Statistical evaluation of the damage potential of earthquake ground motions

This study focuses on the damage potential of earthquake ground motions based on the inelastic dynamic response of equivalent single degree of freedom structures. Their yield resistances are selected in accordance with seismic design codes. An index accounting for the accumulation of damage due to inelastic excursions is used to represent structural damage. A set of 94 ground motions are employed for this analysis, which are all scaled to the same peak ground acceleration of 0.4 g. Earthquake ground motions are classified with respect to both the ratio of peak velocity to peak acceleration (V/A ratio) and their effective excitation duration. The effect of these parameters on damage potential is investigated by using sensitivity analysis and probabilistic techniques. It is concluded that both V/A ratio and effective duration significantly influence the damage potential of earthquake ground motions, although they are not represented appropriately by the spectral definitions of earthquake excitations in seismic design codes.     

Seismic response of shear‐core with sliding support to bi‐directional ground excitation

To study the effectiveness of a sliding support for the isolation of structures from damaging ground motion, the model of a shear‐core supported on a sliding foundation and subjected to random ground motion in two orthogonal directions is considered here. A fictitious spring model is adopted to deal with the discontinuous nature of the sliding structural system. The rigid friction force deformation characteristics of the sliding support are modelled as elasto‐plastic with high elastic stiffness. The sliding support is assumed to remain in the elastic state during non‐sliding and is treated as plastic during the sliding state. An incremental numerical scheme for the solution of a multi‐degree‐of‐freedom system is used for solving the time history responses. The responses (the absolute value of the acceleration of the top of the wall, and the bending moment at the base of the wall), are calculated under various important parametric variations. The result presented here are of interest in the area of the vibration isolation of important structural systems. Copyright © 1999 John Wiley & Sons, Ltd.     

A Wavelet‐Based Adaptive Pole Assignment Method for Structural Control

This article presents a time varying wavelet‐based pole assignment (WPA) method to control seismic vibrations in multi‐degree of freedom (MDOF) structural systems. The discrete wavelet transform is used to determine the energy content over the frequency band of the response in real time. The frequency content was implemented in the Big Bang–Big Crunch algorithm to update the optimum values of the closed‐loop poles of the structural system adaptively. To calculate optimum gain matrix, a robust pole placement algorithm was used. The gain matrix is calculated online based on response characteristic in real time and must not be calculated a priori (offline) choice. The WPA is tested on a 10‐story structural system subject to several historical ground motions. It is observed that the WPA has advantages in some design problems. Numerical examples illustrate that the proposed approach reduces the displacement response of the structure in real time more than conventional linear quadratic regulator (LQR) controller.     

Numerical and comparative study of earthquake intensity indices in seismic analysis

Elastoplastic and time‐dependent analysis of seismic structures has become a major analysis technique in popularly accepted performance‐based seismic design. However, the primary difficulty in using this technique is the lack of a unified criterion in the selection of various intensity indices of ground motions. Various earthquake factors influencing the elastoplastic response of seismic structures are highly sophisticated. Hence, it is vitally important to choose an appropriate and comprehensive earthquake intensity index to achieve an accurate correlation with the structural performance. In this study, a total of 30 earthquake intensity indices published in the literature are reviewed and are evaluated through correlation analysis based on 60 ground motion records. Examined herein is the correlation between existing earthquake intensity indices and the seismic responses of elastoplastic single degree‐of‐freedom and multi degree‐of‐freedom systems. The characteristics and applicability of such indices are also discussed in some detail, based on which appropriate earthquake intensity indices are recommended. Copyright © 2011 John Wiley & Sons, Ltd.     

