Vertical Ground Motion Research Articles

Probabilistic inelastic seismic demand spectra for large-span planar steel structures subjected to vertical ground motions

Severe vertical ground motions (VGMs) may lead to detrimental seismic damages of large-span planar steel structures (LSPSSs), thus the inelastic seismic demand of LSPSSs under VGMs needs to be quantified so as to ensure the structural seismic reliabilities. In view that the uncertainties of VGMs greatly influence the seismic responses of LSPSSs, the VGMs-induced seismic demands of LSPSSs are investigated in a probabilistic way in this paper. Based on 680 strong VGM records, the vertical ductility demands (μ) of 2,100 equivalent single-degree-of-freedom (ESDF) models representing a series of LSPSSs are computed. It is revealed that the influences of VGM properties, including peak ground acceleration, epicentral distance, hypocenter depth, moment magnitude and local site condition, are tiny and irregular on the values of μ. Accordingly, the probabilistic seismic demand model for LSPSSs under VGMs is established regardless of the VGM properties in this paper. From the 1,428,000 computed values of μ, the VGMs-induced seismic demand of LSPSSs follows a positively skewed probabilistic distribution, and the distribution could be well fitted by the lognormal distribution model. The parameters of the lognormal distribution model for μ are simulated by two elementary functions subsequently, in which the effects of vertical strength reduction factor R, post-yield stiffness ratio α and elastic vibrating period T are accounted for. Using the lognormal model and the proposed functions, a group of probabilistic inelastic seismic demand spectra for LSPSSs under VGMs are generated. The established probabilistic spectra could provide the statistic properties of both the peak and the residual seismic demand of LSPSSs in association with pre-set values of T, R and α. Combining the proposed model with certain seismic hazard models that define the probabilistic characteristics of VGMs, the seismic reliability of LSPSSs could be quantified, and a proper structural seismic performance could be guaranteed.

Analysis of influence factors of P-Δ effect considering vertical ground motion

With the development of structure optimization, building materials and construction technology, the study of the P-Δ effect is becoming more and more important in the pursuit of layers, flexibility and light quality. Based on the research status of P-Δ effect at home and abroad, this paper selects thenegative property fictitious member method to calculate the P-Δ effect of the multi-layer frame structure under the combined effect of horizontal and vertical ground motion. This paper discusses the influence of the stiffness-to-weight ratio, structural damping, and the vertical acceleration response of the structure. The results show that the damping and structural acceleration responses have a significant effect on the structural P-Δ effect. Under the premise of considering both, the stiffness-to-weight ratio of the structure, that is, the frequency of the structure, has a greater influence on the P-Δ effect of the structure under earthquakes. With the increase of the stiffness-to-weight ratio, the effect of P-Δ effect on structural response is increased and decreased.

Study on characteristic parameters of near-fault response spectrum

883 vertical earthquake records within the fault distance of 100 km were selected to study that whether the vertical design response spectrum characteristic parameter should be also used for the seismic design of engineering structure in near-fault region. Considering the influence of site conditions, fault distance and velocity pulse characteristics, the platform value, the first turning point period, the characteristic period, and the attenuation index of the dynamic amplification coefficient spectrum were studied respectively. This study concludes: the platform value, the first turning point period, the characteristic period, and the attenuation index are affected by site condition, fault distance, and velocity pulse characteristics. Chinese building seismic design code takes the platform value, the first turning point period, and the attenuation index as fixed values which may not be reasonable, and it should take into account the influence of site condition and fault distance. For the vertical ground motions in near-fault region, the platform values, the first turning point period, and the characteristic period of the dynamic amplification coefficient spectrum should be reasonably increased to improve the safety reserve of the engineering structures in near-fault region.

