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.

Seismic effectiveness evaluation and optimized design of tie up method for securing museum collections

To quantify the seismic effectiveness of the most commonly used fishing line tie up method for securing museum collections and optimize fixed strategies for exhibitions,shaking table tests of the seismic systems used for typical museum collection replicas have been carried out.The influence of body shape and fixed measure parameters on the seismic responses of replicas and the interaction behavior between replicas and fixed measures have been explored.Based on the results,seismic effectiveness evaluation indexes of the tie up method are proposed.Reasonable suggestions for fixed strategies are given,which provide a basis for the exhibition of delicate museum collections considering the principle of minimizing seismic responses and intervention.The analysis results show that a larger ratio of height of mass center to bottom diameter led to more intense rocking responses.Increasing the initial pretension of fishing lines was conducive to reducing the seismic responses and stress variation of the lines.Through comprehensive consideration of the interaction forces and effective securement,it is recommended to apply 20%of breaking stress as the initial pretension.For specific museum collections that cannot be effectively protected by the independent tie up method,an optimized strategy of a combination of fishing lines and fasteners is recommended.

A joint absorbing boundary for the multiple-relaxation-time lattice Boltzmann method in seismic acoustic wavefield modeling

Conventional seismic wave forward simulation generally uses mathematical means to solve the macroscopic wave equation,and then obtains the corresponding seismic wavefield.Usually,when the subsurface structure is finely constructed and the continuity of media is poor,this strategy is difficult to meet the requirements of accurate wavefield calculation.This paper uses the multiple-relaxation-time lattice Boltzmann method(MRT-LBM)to conduct the seismic acoustic wavefield simulation and verify its computational accuracy.To cope with the problem of severe reflections at the truncated boundaries,we analogize the viscous absorbing boundary and perfectly matched layer(PML)absorbing boundary based on the single-relaxation-time lattice Boltzmann(SRT-LB)equation to the MRT-LB equation,and further,propose a joint absorbing boundary through comparative analysis.We give the specific forms of the modified MRT-LB equation loaded with the joint absorbing boundary in the two-dimensional(2D)and three-dimensional(3D)cases,respectively.Then,we verify the effects of this absorbing boundary scheme on a 2D homogeneous model,2D modified British Petroleum(BP)gas-cloud model,and 3D homogeneous model,respectively.The results reveal that by comparing with the viscous absorbing boundary and PML absorbing boundary,the joint absorbing boundary has the best absorption performance,although it is a little bit complicated.Therefore,this joint absorbing boundary better solves the problem of truncated boundary reflections of MRT-LBM in simulating seismic acoustic wavefields,which is pivotal to its wide application in the field of exploration seismology.

Generalized response displacement methods for seismic analysis of underground structures with complex cross section

The response displacement method(RDM)is recommended for the seismic analysis of underground structures in the transverse direction for many codes,including bases for design of structures-seismic actions for designing geotechnical works(ISO 23469)and code for seismic design of urban rail transit structures(GB 50909-2014).However,there are some obvious limitations in the application of RDM.Springs and the shear stress of the soil could be approximately evaluated for the structures having a simple cross section,such as rectangular and circular structures.It is necessary to propose simplified seismic analysis methods for structures with complex cross sections.This paper refers to the idea of RDM and proposes three generalized response displacement methods(GRDM).In GRDM1,a part of the soil surrounding a structure is selected to generate a generalized underground structure with a rectangular cross section,and the same analysis model as RDM is applied to analyze the responses of the structure.In GRDM2,a hollow soil model without a generalized structure is used to compute the equivalent load caused by the relative displacement of the soil,and the soil-structure interaction model is applied to calculate the responses of the structure.In GRDM3,a continuous soil model is applied to compute the equivalent load caused by the relative displacement and shear stress of the soil,and the soil-structure interaction model is applied to analyze the responses of the structure,which is the same as the model used in GRDM2.The time-history analysis method(THAM)is used to evaluate the accuracy of the proposed simplified methods.Results show that the error of GRDM1 is about 20%,while the error is only 5%for GRDM2 and GRDM3.Among the three proposed methods,GRDM3 has obvious advantages regarding calculation efficiency and accuracy.Therefore,it is recommended to use GRDM3 for the seismic response analysis of underground structures that have conventional simple or complex cross sections.

