Collapse period of degrading SDOF systems

Seismic demand estimation for a structure is a critical issue for seismic performance assessment so that the potential damage can be estimated realistically. Many researchers proposed simplified methods to estimate the demand of a structure under strong ground motions. However, most of them did not consider degradation and collapse potential of the structures. Even some of theme considered the degradation effect, stiffness and strength degradation effects were considered separately without collapse potential caused by dynamic instability. In this study, collapse potential of SDOF systems caused by dynamic instability with stiffness and strength degradation has been investigated. Nonlinear time history analyses were performed, using an energy-based, strength and stiffness degraded hysteretic model that considers the collapse potential, with 160 earthquake acceleration time histories. An equation was proposed for the estimation of collapse period of SDOF systems as a function of certain strength reduction factor, ductility level and post-capping stiffness ratio. Finally, effects of parameters of the considered hysteretic model and local site conditions on the collapse period were investigated.     

Seismic response of self‐centring hysteretic SDOF systems

The seismic response of single‐degree‐of‐freedom (SDOF) systems incorporating flag‐shaped hysteretic structural behaviour, with self‐centring capability, is investigated numerically. For a SDOF system with a given initial period and strength level, the flag‐shaped hysteretic behaviour is fully defined by a post‐yielding stiffness parameter and an energy‐dissipation parameter. A comprehensive parametric study was conducted to determine the influence of these parameters on SDOF structural response, in terms of displacement ductility, absolute acceleration and absorbed energy. This parametric study was conducted using an ensemble of 20 historical earthquake records corresponding to ordinary ground motions having a probability of exceedence of 10% in 50 years, in California. The responses of the flag‐shaped hysteretic SDOF systems are compared against the responses of similar bilinear elasto‐plastic hysteretic SDOF systems. In this study the elasto‐plastic hysteretic SDOF systems are assigned parameters representative of steel moment resisting frames (MRFs) with post‐Northridge welded beam‐to‐column connections. In turn, the flag‐shaped hysteretic SDOF systems are representative of steel MRFs with newly proposed post‐tensioned energy‐dissipating connections. Building structures with initial periods ranging from 0.1 to 2.0s and having various strength levels are considered. It is shown that a flag‐shaped hysteretic SDOF system of equal or lesser strength can always be found to match or better the response of an elasto‐plastic hysteretic SDOF system in terms of displacement ductility and without incurring any residual drift from the seismic event. Copyright © 2002 John Wiley & Sons, Ltd.     

单自由度自复位体系设计能量谱研究

本文对具有旗帜型滞回模型的单自由度自复位体系提出了设计能量谱的构造方法,包括设计输入能量谱和设计滞回耗能比谱。首先按中国规范场地类别选取360条实际强震记录进行时程分析,对影响单自由度自复位体系输入能量谱和滞回耗能比谱的参数,包括地震波类型、滞回模型、阻尼比、延性系数等进行研究。在此基础上分别建议了设计输入能量谱和设计滞回耗能比谱及其曲线参数的确定方法,并与实际强震记录计算结果进行比较。结果表明结构滞回模型对能量谱影响明显;阻尼比和延性系数对输入能量谱的影响在整个周期范围内有显著差异,但均有明显的削峰作用。建议的两种设计能量谱综合考虑了结构参数、地震波参数和中国场地类别的影响,可以较好的拟合实际情况,并对弹塑性单自由度自复位体系在地震作用下的耗能需求做出较准确的估计。     

单自由度体系的地震残余变形研究

结构在经受地震动作用后会发生变形和位移,其中在震动结束后不能恢复的这一部分,即为残余变形或永久变形。残余变形取决于结构本身的动力性能和输入地震波的特性以及场地条件等。残余变形能够提供震害评估的信息,同时也是震后加固修复的指标。对单自由度体系进行了研究,考察不同自振周期、阻尼比、延性水准、滞回特性以及输入地震动下的残余变形,得到其影响因素并分析其中机理,为以最大变形和累积耗能为依据的基于性能的抗震工程学提供了补充和新的思路。     

Effect of peak ground velocity on deformation demands for SDOF systems

The effect of peak ground velocity (PGV) on single‐degree‐of‐freedom (SDOF) deformation demands and for certain ground‐motion features is described by using a total of 60 soil site records with source‐to‐site distances less than 23 km and moment magnitudes between 5.5 and 7.6. The observations based on these records indicate that PGV correlates well with the earthquake magnitude and provides useful information about the ground‐motion frequency content and strong‐motion duration that can play a role on the seismic demand of structures. The statistical results computed from non‐linear response history analyses of different hysteretic models highlight that PGV correlates better with the deformation demands with respect to other ground motion intensity measures. The choice of PGV as ground motion intensity decreases the dispersion due to record‐to‐record variability of SDOF deformation demands, particularly in the short period range. The central tendencies of deformation demands are sensitive to PGV and they may vary considerably as a function of the hysteretic model and structural period. The results provided in this study suggest a consideration of PGV as a stable candidate for ground motion intensity measure in simplified seismic assessment methods that are used to estimate structural performance for earthquake hazard analysis. Copyright © 2005 John Wiley & Sons, Ltd.     

