Seismic Response Analysis Method Research Articles

A Review on Seismic Response Analysis Methods for Underground Structures

Seismic safety of underground structures is of paramount importance. This paper reviews the current research status of seismic response analysis methods for underground structures, focuses on the basic principles, advantages and disadvantages, and applicability of the proposed static method and dynamic time course analysis method. It also analyses their applications in engineering. It is shown that the seismic coefficient method, although simple, may have relatively large calculation errors due to oversimplification. The free-field deformation method is simple in form and easy to implement, but ignores soil-structure interaction. The flexibility coefficient method is simple in form and considers soil-structure interaction, but ignores many factors. The reaction displacement method directly reflects the soil-structure interaction, but the foundation spring parameters are difficult to value. The reaction acceleration method has the same advantages as the reaction displacement method, but there is a certain error. The dynamic time-course analysis method is accurate but computationally intensive.

Influence of spatial variability of soil shear-wave velocity considering intralayer correlation on seismic response of engineering site

Shear-wave velocity uncertainty significantly impacts seismic response analysis at engineering sites. Previous studies focused on the correlations of shear-wave velocities within soil layers. However, the influence of the vertical spatial variability of shear-wave velocity within individual soil layers was not considered. This study selected a typical Site Class II engineering site to investigate this influence based on the equivalent linear seismic response analysis method of layered soil deposits. Existing field test data on shear-wave velocity were used to discretize the shear-wave velocity within soil layers into a one-dimensional (1D) random field through covariance matrix decomposition and local average process theory. Monte Carlo simulations generated random shear-wave velocity profiles with different vertical correlation distances. Three artificial records with different earthquake return periods were used as input motions at the engineering bedrock for the 1D free-field model. Considering soil shear-wave velocity uncertainty, the peak shear strain increased by 19–27% with the input ground motion amplitude. Moreover, the site peak shear strain variability increased by 25–34% with the vertical correlation distance. The proposed 1D random field model effectively simulated the interlayer correlation and spatial variability of shear-wave velocity within soil layers, demonstrating its significance in seismic response analysis.

Transformation of the Equivalent Linear Method for solving soil-structure interaction problems in the time domain

Transformation of the Equivalent Linear Method for solving soil-structure interaction problems in the time domain

Static and Dynamic Analysis of Coupled Vibration of Suspension Bridge Structure Under Earthquake Action

This article investigates the coupled vibration problem of suspension bridge structures under earthquake action, and conducts static and dynamic analysis using computer algorithms. In terms of static analysis, complex structures are divided into many small elements, and the stress and deformation of each element are calculated through finite element analysis, thereby obtaining the static characteristics of the entire structure. In terms of dynamic analysis, the seismic response analysis method based on time history considers seismic action as a time-varying external excitation, and calculates and simulates the dynamic response of the suspension bridge structure. In order to achieve efficient and accurate calculations, this article also adopts optimization algorithms and numerical calculation methods. Through a comprehensive study of statics and dynamics analysis, the key characteristics and regularities of coupled vibration of suspension bridge structures under earthquake action have been obtained. These research results not only provide important theoretical guidance and technical support for related engineering practices, but also provide useful references and inspirations for dynamic analysis and optimization design of similar structures. Meanwhile, using computer algorithms and simulation software for static and dynamic analysis can significantly reduce analysis costs and time, improve analysis accuracy and efficiency, and have broad application prospects.

