Near‐fault ground motions,and the response of elastic and inelastic single‐degree‐of‐freedom (SDOF) systems

In order to investigate the response of structures to near‐fault seismic excitations, the ground motion input should be properly characterized and parameterized in terms of simple, yet accurate and reliable, mathematical models whose input parameters have a clear physical interpretation and scale, to the extent possible, with earthquake magnitude. Such a mathematical model for the representation of the coherent (long‐period) ground motion components has been proposed by the authors in a previous study and is being exploited in this article for the investigation of the elastic and inelastic response of the single‐degree‐of‐freedom (SDOF) system to near‐fault seismic excitations. A parametric analysis of the dynamic response of the SDOF system as a function of the input parameters of the mathematical model is performed to gain insight regarding the near‐fault ground motion characteristics that significantly affect the elastic and inelastic structural performance. A parameter of the mathematical representation of near‐fault motions, referred to as ‘pulse duration’ (T_P), emerges as a key parameter of the problem under investigation. Specifically, T_P is employed to normalize the elastic and inelastic response spectra of actual near‐fault strong ground motion records. Such normalization makes feasible the specification of design spectra and reduction factors appropriate for near‐fault ground motions. The ‘pulse duration’ (T_P) is related to an important parameter of the rupture process referred to as ‘rise time’ (τ) which is controlled by the dimension of the sub‐events that compose the mainshock. Copyright © 2004 John Wiley & Sons, Ltd.     

Energy demands for seismic design against low‐cycle fatigue

A seismic design procedure that does not take into account the maximum and cumulative plastic deformation demands that a structure is likely to undergo during severe ground motion could lead to unsatisfactory performance. In spite of this, current design procedures do not take into account explicitly the effect of low‐cycle fatigue. Based on the high correlation that exists between the strength reduction factor and the energy demand in earthquake‐resistant structures, simple procedures can be formulated to estimate the cumulative plastic deformation demands for design purposes. Several issues should be addressed during the use of plastic energy within a practical performance‐based seismic design methodology. Copyright © 2006 John Wiley & Sons, Ltd.     

Design energy input spectra for moderate‐seismicity regions

This paper proposes energy input spectra applicable to seismic design of structures located in low‐to‐moderate‐seismicity regions. These spectra represent the load effect, in terms of input energy, of the most severe earthquake that the construction might encounter during its lifetime. The spectra have been derived through dynamic response analyses of over 100 ground motion records obtained from 48 earthquakes that have occurred in Spain. An empirical equation for estimating the energy input contributable to damage from the total input energy is also suggested. This equation takes into account both the damping and the degree of plastification of the structure. Finally, the proposed design energy input spectra are compared with the provisions of the current Spanish Seismic Code and with the response spectra of recent earthquakes that have occurred in Turkey and Taiwan. Copyright © 2002 John Wiley & Sons, Ltd.     

Correlations between Energy and Displacement Demands for Performance-Based Seismic Engineering

