Strong Earthquake Ground Motion Research Articles

Numerical investigations on dynamic performance of stiffened box steel bridge piers

The aim of this paper is to carry out extensive numerical investigations about the effect of various structural parameters on the dynamic performance of stiffened box steel bridge pier under a strong earthquake ground motion. The considered structural parameters are the local slenderness ratios of stiffener and stiffened wall as well as the global slenderness ratio of the pier. In the present study, all investigated piers are made of high tensile steel with high yield ratio. The non-linear time history analyses are carried out using in-house Finite Element Program DYNAPSS, recently developed by the first author. This program is verified by comparing its results with the results obtained by the general FE program. In this program, the geometrical nonlinearity is considered on the bases of Total Lagrangian formulation, while the non-linearity of structural steel material is considered through implementation of modified multisurface cyclic plasticity model by which real characteristics of high tensile steel material such as, Plateau, Massing type of Bauschinger’s effect, disappearing of Plateau and cyclic strain hardening, are accurately modeled. The results are closely examined in respect with the damage index criterion. From this study, it is found that the increase in slenderness ratios of stiffener does not only increase the damage index, but also may lead to the full collapse. Furthermore, the damage index increases with the increase of local slenderness ratio of stiffened wall and the global slenderness ratio. Also, it is found that when the loacal buckling is not the dominant eigen mode and the pier behave as a single degree of freedom, the natural period has destructive effects when it is close to predominant period of the earthquake. Finally, contour plots of damage index values are presented. These contour plots may be greatly useful for the design of stiffened box steel bridge piers, where, critical values of structural parameters corresponding to certain value of damage index could be determined.

Estimation of seismic hazard in Gujarat region, India

The seismic hazard in the Gujarat region has been evaluated. The scenario hazard maps showing the spatial distribution of various parameters like peak ground acceleration, characteristics site frequency and spectral acceleration for different periods have been presented. These parameters have been extracted from the simulated earthquake strong ground motions. The expected damage to buildings from future large earthquakes in Gujarat region has been estimated. It has been observed that the seismic hazard of Kachchh region is more in comparison with Saurashtra and mainland. All the cities of Kachchh can expect peak acceleration in excess of 500 cm/s2 at surface in case of future large earthquakes from major faults in Kachchh region. The cities of Saurashtra can expect accelerations of less than 200 cm/s2 at surface. The mainland Gujarat is having the lowest seismic hazard as compared with other two regions of Gujarat. The expected accelerations are less than 50 cm/s2 at most of the places. The single- and double-story buildings in Kachchh region are at highest risk as they can expect large accelerations corresponding to natural periods of such small structures. Such structures are relatively safe in mainland region. The buildings of 3–4 stories and tall structures that exist mostly in cities of Saurashtra and mainland can expect accelerations in excess of 100 cm/s2 during a large earthquake in Kachchh region. It has been found that a total of 0.11 million buildings in Rajkot taluka of Saurashtra are vulnerable to total damage. In Kachchh region, 0.37 million buildings are vulnerable. Most vulnerable talukas are Bhuj, Anjar, Rapar, Bhachau, and Mandvi in Kachchh district and Rajkot, Junagadh, Jamnagar, Surendernagar and Porbandar in Saurashtra. In mainland region, buildings in Bharuch taluka are more vulnerable due to proximity to active Narmada-Son geo-fracture. The scenario hazard maps presented in this study for moderate as well as large earthquakes in the region may be used to augment the information available in the probabilistic seismic hazard maps of the region.

CHAOTIC CHARACTERISTIC ANALYSIS OF STRONG EARTHQUAKE GROUND MOTIONS

This paper aims to analyze and understand the irregularity and complexity of earthquake ground motions from the perspective of nonlinear dynamics. Chaotic dynamics theory and chaotic time series analysis are suggested to examine the nonlinear dynamical characteristic of strong earthquake ground motions. Based on the power spectral analysis, principal component analysis and modified false nearest neighbors method, it is illustrated qualitatively that the acceleration time series of earthquake ground motions exhibit chaotic property. Next, the chaotic time series analysis is proposed to calculate quantitatively the nonlinear characteristic parameters of acceleration time histories of near-fault ground motions. Numerical results show that the correlation dimension of these ground motions is fractal dimension. Their Kolmogorov entropy is a limited positive value, and their maximal Lyapunov exponent is larger than 0. It is demonstrated that the strong earthquake ground motions present the chaotic property rather than the pure random signals, and the severe irregularity and complexity of ground motions are the reflection of high nonlinearity of earthquake physical process.

