Live Load Model Research Articles

A Comprehensive Probabilistic Model of Traffic Loads based on Weigh-in-Motion Data for Applications to Bridge Structures

In various efforts to assure safety and serviceability of a bridge structure throughout its lifetime, it is essential to accurately estimate the traffic load effects. Although traffic loads involve large uncertainties and can vary significantly with site-specific traffic environments, bridge design codes and maintenance strategies do not utilize a probabilistic model that can reflect the actual environments and uncertainties of the target bridge. Rapid developments of weigh-in-motion (WIM) technologies now make it possible to collect various types of data describing the characteristics of vehicles and traffic patterns. Based on actual WIM data collected in South Korea, this paper develops a comprehensive probabilistic model describing the characteristics of vehicles and traffic flow so that the traffic load effects of a target bridge can be assessed using a Monte Carlo simulation approach. To describe the characteristics of vehicles and traffic flow in the WIM data, several important random variables are first identified. These key random variables are then incorporated into a comprehensive probabilistic model based on fitted probability distributions and theories of transportation engineering. The developed model is successfully verified by comparing the daily maximum total loads estimated using actual WIM data with those estimated using artificial WIM data generated from the model. Furthermore, bridge traffic load effects, e.g., moment and tension, are estimated using the influence lines of an actual cable-stayed bridge in South Korea (the Incheon Bridge) and are compared with those from the live load model of a design code. Finally, a brief parametric study is performed to explore the possibility that a probabilistic model developed by the proposed approach can be used as a generic probabilistic traffic load model capable of estimating the site-specific traffic loads through customizations based on partial measurements and available information regarding the target bridge.

State-of-the-art review of bridges under rail transit loading

A state-of-the-art review on the global behaviour of bridges under rail transit loading is presented. Of interest is a synthesis of recent technical findings that can bridge the gap between research and practice. The literature review revealed that structural responses have been evaluated and finite-element and analytical models developed. Identification techniques appear to be useful to extract the dynamic characteristics of rail bridges. Impact increases static load in conjunction with dynamic amplification; however, it tends to converge with train speed. The impact force of a wheel–track system is affected by train weight and speed, rail irregularities and rail type. A number of parameters are associated with rail break. The occurrence of rail breaks increases dynamic load allowance and could cause train derailment. Longitudinal forces induced by thermal loading are another important factor in understanding rail–structure interaction. Contrary to highway bridges, limited effort has been made for railway bridges in terms of reliability investigations and the calibration of load and resistance factors. Scarce information is available on bridge responses associated with light rail trains. Several transit agencies have developed design guidelines using their own live load models. A standard live load model for light rail transit is required to achieve uniform design outcomes.

Development of Traffic Live-Load Models for Bridge Superstructure Rating with RBDO and Best Selection Approach

Development of Traffic Live-Load Models for Bridge Superstructure Rating with RBDO and Best Selection Approach

Towards a New Bridge Live Load Model for South Africa

ABSTRACT South Africa’s bridge design code, TMH7, was first introduced in 1981. In deriving the code a fully probabilistic approach was not possible due to insufficient data at the time. Various studies have shown that the code underestimates measured values in hogging, sagging and shear. A new load model, based on seven years of Weigh in Motion (WIM) data, is developed in this contribution. The Weibull distribution offers the best solution to the statistical extrapolation of load effects. A return period of 975 years is used to obtain static characteristic values for the required internal forces. As a result, the most appropriate load model for South African traffic consists of either tridem or quad axle group with an extrapolated axle weight of 160 kN and an appropriate constant UDL loading as specified in this paper. It is shown that TMH7 NA loading produces significantly smaller values than the measured WIM data for all load effects. This serves as motivation to urgently revise TMH7 loading.

Comparison of Bridge Live Loads in US and Europe

The US and European bridge design codes were developed based on a limited amount of traffic data. The design live load for AASHTO LRFD code used in the US is based on traffic data collected by Ontario Ministry of Transportation in 1970s. Eurocode was initially developed using traffic data collected within few weeks in Auxerre, France in the 1980s. An extensive Weigh-in-Motion (WIM) data can serve as a basis to verify the design live load model. The objective of this paper is to analyze and compare statistical parameters of a live load in the US and Europe using available WIM data. WIM measurements from 44 locations in 20 states around the US from 2005 till 2014, containing 118 million records are used. Also, WIM measurements from European countries (Poland, Netherlands, Czech Republic, Slovenia and Slovakia) of about 2 million vehicles are used. The statistical parameters of US are similar to Europe, and US traffic data can be used to recalibrate European bridge design code if required. Also, site-specific live load model in the US can be developed using the statistical parameters developed in this study and also can serve as basis to update national live load model in the US.

