Numerical Simulation of the Seismic Response of a Horizontal Storage Tank Based on a SPH-FEM Coupling Method

A coupled numerical calculation method combining smooth particle hydrodynamics(SPH)and the finite element method(FEM)was implemented to investigate the seismic response of horizontal storage tanks.Anumericalmodel of a horizontal storage tank featuring a free liquid surface under seismic action was constructed using the SPH–FEM coupling method.The stored liquid was discretized using SPH particles,while the tank and supports were discretized using the FEM.The interaction between the stored liquid and the tank was simulated by using the meshless particle contact method.Then,the numerical simulation results were compared and analyzed against seismic simulation shaking table test data to validate the method.Subsequently,a series of numerical models,considering different liquid storage volumes and seismic effects,were constructed to obtain time history data of base shear and top center displacement,which revealed the seismic performance of horizontal storage tanks.Numerical simulation results and experimental data showed good agreement,with an error rate of less than 18.85%.And this conformity signifies the rationality of the SPH-FEM coupling method.The base shear and top center displacement values obtained by the coupled SPH-FEM method were only 53.3% to 69.1% of those calculated by the equivalent mass method employed in the current code.As the stored liquid volume increased,the seismic response of the horizontal storage tank exhibited a gradual upward trend,with the seismic response increasing from 73% to 388% for every 35% increase in stored liquid volume.The maximum von Mises stress of the tank and the supports remained below the steel yield strength during the earthquake.The coupled SPH-FEM method holds certain advantages in studying the seismic problems of tanks with complex structural forms,particularly due to the representation of the flow field distribution during earthquakes by involving reservoir fluid participation.

Optimal design and effectiveness evaluation for inerter-based devices on mitigating seismic responses of base isolated structures

The optimal design and effectiveness of three control systems,tuned viscous mass damper(TVMD),tuned inerter damper(TID)and tuned mass damper(TMD),on mitigating the seismic responses of base isolated structures,were systematically studied.First,the seismic responses of the base isolated structure with each control system under white noise excitation were obtained.Then,the structural parameter optimizations of the TVMD,TID and TMD were conducted by using three different objectives.The results show that the three control systems were all effective in minimizing the root mean square value of seismic responses,including the base shear of the BIS,the absolute acceleration of structural SDOF,and the relative displacement between the base isolation floor and the foundation.Finally,considering the superstructure as a structural MDOF,a series of time history analyses were performed to investigate the effectiveness and activation sensitivity of the three control systems under far field and near fault seismic excitations.The results show that the effectiveness of TID and TMD with optimized parameters on mitigating the seismic responses of base isolated structures increased as the mass ratio increases,and the effectiveness of TID was always better than TMD with the same mass ratio.The TVMD with a lower mass ratio was more efficient in reducing the seismic response than the TID and TMD.Furthermore,the TVMD,when compared with TMD and TID,had better activation sensitivity and a smaller stroke.

An Application of Direct Ritz Method for Random Seismic Responses of Jacket Platforms

In this paper, the jacket platform is simulated by a non-uniform cantilever beam subjected to axial force. Based on the Hamilton theory, the equation of bending motion is developed and solved by the classical Ritz method combined with the pseudo-excitation method for random responses with non-classical damping. Usually, random responses of this continuous structure are obtained by orthogonality of modes, and some normal modes of the structure are needed, causing inconvenience for the analysis of the non-uniform beam whose normal modes are not easy to be obtained. However, if the pseudo-excitation method is extended to calculate random responses by combining it with the classical Ritz method, the responses of a non-uniform beam, such as auto-PSD function, cross-PSD and higher spectral moments, can be solved directly avoiding the calculation of normal modes. The numerical results show that the present method is effective and useful in aseismic design of platforms.

Range of applicability of real mode superposition approximation method for seismic response calculation of non-classically damped industrial buildings

An industrial building is a non-classically damped system due to the different damping properties of the primary structure and equipment.The objective of this paper is to quantify the range of applicability of the real model superposition approximation method to the seismic response calculation of industrial buildings.The analysis using lumped mass-and-shear spring models indicates that for the equipment-to-structure frequency ratiosγf>1.1 orγf<0.9,the non-classical damping effect is limited,and the real mode superposition approximation method provides accurate estimates.For 0.9<γf<1.1,the system may have a pair of closely spaced frequency modes,and the non-zero off-diagonal damping terms have a non-negligible effect on the damping ratios and mode shape vectors of these modes.For 0.9<γf<1.1 and the equipment-to-structure mass ratiosγm<0.07,the real mode superposition approximation method results in large errors,while the approximation method can provide an accurate estimation for 0.9<γf<1.1 andγm>0.07.Furthermore,extensive parametric analyses are conducted,where both steel structures and reinforced concrete structures with equipment with various damping ratios are considered.Finally,the finite element analysis of a five-story industrial building is adopted to validate the proposed range of applicability.

