Seismic response analysis of multidrum classical columns

This paper presents a numerical investigation on the seismic response of multidrum classical columns. The motivation for this study originates from the need to understand: (a) the level of ground shaking that classical multidrum columns can survive, and (b) the possible advantages or disadvantages of retrofitting multidrum columns with metallic shear links that replace the wooden poles that were installed in ancient times. The numerical study presented in this paper is conducted with the commercially available software Working Model 2D?, which can capture with fidelity the sliding, rocking, and slide‐rocking response of rigid‐body assemblies. This paper validates the software Working Model by comparing selected computed responses with scarce analytical solutions and the results from in‐house numerical codes initially developed at the University of California, Berkeley, to study the seismic response of electrical transformers and heavy laboratory equipment. The study reveals that relative sliding between drums happens even when the g‐value of the ground acceleration is less than the coefficient of friction, µ, of the sliding interfaces and concludes that: (a) typical multidrum classical columns can survive the ground shaking from strong ground motions recorded near the causative faults of earthquakes with magnitudes M_w=6.0–7.4; (b) in most cases multidrum classical columns free to dislocate at the drum interfaces exhibit more controlled seismic response than the monolithic columns with same size and slenderness; (c) the shear strength of the wooden poles has a marginal effect on the sliding response of the drums; and (d) stiff metallic shear links in‐between column drums may have an undesirable role on the seismic stability of classical columns and should be avoided. Copyright © 2005 John Wiley & Sons, Ltd.     

Shaking table testing of multidrum columns and portals

A common type of ancient monuments around the Mediterranean is the ancient Greek temple. Unfortunately, very few remain intact; most of them surviving in the form of free‐standing multidrum columns. Composed of stones resting on top of each other without any connection, such columns are considered vulnerable to earthquakes. The paper presents an experimental study of such structures, aiming to explore their seismic vulnerability and derive insights on the key factors affecting their response. Reduced scale models of a single multidrum column and of a portal were tested at the shaking table of the National Technical University of Athens Laboratory of Soil Mechanics. The models, constructed of marble just as the originals, were excited by idealized Ricker pulses and real seismic records. Single columns exhibit a remarkable earthquake resistance. Subjected to the strongest motions ever recorded in Greece, where many such monuments are situated, the columns hardly suffered any permanent deformation. Collapse is probable only for extremely harsh directivity‐affected seismic motions. Portals proved even more robust, surviving extreme seismic excitations. Their superior performance is related to the beneficial role of the epistyle, which adds energy dissipation and restoring force to the system. Their performance is very sensitive to minor changes in geometry or input motion. The complexity increases exponentially with the number of drums, being directly associated with the number of drum‐to‐drum interfaces and the increased probability of interface imperfections. In contrast to PGA, the maximum spectral displacement SD_max and the length scale L_p have turned out to be effective intensity measures. Copyright © 2014 John Wiley & Sons, Ltd.     

Site response analysis with two‐dimensional numerical discontinuous deformation analysis method

The capability of the numerical discontinuous deformation analysis (DDA) method to perform site response analysis is tested. We begin with modeling one‐dimensional shear wave propagation through a stack of horizontal layers and compare the obtained resonance frequency and amplification with results obtained with SHAKE. We use the algorithmic damping in DDA to condition the damping ratio in DDA by changing the time step size and use the same damping ratio in SHAKE to enable meaningful comparisons. We obtain a good agreement between DDA and SHAKE, even though DDA is used with first order approximation and with simply deformable blocks, proving that the original DDA formulation is suitable for modeling one‐dimensional wave propagation problems. The ability of DDA to simulate wave propagation through structures is tested by comparing the resonance frequency obtained for a multidrum column when modeling it with DDA and testing it in the field using geophysical site response survey. When the numerical control parameters are properly selected, we obtain a reasonable agreement between DDA and the site response experiment in the field. We find that the choice of the contact spring stiffness, or the numerical penalty parameter, is directly related to the obtained resonance frequency in DDA. The best agreement with the field experiment is obtained with a relatively soft contact spring stiffness of k = (1/25)(E × L) where E and L are the Young's modulus and mean diameter of the drums in the tested column. Copyright © 2013 John Wiley & Sons, Ltd.     

