Pub Date : 2025-09-16DOI: 10.1016/j.strusafe.2025.102649
Jinheng Song , Jie Li
Poisson white noise is frequently occurring in various engineering applications. Consequently, solving the stochastic dynamic response of structures subjected to Poisson white noise excitation constitutes a crucial research challenge. In this paper, using the Kolmogorov–Feller (KF) and reduced-dimensional KF (RDKF) equations, a highly efficient numerical approach is proposed for determining the probability distribution of the response. The process begins by generating Poisson white noise using stochastic harmonic function and subsequently computing the dynamic response of the structure. The cell renormalized method is then employed to compute the derivate moments at the centers of each cell. Following this, Gaussian Process Regression (GPR) is utilized to model the continuous derivate moments curve or surface within the state space. Finally, the path integral solution is applied to solve the KF and RDKF equations, ultimately yielding the desired probability distribution of the structural response. To highlight the advantages of the proposed methodology, a series of numerical examples, including one and two dimensional scenarios, linear and nonlinear systems, are all employed to substantiate the applicability of proposed method.
{"title":"The cell renormalized method for the solution of KF equation and RDKF equation under additive Poisson white noise","authors":"Jinheng Song , Jie Li","doi":"10.1016/j.strusafe.2025.102649","DOIUrl":"10.1016/j.strusafe.2025.102649","url":null,"abstract":"<div><div>Poisson white noise is frequently occurring in various engineering applications. Consequently, solving the stochastic dynamic response of structures subjected to Poisson white noise excitation constitutes a crucial research challenge. In this paper, using the Kolmogorov–Feller (KF) and reduced-dimensional KF (RDKF) equations, a highly efficient numerical approach is proposed for determining the probability distribution of the response. The process begins by generating Poisson white noise using stochastic harmonic function and subsequently computing the dynamic response of the structure. The cell renormalized method is then employed to compute the derivate moments at the centers of each cell. Following this, Gaussian Process Regression (GPR) is utilized to model the continuous derivate moments curve or surface within the state space. Finally, the path integral solution is applied to solve the KF and RDKF equations, ultimately yielding the desired probability distribution of the structural response. To highlight the advantages of the proposed methodology, a series of numerical examples, including one and two dimensional scenarios, linear and nonlinear systems, are all employed to substantiate the applicability of proposed method.</div></div>","PeriodicalId":21978,"journal":{"name":"Structural Safety","volume":"118 ","pages":"Article 102649"},"PeriodicalIF":6.3,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145105331","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-15DOI: 10.1016/j.strusafe.2025.102654
Filippo Molaioni , Charalampos P. Andriotis , Zila Rinaldi
Reinforced concrete bridges are predominant structural systems in transportation infrastructure. Their exposure to chronic and sudden stressors, such as corrosion and earthquakes, make them prone to risks with severe socioeconomic consequences. While time-dependent single-component seismic fragility formulations have advanced the frontier of life-cycle probabilistic risk assessment, state-dependent multi-component representations of damage and deterioration, paramount for structural integrity management, still lack a systematic probabilistic framework. This paper develops a novel dynamic Bayesian network to evaluate the life-cycle fragility functions of aging bridges, encapsulating the impacts of corrosion and seismic phenomena over time. The network establishes Markovian transitions among deterioration states for various bridge components integrating chloride diffusion and corrosion propagation models with non-stationary Gamma processes. A methodology for deriving and state-dependent fragility at the component and system levels depending on several deterioration scenarios is presented. Our framework is exemplified in an archetypical 4-span bridge, demonstrating the longitudinal effects of corrosion on the system’s seismic fragility for splash and atmospheric conditions. Insights from the multi-component analysis highlight the capabilities in understanding the pathologies and evolving mechanical interactions among components. The adaptability in accommodating on-site observations and advanced decision-making algorithms is discussed, demonstrating the suitability of the framework for applications requiring flexible and updatable virtual environments.