Effect of seismic wave velocity on the dynamic response of multi-story structures on elastic foundation

Traveling wave effects are generally considered with three main cases: (i) Wave passage effect that results with time delay in earthquake motion. (ii) incoherence effect which is defined as loss of coherency in the ground motion due to the reflection and refraction of waves, and (iii) local site effects. For multi-story structures whose supports are close to each other, the incoherence and local site effect may be omitted. In this case, traveling waves result only in a pure time delay in the earthquake motion (wave passage effect). Due to the wave passage effect of vertical and/or horizontal ground motion, the superstructure needs to be analyzed by multi-support excitation. Raft foundations cannot constrain vertical deformations and/or rotations, but they cause a diaphragm effect in the horizontal direction which results in uniform excitation. In this study, the effect of vertical earthquake motions onto multi-story buildings on elastic soil is investigated. Multi support excitation is considered by using displacement loading, which defines the equivalent seismic loads in terms of the ground displacement. According to the performed simulations of the selected structures, it is shown that structural height has a direct influence that results in member force magnifications with slow traveling wave effect. Among these, the ground floor column axial forces are most affected.

Centrifuge shaking table tests on 4 × 4 pile groups in liquefiable ground

A series of centrifuge shaking table model tests are conducted on 4 × 4 pile groups in liquefiable ground in this study, achieving horizontal–vertical bidirectional shaking in centrifuge tests on piles for the first time. The dynamic distribution of forces on piles within the pile groups is analysed, showing the internal piles to be subjected to greater bending moment compared with external piles, the mechanism of which is discussed. The roles of superstructure–pile inertial interaction and soil–pile kinematic interaction in the seismic response of the piles within the pile groups are investigated through cross-correlation analysis between pile bending moment, soil displacement, and structure acceleration time histories and by comparing the test results on pile groups with and without superstructures. Soil–pile kinematic interaction is shown to have a dominant effect on the seismic response of pile groups in liquefiable ground. Comparison of the pile response in two tests with and without vertical input ground motion shows that the vertical ground motion does not significantly influence the pile bending moment in liquefiable ground, as the dynamic vertical total stress increment is mainly carried by the excess pore water pressure. The influence of previous liquefaction history during a sequence of seismic events is also analysed, suggesting that liquefaction history could in certain cases lead to an increase in liquefaction susceptibility of sand and also an increase in dynamic forces on the piles.

SEISMIC RESPONSE OF REINFORCED CONCRETE FRAMES ON FLEXIBLE FOUNDATIONS SUBJECTED TO BOTH HORIZONTAL AND VERTICAL GROUND MOTIONS

This paper investigates the effect of combined horizontal and vertical accelerations on the seismic response of reinforced concrete resting on shallow foundations. Five and nine-storey buildings are considered to represent low- and medium- rise buildings. The building was assumed to be founded on shallow foundation with soil class corresponding to soft soil deposits, The soil of foundation was modeled by an equivalent massless spring coupled with a gap, located at the base of the structure, allowing for the inelastic bearing capacity of the soil and the loss of contact (uplift) of the base from the supporting soil. The accelergrams used in this investigation in the nonlinear range are the horizontal and vertical components of the New Hall earthquake. Although most building codes postulate that SSI generally decreases the force demand of buildings, and increases the deformation demand, it was found that the inclusion of the vertical ground motion with SSI, the horizontal displacement are decreased compared to the case with only the horizontal component.

Examination of the vertical earthquake ground motion component during the September 19, 2017 (Mw = 7.1) earthquake in Mexico City

This technical note aims at investigating the earthquake ground motion and spectral features of the vertical component motions recorded at soft soil sites in Mexico City during the strong September 19, 2017 Puebla-Morelos (Mw = 7.1) earthquake by means of examining ground motion (EQGM) features, vertical-to-horizontal (V/H) spectral ratios, and comparison with design spectra ordinates. EQGM features of vertical components recorded at 10 accelerographic stations revealed that they have shorter mean periods than their corresponding horizontal components, and long significant duration. In addition, V/H spectral ratios are larger than one in 6 stations for periods of vibrations between 0.22 s and 0.56s. Mean V/H ratios confirmed that the trend depends on the period of vibration and the vertical component could be more important for short-period structures than medium-to-long period structures. Since current Mexico City seismic regulations do not include recommendations to account for the vertical component, it is showed that the simple rule of reducing the horizontal acceleration design spectrum prescribed in the recently released 2017 Mexico City seismic regulations by 2/3 is enough to cover the mean + one-standard deviation vertical acceleration response spectrum.

