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.     

Shaking table tests of a reinforced concrete bridge pier with a low-cost sliding pendulum system

After the occurrence of various destructive earthquakes in Japan, extensive efforts have been made to improve the seismic performance of bridges. Although improvements to the ductile capacities of reinforced concrete (RC) bridge piers have been developed over the past few decades, seismic resilience has not been adequately ensured. Simple ductile structures are not robust and exhibit a certain level of damage under extremely strong earthquakes, leading to large residual displacements and higher repair costs, which incur in societies with less-effective disaster response and recovery measures. To ensure the seismic resilience of bridges, it is necessary to continue developing the seismic design methodology of RC bridges by exploring new concepts while avoiding the use of expensive materials. Therefore, to maximize the postevent operability, a novel RC bridge pier with a low-cost sliding pendulum system is proposed. The seismic force is reduced as the upper component moves along a concave sliding surface atop the lower component of the RC bridge pier. No replaceable seismic devices are included to lengthen the natural period; only conventional concrete and steel are used to achieve low-cost design solutions. The seismic performance was evaluated through unidirectional shaking table tests. The experimental results demonstrated a reduction in the shear force transmitted to the substructure, and the residual displacement decreased by establishing an adequate radius of the sliding surface. Finally, a nonlinear dynamic analysis was performed to estimate the seismic response of the proposed RC bridge pier.     

A methodology for defining seismic scenario‐structure‐based limit state criteria for rc high‐rise wall buildings using net drift

As a result of population growth and consequent urbanization, the number of high‐rise buildings is rapidly growing worldwide resulting in increased exposure to multiple‐scenario earthquakes and associated risk. The wide range in frequency contents of possible strong ground motions can have an impact on the seismic response, vulnerability and limit states definitions of RC high‐rise wall structures. Motivated by the pressing need to derive more accurate fragility relations to be used in seismic risk assessment and mitigation of such structures, a methodology is proposed to obtain reliable, Seismic Scenario‐Structure‐Based (SSSB) definitions of limit state criteria. A 30‐story wall building, located in a multi‐seismic scenario study region, is utilized to illustrate the methodology. The building is designed following modern codes and then modeled using nonlinear fiber‐based approach. Uncertainty in ground motions is accounted for by the selection of forty real earthquake records representing two seismic scenarios. Seismic scenario‐based building local response at increasing earthquake intensities is mapped using Multi‐Record Incremental Dynamic Analyses (MRIDAs) with a new scalar intensity measure. Net Inter‐Story Drift (NISD) is selected as a global damage measure based on a parametric study involving seven buildings ranging from 20 to 50 stories. This damage measure is used to link local damage events, including shear, to global response under different seismic scenarios. While the study concludes by proposing SSSB limit state criteria for the sample building, the proposed methodology arrives at a reliable definition of limit state criteria for an inventory of RC high‐rise wall buildings under multiple earthquake scenarios. Copyright © 2016 John Wiley & Sons, Ltd.     

Direct displacement‐based seismic assessment procedure for multi‐span reinforced concrete bridges with single‐column piers

In Italy, as in other high seismic risk countries, many bridges, nowadays deemed ‘strategic’ for civil protection interventions after an earthquake, were built without antiseismic criteria, and therefore their seismic assessment is mandatory. Accordingly, the development of a seismic assessment procedure that gives reliable results and, at the same time, is sufficiently simple to be applied on a large population of bridges in a short time is very useful. In this paper, a displacement‐based procedure for the assessment of multi‐span RC bridges, satisfying these requirements and called direct displacement‐based assessment (DDBA), is proposed. Based on the direct displacement‐based design previously developed by Priestley et al., DDBA idealizes the multi DOF bridge structure as an equivalent SDOF system and hence defines a safety factor in terms of displacement. DDBA was applied to hypothetical bridge configurations. The same structures were analyzed also using standard force‐based approach. The reliability of the two methods was checked performing IDA with response spectrum compatible accelerograms. Copyright © 2012 John Wiley & Sons, Ltd.     

Probabilistic performance assessment of low‐ductility reinforced concrete frames retrofitted with dissipative braces

The paper illustrates a probabilistic methodology for assessing the vulnerability of existing reinforced concrete (RC) buildings with limited ductility capacity retrofitted by means of dissipative braces. The aim is to highlight the most important parameters controlling the capacity of these coupled systems and specific aspects concerning the response uncertainties. The proposed methodology is based on the use of local engineering demand parameters for monitoring the seismic response and on the development of component and system fragility curves before and after the retrofit. In the first part of the paper, the methodology is illustrated by highlighting its advantages with respect to the existing approaches. Then, its capability and effectiveness are tested by considering a benchmark two‐dimensional RC frame designed for gravity‐loads only. The frame is retrofitted by introducing elasto‐plastic dissipative braces designed for different levels of base shear capacity. The obtained results show the effectiveness of the methodology in describing the changes in the response and in the failure modalities before and after the retrofit, for different retrofit levels. Moreover, the retrofit effectiveness is evaluated by introducing proper synthetic parameters describing the fragility curves and by stressing the importance of employing local engineering demand parameters (EDPs) rather than global EDPs in the seismic risk evaluation of coupled systems consisting in low‐ductility RC frames and dissipative braces. Copyright © 2012 John Wiley & Sons, Ltd.     