{"title":"Life-cycle fragility analysis of aging reinforced concrete bridges: A dynamic Bayesian network approach","authors":"Filippo Molaioni , Charalampos P. Andriotis , Zila Rinaldi","doi":"10.1016/j.strusafe.2025.102654","DOIUrl":"10.1016/j.strusafe.2025.102654","url":null,"abstract":"<div><div>Reinforced concrete bridges are predominant structural systems in transportation infrastructure. Their exposure to chronic and sudden stressors, such as corrosion and earthquakes, make them prone to risks with severe socioeconomic consequences. While time-dependent single-component seismic fragility formulations have advanced the frontier of life-cycle probabilistic risk assessment, state-dependent multi-component representations of damage and deterioration, paramount for structural integrity management, still lack a systematic probabilistic framework. This paper develops a novel dynamic Bayesian network to evaluate the life-cycle fragility functions of aging bridges, encapsulating the impacts of corrosion and seismic phenomena over time. The network establishes Markovian transitions among deterioration states for various bridge components integrating chloride diffusion and corrosion propagation models with non-stationary Gamma processes. A methodology for deriving and state-dependent fragility at the component and system levels depending on several deterioration scenarios is presented. Our framework is exemplified in an archetypical 4-span bridge, demonstrating the longitudinal effects of corrosion on the system’s seismic fragility for splash and atmospheric conditions. Insights from the multi-component analysis highlight the capabilities in understanding the pathologies and evolving mechanical interactions among components. The adaptability in accommodating on-site observations and advanced decision-making algorithms is discussed, demonstrating the suitability of the framework for applications requiring flexible and updatable virtual environments.</div></div>","PeriodicalId":21978,"journal":{"name":"Structural Safety","volume":"119 ","pages":"Article 102654"},"PeriodicalIF":6.3,"publicationDate":"2025-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145467586","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-08DOI: 10.1016/j.strusafe.2025.102650
Sushreyo Misra, Paolo Bocchini
Extreme events such as earthquakes and hurricanes cause widespread damage and disruption to infrastructure assets such as buildings and bridges. Catastrophe modeling and accurate extreme event risk and resilience assessment require portfolio-level fragility functions of these assets, which involve the establishment of functional relationships between a relevant peak response quantity, also known as the engineering demand parameter (EDP), and select features characterizing the hazard. Given the computational demands of analyzing several statistical combinations of hazard and structural features, while running nonlinear time history analyses for each combination, surrogate demand models relating peak EDP to relevant intensity measures (IMs) of the input time history are popular. Although traditional IMs such as peak accelerations and velocities, average velocities, and peak spectral accelerations determined a priori have been traditionally found to be effective predictors of response and damage, their use in surrogate models in fragility model development introduces additional model uncertainties. In a bid to enable more robust and accurate surrogate modeling, we propose MetaIMNet; a physics-informed framework based on a neural network that simultaneously extracts key features from the time history of the load and leverages these features for structure specific response prediction. The framework is illustrated through a case study which shows that it outperforms traditional surrogate modeling strategies at a nominal added computational cost associated with model training, and can be used as an effective surrogate model for developing fragility functions for a wide range of hazards and structures.
