Horizontal Seismic Excitation Research Articles

Seismic Vibration Control of Multiple-Degrees-of-Freedom Steel Structures Through Optimal Impact Mass Dampers

ABSTRACT A novel device based on the energy transfer concept, named impact mass damper (IMD), is presented for the mitigation of large structural vibrations due to horizontal seismic excitations. To achieve the optimal performance of the nonlinear device, coupled with different standard steel buildings, an optimization procedure is set both employing the design of experiments (DOEs) method and the Kriging surrogate modelling. Concerning the seismic input, site-specific ground motions and record-to-record variability are taken into account, in agreement with the new European standards. The validated performance of the IMD device demonstrates its benefits, in particular for short-period steel buildings.

Investigating the influence of an approach bridge on a pile-supported wharf at a liquefiable site under horizontal and vertical seismic excitations

The approach bridge of the pile-supported wharf is an important structure that connects the pile foundation platform and the land, and it has a significant impact on the safety of the high-pile wharf. However, the influence of an approach bridge on the seismic dynamic response of a pile-supported wharf has often been neglected in previous studies. Besides, the excess pore water pressure (Δu) generated under combined vertical and horizontal seismic components is typically greater than that induced by unidirectional excitations, which may further impact the dynamic response of pile-supported wharf. Firstly, this study developed a numerical method for simulating the approach bridge of a pile-supported wharf. Secondly, the three-dimensional finite element model of a pile-supported wharf with an approach bridge is established to investigate the dynamic response during horizontal and vertical seismic components. Additionally, the effects of seismic frequency and relative density of liquefied layer on the dynamic response of pile-supported wharf were also studied. By comparing with the experimental results, the numerical model effectively simulated the overall response of the pile-supported wharf and the liquefaction behavior of the surrounding soil. During high-frequency earthquakes, the influence of the approach bridge on the dynamic response of the pile-supported wharf is minimal, whereas it has a more significant impact during low-frequency earthquakes. Furthermore, vertical seismic components significantly amplify the effect of approach bridge on the lateral displacement and internal forces of piles. The effect of the approach bridge on the lateral displacement and internal force of the pile decreases with the increase of the relative density of the liquefaction layer.

Seismic response of tripod suction bucket foundation for offshore wind turbine considering multidirectional earthquake loads

Tripod suction buckets offer several advantages as offshore wind turbine (OWT) foundations, including cost-effective installation, high stability, and resistance to overturning. In seismically active regions, OWTs experience horizontal and vertical directions seismic excitations. This study employed an advanced three-dimensional nonlinear finite element analysis to investigate the influence of vertical seismic motions on the dynamic behavior of tripod bucket foundations installed in nonhomogeneous clay deposits. By adopting a simple kinematic hardening model to capture the foundation-soil nonlinear dynamic interaction, parametric analyses were conducted to study the effect of vertical seismic motions, considering several earthquake types and undrained shear strengths of the clay deposit. The results show that the influence of the vertical seismic motion on the dynamic response and deformation of the nacelle depends on the dominant frequency of the vertical seismic motion and the overturning resistance capacity of the OWT in different horizontal directions. The deformation mechanisms of an OWT vary with the strengths of the clay deposits. Based on these analyses, this study offers insights into the influence of vertical seismic motions on the dynamic response of tripod suction bucket foundations.

An uncoupled approach for estimating seismic-induced pore water pressures in liquefiable sandy soils

Proper evaluation of seismic-induced excess pore water pressures in saturated sandy soils is still an open issue, which can be tackled with fully coupled to uncoupled approaches. The former are more accurate but computationally onerous, while the latter require seismic demand and pore pressure build-up to be computed in two successive steps, typically employing simple constitutive assumptions.Starting from the work by Seed et al. (1975), this paper presents a novel uncoupled procedure to compute excess water pressures developing in a 1D soil column under partially drained conditions, when subjected to horizontal seismic excitations. Fundamental modifications are introduced to account for: non-uniform distribution of equivalent loading cycles; soil stiffness degradation; and modification of the frequency content of ground motion due to pore pressure build-up.The approach was implemented in Matlab via the Finite Difference Method and validated against both fully-coupled Finite Element analyses and one centrifuge test. An extensive parametric study was also performed for a two-layer soil column, by varying the thickness and hydraulic conductivity of the shallow layer, as well as the seismic input. The good agreement with both numerical and experimental data demonstrates that key features of liquefaction are well-captured by the proposed uncoupled approach.

