Earthquake Spectra

We establish and test a shake map methodology for intermediate-depth Vrancea earthquakes, based on seismological information gathered in Romania during recent years. We use region- (azimuth-) dependent attenuation relations derived from stochastic simulations of ground motions using spectral models of Vrancea earthquakes. Both region boundaries and Fourier amplification spectra for the characterization of seismic site effects are based on several hundred weak, moderate and strong-motion records and macroseismic intensity maps. We determine region-specific, magnitude- and distance-dependent amplification factors of peak values and instrumental intensity relative to rock. We interpolate recorded ground motions and ground motion estimates from the obtained amplification factors and attenuation relations for rock conditions. The resulting shake maps show a good agreement with macroseismic descriptions of moderate-sized and large Vrancea earthquakes, demonstrating the feasibility of a seismological approach to shake map generation. Unlike previous methodologies, this approach requires neither expensive assessments of geology-dependent site amplification factors, nor large numbers of strong-motion records. Our results are in good agreement with empirical topographic slope-site amplification relations, but give a better reflection of the abnormal attenuation of seismic waves in the Transylvanian region and the strong amplification in the Focsani basin.

A new representation of seismic hazard is proposed for Italy based on displacement elastic response spectra in a vibration period range that extends from 0 s to 20 s . This relies on an available seismotectonic zonation and earthquake catalogue, but makes use of a set of very recent, expressly developed attenuation relations. The long period picture of ground motion hazard is illustrated vis-à-vis the conventional one based on ground acceleration, and the feasibility of simple approximations of the displacement spectra, useful for design purposes, is shown. We give some foresight on the differences to be expected in hazard maps resulting from the use of a predominantly fault-based seismic source model, as opposed to the more conventional model that includes only spatially extended zones. Finally, we highlight the different hazard exposure of different regions depending on whether we represent hazard with a long or a short period parameter and we discuss the adequacy of recent code provisions regarding elastic displacement spectra.

It is common for ground motions to be estimated using a combination of probabilistic and deterministic procedures. Probabilistic seismic hazard analyses (PSHA) are performed to estimate intensity measures (IMs) for reference site conditions (usually rock). This is followed by a deterministic modification of the rock IMs to account for site effects, typically using site factors from the literature or seismic codes. We demonstrate for two California sites and three site conditions that the deterministic application of nonlinear site factors underestimates ground motions evaluated probabilistically for return periods of engineering interest. Reasons for this misfit include different standard deviation terms for rock and soil sites, different controlling earthquakes, and overestimation of the nonlinear component of the site response in the deterministic procedure. This problem is solved using site-specific PSHA with appropriate consideration of nonlinear site response, within the hazard integral.

The seismic response of levees in the Sacramento-San Joaquin Delta, where the subsurface soils include thick deposits of highly organic soils, is evaluated. One-dimensional (1-D) and two-dimensional (2-D) equivalent-linear analyses were performed that accounted for variability in ground motions, dynamic properties, and soil profiles. Regression models were developed for: (1) the ratio of spectral accelerations at levee crests computed by 2-D versus 1-D response analyses, (2) stress reduction factors from 1-D site response analyses and seismic coefficient reduction factors for various failure surface depths from the 2-D response analyses, and (3) Newmark sliding block displacements computed for the input NEHRP site D ground motions and the computed seismic coefficient time series. The results of these regression models are compared to those obtained in previous studies involving different soil conditions, geometries, and motions. Newmark sliding block displacement hazard curves were calculated for a representative site in the Sacramento-San Joaquin Delta, and the contributions of various uncertainties to the displacement hazard curves are described.

This paper presents a direct displacement design (DDD) procedure that can be used for seismic design of multistory wood-framed structures. The proposed procedure is applicable to any pure shear deforming system. The design procedure is a promising design tool for performance-based seismic design since it allows consideration of multiple performance objectives (e.g., damage limitation, safety requirements) without requiring the engineer to perform a complex finite element or nonlinear time-history analysis of the complete structure. A simple procedure based on normalized modal analysis is used to convert the code-specified acceleration response spectrum into a set of interstory drift spectra. These spectra can be used to determine the minimum stiffness required for each floor based on the drift limit requirements. Specific shear walls can then be directly selected from a database of backbone curves. The procedure is illustrated on the design of two three-story ATC-63 archetype buildings, and the results are validated using nonlinear time-history analysis.

In another work, the “open safe” of the HAZUS-MH methodology was cracked to create seismic vulnerability functions that honor all HAZUS-MH methodologies and data, yet that appear in the form of tables of mean casualty rates (indoor deaths and injuries as four fractions of total occupancy) versus a structure-independent intensity measure, in particular, _Sa (0.3 sec,5%) or _Sa (1.0 sec,5%). In this work, mean repair cost is tabulated against both these intensity measures, for various combinations of model building type, code design level, occupancy class, seismic environment, NEHRP site soil class, magnitude range and distance range.

