Paolo Franchin - Profile on Academia.edu (original) (raw)
Papers by Paolo Franchin
Earthquake Spectra, 2014
This study focuses on the evaluation of the seismic vulnerability of the Italian roadway bridge s... more This study focuses on the evaluation of the seismic vulnerability of the Italian roadway bridge stock, within the framework of a Civil Protection sponsored project. A comprehensive database of existing bridges (17,000 bridges with different level of knowledge) was implemented. At the core of the study stands a procedure for automatically carrying out state-of-the-art analytical evaluation of fragility curves for two performance levels—damage and collapse—on an individual bridge basis. A WebGIS was developed to handle data and results. The main outputs are maps of bridge seismic risk (from the fragilities and the hazard maps) at the national level and real-time scenario damage-probability maps (from the fragilities and the scenario shake maps). In the latter case, the WebGIS also performs network analysis to identify routes to be followed by rescue teams. Consistency of the fragility derivation over the entire bridge stock is regarded as a major advantage of the adopted approach.
Reliability of Uncertain Inelastic Structures under Earthquake Excitation
Journal of Engineering Mechanics-asce, 2004
The assessment of safety for structures subjected to earthquake excitation is a time-variant reli... more The assessment of safety for structures subjected to earthquake excitation is a time-variant reliability problem whose practical solution, when the structure behaves inelastically and uncertainty in the mechanical parameters is taken into account, is traditionally sought by ...
Earthquake Engineering & Structural Dynamics, 2007
A scalar damage measure (DM) for probabilistic performance assessment of structures can be expres... more A scalar damage measure (DM) for probabilistic performance assessment of structures can be expressed as the critical demand-to-capacity ratio corresponding to the component or mechanism that leads the structure closest to failure at the onset of which, the DM assumes the value of one. This DM can be employed to make probabilistic performance assessments taking into account the uncertainty in the ground motion, in the structural modelling parameters, and also in the model(s) used for determining components capacity. Nonlinear dynamic analysis methods can be used to estimate this DM in two ways: (a) applying a (small-size) set of un-scaled ground motion records to the structure and (b) using incremental dynamic analysis. Case (a) is suitable for making performance assessments based on demand and capacity factor design format and case (b) is suitable for estimating directly the probability of failure using numerical integration. Performance assessments using this DM are described in a case study of a RC frame in which the critical demand-to-capacity ratio is determined by taking into account various modes of failure for the limit state of collapse, such as weak storey mechanisms, shear failure in the columns, and ultimate deformations in the columns. For events with a very small probability of occurrence-such as strong earthquakes-the numerical values of (mean) annual frequency of occurrence and of the probability of occurrence (in one year) are very close.
Journal of Earthquake Engineering, 2010
Eurocode 8 Part 3 (EC8-3) is devoted to assessment and retrofitting of existing buildings. In ord... more Eurocode 8 Part 3 (EC8-3) is devoted to assessment and retrofitting of existing buildings. In order to take into account the uncertainty in the knowledge of structural properties, EC8-3 defines, analogously to the ordinary material partial factors, an adjustment factor, called “confidence factor (CF),” whose value depends on the level of knowledge (KL) of properties such as geometry, reinforcement layout and detailing, and materials. This solution is plausible from a logical point of view but it cannot yet profit from the experience of its use in practice, hence it needs to be substantiated by a higher level probabilistic analysis accounting for and propagating epistemic uncertainty (i.e., incomplete knowledge of a structure) throughout the seismic assessment procedure. This article investigates the soundness of the format proposed in EC8-3. The approach taken rests on the simulation of the entire assessment procedure and the evaluation of the distribution of the assessment results (distance from the limit state of interest) conditional on the acquired knowledge. Based on this distribution, a criterion is employed to calibrate the CF values. The obtained values are then critically examined and compared with code-specified ones. The results pinpoint a number of deficiencies that appear to somewhat invalidate the approach. The methodological significance of the work extends beyond the assessment procedure in EC8-3, since similar factors appear in other international guidelines (e.g., the knowledge factor of FEMA356).
