基于轮轴特征的公路桥梁车辆荷载模型研究
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摘要
公路桥梁车辆荷载模型对于桥梁设计、旧桥加固分析、可靠度评估与决策研究等具有十分重要的作用。日益严重的超载汽车在桥上通行，使桥梁的安全运营面临严峻考验和被动局面。对桥梁的研究在材料、结构分析等方面做得较多，对车辆荷载模型则研究较少。常见的桥梁车辆荷载模型，如我国现行的公路桥梁设计荷载标准等，研究的是在设计基准期内车辆总重量的随机过程及其最大值分布等情况，忽略了各车辆的轮轴数量、轮轴间距、车辆总重在各轮轴上的分配情况等对桥梁荷载效应的影响，使得模型与实际情况存在差异。
本文摒弃了桥梁荷载模型研究的一般方法，将桥上的车辆分解为各种轮轴来研究，由实测桥上车辆的信息分析得到车辆轮轴重量和间距等特征，并在此基础上提出了公路桥梁车辆荷载的车队模型和更新随机场模型。主要工作内容如下：
1、论述了基于应变测量的弯板式动态称重系统的优点，介绍了基于光纤光栅传感技术的汽车动态称重系统的研发过程，并与商用动态称重系统的实测对比，通过非参数检验表明，两系统的总体分布相等，证明了称重系统的精度和可靠性；
2、在桥上实测大量车辆信息的基础上，得到各车道上车辆轮轴重量的分布情况，通过非线性最小二乘拟合，得到采用三峰正态分布进行描述的参数。并得到各种不同类型车辆的前轴重分布情况以及后轴重与前轴重比值的分布情况。
3、在桥上实测大量车辆信息的基础上，得到构成车辆各轮轴间距的分布情况，通过非线性最小二乘法拟合，得到采用三峰正态分布进行描述的参数。分析得在一般运行状态和混合运行状态下车辆的行驶距离和跟随距离服从指数分布，在密集运行状态下则服从正态分布。进一步分析得到桥上各种运行状态下的轮轴队列间距的分布情况及其参数，分别服从多峰正态－指数分布和多峰正态分布。
4、在轮轴特征分析的基础上，根据各行车道上车辆轮轴重和轮轴间距的分布特征及其规律的基础上，与实际桥上各车道车辆构成相结合，构建出由小型客车、主要货车和大型货车组成的车队荷载模型，并分析了模型参数及其应用规则。算例结果表明，采用本车队荷载模型计算得到的桥梁活载内力较按规范标准计算得的结果大。
5、在实测分析得到轮轴重量和轮轴间距特征的基础上，提出了以车辆轮轴间距为变量的随机场描述方法，应用随机场理论诠释了一般运行状态下的车辆间距服从指数分布这一现象。提出了将车辆分解为桥上轮轴队列的多峰正态—泊松更新随机场和多峰正态更新随机场描述方法，进而提出了桥上车辆荷载的更新随机场模型及其参数。采用该更新随机场模型进行桥梁活载内力计算，结果表明，对于大跨径桥梁其结果较按规范标准计算的结果大，对于小跨径桥梁或影响线加载长度较短的桥梁，其结果偏小，主要由于随机场模型考察的是车辆的一般意义上的轮轴特征，剔除了轮轴特征的极端情况的结果。
Live load model plays an important role in many aspects of bridges, such as bridgedesign, analysis of bridges in-service, reliability and decision assessment of bridges. Moreand more overloaded vehicles drive on bridges, which imposes a severe situation for bridgemanagement. Less effort is put in the research on the live load model for bridges than otheraspects such as the material feature and the structural performance of bridges. Generally,gross weight of vehicles on bridges is treated as a stochastic process during bridge lifetime,and the distribution of the maximum load of it is deduced while researching into bridgelive load model, like the load model in the code for highway bridge design in China. Sucha treatment neglects the contribution of the characters of wheel axles, such as the amountof vehicles wheels, the distance of wheel axles and the apportionment of the gross weighton each wheel. As a result, such a model will not describe the real loads of vehicles.
In this paper, the general method to research the live load models for bridges isdiscarded. Vehicles are separated into individual wheel axles on bridge. With theinformation of vehicles tested on bridges, chracters of wheel axles, like the axle distanceand the axle weight, are analysed, based on which the live load models of motorcade trafficand of renewal random field are proposed. The main wok and conclusion are stated asfollows.
