Multi‐scale modelling approach for the pushover analysis of existing RC shear walls—Part I: Model formulation

This work focuses on the modelling issues related to the adoption of the pushover analysis for the seismic assessment of existing reinforced concrete (RC) structures. To this purpose a prototype reference structure, one of the RC shear walls designed according to the multi‐fuse concept and tested on shaking table for the CAMUS project, is modelled at different levels of refinement. The meso‐scale of a stiffness‐based fibre element and the micro‐scale of the finite element (FE) method are herein adopted; in the latter separate elements are adopted for the concrete, the steel and the steel–concrete interface. This first of the two companion papers presents in detail the wall under study, illustrating the design philosophy, the geometry of the wall, the instrumentation set‐up and the test programme. The two modelling approaches are then described; the most important points in terms of element formulation and constitutive relations for materials are presented and discussed for each approach, in the light of the particular design of the wall and of its experimental behaviour. Copyright © 2007 John Wiley & Sons, Ltd.     

An improvement to linear‐elastic procedures for seismic performance assessment

An improved linear‐elastic analysis procedure is developed in this paper as a simple approximate method for displacement‐based seismic assessment of the existing buildings. The procedure is mainly based on reducing the stiffness of structural members that are expected to respond in the inelastic range in a single global iteration step. Modal spectral displacement demands are determined from the equal displacement rule. Response predictions obtained from the proposed procedure are evaluated comparatively by using the results of benchmark nonlinear response history analysis, and both the conventional and the multi‐mode pushover analyses. In comparative evaluations, a twelve‐story RC plane frame and a six‐story unsymmetrical‐plan RC frame are employed by using 91 ground motion components. It is observed that the proposed procedure estimates the flexural deformation demands in deformation‐controlled members and the shear forces in force‐controlled members with reasonable accuracy. Copyright © 2010 John Wiley & Sons, Ltd.     

Updating of nonlinear analytical modeling of soft storey RC frame building models based on cyclic test results

Cyclic testing has been carried out on two 1/4 scale of (G+2) soft storey RC frame building models to evaluate the nonlinear performance under cyclic loading. The first model has been designed only for gravity loading and the second model has been designed for gravity and earthquake loading. The different pushover parameters of the frames such as load-deformation curve, displacement and storey drift profile and the failure pattern have been evaluated. These parameters are used for up-gradation and comparison of the nonlinear analytical modeling of the soft storey RC frame building. The nonlinear analytical models have been updated at three stages i.e. linear range, nonlinear range and finally at failure stage. The % of error between the experimental and analytical results for different pushover parameters has also been evaluated.     

Approximate seismic risk assessment of building structures with explicit consideration of uncertainties

An approximate seismic risk assessment procedure for building structures, which involves pushover analysis that is performed utilizing a deterministic structural model and uncertainty analysis at the level of the equivalent SDOF model, is introduced. Such an approach is computationally significantly less demanding in comparison with procedures based on uncertainty analysis at the level of the entire structure, but still allows for explicit consideration of the effect of record‐to‐record variability and modelling uncertainties. A new feature of the proposed pushover‐based method is the so‐called probabilistic SDOF model. Herein, the proposed methodology is illustrated only for reinforced concrete (RC) frames, although it could be implemented in the case of any building structure, provided that an appropriate probabilistic SDOF model is available. An extensive parametric analysis has been performed within the scope of this study in order to develop a probabilistic SDOF model, which could be used for the seismic risk assessment of both code‐conforming and old, that is, non code‐conforming RC frames. Based on the results of risk analysis for the four selected examples, it is shown that the proposed procedure can provide conservative estimates of seismic risk with reasonable accuracy, in spite of the employed simplifications and the relatively small number of Monte Carlo simulations with Latin hypercube sampling, which are performed at the level of the SDOF model. An indication of the possible default values of dispersion measures for limit‐state intensities in the case of low to medium‐height RC frames is also presented. Copyright © 2014 John Wiley & Sons, Ltd.     