A Simplified Approach of Analytical Seismic Fragility Analysis Using the Endurance Time Method

ABSTRACT The endurance time (ET) method is an effective dynamic analysis method for seismic response analysis of structures. It has been recently used for analytical fragility analysis. However, the available ET-based fragility analysis methods have two limitations: 1) the prediction error of the structural median responses estimated by the ET method is ignored; and 2) the record-to-record variability inherent earthquake ground motions is not well considered. To overcome the above limitations, another ET-based fragility analysis method is proposed, where only three times of ET nonlinear analyses are required. To do this, three specific endurance time excitation functions (ETEFs) are generated in correspondence to the mean and 16% and 84% percentile of response spectra of a selected suite of ground motion records (i.e. ETE F m , ETE F v 1 and ETE F v 2 , respectively). The structural response under ETE F m is used to estimate the median response of structures under the selected suite of ground motion. Moreover, the structural responses under ETE F v 1 and ETE F v 2 are used to quantify the record-to-record variability in earthquake ground motions. The fragility relationships are developed by both point and interval estimate methods since another logarithmic standard deviation is introduced to account for the difference between the median responses predicted using ETE F m and those predicted by the dynamic analysis. To validate the proposed method, two RC frame structures with six and nine stories are taken as the study cases. The fragility results based on the proposed ET-based method and those based on the cloud method are compared. It is found that the proposed ET-based fragility analysis method could generate reliable fragility estimation, whereas requiring limited computation cost. The proposed method would provide another simplified way for the rapid fragility assessment of structures.

The inter‐history iteration method for seismic response analysis of seismically isolated structures and its secondary development based on ABAQUS

SummaryIn seismic response analysis of seismically isolated structures (SISs), the nonlinearity is concentrated in the isolation layer while the upper structure behaves linearly, making SISs locally nonlinear systems. This paper proposed a novel seismic analysis method based on equivalent linearization (EL) and iterative solution for SISs. In this method, the equilibrium equations of an SIS are expressed by the second‐order ordinary differential equations of the structural system as well as the hysteretic force of seismic isolation bearings (SIBs). Based on EL theory, the linearized equilibrium equations of the overall system were reconstructed in which the EL parameters are derived theoretically. The inter‐history iteration (IHI) method was proposed to solve the linearized equation system and calculate the EL parameters in sequence iteratively for seismic response analysis of SISs, thus reducing computational cost without excessive loss of accuracy. In addition, the secondary development of the proposed method was programmed in ABAQUS for ease of engineering applications. Finally, the convergence and accuracy of the method were investigated through numerical simulation of an SIS case study. As the numerical investigation indicates, the proposed method considers the coupling between structural response and the EL parameters, achieving a high convergence rate and satisfactory solution accuracy. The ABAQUS secondary development program utilizes the powerful pre‐processor, post‐processor, and solvers of ABAQUS, making the IHI method more appropriate for engineering applications.

Simplified Method for Nonlinear Seismic Response Analysis of Corroded Pile-Supported Wharf

Fiber-based finite element analysis (FB-FEA) has been widely recognized for its ability to reproduce experimental results and is also a reliable method for evaluating the nonlinear seismic response of pile-supported wharves (PSWs). Design practice often employs frame analysis (FA) due to its easy implementation. To precisely reproduce the nonlinear seismic response of PSW using FA, it is necessary to configure mechanical properties such as the hinge property correctly. However, it is unclear whether the hinge properties proposed in previous studies can be applied to PSWs with spun piles. In this study, a novel FA method was developed to investigate the nonlinear seismic response of PSWs with corroded spun piles considering PC bar area reduction, deteriorated material properties, the bending stiffness reduction factor, and the moment–curvature relationship of the spun pile. The nonlinear seismic response of corroded PSWs was determined by performing pushover analysis using three methods: FA using the method of the previous study (FA-1), the proposed FA method (FA-2), and FB-FEA. As regards PSW foundations, vertical pile and batter pile configurations were considered. The pushover analysis results were compared in terms of several parameters, such as the natural period, plastic hinge formation, and load capacity of the corroded PSWs. The FA-2 results agreed very well with the FB-FEA results, while the FA-1 results were less precise with respect to the natural periods and load capacities of corroded PSWs. The results indicated that the bending stiffness reduction factor, moment–curvature relationship, and axial load–bending moment (P–M) capacity of the corroded spun piles should be appropriately defined. Corrosion had greater negative impacts on the compressive axial load and bending moment capacities of the spun pile than on its tensile axial load capacity.