Inelastic dynamic analysis of RC bridges accounting for spatial variability of ground motion,site effects and soil–structure interaction phenomena. Part 1: Methodology and analytical tools

During strong ground motion it is expected that extended structures (such as bridges) are subjected to excitation that varies along their longitudinal axis in terms of arrival time, amplitude and frequency content, a fact primarily attributed to the wave passage effect, the loss of coherency and the role of local site conditions. Furthermore, the foundation interacts with the soil and the superstructure, thus significantly affecting the dynamic response of the bridge. A general methodology is therefore set up and implemented into a computer code for deriving sets of appropriately modified time histories and spring–dashpot coefficients at each support of a bridge with account for spatial variability, local site conditions and soil–foundation–superstructure interaction, for the purposes of inelastic dynamic analysis of RC bridges. In order to validate the methodology and code developed, each stage of the proposed procedure is verified using recorded data, finite‐element analyses, alternative computer programs, previous research studies, and closed‐form solutions wherever available. The results establish an adequate degree of confidence in the use of the proposed methodology and code in further parametric analyses and seismic design. Copyright © 2003 John Wiley & Sons, Ltd.     

Seismic fragility methodology for highway bridges using a component level approach

Bridge fragility curves, which express the probability of a bridge reaching a certain damage state for a given ground motion parameter, play an important role in the overall seismic risk assessment of a transportation network. Current analytical methodologies for generating bridge fragility curves do not adequately account for all major contributing bridge components. Studies have shown that for some bridge types, neglecting to account for all of these components can lead to a misrepresentation of the bridges' overall fragilities. In this study, an expanded methodology for the generation of analytical fragility curves for highway bridges is presented. This methodology considers the contribution of the major components of the bridge, such as the columns, bearings and abutments, to its overall bridge system fragility. In particular, this methodology utilizes probability tools to directly estimate the bridge system fragility from the individual component fragilities. This is illustrated using a bridge whose construction and configuration are typical to the Central and Southeastern United States and the results are presented and discussed herein. This study shows that the bridge as a system is more fragile than any one of the individual components. Assuming that the columns represent the entire bridge system can result in errors as large as 50% at higher damage states. This provides support to the assertion that multiple bridge components should be considered in the development of bridge fragility curves. The findings also show that estimation of the bridge fragilities by their first‐order bounds could result in errors of up to 40%. Copyright © 2006 John Wiley & Sons, Ltd.     

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.     

Life‐cycle reliability of RC bridge piers under seismic and airborne chloride hazards

Over the last two decades, the probabilistic assessment of reinforced concrete (RC) structures under seismic hazard has been developed rapidly. However, little attention has been devoted to the assessment of the seismic reliability of corroded structures. For the life‐cycle assessment of RC structures in a marine environment and earthquake‐prone regions, the effect of corrosion due to airborne chlorides on the seismic capacity needs to be taken into consideration. Also, the effect of the type of corrosive environment on the seismic capacity of RC structures has to be quantified. In this paper, the evaluation of the displacement ductility capacity based on the buckling model of longitudinal rebars in corroded RC bridge piers is established, and a novel computational procedure to integrate the probabilistic hazard associated with airborne chlorides into life‐cycle seismic reliability assessment of these piers is proposed. The seismic demand depends on the results of seismic hazard assessment, whereas the deterioration of seismic capacity depends on the hazard associated with airborne chlorides. In an illustrative example, an RC bridge pier was modeled as single degree of freedom (SDOF). The longitudinal rebars buckling of this pier was considered as the sole limit state when estimating its failure probability. The findings show that the life‐cycle reliability of RC bridge piers depends on both the seismic and airborne chloride hazards, and that the cumulative‐time failure probabilities of RC bridge piers located in seismic zones can be dramatically affected by the effect of airborne chlorides. Copyright © 2011 John Wiley & Sons, Ltd.     

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.     

