Simplified Estimation of Economic Seismic Risk for Buildings

A seismic risk assessment is often performed on behalf of a buyer of commercial buildings in seismically active regions. One outcome of the assessment is that a probable maximum loss (PML) is computed. PML is of limited use to real-estate investors as it has no place in a standard financial analysis and reflects too long a planning period. We introduce an alternative to PML called probable frequent loss (PFL), defined as the mean loss resulting from shaking with 10% exceedance probability in 5 years. PFL is approximately related to expected annualized loss (EAL) through a site economic hazard coefficient (H) introduced here. PFL and EAL offer three advantages over PML: (1) meaningful planning period; (2) applicability in financial analysis (making seismic risk a potential market force); and (3) can be estimated using a single linear structural analysis, via a simplified method called linear assembly-based vulnerability (LABV) that is presented in this work. We also present a simple decision-analysis framework for real-estate investments in seismic regions, accounting for risk aversion. We show that market risk overwhelms uncertainty in seismic risk, allowing one to consider only expected consequences in seismic risk. We illustrate using 15 buildings, including a 7-story nonductile reinforced-concrete moment-frame building in Van Nuys, California, and 14 buildings from the CUREE-Caltech Woodframe Project

Sensitivity of Building Loss Estimates to Major Uncertain Variables

This paper examines the question of which sources of uncertainty most strongly affect the repair cost of a building in a future earthquake. Uncertainties examined here include spectral acceleration, ground-motion details, mass, damping, structural force-deformation behavior, building-component fragility, contractor costs, and the contractor's overhead and profit. We measure the variation (or swing) of the repair cost when each basic input variable except one is taken at its median value, and the remaining variable is taken at its 10th and at its 90th percentile. We perform this study using a 1960s highrise nonductile reinforced-concrete moment-frame building. Repair costs are estimated using the assembly-based vulnerability (ABV) method. We find that the top three contributors to uncertainty are assembly capacity (the structural response at which a component exceeds some damage state), shaking intensity (measured here in terms of damped elastic spectral acceleration, Sa), and details of the ground motion with a given Sa

Simplified Estimation of Seismic Life-Cycle Costs

Most seismic risk assessments for economic decision-making of commercial buildings are based on a risk metric called probable maximum loss (PML) that is associated with losses from an earthquake shaking severity with a 500-year return period. For various reasons, PML is a poor metric for economic performance assessment. This paper introduces an analogous measure, the probable frequent loss (PFL), defined as the mean loss resulting from shaking with 10% exceedance probability in 5 years (an approximately 50-year event). It overcomes many of the problems of PML, and offers the advantage that expected seismic life-cycle costs and expected annualized loss are approximately proportional to PFL through a seismic hazard coefficient that depends on site characteristics, fundamental period, and damage shaking threshold, and can be tabulated for ready use. A brief review is given of a building-specific seismic vulnerability method that may be used to calculate PFL

Real-time Bayesian State Estimation of Uncertain Dynamical Systems

The focus of this report is real-time Bayesian state estimation using nonlinear models. A recently developed method, the particle filter, is studied that is based on Monte Carlo simulation. Unlike the well-known extended Kalman filter, it is applicable to highly nonlinear systems with non-Gaussian uncertainties. Recently developed techniques that improve the convergence of the particle filter simulations are also introduced and discussed. Comparisons between the particle filter and the extended Kalman filter are made using several numerical examples of nonlinear systems. The results indicate that the particle filter provides consistent state and parameter estimates for highly nonlinear systems, while the extended Kalman filter does not. The particle filter is applied to a real-data case study: a 7-story hotel whose structural system consists of non-ductile reinforced-concrete moment frames, one of which was severely damaged during the 1994 Northridge earthquake. Two identification models are proposed: a timevarying linear model and a simplified time-varying nonlinear degradation model. The latter is derived from a nonlinear finite-element model of the building previously developed at Caltech. For the former model, the resulting performance is poor since the parameters need to vary significantly with time in order to capture the structural degradation of the building during the earthquake. The latter model performs better because it is able to characterize this degradation to a certain extent even with its parameters fixed. Once again, the particle filter provides consistent state and parameter estimates, in contrast to the extended Kalman filter. It is concluded that for a state estimation procedure to be successful, at least two factors are essential: an appropriate estimation algorithm and a suitable identification model. Finally, recorded motions from the 1994 Northridge earthquake are used to illustrate how to do real-time performance evaluation by computing estimates of the repair costs and probability of component damage for the hotel

PEER Testbed Study on a Laboratory Building: Exercising Seismic Performance Assessment

