Cloud to IDA: Efficient fragility assessment with limited scaling

Incremental dynamic analysis (IDA) leads to curves expressed in terms of structural response versus intensity, commonly known as the IDA curves. It is known that implementation of IDA usually involves significant computational effort and most often significant scaling of the original records to various intensity levels. Employing as the performance variable the critical demand to capacity ratio (DCR) throughout the structure, which is equal to unity at the onset of the limit state, facilitates the identification of the intensity values at the onset of a desired limit state and hence the implementation of the IDA procedure. Employing the structural response to un‐scaled records and the corresponding regression‐based response predictions (a.k.a., the “Cloud Analysis”) helps in identifying the range of intensity values corresponding to demand to capacity ratio values in the vicinity of unity. The Cloud to IDA procedure for structural fragility assessment is proposed on the premise of exploiting the Cloud Analysis results to obtain the IDA curves both with minimum number of analyses and minimum amount of scaling. The transverse frame of a shear‐critical 7‐story older RC building in Van Nuys, CA, which is modeled in Opensees with fiber‐section considering the flexural‐shear‐axial interactions and the bar slip, is employed as a case study. It is demonstrated, by comparing the results to IDA and other state of the art non‐linear dynamic procedures based on no scaling or spectral‐shape‐compatible scaling, that the Cloud to IDA procedure leads to reliable results in terms of structural fragility and risk for the prescribed limit state.     

Record selection for aftershock incremental dynamic analysis

The back‐to‐back application of mainshock records as aftershock is often considered in conducting aftershock incremental dynamic analysis. In such an approach, the characteristics of mainshock records are considered to be similar to those of major aftershock records within the same mainshock–aftershock sequences. The underlying assumption is that the characteristics of selected mainshocks, other than those used for record selection, are not significant in the assessment of structural responses. A case study is set up to investigate the effects of aftershock record selection on the collapse vulnerability assessment. The numerical results for a specific wood‐frame structure indicate that the aftershock fragility can be affected by the aftershock record characteristics, particularly response spectral shape. Copyright © 2014 John Wiley & Sons, Ltd.     

Modal pushover‐based scaling of earthquake records for nonlinear analysis of single‐story unsymmetric‐plan buildings

The modal pushover‐based scaling (MPS) procedure, currently restricted to symmetric‐plan buildings, is extended herein to unsymmetric‐plan buildings. The accuracy of the extended MPS procedure was evaluated for a large set of three‐degree‐of‐freedom unsymmetric‐plan structures with variable stiffness and strength. The structures were subjected to nonlinear response history analysis considering sets of seven records scaled according to the MPS procedure. Structural responses were compared against the benchmark values, defined as the median values of the engineering demand parameters due to 30 unscaled records. This evaluation of the MPS procedure has led to the following conclusions: (i) the MPS procedure provided accurate estimates of median engineering demand parameter values and reduced record‐to‐record variability of the responses; and (2) the MPS procedure is found to be much superior compared to the ASCE/SEI 7‐10 scaling procedure for three‐dimensional analysis of unsymmetric‐plan buildings. Copyright © 2013 John Wiley & Sons, Ltd.     

Seismic collapse capacity of basic inelastic structures vulnerable to the P‐delta effect

The collapse capacity of earthquake‐excited inelastic nondeteriorating SDOF systems, which are vulnerable to the destabilizing effect of gravity loads (P‐delta effect), is evaluated. In this paper, the collapse capacity of the system subjected to a ground motion is defined as spectral acceleration at its initial structural period, at which the structure becomes unstable. Characteristic structural parameters, which affect the collapse capacity, are identified. Ground motion records of the ATC 63 far‐field set characterize severe earthquake excitation. In extensive incremental dynamic analyses studies, the impact of these parameters and of aleatory uncertainties on the collapse capacity is assessed and quantified. Median and percentile collapse capacities are plotted against the initial structural period leading to collapse capacity spectra. Nonlinear regression analyses are applied to derive analytical expressions of the design collapse capacity spectra and collapse fragility curves. The ultimate objective is to provide collapse capacity spectra for easy application and yet sufficient accurate assessment of the dynamic stability of flexible multistory buildings. Copyright © 2011 John Wiley & Sons, Ltd.     

