Inelastic displacement ratios for evaluation of existing structures

Results of a detailed statistical study of constant relative strength inelastic displacement ratios to estimate maximum lateral inelastic displacement demands on existing structures from maximum lateral elastic displacement demands are presented. These ratios were computed for single‐degree‐of‐freedom systems with different levels of lateral strength normalized to the strength required to remain elastic when subjected to a relatively large ensemble of recorded earthquake ground motions. Three groups of soil conditions with shear wave velocities higher than 180m/s are considered. The influence of period of vibration, level of lateral yielding strength, site conditions, earthquake magnitude, distance to the source, and strain‐hardening ratio are evaluated and discussed. Mean inelastic displacement ratios and those associated with various percentiles are presented. A special emphasis is given to the dispersion of these ratios. It is concluded that distance to the source has a negligible influence on constant relative strength inelastic displacement ratios. However, for periods smaller than 1s earthquake magnitude and soil conditions have a moderate influence on these ratios. Strain hardening decreases maximum inelastic displacement at a fairly constant rate depending on the level of relative strength for periods of vibration longer than about 1.0s while it decreases maximum inelastic displacement non‐linearly as the period of vibration shortens and as the relative‐strength ratio increases for periods of vibration shorter than 1.0s. Finally, results from non‐linear regression analyses are presented that provide a simplified expression to be used to approximate mean inelastic displacement ratios during the evaluation of existing structures built on firm sites. Copyright © 2003 John Wiley & Sons, Ltd.     

Inelastic displacement ratios for soil–structure systems allowed to uplift

The simultaneous effects of soil–structure interaction, foundation uplift and inelastic behavior of the superstructure on total displacement response of soil–structure systems are investigated. The superstructure is modeled as an equivalent single‐degree‐of‐freedom system with bilinear behavior mounted on a rigid foundation resting on distributed tensionless Winkler springs and dampers. It is well known that the behavior of soil–structure systems can be well described using a limited number of nondimensional parameters. Here, by introducing two new parameters, the concept is extended to inelastic soil–structure systems in which the foundation is allowed to uplift. An extensive parametric study is conducted for a wide range of the key parameters through nonlinear time history analyses. It is shown that while uplifting soil–structure systems experience excessive displacements, in comparison with systems that are not allowed to uplift, ductility demand in the superstructure generally decreases owing to foundation uplift. A new inelastic displacement ratio (IDR) is proposed in conjunction with a nonlinear static analysis of uplifting soil–structure systems. Simplified expressions are also provided to estimate the proposed IDR. Copyright © 2014 John Wiley & Sons, Ltd.     

Evaluation of seismic displacement demands from the September 19, 2017 Puebla‐Morelos (Mw = 7.1) earthquake in Mexico City

This short communication presents the assessment of seismic inelastic and elastic displacement demands computed from earthquake ground motions (EQGMs) recorded in Mexico City during the intermediate‐depth intraslab Puebla‐Morelos earthquake on 19 September 2017 (Mw = 7.1). Evaluation is conducted by means of peak elastic and inelastic displacement demand spectra, inelastic displacement ratio, C_R, spectra, and generalized interstory drift spectra computed for selected recording stations located in different soil sites of Mexico City, including those located in areas of reported collapsed buildings. Results of this study confirm previous observations made from interplate (subduction) EQGMs that peak inelastic displacement demands are greater than corresponding elastic counterparts for short‐to‐medium period structures, while the opposite is true for medium‐to‐long period structures. Possible basin site effects were identified from generalized interstory drift spectra. It is also shown that an equation introduced in the literature to obtain estimates of C_R developed from interplate EQGMs provides also a good estimate for mean C_R computed from the intermediate‐depth intraslab EQGMs.     

