Fragility Analysis Using A New 3D Damage Index

In this paper, an advanced analytical assessment methodology for the assessment of irregular buildings is presented. In the proposed method, 3D modeling is utilized to capture the torsional and bi-directional response of buildings. A layering technique, termed ‘Planar Decomposition’, is proposed and shown to furnish detailed information on the demand and capacity of critical members. Through its application to fragility analysis of an example structure and comparison to fragility analysis using conventional damage indices, it is shown that constructing vulnerability function of irregular structures using the conventional damage index may be inaccurate and even unconservative. The proposed approach is therefore recommended for use in seismic assessment of irregular and torsionally-imbalanced structures. INTRODUCTION Earthquake field investigations repeatedly confirm that irregular structures suffer more damage than their regular counterparts. This is recognized in seismic design codes, and restrictions on abrupt changes in mass and stiffness are imposed. Irregularities in dimensions affect the distribution of stiffness, and in turn affect capacity, while mass irregularities tend to influence the imposed demand. Elevation irregularities have been observed to cause storey failures due to non-uniform distribution of demand-to-supply ratios along the height. Plan irregularities, on the other hand, cause non-uniform demand-to-capacity ratios amongst the columns within a single floor. Quantitative measures of seismic assessment on a floor-by-floor basis have been used for many years, in the form of storey drift ratios that provide a single number that portrays the demand-to-supply picture along the height of a structure. Quantitative, readily available and verified measures of demand-tocapacity ratios over the plan of a structure subjected to bidirectional transient dynamic loading and responding in the inelastic range are still lacking. In this paper, an analytical index is derived based on generic response characteristics. The index accounts for the multi-directionality of earthquake motion as well as the asymmetry of the structure; hence it captures the true three-dimensional inelastic effects that govern the response of RC structures. The adoption of such a damage measure opens to door to the reliable and accurate fragility analysis of irregular structures which have threedimensional (3D) responses; bi-directional deformation and torsion. NEW DAMAGE MONITORING PROCEDURE 1 Research Assistant, Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, USA 2 Willett Professor, Director, Mid-America Earthquake Center , Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, USA Existing Damage Indexes The importance of an appropriate damage index as a means of limit state characterization to assess the status of structures is shown by Bento and Azevedo (2000). Two significant reviews of damage indices were conducted by Williams and Sexsmith (1995) and by Ghobarah et al. (1999). Damage indices may be sub-divided into three groups: non-cumulative, cumulative, and combined. The response parameters used to classify the three types of damage indices are the maximum deformation, the hysteric behavior or fatigue, and the deformation and energy absorption. The Park and Ang (1985a) index is widely used in the literature owing to its calibration to a number of experimental programs. From a practical point of view, the deformation-based non-cumulative damage index may be meaningful enough, taking into account that few earthquakes apply a large number of cycles to structures in the conventional period range. Moreover, according to Williams and Sexsmith (1995) and Kappos and Xenos (1996), adding the energy component to the index may be insignificant. Additionally, a deformation-based non-cumulative damage index has the advantages of simplicity in calculations, while the combined damage index necessitates calibrations to determine its empirical parameters. The overall damage state should be determined when assessing the seismic performance of a structure. Williams and Sexsmith (1995) divided global damage indices into two groups: (a) weighted average indices and (b) measures based on modal parameters. Weighted average indices have been presented by Park and Ang (1985b), Park, Ang and Wen (1987), Chung et al. (1987, 1990), Kunnath et al. (1990, 1992) and Bracci et al. (1989). On the other hand, Roufaiel and Meyer (1987), DiPasquale and Cakmak (1987, 1988) and DiPasquale et al. (1990) presented damage measures based on modal parameters. Whereas existing damage indices present many choices for the analyst, their applicability is restricted to local and 2D global assessments, as shown in Figure 1. Non-cumulative damage index Cumulative damage index Combined damage index Interstory drift Weighted average index Modal parameter index