A theoretical calculation method of seismic shear key pounding based on continuum model

The evolution of shear key design for bridges is accompanied by research on structural earthquake resistance. However, the vast majority of pounding forces, responses, and corresponding data for the study and design of shear keys have been based on expensive experimentalism and imprecise empiricism approaches for decades. Hence, strengthening theoretical study on seismic performance of shear key is essential. In this paper, a “Beam-Spring-Beam + Concentrated Mass” continuum dynamic model is proposed. Meanwhile, the transient wave function expansion method and the mode superposition method are applied to determine the analytical expression of the dynamic response from the girder and pier system (pier and cap beam). Furthermore, the combined transient internal force method and Duhamel integration method are introduced to assess the elastic pounding process. Through programming and numerical analysis, a series of pounding response data related to the shear key under various working circumstances will be explored. As mentioned above, the proposed theoretical method can optimize shear key design and boost the reliability of seismic limiting devices in the future.•Establishing a feasible “Beam-Spring-Beam + Concentrated Mass” continuum model of girders and piers based on a two-span continuous girder bridge.•Deriving the analytical solutions of responses by conducting the response equations under horizontal seismic excitation (containing orthonormality verification).•Simulating the pounding process by embedding elastic pounding calculation methods into Continuum Model.

Experimental Investigations of the Seismic Response of a Large Underground Structure at a Soft Loess Site

Based on an underground structure located at a soft loess site in Xi’an as the engineering background, this paper investigated a seismic response and damage model of subway stations at a soft loess site using a large-scale shaking table test, considering the different characteristics of ground motions. The quantitative analysis of the acceleration response and the seismic subsidence of the soft loess site were subjected to different earthquake excitations; based on the experimental results and the corresponding analysis, the development and distribution of seismic structural damage were studied, and the damage mechanism of underground structures in a soft loess area under a strong earthquake was explored. The results indicate that the peak accelerations of the site soil first remained unchanged then increased significantly along the soil height, and the amplification effect of the acceleration response was the most significant at the soil surface. The soft loess soil underwent significant subsidence, and the underground structure was raised compared to both sides of the cover soil; the collapsibility of the soft loess soil was sensitive to strong earthquakes with vertical components. The underground structures in soft loess suffered heavy damage, which rapidly entered the elastic–plastic stage. The composite effect of the collapsibility and vertical seismic excitation impaired the load-carrying capacity of the middle columns, and the strong horizontal seismic excitation enlarged the lateral force and accelerated structural damage development; the underground structure reached failure when plastic damage expended most of the middle columns and structural joints. These results are significant for the seismic design of underground structures in adverse soil conditions.

An Efficient Straightforward Pushover Method for Buildings with Two-Way Unsymmetric-Plan Subjected to Two Components of Ground Motions

ABSTRACT A straightforward pushover method is developed for unsymmetric-plan buildings under bidirectional seismic excitation. To this end, a single innovative torsional-lateral load pattern is introduced based on the response spectrum analysis. The joint contribution of two horizontal seismic excitations and the joint contribution of all considered modes to internal structural forces in forming plastic hinges are considered by implementing the single load pattern. An equivalent dominant mode shape derived from the load pattern is defined to establish capacity spectra in both directions. The accuracy of the proposed procedure in estimating the seismic demands of buildings is demonstrated through two unsymmetric-plan buildings.

