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Short-span railway bridges subjected to high-speed traffic are structures where dynamic effects are mandatory. Additionally, the variability associated with materials and geometric characteristics introduces uncertainty to the safety assessment of railway traffic. This work discusses the current norms limit for vertical deck acceleration regarding the evaluation of stability on ballasted tracks, as stated on Annex A2 of EN1990. A probabilistic methodology to define a partial safety factor is presented, employing dynamic analyses and Monte Carlo simulations. The evaluation of a case study is presented for a single-span filler-beam bridge of the Portuguese Railways Network. The results allow the definition of deterministic design scenarios that are compared to the simulations outcome. Conclusions show consistent partial safety factors with the norms limit, contributing to further discussion of this factor. (c) 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

The First International Symposium on Risk Analysis and Safety of Complex Structures and Components (IRAS 2019) was organised in-teamed with the ESIS/TC12 Technical Committee on Risk Analysis and Safety of Large Structures and Components, which took place between 1-2 July 2019 at the Faculty of Engineering of the University of Porto (FEUP), in the City of Porto, located at seaside in the northwest region of Portugal. The guest editors of the IRAS 2019 deeply acknowledges all members of the International Scientific Committee, Thematic Sessions Organizers, Keynote Speakers and authors that contributed to the success of this event, that gathered more than 126 participants presenting more than 168 papers and posters. Sponsors are also fully acknowledged for their important contributions. The ESIS/TC12 2019 winners of the Robert Moskovic Award, Award of Merit TC12, and ESIS/TC12 Young Scientist Award were announced during the conference. Additionally, the guest editors (conference chairs) sincerely thank the tireless efforts of the Organizing Committee members as well as students and other FEUP and Construction Institute staff involved in the organization. Finally, the guest editors are pleased to inform that the second edition of the IRAS event will be organised by Prof. Aleksandar Sedmak (University of Belgrade, Serbia) which will take place in Belgrade in Serbia in the year 2021.

In the design of reinforced concrete structures several limit states are usually verified using simplified methods instead of using complex direct calculation. Span-to-depth ratio limits are applied for deflection control. In the same way, a redistribution factor and the relative depth of the compression zone are applied for the required ductility, but this is not enough. In fact, specific span-to-depth ratio limits, which are developed in this paper, should also complement the conditions referred to here. A numerical study is developed to compute the deflection ductility index of a wide range of continuous beams (or one-way slabs) considering as ultimate point when the rotation capacity (given by MC2010 and EC2) is achieved. From the boundary between fragile and ductile failures, the new span-to-depth ratio limits for the required ductility are defined and compared with the existing similar limits for deflection control. The results indicate that: (i) for normal strength concrete (up to 50 MPa), the ductility limit is more restrictive than the deflection limit when the redistribution factor delta is lower than 0.9, being always more restrictive for high strength concrete; (ii) for the current building beams, the slenderness used (10 < 1/d < 20) allows ductile failures, while for typical building slabs (low reinforcement ratio, but high redistribution), the slenderness should be 1/d

Bridges present valuable assets for the rail and road network by providing cross at critical links such as waterways, valleys, and other types of facilities. However, these types of structures are exposed to several threats during their lifecycle such as natural hazards and deterioration, which compromise their performance. To assess the condition state of such infrastructure and define maintenance and mitigation strategies, several performance indicators of quantitative nature have been proposed during the last decades by several researchers. Among those indicators, risk has received great attention as it enables to account for both the performance of infrastructures subjected to hazard events, and the consequences associated to an inadequate level of service of the infrastructure. Nevertheless, risk is not a stationary indicator, i.e. several parameters involved in the estimation of risk are time-dependent. One of them comprises the structural capacity of infrastructures, which is affected by deterioration effects over time. This gradual deterioration can be regarded as an interceptable hazard, which may act simultaneously with other non-interceptable hazards such as natural events (e.g. earthquakes). Therefore, a risk assessment framework should account for the probability of having these multiple hazards acting during the service life of infrastructures. The aim of this paper is to conduct a risk assessment for a railway bridge subjected to a multi-hazard scenario, i.e. an observable interceptable hazard corresponding to chloride induced corrosion of the reinforcing steel in reinforced concrete elements, together with seismic hazard. The results of the study demonstrate the relevance of considering time-dependent deterioration effects on the risk assessment of bridges, as the increase in the seismic fragility over time is significant. These findings are relevant for decision-making to plan and execute optimal interventions., FCT -Fundação para a Ciência e a Tecnologia(PEst-C/ECI/UI4029/2011 FCOM-01–0124-FEDER-022681)