Duration of strong ground motion during Northridge, California, earthquake of January 17, 1994

Contours of spatial variations of the duration of strong earthquake ground motion during the 1994 Northridge, California earthquake are smooth over distances as large as tens of kilometers. Visual comparison of those contours with the depth of sediments and with vertical offsets of the basement rocks along the faults in the Los Angeles basin are in excellent qualitative agreement with the trends predicted by the previously published empirical scaling equations of strong-motion duration. It is argued that if the source-to-station distances were measured along the three-dimensional wave paths through the sedimentary wave-guides, rather than along straight lines as is common at present, the accuracy of empirical scaling equations could be improved significantly.

Attenuation characteristics of coda waves in Mainland Gujarat (India)

The attenuation characteristics based on coda waves of Mainland Gujarat (India) have been investigated in the present study. The broadband waveforms of 53 local earthquakes (Mw 1.1–3.3) having focal depths in the 6.0–33.6km range recorded at five stations of Mainland Gujarat region has been used for the analysis. The frequency-dependent relationships (Q=Q0fn) for coda-Q (Qc) and dependency of coda-Q on lapse time windows have been determined for the said region. The average lapse time dependent coda-Q relations estimated for the region are: Qc=(87±13)f(1.01±0.06) (lapse time: 30s), Qc=(112±20)f(0.94±0.08) (lapse time: 40s) and Qc=(120±22)f(0.76±0.07) (lapse time: 50s). The increase in Qc values with lapse time shows the depth dependence of Qc as longer lapse time windows will sample larger area. The observed quality factor is strongly dependent on frequency and lapse time, which indicates that the upper lithosphere, is more heterogeneous and seismotectonically active, while the lower lithosphere is homogeneous and relatively less active. A comparison of the coda-Q estimated for Mainland Gujarat region with those of nearby Kachchh and Saurashtra regions shows that Mainland Gujarat region is more heterogeneous. The rate of decay of attenuation (Q−1) with frequency for the relations obtained here is found to be comparable with those of other regions of the world though the absolute values differ. The obtained relations are expected to be useful for the estimation of source parameters of the earthquakes in the Mainland Gujarat region where no such relations were available earlier. These relations are also important for the simulation of earthquake strong ground motions in the region.

APPLICATION OF RHEOLOGY MODELING TO NATURAL RUBBER AND LEAD RUBBER BEARINGS: A SIMPLIFIED MODEL AND LOW TEMPERATURE BEHAVIOR

A rheology originally proposed for high damping rubber bearing (HDRB) is applied to natural rubber bearing (RB) and lead rubber bearing (LRB) along with its simplified form. Comparing HDRB, the elasticplastic equilibrium responses were found to be more dominant than the rate-dependent response due to viscosity for RB and LRB. Moreover, the overstress in loading/unloading was found to be analogous. The dependency of nonlinear viscosity on current strain was found to be weak in contrast to the existence of considerable nonlinearity in elastic response. The original rheology model considers the nonlinear elastoplastic and viscosity induced rate-dependent behavior into account, while the viscosity effect is eliminated in the simplified version. The models are implemented in a finite element code. The modeling effects of bearings on the seismic responses of a multi-span continuous highway bridge are investigated via nonlinear dynamic analyses for two strong earthquake ground motions. Three analytical models of isolation bearings are considered for comparison: the conventional design models and the proposed two models. Model parameters for the bearings were determined for two temperature conditions: the room temperature (+23 ◦ C) and the low temperature ( 20 ◦ C) based on experimental data. The implication of the rheology models for response prediction of a prototype bridge is studied by comparing the rotation of a plastic hinge in pier and shear strain at the top of the bearing. The comparison suggests that the modeling of RB and LRB considering rheology properties is important for rational prediction of the seismic response of highway bridges, particularly at low temperature condition.