Inelastic displacement demands in steel structures and their relationship with earthquake frequency content parameters

This paper deals with the estimation of peak inelastic displacements of SDOF systems, representative of typical steel structures, under constant relative strength scenarios. Mean inelastic deformation demands on bilinear systems (simulating moment resisting frames) are considered as the basis for comparative purposes. Additional SDOF models representing partially‐restrained and concentrically‐braced (CB) frames are introduced and employed to assess the influence of different force‐displacement relationships on peak inelastic displacement ratios. The studies presented in this paper illustrate that the ratio between the overall yield strength and the strength during pinching intervals is the main factor governing the inelastic deformations of partially‐restrained models and leading to significant differences when compared with predictions based on bilinear structures, especially in the short‐period range. It is also shown that the response of CB systems can differ significantly from other pinching models when subjected to low or moderate levels of seismic demand, highlighting the necessity of employing dedicated models for studying the response of CB structures. Particular attention is also given to the influence of a number of scalar parameters that characterise the frequency content of the ground motion on the estimated peak displacement ratios. The relative merits of using the average spectral period T_aver, mean period T_m, predominant period T_g, characteristic period T_c and smoothed spectral predominant period T_o of the earthquake ground motion, are assessed. This paper demonstrates that the predominant period, defined as the period at which the input energy is maximum throughout the period range, is the most suitable frequency content scalar parameter for reducing the variability in displacement estimations. Finally, noniterative equivalent linearisation expressions based on the secant period and equivalent damping ratios are presented and verified for the prediction of peak deformation demands in steel structures. Copyright © 2011 John Wiley & Sons, Ltd.     

AP/VP specific inelastic displacement ratio for seismic response estimation of structures

In this study, two new site specific statistical equations are proposed to estimate the inelastic displacement ratio, C₁ of structures subjected to far fault (FF) and near fault (NF) ground motions. The proposed equations consider the effects of fundamental vibration period of the structure, T, lateral strength ratio, R and frequency content of the design earthquake record represented by the A_p/V_p ratio (or T₀ = 2π/A_p/V_p), which is a function of the earthquake magnitude, distance to fault, faulting mechanism and site class. It was observed that the C₁ values obtained from the proposed equations are in good agreement with the calculated results. The flare of the plotted C₁ vs. T/T₀ curves enables the proposed equations to cover nearly all the calculated C₁ data range and give satisfactory results. However, the curves obtained using the C₁ equations of several codes and those available in the literature do not cover the whole calculated C₁ data range and generally give unconservative results (smaller C₁ values) especially in the shorter period range. For the longer period range, the predictions of C₁ obtained from the proposed equation and the ones available in the literature are in good agreement with the calculated C₁ data. Copyright © 2014 John Wiley & Sons, Ltd.     

Estimation of inelastic displacement ratio for base‐isolated structures

This study develops a straightforward approximate method to estimate inelastic displacement ratio, C₁ for base‐isolated structures subjected to near‐fault and far‐fault ground motions. Taking into account the inelastic behavior of isolator and superstructure, a 2 degrees of freedom model is employed. A total of 90 earthquake ground motions are selected and classified into different clusters according to the frequency content features of records represented by the peak ground acceleration to peak ground velocity ratio, A_p/V_p. A parametric study is conducted, and effective factors in C₁ (i.e., fundamental vibration period of the superstructure, T_s; postyield stiffness ratio of the superstructure, α_s; strength reduction ratio, R; vibration period of the isolator, T_b; strength of the isolator, Q; ratio of superstructure mass to total mass of the system, γ_m) are recognized. The results indicate that the practical range of C₁ values could be expected for base‐isolated structures. Subsequently, effective parameters are included in simple predictive equations. Finally, the accuracy of the proposed approximate equations is evaluated and verified through error measurement, and comparisons are made in the analyses.     