The corrosion of reinforced concrete structures influences not only their structural strength but also their ductility. In this scenario, the use of Special Ductility Tempcore rebars, which belong to the highest ductility class, can reduce the risk of having a brittle failure when corrosion occurs. Therefore, this paper presents experimental and numerical studies to evaluate the rotation capacity of corroded RC beams with this type of steel. The experimental part consists of testing five beams to rupture and the numerical part uses the non-linear finite element method to correctly model the beam’s behaviour. The results indicate that for 20% damage, the rotation capacity reduced about 50%; however, these values are still higher than the Eurocode 2 normalized curve. In this scenario, the ultimate load only reduces 12%. Nevertheless, corrosion affects the ultimate deflection of isostatic beams much more than hyperstatic beams.

Bridges present valuable assets for the rail network by providing cross critical links such as waterways, valleys, and other types of facilities. However, these types of structures, during their life-cycle, are exposed to several threats such as natural hazards and deterioration. In fact, the lack of maintenance can lead to large consequences either for the structure, such as the partial or total collapse of the system, or for people. To assess the condition state of bridges, several performance indicators, of both quantitative and qualitative nature, have been proposed over these last decades by several researchers. Such indicators present a valuable information about the actual condition of the bridge to avoid undesirable consequences. These performance indicators are assessed over time through predictive models and can be determinist or probabilistic. The latter has been largely applied once they allow considering uncertainties associated with deterioration of the bridge. It is known that the deterioration of an infrastructure it is due to progressive deterioration (e.g., corrosion of the reinforcement, cracking of the concrete) and shock deterioration (e.g. earthquakes, collisions, floods). The idea of this paper is then to analyse a railway bridge and develop a framework that can consider gradual degradation to develop an optimal maintenance schedule.

In the scope of infrastructure risk assessment, structural reliability analysis leads to a challenging problem in order to deal with conflicting objectives: accurate estimation of failure probabilities and computational efficiency. Since the application of classical reliability methods is limited and often leads to a prohibitive computational cost, metamodeling techniques (e.g. polynomial chaos, kriging, response surface methods (RSM), etc.) have been widely used. Nevertheless, existing RSM present limitations handling with highly non-linear limit states, large-scale problems and approximation error. To overcome these problems, this paper describes a cutting-edge response surface algorithm covering the following issues: (i) dimensionality reduction by a variable screening procedure; (ii) definition of a promising search domain; (iii) initial experimental design based on an optimized space-filling scheme; (iv) model selection according to a stepwise regression procedure; (v) model validation by a cross-validation approach; (vi) model fitting using a double weighted regression technique; (vii) sequential sampling scheme by exploring a defined region of interest; (viii) confidence interval of reliability estimates based on a bootstrapping technique. With the aim of proving its efficiency, a wide collection of six illustration examples, concerning both analytical and FE-based problems, was selected. By benchmarking obtained results with literature findings, proposed method not only outperforms existing RSM, but also provides a powerful alternative to the use of other metamodeling techniques, ISISE Institute for Sustainability and Innovation in Structural Engineering (PEst-C/ECI/UI4029/2011 FCOM-01-0124-FEDER-022681), FCT Portuguese Scientific Foundation for the research grant PD/BD/113677/2015 under the PhD Programme “Analysis and Mitigation of Risks in Infrastructures InfraRisk-”. The third author would also like to thank the project POCI-01-0145-FEDER-007457 – CONSTRUCT – Institute of R&D in Structures and Construction. This work was also partly financed by FEDER funds through the Competitivity Factors Operational Programme – COMPETE and by national funds through FCT Foundation for Science and Technology within the scope of the project POCI-01-0145-FEDER-007633, info:eu-repo/semantics/publishedVersion