Evaluation of predictors of non‐linear seismic demands using ‘fishbone’ models of SMRF buildings

Predictors (or estimates) of seismic structural demands that are less computationally time‐consuming than non‐linear dynamic analysis can be useful for structural performance assessment and for design. In this paper, we evaluate the bias and precision of predictors that make use of, at most, (i) elastic modal vibration properties of the given structure, (ii) the results of a non‐linear static pushover analysis of the structure, and (iii) elastic and inelastic single‐degree‐of‐freedom time‐history analyses for the specified ground motion record. The main predictor of interest is an extension of first‐mode elastic spectral acceleration that additionally takes into account both the second‐mode contribution to (elastic) structural response and the effects of inelasticity. This predictor is evaluated with respect to non‐linear dynamic analysis results for ‘fishbone’ models of steel moment‐resisting frame (SMRF) buildings. The relatively small number of degrees of freedom for each fishbone model allows us to consider several short‐to‐long period buildings and numerous near‐ and far‐field earthquake ground motions of interest in both Japan and the U.S. Before doing so, though, we verify that estimates of the bias and precision of the predictor obtained using fishbone models are effectively equivalent to those based on typical ‘full‐frame’ models of the same buildings. Copyright © 2003 John Wiley & Sons, Ltd.     

Axially equilibrated displacement‐based beam element for simulating the cyclic inelastic behaviour of RC members

Distributed plasticity beam elements are commonly used to evaluate limit state demands for performance‐based analysis of reinforced concrete (RC) structures. Strain limits are often preferred to drift limits because they directly relate to damage and are therefore less dependent on member geometry and boundary conditions. However, predicting accurately strain demands still represents a major simulation challenge. Tension shift effects, which induce a linear curvature profile in the plastic hinge region of RC columns and walls, are one of the main causes for the mismatch between experimental and numerical estimates of local level quantities obtained through force‐based formulations. Classical displacement‐based approaches are instead suitable to simulate such linear curvature profile. Unfortunately, they verify equilibrium only on an average sense due to the wrong assumption on the axial displacement field, leading to poor deformation and force predictions. This paper presents a displacement‐based element in which axial equilibrium is strictly verified along the element length. The assumed transversal displacement field ensures a linear curvature profile, connecting accurately global displacement and local strain demands. The proposed finite element is validated against two sets of quasi‐static cyclic tests on RC bridge piers and walls. The results show that curvature and strain profiles for increasing ductility demands are significantly improved when axially equilibrated rather than classical displacement‐based or force‐based elements are used to model the structural members. Copyright © 2017 John Wiley & Sons, Ltd.     

基于FENAP平台的RC高桥墩破坏过程模拟及分析

为精细模拟钢筋混凝土高桥墩在静力推覆荷载作用下的破坏过程,本文基于钢筋混凝土精细化纤维梁柱单元模型分析平台FENAP,对一实际的西部山区空心截面高桥墩进行了Pushover分析,通过对构件、截面和纤维层次的力-位移关系曲线分析,模拟了桥墩从墩底混凝土开裂、纵筋屈服到受压区混凝土压碎的完整破坏过程。并将FENAP平台与OpenSees计算结果进行对比,结果表明,FE-NAP平台可有效地模拟高墩在静力推覆荷载下的破坏过程和软化行为,具有较高的求解精度。进一步比较了不同轴压比、是否考虑约束混凝土效应及纵筋屈曲效应等因素对分析结果的影响,得出结论,轴压比和约束混凝土效应对高桥墩的破坏过程发展有较大影响,而纵筋屈曲效应影响较小,可忽略不计。     

Rapid evaluation and damage assessment of instrumented highway bridges

This study focuses on the use of strong motion data recorded during earthquakes and aftershocks to provide a preliminary assessment of the structural integrity and possible damage in bridges. A system identification technique is used to determine dynamical characteristics and high‐fidelity first‐order linear models of a bridge from low level earthquake excitations. A finite element model is developed and updated using a genetic algorithm optimization scheme to match the frequencies identified and to simulate data from a damaging earthquake for the bridge. Here, two criteria are used to determine the state of the structure. The first criteria uses the error between the data recorded or simulated by the calibrated nonlinear finite element model and the data predicted by the linear model. The second criteria compares relative displacements of the structure with displacement thresholds identified using a pushover analysis. The use of this technique can provide an almost immediate, yet reliable, assessment of the structural health of an instrumented bridge after a seismic event. Copyright © 2011 John Wiley & Sons, Ltd.     

