Biaxial effects in modelling earthquake response of R/C structures

Recent studies reveal that R/C structural members subjected to biaxial flexure due to two-dimensional earthquake excitation can deform much more than would be predicted by conventional one-dimensional response analysis. The biaxial flexure may therefore have a significant effect on the dynamic collapse process of structures subjected to intense ground motions. The present paper is intended to develop a new formulation of the two-dimensional restoring force model of R/C columns acted upon by biaxial bending moments, and to discuss the dynamic response properties of R/C structures. The model considered is a two-dimensional extension of various non-linear models for one-dimensional response analysis, including the degrading trilinear stiffness model which is one of the simpler idealizations of the restoring force characteristics of flexural-failure-type R/C structures. The modelling validity is then examined by comparison with experimental data on the biaxial bending behaviour of R/C columns. Calculations are made to study the role of different system properties on the influence of inelastic biaxial bending on the dynamic structural response. It is shown that the inelastic biaxial effect is generally significant and, in some cases, critical in the case of R/C structures with stiffness-degrading properties, while the effect is not so important for the non-degrading inelastic cases.     

Earthquake response analysis of the olive view hospital psychiatric day clinic

The collapse of the Olive View Hospital Psychiatric Day Clinic is studied using three biaxial force-deflection models to represent the columns of the building. These models are: shear collapse, elastic and inelastic. The biaxial models for shear and inelastic behaviour are new developments and are useful for non-linear structural dynamic studies. In the present study, the shear collapse model is intended to represent the actual prototype behaviour. The inelastic model, which is based on a hardening rule of plasticity, is used to study the performance of a hypothetical structure with the same storey shear capacity as the prototype but which exhibits ductile behaviour. The prototype structure had a base storey shear capacity of 25 per cent, and actually failed by shearing of all of the first floor columns. In the present study, the shear collapse model predicted this behaviour even with the El Centro accelerogram as input. This result may have far-reaching significance because many low-rise reinforced concrete buildings which were designed according to recent codes have similar storey shear capacity coefficients and column properties. According to this study, such buildings may collapse even in a moderate earthquake. In the inelastic representation, the structure was found to have a base storey shear capacity of 80 per cent when moment hinging was assumed to occur at the top and bottom of the columns. Even with this high strength capacity, the permanent offset computed from the inelastic model corresponded to a ductility factor of 5 when the Pacoima Dam accelerogram was used as input. On the basis of damage to other structures observed on the site, it seems likely that ground motion of about the Pacoima Dam intensity occurred at Olive View. From this it is concluded that a low-rise ductile frame concrete building, even with this high shear force capacity, may not prove satisfactory for hospital use when subjected to strong ground motion.     

A new approach of selecting real input ground motions for seismic design: The most unfavourable real seismic design ground motions

This paper presents a new way of selecting real input ground motions for seismic design and analysis of structures based on a comprehensive method for estimating the damage potential of ground motions, which takes into consideration of various ground motion parameters and structural seismic damage criteria in terms of strength, deformation, hysteretic energy and dual damage of Park & Ang damage index. The proposed comprehensive method fully involves the effects of the intensity, frequency content and duration of ground motions and the dynamic characteristics of structures. Then, the concept of the most unfavourable real seismic design ground motion is introduced. Based on the concept, the most unfavourable real seismic design ground motions for rock, stiff soil, medium soil and soft soil site conditions are selected in terms of three typical period ranges of structures. The selected real strong motion records are suitable for seismic analysis of important structures whose failure or collapse will be avoided at a higher level of confidence during the strong earthquake, as they can cause the greatest damage to structures and thereby result in the highest damage potential from an extended real ground motion database for a given site. In addition, this paper also presents the real input design ground motions with medium damage potential, which can be used for the seismic analysis of structures located at the area with low and moderate seismicity. The most unfavourable real seismic design ground motions are verified by analysing the seismic response of structures. It is concluded that the most unfavourable real seismic design ground motion approach can select the real ground motions that can result in the highest damage potential for a given structure and site condition, and the real ground motions can be mainly used for structures whose failure or collapse will be avoided at a higher level of confidence during the strong earthquake. Copyright © 2007 John Wiley & Sons, Ltd.     