Seismic reliability assessment of classical columns subjected to near‐fault ground motions

A methodology for the performance‐based seismic risk assessment of classical columns is presented. Despite their apparent instability, classical columns are, in general, earthquake resistant, as proven from the fact that many classical monuments have survived many strong earthquakes over the centuries. Nevertheless, the quantitative assessment of their reliability and the understanding of their dynamic behavior are not easy, because of the fundamental nonlinear character and the sensitivity of their response. In this paper, a seismic risk assessment is performed for a multidrum column using Monte Carlo simulation with synthetic ground motions. The ground motions adopted contain a high‐ and low‐frequency component, combining the stochastic method, and a simple analytical pulse model to simulate the directivity pulse contained in near source ground motions. The deterministic model for the numerical analysis of the system is three‐dimensional and is based on the Discrete Element Method. Fragility curves are produced conditional on magnitude and distance from the fault and also on scalar intensity measures for two engineering demand parameters, one concerning the intensity of the response during the ground shaking and the other the residual deformation of the column. Three performance levels are assigned to each engineering demand parameter. Fragility analysis demonstrated some of the salient features of these spinal systems under near‐fault seismic excitations, as for example, their decreased vulnerability for very strong earthquakes of magnitude 7 or larger. The analysis provides useful results regarding the seismic reliability of classical monuments and decision making during restoration process. Copyright © 2013 John Wiley & Sons, Ltd.     

黄土斜坡动力响应特征分析

斜坡动力响应特征与斜坡形态密切相关,若入射地震波主频接近斜坡卓越频率就会放大斜坡动力响应,甚至造成斜坡失稳。汶川地震对远离震中的黄土地区造成了较为严重的破坏,局部场地震害和地震动放大效应显著。选取汶川地震典型黄土斜坡场地,利用地形台阵流动观测和数值模拟计算相结合的方法,系统开展强震动作用下黄土斜坡场地动力响应特征研究。结果表明:坡顶卓越频率最小,其PGA放大系数甚至达到坡底的1.98,这种现象可能与斜坡高差和入射波波长之比密切相关,比值0.2时坡顶放大效应达到最大。随斜坡坡度增加,放大效应增强,坡顶反应谱卓越周期放大系数可达5,说明斜坡地形对强震地面运动有显著影响。数值计算结果与实际强震观测基本吻合,其结果对黄土地区建设工程抗震设防具有重要的科学与实际意义。     

Analysis of the rocking response of rigid blocks standing free on a seismically isolated base

This paper examines the rocking response and stability of rigid blocks standing free on an isolated base supported: (a) on linear viscoelastic bearings, (b) on single concave and (c) on double concave spherical sliding bearings. The investigation concludes that seismic isolation is beneficial to improve the stability only of small blocks. This happens because while seismic isolation increase the ‘static’ value of the minimum overturning acceleration, this value remains nearly constant as we move to larger blocks or higher frequency pulses; therefore, seismic isolation removes appreciably from the dynamics of rocking blocks the beneficial property of increasing stability as their size increases or as the excitation pulse period decreases. This remarkable result suggests that free‐ standing ancient classical columns exhibit superior stability as they are built (standing free on a rigid foundation) rather than if they were seismically isolated even with isolation system with long isolation periods. The study further confirms this finding by examining the seismic response of the columns from the peristyle of two ancient Greek temples when subjected to historic records. Copyright © 2011 John Wiley & Sons, Ltd.     

