Pulses in ground motions identified through surface partial matching and their impact on seismic rocking consequence

In seismology and earthquake engineering,it is fundamental to identify and characterize the pulse-like features in pulse-type ground motions.To capture the pulses that dominate structural responses,this study establishes congruence and shift relationships between response spectrum surfaces.A similarity search between spectrum surfaces,supplemented with a similarity search in time series,has been applied to characterize the pulse-like features in pulse-type ground motions.The identified pulses are tested in predicting the rocking consequences of slender rectangular blocks under the original ground motions.Generally,the prediction is promising for the majority of the ground motions where the dominant pulse is correctly identified.

Seismic response and correlation analysis of a pile-supported wharf to near-fault pulse-like ground motions

Earthquake investigations have shown that near-fault pulse-like(NF-P)ground motions have unique characteristics compared to near-fault non-pulse-like(NF-NP)and far-field(FF)ground motions.It is necessary to study the seismic response of pile-supported wharf(PSW)structures under NF-P ground motions.In this study,a three-dimensional finite element numerical model is created to simulate a PSW.By imparting three types of ground motion,the engineering demand parameters(EDPs)of PSW under NF-P ground motions were analyzed and compared,in which EDPs are the maximum displacement and bending moment of the piles.Twenty intensity measures(IMs)were selected to characterize the properties of ground motions.The correlation between IMs and EDPs was explored.The results show that the piles present larger displacement and bending moment under NF-P ground motions compared to NF-NP and FF ground motions.None of the IMs have a high correlation with EDPs under NF-P ground motions,and these IMs are more applicable to FF ground motions.The correlation coefficients between EDPs and IMs under three types of ground motion were obtained,which will provide a valuable reference for the seismic design of PSWs.

Structural failure analysis with CMS-based ground motion selection using innovative cost function and weight factors

The selection and scaling of ground motion records is considered a primary and essential task in performing structural analysis and design.Conventional methods involve using ground motion models and a conditional spectrum to select ground motion records based on the target spectrum.This research demonstrates the influence of adopting different weighted factors for various period ranges during matching selected ground motions with the target hazard spectrum.The event data from the Next Generation Attenuation West 2(NGA-West 2)database is used as the basis for ground motion selection,and hazard de-aggregation is conducted to estimate the event parameters of interest,which are then used to construct the target intensity measure(IM).The target IMs are then used to select ground motion records with different weighted vector-valued objective functions.The weights are altered to account for the relative importance of IM in accordance with the structural analysis application of steel moment resisting frame(SMRF)buildings.Instead of an ordinary objective function for the matching spectrum,a novel model is introduced and compared with the conventional cost function.The results indicate that when applying the new cost function for ground motion selection,it places higher demands on structures compared to the conventional cost function.Moreover,submitting more weights to the first-mode period of structures increases engineering demand parameters.Findings demonstrate that weight factors allocated to different period ranges can successfully account for period elongation and higher mode effects.

Simulation of non-stationary ground motion processes(I)

This paper proposes a method for simulation of non-stationary ground motion processes having the identical statistical feature, time-dependent power spectrum, with a given ground motion record, on the basis of review of simulation of non-stationary ground motion processes. The method has the following advantages: the sample processes are non-stationary both in amplitude and frequency, and both the amplitude and frequency non-stationarity depend on the target power spectrum; the power spectrum of any sample process does not necessarily accord with the target power spectrum, but statistically, it strictly accords with the target power spectrum. Finally, the method is verified by simulation of one acceleration record in Landers earthquake.

A modified method for simulating non-stationary multi-point earthquake ground motion

A spectral-representation-based algorithm is proposed to simulate non-stationary and stochastic processes with evolutionary power,according to a prescribed non-stationary cross-spectral density matrix. Non-stationary multi-point seismic ground motions at different locations on the ground surface are generated for use in engineering applications. First,a modified iterative procedure is used to generate uniformly modulated non-stationary ground motion time histories which are compatible with the prescribed power spectrum. Then,ground motion time histories are modeled as a non-stationary stochastic process with amplitude and frequency modulation. The characteristic frequency and damping ratio of the Clough-Penzien acceleration spectrum are considered as a function of time in order to study the frequency time variation. Finally,two numerical examples are presented to validate the efficiency of the proposed method,and the results show that this method can be effectively applied to the dynamic seismic analysis of long and large scale structures.

