Seismic Analysis Method Research Articles

Automatic stack velocity picking using a semi‐supervised ensemble learning method

AbstractPicking stack velocity from seismic velocity spectra is a fundamental method in seismic stack velocity analysis. With the increase in the scale of seismic data acquisition, manual picking cannot achieve the required efficiency. Therefore, an automatic picking algorithm is urgently needed now. Despite some supervised deep learning–based picking approaches that have been proposed, they heavily rely on sufficient training samples and lack interpretability. In contrast, utilizing physical knowledge to develop semi‐data‐driven methods has the potential to efficiently solve this problem. Thus, we propose a semi‐supervised ensemble learning method to reduce the reliance on manually labelled data and improve interpretability by incorporating the interval velocity constraint. Semi‐supervised ensemble learning fuses the information of the estimated spectrum, nearby velocity spectra and few‐shot manual picking to recognize the velocity picking. Test results of both the synthetic and field datasets indicate that semi‐supervised ensemble learning achieves more reliable and precise picking than traditional clustering‐based techniques and the currently popular convolutional neural network method.

Study on seismic risk assessment model of water supply systems in mainland China

Abstract. Using the peak ground acceleration (PGA) under four exceedance probabilities calculated via a probabilistic seismic hazard analysis method for China, the probability density function of PGA was obtained by fitting with the Cornell seismic hazard exceedance probability PGA function model. Combined with the seismic fragility function of the water supply system calculated on the basis of the empirical matrix of actual earthquake damage and the exposure of fixed assets, the expected seismic loss and expected loss rate models of the water supply system were established, and the classification standard with the expected seismic loss rate of the water supply system as the index was proposed. The seismic fragility of the water supply system was classified, and the exposure of the water supply system was analyzed. The total fixed assets in the Statistical Yearbook of Urban Water Supply, henceforth called Water Supply Yearbook, were taken as the exposure to earthquake in the region. The accuracy of the fragility model in this paper was verified through the actual earthquake damage losses in Deyang. Taking the water supply system of 720 cities in mainland China as an example, the distribution maps of expected seismic loss and expected loss rate were calculated and drawn. The expected loss rate model was verified by the key earthquake prevention areas in mainland China. The assessment model based on the expected loss and expected loss rate was taken as the seismic risk assessment model of water supply systems in mainland China.

A new performance‐based seismic design method using endurance time analysis for linked column frame system and a comparison of structural systems and seismic analysis methods

SummaryThis paper presents a new performance‐based seismic design method for the design of repairable linked column frame (LCF) and linked column system (LCS). Currently, the biggest problem of these systems is the lack of a simple and practical design method that leads to the design of optimal models with sufficient seismic capacity. The interaction of the primary and secondary systems, changing the lateral load pattern during an earthquake, and the implementation of the target performance objectives have complicated the design of these systems. The evaluations carried out in this research show that the rotation of link beams must be controlled in the design. Therefore, the ultimate plastic rotation of links is determined to be 0.01 rad for the seismic intensity of design base earthquake and 0.015 rad for maximum considered earthquake. The results show that the models designed using the presented method are optimal, have sufficient seismic capacity, and achieve the target performance objectives. In addition, although previous researches have shown that these systems have a suitable seismic behavior, their seismic behavior have not been compared with other structural systems. Comparing can show the behavioral characteristics of a new structural system; hence, the elastic and plastic behavior of the LCF and LCS models have been compared with other common steel structural systems using all analysis methods. Moreover, in the presented method for the design of LCF and LCS systems, nonlinear time history analysis using the endurance time method (ETM) is used, and due to the newness of the endurance time method, its results are compared with the median results of nonlinear time history analysis at different seismic hazard levels and incremental dynamic analysis (IDA), in 45 samples. The results show that the endurance time analysis is a reasonable and efficient method, and in this comparison, the difference between the results of ETM and IDA methods is 6% on average.

