The availability of data for Bucharest shaped the selection of methods for the quantification of vulnerability, and the development of new procedures. The overall methodology can be considered hybrid—integrating empirical assumptions and relations, analytical methods for the evaluation of building behavior or statistical analysis, with the goal of explaining the potential distribution of vulnerability due to a credible earthquake.
Our research belongs to the broad field of semi-quantitative vulnerability assessment and index construction. It integrates GIS-based modeling along with a spatial multicriteria analysis of social vulnerability (Ouma et al. 2011). To this our approach adds a building loss estimation component obtained by using analytical methods. The GIS-based multicriteria technique combines the information from several indicators (criteria) to form a single index of social vulnerability (Chen et al. 2010). Figure 3 shows the flowchart guiding the analytical process.
The social vulnerability index construction involved literature review and expert judgement followed by the selection of a core set of social vulnerability dimensions and indicators (Blaikie et al. 1994; Fekete 2009). The census data variables included in the construction of social vulnerability indicators are presented in Table 1, and were selected due to availability and their capability to reflect social vulnerabilities over multiple dimensions, such as social structure, education, housing, and social dependence. This capability was demonstrated also in a preliminary study (Armaş and Gavriş 2013), where the same variables were selected, but the overall level of detail of the analysis was lower.
The analytical steps in the construction of the social vulnerability index relied on principal component analysis (PCA). The four social vulnerability dimensions—social, education, housing, and social dependence, as identified in Table 2—explained over 88% of the variance within a middling value for Kaiser–Meyer–Olkin (KMO) Measure of Sampling Adequacy. The advantage of KMO is found in the fact that it suggests the presence of latent factors, meaning that the statistical exploration of the data may be conducted easily; it is also a double check diagnostic alongside Bartlett’s test. A more detailed description of this procedure can be found in Armaş and Gavriş (2016).
The four dimensions for which we were able to associate statistical results were further integrated into a criteria tree using the SMCE (Spatial Multi-Criteria Evaluation) module of the Ilwis software (ITC 2001), and weighted according to expert judgment and scenario testing. In the criteria tree, there were also spatial constrains (barren land and parks) as Boolean inputs (true/false), but these constrains were not considered during weighting.
Input values were normalized from 0 to 1, by dividing them based on the maximum value in the range (that is the maximum value-function approach). For the normalization of the average dwelling room area per census tract we used a combination of cost-benefit assumptions relative to social vulnerability increase (with a U-shape up to 23 m2 and a descending curve to the maximum value of over 34 m2 room space), according to the values offered by Eurostat (2014). In 2012, Romania had the highest rates of overcrowding in Europe at 51.6%, and an average floor area of 46.9 m2 per dwelling. It should be noted that the average dwelling size in Europe was significantly larger, at 102.3 m2 (Eurostat 2014). All indicators were understood as increasing conditions for social vulnerability, except for the “Average no. of private/owned houses with five or more rooms” variable in Table 2. The presence of large private houses in an area was considered an indication of decreased social vulnerability. It was also normalized using the maximum value-function approach. All other indicators were understood as increasing conditions for social vulnerability.
Weights were assigned to the indicators describing a dimension, as well as to the four groups of dimensions introduced in the criteria tree to indicate their relative importance with respect to social vulnerability. In assigning weights, we applied the pairwise comparative method, developed by Saaty (1980) in the Analytic Hierarchy Process (AHP) and implemented in the SMCE-Ilwis module. The AHP method is based on expert opinion and reduces the complexity of the conversion of subjective assessments of relative importance to a sequence of pairwise comparisons. Each comparison is a two-part question: “How important is indicator I
relative to indicator I
?” The set of overall weights was based on rank orders provided by national and international experts (one or two experts representing the fields of seismology, geology, geomorphology, civil protection, civil constructions, psychology, and sociology) who proved through their results by questionnaire forms on the importance of each criterion for the social vulnerability model (for example, Armaş 2006, 2008; Armaş and Avram 2008).