Probabilistic Engineering Mechanics, 2002
The model correction factor method (MCFM) is used in conjunction with the first-order reliability... more The model correction factor method (MCFM) is used in conjunction with the first-order reliability method (FORM) to solve structural reliability problems involving integrals of non-Gaussian random fields. The approach replaces the limit-state function with an idealized one, in which the integrals are considered to be Gaussian. Conventional FORM analysis yields the linearization point of the idealized limit-state surface.
The model correction factor method (MCFM) is used in conjunction with the first-order reliability... more The model correction factor method (MCFM) is used in conjunction with the first-order reliability method (FORM) to solve structural reliability problems involving integrals of non-Gaussian random fields. The approach replaces the limit-state function with an idealized one, in which the integrals are considered to be Gaussian. Conventional FORM analysis yields the linearization point of the idealized limit-state surface. A model correction factor is then introduced to push the idealized limit-state surface onto the actual limit-state surface. A few iterations yield a good approximation of the reliability index for the original problem. This method has application to many civil engineering problems that involve random fields of material properties or loads. An application to reliability analysis of foundation piles illustrates the proposed method.
Thin-walled Structures, 2000
In this paper, the effect of the interaction between one overall buckling mode and many local mod... more In this paper, the effect of the interaction between one overall buckling mode and many local modes on the post-buckling behaviour of uniformly compressed corrugated sheets is analysed by means of the general theory of elastic stability. The analysis is restricted to third order terms of the energy expansion and, therefore, it can be fruitfully applied to the investigation of structures with asymmetric post-buckling behaviour only. Initial imperfection effect is taken into account. By using the finite strip method, an extensive parametric analysis is performed.
EC8-3, devoted to assessment/retrofitting of existing buildings, accounts for epistemic uncertain... more EC8-3, devoted to assessment/retrofitting of existing buildings, accounts for epistemic uncertainty with an adjustment factor, called "confidence factor (CF)", whose value depends on the knowledge of properties such as geometry, reinforcement layout and detailing, and materials. This solution, plausible from a logical point of view, cannot yet profit from the experience of use in practice, hence it needs to be substantiated by a higher level probabilistic analysis accounting for and propagating epistemic uncertainty (i.e., incomplete knowledge of a structure) throughout the seismic assessment procedure. The paper investigates the soundness of the proposed format and pinpoints some problematic aspects that would require refinement. The approach taken rests on the simulation of the entire assessment procedure and the evaluation the distribution of the assessment results conditional on the acquired knowledge. Based on this distribution a criterion is proposed to calibrate the CF values. The obtained values are then critically examined and compared with code-specified ones.
Increased Accuracy of Vector-IM-Based Seismic Risk Assessment
Journal of Earthquake Engineering, 2008
The vector-valued ground motion intensity measure (IM) consisting of spectral acceleration at two... more The vector-valued ground motion intensity measure (IM) consisting of spectral acceleration at two different periods is considered for seismic risk assessment of structures. The first component of the IM is the spectral acceleration at the first-mode structural period T 1. The second period is selected to increase efficiency in the estimation of seismic risk (i.e., minimizing dispersion). A method to assess vector structural fragility using a scalar global measure of structural performance is proposed. With reference to an example RC frame structure, the accuracy of prediction of the seismic risk using the considered vector IM vs. a conventional scalar IM is presented. In both cases, probabilistic seismic hazard analysis (scalar and vector) is carried out by means of a subset simulation approach that employs a stochastic model of ground motion. Results show that an effective choice of the second period T2 leads to an estimate of the seismic risk close to that obtained employing the scalar IM consisting of Sa(T1) only, while reducing the associated dispersion in the estimate. For the examined example structure, however, the reduction is negligible in light of the effort required for switching from a scalar to a vector IM.
