Fragility Functions for Tall URM Buildings around Early 20th Century in Lisbon. Part 1: Methodology and Application at Building Level

Abstract: The article addresses the seismic vulnerability assessment of a typology of unreinforced masonry buildings constructed in Lisbon between the nineteenth and the twentieth centuries. The main architectural and structural features of these buildings are presented. This supported the identification of the main uncertainties affecting their seismic performance and the definition of classes of buildings representative of the typology. The seismic assessment includes the generation of fragility curves that combine the in-plane and out-of-plane response following different criteria and methods of analyses. The results put in evidence the seismic vulnerability of this class of buildings. Considering the earthquake-resistant code for Lisbon with a return period of 475 years, about 50% probability of having heavy damage and about 30% probability of collapse were estimated. The structural intervention on these buildings is urgent in order to reduce losses due to future earthquakes. Further studies for the assessment of similar buildings in Lisbon and elsewhere can be developed using the adopted procedure.

Abstract: This article describes the application of the procedure for the derivation of fragility functions presented in the companion article entitled Fragility functions for tall URM buildings around early...

Abstract: A high percentage of reinforced concrete (RC) buildings in Portugal were designed and built before the introduction of modern seismic codes. This research aims to assess the seismic capacity and vulnerability of RC buildings in the city of Lisbon. For that purpose, nonlinear static procedures have been used and fragility curves have been developed. These buildings are reaching the end of their nominal life. Therefore, ageing effects have been taken into account, as well as the presence of smooth rebar. To do so, a sensitivity analysis has been performed by considering the chloride-induced corrosion of the reinforcement steel rebar and the degradation of the concrete cover. To illustrate the effects of ageing and the procedure adopted for the seismic fragility assessment of old RC structures, three RC buildings with masonry infills have been selected as case studies. They were all built between 1960 and 1980, and they are representative of the current building stock in Lisbon. The seismic capacity of the buildings has been determined by means of nonlinear static analyses of three-dimensional numerical models. The N2 method and its extended version have been considered to determine the target displacement. The seismic safety of the buildings has been estimated in terms of the demand/capacity ratio for each vertical structural element (columns and walls) according to the bending and the shear failures. Then, a set of fragility curves has been developed for all buildings to represent the probability of RC elements reaching or exceeding the significant damage limit state. Results have shown that the concrete strength degradation has had more influence than reduction of the rebar diameter in the seismic capacity. When considering steel corrosion, it has been demonstrated that the corrosion rate has reduced the capacity more than the time of exposure. It can be concluded that ageing affects the seismic behaviour of RC structures, increasing the vulnerability of these buildings.

Abstract: According to the Sendai Framework for Disaster Risk Reduction (2015–2030), disasters have demonstrated that the recovery, rehabilitation and reconstruction phase, which needs to be prepared ahead of a disaster, is a critical opportunity to “Build Back Better”, integrating disaster risk reduction into development measures. In this respect, a significant number of structures, that constitute several European urban nuclei, belong to old constructive typologies, which were designed and built without any consideration for the seismic hazard. One of the most used typologies exhibiting this shortcoming is unreinforced masonry (URM). Therefore, an important step towards increasing resilience of European cities is to deeply understand the seismic behavior of this frequent typology. In order to do so properly, detailed probabilistic nonlinear building models should be developed. However, including the uncertainties associated with this typology is challenging due to the heterogeneity of the different manufacturing techniques, executed under primitive industrial standards, and to the construction techniques, which are dependent on regional uses and criteria in a pre-code scenario. The object of this research is twofold. First, a detailed quantification of the uncertainties related to the mechanical properties of this construction material is conducted. Then, the influence of this variability on the seismic performance of a representative building model of the Eixample district in Barcelona, Spain, is analysed. This building typology represents 72% of the building stock in this district with an average age of 90 years, which means that the construction practice, at that time, was only regulated by early council guidelines that are considered pre-code rules. Specifically, the probabilistic approach is illustrated with a case study performed on an existing seven-story (high-rise) URM. A detailed numerical model of this structure has been developed and randomized taking into account the variability of the material properties. Accordingly, 1000 models were generated and analysed by considering as input different sets of material random variables. The compressive strength, Young modulus, shear modulus and shear strength are chosen and modelled to encompass the material uncertainties. The seismic response of each variant (i.e. selected set of mechanical properties) is obtained through a simplified non-linear static procedure aiming to compare and categorize the influence of the probabilistic input on the seismic performance of the building. Results are presented in terms of correlations between damage parameters and material properties. The analysis carried out shows that the variability in the material properties generates significant uncertainties in the seismic response of URM buildings, leading to over or underestimate expected damage when compared with results based on approaches that do not consider the probabilistic nature of the problem.

