This paper summarizes the findings of the National Cooperative Research Program, NCHRP reports 458 and 776 that presented a procedure to calibrate system factors that account for the level of structural redundancy in typical highway bridge substructures under lateral loads. A proposed set of system factor equations are presented in a format suitable for inclusion in the American Association of State Highway and Transportation Officials (AASHTO) Load and Resistance Factor Design Bridge Design Specifications and the Manual for Bridge Evaluation. In a first step, the study proposes a set of empirical equations to estimate the lateral load carrying capacity of substructure systems. A comparison between the results of a nonlinear pushover analysis and the empirical equation showed an error of about 8.7%. In a second step, a reliability-based approach is used to calibrate system factors that account for the redundancy and ductility in bridge substructures. The proposed approach replaces the subjectively assigned load modifiers in the current AASHTO design equations with properly calibrated equations. The results show that a system factor equal to 0.74 would ensure that the system reliability of a substructure under seismic loads will be 0.50 higher than the reliability level implied in current member-focused design specifications.

Climate change may lead to regional increases in the frequencies and intensities of several types of environmental hazards raising the risk to infrastructure systems and their users. This paper reviews the fundamental principles behind structural code developments and their underlying assumptions. It also examines methods to assess the safety of structural systems accounting for the nonstationary nature of climatic hazards. Numerical examples illustrate the application of these approaches for the safety assessment and the design of riverine and coastal flood walls to mitigate the risk of future floods.

In recent years, several bridge failures have been observed around the world. These bridge failures are partially due to the lack of financial resources that forces owners to keep bridges in service under undesired circumstances. Given the importance that fatigue and overloading have been playing on bridge failures, the objective of this paper is to present an approach to assess the probability of failure of continuous highway steel bridge superstructures under the combined effect of fatigue damage and overloading. This objective is achieved by performing Monte Carlo simulations on a representative sample of medium length I-girder bridge configurations based on statistical data collected in North America. Damage location, permanent loads, truck gross weight, and axle configurations were assumed to be random variables. The probability of overloading events was modeled as a Poisson’s process. Accordingly, the probability of overloading events was found close to 10

A significant number of recent highway bridge failures have been attributed to the lack of financial resources that constrained owners to keep bridges in service under undesired circumstances. Given that many highway bridge failures were related to cyclic fatigue and overloaded trucks, or some combination thereof, the objective in this paper is to present an approach to assess the reliability of continuous highway steel I-multigirder bridge superstructures under the combined effects of fatigue damage and overloading. To that effect, Monte Carlo simulations were run for 42 short to medium-length steel I-multigirder bridges having configurations representative of bridges in North America. Fatigue damage locations, permanent loads, truck gross weights, and axle configurations were assumed to be random variables. The fatigue model used is consistent with the model implemented during calibration according to AASHTO's specifications for a 75-year design life. Simple equations were constructed to quantify the probability of bridge system collapse resulting from the combined effects of fatigue and overloading events for typical continuous steel I-multigirder bridge superstructures. Accordingly, the expected service life of bridges would reduce by about 7 years if the percentage of overweight trucks increases from the national average of 5.1% to 12.0%. The proposed model can eventually be implemented in bridge management systems to account for the effects of truck loads, complementing these systems' current focus on bridge condition ratings.

Standards for the design of bridges, buildings and other infrastructure specify design loads for climatic hazards such as temperature, snow, wind, and floods based on return periods presented in maps or tables that account for regional differences. These design loads were developed from statistical analyses of historical hazard data under the assumption that the past is representative of the future. Climate change may affect the frequencies and intensities of environmental hazards which, depending on regional variations, raises questions as to whether structures designed to current specifications will meet minimum safety standards over their future service lives. This paper critically appraises issues related to using historical hazard data for future designs. It reviews basic principles of uniform reliability, that modern design codes use as the basis for ensuring minimum levels of safety, describing the relationship between hazard return periods, structural reliability, risk and the maximum loads expected within a structure's service life. Simple examples involving wind effects on structures demonstrate how to calibrate structural design hazard maps for climate-related extreme events to meet the minimum standards of safety implied in current specifications. The paper also introduces a possible practical approach to account for climate change when designing new structures and assessing the safety of existing facilities.

