Vertical Ground Motion Research Articles

Effects of Vertical Ground Motion on Pedestrian-Induced Vibrations of Footbridges: Numerical Analysis and Machine Learning-Based Prediction

Current codes and guidelines for the dynamic design of footbridges often only specify the pedestrian-induced excitations. However, earthquakes may occur during the passing stage of pedestrians in earthquake-prone regions. In addition, modern footbridges tend to be slender and are sensitive to vertical ground motions. Therefore, we investigate the effects of vertical ground motion on pedestrian-induced vibrations of footbridges. A total of 138 footbridges with different materials, dimensions, and structural types are considered as the target structures. The classical social force model combined with the pedestrian-induced load is used to simulate crowd loads for the scenarios with six typical pedestrian densities. Furthermore, 59 vertical ground motions with four seismic intensities are taken as the seismic inputs. An amplification factor is introduced to quantify the amplification effects of vertical ground motion on human-induced vibrations of footbridges. Four machine learning (ML) algorithms are used to predict the amplification factor. The feature importance indicates that the scaled peak ground acceleration, the pedestrian density, and the bridge span are the three most important parameters influencing the amplification factor. Finally, the vibration serviceability of the footbridge subjected to both crowd load and vertical ground motion is assessed.

The Intensity Measures Parameters of Horizontal and Vertical Ground Motions

The Intensity Measures Parameters of Horizontal and Vertical Ground Motions

Response of soil–pile–superstructure–quay wall system to lateral displacement under horizontal and vertical earthquake excitations

The excess pore water pressure generated under the combined vertical and horizontal earthquake excitations is generally greater than that under the unidirectional excitation, which may further affect the dynamic response of soil-pile-superstructure-quay wall (SPSQ) system. This study conducted a coupled effective-stress analysis for the response of SPSQ system to liquefaction-induced lateral displacement under horizontal and vertical earthquake excitations. To accurately describe the lateral displacement behind the quay wall, the liquefaction behavior of soils was described by a modified generalized plasticity model with parameters properly determined from laboratory tests. The numerical model of the SPSQ system was validated against the previously reported centrifuge model tests. The results show that the earthquake excitation with abundant low-frequency component causes greater residual lateral displacements of pile cap (ux,RC) and quay wall (ux,RQ) than that with abundant high-frequency component. The ux,RC and ux,RQ tend to increase as the peak vertical acceleration increases for both vertical and inclined piles. Increasing the fixity of the quay wall significantly reduces the influence of vertical ground motion on the ux,RC and ux,RQ. The polarity reversal of the vertical ground motion also has a significant effect on the ux,RC and ux,RQ and should be considered in the analyses. In addition, the lateral displacement of liquefied ground causes an amount of rotation of the cap of the inclined pile, probably leading to the potential shear failure at the head of piles. Special consideration should be given to the earthquake-induced shear force at deeper location because the shear force could be significantly greater than that at the head of both inclined and vertical piles in certain cases.

Seismic Assessment of Steel Frames Subjected to Multi-hazards

This paper investigates the effects induced by thunderstorm downbursts to steel building structures that have been previously damaged during strong directivity ground motion events. To achieve this objective, one four-story steel moment-resisting frame that was tested at the E-defense laboratory, Japan was analyzed in the nonlinear range using OpenSees. The seismic response was numerically simulated, obtaining a satisfactory agreement with the experimental evidence, revealing that the effects of such wind events and vertical ground motions were significant. These effects should be addressed during the design of low and medium buildings subjected to initial damage and subsequent thunderstorm downbursts and the ductility demands on structures subjected to multi-hazards can be quantified. The wind loads are applied as an externally applied dynamic load and the revised ductility demands are determined directly. The obtained results are compared to what is expected by experimental tests.