A novel Woodbury solution method for nonlinear seismic response analysis of large‐scale structures

AbstractThe Woodbury formula is an efficient tool in mathematics to calculate low‐rank perturbation problems and has been applied to improve the computational efficiency of nonlinear seismic response analysis (NSRA) of structures with local nonlinearity. Using the Woodbury formula for NSRA can avoid the time‐consuming recalculation and factorization of the large‐dimensional global stiffness matrix of a structure by only solving a small‐dimensional Schur complement system representing local nonlinearity per iteration. Because the dimension of the Schur complement matrix is determined by the inelastic degree of freedom (IDOF) number, which represents the scale of local nonlinear regions, a small IDOF number is helpful for achieving the high‐efficiency advantage of the Woodbury formula. However, when performing NSRA for large‐scale structures, the IDOF number is usually relatively large, which contradicts the efficiency requirement of the Woodbury formula. To solve this problem and extend the advantage of the Woodbury formula to the NSRA of large‐scale structures, this paper first proposes a two‐stage IDOF number reduction method by eliminating the IDOFs that have insignificant effects on the results, and consequently, a variant Woodbury formula is derived. Because only the principal component in the Schur complement matrix is retained, the dimension of this matrix and the cost for factorizing it can be reduced significantly without losing accuracy, thus greatly improving the efficiency of the proposed method. Moreover, to reduce the additional computational time introduced by the IDOF number reduction procedure and to further improve the computational performance of the proposed method, an OpenMP parallel computational strategy is incorporated. Finally, the validity of the proposed method is verified by implementing incremental dynamic analysis for a large‐scale reinforced concrete structure.

A real-time approach to structural seismic response analysis

This paper presents a real-time seismic response analysis method based on the Proper Orthogonal Decomposition (POD) and Proper Generalized Decomposition (PGD) theories. Initially, the damping matrix and ground motion load are incorporated using the parametric form of the solid dynamic equation. By leveraging the POD method, the computational challenge arising from the high number of parameters in the equation (one parameter for each degree of freedom of the entire model) is overcome, enabling the calculation of complex computational models. Subsequently, the proposed method's effectiveness, stability, and accuracy are demonstrated through the analysis of various seismic waves characterized by different magnitudes, durations, and frequencies. Furthermore, the method successfully achieves real-time response feedback of the structure to arbitrary seismic waves. Importantly, this approach exhibits significant potential for engineering applications.

Seismic Performance Assessment of Pile-Supported Wharfs: 2D Frame Analysis Method Considering Both Inertial and Kinematic Forces

Frame analysis (FA) is known for its efficiency and low computer resource requirements. However, compared to finite element analysis (FEA), the applicability of FA for the seismic performance assessment of pile-supported wharves (PSWs) is limited, particularly in the ability to account for the kinematic force caused by ground displacement during an earthquake. This study aimed to develop a two-dimensional FA method for PSW seismic response analysis that considers a combination of inertial and kinematic forces. We performed FA and FEA and compared the results. First, we targeted the PSW model without considering the soil slope and discussed the spectral acceleration (SA) evaluation method for calculating inertial force. As a result, an equation for estimating a damping coefficient to evaluate the SA in accordance with the PSW width and natural period was proposed. Next, we targeted the PSW model by considering the soil slope and proposed a method to evaluate the kinematic force based on the amount of ground displacement and the soil spring characteristics. The results revealed that using the proposed method, FA, by considering kinematic and inertial forces, could reproduce the bending moments of the piles comparable to those calculated using FEA. Therefore, solely considering the inertial force for a PSW on a soil slope may cause the bending moment to be underestimated.

