CQC modal combination rule for high-frequency modes

The CQC rule for modal combination is extended to include the quasi-static contribution of truncated modes and the effects of input narrow-bandedness and cut-off frequency. A simple measure of the error in approximating a high-frequency modal response by its quasi-static contribution is derived. The extended rule is applicable to structures with high-frequency modes and to seismic inputs which may not be regarded as wide band. Numerical examples demonstrate the significance of input bandwidth and cut-off frequency on modal cross-correlation coefficients, and on the error resulting from truncation of high-freqeuncy modes.     

A response spectrum method for random vibration analysis of mdf systems

A response spectrum method for stationary random vibration analysis of linear, multi-degree-of-freedom systems is developed. The method is based on the assumption that the input excitation is a wide-band, stationary Gaussian process and the response is stationary. However, it can also be used as a good approximation for the response to a transient stationary Gaussian input with a duration several times longer than the fundamental period of the system. Various response quantities, including the mean-squares of the response and its time derivative, the response mean frequency, and the cumulative distribution and the mean and variance of the peak response are obtained in terms of the ordinates of the mean response spectrum of the input excitation and the modal properties of the system. The formulation includes the cross-correlation between modal responses, which is shown to be significant for modes with closely spaced natural frequencies. The proposed procedure is demonstrated for an example structure that is subjected to an ensemble of earthquake-induced base excitations. Computed results based on the response spectrum method are in close agreement with simulation results obtained from time-history dynamic analysis. The significance of closely spaced modes and the error associated with a conventional method that neglects the modal correlations are also demonstrated.     

Response spectrum analysis for floor acceleration

The peak floor acceleration (PFA) is a critical parameter influencing the performance of non‐structural elements in buildings. This paper develops a response spectrum analysis method based on the complete quadratic combination (CQC) rule to estimate the PFA. The method accounts for the rigid contribution of truncated higher modes and the cross‐correlations between all pairs of modes. The approximation is introduced in the time domain and then formulated in the frequency domain by CQC. Application of the method to a continuous cantilever beam idealizing a building with shear walls is presented and compared with alternative formulations. The proposed method is able to provide a consistent estimation of the PFA along the entire structure, not only where the PFA is principally influenced by the first few flexible modes but also where the PFA is mainly related to the rigid response of the structure, for example, near its base. Copyright © 2015 John Wiley & Sons, Ltd.     

Development and validation of nonlinear computational models of dispersed structures under strong earthquake excitation

Structural health monitoring of large multispan flexible bridges is particularly important because of their important role in civil infrastructure and transportation systems. In this study, the response of the Yokohama Bay Bridge (YBB), a three‐span cable‐stayed bridge, to the 2011 Great East Japan Earthquake is used to perform multi‐input multi‐output system identification studies. The extensive multicomponent measurements are also used to develop and validate data‐driven nonlinear mathematical models that can predict the response of YBB to various earthquake records and can accurately estimate its damping characteristics when the system is driven into the nonlinear response range. A combination of least‐square (parametric) and neural network (nonparametric) approaches is used to develop the mathematical models, along with time‐marching techniques for dynamic response calculations. It is shown that the nonlinear mathematical models perform better than the equivalent linear models, both for response prediction and damping estimation. The importance of having an accurate approach for quantifying the damping due to the variety of nonlinear features in the YBB response is shown. This study demonstrates the significance of constructing robust mathematical models that can capture the correct physics of the underlying system and that can be used for computational purposes to augment experimental studies. Given the lack of suitable data sets for full‐scale structures under extreme loads, the availability of the long‐duration measurements from the 2011 Great East Japan Earthquake and its many strong aftershocks provides an excellent opportunity to perform the analyses presented in this study. Copyright © 2013 John Wiley & Sons, Ltd.     

Geophysical constraints on deep weathering and water storage potential in the Southern Sierra Critical Zone Observatory

The conversion of bedrock to regolith marks the inception of critical zone processes, but the factors that regulate it remain poorly understood. Although the thickness and degree of weathering of regolith are widely thought to be important regulators of the development of regolith and its water‐storage potential, the functional relationships between regolith properties and the processes that generate it remain poorly documented. This is due in part to the fact that regolith is difficult to characterize by direct observations over the broad scales needed for process‐based understanding of the critical zone. Here we use seismic refraction and resistivity imaging techniques to estimate variations in regolith thickness and porosity across a forested slope and swampy meadow in the Southern Sierra Critical Zone Observatory (SSCZO). Inferred seismic velocities and electrical resistivities image a weathering zone ranging in thickness from 10 to 35 m (average = 23 m) along one intensively studied transect. The inferred weathering zone consists of roughly equal thicknesses of saprolite (P‐velocity < 2 km s^?1) and moderately weathered bedrock (P‐velocity = 2–4 km s^?1). A minimum‐porosity model assuming dry pore space shows porosities as high as 50% near the surface, decreasing to near zero at the base of weathered rock. Physical properties of saprolite samples from hand augering and push cores are consistent with our rock physics model when variations in pore saturation are taken into account. Our results indicate that saprolite is a crucial reservoir of water, potentially storing an average of 3 m³ m^?2 of water along a forested slope in the headwaters of the SSCZO. When coupled with published erosion rates from cosmogenic nuclides, our geophysical estimates of weathering zone thickness imply regolith residence times on the order of 10⁵ years. Thus, soils at the surface today may integrate weathering over glacial–interglacial fluctuations in climate. Copyright © 2013 John Wiley & Sons, Ltd.     