{"title":"MetaIMNet: A physics-informed neural network architecture for surrogate response and fragility modeling of structures subjected to time-varying hazard loads","authors":"Sushreyo Misra, Paolo Bocchini","doi":"10.1016/j.strusafe.2025.102650","DOIUrl":"10.1016/j.strusafe.2025.102650","url":null,"abstract":"<div><div>Extreme events such as earthquakes and hurricanes cause widespread damage and disruption to infrastructure assets such as buildings and bridges. Catastrophe modeling and accurate extreme event risk and resilience assessment require portfolio-level fragility functions of these assets, which involve the establishment of functional relationships between a relevant peak response quantity, also known as the engineering demand parameter (EDP), and select features characterizing the hazard. Given the computational demands of analyzing several statistical combinations of hazard and structural features, while running nonlinear time history analyses for each combination, surrogate demand models relating peak EDP to relevant intensity measures (IMs) of the input time history are popular. Although traditional IMs such as peak accelerations and velocities, average velocities, and peak spectral accelerations determined <em>a priori</em> have been traditionally found to be effective predictors of response and damage, their use in surrogate models in fragility model development introduces additional model uncertainties. In a bid to enable more robust and accurate surrogate modeling, we propose MetaIMNet; a physics-informed framework based on a neural network that simultaneously extracts key features from the time history of the load and leverages these features for structure specific response prediction. The framework is illustrated through a case study which shows that it outperforms traditional surrogate modeling strategies at a nominal added computational cost associated with model training, and can be used as an effective surrogate model for developing fragility functions for a wide range of hazards and structures.</div></div>","PeriodicalId":21978,"journal":{"name":"Structural Safety","volume":"118 ","pages":"Article 102650"},"PeriodicalIF":6.3,"publicationDate":"2025-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145045448","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-08DOI: 10.1016/j.strusafe.2025.102651
Xiaowei Wang , Dang Yang , Aijun Ye
Highway bridges are critical lifelines vulnerable to seismic hazards, yet balancing computational efficiency and modeling fidelity in their resilience assessment remains a persistent challenge. This study develops a machine learning (ML)-aided framework integrating three multi-fidelity methods—deterministic (DT), partially probabilistic (PP), and fully probabilistic (FP)—to enable rapid seismic resilience quantification for highway bridges. Four ML algorithms are rigorously optimized and compared, with Random Forests emerging as the most effective for predicting engineering demand parameters (EDPs) such as column drift ratios, bearing displacements, and joint movements. The Random Forests-based surrogate models, publicly shared via Zenodo, significantly reduce computational costs while maintaining accuracy. A case study reveals that DT methods, while computationally lean, underestimate restoration time particularly under strong excitations due to the neglection of uncertainties in structural damage evaluation and restoration model parameters. The FP method integrates uncertainties in damage and restoration, achieving the highest fidelity but with computational costs and technical requirements. The PP method balances accuracy and efficiency by probabilistically evaluating damage while using deterministic restoration models. The hierarchical DT-PP-FP approach provides practitioners with adaptable tools for diverse precision, data availability, and resource constraints, advancing seismic resilience assessment of bridges through ML-driven efficiency and probabilistic rigor.
{"title":"Machine learning-aided deterministic, partially probabilistic, and fully probabilistic seismic resilience assessment methods for highway bridges","authors":"Xiaowei Wang , Dang Yang , Aijun Ye","doi":"10.1016/j.strusafe.2025.102651","DOIUrl":"10.1016/j.strusafe.2025.102651","url":null,"abstract":"<div><div>Highway bridges are critical lifelines vulnerable to seismic hazards, yet balancing computational efficiency and modeling fidelity in their resilience assessment remains a persistent challenge. This study develops a machine learning (ML)-aided framework integrating three multi-fidelity methods—deterministic (DT), partially probabilistic (PP), and fully probabilistic (FP)—to enable rapid seismic resilience quantification for highway bridges. Four ML algorithms are rigorously optimized and compared, with Random Forests emerging as the most effective for predicting engineering demand parameters (EDPs) such as column drift ratios, bearing displacements, and joint movements. The Random Forests-based surrogate models, publicly shared via Zenodo, significantly reduce computational costs while maintaining accuracy. A case study reveals that DT methods, while computationally lean, underestimate restoration time particularly under strong excitations due to the neglection of uncertainties in structural damage evaluation and restoration model parameters. The FP method integrates uncertainties in damage and restoration, achieving the highest fidelity but with computational costs and technical requirements. The PP method balances accuracy and efficiency by probabilistically evaluating damage while using deterministic restoration models. The hierarchical DT-PP-FP approach provides practitioners with adaptable tools for diverse precision, data availability, and resource constraints, advancing seismic resilience assessment of bridges through ML-driven efficiency and probabilistic rigor.</div></div>","PeriodicalId":21978,"journal":{"name":"Structural Safety","volume":"118 ","pages":"Article 102651"},"PeriodicalIF":6.3,"publicationDate":"2025-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145045449","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-08-28DOI: 10.1016/j.strusafe.2025.102648
Yu Leng , Chao-Huang Cai , Zhao-Hui Lu
Failure probability of a structure is dominated by the importance domain whose extent is much smaller than the whole random variable space. Once the importance domain is identified, the failure probability can be evaluated efficiently through compressing the sampling space into the importance domain. Recently, ring simulation has attempted to identify the importance interval in one dimension (i.e., the radius). To obtain a complete importance domain in all dimensions, a new simulation method, called “partial ring simulation”, is proposed for the efficient estimation of the failure probability. In the proposed method, the importance domain, consisting of importance radius and importance direction, is adaptively identified by a stepwise strategy utilizing the information from prior steps. For generating samples located in the importance domain, a Markov chain Monte Carlo sampling is then constructed. The effectiveness of the proposed method is validated by four examples involving parallel, series, and nonlinear limit state functions, small failure probabilities, and high-dimensional problems. The results indicate that the proposed method greatly improves the computational efficiency of ring simulation.