SEISMIC LOSS ESTIMATION BY EFFICIENT SIMULATION
Journal of Earthquake Engineering, 2006
This paper presents a probabilistic method for seismic loss estimation. The method accounts for t... more This paper presents a probabilistic method for seismic loss estimation. The method accounts for the dependence of the structural response on the ground-motion and on the mechanical properties through an approximate response model based on a limited number of nonlinear structural analyses using recorded ground-motions. This response model is the key element in keeping affordable the procedure that uses simulation to compute the distribution of monetary loss. The main advantage of the formulation is that all sources of uncertainty and correlation among loss terms are accounted for. The procedure is illustrated by way of an application to an RC arch bridge. The application highlights the need for further research on models that describe states of increasing damage in terms of repair actions.
Journal of Earthquake Engineering, 2010
The last 15 years have seen fundamental advances in both the definition of the hazard and on the ... more The last 15 years have seen fundamental advances in both the definition of the hazard and on the criteria in codified seismic design, creating a situation whereby even relatively modern constructions may represent an unchecked risk. This article deals with a case of particular relevance, i.e., the seismic risk of bridges and viaducts on the Italian highway network. After a brief outline of the present state of the network, the article concentrates on the solutions adopted in the upgrading, for increasing both the traffic and the seismic capacities, through the illustration of two case studies. The second, main part of the article deals in more detail with one of the case studies, examining alternative design options and the corresponding analytical aspects. Finally, the opportunity is taken to investigate the relevance of two aspects not commonly taken into account in design practice, i.e., differential support motion and soil-structure interaction.
METHODS FOR SEISMIC RISK ANALYSIS: STATE OF THE ART VERSUS ADVANCED STATE OF THE PRACTICE
Journal of Earthquake Engineering, 2002
The core of the paper consists of the illustration of a method for seismic reliability analysis o... more The core of the paper consists of the illustration of a method for seismic reliability analysis of non-linear structures. The method, which is a development over a recent previous proposal, is quite comprehensive in scope since it includes consideration of randomness in the input, in the mechanical properties of the structure and in the limit-state, or capacity, conditions. Essentially, the problem is formulated as the out-crossing of the response process out of a (scalar) safe threshold, and this problem is solved by time-invariant FORM methods. An application to an idealised five-storey building demonstrates the salient theoretical and computational features of the method. The new approach is presented in a broader framework, which involves a discussion on present trends and capabilities in the area of probabilistic seismic design. For the sake of this discussion, two approaches just appeared in the literature are outlined, which are less demanding from a theoretical standpoint, and hence closer to engineering practice, but also less general in scope. It is argued that their introduction on code-assisted design would be feasible immediately with obvious advantages, while approaches of more rigorous nature would be given some more time to mature and to become more accessible to professional use.
the paper contains a few reflections stimulated by the experience of applying EC8 Part 3 to real ... more the paper contains a few reflections stimulated by the experience of applying EC8 Part 3 to real cases. Some of them are of more conceptual character, such as that on the definition and quantitative evaluation of a limit state for the structure, or that on the treatment of the uncertainty. Their intention is more to raise a discussion than to provide answers ready for application. Others deal with more applicative aspects for which an opinion is offered on possible concrete solutions, such as suitable extension of the codified non linear static analysis method and the verification of members under bidirectional loading.
The applicability of non-linear static analyses for the assessment of less-thanregular bridges ha... more The applicability of non-linear static analyses for the assessment of less-thanregular bridges has been subject of recent research by a number of authors ([11,13,14]), with mixed results. The study presented in the paper intends to provide a further example of application of the approach to a bridge whose characteristics are such as to test it in a rather extreme case. This is an existing important highway viaduct built in the sixties, of total length equal to 420m, with 11 spans of 33m each and a continuous RC deck pinned over the piers. These latter, whose height varies irregularly between 14m and 41m, consist of slender single-bay frames with intermediate transverse beams. Among the numerous proposals available, the multi-modal nonadaptive approach as proposed by Chopra et al. has been chosen as the preferred compromise between accuracy and complexity. The selected structure is characterised by at least two modes providing comparable contributions to the transversal response. In view of the final comparison of the results with those from non-linear dynamic analyses, the critical question of the choice of the reference response dof to be monitored has been investigated as well as the approximation of the method as a function of the intensity of the seismic action (inducing a variable degree of inelasticity in the structure).