Ground-Motion Similarities in the Valley of Mexico from Subduction Earthquakes

ABSTRACT Since the eighties, several subduction earthquakes on the Mexican Pacific coast have been recorded at accelerometric networks in the Valley of Mexico (VM). Such are the cases of the 19 September 1985 M 8.1 Michoacán earthquake and the recent 7 September 2021 M 7.1 Guerrero earthquake. These events have caused from minor damages to widespread structural collapses in the VM. The vertical ground motion recorded at several sites in the VM clearly show recurrent Rayleigh wavetrains, which present similar characteristics in period, amplitude, and duration among stations. These characteristics are very stable in space and time. On the other hand, the corresponding horizontal ground motion are strongly affected by the surface geology of the valley because of the shear wave-energy trapped at the uppermost soft layers. In addition, the horizontal response at several soft-ground sites displays significant azimuthal effects. Based on these observations, we analyze thrust-faulting subduction earthquakes that occurred along the Mexican Pacific coast from Michoacán to Chiapas states, all recorded at the VM accelerometric networks. We identified similarities in the vertical and horizontal ground motion not only among stations but also between seismic events recorded at the same station. The local generation of surface waves is studied using a kinematic analysis in the frequency–wavenumber domain (f-k), and sundry techniques in frequency and time domains. As a preliminary explanation, our analysis suggests that azimuthal effects related to thrust faulting subduction earthquakes strongly influence the local generation of surface waves affecting the 3D response of the valley. Moreover, for all earthquakes in all stations, our results show that while the vertical ground motion is similar and its amplifications are small and governed by earthquake size, the two horizontal components reveal strong site effects.

Influence of vertical seismic component on the response of reinforced concrete regular planar frames

The objective of the present paper is to investigate the influence of the vertical seismic component on the response of reinforced concrete regular planar frames. For this purpose, 20 reinforced concrete single- and multi-storey frames with various span lengths are designed according to Eurocodes 2 and 8 and analyzed by means of inelastic dynamic analysis for 20 recorded near-fault ground motions. In particular, two series of time-history analyses are conducted: one taking into account the horizontal seismic component only and a second considering concurrent action of horizontal and vertical components. For each analysis, the values of representative response quantities (axial forces, displacements, plastic hinge rotations) are calculated. The differences of the response quantities resulting from the two series of analyses provide a measure of the vertical seismic component impact on the response of regular planar frames. The whole study demonstrates that the role of the vertical ground motion is quite underestimated by modern seismic codes.

Empirical Correlations Between Horizontal and Vertical Ground-Motion Intensity Measures

ABSTRACTThis study examined empirical correlations among several horizontal and vertical ground-motion intensity measures (IMs), including spectral acceleration (SA), peak ground acceleration (PGA), peak ground velocity, acceleration spectrum intensity, velocity spectrum intensity, displacement spectrum intensity, spectrum intensity, effective peak acceleration (EPA), effective peak velocity (EPV), and effective peak displacement (EPD). The theoretical basis for the prediction equations of EPA, EPV, and EPD were developed based on the ground-motion model (GMM) of SA(T). Horizontal and vertical Next Generation Attenuation (NGA)-West2 GMMs and associated ground motions from active shallow crustal earthquakes in the NGA-West2 database were used to calculate empirical correlations. Fisher ? transformation and nonparametric bootstrapping methods were able to accurately describe the uncertainty caused by the limited sample size. The multivariate normality of the total residuals of the horizontal and vertical ground-motion IMs was verified. The results have shown a moderate correlation between the same IMs of horizontal and vertical ground motions. The difference in correlations between the IMs for two different combination cases (IMi,H–IMj,V and IMj,H–IMi,V) was not significant. The trends of ρlnIMV,lnSAH and ρlnIMH,lnSAV were almost the same, except that ρlnIMV,lnSAH was greater than ρlnIMH,lnSAV in the 0–0.3 s period, except for ρlnPGAV,lnSAH. Moreover, the median correlation coefficients were parametrically fitted to establish a correlation coefficient prediction model. Finally, an example of constructing the conditional distribution using the correlation coefficient models for horizontal and vertical ground motions IMs was given. The correlation coefficient models by this study provide the theoretical basis for the selection of horizontal and vertical ground motions using generalized conditional intensity measure.

