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.     

Acceptance limits for performance‐based seismic design of RC walls for low‐rise housing

Acceptance limits of the structural response of walls for low‐rise concrete housing were developed. Proposed values are applicable within a performance‐based seismic design framework. Acceptance limits are based on performance indicators of structural response–allowable story drift ratios, width of residual cracks and residual damage index, and expected damage of walls. Cracking limits were defined from parameters obtained at the unloading stage of walls (i.e., residual cracking stage). The residual cracking stage may be used for structural damage evaluation and cost estimation of structural rehabilitation after an earthquake has occurred. The performance indicators proposed herein were derived from test observations and measured response of 39 RC walls' specimens during shaking table and quasistatic testing, as well as from limiting values and results of previous studies. Copyright © 2012 John Wiley & Sons, Ltd.     

A preliminary prediction of seismic damage‐based degradation in RC structures

Estimation of structural damage from a known increase in the fundamental period of a structure after an earthquake or prediction of degradation of stiffness and strength for a known damage requires reliable correlations between these response functionals. This study proposes a modified Clough–Johnston single‐degree‐of‐freedom oscillator to establish these correlations in the case of a simple elasto‐plastic oscillator. It is assumed that the proposed oscillator closely models the response of a given multi‐degree‐of‐freedom system in its fundamental mode throughout the duration of the excitation. The proposed model considers the yield displacement level and ductility supply ratio‐related parameter as two input parameters which must be estimated over a narrow range of ductility supply ratio from a frequency degradation curve. This curve is to be identified from a set of recorded excitation and response time‐histories. Useful correlations of strength and stiffness degradation with damage have been obtained wherein a simple damage index based on maximum and yield displacements and ductility supply ratio has been considered. As an application, the proposed model has been used to demonstrate that ignoring the effects of aftershocks in the case of impulsive ground motions may lead to unsafe designs. Copyright © 2001 John Wiley & Sons, Ltd.     

Energy demands for seismic design against low‐cycle fatigue

A seismic design procedure that does not take into account the maximum and cumulative plastic deformation demands that a structure is likely to undergo during severe ground motion could lead to unsatisfactory performance. In spite of this, current design procedures do not take into account explicitly the effect of low‐cycle fatigue. Based on the high correlation that exists between the strength reduction factor and the energy demand in earthquake‐resistant structures, simple procedures can be formulated to estimate the cumulative plastic deformation demands for design purposes. Several issues should be addressed during the use of plastic energy within a practical performance‐based seismic design methodology. Copyright © 2006 John Wiley & Sons, Ltd.     

Seismic energy dissipation in deteriorating systems through low‐cycle fatigue

Energy dissipation characteristics of structural members which exhibit both strength and stiffness deterioration under imposed displacement reversals are investigated. In the experimental part, 17 reinforced concrete beam specimens were tested under constant and variable amplitude inelastic displacement cycles. The constant‐amplitude tests were employed to determine the low‐cycle fatigue behaviour of specimens where the imposed displacement amplitude was the major variable. A two‐parameter fatigue model was developed in order to express the variation of dissipated energy with the number of displacement cycles. This model was then used to predict the energy dissipation of test specimens subjected to variable‐amplitude displacement cycles simulating severe seismic excitations. It has been demonstrated that the remaining energy dissipation capacity in a forthcoming displacement cycle is dependent on the energy dissipated along the completed displacement path. Moreover, it is observed that total energy dissipation is dependent on the length of the displacement path. Copyright © 2003 John Wiley & Sons, Ltd.     

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.     