The role of ground motion duration and pulse effects in the collapse of ductile systems

The seismic collapse capacity of ductile single-degree-of-freedom systems vulnerable to P-Δ effects is investigated by examining the respective influence of ground motion duration and acceleration pulses. The main objective is to provide simple relationships for predicting the duration-dependent collapse capacity of modern ductile systems. A novel procedure is proposed for modifying spectrally equivalent records, such that they are also equivalent in terms of pulses. The effect of duration is firstly assessed, without accounting for pulses, by assembling 101 pairs of long and short records with equivalent spectral response. The systems considered exhibit a trilinear backbone curve with an elastic, hardening and negative stiffness segment. The parameters investigated include the period, negative stiffness slope, ductility and strain hardening, for both bilinear and pinching hysteretic models. Incremental dynamic analysis is employed to determine collapse capacities and derive design collapse capacity spectra. It is shown that up to 60% reduction in collapse capacity can occur due to duration effects for flexible bilinear systems subjected to low levels of P-Δ. A comparative evaluation of intensity measures that account for spectral shape, duration or pulses, is also presented. The influence of pulses, quantified through incremental velocity, is then explicitly considered to modify the long records, such that their pulse distribution matches that of their short spectrally equivalent counterparts. The results show the need to account for pulse effects in order to achieve unbiased estimation of the role of duration in flexible ductile systems, as it can influence the duration-induced reduction in collapse capacity by more than 20%.     

双向地震荷载下崩塌堆积体盲数稳定可靠性分析

为了能考虑地震双向性和岩土体参数多种不确定性,提出了地震荷载下崩塌堆积体稳定可靠性分析方法,进一步研究水平和竖向地震荷载对崩塌堆积体的可靠性影响.运用极限平衡法和拟静力法分析了双向地震下崩塌堆积体的安全稳定性,采用响应面法和JC法建立崩塌堆积体的地震极限状态方程,然后,运用盲数理论对岩土体参数进行盲数化处理,进一步推导...     

Seismic collapse capacity of basic inelastic structures vulnerable to the P‐delta effect

The collapse capacity of earthquake‐excited inelastic nondeteriorating SDOF systems, which are vulnerable to the destabilizing effect of gravity loads (P‐delta effect), is evaluated. In this paper, the collapse capacity of the system subjected to a ground motion is defined as spectral acceleration at its initial structural period, at which the structure becomes unstable. Characteristic structural parameters, which affect the collapse capacity, are identified. Ground motion records of the ATC 63 far‐field set characterize severe earthquake excitation. In extensive incremental dynamic analyses studies, the impact of these parameters and of aleatory uncertainties on the collapse capacity is assessed and quantified. Median and percentile collapse capacities are plotted against the initial structural period leading to collapse capacity spectra. Nonlinear regression analyses are applied to derive analytical expressions of the design collapse capacity spectra and collapse fragility curves. The ultimate objective is to provide collapse capacity spectra for easy application and yet sufficient accurate assessment of the dynamic stability of flexible multistory buildings. Copyright © 2011 John Wiley & Sons, Ltd.     

On the estimation of hysteretic energy demands for SDOF systems

Based on a statistical study of the dynamic response of single degree of freedom (SDOF) systems subjected to earthquake ground motions, a rule to estimate hysteretic energy demands is proposed. Expressions for elastic–perfectly plastic, stiffness degrading and pinching SDOF systems were obtained. The proposed rule does not explicitly depend on the period of the system; instead, it depends on the elastic pseudo‐acceleration and elastic velocity spectra. It is shown that the proposed rule can be applied to compute hysteretic energy demands for systems located at different soil conditions. In addition, information about scatter and bias of the proposed rule is also presented. Copyright © 2007 John Wiley & Sons, Ltd.     

Multi-step prediction of strong earthquake ground motions and seismic responses of SDOF systems based on EMD-ELM method

This paper proposes a new multi-step prediction method of EMD-ELM (empirical mode decomposition-extreme learning machine) to achieve the short-term prediction of strong earthquake ground motions. Firstly, the acceleration time histories of near-fault ground motions with nonstationary property are decomposed into several components of intrinsic mode functions (IMFs) with different characteristic scales by the technique of EMD. Subsequently, the ELM method is utilized to predict the IMF components. Moreover, the predicted values of each IMF component are superimposed, and the short-term prediction of ground motions is attained with low error. The predicted results of near-fault acceleration records demonstrate that the EMD-ELM method can realize multi-step prediction of acceleration records with relatively high accuracy. Finally, the elastic and inelastic acceleration, velocity and displacement responses of single degree of freedom (SDOF) systems are also predicted with satisfactory accuracy by EMD-ELM method.     

