Scaling of residual displacements in terms of elastic and inelastic spectral displacements for existing SDOF systems

Structures undergoing inelastic displacements during earthquake ground motions are known to sustain some amount of residual displacements, which may make them 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 lateral strength ratio. It is observed in the case of a class of ground motions that there are no trends in the dependence of residual displacement on the temporal features of the ground motion, and thus any estimation of residual displacements should be carried out only in the statistical sense. Statistical estimation of residual displacement spectrum via normalization with respect to inelastic or elastic spectral displacements is considered, and it is found that normalization with respect to inelastic spectral displacements is preferable. Expressions for residual displacement spectra are proposed for both types of normalizations and for the givenlateral-strength-ratio type oscillators.     

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.     

Post‐earthquake damage assessment using residual displacements

This paper presents a new, improved, post‐earthquake damage assessment method that takes into account residual deformations attained by the damaged structure during the earthquake. Local and global residual deformations and visual damage indicators are considered to estimate the maximum deformations experienced by the structure. As a particular development, the method allows measured displacements and rotations to be considered jointly. Uncertainties associated with both the excitation and the damaged structure are explicitly accounted for. The resulting maximum displacement estimates allow a more accurate evaluation of the extent of structural damage when judging the usability/reparability of the investigated structure. A trial application of the method to a real structure tested on a shaking table is presented. The results confirm the capability of the method to estimate the maximum displacement and the residual stiffness of the damaged structure. Copyright © 2011 John Wiley & Sons, Ltd.     

Research on the influencing factors for residual displacements of RC bridge columns subjected to earthquake loading

Following the 1995 Kobe earthquake, many RC bridge columns were demolished due to a residual drift ratio of more than 1.75 % even though they did not collapse. The residual drift ratio is a quantitative index for the performance objective of reparability in the bridge seismic design. Numerical models of the columns are built to study the factors that influence the residual displacement of RC bridge columns. In these models, both column bending and bar pulling out deformation are considered using the fiber column-beam element and zero-length section element, respectively. Then, nonlinear time history analyses are performed. The factors that influence column residual displacement, such as the characteristics of ground motion, the structural responses (the maximum lateral drift ratio and the displacement ductility factor), and the structural characteristics (the aspect ratio and the longitudinal reinforcement ratio) are investigated. It is found that the near-fault ground motion induces a larger residual drift ratio than the far-fault ground motion. The residual drift ratio becomes larger due to the increase of the maximum lateral drift ratio, the displacement ductility factor, and the aspect ratio. Further, a larger longitudinal reinforcement ratio can induce a larger residual drift ratio due to the contribution of the bar pulling out deformation.     

Evaluation of seismic displacements of quay walls

A new simplified dynamic analysis method is proposed to predict the seismic sliding displacement of quay walls by considering the variation of wall thrust, which is influenced by the excess pore pressure developed in backfill during earthquakes. The method uses the Newmark sliding block concept and the variable yield acceleration, which varies according to the wall thrust, to calculate the quay wall displacement.A series of 1 g shaking table tests were executed to verify the applicability of the proposed method, and a parametric study was performed. The shaking table tests verified that the proposed method properly predicts the wall displacement, and the parametric study showed that the evaluation of a realistic wall displacement is as important as the analysis of liquefaction potential for judging the stability of quay walls.     

Fault dimensions,displacements and growth

Maximum total displacement (D) is plotted against fault or thrust width(W) for 65 faults, thrusts, and groups of faults from a variety of geological environments. Displacements range from 0.4 m to 40 km and widths from 150 m to 630 km, and there is a near linear relationship betweenD andW ². The required compatibility strains (e _s) in rocks adjacent to these faults increases linearly withW and with and ranges frome _s=2×10^–4 toe _s=3×10^–1. These are permanent ductile strains, which compare with values ofe _s=2×10^–5 for the elastic strains imposed during single slip earthquake events, which are characterised by a linear relationship between slip (u) andW.The data are consisten with a simple growth model for faults and thrusts, in which the slip in successive events increases by increments of constant size, and which predicts a relationship between displacement and width of the formD=cW ². Incorporation of constant ductile strain rate into the model shows that the repreat time for slip events remains constant throughout the life of a fault, while the displacement rate increases with time. An internally consistent model withe _s=2×10^–5, giving repeat times of 160 years and instantaneous displacement rates of 0.02 cm/yr, 0.2 cm/yr, and 2.0 cm/yr when total displacement is 1 m, 100 m, and 10 km, and slip increasing by 0.5 mm with each event, gives a good approximation of the data. The model is also applicable to stable sliding, the slip rate varying with ductile strain rate and withW ².     