Effect of near-fault vertical ground motions on failure mode of long-span sea-crossing cable-stayed bridges

Existing investigations have proved that the near-fault vertical ground motion (VGM) would have a significant effect on the seismic performance of bridge structures. This study mainly investigates the combined effect of VGM and horizontal ground motion (HGM) on failure mode and component damage sequence of long-span sea-crossing cable-stayed bridges. For this purpose, a long-span sea-crossing cable-stayed bridge considering the pile-soil effect and hydrodynamic effects is selected in this paper. The seismic demand models and limit state models are developed under the combination of VGM and HGM to perform the component fragility analysis, which aims to evaluate the damage state and sequence of key components. The results indicate that VGM has little effect on the damage probability of the bearings, but an adverse effect on the damage probability of the pylons and piers. The vulnerable component would be changed from the bearing to the pier and pylon with strong VGM. Meanwhile, the three-dimensional fragility surface of each component based on the horizontal peak ground velocity (Vx) and the ratio of vertical to horizontal component (αV/H) is obtained by convolution. Thus, the effects of Vx and αV/H on the damage mechanism of the cable-stayed bridge in different damage states are quantified.

A probabilistic framework for the stability analysis of slopes considering the coupling influence of random ground motion and conditional random field

The uncertainty of the input parameters can have a significant influence on the evaluation of the slope stability. A simple probabilistic framework is presented in this paper to quantify the influence of the uncertainties of the stochastic ground motion coupled with the spatial variability of soil parameters. The robust quasi–Monte Carlo simulation in the proposed framework is employed to estimate the failure probability of slopes. The conditional random field (CRF) is manipulated to simulate the spatial variability of soil properties with the sample points where the soil parameters are determined, and the spectral representation of stochastic process is applied to generate the horizontal and vertical stochastic ground motions. In each run of the Quasi–Monte Carlo simulation, a modified Newmark method based on an infinite slope failure model is applied to determine the permanent displacement of slopes under horizontal and vertical ground motions. The originality and significance of this proposed probabilistic framework are validated by a real slope case. The results of the case show that the uncertainty affecting the stability of the slope can decrease when CRF is used in a random field simulation to incorporate the real values of soil parameters at sample points, and the failure probability of slopes can be underestimated without considering stochastic vertical ground motion. Moreover, the correlated distance and critical permanent displacement are significant in predicting the failure probability of slopes.

Near-source ground motion estimation for assessing the seismic hazard of critical facilities in central Italy

We apply the Probabilistic Seismic Hazard Analysis (PSHA) and compute Physics-Based Simulations (PBS) of ground motion for three dams in the Campotosto area (Central Italy). The dams, which confine an artificial water reservoir feeding hydroelectric power plants, are located in an active seismic zone between the areas that experienced the 2009 L’Aquila and 2016–2017 Central Italy seismic sequences. The probabilistic disaggregation estimated for a return period of 2475 years, corresponding to the collapse limit state for critical facilities, indicates that the most dangerous fault is associated with a maximum magnitude of 6.75 ± 0.25 within a distance of 10 km. This fault is used in PBS to emulate the Maximum Credible Earthquake scenario. To capture the ground motion variability, we input a pseudo-dynamic source model to encompass spatial and temporal variations in the slip, rise time and rupture propagation, heavily affecting the near-source ground motion. Indeed, the ground motion above the rupture volume is mainly influenced by the epistemic uncertainties of rupture nucleation and slip distribution. The computed broadband seismograms are consistent with the near-source shaking recorded during the 2016 MW 6.6 Norcia earthquake and constrain the upper bound of the simulated ground motion at specific sites. Our modelling reinforces the importance of considering vertical ground motion near the source in seismic design. It could reach shaking values comparable to or larger than those of the horizontal components. This approach can be applied in other areas with high seismic hazard to evaluate the seismic safety of existing critical facilities.