Quantitative investigation on collapse margin of steel high-rise buildings subjected to extremely severe earthquakes

Reponses of structures subjected to severe earthquakes sometimes significantly surpass what was considered in the design. It is important to investigate the failure mechanism and collapse margin of structures beyond design, especially for high-rise buildings. In this study, steel high-rise buildings using either square concrete-filled-tube (CFT) columns or steel tube columns are designed. A detailed three-dimensional (3D) structural model is developed to analyze the seismic behavior of a steel high-rise towards a complete collapse. The effectiveness is verified by both component tests and a full-scale shaking table test. The collapse margin, which is defined as the ratio of PGA between the collapse level to the design major earthquake level (Level 2), is quantified by a series of numerical simulations using incremental dynamic analyses (IDA). The baseline building using CFT columns collapsed with a weak first story mechanism and presented a collapse margin ranging from 10 to 20. The significant variation in the collapse margin was caused by the different characteristics of the input ground motions. The building using equivalent steel columns collapsed earlier due to the significant shortening of the locally buckled columns, exhibiting only 57% of the collapse margin of the baseline building. The influence of reducing the height of the first story was quite significant. The shortened first story not only enlarged the collapse margin by 20%, but also changed the collapse mode.     

Ductility‐dependent intensity measure that accounts for ground‐motion spectral shape and duration

The calculated nonlinear structural responses of a building can vary greatly, even if recorded ground motions are scaled to the same spectral acceleration at a building's fundamental period. To reduce the variation in structural response at a particular ground‐motion intensity, this paper proposes an intensity measure (IM_comb) that accounts for the combined effects of spectral acceleration, ground‐motion duration, and response spectrum shape. The intensity measure includes a new measure of spectral shape that integrates the spectrum over a period range that depends on the structure's ductility. The new IM is efficient, sufficient, scalable, transparent, and versatile. These features make it suitable for evaluating the intensities of measured and simulated ground motions. The efficiency and sufficiency of the new IM is demonstrated for the following: (i) elastic‐perfectly plastic single‐degree‐of‐freedom (SDOF) oscillators with a variety of ductility demands and periods; (ii) ductile and brittle deteriorating SDOF systems with a variety of periods; and (iii) collapse analysis for 30 previously designed frames. The efficiency is attributable to the inclusion of duration and to the ductility dependence of the spectral shape measure. For each of these systems, the transparency of the intensity measure made it possible to identify the sensitivity of structural response to the various characteristics of the ground motion. Spectral shape affected all structures, but in particular, ductile structures. Duration only affected structures with cyclic deterioration. Copyright © 2015 John Wiley & Sons, Ltd.     

采用纤维模型的钢管混凝土框架-中心支撑结构抗连续倒塌非线性分析

为研究不同形式的中心支撑对钢管混凝土结构抗连续倒塌性能的影响,基于纤维梁模型建立5种钢管混凝土框架-中心支撑结构数值模型,在合理选取钢材和混凝土材料本构模型的基础上,计算不同失效工况下结构的抗连续倒塌非线性动力响应,通过非线性静力加载获得结构的整体刚度和极限承载力。研究结果表明：设置中心支撑均可以提高结构的整体刚度和抗倒塌承载能力,其中对边柱失效工况的提升效果好于中柱失效工况;设置中心支撑提供了新的荷载传递路径,可以有效减小失效柱相邻构件的分配内力;X型支撑在不同失效工况下都能显著提升框架刚度和承载能力,降低失效节点的竖向位移,反斜支撑框架表现出更好的延性和极限承载能力,研究结果可为建筑结构抗连续倒塌设计提供参考。     