Loss estimation for non‐ductile reinforced concrete building in Victoria,British Columbia,Canada: effects of mega‐thrust Mw9‐class subduction earthquakes and aftershocks

This paper presents, within the performance‐based earthquake engineering framework, a comprehensive probabilistic seismic loss estimation method that accounts for main sources of uncertainty related to hazard, vulnerability, and loss. The loss assessment rigorously integrates multiple engineering demand parameters (maximum and residual inter‐story drift ratio and peak floor acceleration) with consideration of mainshock–aftershock sequences. A 4‐story non‐ductile reinforced concrete building located in Victoria, British Colombia, Canada, is considered as a case study. For 100 mainshock and mainshock–aftershock earthquake records, incremental dynamic analysis is performed, and the three engineering demand parameters are fitted with a probability distribution and corresponding dependence computed. Finally, with consideration of different demolition limit states, loss assessment is performed. From the results, it can be shown that when seismic vulnerability models are integrated with seismic hazard, the aftershock effects are relatively minor in terms of overall seismic loss (1–4% increase). Moreover, demolition limit state parameters, uncertainties of collapse fragility, and non‐collapse seismic demand prediction models have showed significant contribution to the loss assessment. The seismic loss curves for the reference case and for cases with the varied parameters can differ by as large as about 150%. Copyright © 2015 John Wiley & Sons, Ltd.     

Seismic response prediction of reinforced concrete buildings through nonlinear combinations of intensity measures

A widespread approach for the prediction of the structural response as function of the ground motion intensity is based on the Cloud Analysis: once a set of points representing the engineering demand parameter (EDP) values is obtained as function of the selected seismic intensity measure (IM) for a collection of unscaled earthquake records, a regression analysis is performed by assuming a specific functional form to correlate these variables. Within this framework, many studies have been devoted so far to evaluate the effectiveness of several IMs in estimating the EDPs through intrinsically linear functional forms, but it is still unknown to what extent the use of the linear regression analysis affects the quality of the final results. This paper is intended to provide an answer to such question by means of the calibration of suitable nonlinear combinations of scalar IMs, whose statistical performances are compared with those obtained by using the functional form usually adopted for linear regression-based calibrations. Specifically, the Evolutionary Polynomial Regression technique is adopted to calibrate nonlinear regression models for the prediction of maximum inter-story drift ratio and maximum floor acceleration. The comparative analysis is performed for fixed-base and base-isolated reinforced concrete buildings subjected to ordinary or pulse-like ground motion taking into account accuracy, complexity, efficiency and sufficiency. Final results demonstrate that the linear regression analysis is suitable for fixed-base reinforced concrete buildings, but nonlinear regression models provide better estimates. On the other hand, the linear regression analysis can introduce a significant bias in the seismic response prediction of base-isolated buildings, and nonlinear regression models are deemed more appropriate.     

Modelling of R/C members accounting for shear failure localisation: Hysteretic shear model

Reinforced concrete (R/C) frame buildings designed according to older seismic codes represent a large part of the existing building stock worldwide. Their structural elements are often vulnerable to shear or flexure‐shear failure, which can eventually lead to loss of axial load resistance of vertical elements and initiate vertical progressive collapse of a building. In this study, a hysteretic model capturing the local shear response of shear‐deficient R/C elements is described in detail, with emphasis on post‐peak behaviour; it differs from existing models in that it considers the localisation of shear strains after the onset of shear failure in a critical length defined by the diagonal failure planes. Additionally, an effort is made to improve the state of the art in post‐peak shear response modelling, by compiling the largest database of experimental results for shear and flexure‐shear critical R/C columns cycled well beyond the onset of shear failure and/or up to the onset of axial failure, and developing empirical relationships for the key parameters defining the local backbone post‐peak shear response of such elements. The implementation of the derived local hysteretic shear model in a computationally efficient beam‐column finite element model with distributed shear flexibility, which accounts for all deformation types, will be presented in a companion paper.     