Traffic load patterning on long span bridges: A rational approach

For highway bridges, current live load models from design standards typically replicate the effects of real traffic streams at a certain return period. Most standards stipulate that the worst load effect should be considered, obtained by patterning the live load on the adverse portion of the influence line only. Certainly, this is a worst-case scenario, but the probability of this occurring is surely very low and daily traffic does not pattern in this manner. This paper examines design standards’ approach to load patterning and proposes a relatively simple approach to better reflect the reality of traffic load patterning. As an illustrative example, traffic microsimulation is adopted to simulate the traffic flows on a hypothetical 1200 m bridge. We consider the possible road topologies that might give rise to design standard loading patterns, showing that it is not possible to achieve the code-implied traffic pattern in reality. The load effects results are extrapolated to 5, 75 and 1000 year return periods, representing typical assessment and design return periods respectively. From these results, a rational and practical load patterning method is proposed, based on traffic topologies obtained from an adverse combination of congested and free flow traffic. It is applied to two case study bridges and the results indicate that our proposal can reduce the traffic loading demand by up to 45%. Such reductions can be invaluable in the design of super-long span bridges, or the assessment of existing bridges.

Impact of Specialized Hauling Vehicles on Load Rating Older, Bridge-Class, Reinforced Concrete Box Culverts

This paper describes the comparison of load ratings associated with application of three live load models recognized by AASHTO—AASHTO legal loads, the notional rating load including single-unit specialized hauling vehicles (SHVs), and the HL-93 design tandem live load—versus load ratings associated with application of the typical HS-20 standard truck. The test bed for this study was a statistically representative sample of Texas’ older bridge-class reinforced concrete box culvert structures. Rating factors were determined using the load factor rating method with demands calculated from a production-simplified, calibrated, two-dimensional soil–structure interaction model using linear elastic constitutive models for both concrete and soil. The study was motivated in part by research which showed that SHVs create force effects significantly greater than those from the HS-20 truck (for bridges proper), and recent federal policy mandating that states load rate their bridges for SHVs. Findings from this study indicate the standard HS-20 truck, and not SHVs or other legal or design loads, is the critical model for most culvert load rating applications. In particular, operating rating factors calculated from both the AASHTO legal loads and SHV models tend to be higher than corresponding rating factors calculated using the HS-20 standard truck, most of the time. The response is explained primarily by considering the relatively short span length of culvert structures and the load-attenuating benefit of cover soil above the culvert top slab. More detailed exploration of rating variables suggests interactions between culvert geometry, cover soil thickness, and the various types of applied vehicle loads.

A new live load model for bridges carrying light rail transit

This paper presents the development of a standard live load model for light rail bridges. It is recognized that the absence of a standard load model causes design outcomes varying from agency to agency, which is problematic from performance and reliability standpoints. A blend of deterministic and probabilistic approaches is employed to propose a new load model. Pursuant to light rail transit guidelines, benchmark bridges are designed (steel plate, prestressed concrete multicell box, reinforced concrete tee-beam, prestressed concrete I and bulb-tee, and steel box girder bridges). Finite element analysis is conducted to examine the response of the bridges when loaded by representative light rail trains operated in the United States (Colorado, Massachusetts, Minnesota, and Utah). Parametric investigations in conjunction with numerous loading configurations (48,256 model cases) characterize light rail train loadings, and corresponding results are exploited to determine the extreme bending moments and shear forces of the bridges at four probability levels (the average, upper 20%, 99.9%, and 75-year categories). The upper 20% model shows load effects similar to the standard live load model (HL-93) of the American Association of State Highway and Transportation Officials (AASHTO) Load and Resistance Factor Design (LRFD) Bridge Design Specifications (BDS). The 99.9% and 75-year models envelop the moments and shear forces resulting from the representative light rail trains. These candidate load models are further assessed against site-based load inference. The 75-year model is selected and proposed to be the standard live load model entitled LRT-16 (a uniformly distributed load of 14 kN/m plus three axles of 150 kN at a spacing of 4.3 m, which is configured similarly to those of HL-93 in AASHTO LRFD BDS). The applicability of the standard load model is evaluated using 33 light rail tra.