{"title":"Partial ring simulation: An efficient method identifying importance domain for structural reliability analysis","authors":"Yu Leng , Chao-Huang Cai , Zhao-Hui Lu","doi":"10.1016/j.strusafe.2025.102648","DOIUrl":"10.1016/j.strusafe.2025.102648","url":null,"abstract":"<div><div>Failure probability of a structure is dominated by the importance domain whose extent is much smaller than the whole random variable space. Once the importance domain is identified, the failure probability can be evaluated efficiently through compressing the sampling space into the importance domain. Recently, ring simulation has attempted to identify the importance interval in one dimension (i.e., the radius). To obtain a complete importance domain in all dimensions, a new simulation method, called “partial ring simulation”, is proposed for the efficient estimation of the failure probability. In the proposed method, the importance domain, consisting of importance radius and importance direction, is adaptively identified by a stepwise strategy utilizing the information from prior steps. For generating samples located in the importance domain, a Markov chain Monte Carlo sampling is then constructed. The effectiveness of the proposed method is validated by four examples involving parallel, series, and nonlinear limit state functions, small failure probabilities, and high-dimensional problems. The results indicate that the proposed method greatly improves the computational efficiency of ring simulation.</div></div>","PeriodicalId":21978,"journal":{"name":"Structural Safety","volume":"118 ","pages":"Article 102648"},"PeriodicalIF":6.3,"publicationDate":"2025-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145045447","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-08-19DOI: 10.1016/j.strusafe.2025.102647
Si-Qi Li, Lin-Lin Zheng
The impact of the mainshock earthquake on the regional building cluster is significant, directly causing varying degrees of damage to many houses. A large amount of onsite seismic loss observation data indicate that aftershocks after the main earthquake also impact the damage to and vulnerability of regional buildings. To study the seismic fragility and risk of typical building clusters under mainshock-aftershock sequences, this paper innovatively proposes a structural seismic fragility model that considers the intensity measures of the mainshock-aftershock by combining total probability and Bayesian theory. A computational intensity model has been developed that considers the directionality of ground motion under mainshock-aftershock sequences. The established model was verified and analyzed on the basis of 384,882 accelerations monitored by nine strong motion stations during the Jiuzhaigou earthquake on August 8, 2017, in China. The calculated intensity point cloud and stripe models were generated on the basis of the directional effect of ground motion. Using the Chinese earthquake intensity scale and the proposed computational intensity model, the fragility of three types of building clusters (1212 buildings) affected by the Jiuzhaigou earthquake was estimated, and a structural failure probability model considering mainshock-aftershock sequences was established. A seismic fragility curve of a building cluster considering the influence of mainshock-aftershock sequences was plotted via the Gaussian process, least squares regression algorithm, and data-driven techniques. An innovative structural fragility correlation surface was generated to analyze the correlation characteristics between different fragility levels under the influence of mainshock-aftershock sequences. The traditional earthquake damage index method has been improved, and a structural fragility index function considering the impact of mainshock-aftershocks has been proposed.