Nonlinear random vibration of the slender deep-water pier under seismic excitation

The present study investigates the nonlinear random vibration of the deep-water pier exposed to horizontal seismic excitation. First of all, the stochastic dynamic model of the pier is formulated. During the process, the pier is simplified as a cantilever beam fixed on the rock foundation, the seismic excitation is treated as Gaussian white noise, the hydrodynamic pressure is described with the radiation wave theory, and the equation for the nonlinear kinematic of the pier is deduced by the means of Kane’s method. Then, with the application of the stochastic averaging (SA) technique, the Fokker–Plank–Kolmogorov (FPK) equation governing the transient probability density function (PDF) of the amplitude envelope and the backward Kolmogorov (BK) equation for the conditional reliability function (CRF) are derived, respectively. The closed-form stationary PDF can be yielded directly from the reduced FPK equation, while the CRF and the conditional PDF of first-passage time are given after solving the BK equation numerically. Numerical discussions are performed to illustrate the trend of excitation intensity, mass ratio, immersion ratio, and inner and outer hydrodynamic effect on the stationary response and first-passage failure are examined, respectively. It has been shown that increases in the excitation intensity, mass ratio, and immersion ratio can amplify the response and reduce the reliability of the deep-water pier system. The hydrodynamic effect also leads to an amplification of the system response and a reduction in the reliability of the system. Similarly, the presence of inner water can also exacerbate these effects, and this phenomenon becomes more pronounced with increasing immersed ratios. Additionally, the analytical solution is validated by the result obtained by pertained Monte Carlo simulations (MCS). It is noted that this work will be helpful for the optimal seismic design of deep-water piers.

Dynamic analysis of three-directional vibration isolation and mitigation for long-span grid structure

With the rapid development of the long-span space structures, some seismic isolation methods of ordinary buildings are also gradually applied in these structures. The special feature of the long-span space structure is that the vertical seismic property cannot be ignored, in addition to considering the horizontal property under multi-dimensional earthquake action. This study proposes a novel multi-dimensional earthquake isolation and mitigation device (MEIMD) consisted of viscoelastic core bearing and viscoelastic damper. This device provides certain stiffness that can satisfy the load-bearing capacity requirement of the structure and strong energy dissipation ability in the horizontal and vertical seismic directions. A mathematical model is presented to characterize the mechanical behavior of the MEIMD. The device is installed at the top of the support column, which creates a seismic isolation layer between the column and the upper grid model. The shaking table tests of the long-span grid structure with and without MEIMD under horizontal seismic excitations of various intensities were carried out. The experimental results showed that the acceleration response peak value on the isolation structure was significantly reduced. The novel device has a good horizontal isolation effect on the grid structure. To determine the vertical and three-direction seismic isolation properties of the MEIMD on the grid structure, finite element models of the long-span grid structure with MIEMD and without MEIMD were established for dynamic time history analysis. The numerical results revealed that the dynamic responses of the isolation grid in horizontal and vertical directions have been decreased compared to the non-isolated structure.

Effects of biaxial loading path on seismic behavior of T-shaped RC walls

T-shaped RC walls are commonly used to resist horizontal seismic excitations in multiple directions. The differences in the intensity and spectrum characteristics of two translational components of ground motion cause the wall to experience complex biaxial displacement trajectories, resulting in a different seismic response compared to the behavior derived from conventional uniaxial cyclic tests. Thus, to investigate the seismic behavior and coupling mechanism of T-shaped walls subjected to different magnitudes of loading in two orthogonal directions, this study examined five identical T-shaped walls under uniaxial loading along two principal axes and biaxial loading with three represented loading paths. The test results showed that the mechanical behavior in one direction was significantly affected by the loading in the orthogonal direction owing to internal force redistribution and additional stress caused by the biaxial coupling bending, resulting in vertical variation and intersection of their hysteretic curves. Further, the biaxial loading primarily aggravated the cracking and damage of the flange, which accelerated the performance degradation in the flange direction and reduced the effective flange width involved in resisting web direction load. In addition, the biaxial coupling effect was found to be proportional to the area enclosed by the loading path. Thus, the most severe damage and performance degradation were observed under a square path, followed by an eight-shaped path, with the cruciform path exhibiting the least effect. Consequently, based on the results, recommendations for the design of T-shaped walls subjected to biaxial earthquake actions were proposed.

Investigation on Rupture Initiation and Propagation of Traffic Tunnel under Seismic Excitation Based on Acoustic Emission Technology.