Energy‐based hysteresis and damage models for deteriorating systems

The low‐cycle fatigue model presented in the companion paper is employed for developing hysteresis and damage models for deteriorating systems. The hysteresis model performs strength reduction at a current displacement cycle by evaluating the loss in the energy dissipation capacity along the completed displacement path. Hence it is completely memory dependent. Pinching is accounted for implicitly by a reduced energy dissipation capacity in a displacement cycle. The model predicts the experimental results obtained from variable‐amplitude tests reasonably well. Response analysis under earthquake excitations reveals that both the maximum displacements and the number of large‐amplitude displacement response cycles increase significantly with the reduction in energy dissipation capacity, resulting in higher damage. Damage is defined as the deterioration in the effective stiffness of a displacement cycle, which is in turn related to the reduction in the energy dissipation capacity. A simple damage function is developed accordingly, consisting of displacement and fatigue components. It is observed that the fatigue component of damage is more significant than the displacement component for deteriorating systems under ground motions with significant effective durations. Copyright © 2003 John Wiley & Sons, Ltd.     

Developing high‐performance aluminum alloy buckling‐restrained braces based on series of low‐cycle fatigue tests

In order to enhance the durability of high‐performance buckling‐restrained braces (BRBs) used in bridge engineering, which are expected to withstand severe earthquakes three times without being replaced, aluminum alloys were employed to manufacture BRBs. A series of low‐cycle fatigue tests, including 18 specimens, were conducted to address the low‐cycle fatigue strength of the aluminum alloy BRB. Test results of all specimens show that stable hysteretic curves were obtained without overall buckling occurrence. Failure mode of the welded aluminum alloy BRB is obviously affected by the ribs' welding under the variable or constant strain amplitude condition. Therefore, another type of aluminum alloy BRB, the bolt‐assembled BRB with or without spot‐welded stoppers, is proposed and tested. Results showed that the low‐cycle fatigue performance of bolt‐assembled BRBs with stoppers improved four to five times compared with welded BRBs. However, the stoppers' spot welding has an adverse effect on the failure mode because the crack, which induced the specimen's failure, initiated from the spot weld toes of the stoppers. Both bolt‐assembled BRBs with and without stoppers can meet the cumulative inelastic deformation requirement proposed for high‐performance BRBs under the constant strain amplitude, not larger than 2%. In addition, under the variable strain amplitude condition, only the bolt‐assembled BRB without stoppers has an excellent cumulative inelastic deformation capacity and sustains two cycles of 2.5% strain amplitude. Finally, recommended Manson–Coffin equations and preliminary cumulative damage formulae for welded and bolt‐assembled BRBs are given as the references of the strain‐based damage evaluation. Copyright © 2011 John Wiley & Sons, Ltd.     

Tests on low‐ductility RC frames under high‐ and low‐frequency excitations

The response of low‐ductility reinforced concrete (RC) frames, designed typically for a non‐seismic region, subjected to two frequencies of base excitations is studied. Five half‐scaled, two‐bay, two‐storey, RC frames, each approximately 5 m wide by 3.3 m high, were subjected to both horizontal and/or vertical base excitations with a frequency of 40 Hz as well as a lower frequency of about 4 Hz (close to the fundamental frequency) using a shake table. The imposed acceleration amplitude ranged from 0.2 to 1.2g. The test results showed that the response characteristics of the structures differed under high‐ and low‐frequency excitations. The frames were able to sustain high‐frequency excitations without damage but were inadequate for low‐frequency excitations, even though the frames exhibited some ductility. Linear‐elastic time‐history analysis can predict reasonably well the structural response under high‐frequency excitations. As the frames were not designed for seismic loads, the reinforcement detailing may not have been adequate, based on the crack pattern observed. The effect of vertical excitation can cause significant additional forces in the columns and moment reversals in the beams. The ‘strong‐column, weak‐beam’ approach for lateral load RC frame design is supported by experimental observations. Copyright © 2001 John Wiley & Sons, Ltd.     

