Damage index based on stiffness degradation of low‐rise RC walls

Widely used damage indices, such as ductility and drift ratios, do not account for the influences of the duration of strong shaking, the cumulative inelastic deformation or energy dissipation in structures. In addition, the formulation and application of most damage indices have until now been based primarily on flexural modes of failure. However, evidence from earthquakes suggests that shear failure or combined shear‐flexure behavior is responsible for a large proportion of failures. Empirical considerations have been made in this paper for evaluating structural damage of low‐rise RC walls under earthquake ground motions by means of a new energy‐based low‐cycle fatigue damage index. The proposed empirical damage index is based on the results of an experimental program that comprised six shake table tests of RC solid walls and walls with openings; results of six companion walls tested under QS‐cyclic loading were used for comparison purposes. Variables studied were the wall geometry, type of concrete, web shear steel ratio, type of web shear reinforcement, and testing method. The index correlates the stiffness degradation and the destructiveness of the earthquake in terms of the duration and intensity of the ground motions. The stiffness degradation model considers simultaneously the increment of damage associated to the low‐cycle fatigue, energy dissipation, and the cumulative cyclic parameters, such as displacement demand and hysteretic energy dissipated. Copyright © 2014 John Wiley & Sons, Ltd.     

附设黏滞阻尼器的传统风格建筑混凝土梁-柱节点动力循环荷载累积损伤分析

为研究附设黏滞阻尼器的传统风格建筑混凝土梁-柱节点地震损伤演化规律,进行6个该类型构件的动力荷载试验,并分别采用位移型、能量型及位移-能量混合型损伤模型对其进行全过程评价,采用Park-Ang模型分析试件黏滞阻尼器型号、试件类型等因素对混凝土传统风格建筑梁柱节点损伤行为的影响。研究结果表明：附设黏滞阻尼器可显著提升传统风格建筑节点的承载能力、延性性能及耗能能力,结构的抗震性能得到较大幅度的提升;Park-Ang损伤模型与Banon损伤模型适用于传统风格建筑节点损伤演化规律的描述,建议对该类型节点的损伤规律表征选用该损伤模型。黏滞阻尼器型号可在一定程度上影响传统风格建筑的损伤演化发展;设计阻尼力大的试件虽然延性有所提高,但受荷过程中累积损伤也较大。     

Inelastic seismic spectra including a damage criterion: A stochastic approach

In this paper, a stochastic approach for obtaining damage-based inelastic seismic spectra is proposed. The Park and Ang damage model, which includes displacement ductility and hysteretic energy, is adopted to take into account the cumulative damage phenomenon in structural systems under strong ground motions. Differently from previous studies in this field, damage-based seismic spectra are obtained by means of peak theory of stochastic processes. The following stochastic inelastic seismic spectra are constructed and then analyzed: damage-based displacement and acceleration inelastic spectra, damage-based response modification factor spectra, damage-based yield strength demand spectra and damage-based inelastic displacement ratio spectra.     

Equivalent ductility factors,taking into account low-cycle fatigue

During strong earthquakes, the deformation capacity of structures is reduced due to the cumulative damage caused by cyclic load reversals. In the paper, equivalent (reduced) ductility factors have been proposed, which take into account this effect. They are based on different failure hypotheses. Ductility reduction due to low-cycle fatigue is controlled by a dimensionless parameter γ, which is a function of dissipated hysteretic energy, maximum displacement and the natural frequency of the structural system, and which has been proved to be a relatively stable quantity in the whole period range. If approximate values for γ are used, the determination of equivalent ductility is very simple, and thus appropriate for design purposes. The formulae for equivalent ductility factors include damage indices, and permit the designer to choose acceptable level of structural damage explicitly. As an example, equivalent ductility factors have been used to construct inelastic acceleration spectra, which are proportional to strength demand, for the El Centro 1940 SOOE record. The results have been compared with the ‘exact’ spectra obtained by non-linear dynamic analysis.     

