Multiscale seismic vulnerability assessment and retrofit of existing masonry buildings

buildings Article Multiscale Seismic Vulnerability Assessment and Retrofit of Existing Masonry Buildings Tiago Miguel Ferreira * , Nuno Mendes and Rui Silva ISISE, Institute of Science and Innovation for Bio-Sustainability (IB-S), Department of Civil Engineering, University of Minho, 4710-057 Braga, Portugal; [email protected] (N.M.); [email protected] (R.S.) *Correspondence: [email protected]; Tel.: +351-253-510-200 Received: 30 March 2019; Accepted: 17 April 2019; Published: 19 April 2019   Abstract: The growing concern about the protection of built heritage and the sustainability of urban areas has driven the reoccupation of existing masonry buildings, which, in the great majority of the cases, were not designed or constructed to withstand significant seismic forces. This fact, associated with territorial occupation often concentrated in areas with high seismic hazard, makes it essential to look at these buildings from the point of view of the assessment of their seismic vulnerability and retrofitting needs. However, to be effective and efficient, such an assessment must be founded on a solid knowledge of the existing methods and tools, as well as on the criteria that should underlie the selection of the most appropriate to use in each context and situation. Aimed at contributing to systematise that knowledge, this paper presents a comprehensive review of the most relevant vulnerability assessment methods applicable at different scales, as well as the most significant traditional and innovative seismic retrofitting solutions for existing masonry buildings. Keywords: seismic vulnerability assessment; large-scale vulnerability analysis; numerical modelling; seismic retrofit 1. Introduction Devastating seismic events keep raising the awareness of scientific, technical and political community to the need of identifying assets at risk and developing more effective and cost-efficient risk mitigation strategies. The capacity to accurately assess the seismic vulnerability of these assets plays a fundamental role in this context, mainly because among the three factors that make up the standard formulation of risk (hazard, vulnerability and exposure), the vulnerability is the only factor in which engineering research can intervene. Nevertheless, and despite the significant advances in the field of seismic engineering and risk assessment, there is still much to be done, particularly with regard to existing buildings, most of them built without antiseismic provisions. Moreover, the wide variety of construction and structural systems, associated with the complex behaviour of their materials (raw earth, timber, masonry, steel and reinforced concrete), greatly limit the application of current codes and building standards to the existing building stock. To tackle this global issue, it is fundamental to enhance the engagement between innovation and technical stakeholders towards the development and application of more sophisticated and reliable methods of analysis, as well as improved seismic retrofitting techniques compliant with buildings conservation principles, a goal that can only be achieved on the basis of a solid knowledge of the current state of the art. Based on this assumption, the present paper provides a general framework on the issue of the seismic vulnerability assessment of existing masonry buildings by reviewing the most relevant vulnerability assessment methods applicable at different evaluation scales (from large to Buildings 2019,9, 91; doi:10.3390/buildings9040091 www.mdpi.com/journal/buildings Buildings 2019,9, 91 2 of 22 building scale assessment) and the most successful traditional and innovative solutions used in the retrofitting of existing masonry buildings. 2. Seismic Vulnerability Assessment Approaches at Different Scales The selection of the most appropriate seismic vulnerability assessment method to use must be made based on a proper balance between simplicity (of the tool) and accuracy (of the results), keeping always in mind that vulnerability outputs can be affected by several sources of uncertainty that should acknowledges and addressed, namely those related to the limitations of the model itself and to the inherent randomness of both the sample and the response. Over the last decade, several European consortiums have been working on different aspects related to the assessment and mitigation of vulnerability and seismic risk, namely on the classification and categorisation of existing seismic vulnerability assessment approaches at different scales. According to their classification, methodologies can be grouped into three main categories taking into account their level of detail, scale of evaluation and use of data: (1) first level approaches, (2) second level approaches and (3) third level approaches (see Figure 1). Buildings 2019, 8, x FOR PEER REVIEW 2 of 21 2. Seismic Vulnerability Assessment Approaches at Different Scales The selection of the most appropriate seismic vulnerability assessment method to use must be made based on a proper balance between simplicity (of the tool) and accuracy (of the results), keeping always in mind that vulnerability outputs can be affected by several sources of uncertainty that should acknowledges and addressed, namely those related to the limitations of the model itself and to the inherent randomness of both the sample and the response. Over the last decade, several European consortiums have been working on different aspects related to the assessment and mitigation of vulnerability and seismic risk, namely on the classification and categorisation of existing seismic vulnerability assessment approaches at different scales. According to their classification, methodologies can be grouped into three main categories taking into account their level of detail, scale of evaluation and use of data: (1) first level approaches, (2) second level approaches and (3) third level approaches (see Figure 1). First level approaches are mainly based on the use of qualitative information and therefore they are ideal for the development of large-scale seismic vulnerability analysis. Second level approaches are based on mechanical models, which rely on detailed geometrical and mechanical information. For this reason, second level approaches are particularly suited to the assessment of small building stocks (aggregates or single buildings). Finally, third level approaches involve the use of complex numerical modelling techniques, which require a comprehensive and rigorous geometrical, material and mechanical characterisation of the building. ○ Particularly suitable • Possible to apply Large-scale Small building stocks Building scale First level approaches • ○ Second level approaches • ○ Third level approaches ○ • Level of detail Low Medium High Figure 1. Analysis techniques versus assessment scales. 