Varying Earthquake Ground Motions Research Articles

Nonstationary elastoplastic response analysis of curved beam bridges under spatial variability of earthquake ground motion using absolute displacement method

Current studies indicate that curved beam bridges are more sensitive to the spatial variability of earthquake ground motion (SVEGM) than straight bridges. However, research methods used currently typically disregard the nonlinear characteristics of bridges or use only deterministic excitations for analysis. Furthermore, the sensitivity of curved beam bridges with different curvature radii to the SVEGM has not been investigated comprehensively. Hence, in this study, a nonlinear finite element model of curved beam bridges is established using the ANSYS platform and the MATLAB is then employed to reduce and decouple the non-stationary seismic evolutionary power spectral density (EPSD) matrix. The absolute displacement method is employed for the multidimensional and multipoint nonlinear time-history analysis of the bridges. Considering different wave velocities, site conditions, and coherence types, this study comprehensively analyses the random response and frequency domain characteristics of curved continuous beam bridges under different SVEGMs. The analysis includes a verification of curved beam bridges with different curvature radii based on 48 cases (six SVEGMs with eight curvature radii). The results indicate that the presence of curvature renders curved beam bridges more sensitive to the SVEGM. The SVEGM significantly affects the random response and response frequency domain distribution of curved beam bridges, with smaller curvature radii contributing more significantly to the response. Therefore, the SVEGM must be considered in the seismic analysis of curved beam bridges, particularly those with smaller radii, to avoid an inaccurate estimation of the seismic performance of the bridges. The findings of this study can improve the seismic design and evaluation of curved beam bridges as well as enhance their seismic performance and reliability.

Ground-Motion Variability from Kinematic Rupture Models and the Implications for Nonergodic Probabilistic Seismic Hazard Analysis

Abstract The variability of earthquake ground motions has a strong control on probabilistic seismic hazard analysis (PSHA), particularly for the low frequencies of exceedance used for critical facilities. We use a crossed mixed-effects model to partition the variance components from simulated ground motions of Mw 7 earthquakes on the Salt Lake City segment of the Wasatch fault zone. Total variability of simulated ground motions is approximately equivalent to empirical models. The high contribution from rupture speed suggests an avenue to reducing variability through research on the causes and predictions of rupture speed on specific faults. Simulations show a strong spatial heterogeneity in the variability that manifests from directivity effects. We illustrate the impact of this spatial heterogeneity on hazard using a partially nonergodic PSHA framework. The results highlight the benefit of accounting for directivity effects in nonergodic PSHA, in which models that account for additional processes controlling ground motions are paired with reductions in the modeled ground-motion variability.

Effects of site response on ground motion directionality based on KiK-net records and numerical analysis

The orientation variability of earthquake ground motions (i.e., GM directionality) is an important engineering characteristic in the seismic design of structures. The GM directionality is believed to be mainly related to source and site contributions. This paper investigated the effect of site response on the change of GM directionality from the borehole depth to the ground surface. Distribution of the range for orientation variability level at both borehole and surface was presented for different intensity measures of 3006 records from downhole arrays in the KiK-net database. It was observed that both the maximum direction orientation of intensity measures and the ratio at various orientations may change significantly from depth to surface, and it is dependent on the specific intensity measures and site class. The numerical analysis of soil column considering bi-directional shaking was demonstrated to have a good ability to capture the influence of site response on the GM directionality. Thereafter, some preliminary insights into the linear and nonlinear site response effects on the GM directionality were provided. The azimuthal variation associated with the predominant period of the input borehole motion is an important factor that results in the change of GM directionality at the surface.

Saturation Effect on the Coherency Loss of Spatially Varying Vertical Ground Motions

The effect of the influence regularity of site saturation and water level on the coherency loss between spatially varying earthquake ground motions (SVEGMs) in a vertical direction is not yet clear. Therefore, taking an onshore-offshore site as an example, the influence regularity of site saturation and water level on the coherency loss of SVEGMs in a vertical direction was studied, in which the saturation degree of the whole site (SD), the groundwater level (GWL), and the thickness of the surface water layer (WLT) were considered. Under each case mentioned above, a large number of vertical in-plane SVEGMs were synthesized and then correspondingly, the mean lagged coherency loss and phase angle of coherence function were obtained, and a series of comparisons were carried out to shed light on the varying trend of the value of lagged coherency loss and phase angle, with predefined parameters. The results showed that SD, GWL, and WLT possess significant effects on the varying trend of the coherence function of vertical SVEGMs.

