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.     

Seismic fragilities of non-ductile reinforced concrete frames with consideration of soil structure interaction

Seismic fragilities of buildings are often developed without consideration of soil-structure interaction (SSI), where base of the building is assumed to be fixed. This study highlights effect of SSI and uncertainty in soil properties such as friction angle, cohesion, density, shear modulus and Poisson's ratio and foundation parameters on seismic fragilities of non-ductile reinforced concrete frames resting in dense silty sand. Three-, five-, and nine-storey three-bay moment resisting reinforced concrete frames resting on isolated shallow foundation are studied and the numerical models for SSI are developed in OpenSees. Three sets of 10 ground motions, with mean spectrum of 100, 500, and 1000 yr return period hazard level (matching EC-8 design spectrum), are used for the nonlinear time history analyses. An optimized Latin Hyper Cube sampling technique is used to draw the sample of soil properties and foundation parameters. The fragilities are developed for the fixed base model and SSI models. However, the fragilities that incorporate the soil parameter and foundation uncertainties are only slightly different from those based solely on the uncertainty in seismic demand from earthquake ground motion, suggesting that fragilities that are developed under the assumption that all soil and foundation parameters at their median (or mean) values are sufficient for the purpose of earthquake damage or loose estimation of structures resting on dense silty sand. But the consideration of the SSI effect has the significant influence on the fragilities compare to the fixed base model. The structural parameter uncertainty and foundation modeling uncertainty are not considered in the study.     

Seismic fragility assessment of existing sub-standard low strength reinforced concrete structures

An analytical seismic fragility assessment framework is presented for the existing low strength reinforced concrete structures more common in the building stock of the developing countries.For realistic modelling of such substandard structures,low strength concrete stress-strain and bond-slip capacity models are included in calibrating material models.Key capacity parameters are generated stochastically to produce building population and cyclic pushover analysis is carried out to capture inelastic behaviour.Secant period values are evaluated corresponding to each displacement step on the capacity curves and used as seismic demand.A modified capacity demand diagram method is adopted for the degrading structures,which is further used to evaluate peak ground acceleration from back analysis considering each point on the capacity curve as performance point.For developing fragility curves,the mean values of peak ground acceleration are evaluated corresponding to each performance point on the series of capacity curves.A suitable probability distribution function is adopted for the secant period scatter at different mean peak ground acceleration values and probability of exceedance of limit states is evaluated.A suitable regression function is used for developing fragility curves and regression coefficients are proposed for different confidence levels.Fragility curves are presented for a low rise pre-seismic code reinforced concrete structure typical of developing countries.     

Development of computing environment for the seismic performance assessment of reinforced concrete frames by using simplified nonlinear models

A computing environment for the seismic performance assessment of reinforced concrete frames has been developed in Matlab in combination with OpenSees. It includes several functions which provide calculations of the moment-rotation relationship of plastic hinges in columns and beams, rapid determination of simplified nonlinear structural models, the post-processing of the results of analyses and structural performance assessment with different methods. The user can add new functions to the PBEE toolbox in order to support additional procedures for the seismic performance assessment of RC frames, or can just change the rules for determining the moment-rotation relationship of plastic hinges in columns and beams, which are the main source of uncertainty in simplified nonlinear models. In the paper, the capabilities of the computing environment (PBEE toolbox) are first explained by focusing on the procedures for determining the moment-rotation relationship of plastic hinges. Different examples are then presented, starting with a comparison between the calculated response of a four-storey RC frame building and the response obtained in a pseudo-dynamic experiment. The calculated response was determined with the two different structural models which are later on used for the demonstration of the seismic performance assessment of the same structure by the N2 method. Lastly, seismic performance assessment of an eight-storey frame is performed by using incremental dynamic analysis with consideration of the modelling uncertainties.     

Modelling exterior unreinforced beam‐column joints in seismic analysis of non‐ductile RC frames

The seismic response of non‐ductile reinforced concrete (RC) buildings can be affected by the behaviour of beam‐column joints involved in the failure mechanism, especially in typical existing buildings. Conventional modelling approaches consider only beam and column flexibility, although joints can provide a significant contribution also to the overall frame deformability. In this study, the attention is focused on exterior joints without transverse reinforcement, and a possible approach to their modelling in nonlinear seismic analysis of RC frames is proposed. First, experimental tests performed by the authors are briefly presented, and their results are discussed. Second, these tests, together with other tests with similar features from literature, are employed to calibrate the joint panel deformability contribution in order to reproduce numerically the experimental joint shear stress–strain behaviour under cyclic loading. After a validation phase of this proposal, a numerical investigation of the influence of joints on the seismic behaviour of a case study RC frame – designed for gravity loads only – is performed. The preliminary failure mode classification of the joints within the analysed frame is carried out. Structural models that (i) explicitly include nonlinear behaviour of beam‐column joints exhibiting shear or anchorage failure or (ii) model joints as elements with infinite strength and stiffness are built and their seismic performance are assessed and compared. A probabilistic assessment based on nonlinear dynamic simulations is performed by means of a scaling approach to evaluate the seismic response at different damage states accounting for uncertainties in ground‐motion records. Copyright © 2016 John Wiley & Sons, Ltd.     