RC框架基于典型相关分析的地震动多元破坏势评估

为了更加全面地评估地震动对结构的潜在破坏势,考虑多个地震动强度参数和多个结构损伤参数对地震动破坏势的影响,提出一种基于典型相关分析的地震动多元破坏势评估方法。为说明所提方法,以具有不同高度和不同抗震设防水平的16个钢筋混凝土框架结构为研究对象,采用100条真实地震动记录作为地震输入。将与地震动加速度、速度和位移相关的8个地震动强度参数进行对数线性组合,构造成地震动多元强度参数的典型变量。将结构最大层间位移角、整体损伤指数、最大楼层加速度进行对数线性组合,构造成结构多元损伤参数的典型变量。通过使地震动强度参数的典型变量和结构损伤参数的典型变量的相关系数达到最大,获得可以较好评估地震动破坏势的复合地震动参数。研究结果表明：相比于单一地震动参数,复合地震动参数可以更好地评估地震动的破坏势,其与结构损伤的相关性也更强。     

Wavelet‐Based Method for Generating Nonstationary Artificial Pulse‐Like Near‐Fault Ground Motions

A method to generate a suite of artificial near‐fault ground motion time histories for specified earthquakes is presented. A wavelet‐based nonstationary (WB‐NS) model has been employed to effectively capture the time‐varying frequency content of a particular acceleration record and continuous wavelet transform has been used to simulate the largest velocity pulse. Furthermore, an iterative procedure using discrete wavelet transform is utilized to modify an earthquake ground motion and generate energy‐compatible ground motion. Eventually, the artificial near‐fault accelerogram is achieved via the superposition of a coherent extracted velocity pulse with a random acceleration record corresponding to a WB‐NS model and multiplied by a time‐modulating envelope function. The effectiveness of the method is demonstrated by comparing the spectral response and Arias intensity curves of the simulated accelerograms with those of the real records.     

A Computationally Efficient Algorithm for Real‐Time Tracking the Abrupt Stiffness Degradations of Structural Elements

Real‐time structural identification and damage detection are necessary for on‐line structural damage detection and optimal structural vibration control during severe loadings. Frequently, structural damage can be reflected in the stiffness degradation of structural elements. In this article, a time‐domain three‐stage algorithm with computational efficiency is proposed for real‐time tracking the onsets, locations, and extents of abrupt stiffness degradations of structural elements using measurements of structural acceleration responses. Structural dynamic parameters before damage are recursively estimated in stage I. Then, the time instants and possible locations of degraded structural elements are detected by tracking the errors between the measured data and the corresponding estimated values in stage II. Finally, the exact locations and extents of stiffness degradations of structural elements are determined by solving simple constrained optimization problems in stage III. Both numerical examples and an experimental test are used to validate the proposed algorithm for real‐time tracking the abrupt stiffness degradations of structural elements in linear or nonlinear structures using measurements of structural acceleration responses polluted by noises.     

Mechanism and optimum design of shared tuned mass damper for twin‐tower structures connected at the top by an isolated corridor

The concept of shared tuned mass damper (STMD) for twin towers linked by a sky corridor using flexible joints is proposed in this paper. The analytical expressions of the transform functions and random earthquake responses of the flexibly connected structures are derived using a three‐degrees‐of‐freedom model system. The seismic reduction mechanism of the STMD is revealed using comparative analysis between the structures with STMD and those connected using a viscoelastic damper. The effect of the nondimensional parameters such as the frequency ratio of the two primary structures, mass ratio, tuning frequency ratio of the corridor, and damping ratio of the passive control devices on the structural seismic response is investigated. Optimum parametric analysis is performed using the principle of minimizing the displacements of both towers, and the optimal parameter formulas are established. Numerical analysis is conducted to verify the control effectiveness of the connected multi‐degree‐of‐freedom system subjected to the El Centro earthquake ground motion. The results show that the earthquake responses of the towers can be effectively reduced if the parameters of the flexible connecting elements are appropriately selected for a certain corridor mass. Moreover, a remarkable seismic reduction effect can be achieved if the towers have similar dynamic properties.     

