Applied Science, Faculty of
Non UBC
Civil Engineering, Department of
DSpace
Buildings 13 (2): 344 (2023)
Predari, Giorgia
Stefanini, Lorenzo
Marinković, Marko
Stepinac, Mislav
Brzev, Svetlana, 1959-
The paper describes a novel Adriseismic method for expeditious assessment of seismic risk associated with unreinforced masonry buildings. The methodology was developed for the Adriseismic project of the Interreg ADRION programme, with the aim to develop and share tools for increasing cooperation and reducing seismic risk for six participating countries within the region surrounding the Adriatic and the Ionian Seas. The method is applicable to unreinforced masonry buildings characterised by three main seismic failure mechanisms, namely masonry disintegration, out-of-plane failure, and in-plane damage/failure. Depending on the input parameters for a specific structure, the assessment yields a qualitative output that consists of the masonry quality index, the index of structural response, the level of seismic risk, and the most probable collapse mechanism. Both input and output of the method are applied in the spreadsheet form. The method has so far been applied in urban areas of participating countries in the project, including Mirandola, Italy; Kaštela, Croatia; Belgrade, Serbia. In parallel, the methodology has been validated by performing a detailed seismic assessment of more than 25 buildings, and the results have been compared with the results of the proposed expeditious method. The results show a good correlation between the two methods, for example, the structural response index obtained from the expeditious method and the capacity/demand ratio obtained from the conventional assessment method.
Citation: Predari, G.; Stefanini, L.;Marinkovic´, M.; Stepinac, M.; Brzev,S. Adriseismic Methodology forExpeditious Seismic Assessment ofUnreinforced Masonry Buildings.Buildings 2023, 13, 344. https://doi.org/10.3390/buildings13020344Academic Editor: Rita BentoReceived: 23 December 2022Revised: 19 January 2023Accepted: 23 January 2023Published: 26 January 2023Copyright: © 2023 by the authors.Licensee MDPI, Basel, Switzerland.This article is an open access articledistributed under the terms andconditions of the Creative CommonsAttribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).buildingsArticleAdriseismic Methodology for Expeditious Seismic Assessmentof Unreinforced Masonry BuildingsGiorgia Predari 1 , Lorenzo Stefanini 1,* , Marko Marinkovic´ 2 , Mislav Stepinac 3 and Svetlana Brzev 41 Department of Architecture, University of Bologna, 40136 Bologna, Italy2 Faculty of Civil Engineering, University of Belgrade, 11000 Belgrade, Serbia3 Faculty of Civil Engineering, University of Zagreb, 10000 Zagreb, Croatia4 Department of Civil Engineering, University of British Columbia, Vancouver, BC V6T 1Z4, Canada* Correspondence: lorenzo.stefanini2@unibo.itAbstract: The paper describes a novel Adriseismic method for expeditious assessment of seismicrisk associated with unreinforced masonry buildings. The methodology was developed for theAdriseismic project of the Interreg ADRION programme, with the aim to develop and share tools forincreasing cooperation and reducing seismic risk for six participating countries within the regionsurrounding the Adriatic and the Ionian Seas. The method is applicable to unreinforced masonrybuildings characterised by three main seismic failure mechanisms, namely masonry disintegration,out-of-plane failure, and in-plane damage/failure. Depending on the input parameters for a specificstructure, the assessment yields a qualitative output that consists of the masonry quality index, theindex of structural response, the level of seismic risk, and the most probable collapse mechanism.Both input and output of the method are applied in the spreadsheet form. The method has so farbeen applied in urban areas of participating countries in the project, including Mirandola, Italy;Kaštela, Croatia; Belgrade, Serbia. In parallel, the methodology has been validated by performing adetailed seismic assessment of more than 25 buildings, and the results have been compared with theresults of the proposed expeditious method. The results show a good correlation between the twomethods, for example, the structural response index obtained from the expeditious method and thecapacity/demand ratio obtained from the conventional assessment method.Keywords: unreinforced masonry structures; Adriseismic project; seismic vulnerability assessment;risk prediction; seismic failure mechanisms; existing buildings1. IntroductionThe countries surrounding the Adriatic and Ionian Seas, including Italy, Slovenia,Croatia, Bosnia and Herzegovina, Serbia, Montenegro, Albania, and Greece, have beenhistorically exposed to major seismic events, both in terms of intensity and frequency [1,2].These countries are characterised by the high seismic exposure and significant stock ofvulnerable unreinforced masonry (URM) buildings, which were designed to withstandonly gravity loads and were unable to sustain the effects of moderate to strong earthquakeswithout substantial damage. Historical URM buildings located in urban centres appearto be most vulnerable due to numerous transformations which they have undergoneover time, and the challenges encountered while carrying out structural interventions, asdemonstrated by the many seismic retrofitting techniques introduced since the 1970s [3].At the same time, these urban areas are also characterised by the highest population densityand the unique identity of a specific place. The combination of high seismic hazard, highvulnerability, and high exposure makes seismic risk reduction an issue of fundamentalimportance for these urban areas. Recent earthquakes in the region, including Albania [4],Greece [5,6], and Croatia [7,8], once again confirmed the high seismic vulnerability of URMbuildings, which experienced substantial damage or collapse due to these seismic events.Buildings 2023, 13, 344. https://doi.org/10.3390/buildings13020344 https://www.mdpi.com/journal/buildingsBuildings 2023, 13, 344 2 of 30It was estimated that URM buildings account for 45% to 61% of the existing build-ing stock within the region surrounding the Adriatic and Ionian Seas [9]. Seismic as-sessment of URM buildings is often challenging because an in-depth seismic analysisis both time-consuming and expensive. For this reason, methods for expeditious seis-mic assessment have been considered as an alternative to detailed approaches. They areless time-consuming, but accurate enough to guide informed planning at the urban orregional level.It is possible to classify seismic vulnerability assessment methods into analyticaland empirical ones [10], although hybrid assessment procedures are also available [11].Empirical methods are mainly based on rapid post-earthquake damage observations, whileanalytical methods are usually based on performance limit states, mechanical characteristicsof construction materials, and include detailed vulnerability assessment algorithms [12].Hybrid methods are a combination of empirical and analytical ones—they are derived fromstatistical approaches and consider the actual effects of past earthquakes on different typesof structures, as well as the results from analytical methods [13,14].Probable damage matrices are classic examples of empirical methods, which attempt topredict the effect of an earthquake on structures with known characteristics [15]. Empiricalmethods of this type have evolved over time. For example, the study by Braga [16] used themacroseismic intensity scale MSK-76 [17] to define damage matrices based on the observeddamage after the Irpinia earthquake (Campania, Italy). The same method, implementedby Giovinazzi and Lagomarsino [18], proved particularly effective for application to largeurban areas, such as the cities of Faro, Portugal [19], Barcelona, Spain [20], and Lisbon,Portugal [21]. Another widespread empirical method is the Rapid Visual Screening Method,presented in FEMA154 [22], which assigns a score for the building on the basis of visualsidewalk screening, providing results to the user in about 30 min. Approaches basedon general considerations, inspired by field experience, have been developed in severalcountries, including Japan [23], Turkey [24], and Canada [25].Analytical methods can generally rely on more accurate results but are more time-consuming. They may include the use of collapse multipliers, e.g., the Vulnus System,developed in Italy [26], or the FaMIVE method [27]. Calvi [28] proposed a displacement-based vulnerability assessment approach applicable to both reinforced concrete and URMbuildings, and served as the basis for other methods for URM buildings [29–31].The expeditious method presented in this paper was developed for application inseveral countries within the region surrounding the Adriatic and Ionian Seas. Similarto the EMS-98 scale [32] which is applicable in Europe, the proposed method aims atperforming seismic risk assessment at the international (regional) level. It can be usedto expeditiously evaluate individual buildings, and potentially large areas within a shorttimeframe, without the need to define complex frameworks or acquire empirical datafrom previous seismic events [33]. Building-specific vulnerabilities depend on regionalconstruction characteristics [9] and are different from seismic risk, which is the product ofvulnerability, exposure, and hazard. The procedure yields the following output indicators:(i) index of structural response, defined as an inverse value to the vulnerability; (ii) masonryquality index (MQI) [34,35]; (iii) the most probable collapse mechanism; (iv) seismic riskindex. Both input and output values were simplified as much as possible, often usinggeneral categories (I, II, III, etc.), with the values that were attributed a priori. The methodenables fast data input in the spreadsheet form, easy interpretation of the results, andwas designed to be implemented on Geographical Information System (GIS) platforms tofacilitate large-scale applications.During the Adriseismic project [36], three pilot cases were performed to assess the real-life applicability of the procedure. The selected sites were located in Bologna (Italy) [37],Kaštela (Croatia), and Rethymno (Greece). This paper presents instead the results obtainedfor three urban sites located in the cities of Mirandola (Italy), Kaštela (Croatia), and Belgrade(Serbia), which were considered relevant for the case study purposes, too. These casestudies enabled evaluation and testing of the procedure, in terms of its applicability to sitesBuildings 2023, 13, 344 3 of 30characterised by different seismic hazard levels and masonry buildings constructed usingdifferent techniques. Furthermore, the expeditious method was verified on a pilot sampleof 25 buildings, for which the results of seismic assessment were previously determinedusing conventional seismic assessment methods. Some of the buildings were previouslyassessed using the LV1 expeditious method [38], while others were assessed by means oflinear elastic dynamic analysis.The features such as expeditiousness, applicability at different localities, and qualita-tive, easily interpretable output distinguish the proposed method from existing approachesand facilitate its large-scale application, thereby increasing knowledge of the state of theexisting heritage, therefore targeting more in-depth analyses on the most critical buildings.2. The Adriseismic Method2.1. An Overview of the MethodThe Adriseismic method was developed based on the following criteria:1. Input information is easily accessible: to be effective, the method must be applica-ble on a large scale. For that reason, assessment of an individual building shouldnot require in-depth investigations, such as detailed condition surveys or historicalanalysis, instead, an