-plane failures of the PartialwithPartial diagonal overturning overturning rotation upperwithmechanism, providespart of withthe local walls provides failures and collapse,local of failures the is due of tothe withwith diagonal diagonalaxis rotation theupperupper stress part concentrations of of the the walls walls and that and collapse, occur collapse, at theis due to rotationaxis axis intersectionisthe due stress to theconcentrations of stresstransverse concentrations wallsthat occur and to at the thatthe presenceoccurintersection at of the large of intersection transverse openings. walls of transverse and to the wallspresence and of to large the openings. presence of large openings. Buildings 2020, 10, x FOR PEER REVIEW 10 of 32 Cracks in the façades: Cracks in the façades: Cracks• X-shaped inX-shaped the façades: shear shear cracks cracks • Vertical, horizontal, and diagonal thin cracks Shear mechanism in Vertical, horizontal,• •Central CentralX-shaped and vertical vertical diagonal shear crack crack cracksthin or cracksor arched arched Shear mechanismOverturning inof the • in the four sides of the tower, due to long-term SheartheOverturning façade mechanism plane of thein in the four•cracks sides cracksCentral of nearthe neartower, vertical the the cornerdue corner crackto long-term or arched the façadetower plane top compressive actions and seismic bending the façadetower plane top compressive• Diagonal actionsDiagonalcracks and cracks near seismiccracks the (single bending(singlecorner and and crossed) • actions. actions. •crossed) inDiagonal masonry in masonry cracks panels. (single panels. and crossed) in masonry panels.

Vertical,Vertical, horizontal,horizontal, and and diagonal diagonal thin thin cracks OverturningOverturning of theof the cracksin the four in the sides four of sidesthe tower, of the due tower, to long-term towertower top top duecompressive to long-term actions compressive and seismic actionsbending andactions. seismic bending actions.

Shear cracks of the Diagonal and vertical cracks in the inner internal walls partition walls. Shear cracksShear cracks of the of the DiagonalDiagonal and and vertical vertical cracks cracks in the inner internalinternal walls walls innerpartition partition walls. walls.

CracksCracks in the invaults. the Pa vaults.rtial expulsion Partial of expulsion the Floor damageFloor damage upperof story the upperand detachment story and of steel detachment IPN of Shear cracks of the beamssteelDiagonal from IPN side beamsand walls. vertical from cracks side walls.in the inner Cracks in the vaults. Partial expulsion of the internal walls partition walls. Floor damage upper story and detachment of steel IPN beams from side walls.

5.2. Numerical Analyses 5.2. Numerical Analyses Presently, no in situ investigation campaign has been conducted on the structures of the Bengut Presently, no in situ investigation campaign has been conducted on the structures of the Bengut Lighthouse for identifying the mechanical properties of in situ materials. It should be remembered Lighthouse for identifying the mechanical properties of in situ materials. It should be remembered 5.2. Numerical Analyses that thethat evaluation the evaluation of seismic of seismic behavior behavior of of masonrymasonry structures structures is extremely is extremely complex complex and relies and on relies the on the possibilitypossibilityPresently, of of retrieving retrieving no in situ specific specific investigation and and accurate accurate campaign inform informationation has aboutbeen about eachconductedCracks eachcase in thestud case on vaults.y: the study:unfortunately, Pastructuresrtial unfortunately, expulsion ofthis theof the Bengut this isLighthouseis often oftenFloor very verydamage di fordifficultffi cultidentifying because because the ofof thethe mechanical costcost and invasiveness invasivenessproperties of of investigationsin investigations uppersitu materials.story and and detachment and testsIt should tests aimed aimedof steelbe at rememberedthe IPN at the beams from side walls. classificationthatclassification the of evaluation the of mechanical the mechanical of seismic properties properties behavior of of materials of materi masonryals and and structures knowledgeknowledge is ofextremely of the the structural structural complex details. details. and In therelies In the on the practice, it is almost impossible to perform extensive and detailed destructive tests, less destructive practice,possibility it is almost of impossibleretrieving specific to perform and extensive accurate andinform detailedation destructiveabout each tests, case lessstud destructivey: unfortunately, tests this tests such as flat-jack tests are not reliable for many ancient masonry typologies, the simple such asis flat-jack often very tests difficult are not reliablebecause for of many the cost ancient and masonryinvasiveness typologies, of investigations the simple relationshipsand tests aimed that at the relationships that extend the experimental properties of blocks and mortars to the whole masonry, classificationwhich are provided of the for mechanical new masonry properties buildings, of are materi not valid.als and knowledge of the structural details. In the practice, it is almost impossible to perform extensive and detailed destructive tests, less destructive 5.2. Numerical Analyses tests such as flat-jack tests are not reliable for many ancient masonry typologies, the simple relationshipsPresently, nothat in extend situ investigation the experimental campaign properti has beenes of conductedblocks and on mortars the structures to the whole of the masonry,Bengut Lighthousewhich are forprovided identifying for new the masonry mechanical buildings, properties are notof in valid. situ materials. It should be remembered that the evaluation of seismic behavior of masonry structures is extremely complex and relies on the possibility of retrieving specific and accurate information about each case study: unfortunately, this is often very difficult because of the cost and invasiveness of investigations and tests aimed at the classification of the mechanical properties of materials and knowledge of the structural details. In the practice, it is almost impossible to perform extensive and detailed destructive tests, less destructive tests such as flat-jack tests are not reliable for many ancient masonry typologies, the simple relationships that extend the experimental properties of blocks and mortars to the whole masonry, which are provided for new masonry buildings, are not valid. Buildings 2020, 10, 247 10 of 30 extend the experimental properties of blocks and mortars to the whole masonry, which are provided for new masonry buildings, are not valid. In the case of existing masonry buildings, the approach of the Italian code [40], which will be here followed, is to define a reference set of historical masonry types associated with specific range of variation (based on past experience and technical knowledge) and using both qualitative and experimental investigations for choosing the appropriate class and the value within the interval, also accounting for the factors of degradation of materials or, on the contrary, of reinforcement. Especially in the case of monumental buildings that have very peculiar features, a very effective approach would be the application of dynamic monitoring and structural identification procedures [41–44], to calibrate the parameters of the numerical models to be used in the verifications. Anyway, it is important to observe that the objective of this study is not to perform a technical assessment for determining a safety level, but to define a general methodological framework for the seismic modeling of historical lighthouse, focusing the main aspects influencing seismic vulnerability (morphology, typology, construction quality, conceptual design) and the significant damage modes. This is a fundamental basis on which in the operational phases, then, it will be possible to assess the final effect of the variability of mechanical parameters (which for historical masonry is particularly high) by means of wide sensitivity analyses. In view of the numerical modeling and analysis, it was necessary to assume a range of reference for the mechanical parameters of materials. It is worth observing that in Algerian building codes there is no specific provision regarding the verification of existing buildings or the design of URM buildings [45]. Even after the 2003 Boumerdès Earthquake, the recent Algerian seismic code RPA2003 has not taken into consideration these aspects. In the lack of indications given by local standards, it was decided to refer to the Italian Technical Standards NT2018 [41] both for the assumption of the reference values of the mechanical parameters of materials (Table4) and for the application of the non-linear static analysis.

