Abstract

The incremental dynamic analysis is a powerful tool for evaluating the seismic vulnerability and risk of buildings. It allows calculating the global damage of structures for different peak ground accelerations, PGA, and representing this result by means of damage curves. Such curves are currently used to obtain seismic risk scenarios at urban level. Even if the application of this method in a probabilistic environment requires a relevant computational effort, this has to be the reference method for determining those curves. Nevertheless, it would be of high practical interest to have a simpler method based, for instance, on pushover analysis, for assessing the seismic vulnerability and risk of buildings, which allows obtaining results similar to those based on the incremental dynamic analysis. Referring to the capacity-spectrum-based-methods, expert opinions have been used in previous researches for defining damage states thresholds starting from the yielding and the ultimate spectral displacement identified in the bilinear capacity spectrum. Therefore, we propose in this article a new procedure for defining the damage states thresholds, based on the stiffness degradation of reinforced concrete building, and a fully probabilistic approach is tackled by means of Monte Carlo simulations. It is demonstrated in the paper that the obtained results are in good agreement with those calculated using the incremental dynamic analysis.

Abstract

Capacity-spectrum-based-methods areused for assessing the vulnerability and risk of existing buildings. Capacity curves are usually obtained by means of nonlinear static analysis. Incremental Dynamic Analysis is a powerful tool based on nonlinear dynamic analysis. This method can provide results similar to the pushover analysis as the input is increasingly enlarged. It is well known that the randomness associated to the structural response can be significant, because of the uncertainties involved in the mechanical properties of the materials, among others uncertainty sources, and because the expected seismic actions are also highly stochastic. In this chapter, selected mechanical properties are considered as random variables and the seismic hazard is considered in a probabilistic way. A number of accelerograms of actual European seismic events have been selected in such a way that their response spectra fit well the response spectra provided by the seismic codes for the area where the building is constructed.A fully probabilistic approach is tackled herein by means of Monte Carlo simulation. The method is applied to a detailed study of the seismic response of a reinforced concrete building. The main purposes of this work are 1) to analyze the differences when static and dynamic techniques are used and 2) to obtain a measure of the uncertainties involved in the assessment of the vulnerability of structures. The results show that static based procedures are somehow conservative and that uncertainties increase with the severity of the seismic actions and with the damage. Low damage state fragility curves have little uncertainty while high damage grades fragility curves show great scattering.

Abstract

The out-of-plane response is a complex and at the same time key aspect of the seismic vulnerability of masonry structures. It depends on several factors, some of which are the material properties, the quality of the walls, the geometry of the structure, the connections between structural elements and the stiffness of the diaphragms. During the last years, a wide variety of numerical methods has been employed to assess the out-ofplane behaviour of unreinforced masonry structures. Finite element macro-modelling approaches are among the most famous as they allow modelling large structures at a reasonable computational cost. However, macro-modelling approaches may result in a non-realistic representation of localized cracks and a dependency of the numerical solution on the finite element mesh. Mixed strain/displacement finite elements have been recently proposed as a remedy to the above numerical pathologies. Due to the independent interpolation of strains and displacements these finite element formulations are characterized by an enhanced accuracy in strain localization and crack propagation problems, being at the same time practically mesh independent. For these reasons, mixed finite elements are employed in this work for the out-of-plane assessment of unreinforced masonry structures, being at the same time their first real-scale application. A full-scale experimental campaign of two masonry structures, a stone and a brick one, subjected to shaking-table tests is chosen as reference benchmark. Their structural response under seismic actions is numerically assessed through nonlinear static analysis. The proposed approach is validated through the comparison of the numerical results with the experimental ones, as well as with the results obtained using standard irreducible finite elements.

Abstract

The most important aspects of the design, seismic damage evaluation and safety assessment of structures with low ductility like waffle slabs buildings or flat beams framed buildings are examined in this work. These reinforced concrete structural typologies are the most used in Spain for new buildings but many seismic codes do not recommend them in seismic areas. Their expected seismic performance and safety are evaluated herein by means of incremental non linear structural analysis (pushover analysis) and incremental dynamic analysis which provides capacity curves allowing evaluating their seismic behaviour. The seismic hazard is described by means of the reduced 5% damped elastic response spectrum of the Spanish seismic design code. The most important results of the study are the fragility curves calculated for the mentioned building types, which allow obtaining the probability of different damage states of the structures as well as damage probability matrices. The results, which show high vulnerability of the studied low ductility building classes, are compared with those corresponding to ductile framed structures.

Abstract

Considering the effects of earthquakes occurred during the last 15 years, this article focusses on finding solutions to minimize the human and economic losses. Several methodologies were developed in order to assess the vulnerability of the built environment with special reference to one of the most suitable structural systems in seismic areas for dwellings, offices or other functionalities, which is the reinforced concrete framed structure. Thus, the present article studies the influence on the vulnerability of reinforced concrete framed structures of geometric structural characteristics like the slab thickness, the building height and the plan configuration. Referring to the slab, it adds supplementary stiffness to the structure that can significantly influence upon its overall failure mechanism. 3D static nonlinear analyses are conducted by means of the SAP2000 computer program. The results are capacity curves which are used to develop the vulnerability curves. Three thicknesses are considered for the slab: 0.1 cm, 0.12 cm and 0.15 m. Medium and high rise structures are considered, with 4, and 8 levels, respectively, in order to determine the influence of the building height on the
vulnerability index. Three plan configurations of the buildings are compared: a square one, a rectangular one and an L shaped one. For all the analyzed cases, the corresponding vulnerability curves are compared. The obtained results reveal that more realistic results for the behavior of the structure can be obtained if special attention is given to the structural characteristics, especially during the conceptual design process.

Abstract

Finite element macro-modeling approaches are widely used for the analysis of large-scale masonry structures. Despite their efficiency, they still face two important challenges: the realistic representation of damage and a reasonable independency of the numerical results to the used discretization. In this work, the classical smeared crack approach is enhanced with a crack-tracking algorithm, originating from the analysis of localized cracking in quasi-brittle materials. The proposed algorithm is for the first time applied to a large-scale wall exhibiting multiple shear and flexural cracking. Discussion covers structural aspects, as the response of the structure under different assumptions regarding the floor rigidity, but also numerical issues, commonly overlooked in the simulation of large structures, such the mesh-dependency of the numerical results.

Abstract

In this work a numerical model to obtain the pushover curves of clay masonry walls with openings is presented. These curves represent the non-linear structural behavior of masonry walls with openings subjected to loads in their own plane. The openings represent non-structural elements like doors, windows, among others. These walls can be considered as reinforced or confined masonry and the opening must be rectangular and may have different dimensions and a variable position inside the wall. The main result of the model was a pushover curve, which is compared with the curves obtained from laboratory tests (for walls with and without openings). The model was developed using the software ANSYS [1] version 14.5, based on the model proposed by Campbell and Durán [2].

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