Experimental investigation of damage behavior of RC frame members including non-seismically designed columns

Reinforced concrete (RC) frame structures are one of the mostly common used structural systems, and their seismic performance is largely determined by the performance of columns and beams. This paper describes horizontal cyclic loading tests often column and three beam specimens, some of which were designed according to the current seismic design code and others were designed according to the early non-seismic Chinese design code, aiming at reporting the behavior of the damaged or collapsed RC frame strctures observed during the Wenchuan earthquake. The effects of axial load ratio,shear span ratio, and transverse and longitudinal reinforcement ratio on hysteresis behavior, ductility and damage progress were incorporated in the experimental study. Test results indicate that the non-seismically designed columns show premature shear failure, and yield larger maximum residual crack widths and more concrete spalling than the seismically designed columns. In addition, longitudinal steel reinforcement rebars were severely buckled. The axial load ratio and shear span ratio proved to be the most important factors affecting the ductility, crack opening width and closing ability, while the longitudinal reinforcement ratio had only a minor effect on column ductility, but exhibited more influence on beam ductility. Finally, the transverse reinforcement ratio did not influence the maximum residual crack width and closing ability of the seismically designed columns.     

Post‐repair effect of column jackets on aftershock fragilities of damaged RC bridges subjected to successive earthquakes

In light of recent earthquakes, structures damaged during an initial seismic event (mainshock) may be more vulnerable to severe damage and collapse during a subsequent event (aftershock). In this paper, a framework for the development of aftershock fragilities is presented; these aftershock fragilities define the likelihood that a bridge damaged during an initial event will exhibit a given damage state following one or more subsequent events. The framework is capable of (i) quantifying the cumulative damage of unrepaired bridges subjected to mainshock–aftershock sequences (effect of multiple earthquakes) and (ii) evaluating the effectiveness of column repair schemes such as steel and fiber‐reinforced‐polymer jackets (post‐repair effect of jackets). To achieve this aim, the numerical model of repaired columns is validated using existing experimental results. A non‐seismically designed bridge is chosen as a case study and is modeled for three numerical bridge models: a damaged (but unrepaired) bridge model, and two bridge models with columns repaired with steel and fiber‐reinforced polymer jackets. A series of back‐to‐back dynamic analyses under successive earthquakes are performed for each level of existing damage. Using simulated results, failure probabilities of components for multiple limit states are computed for each bridge model and then are used to evaluate the relative vulnerability of components associated with cumulative damage and column repair. Copyright © 2016 John Wiley & Sons, Ltd.     

Laboratory tests of steel simple torsionally unbalanced models

The objective of this work is to obtain estimations of the amplification factors α and δ used for torsion design of buildings, from experiments. For this study, simple one‐storey torsionally unbalanced (TU) steel models were considered. Models consisted of a deck supported on four columns with a selected arrangement of hinges at column ends. Two theoretical structural eccentricities (e = 0.05 and 0.15) were considered. Models were excited with a simple long‐period pendulum consisting of a hanging platform with a forced‐vibration generator on it. Eight models were tested at several excitation levels (frequencies and force magnitudes) in both ranges of behaviour: elastic and inelastic. Experiments were conducted at three frequency ratios of excitation. Registered accelerations of the pendulum platform indicate that the experimental set‐up leads to excitations that resemble narrow‐band seismic ground motions. Frame shear force estimations, based on accelerations recorded at both deck sides, indicate that torsion design factors (α and δ) depend on eccentricity. Estimations of frame shears based on measurements indicate that for normalized eccentricities e ? 0.025, the amplification α can be between 2 and 3; while δ factor resulted between 0.0 and 1.6. Copyright © 2006 John Wiley & Sons, Ltd.     

