Earthquake Spectra

Seismic input to nonlinear dynamic analyses of structures is usually defined in terms of acceleration time series whose response spectra are compatible with a specified target response spectrum. Time domain spectral matching used to generate realistic design acceleration time series is discussed in this paper. A new and improved adjustment function to be used in modifying existing accelerograms while preserving the nonstationary character of the ground motion is presented herein. The application of the new adjustment wavelet ensures stability, efficiency and speed of the numerical solution and prevents drift in the resulting velocity and displacement time series.

Exposure data available to developers of earthquake loss models are often very crudely aggregated spatially, and in such cases very considerable effort can be required to refine the geographical resolution of the building stock inventory. The influence of the geographical resolution of the exposure data for the Sea of Marmara region in Turkey is explored using several different levels of spatial aggregation to estimate the losses due to a single earthquake scenario. The results show that the total damage over an urban area, expressed as a mean damage ratio (MDR), is rather insensitive to the spatial resolution of the exposure data if a sufficiently large number of ground-motion simulations are used. However, the variability of the MDR estimates does reduce as the spatial resolution becomes higher, reducing the number of simulations required, although there appears to be a law of diminishing returns in going to very high exposure data resolution. This is largely due to the inherent and irreducible spatial variability of ground motion, which suggests that if only mean MDR estimates are needed, the effort required to refine the spatial definition of exposure data is not justified.

Cumulative absolute velocity (CAV), defined as the integral of the absolute acceleration time series, has been used as an index to indicate the possible onset of structural damage to nuclear power plant facilities and liquefaction of saturated soils. However, there are very few available ground motion prediction equations for this intensity measure. In this study, we developed a new empirical prediction equation for the horizontal component of CAV using the strong motion database and functional forms that were used to develop similar prediction equations for peak response parameters as part of the PEER Next Generation Attenuation (NGA) Project. We consider this relationship to be valid for magnitudes ranging from 5.0 up to 7.5–8.5 (depending on fault mechanism) and distances ranging from 0–200 km. We found the interevent, intra-event, and intracomponent standard deviations from this relationship to be smaller than any intensity measure we have investigated thus far.

The normal-faulting earthquake of 6 April 2009 in the Abruzzo Region of central Italy caused heavy losses of life and substantial damage to centuries-old buildings of significant cultural importance and to modern reinforced-concrete-framed buildings with hollow masonry infill walls. Although structural deficiencies were significant and widespread, the study of the characteristics of strong motion data from the heavily affected area indicated that the short duration of strong shaking may have spared many more damaged buildings from collapsing. It is recognized that, with this caveat of short-duration shaking, the infill walls may have played a very important role in preventing further deterioration or collapse of many buildings. It is concluded that better new or retrofit construction practices that include reinforced-concrete shear walls may prove helpful in reducing risks in such seismic areas of Italy, other Mediterranean countries, and even in United States, where there are large inventories of deficient structures.

Squat reinforced concrete (RC) shearwalls are often used to contain nuclear material or other dangerous gases in the U.S. Department of Energy's (DOE) complex. Damage to such walls can be expected even during minor earthquake shaking. The escape of dangerous gases post-event is therefore of concern. In this paper, the flow rate of air through damaged squat RC walls is analytically predicted for a broad range of structural configurations, loading conditions, and concrete compressive strengths at different differential pressures. Design charts relating shearwall lateral drift ratio and air leakage rate are presented. Among the parameters considered in this study, the shearwall boundary element size has the most significant effect on the flow rate. The paper concludes with a design example demonstrating the use of the design charts.

Poor performance of reinforced concrete (RC) frame buildings in India during past earthquakes has been a matter of serious concern. Hence, it becomes important to identify and strengthen the deficient buildings. When dealing with a large building stock, one needs evaluation methods for quick assessment of the seismic safety of existing buildings so that corrective retrofitting measures may be undertaken on the deficient buildings. This paper presents a review of some of the available methods for rapid visual screening (RVS) of RC-frame buildings and proposes a RVS method for RC-frame buildings in India based on systematic studies on damage data of the 2001 Bhuj earthquake.

We develop a global database of building inventories using taxonomy of global building types for use in near-real-time post-earthquake loss estimation and pre-earthquake risk analysis, for the U.S. Geological Survey's Prompt Assessment of Global Earthquakes for Response (PAGER) program. The database is available for public use, subject to peer review, scrutiny, and open enhancement. On a country-by-country level, it contains estimates of the distribution of building types categorized by material, lateral force resisting system, and occupancy type (residential or nonresidential, urban or rural). The database draws on and harmonizes numerous sources: (1) UN statistics, (2) UN Habitat's demographic and health survey (DHS) database, (3) national housing censuses, (4) the World Housing Encyclopedia and (5) other literature.

An innovative tuned mass damper, referred to as a coupled tuned mass damper (CTMD), is proposed for the control of a coupled vibration mode of one-way asymmetric-plan buildings. The CTMD simultaneously translates and rotates almost resonantly with the vibration of the controlled mode, which actually vibrates in translation, as well as rotation. Thus, the CTMD can be viewed as a direct approach for controlling the modal vibration of asymmetric-plan buildings. First, the CTMD is developed from the two-degree-of-freedom modal system, which has one active and one spurious vibration frequency. It is illustrated that the optimum parameter values of the CTMD can be conveniently determined from those of the corresponding tuned mass damper (TMD). Second, in order to apply the CTMD to a building structure, the properties of the CTMD obtained in the modal space are transformed into the physical space. Finally, the effectiveness of the CTMD in reducing the vibrations of asymmetric-plan structures is verified by investigating the frequency response functions and the response histories of three eight-story asymmetric-plan buildings with and without dampers. These three buildings are respectively torsionally stiff, torsionally similarly stiff, and torsionally flexible. This study confirms that the CTMD is an effective alternative for the seismic control of asymmetric-plan buildings.

