Maximum Seismic Response Research Articles

A new processing method of ground acceleration data for fast and accurate evaluation of maximum seismic structural response

AbstractA new processing method of ground acceleration data is proposed for the fast and accurate evaluation of the maximum seismic structural responses. The proposed method consists of a trimming method and a down‐sampling method. The proposed trimming method is based on ground acceleration power and contains compensation procedures for the trimmed ground acceleration. The proposed down‐sampling method effectively uses FIR filter, whose weight coefficients are derived from the correspondence between the responses under a triangular wave and the equivalent impulse input. It is demonstrated through numerical examples for response spectrums and a full‐scale high‐rise building model that the proposed method enables fast and accurate evaluation of the maximum seismic structural responses.

Seismic response of a mid-story isolated stilted structure in mountainous areas

Research on the SSI effect on flat sites has yielded many valuable conclusions. However, current research on the impacts of various special local terrains on structural dynamics remains limited. For mountainous areas, it is common to construct houses in a multi-step, climbing, and laterally staggered architectural form that follows the mountain terrain. Only through the analysis of the combined action of the upper and lower parts can the seismic performance of this type of structural form be better revealed; considering the influence of SSI effects will be closer to the actual seismic effects. Therefore, to identify the damage factors of the mid-story isolated stilted structures under earthquakes and provide optimized design plans for the structures, six models are established considering three slopes and two types of foundations based on the engineering case in Chongqing, China. Through the elastic-plastic time-history analysis under earthquakes in the down and transverse-slope directions, concludes, compared with not considering SSI, the seismic response of the mid-story isolated stilted structures considering SSI in mountainous areas is amplified. With the increase of the mountain slope, the seismic response of the structures considering SSI increases, and the amplification coefficients are between 1–1.8. The amplification coefficients of the structures without SSI are concentrated around 1, which is less influenced by the slope. The damage to the stilted isolated layer is mainly concentrated in the column and the beam end, and the maximum seismic response appears in the short columns. The foundation soil stress increases with the increase of the mountain slope.

Application of optimized polynomial controllers based on Bayesian optimization and weight matrix adjustment

AbstractThis paper uses a polynomial controller with non‐linear performance that is a summation of polynomials in non‐linear states. The optimal performance of this controller depends to a large extent on the weighting matrices elements whose determination is not easy via analytical methods for high dimension control systems. This paper focuses on optimizing a polynomial controller applied to a 20‐story non‐linear benchmark building using the Bayesian optimization (BO). BO is a powerful strategy for optimizing functions that are expensive to evaluate. In setting up the optimization problem, design variables are the parameters of weighting matrices. The objective function is a ratio of the controlled and uncontrolled response for the maximum absolute acceleration of the building, and the maximum inter‐story drift is taken as the constraint. The efficiency of the proposed control scheme is tested on a 20‐story non‐linear benchmark building equipped with magnetorheological dampers. The considered evaluation criteria are compared with other control methods. The results show that the considered algorithm is desirable in reducing the maximum seismic response under different earthquakes.

Local Site Effect of Fault Site and Its Impact on Seismic Response of Fault-Crossing Tunnel

ABSTRACT The areas where tunnels crossing faults are especially susceptible to seismic damage. Local site effects associated with fault site notably contribute to the unfavourable impact on the seismic behaviour of tunnels. In this study, large-scale shaking table tests were conducted to investigate the fault site effect and its impact on the seismic response of tunnels. Real earthquake records, synthetic seismic wave, and sinusoidal waves were selected as input motions, excited in both transverse and longitudinal directions of the tunnel. The local site effect of the fault site was evaluated by time-frequency analysis. The test results indicate that the acceleration response within the fault is significantly greater than those on both sides, regardless of excitation direction. Dynamic characteristics of different regions of the fault site exhibit distinct variations under different excitation directions, with the dynamic behaviour of the strata within the fault playing a crucial role. Marked waveform distortion and trapped waves can be observed within the fault, attributed to harmonic distortion, waveform conversion at fault interfaces, and varying seismic wave propagation pathways. The region of maximum seismic response of the fault-crossing tunnel predominantly occurs near the interface between the fault and the hanging wall. The seismic response of the tunnel located in the hanging wall exceeds that in the footwall. The dynamic characteristics of the fault-crossing tunnel are significantly affected by the dynamic characteristics of the strata around the tunnel, highlighting the necessity of comprehending strata dynamics in the seismic design of such tunnels. The aforementioned findings could offer valuable insights for the seismic design of mountain tunnels crossing fault zones.