The influence of steel strain in bond–slip relationship has been the subject of recent literature, especially steel strain after yielding. This paper presents a new bond element for finite element packages which performs the bond–slip relationship, including steel strain effect. The developed element consists of an orthotropic four-node plane stress element whose constitutive material laws were changed. In order to verify the accuracy of this element several 2D numerical results were compared with experimental data. The results obtained with this element showed the need for its use to achieve good results and the relevance of steel strain effect on bond–slip relationship, especially in tension elements.

In this work the running safety of high-speed trains on a short-span bridge is assessed. A probabilistic approach that combines Monte Carlo simulation with the extreme value theory is used and the existence of track irregularities is taken into account along with the variability of parameters related to the bridge, the track and the train. As case study, a 12 m span filler beam bridge was selected as the train–bridge interaction effects are most significant for short spans. The running safety is assessed for the case of loss of contact between the wheel and the rail, taking into consideration only the vertical wheel–rail interaction and assuming that no lateral forces act on the train. This research enables the characterisation of the wheel unloading coefficient, the identification of the critical wheel and also the definition of the maximum allowable speed for trains to run safely on the bridge.

The Tempcore rebars behaviour results from the interaction of the three layers that compose them, with different initial stresses. Therefore,their mechanical properties study is important for the understanding of the rebar overall behaviour. In this paper it is presentedand discussed the results of hardness, strength and ductility obtained in tensile and hardness tests of several samples from Tempcore rebars (with high ductility) with various damage levels. The assessment of strength and ductility in locally damaged rebars concluded that the ultimate strain decrease is the main anomaly, mainly due tothe hardening of steel that allows overcoming theyield stress decreaseuntil damagesof 20%.

A probabilistic methodology for the safety assessment of short span railway bridges for high-speed traffic is presented. The purpose is to create a simple, efficient and automatic procedure that allows identifying the critical train speeds over the bridge and assessing the safety of the train–bridge system. The methodology combines simulation techniques with the extreme value theory in order to minimise the required computational time and guarantee accurate results. Stochastic simulation is employed as it allows reflecting the real variability of the parameters that characterise the dynamic response of the train–bridge system. As a case study the safety of a short span filler beam railway bridge crossed by a TGV double train is assessed. The behaviour of short span railway bridges is known to be particularly difficult to predict due to the complexity of the coupled train–track–bridge system, as well as for being particularly sensitive to resonant phenomena. The variability of the bridge, the track and the train was accounted for, as well as the existence of track irregularities. The proposed probabilistic methodology proved to be efficient as it allowed identifying the critical train speeds with a reduced computational cost. Furthermore, for these critical train speeds two different methods were used to estimate the probability of failure. The obtained results showed a good agreement guaranteeing the accuracy of the methodology.

Robustness has been recognized as interesting research topic due to several collapses that have been occurring over last years. Indeed, this subject is related with global failure or collapse. However, its definition is not consensual since several definitions have been proposed in the literature. This short-paper aims to present a framework for assessing bridge’s robustness as a probabilistic performance indicator. In this study, a non-linear model of a clamped beam with two point loads using DIANA software was developed to validate the framework presented. By means of a probabilistic approach, the load carrying capacity and structural safety were evaluated. In this regard, special focus is placed on an adaptive Monte Carlo simulation procedure to achieve a proper meta-model., The authors would like to thank ISISE—Institute for Sustainability and Innovation in Structural Engineering (PEst-C/ECI/UI4029/2011 FCOM-01-0124-FEDER022681), FCT– Portuguese Scientific Foundation for the research grant PD/BD/113677/2015. This study also received funding from the European Union’s Seventh Framework Programme for research, technological development and demonstration under grant agreement No. 606229. Also the collaboration and information provided by the professor António Abel Henriques is gratefully acknowledged.