APPLICATION OF RHEOLOGY MODELING TO NATURAL RUBBER AND LEAD RUBBER BEARINGS: A SIMPLIFIED MODEL AND LOW TEMPERATURE BEHAVIOR

A rheology originally proposed for high damping rubber bearing (HDRB) is applied to natural rubber bearing (RB) and lead rubber bearing (LRB) along with its simplified form. Comparing HDRB, the elasticplastic equilibrium responses were found to be more dominant than the rate-dependent response due to viscosity for RB and LRB. Moreover, the overstress in loading/unloading was found to be analogous. The dependency of nonlinear viscosity on current strain was found to be weak in contrast to the existence of considerable nonlinearity in elastic response. The original rheology model considers the nonlinear elastoplastic and viscosity induced rate-dependent behavior into account, while the viscosity effect is eliminated in the simplified version. The models are implemented in a finite element code. The modeling effects of bearings on the seismic responses of a multi-span continuous highway bridge are investigated via nonlinear dynamic analyses for two strong earthquake ground motions. Three analytical models of isolation bearings are considered for comparison: the conventional design models and the proposed two models. Model parameters for the bearings were determined for two temperature conditions: the room temperature (+23 ◦ C) and the low temperature ( 20 ◦ C) based on experimental data. The implication of the rheology models for response prediction of a prototype bridge is studied by comparing the rotation of a plastic hinge in pier and shear strain at the top of the bearing. The comparison suggests that the modeling of RB and LRB considering rheology properties is important for rational prediction of the seismic response of highway bridges, particularly at low temperature condition.

Analysis and Simulation of Strong Earthquake Ground Motions Using ARMA Models

The acceleration record of an earthquake ground motion is a nonstationary process with both amplitude and frequency content varying in time. The paper presents a general procedure for the analysis and simulation of strong earthquake ground motions based on parametric ARMA models. Structural design spectra are based on smoothed linear response spectra obtained from different events scaled by their peak values. Such an approach does not incorporate other characteristics of the excitation represented by measured data. This study investigate the use of non-stationary models which can be considered characteristic and representative of specific historical earthquakes. An earthquake record is regarded as a sample realization from a population of such samples, which could have been generated by the stochastic process characterized by an Autoregressive Moving Average (ARMA) model. This model is capable of reproducing the nonstationary amplitude as well as the frequency content of the earthquake ground accelerations. The moving time-window technique is applied to synthesize the near field earthquakes, Boumerdes-1, Boumerdes -2, and Boumerdes -3 2003 recorded on dense soils in Algeria. This model, is based on a low-order, time-invariant ARMA process excited by Gaussian white noise and amplitude modulated using a simple envelope function to account for the non-stationary characteristics. This simple model gives a reasonable fit to the observed ground motion. It is shown that the selected ARMA (2,1) model and the algorithm used for generating the accelerograms are able to preserve the features of the real earthquake records with different frequency content. In this evaluation, the linear and non linear responses of a given soil layer have been adopted. This study suggests the ability to characterize the earthquake by a minimum number of parameters.

Seismic stability of embankment on soft soil deposit

Well-compacted embankments resting on non-liquefiable foundation soils with a level ground surface are usually considered stable even during strong earthquake ground motions. Some case histories, however, suggest that such embankments may be damaged if the foundation soil is highly compressible, such as thick soft clay and peat deposits. An increase in the thickness of the saturated zone in the embankment and reduction of stresses of embankment soil in the saturated zone, both owing to subsidence of the embankment, are surmised as underlying mechanisms. In this study, centrifuge tests were conducted to verify this hypothesis. Two types of models – embankments on a stiff foundation soil layer and embankments on a soft clay deposit – were prepared, and horizontal base shakings were imparted. Crest settlement and deformation of the embankment during shaking were larger for the embankment on the clay.

Workshop Report: Applications of Precarious Rocks and Related Fragile Geological Features to U.S. National Hazard Maps

The Workshop on the Applications of Precarious Rocks and Related Fragile Geological Features to U.S. National Hazard Maps met on the University of Nevada campus in Reno (UNR), Nevada, on 4–5 October 2010. The goal of this workshop was to develop recommendations to the U.S. Geological Survey (USGS) on the use of precariously balanced rocks and related fragile geological features to improve the national seismic hazard maps (NSHM). The context of the workshop is the growing realization that it is essential to regard hazard maps as the calculated output of hazard models that should be tested, and that fragile geological features provide the only data to validate the predictions of these models at low probabilities. A fragile geological feature (FGF) was defined as a feature that might be easily destroyed by strong earthquake ground motions and is mechanically simple enough to allow for analysis of the ground motions that might cause it to be destroyed. For testing the prediction of a seismic hazard model, an FGF must also have been in essentially the present geometry for enough time to constrain past ground motions. A precariously balanced rock (PBR) is the type example of an FGF. A PBR is a rock that is balanced on, but not mechanically attached to, its pedestal, and it has a high ratio of height to width of the contact with the pedestal, so that it is easily toppled. Brune and Whitney (1992) and Brune (1996) suggested that PBRs might serve as low-resolution seismoscopes to put upper bounds on ground motions over the lifetime of the rock. FGFs were recognized by Hanks et al. (2006) for their critical contribution to evaluation of extreme ground motions at Yucca Mountain. Because PBRs have been studied more than other FGFs, most attention at the workshop focused on their distribution …