assessment should be based on general data, such as cadastralplans and other types of building information.2. The assessment is performed quickly: ideally, it should take no more than a fewminutes to evaluate an individual building once all the information is available.3. The output can be easily understood by non-experts: a long-term goal of the projectis rapid dissemination of the method; hence, it is expected that the results can beincorporated in urban planning tools (through municipal maps), as well as propertyevaluations in the insurance sector.4. The method is internationally applicable: it is essential for the procedure to includefeatures unrelated to a specific country or region.These four criteria guided the method development. On one hand, it was importantto maintain the consistency with the initial objectives, while on the other hand it wasimportant to impose certain constraints, such as international applicability and a balancebetween the accuracy of the results and the speed of processing input data.From the operational point of view, the method comprises the following four mainphases (see Figure 1):Buildings 2023, 13, 344 3 of 30 These case studies enabled evaluation and testing of the procedure, in terms of its applica-bility to sites characterised by different seismic hazard levels and masonry buildings con-structed using different techniques. Furthermore, the expeditious method was verified on a pilot sample of 25 buildings, for which the results of seismic assessment were previously determined using conventional seismic assessment methods. Some of the buildings were previously assessed using the LV1 expeditious method [38], while others were assessed by means of linear elastic dynamic analysis. The features such as expeditious ess, applicability at different localities, and qualita-tive, easily terpretable output distinguish the proposed method from existing ap-proaches and facilitate its large-scale application, thereby increasing knowledge of the state of the existing heritage, therefore targeting more in- epth analyses on the most crit-ical buildings. 2. The Adriseismic Method 2.1. An Overview of the Method The Ad is ismic metho was developed based on the following criteria: 1. Input information is easily accessible: to be effective, the method must be applicable on a large scale. For that re son, ass ssment of an individual building should not require in-depth investigations, such as detail d c ndit on surveys or h storical anal-ysis, instead, an assessm nt should be based on g neral ata, s ch as cadastral plans and other types of building information. 2. The assessment is performed quickly: ideally, it should take no more than a few minutes to evaluate an individual building once all the information is available. 3. The output can be easily understood by non-experts: a long-term goal of the project is rapid dissemination of the method; hence, it is expected that the results can be incorporated in urban planning tools (through municipal maps), as well as property evaluations in the insurance sector. 4. The method is internationally applicable: it is essential for the procedure to include features unrelated to a specific country or region. These four criteria guided the method development. On one hand, it was important to maintain the consistency with the initial objectives, while on the other hand it was im-portant to impose certain constraints, such as international applicability and a balance between the accuracy of the results and the speed of processing input data. From the operati l i t f ie , the method comprises the following four main phases (se Figure : Figure 1. General structure of the proposed Adriseismic method, showing macro-phases and inter-mediate steps. Figure 1. General structure of the proposed Adriseismic method, showing macro-phases and inter-mediate steps.Buildings 2023, 13, 344 4 of 301. Data input: the user needs to enter input data related to specific building.2. Processing: the input data are processed according to the algorithm.3. Output: the system provides output (results).4. Retrofitting: this phase is currently not directly linked to the seismic assessment of abuilding, but a structure intervention strategy can be suggested for enhancing seismicresistance of a specific building.The expeditious method can be applied using a Microsoft Excel spreadsheet. Inputdata are organised into the following sections:1. General data—this section provides general information related to a specific buildingand does not affect the assessment results.2. Construction characteristics—information related to the prevalent construction tech-niques for foundations, vertical structural elements, floors, and roofs is selected froman existing database via a drop-down menu [9,39]. The provided information doesnot affect the assessment results.3. Masonry quality—masonry assessment is performed using the Masonry QualityImethod, M.Q.I. [34,35]. The user is requested to input nine masonry characteristicsfor the building, which strongly influence the seismic vulnerability assessment.4. Building characteristics—this section requires the user to provide 12 input datarelated to the intended use of the building and its morphological and structuralconfiguration. Whenever possible, the weights attributed to each parameter weredefined using normative values or considerations based on simplified schemes. Inputdata, such as intended use, irregularities, and expected ductility, were derived usingindirect considerations from Eurocode 8 [40,41]. (See Appendix B.) Other parameterswere set using equilibrium-based considerations, as explained in the next section.Input data influence the key results, namely the index of structural response, theseismic risk, and the most probable collapse mechanism.5. Site data—this section consists of three input parameters referring to the seismic zoneof the building site according to the Eurocode 8 requirements [40] and is used todetermine the seismic hazard level.Detailed information related to each input section is contained in Appendix A.The following output indicators are obtained as a result of the assessment:1. Masonry category—it depends exclusively on the masonry quality. According tothe M.Q.I. method, which serves as the basis for determining the masonry category,there are three possible categories (A to C), depending on the capacity of a masonrystructure to resist vertical, out-of-plane, and in-plane load actions.2. Index of structural response—associates the presumed building capacity to a numer-ical value (in the range from 0 to 1) and the corresponding category (from I to VI). Aspecific value is determined by analysing the following three main masonry failuremechanisms (in a decreasing extent of impact): wall disintegration, out-of-plane fail-ure, and in-plane failure. The masonry quality and the building characteristics inputdata also influence the failure mechanism.3. Probable collapse mechanism—a hypothesis regarding the most probable collapsemechanism (disintegration of masonry, out-of-plane kinematic mechanism, or in-planefailure) is formulated for the building based on the input data;4. Seismic risk—it is calculated based on the index of structural response and therequired site data (the higher the number, the greater the risk); the risk is also presentedas a category (ranging from “none” to “very high”).5. Retrofitting—when specific structural deficiencies are noted, the user may wish tosuggest specific actions to mitigate the risk. According to the possible choices in termsof the type of the structural intervention, simple qualitative information is providedto indicate its feasibility for a specific building.Both input and output were simplified as much as possible. Instead of providinga numerical input to describe the building characteristics, general categories (I, II, andBuildings 2023, 13, 344 5 of 30III) were used. The use of qualitative indicators instead of numerical values also appearsto be useful since it facilitates the application in different contexts by partially removinga language barrier. For example, “I” indicates a low quantity in an absolute sense, e.g.,a regular building is assigned category “I” to indicate the absence of irregularity, “III”indicates a very high amount/abundance (e.g., high energy dissipation capacity), while“II” is used for intermediate values.Figure 2 compares the assessment form of the Adriseismic method to the general diagram.Buildings 2023, 13, 344 5 of 30 were used. The use of qualitative indicators instead of numerical values also appears to be useful since it facilitates the application in different contexts by partially removing a language barrier. For example, “I” indicates a low quantity in an absolute sense, e.g., a regular building is assigned category “I” to indicate the absence of irregularity, “III” indi-cates a very high amount/abundance (e.g., high energy dissipation capacity), while “II” is used for intermediate v lues. Figure 2 compares the assessment form of the Adriseismic method to the general di-agram. (a) (b) Figure 2. Adriseismic method: (a) assessment form, generated via a Microsoft Excel spreadsheet, showing input data and output (results), and (b) a diagram showing the main input categories (note that the processing phase is shown in grey). Input data related to the masonry quality have been presented as proposed by the M.Q.I. method [34,35]. Each input characteristic is assigned a qualitative indicator, e.g., F. (fulfilled), P.F. (partially fulfilled), or N.F. (not fulfilled), as seen in Table 1. These qualita-tive input categories (I, II, III, F., P.F., N.F.) are associated with numerical data, which are essential for obtaining the output. Table 1. Input parameters: main values. Building Characteristics MQI I Low Value N.F. Not fulfilled II Medium Value P.F. Partially fulfilled III High Value F. Fulfilled The output (results) was presented using the same quantitative indicators as the in-put. For example, the parameter “index of structural response” is defined by six different classes (I to VI), where I indicates a highly vulnerable building and VI indicates a building without obvious structural deficiencies. The class of a building was assigned based on the numerical value (ranging from 0 to 1), which describes the structural behaviour and di-rectly depends on the inputs. The ranges shown in Table 2 were assigned considering Figure 2. Adriseismic method: (a) assessment form, generated via a Microsoft Excel spreadsheet,showing input d ta and output ( sults), and (b) a diagram showing the main input categor es (no ethat the processing phase is sho n in grey).Input data related to the masonry quality have been presented as proposed by theM.Q.I. method [34,35]. Eac input characteristic is assigned a qualitative indicator, e.g., F.