A stochastic ground motion model with separable temporal and spectral nonstationarities

A fully nonstationary stochastic model for strong earthquake ground motion is developed. The model employs filtering of a discretized white‐noise process. Nonstationarity is achieved by modulating the intensity and varying the filter properties in time. The formulation has the important advantage of separating the temporal and spectral nonstationary characteristics of the process, thereby allowing flexibility and ease in modeling and parameter estimation. The model is fitted to target ground motions by matching a set of statistical characteristics, including the mean‐square intensity, the cumulative mean number of zero‐level up‐crossings and a measure of the bandwidth, all expressed as functions of time. Post‐processing by a second filter assures zero residual velocity and displacement, and improves the match to response spectral ordinates for long periods. Copyright © 2008 John Wiley & Sons, Ltd.     

Investigation of ‘equal displacement’ rule for bridges subjected to differential support motions

The ‘equal displacement’ rule is employed in seismic design practice to predict inelastic displacements from analyses of the corresponding linear elastic structural models. The accuracy and limitations of this rule have been investigated for ordinary structures but not for bridges subjected to spatially varying ground motions. The present study investigates this rule for moderate levels of inelastic behavior for four highway bridges in California accounting for the effects of spatial variability of the support motions due to incoherence, wave passage and differential site response. The bridge models vary significantly as to their fundamental periods and their overall configurations. Statistical analyses of pier‐drift responses are performed using as input simulated arrays of nonstationary ground motions in accordance with prescribed coherency models. It is found that the ‘equal displacement’ rule is fairly accurate for cases when the fundamental period of the bridge is longer than the transition period between the acceleration‐controlled and velocity‐controlled ranges of the response spectrum. Otherwise, the rule is non‐conservative for cases with large ductility factors and conservative for cases with small ductility factors. Wave passage and incoherence tend to reduce ratios of mean peak inelastic to elastic pier drifts, whereas incorporation of the differential site‐response effect by locating piers on softer soils tends to increase the same ratios. Mild or moderate positive correlation between these ratios and ductility demands is observed in most cases. Effects of spatial variability are more pronounced for longer and stiffer bridges. Copyright © 2013 John Wiley & Sons, Ltd.     

Coherency analysis of accelerograms recorded by the UPSAR array during the 2004 Parkfield earthquake

Spatial variability of near‐fault strong motions recorded by the US Geological Survey Parkfield Seismograph Array (UPSAR) during the 2004 Parkfield (California) earthquake is investigated. Behavior of the lagged coherency for two horizontal and the vertical components is analyzed by separately examining the decay of coherency with frequency and distance. Assumptions, approximations, and challenges that are involved in estimation of the coherency from recorded data are presented in detail. Comparison of the UPSAR coherency estimates with coherency models that are commonly used in engineering practice sheds light on the advantages and limitations of different approaches to modeling the coherency, as well as on similarities and differences in the spatial variability exhibited by seismic ground motion arrays at different sites. Copyright © 2013 John Wiley & Sons, Ltd.     

Vortex–interface interactions and generation of glitches in pulsars

We show that the crust–core interface in neutron stars acts as a potential barrier to the peripheral neutron vortices approaching the interface in the model in which these are coupled to the proton vortex clusters. This elementary barrier arises because of the interaction of vortex magnetic flux with the Meissner currents set up by the crustal magnetic field at the interface. The dominant part of the force is derived from the cluster–interface interaction. As a result of the stopping of the continuous neutron vortex current through the interface, angular momentum is stored in the superfluid layers in the vicinity of the crust–core interface during the interglitch period. Discontinuous annihilation of proton vortices at the boundary restores the neutron vortex current and spins up the observable crust on short time-scales, leading to a glitch in the spin characteristics of a pulsar.     

Simulation of synthetic ground motions for specified earthquake and site characteristics

A method for generating a suite of synthetic ground motion time‐histories for specified earthquake and site characteristics defining a design scenario is presented. The method employs a parameterized stochastic model that is based on a modulated, filtered white‐noise process. The model parameters characterize the evolving intensity, predominant frequency, and bandwidth of the acceleration time‐history, and can be identified by matching the statistics of the model to the statistics of a target‐recorded accelerogram. Sample ‘observations’ of the parameters are obtained by fitting the model to a subset of the NGA database for far‐field strong ground motion records on firm ground. Using this sample, predictive equations are developed for the model parameters in terms of the faulting mechanism, earthquake magnitude, source‐to‐site distance, and the site shear‐wave velocity. For any specified set of these earthquake and site characteristics, sets of the model parameters are generated, which are in turn used in the stochastic model to generate the ensemble of synthetic ground motions. The resulting synthetic acceleration as well as corresponding velocity and displacement time‐histories capture the main features of real earthquake ground motions, including the intensity, duration, spectral content, and peak values. Furthermore, the statistics of their resulting elastic response spectra closely agree with both the median and the variability of response spectra of recorded ground motions, as reflected in the existing prediction equations based on the NGA database. The proposed method can be used in seismic design and analysis in conjunction with or instead of recorded ground motions. Copyright © 2010 John Wiley & Sons, Ltd.