Discussion on ‘‘Seismic displacement along a log-spiral failure surface with crack using rock Hoek–Brown failure criterion’’

This discussion is based on the paper by Zhao et al. [4] (hereafter identified as “the authors” or “the original paper”). In the original paper, the authors presented a numerical model to calculate the seismic displacement for rock slopes with cracks using the Hoek-Brown yield criterion. For the proposed numerical model, the upper bound limit analysis and rigid block displacement technique were employed in which the actual horizontal and vertical earthquake ground motion records were utilized in the analyses. This discussion addresses the theoretical issues of the computed permanent seismic displacements in conjunction with the upper bound limit analysis using the rigid block displacement technique. In addition, the discussion comments on some issues related to the assumption of using the factor of safety being less than 1 for a calculation of induced seismic displacement under an actual time history of horizontal and vertical accelerations, and the use of fixed crack depth ratios of 0.1 and 0.2 in the parametric studies of the original paper.

Vertical strong ground motion effects on seismic damage propagations of historical masonry rectangular minarets

Abstract Masonry towers and minarets are slender tall structures and highly vulnerable to strong ground motions due to their structural and material characteristics. The paper aims to investigate the effect of vertical ground motion on damage propagations of historical masonry slender tall rectangular stone minarets numerically. The Ulu Mosque minaret with height of 42.90 m constructed in 639 in Diyarbakir, Turkey, is selected as an application. Firstly, three dimensional solid and continuum finite element models of the minaret are obtained from the surveys. Since the foundation of the minaret is sitted on the hard soil, soil-structure interaction is not considered in the finite element model. The finite element model of the minaret is updated by modal analyses results and an empirical frequency formulation developed using the measurement results. Mechanical material properties of the masonry unit are determined using the properties of the stone and mortar used in the minaret. Concrete damaged plasticity (CDP) material model adjusted to masonry structures is considered in the nonlinear analyses. The acceleration records of horizontal (N-S) and vertical (V) components of May 1, 2003 Bingol earthquake (Mw = 6.4), which was recorded in hard soil and occurred in the near region of Diyarbakir city, are chosen as a strong ground motion. Then, linear time history and nonlinear step by step seismic analyses of the minaret are implemented for only horizontal, and combined horizontal and vertical components of the earthquake. The time histories of displacements, minimum and maximum principal strains and stresses, and damage propagations on the minaret are compared for only horizontal, and combined horizontal and vertical load cases including self-weight. It can be stated that consideration of vertical ground motion component in combination with horizontal component affects damage percentages and propagations on slender tall rectangular stone minarets.

Real‐time hybrid simulation for an RC bridge pier subjected to both horizontal and vertical ground motions

SummaryIt is well known that real‐time hybrid simulation (RTHS) is an effective and viable dynamic testing method. Numerous studies have been conducted for RTHS during the last 2 decades; however, the application of RTHS toward practical civil infrastructure is fairly limited. One of the major technical barriers preventing RTHS from being widely accepted in the testing community is the difficulty of accurate displacement control for axially stiff members. For such structures, a servo‐hydraulic actuator can generate a large force error due to the stiff oil column in the actuator even if there is a small axial displacement error. This difficulty significantly restricts the implementation of RTHS for structures such as columns, walls, bridge piers, and base isolators. Recently, a flexible loading frame system was developed, enabling a large‐capacity real‐time axial force application to axially stiff members. With the aid of the flexible loading frame system, this paper demonstrates an RTHS for a bridge structure with an experimental reinforced concrete pier, which is subjected to both horizontal and vertical ground motions. This type of RTHS has been a challenging task due to the lack of knowledge for satisfying the time‐varying axial force boundary condition, but the newly developed technology for real‐time force control and its incorporation into RTHS enabled a successful implementation of the RTHS for the reinforced concrete pier of this study.