(fulfilled), P.F. (partially fulfilled), or N.F. (not fulfilled), as seen in Table 1. These qualitativeinput categories (I, II, III, F., P.F., N.F.) are associated with numerical data, which areessential for obtaining the output.Table 1. Input parameters: main values.Building Characteristics MQII Low Value N.F. Not fulfilledII Medium Value P.F. Partially fulfilledIII High Value F. FulfilledBuildings 2023, 13, 344 6 of 30The output (results) was presented using the same quantitative indicators as the input.For example, the parameter “index of structural response” is defined by six different classes(I to VI), where I indicates a highly vulnerable building and VI indicates a building withoutobvious structural deficiencies. The class of a building was assigned based on the numericalvalue (ranging from 0 to 1), which describes the structural behaviour and directly dependson the inputs. The ranges shown in Table 2 were assigned considering wider ranges forthe lower classes and narrower ranges for the higher ones; this increases the probability ofassigning precautionary values.Table 2. Index of structural response: categories and values.Class Minimum Value Maximum ValueI 0.00 0.20II 0.21 0.40III 0.41 0.55IV 0.56 0.70V 0.71 0.85VI 0.86 1.00The use of building class is similar to the decree “Sismabonus” [42], which is used toevaluate the seismic capacity of existing buildings by means of letters (A to F). The useof defined classes and numerical ranges facilitates ease of application and interpretation,and the results can be transferred to urban planning maps or GIS for use by a widercommunity (non-experts).2.2. Processing of Input DataAfter the input data have been entered in the assessment form, the processing takesplace in the background (it is not visible to the user). One of the key aspects of theprocessing stage is determination of the most critical masonry failure mechanism for aspecific building. The Adriseismic method takes into account realistic seismic behaviourand failure mechanisms for URM structures, including (i) masonry disintegration, (ii) out-of-plane kinematic mechanisms, (iii) and in-plane failure. Figure 3 shows a schematicrepresentation of these failure mechanisms.Buildings 2023, 13, 344 6 of 30 wider ranges for the lower classes and narrower ranges for the higher ones; this increases the probability of assigning precautionary values. Table 2. Index of structural response: categories and values. Class Minimum Value Maximum Value I 0.00 0.20 II 0.21 0.40 III 0.41 0.55 IV 0.56 .70 V 0.71 0.85 VI 0.86 1.00 The use of building class is similar to the decree “Sismabonus” [42], which is used to evaluate the seismic capacity of existing buildings by means of letters (A to F). The use of defined classes and numerical ranges facilitates ease of application and interpretation, and the results can be transferred to urban planning maps or GIS for use by a wider commu-nity (non-experts). 2.2. Processing of Input Data After the input data have been entered in the assessment form, the processing takes place in the background (it is not visible to t e user). O e f the key aspects of the pro-cessing stage is determination of the most critical masonry failure mechanism for a spe-cific building. The Adriseismic method takes into account realistic seismic behaviour and failure mechanisms for URM structures, including i) masonry disintegration, ii) out-of-plane kinematic mechanisms, iii) and in-plane failure. Figure 3 shows a schematic repre-sentation of these failure mechanisms. (a) (b) (c) Figure 3. Masonry failure mechanisms—(a) masonry disintegration, (b) out-of-plane kinematic mechanism, and (c) in-plane failure. Disintegration concerns the loss of cohesion of the wall and is typical of loose (poorly cohesive) and weak (low strength) masonry, (Figure 3a). Out-of-plane kinematic mecha-nism, such as overturning (Figure 3b), can be simulated by a rigid macro-element, which does not depend on material strength characteristics. Collapse due to reaching the ulti-mate resistance in plane, also known as in-plane failure (Figure 2, C), usually requires the greatest seismic energy and can be expected in cohesive masonry which is found in struc-tures with well-connected load-bearing elements [43]. Figure 3. Masonry failure mechanisms—(a) masonry disintegration, (b) out-of-plane kinematicmechanism, and (c) in-plane failure.Buildings 2023, 13, 344 7 of 30Disintegration concerns the loss of cohesion of the wall and is typical of loose (poorlycohesive) and weak (low strength) masonry, (Figure 3a). Out-of-plane kinematic mecha-nism, such as overturning (Figure 3b), can be simulated by a rigid macro-element, whichdoes not depend on material strength characteristics. Collapse due to reaching the ultimateresistance in plane, also known as in-plane failure (Figure 3c), usually requires the greatestseismic energy and can be expected in cohesive masonry which is found in structures withwell-connected load-bearing elements [43].Parameters related to building characteristics directly influence the activation offour out-of-plane kinematic mechanisms, including simple masonry overturning, verticalbending, horizontal bending, and corner overturning, [44] which were considered in thisstudy. Each parameter was assigned a 0 value if it does not influence the activation of aspecific out-of-plane mechanism, 0.5 for the case of a small effect, and 1 in the case of alarge effect (see Table 3).Table 3. Building characteristics related to out-of-plane mechanisms and the corresponding weights attributed.Name and Description InputWeights Attributed to Kinematic MechanismSimple MasonryOverturning Vertical BendingHorizontalBendingCornerOverturningTransversal wall distanceI 0.00 0.00 1.00 0.00II 0.00 0.00 0.50 0.00III 0.00 0.00 0.00 0.00Wall thicknessI 0.00 0.00 0.00 0.00II 0.50 0.50 0.50 0.50III 1.00 1.00 1.00 1.00Floor heightI 1.00 1.00 1.00 1.00II 0.50 0.50 0.50 0.50III 0.00 0.00 0.00 0.00Permanent floor weightsI 0.00 1.00 0.00 0.00II 0.00 0.50 0.00 0.50III 0.00 0.00 0.00 1.00Thrusts due to archesand vaultsI 1.00 1.00 1.00 0.00II 0.50 0.50 0.50 0.00III 0.00 0.00 0.00 0.00Thrusts due to the roofI 1.00 0.00 0.00 1.00II 0.50 0.00 0.00 0.50III 0.00 0.00 0.00 0.00The influence of these characteristics was assessed by monitoring the variation inspectral acceleration for the activation of each kinematic mechanism while the other pa-rameters remained unchanged. C.I.N.E. spreadsheets developed in Italy [45] were usedfor this purpose. The impact was defined as irrelevant when the variation in a parame-ter changed the original spectral acceleration by less than 25%, moderate when changesin spectral acceleration ranged from 25 to 75%, and large when changes were greaterthan 75%.As for the other input parameters, the categories “I”, “II”, and “III” indicate poor orabundant values. For example, in the case of small transversal wall distances, category ‘I’ isused, while for very thick walls the category ‘III’ should be selected. In order to minimisethe complexity of survey and data acquisition, the parameters “thrust due to arches andvaults” and “thrusts due to the roof” were set to depend on the floor weight. For example,in case of a construction solution that generates a thrust on the vertical masonry, a higherfloor weight corresponds to a higher thrust.Buildings 2023, 13, 344 8 of 302.3. Results of the Assessment2.3.1. Masonry CategoriesThe M.Q.I. method assigns masonry categories ranging from A to C, where A is theleast vulnerable, B is intermediate, and C is the most vulnerable. The rating is assigned forall possible load actions, namely vertical actions (gravity) (MQIv), horizontal out-of-planeactions (MQIop), and horizontal in-plane actions (MQIip).The M.Q.I. ratings are formulated for each load action based on Equations (1)–(3).The symbols in the equations are explained in the nomenclature section. The results areassociated with the corresponding masonry category (A, B, or C).MQIv = rv·g·m·Ss·(Hj + Wc + Sr + Vj + Sd + Mm)(1)MQIop = rop·g·m·Ss·(Hj + Wc + Sr + Vj + Sd + Mm)(2)MQIip = rip·g·m·Ss·(Hj + Wc + Sr + Vj + Sd + Mm)(3)Table 4 shows the ranges of values associated with each category. The numericalvalues obtained from equations are divided by a factor of 10 for the sake of convenience.Table 4. Masonry categories and M.Q.I. values.Load Action Masonry Categories Min MaxMQIv—Vertical actionA 0.50 1.00B 0.25 0.499C 0.00 0.249MQIop—Horizontal out-of-plane actionA 0.70 1.00B 0.40 0.699C 1.00 0.399MQIip—Horizontal in-plane actionA 0.50 1.00B 0.30 0.499C 0.00 0.2992.3.2. Index of Structural ResponseIndex of structural response is the key parameter used for assessing the seismicbehaviour of the construction. It is defined considering an M.Q.I. rating and buildingcharacteristics. In order to evaluate all masonry damage mechanisms, the followingequations have been proposed:Psd = Du + Ip + Ih + Ed + Fn (4)Smo = Sw + Wt + Inh + Pf w + Pa + Pr (5)Vb = Sw + Wt + Inh + Pf w + Pa + Pr (6)Hb = Sw + Wt + Inh + Pf w + Pa + Pr (7)Co = Sw + Wt + Inh + Pf w + Pa + Pr (8)The equations assign a numerical value to parameters linked to seismic demand Psd(Equation (4)), simple masonry overturning Smo (Equation (5)), vertical bending Vb (Equation (6)),horizontal bending Hb (Equation (7)), and corner overturning Co (Equation (8)). The meaningof the symbols can be found in the Nomenclature section at the end of the paper. Theresulting values for these parameters have been normalised using the traditional max–minformulation (Equation (9)) to make them comparable. The maximum value was set equalto 1, and the minimum value was 0 (the same applies to the index of structural responseand the M.Q.I.).norm =vi − vminvmax − vmin (9)Buildings 2023, 13, 344 9 of 30Once the five values have been defined according to Equations (4)–(8), it is possibleto calculate the index of structural response, Isr. Two alternative formulations are used:the first considers the main structural elements disconnected from each other (input n.25set “off”, see Appendix A, Table A4), and the second assumes them as linked (input n.25set “on”):Isr,1 =Psd,n + min(Smo,n; Vb,n; Hb,n; Co,n; MQIv; MQIop; MQIip)2(10)Isr,2 =Psd,n + min(MQIv; MQIo; MQIi)2(11)Equation (10) offers the index of structural response as the mathematical average of theseismic demand parameters (normalised) and the minimum value for the four kinematicmechanisms and the M.Q.I. results. In this way, the most probable damage mechanism ofthe analysed structure is evaluated, choosing the one with the lowest numerical value on a0–1 scale. For example, a building constructed with poor masonry quality but with goodconstruction characteristics will still have a low index of structural response.Equation (11) is related to the hypothesis of well-connected structural elements. Thefour out-of-plane kinematic mechanisms are not included in the equation. In this case,the index only depends on the parameters that directly influence the seismic demand(designated use, floors above ground, irregularity in plan, irregularity in height, expectedductility) and the quality of masonry.A numerical value, ranging from 0 (very vulnerable building) to 1 (building withoutvulnerability), is used to assign a class (from I to VI), according to the range shown inTable 2. The assigned class allows for comparison with other buildings and can be used forurban planning purposes.2.3.3. Most Probable Collapse MechanismThe previously presented Equations (5)–(8), together with the M.Q.I. results and thedata provided by the user about the “connections between structural elements”, allowhypotheses to be formulated regarding the most probable collapse mechanism for thebuilding. The output is provided based on the following criteria:• When the masonry quality is class C, for one or all three actions, the masonry maydisaggregate for very low seismic values.• When the masonry quality is average or good class A or B, but the connectionsbetween structural elements are good, the evaluation system indicates the out-of-planekinematic as the most probable collapse mechanism with the lowest value among thefour investigated in the method, Equations (5)–(8).