3. Large-Scale Seismic Vulnerability Assessment Methods When assessing the vulnerability of a large number of buildings, the amount of information to collect and treat can be massive and thus the use of more expedite approaches is more adequate. Large-scale seismic vulnerability assessment methods, either at the national or urban level, should be based on few vulnerability indicators, which are usually defined from the statistical treatment of past earthquake damage data. The definition and nature of such methods (some of them are much more quantitative while others are more qualitative) naturally limits their methodological formulation and the level at which the assessment is conducted, from the expedite evaluation of an entire area based on the identification and characterisation of representative building typologies to the individual assessment of each building. Thus, and according to the scheme in Figure 1, some remarkable examples of the application of first and second level approaches are given in the following subsections, categorising them into four different groups of methods: typological, indirect, conventional and hybrid. 3.1. Typological Methods According to typological methods, buildings are classified into different classes depending on a series of aspects (structural, construction, material, etc.) that either directly or indirectly influence their seismic response. In these methods, vulnerability is described as the probability of a structure Figure 1. Analysis techniques versus assessment scales. First level approaches are mainly based on the use of qualitative information and therefore they are ideal for the development of large-scale seismic vulnerability analysis. Second level approaches are based on mechanical models, which rely on detailed geometrical and mechanical information. For this reason, second level approaches are particularly suited to the assessment of small building stocks (aggregates or single buildings). Finally, third level approaches involve the use of complex numerical modelling techniques, which require a comprehensive and rigorous geometrical, material and mechanical characterisation of the building. 3. Large-Scale Seismic Vulnerability Assessment Methods When assessing the vulnerability of a large number of buildings, the amount of information to collect and treat can be massive and thus the use of more expedite approaches is more adequate. Large-scale seismic vulnerability assessment methods, either at the national or urban level, should be based on few vulnerability indicators, which are usually defined from the statistical treatment of past earthquake damage data. The definition and nature of such methods (some of them are much more quantitative while others are more qualitative) naturally limits their methodological formulation and the level at which the assessment is conducted, from the expedite evaluation of an entire area based on the identification and characterisation of representative building typologies to the individual assessment of each building. Thus, and according to the scheme in Figure 1, some remarkable examples of the application of first and second level approaches are given in the following subsections, categorising them into four different groups of methods: typological, indirect, conventional and hybrid. Buildings 2019,9, 91 3 of 22 3.1. Typological Methods According to typological methods, buildings are classified into different classes depending on a series of aspects (structural, construction, material, etc.) that either directly or indirectly influence their seismic response. In these methods, vulnerability is described as the probability of a structure to suffer a certain level of damage for a given ground motion intensity level, and damage probabilities are defined on the basis of past earthquake damage data and expert judgement. Since results obtained using typological methods are based on field investigation, they have to be considered in terms of their statistical accuracy. In this sense, they are valid only for either that particular area or for other areas with similar field conditions (in terms building typology and seismic hazard). A striking example of the use of a typological approach are the Damage Probability Matrices (DPMs) developed by Whitman et al. [ 1 ]. In this work, the authors have compiled DPMs for several building typologies according to the damaged sustained in over 1600 buildings after the 1971 San Fernando earthquake. According to different authors [ 2 , 3 ], one of the first European versions of a DPM was produced in Italy by Braga et al. [4] from the statistical treatment of the damage data collected after the 1980 Irpinia earthquake. The authors have used a binomial distribution to describe the damage distributions of each class for different seismic intensities. Buildings were separated into three vulnerability classes (A, B and C) and a DPM based on the MSK scale [ 5 ] was evaluated for each class [ 6 ]. The Italian National Seismic Service has processed the same Irpinia 1980 database, in order to obtain DPMs, see Di Pasquale et al. [7] . The main differences between this work and the original DPMs proposed by Braga et al [ 4 ] lies in the use of dwellings instead of buildings and in the quantification of the earthquake intensity in terms of MCS scale [8], instead of the MSK scale [5]. Although, as already referred, its origin goes back to the 1970s, the use of DPMs is still very popular. In 2003, as part of the ENSeRVES project (European Network on Seismic Risk, Vulnerability and Earthquake Scenarios), Dolce et al. [ 9 ] have derived DPMs for the Italian town of Potenza. An additional vulnerability class (D) was included by the authors in the formulation using the EMS-98 scale [ 10 ] in order to account for the buildings constructed after 1980 (i.e., buildings that have either been retrofitted or designed to comply with recent seismic codes) [ 2 , 6 ]. More recently, Lagomarsino and Giovinazzi [ 11 ] proposed a set of DPMs from the European Macroseismic Scale (EMS) aimed at providing a model for estimating seismic damages in five increasing and perfectly defined levels of damage. 