Table 4. Reference average values adopted for the mechanical properties of masonry (E = Young modulus; G = shear modulus; W = specific weight).

Rubble Stone Cut Soft Stone Block Stone Min–Max Average Min–Max Average Min–Max Average E (N/mm2) 690–1050 870 900–1260 1080 2400–3200 2800 G (N/mm2) 230–350 290 300–420 360 780–940 860 W (kN/m3) 19 16 22

Based on available documentation and visual inspections, the types and quality of the masonry composing the structure of the Bengut Lighthouse have been classified. The main building provides the presence of a rubble stone masonry type, whereas the tower presents two different types: regular block stone in the lower part, light cut stone in the upper part. After the visual inspections and the evaluation of the quality of the different masonry types (based on geometry, in-plane and out-of-plane texture, homogeneity, qualitative appraisal of degradation) [46], the masonry walls of the main building have been classified within the range “poor”-“bad”, whereas those of the tower, which exhibit much more homogeneity and with masonry quality, have been classified as “good”. Considering the type of masonry and the level of quality detected, the reference ranges and average values reported in Table4 have been assumed for the numerical models. The choice of the ranges has been based on Table C8A.2.1C8.5.I contained in the Italian Circular of NT 2008 [47] and the typical values adopted in the scientific literature [16,17,19–21,36]. Regarding the seismic hazard, the response spectrum analysis has been performed referring to the RPA2003 [34]: Buildings 2020, 10, x FOR PEER REVIEW 11 of 31

BuildingsRegarding2020, 10the, 247 seismic hazard, the response spectrum analysis has been performed referring11 of 30 to the RPA2003 [34]:

• By followingBy following the theclassification classification table table of of RPA2003, RPA2003, thethe BengutBengut Lighthouse Lighthouse is classifiedis classified as a as building a building • of greatof great importance importance (group (group 1B). 1B). • It is in a high seismic hazard region (zone III), in which PGA is 0.3 g. •It is in a high seismic hazard region (zone III), in which PGA is 0.3 g. • The soil classification is “hard rock”—S12. •The soil classification is “hard rock”—S12. • A behavior factor R = 2 is assigned, by assuming the lowest class for existing URM buildings. •A behavior factor R = 2 is assigned, by assuming the lowest class for existing URM buildings. The quality factor “Q” of the structure defined by the Algerian code RPA 2003 depends on: • •The quality factor “Q” of the structure defined by the Algerian code RPA 2003 depends on: redundancy in plan, regularity both in plan and elevation, quality control and execution of redundancy in plan, regularity both in plan and elevation, quality control and execution of materials, and is Q = 1.35 for the building group 1B. materials, and is Q = 1.35 for the building group 1B. For the site of Bengut Lighthouse, the RPA03 response spectrum plotted in Figure5 is adopted • • For the(the site highest of Bengut acceleration Lighthouse, value is 0.483the RPA03 g = 4.83 resp m/s).onse spectrum plotted in Figure 5 is adopted (the highest acceleration value is 0.483 g = 4.83 m/s).

FigureFigure 5. RPA03 5. RPA03 Response Response Spectrum Spectrum for thethe SiteSite of of Bengut Bengut Lighthouse. Lighthouse.

The Thenon-linear non-linear macro-element macro-element model model (NLM) (NLM) approach approach usedused TreMuri TreMuri computer computer code code [39, 48[39,48,49],49] is based on the original formulation by Gambarotta and Lagomarsino [50]. The 3D model of Bengut is based on the original formulation by Gambarotta and Lagomarsino [50]. The 3D model of Bengut Lighthouse implemented within TreMuri is presented in Figure6. The numerical model is composed Lighthouse implemented within TreMuri is presented in Figure 6. The numerical model is composed of three types of macro-elements: pier elements, spandrel elements and rigid nodes (213 elements, of three76 rigidtypes nodes, of macro-elements: that are rigid elements pier elements, connecting spandrel the resisting elements elements and rigid “pier” nodes and (213 “spandrels”). elements, 76 rigidThe nodes, mass that of the are lantern rigid ofelements the cupola connecting is modeled th ase aresisting dead load elements (16.21 kN “pier”/m2). and “spandrels”). The mass of the lantern of the cupola is modeled as a dead load (16.21 kN/m2).

Buildings 2020, 10, 247 12 of 30 Buildings 2020, 10, x FOR PEER REVIEW 12 of 31

Figure 6. The non-linear macro-element model (NLM) of the Bengut Lighthouse implemented in Figure 6. The non-linear macro-element model (NLM) of the Bengut Lighthouse implemented in TreMuri computer code. TreMuri computer code.