Reliability-based design optimization of a vehicular live load model

Typically, RBDO is used to select physical characteristics of a structure in order to optimize performance under uncertainty, where design variables are often taken as geometric or material parameters defining the structure. In this study, the effectiveness of using RBDO to develop a design load model is explored, which is to be used to design a wide range of bridge girders subjected to location-specific traffic loads. The objective is to minimize variation in reliability index among different bridge girders designed using the load model. Design variables are taken as the number of axles, axle spacing, and axle weights of the design vehicle representing the live load model. A probabilistic constraint is imposed, limiting the minimum reliability index of each girder design. Random variables considered are girder resistance in moment and shear, and bridge dead load and vehicular live load components. A single loop procedure is implemented by using a non-iterative, modified reliability method, the final results of which are verified with direct Monte Carlo Simulation. The optimization problem is solved with a genetic algorithm. It was found that procedure employed could be used to develop a design load model that resulted in substantial improvement over the design models in current use, where the optimized models significantly reduced the range and coefficient of variation of reliability index among the bridge cases considered.

Development of Live Load Model for Strength II Limit State in AASHTO LRFD Design Specifications

The AASHTO LRFD Bridge Design Specifications defines Strength II limit state for agencies to consider the load combination by owner-specified special design vehicles, evaluation permit vehicles, or both. The configuration and characteristics of permit vehicles vary from state to state. In addition, the code calibration process performed in 1994 for the development of the live load factors was applied only to the Strength I limit state. In New Jersey, the design permit vehicle was not developed based on actual permit records or weigh-in-motion (WIM) data. Recently, with the development of permit-issuing management and WIM technology, there is a need to evaluate the effectiveness of design permit vehicles. This study aims to develop a live load model for the assessment of Strength II limit state for New Jersey Department of Transportation (NJDOT). Five years of permit vehicle records are provided by NJDOT for the development of the live load model. The distribution of Gross Vehicle Weight is best described as the Generalized Extreme Value distribution. Load effects are simulated for different span lengths. The mean and standard deviation (SD) of the 75-year maximum loads are predicted using different extrapolation approaches. The results show that NJDOT Design Permit Vehicle provides stable mean and SD of bias ratios at 75-year level. In comparison with the current AASHTO live load factor of 1.35, the averages of the bias ratios at the 75-year level are found to be 1.31, 1.23, and 1.16 for the positive moment, shear, and negative moment, respectively.

Methodology for development of live load models for refined analysis of short and medium-span highway bridges

The accuracy of bridge system safety evaluations and reliability assessments obtained through refined structural and finite element analyses depends not only on the accuracy of the structural model itself but also on the proper modelling of the maximum traffic loads. While current code-specified live load models were calibrated to properly reflect the safety levels of bridge structures analysed using the simplified methods adopted in bridge design and evaluation manuals, these load models may not lead to accurate results when implemented during refined structural analysis procedures. This paper describes a method to calibrate appropriate live load models that can be used for advanced analyses of bridges. The calibration procedure is demonstrated using actual traffic data collected at a representative weigh-in-motion station in New York State. The proposed calibration methodology is applicable for developing live load models for different bridge service periods, bridge types and design/assessment codes or standards. Live load models obtained using the proposed calibration procedure are readily implementable for deterministic refined analyses of highway bridges to produce similar results to those of complex traffic load simulations. Examples are presented that describe how results of such calibrated live load models would be used in engineering practice.