A seismic risk assessment methodology based on socioeconomic clustering of urban habitat is presented in this paper. In this methodology, the city is divided into different housing clusters based on socioeconomic level of occupants, representing reasonably uniform seismic risk. It makes an efficient utilization of high resolution satellite data and stratified random sample survey to develop the building stock database. Ten different classes of socioeconomic clusters found in Indian cities are defined and 34 model building types (MBTs) prevalent on the Indian subcontinent have been identified and compared with the Medvedev-Sponheuer-Karnik (MSK) scale, European macroseismic scale (EMS), parameterless scale of seismic intensity (PSI), and HAZUS classifications. Lower and upper bound damage probability matrices (DPMs) are estimated, based on the MSK and EMS intensity scales and experience from past earthquakes in India. A case study of Dehradun, a city in the foothills of Himalayas, is presented. The risk estimates using the estimated DPMs have been compared with those obtained using the PSI scale. It has been observed that poorer people are subjected to higher seismic risk, both in terms of casualties and in terms of percent economic losses.

Performance evaluation of sacrificial exterior shear keys in bridge abutments under simulated seismic loading was conducted in terms of damage levels that were observed during testing. These experiments provided results that were used to make realistic assumptions on the load-deformation response of as-built sacrificial exterior shear keys as well as their peak and post-peak performance under cyclic loads. Experimental results were subsequently used to develop a two-spring component hysteretic model for modeling the seismic response of shear keys at the abutments. The mathematical rules used to describe the hysteretic model are presented. Analyses show that this model was able to reproduce reasonably well the cyclic response of the investigated keys. The hysteretic model and key experimental results are presented in this paper.

We propose a method to calculate damage and human losses for cities in the developing world by averaging over an entire city, or its administrative districts. Bucharest, Romania, serves as an example. First, we modeled this city as located at a single coordinate point. We transformed the census information on building types, ages and height into EMS-98 vulnerability classes and distribute the population into them. We assumed a seismic load of MSK Intensity=8 (M7.4 1977 Vrancea earthquake). Validating our model by comparison with casualties reported in 1977, we find differences of 20% to 30%. We reduced these errors to about 4%, by adjusting the distribution of building types into vulnerability classes, based on their performance in the 1977 earthquake. Calibrations of this type will be necessary for most developing countries. In a second step, we modeled Bucharest with six districts, in which the distribution of people into building types and the average soil conditions are known. This is our preferred model. We also calculated the soil properties that would be estimated from topography, if microzonation would not be available. The agreement was satisfactory. We propose this method to model important cities in earthquake prone areas of the developing world.

We demonstrate a direct method for the calculation of the annual frequency of exceedance for earthquake losses (or the probability distribution for annual losses) to a portfolio. This method parallels the classic method of probabilistic seismic hazard analysis for the calculation of the annual frequency of exceedance for earthquake ground motions. The method assumes conditional independence of the random component of ground motions and losses at different sites for each earthquake, given magnitude, distance to the sites, and so-called interevent epsilon. Examples show that the method is realizable, and can take into account different loss functions and site conditions in the portfolio. The main advantage of this method is that it does not require a separate set of scenario earthquakes, as do Monte Carlo-based approaches, but can be calculated directly from the inputs used for hazard maps.

An orientation-dependent parameter, _{R¯ Sa} (θ), is used to investigate the orientation of maximum elastic spectral demand for near-fault ground motions. The upper bound on _{R¯ Sa} (θ), equal to 1, occurs when the spectral demands for an orientation θ are equal to the maximum demands at all periods considered. One hundred forty-seven pairs of near-fault ground motions were used to identify the orientation associated with the maximum value of _{R¯ Sa} for each pair of ground motions. The maximum value of _{R¯ Sa} is greater than 0.9 for over 80% of the records in the dataset, meaning that there is generally an axis where the spectral demands are equal or very close to the maximum spectral demands for a wide range of period. The strike-normal direction should not be used as a surrogate for the direction of maximum shaking for a) closest site-to-source distance less than 5 km and periods less than 1 second, and b) closest site-to-source distance greater than 5 km .

Fragility functions are vital for the risk assessment of critical facilities and to calculate component probability of damage in performance-based earthquake engineering. Seismic qualification is used to prove the adequacy of components in existing facilities or to satisfy their design criteria in new facilities. This technical note describes an approach for component fragility development and seismic qualification using data for seismic demand experienced by similar components and their resulting performance. Depending on the observed component failure or survival, the seismic demand values either exceed or fall short of the random component capacity. The concept of censoring, which captures this excess or shortfall, is introduced to model such data and account for the different statistical characteristics of failure and survival data. The censored data are analyzed by survival analysis, which provides a rigorous and efficient approach to extract information from the data set.