1) Preponderance of weigh-in-motion (WIM) by means of bending plate based on themeasurement of strains is demonstrated. A fiber-optic WIM system based on fiber Bragggratting technology is developed. Such a WIM system is employed for in-site testingaccompanied by a commercial one. Datum from them is compared by nonparametric test.As a result, the population distribution of such two systems is equal, which demonstratedthe reliability and accuracy of the developed WIM system.
2) Based on a dreat deal of vehicle information tested in-site, distributions of theweight of the wheel axles on each lane are analysed and described by a3-peak normaldistribution by means of nonline least square fitting. Distributions of the weight of thefront wheel axle of all kinds of vehicle are analysed. Distributions of the ratio of the weightof back wheel axles to the front wheel axle are also analysed. Parameters of them are alsoobtained.
3) Based on the vehicles’ information, distributions of axle distance of each vehicleare analysed and alse described by a3-peak normal distribution. Distributions of the headdistance and the following distance of vehicles in every running conditons are analysed. Asa result, the distribution of distances sumit to exponential distribution while vehicles run inordinary condition and composite condition, and sumit to normal distribution in crowdedcondition. Further more, distribution of the distance of the wheel axles separated fromvehicles are analysed, which sumit to multi-peak normal-exponential distribution ormulti-peak normal distribution.
4) Based on the characters of wheel axles and the reguralities of the distributionparameters on each lane, combined with real traffic on bridge, a live load model ofmotorcade traffic is proposed. Such a model consists of cars, trucks and heavy lorries.Parameters and regulations of their association are also analysed. Bridges of various spansand different patterns are used as example to calculate the effect of such a live load model,which is greater than the effet of the live load model specified by the code for bridgedesign.
5) Based on the characters of wheel axles, methodology of describing the axle distanceby means of random field is proposed. Theory of random field is also applied tointerpretate why the distribution of vehicles sumit to exponential one in ordinary andcomposed running condition. Methodologies of multi-peak normal-Poisson renewalrandom field and multi-peak normal renewal random field are used to describe the distanceof wheel axles on bridges separated from vehicles. Live load model of renewal randomfield is proposed and parameters of the model are acquired simultaneously. Examples ofbridges for the effect of such a model show that, to the bridges of large span, the effect ofthe renewal model is greater than that from the code for bridge design, and it will beopposite to bridges of short span. Such a model eyes on the average characters of wheelaxles and kicks away the extreme characters of them.
本文摒弃了桥梁荷载模型研究的一般方法，将桥上的车辆分解为各种轮轴来研究，由实测桥上车辆的信息分析得到车辆轮轴重量和间距等特征，并在此基础上提出了公路桥梁车辆荷载的车队模型和更新随机场模型。主要工作内容如下：
1、论述了基于应变测量的弯板式动态称重系统的优点，介绍了基于光纤光栅传感技术的汽车动态称重系统的研发过程，并与商用动态称重系统的实测对比，通过非参数检验表明，两系统的总体分布相等，证明了称重系统的精度和可靠性；
2、在桥上实测大量车辆信息的基础上，得到各车道上车辆轮轴重量的分布情况，通过非线性最小二乘拟合，得到采用三峰正态分布进行描述的参数。并得到各种不同类型车辆的前轴重分布情况以及后轴重与前轴重比值的分布情况。
3、在桥上实测大量车辆信息的基础上，得到构成车辆各轮轴间距的分布情况，通过非线性最小二乘法拟合，得到采用三峰正态分布进行描述的参数。分析得在一般运行状态和混合运行状态下车辆的行驶距离和跟随距离服从指数分布，在密集运行状态下则服从正态分布。进一步分析得到桥上各种运行状态下的轮轴队列间距的分布情况及其参数，分别服从多峰正态－指数分布和多峰正态分布。
4、在轮轴特征分析的基础上，根据各行车道上车辆轮轴重和轮轴间距的分布特征及其规律的基础上，与实际桥上各车道车辆构成相结合，构建出由小型客车、主要货车和大型货车组成的车队荷载模型，并分析了模型参数及其应用规则。算例结果表明，采用本车队荷载模型计算得到的桥梁活载内力较按规范标准计算得的结果大。
5、在实测分析得到轮轴重量和轮轴间距特征的基础上，提出了以车辆轮轴间距为变量的随机场描述方法，应用随机场理论诠释了一般运行状态下的车辆间距服从指数分布这一现象。提出了将车辆分解为桥上轮轴队列的多峰正态—泊松更新随机场和多峰正态更新随机场描述方法，进而提出了桥上车辆荷载的更新随机场模型及其参数。采用该更新随机场模型进行桥梁活载内力计算，结果表明，对于大跨径桥梁其结果较按规范标准计算的结果大，对于小跨径桥梁或影响线加载长度较短的桥梁，其结果偏小，主要由于随机场模型考察的是车辆的一般意义上的轮轴特征，剔除了轮轴特征的极端情况的结果。