Simulation of non-stationary ground motion processes (II)

This paper proposes a method for simulation of non-stationary ground motion processes having the identical statis-tical feature, time-dependent power spectrum, with a given ground motion record, on the basis of review of simu-lation of non-stationary ground motion processes. The method has the following advantages: the sample processes are non-stationary both in amplitude and frequency, and both the amplitude and frequency non-stationarity depend on the target power spectrum; the power spectrum of any sample process does not necessarily accord with the tar-get power spectrum, but statistically, it strictly accords with the target power spectrum. Finally, the method is veri-fied by simulation of one acceleration record in Landers earthquake.

Spatial distribution of near-fault ground motion

Near-fault strong ground motion of strike-slip and dip-slip of vertical and inclined rectangular fault in half-space and layered half-space is analyzed by dislocation source model. The Fourier spectra ratio of ground motion is adopted to study the characteristics of near-fault ground motion. For both slip models, near-fault strong ground motion with high amplitude is located in a narrow belt area along the projection of the fault on the ground and mainly controlled by the sub-faults nearby. Directivity of strike-slip fault is more dominant in long period for components perpendicular to the fault, and more dominant in long period for components parallel to the fault for dip-slip fault. The deeper the location of the source is, the more slowly the amplitude of ground motion attenuates. There is obvious hanging wall effect in ground motion of inclined fault, and the spatial distribution of ground motion is asymmetric which coincides with observational data. Finally, a fitting function of spatial distribution for near-fault ground motion is proposed and compared with near source factors of the 1997 Uniform Building Code of USA.

Effect of seawater on incident plane P and SV waves at ocean bottom and engineering characteristics of offshore ground motion records off the coast of southern California, USA

The effect of seawater on vertical ground motions is studied via a theoretical method and then actual offshore ground motion records are analyzed using a statistical method. A theoretical analysis of the effect of seawater on incident plane P and SV waves at ocean bottom indicate that on one hand, the affected frequency range of vertical ground motions is prominent due to P wave resonance in the water layer if the impedance ratio between the seawater and the underlying medium is large, but it is greatly suppressed if the impedance ratio is small; on the other hand, for the ocean bottom interface model selected herein, vertical ground motions consisting of mostly P waves are more easily affected by seawater than those dominated by SV waves. The statistical analysis of engineering parameters of offshore ground motion records indicate that:(1) Under the infl uence of softer surface soil at the seafl oor, both horizontal and vertical spectral accelerations of offshore motions are exaggerated at long period components, which leads to the peak spectral values moving to a longer period.(2) The spectral ratios(V/H) of offshore ground motions are much smaller than onshore ground motions near the P wave resonant frequencies in the water layer; and as the period becomes larger, the effect of seawater becomes smaller, which leads to a similar V/H at intermediate periods(near 2 s). These results are consistent with the conclusions of Boore and Smith(1999), but the V/H of offshore motion may be smaller than the onshore ground motions at longer periods(more than 5 s).

Dominant pulse simulation of near fault ground motions

In this study, a new mathematical model is developed composed of two parts, including harmonic and polynomial expressions for simulating the dominant velocity pulse of near fault ground motions. Based on a proposed velocity function, the corresponding expressions for the ground acceleration and displacement time histories are also derived. The proposed model is then fitted using some selected pulse-like near fault ground motions in the Next Generation Attenuation （NGA） project library. The new model is not only simple in form but also simulates the long-period portion of actual velocity near fault records with a high level of precision. It is shown that the proposed model-based elastic response spectra are compatible with the near fault records in the neighborhood of the prevailing frequency of the pulse. The results indicate that the proposed model adequately simulates the components of the time histories. Finally, the energy of the proposed pulse was compared with the energy of the actual record to confirm the compatibility.

Time-frequency response spectrum of rotational ground motion and its application

The rotational seismic motions are estimated from one station records of the 1999 Jiji （Chi-Chi）, Taiwan, earthquake based on the theory of elastic plane wave propagation. The time-frequency response spectrum （TFRS） of the rotational motions is calculated and its characteristics are analyzed, then the TFRS is applied to analyze the damage mechanism of one twelve-storey frame concrete structure. The results show that one of the ground motion components can not reflect the characteristics of the seismic motions completely; the characteristics of each component, especially rotational motions, need to be studied. The damage line of the structure and TFRS of ground motion are important for seismic design, only the TFRS of input seismic wave is suitable, the structure design is reliable.