Hydraulic events threaten highway bridge safety as more than 55% of bridge failures in the United States (U.S.) are attributed to floods. It is now well-documented that climate change could cause an increase in extreme precipitation leading to larger and more frequent floods in many U.S. regions. This study presents a systematic framework for the reliability analysis of bridges under future changing flood conditions. The bridge scour safety assessment process is demonstrated using a case study representing bridges over Schoharie Creek in Upstate New York, with more than 100 years of peak flow data and evidence of an increasing trend. Our results show that this trend could cause about an 18% increase in the probability of scour failure over the 75-year service life of bridges designed using current procedures. The reliability index for foundation scour should ideally surpass β = 2.5 to effectively lower the risk to acceptable levels.

Engineers use an array of yardsticks, ranging from visual inspection to physical measurements, occasionally combined with users' costs assessed from average long-term traffic data, to characterize a transportation facility's condition and prioritize maintenance needs. This approach is inconsistent with basic economics principles that recognize that transportation facility users optimize their well-being by making rational decisions regarding travel choices. This paper outlines a joint engineering-economic modeling framework that converts engineering indicators of facility condition to a measure of consumer welfare. The feasibility of this framework is demonstrated by applying it to a case study that assesses the welfare of users of a network composed of two substitutable bridges with deteriorating riding surfaces. The analysis accounts for increased users' costs as well as the reduction in traffic volume on a deteriorating facility due to partial diversion of its traffic to the alternate facility. Such joint engineering-economic analyses would give better appreciation of the economic impact of facility deterioration and maintenance deferrals, eventually leading to more informed maintenance decisions compared with those that rely solely on traditional engineering criteria.

The objective of this study is to comprehend the performance of twin steel box girder (TSBG) bridges after complete fracture of one girder and to establish an outline of an approach for reliability analysis required for assessing their levels of structural redundancy. The earlier work has concluded that the main mode of failure for the bridge in such case is a failure in the deck. This conclusion obtained through a series of experimental and numerical studies significantly reduces the efforts for assessing the safety of TSBG bridges. For the purpose of developing an approach for reliability analysis, a simply-supported single-span bridge tested at the University of Texas (UT) at Austin was selected as a baseline model. The results of the current study through an extensive finite element analysis confirmed the earlier findings that concrete deck failure is the dominant failure mode of the bridge after the occurrence of a fracture in one of the girders. Building on the work at UT, an improved simple and unified yield line analysis method was developed to determine the bridge deck capacity. For the first time, a comprehensive and coherent reliability approach was used to assess the safety of TSBG bridges after the complete fracture of one steel girder. Though the developed safety assessment approach was applied to one example bridge, nevertheless, the method described in this paper could easily be extended to evaluate other TSBG bridges. Although the results of this study cannot readily be generalized for all TSBG bridges without further evaluation, this study shows that simply supported twin steel box girder bridges could indeed be safe and potentially removed from the fracture critical list.

Performance-based design and system-level assessment methods are becoming the preferred approaches for evaluating the safety of structures. This is particularly important for highway bridges where, because of their exposure to long-term deterioration as well as sudden localized failures, the generally conservative traditional member-oriented approach does not necessarily lead to an accurate evaluation of the actual structural system's safety levels nor, consequently, to the efficient allocation of the limited resources available for infrastructure management. The objective of this paper is to quantify the effect of damage size and location on bridge elements and how this affects the performance of the entire superstructure system. The paper also presents a simplified equation for estimating the structural robustness of typical highway girder bridge superstructures as a function of the damage type. A numerical example is presented to illustrate alternative approaches for how these concepts could be implemented during the design and safety assessment of highway bridges. In particular, the analysis showed that the occurrence of damage directly under the live load reduced the ultimate capacity of the system in the range of 70%-95%. This reduction was between 40% and 70% when the damage was located away from the loaded zone.

This paper describes the life-cycle analysis of the risk to highway bridge networks subjected to overweight traffic loads under maintenance budget constraints. The risk to the network is initially evaluated based on the current condition of its constituent bridges and then the life-cycle analysis is performed to identify the level of risk reduction that is possible given a particular budget allocation. The deterioration rate is extracted from National Bridge Inventory data. The risk is monitored as the deterioration of bridges progresses over the years. Bridges are ranked in descending order starting from the bridge whose failure has the highest impact on network risk. Maintenance is scheduled sequentially on the riskiest bridges until the entire budget allocation is depleted. The methodology is illustrated using as an example the highway network of major interstate and state roads in New York State. The paper compares the results of the proposed life-cycle risk analysis for several budget levels. The results show that network risk can be reduced from its present level by 20% if current expenditure rates are maintained. Risk reduction can reach 37% if the budget for bridge rehabilitation is increased to match that recommended in the ASCE report card for America's infrastructure.