SEISMIC FRAGILITY OF REINFORCED CONCRETE STRUCTURES USING A RESPONSE SURFACE APPROACH
Journal of Earthquake Engineering, 2003
A statistical approach for time-variant system-reliability problems has been developed and invest... more A statistical approach for time-variant system-reliability problems has been developed and investigated in this study. The basic proposal is to use a response surface, characterised by a statistical model of the mixed type, to represent the capacity part in an analytical limit state function. The fragility of the system is then calculated by SORM analysis, with the constructed empirical limit state function as input. The developed method has been applied to a reinforced concrete frame: investigations have been carried out to check the stability and accuracy of the suggested procedure.
Journal of Earthquake Engineering, 2009
A criterion is proposed for deciding whether, after a damaging mainshock, a bridge can still be o... more A criterion is proposed for deciding whether, after a damaging mainshock, a bridge can still be open for either emergency or ordinary traffic. The criterion is based on the comparison between the collapse risk of the mainshock-damaged structure and the pre-mainshock risk of the intact structure. The approach requires fragilities for multiple damage states for the intact structure, and transition probabilities from these states to collapse for the damaged structure. The aftershock risk decreases with time, hence a decision for reopening might have to wait until the risk level goes down to an acceptable value. A realistic application demonstrates the approach.
Seismic risk evaluation of RC bridge structures
Earthquake Engineering & Structural Dynamics, 2003
In this work a probabilistic methodology, recently developed by Cornell and co-workers for seismi... more In this work a probabilistic methodology, recently developed by Cornell and co-workers for seismic risk assessment of moment-resisting steel frames, is investigated for possible applications to RC bridge structures. The basic theory is first illustrated; it is characterized by a remarkably simple but accurate mathematical formulation and by a light computational effort to estimate the risk. A simple extension to account for uncertainties in the mechanical parameters is then proposed. The methodology is applied to an existing RC bridge. The study has confirmed the robustness of the methodology with respect to the simplifying assumptions on which it is based, in particular to the reduced number of accelerograms required for a stable and accurate estimate of risk, and demonstrates the applicability to the case of RC bridges. Copyright © 2003 John Wiley & Sons, Ltd.
The chapter presents an overview of recent research on the seismic assessment/retrofit and design... more The chapter presents an overview of recent research on the seismic assessment/retrofit and design of bridges, focussing on some of the aspects which are still not adequately covered in the codes. These are: The level of protection to be provided when upgrading an existing bridge, and in particular whether this should be differentiated between new designs and retrofit of existing bridges; The appropriate methods of analysis and modelling, with emphasis on the scope of nonlinear static methods and to the problems related to the selection of the input for dynamic analysis; Soil-foundation-structure interaction and non uniform support input, representing two controversial issues that may be mature for an inclusion in routine bridge analysis.
Seismic fragility analysis of 3D structures
Structural Safety, 2004
A statistical approach for time-variant system reliability problems is developed and investigated... more A statistical approach for time-variant system reliability problems is developed and investigated. The basic proposal is to use a response surface, characterised by a statistical model of the mixed type, to represent the capacity in an analytical limit-state function. The ...
Journal of Engineering Mechanics-asce, 2006
A method is presented for the evaluation of the seismic fragility function of realistic structura... more A method is presented for the evaluation of the seismic fragility function of realistic structural systems. The method is based on a preliminary, limited, simulation involving non linear dynamic analyses performed to establish the probabilistic characterization of the demands on the structure, followed by the solution of a system reliability problem with correlated demands and capacities. The results compare favorably well with the fragility obtained by plain Monte Carlo simulation, while the associated computational effort is orders of magnitude lower. The method is demonstrated with an application to a RC bridge structure subjected to both rigid and spatially varying excitation.