{"title":"Seismic fragility analysis of building clusters considering the effects of mainshock-aftershock sequences","authors":"Si-Qi Li, Lin-Lin Zheng","doi":"10.1016/j.strusafe.2025.102647","DOIUrl":"10.1016/j.strusafe.2025.102647","url":null,"abstract":"<div><div>The impact of the mainshock earthquake on the regional building cluster is significant, directly causing varying degrees of damage to many houses. A large amount of onsite seismic loss observation data indicate that aftershocks after the main earthquake also impact the damage to and vulnerability of regional buildings. To study the seismic fragility and risk of typical building clusters under mainshock-aftershock sequences, this paper innovatively proposes a structural seismic fragility model that considers the intensity measures of the mainshock-aftershock by combining total probability and Bayesian theory. A computational intensity model has been developed that considers the directionality of ground motion under mainshock-aftershock sequences. The established model was verified and analyzed on the basis of 384,882 accelerations monitored by nine strong motion stations during the Jiuzhaigou earthquake on August 8, 2017, in China. The calculated intensity point cloud and stripe models were generated on the basis of the directional effect of ground motion. Using the Chinese earthquake intensity scale and the proposed computational intensity model, the fragility of three types of building clusters (1212 buildings) affected by the Jiuzhaigou earthquake was estimated, and a structural failure probability model considering mainshock-aftershock sequences was established. A seismic fragility curve of a building cluster considering the influence of mainshock-aftershock sequences was plotted via the Gaussian process, least squares regression algorithm, and data-driven techniques. An innovative structural fragility correlation surface was generated to analyze the correlation characteristics between different fragility levels under the influence of mainshock-aftershock sequences. The traditional earthquake damage index method has been improved, and a structural fragility index function considering the impact of mainshock-aftershocks has been proposed.</div></div>","PeriodicalId":21978,"journal":{"name":"Structural Safety","volume":"118 ","pages":"Article 102647"},"PeriodicalIF":6.3,"publicationDate":"2025-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144880339","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-07-16DOI: 10.1016/j.strusafe.2025.102637
Zihang Liu , Genshen Fang , Nikolaos Nikitas , Yizhe Lan , Lin Zhao , Yaojun Ge
Most current bridge wind-resistant design standards adopt “uniform hazard” basis, ensuring the resistance exceeds design wind speed at a given return period. However, wind-induced failure probabilities for bridge structures, especially accounting for multi-level performances, are ambiguous, leading to significant differences in risk levels. To achieve the controllability and consistency in aerodynamic performances of long-span bridges, this study introduces the “uniform risk” into bridge wind engineering to determine the risk-targeted design wind speeds. Four performance objectives (occupant comfort, operational, continuous occupancy and instability), associated with the annual failure probability, are summarized. A case study is performed for Xihoumen Bridge by developing fragility curves corresponding to different vibration thresholds. Buffeting-related fragility curves are derived through a data-driven random model based on long-term measurements, while flutter fragility curve is obtained by Monte Carlo simulations incorporating various uncertainties. By combining with the wind hazard curves, failure probabilities for multi-level performances are estimated. Risk-targeted design wind speeds are calculated through the risk integral method, and the annual failure probabilities for code-recommended versus risk-targeted flutter design speeds are compared. Results indicate that Xihoumen Bridge has excessive wind resistance for the continuous occupancy and instability, while the annual failure risk for occupant comfort is relatively high. The code-recommended design wind speed falls short of ensuring multi-level performance objectives, whereas the risk-targeted design wind speeds effectively meet these criteria. This study provides a forward step in bridge wind engineering to develop the “uniform risk” design basis, serving the uptake of performance-based wind engineering design.