Aftershock collapse fragility curves for non‐ductile RC buildings: a scenario‐based assessment

Recent studies have addressed the computation of fragility curves for mainshock (MS)‐damaged buildings. However, aftershock (AS) fragilities are generally conditioned on a range of potential post‐MS damage states that are simulated via static or dynamic analyses performed on an intact building. Moreover, there are very few cases where the behavior of non‐ductile reinforced concrete buildings is analyzed. This paper presents an evaluation of AS collapse fragility conditioned on various return periods of MSs, allowing for the rapid assessment of post‐earthquake safety variations based solely on the intensity of the damaging earthquake event. A refined multi‐degree‐of‐freedom model of a seven‐storey non‐ductile building, which includes brittle failure simulations and the evaluation of a system level collapse, is adopted. Aftershock fragilities are obtained by performing an incremental dynamic analysis for a number of MS–AS ground motion sequences and a variety of MS intensities. The AS fragilities show that the probability of collapse significantly increases for higher return periods for the MS. However, this result is mainly ascribable to collapses occurred during MSs. When collapse cases that occur during a MS are not considered in the assessment of AS collapse probability, a smaller shift in the fragility curves is observed as the MS intensity increases. This result is justified considering the type of model and collapse modes introduced, which strongly depend on the brittle behavior of columns failing in shear or due to axial loads. The analysis of damage that is due to MSs when varying the return period confirms this observation. Copyright © 2017 John Wiley & Sons, Ltd.     

Use of the conditional spectrum to incorporate record‐to‐record variability in simplified seismic assessment of RC wall buildings

A procedure for incorporating record‐to‐record variability into the simplified seismic assessment of RC wall buildings is presented. The procedure relies on the use of the conditional spectrum to randomly sample spectral ordinates at relevant periods of vibration. For inelastic response, displacement reduction factors are then used to relate inelastic displacement demand to the spectral displacement at the effective period for single‐degree‐of‐freedom systems. Simple equations are used to convert back and forth between multi‐degree‐of‐freedom RC wall buildings and equivalent single‐degree‐of‐systems so that relevant engineering demand parameters can be obtained. Consideration is also given to higher‐mode effects by adapting existing modal combination rules. The proposed method is applied to several case study buildings, showing promising results in the examination of inter‐storey drift ratio and shear forces. The proposed method captures the variation in the distribution of structural response parameters that occurs with variations in structural configuration, intensity, engineering demand parameter of interest and site characteristics. Discussion is provided on possible ways to improve the accuracy of the procedure and suggestions for additional future work. Copyright © 2015 John Wiley & Sons, Ltd.     

Critical uncertainty parameters influencing seismic performance of bridges using Lasso regression

Recent efforts of regional risk assessment of structures often pose a challenge in dealing with the potentially variable uncertain input parameters. The source of uncertainties can be either epistemic or aleatoric. This article identifies uncertain variables exhibiting strongest influences on the seismic demand of bridge components through various regression techniques such as linear, stepwise, Ridge, Lasso, and elastic net regressions. The statistical results indicate that Lasso regression is the most effective one in predicting the demand model as it has the lowest mean square error and absolute error. As the sensitivity study identifies more than 1 significant variable, a multiparameter fragility model using Lasso regression is suggested in this paper. The proposed fragility methodology is able to identify the relative impact of each uncertain input variable and level of treatment needed for these variables in the estimation of seismic demand models and fragility curves. Thus, the proposed approach helps bridge owners to spend their resources judiciously (e.g., data collection, field investigations, and censoring) in the generation of a more reliable database for regional risk assessment. This proposed approach can be applicable to other structures.     

Modelling of R/C members accounting for shear failure localisation: Finite element model and verification

Reinforced concrete (R/C) frame buildings designed according to older seismic codes represent a large part of the existing building stock worldwide. Their structural elements are often vulnerable to shear or flexure‐shear failure, which can eventually lead to loss of axial load resistance of vertical elements and initiate vertical progressive collapse of a building. In this study, a computationally efficient member‐type finite element model for the hysteretic response of shear critical R/C frame elements up to the onset of axial failure is presented; it accounts for shear‐flexure interaction and considers, for the first time, the localisation of shear strains, after the onset of shear failure, in a critical length defined by the diagonal failure plane. Its predictive capabilities are verified against experimental results of column and frame specimens and are shown to be accurate not only in terms of total response, but also with regard to individual deformation components. The accuracy, versatility, and simplicity of this finite element model make it a valuable tool in seismic analysis of complex R/C buildings with shear deficient structural elements.     