Collapse of a nonductile concrete frame: Shaking table tests

Post‐earthquake reconnaissance has reported the vulnerability of older reinforced concrete (RC) columns lacking details for ductile response. Research was undertaken to investigate the full‐range structural hysteretic behavior of older RC columns. A two‐dimensional specimen frame, composed of nonductile and ductile columns to allow for load redistribution, was subjected to a unidirectional base motion on a shaking table until global collapse was observed. The test demonstrates two types of column failure, including flexure‐shear and pure flexural failure. Test data are compared with various simplified assessment models commonly used by practicing engineers and researchers to identify older buildings that are at high risk of structural collapse during severe earthquake events. Comparison suggests that ASCE/SEI 41‐06 produces very conservative estimates on load–deformation relations of flexure‐shear columns, while the recently proposed ASCE/SEI 41‐06 update imposes significant modifications on the predictive curve, so that improved accuracy has been achieved. Copyright © 2008 John Wiley & Sons, Ltd.     

基于能量方法设计的RC框架结构易损性分析

基于“强柱弱梁”的屈服机制,依据能量平衡方法设计了某6层RC框架结构,采用震级-震中距条带地震动记录选取方法,选取12条随机地震动,利用Perform-3D有限元分析软件对结构进行增量动力（IDA）分析,得到了结构的地震易损性曲线、破坏状态概率曲线以及结构破坏概率矩阵。分析结果表明:该方法设计的结构能够形成预设的“强柱弱梁”屈服机制,可以保证结构中梁充分参与耗能,同时结构具有较强的抗倒塌能力,可以满足“小震不坏,中震可修,大震不倒”的性能要求。     

Effects of near-fault ground motions on the nonlinear behaviour of reinforced concrete framed buildings

The design provisions of current seismic codes are generally not very accurate for assessing effects of near-fault ground motions on reinforced concrete(r.c.)spatial frames,because only far-fault ground motions are considered in the seismic codes.Strong near-fault earthquakes are characterized by long-duration(horizontal)pulses and high values of the ratio α_(PGA)of the peak value of the vertical acceleration,PGA_V,to the analogous value of the horizontal acceleration,PGA_H,which can become critical for girders and columns.In this work,six- and twelve-storey r.c.spatial frames are designed according to the provisions of the Italian seismic code,considering the horizontal seismic loads acting(besides the gravity loads)alone or in combination with the vertical ones.The nonlinear seismic analysis of the test structures is performed using a step-by-step procedure based on a two-parameter implicit integration scheme and an initial stress-like iterative procedure.A lumped plasticity model based on the Haar-Karman principle is adopted to model the inelastic behaviour of the frame members.For the numerical investigation,five near-fault ground motions with high values of the acceleration ratio α_(PGA) are considered.Moreover,following recent seismological studies,which allow the extraction of the largest(horizontal) pulse from a near-fault ground motion,five pulse-type(horizontal)ground motions are selected by comparing the original ground motion with the residual motion after the pulse has been extracted.The results of the nonlinear dynamic analysis carried out on the test structures highlighted that horizontal and vertical components of near-fault ground motions may require additional consideration in the seismic codes.     

The role of ground motion duration and pulse effects in the collapse of ductile systems