Attenuation of Coda Waves in the Saurashtra Region, Gujarat (India)

The attenuation characteristics based on coda waves of two areas—Jamnagar and Junagarh of Saurashtra, Gujarat (India)—have been investigated in the present study. The frequency dependent relationships have been developed for both the areas using single back scattering model. The broadband waveforms of the vertical components of 33 earthquakes (Mw 1.5–3.5) recorded at six stations of the Jamnagar area, and broadband waveforms of 68 earthquakes (Mw 1.6–5) recorded at five stations of the Junagarh area have been used for the analysis. The estimated relations for the Junagarh area are: Qc = (158 ± 5)f(0.99±0.04) (lapse time : 20 s), Qc = (170 ± 4.4)f(0.97±0.02) (lapse time : 30 s) and Qc = (229 ± 6.6)f(0.94±0.03) (lapse time : 40 s) and for the Jamnagar area are: Qc = (178 ± 3)f(0.95±0.05) (lapse time : 20 s), Qc = (224 ± 6)f(0.98±0.06) (lapse time : 30 s) and Qc = (282 ± 7)f(0.91±0.03) (lapse time : 40 s). These are the first estimates for the areas under consideration. The Junagarh area appears to be more attenuative as compared to the Jamnagar area. The increase in Qc values with lapse time found here for both the areas show the depth dependence of Qc as longer lapse time windows will sample larger area. The rate of decay of attenuation (Q−1) with frequency for the relations obtained here is found to be comparable with those of other regions of the world though the absolute values differ. A comparison of the coda-Q estimated for the Saurashtra region with those of the nearby Kachchh region shows that the Saurashtra region is less heterogeneous. The obtained relations are expected to be useful for the estimation of source parameters of the earthquakes in the Saurashtra region of Gujarat where no such relations were available earlier. These relations are also important for the simulation of earthquake strong ground motions in the region.

Modelling of Strong Ground Motions from 1991 Uttarkashi, India, Earthquake Using a Hybrid Technique

We present a simple and efficient hybrid technique for simulating earthquake strong ground motion. This procedure is the combination of the techniques of envelope function (Midorikawaet al. Tectonophysics 218:287–295, 1993) and composite source model (Zenget al. Geophys Res Lett 21:725–728, 1994). The first step of the technique is based on the construction of the envelope function of the large earthquake by superposition of envelope functions for smaller earthquakes. The smaller earthquakes (sub-events) of varying sizes are distributed randomly, instead of uniform distribution of same size sub-events, on the fault plane. The accelerogram of large event is then obtained by combining the envelope function with a band-limited white noise. The low-cut frequency of the band-limited white noise is chosen to correspond to the corner frequency for the target earthquake magnitude and the high-cut to the Boore’s fmax or a desired frequency for the simulation. Below the low-cut frequency, the fall-off slope is 2 in accordance with the ω2 earthquake source model. The technique requires the parameters such as fault area, orientation of the fault, hypocenter, size of the sub-events, stress drop, rupture velocity, duration, source–site distance and attenuation parameter. The fidelity of the technique has been demonstrated by successful modeling of the 1991 Uttarkashi, Himalaya earthquake (Ms 7). The acceptable locations of the sub-events on the fault plane have been determined using a genetic algorithm. The main characteristics of the simulated accelerograms, comprised of the duration of strong ground shaking, peak ground acceleration and Fourier and response spectra, are, in general, in good agreement with those observed at most of the sites. At some of the sites the simulated accelerograms differ from observed ones by a factor of 2–3. The local site geology and topography may cause such a difference, as these effects have not been considered in the present technique. The advantage of the technique lies in the fact that detailed parameters such as velocity-Q structures and empirical Green’s functions are not required or the records of the actual time history from the past earthquakes are not available. This method may find its application in preparing a wide range of scenarios based on simulation. This provides information that is complementary to the information available in probabilistic hazard maps.