Earthquake Spectra, 2014
This study focuses on the evaluation of the seismic vulnerability of the Italian roadway bridge s... more This study focuses on the evaluation of the seismic vulnerability of the Italian roadway bridge stock, within the framework of a Civil Protection sponsored project. A comprehensive database of existing bridges (17,000 bridges with different level of knowledge) was implemented. At the core of the study stands a procedure for automatically carrying out state-of-the-art analytical evaluation of fragility curves for two performance levels—damage and collapse—on an individual bridge basis. A WebGIS was developed to handle data and results. The main outputs are maps of bridge seismic risk (from the fragilities and the hazard maps) at the national level and real-time scenario damage-probability maps (from the fragilities and the scenario shake maps). In the latter case, the WebGIS also performs network analysis to identify routes to be followed by rescue teams. Consistency of the fragility derivation over the entire bridge stock is regarded as a major advantage of the adopted approach.
Reliability of Uncertain Inelastic Structures under Earthquake Excitation
Journal of Engineering Mechanics-asce, 2004
The assessment of safety for structures subjected to earthquake excitation is a time-variant reli... more The assessment of safety for structures subjected to earthquake excitation is a time-variant reliability problem whose practical solution, when the structure behaves inelastically and uncertainty in the mechanical parameters is taken into account, is traditionally sought by ...
Earthquake Engineering & Structural Dynamics, 2007
A scalar damage measure (DM) for probabilistic performance assessment of structures can be expres... more A scalar damage measure (DM) for probabilistic performance assessment of structures can be expressed as the critical demand-to-capacity ratio corresponding to the component or mechanism that leads the structure closest to failure at the onset of which, the DM assumes the value of one. This DM can be employed to make probabilistic performance assessments taking into account the uncertainty in the ground motion, in the structural modelling parameters, and also in the model(s) used for determining components capacity. Nonlinear dynamic analysis methods can be used to estimate this DM in two ways: (a) applying a (small-size) set of un-scaled ground motion records to the structure and (b) using incremental dynamic analysis. Case (a) is suitable for making performance assessments based on demand and capacity factor design format and case (b) is suitable for estimating directly the probability of failure using numerical integration. Performance assessments using this DM are described in a case study of a RC frame in which the critical demand-to-capacity ratio is determined by taking into account various modes of failure for the limit state of collapse, such as weak storey mechanisms, shear failure in the columns, and ultimate deformations in the columns. For events with a very small probability of occurrence-such as strong earthquakes-the numerical values of (mean) annual frequency of occurrence and of the probability of occurrence (in one year) are very close.
Journal of Earthquake Engineering, 2010
Eurocode 8 Part 3 (EC8-3) is devoted to assessment and retrofitting of existing buildings. In ord... more Eurocode 8 Part 3 (EC8-3) is devoted to assessment and retrofitting of existing buildings. In order to take into account the uncertainty in the knowledge of structural properties, EC8-3 defines, analogously to the ordinary material partial factors, an adjustment factor, called “confidence factor (CF),” whose value depends on the level of knowledge (KL) of properties such as geometry, reinforcement layout and detailing, and materials. This solution is plausible from a logical point of view but it cannot yet profit from the experience of its use in practice, hence it needs to be substantiated by a higher level probabilistic analysis accounting for and propagating epistemic uncertainty (i.e., incomplete knowledge of a structure) throughout the seismic assessment procedure. This article investigates the soundness of the format proposed in EC8-3. The approach taken rests on the simulation of the entire assessment procedure and the evaluation of the distribution of the assessment results (distance from the limit state of interest) conditional on the acquired knowledge. Based on this distribution, a criterion is employed to calibrate the CF values. The obtained values are then critically examined and compared with code-specified ones. The results pinpoint a number of deficiencies that appear to somewhat invalidate the approach. The methodological significance of the work extends beyond the assessment procedure in EC8-3, since similar factors appear in other international guidelines (e.g., the knowledge factor of FEMA356).