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 full‐probabilistic cloud analysis for structural seismic fragility via decoupled M‐PDEM

AbstractPerformance‐based earthquake engineering (PBEE) is essential for ensuring engineering safety. Conducting seismic fragility analysis within this framework is imperative. Existing methods for seismic fragility analysis often rely heavily on double loop reanalysis and empirical data fitting, leading to challenges in obtaining high‐precision results with a limited number of representative structural analysis instances. In this context, a new methodology for seismic fragility based on a full‐probabilistic cloud analysis is proposed via the decoupled multi‐probability density evolution method (M‐PDEM). In the proposed method, the assumption of a log‐normal distribution is not required. According to the random event description of the principle of preservation of probability, the transient probability density functions (PDFs) of intensity measure (IM) and engineering demand parameter (EDP), as key response quantities of the seismic‐structural system, are governed by one‐dimensional Li‐Chen equations, where the physics‐driven forces are determined by representative analysis data of the stochastic dynamic system. By generating ground motions based on representative points of basic random variables and performing structural dynamic analysis, the decoupled M‐PDEM is employed to solve the one‐dimensional Li‐Chen equations. This yields the joint PDF of IM and EDP, as well as the conditional PDF of EDP given IM, resulting in seismic fragility analysis outcomes. The numerical implementation procedure is elaborated in detail, and validation is performed using a six‐story nonlinear reinforced concrete (RC) frame subjected to non‐stationary stochastic ground motions. Comparative analysis against Monte Carlo simulation (MCS) and traditional cloud analysis based on least squares regression (LSR) reveals that the proposed method achieves higher computational precision at comparable structural analysis costs. By directly solving the physics‐driven Li‐Chen equations, the method provides the full‐probabilistic joint information of IM and EDP required for cloud analysis, surpassing the accuracy achieved by traditional methods based on statistical moment fitting and empirical distribution assumptions.

Conservativeness Study on the Seismic Analysis Method for Research Reactor Plant Structure Based on TMSR-LF1

The seismic performance analysis of research reactor plants is crucial for ensuring the safety of the entire reactor system. This paper analyzes the plant structure seismic performance of the 2WMt Thorium Molten Salt Reactor-Liquid Fuel 1 (TMSR-LF1) at the Shanghai Institute of Applied Physics, Chinese Academy of Sciences under the action of frequent earthquakes, fortification earthquakes, and rare earthquakes was analyzed by finite element software PKPM based on the seismic design method of civil code +1°. On this basis, a comparison was made between the seismic responses of structural pushover analysis and elastoplastic time history analysis under the action of rare earthquakes, and the conservatism of these two commonly used methods for elastoplastic analysis was systematically analyzed. The results indicate that the TMSR-LF1 plant structure exhibits well bearing and deformation capacity. It meets the seismic design goal of “no damage under small earthquakes,” “no unrepairable damage under medium earthquakes,” and “no collapse under large earthquakes (using static pushover analysis),” and the critical regions are entirely within the elastic range. Furthermore, the analysis reveals that the elastoplastic time history analysis method produced a significantly higher seismic response than the pushover analysis method, which indicates the conservativeness of the time history method. Therefore, it is recommended to use the elastoplastic time history analysis method to evaluate the seismic performance of research reactor plants under rare earthquake actions. The research in this paper provides important references for the seismic performance analysis of other Class II research reactor plants.

Fuzzy seismic fragility analysis of underground structures considering multiple failure criteria

To avoid the deficiency of a single failure criterion and deterministic thresholds of limit states in seismic fragility analysis of underground structures, a method of fuzzy seismic fragility analysis of underground structures considering multiple failure criteria is proposed by combining fuzzy-random theory and copula theory. In this method, probabilistic seismic demand and capacity analyses based on different failure criteria are first performed. Then, the fuzziness of the limit states of different failure criteria is characterized by using membership functions, and the fuzzy seismic fragility of underground structures considering a single failure criterion with different membership functions is further calculated. On this basis, the copula function and the combination of membership functions are optimized to characterize the correlation between multiple failure criteria and establish fuzzy seismic fragility curves considering multiple failure criteria. Taking the Daikai subway station as the background, the effects of different failure criteria and the fuzziness of limit states on the seismic fragility are discussed, and the optimal combination of membership functions that characterizes the fuzziness of limit states under the failure criteria of deformation and strength is also presented. The results show that the failure criteria and fuzziness of limit states have significant effects on the seismic fragility of underground structures, and the combination of trigonometric membership functions is the optimal combination that characterizes the fuzziness of multiple failure criteria. Moreover, the fuzzy seismic fragility of underground structures considering multiple failure criteria is more sensitive to the fuzziness of limit states under frequent earthquakes and basic earthquakes, while the multiple failure criteria and the correlation between different failure criteria have more significant effects on the fuzzy seismic fragility considering multiple failure criteria under rare earthquakes and extremely rare earthquakes.