The purpose of this paper is to examine the influence of geotechnical uncertainties on the reliability of vertically loaded pile foundations and the use of this information in decision-making support, especially when gathering the information necessary for reliability analyses. Two case studies of single pile foundations were selected, and each uncertainty source was investigated to identify which are the most important and influential in the evaluation of vertical pile resistance under axial loading. Reliability sensitivity analyses were conducted using FORM (the first-order reliability method) and MCS (Monte Carlo simulations). The characterisation of uncertainties is not an easy task in geotechnical engineering. The aim of the analyses described in this paper is to optimise resources and investments in the investigation of the variables in pile reliability. The physical uncertainties of actions, the inherent variability of soil and model error were assessed by experimental in situ standard penetration tests (SPT) or from information available in the literature. For the cases studied, the sensitivity analysis results show that, in spite of the high variability of the soils involved, model error also plays a very important role in geotechnical pile reliability and was considerably more important than soil variability in both case studies. From a comparison of the two reliability methods (FORM and MCS), it was concluded that FORM is applicable in simple cases and as a first approach because it is an approximate method and sometimes does not have the capability to incorporate every detail of the problem, namely a specific probability density function or more specific limit conditions.

Advances in computer technology allow nowadays the use of powerful computational models to describe the non-linear structural behavior of reinforced concrete (RC) structures. However their utilization for structural analysis and design is not so easy to be combined with the partial safety factors criteria presented in civil engineering international codes. Trying to minimize this type of difficulties, it is proposed a method for safety verification of RC structures based on a probabilistic approach. This method consists in the application of non-linear structural numerical models and simulation methods. In order to reduce computational time consuming the Latin Hypercube sampling method was adopted, providing a constrained sampling scheme instead of general random sampling like Monte Carlo method. The proposed methodology permits to calculate the probability of failure of RC structures, to evaluate the accuracy of any design criteria and, in particular, the accuracy of simplified structural design rules, like those proposed in civil engineering codes.

The dynamic behaviour of railway bridges in high-speed lines has been the subject of several studies in recent years. Nevertheless, most of the work was developed assuming a deterministic perspective. In this paper a probabilistic approach is used to analyse the sensitivity of the dynamic response of a small span bridge due to the variability of the main structural parameters. A filler beam railway bridge was selected as case study and random variables were identified. A variable screening procedure was performed in order to determine which variables had a higher influence on the dynamic response of the bridge. Simulation techniques were applied to analyse the variability of the dynamic response of the bridge, as these methods allow an accurate consideration of the randomness of the main structural parameters. Based on the simulation results, a traffic safety assessment of the bridge was performed. As conclusion, the safety assessment results are discussed, with special focus on the comparison between the results obtained when adopting the European standards approach and when considering a probabilistic approach.

This paper presents probabilistic models for mechanical properties of pre-cast and cast-on-site concrete as well as of reinforcing and pre-stressing steel. An extended review of models available in the literature is made and new probabilistic models are developed based on a significant amount of data collected by the authors. New probabilistic models are proposed for concrete ultimate strength (separately for precast and cast-in-place concretes), for yield and ultimate strength of reinforcing steel and for proportionality limit and ultimate strength of pre-stressing steel. The new models account for a recent improvement of production and are more appropriate for the probabilistic assessment of modern concrete structures then the models available in the literature.

This paper presents newly established probabilistic models of ultimate shear and bending resistance of typical reinforced concrete (RC) and prestressed concrete (PC) bridge cross-sections. These ne...