5.2.1. Preliminary Modal Analysis The seismic vulnerability study of the Bengut Li Lighthouseghthouse has been carri carrieded out by performing, first,first, a preliminary modal analysis to assess the dynamicdynamic behavior of the structure and the potential damage modes. This analysis is useful to verify the consistency of the assumptions made in terms of material parameters and connections with respectrespect toto thethe generalgeneral damagedamage modesmodes observedobserved [[51,52].51,52]. It is worthwhile remembering that the current Al Algeriangerian legislation RPA 2003 [[34]34] definesdefines for the mass participation a limit value equal to 90% in bothboth directionsdirections XX andand YYin in cases of existing and new buildings. In In the the Italian Italian [40] [40] and European Codes [53], [53], the application of linear dynamicdynamic analysis requires considering severalseveral modesmodes thatthat activatesactivates atat leastleast 85%85% ofof thethe participatingparticipating mass.mass. Table5 5 reports reports the the first first 12 12 vibration vibration modes modes provided provided by by the the modal modal analysis: analysis: thethe participating participating masses in directions X and Y reaches the values 95.23% and 95.97%, respectively, before the 12th vibration mode. By looking at the results of the modal analysis, we can observe that the 1st and the 6th vibration modes are translational along X, with a period respectively of 1.22 s and 0.34 s, with a participating mass of 42.28% for the 1st mode and 34.09%34.09% the 6th6th one.one. The 2nd and the 5th modal forms are translational along Y and involve a participating mass respectively of 47.82% and 41.09%, with a periodperiod of 1.211.21 ss andand 0.370.37 s.s. TheThe 11th11th modalmodal formform isis torsional,torsional, withwith 55.05%55.05% participatingparticipating mass along Z directions. It should be noted that the 3rd, 4th, 8th and 10th 10th vibration vibration modes are translational along X, with a very small mass participation, andand represent locallocal modes.modes. All the other modal forms show a small and negligible participating mass. As a general comment we can say that the results of the modalmodal analysis,analysis, withwith thethe presence presence of of low low participating participating mass mass in in the the first first translational translational modes modes and and of aof relevant a relevant torsional torsional mode, mode, point point out that out athat regular a re behaviorgular behavior cannot becannot clearly be recognized,clearly recognized, as typically as encounteredtypically encountered for masonry for buildings masonry which buildings are not which simple are and not regular simple in planand andregular in elevation. in plan Fromand in a physicalelevation. point From of a view,physical this point means of thatview, under this me theans earthquake that under the the response earthquake of the the building response will of the be stronglybuilding awillffected be strongly by additional affected torsional by additional effects, torsional which can effects, be particularly which can dangerous be particularly for the dangerous masonry walls,for the both masonry in terms walls, of additionalboth in terms in-plane of additional bending in-plane and shear bending and in and terms shear of out-of-planeand in termsstresses. of out-of- plane stresses.

Table 5. Results of the modal analysis for the first 12 modes (natural period—T, mass x—mx,

participating mass along x—Mx, mass y—my, participating mass along y—My, mass z—mz, participating mass along z—Mz).

Mode T (s) mx (kg) Mx (%) my (kg) My (%) mz (kg) Mz (%) 1 1.22975 1281492 42.28 2 0.00 0 0.00 2 1.21589 2 0.00 1449487 47.82 1 0.00 3 0.79637 20245 0.67 0 0.00 0 0.00 4 0.43207 31977 1.05 3 0.00 0 0.00 Buildings 2020, 10, 247 13 of 30

Table5. Results of the modal analysis for the first 12 modes (natural period—T, mass x—mx, participating mass along x—Mx, mass y—my, participating mass along y—My, mass z—mz, participating mass along z—Mz).

Mode T (s) mx (kg) Mx (%) my (kg) My (%) mz (kg) Mz (%) 1 1.22975 1,281,492 42.28 2 0.00 0 0.00 2 1.21589 2 0.00 1,449,487 47.82 1 0.00 3 0.79637 20,245 0.67 0 0.00 0 0.00 4 0.43207 31,977 1.05 3 0.00 0 0.00 5 0.37531 2 0.00 1,245,551 41.09 22 0.00 6 0.34775 1,033,403 34.09 4 0.00 0 0.00 7 0.31534 258,212 8.52 1 0.00 0 0.00 8 0.28018 87,862 2.90 0 0.00 4 0.00 9 0.25022 0 0.00 213,320 7.04 0 0.00 10 0.23033 153,386 5.06 0 0.00 1,668,540 0.00 11 0.20577 0 0.00 610 0.02 - 55.05 12 0.20502 20,023 0.66 0 0.00 - 0.00 Σ - - 95.23 - 95.97 - 55.05

5.2.2. Pushover Analysis The computational model of the structure has been loaded with a proper distribution of lateral loads that are gradually increased with the aim of “pushing” the structure into the non-linear field. In each direction, two profiles of lateral loads have been used: a pattern that represents lateral forces proportional to masses (uniform acceleration distribution)—LP-masses—and a modal pattern proportional to the first modal shape—LP-1st mode. The control node is placed at the corner of the top section of the tower (see Figure6). The value of the horizontal displacements of this node is used to trace the capacity curves. In Figures7 and8, capacity curves in the X and +Y directions, considering both the load profile − proportional to the masses (LP-masses) and the load profile proportional to the first modal shape (LP-1st modal shape), are reported. In the plot, the ultimate displacement Du and the equivalent bilinear curve are also displayed. The damage state in the structure walls is depicted in Figure9a,b and Figure 10a,b. The capacity curve (a) obtained in X direction with the load profile proportional to masses shows that the structure − has mainly an elastic response, with an ultimate displacement Du = 6.78 cm. In Figure9a, it is possible to observe that the damage concentration is approximately symmetric on the East and a West side of the building and the main façade (P1, P11 and P3): a concentration of shear damage is located at the corner of the wall P3 (between P2 and P3, P4). The formation of a shear failure at the base and at the areas in contact with the tour (walls: P1, P11) can be observed. The bending damages are located at the corner of the walls P1 and P11. The piers of the openings at the walls P1, P11, and P3 develop a bending and compression failures. In the tower, the wall P12 fails for the formation of a shear hinge near the base and in the central part near the openings. A compressive failure appears in the walls P5 and P12. Buildings 2020, 10, x FOR PEER REVIEW 13 of 31

