Quantitative approach for damage detection of reinforced concrete frames

The objective of this paper is to provide an analytical basis for the quantitative evaluation of damage to a reinforced concrete structure based on the vibration data obtained by using the damage detection technique. A partial reinforced concrete system of a weak beam/strong column moment frame is chosen as an example. A pushover analysis is carried out in order to numerically examine both the story shear-relative displacement characteristics and the associated damage level. In the analysis, a two dimensional nonlinear finite element analysis is employed considering several constitutive models. As a result, the degradation of the stiffness at the damaged story is characterized in association with the story relative displacement. It is also pointed out that the rotation angle of the column-base is highly correlated with the story relative displacement. Based on the analytical findings, quantitative approaches for a structural health monitoring system are suggested considering both the current sensor technologies and those available in the future. Supported by: Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Scientific Research (Base Research (c) (1), Research No. 14550555)     

Bayesian model selection for ARX models and its application to structural health monitoring

A Bayesian framework for model order selection of auto‐regressive exogenous (ARX) models is developed and applied to actual earthquake response data obtained by the structural health monitoring system of a high‐rise building. The model orders of ARX models are selected appropriately by the Bayesian framework, and differ significantly from the optimal order estimated by AIC; in fact, in many cases AIC does not even give an optimal order. A method is also proposed for consistently selecting the same ‘genuine’ modes of interest from the whole set of modes corresponding to each of the identified models from a sequence of earthquake records. In the identification analysis based on building response records from 43 earthquakes over 9 years, the modal parameters of the first four modes in each horizontal direction are estimated appropriately in all cases, showing that the developed methods are effective and robust. As the estimates of natural frequency depend significantly on the response amplitude, they are compensated by an empirical correction so that the influence of the response amplitude is removed. The compensated natural frequencies are much more stable over the nine‐year period studied, indicating that the building had no significant change in its global dynamic characteristics during this period. Copyright © 2010 John Wiley & Sons, Ltd.     

Evaluation of fundamental period of low‐rise and mid‐rise reinforced concrete buildings

Fundamental period of vibration appears to be one of the most critical parameter for the seismic design of buildings because this period strongly affects the magnitude of seismic forces. In this paper, an empirical formula for estimating the fundamental period of reinforced concrete structures is recommended, on the basis of the vibration analysis of 20 different real building configurations. These structures have already been constructed in Greece, and they are analyzed by using in detail 3‐D finite element models and modal eigenvalue analysis. These models take into account the presence of external and internal infill walls, which are usually ignored as nonstructural elements. This neglect leads to unreliable evaluation of period because the infill walls' contribution to the lateral stiffness and therefore to the fundamental period of vibration is also ignored. Furthermore, taking into account that the flexibility of soil elongates the fundamental period, the soil–structure interaction effect is also considered. To achieve a unique, simple, and effective empirical expression for the fundamental period of vibration, a comprehensive nonlinear regression analysis is applied for the datasets of buildings under consideration. This empirical expression is also compared with the similar expressions from the pertinent literature. Copyright © 2013 John Wiley & Sons, Ltd.     

Composed analytical models for seismic assessment of reinforced concrete bridge columns

This paper presents general composed analytical models to predict the behavior of reinforced concrete (RC) bridge columns. The analytical models were developed in OpenSees to represent the common hysteretic behavior of RC bridge columns. The proposed composed models can accommodate flexure failure, flexure‐shear failure, and pure shear failure, which are observed in existing RC bridge piers. The accuracy of the models was verified using data from the static cyclic‐loading experiments of 16 single columns and one multi‐column bent and dynamical experiment from two pseudo‐dynamic tests. The results showed that the analytical models could simulate the nonlinear behavior until the post‐failure behavior, including the strength degradation, the buckling of the reinforcement, and the pinching effect. Therefore, a global view of the behavior of reinforcement concrete is prescribed as simply as possible from the academic perspective, and these models are expected to provide sufficient accuracy when applied in engineering practice. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

Empirical formula for fundamental vibration periods of reinforced concrete buildings in Taiwan

More than 30 buildings around Taiwan have been selected to monitor the floor responses under seismic excitation. The structural array monitoring system in each building controls at most 27 channels of accelerometers distributed in several floors. Those buildings were triggered by many events during the past five years of operation. In each building, the records at the basement can be considered as the ground excitation, and the others at the upper floors are the structural responses. The frequency transfer functions of those buildings can be identified by ARX models, and then the fundamental vibration periods are estimated. The identified fundamental vibration periods using different events are compared in order to ensure the reliability of system identification. An empirical formula in predicting the fundamental vibration period is presented through the regression analysis to the identified fundamental vibration periods of 21 reinforced concrete (RC) moment‐resisting frame (MRF) buildings. It is found that the height of a building plays an important role in predicting the fundamental vibration period, compared with the length, width, and time after completion of the building. It is also found that the RC MRF buildings in Taiwan tend to be stiffer than those in the U.S. Copyright © 2000 John Wiley & Sons, Ltd.     