How Can Vernacular Construction Techniques Sustain Earthquakes: The Case of the Bhatar Buildings

After the 2005 M7.6 Kashmir earthquake (Pakistan), field observations reported that several buildings manufactured with local traditional techniques resisted well to that strong seismic event. In this paper the attention is focused on a typical vernacular construction technique commonly named as “Bhatar”, still practiced in the Himalayan regions of India and Pakistan. It is grounded upon the lacing or reinforcement masonry concept, i.e. the combination of dry-stacked loose stones with timber beams to increase the wall confinement. Despite its good seismic performances, it has still not been deeply studied from a structural engineering point of view. This paper represents a first attempt to fill this gap. It presents a full analytical study on the structural behaviour of a simple one-storey building unit characterized by a 3.6 m x 3.6 m square plan covered by an heavy wooden roof with 20 cm thick earth coverage, in order to investigate its response under gravity and seismic inertial loadings. Materials properties, static analysis and seismic analysis are discussed. In detail, Shorea Robusta wood and limestone rocks are identified as the most used construction materials for the Bhatar buildings. The Barton's model is applied to characterise the shear strength of the rubble stone layers in the wall. Static analysis reveals that normal stresses at the ground level are around 92 kPa, which can be considered acceptable for common soils. With respect to earthquake, the Bhatar technique can absorb wall cracking and distortion mechanisms, and can dissipate energy through friction between stones. Under the assumption of no vertical ground motion, the acceleration which activates in-plane sliding mechanisms is found to be around 0.5 g, being dependent on the interface friction between adjacent layers. Some preliminary considerations about the out-of-plane seismic behaviour are also provided concerning overturning and bending failure mechanisms. The results are based on assumptions taken by several authors and have not been verified with experimental tests. Nevertheless, some practical suggestions can be derived to improve the seismic shear strength and to ensure friction also in the case of significant vertical component of earthquake ground motions.

Reef Carbonate Productivity During Quaternary Sea Level Oscillations

AbstractGlobal variations in reef productivity during the Quaternary depend on external parameters that may alter the global chemical balance in the oceans and atmosphere. We designed a numerical model that simulates reef growth, erosion, and sedimentation on coastlines undergoing sea level oscillations, and uplift or subsidence. We further develop a probabilistic evaluation that accounts for variable vertical ground motion, erosion, and foundation morphologies. Absolute sea level change appears primordial, as productivity must have increased by an order of magnitude since the onset of the glacial cycles, ∼2.6 Ma. But most important is relative sea level change, i.e., eustasy modulated by uplift or subsidence, that rejuvenates the accommodation space and exposes pristine domains of the shore to active reefs at each cycle. Integrated over the long‐term, vertical land motion sets the pace of reef growth: productivity in tectonically unstable domains is thus expected to be up to 10 times higher than in stable regions, if any. We quantify the global length of reef coasts and the probability density functions for slopes and uplift rates. Productivity waxes during transgressions to reach 2–8 and wanes during highstands, which may contribute to increase atmospheric pCO2 by several tens of ppm during deglaciations. Over the last 1.5 Ma, reefs precipitated ∼0.8 × 106 (∼500 × 103 km3), the equivalent of a 1 m‐thick layer spread over the entire surface of the Earth. This production modulates the calcium budget, for it represents some 30% of the modern Ca flux in the ocean.

Development of hazard- and amplification-consistent elastic design spectra

In the framework of the definition of a new building code for dams, the Swiss Federal Office for Energy (SFOE) has commissioned a study on the effect of site response variability on elastic design spectra for different soil conditions and seismic hazard scenarios. The goal of the study presented herein is the definition of a new set of site-dependent design spectra for horizontal and vertical ground-motion, whose design shape (scaled to peak ground acceleration) is to be compared with the present Swiss normative (SIA261, revision 2014) [43].To accomplish the task, we have created a large dataset of Fourier-domain seismic amplification functions by collecting empirical observations and site-specific ground motion models from both measured and stochastically generated velocity profiles. Fourier spectra were then converted to response spectral amplification using a combination of spectral modeling techniques and random vibration theory. Average amplification models are thus derived for different soil classes (SIA class A–E), according to the Swiss building code provisions, and for a set of magnitude-distance combinations chosen as representative of the Swiss hazard disaggregation scenario at the Sion site in Switzerland.Finally, the response spectral amplification functions from the database have been combined with the normalized uniform hazard spectra computed at Sion for return periods of 500, 1000, 5000 and 10,000 years. Based on those results, a new set of design spectral shapes is proposed for the different SIA soil classes, accounting for investigated scenario variability and including a reasoned level of conservatism dependent on the distribution of the site-specific amplification models.The proposed methodology targets the reduction in uncertainty associated with seismic design and, although originally focused and applied to the Swiss norm, it could be potentially applied to any national seismic code as a tool for developing, updating or benchmarking the current provisions in a holistic framework.