Abstract: Unreinforced masonry buildings undergoing seismic actions often exhibit local failure mechanisms which represent a serious life-safety hazard, as recent strong earthquakes have shown. Compared to new buildings, older unreinforced masonry buildings are more vulnerable, not only because they have been designed without or with limited seismic loading requirements, but also because horizontal structures and connections amid the walls are not always effective. Also, Out-Of-Plane (OOP) mechanisms can be caused by significant slenderness of the walls even if connections are effective. The purpose of this paper is to derive typological fragility functions for unreinforced masonry walls considering OOP local failure mechanisms. In the case of slender walls with good material properties, the OOP response can be modeled with reference to an assembly of rigid bodies undergoing rocking motion. In particular, depending on its configuration, a wall is assumed either as a single rigid body undergoing simple one-sided rocking or a system of two coupled rigid bodies rocking along their common edge. A set of 44 ground motions from earthquake events occurred from 1972 to 2017 in Italy is used in this study. The likelihood of collapse is calculated via Multiple Stripe Analysis (MSA) from a given wall undergoing a specific ground motion. Then, the single fragility functions are suitably combined to define a typological fragility function for a class of buildings. The procedure is applied to a historical aggregate in the city center of Ferrara (Italy) as a case study. The fragility functions developed in this research can be a helpful tool for assessing seismic damage and economic losses in unreinforced masonry buildings on a regional scale.

Abstract: During the Chilean earthquakes of May, 1960, a number of tall, slender structures survived the ground shaking whereas more stable appearing structures were severely damaged. An analysis is made of the rocking motion of structures of inverted pendulum type. It is shown that there is a scale effect which makes tall slender structures more stable against overturning than might have been expected, and, therefore, the survival of such structures during earthquakes is not surprising.

Abstract: A relatively simple nonlinear method for the seismic analysis of structures (the N2 method) is presented. It combines the pushover analysis of a multi‐degree‐of‐freedom (MDOF) model with the response spectrum analysis of an equivalent single‐degree‐of‐freedom (SDOF) system. The method is formulated in the acceleration‐displacement format, which enables the visual interpretation of the procedure and of the relations between the basic quantities controlling the seismic response. Inelastic spectra, rather than elastic spectra with equivalent damping and period, are applied. This feature represents the major difference with respect to the capacity spectrum method. Moreover, demand quantities can be obtained without iteration. Generally, the results of the N2 method are reasonably accurate, provided that the structure oscillates predominantly in the first mode. Some additional limitations apply. In the paper, the method is described and discussed, and it basic derivations are given. The similarities a...

Abstract: The Applied Technology Council is adapting PEER's performance-based earthquake engineering methodology to professional practice. The methodology's damage-analysis stage uses fragility functions to calculate the probability of damage to facility components given the force, deformation, or other engineering demand parameter (EDP) to which each is subjected. This paper introduces a set of procedures for creating fragility functions from various kinds of data: (A) actual EDP at which each specimen failed; (B) bounding EDP, in which some specimens failed and one knows the EDP to which each specimen was subjected; (C) capable EDP, where specimen EDPs are known but no specimens failed; (D) derived, where fragility functions are produced analytically; (E) expert opinion; and (U) updating, in which one improves an existing fragility function using new observations. Methods C, E, and U are all introduced here for the first time. A companion document offers additional procedures and more examples.