Inelastic earthquake control of weld failure Part I: Limit state approach

Active structural control of inelastic response is proposed for the first time on existing buildings. The optimal linear control theory and the force analogy method are combined in state space form to calculate the response of the structure. Application of this combined method is performed to reduce the risk of weld failure in steel buildings. A six‐story moment resisting building damaged during the 1994 Northridge earthquake is used to study the sensitivity of the response and the magnitude of the structural control force to the earthquake ground motion. The limit state approach is used to design the structural control system by limiting the maximum plastic rotations in the building to an acceptable level. In the process, structural control is shown to be very effective in reducing the plastic rotations during excitations, and therefore reducing the risk of weld failure. In addition, structural control is effective in reducing the responses, which include displacement, velocity, acceleration and drift of the structure. Copyright © 1999 John Wiley & Sons, Ltd.     

半主动电涡流单摆式调谐质量阻尼器减震性能研究

为了提高传统的调谐质量阻尼器（TMD）对建筑结构的减震效果,提出了一种可实时调整频率和阻尼的半主动电涡流单摆式调谐质量阻尼器(SAEC-PTMD)。由Hilbert-Huang变换(HHT)识别结构的瞬时频率,通过基于HHT的控制算法实时调节SAEC-PTMD的摆长进行频率的调节。研究并拟合了电涡流有效阻尼系数与磁导间距之间的关系,通过基于线性二次型高斯(LQG)的控制算法实时调节磁导间距,以实时调节阻尼系数。为了验证SAEC-PTMD对建筑结构的减震效果,对一单自由度结构模型在地震激励下的震动响应进行数值模拟。数值模拟中,采用一经优化设计的被动TMD (PTMD)作为对比,并考虑由主结构的累积损伤引起自身频率下降而造成PTMD的失调效应。以主结构的加速度和位移时程峰值、整体均方根值及其加速度和位移反应谱作为评价指标,评估了SAEC-PTMD在结构发生损伤前后对PTMD的改良效果。数值模拟结果表明,在结构发生损伤前后,SAEC-PTMD均比经优化设计的PTMD具有更好的减震效果。     

地震作用下结构振动瞬时最优控制的一种改进算法

模拟地震波输入结构的过程,在每一个时间步长建立控制目标函数,推导出了一种更为一般的瞬时最优控制算法,并用状态转移的数值方法加以实现.所获得的最优控制力表达式同时包含了当前时间步长初时刻结构响应和地震激励两部分的影响,从概念上改进了现有的瞬时最优控制算法;还导出了最优控制力系数表达式,用代数公式取代了传统的Riccati微分方程的求解,提高了计算效率.算例表明,该算法的控制效率优于现有的两种结构最优控制算法,具有更高的精度,且稳定性良好.     

Energy evaluation of inelastic structures subjected to random earthquake excitations

The modified force analogy method combined with static condensation is applied to study the seismic behaviour of inelastic structures, while energy transfer and dissipation in the structure during an earthquake hazard are investigated through energy formulation based on the equation of motion. The earthquake ground motion is modelled as a non‐stationary Gaussian random process. Rigid‐end offsets of the plastic hinges forming on the members, as well as the ability for panel zones to deform, are included in the structural analysis model. Monte Carlo simulation method is performed on a six‐story real moment‐resisting frame to determine the mean and the standard deviation of seismic energy dissipation time histories. Based on this combination of the force analogy method and energy formulation in the equation of motion with the stochastic earthquake model, the feasibility of the analysis procedure for studying the dynamics of inelastic structures is demonstrated through varying the rigidity of panel zones. Copyright © 2008 John Wiley & Sons, Ltd.     

Active Tendon Control of Torsionally Irregular Structures under Near‐Fault Ground Motion Excitation

In this study, torsionally irregular single‐story and multistory structures under the effect of near‐fault ground motion excitation were controlled by active tendons. Near‐fault ground motions contain two impulsive characters. These impulsive characters are the directivity effect perpendicular to fault and the flint step parallel to fault. The structural models were simulated under bidirectional earthquake records superimposed with impulsive motions to examine the response of active control under near‐fault effects. Also, the structures were analyzed only under the effect of bidirectional impulsive pulses. The control signals were obtained by Proportional–Integral–Derivative (PID) type controllers and the parameters of the controllers were obtained by using a numerical algorithm depending on time domain analyses. Time delay effect was also considered for active control system. Different cases of orientation of active tendons were examined and the results of the single‐story structure were compared with another control strategy using frequency domain responses in the optimization process. As a conclusion, the control concept is significantly effective on reducing maximum responses in translational and rotational directions and obtaining a steady‐state response.     

