Characteristic traffic load effects from a mixture of loading events on short to medium span bridges

In recent years, highway bridge load assessment has been recognised as an area through which savings can be made by avoiding unnecessary bridge refurbishment and replacement. Load effects in bridges result from single truck crossings or multiple-truck presence events which are, statistically, not identically distributed. Conventional approaches fit statistical distributions to mixtures of non-identically distributed load effects. Inaccuracies in the conventional approach are identified and an alternative approach is developed to find the characteristic load effects. Theoretical and field data are used to show the potential implications of conventional techniques and to demonstrate the application of the new approach.     

Assessment dynamic ratio for traffic loading on highway bridges

The determination of characteristic bridge load effect is a complex problem. Usually, statistical extrapolation of simulated static load effects is used to derive a lifetime characteristic static load effect. However, when a vehicle crosses a bridge, dynamic interactions occur which often cause greater total load effect. This total load effect is related to the static load effect through a dynamic amplification factor (DAF). Specifications often recommend a conservative level for DAF, based on bridge length, number of lanes, and type of load effect only. Therefore significant improvements in the accuracy of this calculation are possible if a DAF, specific to the considered bridge, is applied. In this paper, the authors develop a novel method that considers site-specific bridge and traffic load conditions and allows for the reduced probability of both high static loading and high dynamic interaction occurring simultaneously. This approach utilises multivariate extreme value theory, in conjunction with static simulations and finite element vehicle–bridge dynamic interaction models. It is found that the dynamic allowance for the sample bridge and traffic considered is significantly less than recommended by bridge codes. This finding can have significant implications for the assessment of existing bridge stock.     

An efficient approach for traffic load modelling of long span bridges

Traffic micro-simulation is the newly developed approach for loading calculation of long span bridges. The approach is quite precise, but computationally expensive to consider the full extent of traffic loading scenarios during a bridge lifetime. To address this shortfall, an efficient multi-scale traffic modelling approach is proposed. The proposed approach uses micro- and macro-simulation with different load model varieties (LMVs), or fidelities (levels of detail) of traffic loading in different bridge regions, to achieve optimal computation efficiency while maintaining the precision of loading calculation. Metrics of influence line (IL) characteristics, such as degree of nonlinearity, are proposed to evaluate the appropriateness of the choice of LMV, and standards of the metrics are also investigated to quantify the implementation of LMVs on bridge IL regions in the multi-scale modelling. Finally, two typical ILs are used along with random traffic modelling to study the feasibility of the proposed approach. It is shown that the multi-scale modelling approach proposed here achieves high computational efficiency and accuracy, which is significant for the massive traffic load simulation for lifetime bridge load effect analysis.     

Optimal extrapolation of traffic load effects

This paper proposes a method for determining optimal fittings of the Rice formula to the tails of outcrossing rate histograms related to traffic load effects. An optimal fitting is obtained through a series of statistical tests between successive fittings and the histogram tails. Optimality is found when a confidence level β₀ for the Kolmogorov test is verified. That provides the optimal number of class intervals to take into account the load-effect extrapolation under the hypothesis that the process is stationary and Gaussian. Extrapolations are given for minimal and maximal load effects for any return period. Some examples highlight the use of the method.     

The use of micro-simulation for congested traffic load modeling of medium- and long-span bridges

This paper presents a new approach to the modeling of congested traffic loading events on long span bridges. Conventional traffic load models are based on weigh-in-motion data of non-congested traffic, or something similar to a Poisson Arrival process. In neither case do they account for the mixing between lanes that takes place as traffic becomes congested. It is shown here that cars move out from between trucks as traffic slows down which results in a higher frequency of long platoons of trucks in the slow lane of the bridge. These longer platoons increase some characteristic load effects under the slow lane by a modest but significant amount. Micro-simulation, the process of modeling individual vehicles that is widely used in traffic modeling, is presented here as a means of predicting imposed traffic loading on long-span bridges more accurately. The traffic flow on a congested bridge is modelled using a random mixing process for trucks and cars in each lane, where each vehicle is modelled individually with driver behaviour parameters assigned randomly in a Monte Carlo process. Over a number of simulated kilometres, the vehicles move between lanes in simulated lane-changing manoeuvres. The algorithm was calibrated against video recordings of traffic on a bridge in the Netherlands. Extreme value statistics of measured strains on the bridge are then compared to the corresponding simulation statistics to validate the model. The micro-simulation algorithm shows that the histograms of truck platoon length are moderately affected by lane changing. This in turn is shown to influence some characteristic load effects of the bridge deck.     