结构震后残余位移研究进展

结构在强震作用下进入非线性阶段会产生不可恢复的永久位移或残余变形,结构残余位移是震后结构抗震性能和地震损失评估的重要参数,具有重要的理论意义和工程实用价值。为了深入分析残余位移的研究现状,为面向性态抗震设计和抗震韧性评估的地震动强度指标研究提供参考,全面和系统分析了国内外结构残余位移相关文献,介绍了残余位移的定义,重点论述了影响结构残余位移的主要因素,总结归纳了残余位移计算模型、残余位移控制方法及考虑残余位移的抗震性能评估方法,最后讨论了残余位移研究中存在的问题和建议。     

Seismic displacements on shear surfaces in cohesive soils

The paper is concerned with the earthquake-induced displacements on pre-existing shear surfaces in cohesive soils. Results from ring shear tests have shown that during fast shearing the strength of such surfaces depends on displacement and rate of shearing. The test results have been used in a numerical analysis to assess the displacement of a rigid block sliding on a plane surface. The results from the analysis show that the earthquake-induced displacements on pre-existing shear surfaces are influenced significantly by the soil behaviour under earthquake loading conditions. The results are consistent with the field performance of pre-existing slides in cohesive soils during earthquakes.     

Seismic assessment of the rigid sliding displacements caused by pulse motions

This paper presents a comprehensive study on the rigid block sliding displacement of slopes subjected to ground motions with large velocity pulses. A comparison of the performance of various existing empirical displacement models is provided through analyses of the displacement residuals of slopes subject to pulse-like motions. Except for the PGA- and PGV-based Saygili and Rathje model (2008, referred to as SR08), positive medians of residuals are observed for selected models, indicating an under-estimation. There is a negative constant shift in the total residuals for the SR08 model, which can be easily fixed by changing the constant term in the predictive equation. The residuals from the SR08 model also have the smallest standard deviation compared to the other models. A modified SR08 model is developed for predicting rigid block sliding displacements for pulse-like motions. The modified predictive model is used in probabilistic seismic displacement analyses of slopes in a hypothetical near-fault region.     

Deterministic sliding block methods for estimating seismic displacements of earth structures

A review and quantitative comparison of existing deterministic sliding block methods for predicting permanent displacements of earth structures subjected to seismic loading is presented. The reviewed sliding block methods are divided into two main groups based on the characteristic earthquake parameters referenced in each method. One group uses the maximum horizontal ground acceleration and velocity, and the other uses the maximum horizontal ground acceleration and the predominant period of the acceleration spectrum. Displacement functions published by previous authors are reformulated to give common non-dimensionalized displacement functions of the critical acceleration ratio which are then used to compare the different methods for the estimate of permanent seismic displacement of soil structures. The results show that despite the fact that the different methods were formulated using a wide range of earthquake records and different characteristic seismic parameters, permanent displacement values predicted using these methods fall within a reasonably narrow band. Selected acceleration data from three recent earthquakes that occurred in California are used to evaluate and compare the accuracy of the reviewed displacement methods for practical applications.     

Seismic displacements of torsionally unbalanced buildings

A parametric study is carried out to evaluate the seismic displacements at the flexible edge of torsionally unbalanced (TU) structural systems. Guidelines are provided to estimate these displacements so that they can be incorporated in the formulation of the displacement-based seismic design approach for the design of TU buildings. The ability of three code procedures to estimate the flexible-edge displacement is examined to show that not all procedures lead to conservative estimates. Finally, it is shown that elastic spectrum analysis incorporating accidental torsion effect is a viable means to estimate the flexible-edge displacements.     

