Conditional Spectrum-Based Ground Motion Selection. Part I: Hazard Consistency for Risk-Based Assessments

The conditional spectrum (CS, with mean and variability) is a target response spectrum that links nonlinear dynamic analysis back to probabilistic seismic hazard analysis for ground motion selection. The CS is computed on the basis of a specified conditioning period, whereas structures under consideration may be sensitive to response spectral amplitudes at multiple periods of excitation. Questions remain regarding the appropriate choice of conditioning period when utilizing the CS as the target spectrum. This paper focuses on risk-based assessments, which estimate the annual rate of exceeding a specified structural response amplitude. Seismic hazard analysis, ground motion selection, and nonlinear dynamic analysis are performed, using the conditional spectra with varying conditioning periods, to assess the performance of a 20-story reinforced concrete frame structure. It is shown here that risk-based assessments are relatively insensitive to the choice of conditioning period when the ground motions are carefully selected to ensure hazard consistency. This observed insensitivity to the conditioning period comes from the fact that, when CS-based ground motion selection is used, the distributions of response spectra of the selected ground motions are consistent with the site ground motion hazard curves at all relevant periods; this consistency with the site hazard curves is independent of the conditioning period. The importance of an exact CS (which incorporates multiple causal earthquakes and ground motion prediction models) to achieve the appropriate spectral variability at periods away from the conditioning period is also highlighted. The findings of this paper are expected theoretically but have not been empirically demonstrated previously

Conditional Spectrum-Based Ground Motion Selection. Part II: Intensity-Based Assessments and Evaluation of Alternative Target Spectra

In a companion paper, an overview and problem definition was presented for ground motion selection on the basis of the conditional spectrum (CS), to perform risk-based assessments (which estimate the annual rate of exceeding a specified structural response amplitude) for a 20-story reinforced concrete frame structure. Here, the methodology is repeated for intensity-based assessments (which estimate structural response for ground motions with a specified intensity level) to determine the effect of conditioning period. Additionally, intensity-based and risk-based assessments are evaluated for two other possible target spectra, specifically the uniform hazard spectrum (UHS) and the conditional mean spectrum (CMS, without variability).It is demonstrated for the structure considered that the choice of conditioning period in the CS can substantially impact structural response estimates in an intensity-based assessment. When used for intensity-based assessments, the UHS typically results in equal or higher median estimates of structural response than the CS; the CMS results in similar median estimates of structural response compared with the CS but exhibits lower dispersion because of the omission of variability. The choice of target spectrum is then evaluated for risk-based assessments, showing that the UHS results in overestimation of structural response hazard, whereas the CMS results in underestimation. Additional analyses are completed for other structures to confirm the generality of the conclusions here. These findings have potentially important implications both for the intensity-based seismic assessments using the CS in future building codes and the risk-based seismic assessments typically used in performance-based earthquake engineering applications

An Assessment to Benchmark the Seismic Performance of a Code-Conforming Reinforced-Concrete Moment-Frame Building