Spatially varying earthquake ground motion: artificial generation and effects on earth-fill dam behavior

ABSTRACT The observed amplitude and phase differences of seismic ground motions recorded at different locations over extended areas are termed as spatially varying earthquake ground motion (SVEGM). Earthquake-resistant design and seismic risk assessment of extended structures require three-dimensional dynamic analyses for which the excitation is needed in the form of three-directional SVEGM components, where each component needs to be consistent with the coherency model. In this paper, the principal features of the performed analyses are as follows: (1) discretisation of the spatial domain at the foundation base, (2) the selection of coherency model and (3) propagation angle of the seismic waves. In the first part of the paper, three cases for the generation of three-directional SVEGM are presented. First, the two-dimensional spatial domain, representing the foundation base of the extended structure, is discretised. Second, for case 1, the three-directional SVEGM is generated using the Liu and Hong coherency model at the cells of the grid. In this case, the loss of coherency is considered independent of the direction of the wave propagation (case general). Then, for the case 2, the two different propagation angles of 30 and 60 degrees of seismic waves and the Liu and Hong coherency model are considered. Finally, using the anisotropic coherency model of Hao et al. and the propagation angle 45 degree, the three-directional SVEGM is generated, in case 3. Results show that each component of the generated SVEGM records is affected by propagation angle and directional dependency of the coherency model. The second part of the paper is devoted to two-dimensional analyses of Marun earthfill dam and three-dimensional analyses of earthfill dams with different length-to-height ratios subjected to uniform input motion and artificially generated SVEGM.

Loss estimation of curved bridges considering the incidence angle and spatial variability of earthquake ground motion

The consideration for the angle of seismic incidence (ASI) is critical for the seismic design of curved bridges. Previous studies indicate that the effect of ASI weakens as the damage develops throughout the structure. Since curved bridges often extend over long distances and cross varied geological conditions, the spatial variability of earthquake ground motions (SVEGMs) may significantly affect their responses. However, the concurrent effects of ASI and SVEGM on the system performance of curved bridges have yet to be explored, and there are currently few reliable methodologies for conducting relevant research. To this end, this study takes the monetary repair costs as the metric for representing the entire performance of the bridge, and the impact of ASI on the total loss of long multi-span curved bridges considering the spatially variable nature of earthquake ground motions is investigated in a probabilistic manner. A multi-directional loss assessment approach is derived based on the extension of an existing loss methodology, and an already constructed, 638-m-long, twelve-span prestressed concrete curved bridge is selected as the test-bed. Twenty non-stationary and spectrum-compatible spatially variable earthquake ground motion (SVEGM) pairs are generated based on the Eurocode 8 (EC8) design spectrum and soil conditions of the bridge site for each ASI. Three seismic input motion scenarios are assumed according to the characteristics of SVEGMs, and variabilities of bridge loss with respect to the ASI under the scenario earthquakes are investigated for each excitation case. On these bases, the original ground motion records are amplified by 2 and 4 times, respectively, and 4320 (3 earthquake intensity levels × 3 excitation scenarios × 24 ASIs × 20 ground motion pairs) nonlinear response-history analyses (NRHAs) are implemented to identify the influence induced by the ground motion intensity on the loss variability. Results indicate that the impacts of ASI and SVEGMs weaken as the ground shaking intensity increases and the damage accumulates in the structure.

Response of Aswan cable-stayed bridge to spatial non-synchronous seismic excitations

Cable-stayed bridges are important infrastructure facilities serving the world today. Therefore, their safety against earthquake ground motions is crucial. However, due to their long spans, the affecting seismic excitations might be spatially non-synchronous. This paper presents a study of the effect of non-synchronous seismic excitations on Aswan cable-stayed bridge located at southern Egypt. Nonlinear time history analysis was conducted on a three-dimensional finite element model of the bridge. The spatial variability was represented in terms of the wave passage effect which was simulated via different delay times between the arrivals of the ground motion to bridge supports. Results indicated that spatial variability of earthquake ground motion has, in general, a favorable effect on most bridge response parameters. This is attributed to the flexibility of the overall bridge provided by the flexibility of the bridge structural system and/or by existence of seismic isolation.