The development of a scientific framework for performance-based seismic engineering requires, among other steps, the evaluation of ground motion intensity measures at a site and the characterization of their relationship with suitable engineering demand parameters (EDPs) which describe the performance of a structure. In order to be able to predict the damage resulting from earthquake ground motions in a structural system, it is first necessary to properly identify ground motion parameters that are well correlated with structural response and, in turn, with damage. Since structural damage during an earthquake ground motion may be due to excessive deformation or to cumulative cyclic damage, reliable methods for estimating displacement demands on structures are needed. Even though the seismic performance is directly related to the global and local deformations of the structure, energy-based methodologies appear more helpful in concept, as they permit a rational assessment of the energy absorption and dissipation mechanisms that can be effectively accomplished to balance the energy imparted to the structure. Moreover, energy-based parameters are directly related to cycles of response of the structure and, therefore, they can implicitly capture the effect of ground motion duration, which is ignored by conventional spectral parameters. Therefore, the identification of reliable relationships between energy and displacement demands represents a fundamental issue in both the development of more reliable seismic code provisions and the evaluation of seismic vulnerability aimed at the upgrading of existing hazardous facilities. As these two aspects could become consistently integrated within a performance-based seismic design methodology, understanding how input and dissipated energy are correlated with displacement demands emerges as a decisive prerequisite. The aim of the present study is the establishment of functional relationships between input and dissipated energy (that can be considered as parameters representative of the amplitude, frequency content and duration of earthquake ground motions) and displacement-based response measures that are well correlated to structural and non-structural damage. For the purpose of quantifying the EDPs to be related to the energy measures, for comprehensive range of ground motion and structural characteristics, both simplified and more accurate numerical models will be used in this study for the estimation of local and global displacement and energy demands. Parametric linear and nonlinear time-history analyses will be performed on elastic and inelastic SDOF and MDOF systems, in order to assume information on the seismic response of a wide range of current structures. Hysteretic models typical of frame force/displacement behavior will be assumed for the local inelastic cyclic response of the systems. A wide range of vibration periods will be taken into account so as to define displacement, interstory drift and energy spectra for MDOF systems. Various scalar measures related to the deformation demand will be used in this research. These include the spectral displacements, the peak roof drift ratio, and the peak interstory drift ratio. A total of about 900 recorded ground motions covering a broad variety of condition in terms of frequency content, duration and amplitude will be used as input in the dynamic analyses. The records are obtained from 40 earthquakes and grouped as a function of magnitude of the event, source-to-site condition and site soil condition. In addition, in the data-set of records a considerable number of near-fault signals is included, in recognition of the particular significance of pulse-like time histories in causing large seismic demands to the structures.     

Damage index based on stiffness degradation of low‐rise RC walls

Widely used damage indices, such as ductility and drift ratios, do not account for the influences of the duration of strong shaking, the cumulative inelastic deformation or energy dissipation in structures. In addition, the formulation and application of most damage indices have until now been based primarily on flexural modes of failure. However, evidence from earthquakes suggests that shear failure or combined shear‐flexure behavior is responsible for a large proportion of failures. Empirical considerations have been made in this paper for evaluating structural damage of low‐rise RC walls under earthquake ground motions by means of a new energy‐based low‐cycle fatigue damage index. The proposed empirical damage index is based on the results of an experimental program that comprised six shake table tests of RC solid walls and walls with openings; results of six companion walls tested under QS‐cyclic loading were used for comparison purposes. Variables studied were the wall geometry, type of concrete, web shear steel ratio, type of web shear reinforcement, and testing method. The index correlates the stiffness degradation and the destructiveness of the earthquake in terms of the duration and intensity of the ground motions. The stiffness degradation model considers simultaneously the increment of damage associated to the low‐cycle fatigue, energy dissipation, and the cumulative cyclic parameters, such as displacement demand and hysteretic energy dissipated. Copyright © 2014 John Wiley & Sons, Ltd.     

Non‐structure‐specific intensity measure parameters and characteristic period of near‐fault ground motions

This paper focuses on the effects of long‐period pulse of near‐fault ground motions on the structural damage potential. Two sets of near‐fault ground motion records from Chi‐Chi, Taiwan earthquake and Northridge earthquake with and without distinct pulse are selected as the input, and the correlation analysis between 30 non‐structure‐specific intensity measure parameters and maximum inelastic displacements and energy responses (input energy and hysteretic energy) of bilinear single degree of freedom systems are conducted. Based on the frequency characteristic of near‐fault ground motions with remarkable long‐period components, two intensity indices are proposed, namely, the improved effective peak acceleration (IEPA) and improved effective peak velocity (IEPV). In addition a new characteristic period of these ground motions is defined based on IEPA and IEPV. Numerical results illustrate that the intensity measure parameters related to ground acceleration present the best correlation with the seismic responses for rigid systems; the velocity‐related and displacement‐related parameters are better for medium‐frequency systems and flexible systems, respectively. The correlation curves of near‐fault ground motions with velocity pulse differ from those of ground motions without pulse. Moreover, the improved parameters IEPA and IEPV of near‐fault impulsive ground motions enhance the performance of intensity measure of corresponding conventional parameters, i.e. EPA and EPV. The new characteristic period based on IEPA and IEPV can better reflect the frequency content of near‐fault ground motions. Copyright © 2009 John Wiley & Sons, Ltd.     