An efficient health monitoring system for damage detection in civil engineering structures using on-line monitoring data is being developed to identify any possible damage in short time. The present work is based on the treatment of uncertainties, which is one of the basic common difficulties faced when modelling structures. A methodology, based on interval analysis (IA) theory [R.E. Moore, Interval Analysis, Prentice-Hall, Englewood Cliffs, NJ, 1966] applied to a numerical constraint satisfaction problem (CSP) [J.R. Casas, J.C. Matos, J.A. Figueiras, J. Vehí, O. García, P. Herrero, Bridge monitoring and assessment under uncertainty via interval analysis, in: Ninth International Conference On Structural Safety And Reliability—ICOSSAR2005, 2005. pp. 487–494], is implemented in the damage detection [J.R. Casas, J.C. Matos, J.A. Figueiras, J. Vehí, O. García, P. Herrero, Bridge monitoring and assessment under uncertainty via interval analysis, in: Ninth International Conference On Structural Safety And Reliability—ICOSSAR2005, 2005. pp. 487–494] and modelling system of a long-term monitoring project in order to achieve such an objective. An algorithm is being developed for using such methodology with the obtained data.Such methodology has been first checked in the laboratory with a simple reinforced concrete structure (loaded up to failure). The obtained results are useful for identifying the load where the structure presents changes in its behaviour. The majority of the structures present a linear elastic behaviour throughout their life. However, they tend to deteriorate; such degradation reflects on results obtained from the long term monitoring system. Structural assessment was successfully performed in this case, enabling its application to real structures.

Probabilistic and reliability techniques have been used increasingly to evaluate uncertainty and structural safety. However, when sophisticated methods of structural analysis are used, the current probabilistic techniques require the execution of various simulations for the same problem. This has been one of the main factors to restrain the use of this type of techniques. In this work, the formulation of an efficient method to evaluate the uncertainty of the structural response by applying perturbation techniques is described. The procedure used to implement this method in a structural non-linear finite element framework is presented. The implemented computational program allows, in only one structural analysis, to evaluate the mean value and the standard deviation of the structural response, defined in terms of displacements or forces. The results are exact for linear problems and normal distributed random variables. Calculated values remain accurate when the non-linear problem can be approximated by a linear combination of the basic random variables more correlated with the structural response.

The formulation of an efficient method to evaluate the uncertainty of the structural response by applying perturbation techniques is described. Structural random variables are defined by their mean values, standard deviations and correlations. The uncertainty of structural behaviour is evaluated by the covariance matrix of response according to the developed perturbation methodology. It is also presented the procedure used to implement this method in a structural finite element framework. The implemented computational program allows, in only one structural analysis, to evaluate the mean value and the standard deviation of the structural response, defined in terms of displacements or forces. The proposed method is exact for problems with linear design functions and normal-distributed random variables. Results remain accurate for non-linear design functions if they can be approximated by a linear combination of the basic random variables.

A contribution to the definition of a novel safety format for the design of concrete structures based on non‐linear methods of analysis is the main purpose of this work. A brief discussion of design formats proposed by codes of practice is introduced. Probabilistic analyses of current concrete frames are performed and the corresponding results are used as a basis to derive simplified and coherent practical rules. The analyses have been carried out taking into account the non‐linear material behaviour and the variability of the structural parameters by simulation of probabilistic density functions. A simple procedure is proposed to evaluate the structural safety of concrete frame structures. Mean values are recommended to characterise the material properties to be used in the analysis and a global safety factor is defined to evaluate the structural design resistance.

In this paper a probabilistic methodology for the safety assessment of short span railway bridges for high-speed traffic is presented. The proposed methodology combines simulation techniques with the extreme value theory in order to minimize the required computational time and guarantee accurate results. Stochastic simulation is employed as it enables reflecting the real variability of the parameters that characterize the dynamic response of the train-bridge system. The variability of the bridge, the track and the train was accounted for, as well as the existence of track irregularities. As a case study the safety of a short span filler beam railway bridge crossed by a TGV double train is analysed. The safety of the train-bridge system is assessed for the two most critical aspects of the dynamic response: the deck accelerations and the wheel-rail contact forces. Two stopping criteria for the simulation analysis were defined in order to direct the computational effort to the critical train speeds. For cases where the probability of failure is one order of magnitude apart from the safety threshold proved the efficiency of these criteria, as ruling them out as critical required a reduced number of simulations. Moreover, it was concluded that the track instability due to excessive deck accelerations is the governing aspect of the dynamic response and the Ÿ span the critical section, limiting the train speed over the bridge to 280 km/h. In terms of number of simulations it was observed that less than 25,000 simulations were needed to accurately estimate the probability of failure for the critical train speed for both safety criteria. Since the probability of failure threshold was set at 10-4 used, this is a good indicator of the efficiency of the proposed methodology.