• When neither of the two conditions presented is verified, the building may developglobal behaviour, and collapse may occur due to reaching ultimate strength in verti-cal plane.2.3.4. Seismic RiskThe final output is related to seismic risk, Sh. Using the same concept as before, anumerical value is assigned to a qualitative risk category for the building. The risk Sh iscalculated using the widely used formulation [46]:Sh = Iv·E·H (12)Unlike the index of structural response, the risk is not determined as a numerical valuebecause its magnitude depends on the ground acceleration provided by the user. However,as the number describing the risk increases, the risk category increases, as shown in Table 5.Buildings 2023, 13, 344 10 of 30Table 5. Seismic risk categories and values.Categories Min MaxVery high 1.40High 0.90 1.39Medium 0.45 0.89Low 0.10 0.44None 0.00 0.09The ranges in the table were calibrated for different conditions within the entireAdriatic–Ionian Sea region. For example, the risk was differentiated into high and veryhigh for buildings located in areas subject to significant acceleration, but characterised bydifferent exposures.2.3.5. RetrofittingFinally, the method provides recommendations related to the possible seismic interven-tion (retrofitting). The output is intended to be qualitative and identifies the interventionbased on deficiencies that may have emerged during the investigation phase and con-firmed by the results. The section is also organised into input and output, but there is nointermediate processing phase for the input information and the output. The interventioncan be selected from a defined list. As shown in Table 6, it is possible to select the extentof intervention and the main material that should be used. Based on these preferences,compatible interventions are offered by the method.Table 6. Seismic retrofitting intervention.Name and Description Possible ValuesExtent of intervention(How extensive the intervention is) Extensive, localised, noneMaterial preference(Main material used for the retrofitting)Concrete, composite (fibre-reinforcedpolymers), masonry, wood, steelCurrently, 56 possible interventions have been included in the database; out of these,28 interventions are localised, while the remaining ones are extensive.Figure 4 shows five main types of materials that can be used for interventions. Theblue colour shows the total number of interventions for each material, while a beige bargives an indication of the extent (extensive or localised). For each intervention, a few quali-tative indications are available to help guide the choice. Based on the Adriseismic projectdeliverable D.T.2.1.2 [9], the cost, technical complexity, and critical issues are indicated, asseen in Table 7. For the Croatian scenario, the retrofitting prices were based on World Bankreports and Croatian methodology [47–50].Table 7. Qualitative indicators for seismic retrofitting.Indications Provided Range of ValuesCost Low/medium/highTechnical complexity Low/medium/highExplanation A brief summary of seismic deficienciesaddressed by the interventionBuildings 2023, 13, 344 11 of 30il i , , 1 of Figure 4. Interventions classified based on the main material and type (localised and extensive). Table 7. Qualitative indicators for seismic retrofitting. Indications Provided Range of Values Cost Low/medium/high Technical complexity Low/medium/high Explanation A brief summary of seismic deficiencies addressed by the intervention 3. Application of the Adriseismic Method on Urban Case Studies At the end of the development phase, the method was initially applied on real build-ings. The aim was to verify the adaptability of the procedure in varied contexts and its compliance with the four guiding criteria illustrated in Section 2 (easily accessible infor-mation, quick assessment, outputs easily understandable, and international use). For this purpose, buildings in three different areas within three cities were studied: Mirandola (Italy), Kaštela (Croatia), and Belgrade (Serbia). The areas were selected according to Adriseismic project objectives; hence, URM buildings facing squares and having a histor-ical identity for the place were considered. 3.1. The Mirandola Case Study The city of Mirandola is a small town (approx. 23,000 inhabitants), located in north-ern Italy, in the region of Emilia-Romagna. It has an ancient history and dates back to the year 1000. Like many other settlements in the area, it is organised on an initial fortified structure and successive stratifications added over the centuries. The site is highly active from a seismic point of view, although the acceleration (PGA) expected for the area, at the Life Safety limit state, is 0.14 g, which is about half of that actually recorded in the last major earthquake that occurred in 2012. The combination of these two elements (settle-ment with a long history and high seismic hazard) made the area very relevant for apply-ing the Adriseismic method. Figure 5 shows a satellite view of the case study location. Figure 4. Interventions classified based on the main material and type (localised and extensive).3. Application of the Adriseismic Method on Urban Case StudiesAt the end of the development phase, the method was initially applied on real build-ings. The aim was to verify the adaptability of the procedure in varied contexts and itscompliance with the four guiding criteria illustrated in Secti n 2 ( asily accessible infor-mation, quick assessment, outputs easily understandable, and international use). For thipurpose, buildings in three different areas within three cities were studi d: Mira dola(Italy), Kaštela (Croatia), and Belgrade (Serbia). The areas were selected according toAdriseismic project objectives; hence, URM buildings facing squares and having a historicalidentity for the place were considered.3.1. The Mirandola Case StudyThe city of Mirandola is a small town (approx. 23,000 inhabitants), located in northernItaly, in the region of Emilia-Romagna. It has an ancient history and dates back to theyear 1000. Like many other settlements in the area, it is organised on an initial fortifiedstructure and successive stratifications added over the centuries. The site is highly activefrom a seismic point of view, although the acceleration (PGA) expected for the area, at theLife Safety limit state, is 0.14 g, which is about half of that actually recorded in the lastmajor earthquake that occurred in 2012. The combination of these two elements (settlementwith a long history and high seismic hazard) made the area very relevant for applying theAdriseismic method. Figure 5 shows a satellite view of the case study location.Buildings 2023, 13, 344 12 of 30 Figure 5. A view of the Mirandola case study site and the three buildings analysed. Three buildings facing the Conciliation Square were selected for the study, as seen in Figure 6. All three buildings have masonry load-bearing structures and are a part of larger aggregates. (a) (b) (c) Figure 6. Selected buildings in Mirandola, Italy: (a) Building 1, (b) Building 2, and (c) Building 3; © Google. The information to assess the seismic response was obtained through cadastral plans and site surveys. In parallel, historical analyses were carried out to reconstruct the main events that affected the buildings over time. Following the project objectives, no specific material investigations were carried out. Building (a) (Figure 6) has three floors above ground and an attic. The lowest level is intended for commercial use, while the others are for residential use. The original struc-ture dates back to the 16th century and has been modified over time. A central block has undergone numerous extensions until it was connected to the other units, generating a complex aggregate. Building (b) is of the most recent construction, dating back to the 1930s. As in the previous case, the structure is part of a large aggregate, characterised by an internal courtyard and a highly irregular planimetric configuration. The assessment was carried out on the part of the building with homogeneous construction characteristics. The floors are composite, made of hollow bricks and reinforced concrete, while the walls are made of bricks that are not always interlocked well. The use of the building is public. Building (c) dates back to the 16th century. It is the largest in plan and has probably undergone the largest number of structural interventions over the centuries. The current configuration is certainly different from the original intention and is the result of numer-ous extensions over time. The roof and floors are made of wood, although, given the many transformations that have taken place, they are made using different construction tech-niques. Figure 5. A view of the Mirandola case study site and the three buildings analysed.Buildings 2023, 13, 344 12 of 30Three buildings facing the Conciliation Square were selected for the study, as seenin Figure 6. All three buildings have masonry load-bearing structures and are a part oflarger aggregates.Buildings 2023, 13, 344 12 of 30 Figure 5. A view of the Mirandola case study site and the three buildings analysed. Three the Conciliation Square were sel cted for the study, as seen i Figure 6. All three buildings have masonry load-bearing structu es and are a part of l ger g regates. (a) (b) (c) Figure 6. Selected buildings in Mirandola, Italy: (a) Building 1, (b) Building 2, and (c) Building 3; © Google. The information to assess the seismic response was obtained through cadastral plans and site surveys. In parallel, historical analyses were carried out to reconstruct the main events that affected the buildings over time. Following the project objectives, no specific material investigations were carried out. Building (a) (Figure 6) has three floors above ground and an attic. The lowest level is intended for commercial use, while the others are for residential use. The original struc-ture dates back to the 16th century and has been modified over time. A central block has undergone numerous extensions until it was connected to the other units, generating a complex aggregate. Building (b) is of the most recent construction, dating back to the 1930s. As in the previous case, the structure is part of a large aggregate, characterised by an internal courtyard and a highly irregular planimetric configuration. The assessment was carried out on the part of the building with homogeneous construction characteristics. The floors are composite, made of hollow bricks and reinforced concrete, while the walls are made of bricks that are not always interlocked well. The use of the building is public. Building (c) dates back to the 16th century. It is the largest in plan and has probably undergone the largest number of structural interventions over the centuries. The current configuration is certainly different from the original intention and is the result of numer-ous extensions over time. The roof and floors are made of wood, although, given the many transformations that have taken place, they are made using different construction tech-niques. Figure 6. Selected buildings in Mirandola, Italy: (a) Building 1, (b) Building 2, and (c) Building 3;© Google.The infor ation to assess the seis ic response as obtained through cadastral plansand site surveys. In parallel, historical analyses ere carried out to reconstruct the ainevents that affected the buildings over ti e. Follo ing the project objectives, no specificaterial investigations ere carried out.Building (a) (Figure 6) has three floors above ground and an attic. The lo est level isintended for commercial use, while the others are for residential use. The original structuredates back to the 16th century and has been modified over time. A central l c asundergo e er s e te si s til it s c ecte t t e t er its, e er tico ple ag re t . il i ( ) is f t st r c t c str cti , ti c t t1930s. As in the previous case, the structure is part of a large aggregate, characterised by aninter al courtyard nd a highly irregular pl nimetric configuration. The assessment wascarried out on the part of the building with homogeneous construction characteristics. Thefloors are comp site, made of hollow bricks and reinforced on rete, while th walls aremade of bricks that are not always interlocked well. The us of the building s public.Buil i ack to the 16th century. It is the largest in pl and has prob-ably undergone the largest numbe of structural i erventions over he centuries. Thecurrent configuration is certainly different from the original i tention and is the resultof num rous extensions ov r time. The oof and flo rs are made of