A review of the wave gradiometry method for seismic imaging

As dense seismic arrays at different scales are deployed,the techniques to make full use of array data with low computing cost become increasingly needed.The wave gradiometry method(WGM)is a new branch in seismic tomography,which utilizes the spatial gradients of the wavefield to determine the phase velocity,wave propagation direction,geometrical spreading,and radiation pattern.Seismic wave propagation parameters obtained using the WGM can be further applied to invert 3D velocity models,Q values,and anisotropy at lithospheric(crust and/or mantle)and smaller scales(e.g.,industrial oilfield or fault zone).Herein,we review the theoretical foundation,technical development,and major applications of the WGM,and compared the WGM with other commonly used major array imaging methods.Future development of the WGM is also discussed.

An extended multiple-support response spectrum method incorporating fluid-structure interaction for seismic analysis of deep-water bridges

The effects of ground motion spatial variability(GMSV)or fluid-structure interaction(FSI)on the seismic responses of deep-water bridges have been extensively examined.However,there are few studies on the seismic performance of bridges considering GMSV and FSI effects simultaneously.In this study,the original multiple-support response spectrum(MSRS)method is extended to consider FSI effect for seismic analysis of deep-water bridges.The solution of hydrodynamic pressure on a pier is obtained using the radiation wave theory,and the FSI-MSRS formulation is derived according to the random vibration theory.The influence of FSI effect on the related coefficients is analyzed.A five-span steel-concrete continuous beam bridge is adopted to conduct the numerical simulations.Different load conditions are designed to investigate the variation of the bridge responses when considering the GMSV and FSI effects.The results indicate that the incoherence effect and wave passage effect decrease the bridge responses with a maximum percentage of 86%,while the FSI effect increases the responses with a maximum percentage of 26%.The GMSV and FSI effects should be included in the seismic design of deep-water bridges.

Comparative Analysis of Application of Seismic Wave Reflection Method in Advanced Geological Prediction

Seismic wave reflection method is an advanced geophysical detection method in tunnel geological prediction.It is more sensitive and effective in detecting geological anomalies such as fault fracture zone and karst.In order to verify the prediction efficacy and accuracy of the seismic wave reflection method with different instruments and equipment(tunnel geological prediction[TGP]/tunnel seismic prediction[TSP])and different vibration modes(hammering,explosives),a comparison test was carried out in Jinping Tunnel.The test results showed that the time-consumption of the hammering source was short,which can greatly reduce the impact on the construction site;different vibration sources methods of seismic wave reflection can predict the unfavorable geological sections accurately.

Impact of surface-reflected seismic waves on the seismic isolation performance of circular tunnel isolation layers

Seismic isolation is an effective strategy to mitigate the risk of seismic damage in tunnels.However,the impact of surface-reflected seismic waves on the effectiveness of tunnel isolation layers remains under explored.In this study,we employ the wave function expansion method to provide analytical solutions for the dynamic responses of linings in an elastic half-space and an infinite elastic space.By comparing the results of the two models,we investigate the seismic isolation effect of tunnel isolation layers induced by reflected seismic waves.Our findings reveal significant differences in the dynamic responses of the lining in the elastic half-space and the infinitely elastic space.Specifically,the dynamic stress concentration factor(DSCF)of the lining in the elastic half-space exhibits periodic fluctuations,influenced by the incident wave frequency and tunnel depth,while the DSCF in the infinitely elastic space remain stable.Overall,the seismic isolation application of the tunnel isolation layer is found to be less affected by surface-reflected seismic waves.Our results provide valuable insights for the design and assessment of the seismic isolation effect of tunnel isolation layers.