In SMCE-Ilwis module, the responses use the following nine-point scale expressing the intensity of the preference for one indicator versus another, and also calculates a consistency of judgements between pairs: 1 = Equal importance or preference; 3 = Moderate importance or preference of one over another; 5 = Strong or essential importance or preference; 7 = Very strong importance or preference; 9 = Extreme importance or preference. Based on Saaty (1980), if the consistency of the conducted comparisons is lower than 0.10, the pairwise comparison matrix has an acceptable consistency and the weight values are deemed valid.
Table 3 summarizes the normalized weights for the indicators saturating the four dimensions of the complex social vulnerability index. The overall earthquake vulnerability index for Bucharest was computed as an aggregate of weighted linear combination. As can be seen in Table 3 and Fig. 3, the vulnerability patterns of residential buildings are added as an additional fifth dimension; they are the result of a different computation procedure, described in the following subsection.
The result of the weighting process was reclassified into four vulnerability classes, based on the distance from the average of the value obtained by each census tract. Average vulnerability of census tracts after weighting was 0.51 with a median value of 0.59 and a standard deviation of 0.15. The low vulnerability class result included vulnerability values smaller than 0.4, the upper bound of the medium vulnerability class was 0.6; for the high vulnerability class the upper bound was 0.7, and the very high vulnerability class included values over 0.7.
Since spatial multicriteria analysis involves many indicators, it is increasingly recognized that the outcomes of this approach are prone to inherent uncertainties related to the errors and variability in model choice, availability, heterogeneity, errors in the input data, and/or errors in the weighting process based on human judgment (Crosetto et al. 2000; Crosetto and Tarantola 2001; Chen et al. 2011; Feizizadeh et al. 2014). Therefore, we decided to test the influence of assumptions made in the weighting process (Table 3) and input data values (Table 1) on the specific outcomes and included uncertainty and sensitivity analyses of the building-vulnerability model results, as further analysed in Sect. 4.
Uncertainty analysis aimed to identify if rank reversals occur with changes in weights and input data values (Crosetto and Tarantola 2001). Sensitivity analysis explored the model response to changes in input values by testing the relationships between the inputs and the output of the applied model (Saltelli et al. 2000; Crosetto and Tarantola 2001; Chen et al. 2010; Ravalico et al. 2010). The robustness of the results were analyzed using the methods for sensitivity analysis from DEFINITE toolbox, based on frequency tables from 10,000 simulations run after introducing uncertainty ranges in input values and assigned weights (Janssen and van Herwijnen 1994).
Although the methodology seems to focus on simplified aspects of a complex system (the urban environment), its flexibility allows the integration of multiple types of input data (whether statistical indices or variables obtained through other methods) and facilitates the testing of multiple hypotheses in an effort to explain links between different socioeconomic and habitat dimensions.
Vulnerability Assessment for Residential Buildings
As represented in Table 3, residential building vulnerability, seen as dependent on hazard variability, was introduced as a separate condition in the criteria tree, normalized, and weighted in the final total vulnerability complex index. Through this choice, we emphasized the importance of building vulnerability in the analysis, especially in the urban context, since buildings are the elements that cause most of the seismic losses. This line of thought is aptly captured by the common phrase: earthquakes don’t kill people, buildings do.
That is why we tried to determine which areas of the city have the greatest residential building vulnerability. The assessment of individual buildings can yield the best results, but the process is both time and cost consuming. In Bucharest, only 855 buildings (located mostly in the city center) were evaluated and classified according to their vulnerability by the Bucharest General Municipality (2016), although the total number of residential buildings in Bucharest is 131,875. Approximately 40,000 of these structures are older than 1963; they date from a construction period when no seismic design regulations were available. In other words, reliable information about building vulnerability can only be found for <0.65% of the city’s buildings. Thus, to have a wider perspective, we used a more generalized approach as is found in other contemporary studies, like Erdik et al. (2011) or Karmizadeh et al. (2017). This approach relies on analytical methods, especially the Improved Displacement Coefficient Method (IDCM), as well as statistical data such as the number of buildings per construction period, building material, and structure height. These data provide valuable insight into building damage patterns at the city level.