密肋复合墙板耗能性能及地震损伤分析

根据15榀1/2比例密肋复合墙板在单调及低周反复荷载作用下的试验结果,对这种新型复合墙板的破坏形态、滞回性能、耗能能力和累积损伤模型等进行了分析,探讨了墙板累积损伤的发展过程和发育规律,提出了阶段损伤指数的概念,并通过损伤模型计算的破损结果与试件实际破坏特征对比,确定了墙板的阶段损伤界限值,可供工程实际抗震设计和评估参考。     

Effect of cumulative seismic damage and corrosion on the life‐cycle cost of reinforced concrete bridges

Bridge design should take into account not only safety and functionality, but also the cost effectiveness of investments throughout a bridge life‐cycle. This paper presents a probabilistic approach to compute the life‐cycle cost (LCC) of corroding reinforced concrete (RC) bridges in earthquake‐prone regions. The approach is developed by combining cumulative seismic damage and damage associated with corrosion due to environmental conditions. Cumulative seismic damage is obtained from a low‐cycle fatigue analysis. Chloride‐induced corrosion of steel reinforcement is computed based on Fick's second law of diffusion. The proposed methodology accounts for the uncertainties in the ground motion parameters, the distance from the source, the seismic demand on the bridge, and the corrosion initiation time. The statistics of the accumulated damage and the cost of repairs throughout the bridge life‐cycle are obtained by Monte‐Carlo simulation. As an illustration of the proposed approach, the effects of design parameters on the LCC of an example RC bridge are studied. The results are valuable in better estimating the condition of existing bridges and, therefore, can help to schedule inspection and maintenance programs. In addition, by taking into consideration the two deterioration processes over a bridge life‐cycle, it is possible to estimate the optimal design parameters by minimizing, for example, the expected cost throughout the life of the structure. A comparison between the effects of the two deterioration processes shows that, in seismic regions, the cumulative seismic damage affects the reliability of bridges over time more than the corrosion even for corrosive environments. Copyright © 2008 John Wiley & Sons, Ltd.     

Out‐of‐plane seismic response of vertically spanning URM walls connected to flexible diaphragms

A simplified numerical model was used to investigate the out‐of‐plane seismic response of vertically spanning unreinforced masonry (URM) wall strips. The URM wall strips were assumed to span between two flexible diaphragms and to develop a horizontal crack above the wall mid‐height. Three degrees of freedom were used to accommodate the wall displacement at the crack height and at the diaphragm connections, and the wall dynamic stability was studied. The equations of dynamic motion were obtained using principles of rocking mechanics of rigid bodies, and the formulae were modified to include semi‐rigid wall behaviour. Parametric studies were conducted that included calculation of the wall response for different values of diaphragm stiffness, wall properties, applied overburden, wall geometry and earthquake ground motions. The results of the study suggest that stiffening the horizontal diaphragms of typical low‐rise URM buildings will amplify the out‐of‐plane acceleration demand imposed on the wall and especially on the wall–diaphragm connections. It was found that upper‐storey walls connected to two flexible diaphragms had reduced stability for applied earthquake accelerograms having dominant frequency content that was comparable with the frequency of the diaphragms. It was also found that the applied overburden reduced wall stability by reducing the allowable wall rotations. The results of this study suggest that the existing American Society of Civil Engineers recommendations for assessment of vertically spanning walls overestimate the stability of top‐storey walls in multi‐storey buildings in high‐seismic regions or for walls connected to larger period (less stiff) diaphragms. Copyright © 2015 John Wiley & Sons, Ltd.     

Dispersions for the pushover‐based risk assessment of reinforced concrete frames and cantilever walls

The paper presents the results of an investigation into the dispersion values, expressed in terms of limit‐state spectral accelerations, which could be used for the pushover‐based risk assessment of low‐height to mid‐height reinforced concrete frames and cantilever walls. The results of an extensive parametric study of a portfolio of test structures indicated that the dispersion values due to record‐to‐record variability and modelling uncertainty (β_LS,RU) are within the range from 0.3 to 0.55 for the near collapse limit state, and between 0.35 and 0.60 for the collapse limit state. The dispersions β_LS,RU proposed for the code‐conforming and the majority of old (non code‐conforming) frames are in between these values. On the other hand, the dispersions proposed for the old frames with a soft storey and an invariant plastic mechanism, and for the code‐conforming cantilever walls, are at the lower and upper bounds of the presented values, respectively. The structural parameters that influence these dispersions were identified, and the influence of different ground motion sets, and of the models used for the calculation of the rotation capacities of the columns, on the calculated fragility parameters was examined and quantified. The proposed dispersion values were employed in a practice‐oriented pushover‐based method for the estimation of failure probability for eight selected examples. The pushover‐based risk assessment method, although extremely simple and economical when compared with more rigorous probabilistic methods, was able to predict seismic risk with reasonable accuracy, thus showing it to be a practical tool for engineers. Copyright © 2016 John Wiley & Sons, Ltd.     