An analytical description of the behaviour of a connection has to cover all sources of deformabilities, local yielding, local instabilities, etc. Due to the multitude of influencing parameters, a macroscopic inspection of a complex connection — by subdividing it into components — has proved to be most appropriate. This is the approach recently proposed by the Eurocode 3. One of the basic components is the equivalent T-stub, which adequately models several parts of a connection: column flange in bending, end plate in bending and flange cleat in bending. Reliability techniques combined with non-linear analysis of structures have been applied to interpret the effects of parameter variability on the T-stub behaviour. Simplified safety rules are derived from this probabilistic high-level approach.

Nowadays, social concerns, such as the sustainability and the economy, and also the new regulation design codes are imposing geotechnical engineers to adjust the design methodologies. The new design methodologies should be reliability-based and provide more rational designs that should also be economic and sustainable. On this matter, this work presents a combination of the reliability-based analyses with a cost-effect study in pile foundation design. The mail goal is to match the needs for a particular problem and adequate the efforts to gather the information necessary to achieve a certain reliability level and decrease the chances of additional costs and/or other implications due to unforeseen ground conditions or pile capacity. An example is provided to demonstrate the use of such methodology both in the site investigation stage and the pile design stage.

The behaviour of continuous reinforced concrete elements subjected to bending is characterized by a non-linear response whose extent depends on the available rotation capacity. In this paper the rotation capacity is reviewed and a numerical study for calculating the deflection ductility index in continuous reinforced concrete beams or one way spanning slabs is presented. The results indicate comfortable values between 1.0 and 2.0 for current beams used on building construction, while for slabs with high redistribution the limit values of slenderness and mechanical reinforcement ratios require some attention because slabs may not reach its total loading capacity.

This paper is a contribution for the application of Eurocode 7 design methodology and analysis of related features in geotechnical engineering, such as uncertainty, risk and reliability. The design methodology of Eurocode 7 is applied to a strip foundation resting on a relatively homogeneous c-φ soil, and the different design approaches are compared to deterministic and semi-probabilistic solutions. A reliability assessment is performed for different conditions, particularly selecting different characteristic values and coefficients of variation of soil properties. Several uncorrelated and correlated random variables are considered, and probabilistic solutions are achieved and compared with a target reliability index. For this purpose, reliability techniques such as the first-order reliability method (FORM) and the Monte Carlo simulation (MCS) are applied and compared to other methodologies. Based on the obtained results, the Eurocode 7 design methodology is discussed, and the indispensable engineering judgment is outlined.

En este trabajo se describen las características principales de la metodología desarrollada para la evaluación probabilística de la seguridad y funcionalidad de puentes de hormigón teniendo en cuenta las relaciones constitutivas no lineales de los materiales, los efectos diferidos y las incertidumbres asociadas a los parámetros del proyecto de este tipo de estructuras. El modelo estructural está basado en las técnicas de los elementos finitos usando una formulación elasto-viscoplástica para la estimación precisa de la respuesta y de la capacidad resistente de estructuras de hormigón. Se presenta la aplicación de esta metodología a un viaducto de hormigón pretensado para evaluar el código computacional y para ilustrar su campo de aplicación. Los resultados obtenidos de los análisis fueron usados para identificar los parámetros más importantes para cada estado límite y las zonas críticas que deben ser cuidadosamente controladas para conseguir un mantenimiento racional. This study describes the main features of the methodology developed for the probabilistic assessment of safety and serviceability of concrete bridges, taking into account the non-linear constitutive relationships of the materials, time dependent effects, and uncertainty associated with the design parameters of these types of structure. The structural model is based on finite element techniques using an elasto-viscoplastic formulation for precise estimation of the response and ultimate strength of concrete structures. Application of this methodology to a prestressed concrete viaduct is presented to evaluate the computational code and to illustrate its scope of applicability. The results obtained from the analyses were used to identify the most important parameters for each limiting state studied, and the critical zones that should be carefully controlled to obtain rational maintenance.