Machine Learning Algorithms for the Prediction of the Seismic Response of Rigid Rocking Blocks

A variety of structural members and non-structural components, including bridge piers, museum artifacts, furniture, or electrical and mechanical equipment, can uplift and rock under ground motion excitations. Given the inherently non-linear nature of rocking behavior, employing machine learning algorithms to predict rocking response presents a notable challenge. In the present study, the performance of supervised ML algorithms in predicting the maximum seismic response of free-standing rigid blocks subjected to ground motion excitations is evaluated. As such, both regression and classification algorithms were developed and tested, aiming to model the finite rocking response and rocking overturn. From this point of view, it is essential to estimate the maximum rocking rotation and to efficiently classify its magnitude by successfully assigning respective labels. To this end, a dataset containing the response data of 1100 rigid blocks subjected to 15,000 ground motion excitations, was employed. The results showed high accuracy in both the classification (95% accuracy) and regression (coefficient of determination R2=0.89) tasks.

Seismic performance assessment of a retrofitted pile-supported wharf considering soil-cement uncertainties using artificial neural network

Seismic fragility analysis is an effective method to evaluate the seismic performance of retrofitted wharf systems affected by the uncertainty of soil-cement strength. Nevertheless, fragility analysis usually consumes a large consumption of computational power. In this study, seismic fragility analysis using the artificial neural network (ANN) for the retrofitted wharf, considering the aleatory uncertainty of soil-cement strength and the epistemic uncertainty of the ANN, is carried out; On this basis, the fragility surface for two types of damage limit states considering the uncertainty of soil-cement strength is obtained. It was found that: (1) overall, the soil-cement strengthening strategy is effective for improving the seismic safety of wharf systems, however, the strengthening effect is limited, especially under strong earthquakes, will be further weakened; (2) ANN can effectively predict the maximum seismic response of retrofitted pile-supported wharves, so as to quickly carry out seismic fragility analysis. Examples show that the prediction method has good generalization; and (3) the fragility surface model considers the aleatory uncertainty of soil-cement strength and the epistemic uncertainty of the ANN, which makes the performance-based evaluation of retrofitted pile-supported wharves more comprehensive.

Optimal design of tuned inerter negative stiffness dampers with linear viscous and nonlinear eddy current damping for structural effective damping ratio enhancement

Tuned inerter negative stiffness damper (TINSD) has demonstrated its effectiveness in controlling structural vibrations. However, the potential to improve the effective damping ratio of primary structures remains unexplored, and thus far, TINSD has solely featured linear viscous damping. In this study, we explored two damping types for TINSD: linear viscous damping (abbreviated as TINSD) and nonlinear eddy current damping (termed EC-TINSD). The optimal design of the TINSD was conducted based on the effective damping ratio enhancement (EDRE) effect. Our findings reveal that an increase in the absolute value of the negative stiffness does not result in a continuous improvement in the control efficiency and effectiveness of TINSD, which correspond to the EDRE effect and the structural effective damping ratio, respectively. Importantly, we observe that the proposed optimal TINSD solution outperforms the one derived from the fixed-point method, particularly when the inertance ratio is less than 0.15. For EC-TINSD, its optimal design was performed based on the EDRE effect using statistical linearization techniques that employ both force-based and energy-based equivalent criteria. The control efficiency and effectiveness of optimal EC-TINSD were then validated through Monte Carlo simulation. This analysis highlights the significance of a large critical velocity for EC-TINSD to achieve greater accuracy in vibration control. Numerical studies were further conducted to investigate the control efficiency and effectiveness of EC-TINSD under three types of real seismic excitations. The results demonstrate that both TINSD and EC-TINSD exhibit similar effectiveness in mitigating the maximum seismic responses of primary structures, and their efficiency surpasses that of viscous dampers and eddy current dampers with identical damping parameters. Additionally, the distinctive damping force limiting characteristic of EC-TINSD should be commended as it can protect the security and dependability of both the dampers and their connections to the structures.