An improved 2DOF system for predicting the seismic performance of isolated steel moment frames

This paper proposes an improved two-degree-of-freedom (i2DOF) system with an incorporated effective base-level mass (EBLM) for evaluating the P-Delta and cyclic deterioration effects of nonlinear isolated superstructures. This study verifies the dynamic response and collapse accuracy of the i2DOF system for actual isolated buildings. The case study buildings are the National Institute of Standards and Technology’s (NIST) steel special moment-resisting frames (MRFs) of 4, 8, and 12-stories base-isolated by a friction pendulum bearing (FPB) system. Nonlinear time-history analyses of 22 coupled horizontal–vertical ground motions are performed to verify the i2DOF maximum response when subjected to uplift and pounding effects. The collapse fragility curves of the i2DOF system are compared to those of each corresponding isolated MRF using incremental dynamic analyses (IDA). The results indicate that MRF corner uplifts occur rapidly and do not significantly differ between the i2DOF system and maximum MRF results. The i2DOF system obtains median collapse intensities slightlyhigher than isolated MRFs, indicating that the i2DOF system somewhat overestimates the accurate collapse results. All types of symmetrical and regular low-to-medium-rise isolated steel MRFs with FPBs are designed using a simplified design procedure based on the proposed i2DOF system with a reasonable seismic response precision.

Self-Centering Prestressed Concrete Pier Considering the Effect of Vertical Earthquake Motions with External Aluminum Dissipators

A prototype self-centering prestressedconcrete (SCPC) bridge pier andconventional reinforced concrete (RC) pier with similar backbone curves are designed and modeled. The objective of this study is to investigate the seismic performance of the SCPC bridge pier considering the effect of vertical earthquake ground motions. Under a severe vertical earthquake motion, the RC pier damage is much greater than the SCPC pier. The SCPC bridge pier shows a great capability in reducing residual drift at the top of the structure, therefore, the probability of bridge survival is increased. In this study, the external aluminum bars were used to reduce the seismic energy impacts on the bridge pier structure. In addition, the averages of the maximum and residual drifts of bridge piers under a set of 20 earthquake ground motion records impact with different vertical-to-horizontal peak acceleration ratios on the bridge seismic response are presented. The results are compared with the case of horizontal-only excitations, to clarify the effect of the vertical earthquake on the SCPC and RC bridge pier. Hence, the designers can find good solutions for structures in earthquakes resistance.

Earthquake-induced persistent and instantaneous groundwater variations caused by volumetric strain of soil in Taiwan from 1999 to 2020

Estimating the magnitude of earthquake-induced groundwater level (GWL) based on poroelastic theory is a challenge for researchers. To address this challenge, the present study explores this topic in the context of volumetric strain induced by ground shaking. Specifically, GWL records on the Chi-Chi earthquake in Taiwan, along with other selected events from 2004 to 2020, are analyzed to identify the persistent and instantaneous changes of GWL under distinct geological conditions. The magnitude of the persistent GWL change is highly correlated with peak ground acceleration, and thickness and density of sandy layers. This finding is explained by the magnitude of volumetric strains caused by soil particle rearrangement associated with ground motion intensities and site-specific conditions. Meanwhile, the instantaneous GWL change caused by seismic wave propagation exhibits a highly negative correlation with the vertical ground motion velocity time history because the compression wave induces instantaneous contraction or dilation of the soil. Moreover, the peak instantaneous GWL change correlates well with the peak ground velocity (PGV) in the vertical direction because the compressional (volumetric) strain is theoretically proportional to the PGV of vertical motion.

Seismic response prediction of RC bridge piers through stacked long short-term memory network

