A parametric model for capacity curves and capacity spectra is proposed. The

In this study the main results of a detailed analysis of an actual building, which was severely damaged during the Mw 5.1, May 11th 2011, Lorca earthquake (Murcia, Spain) are presented. The dynamic behavior of the building was analyzed by means of empirical and numerical approaches. The displacement response of the building submitted to ambient noise was recorded by using a Real Aperture Radar (RAR). This approach provides a secure remote sensing procedure that does not require entering the building. Based on the blueprints and other available graphical information about the building, a numeric 3D model was also set up, allowing obtaining capacity spectra and fragility curves in the two main resistant directions of the building. The main purpose of this study was to check out the feasibility of the RAR-based method to detect the safety state of a damaged building after an earthquake, without the need of entering unsafe structures. A good consistency of the numerical and experimental approaches and the observed damage was obtained, showing that RAR interferometric-based tools may provide promising supplementary remote sensing methods to safely survey and report about the structural health and the operative conditions of buildings in post-earthquake scenarios.

The equal displacement approximation is a well-known procedure for estimating the non-linear behavior of structures subjected to earthquake ground motions. This procedure plays a significant role in current seismic design, since it constitutes the basic assumption for defining strength reduction factors. In this paper, calculation of the performance point based on this rule is used to estimate engineering demand parameters such as those obtained by advanced probabilistic non-linear dynamic analysis, NLDA. We present a modification to the classic approach, to improve the predictability of the equal displacement rule. Uncertainties in seismic action and structural properties are considered. Mid-rise reinforced concrete buildings will be used as a testbed. To obtain a representative sample of buildings for statistical analysis, we describe the development through implementation of a numerical tool for calculating probabilistic NLDA. This tool, which is expected to evolve into interoperable software for assessing the seismic risk of structures, is developed within the framework of the KaIROS project. The results presented in this paper could be used to estimate the seismic risk of structures in a very simplified manner.

Most of buildings and structures are usually projected according to two main axes. However, the geographical position of these buildings varies randomly. Such random distributions of the azimuthal positions of structures, in most of the cities, generally, are not accounted for when assessing their seismic risk; certainly, the direction of the seismic loads is another highly random variable. Moreover, an additional important source of uncertainty is related to the structural response, mainly due to the random character of the mechanical properties. There is a consensus that uncertainties must be considered for adequately assessing the seismic risk of structures, but these directionality effects have not been deeply explored so far. In this article, the influence of the high uncertainty involved in these input variables on the expected seismic damage is analysed. Thus, an actual earthquake, which affected the southern part of Spain, is studied. Notably, damages on a group of affected buildings, located close to the epicentre, are analysed and discussed in detail. The results show that the influence of the random azimuthal position of structures is an important source of uncertainty and that it should be taken into account when estimating the expected seismic risk in urban areas.

The basic input when seismic risk is estimated in urban environments is the expected physical damage level of buildings. The vulnerability index and capacity spectrum-based methods are the tools that have been used most to estimate the probability of occurrence of this important variable. Although both methods provide adequate estimates, they involve simplifications that are no longer necessary, given the current capacity of computers. In this study, an advanced method is developed that avoids many of these simplifications. The method starts from current state-of-the-art approaches, but it incorporates non-linear dynamic analysis and a probabilistic focus. Thus, the method considers not only the nonlinear dynamic response of the structures, modeled as multi degree of freedom systems (MDoF), but also uncertainties related to the loads, the geometry of the buildings, the mechanical properties of the materials and the seismic action. Once the method has been developed, the buildings are subjected to earthquake records that are selected and scaled according to the seismic hazard of the site and considering the probabilistic nature of the seismic actions. The practical applications of the method are illustrated with a case study: framed reinforced concrete buildings that are typical of an important district, the Eixample, in Barcelona (Spain). The building typology and the district were chosen because the seismic risk in Barcelona has been thoroughly studied, so detailed information about buildings' features, seismic hazard and expected risk is available. Hence, the current results can be compared with those obtained using simpler, less sophisticated methods. The main aspects of the method are presented and discussed first. Then, the case study is described and the results obtained with the capacity spectrum method are compared with the results using the approach presented here. The results at hand show reasonably good agreement with previous seismic damage and risk scenarios in Barcelona, but the new method provides richer, more detailed, more reliable information. This is particularly useful for seismic risk reduction, prevention and management, to move towards more resilient, sustainable cities.Sustainability 2020, 12, 1308 2 of 21 software useful for estimating the stochastic response of multi degree of freedom systems (MDoF) systems by considering uncertainties in the seismic hazard and in the main features of the structures. Uncertainties were considered in relation to the geometry of the structure, the mechanical properties of the materials and the seismic action, amongst many other variables. In that study, thousands of non-linear dynamic analyses (NLDA) were executed using thousands of structural models and earthquake records. The procedure for combining the structural models and the earthquake records was based on the Latin hypercube and Monte Carlo sampling methods.From the NLDA results presented in Vargas-Alzate et al. 2019 [2], a simplified methodology was proposed to estimate maximum inter-story drifts ...