Comparison between seismic analysis of twisting and regular 52-story towers considering soil-structure interaction

A dynamic analysis of both twisting and regular towers is carried out to determine the results of considering soil-structure interaction(SSI)on high-rise buildings.In addition,the difference between the seismic performance of using twisting towers over regular ones is investigated.The twisting tower is a simulation of the Evolution Tower(Moscow).The towers’skeletons consist of RC elements and rest on a reinforced concrete piled-raft foundation.The soil model is considered as multi-layered with the same soil properties as the zone chosen for the analysis(New Mansoura City,Egypt).The only difference between both towers is their shape in elevation.The whole system is modelled and analyzed in a single step as one full 3D model,which is known as the direct approach in SSI.All analyses are carried out using finite-element software(Midas GTS NX).Dynamic output responses due to three records of seismic loads are proposed and presented in some graphs.Based on the results,it is concluded that SSI has a considerable effect on the dynamic response of tall buildings mainly because of the foundation flexibility,as it leads to lengthening the vibration period,increasing the story drift and the base shear for both cases.

Numerical investigation of the effects of soil-structure and granular material-structure interaction on the seismic response of a flat-bottom reinforced concrete silo

In this work,a numerical study of the effects of soil-structure interaction(SSI)and granular material-structure interaction(GSI)on the nonlinear response and seismic capacity of flat-bottomed storage silos is conducted.A series of incremental dynamic analyses(IDA)are performed on a case of large reinforced concrete silo using 10 seismic recordings.The IDA results are given by two average IDA capacity curves,which are represented,as well as the seismic capacity of the studied structure,with and without a consideration of the SSI while accounting for the effect of GSI.These curves are used to quantify and evaluate the damage of the studied silo by utilizing two damage indices,one based on dissipated energy and the other on displacement and dissipated energy.The cumulative energy dissipation curves obtained by the average IDA capacity curves with and without SSI are presented as a function of the base shear,and these curves allow one to obtain the two critical points and the different limit states of the structure.It is observed that the SSI and GSI significantly influence the seismic response and capacity of the studied structure,particularly at higher levels of PGA.Moreover,the effect of the SSI reduces the damage index of the studied structure by 4%.

Seismic safety assessment with non-Gaussian random processes for train-bridge coupled systems

Extensive high-speed railway(HSR)network resembled the intricate vascular system of the human body,crisscrossing mainlands.Seismic events,known for their unpredictability,pose a significant threat to both trains and bridges,given the HSR’s extended operational duration.Therefore,ensuring the running safety of train-bridge coupled(TBC)system,primarily composed of simply supported beam bridges,is paramount.Traditional methods like the Monte Carlo method fall short in analyzing this intricate system efficiently.Instead,efficient algorithm like the new point estimate method combined with moment expansion approximation(NPEM-MEA)is applied to study random responses of numerical simulation TBC systems.Validation of the NPEM-MEA’s feasibility is conducted using the Monte Carlo method.Comparative analysis confirms the accuracy and efficiency of the method,with a recommended truncation order of four to six for the NPEM-MEA.Additionally,the influences of seismic magnitude and epicentral distance are discussed based on the random dynamic responses in the TBC system.This methodology not only facilitates seismic safety assessments for TBC systems but also contributes to standard-setting for these systems under earthquake conditions.

Seismic Design Strategy of High Pier Bridge

China’s infrastructure construction has been continuously improving in recent years,especially its highway construction,which spans from north to south and connects east to west.Some special areas are also interconnected through bridges,but constructing highway bridges through complex terrains or across valleys and mountain gullies presents significant challenges,requiring an increase in the height of bridge piers.These bridge piers generally reach tens or even hundreds of meters in height.Furthermore,the construction of these high-pier bridges is becoming increasingly widespread.Not only do they pose greater construction challenges,but they also have higher requirements for seismic resistance.This article primarily analyzes the characteristics of high-pier bridges and proposes seismic design schemes,calculation methods,and design strategies to enhance the construction quality of high-pier bridges.