Seismic energy dissipation under variable amplitude loading for rectangular RC members in flexure

The energy dissipation characteristics of reinforced concrete members that exhibit both strength and stiffness deterioration under imposed displacement reversals were investigated. To do this, 24 symmetrically reinforced concrete rectangular specimens were tested under stable variable and random variable amplitude inelastic displacement cycles. Stable variable amplitude tests were employed to determine the low‐cycle fatigue behavior of specimens where the loading sequence was the major variable. A 2‐parameter fatigue model was developed in order to express the variation of the dissipated energy in displacement cycles with the cumulative hysteretic energy. This model was then used to predict the energy dissipation of test specimens subjected to random variable amplitude displacement cycles simulating severe seismic excitations. It has been demonstrated that the remaining energy dissipation capacity for the next displacement cycle was dependent on the relative relationship between the maximal displacement cycle and the energy dissipated along the completed displacement path. The plastic energy dissipation capacity of reinforced concrete members is both displacement path dependent and cumulative hysteretic energy dependent.     

A damage model for structures with degrading response

The paper presents a hysteretic damage model for the response simulation of structural components with strength and stiffness deterioration under cyclic loading. The model is based on 1D continuum damage mechanics and relates any 2 work‐conjugate response variables such as force‐displacement, moment‐rotation, or stress‐strain. The strength and stiffness deterioration is described by a continuous damage variable. The formulation uses a criterion based on the hysteretic energy and the maximum or minimum deformation for damage initiation with a cumulative probability distribution function for the damage evolution. A series of structural component response simulations showcase the ability of the model to describe different types of hysteretic behavior. The relation of the model's damage variable to the Park‐Ang damage index is also discussed. Because of its consistent and numerically robust formulation, the model is suitable for the large‐scale seismic response simulation of structural systems with strength and stiffness deterioration.     

远场长周期地震下高层建筑的地震损伤模型研究

传统高层建筑地震损伤模型不能反映构件极限滞回耗能随累积幅值的改变情况,无法有效确定组合参数,离散性较大。为此,设计一种远场长周期地震下高层建筑的地震损伤模型。针对不同层次高层建筑结构,依据广义力-广义变形曲线,构建变形损伤模型。结合累积能量比、远场长周期地震瞬时输入能比构建能量损伤模型。从变形与能量两方面综合评价损伤,依据钢筋混凝土结构构建最大反应变形与耗损能量的线性组合地震损伤模型,并对其进行改进。实验选用ILA003、ILA048和TCU115三种长周期地震波,计算不同构件和高层建筑结构整体损伤结果,验证所提模型的可靠性。将所提模型应用于实际高层建筑中,发现其实用性强。     

Cumulative damage‐based inelastic cyclic demand spectrum

The estimation of cyclic deformation demand resulting from earthquake loads is crucial to the core objective of performance‐based design if the damage and residual capacity of the system following a seismic event needs to be evaluated. A simplified procedure to develop the cyclic demand spectrum for use in preliminary seismic evaluation and design is proposed in this paper. The methodology is based on estimating the number of equivalent cycles at a specified ductility. The cyclic demand spectrum is then determined using well‐established relationships between seismic input energy and dissipated hysteretic energy. An interesting feature of the proposed procedure is the incorporation of a design spectrum into the proposed procedure. It is demonstrated that the force–deformation characteristics of the system, the ductility‐based force‐reduction factor R_μ, and the ground motion characteristics play a significant role in the cyclic demand imposed on a structure during severe earthquakes. Current design philosophy which is primarily based on peak response amplitude considers cyclic degradation only in an implicit manner through detailing requirements based on observed experimental testing. Findings from this study indicate that cumulative effects are important for certain structures, classified in this study by the initial fundamental period, and should be incorporated into the design process. Copyright © 2003 John Wiley & Sons, Ltd.     