Envelope‐based pushover analysis procedure for the approximate seismic response analysis of buildings

An envelope‐based pushover analysis procedure is presented that assumes that the seismic demand for each response parameter is controlled by a predominant system failure mode that may vary according to the ground motion. To be able to simulate the most important system failure modes, several pushover analyses need to be performed, as in a modal pushover analysis procedure, whereas the total seismic demand is determined by enveloping the results associated with each pushover analysis. The demand for the most common system failure mode resulting from the ‘first‐mode’ pushover analysis is obtained by response history analysis for the equivalent ‘modal‐based’ SDOF model, whereas demand for other failure modes is based on the ‘failure‐based’ SDOF models. This makes the envelope‐based pushover analysis procedure equivalent to the N2 method provided that it involves only ‘first‐mode’ pushover analysis and response history analysis of the corresponding ‘modal‐based’ SDOF model. It is shown that the accuracy of the approximate 16th, 50th and 84th percentile response expressed in terms of IDA curves does not decrease with the height of the building or with the intensity of ground motion. This is because the estimates of the roof displacement and the maximum storey drift due to individual ground motions were predicted with a sufficient degree of accuracy for almost all the ground motions from the analysed sets. Copyright © 2013 John Wiley & Sons, Ltd.     

A comparison of single‐run pushover analysis techniques for seismic assessment of bridges

Traditional pushover analysis is performed subjecting the structure to monotonically increasing lateral forces with invariant distribution until a target displacement is reached; both the force distribution and target displacement are hence based on the assumption that the response is controlled by a fundamental mode, that remains unchanged throughout. However, such invariant force distributions cannot account for the redistribution of inertia forces caused by structural yielding and the associated changes in the vibration properties, including the increase of higher‐mode participation. In order to overcome such drawbacks, but still keep the simplicity of using single‐run pushover analysis, as opposed to multiple‐analyses schemes, adaptive pushover techniques have recently been proposed. In order to investigate the effectiveness of such new pushover schemes in assessing bridges subjected to seismic action, so far object of only limited scrutiny, an analytical parametric study, conducted on a suite of continuous multi‐span bridges, is carried out. The study seems to show that, with respect to conventional pushover methods, these novel single‐run approaches can lead to the attainment of improved predictions. Copyright © 2007 John Wiley & Sons, Ltd.     

A simple displacement control technique for pushover analyses

This paper explains how to control in displacement any force proportional loading. Such a procedure makes it possible to derive the complete (i.e. including the possible softening branch) response curve of a structure along any radial loading path in the force space. This is exactly what is required in the so‐called pushover analysis used in the seismic assessment of structures. The proposed procedure is simple in the sense that it can be easily implemented in any classical (displacement‐based) finite element code through a standard displacement control loading process. Furthermore, it leads to an interesting definition of the controlled degree‐of‐freedom, which, in the case of the pushover analysis, could substitute the classical roof displacement. Copyright © 2006 John Wiley & Sons, Ltd.     

Seismic response analysis using characteristic ground motion records for risk‐based decision‐making (3R method)

The concept of intensity‐based assessment for risk‐based decision‐making is introduced. It is realized by means of the so‐called 3R method (response analysis, record selection and risk‐based decision‐making), which can be used to check the adequacy of design of a new building or of the strengthening of an existing building by performing conventional pushover analysis and dynamic analysis for only a few ground motions, which are termed characteristic ground motions. Because the objective of the method is not a precise assessment of the seismic risk, a simple decision model for risk acceptability can be introduced. The engineer can decide that the reliability of a no‐collapse requirement is sufficient when collapse is observed in the case of less than half of, for example, seven characteristic ground motions. From the theoretical point of view, it is shown that the accuracy of the method is acceptable if the non‐linear response history analyses are performed at a low percentile of limit‐state intensity, which is also proven by means of several examples of multi‐storey reinforced concrete frame buildings. The 3R method represents a compromise between the exclusive use of either pushover analysis or dynamic analysis and can be easily introduced into building codes provided that its applicability is further investigated (e.g. asymmetric structures and other performance objectives) and that the procedure for the selection of characteristic ground motions is automated and readily available to engineers (www.smartengineering.si).     