3.2. Indirect Methods Indirect methods involve the determination of a vulnerability index and the establishment of a series of relationships between damage and seismic intensity [ 6 ], which are generally supported by statistical studies of postearthquake damage data. As schematised in Figure 1, indirect methods have been applied extensively to assess the seismic vulnerability of large areas and/or building stocks. The “Vulnerability Index Method”, originally proposed by Benedetti and Petrini [ 12 ] (see also [ 13 ]), is one of the most applied indirect methods, involving the computation of a vulnerability index (i.e., a building vulnerability classification system), which aims at traducing the physical and structural characteristics of the building into a quantitative form. According to this approach, each building is classified in terms of a vulnerability index related to a damage grade determined via the use of vulnerability functions. These functions enable the formulation of the damage suffered by buildings for each level of seismic intensity (or peak ground acceleration, PGA) and vulnerability index, see Figure 2. Indirect methods use extensive databases of building characteristics (typological and mechanical properties) and rely on observed damage after recent earthquakes to classify vulnerability, based on a score assignment. An adapted vulnerability index method has been developed and used to assess the seismic vulnerability of both unreinforced masonry and reinforced concrete building under the scope of “Catania Project” [ 14 ]. Following the guidelines of ATC-21 [ 15 ], a rapid screening approach was used in this project to define the vulnerability scores of the buildings. Buildings 2019,9, 91 4 of 22 Among the main advantages of indirect techniques, it is worth highlighting their ability to determine the vulnerability characteristics of the building stock under consideration, rather than base the vulnerability definition of a certain building typology considered as representative of the that building stock. Nonetheless, since they are based on vulnerability indices that are defined on the basis of empirical-based coefficients (weights), the uncertainty associated to the results is potentially high and should therefore be taken into account. Moreover, large-scale assessment using indirect techniques (at a regional or a national scale) must be based on data gathered from a large number of buildings, assumed to be representative of the building stock [16]. Buildings 2019, 8, x FOR PEER REVIEW 4 of 21 techniques (at a regional or a national scale) must be based on data gathered from a large number of buildings, assumed to be representative of the building stock [16]. Figure 2. Unified relationships between vulnerability, damage and peak ground acceleration, adapted from Petrini [17]. 3.3. Conventional Methods Conventional techniques are essentially heuristic, proposing a correspondence between a vulnerability index and a certain level of damage. According to Vicente et al. [18], there are essentially two groups of conventional approaches: the group that qualify the different physical characteristics of structures empirically and the group of those based on the criteria defined in seismic design standards for structures, evaluating the capacity–demand relationship of buildings. One of the bestknown approaches of the first group is probably ATC-13 [19]. Damage probability matrices were defined therein based on the know-how of more than 50 senior earthquake engineering experts who were asked to estimate damage factors (the ratio of loss to replacement cost, expressed as a percentage) for Modified Mercalli Intensities [20] from VI to XII, and for 36 different building classes. Some large-scale risk and loss assessment works based on ATC-13 can be found in the literature [21– 25]. As an example, Table 1 presents the damage factors for each damage state, computed by Eleftheriadou and Karabinis [22] for the city of Basel. Table 1. Damage probability matrix (DPM) presented by Eleftheriadou and Karabinis [23] for Basel. Damage grade CDF (%) Intensity V VI VII VIII IX X 1 5 8 35 20 20 5 0 2 20 0 8 37 37 15 7 3 55 0 0 35 35 37 15 4 90 0 0 8 8 35 37 5 100 0 0 0 0 8 41 MDF 0.4 3 14 35 63 84 3.4. Hybrid Methods As its name suggests, the hybrid techniques combine features of the above-mentioned techniques. A representative example of a hybrid technique is the macroseismic approach proposed by Faccioli et al. [11], which combines the characteristics of the typological and indirect methods using the referred vulnerability classes and a vulnerability index improved by the use of modifier parameters. This macroseismic method, either in its original format or with some minor adaptations, has been widely applied for assessing the seismic risk of various urban areas, such as Barcelona (Spain) [21], Faro (Portugal) [26] or Annaba (Algeria) [27], just to mention some, as well as of neighbourhoods [28] and building aggregates [29]. An interesting example of the combined application of a hybrid approach and a GIS tool was recently presented by Ferreira et al. [30]. In that Figure 2. Unified relationships between vulnerability, damage and peak ground acceleration, adapted from Petrini [17]. 3.3. Conventional Methods Conventional techniques are essentially heuristic, proposing a correspondence between a vulnerability index and a certain level of damage. According to Vicente et al. [ 18 ], there are essentially two groups of conventional approaches: the group that qualify the different physical characteristics of structures empirically and the group of those based on the criteria defined in seismic design standards for structures, evaluating the capacity–demand relationship of buildings. One of the best-known approaches of the first group is probably ATC-13 [ 19 ]. Damage probability matrices were defined therein based on the know-how of more than 50 senior earthquake engineering experts who were asked to estimate damage factors (the ratio of loss to replacement cost, expressed as a percentage) for Modified Mercalli Intensities [ 20 ] from VI to XII, and for 36 different building classes. Some large-scale risk and loss assessment works based on ATC-13 can be found in the literature [ 21 – 25 ]. As an example, Table 1 presents the damage factors for each damage state, computed by Eleftheriadou and Karabinis [ 22 ] for the city of Basel. Table 1. Damage probability matrix (DPM) presented by Eleftheriadou and Karabinis [23] for Basel. Damage Grade CDF (%) Intensity V VI VII VIII IX X 1 5 8 35 20 20 5 0 2 20 0 8 37 37 15 7 3 55 0 0 35 35 37 15 4 90 0 0 8 8 35 37 5 100 0 0 0 0 8 41 MDF 0.4 3 14 35 63 84 Buildings 2019,9, 91 5 of 22 3.4. Hybrid Methods As its name suggests, the hybrid techniques combine features of the above-mentioned techniques. A representative example of a hybrid technique is the macroseismic approach proposed by Faccioli et al. [11] , which combines the characteristics of the typological and indirect methods using the referred vulnerability classes and a vulnerability index improved by the use of modifier parameters. This macroseismic method, either in its original format or with some minor adaptations, has been widely applied for assessing the seismic risk of various urban areas, such as Barcelona (Spain) [ 21 ], Faro (Portugal) [ 26 ] or Annaba (Algeria) [ 27 ], just to mention some, as well as of neighbourhoods [ 28 ] and building aggregates [ 29 ]. An interesting example of the combined application of