This paper focuses on the probabilistic analysis of Intensity Measures (IMs) and Engineering Demand Parameters (EDPs) in the context of earthquake-induced ground motions. Several statistical properties, which are desirable inIMs when they are used to predictEDPs, have been analysed. Specifically, efficiency, sufficiency andsteadfastnesshave been quantified for a set ofIMs with respect to twoEDPs: the maximum inter-storey drift ratio,MIDR, and the maximum floor acceleration,MFA. Steadfastness is a new statistical property proposed in this article, which is related to the ability ofIMs to forecastEDPs for large building suites. In other words, this means that efficiency does not significantly vary when different types of buildings are simultanously considered in the statistical analyses. This property allows reducing the number of calculations when performing seismic risk estimations at urban level since, for instance, a large variety of fragility curves, representing specific building typologies, can be grouped together within a more generic one. The main sources of uncertainty involved in the calculation of the seismic risk have been considered in the analysis. To do so, the nonlinear dynamic responses of probabilistic multi-degree-of-freedom building models, subjected to a large data set of ground motion records, have been calculated. These models have been generated to simulate the dynamic behavior of reinforced concrete buildings whose number of stories vary from 3 to 13. 18 spectrum-, energy- and direct-accelerogram-basedIMs have been considered herein. Then, from clouds ofIM-EDPpoints, efficiency, sufficiency and steadfastness have been quantified. ForMIDR, results show thatIMs based on spectral velocity are more efficient and steadfast than the ones based on spectral acceleration; spectral velocity averaged in a range of periods,AvSv, has shown to be the most efficientIMwith an adequate level of steadfastness. ForMFA, spectral acceleration-based-IMs are more efficient than velocity-based ones. A comparison is also presented on the use of linear vs quadratic regression models, and their implications on the derivation of fragility functions. Concerning sufficiency, most of the 18IMs analysed do not have this property. Nonetheless, multi-regression models have been employed to address this lack of sufficiency allowing to obtain a so-called ‘ideal’IM.

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.

This paper focuses on the identification of high-efficiency intensity measures to predict the seismic response of buildings affected by near- and far-fault ground motion records. Near-fault ground motion has received special attention, as it tends to increase the expected damage to civil structures compared to that from ruptures originating further afield. In order to verify this tendency, the nonlinear dynamic response of 3D multi-degree-of-freedom models is estimated by using a subset of records whose distance to the epicenter is lower than 10 km. In addition, to quantify how much the expected demand may increase because of the proximity to the fault, another subset of records, whose distance to the epicenter is in the range between 10 and 30 km, has been analyzed. Then, spectral and energy-based intensity measures as well as those obtained from specific computations of the ground motion record are calculated and correlated to several engineering demand parameters. From these analyses, fragility curves are derived and compared for both subsets of records. It has been observed that the subset of records nearer to the fault tends to produce fragility functions with higher probabilities of exceedance than the ones derived for far-fault records. Results also show that the efficiency of the intensity measures is similar for both subsets of records, but it varies depending on the engineering demand parameter to be predicted.

A simplified procedure is developed to consider the azimuthal orientation of buildings when estimating seismic risk. Two square‐plan reinforced concrete building models are considered as a testbed, one with similar and one with dissimilar properties along the two principal horizontal axes. The fragility of both structures is analysed using a set of ground motion records rotated to multiple incidence angles to develop orientation‐dependent fragility functions. It has been observed that, re‐orienting all records so that these structures have the same azimuth vis‐à‐vis the corresponding epicentre leads to significant differences compared to assuming random orientations. Additional results stemming from single‐degree‐of‐freedom oscillators further confirm such findings, showing a dependence to the proximity to the faults and the level of dissimilarity in the principal horizontal axes of the structure. The end results point to a non‐negligible bias in assessment studies when a structure's orientation with respect to governing rupture scenarios is not taken into account. It is shown that the median of fragility curves calculated for un‐rotated incidence angles can be bias‐corrected through shifted by an amount that depends on the azimuthal orientation and level of axes‐dissimilarity of structures.