Nonlinear dynamic tests of a reinforced concrete frame building at different damage levels

This paper discusses the dynamic tests of a two-story infilled reinforced concrete (RC) frame building using an eccentric-mass shaker. The building, located in El Centro, CA, was substantially damaged prior to the tests due to the seismic activity in the area. During the testing sequence, five infill walls were removed to introduce additional damage states and to investigate the changes in the dynamic properties and the nonlinear response of the building to the induced excitations. The accelerations and displacements of the structure under the forced and ambient vibrations were recorded through an array of sensors, while lidar scans were obtained to document the damage. The test data provide insight into the nonlinear response of an actual building and the change of its resonant frequencies and operational shapes due to varying damage levels and changes of the excitation amplitude, frequency, and orientation.     

Damage evaluation models of reinforced concrete buildings based on the damage statistics and simulated strong motions during the 1995 Hyogo‐ken Nanbu earthquake

We have tried to estimate the yield shear strengths of reinforced concrete (RC) buildings based on the damage statistics in Kobe surveyed after the Hyogo‐ken Nanbu, Japan, earthquake of 1995 and the non‐linear response analyses for synthetic waveforms calculated from a complex seismic source and a three‐dimensional basin structure. First, a set of building models that represented the RC building stock in Kobe was constructed and plausible non‐linear multi‐degree‐of‐freedom models with four different numbers of stories were created based on the current seismic code and construction practice. For response analysis the damage criterion and the strength distribution should be assumed a priori. When the damage ratios for these standard models were calculated it was found that the damage ratios were so high that we had to increase the average yield strengths in order to match the calculated damage ratios to those observed. After searching the best models it was found that the estimated average yield strengths should be much higher than those based on the code, especially for low‐rise buildings. Using this set of building models we succeeded in reproducing the belt‐shaped area with high damage ratios in Kobe. One can apply the proposed methodology to different countries if there is enough damage data, strong motion records, and building statistics. If there is sparse damage data at several locations only, then our models can be adjusted to reproduce observed damage data and used for damage prediction as a first‐order approximation. Copyright © 2004 John Wiley & Sons, Ltd.     

Nonparametric estimation of wave dispersion in high‐rise buildings by seismic interferometry

Interferometric identification and health monitoring of high‐rise buildings has been gaining increasing interest in recent years. The wave dispersion in the structure has been largely ignored in these efforts but needs to be considered to further develop these methods. In this paper, (i) the goodness of estimation of vertical wave velocity in buildings, as function of frequency, by two nonparametric interferometric techniques is examined, using realistic fixed‐base Timoshenko beam benchmark models. Such models are convenient because the variation of phase and group velocities with frequency can be derived theoretically. The models are those of the NS and EW responses of Millikan Library. One of the techniques, deconvolution interferometry, estimates the phase velocity on a frequency band from phase difference between motions at two locations in the structure, while the other one estimates it approximately at the resonant frequencies based on standing wave patterns. The paper also (ii) examines the modeling error in wave velocity profiles identified by fitting layered shear beam in broader band impulse response functions of buildings with significant bending flexibility. This error may affect inferences on the spatial distribution of damage from detected changes in such velocity profiles. Copyright © 2014 John Wiley & Sons, Ltd.     

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

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

Design and application of structural health monitoring system in long-span cable-membrane structure

Cable-membrane structures have small rigidity and are highly sensitive to wind. Structural health monitoring is necessary to ensure the serviceability and safety of the structure. In this research, the design method of a structural health monitoring system is using the characteristics of a cable-membrane structure. Taking the Yueyang Sanhe Airport Terminal as an example, a finite element model is established to determine the critical structural components. Next, the engineering requirements and the framework of the monitoring system are studied based on the results of numerical analysis. The specific implementation of the structural health monitoring is then carried out, which includes sensor selection, installation and wiring. The proposed framework is successfully applied to the monitoring system for the Yueyang Airport terminal building, and the synchronous acquisition of fiber Bragg grating and acceleration sensor signals is implemented in an innovative way. The successful implementation and operation of structural health monitoring will help to guarantee the safety of the cablemembrane structure during its service life.     