a hybrid approach and a GIS tool was recently presented by Ferreira et al. [ 30 ]. In that work, the authors make use of a simplified index-based approach to evaluate the impact resulting from the adoption of different large-scale retrofitting strategies, measured in terms of material, human and economic losses. In order to improve their interpretation, the results are mapped using a commercial GIS software, wherein georeferenced graphical information was combined and connected to a relational database containing the main structural characteristics of the buildings, see Figure 3. Various modules with different objectives were developed and integrated into the GIS, including vulnerability assessment, damage and loss estimation (number of collapsed buildings, casualty rate, number of unusable buildings and repair costs) for different macroseismic intensities, allowing for the construction of multiple physical damage and loss scenarios. With this discussion, the authors intended not only to demonstrate how simplified seismic vulnerability assessment approaches can be used to analyse the impacts resulting from the implementation of large-scale retrofitting programs (Figure 3a versus Figure 3b), but also to prove that investing in prevention strategies designed to mitigate urban vulnerability is one of the most effective strategies, both from the social and economic standpoint. Buildings 2019, 8, x FOR PEER REVIEW 5 of 21 work, the authors make use of a simplified index-based approach to evaluate the impact resulting from the adoption of different large-scale retrofitting strategies, measured in terms of material, human and economic losses. In order to improve their interpretation, the results are mapped using a commercial GIS software, wherein georeferenced graphical information was combined and connected to a relational database containing the main structural characteristics of the buildings, see Figure 3. Various modules with different objectives were developed and integrated into the GIS, including vulnerability assessment, damage and loss estimation (number of collapsed buildings, casualty rate, number of unusable buildings and repair costs) for different macroseismic intensities, allowing for the construction of multiple physical damage and loss scenarios. With this discussion, the authors intended not only to demonstrate how simplified seismic vulnerability assessment approaches can be used to analyse the impacts resulting from the implementation of large-scale retrofitting programs (Figure 3a versus Figure 3b), but also to prove that investing in prevention strategies designed to mitigate urban vulnerability is one of the most effective strategies, both from the social and economic standpoint. (a) (b) Figure 3. Mapping of damage scenarios for the old city centre of Horta: (a) before and (b) after the application of seismic retrofitting strategies, adapted from Ferreira et al. [30]. In the same line, Aguado et al. [31] took advantage of a hybrid approach to discuss the potential benefit resulting from the application of different seismic retrofitting strategies, not only accounting for their effect on the reduction of individual and global damages resulting from different seismic scenarios, but also regarding their global impact in terms of civil protection and urban accessibility. For such, the authors applied a hybrid seismic vulnerability assessment approach for façade walls to obtain vulnerability and damage scenarios for the historical city centre of Coimbra. Resorting to a GIS tool, these scenarios were subsequently used to map evacuation routes with different levels of accessibility, see Figure 4a. Blocked, restricted access and free roads were plotted considering both the façade walls prone to partial or total collapse and the narrowness of streets. Moreover, the urban areas that may be potentially inaccessible in the case of a seismic event were also identified, as well as the number of people that, in consequence, may be affected. Finally, the author has analysed the impact, in terms of urban accessibility, of retrofitting the building façade walls that define the areas more prone inaccessibility, see Figure 4b. Due to its immediate and practical application, it is easy to understand that this kind of information is of major significance for decision-makers and civil protection agencies. Figure 3. Mapping of damage scenarios for the old city centre of Horta: ( a ) before and ( b ) after the application of seismic retrofitting strategies, adapted from Ferreira et al. [30]. Buildings 2019,9, 91 6 of 22 In the same line, Aguado et al. [ 31 ] took advantage of a hybrid approach to discuss the potential benefit resulting from the application of different seismic retrofitting strategies, not only accounting for their effect on the reduction of individual and global damages resulting from different seismic scenarios, but also regarding their global impact in terms of civil protection and urban accessibility. For such, the authors applied a hybrid seismic vulnerability assessment approach for façade walls to obtain vulnerability and damage scenarios for the historical city centre of Coimbra. Resorting to a GIS tool, these scenarios were subsequently used to map evacuation routes with different levels of accessibility, see Figure 4a. Blocked, restricted access and free roads were plotted considering both the façade walls prone to partial or total collapse and the narrowness of streets. Moreover, the urban areas that may be potentially inaccessible in the case of a seismic event were also identified, as well as the number of people that, in consequence, may be affected. Finally, the author has analysed the impact, in terms of urban accessibility, of retrofitting the building façade walls that define the areas more prone inaccessibility, see Figure 4b. Due to its immediate and practical application, it is easy to understand that this kind of information is of major significance for decision-makers and civil protection agencies. Buildings 2019, 8, x FOR PEER REVIEW 6 of 21 (a) (b) Figure 4. Mapping of (a) evacuation routes and (b) configuration of the most critical urban area before (top) and after (bottom) retrofit, adapted from Aguado et al. [31]. 4. Seismic Vulnerability Assessment at Building Scale The seismic behaviour of existing masonry buildings is complex and depends on several aspects. The evaluation of the seismic response of this type of buildings can be divided in two main types of behaviour: (1) in-plane behaviour and (2) out-of-plane behaviour. In the last decades, several experimental and numerical studies on the in-plane and out-of-plane of existing masonry buildings were carried out, which allowed for significant improvement of the knowledge on its seismic performance. Furthermore, these studies helped develop new tools for the seismic assessment of existing masonry buildings. In the next sections, an overview on the numerical modelling approaches at material level, and the numerical modelling methods, the types of analysis and the assessment criteria for the seismic assessment of existing masonry structures at the building scale are presented. 