Frame‐type load bearing system for long‐span cantilevers

SummaryCantilevers experience high risks of vulnerability against progressive collapse and vertical ground motion effects. In addition, despite common engineering practice that regards cantilevers dominated by vertical loads, it is shown that while subjected to lateral forces, they might undergo large deflections due to the formation of plastic hinges in the supporting structural subassemblage; even if cantilevers satisfy deflection limits proposed by design codes. To overcome such vulnerabilities, successive cantilever beams can be coupled in the height of the structure using vertical elements to develop a framed cantilever system. Frame behavior in cantilevers is formulized using spring models and by employing optimization procedures, economic efficiency is compared to the conventional method. The optimization results for 6 2‐D steel moment frames showed that employing framed cantilever system has the potential to reduce required material weight up to 40%. Furthermore, nonlinear pushdown and incremental dynamic analyses were conducted to extract capacity and fragility curves. The results reveal the superior performance of framed cantilevers in both lateral and vertical loads while offering better resistance against the progressive collapse.

Combined horizontal–vertical seismic isolation system for high-voltage–power transformers: development, testing and validation

The electric power network is considered to be critical infrastructure. Electric utility companies and electric power administrators are increasingly interested in strengthening the security and resilience of their networks against earthquakes. Important components of these networks are high-voltage electrical transformers. Earlier studies in the use of seismic isolation systems for electrical transformers and other equipment produced results that clearly show the benefits of seismic isolation in the horizontal direction. However, vertical ground motions were transmitted through the isolation system unchanged or even magnified. In response to this problem, this paper presents the development and validation of a compact, effective, reliable and cost-effective combined horizontal–vertical seismic isolation system for use in electrical equipment.

Analytical Assessment of the Effect of Vertical Ground Motion on RC Frames Designed for Gravity Loads with Various Geometric Configurations

The paper presents an analytical investigation of the effect of vertical ground motion on the selected 13 reinforced concrete (RC) frames with different geometric configurations. For this purpose, earthquake ground motions with various vertical‐to‐horizontal peak acceleration ratios are selected to which a suitable scale factor is applied to match with seismic hazards of Korea. The methodology involves the evaluation of the structural responses of RC frames subjected to the selected records by means of nonlinear time history analyses. The results from the analysis are compared with results from studies of the case of horizontal‐only excitation. The effect of the vertical earthquake component on damage of RC frames is considered at both the global and the local levels. The effect of vertical ground motion on axial force, shear demand, and shear capacity of RC columns is investigated to assess failure on a local level. In particular, the shear capacity is evaluated by using both the conservative method of a design code and more realistic predictive approaches. The results of the extensive analyses indicate that vertical ground motion can significantly affect the response of RC members in terms of axial force variation and shear capacity. These results point to the conclusion that vertical ground motion needs to be included in analysis for assessment and design.

Combined Effect of Vertical and Horizontal Ground Motions on Failure Probability of RC Chimneys

Previous earthquake events have shown that chimneys are one of the most fragile structures. Studies have focused on the seismic behavior of reinforced concrete (RC) chimney structures subjected to earthquake load only along the horizontal direction. However, the vertical component of strong ground motion has been proven to damage or completely destroy civil structures. Therefore, it is essential to determine the failure probability of RC chimneys under both horizontal and vertical directions. In this study, the seismic behavior of an RC chimney was studied through seismic fragility analysis, wherein a fragility model based on the intensity ratio between the vertical and horizontal components was proposed. In the fragility analysis, different intensity ratios of near‐fault ground motions (NFGMs) between the vertical and horizontal components were considered. The findings indicate that the NFGMs along the vertical and horizontal directions significantly affect the failure probability if the intensity of the horizontal component is above a certain threshold. Moreover, the failure probability increases with the intensity of the vertical and horizontal ground motions. Therefore, the influence of the combination of the vertical and horizontal components of the NFGMs should be considered in the safety evaluation of RC chimney structures.

