PSI - Issue 55

Isabel Turbay et al. / Procedia Structural Integrity 55 (2024) 168–176 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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centres such as: the periodicity of the maintenance of the building, the use of the land, the inadequate occupation of the public space, the vehicular traffic in the immediate environment, the seismic vulnerability and the inadequate interventions carried out in the building.

Table 1. Vulnerability indexes and the factors involved (VI, VIp, VIe1, VIe2). Building variables and its environment

Physical-chemical characteristics Texture Foundation Structure Construction system (finishes) Urban Landscape Fire resistance Roofs Installations Seismic vulnerability Simplicity of the construction solution Traffic Land use Inadequate occupation of public space Maintenance Inappropriate interventions

VI - VIp

VIe2

VIe1

Alteration factors

Cataloguing Level of use

Soils, climate, natural phenomena, anthropogenic action

21 churches located in three cities (Popayán and Cartagena de Indias in Colombia and La Antigua in Guatemala) were studied in situ and 18 variables were identified as their vulnerability factors. There are several multivariate statistical techniques that help to perceive what is not visible in the data sets, the PCA, reduces the number of observations (variables) that also allows to discover the hidden relationships between them, preserving the most relevant information of the set with its interdependent relationships, i.e., it does not distinguish between dependent and independent variables, but examines the interdependent relationships between the complete set of variables. In addition, the analysis of results is simple and can be the first step for other complementary studies such as the statistical analysis by clusters in charge of the search for relationships in a large symmetric matrix and whose variables or groups of variables specified can then be used to group the samples by distance function, which can be a good option having a clearer grouping criterion. The Excel program Xlstat was used to carry out the PCA. The procedure for data analysis is explained below. • The PCA in the vulnerability study in Colombia and Guatemala is carried out to reduce the dimensions of the original data matrix and calculate the statistical weight of the sets of variables. • The correlation between the variables was analyzed in the factorial space represented with the F1 and F2 axes. And it is explained by the circle of correlations that shows a projection of the initial variables in the factor space represented in two dimensions with the axes F1 and F2. • The data was also analyzed to understand global vulnerability with a Biplot graph, observing the relationship between vulnerability, the variables that affect it and the churches studied. • Finally, PCA was employed to propose preventive conservation, determining groups of churches in the factorial space and their location with respect to the variable incident on the vulnerability and the axes of the Cartesian plane.