5 0.37531 2 0.00 1,245,551 41.09 22 0.00 6 0.34775 1033403 34.09 4 0.00 0 0.00 7 0.31534 258212 8.52 1 0.00 0 0.00 8 0.28018 87862 2.90 0 0.00 4 0.00 9 0.25022 0 0.00 213320 7.04 0 0.00 10 0.23033 153386 5.06 0 0.00 1,668,540 0.00 11 0.20577 0 0.00 610 0.02 - 55.05 12 0.20502 20023 0.66 0 0.00 - 0,00 Σ - - 95.23 - 95.97 - 55.05

5.2.2. Pushover Analysis The computational model of the structure has been loaded with a proper distribution of lateral loads that are gradually increased with the aim of “pushing” the structure into the non-linear field. In each direction, two profiles of lateral loads have been used: a pattern that represents lateral forces proportional to masses (uniform acceleration distribution)—LP-masses—and a modal pattern proportional to the first modal shape—LP-1st mode. The control node is placed at the corner of the top section of the tower (see Figure 6). The value of the horizontal displacements of this node is used to trace the capacity curves. In Figures 7 and 8, capacity curves in the -X and +Y directions, considering both the load profile proportional to the masses (LP-masses) and the load profile proportional to the first modal shape Buildings(LP-1st 2020modal, 10, 247shape), are reported. In the plot, the ultimate displacement Du and the equivalent14 of 30 bilinear curve are also displayed.

FigureFigure 7. Plots 7. ofPlots the capacity of the capacity curves, curves,corresponding corresponding equivalent equivalent bilinear curves, bilinear and curves, maximum and maximum available displacementavailable D displacementu. (a) Pushover D uin.( -Xa) Pushoverdirection, inLP-masses.X direction, (b) +Y LP-masses. direction,( LP-masses.b) +Y direction, LP-masses. −

Figure 8. Plots of the capacity curves with the corresponding equivalent bilinear curves and maximum available displacement Du.(a) Pushover in X direction, LP-masses. (b) +Y direction, LP-masses. −

1

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Figure 9. Damage state of the main walls in X andand YY directions:directions: (a)) DamageDamage statestate inin thethe -XX direction, direction, − LP-masses. ( b) +Y+Y direction, direction, LP-masses. LP-masses. Buildings 2020, 10, 247 16 of 30 Buildings 2020, 10, x FOR PEER REVIEW 16 of 31

(a)

(b)

FigureFigure 10. 10. DamageDamage state state of of the the main main walls walls in in X Xand and Y Ydirections: directions: (a ()a Damage) Damage state state in in the the -X Xdirection, direction, − LP-1stLP-1st mode. mode. (b ()b +Y) + Ydirection, direction, LP-1st LP-1st mode. mode.

InThe Figure capacity 9a, it curve is possible in the to+Y observe direction that proportional the damage to concentration masses is shown is approximately in Figure8b and symmetric shows that onthe the structure East and has a West an elastic-plastic side of the building response and with the an main ultimate façade displacement (P1, P11 and of 5.37P3): cm.a concentration The localization of shear damage is located at the corner of the wall P3 (between P2 and P3, P4). The formation of a shear failure at the base and at the areas in contact with the tour (walls: P1, P11) can be observed. The Buildings 2020, 10, x FOR PEER REVIEW 17 of 31 bending damages are located at the corner of the walls P1 and P11. The piers of the openings at the walls P1, P11, and P3 develop a bending and compression failures. In the tower, the wall P12 fails for the formation of a shear hinge near the base and in the central part near the openings. A compressive Buildingsfailure appears2020, 10, 247 in the walls P5 and P12. 17 of 30 The capacity curve in the +Y direction proportional to masses is shown in Figure 8b and shows that the structure has an elastic-plastic response with an ultimate displacement of 5.37 cm. The of the shear damage is mainly visible on the walls P6 and P13 along the height of the tower and on localization of the shear damage is mainly visible on the walls P6 and P13 along the height of the the building wall (areas in contact with the tower). The shear damage is concentrated at the base tower and on the building wall (areas in contact with the tower). The shear damage is concentrated of the walls P2 and P13. In the case of load acting in +X direction proportional to the first mode, at the base of the walls P2 and P13. In the case of load acting in +X direction proportional to the first the capacity curve (c) shows an elastic-plastic trend. The ultimate displacement D is found to be mode, the capacity curve (c) shows an elastic-plastic trend. The ultimate displacementu Du is found to higher than other directions: Du = 8.19 cm. A shear failure is evident in the central area of the walls be higher than other directions: Du = 8.19 cm. A shear failure is evident in the central area of the walls P5 and P12 of the tower. The formation of compressive failure in the piers of the tower can also be P5 and P12 of the tower. The formation of compressive failure in the piers of the tower can also be observed. The building’s walls P1 and P11 develop shear failure in the corner near the tower and observed. The building’s walls P1 and P11 develop shear failure in the corner near the tower and bending damage in the other one. bending damage in the other one. The curve corresponding to the Y direction proportional to the first mode (Figure9b) is also The curve corresponding to the −-Y direction proportional to the first mode (Figure 9b) is also elastic-plastic with an ultimate displacement Du = 5.54 cm. The damage map at the end of the analysis elastic-plastic with an ultimate displacement Du = 5.54 cm. The damage map at the end of the analysis is basically the same as the one in +Y direction proportional to masses. It is possible to observe the is basically the same as the one in +Y direction proportional to masses. It is possible to observe the formation of shear failure on the walls P1 and P11 at the corner. However, most of the shear failures formation of shear failure on the walls P1 and P11 at the corner. However, most of the shear failures are located, as expected, in the central part of tower and the base of the wall building (P6 and P13). are located, as expected, in the central part of tower and the base of the wall building (P6 and P13). It is worth noting that the results provided by the pushover analyses in terms of in-plane damage It is worth noting that the results provided by the pushover analyses in terms of in-plane damage pattern is in a good agreement with the actual distribution of cracks observed after post-earthquake pattern is in a good agreement with the actual distribution of cracks observed after post-earthquake surveys (Figure4 and Table3). Anyway, not all the post-earthquake damage observed in the surveys surveys (Figure 4 and Table 3). Anyway, not all the post-earthquake damage observed in the surveys are captured by the numerical analyses, especially in the building, which exhibits significant damage are captured by the numerical analyses, especially in the building, which exhibits significant damage modes related to local out-of-plane collapse mechanisms that cannot be captured by the global pushover modes related to local out-of-plane collapse mechanisms that cannot be captured by the global analysis. The activation of local out-of-plane mechanisms is evident by looking at the actual cracks, pushover analysis. The activation of local out-of-plane mechanisms is evident by looking at the actual as shown in Figure 11, which points out the presence of tree main local failure mechanisms: (a) Global cracks, as shown in Figure 11, which points out the presence of tree main local failure mechanisms: overturning of the right back façade, (b) Partial overturning of the left back façade; (c) Overturning of (a) Global overturning of the right back façade, (b) Partial overturning of the left back façade; (c) the tower top. Overturning of the tower top.

