Seismic Vulnerability Assessment of Historic Constructions in the Downtown of Mexico City

: Seismic risk is determined by the sum of multiple components produced by a certain seismic intensity, being represented by the seismic hazard, the structural vulnerability and the exposure of assets at a speciﬁed zone. Most of the methods and strategies applied to evaluate the vulnerability of historic constructions are specialized in buildings with higher importance, either public or private, by relegating ordinary dwellings to a second plane. On account of this, this paper aims to present a seismic vulnerability assessment, considering a limited urban area of the Historic Downtown of Mexico City (La Merced Neighborhood), thus showing the analysis of 166 historic buildings. The seismic vulnerability assessment of the area was performed resorting to a simpliﬁed seismic vulnerability assessment method, composed of both qualitative and quantitative parameters. To better manage and analyze the human and economic exposure, the results were integrated into a Geographic Information System (GIS) tool, which allowed to map vulnerability and damage scenarios for di ﬀ erent earthquake intensities.


Introduction
As is widely known, while seismic hazard involves the probability of occurrence of a seismic event [1], which can be represented by an exposure model [2], seismic vulnerability can be defined as the intrinsic predisposition of an element to suffer damage from a seismic event of a given intensity. Specifically concerning Heritage Sites, the elements considered are the inherent features of a cultural heritage site, a group of buildings, monuments or objects, as well as their institutional and/or socio-economic context [3]. In terms of the vulnerability of historic buildings, it is fundamental that vulnerability studies address the assessment of potential damages and, based on those, discuss possible rehabilitation and/or retrofit interventions and supported pre-and post-disaster decisions [4][5][6].
Aimed at contributing to this discussion, a pilot area of the Mexico City Downtown is comprehensively investigated herein by analyzing and intercrossing its historical seismicity with the most relevant architectural, construction and structural features of the buildings. For this purpose, a matrix of thirty-six typologies of residential and historical buildings was assessed, resorting to a simplified seismic vulnerability assessment. Over this assessment, the identification of the most vulnerable aspects of the building stock allowed the presentation of damage scenarios, generated by different macroseismic intensities. Geographical Information Systems (GIS) tools play an essential role in the establishment of urban management, civil protection, and risk disaster strategies. For that reason, this analysis was established by mapping and discussing all outputs through the free and open-source software QGIS ver. 3.8.1 (QGIS Development Team: Zanzibar) [7].
Recently, in 2017, two intense earthquakes occurred on 7th of September and 19th of September. The first (7th September) occurred near the coast of Oaxaca with a subduction event of M s = 8.2, while the second was a local event with an epicenter located in Axochiapan, Morelos with M s = 7.1 (19th September). Due to these seismic events, a large number of losses affecting immovable cultural heritage were reported in different zones of the Central and Southwest part of the country. The earthquake of the 7th of September 2017 could correspond to the absence of seismic activity located at the Tehuantepec Gap, in the State of Oaxaca, as seen in Figure 1b.  Figure 1b shows not only the earthquake near the Tehuantepec Gap but also the seismic activity that occurred during the 20th century and was recorded by the National Seismologic Service of Mexico (SSN). The map (Figure 1b) depicts, along the coast of Guerrero, the absence of seismic activity, which is well-known as the Guerrero Gap. This Gap, located about 300 km from Mexico City, can signify possible future seismic events produced by interplate movements (i.e., subduction trust events), with similar or higher magnitudes than those that occurred in 1985 and 2017 with significant impact on Mexico City. However, the consequences of these seismic events in the city do not depend only on interplate movements, but also on volcanic activity (i.e., the Popocatepetl volcano) [13], denoting a seismic risk between two possible geologic phenomena.

Buildings Exposure Model
Numerous researches have proposed different methodologies to achieve closer approaches to the history of construction and architecture related to buildings from the 16th century to the beginning of the 20th century. Most of the buildings in the historic center are considered of cultural heritage, catalogued by the National Institution of Anthropology and History (INAH) or by the National Institute of the Fine Arts (Instituto Nacional de Bellas Artes-INBA). Nonetheless, over their lifespan, some of the buildings have been refurbished or retrofitted, resorting to different construction technologies and materials, some of them poorly compatible with the original characteristics of these buildings. A categorical example of such inadequate intervention is the use of concrete or cement-based materials, which are chemically, physically and mechanically incompatible with traditional construction technologies. A comprehensive discussion on this aspect was recently given by Correia Lopes et al. [16]. To determine the characterization of the buildings, highlighting the wide ranges and complex task of collecting the data, the typology matrix presented in Tables 1-3   not depend only on interplate movements, but also on volcanic activity (i.e., the Popocatepetl volcano) [13], denoting a seismic risk between two possible geologic phenomena.