A hybrid reliability analysis procedure that combines the advantages of the Subset Simulation method, the application of surrogate models and clustering techniques is proposed to efficiently assess the failure probability of complex structural systems that may exhibit multiple failure modes. The proposed procedure, herein called SS-KK, integrates the Kriging surrogate modeling technique, K-means clustering algorithm into the original Subset Simulation (SS) method. The approach is found to not only improve the efficiency of the Subset Simulation method in finding the reliability of a structural system but to also help identify the important failure modes and controlling random variables. This information is important to aid engineers optimize the structural design process by focusing on the critical failures modes and design variables. The method consists of first constructing a relatively coarse global Kriging model at each subset level of SS by applying an appropriate active learning strategy. Subsequently, the initial global Kriging model is partitioned into several local Kriging models that coincide with the important failure modes identified by the K-means clustering algorithm. This partitioning, which helps identify the important failure modes, also gives a better representation of the entire failure region leading to improved estimates of the system reliability. Finally, FORM is implemented for each local Kriging to rank the importance of each identified failure mode based on its Hasofer-Lind reliability index and to use the associated design point and sensitivity coefficients to identify the most critical random variables. Several examples extracted from the available literature are analyzed to illustrate the advantages of the proposed SS-KK methodology and demonstrate its accuracy and efficiency.

In the U.S. overloading represents the third cause of bridge failures just after hydraulic events and collisions. Large data assembled by Weigh-In-Motion (WIM) systems can be used to obtain improved region-specific or network-specific characterization of vehicle loads on highway bridges for a more accurate evaluation of the safety of critical bridges and the failure consequences to the concerned communities. To achieve this goal it is important to develop tools that allow engineers to estimate the reliability of various types of bridges subjected to realistic ranges of heavy truck load intensities as encountered on highway networks. The objective of this paper is to describe an approach that combines field data and numerical simulations to perform the fragility analysis of bridges due to different percentages of overweight loads and truck traffic. Numerical examples are provided by analyzing typical bridges using field truck data collected at WIM sites in upstate New York. The results of the analysis show that the fragility curves for fatigue are function of the percentage of overweight trucks in New York as a second order polynomial, while the fragility curves of bridges for overstress can be modeled with a copula using both normal distributions for the overweight percentages and Average Daily Truck Traffic.

This paper proposes a risk analysis framework for the quantification of the importance to a highway network of bridges subjected to overweight traffic loads. First, the level of risk to the network is quantified taking into consideration current bridge safety levels and the consequences of their failures. A risk mitigation strategy is proposed through the calibration of importance factors that can be used during bridge design and rating processes to induce different levels of risk reduction in the network. The applicability of the method is illustrated through the analysis and the calibration of importance factors for bridges of a network composed by interstate highways and principal state roads in New York State (NYS) which includes 1,315 typical bridges. Analysis results show that traffic delays constitute the major consequence of bridge failure representing 61% of the total risk while the second major risk component is the maintenance of bridges that accounts for about 21%. It is also observed that the relationship between bridge importance factors and risk is well represented by a power law equation.

This paper presents an improved reinforced concrete steel bar deterioration model that incorporates pitting corrosion and considers the change in after-cracking corrosion rate to assess the time-dependent seismic fragility of RC bridge substructures in marine environments. The proposed deterioration model is applicable for both existing and new RC bridge substructures and could be employed for life-cycle analysis of RC bridge substructures in marine environments. In this paper, the model is implemented to conduct a probabilistic seismic fragility analysis of a three-span continuous box girder bridge accounting for uncertainties in establishing bridge geometry, material properties, ground motion and corrosion parameters. Differences in the results obtained when reinforcing steel is subjected to general and pitting corrosion are investigated. The results show that the effect of chloride-induced corrosion cannot be neglected when performing the seismic fragility analysis of RC bridge substructures in marine environments. Additionally, the calculated time-dependent fragility curves indicate that there is a nonlinear accelerated growth of RC column vulnerability along the service life of highway bridges, especially after twenty-five years of exposure to chlorides.