Elsevier

Engineering Structures

Volume 31, Issue 1, January 2009, Pages 125-137
Engineering Structures

Seismic fragility analysis of low-rise unreinforced masonry structures

https://doi.org/10.1016/j.engstruct.2008.07.021Get rights and content

Abstract

Unreinforced masonry (URM) is one of the most common structural types for low-rise buildings in the United States. Its dynamic behavior is highly nonlinear, and generally shows high vulnerability to seismic loading. Despite the need for seismic risk assessment of this class of structures, the fragility curves for URM buildings based on analytical models are scarce in the field of earthquake engineering. This study performs seismic fragility analysis of a URM low-rise building. Fragility curves are developed for a two-story URM building designed to represent a typical essential facility (i.e., a firehouse) in the central and southern US (CSUS) region. A structural modeling method is proposed such that it can be effectively used for fragility analysis without significant increase in computational time, and maintains an acceptable level of accuracy in representing the nonlinear behavior of the structures. A set of fragility curves are developed and include different configurations of the out-of-plane walls and their associated stiffness. The fragility analysis shows that the seismic performance of URM buildings is well below the desirable building seismic performance level recommended by current seismic codes, indicating high vulnerability of URM buildings within the CSUS region. It is also shown that the out-of-plane wall stiffness should not be ignored in the risk assessment of URM buildings because the overall seismic performance of URM buildings is rather sensitive to the out-of-plane wall stiffness. The analytical fragility curves developed are compared with those of HAZUS. The comparison shows that the analytical fragility curves developed have lower variation in the seismic response than those of HAZUS. Several reasons for the discrepancy are discussed. The model-based analytical fragility curves developed in this study can increase the accuracy and effectiveness of seismic risk assessment of essential facilities of the CSUS region. Moreover, the structural modeling method introduced in this study can be effectively used for development of the fragility curves of URM buildings.

Introduction

Unreinforced masonry (URM) is one of the most common structural types for low-rise buildings in the United States. In particular, French and Olshansky [1] have showed that nearly one third of the essential facilities (i.e., firehouses, police stations, emergency management centers, etc.) distributed within the central and southern US (CSUS) region are low-rise (i.e., two stories or less) URM structures. Due to the infrequent nature of major earthquakes in the CSUS region, however, most existing URM building structures have been designed considering only gravity and/or wind loads. Moreover, past earthquake reconnaissance reports have suggested that unreinforced masonry structures are highly susceptible to damage from earthquakes. Therefore, URM structures have high seismic vulnerability over the CSUS region. This means that a moderate or major earthquake might result in a disastrous consequence associated with the URM structures in the region.

For rational estimation and reduction of the potential seismic losses associated with URM structures, the seismic performance level should be quantitatively measured through risk assessment of such structures. Fragility analysis is an effective tool for risk assessment of structural systems as it can be used for probabilistic estimation of seismic losses and eventually enables decision-making activities for seismic risk reduction.

Fragility curves for URM structures are currently available from HAZUS [2], a seismic loss estimation framework developed by the Federal Emergency Management Agency (FEMA). HAZUS uses a systematic approach for probabilistic damage assessment of building structures, in which building response is characterized by building capacity curves and seismic hazard is represented by demand spectra (i.e., capacity spectrum method). The building fragility curves are then generated assuming a lognormal distribution in which distribution parameters consist of the median capacity and damage variability. Although it is desirable to obtain these distribution parameters from either an analytical or experimental approach, HAZUS defines these parameters in most cases based on expert judgment [3]. More accurate fragility curves incorporating rigorous modeling of nonlinear behavior of URM structures are scarce in the field of earthquake engineering at the present time. This study performs seismic fragility analysis of low-rise URM building structures using a simplified modeling method that can be effectively used for fragility analysis without significant loss of computation time, and which maintains an acceptable level of accuracy in representing the nonlinear behavior of the structures.