Effect of Spatial Variation of Earthquake Ground Motions on Seismic Vulnerability of Urban Road Network Considering Building Environment

Evaluating the seismic damage of urban road infrastructure systems is of vital importance in reducing the earthquake hazard risk of cities. Urban road infrastructure systems are commonly represented as a spatial network that covers the whole city, and in its seismic damage analysis the spatial variation of earthquake ground motions cannot be ignored. However, the effect of the spatial variation of ground motions on the seismic vulnerability of urban road networks is unknown. In this article, based on the case study on Datong, China, it is shown that the spatially variation of ground motions may increase the damage risk of urban road networks and should be considered in the seismic vulnerability analysis. This was achieved by developing a method to evaluate the performance of a post-earthquake road network considering the structural damage of road components and the building environment. This work is anticipated to be a starting point for more sophisticated studies on the earthquake risk analysis of spatially extended urban lifeline systems.

Study on the Influence of a Soft Soil Interlayer on Spatially Varying Ground Motions

The existence of local soft interlayer can significantly amplify or attenuate the ground motion and thus might influence the lagged spatial coherency between spatially varying earthquake ground motions. A target site with a local soft interlayer was assumed first, and then two numerical examples were set. In example 1, linear soil behavior was considered and a large amount of quasi-stationary spatially varying earthquake ground motions were generated by combining the one-dimensional wave propagation theory and the classical spectral representation method. The influence regularity of varying shear wave velocity, buried depth, and thickness of the soft interlayer on the characteristics of lagged spatial coherency was investigated. In example 2, non-linear soil behavior was taken into account and fully non-stationary spatially varying earthquake ground motions were thus generated by using time-varying transfer function and spectral representation method. An overall evaluation was carried out to shed light on the differences of characteristics of spatial coherency between non-linear soil and linear soil cases. It showed that: (i) As the shear wave velocity of interlayer declines and as the buried depth and thickness increase, remarkable reduction of spatial coherency showed up; (ii) the reduction of lagged spatial coherency caused by varying buried depth may be more inclined to concentrate in the lower frequency range; (iii) the non-linear soil behavior can cause greater further reduction of lagged spatial coherency in comparison with linear soil behavior, especially in the higher frequency range; (iv) the troughs of lagged spatial coherency curve tend to be located in the variation range of vibration frequency of time-varying spectral ratio.

Investigating the Effect of Pseudo-Static Components on Bridge Structures under Multiple Support Excitations Using Conditional Simulated Records

Long-span bridges, as vital structures, play an important role in economic development. Previous studies revealed that the seismic responses of such structures, under non-uniform excitations, are different from the same result due to uniform excitations. Furthermore, the results of several earthquake-damaged bridges showed that their seismic behavior was different from that predicted under uniform excitation and, in some cases; the responses were more than predicted results. Therefore, the damaged bridges under non-uniform excitations were re-analyzed and the obtained results were in good agreement with the recorded outcomes. Considering current bridge designing codes it is clear that almost all of them ignored it and just the Euro Code 2008 prepared some recommendations. It is found that the main reason for the differences in results from the uniform and non-uniform excitations is the spatial variation of earthquake ground motions. Based on the papers three phenomena were introduced for spatial variability of ground motion: the wave-passage, the incoherence, and also the site-response effects. The responses of structures under non-uniform excitations obtained from the superposition of dynamic and pseudo-static components. This paper investigated the seismic behavior of a long-span structure under non-uniform movements to evaluate the most undesirable conditions. So, different soils and load combinations considered and soil-structure effects included. The effect of wave-passage, incoherence, and site-response on the structure was measured and the results were compared with the uniform excitation. The results indicate that the variation in soil condition significantly affects the seismic responses under non-uniform excitations. Also, it is found that the results from uniform excitations with considering soil-structure interactions are remarkably increased. Moreover, the outcomes of analysis under-considered load cases and soil conditions showed that ignoring the spatially varying ground motions may lead to a non-conservative design.

