Fragility of Hydraulic Elevators for Use in Performance-Based Earthquake Engineering

New performance-based earthquake engineering methods developed by the Pacific Earthquake Engineering Research Center, the Applied Technology Council, and others include damage analysis at a highly detailed level, requiring the compilation of fragility functions for a large number of damageable generic structural and nonstructural components. This brief paper presents the development of a fragility function for hydraulic elevators. It uses post-earthquake survey data from 91 elevators in nine California locations after two earthquakes. Surveys were used to collect data on facilities and elevators. Ground-motion records from the California Integrated Seismic Network were used to estimate engineering demands at each site. Binary regression analysis was used to fit a fragility function, which takes the form of a lognormal cumulative distribution function with median value of PGA=0.42 g and logarithmic standard deviation of 0.3. The fragility function appears to be reasonable based on four criteria

A Survey of Bridge Practitioners to Relate Damage to Closure

The Pacific Earthquake Engineering Research (PEER) Center's second-generation performance-based earthquake engineering (PBEE) methodology is intended in part to model highway bridge performance in terms of collapse, closure, repair duration, speed or load limitations, and possibly other performance measures. Some of these are difficult to model, particularly closure decisions where the engineering evidence of safety is inconclusive and must be supplemented by the inspector's judgment. This paper presents results of a limited, initial survey of department of transportation (DOT) engineers' beliefs about the relationship between physical damage and closure. The initial survey addresses a common class of reinforced-concrete bridges. The author and others developed and administered to a select, nationwide group of DOT engineers a one-page, multiple-choice survey form with expert self-rating, asking the engineers to relate ten damage measures (DM) to four closure levels. The DMs include approach settlement, offsets at abutments and expansion joints, flexural and shear cracks in beams, columns, shear keys, and backwalls. The performance levels considered are: leave open, close briefly for quick repairs, close for an extended period, and reduce speed. The survey results are analyzed to produce a number of preliminary relationships between damage and post-earthquake decisions by inspectors, relationships that can be used in probabilistic seismic performance evaluation in PEER's developing PBEE methodology. This preliminary test of a survey form also yielded insight into a number of desirable improvements for a second round of survey, possibly to be administered via the Internet early in 2004

Value of Injuries in the Northridge Earthquake

The economic equivalent value of deaths and injuries in the 1994 Northridge earthquake has not previously been calculated, although number of injuries by category of treatment has. Using dollar-equivalent values for injuries accepted and used by the U.S. government for evaluating the cost-effectiveness of risk-mitigation efforts, the value of injuries in the 1994 Northridge earthquake is estimated to be $1.3 to 2.2 billion in 1994 (90$1.8 to 2.9 billion in 2005). This is equivalent to 3–4% of the estimated $50 billion (in 1994) estimated direct capital losses and direct business interruption losses. If injuries in the 1994 Northridge earthquake are representative of injuries in future U.S. events, then the economic value of future earthquake injuries—the amount that the U.S. government would deem appropriate to expend to prevent all such injuries—is on the order of$200 million per year (in 2005 constant dollars). Of this figure, 96% is associated with nonfatal injuries, an issue overlooked by current experimental research. Given the apparently high cost of this type of loss, this appears to represent an important gap in the present earthquake research agenda

Creating Fragility Functions for Performance-Based Earthquake Engineering

The Applied Technology Council is adapting PEER's performance-based earthquake engineering methodology to professional practice. The methodology's damage-analysis stage uses fragility functions to calculate the probability of damage to facility components given the force, deformation, or other engineering demand parameter (EDP) to which each is subjected. This paper introduces a set of procedures for creating fragility functions from various kinds of data: (A) actual EDP at which each specimen failed; (B) bounding EDP, in which some specimens failed and one knows the EDP to which each specimen was subjected; (C) capable EDP, where specimen EDPs are known but no specimens failed; (D) derived, where fragility functions are produced analytically; (E) expert opinion; and (U) updating, in which one improves an existing fragility function using new observations. Methods C, E, and U are all introduced here for the first time. A companion document offers additional procedures and more examples

Simplified PBEE to Estimate Economic Seismic Risk for Buildings

A seismic risk assessment is often performed on behalf of a buyer of large 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 for what-if scenarios. We introduce an alternative to PML called probable frequent loss (PFL), defined as the mean loss resulting from an economic-basis earthquake such as 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 by a rigorous but simplified PBEE method that relies on a single linear structural analysis. We illustrate using 15 example buildings, including a 7-story nonductile reinforced-concrete moment-frame building in Van Nuys, CA and 14 buildings from the CUREE-Caltech Woodframe Project

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

Uncertainty Propagation and Feature Selection for Loss Estimation in Performance-based Earthquake Engineering

This report presents a new methodology, called moment matching, of propagating the uncertainties in estimating repair costs of a building due to future earthquake excitation, which is required, for example, when assessing a design in performance-based earthquake engineering. Besides excitation uncertainties, other uncertain model variables are considered, including uncertainties in the structural model parameters and in the capacity and repair costs of structural and non-structural components. Using the first few moments of these uncertain variables, moment matching requires only a few well-chosen point estimates to propagate the uncertainties to estimate the first few moments of the repair costs with high accuracy. Furthermore, the use of moment matching to estimate the exceedance probability of the repair costs is also addressed. These examples illustrate that the moment-matching approach is quite general; for example, it can be applied to any decision variable in performance-based earthquake engineering. Two buildings are chosen as illustrative examples to demonstrate the use of moment matching, a hypothetical three-story shear building and a real seven-story hotel building. For these two examples, the assembly-based vulnerability approach is employed when calculating repair costs. It is shown that the moment-matching technique is much more accurate than the well-known First-Order-Second-Moment approach when propagating the first two moments, while the resulting computational cost is of the same order. The repair-cost moments and exceedance probability estimated by the moment-matching technique are also compared with those by Monte Carlo simulation. It is concluded that as long as the order of the moment matching is sufficient, the comparison is satisfactory. Furthermore, the amount of computation for moment matching scales only linearly with the number of uncertain input variables. Last but not least, a procedure for feature selection is presented and illustrated for the second example. The conclusion is that the most important uncertain input variables among the many influencing the uncertainty in future repair costs are, in order of importance, ground-motion spectral acceleration, component capacity, ground-motion details and unit repair costs