Scaling of strength reduction factors for degrading elasto‐plastic oscillators

The inelastic (design) spectra characterizing a seismic hazard are generally obtained by the scaling‐down of the elastic (design) spectra via a set of response modification factors. The component of these factors, which accounts for the ductility demand ratio, is known as the strength reduction factor (SRF), and the variation of this factor with initial period of the oscillator is called an SRF spectrum. This study considers scaling of the SRF spectrum in the case of an elasto‐plastic oscillator with strength and stiffness degradation characteristics. Two models are considered: one depending directly on the characterization of source and site parameters and the other depending on the normalized design spectrum characterization of the seismic hazard. The first model is the same as that proposed earlier by the second author, and is given in terms of earthquake magnitude, strong‐motion duration, predominant period, geological site conditions, ductility demand ratio, and ductility supply‐related parameter. The second model is a new model proposed here in terms of the normalized pseudo‐spectral acceleration values (to unit peak ground acceleration), ductility demand ratio and ductility supply‐related parameter. For each of these models, least‐square estimates of the coefficients are obtained through regression analyses of the data for 956 recorded accelerograms in western U.S.A. Parametric studies carried out with the help of these models confirm the dependence of SRFs on strong‐motion duration and earthquake magnitude besides predominant period and site conditions. It is also seen that degradation characteristics make a slight difference for high ductility demands and may lead to lower values of SRFs, unless the oscillators are very flexible. Copyright © 2004 John Wiley & Sons, Ltd.     

Cumulative damage‐based inelastic cyclic demand spectrum

The estimation of cyclic deformation demand resulting from earthquake loads is crucial to the core objective of performance‐based design if the damage and residual capacity of the system following a seismic event needs to be evaluated. A simplified procedure to develop the cyclic demand spectrum for use in preliminary seismic evaluation and design is proposed in this paper. The methodology is based on estimating the number of equivalent cycles at a specified ductility. The cyclic demand spectrum is then determined using well‐established relationships between seismic input energy and dissipated hysteretic energy. An interesting feature of the proposed procedure is the incorporation of a design spectrum into the proposed procedure. It is demonstrated that the force–deformation characteristics of the system, the ductility‐based force‐reduction factor R_μ, and the ground motion characteristics play a significant role in the cyclic demand imposed on a structure during severe earthquakes. Current design philosophy which is primarily based on peak response amplitude considers cyclic degradation only in an implicit manner through detailing requirements based on observed experimental testing. Findings from this study indicate that cumulative effects are important for certain structures, classified in this study by the initial fundamental period, and should be incorporated into the design process. Copyright © 2003 John Wiley & Sons, Ltd.     

Scaling of ductility and damage‐based strength reduction factors for horizontal motions