Influence of the Site-Specific Component of Kappa on the Magnitude-Dependency of Within-Event Aleatory Variabilities in Ground-Motion Models

AbstractThe aleatory-variability component (standard deviation) of a ground motion has a large influence on results of a probabilistic seismic hazard assessment. kappa, a measure of high-frequency attenuation, has site- and record-specific effects that have been suggested as reasons for observing heteroscedastic aleatory variability within earthquake ground motions. Specifically, kappa has been proposed as a reason why ground motions from small earthquakes are more variable than those from large earthquakes, which is modeled by magnitude-dependent within-event standard deviations in ground-motion prediction equations (GMPEs). In this study, we use ground motions simulated using the stochastic method to examine the influence of the site-specific component of kappa on aleatory variability of earthquake ground motions and examine the hypothesis that this could be a cause of the observed heteroscedasticity in this variability. We consider simulations with both fixed and continuous stress drop distributions and the site-specific component of kappa to demonstrate that variation in the stress drop parameter contributes minimally to magnitude-dependency, unlike the site-specific component of kappa, which causes significant magnitude-dependency. Variation in the site-specific component of kappa is, therefore, proposed to be at least partially responsible for the magnitude-dependency captured in the aleatory-variability components of some recent GMPEs. It is found, however, that the expected impact of the site-specific component of kappa on aleatory variability is much greater than modeled in these GMPEs, which suggests that there could be a mitigating effect that is not captured within the simulations (e.g., correlated inputs to the simulations).

Vs30 değerine bağlı koherans modeli

Strong ground motion caused by earthquakes at every point of extended structures would not be same. This difference in ground movement has an important effect on the design of these types of structures. Meanwhile, the seismic resistant design has been lead to investigate the variability of earthquake ground motion over last decades. This variability of strong ground motion can define in terms of frequency or time. In this study, frequency domained variability named coherency is considered. Several coherency models have been proposed without considering soil effect. In this context, spatial variation of seismic ground motion based on the average shear wave velocity over the upper 30 m of depth, Vs30 is analyzed. Initially, coherency values are calculated using data triggered during six earthquakes recorded by the Istanbul Earthquake Rapid Response System. Lagged coherency data is considered in the process to get the coherency model. Nonlinear regression analysis is used for the model to obtain a good-fit to observed data. A coefficient is defined based on Vs30 values of the station-pairs. The cohereny model based on this coefficient of Vs30 is derived for EW and NS components. It is expected that coherency function decreases with the increase of frequency and separation distance. The decrease in the coefficient of Vs30 causes decrease in coherency. The variance in the coherency model between EW and NS components is small. This coherency model is used to simulate spatial variable ground motion for the accurate seismic design of elongated structures for the future studies.

Effect of spatial variability of earthquake ground motions on the reliability of road system

This paper presents an approach for assessing the failure probability of a road system due to its interaction with landslides induced by the earthquake. The landslide occurrence and failure probability of the road system is estimated by considering the spatial variation of earthquake ground motion. Since significant incoherence in earthquake ground motions is usually observed within the spatial dimensions of large horizontally expanded structures like roads, bridges and dams, it is important to consider the uncertainty due to spatially varying ground motion. The stochastic nature of seismic loading is incorporated in the study by generating a series of earthquake ground motions while the spatial variation of ground motion is accounted for by using cross power spectral density function. Two phase material point method (MPM) is used to simulate the dynamic behaviour of saturated slopes. MPM is able to capture the failure mechanism of slopes under seismic loading and evaluates the travel distance of sliding mass.

3D seismic responses of a long lined tunnel in layered poro-viscoelastic half-space by a hybrid FE-BE method

This paper aims to study the seismic responses of a long lined tunnel embedded in a water-saturated poro-viscoelastic half-space, with focus on wave passage effects. The poro-viscoelastic half-space is modeled by the Biot's theory and the soil nonlinearity is considered via an equivalent linear approach. The seismic responses of the tunnel structure are simulated by a 2.5D hybrid FE-BE method. A total of 72 cases of different incident angles for plane SV- and P1-waves are simulated, in order to conduct a systematic study on the tunnel seismic responses, in terms of longitudinal internal forces and strains, as well as seismic pore pressure and soil stresses. It is shown that the spatial variation of earthquake ground motion due to wave passage effects results in considerable longitudinal internal forces of the tunnel lining, which cannot be overlooked for seismic design. The responses of the tunnel depend on both the horizontal and vertical incident angles of the seismic waves. It is also shown that the 2D scenario with perpendicularly incident SV-waves, which is commonly considered in engineering practice, may lead to nonconservative seismic design, especially for tunnels in saturated soil.