基于推覆分析的RC框架地震倒塌易损性预测

基于倒塌率的结构倒塌易损性分析是目前评价结构抗倒塌能力最合理的方法.但是,目前基于增量动力分析(IDA)的倒塌率分析方法,工作量和实施难度大,很难直接用于工程设计,因此有必要研究便于工程应用的新方法.本文基于18个典型多层RC框架结构的IDA倒塌率分析和静力推覆分析,发现RC框架在大震下的倒塌率及抗倒塌安全储备(CMR)与静力推覆得到的结构位移安全储备之间存在较好的相关关系.依据此关系,建议了保证大震倒塌率的推覆位移安全储备,并通过9个RC框架结构算例进行了验证.本文方法简单易行,可供规则多层RC框架结构抗倒塌设计参考.     

Effect of masonry infills on seismic performance of a 3‐storey R/C frame with non‐seismic detailing

The objective of this study is to investigate the effect of masonry infills on the seismic performance of low‐rise reinforced concrete (RC) frames with non‐seismic detailing. For this purpose, a 2‐bay 3‐storey masonry‐infilled RC frame was selected and a 1 : 5 scale model was constructed according to the Korean practice of non‐seismic detailing and the similitude law. Then, a series of earthquake simulation tests and a pushover test were performed on this model. When the results of these tests are compared with those in the case of the bare frame, it can be recognized that the masonry infills contribute to the large increase in the stiffness and strength of the global structure whereas they also accompany the increase of earthquake inertia forces. The failure mode of the masonry‐infilled frame was that of shear failure due to the bed‐joint sliding of the masonry infills while that of the bare frame appeared to be the soft‐storey plastic mechanism at the first storey. However, it is judged that the masonry infills can be beneficial to the seismic performance of the structure since the amount of the increase in strength appears to be greater than that in the induced earthquake inertia forces while the deformation capacity of the global structure remains almost the same regardless of the presence of the masonry infills. Copyright © 2001 John Wiley & Sons, Ltd.     

Direct displacement‐based seismic assessment procedure for multi‐span reinforced concrete bridges with single‐column piers

In Italy, as in other high seismic risk countries, many bridges, nowadays deemed ‘strategic’ for civil protection interventions after an earthquake, were built without antiseismic criteria, and therefore their seismic assessment is mandatory. Accordingly, the development of a seismic assessment procedure that gives reliable results and, at the same time, is sufficiently simple to be applied on a large population of bridges in a short time is very useful. In this paper, a displacement‐based procedure for the assessment of multi‐span RC bridges, satisfying these requirements and called direct displacement‐based assessment (DDBA), is proposed. Based on the direct displacement‐based design previously developed by Priestley et al., DDBA idealizes the multi DOF bridge structure as an equivalent SDOF system and hence defines a safety factor in terms of displacement. DDBA was applied to hypothetical bridge configurations. The same structures were analyzed also using standard force‐based approach. The reliability of the two methods was checked performing IDA with response spectrum compatible accelerograms. Copyright © 2012 John Wiley & Sons, Ltd.     

Integrated foundation–structure seismic assessment through non‐linear dynamic analyses

This paper aims at clarifying the role of dynamic soil–structure interaction in the seismic assessment of structure and foundation, when the non‐linear coupling of both subsystems is accounted for. For this purpose, the seismic assessment of an ideal set of bridge piers on shallow foundations is considered. After an initial standard assessment, based on capacity design principles, the evaluation of the seismic response of the piers is carried out by dynamic simulations, where both the non‐linear responses of the superstructure and of the foundation are accounted for, in the latter case through the macro‐element modeling of the soil–foundation system. The results of the dynamic simulations point out the beneficial effects of the non‐linear response of the foundation, which provides a substantial contribution to the overall energy dissipation during seismic excitation, thus allowing the structural ductility demand to decrease significantly with respect to a standard fixed‐base or linear‐elastic base assessment. Permanent deformations at the foundation level, such as rotation and settlement, turn out to be of limited amount. Therefore, an advanced assessment approach of the integrated non‐linear system, consisting of the interacting foundation and superstructure, is expected to provide more rationale and economic results than the standard uncoupled approach, which, neglecting any energy dissipation at the foundation level, generally overestimates the ductility demand on the superstructure. Copyright © 2016 John Wiley & Sons, Ltd.     