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.

Seismic fragility analysis of nuclear containment structure using Bayesian logistic regression model

Nuclear containment structure serves as the critical shielding structure in nuclear power plants, and must maintain structural integrity under various conditions. Following the Fukushima nuclear accident, seismic safety of nuclear power plant structures has become a significant concern in nuclear engineering community. This study presents seismic fragility analysis of the nuclear containment structure subjected to far-fault ground motion based on Bayesian logistic regression model. A refined finite element model of the nuclear containment structure was developed using layered shell element with considering material nonlinear behavior. The maximum tensile strain and roof drift of the nuclear containment structure were analyzed. MATLAB scripts for the seismic fragility analysis method based on Bayesian logistic regression model were developed. Posterior samples for the parameter of fragility function parameters were obtained using developed scripts. The sensitivity of the proposed Bayesian logistic regression based seismic fragility analysis method was verified. Seismic fragility curves of the nuclear containment structure obtained with the minimized sum of squared error, maximum likelihood estimation and Bayesian logistic regression methods were compared in depth.

Rapid recovery strategy for seismic performance of seismic-damaged structures considering imperfect repair and seismic resilience

In the emergency repair process of seismic-damaged structures, it is necessary to determine the optimal repair strategy according to damage assessment results, available repair resources and repair time. In this study, the applicable conditions of various member-level and structure-level damage indexes or models are compared. Then, considering the actual conditions of limited available repair resources and repair time in the emergency repair process, the determination method of the optimal imperfect repair strategy is established. On this basis, the determination method of the optimal repair sequence is proposed by taking seismic resilience as the evaluation index. Finally, a seismic fragility analysis method that considers uniform collapse risk and residual service life of structures is introduced, which can be used to analyze the seismic performance of seismic-damaged structures and to compare the repair effectiveness of different repair strategies. Taken a 5-story reinforced concrete structure as an example for analysis. The analysis results show the optimal imperfect repair strategy and the optimal repair sequence determined by the proposed methods can effectively improve the seismic performance of seismic-damaged structures. The fragility analysis results further confirm that the repair based on the optimal imperfect repair strategy can effectively reduce the collapse risk of seismic-damaged 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.

Application of a Deep Learning Method to the Seismic Vulnerability Analysis of Cross-Fault Hydraulic Tunnels Based on MLE-IDA

Rapidly developed deep learning methods, widely used in various fields of civil engineering, have provided an efficient option to reduce the computational costs and improve the predictive capabilities. However, it should be acknowledged that the application of deep learning methods to develop prediction models that efficiently assess the nonlinear dynamic responses of cross-fault hydraulic tunnels (CFHTs) is lacking. Thus, the objective of this study is to construct a rational artificial neural network (ANN) prediction model to generate the mass data and fragility curves of CFHTs. Firstly, an analysis of 1080 complete nonlinear dynamic time histories via incremental dynamic analysis (IDA) is conducted to obtain the mass data of the drift ratio of the CFHT. Then, the hyper-parameters of the ANN model are discussed to determine the optimal parameters based on four examined approaches to improve the prediction capacity and accuracy. Meanwhile, the traditional probabilistic seismic demand models of the predicted values obtained by the ANN model and the numerical results are compared with the statistical parameters. Eventually, the maximum likelihood estimation couping IDA method is applied to assess the seismic safety of CFHTs under different damage states. The results show that two hidden layers, ten neurons, and the ReLU activation function for the ANN model with Bayesian optimization can improve the reliability and decrease the uncertainty in evaluating the structural performance. Moreover, the amplitude of the seismology features can be used as the neurons to build the input layers of the ANN model. It is found through vulnerability analysis that the traditional seismic fragility analysis method may overestimate the earthquake resistance capacity of CFHTs compared with maximum likelihood estimation. In practical engineering, ANN methods can be regarded as an alternative approach for the seismic design and performance improvement of CFHTs.