FigureFigure 11. 3d3d sketches sketches of of the the failure failure mechanisms: mechanisms: (a) ( aGlobal) Global overturning overturning of the of the right right back back façade, façade, (b) (Partialb) Partial overturning overturning of the of theleft left back back façade; façade; (c) (Overturningc) Overturning of the of the tower tower top. top. 6. Proposal of Retrofitting Solutions for the Bengut Lighthouse 6. Proposal of Retrofitting Solutions for the Bengut Lighthouse 6.1. A Literature Review of Seismic Repair and Retrofitting for Masonry Structures 6.1. A Literature Review of Seismic Repair and Retrofitting for Masonry Structures The seismic repair and retrofitting of damaged masonry buildings require specific training and The seismic repair and retrofitting of damaged masonry buildings require specific training and multi-disciplinary approach based on theoretical background and experimental basis. multi-disciplinary approach based on theoretical background and experimental basis. As can be found in the literature review, seismic retrofitting techniques for masonry structures have been widely developed and practiced in recent decades. The first guidelines for the earthquake resistance of non-engineered constructions were published in 1986 by the International Association for Earthquake Engineering IAEE. Then, a series of documents on the assessment and strengthening was Buildings 2020, 10, 247 18 of 30 issued by the United States federal emergency management agency (FEMA). The reference European standards for the assessment for earthquake resistance and retrofitting of masonry structures are the Eurocode 6 [53] and Eurocode 8 [54]. Among national codes, the Italian NTC 2018 [41] presents the most comprehensive approach about retrofitting of masonry structures. To prevent collapse under future seismic events, existing masonry buildings often require the implementation of adequate strengthening solutions aimed at enhancing their seismic response and, in general, the global structural performance. The present conditions of the Bengut Lighthouse are quite severe, and the vulnerability analysis carried out confirmed the visual evaluation, with a possible collapse of the tower. Therefore, the design of retrofitting interventions is an urgent step to be taken. The proposal of retrofitting solutions for the Bengut Lighthouse is based first on the analysis of the morphological and constructive aspects discussed in Section4, whereas specific guidelines are derived by the diagnosis of collapse mechanisms presented in Section 5.1 and by the results of non-linear static analysis discussed in Section 5.2. The reference technical law is the Algerian seismic code—recommendations RPA—and integrative orientations are provided by Eurocode 6 [53] about masonry structures. Regarding the approach to restoration, important references are the historic lighthouse preservation handbook [55] and several research studies reporting the techniques of retrofitting and structural strengthening schemes for masonry buildings [18,52,56–62]. These documents present some significant recent examples that illustrate interventions of retrofitting and repairing for masonry towers: the Monza cathedral belltower in Italy; the Church of Santa Maria Maggiore in Mirandola in Italy; the Church of Saint Christ in Outeiro in the North of Portugal and several American lighthouses: block island Southeast Lighthouse, cape Florida Lighthouse, and the Great Mosque of Dellys in Algeria. The general framework is that of seismic retrofitting of existing buildings. Anyway, it should be remembered that any structural intervention on h buildings should respect as much as possible the original materials, construction techniques, and historical character of the structure. It is worth remembering, according to the fundamental principles of restoration, that the approach should provide at the same time effectiveness and minimum degree of invasiveness, maximum compatibility, and reversibility of the repair intervention. More exhaustive concepts and guidelines about the conservation and restoration of historical masonry buildings can be found in the different restoration charters (Venice, Athens, etc.) [63–65]. The choice of guidelines for the structural strengthening interventions on the Bengut Lighthouse will be supported by a numerical seismic re-evaluation to appraise the effectiveness of the adopted solutions on the global seismic behavior of the building. The proposed strengthening techniques have been modeled in a new numerical model and analyzed in terms of natural periods and vibration modes, ultimate displacements, and damage patterns.

6.2. Suggestions for Seismic Retrofitting Techniques The general scheme of the repair and retrofitting proposed for the Bengut Lighthouse is described in Figures 12 and 13. Two principal kind of structural techniques, acting both at a local and global level, are proposed to improve the structural stability and the seismic behavior of the building. In the reference scientific literature, these structural solutions are considered to be particularly adequate for masonry towers and can be classified as follows: Retrofitting techniques aimed at restoring the initial seismic behavior of the structure To guarantee the continuity in the transmission of vertical loads under seismic excitation, the interventions suggested for repairing walls and floors are: rebuilding the collapsed parts of the north-east façade; reconstructing the collapsed part of the upper story; repairing the passing cracks; applying repointing technique to walls and substituting damaged stone (Figure 12[ 18,56,57,59,60,66]). More in detail: Buildings 2020, 10, 247 19 of 30

The collapsed part of the north-east façade shall be reconstructed by using materials with • mechanical characteristics similar to the original ones. The objective of this intervention is only to restore the restore the original bearing capacity of the damaged parts. The partial collapse of the roof has caused severe degradation to the whole structure because of • water infiltration, humidity and corrosion of the steel IPE beams, and is a very urgent intervention to be taken. Therefore, the collapsed part of the floor will be rebuilt using bricks similar to the original ones and the steel IPE beams detached from the collapsed wall will be replaced with new ones and anchored to the supporting walls. The masonry on both sides of passing cracks will be disassembled, restoring the gaps using stones • of the same original material, stainless metal staples, and oblique mortar injections (Figure 12a). This technique is known “indenting” (“cuci e scuci” in Italy). The mortar joints damaged by superficial cracks or infested by plant roots plants will be cleaned • with compressed air and stripped to a depth of 3 cm, then moistened, and finally a liquid mortar will be introduced under pressure till the complete filling of vacuum (Figure 12b). The compatibility of the repointing mortars with the existent ones is a fundamental condition to assure the proper effectiveness of this intervention.

