New Model Predicts Extreme Traffic Loads on Chinese Bridges from WIM Data

Engineers have long struggled to predict the heaviest loads that traffic will ever place on a bridge, because the answer depends on a tangle of factors: how heavy the trucks are, how closely they follow one another, how many lanes are loaded, and how long the span is. A new study published in Advances in Bridge Engineering offers a way to cut through that complexity. Researchers led by Jean Claude Sugira, Xiaoyi Zhou and Jean de Dieu Ninteretse have built an analytical probability distribution model that links weigh-in-motion (WIM) measurements from a Chinese highway directly to the statistical parameters governing extreme bridge load effects, allowing rapid prediction without running a fresh simulation for every bridge.

The work builds on a classical framework from extreme value theory, which describes how the largest values in a series of measurements behave statistically. When engineers fit an extreme value distribution to samples of maximum load effect, they can extrapolate to rare events such as the load a bridge might experience once in a hundred or five hundred years. The trouble, the authors note, is that this approach is site-specific: each bridge requires its own simulation campaign and calibration, which becomes impractical when evaluating an entire road network. An earlier analytical shortcut proposed by Bailey and Hirt in 1996 connected traffic and bridge parameters directly to the parameters of the Type III extreme value distribution, enabling simulation-free prediction, but it was calibrated exclusively on European weigh-in-motion data.

That European calibration is the crux of the problem. Empirical evidence from multiple WIM-based studies indicates that Chinese traffic exhibits heavier gross vehicle weights, higher overloading rates, shorter headways and a greater prevalence of multi-axle heavy trucks compared with European traffic. Previous research reported that heavy vehicles in China frequently exceed legal weight limits by more than 150 percent, with mean gross vehicle weights and standard deviations often two to three times higher than in Europe. Models calibrated on lighter, more regulated European fleets therefore risk systematically underestimating extreme load effects on Chinese bridges, potentially compromising safety assessments.

To close that gap, the team collected approximately two months of WIM data from a highway site in China, ultimately yielding 915,000 validated vehicle records for a 60-metre simply supported, bi-directional highway bridge. Before any modelling, the raw records passed through systematic filtering and quality control: incomplete entries were removed, physically implausible speeds, weights and axle spacings were screened out, axle information was checked for internal consistency, and duplicate or abnormal records were discarded. The measured traffic was dominated by two-axle trucks, which made up 80.7 percent of the fleet, with heavier multi-axle vehicles accounting for progressively smaller shares.

The statistical characterisation of that traffic revealed a distinctive feature of Chinese loading conditions: the gross vehicle weight histograms for heavy vehicle classes consistently displayed three distinct peaks, reflecting the coexistence of legally loaded, overloaded and severely overloaded trucks. The researchers therefore modelled vehicle weights, axle load proportions and axle spacings using three-component Gaussian mixture models, while vehicle speeds followed a single normal distribution and headways a composite model combining a polynomial fit for short gaps under four seconds with a shifted exponential distribution for longer gaps. Goodness-of-fit was checked with Kolmogorov–Smirnov tests; for example, the test for Type VII gross vehicle weight yielded a p-value of 0.6124, and all fitted distributions passed with p-values above 0.05.

With these distributions in hand, the team used Monte Carlo simulation to extend the two-month measurement into a synthetic traffic stream of 1,000 days. Because multi-year WIM records were not available at the site, traffic growth was treated as a scenario input: volume was assumed to grow at 3 percent per year and maximum gross vehicle weight at 2 percent per year, applied uniformly across vehicle classes in the baseline model. Vehicles were generated sequentially with sampled arrival times, classes, weights, axle configurations and speeds, and moved across the bridge’s influence line with a time step of 0.02 seconds. Dynamic effects were captured through a stochastic dynamic amplification factor with a mean of 1.1 and a standard deviation of 0.1, adopted from literature values for similar bridge types because site-specific dynamic measurements were unavailable.

The simulation produced hourly maximum bending moments and shear forces for spans ranging from 20 to 120 metres, vehicle speeds from 30 to 180 kilometres per hour, and one or two loaded lanes, generating more than 1,500 parameter combinations. The envelopes confirmed expected structural behaviour: peak bending moments occurred near midspan and grew steeply with span, with the fitted upper bound rising from 66.2 kilonewton-metres for a 20-metre span to 2,382.6 kilonewton-metres at 120 metres, while peak shear forces concentrated near the supports. The fitted upper bound also increased as mean speed decreased, a consequence of denser traffic and reduced inter-vehicle spacing putting more vehicles on the bridge simultaneously.

The central result concerns how the three parameters of the Type III extreme value distribution translate from European to Chinese conditions. The upper bound parameter, which reflects physical and regulatory limits on how heavy a single truck or axle group can be, remained consistent with Bailey’s original formulation. The shape parameter, however, came out at roughly 0.32 to 0.36 of the European value, reflecting the wider dispersion and heavier upper tail of Chinese heavy-vehicle weights, where the measured standard deviation of linear weight was 18.6 kilonewtons per metre compared with 6 in the European data. The position parameter was revised to 2.2 times its original value, driven by the much larger gap between maximum and mean heavy-vehicle linear weights in China, 151.4 versus 38.9 kilonewtons per metre, compared with 70 versus 14 in Europe.

Verification supported the calibrated model across multiple configurations. Comparing theoretical distributions implied by the analytical formulas with distributions fitted from simulated hourly maxima at spans of 30, 60 and 120 metres showed close agreement, with root-mean-square errors below 5 percent. A quantile–quantile plot of simulated versus measured maxima for a 60-metre span yielded a coefficient of determination of 0.998, and return-level plots comparing 100-year and 500-year values from measured data and the 1,000-day simulation tracked each other closely. The authors report that the derived relationships predict the distribution parameters with 95 percent agreement against direct simulation across the tested spans and speeds.

The practical payoff is a tool that can estimate extreme traffic load effects for any chosen return period without a bespoke simulation campaign, supporting reliability-based assessment and design of highway bridges, including China’s ageing stock, and offering a data-driven alternative to codified load models that the authors argue often underestimate site-specific extremes. The framework does carry stated limitations: the traffic input came from a single WIM site, the growth rates and dynamic amplification parameters were scenario inputs rather than site measurements, and the calibration coefficients should be interpreted as data-driven parameters rather than universal constants. The researchers identify external validation using independent WIM sites as a key next step, alongside extending the model to other bridge types such as arch, box girder and suspension bridges, benchmarking it against other distribution families, and combining extreme traffic loads with other hazards such as seismic and environmental effects in multi-hazard reliability assessments.

Subject of Research: An analytical probability distribution model linking WIM traffic data and extreme value theory to predict extreme bridge traffic load effects in China.

Article Title: An analytical probability distribution model for extreme bridge traffic load effects based on WIM data and extreme value theory

Article References: Sugira, J. C., Zhou, X., & de Dieu Ninteretse, J. (2026). An analytical probability distribution model for extreme bridge traffic load effects based on WIM data and extreme value theory. Advances in Bridge Engineering, 7(1), Article 33. https://doi.org/10.1186/s43251-026-00210-x

Image Credits: AI Generated

DOI: 10.1186/s43251-026-00210-x

Keywords: bridge engineering, extreme value theory, weigh-in-motion, traffic load effects, Monte Carlo simulation, Type III extreme value distribution, structural safety, Chinese highway traffic, reliability-based design, influence line analysis, Gaussian mixture model, load effect prediction