Strength capacity of unreinforced masonry cylindrical columns under seismic transverse forces

In this paper, the seismic resistance of unreinforced masonry (URM) cylindrical columns is investigated with an equivalent static analysis procedure. To this end, an existing numerical model developed for the stability analysis of masonry elements with rectangular cross-section is utilized and modified for the cylindrical columns. In the numerical model which takes into account the cracking of the sections and the second-order effects, the columns are divided ideally into sufficiently high number of elements, each having uniform curvature. The columns are modeled as prismatic cantilevers undergoing their own weights, eccentric vertical loads and distributed and concentrated static horizontal loads equivalent to the inertia actions. By considering two examples of columns, firstly a reference column and secondly a column from a real building, lateral seismic coefficient versus top drift level curves are obtained. On the basis of these curves, lateral load behavior of the columns is interpreted and maximum seismic load values which can be resisted by each column are determined. Implementing parametric analyses on the reference column, sensitivity of the seismic resistance to parameters such as column slenderness, magnitude and eccentricity of vertical top load, and the flexibility parameter is determined. The influence of some structural imperfections such as the deviation from vertical on the seismic resistance is also discussed in the paper.     

Experimental investigation of seismic behaviour of the ancient Protiron monument model

Throughout history, dry-stone masonry structures have been strengthened with different types of metal connectors in order to increase their resistance which enabled their survival, especially in the seismically active area. One such example is the ancient Protiron monument placed in the Peristyle square of the Diocletian's Palace in Split, Croatia. The Protiron was built at the turn of the 3rd century as a stone masonry structure with dowels embedded between its base, columns, capitals and broad gable. The stone blocks in the broad gable were connected by metal clamps during restoration at the beginning of the 20th century. In order to study the seismic performance of the strengthened stone masonry structures, an experimental investigation of seismic behaviour of a physical model of the Protiron was performed on the shaking table. The model was designed as a true replica model in a length scale of 1:4 and exposed to representative earthquake with increasing intensities up to collapse. The tests provided a clear insight into system behaviour, damage mechanism and failure under intensive seismic load, especially into the efficiency of connecting elements, which had a special role in increasing seismic resistance and protection of the structure from collapse. Additionally, this experiment provided valuable data for verification and calibration of numerical models for strengthened stone masonry structures.     

Planar investigation of the seismic response of ancient columns and colonnades with epistyles using a custom-made software

In this paper, the dynamic behavior of multi-drum columns and colonnades with epistyles under earthquake excitations is examined through planar numerical simulations. A specialized software application, developed utilizing the discrete element methods (DEM), is used to investigate the influence of certain parameters on the seismic response of such multi-body structural systems. First, this custom-made software is extensively validated by comparing the computed responses of various problems, such as sliding, rocking and free vibration dynamics of rigid bodies, with the corresponding analytical solutions. Then, the developed software is used to study the influence of the frequency content and amplitude of the ground motions on the columns and colonnades, as well as the geometric characteristics of these structures. Parameters such as the number of drums that assemble each column and the number of columns of a colonnade appear to be defining parameters that affect the seismic response of colonnades with epistyles. For ground motions with relatively low predominant frequencies, rocking is the dominant effect in the response, while with the increase of the excitation frequency the response becomes even more complex involving both sliding and rocking phenomena. The numerical simulations show that earthquakes with relatively low predominant frequencies seem to endanger both standalone columns and colonnades with epistyles more than earthquakes with higher predominant frequencies.     

Dynamic response analysis of solitary flexible rocking bodies: modeling and behavior under pulse‐like ground excitation

Results obtained for rigid structures suggest that rocking can be used as seismic response modification strategy. However, actual structures are not rigid: structural elements where rocking is expected to occur are often slender and flexible. Modeling of the rocking motion and impact of flexible bodies is a challenging task. A non‐linear elastic viscously damped zero‐length spring rocking model, directly usable in conventional finite element software, is presented in this paper. The flexible rocking body is modeled using a conventional beam‐column element with distributed masses. This model is verified by comparing its pulse excitation response to the corresponding analytical solution and validated by overturning analysis of rocking blocks subjected to a recorded ground motion excitation. The rigid rocking block model provides a good approximation of the seismic response of solitary flexible columns designed to uplift when excited by pulse‐like ground motions. Guidance for development of rocking column models in ordinary finite element software is provided. Copyright © 2014 John Wiley & Sons, Ltd.     