Peak earthquake response of structures under multi-component excitations

Accurate estimation of the peak seismic responses of structures is important in earthquake resistant design. The internal force distributions and the seismic responses of structures are quite complex, since ground motions are multi- directional. One key issue is the uncertainty of the incident angle between the directions of ground motion and the reference axes of the structure. Different assumed seismic incidences can result in different peak values within the scope of design spectrum analysis for a given structure and earthquake ground motion record combination. Using time history analysis to determine the maximum structural responses excited by a given earthquake record requires repetitive calculations to determine the critical incident angle. This paper presents a transformation approach for relatively accurate and rapid determination of the maximum peak responses of a linear structure subjected to three-dimensional excitations within all possible seismic incident angles. The responses can be deformations, internal forces, strains and so on. An irregular building structure model is established using SAP2000 program. Several typical earthquake records and an artifi cial white noise are applied to the structure model to illustrate the variation of the maximum structural responses for different incident angles. Numerical results show that for many structural parameters, the variation can be greater than 100%. This method can be directly applied to time history analysis of structures using existing computer software to determine the peak responses without carrying out the analyses for all possible incident angles. It can also be used to verify and/or modify aseismic designs by using response spectrum analysis.     

Inelastic torsion of multistorey buildings under earthquake excitations

The inelastic earthquake response of eccentric, multistorey, frame‐type, reinforced concrete buildings is investigated using three‐ and five‐storey models, subjected to a set of 10, two‐component, semi‐artificial motions, generated to match the design spectrum. Buildings designed according to the EC8 as well as the UBC‐97 code were included in the investigation. It is found that contrary to what the simplified one‐storey, typical, shear‐beam models predict, the so‐called ‘flexible’ side frames exhibit higher ductility demands than the ‘stiff’ side frames. The substantial differences in such demands between the two sides suggest a need for reassessment of the pertinent code provisions. This investigation constitutes one of the first attempts to study the problem of inelastic torsion by means of realistic, multistorey inelastic building models. Additional studies with similar or even more refined idealizations will certainly be required to arrive at definite results and recommendations for possible code revisions. Copyright © 2005 John Wiley & Sons, Ltd.     

Prediction and validation of sidesway collapse of two scale models of a 4‐story steel moment frame

A research program is summarized in which collapse of a steel frame structure is predicted numerically and the accuracy of prediction is validated experimentally through earthquake simulator tests of two 1:8 scale models of a 4‐story code‐compliant prototype moment‐resisting frame. We demonstrate that (1) sidesway collapse can occur for realistic combinations of structural framing and earthquake ground motion; (2) P?Δeffects and component deterioration dominate behavior of the frame near collapse; (3) prediction of collapse is feasible using relatively simple analytical models provided that component deterioration is adequately represented in the analytical model; and (4) response of the framing system near collapse is sensitive to the history that every important component of the frames experiences, implying that symmetric cyclic loading histories that are routinely used to test components provide insufficient information for modeling deterioration near collapse. Copyright © 2010 John Wiley & Sons, Ltd.     

Residual displacements of RC structures as SDOF systems

Residual displacements are sensitive to ground motion details, hence more random than peak inelastic displacements. Among the factors with systematic impact on residual displacements, the post‐yield‐stiffness‐ratio has been studied thoroughly; its effects are not investigated further. Concerning another important factor, the hysteresis law, past studies have focused on the bilinear model, which does not represent concrete structures. Residual displacements from nonlinear response‐history analyses of bilinear systems are compared to those from models tuned to concrete structures, conforming to modern codes, deficient or intermediate. Deficient‐type structures, with their narrow, almost self‐centering hysteresis loops, develop markedly smaller residual displacements than those with stable energy‐dissipating behavior. A velocity pulse in the motion increases peak inelastic and residual displacements by about the same proportion. As a fraction of the peak inelastic or spectral displacement, residual displacements are on average almost independent of the period and increase when the lateral strength ratio increases, reaching a limit at a lateral strength ratio of 2 to 5. Peak inelastic displacements are a better basis for estimation of residual displacements than spectral ones: the ratio of the two is almost independent of the period, the lateral strength ratio (beyond values of 2 to 3) and velocity pulses. The spectrum of the ratio of residual displacement to peak inelastic or spectral displacement is considered as a random process of period; its mean and variance functions, marginal probability distributions and autocorrelation functions are given in terms of the lateral strength ratio, the hysteresis model and the presence of a velocity pulse. Copyright © 2014 John Wiley & Sons, Ltd.     