Buildings Exposure Model
Numerous researches have proposed different methodologies to achieve closer approaches to the history of construction and architecture related to buildings from the 16th century to the beginning of the 20th century. Most of the buildings in the historic center are considered of cultural heritage, catalogued by the National Institution of Anthropology and History (INAH) or by the National Institute of the Fine Arts (Instituto Nacional de Bellas Artes-INBA). Nonetheless, over their lifespan, some of the buildings have been refurbished or retrofitted, resorting to different construction technologies and materials, some of them poorly compatible with the original characteristics of these buildings. A categorical example of such inadequate intervention is the use of concrete or cement-based materials, which are chemically, physically and mechanically incompatible with traditional construction technologies. A comprehensive discussion on this aspect was recently given by Correia Lopes et al. [16]. To determine the characterization of the buildings, highlighting the wide ranges and complex task of collecting the data, the typology matrix presented in Tables 1-3     The next on the list is typology T14 with 7% and 12 buildings, which results from the consideration of geometry B and material M5; and T13 with approximately 5.8% corresponding to 10 buildings (B and M4). These are followed by T34 (D and M7) and T22 (C and M4), which have a percentage of almost 5.2% each (nine buildings respectively). T30 (correlation between D and M3) has 4.6% that is equivalent to eight buildings. The ratio of T10 (B and M1), T28 (D and M1), T29 (D and M2) and T32 (D and M5) is almost 3.4% each (six buildings each). Typologies T2, T3, T5, T8, T9,  T15, T16, T17, T18, T19, T20, T21, T23, T24, T25, T26  The next on the list is typology T14 with 7% and 12 buildings, which results from the consideration of geometry B and material M5; and T13 with approximately 5.8% corresponding to 10 buildings (B and M4). These are followed by T34 (D and M7) and T22 (C and M4), which have a percentage of almost 5.2% each (nine buildings respectively). T30 (correlation between D and M3) has 4.6% that is equivalent to eight buildings. The ratio of T10 (B and M1), T28 (D and M1), T29 (D and M2) and T32 (D and M5) is almost 3.4% each (six buildings each). Typologies T2, T3, T5, T8, T9,  T15, T16, T17, T18, T19, T20, T21, T23, T24, T25, T26  The next on the list is typology T14 with 7% and 12 buildings, which results from the consideration of geometry B and material M5; and T13 with approximately 5.8% corresponding to 10 buildings (B and M4). These are followed by T34 (D and M7) and T22 (C and M4), which have a percentage of almost 5.2% each (nine buildings respectively). T30 (correlation between D and M3) has 4.6% that is equivalent to eight buildings. The ratio of T10 (B and M1), T28 (D and M1), T29 (D and M2) and T32 (D and M5) is almost 3.4% each (six buildings each). Typologies T2, T3, T5, T8, T9,  T15, T16, T17, T18, T19, T20, T21, T23, T24, T25, T26, T27, T31, T33 and T35   The next on the list is typology T14 with 7% and 12 buildings, which results from the consideration of geometry B and material M5; and T13 with approximately 5.8% corresponding to 10 buildings (B and M4). These are followed by T34 (D and M7) and T22 (C and M4), which have a percentage of almost 5.2% each (nine buildings respectively). T30 (correlation between D and M3) has 4.6% that is equivalent to eight buildings. The ratio of T10 (B and M1), T28 (D and M1), T29 (D and M2) and T32 (D and M5) is almost 3.4% each (six buildings each). Typologies T2, T3, T5, T8, T9,  T15, T16, T17, T18, T19, T20, T21, T23, T24, T25, T26, T27, T31, T33 and T35  The next on the list is typology T14 with 7% and 12 buildings, which results from the consideration of geometry B and material M5; and T13 with approximately 5.8% corresponding to 10 buildings (B and M4). These are followed by T34 (D and M7) and T22 (C and M4), which have a percentage of almost 5.2% each (nine buildings respectively). T30 (correlation between D and M3) has 4.6% that is equivalent to eight buildings. The ratio of T10 (B and M1), T28 (D and M1), T29 (D and M2) and T32 (D and M5) is almost 3.4% each (six buildings each). Typologies T2, T3, T5, T8, T9, T15, T16, T17, T18,  T19, T20, T21, T23, T24, T25, T26, T27, T31, T33 and T35 have between 0.4% (one building) and 2.9% (five buildings) on the analyzed site.