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.     

Alternative non‐linear demand estimation methods for probability‐based seismic assessments

Alternative non‐linear dynamic analysis procedures, using real ground motion records, can be used to make probability‐based seismic assessments. These procedures can be used both to obtain parameter estimates for specific probabilistic assessment criteria such as demand and capacity factored design and also to make direct probabilistic performance assessments using numerical methods. Multiple‐stripe analysis is a non‐linear dynamic analysis method that can be used for performance‐based assessments for a wide range of ground motion intensities and multiple performance objectives from onset of damage through global collapse. Alternatively, the amount of analysis effort needed in the performance assessments can be reduced by performing the structural analyses and estimating the main parameters in the region of ground motion intensity levels of interest. In particular, single‐stripe and double‐stripe analysis can provide local probabilistic demand assessments using minimal number of structural analyses (around 20 to 40). As a case study, the displacement‐based seismic performance of an older reinforced concrete frame structure, which is known to have suffered shear failure in its columns during the 1994 Northridge Earthquake, is evaluated. Copyright © 2008 John Wiley & Sons, Ltd.     

Seismic performance of wood‐frame houses in south‐western British Columbia

The seismic performance of conventional wood‐frame structures in south‐western British Columbia is analytically investigated through incremental dynamic analysis by utilizing available UBC‐SAWS models, which were calibrated based on experimental test results. To define an adequate target response spectrum that is consistent with information from national seismic hazard maps, record selection/scaling based on the conditional mean spectrum (CMS) is implemented. Furthermore, to reflect complex seismic hazard contributions from different earthquake sources (i.e. crustal events, interface events, and inslab events), we construct CMS for three earthquake types, and use them to select and scale an adequate set of ground motion records for the seismic performance evaluation. We focus on the impacts of adopting different record selection criteria and of using different shear‐wall types (Houses 1–4; in terms of seismic resistance, House 1>House 2>House 3>House 4) on the nonlinear structural response. The results indicate that the record selection procedures have significant influence on the probabilistic relationship between spectral acceleration at the fundamental vibration period and maximum inter‐story drift ratio, highlighting the importance of taking into account response spectral shapes in selecting and scaling ground motion records. Subjected to ground motions corresponding to the return period of 2500 years, House 1 is expected to experience very limited extent of damage; Houses 2 and 3 may be disturbed by minor damage; whereas House 4 may suffer from major damage occasionally. Finally, we develop statistical models of the maximum inter‐story drift ratio conditioned on a seismic intensity level for wood‐frame houses, which is useful for seismic vulnerability assessment. Copyright © 2010 John Wiley & Sons, Ltd.     

Effect of ground motion selection methods on seismic collapse fragility of RC frame buildings

Variation in the seismic collapse fragility of reinforced concrete frame buildings predicted using different ground motion (GM) selection methods is investigated in this paper. To simulate the structural collapse, a fiber‐element modelling approach with path‐dependent cyclic nonlinear material models that account for concrete confinement and crushing, reinforcement buckling as well as low cycle fatigue is used. The adopted fiber analysis approach has been found to reliably predict the loss in vertical load carrying capacity of structural components in addition to the sidesway mode of collapse due to destabilizing P–Δ moments at large inelastic deflections. Multiple stripe analysis is performed by conducting response history analyses at various hazard levels to generate the collapse fragility curves. To select GMs at various hazard levels, two alternatives of uniform hazard spectrum (UHS), conditional mean spectrum (CMS) and generalized conditional intensity measure (GCIM) are used. Collapse analyses are repeated based on structural periods corresponding to initial un‐cracked stiffness and cracked stiffness of the frame members. A return period‐based intensity measure is then introduced and applied in estimating collapse fragility of frame buildings. In line with the results of previous research, it is shown that the choice of structural period significantly affects the collapse fragility predictions. Among the GM selection methods used in this study, GCIM and CMS methods predict similar collapse fragilities for the case study building investigated herein, and UHS provides the most conservative prediction of the collapse capacity, with approximately 40% smaller median collapse capacity compared to the CMS method. The results confirm that collapse probability prediction of buildings using UHS offers a higher level of conservatism in comparison to the other selection methods. Copyright © 2017 John Wiley & Sons, Ltd.     