Investigation of the Parameters of Hertz Impact Model for the Pounding Analysis of Highway Bridge

Under the strong earthquake ground motions, the adjacent buildings with small distance and the highway bridges with expansion joints are sensitive to the pounding damage. Contact element approach was usually used to analyze the structure responses with pounding effect. The impact stiffness is the key parameter of the several existing contact models, such as the linear viscoelastic impact model and the nonlinear viscoelastic impact model. However, the linear spring model cannot account for the energy loss during impact, and the Kelvin model is untenable as it results in tensile forces acting just before separation. Alternatively, a non-linear spring based on the Hertz contact law can be used to model impact, but the impact stiffness in Hertz impact model is not easy to determined, when the impact surfaces between two segments are plain. In this study, the model of the Hertz-damper impact model is investigated. Firstly, the stiffness of the impact model is analyzed considering the surface roughness based on Hertz theory. Then, the structural responses of a highway bridge with pounding are analyzed using the proposed method for the Hertz impact model to validate the accuracy of the theory. Finally, the effect of the various pounding models on the structural response of the colliding structures is compared.

Sectional forces for seismic design of R/C frames by linear time history analysis and application to 3D single-story buildings

The aim of the present paper is to present a rational procedure for the appropriate selection of the sectional forces needed for the calculation of the longitudinal reinforcement to R/C elements within the context of linear time history analysis. The proposed procedure is based on the maximum normal stresses, which occurs in each relevant cross section, and takes into consideration the critical angle of the seismic excitation, i.e., the angle that yields the maximum value of each response quantity of interest. Moreover, in an attempt to realistically interpret pertinent code provisions, three other code compatible methods of selecting the cross sectional forces are presented and compared to the here proposed method. For this purpose, three single-story buildings subjected to 47 bi-directional strong earthquake ground motions are analyzed. For each ground motion, the longitudinal reinforcement at all critical cross sections is calculated using the above four methods. Furthermore, the necessary reinforcement due to 3 and 7 representative earthquake records, required by the seismic code provisions, is determined. Comparison of results clearly shows that methods compatible with current seismic code provisions can significantly underestimate the necessary reinforcement with regards to the proposed method.

Broadband Kinematic Stochastic Simulation of an Earthquake Source: a Refined Procedure for Application in Seismic Hazard Studies

To carry out a realistic simulation of earthquake strong ground motion for applied studies, one needs an earthquake fault/source simulator that can integrate most relevant features of observed earthquake ruptures. A procedure of this kind is proposed that creates a broadband kinematic source model. At lower frequencies, the source is described as propagating slip pulse with locally variable velocity. The final slip is assumed to be a two-dimensional (2D) random function. At higher frequencies, radiation from the same running strip is assumed to be random and incoherent in space. The model is discretized in space as a grid of point subsources with certain time histories. At lower frequencies, a realistic shape of source spectrum is generated implicitly by simulated kinematics of slip pulse propagation. At higher frequencies, the original approach is used to generate signals with spectra that plausibly approximate the prescribed smooth far-field source spectrum. This spectrum is set on the basis of the assumedly known regional empirical spectral scaling law, and subsource moment rate time histories are conditioned so as to fit this expected spectrum. For the random function that describes final slip over the fault area, lognormal probability distribution of amplitudes is assumed, on the basis of exploratory analysis of inverted slip distributions. Similarly, random functions that describe local slip rate time histories are assumed to have lognormal distribution of envelope amplitudes. In this way one can effectively emulate expressed “asperities” of final slip and occasional occurrence of large spikes on near-source accelerograms. A special procedure is proposed to simulate the spatial coherence of high-frequency fault motion. This approach permits the simulation of fault motion plausibly at high spatial resolution, fulfilling the prerequisite for simulation of strong motion in the vicinity of a fault. A particular realization (sample) of a source created in a simulation run depends on several random seeds, and also on a considerable number of parameters. Their values can be selected so as to take into account expected source features; they can also be perturbed to examine the source-related component of uncertainty of strong motion. The proposed approach to earthquake source specification is well adapted to the study of deterministic seismic hazard: it may be used for simulation of individual scenario events, or suites of such events, as well as for analysis of uncertainty for expected ground motion parameters from a particular class of events. Examples are given of application of the proposed approach to strong motion simulations and related uncertainty estimation.

Should average shear-wave velocity in the top 30 m of soil be used to describe seismic amplification?

The average velocity of shear waves in the top 30 m of soil, ν L , has become the parameter used by many engineering design codes and most recently by published empirical-scaling equations to estimate the amplitudes of strong ground motion. Yet there are few studies to determine whether this is a meaningful parameter to use—and whether estimates that do use it are reliable. In 1995, the authors studied this problem and concluded that ν L should not be used. We reported then that an older site characterization in terms of the soil site parameter proposed by Seed et al. [1], s L , worked better because it included a measure of the thickness of the soil layers to considerably greater depths. Our report, however, made no difference; numerous papers continued to be published based only on scaling in terms of ν L , and worse, they also ignored the geological site conditions. The purpose of this paper is to emphasize that the average shear-wave velocity in the top 30 m of soil should not be the only site parameter used to scale strong-motion amplitudes. While the search continues for the more meaningful site parameters to use in empirical scaling of strong earthquake ground motion, it is better to use s L to describe the amplification of seismic waves by soil deposits near the surface.