This paper aims at addressing the prediction of the displacement time histories and subsequently hysteresis curves of reinforced concrete bridge piers using a real-time hybrid simulation. A deep recursive long short-term memory (LSTM) network combined with a bidirectional LSTM, as a powerful deep learning algorithm, is utilized to achieve this goal. The designed stacked LSTM network includes multiple uncertain input variables, horizontal and vertical ground motions, horizontal and vertical actuator loads, the effective height of the bridge pier, the moment of inertia, and the mass assumed for hybrid simulation. The functional application programming interface in the Keras Python library is utilized to develop a complex model with these multiple inputs. Considering all these variables helps to predict the hysteresis curves of reinforced concrete bridge piers more accurately. The database for the training, validation, and unseen dataset of the proposed LSTM network during the prediction process comprises 12 experimental hybrid simulation tests on the bridge piers considering various aforementioned characteristics. The results reveal that the mean square error, as a loss function, is monotonically decreased to zero for both the training and validation datasets after 5000 epochs, and a high level of correlation is observed between the predicted and the reference values of the displacement time series for all the datasets. The Box-Whisker plot and Gaussian distribution of normalized error are also investigated for all the predictions to have more confidence in the estimations. It can be concluded that the maximum mean of the normalized error is about 0.05 for unseen data. Finally, it brings to an end that the LSTM method implemented in this study can successfully reduce the time and experimental costs to conduct new experimental hybrid simulation tests in the future.

Empirical H/V spectral ratios at the InSight landing site and implications for the martian subsurface structure

SUMMARY The horizontal-to-vertical (H/V) spectral ratio inversion is a traditional technique for deriving the local subsurface structure on Earth. We calculated the H/V from the ambient vibrations at different wind levels at the InSight landing site, on Mars, and also computed the H/V from the S-wave coda of the martian seismic events (marsquakes). Different H/V curves were obtained for different wind periods and from the marsquakes. From the ambient vibrations, the recordings during low-wind periods are close to the instrument self-noise level. During high-wind periods, the seismic recordings are highly contaminated by the interaction of the lander with the wind and the martian ground. Therefore, these recordings are less favourable for traditional H/V analysis. Instead, the recordings of the S-wave coda of marsquakes were preferred to derive the characteristic H/V curve of this site between 0.4 and 10 Hz. The final H/V curve presents a characteristic trough at 2.4 Hz and a strong peak at 8 Hz. Using a full diffuse wavefield approach as the forward computation and the Neighbourhood Algorithm as the sampling technique, we invert for the 1-D shear wave velocity structure at the InSight landing site. Based on our inversion results, we propose a strong site effect at the InSight site to be due to the presence of a shallow high-velocity layer (SHVL) over low-velocity units. The SHVL is likely placed below a layer of coarse blocky ejecta and can be associated with Early Amazonian basaltic lava flows. The units below the SHVL have lower velocities, possibly related to a Late Hesperian or Early Amazonian epoch with a different magmatic regime and/or a greater impact rate and more extensive weathering. An extremely weak buried low velocity layer (bLVL) between these lava flows explains the data around the 2.4 Hz trough, whereas a more competent bLVL would not generate this latter feature. These subsurface models are in good agreement with results from hammering experiment and compliance measurements at the InSight landing site. Finally, this site effect is revealed only by seismic events data and explains the larger horizontal than vertical ground motion recorded for certain type of marsquakes.

Myths and Realities of the Salt Lake Temple Foundation

Myths and Realities of the Salt Lake Temple Foundation

Effect of submarine permafrost degradation on the vertical ground motions and vertical response spectrum of a single-degree-of-freedom system in polar ocean

Owing to global warming, the rise in sea temperature is causing degradation of submarine permafrost, which has an impact on the seismic responses of submarine strata. Based on the revised dynamics of nearly saturated frozen porous media, a simplified model of the vertical seismic responses of submarine permafrost is established considering the degradation of its upper layer, and an analytical solution is obtained using the Laplace transform method. The governing equation of a single-degree-of-freedom system on the seafloor is further proposed, and the vertical response spectrum is obtained using the numerical inverse transformation method. The numerical results show that the vertical ground motions of the seafloor agree well with those of saturated and nearly saturated soil layers with a free surface on land and under deep-water conditions. Parametric studies show that saturation strongly affects the vertical ground motions of the seafloor, and this effect is closely related to the water depth ratio. In addition, the structural stratum parameters, including the active layer thickness ratio, permafrost thickness, and temperature, have significant effects on the vertical ground motions of the seafloor and the vertical response spectrum of the submarine lumped parameter system. Therefore, attention should be paid to the impact of submarine permafrost degradation on the vertical seismic responses of oil and gas exploitation systems in polar oceans.