wood, although,given the ma y r nsformatio s that have taken place, they are made using differentconstruction techniques.Table 8 shows the main results of the expeditious assessment: index of structuralresponse, masonry category, most probable collapse mechanism, seismic risk, and seismicrisk category.Table 8. Result of the evaluation of buildings in Mirandola.Building Code Index of StructuralResponse Masonry CategoriesMost ProbableCollapse Mechanism Seismic RiskSeismic RiskCategoryBuilding a II (0.35) B, B, A Cantonal Overturning 0.60 MediumBuilding b III (0.54) A, A, C Disintegration 0.39 LowBuilding c II (0.32) A, A, A Horizontal deflection 0.66 Medium3.2. The Kaštela Case StudySimilar to Italy, Croatia is affected by a high seismic hazard. A few disastrous earth-quakes that have occurred in recent years, such as the 2020 one in Petrinja with a magnitude6.4 on the Richter scale, have raised awareness of the scientific and political communitywho started to evaluate innovative measures to reduce seismic risk. The chosen area,Podvorje Square, is located in the south of Kaštel Suc´urac, the administrative area of thecity of Kaštela (Croatia), as seen in Figure 7.Buildings 2023, 13, 344 13 of 30Buildings 2023, 13, 344 13 of 30 Table 8 shows the main results of the expeditious assessment: index of structural re-sponse, masonry category, most probable collapse mechanism, seismic risk, and seismic risk category. Table 8. Result of the evaluation of buildings in Mirandola. Building Code Index of Structural Response Masonry Categories Most Probable Collapse Mechanism Seismic Risk Seismic Risk Category Building a II (0.35) B, B, A Cantonal Overturning 0.60 Medium Building b III (0.54) A, A, C Disintegration 0.39 Low Building c II (0.32) A, A, A Horizontal deflection 0.66 Medium 3.2. The Kaštela Case Study Similar to Italy, Croatia is affected by a high seismic hazard. A few disastrous earth-quakes that have occurred in recent years, such as the 2020 one in Petrinja with a magni-tude 6.4 on the Richter scale, have raised awareness of the scientific and political commu-nity who started to evaluate innovative measures to reduce seismic risk. The chosen area, Podvorje Square, is located in the south of Kaštel Sućurac, the administrative area of the city of Kaštela (Croatia), as seen in Figure 7. Figure 7. A view of Kaštela case study site and the five buildings analysed. The city, located just north of Split, is a small town (around 40,000 inhabitants), char-acterised by a very ancient history dating back to prehistoric times, which has resulted in a building heritage rich in dated constructions. The presence of potentially vulnerable buildings and a high seismic hazard, the expected acceleration (PGA) at the site at the Life Safety limit state is equal to 0.22 g, made the square relevant for the application of the Adriseismic method. The area dates back to the 15th century and was built at the behest of Archbishop Bartul Averaldo, who intended to create fortifications at the centre of the present Arch-bishop’s palace. The assessment was carried out on five buildings, characterised by dif-ferent construction techniques, construction periods, and functions; see Figure 8. Figure 7. A view of Kaštela case study site and the five buildings analysed.The city, located just north of Split, is a small town (around 40,000 inhabitants),characterised by a very ancient history dating back to prehistoric times, which has resultedin a building heritage rich in dated constructions. The presence of potentially vulnerablebuildings and a high seismic hazard, the expected acceleration (PGA) at the site at the LifeSafety limit state is equal to 0.22 g, made the square relevant for the application of theAdr seismic method.The area dates back to the 15th century and was built at the behest of Archbishop BartulAveraldo, who intended to create fortifications at the centre of the present Archbishop’spalace. The assessment was carried out on five buildings, characterised by differentconstruction techniques, construction periods, and functions; see Figure 8.Buildings 2023, 13, 344 14 of 30 Figure 8. Selected five buildings for the Kaštela study area. Elevations photographed or recon-structed by photogrammetry. The input information was obtained using: (i) historical surveys which were used to find information to demonstrate the building modifications that have occurred over time or the presence of structural interventions; (ii) physical surveys such as on-site measure-ments and aerial-photogrammetric surveys. The full laser scanning of the area from the ground was conducted to create a 3D cloud of points (Figure 9). The laser scanner was a compact Leica BLK360 3D imaging laser scanner with an integrated spherical imaging system and thermography panorama sensor system. Laser scanning facilitates and speeds up, documenting and reviewing geometry, especially for large and complex buildings [51]. The point cloud was used to create an accurate 3D model of the area (Figure 8). Sim-ilarly, full 3D photogrammetry scanning was performed by unmanned aerial devices (drones), which produced several 360° images that were used in the post-analysis stage [52]. Figure 9. Plan view of the point cloud showing camera stations. Figure 8. Selected five b il i gs for the Kaštela study area. Elevations photographed or reconstructedby photogrammetry.Buildings 2023, 13, 344 14 of 30The input information was obtained using: (i) historical surveys which were used tofind information to demonstrate the building modifications that have occurred over time orthe presence of structural interventions; (ii) physical surveys such as on-site measurementsand aerial-photogrammetric surveys. The full laser scanning of the area from the groundwas conducted to create a 3D cloud of points (Figure 9). The laser scanner was a compactLeica BLK360 3D imaging laser scanner with an integrated spherical imaging systemand thermography panorama sensor system. Laser scanning facilitates and speeds up,documenting and reviewing geometry, especially for large and complex buildings [51]. Thepoint cloud was used to create an accurate 3D model of the area (Figure 8). Similarly, full3D photogrammetry scanning was performed by unmanned aerial devices (drones), whichproduced several 360◦ images that were used in the post-analysis stage [52].Buildings 2023, 13, 344 14 of 30 Figure 8. Selected five buildings for the Kaštela study area. Elevations photographed or recon-structed by photogrammetry. The input information was obtained using: (i) historical surveys which were used to find information to demonstrate the building modifications that have occurred over time or the presence of structural interventions; (ii) physical surveys such as on-site measure-ments and aerial-photogrammetric surveys. The full la er scanning of the area from the ground was conducted to create a 3D cloud of points (Figure 9). The laser scanner was a compact Leica BLK360 3D imaging laser scanner with an integrated spherical imaging system and thermography panorama sensor system. Laser scanning facilitates and speeds up, documenting and reviewing geometry, specially for large and complex buildings [51]. The point cloud was used to create an accurate 3D odel of the area (Figure 8). Sim-ilarly, full 3D photogrammetry scanning was performed by unmanned aerial devices (drones), which produced several 360° images that were used in the post-analysis stage [52]. Figure 9. Plan view of the point cloud showing camera stations. Figure 9. Plan view of the point cloud showing camera stations.The first building (a) is public which dates back to the 15th century (Figure 8). Con-figuration is irregular both in height and plan, with one side being much longer than theother. The building has stone masonry walls and wooden floors and roof.The second building (b) has a residential function. The building has brick masonrywalls and wooden floors and roof. The construction period is between the 1920s and 1940s.The third building (c) is very similar to the second, as they share the same constructionperiod and construction features. There are no noticeable irregularities in plan and elevation;it has a wooden load-bearing structure with brick tiles to characterise the floors.The fourth (d) and fifth buildings (e) are part of the same aggregate and have residentialuse. The walls were constructed using stone masonry, while the floors and roof are mainlywooden structures. In terms of configuration, no particular irregularities in height werefound. The structures probably date back to the early 1900s and may not have been builtsimultaneously. The aggregate effect was not considered in this study.Table 9 shows the results obtained by applying the method to these five buildings.Buildings 2023, 13, 344 15 of 30Table 9. Results of evaluation of building around the Podvorje square.Building ID Index of StructuralResponse Masonry CategoriesMost ProbableCollapse Mechanism Seismic RiskSeismic RiskCategoryBuilding a III (0.43) A, B, A Horizontal deflection 0.59 LowBuilding b IV (0.68) A, A, A Horizontal deflection 0.37 LowBuilding c IV (0.56) A, B, A Vertical deflection 0.45 LowBuilding d III (0.45) A, B, B Horizontal deflection 0.56 LowBuilding e IV (0.65) A, A, A Horizontal deflection 0.39 Low3.3. The Belgrade Case StudyThe last case study site is located in Belgrade the capital of Serbia. Belgrade is oneof the oldest settlements in Europe, and its considerable size (population 1,400,000) andrich history have resulted in a heterogeneous building heritage in terms of constructiontechniques. Seismic hazard of the area can be characterised as moderate, the PGA is 0.1 g,the lowest for the three selected case studies. Due to its geographical location [53], the cityhas not been affected by earthquakes since 1992.The chosen area is close to the city centre, in immediate proximity to the Cyril andMethodius Park, as shown in Figure 10. It is a very busy area (resulting in a high exposure),surrounded by ancient buildings which were not designed to resist horizontal actions. Thisfact, together with the historical stratifications that characterise the site, make it the perfectlocation for applying the method. In this context, eight different load-bearing masonrybuildings characterised by varied construction techniques and functions were assessed(Figure 11).Buildings 2023, 13, 344 16 of 30 Figure 10. Belgrade case study and the eight buildings analysed. Figure 11. The buildings assessed for the Belgrade study; © Google. Similar to other case studies, expeditious assessment was initially conducted on the observation of structural elements, and archival material was used to reconstruct the con-struction history. Structural and architectural plans were also found for all the buildings. No surveys were carried out using advanced techniques. Building (a) is currently used as the University canteen and dormitory (public build-ing). It was built in 1926 and has a load-bearing structure composed of brickwork. The floors consist of RC cast-in-situ ribbed slabs. The building has a large inner courtyard and is developed as a trapezoid on the four perimeter sides. Building (b) is used for shops on the ground floor and as a residential building on the other levels. It has a highly irregular plan and is characterised by load-bearing brick masonry walls. The investigations carried out did not reveal any recent structural interventions. The other buildings have many common features: they were made of load-bearing masonry, have at least four floors above ground, and were built between 1930 and 1960. The main differences are related to Figure 10. Belgrade case study and the eight buildings analysed.Buildings 2023, 13, 344 16 of 30Buildings 2023, 13, 344 16 of 30 Figure 10. Belgrade case study and the eight buildings analysed. Figure 11. The buildings assessed for the Belgrade study; © Google. Similar