Shaking table tests on braced reinforced concrete frame structure across the earth fissure under earthquake

A series of shaking table tests on a scaled model were conducted to investigate the effect of steel braces on reinforced concrete frame structure across earth fissure under earthquake. In the test, a 1/15 scaled model structure taking into account soil–structure interaction was designed on the basis of similarity theorem. Seismic response data, including acceleration responses, displacement responses, shear force distributions, and strain amplitudes of column reinforcement were obtained and analyzed by comparing the results of unbraced and braced structure. Results show that with the peak ground acceleration of input motions increased, maximum of inter‐story drifts, shear forces, and strain amplitudes increased, whereas the acceleration amplification factors decreased. Steel braces could obviously reduce the seismic response of the structure, indicating that this retrofit method is an effective control measure for structures across the earth fissure under earthquake. These results are significant for studying the effect of earth fissure on seismic responses of structures.     

Seismic response control of asymmetric buildings using tuned mass dampers

The aim of the present study is to investigate the efficiency of the torsional tuned mass dampers (T‐TMDs) in response control of asymmetric buildings under bidirectional earthquake ground excitations. The efficiency of the T‐TMDs is compared with bidirectional tuned mass dampers (BTMDs). The T‐TMDs are oriented to the rotation of the structures about vertical axis with a single torsional mass attached to spring–dashpot elements, whereas the BTMD connects a single mass to two orthogonal sets of spring–dashpot elements oriented to principal axes of the building. The buildings are idealized three‐dimensional models with two translational and one torsional degrees of freedom for each floor. Three different configurations (cruciform‐shaped, L‐shaped, and T‐shaped) of multistory buildings are considered. The 5‐, 15‐, and 20‐story buildings with and without the tuned mass damper schemes are subjected to bidirectional earthquake ground excitation. In order to evaluate the effectiveness of the T‐TMDs and BTMD, the rotation, displacement, acceleration, and base shear force responses are computed. Parametric studies are conducted for all the configurations installed with the T‐TMDs and BTMD by varying their mass ratio, damping ratio, and ground motions. It is concluded that the T‐TMDs are more effective in mitigating the torsional response of asymmetric buildings as compared with the BTMD.     

Model‐Reference Health Monitoring of Hysteretic Building Structure Using Acceleration Measurement with Test Validation

A model‐reference health monitoring algorithm with two damage sensitive features is presented in this study, utilizing structural acceleration measurements from earthquake‐damaged building structure. A virtual linear healthy model, representing linear behavior of the instrumented structure, is used to generate real‐time reference response signals for health monitoring during a disastrous earthquake. The tracking error of acceleration and a relevant statistical factor are first proposed for identifying damage occurrence and location at story level. The severity of the hysteretic damage is estimated numerically using a model‐based prediction curve in an equivalent stiffness reduction manner with the implementation of robust Kalman filtering. The performance of damage detection and evaluation in the presented algorithm are illustrated by numerical simulation of structural models with different hysteretic characteristics, and further validated by experimental investigation employing a base‐isolated three‐story structure and real‐world case study of a seven‐story frame structure. The influence of measurement noise and uncertain stiffness in linear healthy model is also discussed through a parametric study.     

Effects of hysteretic model on seismic demands: consideration of near‐fault ground motions

This paper summarizes the results of a study that is to evaluate the structural response attributes of near‐fault ground motion. Ground motion recordings from the Chi‐Chi earthquake are used as inputs to the structural system. An improved nonlinear hysteretic model, based on the experimental study, was used to calculate the response of the single degree‐of‐freedom inelastic system. Comparison of the results of analysis with traditional elastic–perfect plastic mode calculations was made. Discussions on the inelastic design spectrum, particularly the code‐specified base shear coefficients, using the improved nonlinear hysteretic model incorporated with the near‐fault input ground motion are made. Copyright © 2002 John Wiley & Sons, Ltd.     