The conventional approach of obtaining the inelastic response spectra for the aseismic design of structures involves the reduction of elastic spectra via response modification factors. A response modification factor is usually taken as a product of (i) strength factor, R_S, (ii) ductility factor, R_μ, and (iii) redundancy factor, R_R. Ductility factor, also known as strength reduction factor (SRF), is considered to primarily depend on the initial time period of the single‐degree‐of‐freedom (SDOF) oscillator and the displacement ductility demand ratio for the ground motion. This study proposes a preliminary scaling model for estimating the SRFs of horizontal ground motions in terms of earthquake magnitude, strong motion duration and predominant period of the ground motion, geological site conditions, and ductility demand ratio, with a given level of confidence. The earlier models have not considered the simultaneous dependence of the SRFs on various governing parameters. Since the ductility demand ratio is not a complete measure of the cumulative damage in the structure during the earthquake‐induced vibrations, the existing definition of the SRF is sought to be modified with the introduction of damage‐based SRF (in place of ductility‐based SRF). A parallel scaling model has been proposed for estimating the damage‐based SRFs. This model considers damage and ductility supply ratio as parameters instead of ductility demand ratio. Through a parametric study on ductility‐based SRFs, it has been shown that the hitherto assumed insensitivity of earthquake magnitude and strong motion duration may not be always justified and that the initial time period of the oscillator plays an important role in the dependence of SRF on these parameters. Further, the damage‐based SRFs are found to show similar parametric dependence as observed in the case of the ductility‐based SRFs. Copyright © 2000 John Wiley & Sons, Ltd.     

Wavelet‐based characterization of design ground motions

With the recent emergence of wavelet‐based procedures for stochastic analyses of linear and non‐linear structural systems subjected to earthquake ground motions, it has become necessary that seismic ground motion processes are characterized through statistical functionals of wavelet coefficients. While direct characterization in terms of earthquake and site parameters may have to wait for a few more years due to the complexity of the problem, this study attempts such characterization through commonly available Fourier and response spectra for design earthquake motions. Two approaches have been proposed for obtaining the spectrum‐compatible wavelet functionals, one for input Fourier spectrum and another for input response spectrum, such that the total number of input data points are 30–35% of those required for a time‐history analysis. The proposed methods provide for simulating ‘desired non‐stationary characteristics’ consistent with those in a recorded accelerogram. Numerical studies have been performed to illustrate the proposed approaches. Further, the wavelet functionals compatible with a USNRC spectrum in the case of 35 recorded motions of similar strong motion durations have been used to obtain the strength reduction factor spectra for elasto‐plastic oscillators and to show that about ±20% variation may be assumed from mean to 5 and 95% confidence levels due to uncertainty in the non‐stationary characteristics of the ground motion process. Copyright © 2002 John Wiley & Sons, Ltd.     

Earthquake‐resistant structural design through energy demand and capacity

An energy‐based earthquake‐resistant structural design method is proposed. The proposed method uses specific input energy spectra, modal or time‐history analyses, and energy distribution among structural members. For a given member strength and stiffness, a relationship between the energy attributable to damage absorbed by a member and its cumulative ductility demand can be determined. Member strength, stiffness and energy capacity are design parameters which are simultaneously used in the design. The method can avoid soft‐storey design. The damage is measured based on a cumulative basis considering earthquake magnitude, frequency, and duration. Tests have been carried out to determine energy absorbing capacities of various structural components. More efforts are needed to make the energy‐based earthquake‐resistant structural design practical, but ssimple formulations for this method are possible. Copyright © 2007 John Wiley & Sons, Ltd.     

Ground motion duration effect on responses of hydraulic shallow-buried tunnel under SV-waves excitations

Although intensive research of the influence of ground motion duration on structural cumulative damage has been carried out, the influence of dynamic responses in underground tunnels remains a heated debate. This study attempts to highlight the importance of the ground motion duration effect on hydraulic tunnels subjected to deep-focus earthquakes. In the study, a set of 18 recorded accelerograms with a wide-range of durations were employed. A spectrally equivalent method serves to distinguish the effect of duration from other ground motion features, and then the seismic input model was simulated using SV-wave excitation based on a viscous-spring boundary, which was verified by the time-domain waves analysis method. The nonlinear analysis results demonstrate that the risk of collapse of the hydraulic tunnel is higher under long-duration ground motion than that of short-duration ground motion of the same seismic intensity. In a low intensity earthquake, the ground motion duration has little effect on the damage energy consumption of a hydraulic tunnel lining, but in a high intensity earthquake, dissipation of the damage energy and damage index of concrete shows a nonlinear growth trend accompanied by the increase of ground motion duration, which has a great influence on the deformation and stress of hydraulic tunnels, and correlation analysis shows that the correlation coefficient is greater than 0.8. Therefore, the duration of ground motion should be taken into consideration except for its intensity and frequency content in the design of hydraulic tunnel, and evaluation of seismic risk.

