Earthquake Spectra

We examine the characteristics of long-period near-source ground motions by conducting a sensitivity study with variations in six earthquake source parameters for both a strike-slip fault (M 7.0-7.1) and a thrust fault (M 6.6-7.0). The directivity of the ruptures creates large displacement and velocity pulses in the forward direction. The dynamic displacements close to the fault are comparable to the average slip. The ground motions exhibit the greatest sensitivity to the fault depth with moderate sensitivity to the rupture speed, peak slip rate, and average slip. For strike-slip faults and thrust faults with surface rupture, the maximum ground displacements and velocities occur in the region where the near-source factor from the 1997 Uniform Building Code is the largest. However, for a buried thrust fault the peak ground motions can occur up-dip from this region.

In this paper, the validity of the energy balance equation is verified by statistical analysis. An ensemble of two hundred artificial earthquakes are generated and used as input to a structure on whose floors unanchored bodies are placed. The equation of motion governing the rocking motion of an unanchored body is solved and the probabilities of overturning are obtained. This information is used to show that the energy balance equation proposed by Housner is indeed valid. A few examples are given to demonstrate the use of the energy balance equation.

A new measure of earthquake demand, the drift spectrum has been developed as an adjunct to the response spectrum, a central concept in earthquake engineering, in calculating the internal deformations of a structure due to near-fault ground motions with pronounced coherent pulses in the velocity and displacement histories. Compared in this paper are certain aspects of the elastic structural response to near-fault and far-fault ground motions. It is demonstrated that (1) the difference between drift and response spectra are not unique to near-fault ground motions; these differences simply reflect higher-mode response, which is larger due to near-fault ground motions; (2) response spectrum analysis (RSA) using existing modal combination rules can provide an estimate of structural response that is accurate to a useful degree; (3) these modal combination rules are similarly accurate for near-fault and far-fault ground motions although the underlying assumptions are not satisfied by near-fault excitations; and (4) RSA is preferable over the drift spectrum in computing structural response because it represents standard engineering practice and is applicable to a wide variety of structures.

Energy dissipation as a means of reducing the seismic response of structures has become a popular topic among researchers and structural engineers who have developed and implemented devices, such as friction dampers, fluid dampers, and isolators, in the design or retrofit of structures. However, a natural source of energy dissipation is the interaction between a structure, its foundation, and the supporting soil medium. To account for this frequency-dependent energy dissipation in dynamic analysis based on modal superposition, relatively simple and practical systems-identification methods are presented to estimate the composite modal damping ratios for the significant modes of vibration. SSI experiments and analysis of simple theoretical models using this method have yielded relatively large modal damping ratios in certain situations for structures such as short to mid-rise buildings, short-span bridges, flat bottom fuel storage tanks, offshore concrete gravity platforms, nuclear power plant containments, and nuclear waste processing plants.

This paper defines a damage index based on the predicted hysteretic behavior of a concrete column. The model yields a damage index at a point in the time history for the element, based on the predicted monotonic response from the point in time to failure. The model takes into account the parameters that describe the hysteretic behavior: stiffness degradation, strength deterioration, and ultimate displacement reduction. Therefore, the damage model is accumulative and it combines energy, ductility, and low-cycle fatigue. The model is based on the work needed to fail a reinforced concrete column monotonically after it experiences a cyclic loading. The model modifies the ultimate displacement that the column can achieve, due to low-cycle fatigue in the longitudinal reinforcement using the Coffin-Manson rule in combination with Miner's hypothesis. The proposed model is applied to bridge columns tested by others, and compared to existing damage indices. The proposed model gives a realistic prediction of damage throughout the loading cycles for several test specimens investigated.

Assembly-based vulnerability (ABV) is a framework for evaluating the seismic vulnerability and performance of buildings on a building-specific basis. It utilizes the damage to individual building components and accounts for the building's seismic setting, structural and nonstructural design and use. A simulation approach to implementing ABV first applies a ground motion time history to a structural model to determine structural response. The response is applied to assembly fragility functions to simulate damage to each structural and nonstructural element in the building, and to its contents. Probabilistic construction cost estimation and scheduling are used to estimate repair cost and loss-of-use duration as random variables. It also provides a framework for accumulating post-earthquake damage observations in a statistically systematic and consistent manner. The framework and simulation approach are novel in that they are fully probabilistic, address damage at a highly detailed and building-specific level, and do not rely extensively on expert opinion. ABV is illustrated using an example pre-Northridge welded-steel-moment-frame office building.

We calculated peak ground accelerations and response spectra for the Taipei area using stochastic simulation technique on the basis of recently obtained empirical models. The source, path and site effects were characterized separately on the basis of the analysis of a large collection of ground-motion recordings obtained since 1991 in the Taiwan area. The simple ω-squared Brune's point-source model combined with regional anelastic attenuation (Q) and duration (τ_0.9) models provide a satisfactory estimation of ground-motion parameters for rock sites. Effects of local site response are considered by means of empirical soil/bedrock spectral ratios calculated as ratios between spectra of actual earthquake records and those modeled for hypothetical “hard rock” site. The results of the simulation demonstrate that this combination of source, path and site response models provides an accurate prediction of “site- and region-dependent” ground-motion parameters for the Taipei basin for the broad range of earthquake magnitudes, distances and site conditions. The model, with a set of generic soil profiles, can be considered as an efficient tool for estimating of design input ground motion parameters in the Taipei basin both in deterministic (scenario earthquakes) and probabilistic (“site- and region-dependent” Uniform Hazard response spectra) seismic hazard assessment.

The damage potential of earthquake ground motions compatible with site-specific 2% in 50 year uniform hazard spectra is compared at two North American sites in areas of moderate seismic hazard: Montreal, in the east, and Vancouver, along the west coast. For Vancouver, crustal, subcrustal and Cascadia subduction ground motion earthquake ensembles are considered. Nonlinear dynamic analyses of bi-linear single-degree-of-freedom oscillators exhibiting various ductility levels and damage laws were performed to determine R factors required to prevent structural collapse for each site and each system. Then, inelastic response parameters were computed for the general design case, wherein a prescribed R factor is used for a given system irrespective of tectonic region or structural period. The results show that the R factors vary with the ductility level, the damage law, the structural period, and the tectonic region. Neglecting the latter two dependencies in design, as is current practice, may lead to significant discrepancies in the level of protection achieved for different structures in different regions.

For performance evaluation of buildings and structures, synthetic uniform hazard (10% and 2% in 50 years) ground motions are generated for Memphis, Tennessee, St. Louis, Missouri, and Carbondale, Illinois. The method of simulation is based on the latest regional seismic information and stochastic ground motion models. Both point-source model and finite-fault model are used and the effects of soil profile are considered. The emphasis is on treatment of uncertainty and efficiency in application to evaluation of structural performance in both the linear and nonlinear range. The results show that the uniform hazard response spectra calculated from the simulated motions are comparable to those corresponding to USGS hazard maps. The suites of ten ground motions selected to match the uniform hazard response spectra represent events of different magnitudes, distances, and attenuation. The median value of the structural response to the selected ground motions matches closely the uniform hazard linear and nonlinear response spectra based on nine thousand ground motions and has a coefficient of variation of less than 10%. The suites of uniform hazard ground motions therefore can be used in probabilistic performance evaluation with good accuracy and efficiency.