Dynamic Reliability Assessment of Aging Prestressed Concrete Bridges Under Stochastic Loads


The dynamic serviceability and safety reliability of aging prestressed concrete (PC) girder bridges are major concerns for civil engineers, because these structures face with time-variant increased traffic volumes and vehicle loads. Prestressed concrete bridges are widely used in modern infrastructure due to their enhanced load-carrying capacity and durability. However, their service performance is time-dependent, influenced by factors such as concrete shrinkage, creep, resistance degradation, and stochastic vehicle load flows. These factors contribute to sequential alterations of internal forces and deformations, ultimately affecting the dynamic reliability of the bridges. One of the main challenges in ensuring the longevity and safety of PC girder bridges is accurately predicting and mitigating the effects of concrete shrinkage and creep. These inherent characteristics of concrete induce additional deformations over time, leading to internal force redistribution and potential adverse consequences such as cracking of bridge decks and loss of prestress. These deformations are further compounded by non-stationary vehicle load flows, which can vary significantly and can be unpredictable over time. Another significant challenge is the degradation of structural resistance due to long-term exposure to environmental factors and increasing traffic loads. With more aging bridges, the materials’ properties may deteriorate, leading to a reduction in their load-carrying capacity. This degradation process, combined with the increasing weight and frequency of vehicle loads, poses a significant risk to the structural integrity and safety of the bridges. Therefore, there is an urgent need to develop more precise and reliable methods for assessing the serviceability and safety of aging PC girder bridges. Traditional analysis methods often overlook the coupling effects of concrete shrinkage, creep, and stochastic vehicle loads, resulting in less accurate predictions of bridge performance. By addressing these shortcomings, the researchers aim to provide a robust methodology that incorporates these critical factors, enabling a more comprehensive and accurate assessment of bridge reliability. To this end, new study published in Journal Structures by graduate student Heng Zhou, Associate Professor Xueping Fan, and Associate Professor Yuefei Liu from the School of Civil Engineering and Mechanics at Lanzhou University  developed a detailed load probability model that accounts for the stochastic nature of vehicle loads using motion measurement data and calculates the resulting internal forces and deformations due to shrinkage and creep and offered offers a comprehensive approach to assessing both the serviceability and load-carrying capacity limit states of PC girder bridges with the incorporation of Monte Carlo simulation and validation of the resistance degradation model.

The researchers began by developing a stochastic vehicle flow model to simulate the random traffic conditions experienced by PC girder bridges. This model incorporated various parameters such as vehicle type, weight, spacing, and speed, derived from Weigh-In-Motion (WIM) data. For instance, data collected from the Nanxi-Yangtze River Bridge was used to generate probability distributions for different vehicle types and their associated loads. The researchers employed a Gaussian Mixture Model (GMM) to accurately represent the multimodal distribution characteristics of axle loads. Afterward and by using the Monte Carlo method, they generated random traffic flows and analyzed the sequence of vehicle loads. This approach allowed them to model realistic traffic conditions and assess the impact on bridge responses. The authors found significant temporal variations in vehicle spacing and speed, which in turn influenced the dynamic response of the bridges. The new model provided a detailed understanding of how real traffic loads affect the internal forces and deformations of PC girder bridges over time.