Static pushover test of spring-underground structure system for seismic performance analysis of underground structure

The static test is appropriate for studying the seismic performance of underground structures due to the large size of the model structure and the controllable stress level. By setting elastic elements around the model structure, the static pushover test of the spring-underground structure system could simulate the initial stress state of the underground structure and soil-structure interactions during the pushover process. Taking the Daikai subway station damaged in the 1995 Hanshin earthquake in Japan as the model structure, a series of static pushover tests of underground structures with a geometric scale of 1/5 were performed. The impact of vertical ground motion on the seismic performance of underground structures was studied by conducting two static pushover tests of spring-underground structure system under different vertical loads; the impact of surrounding soil on the seismic performance and failure process of underground structures was studied by conducting static pushover tests with and without springs under the same vertical load. The relationship between the horizontal pushover force and the structural interstory drift, the concrete strain change process of structural weak vertical member, the structural failure phenomenon, and the seismic performance of the test object can be obtained from the tests, which can provide valuable information for experimental research on the seismic performance of underground structures. The test results demonstrate that the vertical ground motion decreases the ductility of underground structure, and the surrounding soil improves the lateral collapse resistance of underground structure.

Seismic Responses of a Tunnel-Soil-Surface Structure System under Multidimensional Near-Field and Far-Field Seismic Waves through a Shaking Table Test

In this paper, a tunnel-soil-surface structure system is taken as the research object, and shaking table tests of multidimensional near-field and far-field seismic waves are carried out to study the dynamic response law of the tunnel, the soil and the surface structure. The test results show that the response of the soil under the far-field seismic wave is relatively stronger, but due to the high-energy velocity pulse of the near-field seismic wave, the difference in acceleration response of the soil under near-field and far-field seismic waves gradually decreases as the input ground motion intensity increases. The existence of the tunnel causes the seismic response of the soil near the tunnel to be obviously different from that of the soil far away from the tunnel. After considering the vertical earthquake action, the acceleration response of the soil slightly increases. The surface structure-pile foundation has a certain influence on the seismic response of the middle section of the shallow tunnel. In addition, the input of vertical ground motion causes greater tensile strain in the tunnel. For the deformation of the surface structure, the period of acceleration response spectra of vertical ground motion close to the fundamental period of the structure in the vertical direction leads to a significant change in the vertical response, which is also the reason for the increase of the lateral deformation. The vertical seismic component has a significant influence on the dynamic response of the tunnel-soil-surface structure system, and the influence of vertical ground motion should be fully considered in seismic design.

The study of ground motion amplification based on an SMASS array site

There is a consensus in earthquake engineering that different soil structures have significant effects on ground motion. Three main methods can be used to study this issue: theoretical analysis, numerical simulation, and earthquake records analysis. Notably, the combined analysis of strong-motion records and station site information appears to be the most effective and reliable approach. In this study, we used site information from the Seismic Monitoring Array of Site and Structure (SMASS) of the Institute of Disaster Prevention and a record of the earthquake that occurred in Guye, China: a point on the bedrock was considered as reference for studying the amplification effect of the soil structure on ground motion through traditional spectral ratio analysis. Our main conclusions are the following. (1) The SMASS array data indicated that the shallow soil had an amplifying effect on ground motion: the frequency bands amplifying the horizontal ground motion were mainly those between 3.4 and 6.8, 11.3–13, and 15–20.8 Hz, while the frequency bands amplifying the vertical ground vibration were mainly those between 5 and 9.9, 13.5–15.9, and 18.5–21.9 Hz (2) The SMASS array data indicated that the influence of the deep soil on the horizontal ground motion frequency component was more significant than that of vertical ground motion. (3) Overall, the SMASS array site amplified the effects of both the high (3.4–20.8 Hz) and low (0.4–2.2 Hz) frequency components of ground motion with the depth decreases of buried depth; notably, the amplification effect of the high-frequency components grew much faster than that of the low-frequency components. (4) The groundwater table had an amplification effect on the vertical ground motion; therefore, its influence is also important to consider.