Direct use of peak ground motion parameters for the estimation of inelastic displacement ratio of SDOF systems subjected to repeated far fault ground motions

This study is aimed at developing statistical equations to estimate the inelastic displacement ratio of singledegree-of-freedom systems subjected to far fault repeated earthquakes. In the study, peak ground motion parameters are used to define the scatter of the original data. The ratio of peak ground acceleration to peak ground velocity, and peak ground velocity of the ground motion records and structural parameters such as period of vibration and lateral strength ratio are used in the proposed equations. For the development of the equations, nonlinear time history analyses of single-degree-offreedom systems are conducted. Then, the results are used in a multivariate regression procedure. The equations are verified by comparing the estimated results with the calculated results. The average error and coefficient of variation of the proposed equations are presented. The analyses results revealed that the direct use of peak ground motion parameters for the estimation of inelastic displacement ratio significantly reduced the scatter in the original data and yielded accurate results. From the comparative results it is also observed that results obtained using equations specific to peak ground velocity or peak ground acceleration to peak ground velocity ratio are similar.

Influence of earthquake ground motion incoherency on multi-support structures

A linear response history analysis method is used to determine the influence of three factors:geometric incoherency,wave-passage,and local site characteristics on the response of lnulti-support structures subjected to differential ground motions.A one-span frame and a reduced model of a 24-span bridge,located in Las Vegas,Nevada are studied,in which the influence of each of the three factors and their combinations are analyzed.It is revealed that the incoherency of earthquake ground motion can have a dramatic influence on structural response by modifying the dynamics response to uniform excitation and inducing pseudo-static response,which does not exist in structures subjected to uniform excitation.The total response when all three sources of ground motion incoherency are included is generally larger than that of uniform excitation.

Traveling wave effect on the seismic response of a steel arch bridge subjected to near fault ground motions

In the 1990s, several major earthquakes occurred throughout the world, with a common observation that near fault ground motion （NFGM） characteristics had a distinct impact on causing damage to civil engineering structures that could not be predicted by using far field ground motions. Since then, seismic responses of structures under NFGMs have been extensively examined, with most of the studies focusing on structures with relatively short fundamental periods, where the traveling wave effect does not need to be considered. However, for long span bridges, especially arch bridges, the traveling wave （only time delay considered） effect may be very distinct and is therefore important. In this paper, the results from a case study on the seismic response of a steel arch bridge under selected NFGMs is presented by considering the traveling wave effect with variable apparent velocities. The effects of fling step and long period pulses of NFGMs on the seismic responses of the arch bridge are also discussed.

A note on near-field site amplification effects of ground motion from a radially inhomogeneous valley

To improve the understanding of the near-field soil and topographic amplification effects, an analytical solution by the authors for the scattering of plane SH waves by a radially inhomogeneous semi-cylindrical valley is extended to the case of a line source of cylindrical SH waves. Upon confirmation of its accuracy with past exact solutions for a homogeneous and an inhomogeneous semi-cylindrical valley under far-field plane SH waves, the extended solution is used to calculate the ground motion amplification factors for both the homogeneous and inhomogeneous valleys subjected to near-field waves. A comprehensive parametric study is conducted with respect to the location of the wave source, the dimensionless frequency of the incident waves, and the inhomogeneity degree of the covering soil layer. It is found that more amplifications and reductions of ground motions will occur within a certain range in and around the valley as the sources are located further. Consistent with the far-field case, it is confirmed that an increase of the degree of inhomogeneity of the covering soil layer generally amplifies the ground motions significantly.

Vertical coherency function model of spatial ground motion

Many studies have focused on horizontal ground motion, resulting in many coherency functions for horizontal ground motion while neglecting related problems arising from vertical ground motion. However, seismic events have demonstrated that the vertical components of ground motion sometimes govern the ultimate failure of structures. In this paper, a vertical coherency function model of spatial ground motion is proposed based on the Hao model and SMART 1 array records, and the validity of the model is demonstrated. The vertical coherency function model of spatial ground motion is also compared with the horizontal coherency function model, indicating that neither model exhibits isotropic characteristics. The value of the vertical coherency function has little correlation with that of the horizontal coherency function. However, the coherence of the vertical ground motion between a pair of stations decreases with their projection distance and the frequency of the ground motion. When the projection distance in the wave direction is greater than 800 meters, the coherency between the two points can be neglected.