Seismic Assessment of Footbridges under Spatial Variation of Earthquake Ground Motion (SVEGM): Experimental Testing and Finite Element Analyses.

In this paper, the seismic assessments of two footbridges, i.e., a single-span steel frame footbridge and a three-span cable-stayed structure, to the spatial variation of earthquake ground motion (SVEGM) are presented. A model of nonuniform kinematic excitation was used for the dynamic analyses of the footbridges. The influence of SVEGM on the dynamic performance of structures was assessed on both experimental and numerical ways. The comprehensive tests were planned and carried out on both structures. The investigation was divided into two parts: in situ experiment and numerical analyses. The first experimental part served for the validation of both the finite element (FE) modal models of structures and the theoretical model of nonuniform excitation as well as the appropriateness of the FE procedures used for dynamic analyses. First, the modal properties were validated. The differences between the numerical and the experimental natural frequencies, obtained using the operational modal analysis, were less than 10%. The comparison of the experimental and numerical mode shapes also proved a good agreement since the modal assurance criterion values were satisfactory for both structures. Secondly, nonuniform kinematic excitation was experimentally imposed using vibroseis tests. The apparent wave velocities, evaluated from the cross-correlation functions of the acceleration-time histories registered at two consecutive structures supports, equaled 203 and 214 m/s for both structures, respectively. Also, the coherence functions proved the similarity of the signals, especially for the frequency range 5 to 15 Hz. Then, artificial kinematic excitation was generated on the basis of the adopted model of nonuniform excitation. The obtained power spectral density functions of acceleration-time histories registered at all supports as well as the cross-spectral density functions between registered and artificial acceleration-time histories confirmed the strong similarity of the measured and artificial signals. Finally, the experimental and numerical assessments of the footbridges performance under the known dynamic excitation generated by the vibroseis were carried out. The FE models and procedures were positively validated by linking full-scale tests and numerical calculations. In the numerical part of the research, seismic analyses of the footbridges were conducted. The dynamic responses of structures to a representative seismic shock were calculated. Both the uniform and nonuniform models of excitation were applied to demonstrate and quantify the influence of SVEGM on the seismic assessment of footbridges. It occurred that SVEGM may generate non-conservative results in comparison with classic uniform seismic excitation. For the stiff steel frame footbridge the maximum dynamic response was obtained for the model of nonuniform excitation with the lowest wave velocity. Especially zones located closely to stiff frame nodes were significantly more disturbed. For the flexible cable-stayed footbridge, in case of nonuniform excitation, the dynamic response was enhanced only at the points located in the extreme spans and in the midspan closely to the pillars.

A numerical study on the transverse seismic response of lined circular tunnels under obliquely incident asynchronous P and SV waves

The numerical analysis of the transverse seismic response of tunnels is an important issue in the design and safety evaluation of tunnel structures, where the spatial variation of earthquake ground motion induced by wave passage effect has been recognized as an important influence factor that cannot be ignored. In this paper, a 2-D transient dynamic finite element modelling technique is applied to investigate the seismic response of two soil-structure interaction systems subjected to obliquely incident plane P and SV waves. Based on the theory of wave input, the incident earthquake motion is modeled as equivalent nodal forces applied on the truncated boundary, and the free field ground response is calculated from the 1-D time-domain finite element method by considering the wave passage effect. The numerical scheme is implemented into the commercial software ABAQUS, and its accuracy is verified by comparing with the analytical solutions of soil-structure interaction problems. Firstly, the verified method is applied to study the transverse seismic response of a circular tunnel embedded in a homogenous elastic half-space under obliquely incident P and SV waves, where the influence of the incident wave type, incident angle, burial depth and tunnel diameter is discussed. Secondly, the response of circular tunnels embedded in a multi-layered non-homogenous elastic foundation is studied, where the influence of tunnel position in the foundation, flexibility ratio between soil and tunnel and stiffness difference of adjacent soil layers in the foundation are extensively investigated. Moreover, comparison is drawn between the tunnel responses in the homogenous and non-homogenous foundation systems, and the importance of conducting asynchronous seismic response analysis of circular tunnels is highlighted.