4.1. Numerical Modelling Approaches at Material Level Masonry is a composite material with units and joints. The units can be adobe bricks, fired bricks, ashlars, irregular stones and others. Two main types of joints can be distinguished, namely, dry joints and mortar joints. The mortar joints can be such as mud mortar, lime-based mortar and cement-based mortar, among others. The structural behaviour of masonry depends on several aspects: (a) material properties of units and joints; (b) geometrical properties of units and joints; (c) quality of the workmanship; and (d) conservation status. The morphology of the cross-section of the masonry element has also influence on the structural, since the masonry can present: (a) different types of unit bonds, such as uncoursed bond and coursed bond with stone units or the English bond and Flemish bond with brick units; (b) different number of layers/leafs that compose the masonry element (single leaf masonry wall, multileaf masonry wall and multilayered vault); and (c) different types of arrangement at the connections between the walls (with and without interlocking). The strategy for the numerical modelling of existing masonry buildings can be defined based on the assumptions assumed at material level. At material level, three elements can be distinguished in Figure 4. Mapping of ( a ) evacuation routes and ( b ) configuration of the most critical urban area before (top) and after (bottom) retrofit, adapted from Aguado et al. [31]. 4. Seismic Vulnerability Assessment at Building Scale The seismic behaviour of existing masonry buildings is complex and depends on several aspects. The evaluation of the seismic response of this type of buildings can be divided in two main types of behaviour: (1) in-plane behaviour and (2) out-of-plane behaviour. In the last decades, several experimentalandnumericalstudieson thein-planeand out-of-plane ofexisting masonry buildingswere carried out, which allowed for significant improvement of the knowledge on its seismic performance. Furthermore, these studies helped develop new tools for the seismic assessment of existing masonry buildings. In the next sections, an overview on the numerical modelling approaches at material level, Buildings 2019,9, 91 7 of 22 and the numerical modelling methods, the types of analysis and the assessment criteria for the seismic assessment of existing masonry structures at the building scale are presented. 4.1. Numerical Modelling Approaches at Material Level Masonry is a composite material with units and joints. The units can be adobe bricks, fired bricks, ashlars, irregular stones and others. Two main types of joints can be distinguished, namely, dry joints and mortar joints. The mortar joints can be such as mud mortar, lime-based mortar and cement-based mortar, among others. The structural behaviour of masonry depends on several aspects: (a) material properties of units and joints; (b) geometrical properties of units and joints; (c) quality of the workmanship; and (d) conservation status. The morphology of the cross-section of the masonry element has also influence on the structural, since the masonry can present: (a) different types of unit bonds, such as uncoursed bond and coursed bond with stone units or the English bond and Flemish bond with brick units; (b) different number of layers/leafs that compose the masonry element (single leaf masonry wall, multileaf masonry wall and multilayered vault); and (c) different types of arrangement at the connections between the walls (with and without interlocking). The strategy for the numerical modelling of existing masonry buildings can be defined based on the assumptions assumed at material level. At material level, three elements can be distinguished in the masonry with mortar (Figure 5a): units, mortar and interface unit/mortar. Two main approaches can be adopted to simulate masonry [ 32 ]: microand macromodelling. Micromodelling can be further divided into [ 32 ] detailed micromodelling and simplified micromodelling. In the macromodelling approach (Figure 5d), the units, the mortar and the interfaces unit/mortar are modelled together as a continuum and composite material. In the simplified micromodelling approach (Figure 5c), the units are expanded (unit and half of the thickness of the mortar) and they are simulated as continuum elements. The behaviour of the mortar and of the interface unit/mortar is modelled by discontinuous elements. The third approach (Figure 5b) corresponds to the most detailed approach, in which the units and the mortar are simulated by independent continuum elements and the behaviour of the interfaces unit/mortar are modelled by discontinuous elements. The mortar with dry joints can be simulated using a micromodelling approach, composed by continuous elements for the units and discontinuous elements to simulate the interfaces unit/mortar (infinite compressive stiffness and strength and no tensile stiffness and strength). In general, the most detailed modelling approaches provide simulations that are more accurate and can be more representative of the real behaviour. However, they are more complex, since they require a high number of material parameters and more computational effort. The number of material parameters is significantly high when the nonlinear analysis is adopted. Thus, the selection of the modelling approach at material level should be based on an equilibrium between the required precision in the results and the effort needed to prepare the model, run the analysis and analyse the results. In general, macromodelling is used to simulate entire buildings, while micromodelling is adopted to model small portions/elements of masonry. For examples of applications of the macromodelling, simplified micromodelling and detailed micromodelling see respectively Mendes and Lourenço, Kurdo et al. and Andreotti et al. [33–35]. 