重载交通作用下沥青路面动剪应力分析

基于动力学分析理论基础,并利用ANSYS软件,建立了三维动力有限元模型,研究了重载作用下半刚性基层沥青路面结构内剪应力的动态响应和分布规律,分析了重载路面受剪破坏的机理,以供参考。     

预应力简支梁桥在移动荷载作用下的非线性动力特性分析

考虑预应力梁的剪切变形和几何非线性,建立梁的动力学基本方程式,应用增量谐波平衡法,分析计算梁在预应力作用下的横向振动问题。通过实例计算,得到梁在移动车辆荷载作用下的幅频响应曲线和力与位移的非线性响应关系,并给出了外激励频率不同且初始预加力变化时动挠度的变化规律。计算结果表明,梁非线性位移明显大于线性位移,且荷载与位移呈明显非线性关系,非线性因素的影响不可忽略;施加预应力可以提高梁的动抗弯刚度,减少梁的动挠度值。为预应力混凝土桥梁的设计和动力特性分析提供一定的理论依据。     

Live load model for highway bridges

Load models are developed for highway bridges. The models are based on the available statistical data on dead load, truck loads and dynamic loads. The paper deals mostly with the static live load. The model is derived from truck surveys, weight-in-motion measurements and other observations. Simple span moments, shears and negative moments are calculated for various spans. Extreme 75 year loads are determined by extrapolation. The important parameters also include girder distribution factors and multiple presence (more than one truck on the bridge). Multiple presence is considered in lane and side-by-side with various degrees of correlation between truck weights. The maximum load is calculated by simulations. The developed live model served as a basis for the development of new design provisions in the United States (LRFD AASHTO) and Canada (Ontario Highway Bridge Design Code).     

车辆荷载下上覆无限大薄板加筋路堤的三维动力响应

利用半解析的方法研究了车辆荷载作用下加筋路堤上覆薄板的动力响应问题。基于Biot多孔弹性介质的波动理论,建立了加筋路堤-道路系统模型。采用上覆Kirchhoff小变形无限大薄板模拟路面板,车辆荷载用4个均布矩形荷载来模拟。在忽略土颗粒自重的情况下,半空间土体引入Biot方程,通过Fourier变换以及边界条件求得变换域里的加筋路堤层位移表达式,采用快速Fourier变换求出时域里的位移。通过数值计算,给出了移动荷载速度、加筋路堤层厚度、板刚度以及加筋率对道路系统位移响应的影响。     

车辆荷载作用下高速公路路基路面动力研究

车辆与道路之间动荷载问题是一个非常复杂的相互过程,在充分考虑振动荷载产生机理的基础上,从车辆荷载的重要形式、车辆荷载的模拟、路基有限元模型的建立等方面,研究了路面在车辆动载作用下的动态响应特征。     

关于水平弯桥活载横向分布探讨

针对T形弯梁桥,利用Midas/civil软件对81座弯桥进行建模分析,然后结合SPSS和Excel数据分析软件对数据进行了敏感性分析,回归出一个基于桥梁弯曲半径、跨长、主梁间距和横梁问距的活载最大荷载计算公式.     

On the dynamic properties of cable-stayed bridges

In the design of cable-stayed bridges, it is generally necessary to take account of the dynamic properties of the structure. The lowest natural frequency for vertical oscillation is shown to be closely constrained by the normal design criteria, so that the designer can make significant change only by altering the overall configuration.By introducing the concept of a design strees level under dead load to provide a standardised design basis, it is possible to compare various configurations; particular attention is paid to the radiating-stay configuration having a large number of stays, in comparison with layouts having a small number of stays.Generalised results are presented for these configurations for the stiffness contribution from the stay system. The combination of the stay system with the deck girder is discussed, and charts are presented for selected geometric proportions, giving values of a convenient general non-dimensional frequency parameter, as a function of the stiffness of the beam relative to the stiffness of the stay system.In all practical cases any deviation from the uniform dead load design stress basis is effectively averaged-out over the length of the bridge, either by the deck beam stiffness or by coupling caused by interconnection at the tower. The charts presented thus provide a generally applicable design tool. A brief discussion is included of practical applications.     