Single and multiple presence statistics for bridge live load based on weigh-in-motion data

Abstract Modeling the traffic loads on bridges has been the subject of numerous studies. Defining a live load model to be used for bridge design is not an easy task. It demands among many other things a reliable dataset, a well-defined procedure for filtering data and also the determination of statistics for single and multiple presence occurrences. This study examines and characterizes the live load statistics for Brazilian concrete bridges. Single and multiple truck presence are evaluated for different bridge spans and truck daily volume. The sample is comprised of the thirteen months of data from a High Speed Weigh-In-Motion station (HS-WIM) in a resolution of one hundredth of a second currently operating on the Fernão Dias highway, also known as BR-381. The system provides eleven thousand records on a daily basis. After the filtering process three thousand trucks remain. The station takes measures in an same-direction two-lane highway, which allows the evaluation and characterization of both single and multiple presence statistics. Three case of multiple presence are considered: following, side-by-side and staggered cases. The consideration of truck multiple presence on concrete bridges is mandatory to understand and characterize live load models. The results show that with the exception of the side-by-side case, the frequency of multiple truck presence is significantly affected by span length. It also shows that the daily truck volume considerably affects the multiple presence statistics for all load patterns. The results show that the general tendency of the occurrence of all multiple presence events is to increase as the truck volume increases.

WIM-Based Live-Load Model for Advanced Analysis of Simply Supported Short- and Medium-Span Highway Bridges

The accuracy of bridge system safety evaluations and reliability assessments obtained through refined structural analysis procedures depends on the proper modeling of traffic load effects. While the live-load models specified in AASHTO procedures were calibrated for use in combination with approximate analysis methods and load-distribution factors commonly used in the United States, these existing models may not produce accurate results when used in association with advanced finite-element analyses of bridge structures. This paper proposes a procedure for calibrating appropriate live-load models that can be used for advanced analyses of multigirder bridges. The calibration procedure is demonstrated using actual truck data collected at a representative set of weigh-in-motion (WIM) stations in New York State. Extreme value theory was used to project traffic-load effects to different service periods. The results are presented as live-load models developed for a 5-year typical rating interval and for a 75-year design life. The outcome of the calibration indicates that maximum traffic-load effects can be calculated using finite-element models with the help of a single truck for short to medium one-lane multigirder bridges and two side-by-side truck configurations for multilane bridges. The proposed analysis trucks have axle configurations of the standard AASHTO 3-S2 and Type 3 legal rating trucks with appropriate factors to amplify their nominal weights. The amplification factors reflected the presence of overweight trucks in the traffic stream and the probability of multiple presence. The proposed live-load models are readily implementable for deterministic refined analyses of highway bridges and for evaluating the reliability of bridges at ultimate limit states considering the system’s behavior.

Design and construction of simple beam bridges for high-speed rails in China: standardization and industrialization

High-speed rail provides a safe, efficient, and economic transportation system for regions with high population density such as eastern China. To accommodate the rapid development of high-speed rails in China, the bridges with standard spans have been identified as the main infrastructure type. This article provides a state-of-the-art review on the design and construction of the standard simply-supported beam (simple beam) bridges for high-speed rails in China. The structural components discussed include the main girder, deck, and substructure. The live load models, deformation limiting values, and construction methods for the bridges are also discussed. Additionally, the experimental tests were conducted to verify the static and dynamic performances of the structure. The main objective of this paper is to provide the latest design and construction experience of Chinese standard simple beam bridges in high-speed rail and show how a quick and quality engineering has been achieved by utilizing these standardized bridges.

Estimation of Live Load Effect of Single Truck Through Probabilistic Analysis of Truck Traffic on Expressway

PURPOSES : This study estimated the load effect of a single heavy truck to develop a live load model for the design and assessment of bridges located on an expressway with a limited truck entry weight. METHODS : The statistical estimation methods for the live load effect acting on a bridge by a heavy vehicle are reviewed, and applications using the actual measurement data for trucks traveling on an expressway are presented. The weight estimation of a single vehicle and its effect on a bridge are fundamental elements in the construction of a live load model. Two statistical estimation methods for the application of extrapolation in a probabilistic study and an additional estimation method that adopts the extreme value theory are reviewed. RESULTS : The proposed methods are applied to the traffic data measured on an expressway. All of the estimation methods yield similar results using the data measured when the weight limit has been relatively well observed because of the rigid enforcement of the weight regulation. On the other hand, when the estimations are made using overweight traffic data, the resulting values differ with the estimation method. CONCLUSIONS : The estimation methods based on the extreme distribution theory and the modified procedure presented in this paper can yield reasonable values for the maximum weight of a single truck, which can be applied in both the design and evaluation of a bridge on an expressway.