to other case studies, expeditious assessment was initially conducted on the observation of structural elements, and archival material was used to reconstruct the con-struction history. Structural and architectural plans were also found for all the buildings. No surveys were carried out using advanced techniques. Building (a) is currently used as the University canteen and dormitory (public build-ing). It was built in 1926 and has a load-bearing structure composed of brickwork. The floors consist of RC cast-in-situ ribbed slabs. The building has a large inner courtyard and is developed as a trapezoid on the four perimeter sides. Building (b) is used for shops on the ground floor and as a residential building on the other levels. It has a highly irregular plan and is characterised by load-bearing brick masonry walls. The investigations carried out did not reveal any recent structural interventions. The other buildings have many common features: they were made of load-bearing masonry, have at least four floors above ground, and were built between 1930 and 1960. The main differences are related to Figure 11. The buildings assessed for the Belgrade study; © Google.Similar to other case studies, expeditious assessment was initially conducted on theobservation of structural elements, and archival material was used to reconstruct econstruction history. Structural and architectural plans were also found for all the buildings.No surveys were carried out using advanced techniques.Building (a) is currently used as the University canteen and dormitory (public build-ing). It wa built in 1926 an has a load-b aring structure composed of brickwork. Thefloors consist of RC cast-in-situ ribbed slabs. The building has a large inner courtyardand is developed as a trapezoid on the four perimeter sides. Building (b) is used forshops on the ground floor nd as a residential building on the other levels. It has ahighly irregular plan and is characterised by load-bearing brick masonry walls. The in-vestigations carried out did not reveal any recent structural interventions. The otherbuildings have many common features: they were made of load-bearing masonry, haveat least four floors above ground, and were built between 1930 and 1960. The main dif-ferences are related to the configuration and the technology used to construct the floors(precast concrete or cast-in-situ reinforced slab). Table 10 shows the results of the Belgradecase study.Buildings 2023, 13, 344 17 of 30Table 10. Result of the evaluation of buildings in Belgrade, Serbia.Building ID Index of StructuralResponse Masonry CategoriesMost ProbableCollapse Mechanism Seismic RiskSeismic RiskCategoryBuilding a III (0.43) B, A, A Vertical Deflection 0.42 LowBuilding b II (0.33) B, A, A Cantonal Overturning 0.33 MediumBuilding c IV (0.67) A, A, A Vertical Deflection 0.22 LowBuilding d IV (0.65) A, A, A Vertical Deflection 0.23 LowBuilding e IV (0.67) A, A, A Vertical Deflection 0.22 LowBuilding f II (0.33) B, A, A Cantonal Overturning 0.45 LowBuilding g V (0.72) A, A, A Vertical Deflection 0.21 LowBuilding h IV (0.59) A, A, A Vertical Deflection 0.25 Low3.4. Results and DiscussionIn most cases, cadastral plans, storey heights, and an on-site inspection (or pho-tographs) were sufficient to carry out the expeditious assessment. Required documentationis usually readily available and it is not required to use advanced equipment or performdetailed surveys, although, in some cases, obtaining all the necessary information couldstill be difficult and time-consuming. Some challenges were encountered while surveyingbuildings with plaster because the correct implementation of the M.Q.I. was difficult. Inthose situations, or even where little or no material is available, it is possible to assumethe building construction period, the most common construction techniques, and the sur-veyor’s experience. Furthermore, the approach is not accurate in the application on specialstructures (such as towers, campaniles, and churches), as it is designed to assess ordinarybuildings such as residences, shops, etc. This method is particularly suitable for applica-tions on a large scale when it is often not possible to find all the information. The loss ofaccuracy of the final results obtained in this way is partly compensated by the use of thecategories (I to VI) associated with the index of structural response. The six categories areintended to simplify the outcome of verifications and to consider wide ranges of values,making inaccurate information input less significant.The analysis of the study areas confirmed that the application of the method takes a fewminutes per building (provided that the information was previously acquired) and givessufficient time for the surveyor to derive the outputs and suggest structural intervention.The use of categories (I, II, III) simplifies the procedure, making it more user-friendly foroperators with different cultural and educational backgrounds. The analysis of the optionscontained in the database, both in terms of proposed improvement measures and selectedconstruction techniques, proved extensive enough to cover all the cases that arose in theapplication phases. In addition, the “notes” box allows the user to specify any details notpresent in the archive.Figure 12 summarises the structural response categories recorded in the three casestudy areas. Analysis of the surveys form showed a good distribution of results, withan exception for the two extreme categories (I–VI). Category IV is the most populated(accounting for 43.8% of the results), followed by categories II and III (25%). Only a singlecase falls in category V. In general, the results showed that the Kaštela area appears to bethe least susceptible to possible seismic actions, having recorded the highest structuralbehaviours (IV, III). In contrast, the Mirandola area showed generally poor structuralresponses (II and III).The analysis of the out-of-plane kinematic mechanisms showed a good distribution ofresults: “vertical deflection” proved to be the most frequent (43.8%), followed by “horizon-tal deflection” (31.2%) and “cantonal overturning” (25%); while the kinematic mechanismof simple masonry overturning was not encountered.Buildings 2023, 13, 344 18 of 30Figure 12. The index of structural response for the three study areas.The results of the M.Q.I. method highlighted the importance of the masonry qualityconcerning the outcome offered by the structural response index. In general, high masonryvalues (majority of categories A and B) were associated with high response categories (asobserved in the Kaštela area).A significant variety of construction techniques, seismic hazards, and seismic ex-posure of the buildings in the three study areas were encountered in the results of theexpeditious method.4. Validation of the Adriseismic Method4.1. A Comparison of Traditional Seismic Analysis and Expeditious MethodThe procedure was verified using seismic analysis results for a sample of 25 buildingsfrom Italy to understand the method’s accuracy. The analysis results were compared withthose obtained for the same constructions using the expeditious method. These buildingshave different characteristics in terms of the construction period, the number of floors, planarticulation, the function of use, etc. Although limited in number, the sample covers abroad spectrum of structural types, but Appendix C lists the main characteristics.The sample of structures, used for the validation, was analysed using two differentmethods: some buildings were assessed using the LV1 system [38] and others usingmulti-modal analysis. Multi-modal analysis is prescribed by Eurocode 8 and is one of thewidely used methods, while the LV1 method is based on an Italian Directive and allowsan expeditious assessment using a limited number of parameters. The validation aimsto verify the results of the proposed expeditious method by comparing them with thoseobtained from a traditional analysis method and those obtained through an establishedexpeditious method.A result of the LV1 method is a seismic safety index (Is, ls), which is defined as theratio between the return fundamental period of the seismic action that leads to the genericlimit state and the corresponding reference period, which is calculated based on the coderequirements. The Is value has a range from 0 (total inadequacy) to 1 (adequate) as averification condition. This indicator is comparable to the index of structural responsewhich is defined in the proposed Adriseismic method. The results obtained from theLV1 and from a traditional analysis method are based on the structural characteristics,the exposure (usually indicated as class of use), and seismic hazard at the site. On theother hand, the proposed method determines the structural response index based on theBuildings 2023, 13, 344 19 of 30structural feature, and then the seismic risk is determined as a product of vulnerability,hazard, and exposure. However, the comparison of these results of the other two methodswith the structural response index appears to be mathematically more effective than theestimated seismic risk determined.The modal analysis applied to a structure produced a capacity/demand ration for eachload-bearing element. This value is expressed in the same range as the index Is, ls of the LV1method (values greater than 1 indicate satisfactory verifications). However, in the case ofnon-linear static analysis, there is no single parameter that summarises the global behaviourof the structure, but there are parameters for each load-bearing element. Therefore, theweighted average for all load-bearing elements, Ima, is considered comparable to thestructural response index and can be determined as follows:Ima =∑ni=1(xi·pi)∑ni=1 pi(13)4.2. Results and DiscussionTable 11 shows the results from the traditional seismic analysis methods in terms ofthe two indices Ima and Is, which are compared with the structural response index for25 buildings.Table 11. Results of the validation—traditional vs. expeditious methods.Building ID(1)Type of Analysis(2)Results fromTraditional Analysis,Ima, and Is (3)Index of StructuralResponse, Isr (4)VulnerabilityCategory (5)|1 − Isr/I|(6)M001 LV1 0.85 0.74 V 0.13M002 LV1 0.02 0.24 II 11.00M003 LV1 0.35 0.25 II 0.29M004 LV1 0.37 0.23 II 0.38M005 LV1 0.38 0.25 II 0.34M006 LV1 0.38 0.25 II 0.34M007 LV1 0.51 0.46 III 0.10M008 LV1 0.34 0.34 II 0.00M009 LV1 0.10 0.17 I 0.70M010 LV1 0.34 0.38 II 0.12M011 LV1 0.27 0.34 II 0.26M012 LV1 0.36 0.38 II 0.06M013 LV1 0.51 0.40 III 0.22M014 LV1 0.48 0.42 III 0.13M015 LV1 0.77 0.43 III 0.44M016 Modal 0.26 0.23 II 0.12M017 Modal 0.51 0.28 II 0.45M018 Modal 0.33 0.32 II 0.03M019 Modal 0.82 0.78 V 0.05M020 Modal 0.42 0.28 II 0.33M021 Modal 0.28 0.34 II 0.21M022 Modal 0.63 0.34 II 0.46M023 Modal 0.69 0.48 III 0.30M024 Modal 0.97 0.75 V 0.23M025 Modal 0.92 0.63 IV 0.32The last column shows the comparison between the values obtained from traditionalanalysis and the structural response index using the formula:∣∣∣∣1− IsrI∣∣∣∣ (14)Buildings 2023, 13, 344 20 of 30Figure 13 shows the same results in a graphical manner. For each building, the resultsfor traditional analysis and the index of structural response obtained from the expeditiousmethods have been compared.Buildings 2023, 13, 344 20 of 30 The last column shows the comparison between the values obtained from traditional analysis and the structural response index using the formula: ฬ1 − 𝐼௦௥𝐼 ฬ (14)Figure 13 shows the same results in a graphical manner. For each building, the results for traditional analysis and the index of structural response obtained from the expeditious methods have been compared. Figure 13. Results of the validation—traditional vs expeditious methods. A comparison of sample buildings analysed using the LV1 method shows a similarity between the structural response index Isr and Is. There is an average variation of about 25% between the results of the traditional and the proposed expeditious method, with a standard deviation of 0.18. Furthermore, in most cases, the expeditious method gives more conservative results compared to the LV1. These considerations excluded building no. 2 (M002) at this stage because the differ-ence between the two results (expeditious and LV1) is small in terms of absolute value (0.22). At the same time, it is important from a relative point of view, and with such a small sample, that the outlier would have affected the outcome of the collected data. An average variation of 25% and a standard deviation of (0.15) were obtained for comparison with modal analysis. Out of ten analysed buildings, only once did the expe-ditious method overestimate the capacity of the building to a very limited extent (6% higher). The aggregation of the two methods (LV1 and modal) gives an average variation of 25% and a standard deviation of 0.167. There are no substantial differences between the two methods in terms of the varia-tion in results proposed by the expeditious method, which gives good accuracy for a qual-itative system. This confirms that the method allows for the identification of the most crit-ical buildings, effectively indicating the ones which require a more in-depth analysis, thereby ensuring a more efficient use of resources. However, a larger building sample will have to be analysed before definitive conclusions can be established. 