IDA-Based Collapse Safety Assessment of Torsional-Irregular Buildings, Considering Ductility and Damage

The complexity in nonlinear behavior of torsional-irregular buildings in combination with uncertainty due to the natural randomness of earthquake records has been always a main challenge for buildings’ seismic design. To find a solution to this challenge, three reinforced concrete (RC) building archetypes were designed and next developed into their nonlinear models. Nonlinear static (pushover) analyses were performed to calculate the capacity of the archetype models in all principal and non-principal directions while incremental dynamic analyses (IDAs) were conducted by applying 30 accelerograms from both near-field and far-field earthquakes. The IDA capacity curves, collapse fragility curves and log-normal cumulative distribution functions (CDFs) were established by including both the aleatory randomness and epistemic uncertainty. Despite previous studies wherein fragility curves were given by evaluating structures’ collapse along structural reference axes or simply on [Formula: see text], [Formula: see text]-axes, in this paper, possible building collapse on a critical non-principal direction (where maximum seismic response was observed) was simulated and its probability was accounted for developing IDA curves and log-normal CDFs. Accordingly, this issue was mirrored in computing available/acceptable collapse margin ratios (CMRs). In addition to the well-known outline used for calculating CMRs in the literature (that is based on estimation of collapse capacity in terms of earthquake intensity measure (IM)), the framework proposed here includes a new method for calculating the CMRs in terms of displacement-based drift, ductility, and damage. The superiority of the proposed method over the former is consistent with the buildings’ design procedure that is governed by storey drift control rather than base-shear strength. Refined statistics of CMRs given by taking into account displacement-based responses illustrate the available CMRs exceed the acceptable CMRs, meaning that a satisfactory safety margin against collapse will be anticipated in the targeted building class if a suitable yielding mechanism with sufficient ductility is provided for seismic force-resisting system by applying seismic design provisions of the current codes.

Investigation on Improved Optimal Fixed Time Step in Time-History Analysis for Aseismic Design of High-Speed Railway Bridge-Track System

ABSTRACT Time-history analysis is currently the main approach to the aseismic design of high-speed railway, and the time step significantly affects the calculation efficiency and accuracy. A 5-span high-speed railway bridge-track system was used as an example in this study. The effect of different fixed time steps on maximum seismic response was analyzed. An approach of improved optimal fixed time step was proposed by introducing maximum frequency and sampling frequency multiple. According to the research findings, for a specified ground motion record, the calculation error and efficiency of the improved fixed time step decrease with the increasing sampling frequency multiple. For a specified sampling frequency multiple, the calculation efficiency decreases with the increasing high-frequency components in ground motion record. The calculation error of secondary sampling signal for random ground motion records approximately obeys the normal distribution, and a stable and deterministic upper bound can be constructed based on the random sample of calculation error. The sampling frequency of secondary sampling signal in aseismic analysis for high-speed railway bridge-track system should be set as 4fmax. The improved optimal fixed time step should be set as (4fmax)−1 to simultaneously satisfy both the calculation error and efficiency requirements.

Seismic Responses and Damage Control of Long-Span Continuous Rigid-Frame Bridges Considering the Longitudinal Pounding Effect under Strong Ground Motions

Continuous rigid-frame bridge (CRFB), a type of bridge adopting the unique form of pier-girder consolidation, combines a T-shaped rigid frame with a continuous girder. CRFBs located in western China are likely to suffer destructive earthquakes, which may result in serious damage to bridges. To study the longitudinal seismic responses and damage control of different structure types of the CRFB under strong ground motions, this work develops three nonlinear dynamic analysis models considering the initial internal force state and longitudinal girder-pier pounding effect based on the OpenSEES (version 3.3.0) platform. Moreover, the present study comparatively analyzes the displacement responses, internal force of piers, pounding force and times, and damage condition of the three models and investigates the effectiveness of tuned inerter-based dampers (TIBDs) in controlling seismic responses of the CRFB. The numerical results show that the longitudinal seismic responses of the main piers in the three models are obviously different, especially when subjected to near-fault ground motions. The peak pounding force at the abutments is much larger than at the transition piers, while the pounding times are the opposite. Under near-fault ground motions with a peak ground acceleration (PGA) of 0.4g, the main piers may be damaged moderately or even more seriously, and the bearings are completely destructive. The TIBDs can effectively control the maximum seismic responses and damage degree of the CRFB under pulse-like near-fault ground motions. Among them, both the tuned viscous mass damper and tuned inerter damper are ideal and useful devices. This study can provide useful references for the seismic design and performance analysis of CRFBs.