Comparison of displacement coefficient method and capacity spectrum method with experimental results of RC columns

For the performance‐based seismic design of buildings, both the displacement coefficient method used by FEMA‐273 and the capacity spectrum method adopted by ATC‐40 are non‐linear static procedures. The pushover curves of structures need to be established during processing of these two methods. They are applied to evaluation and rehabilitation of existing structures. This paper is concerned with experimental studies on the accuracy of both methods. Through carrying out the pseudo‐dynamic tests, cyclic loading tests and pushover tests on three reinforced concrete (RC) columns, the maximum inelastic deformation demands (target displacements) determined by the coefficient method of FEMA‐273 and the capacity spectrum method of ATC‐40 are compared. In addition, a modified capacity spectrum method which is based on the use of inelastic design response spectra is also included in this study. It is shown from the test specimens that the coefficient method overestimates the peak test displacements with an average error of +28% while the capacity spectrum method underestimates them with an average error of ‐20%. If the Kowalsky hysteretic damping model is used in the capacity spectrum method instead of the original damping model, the average errors become ‐11% by ignoring the effect of stiffness degrading and ‐1.2% by slightly including the effect of stiffness degrading. Furthermore, if the Newmark–Hall inelastic design spectrum is implemented in the capacity spectrum method instead of the elastic design spectrum, the average error decreases to ‐6.6% which undervalues, but is close to, the experimental results. Copyright © 2003 John Wiley & Sons, Ltd.     

Shaking table 2‐D models of a concrete gravity dam

One of the most famous and studied cases of dams subjected to earthquake loading is the Koyna Dam in India. In this study, a two‐dimensional model of Koyna Dam at 1/50 scale was used on a shake table to simulate effects and serve as data for non‐linear computer model calibration. A new concrete mix was designed for the non‐linear similitude modelling. This new mix provided the correct kinematic failure of concrete at scale. Two models were tested to failure: one with an initial shrinkage crack and one monolith. Reservoir effects were not modelled. The results of both models are discussed and compared. The ability to model non‐linear effects is discussed. Published in 2000 by John Wiley & Sons, Ltd.     

Evaluation of performance of non‐invasive upgrade strategy for beam–column sub‐assemblages of poorly designed structures under seismic type loading

Beam–column sub‐assemblages are the one of the most vulnerable structural elements to the seismic loading and may lead to devastating consequences. In order to improve the performance of the poorly/under‐designed building structures to the critical loading scenarios, introduction of steel bracing at the RC beam–column joint is found to be one of the modern and implementable techniques. In the present work, a diagonal metallic single haunch/bracing system is introduced at the beam–column joints to provide an alternate load path and to protect the joint zone from extensive damage because of brittle shear failure. In this paper, an investigation is reported on the evaluation of tae influence of different parameters, such as angle of inclination, location of bracing and axial stiffness of the single steel bracing on improving the performance through altering the force transfer mechanism. Numerical investigations on the performance of the beam–column sub‐assemblages have been carried out under cyclic loading using non‐linear finite element analysis. Experimentally validated numerical models (both GLD and upgraded specimen) have been further used for evaluating the performance of various upgrade schemes. Cyclic behaviour of reinforcement, concrete modelling based on fracture energy, bond‐slip relations between concrete and steel reinforcement have been incorporated. The study also includes the numerical investigation of crack and failure patterns, ultimate load carrying capacity, load displacement hysteresis, energy dissipation and ductility. The findings of the present study would be helpful to the engineers to develop suitable, feasible and efficient upgrade schemes for poorly designed structures under seismic loading. Copyright © 2016 John Wiley & Sons, Ltd.     

Three‐dimensional beam‐truss model for reinforced concrete walls and slabs – part 1: modeling approach,validation, and parametric study for individual reinforced concrete walls

A three‐dimensional beam‐truss model for reinforced concrete (RC) walls developed by the first two authors in a previous study is modified to better represent the flexure–shear interaction and more accurately capture diagonal shear failures under static cyclic or dynamic loading. The modifications pertain to the element formulations and the determination of the inclination angle of the diagonal elements. The modified beam‐truss model is validated using the experimental test data of eight RC walls subjected to static cyclic loading, including two non‐planar RC walls under multiaxial cyclic loading. Five of the walls considered experienced diagonal shear failure after reaching their flexural strength, while the other three walls had a flexure‐dominated response. The numerically computed lateral force–lateral displacement and strain contours are compared with the experimentally recorded response and damage patterns for the walls. The effects of different model parameters on the computed results are examined by means of parametric analyses. Extension of the model to simulate RC slabs and coupled RC walls is presented in a companion paper. Copyright © 2016 John Wiley & Sons, Ltd.