Near‐fault effects on residual displacements of RC structures

Residual displacements of single‐degree‐of‐freedom systems due to ground motions with velocity pulses or fling step displacements are presented as a function of period T and of its ratio to the pulse period T_p. Four hysteretic behaviors are considered: bilinear elastoplastic, stiffness‐degrading with cycling, stiffness‐cum‐strength degrading, with or without pinching. When expressed in terms of T/T_p, peak inelastic and residual displacements due to motions with a pulse or fling appear similar to those due to far‐fault motions, if the response to far‐field records are expressed in terms of the ratio of T to the record's characteristic period. However, as the latter is usually much shorter than the pulse period of motions with fling, the range of periods of interest for common structures becomes a short‐period range under fling motions and exhibits very large amplification of residual and peak inelastic displacements. Similar, but less acute, are the effects of motions with a velocity pulse. Wavelets of different complexity are studied as approximations to near‐fault records. Simple two‐parameter wavelets for fling motions overestimate peak inelastic displacements; those for pulse‐type motions overestimate residual displacements. A more complex four‐parameter wavelet for motions with a velocity pulse predicts overall well residual and peak displacements due to either pulse‐ or fling‐type motions; a hard‐to‐identify parameter of the wavelet impacts little computed residual displacements; another significantly affects them and should be carefully estimated from the record. Even this most successful of wavelets overpredicts residual displacements for the periods of engineering interest. Copyright © 2016 John Wiley & Sons, Ltd.     

1-G model tests and hollow cylindrical torsional shear experiments on seismic residual displacements of fill dams from the viewpoint of seismic performance-based design

This paper concerns technological efforts for the general acceptance of performance-based seismic design principle of geotechnical structures. Among many problems to be solved, a particular emphasis was placed on the prediction of residual displacement that remains after a strong earthquake. Because of the complicated behavior of soils undergoing cyclic loading, the prediction is often either complicated/costly or not very accurate. The aim of this study is to examine the capability of existing prediction measures and propose some future scopes. To achieve these goals, shaking table model tests and laboratory shear tests were conducted by taking fill dams as an example target structure. It is concluded that performance-based design is possible if the necessary time and cost are spent and if the required accuracy of prediction is reasonable.     

基于强震记录估算同震位移的研究进展及方法

通过对强震加速度记录估算同震位移技术自20世纪40年代以来国内外研究成果的总结,系统地阐述了通过近断层加速度记录计算同震位移的相关理论、方法的发展历程和成就。首先简述了基于强震记录估算同震位移的意义和普遍存在的漂移现象,然后总结了从模拟记录到数字记录两个阶段计算同震位移所取得的成果,接着归纳了为解决漂移现象所采取的3种基于时程拟合的方法和2种基于小波分析的方法,最后对基于数字强震仪记录估算同震位移的未来研究进行了展望。     

利用GPS和GRACE分析四川地表垂向位移变化

陆地水储量的季节性变化是导致地表周期性负荷形变位移的主要因素,有效地剔除地表位移中的陆地水储量影响,是获取地壳构造垂向运动的必要过程.四川地处青藏高原东边缘,地形分区明显,境内以长江水系为主,水资源丰富,研究四川地区地表负荷形变位移,有助于分析陆地水储量的时空分布特性及地壳构造形变信息.本文利用研究区域内59个CORS站的GPS观测数据,计算了CORS站点的垂向位移,并将其与GRACE所得相应结果进行对比分析.结果显示,GPS和GRACE所得垂向位移时间序列的振幅大小整体相符,但存在明显的相位差.GPS站点振幅最大值为12.7 mm,对应HANY站,最小值为1.5 mm,对应SCMX站.GRACE所得的地表垂向位移振幅大小均为3~4 mm,且最大位移集中出现在7-9月份;而GPS站点出现最大位移的月份和地形相关,东部盆地、西北部高原和南部山地分别出现在7-8月份、10-11月份和10月份.GPS站点时间序列中的周年项与陆地水的季节性变化强相关,为了讨论陆地水储量对GPS站点位移的影响,本文利用改进的总体经验模态分解方法（MEEMD：Modified Ensemble Empirical Mode Decomposition）,从GPS垂向位移时间序列中提取出周年项及约2年的年际变化项.发现利用MEEMD获取的周年项改正原始GPS时间序列时可使其WRMS（Weight Root Mean Square）减少量减小约26%,结果优于最小二乘拟合方法提取的GPS周年项改正效果,验证了MEEMD方法在GPS坐标时间序列处理中的可行性及有效性.     