Probabilistic seismic loss assessment of aging bridges using a component‐level cost estimation approach

Deteriorating highway bridges in the United States and worldwide have demonstrated susceptibility to damage in earthquake events, with considerable economic consequences due to repair or replacement. Current seismic loss assessment approaches for these critical elements of the transportation network neglect the effects of aging and degradation on the loss estimate. However, the continued aging and deterioration of bridge infrastructure could not only increase susceptibility to seismic damage, but also have a significant impact on these economic losses. Furthermore, the contribution of individual aging components to system‐level losses, correlations between these components, and uncertainty modeling in the risk assessment and repair modeling are all crucial considerations to enhance the accuracy and confidence in bridge loss estimates. In this paper, a new methodology for seismic loss assessment of aging bridges is introduced based on the non‐homogeneous Poisson process. Statistical moments of seismic losses can be efficiently estimated, such as the expected value and variance. The approach is unique in its account for time‐varying seismic vulnerability, uncertainty in component repair, and the contribution of multiple correlated aging components. A representative case study is presented with two fundamentally distinct highway bridges to demonstrate the effects of corrosion deterioration of different bridge components on the seismic losses. Using the proposed model, a sensitivity study is also conducted to assess the effect of parameter variations on the expected seismic losses. The results reveal that the seismic losses estimated by explicitly considering the effects of deterioration of bridge components is significantly higher than that found by assuming time‐invariant structural reliability. Copyright © 2011 John Wiley & Sons, Ltd.     

RC structures cyclic behavior simulation with a model integrating plasticity,damage, and bond‐slip

The behavior of reinforced concrete structures under severe demands, as strong ground motions, is highly complex; this is mainly due to the complexity of concrete behavior and to the strong interaction between concrete and steel, with several coupled failure modes. On the other hand, given the increasing awareness and concern on the worldwide seismic risk, new developments have arisen in earthquake engineering; nonetheless, some developments are mainly based on simple analytical tools that are widely used, given their moderate computational cost. This research aims to provide a solid basis for validation and calibration of such developments by using computationally efficient continuum mechanics‐based tools. Within this context, this paper presents a model for 3D simulation of cyclic behavior of RC structures. The model integrates a bond‐slip model developed by one of the authors and the damage variable evolution methodology for concrete damage plastic model developed by some authors. In the integrated model, a new technique is derived for efficient 3D analysis of bond‐slip of 2 or more crossing reinforcing bars in beam‐column joints, slabs, footings, pile caps, and other similar members. The analysis is performed by implementing the bond‐slip model in a user element subroutine of Abaqus and the damage variable evolution methodology in the original concrete damage plastic model in the package. Two laboratory experiments consisting of a column and a frame subjected to cyclic displacements up to failure are simulated with the proposed formulation.     

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.     

Post‐earthquake bridge repair cost and repair time estimation methodology

While structural engineers have traditionally focused on individual components (bridges, for example) of transportation networks for design, retrofit, and analysis, it has become increasingly apparent that the economic costs to society after extreme earthquake events are caused at least as much from indirect costs as direct costs due to individual structures. This paper describes an improved methodology for developing probabilistic estimates of repair costs and repair times that can be used for evaluating the performance of new bridge design options and existing bridges in preparation for the next major earthquake. The proposed approach in this paper is an improvement on previous bridge loss modeling studies—it is based on the local linearization of the dependence between repair quantities and damage states so that the resulting model follows a linear relationship between damage states and repair points. The methodology uses the concept of performance groups (PGs) that account for damage and repair of individual bridge components and subassemblies. The method is validated using two simple examples that compare the proposed method to simulation and previous methods based on loss models using a power–law relationship between repair quantities and damage. In addition, an illustration of the method is provided for a complete study on the performance of a common five‐span overpass bridge structure in California. Intensity‐dependent repair cost ratios (RCRs) and repair times are calculated using the proposed approach, as well as plots that show the disaggregation of repair cost by repair quantity and by PG. This provides the decision maker with a higher fidelity of data when evaluating the contribution of different bridge components to the performance of the bridge system, where performance is evaluated in terms of repair costs and repair times rather than traditional engineering quantities such as displacements and stresses. Copyright © 2009 John Wiley & Sons, Ltd.     

Inelastic dynamic analysis of RC bridges accounting for spatial variability of ground motion,site effects and soil–structure interaction phenomena. Part 2: Parametric study

The methodology for dealing with spatial variability of ground motion, site effects and soil–structure interaction phenomena in the context of inelastic dynamic analysis of bridge structures, and the associated analytical tools established and validated in a companion paper are used herein for a detailed parametric analysis, aiming to evaluate the importance of the above effects in seismic design. For a total of 20 bridge structures differing in terms of structural type (fundamental period, symmetry, regularity, abutment conditions, pier‐to‐deck connections), dimensions (span and overall length), and ground motion characteristics (earthquake frequency content and direction of excitation), the dynamic response corresponding to nine levels of increasing analysis complexity was calculated and compared with the ‘standard’ case of a fixed base, uniformly excited, elastic structure for which site effects were totally ignored. It is concluded that the dynamic response of RC bridges is indeed strongly affected by the coupling of the above phenomena that may adversely affect displacements and/or action effects under certain circumstances. Evidence is also presented that some bridge types are relatively more sensitive to the above phenomena, hence a more refined analysis approach should be considered in their case. Copyright @ 2003 John Wiley & Sons, Ltd.     