Seismic Vulnerability Assessment
Following the proposal of Gruppo Nazionale per la Difesa dai Terremoti (GNDT) [17], a simplified seismic vulnerability assessment approach is used in this work. The method was proposed by Ferreira et al. [18] to assess the seismic vulnerability of traditional masonry buildings and to estimate damages and post-seismic losses for different macroseismic scenarios [19]. The method is based on the assessment of 14 parameters within the vulnerability index, organized in four groups: (1) structural building system; (2) irregularities and interaction; (3) floor slabs and roofs; and (4) conservation status and other elements. The first group (Group 1) involves the building resisting system, namely type P1, the quality of the resisting system (P2), the shear strength capacity of the building (P3), the maximum distance between walls whose indicator constitutes a potential

Seismic Vulnerability Assessment
Following the proposal of Gruppo Nazionale per la Difesa dai Terremoti (GNDT) [17], a simplified seismic vulnerability assessment approach is used in this work. The method was proposed by Ferreira et al. [18] to assess the seismic vulnerability of traditional masonry buildings and to estimate damages and post-seismic losses for different macroseismic scenarios [19]. The method is based on the assessment of 14 parameters within the vulnerability index, organized in four groups: (1) structural building system; (2) irregularities and interaction; (3) floor slabs and roofs; and (4) conservation status and other elements. The first group (Group 1) involves the building resisting system, namely type P1, the quality of the resisting system (P2), the shear strength capacity of the building (P3), the maximum distance between walls whose indicator constitutes a potential

Seismic Vulnerability Assessment
Following the proposal of Gruppo Nazionale per la Difesa dai Terremoti (GNDT) [17], a simplified seismic vulnerability assessment approach is used in this work. The method was proposed by Ferreira et al. [18] to assess the seismic vulnerability of traditional masonry buildings and to estimate damages and post-seismic losses for different macroseismic scenarios [19]. The method is based on the assessment of 14 parameters within the vulnerability index, organized in four groups: (1) structural building system; (2) irregularities and interaction; (3) floor slabs and roofs; and (4) conservation status and other elements. The first group (Group 1) involves the building resisting system, namely type P1, the quality of the resisting system (P2), the shear strength capacity of the building (P3), the maximum distance between walls whose indicator constitutes a potential

Seismic Vulnerability Assessment
Following the proposal of Gruppo Nazionale per la Difesa dai Terremoti (GNDT) [17], a simplified seismic vulnerability assessment approach is used in this work. The method was proposed by Ferreira et al. [18] to assess the seismic vulnerability of traditional masonry buildings and to estimate damages and post-seismic losses for different macroseismic scenarios [19]. The method is based on the assessment of 14 parameters within the vulnerability index, organized in four groups: (1) structural building system; (2) irregularities and interaction; (3) floor slabs and roofs; and (4) conservation status and other elements. The first group (Group 1) involves the building resisting system, namely type P1, the quality of the resisting system (P2), the shear strength capacity of the building (P3), the maximum distance between walls whose indicator constitutes a potential