The seismic collapse capacity of ductile single-degree-of-freedom systems vulnerable to P-Δ effects is investigated by examining the respective influence of ground motion duration and acceleration pulses. The main objective is to provide simple relationships for predicting the duration-dependent collapse capacity of modern ductile systems. A novel procedure is proposed for modifying spectrally equivalent records, such that they are also equivalent in terms of pulses. The effect of duration is firstly assessed, without accounting for pulses, by assembling 101 pairs of long and short records with equivalent spectral response. The systems considered exhibit a trilinear backbone curve with an elastic, hardening and negative stiffness segment. The parameters investigated include the period, negative stiffness slope, ductility and strain hardening, for both bilinear and pinching hysteretic models. Incremental dynamic analysis is employed to determine collapse capacities and derive design collapse capacity spectra. It is shown that up to 60% reduction in collapse capacity can occur due to duration effects for flexible bilinear systems subjected to low levels of P-Δ. A comparative evaluation of intensity measures that account for spectral shape, duration or pulses, is also presented. The influence of pulses, quantified through incremental velocity, is then explicitly considered to modify the long records, such that their pulse distribution matches that of their short spectrally equivalent counterparts. The results show the need to account for pulse effects in order to achieve unbiased estimation of the role of duration in flexible ductile systems, as it can influence the duration-induced reduction in collapse capacity by more than 20%.     

Seismic loss estimation of non‐ductile reinforced concrete buildings

Non‐ductile reinforced concrete buildings represent a prevalent construction type found in many parts of the world. Due to the seismic vulnerability of such buildings, in areas of high seismic activity non‐ductile reinforced concrete buildings pose a significant threat to the safety of the occupants and damage to such structures can result in large financial losses. This paper introduces advanced analytical models that can be used to simulate the nonlinear dynamic response of these structural systems, including collapse. The state‐of‐the‐art loss simulation procedure developed for new buildings is extended to estimate the expected losses of existing non‐ductile concrete buildings considering their vulnerability to collapse. Three criteria for collapse, namely first component failure, side‐sway collapse, and gravity‐load collapse, are considered in determining the probability of collapse and the assessment of financial losses. A detailed example is presented using a seven‐story non‐ductile reinforced concrete frame building located in the Los Angeles, California. Copyright © 2012 John Wiley & Sons, Ltd.     

The influence of interface geometry,stiffness, and crushing on the dynamic response of masonry collapse mechanisms

Failure of masonry structures generally occurs via specific collapse mechanisms which have been well documented. Using rocking dynamics, equations of motion have been derived for a number of different failure mechanisms ranging from the simple overturning of a single block to more complicated mechanisms. However, most of the equations of motion derived thus far assume that the structures can be modelled as rigid bodies rocking on rigid interfaces with an infinite compressive strength—which is not always the case. In fact, crushing of masonry—commonly observed in larger scale constructions and vertically restrained walls—can lead to a reduction in the dynamic capacity of these structures. This paper rederives the rocking equation of motion to account for the influence of flexible interfaces, characterized by a specific interface stiffness as well as finite compressive strength. The interface now includes a continually shifting rotation point, the location of which depends not only on the material properties of the interface but also on its geometry. Expressions have thus also been derived for interfaces of different geometries, and parametric studies conducted to gauge their influence on dynamic response. The new interface formulations are also implemented within a new analytical modelling tool that provides a novel approach to the dynamic analysis of masonry collapse mechanisms. Finally, this tool is exemplified, along with the importance of the interface formulation, by evaluating the collapse of the Dharahara Tower in Kathmandu, which was almost completely destroyed during the 2015 Gorkha earthquake.     

Double deck bridge behavior and failure mechanism under seismic motions using nonlinear analyzes

This paper investigates the behavior and the failure mechanism of a double deck bridge constructed in China through nonlinear time history analysis.A parametric study was conducted to evaluate the influence of different structural characteristics on the behavior of the double deck bridge under transverse seismic motions,and to detect the effect of bidirectional loading on the seismic response of this type of bridge.The results showed that some characteristics,such as the variable lateral stiffness,the foundation modelling,and the longitudinal reinforcement ratio of the upper and lower columns of the bridge pier bents have a major impact on the double deck bridge response and its failure mechanism under transverse seismic motions.It was found that the soft story failure mechanism is not unique to the double deck bridge and its occurrence is related to some conditions and structural characteristics of the bridge structure.The analysis also showed that the seismic vulnerability of the double deck bridge under bi-directional loading was severely increased compared to the bridge response under unidirectional transverse loading,and out-of-phase movements were triggered between adjacent girders.     