The Ultimate Anti-Seismic Design Method

The design mechanisms and methods of the invention are intended to minimize problems related to the safety of structures in the event of natural phenomena such as earthquakes, tornadoes, and strong winds. It is achieved by controlling the deformations of the structure. Damage and deformation are closely related concepts since the control of deformations also controls the damage. The design method of applying artificial compression to the ends of all longitudinal reinforced concrete walls and, at the same time, connecting the ends of the walls to the ground using ground anchors placed at the depths of the boreholes, transfers the inertial stresses of the structure in the ground, which reacts as an external force in the structure’s response to seismic displacements. The wall with the artificial compression acquires dynamic, larger active cross-section and high axial and torsional stiffness, preventing all failures caused by inelastic deformation. By connecting the ends of all walls to the ground, we control the eigenfrequency of the structure and the ground during each seismic loading cycle, preventing inelastic displacements. At the same time, we ensure the strong bearing capacity of the foundation soil and the structure. By designing the walls correctly and placing them in proper locations, we prevent the torsional flexural buckling that occurs in asymmetrical floor plans, and metal and tall structures. Compression of the wall sections at the ends and their anchoring to the ground mitigates the transfer of deformations to the connection nodes, strengthens the wall section in terms of base shear force and shear stress of the sections, and increases the strength of the cross-sections to the tensile at the ends of the walls by introducing counteractive forces. The use of tendons within the ducts prevents longitudinal shear in the overlay concrete, while anchoring the walls to the foundation not only dissipates inertial forces to the ground but also prevents rotation of the walls, thus maintaining the structural integrity of the beams. The prestressing at the bilateral ends of the walls restores the structure to its original position even inelastic displacements by closing the opening of the developing cracks.

Seismic wave input method for three-dimensional soil-structure dynamic interaction analysis based on the substructure of artificial boundaries

The method of inputting the seismic wave determines the accuracy of the simulation of soil-structure dynamic interaction. The wave method is a commonly used approach for seismic wave input, which converts the incident wave into equivalent loads on the cutoff boundaries. The wave method has high precision, but the implementation is complicated, especially for three-dimensional models. By deducing another form of equivalent input seismic loads in the fi nite element model, a new seismic wave input method is proposed. In the new method, by imposing the displacements of the free wave fi eld on the nodes of the substructure composed of elements that contain artifi cial boundaries, the equivalent input seismic loads are obtained through dynamic analysis of the substructure. Subsequently, the equivalent input seismic loads are imposed on the artifi cial boundary nodes to complete the seismic wave input and perform seismic analysis of the soil-structure dynamic interaction model. Compared with the wave method, the new method is simplifi ed by avoiding the complex processes of calculating the equivalent input seismic loads. The validity of the new method is verifi ed by the dynamic analysis numerical examples of the homogeneous and layered half space under vertical and oblique incident seismic waves.

Modeling seismic wave propagation in heterogeneous medium using overlap domain pseudospectral method

Pseudospectral method is an efficient and high accuracy numerical method for simulating seismic wave propaga- tion in heterogeneous earth medium. Since its derivative operator is global, this method is commonly considered not suitable for parallel computation. In this paper, we introduce the parallel overlap domain decomposition scheme and give a parallel pseudospectral method implemented on distributed memory PC cluster system for modeling seismic wave propagation in heterogeneous medium. In this parallel method, the medium is decomposed into several subdomains and the wave equations are solved in each subdomain simultaneously. The solutions in each subdomain are connected through the transferring at the overlapped region. Using 2D models, we compared the parallel and traditional pseudospectral method, analyzed the accuracy of the parallel method. The results show that the parallel method can efficiently reduce computation time for the same accuracy as the traditional method. This method could be applied to large scale modeling of seismic wave propagation in 3D heterogeneous medium.

Slope stability analysis under seismic load by vector sum analysis method

The vibration characteristics and dynamic responses of rock and soil under seismic load can be estimated with dynamic finite element method （DFEM）. Combining with the DFEM, the vector sum analysis method （VSAM） is employed in seismic stability analysis of a slope in this paper. Different from other conventional methods, the VSAM is proposed based on the vector characteristic of force and current stress state of the slope. The dynamic stress state of the slope at any moment under seismic load can he obtained by the DFEM, thus the factor of safety of the slope at any moment during earthquake can be easily obtained with the VSAM in consideration of the DFEM. Then, the global stability of the slope can be estimated on the basis of time-history curve of factor of safety and reliability theory. The VSAM is applied to a homogeneous slope under seismic load. The factor of safety of the slope is 1.30 under gravity only and the dynamic factor of safety under seismic load is 1.21. The calculating results show that the dynamic characteristics and stability state of the slope with input ground motion can be actually analyzed. It is believed that the VSAM is a feasible and practical approach to estimate the dynamic stability of slopes under seismic load.

