Article

Effect of live load on simply supported bridges under a random traffic flow based on weigh-in-motion data

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Abstract

Weight, speed, axle space, and following distance of the vehicles are important factors that determine the live load for simply supported beam bridges. In this study, the effect of live load on simply supported bridges was investigated by considering these parameters. The parameters namely weight, speed, longitudinal following space, and vehicle occupancy ratio on different driving lanes are considered using different numerical models. Then, the random traffic flow is simulated using Monte Carlo method based on Nan-xi Yangzi River Bridge’s weigh-in-motion system data. Finite element models are established for six types of simply supported beam bridges with the span ranging from 6 to 40 m and transient analysis is simulated under the traffic loading. Subsequently, the maximum value distribution of live load for lifetime is obtained for the collected data by the method of extrapolation. This study shows that the mean value of the live load for the simply supported beam bridges under a random traffic flow is lower than the permissible design load as per American Association of State Highway and Transportation Officials; however, it is higher than the permissible design load as per BS5400, and it is 0.82 times the Highway-I standard load.

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... The usage of bridge WIM for overweight truck enforcement was written in [11]. Determination of the effect of live load on simply supported bridges using WIM was presented in [12]. Investigation of the feasibility of using a single-span bridge as a WIM tool to quantify the gross vehicle weights (GVWs) of trucks with a small number of sensors and without using axle detectors was studied in [13]. ...
... The mean value of the combination of the live load and impact load was calculated as: (12) It must be noted that for two lane loaded cases multiple presence factor is 1.0 in the above equation as recommended by [1]. The COV of the combination of live load and dynamic load effect was determined as: where live load part µ LL,S in this equation does not include the bias factor. ...
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... Firstly, the probability density distributions for velocities of each truck type are presented in Fig. 3. It is noticed that Gaussian distribution represents the characteristics of the truck velocities better than other single peak distributions such as Log-normal distribution and Weibull distribution, which was also pointed out in other previous studies [28,29]. Therefore, Gaussian distribution function g(x|μ, σ) was adopted for truck velocity distribution as in Eq. (1). ...
... In which, V is the vehicle velocity for different vehicle types; μ and σ are the mean value and standard deviation of the vehicle velocity respectively. The probability density distributions for the axle weights of the five types of vehicles are also obtained from the WIM data, and hereby only the distributions of 2-axle and 6-axle vehicles are displayed in Fig. 4. It can be found that the distribution of axle weight shows the typical feature as also observed in previous studies on stochastic traffic flow [29][30][31], and they could be represented with Gaussian mixture model (GMM) which is a mixture of a finite number of Gaussian distributions as shown below: ...
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... In this study, the velocity data of each vehicle type was collected as the histogram displayed in Fig. 7. It can be seen that generally the velocity of each vehicle follows Gaussian distribution, which accords with the findings of relevant studies [23,25]. Therefore, the probability density distributions of 6 vehicle types can be fitted by Gaussian distribution. ...
... By observation, it can be found that the distribution of axial weight shows the typical feature of multi-peaks especially for V1 ′ s two axles, which means they could obey Gaussian mixture model (GMM). This finding also accords with former studies of highway bridges [25]. Therefore, the axial weight was fitted using GMM which is a superposition of a certain number of normal distributions as shown below: ...
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Nowadays, the overload issue is becoming more prevalent which inevitably accelerates the degradation of bridges. Restriction on vehicle weight is a practical option to solve this issue. Under the circumstances, a reliability-based method is proposed in this paper to determine the vehicle weight limit of urban bridges. Firstly, the framework of the methodology is presented and a stochastic urban traffic model is established through the site-specific weigh-in-motion data. Then refined vehicle-bridge coupling simulation is incorporated in the framework of the method. Subsequently, reliability analysis is performed based on the probabilistic density evolution method, and uncertainties in both the load and the structural resistance are taken into account. Finally, the vehicle weight limits for 75 urban bridges in Nanjing, China were investigated as a case study. The results showed that the proposed method can obtain more reasonable vehicle weight limits, hich would effectively increase the reliability of urban bridges and provide references for policymakers.