This report describes a state-of-the-art performance-based earthquake engineering methodology that is used to assess the seismic performance of a four-story reinforced concrete (RC) office building that is generally representative of low-rise office buildings constructed in highly seismic regions of California. This “benchmark” building is considered to be located at a site in the Los Angeles basin, and it was designed with a ductile RC special moment-resisting frame as its seismic lateral system that was designed according to modern building codes and standards. The building’s performance is quantified in terms of structural behavior up to collapse, structural and nonstructural damage and associated repair costs, and the risk of fatalities and their associated economic costs. To account for different building configurations that may be designed in practice to meet requirements of building size and use, eight structural design alternatives are used in the performance assessments. Our performance assessments account for important sources of uncertainty in the ground motion hazard, the structural response, structural and nonstructural damage, repair costs, and life-safety risk. The ground motion hazard characterization employs a site-specific probabilistic seismic hazard analysis and the evaluation of controlling seismic sources (through disaggregation) at seven ground motion levels (encompassing return periods ranging from 7 to 2475 years). Innovative procedures for ground motion selection and scaling are used to develop acceleration time history suites corresponding to each of the seven ground motion levels. Structural modeling utilizes both “fiber” models and “plastic hinge” models. Structural modeling uncertainties are investigated through comparison of these two modeling approaches, and through variations in structural component modeling parameters (stiffness, deformation capacity, degradation, etc.). Structural and nonstructural damage (fragility) models are based on a combination of test data, observations from post-earthquake reconnaissance, and expert opinion. Structural damage and repair costs are modeled for the RC beams, columns, and slabcolumn connections. Damage and associated repair costs are considered for some nonstructural building components, including wallboard partitions, interior paint, exterior glazing, ceilings, sprinkler systems, and elevators. The risk of casualties and the associated economic costs are evaluated based on the risk of structural collapse, combined with recent models on earthquake fatalities in collapsed buildings and accepted economic modeling guidelines for the value of human life in loss and cost-benefit studies. The principal results of this work pertain to the building collapse risk, damage and repair cost, and life-safety risk. These are discussed successively as follows. When accounting for uncertainties in structural modeling and record-to-record variability (i.e., conditional on a specified ground shaking intensity), the structural collapse probabilities of the various designs range from 2% to 7% for earthquake ground motions that have a 2% probability of exceedance in 50 years (2475 years return period). When integrated with the ground motion hazard for the southern California site, the collapse probabilities result in mean annual frequencies of collapse in the range of [0.4 to 1.4]x10 -4 for the various benchmark building designs. In the development of these results, we made the following observations that are expected to be broadly applicable: (1) The ground motions selected for performance simulations must consider spectral shape (e.g., through use of the epsilon parameter) and should appropriately account for correlations between motions in both horizontal directions; (2) Lower-bound component models, which are commonly used in performance-based assessment procedures such as FEMA 356, can significantly bias collapse analysis results; it is more appropriate to use median component behavior, including all aspects of the component model (strength, stiffness, deformation capacity, cyclic deterioration, etc.); (3) Structural modeling uncertainties related to component deformation capacity and post-peak degrading stiffness can impact the variability of calculated collapse probabilities and mean annual rates to a similar degree as record-to-record variability of ground motions. Therefore, including the effects of such structural modeling uncertainties significantly increases the mean annual collapse rates. We found this increase to be roughly four to eight times relative to rates evaluated for the median structural model; (4) Nonlinear response analyses revealed at least six distinct collapse mechanisms, the most common of which was a story mechanism in the third story (differing from the multi-story mechanism predicted by nonlinear static pushover analysis); (5) Soil-foundation-structure interaction effects did not significantly affect the structural response, which was expected given the relatively flexible superstructure and stiff soils. The potential for financial loss is considerable. Overall, the calculated expected annual losses (EAL) are in the range of $52,000 to$97,000 for the various code-conforming benchmark building designs, or roughly 1% of the replacement cost of the building ($8.8M). These losses are dominated by the expected repair costs of the wallboard partitions (including interior paint) and by the structural members. Loss estimates are sensitive to details of the structural models, especially the initial stiffness of the structural elements. Losses are also found to be sensitive to structural modeling choices, such as ignoring the tensile strength of the concrete (40 EAL) or the contribution of the gravity frames to overall building stiffness and strength (15 change in EAL). Although there are a number of factors identified in the literature as likely to affect the risk of human injury during seismic events, the casualty modeling in this study focuses on those factors (building collapse, building occupancy, and spatial location of building occupants) that directly inform the building design process. The expected annual number of fatalities is calculated for the benchmark building, assuming that an earthquake can occur at any time of any day with equal probability and using fatality probabilities conditioned on structural collapse and based on empirical data. The expected annual number of fatalities for the code-conforming buildings ranges between 0.05*10 -2 and 0.21*10 -2 , and is equal to 2.30*10 -2 for a non-code conforming design. The expected loss of life during a seismic event is perhaps the decision variable that owners and policy makers will be most interested in mitigating. The fatality estimation carried out for the benchmark building provides a methodology for comparing this important value for various building designs, and enables informed decision making during the design process. The expected annual loss associated with fatalities caused by building earthquake damage is estimated by converting the expected annual number of fatalities into economic terms. Assuming the value of a human life is$3.5M, the fatality rate translates to an EAL due to fatalities of $3,500 to$5,600 for the code-conforming designs, and $79,800 for the non-code conforming design. Compared to the EAL due to repair costs of the code-conforming designs, which are on the order of$66,000, the monetary value associated with life loss is small, suggesting that the governing factor in this respect will be the maximum permissible life-safety risk deemed by the public (or its representative government) to be appropriate for buildings. Although the focus of this report is on one specific building, it can be used as a reference for other types of structures. This report is organized in such a way that the individual core chapters (4, 5, and 6) can be read independently. Chapter 1 provides background on the performance-based earthquake engineering (PBEE) approach. Chapter 2 presents the implementation of the PBEE methodology of the PEER framework, as applied to the benchmark building. Chapter 3 sets the stage for the choices of location and basic structural design. The subsequent core chapters focus on the hazard analysis (Chapter 4), the structural analysis (Chapter 5), and the damage and loss analyses (Chapter 6). Although the report is self-contained, readers interested in additional details can find them in the appendices