4.2. Numerical Modelling Methods In the numerical modelling of existing masonry buildings, four main strategies based on the following methods can be distinguished: (1) Finite Element Method (FEM); (2) Distinct Element Method (DEM); (3) equivalent frame method; and (4) method using rigid macroblocks taking into account the expected collapse mechanisms. Buildings 2019,9, 91 8 of 22 Buildings 2019, 8, x FOR PEER REVIEW 7 of 21 the masonry with mortar (Figure 5a): units, mortar and interface unit/mortar. Two main approaches can be adopted to simulate masonry [32]: microand macromodelling. Micromodelling can be further divided into [32] detailed micromodelling and simplified micromodelling. In the macromodelling approach (Figure 5d), the units, the mortar and the interfaces unit/mortar are modelled together as a continuum and composite material. In the simplified micromodelling approach (Figure 5c), the units are expanded (unit and half of the thickness of the mortar) and they are simulated as continuum elements. The behaviour of the mortar and of the interface unit/mortar is modelled by discontinuous elements. The third approach (Figure 5b) corresponds to the most detailed approach, in which the units and the mortar are simulated by independent continuum elements and the behaviour of the interfaces unit/mortar are modelled by discontinuous elements. The mortar with dry joints can be simulated using a micromodelling approach, composed by continuous elements for the units and discontinuous elements to simulate the interfaces unit/mortar (infinite compressive stiffness and strength and no tensile stiffness and strength). In general, the most detailed modelling approaches provide simulations that are more accurate and can be more representative of the real behaviour. However, they are more complex, since they require a high number of material parameters and more computational effort. The number of material parameters is significantly high when the nonlinear analysis is adopted. Thus, the selection of the modelling approach at material level should be based on an equilibrium between the required precision in the results and the effort needed to prepare the model, run the analysis and analyse the results. In general, macromodelling is used to simulate entire buildings, while micromodelling is adopted to model small portions/elements of masonry. For examples of applications of the macromodelling, simplified micromodelling and detailed micromodelling see respectively Mendes and Lourenço, Kurdo et al. and Andreotti et al. [33–35]. Figure 5. Modelling strategies at material level: (a) masonry sample; (b) detailed micromodelling; (c) simplified micromodelling; and (d) macromodelling, adapted from Lourenço [32]. 4.2. Numerical Modelling Methods In the numerical modelling of existing masonry buildings, four main strategies based on the following methods can be distinguished: (1) Finite Element Method (FEM); (2) Distinct Element Method (DEM); (3) equivalent frame method; and (4) method using rigid macroblocks taking into account the expected collapse mechanisms. In the Finite Element Method (FEM) (Figure 6b), the continuous domain is discretised by a mesh composed by elements connected by nodes. It is a method widely used to solve complex engineering problems, in which the problem is described by differential equations. In structural problems, first a numerical model, composed by elements, is prepared. Then, and after running the analysis, the results are obtained and evaluated. The FEM has several types of 1D, 2D and 3D elements based on different formulations that can be adopted to simulate structural problems, such as beams elements, shell elements or solid elements. FEM has also available other types of elements to simulate particular behaviours/characteristics of the structure, such as interface elements, springs elements, mass Perpend or head joint Unit (brick, block, etc.) Bed joint Unit Mortar Interface Unit/mortar Composite “Joint” “Unit” (a) (b) (c) (d) Figure 5. Modelling strategies at material level: ( a ) masonry sample; ( b ) detailed micromodelling; (c) simplified micromodelling; and (d) macromodelling, adapted from Lourenço [32]. In the Finite Element Method (FEM) (Figure 6b), the continuous domain is discretised by a mesh composed by elements connected by nodes. It is a method widely used to solve complex engineering problems, in which the problem is described by differential equations. In structural problems, first a numerical model, composed by elements, is prepared. Then, and after running the analysis, the results are obtained and evaluated. The FEM has several types of 1D, 2D and 3D elements based on different formulations that can be adopted to simulate structural problems, such as beams elements, shell elements or solid elements. FEM has also available other types of elements to simulate particular behaviours/characteristics of the structure, such as interface elements, springs elements, mass elements, boundary elements or reinforcement elements. This method can be used to solve static and dynamic problems, with linear and nonlinear behaviour. The nonlinear analyses can be adopted to simulate the nonlinear behaviour of the materials (e.g., cracking and crushing of masonry) or the geometric nonlinearity. The FEM models can consider also the anisotropic behaviour of the masonry. The standard FEM method to solve nonlinear problems is implicit, which requires an iterative method, more computational effort and provides an unconditionally stable solution. There are also FEM codes that provide the explicit method, aiming at reducing the computational effort associated to the convergence difficulties of the implicit method. However, this FEM method is unconditionally stable and small steps should be adopted. Several softwares to solve complex structural problems, including the behaviour of existing masonry buildings, are available, such as DIANA TM [ 36 ], ANSYS ® [ 37 ] or Abaqus Unified FEATM [38]. The FEM has been widely used to evaluate the structural performance of existing masonry buildings, including for the seismic action. Most of the FEM models of entire buildings are developed based on the macromodelling approach (Section 4.1), even for historic buildings, since it is the most simple and fast approach to prepare the models and run the analysis. In general, this approach is a good compromise between required accuracy and computational effort to evaluate the global seismic behaviour of an entire masonry building. There are several applications of the macromodelling approach based on the FEM to evaluate the performance of masonry buildings, taking into account the in-plane and out-of-plane behaviour of the walls, and to evaluate the efficiency of strengthening techniques[ 39 – 41 ]. Thenumerical modelsdevelopedintheFEM basedonthe micromodellingapproach (Section 4.1) are detailed, requiring more computational effort. Thus, this modelling strategy is not commonly adopted simulate the seismic behaviour of entire masonry buildings. It is mainly adopted to simulate a small portion of masonry or a masonry element, such a masonry wall (e.g., [42,43]). The Distinct Element Method (DEM) (Figure 6a) was mainly developed to solve problems related to discontinuous materials, such as soils or masonry. Due to high computational effort required to run DEM models, this method was used mainly to simulate behaviour of small models. Nowadays, and to the recent advances in the computer hardware, the DEM is becoming more popular, even to solve Buildings 