Evaluation of the fishbone model in simulating the seismic response of multistory reinforced concrete moment-resisting frames

The fishbone model is a simplified numerical model for moment-resisting frames that is capable of modelling the effects of column-beam strength and stiffness ratios. The applicability of the fishbone model in simulating the seismic responses of reinforced concrete moment-resisting frames of different sets of column-beam strength and stiffness ratios are evaluated through nonlinear static, dynamic and incremental dynamic analysis on six prototype buildings of 4-, 8-and 12-stories. The results show that the fishbone model is practically accurate enough for reinforced concrete frames, although the assumption of equal joint rotation does not hold in all cases. In addition to the ground motion characteristics and the number of stories in the structures, the accuracy of the model also varies with the column-beam stiffness and strength ratios. The model performs better for strong column-weak beam frames, in which the lateral drift patterns are better controlled by the continuous stiffness provided by the strong columns. When the inelastic deformation is large, the accuracy of the model may be subjected to large record-to-record variability. This is especially the case for frames of weak columns.     

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.     

Estimating economic losses of midrise reinforced concrete shear wall buildings in sedimentary basins by combining empirical and simulated seismic hazard characterizations

Studies of recorded ground motions and simulations have shown that deep sedimentary basins can greatly increase the intensity of earthquake ground motions within a period range of approximately 1–4 s, but the economic impacts of basin effects are uncertain. This paper estimates key economic indicators of seismic performance, expressed in terms of earthquake‐induced repair costs, using empirical and simulated seismic hazard characterizations that account for the effects of basins. The methodology used is general, but the estimates are made for a series of eight‐ to 24‐story residential reinforced concrete shear wall archetype buildings in Seattle, WA, whose design neglects basin effects. All buildings are designed to comply with code‐minimum requirements (i.e., reference archetypes), as well as a series of design enhancements, which include (a) increasing design forces, (b) decreasing drift limits, and (c) a combination of these strategies. As an additional reference point, a performance‐based design is also assessed. The performance of the archetype buildings is evaluated for the seismic hazard level in Seattle according to the 2018 National Seismic Hazard Model (2018 NSHM), which explicitly considers basin effects. Inclusion of basin effects results in an average threefold increase in annualized losses for all archetypes. Incorporating physics‐based ground motion simulations to represent the large‐magnitude Cascadia subduction interface earthquake contribution to the hazard results in a further increase of 22% relative to the 2018 NSHM. The most effective of the design strategies considered combines a 25% increase in strength with a reduction in drift limits to 1.5%.     

Impacts of simulated M9 Cascadia Subduction Zone earthquakes considering amplifications due to the Georgia sedimentary basin on reinforced concrete shear wall buildings

Southwest British Columbia has the potential to experience large‐magnitude earthquakes generated by the Cascadia Subduction Zone (CSZ). Buildings in Metro Vancouver are particularly vulnerable to these earthquakes because the region lies above the Georgia sedimentary basin, which can amplify the intensity of ground motions, particularly at medium‐to‐long periods. Earthquake design provisions in Canada neglect basin amplification and the consequences of accounting for these effects are uncertain. By leveraging a suite of physics‐based simulations of M9 CSZ earthquakes, we develop site‐specific and period‐dependent spectral acceleration basin amplification factors throughout Metro Vancouver. The M9 simulations, which explicitly account for basin amplification for periods greater than 1s, are benchmarked against the 2016 BC Hydro ground motion model (GMM), which neglects such effects. Outside the basin, empirical and simulated seismic hazard estimates are consistent. However, for sites within the basin and periods in the 1‐5 s range, GMMs significantly underestimate the hazard. The proposed basin amplification factors vary as a function of basin depth, reaching a geometric mean value as high as 4.5 at a 2‐s period, with respect to a reference site located just outside the basin. We evaluate the impact of the M9 simulations on tall reinforced concrete shear wall buildings, which are predominant in the region, by developing a suite of idealized structural systems that capture the strength and ductility intended by historical seismic design provisions in Canada. Ductility demands and collapse risk conditioned on the occurrence of the M9 simulations were found to exceed those associated with ground motion shaking intensities corresponding to the 975 and 2475‐year return periods, far exceeding the ～500‐year return period of M9 CSZ earthquakes.     