Probabilistic Engineering Mechanics, 2002
The model correction factor method (MCFM) is used in conjunction with the first-order reliability... more The model correction factor method (MCFM) is used in conjunction with the first-order reliability method (FORM) to solve structural reliability problems involving integrals of non-Gaussian random fields. The approach replaces the limit-state function with an idealized one, in which the integrals are considered to be Gaussian. Conventional FORM analysis yields the linearization point of the idealized limit-state surface.
The model correction factor method (MCFM) is used in conjunction with the first-order reliability... more The model correction factor method (MCFM) is used in conjunction with the first-order reliability method (FORM) to solve structural reliability problems involving integrals of non-Gaussian random fields. The approach replaces the limit-state function with an idealized one, in which the integrals are considered to be Gaussian. Conventional FORM analysis yields the linearization point of the idealized limit-state surface. A model correction factor is then introduced to push the idealized limit-state surface onto the actual limit-state surface. A few iterations yield a good approximation of the reliability index for the original problem. This method has application to many civil engineering problems that involve random fields of material properties or loads. An application to reliability analysis of foundation piles illustrates the proposed method.
Thin-walled Structures, 2000
In this paper, the effect of the interaction between one overall buckling mode and many local mod... more In this paper, the effect of the interaction between one overall buckling mode and many local modes on the post-buckling behaviour of uniformly compressed corrugated sheets is analysed by means of the general theory of elastic stability. The analysis is restricted to third order terms of the energy expansion and, therefore, it can be fruitfully applied to the investigation of structures with asymmetric post-buckling behaviour only. Initial imperfection effect is taken into account. By using the finite strip method, an extensive parametric analysis is performed.
EC8-3, devoted to assessment/retrofitting of existing buildings, accounts for epistemic uncertain... more EC8-3, devoted to assessment/retrofitting of existing buildings, accounts for epistemic uncertainty with an adjustment factor, called "confidence factor (CF)", whose value depends on the knowledge of properties such as geometry, reinforcement layout and detailing, and materials. This solution, plausible from a logical point of view, cannot yet profit from the experience of use in practice, hence it needs to be substantiated by a higher level probabilistic analysis accounting for and propagating epistemic uncertainty (i.e., incomplete knowledge of a structure) throughout the seismic assessment procedure. The paper investigates the soundness of the proposed format and pinpoints some problematic aspects that would require refinement. The approach taken rests on the simulation of the entire assessment procedure and the evaluation the distribution of the assessment results conditional on the acquired knowledge. Based on this distribution a criterion is proposed to calibrate the CF values. The obtained values are then critically examined and compared with code-specified ones.
Increased Accuracy of Vector-IM-Based Seismic Risk Assessment
Journal of Earthquake Engineering, 2008
The vector-valued ground motion intensity measure (IM) consisting of spectral acceleration at two... more The vector-valued ground motion intensity measure (IM) consisting of spectral acceleration at two different periods is considered for seismic risk assessment of structures. The first component of the IM is the spectral acceleration at the first-mode structural period T 1. The second period is selected to increase efficiency in the estimation of seismic risk (i.e., minimizing dispersion). A method to assess vector structural fragility using a scalar global measure of structural performance is proposed. With reference to an example RC frame structure, the accuracy of prediction of the seismic risk using the considered vector IM vs. a conventional scalar IM is presented. In both cases, probabilistic seismic hazard analysis (scalar and vector) is carried out by means of a subset simulation approach that employs a stochastic model of ground motion. Results show that an effective choice of the second period T2 leads to an estimate of the seismic risk close to that obtained employing the scalar IM consisting of Sa(T1) only, while reducing the associated dispersion in the estimate. For the examined example structure, however, the reduction is negligible in light of the effort required for switching from a scalar to a vector IM.