5. Conclusions The research study presented in this paper was focused on the development of the Adriseismic method for expeditious seismic assessment of URM buildings. The proposed method was developed to mitigate seismic risk associated with urban heritage buildings 0.850.020.35 0.370.38 0.380.510.340.10.340.270.360.510.480.770.260.510.330.820.420.280.630.690.970.9200.20.40.60.811.2 M001 M002 M003 M004 M005 M006 M007 M008 M009 M010 M011 M012 M013 M014 M015 M016 M017 M018 M019 M020 M021 M022 M023 M024 M025Results from traditional analysis Index of structural responseFigure 13. Results of the validation—traditional vs. expeditious methods.A comparison of sample buildings analysed using the LV1 method shows a similaritybetween the structural response index Isr and Is. There is an average variation of about25% between the results of the traditional and the proposed expeditious method, with astandard deviation of 0.18. Furthermore, in most cases, the expeditious method gives moreconservative results compared to the LV1.These considerations excluded building no. 2 (M002) at this stage because the differ-ence between the two results (expeditious and LV1) is small in terms of absolute value(0.22). At the same time, it is important from a relative point of view, and with such a smallsample, that the outlier would have affected the outcome of the collected data.An average variation of 25% and a standard deviation of (0.15) were obtained for com-parison with modal analysis. Out of ten analysed buildings, only once did the expeditiousmethod overestimate the capacity of the building to a very limited extent (6% higher). Theaggregation of the two methods (LV1 and modal) gives an average variation of 25% and astandard deviation of 0.167.There are no substantial differences between the two methods in terms of the variationin results proposed by the expe itious method, whic gives good accuracy for a qualitativesystem. This confirms that the method allows f r the dentification of the most criticbuildings, effectively i dicating the ones which require a more in-dep h analysis, therebyensuring a more e fi ient use of resources. However, a larger building sampl will have tobe anal sed before definitive co clusi ns can be established.5. ConclusionsThe research study presented in this paper was focused on the development of theAdriseismic method for expeditious seismic assessment of URM buildings. The proposedmethod was developed to mitigate seismic risk associated with urban heritage buildings insix countries located close to the Adriatic and Ionian Seas and is one of the key deliverablesof the Adriseismic project.The first phase of the study involved the development of the expeditious seismicassessment system, with a choice of input parameters and assigned numerical values.The expected seismic performance of the building was estimated based on the proposedmethodology through a Microsoft Excel spreadsheet, and the output included masonryBuildings 2023, 13, 344 21 of 30category, index of structural response, most probable collapse mechanism, and seismicrisk level.Subsequently, the method was applied in three heterogeneous urban areas, namelyMirandola (Italy), Kaštela (Croatia), and Belgrade (Serbia). In parallel, the method wasvalidated on 25 sample buildings, which were previously evaluated using the LV1 method(expeditious assessment) and modal analysis (traditional seismic analysis). In this manner,the method was validated both in terms of its applicability and the accuracy of results. Thevalidation showed an average variation of 25% and a standard deviation of 0.167 betweenthe index of structural response and the indices Ima and Is. These encouraging resultswill need to be confirmed by increasing the number of sample buildings and analysingthe results of damage kinematics and pushover analyses in order to assess the accuracy ofthe method.The application of the method on selected buildings in three urban areas in differentcountries proved to be very important for testing the practical applicability of the procedure.The results showed that information required at the preliminary stage was almost alwayseasy to obtain. It was found that in large-scale applications (a large number of buildingsand limited input data), the loss of accuracy associated with the output was relativelylow, e.g., a category II building tends to remain in the same category for small variationsin input data; therefore, the use of categories (e.g., I, II, III, etc.), rather than a range ofnumerical values, makes it possible to limit the incidence of errors or inaccuracies in datacollection. The distribution of the results and their variety, in terms of response classes,collapse mechanism, and seismic risk, seem consistent with the case studies. However, it isnecessary to perform similar tests on a larger number of buildings and other urban areasin order to collect data related to the distribution of results and the size of the database,especially regarding the construction characteristics and seismic intervention techniques.The final aspect of the expeditious method was related to recommended structuralimprovement measures, which enables the user to identify a deficiency in the building andmake a preliminary suggestion for intervention.In spite of the cultural and technical differences, the development of common seis-mic assessment procedures is the first step towards increasing cooperation in the partnercountries involved in the Adriseismic project, which can lead towards a general mitiga-tion of seismic risk by combining typical earthquake engineering procedures with urbanplanning systems.Author Contributions: Conceptualisation, G.P. and L.S.; methodology, L.S. and G.P.; software, L.S.and G.P.; validation, G.P., L.S., M.M. and M.S.; formal analysis, L.S., G.P. and S.B.; investigation,L.S. and G.P.; resources, L.S. and G.P.; data curation, L.S., G.P. and S.B., writing—original draftpreparation, L.S. and G.P.; writing—review and editing, S.B. and L.S.; visualisation, G.P.; supervision,G.P. and S.B.; project administration, G.P.; funding acquisition, G.P. All authors have read and agreedto the published version of the manuscript.Funding: This research was funded by the Adriseismic project, of the programme Interreg ADRION“https://www.adrioninterreg.eu/ (accessed on 20 December 2022)”. INTERREG V-B ADRIATIC-IONIAN ADRION PROGRAMME 2014–2020: ADRISEISMIC 1019.Data Availability Statement: Data regarding the expeditious method and validation are not availableas they concern studies still in progress.Acknowledgments: The authors would like to thank the Adriseismic project of the Interreg ADRIONprogramme for the financial support.Conflicts of Interest: The authors declare no conflict of interest.Buildings 2023, 13, 344 22 of 30NomenclatureCo Corner overturningCo,n Corner overturning, normalisedDu Designated useE ExposureEd Expected ductilityFn Floors numberg Thickness of mortar jointsH Seismic hazardHb Horizontal bendingHb,n Horizontal bending, normalisedHj Horizontality of mortar bed jointsI Result obtained from traditional analysis (modal or LV1)Ih Irregularity in heightIma Index derived from modal analysisInh Inter-floor heightIp Irregularity in planIsr Index of structural responseIv vulnerability index; (1/Is)m Additional mortar quality coefficientMm Quality of mortarMQIv Quality masonry index for vertical actionsMQIop Quality masonry index for out-of-plane actionsMQIip Quality masonry index for in-plane actionsPa Thrusts due to arches and vaultsPf w Permanent floor weightPi Structural element verificationPr Thrusts due to roofsPsd Parameters influencing seismic demandPsd,n Parameters influencing seismic demand, normalisedr Type of masonry unitsSd Dimensions of the masonry unitsSh Seismic riskSm Mechanical characteristics and quality of masonry unitsSmo Simple masonry overturningSmo,n Simple masonry overturning, normalisedSs Shape of the masonry unitsSw Stiffening wall distanceVb Vertical bendingVj Staggering of vertical mortar jointsVb,n Vertical bending, normalisedWc Level of connection between adjacent wall leaves/headerWt Wall thicknessxi Generic vertical elementAppendix A. Input DataThis section details all the inputs provided in the method divided by category, as seenin Table A1. In the first column is a brief description of the parameter; in the second is thevalues that can be entered. For the inputs that influence the final assessment results, theweights considered in the system are also shown.Buildings 2023, 13, 344 23 of 30Table A1. General data.Name and Description Possible Values1 DataThe date of compilation of the evaluation sheet is requested dd/mm/yy2 Building AddressThe address of the building under evaluation is required Alphanumeric entry3 Presumed year of constructionThe user can enter a year of construction of the building, or a period Alphanumeric entry4 G.P.S. coordinates Coordinates in WGS84 formatTable A2. Construction characteristics.Name and Description Possible Values5FoundationThe prevailing type of foundationdetected or assumed must be enteredStepped foundation, engraved in the rockRegular stone masonry foundationIrregular stone masonry foundationStone rubble foundation with concrete binderBrick masonry foundationsContinuous reinforced concrete foundations (strip footings)Wooden pilesReinforced concrete pilesInverted beams foundationIsolated footingSlab foundation6MasonryThe prevailing type of masonry detectedor assumed must be enteredRubble stone masonryRubble masonry with regular-sized stonesRubble masonry with bricksCut stone with good bondingMasonry in rammed earth blocksTuff masonryDressed rectangular (ashlar) stone masonrySolid brick masonry with lime mortarSolid brick masonry with cement mortarMasonry in brick or cement blocks with cement mortarReinforced masonry with distribution reinforcementConfined masonry with concentrated reinforcementTimber-reinforced masonry7FloorsThe prevailing type of floor detected orassumed must be enteredSingle or double timber floors (beams and joists) with asimple wooden plankSingle or double timber floors (beams and joists) withbrick tilesFloors with metal beams and vaults made with brick tilesFloors with metal beams and hollow bricksBrick vaultsStone vaultsCast-in-situ reinforced concrete slabHollow clay block floor without a reinforced concrete slabHollow clay block floor with reinforced concrete slabPrefabricated