Time-Variant Risk Assessment of Bridges with Partially and Fully Closed Lanes due to Traffic Loading and Scour

This article presents an approach for assessing time-variant risk associated with the closure of bridge lanes due to traffic loading and scour. Scenarios of lane closure are identified for both traffic loading and scour. The time-variant failure probabilities of girders under traffic loading are evaluated using a deterioration model that accounts for the decrease in resistance and a live-load model that considers the increase in maximum load effects. The annual failure probabilities of pier columns due to scour are estimated by comparing pier depth and scour depth caused by the annual peak flow. The probabilities of occurrence of the identified closure scenarios are computed on the basis of the relations between these scenarios and the failure events of girders and pier columns, and the correlations among failure modes are considered. The consequences caused by the lane-closure scenarios are evaluated by considering repair, running, and time-loss costs. Finally, the time-variant risks associated with the identified scenarios are assessed. The proposed approach is illustrated using a highway bridge as an example.

Analysis of Design Live Load of Railway Bridge Through Statistical Analysis of WIM Data for High-speed Rail

In this paper, the live load model for the design of high-speed railway bridge is analyzed by statistic and probabilistic methods and the safety level that is given by the load factors of the load combination is analyzed. This study is a part of the development of the limit state design method for the railway bridge, and the train data collected from the Gyeongbu high-speed railway for about one month are utilized. The four different statistical methods are applied to estimate the design load to match the bridge design life and the results are compared. In order to examine the safety level that the design load combination of the railway bridge gives, the reliability indexes are determined and the results are analyzed. The load effect from the current design live load for the high-speed rail bridge which is 0.75 times of the standard train load is came out greater than at least 30-22% that from the estimated load from the measured data. If it is judged based on the ultimate limit state, there is a possibility of additional reduction of the safety factors through the reliability analysis.

Proposal for the extension of the Eurocode shear formula for one-way slabs under concentrated loads

A large number of existing reinforced concrete solid slab bridges in the Netherlands are found to be insufficient for shear when assessed for the governing live load models. However, due to transverse load redistribution, the shear capacity of reinforced concrete slabs under concentrated loads is larger than the capacity of beams, on which the code provisions for shear are based. Therefore, an extension of the Eurocode shear provisions for the case of slabs under concentrated loads in shear may be warranted. To study the increase in capacity of slabs as compared to beams, a series of experiments on concrete slabs was carried out. These experimental results are combined with Monte Carlo simulations to quantify the increase in shear capacity in slabs as a result of transverse load redistribution. From the analysis of different subsets of experiments follows a proposal to extend the Eurocode shear provisions for the case of slabs under concentrated loads. Using this new expression and allowing larger shear stresses in slabs under concentrated loads results in less shear-critical cross-sections for existing slab bridges.

Towards actual brazilian traffic load models for short span highway bridges

New live load models for highway bridge design in Brazil are under development by assembling real traffic database, traffic simulations, analytical-numerical modeling of the dynamic interaction between vehicle and structure and statistical extrapolations. This paper presents and discusses the results obtained in the first stages of this work which includes the comparison between the static effects due to the actual traffic of heavy vehicles and those generated by the live load model given in the current national code NBR 7188. It is demonstrated that this live load model is not appropriate to represent the actual traffic effects and may be, in some cases, non-conservative. The present work deals with short span bridges for two lanes single carriageway under free flow traffic scenarios. The representative static effects in these bridges due to the actual traffic of heavy vehicles are obtained by extrapolating its probability density functions to a certain return period. To this purpose, a traffic database was constructed by gathering data from several weighing stations in Brazilian highways which was then applied to perform traffic simulations through a specially developed computational tool.

KL-510 하중모형을 적용한 강합성 2거더교 RC 장지간 바닥판의 최소두께

The minimum thickness of long-span deck slab is proposed by checking the limit state according to the Korean highway bridge design code(limit state design). Both minimizing thickness and ensuring safety of deck slab are important design factors to increase a competitive price of the long span deck slabs. The required thicknesses for satisfying flexural capacity, preventing punching shear failure and limiting deflection were calculated by considering KL-510 load model which has increased total load compared to DB 24 from 432 kN to 510 kN. The results of the required thickness for various limit states were compared to propose the minimum thickness as a function of span length of deck slabs. The proposed minimum thickness is influenced by satisfying flexural capacity and limiting deflection. It turns out to be similar compared to the results of the previous study by ultimate strength design method even if the live load model was increased in total weights.