IDCM is an analytical method developed along with the HAZUS initiative (FEMA 2014). The method involves the modification of the displacement demand of an equivalent single-degree of freedom system (this simplifies building characteristics) by multiplying it with a series of coefficients to generate an estimate of the maximum displacement demand of the nonlinear oscillator (Molina et al. 2010). We chose this method due to the good performance it showed for the study area (Toma-Danila et al. 2015a) and its successful implementation within the widely used SELENA (Seismic Loss Estimation using a logic tree Approach) open-source software for seismic loss estimation (Strasser et al. 2008).
Census data—collected by Romania’s National Institute of Statistics in 2011—for residential buildings in 128 distinct census tracts within the city were used for computing building loss estimations. Recently, a set of 48 vulnerability (more specifically capacity and fragility) functions, custom developed as well as adapted from the literature, were associated with major building typologies in Romania and enabled implementation of a near real-time system for estimating Seismic Damage in Romania—SeisDaRo (Toma-Danila et al. 2015b). The SeisDaRo building typologies account for nine types of construction materials (such as adobe, reinforced or unreinforced masonry, wood, and reinforced concrete), three building height classes, and four construction periods representative for Romania (PreCode—before 1963, LowCode—1963–1977, MediumCode—1978–1991, and HighCode—after 1991). In order to adopt this classification, considered relevant to Bucharest (Toma-Danila et al. 2015a), a specific conversion methodology was applied to the 2011 original dataset (Fig. 4; Table 4). The methodology comprises reclassification and statistical derivation, both based on custom-defined profiles and GIS interpretation. Detailed methodological steps can be found in Toma-Danila and Armaş (2017). The arrangement allows for the integration of the 2011 Bucharest data within SeisDaRo, and has proved to be a useful step in the quick estimation of possible earthquake effects in our study.
Since vulnerability functions cannot offer a complete answer to the question of which areas are more endangered, we run simulations with three distinct seismic scenarios. These simulations exposed building damage patterns at minimum, median, and maximum credible damaging levels. As seen in Fig. 1, the Vrancea intermediate-depth seismic source, located at the contact between the East European Plate and the Intra-Alpine and Moesian Subplates, is the only source responsible for damaging acceleration values in Bucharest. Hazard studies such as those by Giardini et al. (2013) and Pavel et al. (2016) reflect this aspect. Therefore, all selected scenarios are for this source. Two of these scenarios are based on real-recorded values (for the 1990 and 1977 Vrancea earthquakes with moment-magnitudes of 6.9 and 7.4, respectively) and one (for the maximum possible Vrancea earthquake, with moment-magnitude of 7.8) is based on a recent approach relying on nonlinear seismic response evaluation to a synthetic signal from a point source with a mechanism similar to the one of the 1940 earthquake (Marmureanu et al. 2010). These scenarios are deterministic and were selected due to their capability to highlight potential differences inflicted by local site effects and due to their different magnitude ranges, which cover the spectrum between maximum and inceptive damage levels (Toma-Danila and Armaş 2017). All ground motion parameters used are at surface level, and consider site conditions, propagation effects, and frequency ranges, a very important aspect for intermediate-depth Vrancea earthquakes. Probabilistic scenarios for Bucharest do not yet provide sufficient insights into the very local variance of ground motion parameters, which, as demonstrated by previous events, vary considerably both within and between events, and were thus considered unsuitable for reflecting vulnerability patterns, but proved more useful in testing seismic risk dynamics.
The individual scenario results consisted of estimated numbers of damaged buildings per census tract, with probabilities for different damage states (none, slight, medium, extensive, and complete damage). The ratio between estimated buildings with complete damage and their total number was used, which allowed normalization between census tracts of different sizes. The ratios of the three earthquake scenarios were averaged and normalized on a scale from 0 to 1 and were introduced as a separate spatial factor in the total vulnerability criteria tree. This procedure is one of the steps that make the proposed methodology innovative and presumably more insightful.