主余震序列型地震动作用下RC框架结构损伤耗能研究

强震发生后通常伴随着余震,余震的发生会加重结构损伤甚至引发倒塌。为了量化研究主余震序列型地震动对结构损伤的影响,以一栋3层钢筋混凝土框架结构为研究对象,选取了10条实际的主余震记录作为地震动输入,采用ABAQUS非线性有限元软件对该框架结构进行非线性动力时程分析,并依据结构局部和整体损伤耗能指标来评价主余震序列型地震动对框架结构累积损伤的影响。研究结果表明:序列地震会加剧结构底层柱的局部损伤耗能,特别是对底层中柱的影响更加明显;序列地震作用下的结构整体损伤耗能平均值相对于单主震作用下增加约30%;当余震与主震的第一周期谱加速度指标的比值Sa （T₁）_余震/Sa （T₁）_主震较大时,序列地震对结构损伤需求的影响更为显著。     

A combined local damage index for seismic assessment of existing RC structures

A new local damage index for existing RC structures is introduced, wherein deterioration caused by all deformation mechanisms (flexure, shear, anchorage slip) is treated separately for each mechanism. Moreover, the additive character of damage arising from the three response mechanisms, and the increase in degradation rate caused by their interaction, are fully taken into consideration. The proposed local damage index is then applied, in conjunction with a finite element model developed previously by the authors, to assess seismic damage response of several RC column and frame test specimens with substandard detailing. It is concluded that in all cases and independently from the prevailing mode of failure, the new local damage index describes well the damage pattern of the analysed specimens. Copyright © 2012 John Wiley & Sons, Ltd.     

Seismic retrofit of low‐rise steel buildings in Canada using rocking steel braced frames

This article examines the use of rocking steel braced frames for the retrofit of existing seismically deficient steel building structures. Rocking is also used to achieve superior seismic performance to reduce repair costs and disruption time after earthquakes. The study focuses on low‐rise buildings for which re‐centring is solely provided by gravity loads rather than added post‐tensioning elements. Friction energy dissipative (ED) devices are used to control drifts. The system is applied to 2‐storey and 3‐storey structures located in 2 seismically active regions of Canada. Firm ground and soft soil conditions are considered. The seismic performance of the retrofit scheme is evaluated using nonlinear dynamic analysis and ASCE 41‐13. For all structures, rocking permits to achieve immediate occupancy performance under 2% in 50 years seismic hazard if the braces and their connections at the building's top storeys are strengthened to resist amplified forces due to higher mode response. Base shears are also increased due to higher modes. Impact at column bases upon rocking induces magnified column forces and vertical response in the gravity system. Friction ED is found more effective for drift control than systems with ring springs or bars yielding in tension. Drifts are sufficiently small to achieve position retention performance for most nonstructural components. Horizontal accelerations are generally lower than predicted from ASCE 41 for regular nonrocking structures. Vertical accelerations in the gravity framing directly connected to the rocking frame are however higher than those predicted for ordinary structures. Vertical ground motions have limited effect on frame response.     