Effective stress analysis method of seismic response for high tailings dam

Based on the analysis method for tailings dam in upstream raising method presently used in metallurgy and nonferrous metals tailings depository in the world, an effective stress analysis method of seismic response for high tailings dam was developed according to the results of engineering geological exploration, static and dynamic test and stability analysis on Baizhishan tailing dam 113.5 m high. The law of generation, diffusion and dissipation of seismic pore water pressure during and after earthquake was investigated, and the results of tailings dam’s acceleration, seismic dynamic stress and pore water pressure were obtained. The results show that the seismic stability and liquefaction resistance of high tailings dam are strengthened remarkably, and the scope and depth of liquefaction area at the top of dam are reduced greatly. The interior stress is compressive stress, the stress level of every element is less than 1.0 and the safety coefficient of every element is greater than 1.0. The safety coefficient against liquefaction of every element of tailing dam is greater than 1.5 according to the effective stress analysis of seismic response by finite element method. The calculated results prove that liquefaction is the main reason of seismic failure of high tailing dams, and the effect of seismic inertia forces on high tailing dams’ stability during earthquake is secondary reason.

Assessment of seismic design response factors of concrete wall buildings

To verify the seismic design response factors of high-rise buildings, five reference structures, varying in height from 20- to 60-stories, were selected and designed according to modern design codes to represent a wide range of concrete wall structures. Verified fiber-based analytical models for inelastic simulation were developed, considering the geometric nonlinearity and material inelasticity of the structural members. The ground motion uncertainty was accounted for by employing 20 earthquake records representing two seismic scenarios, consistent with the latest understanding of the tectonic setting and seismicity of the selected reference region （UAE）. A large number of Inelastic Pushover Analyses （IPAs） and Incremental Dynamic Collapse Analyses （IDCAs） were deployed for the reference structures to estimate the seismic design response factors. It is concluded that the factors adopted by the design code are adequately conservative. The results of this systematic assessment of seismic design response factors apply to a wide variety of contemporary concrete wall buildings with various characteristics.

Seismic response analysis of continuous rigid frame bridge considering canyon topography effects under incident SV waves

To evaluate the importance of the canyon topography effects on large structures, based on a rigid frame bridge across a 137-m-deep and 600-m-wide canyon, the seismic response of the canyon site is analyzed using a two-dimensional finite element model under different seismic SV waves with the assumptions of vertical incidence and oblique incidence to obtain the ground motions, which are used as the excitation input on the pier foundations of the bridge with improved large mass method. The results indicate that canyon topography has significant influences on the ground motions in terms of inci- dent angle. The peak ground acceleration values vary greatly from the bottom of the canyon to the upper comers. Under ver- tical incident SV waves, at the upper comers of canyon the peak ground accelerations greatly increase; whereas the peak ground accelerations diminish at the bottom comers of canyon. Under oblique incident SV waves, the shaking of the canyon slope perpendicular to the incidence direction is much more severe than that of the opposite side of canyon. And the ground surface has been characterized by larger deformations in the case of oblique incident waves. It is also concluded that the low piers and frame of the continuous rigid frame bridge ape more sensitive to the multi-support seismic excitations than the flexible high piers. The canyon topography as well as the oblique incidence of the waves brings the continuous rigid frame bridge severe responses, which should be taken into account in bridge design.

Seismic Response of Submerged Floating Tunnel Tether

A mathematical equation for vibration of submerged floating tunnel tether under the effects of earthquake and parametric excitation is presented. Multi-step Galerkin method is used to simplify this equation and the fourth-order Runge-Kuta integration method is used for numerical analysis. Finally, vibration response of submerged floating tunnel tether subjected to earthquake and parametric excitation is analyzed in a few numerical examples. The results show that the vibration response of tether varies with the seismic wave type; the steady maximum mid-span displacement of tether subjected to seismic wave keeps constant when parametric resonance takes place; the transient maximum mid-span displacement of tether is related to the peak value of input seismic wave acceleration.

Seismic response analysis of arch dam-water-rock foundation systems

The effect of water compressibility on the seismic responses of arch dams is not well understood.In this paper,a numerical model is developed with rigorous representation of the dynamic interaction between arch dam-water- rock foundation.The model is applied to the seismic response analysis of an arch dam with a height of 292m designed to a seismic intensity of IX.It is shown that consideration of the water compressibility clearly decreases the stress responses at key positions of the dam,while the added mass model gives a conservative estimate.

