Seismic loss estimation based on end-to-end simulation

Recently, there has been increasing interest in simulating all aspects of the seismic risk problem, from the source mechanism to the propagation of seismic waves to nonlinear time-history analysis of structural response and finally to building damage and repair costs. This study presents a framework for performing truly “end-to-end” simulation. A recent region-wide study of tall steel-frame building response to a Mw 7.9 scenario earthquake on the southern portion of the San Andreas Fault is extended to consider economic losses. In that study a source mechanism model and a velocity model, in conjunction with a finiteelement model of Southern California, were used to calculate ground motions at 636 sites throughout the San Fernando and Los Angeles basins. At each site, time history analyses of a nonlinear deteriorating structural model of an 18-story steel moment-resisting frame building were performed, using both a pre-Northridge earthquake design (with welds at the moment-resisting connections that are susceptible to fracture) and a modern code (UBC 1997) design. This work uses the simulation results to estimate losses by applying the MDLA (Matlab Damage and Loss Analysis) toolbox, developed to implement the PEER loss-estimation methodology. The toolbox includes damage prediction and repair cost estimation for structural and nonstructural components and allows for the computation of the mean and variance of building repair costs conditional on engineering demand parameters (i.e. inter-story drift ratios and peak floor accelerations). Here, it is modified to treat steel-frame high-rises, including aspects such as mechanical, electrical and plumbing systems, traction elevators, and the possibility of irreparable structural damage. Contour plots of conditional mean losses are generated for the San Fernando and the Los Angeles basins for the pre-Northridge and modern code designed buildings, allowing for comparison of the economic effects of the updated code for the scenario event. In principle, by simulating multiple seismic events, consistent with the probabilistic seismic hazard for a building site, the same basic approach could be used to quantify the uncertain losses from future earthquakes. sulting values for structural response measures such as peak transient inter-story drift ratio (IDR) or peak floor acceleration, which are referred to as engineering demand parameters (EDP). In the damage analysis phase, the EDP is used with experimentally or empirically determined fragility functions to compute damage measures (DM) for the building components. Finally, the DM values are used in a loss analysis, where the losses are calculated using measures such as repair cost, repair duration, and loss of life. The modules are designed to implement a probabilistic approach to hazard analysis, so that the final result is essentially an integral involving a set of conditional probability density functions, which are used to “integrate out” the uncertainties associated with each module. In the PEER methodology, the first two steps are usually carried out using probabilistic seismic hazard and building vulnerability curves. Here, a full seismic risk analysis is not attempted; instead, only the damage and loss steps are implemented by applying an extended version of the MDLA toolbox developed at Caltech (Mitrani-Reiser 2007) to the results of a Southern California-wide study of the response of two steel-frame buildings to a Mw 7.9 scenario earthquake (Krishnan et al. 2006a, 2006b). This effectively extends the PBEE methodology to include simulation of the source rupture mechanism and wave propagation to the building site. Only one scenario event is considered here but work is underway to combine the results presented here with a probabilistic seismic hazard analysis to quantify uncertain losses from future earthquakes and hence, ultimately, to life-cycle costs for a building at one of the sites in the Southern California region. 2 SCENARIO EARTHQUAKE AND BUILDING RESPONSE The regions of interest for this study are the Los Angeles basin and the San Fernando valley, areas with large inventories of high-rise buildings and high levels of seismic risk. The chosen scenario event is a Mw 7.9 earthquake along a 290-km segment of the southern San Andreas fault (similar to the 1857 Fort Tejon earthquake), with the slip model derived from a finite-source inversion of the November 3, 2002 Denali earthquake in Alaska (Ji et al. 2003). The rupture was initiated at Parkfield in central California, propagated in a south-easterly direction, and terminated just north of the San Gabriel valley, as shown in Figure 1 (inset). Krishnan et al. (2006a, 2006b) computed ground motion time histories for the 636 analysis sites (spaced uniformly at approximately 3.5 km, as shown in Figure 1) using the spectral element method (e.g. Komatitsch and Tromp 1999), with peak velocities of up to 2 m/s and peak displacements of about 2 m. -119 ̊ -118.75 ̊ -118.5 ̊ -118.25 ̊ -118 ̊ -117.75 ̊ 33.75 ̊ 34 ̊ 34.25 ̊