Evaluation of bias on the probability of collapse from amplitude scaling using spectral-shape-matched records

Although for many years it was thought that amplitude scaling of acceleration time series to reach a target intensity did not introduce any bias in the results of nonlinear response history analyses, recent studies have showed that scaling can lead to an overestimation of deformation demands with increasing scale factors. Some studies have suggested that the bias can be explained by differences in spectral shape between the response spectra of unscaled and scaled records. On the basis of these studies, some record selection procedures assume that if records are selected using spectral-shape-matching procedures, amplitude scaling does not induce any bias on the structural response. This study evaluates if bias is introduced on lateral displacement demands and seismic collapse risk estimates even when spectral shape is carefully taken into consideration when selecting ground motions. Several single-degree-of-freedom and multiple-degree-of-freedom systems are analyzed when subjected to unscaled and scaled ground motions selected to approximately match the mean and the variance of the conditional spectrum at the target level of intensity. Results show that an explicit consideration of spectral shape is not enough to avoid a systematic overestimation of lateral displacement demands and collapse probabilities as the scale factor increases. Moreover, the bias is observed in practically all cases for systems with strength degradation and it increases with decreasing period and decreasing lateral strength relative to the strength required to remain elastic. Key reasons behind the bias are presented by evaluating input energy, causal parameters, and damaging pulse distributions in unscaled and scaled ground motion sets.     

Response of nonlinear soil‐MDOF structure systems subjected to distinct frequency‐content components of near‐fault ground motions

This paper is devoted to investigate the effects of near‐fault ground motions on the seismic responses of nonlinear MDOF structures considering soil‐structure interaction (SSI). Attempts are made to take into account the effects of different frequency‐content components of near‐fault records including pulse‐type (PT) and high‐frequency (HF) components via adopting an ensemble of 54 near‐fault ground motions. A deep sensitivity analysis is implemented based on the main parameters of the soil‐structure system. The soil is simulated based on the Cone model concept, and the superstructure is idealized as a nonlinear shear building. The results elucidate that SSI has approximately increasing and mitigating effects on structural responses to the PT and HF components, respectively. Also, a threshold period exists above which the HF component governs the structural responses. As the fundamental period of the structure becomes shorter and structural target ductility reduces, the contribution of the HF component to the structural responses increases, elaborately. Soil flexibility makes the threshold period increase, and the effect of the PT component becomes more significant than the HF one. In the case of soil‐structure system, slenderizing the structure also increases this threshold period and causes the PT component to be dominant. Copyright © 2013 John Wiley & Sons, Ltd.     

Seismic reliability‐based ductility demand evaluation for inelastic base‐isolated structures with friction pendulum devices

The aim of this work is to propose seismic reliability‐based relationships between the strength reduction factors and the displacement ductility demand of nonlinear structural systems equipped with friction pendulum isolators (FPS) depending on the structural properties. The isolated structures are described by employing an equivalent 2dof model characterized by a perfectly elastoplastic rule to account for the inelastic response of the superstructure, whereas, the FPS behavior is described by a velocity‐dependent model. An extensive parametric study is carried out encompassing a wide range of elastic and inelastic building properties, different seismic intensity levels and considering the friction coefficient as a random variable. Defined a set of natural seismic records and scaled to the seismic intensity corresponding to life safety limit state for L'Aquila site (Italy) according to NTC08, the inelastic characteristics of the superstructures are designed as the ratio between the average elastic responses and increasing strength reduction factors. Incremental dynamic analyses (IDAs) are developed to evaluate the seismic fragility curves of both the inelastic superstructure and the isolation level assuming different values of the corresponding limit states. Integrating the fragility curves with the seismic hazard curves related to L'Aquila site (Italy), the reliability curves of the equivalent inelastic base‐isolated structural systems, with a design life of 50 years, are derived proposing seismic reliability‐based regression expressions between the displacement ductility demand and the strength reduction factors for the superstructure as well as seismic reliability‐based design (SRBD) abacuses useful to define the FPS properties. Copyright © 2016 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.