Seismic Vulnerability Assessment
Following the proposal of Gruppo Nazionale per la Difesa dai Terremoti (GNDT) [17], a simplified seismic vulnerability assessment approach is used in this work. The method was proposed by Ferreira et al. [18] to assess the seismic vulnerability of traditional masonry buildings and to estimate damages and post-seismic losses for different macroseismic scenarios [19]. The method is based on the assessment of 14 parameters within the vulnerability index, organized in four groups: (1) structural building system; (2) irregularities and interaction; (3) floor slabs and roofs; and (4) conservation status and other elements. The first group (Group 1) involves the building resisting system, namely type P1, the quality of the resisting system (P2), the shear strength capacity of the building (P3), the maximum distance between walls whose indicator constitutes a potential out-of-plane failure mechanism (P4), the number of floors (P5) and the geotechnical conditions of the foundations (P6). The second group (Group 2) considers the irregularities and interaction between adjacent buildings (P7), the regularities in plan (P8) and height (P9) and the alignment of the openings (P10). The parameters integrated into the third group (Group 3) are the quality of the horizontal supporting structures, namely of the horizontal diaphragms (P11), and the roofing system (P12). Finally, the fourth group (Group 4) is linked to the conservation status, considering the fragilities of the building (P13) and the characteristics of non-structural elements (P14).
The vulnerability parameters are influenced by a vulnerability class (A, B, C and D), by choosing the best-described vulnerability option for each parameter, between the values 0 to 50 multiplied by a weight (P i ), which ranges from 0.5 (lower-ranking) to 1.5 (higher-ranking). A vulnerability index (I * v ) value ranging from 0 to 650 can then be obtained. Furthermore, for ease of use, this value is usually normalized (I V ) between 0 and 100. On account of this, the simplified vulnerability assessment method was applied to the study area in Mexico City through a typological-based approach by establishing some empirical facts. As will be discussed further on, this vulnerability indicator can be used as an early step for estimating damages and losses [20].

Seismic Vulnerability Assessment and Damage Scenarios
Once data is collected, the vulnerability assessment was performed for a historic area of Mexico City. The vulnerability assessment is performed herein adopting a typological-based procedure which consists of a pre-assessment of the seismic vulnerability of each one of the typologies identified in Section 3, through the assessment of eight specific vulnerability assessment parameters (P1, P2, P4, P5, P8, P9, P11 and P12), which, as can be seen in Table 2, focus on the structural characteristics of the buildings (Group 1), on their irregularities and the interaction between adjacent buildings (Group 2) and the characteristics of their floor slabs and roof (Group 3), see Table 4. Table 4. Vulnerability index, according to [18], modified for the study area.

Vulnerability Index (I v )
Class Weight Vulnerability Index 1. After the eight refereed parameters have been evaluated (according to the aforementioned typological-based approach), the vulnerability analysis is accomplished by evaluating the remaining parameters of the vulnerability assessment methodology, namely parameters P6, P7, P10, P13 and P14. Following this strategy, it was thus possible to perform a complete vulnerability assessment of the whole study area. It is worth noting, that because of the nature of the data required to evaluate Parameter 3, this parameter was neglected in the present study. For this reason, instead of having 650 as a maximum vulnerability index value, the vulnerability index value is limited in this analysis to 575 (I cc v ).

Analysis and Discussion of the Results
The vulnerability assessment method was applied to 166 historical buildings, resulting in a mean value of the seismic vulnerability index (I cc v ) of 45.91. Non-historic buildings, which include reinforced concrete (RC) and rehabilitated ones, fall outside the scope of the study and are omitted from the data. Figure 2 presents the results of I cc v for the study area, whereas Figure 3a depicts the distribution of the vulnerability index (I cc v ) for the 166 buildings. Almost 75% of the assessed buildings had a vulnerability index value (I v ) greater than 40 (i.e., equivalent to vulnerability class A in the European Macroseismic Scale (EMS-98) [18]). While the maximum and minimum values obtained from the assessment were 75 and 27, respectively, the standard deviation value obtained (σI cc v ) was 8.34. The lower and the upper bond values of the vulnerability distribution are also used in the analyses presented in the following.  Figure 3b presents the frequency distributions of the most important parameters in terms of their influence on the vulnerability index definition. As observed, class D overcomes 50% for parameters P4, P9, P10, P12 and 14 (i.e., the distance between walls, regularity in height, openings and alignments, roofing system and non-structural elements) evidencing a significant number of parameters related to the irregularity and interaction of the buildings. The combination of class D and class C covers more than 50% for parameters P1, P6, P8, P11 and P13 (i.e., type of resisting system, location and soil conditions, plan configuration, horizontal diaphragms, and fragilities and conservation state); at this point, the class D for P1, P6, P8, P11 and P13 is lower than parameters P4, P9, P10, P12 and 14; however, it is still significant with excessive deficiency in the structural building system (Group 1), and the irregularities and interaction (Group 2). The presence of parameters A and B (i.e., the classes corresponding to lower vulnerability) is dominant in the parameters P2, P5 and P7 (quality of the resisting system, number of floors and aggregate position and interaction). Some of the highly vulnerable parameters are related to geometry, such as the alignment of the openings (P10), the height (P9), the characteristics of the foundations when interacting with the soil conditions (P6), the connections between vertical and horizontal systems and the increase of the stiffness on the horizontal diaphragm systems. The latter (i.e., increase of stiffness) is conceivably linked to the incompatibility of the systems (P1, P12), the physical or mechanical properties of the wall itself (P2), and the non-structural elements (P14). Even though the weight (P i ) of parameters P1, P2, P11, P12 and P13 is 1.0 or lower (see Table 4), their individual analysis (i.e., non-typological-based method selection) is essential because the set of these parameters reflects higher levels of individual vulnerability. The following figures illustrate some parameters with major class D such as P4 (Figure 4a Table 1 for a description of the parameters.