To simulate the effects of these vehicle loads and calculate the coupled responses of vehicle-axle interactions, the researchers established a finite element model using ABAQUS software. They modeled a 40-meter span PC simply supported T-beam bridge, incorporating design parameters such as C50 concrete and reinforced girder web plates with prestressing tendons. The finite element model allowed for detailed analysis of how traffic loads induced internal forces and deformations in the bridge structure. Moreover, the team performed simulations to obtain the internal force responses and evaluate time-varying dynamic responses by using the stochastic vehicle load model to this finite element model and found that the bridge experienced significant deformations due to the combined effects of traffic loads, shrinkage, and creep. These deformations were particularly pronounced in the mid-span region of the bridge, where the bending moments were highest. They also conducted dynamic reliability analysis to assess the safety and serviceability of the bridge under the combined effects of shrinkage, creep, and stochastic vehicle loads. The authors’ results showed that while the deflection reliability remained high in the initial 40 years of service, it began to decline significantly as the effects of shrinkage and creep accumulated over time. This decline was especially noticeable when considering the increasing traffic loads, which exacerbated the deformations caused by shrinkage and creep. For the ultimate limit state, they considered the load-carrying capacity degradation due to factors such as steel bar corrosion and concrete carbonization. They represented the time-varying resistance degradation as a product of the initial resistance and a degradation function. Additionally, they combined the stochastic vehicle load model with the degradation function to conduct a time-varying reliability analysis using the first-passage probability method and found that the load-carrying capacity reliability of the bridge decreased significantly over the evaluation period, particularly when the deformation due to shrinkage and creep was considered. The reliability index dropped sharply after 50 years, highlighting the critical need for regular maintenance and risk assessments to ensure the long-term safety of aging bridges. In conclusion the study by Professor Xueping Fan and colleagues introduced comprehensive and robust methodology for assessing the dynamic reliability of PC girder bridges which can provide engineers with a detailed framework for assessing the long-term performance and maintenance needs of PC girder bridges. This enables more informed decisions regarding resource allocation for repairs and maintenance, ultimately extending the operational lifespan of bridges and ensuring safety. Moreover, the new methodology allows for more precise safety assessments because it considers the cumulative effects of shrinkage, creep, and stochastic vehicle loads which can result in better risk management and preventive measures, and reduces the likelihood of sudden bridge failures and associated risks to public safety. The authors’ new method can also inform the design of new bridges and the retrofitting of existing ones. Better understanding on how different factors influence bridge performance over time, engineers can design structures that are more resilient to long-term stresses and environmental conditions.

Dynamic Reliability Assessment of Aging Prestressed Concrete Bridges Under Stochastic Loads - Advances in Engineering

About the author

Mr. Heng Zhou is a research assistant and a postgraduate pursing the master’s degree from School of Civil Engineering and Mechanics at Lanzhou University, China. He held a B.S. in Civil Engineering from Southwest Jiaotong University in China in 2019. His research is focused on bridge reliability. He has published 7 journal papers, 4 of which were in SCI-index journals.

About the author

Dr. Xueping Fan is an Associate Professor of Disaster Prevention and Mitigation Engineering from School of Civil Engineering and Mechanics at Lanzhou University, China. He serves as the members of ASCE IALCCE and IABMAS. Xueping Fan held a B.S. in Civil Engineering from Shijiazhuang Railway Institute (Now renamed Shijiazhuang Tiedao University) in China in 2008; a M.S. in Structural Engineering from Harbin Institute of Technology in China in 2010 and Ph.D. in Engineering Mechanics from Harbin Institute of Technology in 2014. His research interests include Bridge monitoring data processing, Information fusion of bridge reliability prediction and assessment, Dynamic prediction and abnormal monitoring of bridge dynamic responses, Information fusion of building (group) resistance assessment under earthquake and Bridge optimization design theory. He has published 90+ journal/conference papers, more than 30 of which were in SCI-index journals. He is an Academic Editor of an international journal (Advances in Civil Engineering), a Youth editorial board member of Journal of Jilin University (Engineering and Technology Edition) and Reviewers of more than 50 peer-reviewed journals in the areas of civil engineering, engineering mechanics and artificial intelligence.

About the author

Dr. Yuefei Liu is an Associate Professor of Disaster Prevention and Mitigation Engineering from School of Civil Engineering and Mechanics at Lanzhou University, China. Yuefei Liu hold a B.S. in Applied Mathematics from Central South University in China in 2006; a M.S. in Fundamental Mathematics from Changsha University of Science & Technology in China in 2009 and Ph.D. in Engineering Mechanics from Harbin Institute of Technology in China in 2015. Her research interests include Numerical algorithm for structural dynamic differential equations, Bridge reliability, Bridge monitoring data processing, Bridge safety assessment and prognosis and Structural Seismic vulnerability and safety assessment. She is Reviewers of more than 30 peer-reviewed journals in the areas of Civil Engineering, Engineering Mechanics and Mathematics.


Heng Zhou, Xueping Fan, Yuefei Liu, Dynamic serviceability and safety reliability analysis of aging PC girder bridges with non-prestressed reinforcement considering concrete shrinkage, creep and stochastic vehicle load flows, Structures, Volume 64, 2024, 106515,

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