Prestressed partial single-layer twisted reticulated shell seismic performance assessment using endurance time

The endurance time analysis is a method for seismic analysis. This method uses a function with an increasing acceleration value as time passes to reflect the seismic performance of structures at various seismic intensities. It offers the advantages of small discrete and fast calculation. It has not, however, been researched in space structures. In this research, a prestressed partial single-layer twisted reticulated shell with a size of 66 m × 46 m was used as the research object, and the seismic performance of the structure was assessed using three endurance time analysis functions that were compared with the incremental dynamics analysis assessment results under twenty far-field ground motions and twenty near-field ground motions. With a maximum error of 0.011 m in the displacement response, the results indicate that the two methods of assessment produced similar results. In comparison to incremental dynamics analysis, the endurance time analysis reduced computation time by 90%.

Hybrid‐simulation‐based model calibration method for nonlinear seismic analysis

AbstractThe calibration of parameters of hysteretic models that simulate the hysteretic behavior of key structural components is a crucial task in the nonlinear seismic analysis of structures to ensure accurate analysis results. For complicated systems, a direct calibration of model parameters at the system level is almost impossible due to the lack of test data. Consequently, the calibration is usually conducted using test results with lower levels of complexity. Currently, a widely accepted practice in calibrating hysteretic model parameters in structural models is to utilize standardized cyclic tests of a single component. However, due to the simplified and unrealistic loading profile of standardized cyclic tests, the relevance between the calibration and the system‐level prediction capabilities can be weak. In other words, a well‐tuned hysteretic model that matches the standardized cyclic test results very well may not be able to produce the same level of accuracy in estimating the system‐level structural dynamic response where the calibrated components will experience more random and complicated loadings. In this paper, a method is proposed to calibrate hysteretic models in a test method with more realistic loading histories through hybrid simulations. The proposed calibration method is then validated by conducting a large number of hybrid simulations on a type of small‐scale buckling‐restrained brace (BRB) specimen. A framework is also proposed to evaluate the relevance between the calibration and the system‐level response considering uncertainties in hysteretic model parameters. The results demonstrate the superiority of the hybrid‐simulation‐based calibration method over the conventional cyclic‐test‐based calibration method.

Seismic Design of Large-Span, Heavy-Load Transfer Truss for Zhanjiang Bay R&D Building

The Zhanjiang Bay Laboratory R&D Building project aims to create a favorable working, research, and living environment. Zone II of the Zhanjiang Bay Laboratory R&D Building is equipped with a large-span, heavy-load transfer truss to obtain a large space on the ground floor. The overall structure adopts a steel frame-core tube structure system. In order to reduce the deflection of the large-span, heavy-load transfer truss, eight diagonal pull rods are installed between the large-span, heavy-load transfer truss and the core tube. The Q235 cross-shaped replacement section can consume construction load energy. Adopting replacement methods can reduce the stress and damage of diagonal pull rods caused by construction loads. The structure adopts a performance-based seismic design method for seismic calculation and analysis. In addition, a special analysis was conducted on the single frame structure. The major results can be summarized as follows: during small earthquakes, all structural components are in the elastic stage; during large earthquakes, frame beams yield first, but frame columns and core tubes do not yield; even without considering out-of-plane constraints, the structure can still meet the requirements.

Longitudinal seismic displacement analysis of Quasi Seismic Isolation Bridge based on Energy-based Multimodal Pushover Method with and without collision

This paper aims to evaluate the longitudinal seismic displacement of the Quasi Seismic Isolation Bridge (QSIB) based on the Energy-based Multimodal Pushover Method (EMPM), including the pier-beam relative displacement and the collision effect. As a simplified seismic analysis method, the EMPM invokes the concept of energy balance into the modal pushover analysis to assess the nonlinear seismic behavior of Laminated Rubber Bearing (LRB) on bridges. In this method, the energy-based capability curve is obtained by the modal pushover analysis, while the energy-based demand curve is estimated under the ground motion record. The target performance criterion can be derived by intersecting the capability curve with the demand curve. The effect of several key factors in EMPM, such as the mode classification and selection, collision effect, energy coefficient and ductility factor, are studied by a case study of a prototype QSIB under ChiChi and El Centro earthquakes. The results of EMPM are compared with those from Nonlinear Time History Analysis (NTHA), to illustrate the effectiveness and accuracy of this method for evaluating the maximum seismic displacement, and the pier-beam relative displacement with and without collision. Results show that the EMPM is found to be able to estimate the longitudinal seismic displacement of the QSIB with and without collision, and can be used as an effective alternative for rapid assess the seismic performance of bridges. The results also indicate that LRB stiffness for modal analysis should be taken as the stiffness pre- or post-sliding when without or with the gap element. Collision effect enlarges the peak displacement and the maximum bias of EMPM.