{"title":"Risk-targeted design wind speeds for multi-level aerodynamic performances of long-span bridges: A real data-informed case study","authors":"Zihang Liu , Genshen Fang , Nikolaos Nikitas , Yizhe Lan , Lin Zhao , Yaojun Ge","doi":"10.1016/j.strusafe.2025.102637","DOIUrl":"10.1016/j.strusafe.2025.102637","url":null,"abstract":"<div><div>Most current bridge wind-resistant design standards adopt “uniform hazard” basis, ensuring the resistance exceeds design wind speed at a given return period. However, wind-induced failure probabilities for bridge structures, especially accounting for multi-level performances, are ambiguous, leading to significant differences in risk levels. To achieve the controllability and consistency in aerodynamic performances of long-span bridges, this study introduces the “uniform risk” into bridge wind engineering to determine the risk-targeted design wind speeds. Four performance objectives (occupant comfort, operational, continuous occupancy and instability), associated with the annual failure probability, are summarized. A case study is performed for Xihoumen Bridge by developing fragility curves corresponding to different vibration thresholds. Buffeting-related fragility curves are derived through a data-driven random model based on long-term measurements, while flutter fragility curve is obtained by Monte Carlo simulations incorporating various uncertainties. By combining with the wind hazard curves, failure probabilities for multi-level performances are estimated. Risk-targeted design wind speeds are calculated through the risk integral method, and the annual failure probabilities for code-recommended versus risk-targeted flutter design speeds are compared. Results indicate that Xihoumen Bridge has excessive wind resistance for the continuous occupancy and instability, while the annual failure risk for occupant comfort is relatively high. The code-recommended design wind speed falls short of ensuring multi-level performance objectives, whereas the risk-targeted design wind speeds effectively meet these criteria. This study provides a forward step in bridge wind engineering to develop the “uniform risk” design basis, serving the uptake of performance-based wind engineering design.</div></div>","PeriodicalId":21978,"journal":{"name":"Structural Safety","volume":"117 ","pages":"Article 102637"},"PeriodicalIF":5.7,"publicationDate":"2025-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144654440","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-07-16DOI: 10.1016/j.strusafe.2025.102636
Bing Xia , Jianzhuang Xiao , Xiangshuo Guan
Probabilistic low-carbon structural design is an emerging method for mitigating structural embodied carbon, whereas the absence of a rational target for probabilistic regulation hindered its effectiveness. Here, we clarify the necessity of verifying the low-carbon conditional probability in low-carbon design of structures/structural members, and propose methods for determining acceptable and optimal low-carbon conditional probabilities (i.e., PLT,a and PLT,o), respectively based on the carbon mitigation obligation for construction sector and the carbon-related cost minimization for structures/structural members. Based on typical levels of parameter values for target determination, we reveal that PLT,a is primarily influenced by the distributions of structural embodied carbon premised on safety Is and its embodied carbon limit Icr,c, and it typically decreases with the decrease in the difference between the coefficients of variance of Is and Icr,c. The reduction of marginal cost for embodied carbon reduction (k), the increase of relative carbon cost (uc), and the increase of penalty for the excess of carbon emissions (γp) facilitate the attainment of the lowest carbon-related cost at lower embodied carbon levels, where a higher PLT,o could be specified to promote stricter carbon mitigation efforts. The target low-carbon conditional probability PLT is recommended to be taken as the larger of PLT,a and PLT,o, while the γp required to ensure that the lowest carbon-related cost is reached with PLT increases as k increases or uc decreases.
{"title":"Target low-carbon conditional probability for low-carbon structural design","authors":"Bing Xia , Jianzhuang Xiao , Xiangshuo Guan","doi":"10.1016/j.strusafe.2025.102636","DOIUrl":"10.1016/j.strusafe.2025.102636","url":null,"abstract":"<div><div>Probabilistic low-carbon structural design is an emerging method for mitigating structural embodied carbon, whereas the absence of a rational target for probabilistic regulation hindered its effectiveness. Here, we clarify the necessity of verifying the low-carbon conditional probability in low-carbon design of structures/structural members, and propose methods for determining acceptable and optimal low-carbon conditional probabilities (i.e., <em>P</em><sub>LT,a</sub> and <em>P</em><sub>LT,o</sub>), respectively based on the carbon mitigation obligation for construction sector and the carbon-related cost minimization for structures/structural members. Based on typical levels of parameter values for target determination, we reveal that <em>P</em><sub>LT,a</sub> is primarily influenced by the distributions of structural embodied carbon premised on safety <em>I</em><sub>s</sub> and its embodied carbon limit <em>I</em><sub>cr,c</sub>, and it typically decreases with the decrease in the difference between the coefficients of variance of <em>I</em><sub>s</sub> and <em>I</em><sub>cr,c</sub>. The reduction of marginal cost for embodied carbon reduction (<em>k</em>), the increase of relative carbon cost (<em>u</em><sub>c</sub>), and the increase of penalty for the excess of carbon emissions (<em>γ</em><sub>p</sub>) facilitate the attainment of the lowest carbon-related cost at lower embodied carbon levels, where a higher <em>P</em><sub>LT,o</sub> could be specified to promote stricter carbon mitigation efforts. The target low-carbon conditional probability <em>P</em><sub>LT</sub> is recommended to be taken as the larger of <em>P</em><sub>LT,a</sub> and <em>P</em><sub>LT,o</sub>, while the <em>γ</em><sub>p</sub> required to ensure that the lowest carbon-related cost is reached with <em>P</em><sub>LT</sub> increases as <em>k</em> increases or <em>u</em><sub>c</sub> decreases.</div></div>","PeriodicalId":21978,"journal":{"name":"Structural Safety","volume":"117 ","pages":"Article 102636"},"PeriodicalIF":5.7,"publicationDate":"2025-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144687435","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-07-14DOI: 10.1016/j.strusafe.2025.102635
Yazhou Xie
Seismic fragility modeling of bridges has evolved from simplified system-level assessments to high-fidelity, component-based methodologies. However, a key challenge remains in accurately incorporating damage dependency among bridge components, which might influence high-resolution seismic risk estimates that rely upon damage simulations of each bridge component. While previous studies have explored demand and capacity correlations in various structures, a comprehensive framework integrating these dependencies within the component-based bridge fragility modeling approach remains absent. This study addresses this gap by introducing a refined methodology for modeling seismic damage correlations across bridge components and damage states. A correlation-based fragility modeling framework is proposed, leveraging joint probabilistic seismic demand models and a hierarchical capacity correlation structure. The framework is systematically compared against other correlation models, including fully independent, fully correlated, and partially correlated approaches. Using a four-span, multi-column reinforced concrete bridge as a benchmark, the influence of correlation modeling on key seismic risk metrics, such as bridge collapse fragility, repair costs, and recovery durations, is assessed. Results demonstrate that neglecting damage correlation, or treating it perfectly correlated, sometimes would lead to significant biases in risk estimations. The proposed framework provides a practical extension of the existing component-level seismic fragility modeling approach for seamlessly integrating correlation effects, improving its effectiveness and applicability for downstream risk and resilience assessment of bridge systems.
{"title":"Impact of component damage correlations on seismic fragility and risk assessment of multi-component bridge systems","authors":"Yazhou Xie","doi":"10.1016/j.strusafe.2025.102635","DOIUrl":"10.1016/j.strusafe.2025.102635","url":null,"abstract":"<div><div>Seismic fragility modeling of bridges has evolved from simplified system-level assessments to high-fidelity, component-based methodologies. However, a key challenge remains in accurately incorporating damage dependency among bridge components, which might influence high-resolution seismic risk estimates that rely upon damage simulations of each bridge component. While previous studies have explored demand and capacity correlations in various structures, a comprehensive framework integrating these dependencies within the component-based bridge fragility modeling approach remains absent. This study addresses this gap by introducing a refined methodology for modeling seismic damage correlations across bridge components and damage states. A correlation-based fragility modeling framework is proposed, leveraging joint probabilistic seismic demand models and a hierarchical capacity correlation structure. The framework is systematically compared against other correlation models, including fully independent, fully correlated, and partially correlated approaches. Using a four-span, multi-column reinforced concrete bridge as a benchmark, the influence of correlation modeling on key seismic risk metrics, such as bridge collapse fragility, repair costs, and recovery durations, is assessed. Results demonstrate that neglecting damage correlation, or treating it perfectly correlated, sometimes would lead to significant biases in risk estimations. The proposed framework provides a practical extension of the existing component-level seismic fragility modeling approach for seamlessly integrating correlation effects, improving its effectiveness and applicability for downstream risk and resilience assessment of bridge systems.</div></div>","PeriodicalId":21978,"journal":{"name":"Structural Safety","volume":"117 ","pages":"Article 102635"},"PeriodicalIF":5.7,"publicationDate":"2025-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144662089","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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