2019,9, 91 9 of 22 problems of civil engineering, such the evaluation of the seismic performance of masonry structures. In the analysis of masonry structures or masonry components, two approaches can be adopted for DEM models: (1) DEM models developed with rigid or deformable blocks and (2) DEM models developed with spherical particles. The DEM models with spherical particles involve a high number of elements and they are not appropriated to simulate entire masonry buildings. In general, the masonry models based on DEM are prepared with blocks to simulate the units, in which the interaction between the blocks is defined by contact points. The normal and shear stress at the contact points are based on the relative displacement caused by applied forces. In this method, the accuracy is guaranteed if an enough number of contact points are adopted [ 44 ]. When the deformable blocks are adopted, the blocks are discretised into an internal finite element mesh (combined FEM/DEM method [ 45 ]). The DEM allows stimulating the collapse mechanisms at large displacement domains, which is useful to evaluate the behaviour of masonry buildings from the initial damage until near its collapse, including damage caused by the sliding mechanism. The solution is obtained from an explicit time-stepping algorithm, which allows to simulate the nonlinear interaction of a large number of blocks without high computational requirements or to use an iterative method. Thus, small steps should be used. The UDEC [ 46 ], 3DEC [ 47 ] and DEMpack [ 48 ] are examples of software based on DEM. In general, these softwares have also beam and cables elements to simulate strengthening of the structure. The DEM can be useful to take into account the effect of the morphology of the masonry, using one block to simulate each unit, which require a high computational effort for large models. The computational effort can be reduced if the blocks simulate portions of masonry composed by several units. In this simplification, the discretisation should be carefully defined, taking into account the expected collapse mechanisms, since it can have influence on the response of the model. There are several applications of the DEM to evaluate the seismic performance of existing masonry structures, mainly for historic constructions [49–51]. In the equivalent frame method (Figure 6c), the main objective is to represent each type of member of the masonry building (piers, lintels, spandrels, etc.) by a specific structural element that simulate its behaviour (1D or 2D FEM element, macroblock, macroelements, etc.). In general, these structural elements are connected by rigid nodes, springs or interface elements. Thus, a 3D equivalent frame to the structural system of the buildings is created. This type of modelling strategy started to be applied by Tomaževiˇc [ 52 ] in 1978, where the 1D macroelements were adopted to simulate the diagonal shear failure of the piers and assuming that the in-plane global behaviour of masonry walls is mainly controlled by this type of failure (POR method). In the last decades, new formulations based on this modelling strategy have been developed, aiming at including other types of behaviour and failures with influence in the global seismic behaviour of masonry buildings, such as both flexural and shear behaviour of piers and spandrels or the sliding failure of the piers. The analysis based on this numerical modelling strategy is significantly faster than the analysis carried out using the previous methods, since involves a very low number of degrees of freedom. Several software using the equivalent frame method are available for masonry buildings, such as 3Muri [ 53 ], PRO_SAM [ 54 ] and 3DMacro [ 55 ]. In general, this software allows users to take into account the contribution of other types of structural elements, such as timber floors or reinforced concrete floors. The analysis of existing masonry structures based on the equivalent frame methods can be also performed in software’s that were not originally developed for masonry structures and more common in design offices, such SAP2000 ® [ 56 ], simulating the piers and the columns through beam elements with vertical and/or horizontal rigid offsets, connected by plastic hinges (spring elements to simulate the shear and the flexural behaviour) [ 57 ]. For examples of applications of this modelling strategy to existing masonry buildings see Lagomarsino et al., Magenes et al. and Penna et al. [58–60]. Buildings 2019,9, 91 16 of 22 compatibility with masonry substrates [ 90 , 91 ]. Thus, alternative composite solutions have been developed by integrating matrixes with enhanced compatibility, namely cement-, limeor clay-based mortars. The adequate embedding and bond of these mortars also required substituting the sheet textiles by mesh textiles or steel grids with adequate aperture sizes (Figure 8b). These alternative composites are known as Steel Reinforced Grout (SRG), Fibre-Reinforced Cementitious Matrix (FRCM) or Textile-Reinforced Mortar (TRM) [ 92 , 93 ]. Nowadays, several commercial TRM systems are available in the market, as provided by companies such as Ardea Progetti, BASF, Kerakoll, Mapei, Sika and Simpson Strong-Tie. These systems are constituted by meshes of different fibres (steel, glass, carbon, basalt and polyparaphenylene benzobisoxazole) and mortars of different composition; nevertheless, they are in general high mechanical performance materials. Recommendations for designing FRP-based strengthening solutions are sufficiently documented in ACI 440 7R-10 [ 94 ] and CNR-DT 200 R1/2012 [ 95 ] for concrete and masonry elements. These recommendations have also been used for designing TRM strengthening systems for masonry, nevertheless they lack comprehensive instructions, in particular for what concerns application procedures, quality assurance of the materials, durability verification, laboratory and field testing methodologies and the effectiveness of the installation. More recently, the American Concrete Institute published the ACI 549.4R13 [96] to fill this gap. The use of antiseismic devices to reduce the vulnerability of existing masonry buildings is not frequent, but in the last few years has been gaining attention, especially in the seismic protection of buildings with significant cultural value. Several types of devices have been proposed, among which the most interesting for masonry buildings are base isolators and passive dampers. Base isolation consists in isolating the structure from the seismic vibrations by introducing an interface with low horizontal stiffness and sufficient capacity to support the vertical loads. This interface modifies the modes of the structure, namely increases their fundamental period and changes their configuration. Furthermore, theincreasein horizontalflexibility, introducedby thebaseisolators, results