SEISMIC LOSS ESTIMATION BY EFFICIENT SIMULATION
Journal of Earthquake Engineering, 2006
This paper presents a probabilistic method for seismic loss estimation. The method accounts for t... more This paper presents a probabilistic method for seismic loss estimation. The method accounts for the dependence of the structural response on the ground-motion and on the mechanical properties through an approximate response model based on a limited number of nonlinear structural analyses using recorded ground-motions. This response model is the key element in keeping affordable the procedure that uses simulation to compute the distribution of monetary loss. The main advantage of the formulation is that all sources of uncertainty and correlation among loss terms are accounted for. The procedure is illustrated by way of an application to an RC arch bridge. The application highlights the need for further research on models that describe states of increasing damage in terms of repair actions.
Journal of Earthquake Engineering, 2010
The last 15 years have seen fundamental advances in both the definition of the hazard and on the ... more The last 15 years have seen fundamental advances in both the definition of the hazard and on the criteria in codified seismic design, creating a situation whereby even relatively modern constructions may represent an unchecked risk. This article deals with a case of particular relevance, i.e., the seismic risk of bridges and viaducts on the Italian highway network. After a brief outline of the present state of the network, the article concentrates on the solutions adopted in the upgrading, for increasing both the traffic and the seismic capacities, through the illustration of two case studies. The second, main part of the article deals in more detail with one of the case studies, examining alternative design options and the corresponding analytical aspects. Finally, the opportunity is taken to investigate the relevance of two aspects not commonly taken into account in design practice, i.e., differential support motion and soil-structure interaction.
METHODS FOR SEISMIC RISK ANALYSIS: STATE OF THE ART VERSUS ADVANCED STATE OF THE PRACTICE
Journal of Earthquake Engineering, 2002
The core of the paper consists of the illustration of a method for seismic reliability analysis o... more The core of the paper consists of the illustration of a method for seismic reliability analysis of non-linear structures. The method, which is a development over a recent previous proposal, is quite comprehensive in scope since it includes consideration of randomness in the input, in the mechanical properties of the structure and in the limit-state, or capacity, conditions. Essentially, the problem is formulated as the out-crossing of the response process out of a (scalar) safe threshold, and this problem is solved by time-invariant FORM methods. An application to an idealised five-storey building demonstrates the salient theoretical and computational features of the method. The new approach is presented in a broader framework, which involves a discussion on present trends and capabilities in the area of probabilistic seismic design. For the sake of this discussion, two approaches just appeared in the literature are outlined, which are less demanding from a theoretical standpoint, and hence closer to engineering practice, but also less general in scope. It is argued that their introduction on code-assisted design would be feasible immediately with obvious advantages, while approaches of more rigorous nature would be given some more time to mature and to become more accessible to professional use.
the paper contains a few reflections stimulated by the experience of applying EC8 Part 3 to real ... more the paper contains a few reflections stimulated by the experience of applying EC8 Part 3 to real cases. Some of them are of more conceptual character, such as that on the definition and quantitative evaluation of a limit state for the structure, or that on the treatment of the uncertainty. Their intention is more to raise a discussion than to provide answers ready for application. Others deal with more applicative aspects for which an opinion is offered on possible concrete solutions, such as suitable extension of the codified non linear static analysis method and the verification of members under bidirectional loading.
The applicability of non-linear static analyses for the assessment of less-thanregular bridges ha... more The applicability of non-linear static analyses for the assessment of less-thanregular bridges has been subject of recent research by a number of authors ([11,13,14]), with mixed results. The study presented in the paper intends to provide a further example of application of the approach to a bridge whose characteristics are such as to test it in a rather extreme case. This is an existing important highway viaduct built in the sixties, of total length equal to 420m, with 11 spans of 33m each and a continuous RC deck pinned over the piers. These latter, whose height varies irregularly between 14m and 41m, consist of slender single-bay frames with intermediate transverse beams. Among the numerous proposals available, the multi-modal nonadaptive approach as proposed by Chopra et al. has been chosen as the preferred compromise between accuracy and complexity. The selected structure is characterised by at least two modes providing comparable contributions to the transversal response. In view of the final comparison of the results with those from non-linear dynamic analyses, the critical question of the choice of the reference response dof to be monitored has been investigated as well as the approximation of the method as a function of the intensity of the seismic action (inducing a variable degree of inelasticity in the structure).