Retrofitting techniques to improve the structural stability and the seismic behavior of the building

The most important provision to be taken consists of creating a seismic joint between the tower • and the rest of the main building walls. According to RPA recommendations, if two neighboring structures have a steep difference in height, they should be separated by a seismic joint whose minimum displacement dmin satisfies the following condition:

d = 15 mm + (δ + δ ) mm 40 mm (1) min 1 2 ≥ δ1 and δ2 respectively represent the maximum displacements of the main building and of the tower at the roof. Buildings 2020, 10, x FOR PEER REVIEW 19 of 31

Figure 12. North façade of the Bengut Lighthouse with the location of the different types of the Figure 12. North façade of the Bengut Lighthouse with the location of the different types of the reinforcing interventions: (a) Repair of passing cracks; (b) Repointing technique. reinforcing interventions: (a) Repair of passing cracks; (b) Repointing technique.

Buildings 2020, 10, x FOR PEER REVIEW 19 of 31

Buildings 2020Figure, 10, 24712. North façade of the Bengut Lighthouse with the location of the different types of the 20 of 30 reinforcing interventions: (a) Repair of passing cracks; (b) Repointing technique.

Figure 13. Plan view of the Bengut Lighthouse with the different types of the reinforcing interventions and details of the: (a) Seismic joint; (b) Strengthening the tower corners; (c) Location of the reinforcing rings; (d) Reinforcing the brick vault; (e) Reinforcing the flat formed vault; (f) Strengthening the building corner; (g) Increasing the interior walls thickness.

This kind of interventions is surely advisable in the theory, but the operational execution could be difficult. Indeed, we propose that the original tower walls are preserved, whereas in the main building walls are rebuilt to properly support the floors and ensure the box-like behavior of the structure (Figure 13). The foundation of this new wall will be eccentric to preserve the original foundations (Figure 13a). The seismic joint between the original and new walls is calculated from Equation (1): dmin = 40 cm (the displacements δ1 = 2.48 cm, δ2 = 9.84 cm are deduced from the pushover analyses of the two separated structures). A second important intervention to improve the structural behavior of the tower is the reinforcing • of the four tower sides. This technique consists of inserting a series of horizontal stainless steel reinforcing rings all along the height of the tower Figure 13b, to confine the masonry, improve the connection between the orthogonal walls at the corners and assure the box-like behavior of the tower under seismic loads [18]. The position of the rings depends on the damages detected and the structural configuration. They are provided at three levels in the tower walls (Figure 13c): the first series will be inserted at a height of 7.50 m. The choice of reinforcing at this level is due to the proximity of the first floor of the building. The second series will be placed at a height of 15 m, since this zone, located between the openings, is already cracked, and its seismic vulnerability has been confirmed by the pushover analysis. The last series will be placed at the height of 26.50 m due to the presence of a flat vault at this level, to reinforce the connection between walls and floor. Buildings 2020, 10, 247 21 of 30

The structural reinforcement of the floors is another important provision. The interventions will • be applied both on the brick vault of the building and on the flat formed vault of the tower. Additional steel IPE beams will be screwed on the bottom part of the vaulted floor and will be anchored to the walls in a perpendicularly direction to the original IPE beams (Figure 13d) [57]; a diaphragm solution is proposed for the flat formed vault at the height of 26.50 m, consisting of a structure of steel elements and tie rods (Figure 13e) anchored in the exterior of the tower [18]. For guaranteeing the box-like behavior of the main building, the suggested intervention is the • improvement of corner chaining, since the actual connection between the blocks in the external orthogonal walls is insufficient. The corner stone blocks will be dismantled and substituted with new ones of same nature and dimensions (50 cm 70 cm 30 cm), as shown in Figure 13f. × × An additional intervention is proposed for guaranteeing the structural stability of interior walls • and increasing their tensile strength, shear strength, and ductility. This technique has been largely applied in Italy. It consists first in jacketing the existing wall on both faces with wire meshes joined together by transversal steel ties, then in the application of a thick mortar layer on both faces. Overall, the thickness of the wall will be increased from 40 cm to 50 cm (Figure 13g) [56,57,60].

6.3. Seismic Re-Evaluation For each strengthening solution proposed to the Bengut Lighthouse structure, it is important to check the structural effectiveness. This was supported by a modal analysis to estimate the new dynamic characteristics of the structure—natural periods and vibration modes of the two separated structures with the seismic joint—and a non-linear static analysis (pushover), for checking the new capacity curve and the damage state of the walls. Table6 shows the first three vibration modes of the original structure and those of the two separated structures (tower and main building). From the comparative analysis, the following conclusions can be derived:

The principal modes of the tower are similar to those of the original configuration, but with a • strong increase in the participating masses. The 1st mode is translational along the direction X, the 2nd translational along the direction Y, and they have a comparable participating mass over 70%. The 3rd mode has very small mass participation and is a local mode. The mass participation is increased by approximately 30.57% and 25.43% in the 1st and 2nd mode, respectively. Also, the main building, in the new configuration, has much higher values of the translational • participating masses (over 90%). The 1st mode is translational along Y, the 2nd is a local mode with a very small mass participation and the 3rd is translational along X. The mass participation is increased by 50.01% in the X direction and 42.96% in Y direction.