Implications of Seismic Design Values for Economic Losses

In the U.S., seismic design values are determined mostly through a risk-targeting process, which combines information about the expected collapse fragility of code-designed structures with seismic hazard at a site. However, this target only applies where the risk-targeted ground motions govern the design. In other areas, primarily close to active faults, seismic design values are reduced to values calculated from deterministic seismic hazard analysis, increasing seismic risk for near-fault sites by an unknown quantity. This study investigates the implications of designing buildings using deterministic and probabilistic design values in terms of earthquake-induced economic consequences. This investigation is carried out using a performance-based seismic risk assessment of modern code-designed buildings with various structural systems, following the FEMA P-58 framework. Specifically, structural responses and losses associated with code-designed systems (i.e., reinforced concrete, steel, wood light frame, and precast tilt-up buildings) considering different design values (i.e., risk-targeted, deterministic, and uniform-hazard) are assessed. This study finds that, while risk-targeted design maps specify a uniform collapse risk, they do not provide uniform risk of economic losses to modern buildings across the U.S. and are instead dependent on building type and site properties. Also, for the sites in this study governed by deterministic capping, design values in the current code may be up to 30% lower than design values derived from risk-targeted design maps, resulting in up to 40% higher expected seismic losses.Thanks to the Haselton Baker Risk Group to providing access to the SP3 RiskModel and to the CEAE department at CU Boulder

Evaluation of the seismic performance of a code-conforming reinforced-concrete frame building—from seismic hazard to collapse safety and economic losses

A state-of-the-art seismic performance assessment is illustrated through application to a reinforcedconcrete moment-frame building designed per current (2003) building code provisions. Performance is quantified in terms of economic losses and collapse safety. The assessment includes site-specific seismic hazard analyses, nonlinear dynamic structural response simulations to collapse, damage analyses, and loss estimation. When selecting ground motion records for nonlinear dynamic analyses that are consistent with a target hazard level expressed in terms of a response spectral value at the building’s fundamental period, it is important to consider the response spectral shape, especially when considering higher hazard levels. This was done through the parameter commonly denoted by ε. Neglecting these effects during record selection is shown to lead to a factor of 5–10 overestimation of mean annual collapse rate. Structural response simulations, which properly account for uncertainties in ground motions and structural modelling, indicate a 2–7% probability of collapse for buildings subjected to motions scaled to a hazard level equivalent to a 2% probability of exceedance in 50 years. The probabilities of component damage and the means and coefficients of variation of the repair costs are calculated using fragility functions and repair-cost probability distributions. The calculated expected annual losses for various building design variants range from 0.6 to 1.1% of the replacement value, where the smaller losses are for above-code design variants and the larger losses are for buildings designed with minimum-code compliance. Sensitivity studies highlight the impact of key modelling assumptions on the accurate calculation of damage and the associated repair costs