Characteristic Period Value of the Seismic Design Response Spectrum of UHV Electrical Equipment

Characteristic period is an important parameter of the seismic design response spectrum.There is important theoretical significance and engineering application value to the study of the characteristic period of seismic design response spectrum of ultra high voltage(UHV)electrical equipment.In this paper,1448 horizontal earthquake records within the world scope including the United States and Japan for Site Class Ⅲ were analyzed.Results show that both magnitude and epicentral distance have great influence on the characteristic period.About80% of characteristic periods of strong earthquake records are about 0.9s.Statistical analysis was conducted on the seismic hazard assessment results of 312 projects of China in recent years,and it is found that about 70% of characteristic periods are about 0.9s.Combined with the related code comparison and analysis,it is suggested that the characteristic period of the seismic design response spectrum of UHV electrical equipment should select 0.9s in order to effectively guarantee the seismic safety of UHV electrical equipment.

Statistical determination of significant curved I-girder bridge seismic response parameters

Curved steel bridges are commonly used at interchanges in transportation networks and more of these structures continue to be designed and built in the United States. Though the use of these bridges continues to increase in locations that experience high seismicity, the effects of curvature and other parameters on their seismic behaviors have been neglected in current risk assessment tools. These tools can evaluate the seismic vulnerability of a transportation network using fragility curves. One critical component of fragility curve development for curved steel bridges is the completion of sensitivity analyses that help identify influential parameters related to their seismic response. In this study, an accessible inventory of existing curved steel girder bridges located primarily in the Mid-Atlantic United States （MAUS） was used to establish statistical characteristics used as inputs for a seismic sensitivity study. Critical seismic response quantities were captured using 3D nonlinear finite element models. Influential parameters from these quantities were identified using statistical tools that incorporate experimental Plackett-Burman Design （PBD）, which included Pareto optimal plots and prediction profiler techniques. The findings revealed that the potential variation in the influential parameters included number of spans, radius of curvature, maximum span length, girder spacing, and cross-frame spacing. These parameters showed varying levels of influence on the critical bridge response.

Study of Nonlinear Seismic Response and TMD Primary Control of the Cable-Stayed Bridge Section of the Third Macao-Taipa Bridge

The practical design of the cable-stayed bridge of the 3rd Macao-Taipa bridge is investigated by the finite element analysis program ANSYS, and 3-D elements BEAM188 and BEAM4 are adopted to create a dynamic calculation model. In order to analyze the material nonlinear seismic response of the cable-stayed bridge, the nonlinear behaviors of the ductile plastic hinges of the bridge towers are taken into account by employing the nonlinear rotational spring element COMBIN40. To simulate a major earthquake, three earthquake records were chosen using a wave-choosing program and input into the bridge structure along longitudinal and transversal directions. Comparisons of the linear and nonlinear seismic responses of the cable-stayed bridge are performed. In addition, a study of TMD primary control is carried out using element MASS21 and element COMBIN14, and it is indicated that the effects of mitigation monitoring are evident.

Seismic responses of high concrete face rockfill dams:A case study

Seismic responses of the Zipingpu concrete face rockfill dam were analyzed using the finite element method. The dynamic behavior of rockfill materials was modeled with a viscoelastic model and an empirical permanent strain model. The relevant parameters were obtained either by back analysis using the field observations or by reference to parameters of similar rockfill materials. The acceleration responses of the dam,the distribution of earthquake-induced settlement, and the gap propagation under the concrete slabs caused by the settlement of the dam were analyzed and compared with site investigations or relevant studies. The mechanism of failure of horizontal construction joints was also analyzed based on numerical results and site observations. Numerical results show that the input accelerations were considerably amplified near the top of the dam, and the strong shaking resulted in considerable settlement of the rockfill materials, with a maximum value exceeding 90 cm at the crest.As a result of the settlement of rockfill materials, the third-stage concrete slabs were separated from the cushion layer. The rotation of the cantilever slabs about the contacting regions, under the combined action of gravity and seismic inertial forces, led to the failure of the construction joints and tensile cracks appeared above the construction joints. The effectiveness and limitations of the so-called equivalent linear method are also discussed.

Finite element modeling assumptions impact on seismic response demands of MRF-buildings

Recent seismic events have raised concerns over the safety and vulnerability of reinforced concrete moment resisting frame ＂RC-MRF＂ buildings. The seismic response of such buildings is greatly dependent on the computational tools used and the inherent assumptions in the modelling process. Thus, it is essential to investigate the sensitivity of the response demands to the corresponding modelling assumption. Many parameters and assumptions are justified to generate effective structural finite element（FE） models of buildings to simulate lateral behaviour and evaluate seismic design demands. As such, the present study focuses on the development of reliable FE models with various levels of refinement. The effects of the FE modelling assumptions on the seismic response demands on the design of buildings are investigated. the predictive ability of a FE model is tied to the accuracy of numerical analysis; a numerical analysis is performed for a series of symmetric buildings in active seismic zones. The results of the seismic response demands are presented in a comparative format to confirm drift and strength limits requirements. A proposed model is formulated based on a simplified modeling approach, where the most refined model is used to calibrate the simplified model.