... e vehicle loads contain multiple types due to different vehicle load rates. e vehicle load probability model may be described using a Gaussian mixture distribution [20], yielding ...
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The present study proposes a novel fatigue life prediction considering the temperature load, which may be neglected in the traditional assessment of suspension bridge steel deck welds under dynamic vehicle load. Vehicle fatigue, pavement temperature, and temperature gradient models are developed based on the test data from the weight-in-motion system, U-rib welds, pavement temperature, and environment temperature. The U-rib-to-deck and U-rib-to-U-rib welds fatigue stresses are obtained considering both vehicle and temperature loads with transient analysis method in ANSYS package. Then, the temperature gradient fatigue stress spectra are calculated. After that, the fatigue life of two weld types is predicted considering the coupled vehicle-temperature loads. The results indicate that the fatigue stress varies linearly with the temperature of the asphalt concrete. The effect of the temperature on the weld’s fatigue life decreases as the distance increases between the welds and the pavement. The dynamic vehicle load results in a higher fatigue stress than the temperature gradient, indicating that the vehicle load contributes mainly to the bridge’s fatigue damage. Finally, it is calculated that the fatigue damage of two weld types is magnified 5.06 and 1.50 times when the temperature effect is considered after 100-year service of Nanxi Yangtze River Bridge.
... In a free-flowing traffic state, the probability of two trucks in a single lane is extremely low for a short-to medium-span bridge with a span length of less than 40 m. The truck-by-truck analysis in a single-lane was demonstrated to be conservative rather than considering a MPF (Liu et al. 2016). Therefore, the present study focuses on the simultaneous presence of two trucks in neighboring lanes. ...
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This study presents a novel approach to simulating the fatigue stress spectra of short- to medium-span bridges under stochastic and dynamic traffic loads. The stochastic traffic load is simulated based on the weigh-in-motion (WIM) measurements of a heavy-duty highway bridge in China, and the dynamic effects are modeled using a vehicle-bridge coupled vibration system. An interpolation RSM is used to approximate the effective stress ranges of a bridge with respect to road roughness conditions, gross vehicle weights, vehicle configurations, and driving speeds. The RSM provides a platform for an efficient spectrum simulation of bridges under stochastic and dynamic traffic loads. A case study of a simply supported T-girder bridge demonstrates the effectiveness and efficiency of the proposed approach. The proposed computational framework provides an effective approach for simulating the fatigue stress spectra for short- to medium-span bridges with WIM data. However, the efficiency of the approach depends on the number of intervals of driving speed and gross vehicle weight in the interpolation RSM. Additionally, overloading control has a considerable influence on the probability density of the high-amplitude stresses in the fatigue stress spectrum. Even a relatively high overloading limit value will considerably increase the fatigue reliability of a bridge. In addition, the numerical results provide a theoretical basis for bridge deck retrofitting and truck overloading control measures.
... In a free-flowing traffic state, the probability of two trucks in a single lane is extremely low for a short-to medium-span bridge with a span length of less than 40 m. The truck-by-truck analysis in a single-lane was demonstrated to be conservative rather than considering a MPF (Liu et al. 2016). Therefore, the present study focuses on the simultaneous presence of two trucks in neighboring lanes. ...
... The specific classes and their proportions in traffic flow are listed in Table 4. For brevity, the statistics of random variables' probability distributions would not be given here, which could be found in Liu et al. [54]. ...
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Highway bridges are essential infrastructure engineering. To monitor their conditions effectively, bridge structural health monitoring (SHM) techniques have been developed to substitute the manual inspection. Among SHM techniques, the damage detection method is the most promising one utilized for identifying damage location and extent. However, most frequency-domain signal based damage detection methods are not sufficiently sensitive to local damage, while other time-domain signal based methods with a sufficient sensitivity have many limitations, especially on working conditions where those methods are only feasible when just a single vehicle passes over the bridge. This restriction severely differs with actual traffic situations. Under these backgrounds, in this study, a damage detection method based on long-gauge fibre Bragg grating (FBG) was proposed, which can achieve the identification of the damage location and extent under stochastic traffic flow. This method's feasibility was initially verified through a series of indoor bridge model experiments. Then, some numerical case studies were conducted to mimic actual stochastic traffic flow conditions. The results of experiment and numerical simulation demonstrated that this method performs well in detecting the damage location and extent under various designed situations, and it has the potential to be an alternative for the current methods.