Damage Distribution and Loss Scenario
To obtain the damage distribution and loss scenario, the computation of mean damage grade must be considered, through either absolute or relative vulnerability results, depending on the selected methodology [21]. The absolute vulnerability represents the damage as a function of the seismic intensity, or it can be considered as the damage condition attributed to a given seismic intensity. On the contrary, the relative vulnerability is determined by empirical or experimental data, without correlating the damage and the seismic intensity. For this paper, the analysis will be considered absolute. Accordingly, to represent the grade of damage linked to a seismic event, EMS-98 can be used [22]. Nevertheless, the damage grade can be associated, employing phenomena that occurred in a particular location, whose aims entail the assessment of cultural heritage. Thereby, the mean damage grades (µ D ) are estimated for different macro-seismic intensities based on the previous results of the vulnerability index. Under the analytical expression that correlates hazard and a mean damage grade (0 ≤ µ D ≤ 5) of the damage distribution, the vulnerability value (V) is obtained through the Equations (1) and (2) [23]: According to equations above, the vulnerability index value (V) determines the position of the curve, whereas the ductility factor (Q) limits the slope of the vulnerability function (e.g., the rate of damage increases with rising intensity). For the computation of the mean damage grades (µ D ), the input values were the proposed seismic intensities (I) between the range of V and XII, the vulnerability index (I cc v ) calculated previously with a mean value of 45.91 and the proposed ductility factor (Q) of 2.0. The Q factor is based on similar values recommended by the local code (RCDF-NTC) [24] for equivalent buildings. In summary, the vulnerability index value, obtained in the prior assessment (I cc v ), is associated with the vulnerability index (V) through the macroseismic approach seen in Equations (1) and (2). Therefore, the calculation of the mean damage grades (µ D ), and the subsequent estimations of physical, economic and human losses are calculated, by following the initial mean vulnerability index value (I cc v ) [18]. Figure 5a shows the vulnerability curves obtained for the mean value of the vulnerability index (I cc v mean) and the lower and upper bound ranges (I cc v mean − 2σI cc v ; I cc v mean − 1σI cc v ; I cc v mean + 1σI cc v ; I cc v mean + 2σI cc v ) for events with macroseismic intensities ranging from V to XII. Thus, from an overall view, the estimated damages range from 1.02 to 2.29 corresponds to the earthquake scenario of I EMS−98 = VII, the range from 2.06 to 3.48 corresponds to I EMS−98 = VIII and the range from 3.28 to 4.31 is linked to I EMS−98 = IX. The evaluation shows alarming results, due to the high estimation represented by moderate damages (2 ≤ µ D < 3) at I EMS−98 = VII, severe damages (3 ≤ µ D < 4) at I EMS−98 = VIII and possible collapses (4 ≤ µ D < 5) at I EMS−98 = IX.   The damage assessment is an initial step to measure the risk linked to economic and human losses. These studies allow the spatial the global damage distribution, and the representation of the building stock analysis, by integrating GIS tools. The mapping damage distribution enables the practical identification of more vulnerable zones with its correspondent specific constructions, thus enhancing the decision-making for urban management and civil protection strategies [25]. The damage distribution scenarios are presented in Figure 6a

Fragility Curves
Based on a probabilistic approach, the physical building damage distributions are possible to determine through the beta probability function for specific building typologies. Fragility curves are possibly some of the most accepted and used methods for representing estimations of damage, thus defining probabilities that can exceed a specific damage grade D k (∈ [0; 5]) [18]. Fragility curves establish a relationship between five damage states and earthquake intensity, entailed by continuous probability functions, which express the conditional cumulative probability when reaching or exceeding a certain degree of damage state. Equation (3) shows the discrete probabilities, P(D k = d) derived from the difference of accumulative probabilities P D [D i ≥ d].
Influenced by the parameters of the beta distribution function, the estimation of damage can be determined as a continuous probability function. Figure 7a,b shows the fragility curves by inputting a mean vulnerability index of I cc v mean = 45.91 and the mean vulnerability index plus the standard deviation value ( I cc v mean + 1σI cc v = 54.26), respectively.

