Drift-based fragility assessment of confined masonry walls in seismic zones
Introduction
Several seismic events have highlighted the vulnerability of housing dwellings in developing countries, mainly those dwellings located in populated areas near the earthquake source [1], [2]. In Latin-America, low-cost housing dwellings and medium-rise apartment buildings predominantly have load-bearing confined-masonry walls as primary lateral-load resisting systems under earthquake excitation. Confined masonry construction consists of load-bearing walls built of brick units framed by lightly-reinforced small-section, reinforced concrete beams and columns. This building construction type is common in many Latin-American countries, and extensive damage to this type of construction has been reported after moderate to severe seismic events. For example, in the 2003 Tecoman earthquake , that struck the Southwest coast of Mexico causing approximately 123 million dollars in direct and indirect economic losses [1], 25,353 of a sample of 140,572 housing dwellings were affected in the Mexican state of Colima. From the housing dwelling census that suffered structural damage, 31.4% experienced light damage that required minor repair, 53.7% exhibited moderate damage that required major repair, while 14.9% dwellings collapsed [1]. Other examples of the high seismic vulnerability of confined masonry construction observed in Mexico and other Latin-American countries are reported by Ruiz, et al. [2] and Rodriguez [3].
Recently proposed performance-based seismic assessment procedures [4] or, in a more general context, consequence-based engineering procedures [5] are aimed at estimating the seismic risk of man-made constructed facilities, taking into account all potential sources of uncertainty. In particular, seismic performance is measured from decision variables such as the expected annual loss of a building. In this context, Miranda and Aslani [6] have proposed estimating the mean annual frequency of exceedance of loss in a specific building located in a specific seismic environment from computing the losses in individual structural and non-structural components. The mean annual probability of exceedance of loss in a component taking into account discrete damage states is given as follows:
where is the number of damage states in the th component, is the annual probability of exceedance of a loss in the th component conditioned on the damage state , is the probability that the component will be in the damage state , given that the component has been subjected to an engineering demand parameter equal to , which is commonly known as the fragility curve [5], is the exceedance probability of an (e.g. maximum inter-story drift, etc.) given that the ground motion intensity measure reaches a value of , which is referred to as the seismic demand hazard curve, and is the slope of the site-specific seismic hazard curve, evaluated at a intensity measure im. A detailed description of variables involved in Eq. (1) can be found in Ref. [4], [6]. Then, the building-specific expected annual loss is computed by adding the expected losses in each individual component in the building.
There is a consensus among the earthquake engineering community, that structural damage is a consequence of lateral deformation demands imposed to the structures during earthquake ground shaking. Thus, modern performance-based seismic assessment methodologies for reinforced concrete and steel structures are based on the evaluation of the lateral deformation capacity, and demand of structural systems and their components (e.g. [4], [5]). Under this approach, to evaluate Eq. (1), fragility curves based on lateral deformation capacity as well as seismic demand hazard curves and seismic hazard curves based on displacement demand are required. For instance, Aslani and Miranda [7] as well as Pagni and Lowes [8] have developed drift-based fragility curves for slab–column connections and beam–column joints of non-ductile reinforced concrete buildings.
However, there is very little research focused on developing displacement-based fragility curves for confined masonry construction. From the author’s knowledge, the only published work on this topic was developed by Astroza and Schmidt [9]. The authors developed fragility curves from experimental results of 52 specimens, representative of confined masonry walls tested in Chile, Mexico and Venezuela. However, it should be noted that the authors only included the specimen-to-specimen variability in their study as a source of uncertainty.
The objective of this paper is to summarize research results, in order to obtain drift-based fragility curves associated with selected damage states of confined masonry structures for performance-based seismic assessment and earthquake-induced loss estimation. For that purpose, a relatively large database which contains information of lateral drift levels associated to the first diagonal cracking and to lateral strength recorded of 118 confined masonry walls tested under cyclic lateral loading was assembled. Then, drift-based fragility curves for confined masonry walls were developed, taking into account parameters that influence their deformation capacity such as the brick-type, amount of horizontal steel reinforcement, and the vertical compressive stress active during the test. In particular, four sources of uncertainty identified from the experimental database were taken into account. Finally, a discussion on limiting drifts linked to damages states for confined masonry walls based in the developed drift-based fragility curves is offered. It is believed that the information presented in this paper will provide a tool to allow, not only estimating the seismic vulnerability of confined masonry buildings [5], but also to obtain estimates of economic losses during future earthquakes, based on aggregating the estimated damage at the component level for a specific structure (e.g. [6]).
Section snippets
Performance of confined masonry walls under earthquake-type loading
Based on post-earthquake field reconnaissance and ample experimental evidence, three failure modes have been identified in confined masonry (CM) walls: (a) shear failure, (b) bending failure, and (c) sliding failure. The first failure mode is characterized by diagonal cracking crossing the brick units or following the mortar joints. This is produced when the acting principal stresses reach the diagonal tension strength of masonry. The second failure mode occurs in slender CM walls when the
Drift-based fragility curves for confined masonry walls
Displacement-based fragility curves express the conditional probability of exceeding a defined damage state, conditioned on the lateral deformation demand (e.g. maximum inter-storey drift). There are several ways to develop fragility curves for structural components or systems such as from numerical simulation, using post-earthquake field reconnaissance information or experimental data (e.g. [5]). Many studies aimed at developing fragility curves are based on numerical simulation, but they
Drift-based limit states for confined masonry walls
Drift-based fragility curves can also be used for defining and calibrating limiting drifts corresponding to key damage states having uniform exceedance probability. For instance, Alcocer et al. [15] proposed limiting drifts for load-bearing confined masonry (LB-CM) walls made of hand-made clay brick units associated with three limit states (i.e. serviceability, repairability, and safety). The authors suggested limiting drifts, based on the observed experimental behavior and technical
Conclusions
This paper introduced the development of fragility functions aimed at estimating the probability that confined masonry (CM) walls reach, or exceed two levels of observed damage due to earthquake-type loading. Probabilistic estimates are based on the level of lateral drift imposed to the walls. For developing drift-based fragility functions, a relatively large experimental database that included test results of 118 CM walls tested under cyclic lateral loading, as part of research programs
Acknowledgements
The authors would like to express their gratitude to the Universidad Michoacana de San Nicolas de Hidalgo in Mexico for the support provided to develop the research reported in this paper. In addition, the authors wish to thank one anonymous reviewer for his/her comments and suggestions that helped to improve the final version of the paper.
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