Seismic Response of Cable-Stayed Spanning Pipeline Considering Medium-Pipeline Fluid–Solid Coupling Dynamic Effect

With the aim of determining the influence of the fluid–structure coupling dynamic effect of the oil and gas transmission medium and pipeline on the seismic response, an oil pipeline supported by a cable-stayed spanning structure was taken as the study object. Kinetic equations taking into account the action of oil and gas medium were studied, and a finite element model structure considering the additional-mass method and the fluid–structure coupling effect were established separately. In addition, the mechanism of the oil–gas–pipeline coupling action on the seismic response of pipeline structure was analyzed, and the results were obtained. The results show that the pipeline has a minimal seismic response at the abutment location, the seismic response gradually increases along the abutment to the main tower, and the seismic response reach is maximized at about one-fifth of the bridge platform. The seismic response of the oil and gas pipeline model structure using the additional-mass method is generally more significant than that based on the fluid–solid coupled dynamic model; moreover, the maximum displacement response differs by about 24%, and the maximum acceleration response differs by approximately 30%, indicating that the oil and gas medium has a certain viscoelastic damping effect on the seismic response of the oil pipeline, which provides a reference for the seismic response calculation theory and analysis method of cable-stayed spanning oil pipelines.

A novel strong ground motion duration to reduce computation time of structural time history analysis

As a widely used dynamic computation method for seismic response analysis of structures, time history analysis (THA) can be a time-consuming procedure in some situations. In order to reduce the calculation time, this study proposed a novel strong ground motion duration which can truncate the head and tail weak signals of records before THA. The initial point of proposed duration refers to the concept of bracketed duration, while the termination point is determined by the maximum displacement responses of equivalent single-degree-of-freedom (SDOF) systems of the structure. The relationship between the fundamental period and period-lengthening level of structure is counted from previous research and fitted with a formula which is used to compute the period range of equivalent SDOF systems. After comparing the structural responses and time-saved percentage of truncated records by proposed duration with those by other definition of durations, results prove that the proposed duration has significant time-saving procedure and reliable computation results on THA.

Exact artificial boundary condition and 1D time-domain method for seismic response analysis of layered saturated poroelastic half-space

This study proposed a one-dimensional (1D) time-domain finite element method (FEM) for seismic response analysis of a layered saturated soil half-space under obliquely incident plane waves, based on Biot's u-w wave equations. The spatially two-dimensional problem was transformed into an equivalent 1D time-domain problem along the depth according to Snell's law. An exact artificial boundary condition for saturated poroelastic media was developed to simulate the wave absorption and input effects of the truncated half-space. Using the displacement and stress continuity conditions between the adjacent saturated poroelastic-medium layers and combining all finite elements and the exact artificial boundary condition, the total dynamic equation for the spatially 1D problem was obtained. The 1D dynamic equation was solved using the FEM with explicit time integration. The proposed method was verified by analyzing two engineering sites in the time domain and a comparison with the frequency-domain transfer matrix method with fast Fourier transform.

A comparative analysis of seismic response of shallow buried underground structure under incident P, SV and Rayleigh waves

In this study, A time-domain seismic response analysis method and a calculation model of the underground structure that can realize the input of seismic P, SV and Rayleigh waves are established, based on the viscoelastic artificial boundary elements and the boundary substructure method for seismic wave input. After verifying the calculation accuracy, a comparative study on seismic response of a shallow-buried, double-deck, double-span subway station structure under incident P, SV and Rayleigh waves is conducted. The research results show that there are certain differences in the cross-sectional internal force distribution characteristics of underground structures under different types of seismic waves. The research results show that there are certain differences in the internal force distribution characteristics of underground structures under different types of seismic waves. At the bottom of the side wall, the top and bottom of the center pillar of the underground structure, the section bending moments of the underground structure under the incidences of SV wave and Rayleigh wave are relatively close, and are significantly larger than the calculation result under the incidence of P wave. At the center of the side wall and the top floor of the structure, the peak value of the cross-sectional internal force under the incident Rayleigh wave is larger than the calculation result under SV wave. In addition, the floor of the underground structure under Rayleigh waves vibrates in both the horizontal and vertical directions, and the magnification effect in the vertical direction is more significant. Considering that the current seismic research of underground structures mainly considers the effect of body waves such as the shear waves, sufficient attention should be paid to the incidence of Rayleigh waves in the future seismic design of shallow underground structures.