SEISMIC FRAGILITY OF REINFORCED CONCRETE STRUCTURES USING A RESPONSE SURFACE APPROACH
Journal of Earthquake Engineering, 2003
A statistical approach for time-variant system-reliability problems has been developed and invest... more A statistical approach for time-variant system-reliability problems has been developed and investigated in this study. The basic proposal is to use a response surface, characterised by a statistical model of the mixed type, to represent the capacity part in an analytical limit state function. The fragility of the system is then calculated by SORM analysis, with the constructed empirical limit state function as input. The developed method has been applied to a reinforced concrete frame: investigations have been carried out to check the stability and accuracy of the suggested procedure.
Journal of Earthquake Engineering, 2009
A criterion is proposed for deciding whether, after a damaging mainshock, a bridge can still be o... more A criterion is proposed for deciding whether, after a damaging mainshock, a bridge can still be open for either emergency or ordinary traffic. The criterion is based on the comparison between the collapse risk of the mainshock-damaged structure and the pre-mainshock risk of the intact structure. The approach requires fragilities for multiple damage states for the intact structure, and transition probabilities from these states to collapse for the damaged structure. The aftershock risk decreases with time, hence a decision for reopening might have to wait until the risk level goes down to an acceptable value. A realistic application demonstrates the approach.
Seismic risk evaluation of RC bridge structures
Earthquake Engineering & Structural Dynamics, 2003
In this work a probabilistic methodology, recently developed by Cornell and co-workers for seismi... more In this work a probabilistic methodology, recently developed by Cornell and co-workers for seismic risk assessment of moment-resisting steel frames, is investigated for possible applications to RC bridge structures. The basic theory is first illustrated; it is characterized by a remarkably simple but accurate mathematical formulation and by a light computational effort to estimate the risk. A simple extension to account for uncertainties in the mechanical parameters is then proposed. The methodology is applied to an existing RC bridge. The study has confirmed the robustness of the methodology with respect to the simplifying assumptions on which it is based, in particular to the reduced number of accelerograms required for a stable and accurate estimate of risk, and demonstrates the applicability to the case of RC bridges. Copyright © 2003 John Wiley & Sons, Ltd.
The chapter presents an overview of recent research on the seismic assessment/retrofit and design... more The chapter presents an overview of recent research on the seismic assessment/retrofit and design of bridges, focussing on some of the aspects which are still not adequately covered in the codes. These are: The level of protection to be provided when upgrading an existing bridge, and in particular whether this should be differentiated between new designs and retrofit of existing bridges; The appropriate methods of analysis and modelling, with emphasis on the scope of nonlinear static methods and to the problems related to the selection of the input for dynamic analysis; Soil-foundation-structure interaction and non uniform support input, representing two controversial issues that may be mature for an inclusion in routine bridge analysis.
Seismic fragility analysis of 3D structures
Structural Safety, 2004
A statistical approach for time-variant system reliability problems is developed and investigated... more A statistical approach for time-variant system reliability problems is developed and investigated. The basic proposal is to use a response surface, characterised by a statistical model of the mixed type, to represent the capacity in an analytical limit-state function. The ...
Journal of Engineering Mechanics-asce, 2006
A method is presented for the evaluation of the seismic fragility function of realistic structura... more A method is presented for the evaluation of the seismic fragility function of realistic structural systems. The method is based on a preliminary, limited, simulation involving non linear dynamic analyses performed to establish the probabilistic characterization of the demands on the structure, followed by the solution of a system reliability problem with correlated demands and capacities. The results compare favorably well with the fragility obtained by plain Monte Carlo simulation, while the associated computational effort is orders of magnitude lower. The method is demonstrated with an application to a RC bridge structure subjected to both rigid and spatially varying excitation.