As expected, the high irregularity of the structural compound, which was clearly highlighted by the low participating mass of the translational modes and by the presence of a relevant torsional rotation (Mz) is sanitized if the buildings are separated by a seismic joint. To evaluate the efficiency of retrofitting solutions on the structural response of the tower and the main building, the capacity curves obtained by the pushover analysis for the two separate structures—tower and main building—are presented in Figure 14. The control nodes are chosen at the highest level (the average of all floor’s nodes is performed) and the load profiles are proportional to the masses and proportional to the first mode along X and Along Y (the worst situation is then selected and plotted). In Figures 15 and 16 the deformed configurations and damage states of the main structures along X and Y directions are depicted. Buildings 2020, 10, x FOR PEER REVIEW 22 of 31

Table 6. The first three natural modes (periods and mass participations) of the original structural compound), isolated tower, and isolated main building. The participating masses corresponding to the first three modes along x and y are highlighted in bold.

- 1st Mode 2nd Mode 3rd Mode T(s): 1.22 T(s): 1.21 T(s): 1.79 Mx (%): 42.28 Mx (%): 0.00 Mx (%): 0.67 Original structure My (%): 0.00 My (%): 47.82 My (%): 0.00 Mz (%): 0.00 Mz (%): 0.00 Mz (%): 0.00 T(s): 1.35 T(s): 1.34 T(s): 1.90 Buildings 2020, 10, 247 22 of 30 Mx (%): 72.85 Mx (%): 0.04 Mx (%): 0.04 Tower Table 6. The first three natural modesMy (%): (periods 0.04 and massMy (%): participations) 73.25 My of the (%): original 0.00 structural compound, isolated tower, and isolatedMz main(%): building.0.00 The Mz participating(%): 0.00 masses Mz (%): corresponding 0.00 to the first three modes along x and y are highlighted in bold. T(s): 0.43 T(s): 0.33 T(s): 0.30 - 1stMx Mode (%): 0.00 Mx 2nd (%): Mode 1.78 Mx (%): 3rd 92.29 Mode Main building T(s): 1.22 T(s): 1.21 T(s): 1.79 My (%): 90.78 My (%): 0.00 My (%): 0.00 Mx (%): 42.28 Mx (%): 0.00 Mx (%): 0.67 Original structure Mz (%): 0.01 Mz (%): 0.00 Mz (%): 0.00 My (%): 0.00 My (%): 47.82 My (%): 0.00

Mz (%): 0.00 Mz (%): 0.00 Mz (%): 0.00 As expected, the high irregularity of the structural compound, which was clearly highlighted by T(s): 1.35 T(s): 1.34 T(s): 1.90 the low participating mass of the translational modes and by the presence of a relevant torsional Mx (%): 72.85 Mx (%): 0.04 Mx (%): 0.04 rotation (Mz) is sanitizedTower if the buildings are separated by a seismic joint. M (%): 0.04 M (%): 73.25 M (%): 0.00 To evaluate the efficiency of retrofittingy solutions ony the structural responsey of the tower and the main building, the capacity curvesMz (%): obtained 0.00 by the Mz (%): pushover 0.00 analysis Mz (%):for 0.00the two separate structures—tower and main building—areT(s): 0.43 presented in T(s):Figure 0.33 14. The control T(s): nodes 0.30 are chosen at M (%): 0.00 M (%): 1.78 M (%): 92.29 the highest levelMain (the building average of all floor’sx nodes is performed)x and the load profilesx are proportional to the masses and proportional to Mthey (%): first 90.78 mode alongM Xy (%): and 0.00 Along Y (the My worst(%): 0.00 situation is then selected and plotted). In Figures 15M andz (%): 16 0.01 the deformed Mz (%): configurations 0.00 and Mz (%): damage 0.00 states of the main structures along X and Y directions are depicted.

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Figure 14. Cont.

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Figure 14. Cont. Buildings 2020, 10, 247 24 of 30 Buildings 2020, 10, x FOR PEER REVIEW 24 of 31

FigureFigure 14. 14. PlotsPlots ofof the the capacity capacity curves, curves, with thewith corresponding the corresponding equivalent equivalent bilinear curves bilinear and maximum curves and

maximumavailable available displacement displacement Du.(a) Pushover Du. ( ofa) thePushover tower. ( bof) Pushover the tower. of the (b) rectangular Pushover building: of the rectangular (a1,b1) In the X direction and LP-masses. (a ,b ) In the Y direction and LP-masses. (a ,b ) In the X direction building: (a1,b1) In the X direction and2 2LP-masses. (a2,b2) In the Y direction3 and3 LP-masses. (a3,b3) In and LP-1st mode (a4,b4) In the Y direction and LP-1st mode. the X direction and LP-1st mode (a4,b4) In the Y direction and LP-1st mode. Buildings 2020, 10, 247 25 of 30 Buildings 2020, 10, x FOR PEER REVIEW 25 of 31

FigureFigure 15. Damage 15. Damage state state of ofthe the main main wa wallslls in in X X and and Y directions: ( a(a)) Damage Damage state state of theof the tower tower walls. walls. (b) Damage(b) Damage state state of the of the rectangular rectangular building. building. ( a11,b1) In thethe X X direction direction proportional proportional to masses. to masses. (a3,b (3a) 3,b3) In theIn X the direction X direction proportional proportional to to the the first first mode. mode. The plots of the capacity curves and the deformed configurations presented in the figures show that the strengthening solutions are globally efficient. In the strengthened tower model, the displacement registered for the control node at the top of the tower attain a reduction of the approximately 10% on average along Y direction. The stress concentration occurred near the regions of the openings is reduced by comparing it with those in the original configuration. In the other direction, the capacity profiles show that the strengthening solutions have a slight increase of the displacement and the stress concentration in the vicinity of the openings is slightly reduced. This latter is due to the percentage of wall openings and the vulnerability of the tower to seismic action in this direction. Buildings 2020, 10, 247 26 of 30

Buildings 2020, 10, x FOR PEER REVIEW 26 of 31

Figure 16. Damage state of the main wa wallslls in X and Y directions: ( (aa)) Damage Damage state state of of the the tower tower walls. walls. ((b)) DamageDamage statestate ofof thethe rectangularrectangular building.building. ((aa22,,bb22) In the YY directiondirection proportionalproportional toto masses.masses. ((aa44,,b44) In the YY directiondirection proportionalproportional toto thethe firstfirst mode.mode.