基于结构动态响应统计特征的损伤指标研究

为了提高土木工程结构损伤识别的可靠性和有效性,本文提出一种基于结构动态响应统计特征的损伤指标,并对其可行性进行研究。文中首先在结构随机振动理论基础上推导出结构动态响应（包括位移、速度和加速度）的统计特征（包括均值和方差）与结构损伤位置和损伤程度之间的关系;然后通过敏感性分析确定以结构位移的方差作为结构损伤识别的损伤指标;最后,数值模拟-六层钢筋混凝土框架结构在白噪声激励下的动态响应,观察在不同损伤位置和损伤程度下结构动态位移方差的变化,从而对选择结构位移的方差作为损伤指标的可行性进行评估。研究得出结论,使用结构动态响应的统计特征作为土木工程结构损伤识别的损伤指标是可行的。     

Seismic strengthening of existing RC beam‐column joints by wing walls

Numerous non‐ductile reinforced concrete (RC) buildings with little or no shear reinforcement in beam‐column joints can be found in regions of moderate seismicity. To strengthen such substandard beam‐column joints, this study proposes a method in which RC wing walls are installed beside existing columns, which overcomes the lack of realistic strengthening methods for congested connections in RC buildings. The proposed strengthening mechanism improves the joint moment capacity by utilizing tension and compression acting on the beam–wing wall boundaries; thus, brittle joint hinging failure is prevented. Three 3/4‐scale RC exterior beam‐column joint specimens without shear reinforcement, two of which were strengthened by installing wing walls with different strengthening elements, were fabricated and tested. The test results verified the effectiveness of the proposed strengthening method and the applicability of this method to seismically substandard beam‐column joints. © 2017 The Authors. Earthquake Engineering & Structural Dynamics Published by John Wiley & Sons Ltd.     

Low cyclic fatigue and hysteretic behavior of U‐shaped steel dampers for seismically isolated buildings under dynamic cyclic loadings

Energy dissipation devices are necessary for base‐isolated buildings to control the deformation in the isolation system and to dissipate the earthquake‐induced energy. U‐shaped steel dampers (also known as U‐dampers) dissipate energy through plastic deformation of specially designed U‐shaped steel elements. This type of device can be installed at several locations in the isolation system. U‐dampers have been widely used in Japan for different types of isolated structures, such as hospitals, plants and residential buildings, since the 1995 Kobe Earthquake. Previous research has used static tests to estimate the performance of U‐dampers. However, the ultimate plastic deformation capacities and hysteretic behaviors of full‐scale U‐dampers under dynamic excitations still remain unclear. In addition, it is unclear whether the initial temperature has an effect on the hysteretic behavior and plastic deformation capacity of U‐dampers. In this paper, two series of dynamic loading tests of U‐dampers were conducted to evaluate the issues described earlier. The major findings of the study are (i) the loading speed has little effect on the plastic deformation capacity of U‐dampers; (ii) method to evaluate the ultimate plastic deformation capacities of U‐shaped steel dampers of different sizes is established using a Manson–Coffin relation‐based equation that is based on the peak‐to‐peak horizontal shear angle γ_t, which is defined as the lateral deformation amplitude (peak‐to‐peak amplitude) divided by the height of the dampers; (iii) the loading rate and the initial temperature have a minimal effect on the hysteretic behavior of the U‐dampers; and (iv) a bilinear model is proposed to simulate the force‐deformation relationships of the U‐dampers. Copyright © 2014 John Wiley & Sons, Ltd.     

Damage mechanics applied to performance‐based design of reinforced concrete columns

Performance‐based design methodology is based on reaching performance objectives that are associated to certain damage conditions. These performance objectives are related to the seismic hazard and to the performance levels. In actual application, reliable tools are required for capturing the evolution of the damage condition as well as for measuring and locating it. Moreover, it is essential to accurately establish the relationship between the damage and the performance levels. This paper shows the application of damage mechanics to performance‐based design. A layered damage mechanics‐based finite element program is presented with a discussion on modeling for prediction of the response of normal‐strength and high‐strength concrete columns subjected to cyclic flexural loading and various axial load levels. The damage indices derived from these analyses were used to elaborate several damage charts expressed as a function of drift and displacement ductility. This makes it possible to establish a relationship between the damage state and the performance levels. Results have demonstrated the ability of the damage mechanics modeling to accurately predict the behavior of the specimens tested. Copyright © 2017 John Wiley & Sons, Ltd.