Loss Estimation
A wide variety of methods can be currently used to estimate material, human and economic losses [26][27][28][29]. From those, probabilistic-based approaches in which the probability of attaining a specific damage grade for a certain level of action are within the most widely adopted ones. According to these methods, the construction of a damage scenario can be completed through probabilistic distributions, whose input data computation involves the representative vulnerability index values (I cc v mean − 2σI cc v ; I cc v mean; I cc v mean − 1σI cc v ; I cc v mean + 1σI cc v ; I cc v mean + 2σI cc v ). The loss estimation can be considered as part of a damage model, linking the physical damage grades. Thereby, the physical damage grades include the correlations between the probability of exceeding a certain level of damage and the probability of different loss phenomena. These methods are herein applied to estimate the probability of collapsed and unusable buildings or to assess the quantification of probable fatalities and severely injured people after a seismic event.

Collapsed and Unusable Buildings
The method used to calculate the probability of collapsed and unusable buildings was proposed by Servizio Sismico Nazionale (SSN), based on the studies carried out by Bramerini et al. [30]. This approach involves the analysis of data associated with the probability of buildings, considered unusable after minor and moderate seismic actions.
Although such events produce lower levels of structural and non-structural damage, higher mean damage grade values are associated with a higher probability of building collapse. Thus, the probabilities of exceeding a certain damage grade are used in the loss estimation and are affected by multiplier factors, which range from 0 to 1. The following Equations (4) and (5) were used for the computation of the probabilities of collapsed and unusable buildings, respectively: where P(D i ), is the probability of occurrence at a certain damage grade (from D 1 to D 5 ), and W ei, j is the multiplier factor that indicates the percentage of buildings associated with D i . Although [30][31][32][33] have indicated different values for these factors, in this study, the values of W ei,3 and W ei,4 were assumed as equal to 0.4 and 0.6, respectively. Figure 8a,b presents the resultant probability of building collapse and unusable buildings, for the mean value of the vulnerability index (I cc v mean = 45.91) and for other characteristic values of the vulnerability distribution (I cc v mean − 2σI cc v ; I cc v mean; I cc v mean − 1σI cc v ; I cc v mean + 1σI cc v ; I cc v mean + 2σI cc v ), respectively. According to the results in Figure 8a, the building collapse probability curve shows that the probabilities of collapse increase with the higher macroseismic value I EMS−98 . On the other hand, the number of unusable buildings ( Figure 8b) decreases with the increase of seismic intensity, as a result of the ultimate state capacity producing the collapse, and thus its reduction.
The overall results from moderate to large intensity seismic events present an exponential rise between VIII and IX, as seen in Table 5, by considering macroseismic intensities from I EMS−98 = VII to I EMS−98 = X [19], and a mean vulnerability index of I cc v mean = 45.91; this output summarizes the number of units affected and the percentage related to the study area.