Orthogonal expansion of ground motion and PDEM-based seismic response analysis of nonlinear structures

This paper introduces an orthogonal expansion method for general stochastic processes. In the method, a normalized orthogonal function of time variable t is first introduced to carry out the decomposition of a stochastic process and then a correlated matrix decomposition technique, which transforms a correlated random vector into a vector of standard uncorrelated random variables, is used to complete a double orthogonal decomposition of the stochastic processes. Considering the relationship between the Hartley transform and Fourier transform of a real-valued function, it is suggested that the first orthogonal expansion in the above process is carried out using the Hartley basis function instead of the trigonometric basis function in practical applications. The seismic ground motion is investigated using the above method. In order to capture the main probabilistic characteristics of the seismic ground motion, it is proposed to directly carry out the orthogonal expansion of the seismic displacements. The case study shows that the proposed method is feasible to represent the seismic ground motion with only a few random variables. In the second part of the paper, the probability density evolution method （PDEM） is employed to study the stochastic response of nonlinear structures subjected to earthquake excitations. In the PDEM, a completely uncoupled one-dimensional partial differential equation, the generalized density evolution equation, plays a central role in governing the stochastic seismic responses of the nonlinear structure. The solution to this equation will yield the instantaneous probability density function of the responses. Computational algorithms to solve the probability density evolution equation are described. An example, which deals with a nonlinear frame structure subjected to stochastic ground motions, is illustrated to validate the above approach.

An alternative approach for computing seismic response with accidental eccentricity

Accidental eccentricity is a non-standard assumption for seismic design of tall buildings. Taking it into consideration requires reanalysis of seismic resistance, which requires either time consuming computation of natural vibration of eccentric structures or finding a static displacement solution by applying an approximated equivalent torsional moment for each eccentric case. This study proposes an alternative modal response spectrum analysis （MRSA） approach to calculate seismic responses with accidental eccentricity. The proposed approach, called the Rayleigh Ritz Projection-MRSA （RRP-MRSA）, is developed based on MRSA and two strategies： （a） a RRf＂ method to obtain a fast calculation of approximate modes of eccentric structures; and （b） an approach to assemble mass matrices of eccentric structures. The efficiency of RRP-MRSA is tested via engineering examples and compared with the standard MRSA （ST-MRSA） and one approximate method, i.e., the equivalent torsional moment hybrid MRSA （ETM-MRSA）. Numerical results show that RRP-MRSA not only achieves almost the same precision as ST-MRSA, and is much better than ETM-MRSA, but is also more economical. Thus, RRP-MRSA can be in place of current accidental eccentricity computations in seismic design.

Comparative Analysis of Seismic Response of Pile-Soil-Structure Interaction System

一个 pile-soil-structureinteraction 系统的地震抵抗的表演上的学习是在土木工程学实践的一个相对复杂、首先重要的问题。在这篇论文，为 pile-supportedstructures 的一个计算模型和计算过程，它能按时地考虑堆积土壤相互作用完成，被有限单元法建立。数字实现在时间领域被做。为 pile-soil-structure 系统的地震反应分析的简化近似简短被介绍。然后，比较研究为一个设计例子被执行，数字结果由有限单元法和简化方法分别地计算了。通过比较分析，简化方法获得很好的结果同意有限单元法完成的那些，这被显示出。数字结果和调查结果将为有启发性的指南提供支持堆积的结构的 forearthquake 抵抗的分析和设计。

Comparative analysis of seismic response characteristics of pile-supported structure

In order to analyze the seismic response characteristics of pile-supported structure,a computational model considering pile-soil-structure interaction effect was established by finite element method.Then,numerical implementation was made in time domain.At the same time,a simplified approximation for seismic response analysis of pile-soil-structure system was briefly presented.Furthermore,comparative study was performed for an engineering example.Through comparative analysis,it is shown that the results obtained by the simplified method well agree with those achieved by the finite element method.These results show that spectrum characteristics and intensity of input earthquakes are two important factors that can notablely influence the seismic response characteristics of superstructure.When the input ground motion acceleration amplitude gradually increases from 1 to 4 m/s2,the acceleration of pier top will increase,but it will not be simply proportional to the increase of input acceleration amplitude.

Study of Vertical Seismic Response of Concrete Self-Anchored Suspension Bridges

Based on the variational prineiple of incomplete generalized potential energy with large deflection, the vertical nonlinear vibrational differential equation of self-anchored suspension bridge is presented by taking the effect of coupling of flexural and axial action into consideration. The linear vertical equation is obtained by omitting the nonlinear term, and the pseudo excitation method(PEM). Taking the self-anchored concrete suspension bridge over Lanqi Songhua river for an example, the expected peak responses of main beam, towers and cables are calculated. And the seismic spatial effects on vertical seismic response of self-anchored suspension bridges are discussed.