Viaduct seismic response under spatial variable ground motion considering site conditions

The evaluation of the seismic hazard for a given site is to estimate the seismic ground motion at the surface. This is the result of the combination of the action of the seismic source, which generates seismic waves, the propagation of these waves between the source and the site, and site local conditions. The aim of this work is to evaluate the sensitivity of dynamic response of extended structures to spatial variable ground motions (SVGM). All factors of spatial variability of ground motion are considered, especially local site effect. In this paper, a method is presented to simulate spatially varying earthquake ground motions. The scheme for generating spatially varying ground motions is established for spatial locations on the ground surface with varying site conditions. In this proposed method, two steps are necessary. Firstly, the base rock motions are assumed to have the same intensity and are modelled with a filtered Tajimi-Kanai power spectral density function. An empirical coherency loss model is used to define spatial variable seismic ground motions at the base rock. In the second step, power spectral density function of ground motion on surface is derived by considering site amplification effect based on the one dimensional seismic wave propagation theory. Several dynamics analysis of a curved viaduct to various cases of spatially varying seismic ground motions are performed. For comparison, responses to uniform ground motion, to spatial ground motions without considering local site effect, to spatial ground motions with considering coherency loss, phase delay and local site effects are also calculated. The results showed that the generated seismic signals are strongly conditioned by the local site effect. In the same sense, the dynamic response of the viaduct is very sensitive of the variation of local geological conditions of the site. The effect of neglecting local site effect in dynamic analysis gives rise to a significant underestimation of the seismic demand of the structure.

Simulation of fully non-stationary spatially varying ground motions considering nonlinear soil behavior

Taking the nonlinear soil behavior into consideration, a novel method for simulating fully non-stationary spatially varying earthquake ground motions (SVEGMs) was proposed. Based on the one-dimensional (1D) wave propagation model, time-varying shear modulus and damping ratio were introduced into the classical transfer function model, where the evolution characteristics of soil properties (i.e., shear modulus and damping ratio) during earthquake were obtained by using a two-dimensional (2D) site response analysis. By using an example of application, the out-of-plane and in-plane fully non-stationary SVEGMs on ground surface were simulated. The acceleration and displacement time-histories were observed, and the auto power spectral density functions (PSDFs) and coherency loss functions of simulated motions were compared with corresponding targets, respectively. The normalized time-frequency spectra of simulated motions were presented to exhibit the spectral non-stationarity. It was shown that the evolution tendency of predominant frequency of simulated motions reflected similar characteristics with that of shear modulus of soil, which demonstrated the validness of the proposed method.

A simplified reliability estimation method for pile-supported wharf on the residual displacement by earthquake

Pile-supported wharves undergo lateral displacement as well as structural damage due to earthquakes. Therefore, residual displacement and structural safety assessment are necessary for earthquake-resistant design of pile-supported wharves. This study introduces a simplified reliability estimation method for pile-supported wharves, involving the residual displacement caused by earthquakes and the variation of earthquake ground motions. As the residual displacement of wharves is strongly affected by the deformation of subsoil caused by earthquakes, a soil-structure system finite element earthquake response analysis was performed. To reduce the computational load for the evaluation of a probability distribution of residual displacement, a first-order second-moment method estimating the probabilistic response of structures with a small number of trials was applied. Thefinite element analyses demonstrate that the summed squared Fourier amplitudes (SSFAs) of the input seismic motion for a cumulative probability frequency band better estimated the residual displacement. A simplified reliability estimation method utilizing three results of finite element analyses is proposed following the demonstration of its applicability.

Numerical study on site response considering ground motion spatial variation

Identical support excitation (ISE) of ground motion has been utilized to study the site response, whereas, to a large-scale site, multiple support excitation (MSE) considering the ground motion spatial variation may be more applicable. In this paper, the spatially varying earthquake ground motions (SVEGMs) were simulated first. Then, a large-scale four-layered free-field model was established using ABAQUS. Taking ISE and MSE into account, the significant durations of acceleration responses and shear wave velocities at many observation points were obtained. Comparing the results under MSE with those under ISE, it was shown that: i) the significant durations of acceleration responses under MSE were shorter than those under ISE; ii) even though the input peak ground acceleration (PGA) for MSE is lower, the shear wave velocity under MSE is not necessarily higher. Therefore, the spatial variation of ground motion may have important influence on the seismic response of large-scale site.