Artificial ground motion compatible with specified ground shaking peaks and target response spectrum

This article describes a hybrid simulation method to generate artificial ground motion time histories that are compatible with specified peak seismic acceleration, velocity and displacement as well as the target response spectrum of absolute acceleration. First, based on traditional methods that match the target spectrum in the frequency domain, an initial acceleration time history was synthesized to satisfy the specified peak acceleration, target spectral acceleration and intensity envelope. Second, by using the inversion formula of the seismic input to a linear single-degree-of-freedom system and by superimposing a series of narrow-band time histories in the time domain, the initial time history is further modified to allow its peak velocity and displacement to approach the targets and improve its matching precision with the target spectrum. Numerical examples are provided to demonstrate that the proposed method achieves good agreement with the target values.

Dynamic shear modulus of undisturbed soil under different consolidation ratios and its effects on surface ground motion

The dynamic shear modulus for three types of undisturbed soil under different consolidation ratios is presented by using the resonant column test method. Its effects on surface ground motion is illustrated by calculation. The test results indicate that the power function is a suitable form for describing the relationship between the ratio of the maximum dynamic shear modulus due to anisotropic and isotropic consolidations and the increment of the consolidation ratio. When compared to sand, the increment of the maximum dynamic shear modulus for undisturbed soil due to anisotropic consolidation is much larger. Using a one-dimensional equivalent linearization method, the earthquake influence factor and the characteristic period of the surface acceleration are calculated for two soil layers subjected to several typical earthquake waves. The calculated results show that the difference in nonlinear properties due to different consolidation ratios is generally not very notable, but the degree of its influence on the surface acceleration spectrum is remarkable for the occurrence of strong earthquakes. When compared to isotropic consolidation, the consideration of actual anisotropic consolidation causes the characteristic period to decrease and the earthquake influence factor to increase.

Ground motion attenuation of M_s8.0 Wenchuan earthquake

The great Ms8.0 Wenchuan earthquake has been the most destructive earthquake since 1949 in China. The earthquake occurred no more than half a year after the establishment of the National Strong Motion Observation Network System （NSMONS） of China; what is more, the epicenter was located in the area with dense strong motion observation sta- tions so that a large number of strong motion records of the main shock were obtained. In this paper, 501 strong motion re- cords from 167 observation stations are utilized to establish the ground motion attenuation relations in three directions in the range of fault distance less than 600 km. The result shows the difference of seismic motion attenuation in two horizontal di- rections is insignificant. It is the first time that strong-motion records are used to establish the ground motion attenuation relations of the Ms8.0 earthquake in China.

Simulation of spatially correlated earthquake ground motions for engineering purposes

A new model to simulate spatially correlated earthquake ground motions is developed. In the model, the main factors that characterize three distinct effects of spatial variability, namely, the incoherency effect, the wave-passage effect and the site-response effect, are taken into account, and corresponding terms/parameters are incorporated into the well known model of uniform ground motions. Some of these terms/parameters can be determined by the root operation, and others can be calculated directly. The proposed model is first verified theoretically, and examples of ground motion simulations are provided as a further illustration. It is proven that the ensemble expected value and the ensemble auto-/cross-spectral density functions of the simulated ground motions are identical to the target spectral density functions. The proposed model can also be used to simulate other correlated stochastic processes, such as wave and wind loads.

Simulation of multi-support depth-varying earthquake ground motions within heterogeneous onshore and offshore sites

This paper presents a novel approach to model and simulate the multi-support depth-varying seismic motions（MDSMs） within heterogeneous offshore and onshore sites.Based on 1 D wave propagation theory,the three-dimensional ground motion transfer functions on the surface or within an offshore or onshore site are derived by considering the effects of seawater and porous soils on the propagation of seismic P waves.Moreover,the depth-varying and spatial variation properties of seismic ground motions are considered in the ground motion simulation.Using the obtained transfer functions at any locations within a site,the offshore or onshore depth-varying seismic motions are stochastically simulated based on the spectral representation method（SRM）.The traditional approaches for simulating spatially varying ground motions are improved and extended to generate MDSMs within multiple offshore and onshore sites.The simulation results show that the PSD functions and coherency losses of the generated MDSMs are compatible with respective target values,which fully validates the effectiveness of the proposed simulation method.The synthesized MDSMs can provide strong support for the precise seismic response prediction and performance-based design of both offshore and onshore large-span engineering structures.