RC jacketing parameters to retrofit highway bridges

Highway bridges are essential structures in the transportation system of any country in the world. Many highway bridges are reinforced concrete (RC) bridges that were constructed before the 1980s, prior to current seismic regulation codes. The continuous modification of regulation codes makes it necessary to evaluate structures, and in many cases, existing bridges require interventions to increase their seismic capacity. Among the different techniques used to improve bridge capacity, encasing the columns with RC jackets increases the strength and stiffness of the substructure. RC jacketing increases the column cross sections, improves the seismic capacity and reduces the seismic vulnerability of the bridge substructures. This work presents a parametric study to assess the expected demands of seismically deficient medium length highway bridges retrofitted with RC jacketing aimed at determining the best jacket parameters. A suite of twenty strong ground motions, recorded from a subduction seismic source close to the Pacific Coast in Mexico, was selected to characterize the seismic demand. The bridge superstructures are simply supported with five 30 m long spans for a total length of 150 m. The bridge models have five possible pier heights of 5, 10, 15 20 and 25 m and three different jacket thicknesses and steel ratios. Pushover analyses and capacity spectra of the family of accelerograms allow for the determination of the pier demands by obtaining the performance point as the intersection of the capacity and demand curves. The results allow for the determination of the influence of each parameter on the expected seismic behavior of the bridge models, with the aim of selecting the most suitable jacket characteristics to improve the seismic bridge performance.     

Nonlinear numerical assessment of the seismic response of hillside RC buildings

Major damage has been reported in hilly areas after major earthquakes,primarily because of two special conditions:the variation in the seismic ground motion due to the inclined ground surface and the irregularities caused by a stepped base level in the structure.The aim of this study is to evaluate possible differences in the responses of Chilean hillside buildings through numerical linear-elastic and nonlinear analyses.In the first step,a set of response-spectrum analyses were performed on four simplified 2D structures with mean base inclination angles of 0°,15°,30°,and 45°.The structures were designed to comply with Chilean seismic codes and standards,and the primary response parameters were compared.To assess the seismic performance of the buildings,nonlinear static(pushover)and dynamic(time-history)analyses were performed with SeismoStruct software.Pushover analyses were used to compare the nonlinear response at the maximum roof displacement and the damage patterns.Time-history analyses were performed to assess the nonlinear dynamic response of the structures subjected to seismic ground motions modified by topographic effects.To consider the topographic modification,acceleration records were obtained from numerical models of soil,which were calculated using the rock acceleration record of the Mw 8.01985 Chilean earthquake.Minor differences in the structure responses(roof displacements and maximum element forces and moments)were caused by the topographic effects in the seismic input motion,with the highly predominant ones being the differences caused by the step-back configuration at the base of the structures.High concentrations of shear forces in short walls were observed,corresponding to the walls located in the upper zone of the foundation system.The response of the structures with higher angles was observed to be more prone to fragile failures due to the accumulation of shear forces.Even though hillside buildings gain stiffness in the lower stories,resulting in lower design roof displacement,maximum roof displacements for nonlinear time-history analyses remained very close for all the models that were primarily affected by the drifts of the lower stories.Additionally,vertical parasitic accelerations were considered for half the time-history analyses performed here.The vertical component seems to considerably modify the axial load levels in the shear walls on all stories.     

基于OpenSees的巨型SRC柱低周反复试验数值分析

为研究巨型SRC柱抗震性能的数值模拟方法,本文基于有限元分析软件OpenSees,采用纤维单元模拟5根具有不同复杂截面型钢形式的巨型SRC柱试件的低周反复加载试验,并与试验滞回曲线以及骨架曲线进行对比分析。结果表明,该基于纤维单元的有限元模型能够较好模拟巨型SRC柱试件的滞回反应,具有一定的合理性和可靠性。同时采用一种新型高性能分层壳单元对其中一根巨型SRC柱试件进行精细有限元建模分析,分析结果与试验结果对比表明分层壳能够较好地模拟试件的初始刚度和峰值承载力;与纤维单元模拟结果对比表明纤维单元能够更好地模拟试件承载力的下降,结果更加精确,且计算效率更高;新型高性能壳单元DKGQ能够弥补原有壳单元的不足,更好地模拟构件因混凝土大量开裂剥落导致的承载力下降。     