     

Adapting earthquake actions in Eurocode 8 for performance‐based seismic design

Performance‐based seismic design (PBSD) can be considered as the coupling of expected levels of ground motion with desired levels of structural performance, with the objective of achieving greater control over earthquake‐induced losses. Eurocode 8 (EC8) already envisages two design levels of motion, for no collapse and damage limitation performance targets, anchored to recommended return periods of 475 and 95 years, respectively. For PBSD the earthquake actions need to be presented in ways that are appropriate to the estimation of inelastic displacements, since these provide an effective control on damage at different limit states. The adequacy of current earthquake actions in EC8 are reviewed from this perspective and areas requiring additional development are identified. The implications of these representations of the seismic loads, in terms of mapping and zonation, are discussed. The current practice of defining the loading levels on the basis of the pre‐selected return periods is challenged, and ideas are discussed for calibrating the loading‐performance levels for design on the basis of quantitative earthquake loss estimation. Copyright © 2005 John Wiley & Sons, Ltd.     

Analytical modelling of near‐source pulse‐like seismic demand for multi‐linear backbone oscillators

Nonlinear static procedures, which relate the seismic demand of a structure to that of an equivalent single‐degree‐of‐freedom oscillator, are well‐established tools in the performance‐based earthquake engineering paradigm. Initially, such procedures made recourse to inelastic spectra derived for simple elastic–plastic bilinear oscillators, but the request for demand estimates that delve deeper into the inelastic range, motivated investigating the seismic demand of oscillators with more complex backbone curves. Meanwhile, near‐source (NS) pulse‐like ground motions have been receiving increased attention, because they can induce a distinctive type of inelastic demand. Pulse‐like NS ground motions are usually the result of rupture directivity, where seismic waves generated at different points along the rupture front arrive at a site at the same time, leading to a double‐sided velocity pulse, which delivers most of the seismic energy. Recent research has led to a methodology for incorporating this NS effect in the implementation of nonlinear static procedures. Both of the previously mentioned lines of research motivate the present study on the ductility demands imposed by pulse‐like NS ground motions on oscillators that feature pinching hysteretic behaviour with trilinear backbone curves. Incremental dynamic analysis is used considering 130 pulse‐like‐identified ground motions. Median, 16% and 84% fractile incremental dynamic analysis curves are calculated and fitted by an analytical model. Least‐squares estimates are obtained for the model parameters, which importantly include pulse period T_p. The resulting equations effectively constitute an R ? μ ? T ? T_p relation for pulse‐like NS motions. Potential applications of this result towards estimation of NS seismic demand are also briefly discussed. Copyright © 2016 John Wiley & Sons, Ltd.     

Evaluation of site‐dependent constant‐damage design spectra for reinforced concrete structures

An investigation on the validity of the conventional design approach known as constant displacement ductility is carried out. The hysteretic behaviour described by the Modified Takeda model is taken to represent the characteristics of reinforced concrete structural systems. The results presented in the form of seismic damage spectra indicate that the conventional design approach may not be valid because cumulative damage is excessively high. The inelastic design spectra based on the constant‐damage concept are proposed in terms of simplified expressions. The expressions are derived from constant‐damage design spectra computed by non‐linear response analysis for SDOF systems subjected to ground motions recorded on rock sites, alluvium deposits, and soft‐soil sites. The proposed expressions, which are dependent on the local soil conditions, are functions of target seismic damage, displacement ductility ratio and period of vibration. The seismic damage of structures that have been designed based on this new design approach is also checked by a design‐and‐evaluation approach. The results are found to be satisfactory. Copyright © 2004 John Wiley & Sons, Ltd.     