Seismic Response Analysis of an Isolated Structure with QZS under Near‐Fault Vertical Earthquakes

Seismic isolation devices are usually designed to protect structures from the strong horizontal component of earthquake ground shaking. However, the effect of near‐fault (NF) vertical ground motions on seismic responses of buildings has become an important consideration due to the observed building damage caused by vertical excitation. As the structure needs to maintain its load bearing capacity, using the horizontal isolation strategy in vertical seismic isolation will lead to the problem of larger static displacement. In particular, the bearings may generate large deformation responses of isolators for NF vertical ground motions. A seismic isolation system including quasi‐zero stiffness (QZS) and vertical damper (VD) is used to control NF vertical earthquakes. The characteristics of vertical seismic isolated structures incorporating QZS and VD are presented. The formula for the maximum bearing capacity of QZS isolation considering the stiffness of vertical spring components is obtained by theoretical derivation. From the static analysis, it is found that the static capacity of the QZS isolation system with vertical seismic isolation components increases when the configurative parameter reduces. Seismic response analyses of the seismic isolated structure model with QZS and VD subjected to NF vertical earthquakes are conducted. The results show that seismic responses of the structure can be controlled by setting the appropriate static equilibrium position, vertical isolation period, and vertical damping ratio. Adding a damping ratio is effective in controlling the vertical large deformation of the isolator.

Coastal landscape evolution of Naples (Southern Italy) since the Roman period from archaeological and geomorphological data at Palazzo degli Spiriti site

The Posillipo promontory is an elongated tufaceous ridge located on the southern periphery of the Campi Flegrei active volcanic complex that hosts several underwater archaeological structures dated mostly in the 1st century BC and the Imperial age. The so-called Palazzo degli Spiriti, built in the 1st century BC along the coast of the Posillipo hill (Naples, Italy), is one of the most preserved Roman maritime villas on the Gulf of Naples, with clear evidence of the interaction of both human and natural events. At this site, a relative sea level rise due to a sudden subsidence occurred between the 1st century BC and 1st century AD, probably of volcano-tectonic origin, produced a significant amount of adaptation, as the partial closure of the ground floor windows of the villa still visible. Integrated surveys by means of a marine drone and several direct archaeological measurements were carried out both on the coastline and in the underwater portion of this site.A GIS analysis of geophysical, LIDAR, multibeam and archaeological data has returned a 3D reconstruction of the Roman landscape, useful to understand both the natural events occurred in the area since the Roman Period (vertical ground movements, wave erosion, etc.) and the correlative steps of human occupation and adaptation.

Vertical ductility demand and residual displacement of roof-type steel structures subjected to vertical earthquake ground motions

The vertical component of seismic ground motions (VGM) may induce severe responses in roof-type structures such as mega canopies, large floors, etc. This paper proposes a ductility-based approach for estimating the inelastic responses of roof-type steel structures under VGMs. Due to the pre-loaded gravity, a roof-type steel structure exhibits obvious asymmetric hysteresis properties in the vertical direction. Accordingly, this kind of structure could be idealized as “one-side yielding” systems which only yield in the lower side of vibration, wherein the gravity effect and the VGM effect positively super-positions with each other. Based on the idealized model, the vertical ductility demand spectra and the vertical residual displacement spectra for roof-type steel structures are computed using 53 recorded strong near-fault VGMs. Taking into account the vertical strength reduction factor and the vertical post-yielding stiffness ratio, a vertical ductility demand model in the μ-T format is proposed for roof-type steel structures under VGMs. Meanwhile, the vertical residual displacement model is derived from the vertical ductility demand model, since the vertical residual displacement could be computed as the peak vertical displacement subtracted by the recoverable elastic displacement. An application of these proposed models is given in the paper. The vertical seismic responses of a large-span steel floor under VGMs are predicted based on the proposed models, and the obtained results (including both the peak and the residual responses in the vertical direction) show good accuracy as compared with the results given by nonlinear response history analysis.