Traffic tunnels are important engineering structures in transportation, and their stability is critical to traffic safety. In particular, when these tunnels are in an earthquake-prone area, the rupture process under seismic excitation needs to be studied in depth for safer tunnel design. In this paper, based on a construction project on the Nairobi-Malaba railway in East Africa, a laboratory shaking table test with 24 working cases of seismic excitation on a mountain tunnel is designed, and the acoustic emission (AE) technique is employed to investigate the tunnel rupture process. The results show that the high frequency components between 20 and 30 kHz of AE signals are the tunnel rupturing signals under the seismic excitation under such conditions. The tunnel vault and the arch foot are prone to rupture during the seismic excitation, and the initial rupture in the arch foot and vault of the tunnel occur under the horizontal and vertical Kobe wave seismic excitation, respectively, with a maximum acceleration of 0.4 g. After the rupture initiation, the tunnel arch foot continues to rupture in the subsequent working cases regardless of whether the excitation direction is horizontal or vertical, while the tunnel vault does not rupture continuously with the implementation of the subsequent excitations. Moreover, the Kobe seismic wave has a higher degree of damage potential to underground structures than the El seismic wave.

Shaking table test and numerical simulation of shallow foundation structures in seasonal frozen soil regions

Frozen soil layers can induce the formation of double or multilayers on the ground. Such formations change the dynamic characteristics and dominant period of soil, directly influencing the stability and safety of upper buildings. In this paper, the frozen soil-structure interaction system in cold region was taken as the research object. The frozen soil model was made artificially, and two kinds of structure models with different natural frequencies were designed. Through a series of shaking table tests and finite element numerical analysis, the influence of structural natural frequency, soil frozen depth and seismic load on the seismic response of structure were studied. The test results indicate that ground freezing could weaken the soil–structure interaction effect and the nonlinear development of the soil structure. The effect of peak acceleration amplification of the ground is significant close to the surface. The acceleration amplification coefficient of the ground surface decreased as the freezing depth increased, which indicates that the freezing of the ground suppressed the acceleration response of the ground surface. If the peak frequency of a seismic wave is close to the natural frequency of the structure, it can significantly amplify the seismic response of the structure. Owing to the interaction between the soil and the structure, the degree of liquefaction of the ground varied with different structures. Subsequently, a nonlinear finite element program was used to establish the dynamic calculation model of frozen soil-structure interaction system considering the gradient change of stiffness of frozen soil and the dependence of frozen soil on temperature. On the basis of validating the numerical model rationality, the seismic response of frozen soil-structure interaction system under horizontal seismic excitation was further explored. The analysis results show that the seismic response of the structure increased significantly with amplitude excitation; the greater was the freezing depth, the greater was the seismic response of the structure, The influence of the frozen ground on the seismic response of structures in the design of structures in frozen soil areas should be considered. In summary, the dominant period of the ground, the dynamic characteristics of a structure, the type of seismic wave, and the degree of liquefaction of the ground have a significant influence on the seismic response of the structure. Therefore, considerable attention should be paid to the influence of frozen soil on the dynamic characteristics of a structure in frozen soil regions.

Seismic Performance Assessment of a Single-Layer Spherical Lattice Shell Structure with Multifunctional Friction Pendulum Bearings

The dynamic responses of spatial lattice shell structures with friction pendulum bearings (FPBs) under multidimensional seismic excitations are complex. In addition, FPBs may experience uplift and separation of the bearing components owing to excessive displacements. In this study, a novel multifunctional FPB (MFPB) with a multi-defense system was developed, and its effectiveness in reducing and controlling the seismic responses of spherical lattice shell structures was evaluated. The proposed MFPB comprises an FPB, superelastic shape-memory alloy cables, and sleeve restrainers. A mechanical model of the MFPB was established, and its isolation and control behaviors were investigated through numerical simulations. Furthermore, the main characteristics and advantages of the isolation system were analyzed. Subsequently, the MFPB system was applied to a single-layer spherical lattice shell structure with surrounding columns. A computational model of the controlled structure was developed using the OpenSees software. Finally, nonlinear time history analyzes were conducted to analyze the seismic performance of controlled and uncontrolled lattice shells. The results demonstrate that the MFPB isolation system can effectively control the structural responses of isolated spatial lattice shell structures under horizontal and vertical seismic excitations and improve their seismic resilience.