Probabilistic development of shear strength model for reinforced concrete squat walls

In order to reconcile the larger scatter and avoid the biased estimate from deterministic predictions for the shear strength of reinforced concrete (RC) squat structural walls, a probabilistic shear strength model is developed in this paper based on the strut‐and‐tie model and the generalized likelihood uncertainty estimation (GLUE) method. The strut‐and‐tie model is used to derive an appropriate function form for the probabilistic shear strength model, where four unknown model parameters (e.g. k₁, k₂, k₃ and k₄) are defined carefully to guarantee them having a clear physical‐based meaning so that the corresponding prior distribution ranges can be specified reasonably. Then, the GLUE method is adopted to estimate the posterior cumulative distribution of k₁, k₂, k₃ and k₄ with an available experimental database. Furthermore, to demonstrate the stability of the estimated posterior cumulative distribution, the sensitivity of three major aspects in GLUE method is investigated. Finally, based on the estimated cumulative distribution of k₁, k₂, k₃ and k₄, the developed probabilistic shear strength model is simplified as a mean prediction model and a standard deviation prediction model for facilitate using in engineering practice. Therefore, with the developed probabilistic shear strength model, not only can the squat structural walls be designed in confidence, but the accuracy of those deterministic predictions can be evaluated in a probabilistic manner. Copyright © 2016 John Wiley & Sons, Ltd.     

Effects of excitation frequency on detection accuracy of orthogonal wavelet decomposition for structural health monitoring

Accurate estimation of stiffness loss is a challenging problem in structural health monitoring. In this study orthogonal wavelet decomposition is used for identifying the stiffness loss in a single degree of freedom spring-mass-damper system. The effects of excitation frequency on accuracy of damage detection is investigated. Results show that pseudo-alias effects caused by the orthogonal wavelet decomposition (OWD), affect damage detectability. It is demonstrated that theproposed approach is sunable for damage detection when the excitation frequency is relatively low. This study shows how a priori knowledge about the signal and ability to control the sampling frequency can enhance damage detectability.     

Performance‐based seismic assessment of conventional and base‐isolated steel buildings including environmental impact and resilience

Sustainability and resilience are issues that are recognized worldwide, and increased attention should be placed on strategies to design and maintain infrastructure systems that are hazard resilient, damage tolerant, and sustainable. In this paper, a methodology to evaluate the seismic sustainability and resilience of both conventional and base‐isolated steel buildings is presented. Furthermore, the proposed approach is used to explore the difference between the performance associated with these buildings by considering the three pillars of sustainability: economic, social, and environmental. Sustainability and resilience are both considered to cover a comprehensive performance‐based assessment content. The uncertainties associated with performance and consequence evaluation of structural and non‐structural components are incorporated within the assessment process. The proposed performance‐based assessment approach is illustrated on conventional and base‐isolated steel buildings under given seismic scenarios. Copyright © 2015 John Wiley & Sons, Ltd.     

既有钢筋混凝土框架结构的多指标云模型地震损伤评估

目前的既有钢混结构地震损伤研究没有同时考虑不同抗震设计规范差异和耐久性两个因素对结构抗震性能的影响,且损伤指标较简单,在动力损伤分析中也存在局限。基于云模型的特点,提出了包括弹塑性耗能差率、刚度损伤指数、层间位移角和顶点位移角的多元结构损伤状态综合评估方法,能够同时考虑结构各损伤指数的随机性和模糊性。考虑不同版本抗震设计规范造成的结构性能差异和耐久性下降对结构性能的影响,设计3个典型五层钢混框架结构,进行增量动力分析,验证损伤评估方法的准确性。结果表明：随着抗震规范版本的更新,结构的损伤程度有适当减轻;同一结构的损伤程度因混凝土碳化作用先减轻后加重;采用弹塑性耗能差率表征既有结构的地震损伤效果优于刚度损伤指数;基于多指标云模型损伤评估方法获得的云模型综合隶属度和综合损伤值能够更加细化和精确地描述结构损伤状态。     

Evaluation of a recently proposed record selection and scaling procedure for low‐rise to mid‐rise reinforced concrete buildings and its use for probabilistic risk assessment studies

This paper evaluates a recent record selection and scaling procedure of the authors that can determine the probabilistic structural response of buildings behaving either in the elastic or post‐elastic range. This feature marks a significant strength on the procedure as the probabilistic structural response distribution conveys important information on probability‐based damage assessment. The paper presents case studies that show the utilization of the proposed record selection and scaling procedure as a tool for the estimation of damage states and derivation of site‐specific and region‐specific fragility functions. The method can be used to describe exceedance probabilities of damage limits under a certain target hazard level with known annual exceedance rate (via probabilistic seismic hazard assessment). Thus, the resulting fragility models can relate the seismicity of the region (or a site) with the resulting building performance in a more accurate manner. Under this context, this simple and computationally efficient record selection and scaling procedure can be benefitted significantly by probability‐based risk assessment methods that have started to be considered as indispensable for developing robust earthquake loss models. Copyright © 2013 John Wiley & Sons, Ltd.