Feedback-feedforward control of structures under seismic excitation

While the base acceleration resulting from a seismic activity on a civil engineering structure is not known a priori, it can be measured in real time. In this paper, it is shown that this extra information can be used for achieving a better control of the structure with little additional effort. The approach taken is to augment the equations of motion for the structural system with an appropriate model of the earthquake excitation based on filtering a Gaussian white noise process. The augmented equations of motion are used to determine a control which utilizes both feedback and feedforward compensation. The feedback loop incorporates measurements of the response of the structure into the control law. The information from both the structure and the earthquake excitation model is utilized in the feedforward control law with an observer designed to estimate the states of the eartquake model based upon the base acceleration measurements. A quadratic performance index is used as a measure of optimality of the control algorithms. Results are given which indicate that the proposed method offers advantages in performance over the control method employing only state feedback and that it is also able to improve upon results of the recently develped instntaneous control algorithms. It is also shown that the nostationarity in the earthquake excitation can often be neglected in practical design of linear systems. Finally, a discussion is given of how the method might be coupled with equivalent linearization techniques and extended for use with nonlinear structures.     

Strength reduction factor for MDOF soil–structure systems

In most of the seismic design provision, the concept of strength reduction factor has been developed to account for inelastic behavior of structures under seismic excitations. Most recent studies considered soil–structure interaction (SSI) in inelastic response analysis are mainly based on idealized structural models of single degree‐of‐freedom (SDOF) systems. However, an SDOF system might not be able to well capture the SSI and structural response characteristics of real multiple degrees‐of‐freedom (MDOF) systems. In this paper, through a comprehensive parametric study of 21600 MDOF and its equivalent SDOF (E‐SDOF) systems subjected to an ensemble of 30 earthquake ground motions recorded on alluvium and soft soils, effects of SSI on strength reduction factor of MDOF systems have been intensively investigated. It is concluded that generally, SSI reduces the strength reduction factor of both MDOF and more intensively SDOF systems. However, depending on the number of stories, soil flexibility, aspect ratio and inelastic range of vibration, the strength reduction factor of MDOF systems could be significantly different from that of E‐SDOF systems. A new simplified equation, which is a function of fixed‐base fundamental period, ductility ratio, the number of stories, structure slenderness ratio and dimensionless frequency, is proposed to estimate strength reduction factors for MDOF soil–structure systems. Copyright © 2012 John Wiley & Sons, Ltd.     

Seismic response control of base‐isolated buildings using multiple tuned mass dampers

Seismic response of a base‐isolated building equipped with single tuned mass damper (STMD), multiple tuned mass dampers (MTMDs), and distributed multiple tuned mass dampers (d‐MTMDs) under real earthquake ground motions is investigated. Numerical study is carried out using analytical models of five‐, 10‐, and 15‐storey base‐isolated buildings equipped with the STMD, MTMDs, and d‐MTMDs. The buildings are modeled as shear‐type structure with a lateral degree of freedom at each floor level, and the buildings are isolated using the laminated rubber bearing, lead‐core rubber bearing, friction pendulum system, and resilient‐friction base isolator. The coupled differential equation of motion for the buildings are derived and solved in the incremental form using Newmark's step‐by‐step method of integration. From the numerical study conducted, it is concluded that installing a tuned mass damper at each floor level of a base‐isolated building reduces the structural response in terms of top floor acceleration and bearing displacement. It is found that installing the MTMDs and d‐MTMDs are significantly beneficial in reducing top floor acceleration as compared with the STMD. Further, almost comparable reduction in the bearing displacement could be obtained by installing the STMD, MTMDs at top, and d‐MTMDs in the base‐isolated buildings. The d‐MTMDs are more beneficial as compared with the STMD and MTMDs as otherwise huge controller mass can now be divided and distributed on different floor levels.