... Mixture distribution models constructed by combining several unimodal parametric distributions have been widely utilized to fit distributions of vehicle loads that have the feature of multimodal (Guo et al., 2008;Mei et al., 2004). On the other hand, the classical random process theory is also the basis for deriving extreme value distributions of vehicle loads (Guo et al., 2008;Haider & Harichandran, 2007;Lan et al., 2011;Liu, Zhang, Deng, & Jiang, 2017;Mei et al., 2004), together with other classical extreme value extrapolation methods (e.g. block-maxima method (Coles, 2001;O'Brien, Schmidt et al. (2015), peaks-over-threshold method (Coles, 2001;Crespo-Minguill on & Casas, 1997; and levelcrossing method (Cremona, 2001)), forming the basic methodologies for estimating and predicting the corresponding maximum value of vehicle loads or load effects. ...
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... Mixture distribution models constructed by combining several unimodal parametric distributions have been widely utilized to fit distributions of vehicle loads that have the feature of multimodal (Guo et al., 2008;Mei et al., 2004). On the other hand, the classical random process theory is also the basis for deriving extreme value distributions of vehicle loads (Guo et al., 2008;Haider & Harichandran, 2007;Lan et al., 2011;Liu, Zhang, Deng, & Jiang, 2017;Mei et al., 2004), together with other classical extreme value extrapolation methods (e.g. block-maxima method (Coles, 2001;O'Brien, Schmidt et al. (2015), peaks-over-threshold method (Coles, 2001;Crespo-Minguill on & Casas, 1997; and levelcrossing method (Cremona, 2001)), forming the basic methodologies for estimating and predicting the corresponding maximum value of vehicle loads or load effects. ...
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A stochastic model based on Markov random field is proposed to model the spatial distribution of vehicle loads on longspan bridges. The bridge deck is divided into a finite set of discrete grid cells, each cell has two states according to whether the cell is occupied by the heavy vehicle load or not, then a four-neighbor lattice-structured undirected graphical model with each node corresponding to a cell state variable is proposed to model the location distribution of heavy vehicle loads on the bridge deck. The node potential is defined to quantitatively describe the randomness of node state, and the edge potential is defined to quantitatively describe the correlation of the connected node pair. The junction tree algorithm is employed to obtain the systematic solutions of inference problems of the graphical model. A marked random variable is assigned to each node to represent the amplitude of the total weight of vehicle applied on the corresponding cell of the bridge deck. The rationality of the model is validated by a Monte Carlo simulation of a learned model based on monitored data of a cable-stayed bridge.
... Thus, for the various 189 application scenarios, the WIM system has been continuously improved with different types of sensors 190 and supporting equipment since the 1950s. [59][60][61][62][63][64][65]. The typical WIM system is equipped with 191 inductive loop sensors as shown in Fig. 1[79]. ...
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... The second step is to obtain samples of the distribution characteristics of the vehicle load based on MC simulation. This simulation method is easier to operate and is soon widely used in traffic flow simulation, owing to its simple and specific parameters [17][18][19][20][21]. However, none of the above research results considered the statistical dependence of parameters of vehicle loads when performing parameter sampling, and therefore, some scholars have continued to improve the simulation method. ...
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... To verify the proposed method, a numerical simulation of two vehicles applied on a simply supported bridge is conducted. The bridge and vehicle parameters are given in Table 1, which is referenced by Liu et al. 38 The bridge is discretized into Euler beam elements. Suppose 20 LFBG strain sensors are installed onto the bridge in order to record the bridge strain responses, and the flexural stiffnesses of all bridge sections except for the damage sections are identical. ...