MAXIMUM SEISMIC RESPONSE PREDICTION BASED ON CAPACITY SPECTRUM METHOD FOR VIBRATION-CONTROLLED CEILING STRUCTURE EMPLOYED PULLEY MECHANISM

This paper proposes a new procedure for predicting the maximum seismic response based on the capacity spectrum method (CSM) for the passively controlled suspended ceiling structures named “Pulley Damper Ceiling System (PDCS)”. The structural system has a supplemental nonlinear viscous damper and a bilinear hysteretic damper in parallel with displacement amplification mechanisms of block and tackle pulley system. The single degree-of-freedom model of the PDCS is initially discussed. The accuracy of a simplified calculation method for obtaining the structural equivalent damping coefficient, determined by the sum of the inherent damping and the square root of sum of squares (SRSS) of each damping provided by the nonlinear viscous damper and the bilinear hysteretic damper, is verified by comparing with the full-scale shake table test results of the PDCS. Then, the pseudo capacity curve of the structure is generated by continuously plotting the transition of maximum force and displacement values under different amplitudes of sinusoidal waves. Finally, the availability of the response prediction based on proposed CSM procedure considering floor response spectrum (FRS) is examined by the comparison of time history analysis results, and the sufficient accuracy to evaluate the seismic response is confirmed.

Multi-pulse decomposition for nonlinear seismic analysis of structural systems

Large sympathetic, resonance-like, structural behaviour to earthquake excitations with analogous frequency content often plays a critical role in determining its maximum seismic response. Earthquake excitation typically contains a broad spectrum of non-stationary frequency content, wave packets, which are difficult to observe from the recorded time series. Therefore, identifying the root cause of large responses (which act sympathically with the input but do not achieve full-resonance) of a structure is problematic. Hence, this paper proposes a new multi-pulse decomposition method of ground motions, through which components of a ground motion within a specific period range are determined. In this method, a ground motion is approximated with a Gauss-Fourier wave packet series. The decomposed components, wave packets, contain information about its time-position, frequency, amplitude, pulse width and phase angle. Unlike the Ricker (Morlet) wavelet the Gauss-Fourier wave packet is not limited to symmetrical pulses. One ensemble of 40 near-fault ground motions and one ensemble of 44 far-fault ground motions are used to demonstrate the application and efficiency of the proposed method. The method is shown to be precise in reconstructing the original ground motion using its decomposed components. It is also concluded that the method is accurate in replication of elastic and inelastic response spectra of ground motions within a specific period range. It is demonstrated that for some structure/ground motion combinations, only a few Gauss-Fourier components are required to faithfully describe response behaviour. This highlights that, for these systems, most of the recorded earthquake time series acts like noise on a much simpler wave-packet signal.

Finite element modeling of reinforced concrete short columns subjected to shear in two perpendicular directions