Live load model plays an important role in many aspects of bridges, such as bridgedesign, analysis of bridges in-service, reliability and decision assessment of bridges. Moreand more overloaded vehicles drive on bridges, which imposes a severe situation for bridgemanagement. Less effort is put in the research on the live load model for bridges than otheraspects such as the material feature and the structural performance of bridges. Generally,gross weight of vehicles on bridges is treated as a stochastic process during bridge lifetime,and the distribution of the maximum load of it is deduced while researching into bridgelive load model, like the load model in the code for highway bridge design in China. Sucha treatment neglects the contribution of the characters of wheel axles, such as the amountof vehicles wheels, the distance of wheel axles and the apportionment of the gross weighton each wheel. As a result, such a model will not describe the real loads of vehicles.
In this paper, the general method to research the live load models for bridges isdiscarded. Vehicles are separated into individual wheel axles on bridge. With theinformation of vehicles tested on bridges, chracters of wheel axles, like the axle distanceand the axle weight, are analysed, based on which the live load models of motorcade trafficand of renewal random field are proposed. The main wok and conclusion are stated asfollows.
1) Preponderance of weigh-in-motion (WIM) by means of bending plate based on themeasurement of strains is demonstrated. A fiber-optic WIM system based on fiber Bragggratting technology is developed. Such a WIM system is employed for in-site testingaccompanied by a commercial one. Datum from them is compared by nonparametric test.As a result, the population distribution of such two systems is equal, which demonstratedthe reliability and accuracy of the developed WIM system.
2) Based on a dreat deal of vehicle information tested in-site, distributions of theweight of the wheel axles on each lane are analysed and described by a3-peak normaldistribution by means of nonline least square fitting. Distributions of the weight of thefront wheel axle of all kinds of vehicle are analysed. Distributions of the ratio of the weightof back wheel axles to the front wheel axle are also analysed. Parameters of them are alsoobtained.
3) Based on the vehicles’ information, distributions of axle distance of each vehicleare analysed and alse described by a3-peak normal distribution. Distributions of the headdistance and the following distance of vehicles in every running conditons are analysed. Asa result, the distribution of distances sumit to exponential distribution while vehicles run inordinary condition and composite condition, and sumit to normal distribution in crowdedcondition. Further more, distribution of the distance of the wheel axles separated fromvehicles are analysed, which sumit to multi-peak normal-exponential distribution ormulti-peak normal distribution.
4) Based on the characters of wheel axles and the reguralities of the distributionparameters on each lane, combined with real traffic on bridge, a live load model ofmotorcade traffic is proposed. Such a model consists of cars, trucks and heavy lorries.Parameters and regulations of their association are also analysed. Bridges of various spansand different patterns are used as example to calculate the effect of such a live load model,which is greater than the effet of the live load model specified by the code for bridgedesign.
5) Based on the characters of wheel axles, methodology of describing the axle distanceby means of random field is proposed. Theory of random field is also applied tointerpretate why the distribution of vehicles sumit to exponential one in ordinary andcomposed running condition. Methodologies of multi-peak normal-Poisson renewalrandom field and multi-peak normal renewal random field are used to describe the distanceof wheel axles on bridges separated from vehicles. Live load model of renewal randomfield is proposed and parameters of the model are acquired simultaneously. Examples ofbridges for the effect of such a model show that, to the bridges of large span, the effect ofthe renewal model is greater than that from the code for bridge design, and it will beopposite to bridges of short span. Such a model eyes on the average characters of wheelaxles and kicks away the extreme characters of them.
引文
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