Inelastic response analysis of reinforced concrete structures using modified force analogy method

A modified force analogy method (MFAM) is developed to simulate the nonlinear inelastic response of reinforced concrete (RC) structures. Beam–column elements with three different plastic mechanisms are utilized to simulate inelastic response caused by moment and shear force. A multi‐linear hysteretic model is implemented to simulate the nonlinear inelastic response of RC member. The P‐Δ effect of the structure is also addressed in MFAM. Static and dynamic inelastic response of structure, damage condition and failure type for structural element, structural limit state and collapse time can also be simulated using MFAM. Compared with the general algorithm, the MFAM provides less computational time especially in the case of large structural system. It is also easier to be written as computer program. Three test data groups, which include cyclic loading test data of a non‐ductile RC bridge column, a two‐storey RC frame, and dynamic collapse test data of a non‐ductile RC portal frame, are selected to confirm the effectiveness of applying MFAM to simulate the inelastic behaviour of structures. Copyright © 2007 John Wiley & Sons, Ltd.     

Accuracy of nonlinear static procedures for the seismic assessment of shear critical structures

The nonlinear behavior of reinforced concrete (RC) members represents a key issue in the seismic performance assessment of structures. Many structures constructed in the 1980s or earlier were designed based on force limits; thus they often exhibit brittle failure modes, strength and stiffness degradation, and severe pinching effects. Field surveys and experimental evidence have demonstrated that such inelastic responses affect the global behavior of RC structural systems. Efforts have been made to consider the degrading stiffness and strength in the simplified nonlinear static procedures commonly adopted by practitioners. This paper investigates the accuracy of such procedures for the seismic performance assessment of RC structural systems. Refined finite element models of a shear critical bridge bent and a flexure‐critical bridge pier are used as reference models. The numerical models are validated against experimental results and used to evaluate the inelastic dynamic response of the structures subjected to earthquake ground motions with increasing amplitude. The maximum response from the refined numerical models is compared against the results from the simplified static procedures, namely modified capacity spectrum method and coefficient method in FEMA‐440. The accuracy of the static procedures in estimating the displacement demand of a flexure‐critical system and shear‐critical system is discussed in detail. Copyright © 2015 John Wiley & Sons, Ltd.     

Seismic steel jacketing of rectangular RC bridge columns for the mitigation of lap‐splice failures

This paper investigated the use of external steel jacketing for seismic retrofit of non‐ductile reinforced concrete (RC) bridge columns to prevent lap‐splice failure. Three 1/2.5‐scale specimens were tested under cyclic loads. The effectiveness of two types of steel jackets for improving the ductility and strength of specimens using inadequate transverse reinforcing and lap‐splice details were examined. An octagonal steel jacketing scheme for the seismic retrofitting of rectangular RC bridge columns was proposed. In addition, the methods for seismic retrofitting rectangular columns using elliptical steel jacketing were also critically tested. The test results indicated that the octagonal steel jackets can effectively provide confinement thereby mitigating failures as a result of inadequate transverse reinforcing and inadequate lap‐splices. Tests also confirmed that the ductility performance and the energy dissipation capacity of the specimens can be significantly improved by the octagonal steel jacket. Copyright © 2010 John Wiley & Sons, Ltd.     

Methodology for the development of bridge‐specific fragility curves

A new methodology for the development of bridge‐specific fragility curves is proposed with a view to improving the reliability of loss assessment in road networks and prioritising retrofit of the bridge stock. The key features of the proposed methodology are the explicit definition of critical limit state thresholds for individual bridge components, with consideration of the effect of varying geometry, material properties, reinforcement and loading patterns on the component capacity; the methodology also includes the quantification of uncertainty in capacity, demand and damage state definition. Advanced analysis methods and tools (nonlinear static analysis and incremental dynamic response history analysis) are used for bridge component capacity and demand estimation, while reduced sampling techniques are used for uncertainty treatment. Whereas uncertainty in both capacity and demand is estimated from nonlinear analysis of detailed inelastic models, in practical application to bridge stocks, the demand is estimated through a standard response spectrum analysis of a simplified elastic model of the bridge. The simplified methodology can be efficiently applied to a large number of bridges (with different characteristics) within a road network, by means of an ad hoc developed software involving the use of a generic (elastic) bridge model, which derives bridge‐specific fragility curves. Copyright © 2016 John Wiley & Sons, Ltd.