Integrating visual damage simulation,virtual inspection,and collapse capacity to evaluate post‐earthquake structural safety of buildings

A methodology is introduced to assess the post‐earthquake structural safety of damaged buildings using a quantitative relationship between observable structural component damage and the change in collapse vulnerability. The proposed framework integrates component‐level damage simulation, virtual inspection, and structural collapse performance assessment. Engineering demand parameters from nonlinear response history analyses are used in conjunction with component‐level damage simulation to generate multiple realizations of damage to key structural elements. Triggering damage state ratios, which describe the fraction of components within a damage state that results in an unsafe placard assignment, are explicitly linked to the increased collapse vulnerability of the damaged building. A case study is presented in which the framework is applied to a 4‐story reinforced concrete frame building with masonry infills. The results show that when subjected to maximum considered earthquake level ground motions, the probability of experiencing enough structural damage to trigger an unsafe placard, leading to building closure, is more than 2 orders of magnitude higher than the risk of collapse.     

Fiber-based hysteretic model for simulating strength and stiffness deterioration of steel hollow structural section columns under cyclic loading

An efficient component model has been developed that captures strength and stiffness deterioration of steel hollow structural section (HSS) columns. The proposed model consists of two fiber-based segments at a member's ends along with an elastic segment in between. The fibers exhibit nonlinear uniaxial stress–strain behavior, which is explicitly defined by uniaxial monotonic tensile and cyclic round coupon tests. The postbuckling behavior of an HSS column is traced through a proposed uniaxial effective stress–strain constitutive formulation, which includes a softening branch in compression and an energy-based deterioration rule to trace the influence of cyclic deterioration in the inelastic cyclic straining. These may be inferred by uniaxial stub-column tests. The component model captures the coupling between the column axial force and flexural demands. Consistent model parameters for a number of steel materials used in the steel construction in North America and Japan are proposed along with the associated model calibration process. The efficiency of the proposed model in predicting the hysteretic behavior of HSS columns is demonstrated by comparisons with physical steel column tests subjected to various loading histories, including representative ones of ratcheting prior to earthquake-induced collapse. The proposed model is implemented in an open-source finite element software for nonlinear response history analysis of frame structures. The effectiveness of the proposed model in simulating dynamic instability of steel frame buildings is demonstrated through nonlinear response simulations of a four-story steel frame building, which was tested at full-scale through collapse. Limitations as well as suggestions for future work are discussed.     

基于等效单自由度体系的结构地震输入能量的研究

通过对多自由度体系结构在地震作用下的能量分析,考虑地震动因素和结构自身特性,提出一种框架结构地震总输入能量的简化求解方法.实例计算结果表明:基于等效单自由度体系来估计多自由度体系的地震总输入能,是一种计算简便且较为准确的方法.     

地震断层对管道压溃压力的影响

利用有限元软件ABAQUS,结合用户自定义Python程序,开展地震断层作用下深海管道局部变形和压溃过程的数值模拟。分析均质土体和随机分布土体模型的地震断层位移大小对管道局部变形的影响,并分析断层诱发的局部挤压变形对管道压溃压力的影响。研究表明:相比于断层走向与管道轴线方向垂直的走滑断层,断层走向与管道轴线方向夹角为45°的走滑断层作用下管道的压溃压力较小,且当断层走向为管道轴线方向逆时针旋转45°时,左旋走滑断层作用下管道的压溃压力低于右旋走滑断层作用下的管道压溃压力。断层位移相同时,管道径厚比越大,压溃压力越小。考虑土壤随机性时,由于APIX65钢制管道刚性较大,且管道两侧土体内聚力和摩擦角分散于均质土壤土体参数均值两侧,因此断层作用过程中管道受到的土压力在均质土壤模型中的土压力数值处上下波动。     

Identification of soil degradation during earthquake excitations by Bayesian inference

A Bayesian inference approach is introduced to identify soil degradation behaviours at four downhole array sites. The approach of inference is based on a parametric time‐varying infinite impulse response filter model. The approach is shown to be adaptive to the changes of filter parameters and noise amplitudes. Four sites, including the Lotung (Taiwan), Chiba (Japan), Garner Valley (California), and Treasure Island (California) sites with downhole seismic arrays are analysed. Our results show two major types of soil degradation behaviour: the well‐known strain‐dependent softening, and reduction in stiffness that is not instantaneously recoverable. It is also found that both types of soil degradation are more pronounced in sandy soils than in clayey soils. The mechanism for the second type of soil degradation is not yet clear to the authors and suggested to be further studied. Copyright © 2003 John Wiley & Sons, Ltd.