基于累积耗损能量的饱和粉土液化特性试验研究

饱和粉土场地在强地震作用下易发生液化现象。开展饱和粉土的循环三轴试验,以循环加载的累积耗损能量为指标,探讨黏粒含量、密实度、有效围压和循环应力比等因素对粉土液化特性的影响,试验结果表明:粉土液化所需的耗损能量随黏粒含量的增加呈先减小后增大的趋势,当黏粒含量约为8%时粉土的液化耗损能量最低;液化耗损能量随粉土密实程度的增大而逐渐增加,并随初始有效围压的增长而增加,但粉土的液化耗损能量与循环应力比之间的关系不明显。     

Damage evolution in reinforced concrete columns subjected to biaxial loading

An analysis of the damage observed in 24 reinforced concrete (RC) columns tested under uniaxial and biaxial horizontal loading is presented. The test results show that for biaxial loading conditions specific damage occurs for lower drift demands when compared with the corresponding uniaxial demand (a reduction of 50–75 % was found). The damage distribution observed in each column is also analysed. No significant differences are found in the plastic hinge length for uniaxial and biaxial loading. The drift demands associated with each damage state are compared with reference values proposed in international guidelines. Finally, and based on the philosophy of the Park and Ang uniaxial damage index, two new expressions are proposed for the evaluation of damage in RC elements under biaxial loading. The results of the application of these expressions to the experimental results are discussed.     

基于能量原理的Park & Ang损伤模型简化计算方法

Park＆Ang损伤模型综合考虑了结构最大变形和累积滞回耗能的耦合作用,具有一定的先进性,被国内外研究者广泛采用;但由于该模型中参数的计算困难,尤其涉及结构滞回耗能的计算问题时,该模型的应用受到了一定的限制;文中从能量的关系入手,寻找出结构滞回耗能与结构最大位移的关系,利用该关系可方便求解出结构的滞回耗能,从而为该模型的计算提供了一种简便方法;最后,例题分析证明本文的方法简便可行,计算效率高。     

Seismic demand based on damage control model—considering basin effect and source effect

The Park and Ang damage model was used as the "Structural Damage Control Model" to study the seismic design parameters. This damage control model included the displacement ductility and hysteretic energy in the analysis of elastic-perfect-plastic single-degree-of-freedom system. Based on this damage control model, the reduction factor and yield base shear coefficient are discussed. Seismic data collected from Taipei basin were used to examine the code-provided yield base shear coefficient which reflects the influence of using a damage control model in the seismic design parameter. Effects of seismic source as well as Taipei basin topography are also considered in examining the variation of yield base shear coefficient.     

Incorporating low‐cycle fatigue model into duration‐dependent inelastic design spectra

Seismic performance of structures is related to the damage inflicted on the structure by the earthquake, which means that formulation of performance‐based design is inherently coupled with damage assessment of the structure. Although the potential for cumulative damage during a long‐duration earthquake is generally recognized, most design codes do not explicitly take into account the damage potential of such events. In this paper, the classical low‐cycle fatigue model commonly used for seismic damage assessment is cast in a framework suitable for incorporating cumulative damage into seismic design. The model, in conjunction with a seismic input energy spectrum, may be used to establish an energy‐based seismic design. In order to ensure satisfactory performance in a structure, the cyclic plastic strain energy capacity of the structure is designed to be larger than or equal to the portion of seismic input energy contributing to cumulative damage. The resulting design spectrum, which depends on the duration of the ground motion, indicates that the lateral strength of the structure must be increased in order to compensate for the increased damage due to an increased number of inelastic cycles that occur in a long‐duration ground motion. Examples of duration‐dependent inelastic design spectra are developed using parameters currently available for the low‐cycle fatigue model. The resulting spectra are also compared with spectra developed using a different cumulative damage model. Copyright © 2004 John Wiley & Sons, Ltd.     