Inelastic spectra for infilled reinforced concrete frames

In two companion papers a simplified non‐linear analysis procedure for infilled reinforced concrete frames is introduced. In this paper a simple relation between strength reduction factor, ductility and period (R–µ–T relation) is presented. It is intended to be used for the determination of inelastic displacement ratios and of inelastic spectra in conjunction with idealized elastic spectra. The R–µ–T relation was developed from results of an extensive parametric study employing a SDOF mathematical model composed of structural elements representing the frame and infill. The structural parameters, used in the proposed R–µ–T relation, in addition to the parameters used in a usual (e.g. elasto‐plastic) system, are ductility at the beginning of strength degradation, and the reduction of strength after the failure of the infills. Formulae depend also on the corner periods of the elastic spectrum. The proposed equations were validated by comparing results in terms of the reduction factors, inelastic displacement ratios, and inelastic spectra in the acceleration–displacement format, with those obtained by non‐linear dynamic analyses for three sets of recorded and semi‐artificial ground motions. A new approach was used for generating semi‐artificial ground motions compatible with the target spectrum. This approach preserves the basic characteristics of individual ground motions, whereas the mean spectrum of the whole ground motion set fits the target spectrum excellently. In the parametric study, the R–µ–T relation was determined by assuming a constant reduction factor, while the corresponding ductility was calculated for different ground motions. The mean values proved to be noticeably different from the mean values determined based on a constant ductility approach, while the median values determined by the different procedures were between the two means. The approach employed in the study yields a R–µ–T relation which is conservative both for design and performance assessment (compared with a relation based on median values). Copyright © 2004 John Wiley & Sons, Ltd.     

Residual displacement ratios for assessment of existing structures

Results of an analytical study aimed at evaluating residual displacement ratios, C_r, which allow the estimation of residual displacement demands from maximum elastic displacement demands is presented. Residual displacement ratios were computed using response time‐history analyses of single‐degree‐of‐freedom systems having 6 levels of relative lateral strength when subjected to an ensemble of 240 earthquake ground motions recorded in stations placed on firm sites. The results were statistically organized to evaluate the influence of the following parameters: period of vibration, level of relative lateral strength, site conditions, earthquake magnitude, and distance to the source. In addition, the influence of post‐yield stiffness ratio in bilinear systems and of the unloading stiffness in stiffness‐degrading systems was also investigated. A special emphasis is given to the uncertainty of these ratios. From this study, it is concluded that mean residual displacement ratios are more sensitive to changes in local site conditions, earthquake magnitude, distance to the source range and hysteretic behaviour than mean inelastic displacement ratios. In particular, residual displacement ratios exhibit large levels of record‐to‐record variability and, therefore, this dispersion should be taken into account when estimating residual displacements. A simplified expression is presented to estimate mean residual displacements ratios for elastoplastic systems during the evaluation of existing structures built on firm soil sites. Copyright © 2005 John Wiley & Sons, Ltd.     

软土场地基础隔震建筑减震性能研究

本文研究土与结构相互作用(SSI)对多层及中高层基础隔震建筑地震需求及隔震效率的影响规律,隔震层采用LRB铅芯橡胶与LNR普通橡胶隔震支座组合,就我国现行《建筑抗震设计规范》(GB50011-2010)中软土场地设置隔震层问题做探讨。提出土与基础隔震结构相互作用的简化计算模型,对不同场地及隔震设计目标下的多层及中高层基础隔震结构进行时程分析。研究表明:软土场地基础隔震建筑隔震层的有效隔震效率相对于硬土场地有所下降,必须通过设置具有一定规格的LRB支座来满足隔震目标。本文给出了铅芯橡胶支座极限变形需求随建筑层高及隔震目标变化的规律。     

利用等位移原则估计高层结构的非弹性地震反应(二)

通过高层结构弹性和非弹性地震时程反应分析,研究了两者的位移反应关系。结果表明：结构在不同地震作用下非弹性总位移角反应的平均值与弹性反应十分接近,基本符合等位移原则,可以用后者分析结果直接估计前者;结构最大层间位移角反应的平均值在弱和中等非线性阶段亦与弹性反应十分接近,在强非线性阶段则大于弹性反应,经数据拟合,初步提供了一个在此阶段由弹性最大层间位移角反应估计非弹性反应的近似公式。     