抛物线拱桥在移动荷载作用下的动力响应分析

建立抛物线双铰拱桥的强迫振动的运动微分方程,分析了拱桥在移动荷载作用下的横向振动问题,将运动微分方程解耦,得到拱桥在移动荷载作用下振动时的动力响应并加以分析,通过实例计算,得到了拱桥在移动荷载不同行驶速度时的动力挠度曲线,并进行了比较分析。     

Damage due to heavy traffic on three RC road bridges

An investigation of the damage caused by road traffic on three reinforced concrete bridges was performed. This study was performed with a focus on the determination of the damage induced by heavy vehicles in relation to the damage caused by average everyday traffic. A damage model based on fatigue of reinforcement bars was employed. The stress cycles in the reinforcement bars were determined using measurements of the crack widths under traffic loading. Stress cycles were analyzed using the Rainflow Method and Miner’s Rule was employed to gain a measurement for the damage. Monitoring systems were installed on each of the three bridges and operated for several weeks continuously to collect input data for the damage model. Computer software was developed to process the monitoring data in the sense of the damage model. The described methodology was developed and used for the first time in the described project.Heavy traffic was shown to cause a disproportionate high portion of the overall damage on all three bridges. The obtained results indicated that the damage caused by singular events, such as the passage of a heavy vehicle, in relation to the damaging effects of every-day traffic differed significantly between the considered bridges. For one of the bridges the greatest damage from singular traffic events was computed for passages of special transport vehicles. The same bridge was also found to display the highest damage by a single passage in relation to average everyday traffic. Passages of short and heavy trucks with four and five axles were identified as the most detrimental traffic events on the other two bridges.     

Simplified site-specific traffic load models for bridge assessment

Traffic load is identified as one of the greatest sources of uncertainty in the assessment of bridges. In recent years, simulation techniques, using measured traffic data, have been used to predict the characteristic traffic load effects on bridges. However, the techniques are complex, sensitive to the assumptions adopted and require specialist statistical expertise. This work presents a simplified site-specific traffic load model that generates comparable load effects to the corresponding results from a full simulation. While the simplified model is still sensitive to the underlying assumptions, these can be carefully reviewed prior to the method being approved. Further, the simplified method can be employed by practising engineers for bridge assessment.     

Reliability-based condition assessment of deteriorating concrete bridges considering load redistribution

A wide variety of models have been proposed for estimating the reliability of highway bridges. For reinforced concrete bridges subjected to environmental attack, time-variant reliability methods have to be used. In this study, the condition of reinforced concrete girder bridges is assessed using a time-variant system reliability approach in which both load and resistance are time-variant quantities. Several system models are considered, including failure of any girder (series system) and failure of a specified number of adjacent girders (series-parallel system). Adaptive importance sampling is used to determine the cumulative-time system failure probability. An existing reinforced concrete T-beam bridge located near Pueblo, Colorado, is investigated. The influence of resistance degradation and post-failure load redistribution is included. A comparison of reliability estimates for several system models is given, including the influence of correlation among initial girder strengths. The results can be used as a guide for the selection of system models for bridge reliability analysis, identification of critical girders in a bridge system, and for the development of optimal reliability-based maintenance strategies for reinforced concrete highway bridges.     

动荷载作用下杭州粉土动强度试验研究

通过对杭州粉土进行固结不排水动三轴试验,研究围压和固结比在动荷载作用下对杭州粉土动强度的影响,总结了不同固结比、不同围压的条件下,杭州粉土动强度的变化规律。     

系杆拱连续梁桥荷载横向分布研究

采用Midas Civil有限元软件建立空间有限元模型,进行了系杆拱连续梁桥不同的虚拟横、纵梁间距对荷载横向分布影响的研究,并以齐齐哈尔北大桥为例,运用空间支反力法及杠杆法对该桥活载横向分布系数进行了计算,同时对其计算结果进行了对比分析,得出了一些有价值的结论,以供参考。     

A pseudo-microsimulation approach for modelling congested traffic loading on long-span bridges

This paper investigates congested traffic loading on long-span bridges through the use of traffic microsimulation. Six months of Weigh-In-Motion free-flow traffic data (including cars) are used as input for the microsimulation of congested traffic. Key parameters that affect traffic loading are identified in the output of the microsimulation, and these parameters form the basis for a more computationally efficient ‘pseudo-microsimulation of congested traffic’ (PMCT) model. This PMCT model is shown to replicate the traffic loading from full microsimulation accurately and allows long-run simulations, equivalent to 1000 years of congested traffic, to be performed with an acceptably short duration. This reduces the significant uncertainties associated with extrapolating short-run simulation results to long return periods. The 1000-year simulated results from the PMCT are compared with the extrapolated results from full microsimulation, and with the traffic loading from some design codes, for different bridge lengths. Both types of microsimulation are also applied to calculate maximum lifetime loading for two typical long-span bridges – one cable-stayed and one suspension bridge – using influence lines determined from finite-element models.     

输电线在冻雨荷载作用下的动力响应

结合雪灾实际,将输电塔-导线体系简化为柔性支承的单根微斜索计算模型,采用变分法,给出导线弹性和塑性阶段运动方程的计算方法,分析比较了冻雨荷载对输电线动力响应的影响,得出冻雨荷载作用下输电线的动力响应较无冻雨荷载作用时大的结论。