基于OpenSees的防屈曲支撑加固钢筋混凝土框架数值模拟

提出了一种既有钢筋混凝土框架结构的抗震加固方法,该法采用防屈曲支撑提高框架结构体系的水平承载力和耗能能力,利用外包钢进一步提高柱子的抗弯和抗剪承载力。采用开源有限元程序OpenSees,分别建立空钢筋混凝土框架和防屈曲支撑加固钢筋混凝土框架的分析模型,对2榀钢筋混凝土框架的抗震性能进行模拟。防屈曲支撑采用了弹塑性桁架单元模型,加固框架柱混凝土考虑了外包钢的约束作用。将分析结果与拟静力试验结果进行比较,以检验分析模型的准确性,以及研究防屈曲支撑和外包钢对混凝土框架抗震性能的影响。分析结果表明,数值模拟与试验结果吻合较好,验证了基于OpenSees建立的数值模型的准确性;外包钢有效改善了框架柱的抗弯承载力和变形能力;防屈曲支撑显著提高了加固框架体系的水平刚度、水平承载力和耗能能力。     

Modelling methods of historic masonry buildings under seismic excitation

Historic masonry buildings in seismically active regions are severely damaged by earthquakes, since they certainly have not been explicitly designed by the original builders to withstand seismic effects, at least not in a ‘scientific’ way from today’s point of view. The assessment of their seismic safety is an important first step in planning the appropriate interventions for improving their pertinent resistance. This paper presents a procedure for assessing the seismic safety of historic masonry buildings based on measurements of their natural frequencies and numerical simulations. The modelling of the brittle nonlinear behaviour of masonry is carried out on the macro-level. As an example, a recently completed investigation of the seismic behaviour of the Aachen Cathedral is given, this being the first German cultural monument to be included in the UNESCO cultural heritage list in 1978. Its construction goes back to the 9th century a.d. and it is considered as one of the finest examples of religious architecture in Central Europe. The investigation is based on measurements of the natural frequencies at different positions and numerical simulations using a detailed finite element model of the Cathedral.     

An analytical model of a deformable cantilever structure rocking on a rigid surface: development and verification

This paper extends previously developed models to account for the influence of the column and the foundation masses on the behavior of top‐heavy deformable elastic cantilever columns rocking on a rigid support surface. Several models for energy dissipation at impact are examined and compared. A novel Vertical Velocity Energy Loss model is introduced. Rocking uplift and overturning spectra for the deformable elastic cantilever model excited by sinusoidal ground motions are constructed. The effects of non‐dimensional model parameter variations on the rocking spectra and the overturning stability of the model are presented. It is shown that the remarkable overturning stability of dynamically excited large cantilever columns is not jeopardized by their deformability. Copyright © 2015 John Wiley & Sons, Ltd.     

Reinforced concrete scaled columns under cyclic actions

In the area of reduced-scale model testing, increasing the size of model structures as a means of improving the model performance is often inhibited by the capacity limitation of the available seismic testing facilities. This was the case in a recent experimental programme conducted at NTUA in which several 1:5.5-scale model frames were tested on an earthquake simulator. In order to improve the model reliability, the following measures were taken: strictly obeying the geometric scaling in almost all aspects; using deformed bars as model reinforcement; and using stone-aggregate microconcrete for constructing the models, etc. To evaluate the effectiveness of these measures, a parallel column test programme was conducted in which duplicates of typical columns in the test model frames were prepared, along with those of large sizes following similitude laws. The column specimens were tested under reversals of lateral load. Besides the scale effects, general rules regarding the influences of transverse confinement and axial force on the ductility and strength of columns were also confirmed on the small-scale model columns.