reinforced concrete floorHollow brick floor with prefabricated joistsBuildings 2023, 13, 344 24 of 30Table A2. Cont.Name and Description Possible Values8RoofThe prevailing type of roof detected orassumed must be enteredSingle or double timber floors (beams and joists) with asimple wooden plankSingle or double timber floors (beams and joists) withbrick tilesFloors with metal beams and vaults made with brick tilesFloors with metal beams and hollow bricksBrick vaultsStone vaultsCast-in-situ reinforced concrete slabHollow clay block floor without a reinforced concrete slabHollow clay block floor with reinforced concrete slabPrefabricated reinforced concrete floorHollow brick floor with prefabricated joists9Notes on inputSpace is left to allow for specifications onthe building under investigationAlphanumeric entryTable A3. Masonry characteristics.Name and Description Possible ValuesWeight Attributed by the SystemVertical Loads Out-of-Plane Actions In-Plane Actions10 Type of masonry unitsThe values are assignedaccording to the choice ofquality of mortar (N.F., P.F., F.)Stone 1 1 1BrickN.F. 0.2P.F. 0.6F 11110.10.85111 Horizontality of mortarbed jointsN.F. 0 0 0P.F. 1 1 0.5F. 2 2 112 Level of connection betweenadjacent wall leaves/headerN.F. 0 0 0P.F. 1 1.5 1F. 1 3 213Shape of the masonry unitsN.F. 0 0 0P.F. 1.5 1 1F. 3 2 214 Staggering of verticalmortar jointsN.F. 0 0 0P.F. 0.5 0.5 1F. 1 1 215 Dimensions of themasonry unitsN.F. 0 0 0P.F. 0.5 0.5 1F. 1 1 216Quality of mortarN.F. 0 0 0P.F. 0.5 0.5 1F. 2 1 217 Mechanical characteristicsand quality of masonry unitsN.F. 0.3 0.5 0.3P.F. 0.7 0.7 0.7F. 1 1 118 Thickness of mortar joints Large 0.7 0.7 0.7Standard 1 1 119 Additional mortarquality coefficientPoor 0.7 0.7 0.7Standard 1 1 1Buildings 2023, 13, 344 25 of 30Table A4. Building characteristics.Name and Description Possible Values Weight Attributed by the System20Designated useResidential 0.15Commercial 0.12Public 0.0021Floors above ground1 0.112 0.003 0.004 0.015 0.2022Irregularity in planI 0II 1.5III 323Irregularity in heightI 0.25II 0.12III 0.0024Expected ductilityI 0.00II 0.33III 0.6725Connections betweenstructural elementsOn The parameter is not associated with aspecific value but directly influencesthe formula used to define the index ofstructural response, as will beillustrated in the dedicated sectionOffTable A5. Building characteristics (kinematics).Name andDescription Possible ValuesWeight Attributed by the SystemSimple MasonryOverturning Vertical BendingHorizontalBendingCornerOverturning26Transversalwall distanceI 0.00 0.00 1.00 0.00II 0.00 0.00 0.50 0.00III 0.00 0.00 0.00 0.0027Wall thicknessI 0.00 0.00 0.00 0.00II 0.50 0.50 0.50 0.50III 1.00 1.00 1.00 1.0028Floor heightI 1.00 1.00 1.00 1.00II 0.50 0.50 0.50 0.50III 0.00 0.00 0.00 0.0029 Permanentfloor weightsI 0.00 1.00 0.00 0.00II 0.00 0.50 0.00 0.50III 0.00 0.00 0.00 1.0030 Thrusts dueto archesand vaultsI 1.00 1.00 1.00 0.00II 0.50 0.50 0.50 0.00III 0.00 0.00 0.00 0.0031Thrusts due tothe roofI 1.00 0.00 0.00 1.00II 0.50 0.00 0.00 0.50III 0.00 0.00 0.00 0.00Buildings 2023, 13, 344 26 of 30Table A6. Site data.Name and Description Possible Values Weight Attributed by the SystemAg/gThis is the ratio between the designground acceleration, on type A soil, andthe gravity accelerationNumerical value The number entered is replicatedGround typeThe soil type is required according to theguidelines of Eurocode 8 Part 1, chapter3.2.1. it is possible to enter a categoryfrom A to E (type 2 elastic spectrum)A, B, C, D, E A = 1.0; B = 1.35; C = 1.50; D = 1.80;E = 1.60Building exposureThe exposure is assessed using theimportance classes given in Table 4.3 ofEurocode 8, Part 1I, II, III, IV I = 0.8; II = 1.0; III = 1.20; IV = 1.40Appendix B. Building CharacteristicsThe values are derived from simplified formulations or general schematisation, definedwith the specific purpose of evaluating the variation in output parameters due to thevariation in input parameters. Sometimes it was analysed how a single parameter couldinfluence the seismic demand and, other times, the structural response. The complexity ofstudying these variations in virtual situations (e.g., it is unlikely that in reality, one wouldsee an increase in loads, hence greater mass, without an increase in the masonry section,thus an increase in seismic capacity) required a certain flexibility in the interpretation ofthe results, at the expense of rigorous formulations. General considerations for defining theweights of certain input parameters are summarised next:1. Designated use: The parameter considers the typical loads assigned by Eurocode 1 [54].Specifically, residential (200 Kg/sm), commercial (300 Kg/sm), and public (400 Kg/sm)were evaluated. Starting from invariant permanent loads, the mass variation wasanalysed using the coefficients provided for the seismic combination, Eurocode 8. Thevalues were then correlated to obtain the percentage of variation relative to each other.The worst parameter for structural response (Public) was given a value of 0; the othertwo were higher than the first (Commercial 0.12 and Residential 0.15).2. Floors above ground: The analysis of the variation in the structural response asthe number of storeys varied imposed several parallel considerations. Firstly, theseismic design action was determined using the formula: Sq = Se·W/q. Where Se isthe spectral acceleration, assumed by imagining the building located in Bologna onground A (the period is that resulting from the simplified formula in Section 4.3.2.2of Eurocode 8), the mass depends on the number of floors, with fixed dead andlive loads. The behaviour factor varies according to the structure’s greater or lesserdissipative capacity.Secondly, the response capacity of the building was determined using the simplifiedMohr–Coulomb criterion [55], using the quality of the masonry “solid brick and limemortar” as an unchanging parameter [56] and the thickness of the resisting panels (24 cm,24 cm, 36 cm, 36 cm, and 48 cm, respectively) as a factor dependent on the number of floors.The values used in the method are the result of the capacity–demand ratio performedfor each storey, then correlated with each other to provide, as for the designated use, thepercentage of variation in one concerning the other (the worst always have value 0).It is evident that the weights obtained result from choices made in advance andthat different options could have led to slightly different results. Although considera-tions may be made in the future to make the procedure less dependent on specific de-cisions, it is nevertheless believed that the values provided can provide a guideline forexpeditious analyses.Buildings 2023, 13, 344 27 of 303. Irregularity in plan: The values derived from the indications given in paragraph 7.3.1of Italian NTC [57], regarding determining the behaviour factor as the greater or lesserregularity in the plan of a building varies. Again, the three results obtained werecorrelated by formulating them as percentage variations (the less regular building hasa value of 0; the regular one, 0.26). The Italian standard was used because no specificreferences were found in the European one.4. Irregularity in height: The computation was carried out using Section 9.3 of Eurocode8, part 1, in which guidance is given on reducing the q-factor by 20% for buildingsthat are not regular in height. This resulted in: regular buildings = 1.0, partiallyregular = 0.9, and irregular = 0.8. Using the formula, already used for the otherparameters, to correlate the three values: vi = 1− valivalmin where vali denotes the genericvalue and valmin the lowest of the three; the three weights of 0 (worst case), 0.12, and0.25 were obtained.5. Expected ductility: For masonry buildings, it was assumed that the behaviour factorcould be numerically equal to: (1.5; 2.0; 2.5). The three weights were obtained usingthe same procedure as illustrated above (and the same formula for correlating thevalues), which were then implemented in the expeditious method (0.0; 0.33; 0.67). Thevalue 0 was attributed to the worst category (I) and 0.67 to the best (III).6. Connections between structural elements: As already specified, the parameter is notassociated with any specific numerical value, and its presence influences the formulaeused in calculating the structural response index.Appendix C. Summary of Building CharacteristicsAppendix C shows the main characteristics of the 25 buildings analysed.Table A7. Main characteristics of the sample buildings.BuildingCodePeriodof ConstructionDesignedUseHeight(Number ofStoreys)Typeof MasonryTypeof Floor SystemM001 1930–40 Public 3 Solid brick masonrywith lime mortarHollow clay block floor withoutreinforced concrete slabM002 1900–1910 Residential 5 Solid brick masonrywith lime mortarFloors with metal beams andvaults made with brick tilesM003 Before 1900 Residential 3 Rubble stone masonry Floors with metal beams andvaults made with brick tilesM004 Before 1900 Residential 2 Rubble stone masonry Floors with metal beams andvaults made with brick tilesM005 1940 Public 4 Solid brick masonrywith lime mortarHollow clay block floor withoutreinforced concrete slabM006 1940 Public 4 Solid brick masonrywith lime mortarHollow brick floor withprefabricated joistsM007 Before 1900 Public 4 Solid brick masonrywith lime mortarFloors with metal beams andvaults made with brick tilesM008 Before 1900 Public 4 Solid brick masonrywith lime mortarCast-in-situ reinforcedconcrete slabM009 Before 1900 Public 1 Solid brick masonrywith lime mortar Brick vaultsM010 1920–1930 Residential 4 Solid brick masonrywith lime mortarHollow clay block floor withoutreinforced concrete slabM011 Before 1900 Public 4 Solid brick masonrywith lime mortarHollow brick floor withprefabricated joistsM012 Before 1900 Public 3 Solid brick masonrywith lime mortarSingle or double timber floors(beams and joists) with brick tilesBuildings 2023, 13, 344 28 of 30Table A7. Cont.BuildingCodePeriodof ConstructionDesignedUseHeight(Number ofStoreys)Typeof MasonryTypeof Floor SystemM013 Before 1900 Public 3 Solid brick masonrywith lime mortarCast-in-situ reinforcedconcrete slabM014 1930 Public 2 Solid brick masonrywith lime mortarCast-in-situ reinforcedconcrete slabM015 Before 1900 Public 3 Solid brick masonrywith lime mortarFloors with metal beams andvaults made with brick tilesM016 Before 1900 Public 3 Rubble masonrywith bricks Brick vaultsM017 Before 1900 Public 3 Rubble masonrywith bricks Brick vaultsM018 Before 1900 Public 3 Rubble masonrywith bricks Brick vaultsM019 Before 1900 Public 4 Solid brick masonrywith lime mortarHollow clay block floor withoutreinforced concrete slabM020 Before 1900 Public 3 Solid brick masonrywith lime mortar Brick vaultsM021 Before 1900 Public 4 Solid brick masonrywith lime mortarHollow clay block floor withoutreinforced concrete slabM022 Before 1900 Public 4 Solid brick masonrywith lime mortarSingle or double timber floors(beams and joists) with brick tilesM023 Before 1900 Public 3 Solid brick masonrywith lime mortarSingle or double timber floors(beams and joists) with brick tilesM024 Before 1900 Public 2 Rubble masonrywith bricksHollow clay block floor withoutreinforced concrete slabM025 Before 1900 Public 4 Solid brick masonrywith lime mortarHollow clay block floor withoutreinforced concrete slabReferences1. 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eng
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Vancouver : University of British Columbia Library
Multidisciplinary Digital Publishing Institute
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unreinforced masonry structures
Adriseismic project
seismic vulnerability assessment
risk prediction
seismic failure mechanisms
existing buildings
Adriseismic Methodology for Expeditious Seismic Assessment of Unreinforced Masonry Buildings
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