Low-rise URM structures are usually characterized by their relatively stiff yet quite brittle structural behavior. The behavior of URM walls is typically characterized with respect to either in-plane or out-of-plane loadings (referred to hereafter as “in-plane” or “out-of-plane”). URM walls usually exhibit very high in-plane elastic stiffness and very little out-of-plane stiffness. Out-of-plane failures are generally quite brittle unless significant compressive loads are present, but in-plane cracking can lead to relatively ductile behavior of perforated (i.e., by windows, doors, etc.) walls if significant pier rocking is developed. Many of the URM essential facilities located in the CSUS region are constructed with wooden floor and roof diaphragms that are rather flexible and are often poorly tied into the walls. As a result, the seismic response of such URM structures are often more complex than expected. FEMA guidelines for seismic analysis and rehabilitation of building structures [4] states that the out-of-plane stiffness of walls should be neglected while only masses should be considered in structural modeling of URM buildings. This implies that the contribution of the out-of-plane wall stiffness to the dynamic response of URM structures is minimal and should be ignored in the modeling and analysis for conservatism. Some studies, however, show that the dynamic response of an URM building structure could be greatly affected by the out-of-plane wall stiffness [4], [5]. If out-of-plane walls are well-connected to the adjacent URM components such as in-plane walls or floor diaphragms, the out-of-plane walls could contribute more to the overall response of the URM building. As a consequence, we can say that no generally accepted approach exists at the present time as to whether the out-of-plane wall stiffness should be considered in modeling URM structures in the absence of rigid diaphragms.

This study has two objectives. One is to develop model-based analytical fragility curves of low-rise URM buildings, of which fragility curves are only available based on expert opinion at the present time. A low-rise URM building representative of the essential facilities in the CSUS region is selected and structurally modeled with a simplified nonlinear spring model for effectiveness in repetitive computation. The seismic responses of the URM building subject to different levels of earthquake inputs are then probabilistically estimated considering the randomness in its material properties to yield the fragility curves. The model-based analytical fragility curves developed in this study can increase the accuracy and effectiveness of seismic risk assessment of essential facilities of the CSUS region. Moreover, the structural modeling method introduced in this study can be effectively used for development of the fragility curves of an individual URM building with a particular configuration. Another objective of this study is to investigate the effect of considering the out-of-plane wall stiffness on the seismic performance of the URM building structures. The fragility curves are developed for three different configurations of out-of-plane wall stiffness and compared to one another to investigate the effect of the out-of-plane wall stiffness on the seismic performance. This effort demonstrates the needs of considering the effect of the out-of-plane wall stiffness in modeling and analysis of URM building structures for seismic risk assessment.

Section snippets

Representative URM building structure

Typical URM essential facilities in the CSUS region are relatively small and low-rise (one or two-story in height). The structure is composed of two main components: the URM bearing walls and the floor and roof diaphragms. The walls are generally stiff and constructed with many openings or perforations for windows and doors. The diaphragms are usually constructed of timber and, as a result, are much more flexible than the walls. A benchmark building is selected as representative of existing URM

Modeling URM buildings

Masonry is a nonhomogeneous material made up of two components: the masonry bricks and the mortar. Masonry properties are dependent upon the properties of its constituents. Structural behavior of the masonry can be very complex even under static loadings. The most refined approach for analyzing a URM wall is the so-called brick-by-brick approach which models individual masonry brick as a solid element connecting to each other by the interface elements representing the mortar. However, for the

Fragility analysis of the URM building

As shown in Fig. 7, fragility is defined as the probability of the case study structure reaching or exceeding a specified limit state under a given earthquake intensity level [14]. In this figure, the shaded area represents a failure domain defined from specific criteria, where a damage measure, D, exceeds a specific threshold, dsi. Under a given earthquake level San, P[Ddsi|San] is the probability of the structural response exceeding the i-th limit state expressed as a threshold, dsi, and

Fragility comparison

As previously mentioned, HAZUS fragility curves are the only available ones for low-rise URM buildings at this time. The fragility curves of the URM structures developed in this study are compared with the HAZUS fragility curves. Note that the comparison is made for the HAZUS fragility curves developed for pre code low-rise URM building, as it is assumed that the building is designed without any consideration of seismic loading. For the comparison, the fragility curves of HAZUS are converted

Conclusions

Model-based analytical fragility curves for a 2-story unreinforced masonry building typical of the CSUS region are developed in this study. These fragility curves are distinguished from the existing fragility curves in HAZUS, in that the HAZUS fragility curves are derived using selected parameters which are based on the subjective judgments of experts. A simplified spring model is developed to describe the highly nonlinear dynamic behavior of URM structures in an effective manner, and a typical

Acknowledgements

This work was supported primarily by the Mid-America Earthquake Center (MAE) through the Earthquake Engineering Research Centers Program of the National Science Foundation under NSF Award No. EEC-9701785. Any opinions, findings and conclusions or recommendations expressed in this paper are those of the authors and do not necessarily reflect those of the National Science Foundation.

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