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EM algorithm is used to determine the maximum likelihood estimates when the data are progressively Type II censored. The method is shown to be feasible and easy to implement. The asymptotic variances and covariances of the ML estimates are computed by means of the missing information principle. The methodology is illustrated with two popular models in lifetime analysis, the lognormal and Weibull lifetime distributions.
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When formulating an approach to assess bridge traffic loading with allowance for Vehicle-Bridge Interaction (VBI), a trade-off is necessary between the limited accuracy and computational demands of numerical models and the limited time periods for which experimental data is available. Numerical modelling can simulate sufficient numbers of loading scenarios to determine characteristic total load effects, including an allowance for VBI. However, simulating VBI for years of traffic is computationally expensive, often excessively so. Furthermore, there are a great many uncertainties associated with numerical models such as the road surface profile and the model parameter values (e.g., spring stiffnesses) for the heavy vehicle fleet. On site measurement of total load effect, including the influence of VBI, overcomes many of these uncertainties as measurements are the result of actual loading scenarios as they occur on the bridge. However, it is often impractical to monitor bridges for extended periods of time which raises questions about the accuracy of calculated characteristic load effects.Soft Load Testing, as opposed to Proof Load or Diagnostic Load Testing, is the direct measurement of load effects on bridges subject to random traffic. This paper considers the influence of measurement periods on the accuracy of soft load testing predictions of characteristic load effects, including VBI, for bridges with two lanes of opposing traffic. It concludes that, even for relatively short time periods, the estimates are reasonably accurate and tend to be conservative. Provided the data is representative, Soft Load Testing is shown to be a useful tool for calculating characteristic total load effect.
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The problem of selecting one of a number of models of different dimensions is treated by finding its Bayes solution, and evaluating the leading terms of its asymptotic expansion. These terms are a valid large-sample criterion beyond the Bayesian context, since they do not depend on the a priori distribution.
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The history of the development of statistical hypothesis testing in time series analysis is reviewed briefly and it is pointed out that the hypothesis testing procedure is not adequately defined as the procedure for statistical model identification. The classical maximum likelihood estimation procedure is reviewed and a new estimate minimum information theoretical criterion (AIC) estimate (MAICE) which is designed for the purpose of statistical identification is introduced. When there are several competing models the MAICE is defined by the model and the maximum likelihood estimates of the parameters which give the minimum of AIC defined by AIC = (-2)log-(maximum likelihood) + 2(number of independently adjusted parameters within the model). MAICE provides a versatile procedure for statistical model identification which is free from the ambiguities inherent in the application of conventional hypothesis testing procedure. The practical utility of MAICE in time series analysis is demonstrated with some numerical examples.
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This paper describes a new multiresolution representation which tackles the mixture modelling problem head-on. The general approach shares important features with the Classication and Regression Trees (CART) system of [9] and its derivatives [17]. It may also be seen as a generalisation of scale-space [26], in that it uses Gaussian functions and includes spatial co-ordinates, but unlike a conventional basis set, they are adapted to the data and used statistically. Moreover, they are dened in a space whose dimension reects the inference problem, not simply the image data. Thus in dealing with colour images, a 5 D space is required (two spatial and three colour dimensions); for inferring 3 D structure from motion, typically nine dimensions are required (three spatial, three colour and three motion axes). Yet MGMM has no diculty in principle in moving seamlessly between these spaces. The next section of the paper outlines the theory underlying MGMM as a method of approximating an arbitrary density and shows how it can deal with smooth motions of an image. The 1
Live load models based on WIM data In: Proceedings of the probabilistic mechanics and structural and geotechnical reliability
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Nowak AS and Nassif H (2015) Live load models based on WIM data. In: Proceedings of the probabilistic mechanics and structural and geotechnical reliability. Reston, VA: ASCE, 29 November. New York.
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Live load models based on WIM data
  • A S Nowak
  • H Nassif
Nowak AS and Nassif H (2015) Live load models based on WIM data. In: Proceedings of the probabilistic mechanics and structural and geotechnical reliability. Reston, VA: ASCE, 29 November. New York.