软弱土层的厚度及埋深对深厚软弱场地地震效应的影响

就软弱土层的埋深和厚度对深厚场地地震动的影响进行了数值分析。场地1、场地2和场地3分别选自南京、盐城和天津。场地1、场地2用于分析软弱表层土的厚度对地表地震动参数的影响：场地1的软弱表层土厚度从2m依次增加到30m，构造了18个土层剖面；场地2的软弱表层土的厚度从2m依次增加到36m，构造了21个土层剖面。场地3用于分析软弱夹层的埋深和厚度对地表地震动参数的影响：软弱夹层的埋深从2m增加到62m，构造了16个剖面；软弱夹层的厚度从2m增加到10m，构造了5个剖面。选用Taft、E1 Centro和Northridge地震记录作为输入地震动，将Taft、El Centro和Northridge地震波加速度时程的峰值水平调整为0．35m／s^2，0．70m／s^2和0．98m／s^2，利用程序SHAKE91对不同的构造剖面、不同的输入地震波及不同的峰值加速度水平，共进行了507种组合的场地地震反应分析。分析表明：对于给定的输入地震动条件，当软弱表层土的厚度超过一定界限值时，地表加速度峰值及放大系数的变化已不很明显；当软弱表层土的厚度超过一定界限值时，加速度放大系数会小于1。也即软弱表层土可起到减震的作用；对于同一场地，输入地震动强度越大，此软表层厚度值越小。对于给定的输入地震动和峰值加速度水平，随着软弱夹层埋深的增加，地表加速度峰值和放大系数入都有减小的趋势，当埋深超过一定值后，地表加速度放大系数小于1．0；软弱夹层厚度对地表加速度峰值的影响与软弱夹层所处位置有关。     

Scaling of constant-ductility residual displacement spectrum

Structures undergoing inelastic displacements during earthquake ground motions are known to sustain some amount of residual displacements, which may make those unusable or unsafe. In this study an attempt is made to estimate residual displacements for elastic-perfectly-plastic single-degree-of-freedom oscillators with a given ductility ratio. Such oscillators belong to the class of bilinear hysteresis models applicable to steel structures, with post-yield-stiffness ratio taken as zero, and may be used for the conservative estimates of residual displacements when the post-yield-stiffness ratio is unlikely to become negative. Statistical estimation of residual displacement spectrum via normalization with respect to inelastic or elastic spectral displacements is considered and expressions are proposed for both types of normalizations. The statistical dependence of residual displacement on the seismological and site parameters and strong motion duration is also studied and a simple scaling model is proposed in terms of earthquake magnitude, epicentral distance, and geologic site condition parameter for the seismic region of western U.S.A. According to this model, the variation of residual displacement with period primarily depends on the site conditions, and the residual displacements are more sensitive to ductility ratio at low ductility ratios.     

软土层厚度对地铁车站结构地震反应的影响规律研究

为了明确软土层厚度对地铁车站结构地震反应的影响规律,本文中对常见的两层三跨岛式地铁车站结构侧向和底部地基中存在不同厚度软土层时9种软场地条件下地铁车站结构的地震反应进行了数值模拟分析。由本文和作者之前对软土层埋深影响地铁车站结构地震反应的共同研究结果来看：软土层位于地铁车站结构侧向地基时对地铁车站结构的抗震是非常不利的,尤其是软土层位于地铁车站结构侧向地基底部时最为不利,而当软土层位于地铁车站结构底部地基中时对其抗震性能一般是有利的,起到消能减震的作用;当软土层位于地铁车站结构侧向地基顶部时,随着软土层厚度的变大,对地铁车站结构抗震性能的影响越是不利且影响程度越大,而当软土层位于地铁车站结构侧向地基底部和底部地基中时,软土层厚度的变化对地铁车站结构抗震性能的影响规律并不具有很好的一致性。     

Improved evaluation of inelastic displacement demands for short‐period masonry structures

This work discusses the simplified estimation of earthquake‐induced nonlinear displacement demands as required by nonlinear static procedures, with particular attention on short‐period masonry structures. The study focuses on systems with fundamental periods between 0.1 and 0.5 s, for which inelastic amplification of the elastic displacement demand is more pronounced; hysteretic force‐displacement relationships characteristic of masonry structures are adopted, because these structures are more commonly found within the considered period range. Referring to the results of nonlinear dynamic analyses of single‐degree‐of‐freedom oscillators, some limitations of the Eurocode 8 and Italian Building Code formulations are first discussed, then an improved equation is calibrated that relates inelastic and elastic displacement demands. Numerical values of the equation parameters are obtained, considering the amount of hysteretic energy dissipation associated with various damage mechanisms observed in masonry structures. Safety factors are also calculated to determine several percentiles of the displacement demand. It is shown that the proposed equation can be extended to more dissipative systems. Finally, the same formulation is adapted to the estimation of seismic displacements when elastic analysis procedures are employed. Copyright © 2017 John Wiley & Sons, Ltd.     