Progressive Collapse of the Base-Isolated Frame Structures Supported by Stepped Foundation in Mountainous City

Base-isolated frames supported by stepped foundation in mountainous areas possess their own particularity, so its progressive collapse dynamic response performance and dynamic effect propagation path are very different from those of ordinary flat ground-isolated structural systems. In order to study the progressive collapse performance of the base-isolated frames supported by stepped foundation in mountainous areas under two-directional coupled dynamic excitation, a four-span three-story plane frame demolition column test was simulated to verify the reliability of the computing platform. The common ground motion and three types of long-period ground motions were selected, and the two-dimensional dynamic coupling of the ordinary flat ground isolation structure and the base-isolated frames supported by stepped foundation in mountainous areas was obtained based on the demolition method. First, the seismic isolation structure was subjected to the collapse dynamic response under the vertical unbalanced load, then the collapse dynamic response under the vertical unbalanced load and the horizontal seismic coupling excitation was made; the two were compared and analyzed. It can be used as a reference for the design of progressive collapse of the frame structure of the base-isolated frames supported by stepped foundation in mountainous areas.

A mechanical model for soil-rectangular tank interaction effects under seismic loading

In this paper, the dynamic behavior of concrete rectangular tanks subjected to motions caused by an earthquake considering the effects of soil-structure-fluid interaction is studied. An analytical mechanical model for a rectangular tank with flexible walls, taking into consideration the effects of rigid-base rocking motion and lateral translation, is developed. The model with a lumped-parameters idealization of foundation soil is used to evaluate the system's response to ground earthquake motions. Using this model, the soil-structure-fluid interaction effect can be taken into account in the seismic analysis of flexible rectangular tanks in a fast and practical manner. To verify the mechanical model, the numerical results of the fixed-base case are compared with the experimental results. The results show that dynamic soil-tank interaction under horizontal seismic excitations, depending on the type of soil, can cause a profound effect on the amplification of hydrodynamic forces and moments exerted on the tank structure.

Comparison of sodium fast reactor core assembly seismic evaluation using the Japanese and French simulation tools

Launched in 2014, Japan-France collaboration on the ASTRID (Advanced Sodium Technological Reactor for Industrial Demonstration) project is active both in reactor design and in R&D fields. CEA, Framatome, JAEA, MHI and MFBR are in charge of this collaboration. In the design field, Japan-France evaluates core assemblies with interferences on seismic events. The objectives of this collaboration are to determine the core assembly lattice displacements under seismic load in order to demonstrate the safe behavior of the core regarding control rod insertion, structural integrity, and reactivity variation, etc.From this point of view, the object of this study is to verify the seismic evaluation method on core assemblies between Japan and France by comparing the results. Using their evaluation method applied to common the ASTRID core input data, Japan and France will calculate a collision load, a horizontal displacement, and a vertical displacement for core assemblies.As the first step of this work, the comparison of each evaluation (modelling and calculation results) is carried out considering the horizontal seismic excitation and without including the vertical component.The analysis of this benchmark calculation shows a satisfactory agreement between the Japanese and French tools and the figures show a good behavior of the core in horizontal direction under French seismic condition.This paper describes the summary of horizontal seismic analysis comparison and the future analysis plan.

The slab effect of composite frames: From modified fiber modeling to seismic fragility assessment

The slab spatial composite effect (SSCE) is of considerable importance in the field of engineering as it greatly influences the vertical load-bearing capacity and lateral load resistance of composite frame structures. In this study, the existing uniaxial material-constitutive models of concrete (Concrete02) and steel (Steel02) in the Open System for Earthquake Engineering Simulation (OpenSees) were modified based on three effective flange widths of composite beams under two critical limit states. An improved fiber model was developed to capture the SSCE of composite frames by combining the conventional fiber models and new material-constitutive models. Through three validation studies, the ability of the proposed fiber model to trace the SSCE accurately and efficiently was established based on modeling and comparison of the representative composite frames available in literature. Moreover, seismic fragility assessment was conducted for a 10-story spatial composite frame subjected to bidirectional horizontal seismic excitation based on an incremental dynamic analysis. The comprehensive numerical simulation results indicate that the conventional fiber model without constitutive model modifications leads to significant overestimation of the probability of the structure being a specified limit state under different ground motion intensities and site classes. The conventional fiber model results are at most 47.1%, 72.0%, 53.5%, and 49.6% higher than those obtained using the improved fiber model in terms of the structure being slightly, moderately, extensively, and completely damaged, respectively. This means that the potential economic advantages of composite frames can be explored by reasonably considering the SSCE.