A new equivalent acceleration-based non-uniform response spectrum method for efficient seismic SSI analysis

A complex multiple-support response spectrum (CMSRS) method with a concise and universal expression is required to estimate the seismic responses of soil–structure interaction (SSI) systems under non-uniform seismic excitations to replace existing complex methods. This paper introduces and defines a new concept called equivalent acceleration of boundary load (EABL) that converts widely used equivalent loads into equivalent accelerations, and further develops an efficient CMSRS-EABL method for the seismic analysis of the SSI system. First, EABL offers three main benefits: it simplifies the expressions without sacrificing precision, extends the applicable scope of viscous-spring artificial boundary (VSAB) to all stress-type artificial boundaries, and presents dynamic equations in a familiar form. Subsequently, the CMSRS–EABL formula was successfully deduced based on the equivalent simplified dynamic equations. This formula significantly simplifies the traditional method by reducing the effective modal participation factors, mean-square-roots, and cross-correlation coefficients by 4, 5 and 15 items, respectively. Finally, a rectangular construction surrounded by a VSAB–soil combination was used as an example to illustrate the convenience of the developed CMSRS–EABL method and verify its precision. The results indicate that the proposed method is characterized by greater simplicity and ingenuity, and it is capable of high precision similar to that of the conventional methods. We believe this method will be of significant benefit in evaluating the anti-seismic performance of deeply buried and long-standing structures.

Estimation of wave velocity and analysis of dispersion characteristics based on wavelet decomposition

Due to the complexity of the crustal medium and stratigraphic boundaries, seismic waves typically exhibit attenuation and dispersion after propagation through the medium. By studying the regularity of seismic wave dispersion, soil layer information can be extracted. Current spectral decomposition techniques take less account of signal filtering processing of seismic waves, and the complexity of the stratigraphy tends to reduce the accuracy of dispersion analysis. Based on the above, a new method for calculating the dispersion characteristics of a site from surface and downhole ground vibration recordings is proposed, which is simpler than the spectra analysis of surface waves (SASW) method and eliminates the need for multiple pickups and additional equipment. This method is based on wavelet decomposition and seismic wave filtering, and a numerical simulation example is established to verify the effectiveness of the method. Then, the records of the Tohoku earthquake on March 11, 2011 are used as actual strong earthquake examples for filtering and dispersion analysis. Finally, it is concluded that the seismic wave dispersion analysis method based on wavelet decomposition can effectively filter and analyze seismic waves in specific frequency bands.

Overall seismic reliability analysis of aqueduct structure based on different levels under random earthquake

The seismic reliability analysis method of large aqueduct structure is of great significance to its operation and maintenance safety evaluation and seismic toughness evaluation in the life cycle. In this paper, the seismic reliability analysis method of aqueduct structure at different levels is proposed based on the probability density evolution theory and the random ground motion model of engineering physics. Taking Shuangji River aqueduct as an example, 100 random seismic acceleration time-history samples and corresponding probability assignments are generated based on the engineering physical random ground motion model, and combined with the nonlinear response analysis platform of fiber beam element of aqueduct structure，the dynamic response analysis of the aqueduct structure under nonlinear and random coupling conditions is carried out from the perspective of the whole process of nonlinear development. And by introducing different failure criteria of the aqueduct structure, the overall seismic resistance of the aqueduct structure under different fortification targets is quantitatively analyzed. The results show that the coupling of randomness and nonlinearity has a significant impact on the dynamic response of the aqueduct structure. The overall seismic reliability analysis method based on different fortification levels can accurately solve and evaluate the overall seismic reliability of the aqueduct structure under different fortification levels. The research results have important theoretical significance for the overall seismic reliability analysis and design of aqueduct structures based on multi-level fortification targets.