Seismic performance and global ductility of RC frames rehabilitated with retrofitted joints by CFRP laminates

This paper presents a new FRP retrofi tting scheme to strengthen local beam-column joints in reinforced concrete(RC) frames.The new retrofi tting scheme was proposed following a preliminary study of four different existing retrofi tting schemes.A numerical simulation was conducted to evaluate the effectiveness of FRP-strengthened reinforced concrete frames by bridging behavior of local joints to the whole structure.Local confi nement effects due to varying retrofi tting schemes in the joints were simulated in the frame model.The seismic behavior factor was used to evaluate the seismic performance of the strengthened RC frames.The results demonstrated that the new proposed retrofi tting scheme was robust and promising,and fi nite element analysis appropriately captured the strength and global ductility of the frame due to upgrading of the local joints.     

Approximate seismic risk assessment of building structures with explicit consideration of uncertainties

An approximate seismic risk assessment procedure for building structures, which involves pushover analysis that is performed utilizing a deterministic structural model and uncertainty analysis at the level of the equivalent SDOF model, is introduced. Such an approach is computationally significantly less demanding in comparison with procedures based on uncertainty analysis at the level of the entire structure, but still allows for explicit consideration of the effect of record‐to‐record variability and modelling uncertainties. A new feature of the proposed pushover‐based method is the so‐called probabilistic SDOF model. Herein, the proposed methodology is illustrated only for reinforced concrete (RC) frames, although it could be implemented in the case of any building structure, provided that an appropriate probabilistic SDOF model is available. An extensive parametric analysis has been performed within the scope of this study in order to develop a probabilistic SDOF model, which could be used for the seismic risk assessment of both code‐conforming and old, that is, non code‐conforming RC frames. Based on the results of risk analysis for the four selected examples, it is shown that the proposed procedure can provide conservative estimates of seismic risk with reasonable accuracy, in spite of the employed simplifications and the relatively small number of Monte Carlo simulations with Latin hypercube sampling, which are performed at the level of the SDOF model. An indication of the possible default values of dispersion measures for limit‐state intensities in the case of low to medium‐height RC frames is also presented. Copyright © 2014 John Wiley & Sons, Ltd.     

Capacity models for shear strength of exterior joints in RC frames: state-of-the-art and synoptic examination

Damage observed in existing structures after recent earthquake events pointed out the key importance of beam-to-column joints in influencing the global response of reinforced concrete structures. In the last two decades several theoretical and empirical models have been proposed for evaluating shear strength of beam-to-column joints. The present paper reports an overview of the models currently available in the scientific literature for evaluating shear capacity of exterior beam-to-column joints. The present study is the first step of a wide analysis aimed at assessing such models and improving them. Moreover, the uncertainties deriving by applying the mentioned models will be also quantified therein, by means of well-established procedures for probabilistic seismic analysis of structures. The final results of that study are reported within a companion paper.     

Numerical evaluation of seismic response of soft-story RC frames retrofitted with passive devices

This study presents a nonlinear modelling technique for reinforced concrete (RC) frames retrofitted with metallic yielding devices to predict the seismic response using a computer software OpenSees. The numerical model considers the axial–flexure interaction, shear force–displacement response and the bond-slip characteristics of the frame members. The predicted hysteretic response has been compared with the results of slow-cyclic testing. The validated numerical model is then used to predict the seismic response of a five-story RC frame with soft-story. Nonlinear cyclic pushover and dynamic analyses are conducted to investigate the effectiveness of the proposed retrofitting scheme in enhancing the lateral strength and energy dissipation potential and in controlling the premature failure of the study frame. Analysis results showed significant improvement in the seismic response of RC frames with soft-story using the proposed retrofitting technique.     