Human Casualties and Homelessness
To estimate the probability of deaths, severe injuries associated with a disaster, and homelessness, the vulnerability index values are required, both the mean value of the vulnerability index (I cc v mean = 45.91) and the representative values of the vulnerability distribution (I cc v mean − 2σI cc v ; I cc v mean; I cc v mean − 1σI cc v ; I cc v mean + 1σI cc v ; I cc v mean + 2σI cc v ). Hence, the calculation is carried out by resorting to Equations (6)-(8) [18]. P death and severely injured = 0.3 × P(D 5 ) P homelessness = P unusable buildings + 0.7 × P(D 5 ) where P(D i ), is the probability of occurrence at a certain damage grade (from D 1 to D 5 ), W ei,j is the multiplier factor that indicates the percentage of buildings associated with D i , and D i is the damage grade corresponding to collapse or are considered unusable. In Equation (7), it is assumed that 30% of the population, located in a building expected to collapse (i.e., with a probability of exceeding damage grade D 5 ), will perish or be severely injured. The probability of homelessness is determined by the Equations (8) and (9), which considers that 100% of people living in unusable buildings, and the remaining 70% of residents of collapsed buildings will not be able to reoccupy their dwellings after an earthquake [18]. Four seismic intensity scenarios, ranging between VII and X according to the EMS-98 scale [19], were analyzed, and the results were associated with the number of casualties and homeless. As can be observed in Table 6, the percentage of homelessness becomes relevant for intensity equal to or greater than VIII.
With this information, the extrapolation of loss output data for the Downtown area in Mexico City can be possible as a relative value. In other words, if these estimations were extended to the city center, it would have obtained a total number of 14,922 homeless people, which is undoubtedly a concerning result from the risk mitigation point of view. For that reason, appropriate logistical preparedness is required by the stakeholders (i.e., governmental authorities, civil protection, social entities) related to the relocation of residents, which could be performed through pre-seismic simulation exercises. To this end, a logistical plan is essential for having financial resources and thus suggesting the best emergency plan for the inhabitants. Communities and governments should put the same emphasis on planning for post-disaster emergency response by valuing community engagement and decision-making [25]. Figure 9a shows the probability of casualties and Figure 9b presents the probability of homelessness for different vulnerability values.

Economic Losses and Repair Cost Estimation
The estimated damage grade can either be interpreted economically, as defined by Benedetti and Petrini [34] or as an economic damage index, i.e., the ratio between the repair cost and the replacement cost. The correlation between damage grades and the repair and rebuilding costs is obtained through the processing of post-earthquake damage data [16]. According to Ferreira et al. [18], the repair cost probabilities for a certain seismic event characterized by intensity I, ( P[R I] ) can be obtained from the product of the conditional probability of the repair cost for each damage level (P[R|D k ]) with the conditional probability of the damage condition for each level of building vulnerability and seismic intensity ( P[D k I CC V , I] ) given by the following Equation (9): Loss estimation plays an essential role in the implementation of urban planning and retrofitting strategies, enabling costs to be placed alongside various beneficial measures such as reduced repair costs and life safety [35,36]. To estimate the repair costs associated with the different vulnerability values used in the loss evaluation (I cc v mean − 2σI cc v ; I cc v mean; I cc v mean − 1σI cc v ; I cc v mean + 1σI cc v ; I cc v mean + 2σI cc v ), an average cost per unit area of 506 €/m 2 (about MXN 11,716/m 2 ) was considered for the building stock in Mexico City (according to BIMSA-Cámara Mexicana de la Industria de la Construcción, 2015). The estimated global repair costs for the 166 buildings analyzed in this work are illustrated in Figure 10 and summarized in Table 7 for the most relevant macroseismic intensities.

Final Remarks
A simplified seismic vulnerability assessment was applied to a set of historical buildings in the selected area of La Merced at Mexico City. Through an overall description of the study area, an index-based seismic vulnerability assessment methodology was applied to 166 buildings. To this purpose, 31 building typologies were originally defined through a matrix of four geometrical types and nine material types. From the analysis made, it was possible to observe that intrinsic characteristics of the buildings, such as their structural and geometrical features, their current conservation state and their location within the urban mesh are the factors that most contribute to their seismic vulnerability. Furthermore, it was possible to notice that, in several cases, massive incompatible refurbishment or retrofit interventions performed over the lifespan of the building also play a significant role in the increase of the seismic vulnerability of these buildings. From the vulnerability assessment results, a series of damage scenarios were also computed and plotted for the study area. Among those, the scenarios obtained for macroseismic intensities VII, VIII and IX were mapped resorting to a GIS tool in order to better understand and identify the buildings that, in the case of an earthquake within this range of intensities, will probably suffer more damage.
As a final remark, it is worth highlighting that the overall understanding of the selected area (i.e., historical context and characterization of the buildings), the vulnerability assessment, the computation of different damage scenarios and the estimation of losses are all valuable outputs that can be used by the local and national authorities to support the development of informed preand post-earthquake risk mitigation strategies. Moreover, these kinds of large-scale vulnerability assessment outputs can also guide the action of cultural institutions towards creating and fostering programs for the safeguarding of cultural heritage in historic areas.

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