The plots retrofitting of the capacity solutions curves significantly and the reducesdeformed the configurations displacement presented at the top in of the the figures rectangular show buildingthat the bystrengthening approximately solutions 30% in theare X globally direction, ef theficient. stress In distribution the strengthened throughout tower the wallmodel, façades the willdisplacement be more uniform registered and for the the damaged control area node is significantlyat the top of reduced the tower along attain this direction.a reduction However, of the aapproximately slight increase 10% of theon average displacement along Y along direction. the Y The direction stress isconcentration observed, the occurred concentration near the of regions stress isof slightlythe openings reduced is inducingreduced by local comparing damages. it Thiswith is those attributable in the original to the extensive configuration. length In of the wallsother anddirection, the high the percentagecapacity profiles of wall show openings that inthe this stre direction.ngthening It solutions is clear also have that a slight the low increase height of the buildingdisplacement relative and to the that stress of the concentration tower has a direct in the impact vicinity on of the the reduction openings of displacementis slightly reduced. percentage This andlatter stress is due concentration. to the percentage The plotsof wall of openings the capacity and curves the vulnerability and the deformed of the tower configurations to seismic presented action in inthis the direction. figures show that the strengthening solutions are globally efficient. In the strengthened tower model,The the retrofitting displacement solutions registered significantly for the control reduces node the at displacement the top of the towerat the attaintop of a reductionthe rectangular of the approximatelybuilding by approximately 10% on average 30% along in the Y X direction. direction, The the stress stress concentration distribution throughout occurred near the the wall regions façades of thewill openings be more isuniform reduced and by comparingthe damaged it witharea thoseis sign inificantly the original reduced configuration. along this In direction. the other However, direction, thea slight capacity increase profiles of the show displacement that the strengthening along the Y solutionsdirection haveis observed, a slight the increase concentration of the displacement of stress is slightly reduced inducing local damages. This is attributable to the extensive length of the walls and the high percentage of wall openings in this direction. It is clear also that the low height of the building relative to that of the tower has a direct impact on the reduction of displacement percentage Buildings 2020, 10, 247 27 of 30 and the stress concentration in the vicinity of the openings is slightly reduced. This latter is due to the percentage of wall openings and the vulnerability of the tower to seismic action in this direction.

7. Concluding Remarks Offshore lighthouses in Algeria are sometimes more than 150 years old, despite being in a region particularly prone to seismic hazard. They represent a very important element not only of the local historical architecture but also of a world historical patrimony that embodies in the maritime signals dedicated to navigation, the symbol of the history of explorations, and exchanges between peoples. In recent years, great attention has been paid to the theme of protection and conservation of lighthouses in several studies and research that combine architectural and historical aspects with the more technical issues of structural analysis. Within this framework, the paper deals with the study of a case which is representative of the maritime heritage of Algeria: the Cap Bengut Lighthouse, in Dellys, with the objective of giving first an overview of the constructive, architectural, and geometrical features and then performing the seismic vulnerability. The seismic vulnerability evaluation of the lighthouse structure has been preceded by a visual structural diagnosis to identify the main collapse mechanisms. Then, a preliminary modal analysis and, finally, a non-linear static analysis (pushover) have been carried out in the +X, X, +Y, − and Y directions, using profile loads proportional to the masses and the first modal shape. The results − obtained in terms of capacity curves indicate that the structural behavior is mostly elastic, with a reduced level of ductility. The damage states have shown that the seismic damage concentration provided by pushover analysis are in a good agreement with the actual distribution of cracks observed after post-earthquake surveys, especially at the contact zone between the tower and the confining structure. The paper, moreover, discusses some proposals of seismic retrofitting techniques for the Bengut Lighthouse, in the respect of the restoration principle and of the original conception of the building. The structural effectiveness of the retrofitting solutions has been preliminarily investigated by the numerical analysis of the seismic behavior. Nevertheless, future developments will carry out wider investigations by means of dynamic analyses, to properly model the local out-of-plane collapse modes and account for the uncertainty both in the records and in models. Despite the simplicity and generality of the model and of the numerical approach, a good prediction of the actual collapse mode exhibited by the structure has been obtained. The presented study, in perspective, can provide a basis for the seismic risk and vulnerability analysis of whole morpho-typical class of historical lighthouses at a large scale, exploiting a basis of knowledge which is sufficiently detailed from a geometric and constructive point of view but avoids—at least in a preliminary phase—the resort to expensive and time-consuming investigations, both experimental (extensive sampling and tests, monitoring, identification) and numerical (non-linear dynamic analyses). Very often, in fact, the lack of detailed data and the limited economic resources to fill the incomplete frame of knowledge needed to carry on the accurate assessment and design of interventions actually leads to a total absence of actions. The road traced could be a basis to develop mechanical large-scale typological vulnerability models to be used not only for preliminary priority screening but also for the continuous monitoring of the built heritage, thanks for example to the implementation into GIS or DSS platforms that collect and update information and process it, providing alerts and indications about the criticalities.

Author Contributions: Methodology, G.U. and A.A.F.; validation, K.A., G.U. and A.A.F.; investigation, K.A.; data curation, K.A. and M.C.Z.; writing—original draft preparation, K.A. and G.U.; writing—review and editing, G.U. and K.A. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Acknowledgments: The authors kindly acknowledge the members of ONSM (National Board of Lighthouse Authorities) for their help in the documentation research. For the fieldwork in Italy, the authors would like to thank the Erasmus + program; the thanks also go to Sergio Ruggieri and Andrea Nettis for their help in laboratory work. The research was supported by DGRSDT of Algeria (General Directorate of Scientific Research and Technological Development). Buildings 2020, 10, 247 28 of 30

Conflicts of Interest: The authors declare no conflict of interest.

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