Attenuation of High Frequency P and S Waves in the Gujarat Region, India

The local earthquake waveforms recorded on broadband seismograph network of Institute of Seismological Research in Gujarat, India have been analyzed to understand the attenuation of high frequency (2–25 Hz) P and S waves in the region. The frequency dependent relationships for quality factors for P (QP) and S (QS) waves have been obtained using the spectral ratio method for three regions namely, Kachchh, Saurashtra and Mainland Gujarat. The earthquakes recorded at nine stations of Kachchh, five stations of Saurashtra and one station in mainland Gujarat have been used for this analysis. The estimated relations for average QP and QS are: QP = (105 ± 2) f0.82 ± 0.01, QS = (74 ± 2) f1.06 ± 0.01 for Kachchh region; QP = (148 ± 2) f0.92 ± 0.01, QS = (149 ± 14) f1.43 ± 0.05 for Saurashtra region and QP = (163 ± 7) f0.77 ± 0.03, QS = (118 ± 34) f0.65 ± 0.14 for mainland Gujarat region. The low Q ( 0.5) as obtained from present analysis indicate the predominant seismic activities in the region. The lowest Q values obtained for the Kachchh region implies that the area is relatively more attenuative and heterogeneous than other two regions. A comparison between QS estimated in this study and coda Q (Qc) previously reported by others for Kachchh region shows that QC > QS for the frequency range of interest showing the enrichment of coda waves and the importance of scattering attenuation to the attenuation of S waves in the Kachchh region infested with faults and fractures. The QS/QP ratio is found to be less than 1 for Kachchh and Mainland Gujarat regions and close to unity for Saurashtra region. This reflects the difference in the geological composition of rocks in the regions. The frequency dependent relations developed in this study could be used for the estimation of earthquake source parameters as well as for simulating the strong earthquake ground motions in the region.

Research progress of the NSFC Major Research Plan “dynamic disaster evolution of major engineering structures”

The NSFC Major Research Plan aims to conduct researches at the international research frontiers on modeling of strong earthquake ground motions and strong wind or typhoon fields, and investigating the damage and failure evolution process of the major engineering structures under dynamic actions, focusing on the following two key scientific problems: (1) characteristics and laws of strong earthquake ground motions and strong wind or typhoon fields, and (2) process and mechanism of dynamic disaster evolution of the major engineering structures. For these goals, the research work is targeted at (1) modeling and predicting of strong earthquake ground motion and strong wind or typhoon fields, (2) identifying critical parameters influencing the dynamic disaster evolution of the major engineering structures, (3) analyzing the whole dynamic disaster evolution process of the major engineering structures, and (4) integration and verification of simulation systems for dynamic disaster evolution of the major engineering structures.

Equivalent linear substructure approximation of soil–foundation–structure interaction: model presentation and validation

An equivalent linear substructure approximation of the soil–foundation–structure interaction is proposed in this paper. Based on the inherent linearity of the approach, the solution of the structural and the soil domain is obtained simultaneously, incorporating the effects of the primary and secondary soil nonlinearities. The proposed approximation is established theoretically and then validated against centrifuge benchmark soil–foundation–structure interaction tests. The equivalent linear substructure approximation is proved to simulate efficiently the effects of the nonlinear soil behavior on the soil–foundation–structure system under a strong earthquake ground motion.

Empirical Scaling of Rotational Spectra of Strong Earthquake Ground Motion

Abstract Many empirical scaling equations have been developed for scaling Fourier spectrum amplitudes of strong earthquake accelerations and for generation of artificial strong-motion accelerograms for the translational, torsional, and rocking components of strong motion. It has also been shown that rotational components of strong motion significantly contribute to the overall response of structures; however, little progress has been made in the development and deployment of strong-motion instruments to measure rotations. This article presents a simple approximate algorithm for generating torsional and rocking Fourier spectral amplitudes from the corresponding translational motions. The method can be used to generate torsion and rocking spectra from the translational Fourier spectra of actual records. Inverse Fourier transform can be used to generate torsional and rocking time histories.