Parallel partitioned method of seismic response analysis for seawater-seabed-bridge system

我国沿海地区有多座已建或在建的跨海大桥，由于其位于环太平洋地震带上，地震较为频发，如何保障这些跨海大桥的地震安全十分重要。然而，跨海大桥地震反应分析涉及到海水-海床-桥梁的相互作用，问题十分复杂，目前仍缺乏高效的分析方法。本文将地震作用下海水-海床-桥梁系统的反应分析问题看作是地震波经基岩、海床、海水入射到跨海桥梁的散射分析问题，发展了一套地震作用下海水-海床-桥梁系统反应分析的高效方法，并编制了相关分析程序。首先，采用传递矩阵方法得到地震波入射时海水-海床-基岩水平成层场地的自由场，结合人工边界条件，实现地震波散射分析的输入；其次，将海水、饱和海床、基岩采用广义饱和多孔介质模型统一进行描述，将海域场地中海水、饱和海床、基岩间的耦合分析统一在广义饱和多孔介质模型计算框架下，并通过集中质量显式有限元方法实现，可避免不同介质及方程之间的相互耦合，实现海域场地的高效有限元分析；然后，将海域场地-桥梁系统进行分区，海域场地和桥梁分别建模，并选择适合各自特点的分析方法和计算时间步距，实现海域场地-桥梁相互作用的分区并行分析。最后，以港珠澳大桥青州航道桥为例，根据港珠澳大桥青州航道桥地震设防标准、所处海域条件，采用调幅后的3条实际地震动记录作为输入，分析了青州航道桥的地震响应特征。

Extending the Performance-Based Design Method for Seismic Response Analysis of Self-Centering Structures

Extending the Performance-Based Design Method for Seismic Response Analysis of Self-Centering Structures

Effects of temperature, analysis and modelling uncertainties on the reliability of base-isolated bridges in Eastern Canada

The seismic response of base-isolated bridges depends strongly on the seismic isolation system (SIS) properties, which typically vary under the effect of multiple conditions, such as temperature. The North American Bridge Design Codes and the EN-Eurocode 8 recommend a bounding analysis method in order to consider the effect of SIS properties variation with different conditions. However, this method is not founded on a rigorous probabilistic approach, and thus does not impact the reliability of base-isolated bridges. This paper presents an estimate of the seismic reliability and its variation range for a typical two-span concrete base-isolated bridge located in Montreal, a typical site for Eastern Canada. Temperature, bidirectional horizontal seismic hazard and the main parameters affecting the resistance of bridge components, specifically, dimensions, material properties of the bridge pier and SIS properties are all modelled as Random Variables (RVs). Bridge failure associated with two limit states is examined: (1) damage at the pier base by lack of bending moment capacity and (2) SIS failure due to a lack of displacement capacity. The Monte-Carlo method is used to evaluate each limit state’s reliability and probability of failure. In earlier studies, epistemic uncertainties (EUs) associated with the modelling and seismic analysis method were either ignored or not thoroughly considered. A main innovation of the present study is to include EUs associated with the seismic response analysis method and the lead core heating of the lead rubber bearing SIS are modelled as RVs. Their margins of variation are estimated, and their probabilistic distribution parameters are identified. The effects of these EUs on the reliability of the bridge are investigated. The effect of the natural rubber material type on the reliability of the bridge is also studied. Preliminary results show that, due to any of these uncertainties, the global reliability index is within a range of [3.36–3.62], whereas the reliability index when these EUs are not included is 3.49. When including the epistemic uncertainty associated with the response analysis method, the reliability index of the pier base flexural behaviour limit state varies between 3.52 and 3.76(as compared to a value of 3.56 obtained without including the above EUs). Similarly, when including the epistemic uncertainty associated with the heating effect, the reliability index of the SIS displacement limit state varies between 3.31, for an extreme effect, and 3.49 for a more representative effect (as compared toa value of 3.51 obtained without including the above EUs). Earlier studies considering fewer variability sources showed that the global seismic reliability varies between 3.47 and 3.52 for the same typical two-span base-isolated bridge in Montreal. In these studies, the SIS material and geometrical properties were considered deterministic. Other sites in Quebec have shown comparable reliabilities to those at the studied site, with a maximum variation of 3% between sites.