Drift-sensitive non-structural damage to masonry-infilled reinforced concrete frames designed to Eurocode 8

Post-earthquake surveys indicate that losses come from non-structural damage more than from structural damage. Current performance-based design would prevent excessive non-structural damage as well, but the effectiveness of relevant code provisions has not been assessed in depth. This study investigates the drift-sensitive non-structural damage to reinforced concrete frame buildings complying with the European seismic code. Damage to non-structural unreinforced masonry infill walls in contact with the frame is quantified in terms of numerical fragility curves with the same quantities considered in the design: the peak ground acceleration measures the seismic intensity; the peak value of the interstorey drift ratio is the damage index. The methodology for the fragility computation is described in detail. Peculiar is the use of probabilistic parameters of the drift capacity coupled to the fuzziness in the damage state. The drift demand is estimated by member-by-member modelling of typical frame structures and non-linear time–history analyses under spectrum-compatible artificial accelerograms. The kind of the infills and their modelling, the number of storeys, the ground type, and the ductility class are covered. Modelling the infills results to be essential. Any code-compliant verification is on the safe side, but the margin appears to be inconsistent among the frames under consideration. Furthermore, there is one case where occupancy appears to be not ensured despite the code verification is satisfied. The effect of the number of storeys may be misrepresented. The ductility class may be unimportant, however the damage seems to be correlated with the likely strength.     

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.     

Empirical seismic fragility for the precast RC industrial buildings damaged by the 2012 Emilia (Italy) earthquakes

The paper analyses the seismic fragility of precast reinforced concrete buildings using observational damage data gathered after the 2012 Emilia earthquakes that struck Northern Italy. The damage level in 1890 buildings was collected, classified and examined. Damage matrices were then evaluated, and finally, empirical fragility curves were fitted using Bayesian regression. Building damage was classified using a six‐level scale derived from EMS‐98. The completeness of the database and the spatial distribution of the buildings investigated were analysed using cadastral data as a reference. The intensity of the ground motion was quantified by the maximum horizontal peak ground acceleration, which was obtained from ShakeMaps. Copyright © 2017 John Wiley & Sons, Ltd.     

Shaking table test and numerical simulation of a 1/2‐scale self‐centering reinforced concrete frame

Self‐centering reinforced concrete frames are developed as an alternative of traditional seismic force‐resisting systems with better seismic performance and re‐centering capability. This paper presents an experimental and computational study on the seismic performance of self‐centering reinforced concrete frames. A 1/2‐scale model of a two‐story self‐centering reinforced concrete frame model was designed and tested on the shaking table in State Key Laboratory of Disaster Reduction in Civil Engineering at Tongji University to evaluate the seismic behavior of the structure. A structural analysis model, including detailed modeling of beam–column joints, column–base joints, and prestressed tendons, was constructed in the nonlinear dynamic modeling software OpenSEES. Agreements between test results and numerical solutions indicate that the designed reinforced concrete frame has satisfactory seismic performance and self‐centering capacity subjected to earthquakes; the self‐centering structures can undergo large rocking with minor residual displacement after the earthquake excitations; the proposed analysis procedure can be applied in simulating the seismic performance of self‐centering reinforced concrete frames. To achieve a more comprehensive evaluation on the performance of self‐centering structures, research on energy dissipation devices in the system is expected. Copyright © 2015 John Wiley & Sons, Ltd.     

Evaluation of seismic vulnerability of a complex RC existing building by linear and nonlinear modeling approaches

Recent earthquakes, that stroked Italian regions in past decades (Umbria— Marche 1997; Molise 2002; L’Aquila 2009), pointed out the high vulnerability of reinforced concrete existing buildings causing severe damages in the structures and consequently life losses. This is mainly due to the fact that such structures were often built without reference to seismic actions or on the basis of old standard provisions. Nowadays in Italy, Public Authorities are requested to evaluate the seismic vulnerability of their building stock assessing the actual capacity of such structures, as a consequence of new hazard levels and seismic microzonation introduced by new standards. According to Eurocode 8 or Italian standard NTC 2008, the seismic analysis of existing reinforced concrete buildings can be performed by one of the established procedure (i.e. Linear Static Analysis LSA, Linear Dynamic Analysis LDA, Nonlinear Static Analysis NSA, Nonlinear Dynamic Analysis NDA), depending on the achieved knowledge level about the structural system and materials. In order to compare efficiency and differences of previously described approaches, a deep investigation was executed on a reinforced concrete existing building whose dynamic behaviour was evaluated by an experimental dynamic analysis. In such a way, updated models were obtained and adopted for seismic analysis performed by using linear and nonlinear approaches, taking into account the stiffness and strength contribution of masonry infill walls. It was so possible to get useful indications on the reliability and discrepancies of different modelling approaches as well as on the influence of masonry infills on the seismic response of existing r.c. buildings.     