An improved pseudo-static method for seismic resistant design of underground structures

This paper describes a commonly used pseudo-static method in seismic resistant design of the cross section of underground structures. Based on dynamic theory and the vibration characteristics of underground structures, the sources of errors when using this method are analyzed. The traditional seismic motion loading approach is replaced by a method in which a one-dimensional soil layer response stress is differentiated and then converted into seismic live loads. To validate the improved method, a comparison of analytical results is conducted for internal forces under earthquake shaking of a typical shallow embedded box-shaped subway station structure using four methods： the response displacement method, finite element response acceleration method, the finite element dynamic analysis method and the improved pseudo-static calculation method. It is shown that the improved finite element pseudo-static method proposed in this paper provides an effective tool for the seismic design of underground structures. The evaluation yields results close to those obtained by the finite element dynamic analysis method, and shows that the improved finite element pseudo-static method provides a higher degree of precision.

Efficient structural seismic performance evaluation method using improved endurance time analysis

Evaluation of structural performance under seismic excitations from low intensity to high intensity is essential to verify the seismic resistant capacity of a structure, and usually carried out by the incremental dynamic analysis (IDA) method or pushover method. The recently developed endurance time (ET) method is another method that uses dynamic pushover excitations, i.e., endurance time acceleration function, to obtain results similar to those obtained by IDA or pushover methods with low computational cost and acceptable accuracy. This study proposes an improvement on the ET method by considering more restrictions for both the elastic and inelastic response spectra in the generation procedure, and by specifying a target duration. Four reinforced concrete frame structures with 4, 8, 12, and 16 stories are adopted to verify the accuracy of the improved method. Comparison of the results obtained by the proposed method, the ET method and the IDA method shows that the improved method has a higher accuracy than the ET method. For evaluation of structural responses under specifi c ground motion intensity, which is typically required in seismic design codes, the results obtained by the proposed method are compared with fi ve commonly used ground motion selection methods, and shows the proposed method provides acceptable accuracy for engineering applications.

Seismic assessment of unanchored steel storage tanks by endurance time method

Liquid storage tanks are essential structures that are often located in residential and industrial areas; thus an assessment of their seismic performance is an important engineering issue. In this paper, the seismic response ofunanchored steel liquid storage tanks is investigated using the endurance time （ET） dynamic analysis procedure and compared to responses obtained for anchored tanks under actual ground motions and intensifying ET records. In most cases, the results from ground motions are properly obtained with negligible differences using ET records. It is observed that uplifting of the tank base, which is closely related to the tank aspect ratio, has the greatest significance in the responses of the tank and can be predicted with reasonable accuracy by using currently available ET records.

Accelerating the discontinuous Galerkin method for seismic wave propagation simulations using multiple GPUs with CUDA and MPI

We have successfully ported an arbitrary highorder discontinuous Galerkin method for solving the threedimensional isotropic elastic wave equation on unstructured tetrahedral meshes to multiple Graphic Processing Units （GPUs） using the Compute Unified Device Architecture （CUDA） of NVIDIA and Message Passing Interface （MPI） and obtained a speedup factor of about 28.3 for the single-precision version of our codes and a speedup factor of about 14.9 for the double-precision version. The GPU used in the comparisons is NVIDIA Tesla C2070 Fermi, and the CPU used is Intel Xeon W5660. To effectively overlap inter-process communication with computation, we separate the elements on each subdomain into inner and outer elements and complete the computation on outer elements and fill the MPI buffer first. While the MPI messages travel across the network, the GPU performs computation on inner elements, and all other calculations that do not use information of outer elements from neighboring subdomains. A significant portion of the speedup also comes from a customized matrix-matrix multiplication kernel, which is used extensively throughout our program. Preliminary performance analysis on our parallel GPU codes shows favorable strong and weak scalabilities.