Ground motion characteristics of the Chi‐Chi earthquake of 21 September 1999

The purpose of this paper is to investigate the ground motion characteristics of the Chi‐Chi earthquake (21 September 1999) as well as the interpretation of structural damage due to this earthquake. Over 300 strong motion records were collected from the strong motion network of Taiwan for this earthquake. A lot of near‐field ground motion data were collected. They provide valuable information on the study of ground motion characteristics of pulse‐like near‐field ground motions as well as fault displacement. This study includes: attenuation of ground motion both in PGA and spectral amplitude, principal direction, elastic and inelastic response analysis of a SDOF system subjected to near‐field ground motion collected from this event. The distribution of spectral acceleration and spectral velocity along the Chelungpu fault is discussed. Based on the mode decomposition method the intrinsic mode function of ground acceleration of this earthquake is examined. A long‐period wave with large amplitude was observed in most of the near‐source ground acceleration. The seismic demand from the recorded near‐field ground motion is also investigated with an evaluation of seismic design criteria of Taiwan Building Code. Copyright © 2000 John Wiley & Sons, Ltd.     

Development of duration‐dependent damage‐based inelastic response spectra

A simple relationship is proposed in this paper to construct damage‐based inelastic response spectra including the effect of ground motion duration that it can be used for damage control in seismic design of structures. This relation is established for three groups of ground motions with short‐duration, moderate‐duration, and long‐duration ranges. To develop the model, the duration effect is included in the cyclic ductility of structures by an energy‐based method, and then strength reduction factors are computed based on this modified ductility (named ). The strength reduction factors were calculated for 44 stiffness‐degrading oscillators having vibration periods between 0.05 and 4.0 s, four ultimate ductility capacities, and five damage levels subjected to 296 earthquake records. The results showed that ductility capacity, damage level, and ground motion duration are effective parameters in the energy dissipation of structures, which affect the spectra. The values of short‐period oscillators (e.g., low‐rise structures) under short‐duration records are generally greater than those under moderate‐duration and long‐duration records. Residual analysis has been made in terms of magnitude and distance to examine the validity of the proposed simple expression. Finally, the introduced spectra were compared with three previously published proposals. Copyright © 2016 John Wiley & Sons, Ltd.     

Theoretical models and recorded response in the estimation of cumulative seismic damage on non‐linear structures

A damage‐function model is proposed for the inelastic response of structures in terms of initial damage and of displacement amplitudes and secant stiffnesses of response cycles. The model is used to obtain an analytical closed‐form solution for the probability distribution of cumulative damage after an earthquake ground motion given the distribution prior to such excitation and information on the inelastic structural response. The formulation is applied to a reinforced concrete frame and the results show the capabilities of the method to yield updated distributions of damage. Copyright © 2000 John Wiley & Sons, Ltd.     

黄土丘陵河谷场地地震动特征研究

研究黄土丘陵河谷场地在地震作用下强地面运动特征的变化情况,可以揭示强震对该类场地上震害的触发机理。结合黄土高原的地貌特征,建立具有代表性的动力数值分析模型,通过输入不同幅值、频谱特性和持续时间的地震波,对起伏地形和覆盖黄土层共同影响下的黄土河谷场地进行地震反应分析。结果表明:黄土层和地形耦合作用控制了地表的PGA变化,使其趋于复杂,在同一输入波不同振幅作用下,与基岩河谷各测点相比,黄土覆盖河谷场地的地震动频谱幅值均有所增加,并且频谱主峰均向高频移动。在不同地震波输入下,场地不同部位的固有频率受地形高程和土层影响;而地震动大小和频谱幅值不仅与场地的基本频谱和地形起伏有关,也与输入地震波的频谱成分相关。输入波PGA与地震频谱特征都不变时,同一场地输出的地震频谱形状具有相似的特征,随着地震持时增长,能量向场地基本频率附近集中,从而可能导致场地上相应频率建筑物震动幅值增加,造成累积破坏。