A statistical evaluation of shaking damage to wood-framed houses caused by the 2003 M6.5 San Simeon earthquake indicates that both the rate and severity of damage, independent of structure type, are significantly greater on hilltops compared to hill slopes when underlain by Cretaceous or Tertiary sedimentary rocks. This increase in damage is interpreted to be the result of topographic amplification. An increase in the damage rate is found for all structures built on Plio-Pleistocene rocks independent of topographic position, and this is interpreted to be the result of amplified shaking caused by geologic site response. Damage rate and severity to houses built on Tertiary rocks suggest that amplification due to both topographic position and geologic site response may be occurring in these rocks, but effects from other topographic parameters cannot be ruled out. For all geologic and topographic conditions, houses with raised foundations are more frequently damaged than those with slab foundations. However, the severity of damage to houses on raised foundations is only significantly greater for those on hill slopes underlain by Tertiary rocks. Structures with some damage-resistant characteristics experienced greater damage severity on hilltops, suggesting a spectral response to topographic amplification.

Site response characteristics at seismic stations were investigated using horizontal-to-vertical (H/V) spectral ratios calculated from a seismic-motion dataset of the 2003 Boumerdes earthquake, and transfer functions were evaluated from soil profile data. Although high peak ground acceleration (PGA) values were recorded at some sites, the nonlinear effect at these stations was not clear. The H/V spectral ratios calculated from weak and strong motion events did not show a clear difference in the predominant period and amplitudes, and the shapes of the H/V ratios were flat for some stations. These observations are characteristic of the presence of firm to hard layers under the stations; however, one station was located on Quaternary deposits showed a remarkable amplification at the predominant period and a high PGA value.

Non-uniform values of recurrence intervals to seismic failure of structures are shown to occur for different limit states. The median capacity and the capacity and demand factors specified by currently accepted criteria are calculated for a set of 5-, 10-, 15-, and 24-story buildings, built on very soft soil sites and exposed to narrow-band ground motions. Using these values and the demand hazard curves for each structure, the recurrence intervals to failure are obtained for serviceability, life-safety and near-collapse limit states. Based on the results, it is concluded that for the design of structures exposed to the action of narrow-band motions, it may be appropriate to use capacity and demand factors that depend on their fundamental periods of vibration.

As nonlinear response history analysis (NLRHA) becomes a frequently used procedure for the seismic demand evaluation of multistory buildings, it becomes increasingly important to develop a ground motion scaling method which properly includes the dominating modes in the seismic demand estimates. This paper proposes a multimode ground motion scaling (MMS) method, which applies the square root of the sum of the squares (SRSS) or complete quadratic combination (CQC) rule in computing peak seismic demands. The aim is to minimize the weighted sum of the square differences between the spectral responses of a given ground motion and the design response spectrum for the first few modes. Using four case studies, this paper compares the effectiveness of the MMS method with the other common scaling procedures. It is illustrated that the MMS method is effective in reducing the scatter in the peak seismic demands computed from both the response spectral analysis (RSA) and the NLRHA. Recommendations for selecting the ground motion records for the application of MMS method are also provided.

This study introduces a methodology for anticipating the post-earthquake functionality of hospitals in a region. Performance levels for interacting systems (structural, nonstructural, lifeline, and personnel) in a hospital are operationally defined, empirically correlated, and probabilistically modeled using damage data from past earthquakes. Separate models are developed for buildings built before and after the 1973 California Hospital Seismic Safety Act. Performance estimates of the systems are used to anticipate overall hospital functionality. Effects of external power and water outage are also included. As a case study, the methodology is utilized to predict the functionality of hospitals in Los Angeles County for two earthquake scenarios. Findings indicate that in a M6.9 Verdugo fault earthquake scenario, nearly half of county hospitals have at least a 50% chance of experiencing significant loss of functionality. Such findings can support emergency response planning as well as seismic retrofit prioritization.

The “cracking an open safe” methodology has been used to tabulate HAZUS-based seismic vulnerability as functions of structure-independent intensity, while avoiding iteration in the structural analysis. The vulnerability functions give mean damage factor (MDF, defined here as mean repair cost as a fraction of replacement cost) versus 5%-damped elastic spectral acceleration response at 0.3-second and 1.0-second periods, for every combination of occupancy type, model building type, design level, magnitude, distance, site soil classification, etc. Like HAZUS-MH, these prior seismic vulnerability functions give no estimate of uncertainty in damage factor. The coefficient of variation (COV) of damage factor is readily calculated by taking advantage of the fact that that at any level of excitation there is a probability mass function of damage state and an implicit distribution of repair cost conditioned on damage state. COV is calculated here for each combination of occupancy type, model building type, etc., tabulated alongside MDF, and the tables presented for public use at www.risk-agora.org. It is found that a HAZUS-based COV generally decreases with increasing MDF (as has been observed using other analytical vulnerability methods), and the standard deviation of damage factor generally increases with increasing MDF.