Research on the anti-seismic performance of composite precast utility tunnels based on the shaking table test and simulation analysis

In this paper, the parameters of haunch height, reinforcement ratio and site condition were evaluated for the influence on the seismic performance of a composite precast fabricated utility tunnel by shaking table test and numerical simulation. The dynamic response laws of acceleration, interlayer displacement and steel strain under unidirectional horizontal seismic excitation were analyzed through four specimens with a similarity ratio of 1:6 in the test. And a numerical model was established and analyzed by the finite element software ABAQUS based on the structure of utility tunnel. The results indicated that composite precast fabricated utility tunnel with the good anti-seismic performance. In a certain range, increasing the height of haunch or the ratio of reinforcement could reduce the influence of seismic wave on the utility tunnel structure, which was beneficial to the structure earthquake resistance. The clay field containing the interlayer of liquefied sandy soil has a certain damping effect on the structure of the utility tunnel, and the displacement response could be reduced by 14.1%. Under the excitation of strong earthquake, the reinforcement strain at the side wall upper end and haunches of the utility tunnel was the biggest, which is the key part of the structure. The experimental results were in good agreement with the fitting results, and the results could provide a reference value for the anti-seismic design and application of composite precast fabricated utility tunnel.

Frequency response analysis of concrete seawall including soil-structure-seawater interaction

In this study, a frequency-domain finite element model is proposed to evaluate the seismic response of water-structure-sediment-foundation-backfill coupling system. It includes the seawater as a compressible fluid, seawall as viscoelastic solid, backfilled soil, sediment, and foundation as two-phase poroelastic domains with dynamic behavior described by u-p formulation of Biot’s equations. The dynamic interactions among various domains are fully considered and the PML is adopted as an absorbing boundary condition to truncate the computational domain, absorbing all out-going seismic waves. The dynamic responses in the structure, water and soil are assumed to be generated by the vertical propagating shear or compressional waves from the bedrock substrate under the foundation soil. Both the actions of horizontal and vertical seismic excitations at the bottom of foundation are respectively considered. After verifying the accuracy of PML and coupled model of soil-structure-water system, a series of parametric studies are conducted to investigate the effects of sediment thickness, water depth, foundation stiffness, foundation thickness, inclination of seawall, and properties of backfilled soil including soil permeability, shear modulus, and saturation degree, on the frequency response at the top of seawall.

Stability Charts for Pseudostatic Stability Analysis of Rock Slopes Using the Nonlinear Hoek–Brown Strength Reduction Technique

This paper presents a set of stability charts for the stability assessment of rock slopes that satisfy the Hoek–Brown (HB) criterion under various seismic loading conditions. The nonlinear Hoek–Brown strength reduction technique is used to conduct pseudostatic stability analysis of rock slopes subjected to horizontal seismic excitation. Based on an extensive parametric study, first, a set of stability charts with a slope angle of β = 45° under static and pseudostatic conditions are proposed by using ABAQUS 6.10 software. Second, the slope angle weighting factor (fβ) and the seismic weighting factor (fkh) are adopted to characterize the influence of slope angle (β) and horizontal seismic acceleration coefficient (kh) on the rock slope stability. Finally, the reliability of the proposed charts was validated by three typical examples and two case studies, and the results show that the values of the factor of safety (FOS) obtained from the proposed charts are consistent with the values from other methods. The proposed charts provide an efficient and convenient way to determine the FOS of rock slopes directly from the rock mass properties (γ and σci), the HB parameters (mi and GSI), the slope geometry (H and β), and the horizontal seismic coefficients (kh).