A probabilistic framework for estimating the residual drift of idealized SDOF systems of non‐degrading conventional and damped structures

This paper presents a general framework for predicting the residual drift of idealized SDOF systems that can be used to represent non‐degrading structures, including those with supplemental dampers. The framework first uses post‐peak oscillation analysis to predict the maximum ratio of residual displacement to the peak transient displacement in a random sample. Then, residual displacement ratios obtained from nonlinear time‐history analyses using both farfield and near‐fault‐pulse records were examined to identify trends, which were explained using the oscillation mechanics of SDOF systems. It is shown that large errors can result in existing probability models that do not capture the influence of key parameters on the residual displacement. Building on the observations that were made, a general probability distribution for the ratio of residual displacement to the peak transient displacement that more accurately reflects the physical bounds obtained from post‐peak oscillation analysis is proposed for capturing the probabilistic residual displacement response of these systems. The proposed distribution is shown to be more accurate when compared with previously proposed distributions in the literature due to its explicit account of dynamic and damping properties, which have a significant impact on the residual displacement. This study provides a rational basis for further development of a residual drift prediction tool for the performance‐based design and analysis of more complex multi‐degree‐of‐freedom systems.     

Computation of sliding displacements of bridge abutments by pseudo-dynamic method

The paper focuses on seismic sliding displacement calculations of gravity wall bridge abutments when subjected to passive condition during earthquakes. Pseudo-dynamic approach has been used for the calculation of the passive seismic earth pressure. A novel element of the present investigation is the computation of seismic passive earth pressure coefficients by considering the composite curved rupture surface behind the abutment wall in the framework of limit equilibrium method. Sliding failure along the wall base is considered in the new pseudo-dynamic method. The critical seismic acceleration coefficient for sliding and sliding component of the displacement, resulting from horizontal and vertical sinusoidal ground accelerations, are computed by using Newmark's sliding block method. The effect of sliding on the response of earth structures is evaluated and comparisons are made between sliding displacements calculated using planar and composite failure mechanisms. Results of the comparative study showed that the assumption of planar failure mechanism for rough soil–wall interfaces significantly overestimates the critical seismic accelerations for sliding and underestimates the sliding displacements.     

Maximum seismic displacements evaluation of steel frames from their post-earthquake residual deformation

The maximum seismic displacements of a structure can be used for the assessment of its post-earthquake performance. In this paper, a simple and efficient procedure is proposed for determining maximum seismic displacements of planar steel frames from their residual deformation. More specifically, the inelastic behaviour of 36 moment resisting steel frames and 36 concentrically X-braced steel frames under one hundred strong ground motions is investigated. Thus, on the basis of extensive parametric studies for these structures and seismic records, empirical equations are constructed for simple and effective prediction of maximum seismic displacements from residual deformation, which can be measured in-situ after strong seismic events. It is found that the usage of residual deformation can be effectively utilized to evaluate the post-earthquake performance level of steel structures.     

Finite element analysis of buried steel pipelines under strike-slip fault displacements

The present paper investigates the mechanical behavior of buried steel pipelines, crossing an active strike-slip tectonic fault. The fault is normal to the pipeline direction and moves in the horizontal direction, causing stress and deformation in the pipeline. The interacting soil–pipeline system is modelled rigorously through finite elements, which account for large strains and displacements, nonlinear material behavior and special conditions of contact and friction on the soil–pipe interface. Considering steel pipelines of various diameter-to-thickness ratios, and typical steel material for pipeline applications (API 5L grades X65 and X80), the paper focuses on the effects of various soil and pipeline parameters on the structural response of the pipe, with particular emphasis on identifying pipeline failure (pipe wall wrinkling/local buckling or rupture). The effects of shear soil strength, soil stiffness, horizontal fault displacement, width of the fault slip zone are investigated. Furthermore, the influence of internal pressure on the structural response is examined. The results from the present investigation are aimed at determining the fault displacement at which the pipeline fails and can be used for pipeline design purposes. The results are presented in diagram form, which depicts the critical fault displacement, and the corresponding critical strain versus the pipe diameter-to-thickness ratio. A simplified analytical model is also developed to illustrate the counteracting effects of bending and axial stretching. The numerical results for the critical strain are also compared with the recent provisions of EN 1998-4 and ASCE MOP 119.     

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.