Inelastic displacement demand of bridge columns considering shear–flexure interaction

Reinforced concrete bridge columns exhibit complex hysteretic behavior owing to combined action of shear, bending moment, and axial force under multi‐directional seismic shakings. The inelastic displacement of columns can be increased by shear–flexure interaction (SFI). This paper develops a simple yet reliable demand model for estimating the inelastic displacement and ductility based on the nonlinear time history analyses of 24 full‐size columns subject to a suite of near‐fault ground motions. A coupled hysteretic model is used to simulate the shear‐flexure interactive (SFI) behavior of columns and the accumulated material damage during loading reversals, including pinching, strength deterioration, and stiffness softening. Guided by rigorous dimensional analysis, the inelastic displacement responses of bridge columns are presented in dimensionless form showing remarkable order. A dimensionless nonlinearity index is derived taking into account of the column strength, ground motion amplitude, and softening or hardening post‐yield behavior. Strong correlation is revealed between the normalized inelastic displacement and the dimensionless structure‐to‐pulse frequency, the dimensionless nonlinearity index as well as the aspect ratio. Two regressive equations for displacement and ductility demands are proposed and validated against the simulation results. The SFI effects are discussed and included explicitly through the aspect ratio in the proposed model. This study offers a new way to realistically predict the inelastic displacement of columns directly from structural and ground motion characteristics. Copyright © 2010 John Wiley & Sons, Ltd.     

Study on inelastic displacement ratio spectra for near-fault pulse-type ground motions

In displacement-based seismic design, inelastic displacement ratio spectra (IDRS) are particularly useful for estimating the maximum lateral inelastic displacement demand of a nonlinear SDOF system from the maximum elastic displacement demand of its counterpart linear elastic SDOF system. In this study, the characteristics of IDRS for near-fault pulse-type ground motions are investigated based on a great number of earthquake ground motions. The in? uence of site conditions, ratio of peak ground velocity (PGV) to peak ground acceleration (PGA), the PGV, and the maximum incremental velocity (MIV) on IDRS are also evaluated. The results indicate that the effect of near-fault ground motions on IDRS are signifi cant only at periods between 0.2 s - 1.5 s, where the amplifi cation can approach 20%. The PGV/PGA ratio has the most signifi cant in? uence on IDRS among the parameters considered. It is also found that site conditions only slightly affect the IDRS.     

Inferring the location of catchment characteristic soil moisture monitoring sites. Covariance structures in the temporal domain

Information shortage is a fundamental constraint in catchment hydrology that severely affects the possibilities for secure inference of the generic hydrologic landscape, as well as for secure validation of physically deduced distributed models. The introduction of databases with high enough spatiotemporal resolution to properly reflect generic hydrological catchment characteristics may therefore be considered as an inferential breakthrough. The work presented here is part of a project where observations from such an Australian catchment (the Tarrawarra) are utilised to estimate the discrepancy for individual soil moisture monitoring sites in reflecting generic catchment characteristics. With low enough discrepancy, observation sites may be considered as catchment characteristic soil moisture monitoring (CASMM) sites, thus capturing unbiased catchment characteristics and being well suited to represent the catchment in a monitoring effort. In this particular study, covariance structures in the temporal domain are inferred in order to enable subsequent enquiries regarding CASMM discrepancies. This is accomplished with ARMAX filters applied to the conditional auto- and cross-covariance structures that connect observations of soil moisture to the temporal variation of meteorology. The results suggest that weekly observations of Tarrawarra soil moisture are quite consistent realisations of first order auto-regressive processes, which means that the present state of soil moisture is generally acquired through the past week. With auto-correlative effects filtered out, cross-correlative meteorological effects on Tarrawarra soil moisture are identified and generally represented by the present week's accumulation of rainfall, the present week's accumulation of global radiation, and the previous week's maximum wind speed. After successive filtering of conditional cross-correlative effects, residual time-series observations may be considered as temporally independent, and therefore are well suited for subsequent inferences regarding covariance structures in the spatial domain. Since the exclusion of auto-correlative effects is necessary for unambiguous model interpretation, the estimated cross-correlative parameters should reflect the true nature of underlying physical processes.     