强震作用下混凝土框架结构倒塌过程的数值分析

本文引入机械铰概念解释了钢筋混凝土杆件在地震作用下的失效过程，继而建立了以楼层为基本单位的强梁弱柱型框架结构的倒塌分析模型。并将离散单元法的中心算法一动态松弛法运用到结构倒塌分析模型中，成功地模拟了钢筋混凝土框架结构在地震作用下的倒塌全过程反应。     

Field investigation on severely damaged aseismic buildings in 2014 Ludian earthquake

The 2014 magnitude 6.5 Ludian earthquake caused a death toll of 617, many landslides and tens of thousands of collapsed buildings. A field investigation to evaluate the damage to buildings was carried out immediately after the occurrence of the earthquake. Severely damaged aseismic buildings, which were basically observed in the downtown of Longtoushan Town, were carefully examined one by one with the aim to improve design codes. This paper summarizes the damage observed to the investigated aseismic buildings in both the structural and local levels. A common failure mode was observed that most of the aseismic buildings, such as RC frame structures and confined masonry structures, were similarly destroyed by severe damage or complete collapse of the first story. The related strong ground motion, which was recorded at the nearby station, had a short duration of less than 20 s but a very large PGA up to 1.0 g. The RC frames based on the new design codes still failed to achieve the design target for "strong column, weak beam". Typical local failure details, which were related to the interaction between RC columns and infill walls and between constructional columns and masonry walls, are summarized with preliminary analyses.     

Aftershock collapse vulnerability assessment of reinforced concrete frame structures

In a seismically active region, structures may be subjected to multiple earthquakes, due to mainshock–aftershock phenomena or other sequences, leaving no time for repair or retrofit between the events. This study quantifies the aftershock vulnerability of four modern ductile reinforced concrete (RC) framed buildings in California by conducting incremental dynamic analysis of nonlinear MDOF analytical models. Based on the nonlinear dynamic analysis results, collapse and damage fragility curves are generated for intact and damaged buildings. If the building is not severely damaged in the mainshock, its collapse capacity is unaffected in the aftershock. However, if the building is extensively damaged in the mainshock, there is a significant reduction in its collapse capacity in the aftershock. For example, if an RC frame experiences 4% or more interstory drift in the mainshock, the median capacity to resist aftershock shaking is reduced by about 40%. The study also evaluates the effectiveness of different measures of physical damage observed in the mainshock‐damaged buildings for predicting the reduction in collapse capacity of the damaged building in subsequent aftershocks. These physical damage indicators for the building are chosen such that they quantify the qualitative red tagging (unsafe for occupation) criteria employed in post‐earthquake evaluation of RC frames. The results indicated that damage indicators related to the drift experienced by the damaged building best predicted the reduced aftershock collapse capacities for these ductile structures. Copyright © 2014 John Wiley & Sons, Ltd.     

Variance of collapse capacity of SDOF systems under earthquake excitations

The variance of collapse capacity is an important constituent of probabilistic methodologies used to evaluate the probability of collapse of structures subjected to earthquake ground motions. This study evaluates the effect of ground motion randomness (i.e. record‐to‐record (RTR) variability) and uncertainty in the deterioration parameters of single‐degree‐of‐freedom (SDOF) systems on the variance of collapse capacity. Collapse capacity is evaluated in terms of a relative intensity defined as the ratio of ground motion intensity to a structure strength parameter. The effect of RTR variability on the variance of collapse capacity is directly obtained by performing dynamic analyses of deteriorating hysteretic models for a set of representative ground motions. The first‐order second‐moment (FOSM) method is used to quantify the effect of deterioration parameter uncertainty. In addition to RTR variability, the results indicate that uncertainty in the displacement at the peak (cap) strength and the post‐capping stiffness significantly contribute to the variance of collapse capacity. If large dispersion of these parameters exists, the effect of uncertainty in deterioration parameters on the variance of collapse capacity may be comparable to that caused by RTR variability. Copyright © 2011 John Wiley & Sons, Ltd.     