PurposeShort columns can cause serious damage when subjected to an earthquake due to their high stiffness with low ductility. These columns can be exposed to multidirectional shear forces, which encouraged this study to investigate the behavior of structural short columns under bi-directional shear.Design/methodology/approachFinite element analysis (FEA) using ABAQUS is conducted and calibrated based on experimental data tested by previous researchers who studied the uni-directional behavior of short columns subjected to cyclic shear displacements. Then, the calibrated column models are further investigated to study the influence of bidirectional cyclic shear. Two scenarios are investigated, namely “simultaneous” and “sequential,” to compare the performance in terms of shear strength reduction.FindingsThe results show that the shear strength reduction significantly appears when 1:1 simultaneous bi-directional cyclic shear is applied. However, the shear reduction is more significant when the sequential scenario is applied. The seismic forces or deformations applied in orthogonal directions should be combined to achieve the maximum seismic response of structures as specified in Federal Emergency Management Agency (FEMA) 356 Standard. Finally, the combinations presented in literature to consider bi-directional shear are investigated. Based on FE results, the effect of applied 1:0.30 bi-directional cyclic shear simultaneously does not result in significant effect on the considered columns properly design for seismic forces.Originality/valueTo investigate the effect of multidirectional shear forces on the shear strength capacity of short columns, the presented effect of multidirectional shear forces in literature to consider bi-directional shear are investigated.

E-Cloud: Efficient seismic fragility assessment of structures based on enhanced cloud analysis

Cloud analysis is based on linear regression in the logarithmic space using least squares, in which a large number of nonlinear dynamic analyses are required to ensure the regression accuracy. Thus, it needs significant computational effort to derive fragility curves especially for the complicated structures. This article proposed the Enhanced Cloud approach (E-Cloud) to enhance the efficiency but maintain the accuracy of Cloud analysis. The basic concept of the E-Cloud method aims to utilize both maximum and additional seismic responses with corresponding intensity measures (IMs) from ground motions for the logarithmic linear regression in Cloud analysis. The additional seismic responses can be obtained from the engineering demand parameter (EDP)-IM curve, which is generated at the specific time duration when structures are subjected to intensifying dynamic excitations in nonlinear time–history analysis. The required number of nonlinear time–history analyses in Cloud analysis is reduced since additional seismic responses (with their corresponding IM value) are used as additional Cloud points for the Cloud regression. The proposed E-Cloud method is applied for the case study of a typical reinforced concrete (RC) frame structure. By comparison of probabilistic seismic demand models and fragility curves from the E-Cloud method to Cloud analysis, it is demonstrated that the proposed E-Cloud method can significantly improve the computational efficiency of the Cloud analysis, which also leads to accurate fragility estimates of the structures.

A modal displacement-based design method for irregular building frames equipped with elastomeric bearings

In this study, a Modal Displacement-Based Design (MDBD) method for seismic design of base isolated building frames with vertical irregularity has been proposed using principles of the Direct Displacement Based Design method and evaluated through the Nonlinear Time History Analysis (NTHA). The structural models used here are regular and irregular building frames equipped with elastomeric bearings. By comparing the results of the proposed MDBD method with those of the NTHA, it can be concluded that the proposed procedure is able to predict seismic demands of this kind of structures with acceptable accuracy. The advantage of this method is not only that it can predict the design values in a way that the maximum seismic responses of structure reach to the pre-selected values, but also can predict the true displacement profile of frame and find where maximum drifts happen.

Seismic analysis of reinforced concrete building accounting for local uplift, large rotation of the base and soil plasticity

This study provides an analysis of multistory reinforced concrete residential buildings to earthquakes considering local uplift of foundation, soil behaviour, site category and seismicity of area as suggested by the Moroccan seismic regulation. The superstructure was modeled as a flexible column with lumped mass placed at the top of the column under the hypothesis of large rotations or small rotations. The governing equations of the coupled system were obtained by expressing momentum conservation principle and were solved by means of adequate time integration numerical scheme. Then, the maximum seismic response of the coupled system was determined under El Centro ground motion for various configurations of the coupled mat-foundation system: elastic or elastic-perfectly plastic, as well as soil class and seismic magnitude. It was found that the nonlinear seismic demand of a reinforced concrete building, in terms of maximum values of horizontal and vertical displacements and rotation, depends considerably on the assumption regarding rotation magnitude. It is governed also by the height of the structure and the soil stiffness.