Research on the seismic retrofitting performance of RC frames using SC-PBSPC BRBF substructures

A new type of external substructure to upgrade existing reinforced concrete frames (RCFs) is presented in this paper, namely, a self-centering precast bolt-connected steel-plate reinforced concrete buckling-restrained brace frame (SC-PBSPC BRBF). The upgrade mechanism and three-dimensional simulation model were analyzed based on relevant experiment validations. A quasistatic analysis and parameter study was conducted using 21 scenarios to compare the upgrading effects of the outside substructure. Afterwards, a stiffness-based design procedure was developed and modified for this external substructure, including macro-demand analysis, partial component design, and overall structural evaluations. Dynamic analyses were also performed on a frame building for five cases, before and after strengthening. The proposed numerical model reflected the precast characteristics and displayed the ideal fitting accuracy. The external assembled brace provided sufficient initial stiffness and energy dissipation capacity, while the external prestressed tendon decreased residual displacements and facilitated self-centering of the whole structure. The analyses illustrated that the damage to the existing RCF was transferred and seismic demands were significantly reduced within limitations, accompanied with greater capacity reliability. This research provides a reference for the practical applications of the external upgrading substructures in earthquake-prone areas.     

Cyclic tests on large‐scale models of existing bridge piers with rectangular hollow cross‐section

Cyclic tests on two large‐scale models of existing bridge piers with rectangular hollow cross‐section were performed in the ELSA laboratory. The prototype structure is an existing reinforced concrete highway bridge constructed in Austria in 1975. The piers presented several seismic deficiencies and consequently they showed poor hysteretic behaviour and limited deformation capacity as well as undesirable failure modes that do not comply with the requirements of modern codes for seismic‐resistant structures. Experimental data are compared to numerical and empirical predictions. Copyright © 2003 John Wiley & Sons, Ltd.     

An efficient three‐dimensional solid finite element dynamic analysis of reinforced concrete structures

Most of the finite element analyses of reinforced concrete structures are restricted to two‐dimensional elements. Three‐dimensional solid elements have rarely been used although nearly all reinforced concrete structures are under a triaxial stress state. In this work, a three‐dimensional solid element based on a smeared fixed crack model that has been used in the past mainly for monotonic static loading analysis is extended to cater for dynamic analysis. The only material parameter that needs to be input for this model is the uniaxial compressive strength of concrete. Steel bars are modelled as uniaxial elements and an embedded formulation allows them to have any orientation inside the concrete elements. The proposed strategy for loading or unloading renders a numerical procedure which is stable and efficient. The whole process is applied to two RC frames and compared against existing experiments in the literature. Results show that the proposed approach may adequately be used to predict the dynamic response of a structure. Copyright © 2005 John Wiley & Sons, Ltd.     

Static vulnerability of an existing r.c. structure and seismic retrofitting by CFRP and base-isolation: A case study

The assessment of the static vulnerability under gravity loads of existing reinforced concrete (r.c.) framed buildings is a serious problem that requires the use of reliable methodologies to evaluate ductile and brittle mechanisms. The present work compares alternative formulations of member chord rotation and section and joint shear strength, proposed by Italian and European seismic codes and guidelines and other expressions available in the scientific literature. To this end, a r.c. framed building built sixty years ago with bi-directional (perimeter) and mono-directional (interior) plane frames, originally designed for five storeys then elevated to six during construction, is studied. A full characterization of the structure and its materials is carried out by means of destructive and non-destructive methods. Then, retrofitting based on the use of both innovative material, such as carbon fibre reinforced polymers (CFRP), and technology, such as base-isolation, are adopted to improve the static and seismic performances of the original structure. Finally, nonlinear analyses are carried out on a three-dimensional fibre model of the original and retrofitted structures, where an elastic linear law idealizes the behaviour of the CFRP up to tension failure and viscoelastic linear and bilinear models are used to idealize the behaviour of the elastomeric and sliding bearings, respectively.     

Seismic reliability assessment and the nonergodicity in the modelling parameter uncertainties

Modelling uncertainty can significantly affect the structural seismic reliability assessment. However, the limit state excursion due to this type of uncertainty may not be described by a Poisson process as it lacks renewal properties with the occurrence of each earthquake event. Furthermore, considering uncertainties related to ground motion representation by employing recorded ground motions together with modelling uncertainties is not a trivial task. Robust fragility assessment, proposed previously by the authors, employs the structural response to recorded ground motion as data in order to update prescribed seismic fragility models. Robust fragility can be extremely efficient for considering also the structural modelling uncertainties by creating a dataset of one-to-one assignments of structural model realizations and as-recorded ground motions. This can reduce the computational effort by more than 1 order of magnitude. However, it should be kept in mind that the fragility concept itself is based on the underlying assumption of Poisson-type renewal. Using the concept of updated robust reliability, considering both the uncertainty in ground motion representation based on as-recorded ground motion and non ergodic modelling uncertainties, the error introduced through structural reliability assessment by using the robust fragility is quantified. It is shown through specific application to an existing RC frame that this error is quite small when the product of the time interval and the standard deviation of failure rate is small and is on the conservative side.