Probabilistic estimation of inelastic displacement demands in soil–structure interaction systems on cohesive soils

Inelastic displacement ratios (IDRs) of nonlinear soil–structure interaction (SSI) systems located at sites with cohesive soils are investigated in this study. To capture the effects of inelastic cyclic behavior of the supporting soil, the Beam on Nonlinear Winkler Foundation (BNWF) model is used. The superstructure is modeled using an inelastic single-degree-of-freedom (SDOF) system model. Nonlinear SSI systems representing various combinations of unconfined compressive strengths and shear wave velocities are considered in the analysis. A set of strong ground motions recorded at sites with soft to stiff soils is used for considering the record-to-record variability of IDRs. It is observed that IDRs for nonlinear SSI systems are sensitive to the strength and the stiffness properties of both the soil and the structure. For the case of SSI systems on the top of cohesive soils, the compressive strength of the soil has a significant impact on the IDRs, which cannot be captured by considering only the shear wave velocity of the soil. Based on the results of nonlinear time-history analysis, a new equation is proposed for estimating the mean and the dispersion of IDRs of SSI systems depending on the characteristic properties of the supporting soil, dimensions of the foundation, and properties of the superstructure. A probabilistic framework is presented for the performance-based seismic design of SSI systems located at sites with cohesive soils.     

Near-fault acceleration pulses and non-acceleration pulses: Effects on the inelastic displacement ratio

Near-fault ground motions can impose particularly high seismic demands on the structures due to the pulses that are typically observed in the velocity time-histories. The velocity pulses can be further categorized into either a distinct acceleration pulse (acc-pulse) or a succession of high-frequency, one-sided acceleration spikes (non-acc-pulse). The different characteristics of velocity pulses imply different frequency content of the ground motions, potentially causing different seismic effects on the structures. This study aims to investigate the characteristics of the two types of velocity pulses and their impacts on the inelastic displacement ratio (C_R) of single-degree-of-freedom systems. First, a new method that enables an automated classification of velocity pulses is used to compile a ground motion dataset which consists of 74 acc-pulses and 45 non-acc-pulses. Several intensity measures characterizing different seismological features are then compared using the two groups of records. Finally, the influences of acc-pulses and non-acc-pulses on the C_R spectra are studied; the effects of pulse period and hysteretic behavior are also considered. Results indicate that the characteristics of the two types of velocity pulses differ significantly, resulting in clearly distinct C_R spectral properties between acc-pulses and non-acc-pulses. Interestingly, mixing acc-pulses and non-acc-pulses can lead to local “bumps” that were found in the C_R spectral shape by previous studies. The findings of this study highlight the importance of distinguishing velocity pulses of different types when selecting near-fault ground motions for assessing the nonlinear dynamic response of structures.     

Approximate analysis method for displacement responses of structures with active variable stiffness systems

The performance of structures with active variable stiffness (AVS) systems exhibits strong nonlinearity due to the variety with time of the stiffness of each storey unit, in which the AVS system is installed. Hence, the classical dynamic analysis method for linear structures, such as the mode-superposition method, is not applicable to structures with AVS systems. In this paper, an approximate analysis method is proposed for displacement responses of structures with AVS systems. Firstly, an equivalent relationship between single-degree-of-freedom (SDOF) structures equipped with AVS systems and so-called fictitious linear structures is established. Then, an approximate mode-superposition (AMS) method is presented for multi-degree-of-freedom (MDOF) structures equipped with AVS systems. The accuracy of this method is investigated through extensive parametrical study using different types of earthquake excitations, and some modification is made to the method. Numerical calculation results indicate that the modified AMS method is effective for estimating the maximum displacements relative to the ground and the maximum interstorey drifts of MDOF structures equipped with AVS systems. Supported by: National Natural Science foundation of China, Grant number 59895410