Research and development of vibration control device for sedimentation device with inclined plates

Water filtration plants are important facilities that support social infrastructure, and a sedimentation device with inclined plates installed in a sedimentation pool is one of the most important facilities to remove dust in the water efficiently in a slow water flow. Therefore, it is desirable that the sedimentation device is not damaged by the earthquake to ensure a continuous and stable supply of purified water even after a large earthquake. However, the sedimentation pool is a large structure, and seismic damage may be caused by sloshing of water in addition to the response of the sedimentation device itself. Thus, authors conduct research and development of a vibration control device for a sedimentation device. This paper proposes the installation of steel dampers in the upper frame of the sedimentation device to prevent seismic damage. A seismic response analysis method using a mass point system model was proposed to evaluate the performance of the vibration control device. Next the validity of the analysis method was confirmed by experiments. Then the vibration control performance was evaluated by seismic response analysis. As a result, the proposed vibration control device could suppress the response displacement of the sedimentation device and prevent collision with the side wall of the pool. Thus, the proposed vibration control device is effective as a seismic countermeasure for sedimentation devices.

A BOUNDARY FORCED RESPONSE DISPLACEMENT METHOD FOR SEISMIC ANALYSIS OF SYMMETRICAL UNDERGROUND STRUCTURES

A boundary forced response displacement method is proposed for the seismic analysis of symmetrical underground structures based on the requirement of quasi-static pushover test of soil-underground structure systems. The implementation procedure and special features of the method are introduced in detail. We took the Daikai subway station which was damaged during the Kobe earthquake in Japan as an example for the analysis, and compared the results of boundary forced response displacement method, the FEM seismic deformation method and the dynamic time-history analysis method. The results show that the accuracy of the new method was much higher than the FEM seismic deformation method when the width of the model was reasonable. The errors of the internal forces and the story drift were less than 15%. The new method is an effective simplified method for seismic response analysis of symmetrical underground structures. The attenuation law of lateral boundary forced displacement was analyzed. It provides references for the quasi-static pushover test of soil-underground structure system.

A practical method for seismic response analysis of nonlinear soil-structure interaction systems

Soil–structure interaction (SSI) plays an important role in the analysis of seismic structural responses. This study significantly extends an efficient linear SSI analysis method presented previously by the authors and co-workers to realistic nonlinear SSI systems, that is, systems with nonlinear soil, nonlinear structures, and flexible foundations (e.g. single- or multiple-pile foundations). The flexible foundations lying on half-space nonlinear soil are represented by frequency-dependent compliance functions that are fitted numerically instead of obtained by closed-form solution. These functions are then transferred to the time domain using the discrete-time recursive filtering method. A non-iterative algorithm is applied to guarantee the boundary conditions between soil and structure, that is, the displacement continuity and force equilibrium between them. The proposed method is implemented on an open-source FE software framework, called OpenSees. The accuracy and efficiency of the extended coupling method are investigated in detail through the seismic response analyses of typical soil–foundation–structure systems while considering the cases of linear or nonlinear soil, linear or nonlinear structures, and single- or multiple-pile foundations. Results show that the extended coupling method is significantly faster than the traditional FE method and provides acceptably accurate solutions for SSI systems with linear or low-to-moderate nonlinear soil. The paper provides a method for fast evaluation of nonlinear SSI effects in seismic structural response analysis.