Seismic analysis of high-speed railway irregular bridge\u2013track system considering V-shaped canyon effect

To explore the effect of canyon topography on the seismic response of railway irregular bridge–track system that crosses a V-shaped canyon, seismic ground motions of the horizontal site and V-shaped canyon site were simulated through theoretical analysis with 12 earthquake records selected from the Pacific Earthquake Engineering Research Center (PEER) Strong Ground Motion Database matching the site condition of the bridge. Nonlinear seismic response analyses of an existing 11-span irregular simply supported railway bridge–track system were performed under the simulated spatially varying ground motions. The effects of the V-shaped canyon topography on the peak ground acceleration at bridge foundations and seismic responses of the bridge–track system were analyzed. Comparisons between the results of horizontal and V-shaped canyon sites show that the top relative displacement between adjacent piers at the junction of the incident side and the back side of the V-shaped site is almost two times that of the horizontal site, which also determines the seismic response of the fastener. The maximum displacement of the fastener occurs in the V-shaped canyon site and is 1.4 times larger than that in the horizontal site. Neglecting the effect of V-shaped canyon leads to the inappropriate assessment of the maximum seismic response of the irregular high-speed railway bridge–track system. Moreover, engineers should focus on the girder end to the left or right of the two fasteners within the distance of track seismic damage.

Predicting the Maximum Seismic Response of the Soil-Pile-Superstructure System Using Random Forests

ABSTRACT Seismic fragility analysis has been considered an efficient method for seismic performance assessment of soil-pile-superstructure systems (SPSSs). However, seismic fragility analysis based on widely used numerical methods often requires a significant investment of time. In this study, a new approach based on the random forest technique, which can be applied to fragility analysis, is proposed to accurately and efficiently predict the maximum seismic response of SPSSs. Moreover, based on the random forest technique, the velocity RMS is found to exhibit a stronger correlation with the maximum seismic response of SPSSs in liquefiable soils.

Seismic Performance Evaluation of Steel Buildings with Oil Dampers Using Capacity Spectrum Method

This study proposes a capacity spectrum Method (CSM)-based procedure to estimate the maximum seismic performance of steel buildings passively controlled with bilinear oil dampers. In the proposed CSM, the maximum seismic response of a building was estimated, in the acceleration-displacement response spectrum, as the intersection between the capacity curve and the damping-adjusted demand curves, using the equivalent linearization method. The building equivalent damping ratio was determined by the sum of the inherent damping, and the square root of sum of squares (SRSS) of the hysteretic damping and the viscous damping of the supplemental oil devices. The calculation steps of the proposed CSM are explained in detail based on the equivalent single degree of freedom (ESDOF) system, and its accuracy was examined by comparison with time history analysis (THA) results. Two model steel buildings of 4 and 10 stories, uniformly equipped with oil dampers along the height, were subjected to six selected earthquake ground motions scaled to be compatible with Level-2 earthquakes, as defined in the Japanese Building Standard Law. The seismic performance of the buildings was estimated by the proposed CSM procedure and compared with the results of nonlinear THA in terms of the maximum story displacements and the shear forces. It was observed that the proposed CSM scheme provided a satisfactory accuracy to assess the maximum nonlinear response of steel buildings passively controlled with oil dampers.

Seismic Test and Simulation of Spring Vibration Isolated Foundation for Turbo-Generator

The 1 : 8 model of turbo-generator vibration isolated foundation of common islands in nuclear plants was established for vibration characteristic tests and pseudodynamic experiments. The finite element model was established by SeismoStruct for time-history analysis. Frequencies, modal shapes and seismic responses, deformation curves, and spring deformations were compared and analyzed. Results from tests and experiments show that the natural frequencies of spring vibration isolation foundation are lower than those of common frame foundations and the vertical frequencies are far from the working disturbance frequency of the turbo-generator units. The spring vibration isolation device can reduce the acceleration response of the TG (turbo-generator) deck and redistribute the horizontal earthquake action of the foundation according to the stiffness to give full play to the seismic capacity of the columns. The errors of natural vibration frequencies and maximum seismic response are approximately 15% and 10%, respectively, and the simulation results are in good agreement with the test and experiment data. The proportion and distribution of spring deformation are close, and the test study shows the convenient and precise realization of the simulation. Results of seismic experiments and numerical simulations show that the foundation design meets the standard of the “Code for Seismic Design of Buildings” in China, which realizes the goal of spring vibration isolation and seismic resistance. The foundation design is also reasonable, safe, and reliable.