Impact of hazard‐consistent ground motion duration in structural collapse risk assessment

This study evaluates the effect of considering ground motion duration when selecting hazard‐consistent ground motions for structural collapse risk assessment. A procedure to compute source‐specific probability distributions of the durations of ground motions anticipated at a site, based on the generalized conditional intensity measure framework, is developed. Targets are computed for three sites in Western USA, located in distinct tectonic settings: Seattle, Eugene, and San Francisco. The effect of considering duration when estimating the collapse risk of a ductile reinforced concrete moment frame building, designed for a site in Seattle, is quantified by conducting multiple stripe analyses using groups of ground motions selected using different procedures. The mean annual frequency of collapse (λ_collapse) in Seattle is found to be underestimated by 29% when using typical‐duration ground motions from the PEER NGA‐West2 database. The effect of duration is even more important in sites like Eugene (λ_collapse underestimated by 59%), where the seismic hazard is dominated by large magnitude interface earthquakes, and less important in sites like San Francisco (λ_collapse underestimated by 7%), where the seismic hazard is dominated by crustal earthquakes. Ground motion selection procedures that employ causal parameters like magnitude, distance, and Vs₃₀ as surrogates for ground motion duration are also evaluated. These procedures are found to produce poor fits to the duration and response spectrum targets because of the limited number of records that satisfy typical constraints imposed on the ranges of the causal parameters. As a consequence, ground motions selected based on causal parameters are found to overestimate λ_collapse by 53%. Copyright © 2016 John Wiley & Sons, Ltd.     

Dynamic behaviour of R/C highway bridges under the combined effect of vertical and horizontal earthquake motions

Measurements of ground motions during past earthquakes indicate that the vertical acceleration can reach values comparable to horizontal accelerations or may even exceed these accelerations. Furthermore, measurements of structural response show the possibility of significant amplification in the response of bridges in the vertical direction that can be attributed to the vertical component of ground motion. In this study, the relative importance of the vertical component of ground motion on the inelastic response of R/C highway bridges is investigated. Particular emphasis is placed on modelling of the deck and piers to account for complex loading histories under combined vertical and horizontal earthquake motions. Analyses of actual bridges indicate that, in general, the vertical motion will increase the level of response and the amount of damage sustained by a highway bridge. Vertical motion generates fluctuating axial forces in the columns, which cause unstability of the hysteresis loops and increase the ductility demand. Furthermore, vertical motion can generate forces of high magnitude in the abutments and foundations that are not accounted for by the current seismic design guidelines. Thus, it is important to consider this component of the ground motion in the design of highway bridges, especially for those located in regions near seismic faults.     

Near‐collapse response of existing RC building under severe pulse‐type ground motion using hybrid simulation

Column shear‐axial failure is a complex response, which lends itself to physical experimentation. Reinforced concrete structures built prior to the mid‐1970s are particularly susceptible to such failure. Shear‐axial column failure has been examined and studied at the element level, but current rehabilitation practice equates such a column failure with structural collapse, neglecting the collapse resistance of the full structural system following column failure. This system‐level response can prevent a column failure from leading to progressive collapse of the entire structure. In this study, a hybrid simulation was conducted on a representative pre‐1970s reinforced concrete frame structure under severe seismic ground motion, in which three full‐scale reinforced concrete columns were tested at the University of Illinois at Urbana Champaign. The analytical portion of the model was represented in the computer program OpenSees. Failure occurred in multiple physical specimens as a result of the ground motion, and the hybrid nature of the test allowed for observation of the system‐level response of the tested columns and the remaining structural system. The behavior of the system accounting for multiple column shear‐axial failure is discussed and characterized. Copyright © 2016 John Wiley & Sons, Ltd.