From 2002 to 2004 (years five and six of a ten-year funding cycle), the PEER Center organized the majority of its research around six testbeds. Two buildings and two bridges, a campus, and a transportation network were selected as case studies to “exercise” the PEER performance-based earthquake engineering methodology. All projects involved interdisciplinary teams of researchers, each producing data to be used by other colleagues in their research. The testbeds demonstrated that it is possible to create the data necessary to populate the PEER performancebased framing equation, linking the hazard analysis, the structural analysis, the development of damage measures, loss analysis, and decision variables. This report describes one of the building testbeds—the UC Science Building. The project was chosen to focus attention on the consequences of losses of laboratory contents, particularly downtime. The UC Science testbed evaluated the earthquake hazard and the structural performance of a well-designed recently built reinforced concrete laboratory building using the OpenSees platform. Researchers conducted shake table tests on samples of critical laboratory contents in order to develop fragility curves used to analyze the probability of losses based on equipment failure. The UC Science testbed undertook an extreme case in performance assessment—linking performance of contents to operational failure. The research shows the interdependence of building structure, systems, and contents in performance assessment, and highlights where further research is needed. The Executive Summary provides a short description of the overall testbed research program, while the main body of the report includes summary chapters from individual researchers. More extensive research reports are cited in the reference section of each chapter

Investigation of Sensitivity of Building Loss Estimates to Major Uncertain Variables for the Van Nuys Testbed

A major component of a building-specific seismic loss analysis is the estimation of repair costs in future earthquakes. A number of uncertain variables contribute to the uncertainty in these cost estimates. Among these are ground-shaking intensity, details of the ground motion, mass, damping, and force-deformation behavior, component fragility, repair methods, contractor’s direct costs, and contractor’s overhead and profit, among others. This report addresses which of these significantly contribute to the overall uncertainty in future economic performance. We examine gross sensitivity by measuring the variation (or swing) of the economic performance when each variable is taken at its assumed median value and at its extremes, e.g., the 10th and 90th percentiles. Such a study is undertaken for a 1960s nonductile reinforced-concrete moment-frame building located in Van Nuys, California, which is one of two buildings studied by the PEER testbeds program. Here, economic performance is measured in terms of the repair costs associated with the (uncertain) highest shaking intensity the site will experience in the next 50 years. Repair costs are estimated using the assembly-based vulnerability (ABV) method and the site’s seismic hazard. We do not address all uncertainties. Notable among those excluded are the selection among competing models of hysteretic behavior of structural elements, the potential that fragility tests of structural and nonstructural elements do not accurately reflect actual field conditions, the selection among competing repair methods given a component damage state, the choice of nonunion versus union labor to perform repairs, and the potential for repair costs after an earthquake to be increased by demand-driven inflation (a phenomenon often called demand surge). Except for demand surge, all of these uncertainties can be examined in future ABV analyses. The study shows that among the parameters considered here, the top three contributors to uncertainty in earthquake repair cost, in decreasing order, are assembly capacity (i.e., for a building element, the relationship between physical damage and the relevant engineering demand parameter), shaking intensity (measured here in terms of damped elastic spectral acceleration, Sa), and details of the ground motion conditioned on Sa. Uncertainties in parameters of the structural model contribute modestly to overall uncertainty in economic performance, and are comparable in importance to the uncertainty in the unit costs that a contractor will experience in repairing the damage. These observations are based only on the demonstration building, but they do offer intriguing implications for performance-based earthquake engineering. If duplicated for other buildings, it may be that much performance uncertainty could be reduced through more-detailed study and modeling of building component damageability. In addition, seismic loss analyses might reasonably neglect uncertainties in structural modeling parameters, without substantially underestimating overall uncertainty

Comparative Study of Different Methods of Structural Damage Assessment

In a modern performance-based earthquake engineering (PBEE) design framework, component fragility functions are used to relate parameters of structural response to damage. Since common structural response parameters are coupled to structural member properties, the usage of fragility functions in damage analysis after performing the structural analysis is inconsistent. The errors arising from such inconsistency do not seem to have been addressed previously. In the present study, we investigate this issue by comparing the results of damage estimation performed by three different methods. The first method, considered to be the most accurate, represents a coupled structural and damage analysis and utilizes randomized structural properties in the simulations for both the dynamic structural analysis and the damage analysis. The second, uncoupled, method samples the randomized structural properties twice during dynamic simulations, once for structural analysis and once for damage estimation. The third method is analogous to the second method but it uses a deterministic structural model for the dynamic simulation and uncertain structural properties for the damage analysis. Comparison of the results for a reinforced-concrete frame shows that relative to the first method, the second method provides reasonable estimates of the expected values and variances of the damage, while the third method underestimates the damage uncertainty. The variance estimated by a common approach based on a deterministic load and deterministic structure complemented by a probabilistic damage analysis is much less than the variance estimated by the first method