in a reduction in the accelerations of the structure (by avoiding resonance) and a total displacement increase. Nevertheless, the structure behaves as a rigid body, meaning that the relative displacements of thestructurearereducedandthusthe associated damage. Itshouldbe notedthatthe total displacements concentrate at the interface of the system, which constitutes a limitation to the use of this solution if they may affect nearby buildings. Base isolation devices can be classified as elastomeric bearings and sliding bearings. Lead–rubber bearings are among the most established devices, whose installation in existing masonry buildings involves (1) construction of reinforced concrete beams at the base of the walls, (2) construction of the base of the devices, (3) installation of the devices, (4) lifting of the structure and transfer of its dead-weight to the devices and (5) construction of a rigid diaphragm at the level of the beams to promote a joint operation of the full system. The lifting–transfer phase is the most critical of the process, as it requires limiting the induced differential settlements to avoid causing damage to the masonry walls and other structural elements. As is implicit, this strengthening solution has an intrusive implementation and especially it can be very costly due to the complexity of the implementation process. Despite this, base isolation has been successfully applied in the strengthening of notable masonry buildings, such as the Salt Lake City and County Building (USA) [97]. The installation of passive dampers presents as main objective the improvement of the structure capacity to dissipate the energy transmitted by an earthquake, which in turn allows to improve the its seismic performance and reduce the induced damage. Dampers can be classified as (1) viscous dampers, (2) viscoelastic dampers, (3) hysteretic metallic dampers and (4) friction dampers. Viscous dampers are constituted by a hollow metallic cylinder filled with a silicon-based fluid and a piston that forces the fluid to pass through its small holes at high speed. The movement of the fluid originates high forces that oppose to the relative movement of the damper and dissipates energy through heat due to interparticle friction. The resisting forces are proportional to the piston speed and depend on the viscosity of the fluid. The installation of this type of dampers significantly increases the structural damping, which, in case of an earthquake, allows a significant reduction of the induced deformations. Viscoelastic dampers are normally constituted by metallic sheets intercalated by deformable polymeric Buildings 2019,9, 91 17 of 22 sheets. The shear deformation of the polymeric sheets due to relative movements of the damper extremities generates heat and dissipates energy. The dissipated energy is a function of the elastic deformation and deformation speed. In general, the installation of this type of dampers modifies the structural linear parameters for damping and stiffness. Hysteretic metallic dampers dissipate energy by exploiting the plastic deformation capacity of steel, which can be achieved by using low-yielding stress steels or cruciform cross-sections. Finally, friction dampers dissipate energy due to friction generated at the contact surface between two moving solid elements. These dampers are typically constituted by steel plates connected transversally by nuts and bolts fixed with a specific torque, which defines the friction force required to initiate energy dissipation. In general, passive dampers can be installed to strengthen specific structural elements, meaning that they constitute a solution less intrusive and costly than base isolation. The Siena Cathedral (Italy) is an example of a historical monument strengthened with dampers. In this case, two spring viscous dampers were installed to improve the out-of-plane behaviour of the tympanum of the main façade [98]. 6. Conclusions A comprehensive literature review of the main methods and techniques proposed in the last decades to assess and mitigate the seismic vulnerability of existing masonry buildings is presented in this paper. Before making some final remarks, it is worth noting that, despite the authors’ efforts to compile a sample of works as relevant and comprehensive as possible, there are certainly several other important works that, due to space constraints or oversight, are not included herein. From the review given in this paper it is possible to draw some important conclusions. The first regards the selection of the most appropriate seismic vulnerability assessment method to use. As it is mention is Section 2, and easily verifiable from the discussion included in Sections 3and 4, the selection of the most appropriate method or technique to use must be made based on a proper balance between its simplicity and the accuracy of its results. In this sense, it is very important to stress that vulnerability results can be strongly affected by several sources of uncertainty, which, for this reason, must be acknowledged and addressed. Moreover, and perhaps not less important, in order to be effective, it is fundamental that vulnerability indicators can be easily understood and interpreted, not only by the technical and scientific community, but also by citizens and governmental and civil protection authorities [ 99 ]. GIS tools can play a particularly relevant role in this context, making it possible to manage and communicate vulnerability and risk results in a very simple but informative manner. As exemplified in Section 3, such tools can be actually very helpful for the development of strengthening strategies, cost–benefit analyses, civil protection and emergency planning. The fundamental role of vulnerability assessment methods from the risk mitigation standpoint was also clearly demonstrated though the discussion presented herein. In fact, only on the basis of a comprehensive knowledge of the characteristics of the buildings and of their structural vulnerabilities it is possible to select and implement proficient mitigation strategies and to outline strengthening interventions that can contribute to reduce, in an effective and cost-efficient manner, their seismic vulnerability. Author Contributions: All authors contributed to every part of the research described in this paper. Funding: This research was funded by the Portuguese Foundation for Science and Technology (FCT) through the postdoctoral grant SFRH/BPD/122598/2016. Conflicts of Interest: The authors declare no conflict of interest. References 1. Whitman, R.V.; Reed, J.W.; Hong, S.-T. Earthquake Damage Probability Matrices. In Proceedings of the Fifth World Conference Earthquakes Engineering, Rome, Italy, 25–29 June 1973. 2. Calvi, G.M.; Pinho, R.; Magenes, G.; Bommer, J.J.; Crowley, H. 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