基于损伤的累积滞回耗能与延性系数

从地震损伤评价出发, 通过分析与推导, 建立了基于位移延性系数的损伤评价模型。 采用四个柱的破坏性试验数据, 运用推导出来的模型进行了柱的损伤程度评价。 考虑到延性系数计算的困难以及其与累积滞回耗能的关系, 通过分析建立起累积滞回耗能与位移延性系数的关系曲线。     

结构地震弹塑性反应谱——损伤谱

首先,本文基于各国广泛使用的由Park和Ang提出的双参数损伤模型,研究基于损伤性能的弹塑性反应谱（损伤谱）的分析方法。其次,文中考虑结构极限状态设计,并通过自编DBDS程序,研究得到了损伤反应谱（简称“RD谱”）,尺。谱综合考虑了结构最大弹塑性位移和结构累积滞回耗能的耦合影响,更加合理地反映结构在罕遇地震作用下的弹塑性行为。第三,通过大量时程分析和拟合得到回归公式及其相关系数,研究成果可供抗震性能评估使用。最后,由本文提倡的RD谱和已有研究的Rμ谱做了定性比较分析,说明了考虑地震动持时的必要性和重要性。     

Experimental investigation on dynamic and quasi‐static behavior of low‐rise reinforced concrete walls

Experimental evidence supporting the fact that results from quasi‐static (QS) test of low‐rise reinforced concrete walls may be safely assumed as a lower limit of strength and displacement, and energy dissipation capacities are still scarce. The aim of this paper is to compare the seismic performance of 12 reinforced concrete walls for low‐rise housing: six prototype walls tested under QS‐cyclic loading and six models tested under shaking table excitations. Variables studied were wall geometry, type of concrete, web steel ratio, type of web reinforcement and testing method. Comparison of results from dynamic and QS‐cyclic tests indicated that stiffness and strength properties were dependent on the loading rate, the strength mechanisms associated with the failure mode, the low‐cycle fatigue, and the cumulative parameters, such as displacement demand and energy dissipated. Copyright © 2012 John Wiley & Sons, Ltd.     

钢筋混凝土柱低周疲劳性能的试验研究

结构的地震破坏可看作是超过屈服后的非弹性阶段的低周疲劳问题,而单根柱的破坏分析是整个框架失效分析的基础,本文通过八根１／２比例的钢筋混凝土柱在不同位移幅值下的等幅低周疲劳试验和六根非对称位移循环下低疫疲劳试验,探讨了在不同位移幅值下降筋混凝土柱累积损伤的发展规划以及低周疲劳寿命的表达式,给出了低周疲劳寿命不同位移水平下正负位移幅值比之间关系的表达式。希望以此为基础,建立更为合理的结构抗震破坏准则。     

橡胶集料风积沙混凝土柱抗震性能试验研究

为研究橡胶集料风积沙混凝土柱的抗震性能,制作了4根相同尺寸的混凝土柱试件,其中包括普通混凝土柱、风积沙混凝土柱、橡胶集料混凝土柱和橡胶集料风积沙混凝土柱。通过低周反复荷载试验,分析各试件的破坏现象、滞回曲线、骨架曲线、刚度退化和延性等抗震性能指标。在试验的基础上,根据能量耗散原理建立累积损伤评价模型,并对结构进行了累积损伤分析。研究结果表明:10%橡胶集料的掺入能够改善混凝土柱的变形能力,但混凝土柱的承载力有所降低;30%风积沙的掺入可以改善混凝土柱的抗震性能;橡胶集料风积沙混凝土柱具有较好的滞回性能,且耗能能力和延性性能明显高于其余试件,柱的抗震性能得到提高;通过累积损伤分析表明:适量掺入橡胶集料和风积沙的可以有效减缓试件的损伤,且该累积损伤模型能够较好的反映出各试件的损伤程度。     

Prediction of seismic energy dissipation in SDOF systems

A simple analytical procedure is developed for calculating the seismic energy dissipated by a linear SDOF system under an earthquake ground excitation. The ground excitation is specified by its pseudo-velocity spectra and effective duration whereas the SDOF system is defined by its natural period of vibration and viscous damping ratio. However, the derived relationship for the energy dissipation demand under an earthquake excitation is sensitive neither to the viscous damping ratio nor the ductility ratio when the SDOF system undergoes inelastic response. Accordingly, the proposed relationship can be employed in an energy-based seismic design procedure for determining the required energy dissipation capacity of a structural system.