Transportation structures such as roads and bridges are designed to carry moving traffic loads. However, with the rapid economic development, the load capacity and occupancy of heavy vehicles are increasing [
1,
2], generating greater safety hazards to in-service highway bridges and even leading to serious accidents [
3]. The heavy vehicle weight parameters indicate strong randomness and significant correlation between parameters; therefore, it is of great importance to fully study the randomness and correlation of heavy vehicle weights and propose a more realistic simulation method for heavy vehicle flow to evaluate the safety of bridge structures.
Several scholars have implemented random traffic flow simulations considering several parameters, such as vehicle type, vehicle weight, axle weight, and vehicle speed, based on data measured utilizing a dynamic weighing system, weigh-in-motion (WIM). For example, Zhouhong et al. [
4], Yang et al. [
5], and Liang and Xiong [
6] developed random traffic flow models applicable to specific regions using Monte Carlo simulation methods. Notably, mass parameters, such as vehicle weight and axle weight, are important for the load effect, and there is a significant correlation between the mass parameters of each traffic model. To build a model closer to a real traffic flow, numerous scholars have used the Copula theory to describe the nonlinear correlation of random parameters. For example, Li et al. [
7] analyzed the correlation between vehicle axle weights using the t-Copula function and established a random traffic flow model based on a Monte Carlo simulation. Li [
8] analyzed the axle weight correlation according to the Copula distribution function, established a two-dimensional compound Poisson process for vehicle speed and weight using the Levy Copula function, and finally established a random traffic flow model utilizing Monte Carlo simulations. Torres-Alves et al. [
9] used the vine Copula model to analyze the axle weight, wheelbase, and vehicle distance to establish a random traffic flow model that considered the correlations through random sampling. Sorianoa et al. [
10] used the binary Copula function to construct a joint distribution model for overweight trucks with regard to occupancy and average daily traffic flow. In general, the accuracy of random traffic flow simulations can be improved by considering the correlation between the mass parameters of each vehicle. However, existing simulation methods have the following two shortcomings: First, the parameters of the C-vine and D-vine Copula models used in random traffic flow simulations are all based on fixed-type subjective assumptions, whereas the correlation structure between the variables of each dimension in actual engineering is complex and variable. Furthermore, accurately describing the parameters using a fixed structure is difficult. Therefore, accurately constructing a high-dimensional variable correlation model using the vine Copula model still has certain limitations [
11,
12]. Second, random traffic flow simulations are mainly conducted by considering the correlation between parameters through the Copula theory and Monte Carlo sampling. The correlation between parameters is difficult to determine using solely the Monte Carlo sampling method because it leads to inaccurate sampled parameters when correlating them. Therefore, a more rational sampling method is urgently needed.
A literature review found the following theories to resolve the above two problems. Morales-Nápoles et al. [
13] proposed an R-vine Copula model for topology optimization based on the data-driven nonparametric estimation of the decomposed Copula function, which has better flexibility and practicality. Latin hypercube sampling (LHS), proposed by McKay et al. [
14], can achieve stratified sampling to avoid the sampling aggregation phenomenon induced in Monte Carlo sampling while achieving improved accuracy and efficiency. Iman and Conover [
15] proposed a simulation method independent of the data distribution. It derives the expected rank correlation matrix using multi-parameter input random variables through matrix transformation to fully preserve the data correlation characteristics. This method can be applied to any type of distribution sampling.
In light of this, 2020 WIM data was collected from the 49,010 Census Station of Interstate 80 in the U.S. to analyze the statistical characteristics of daily traffic flow, vehicle type, vehicle weight, vehicle speed, and other heavy vehicle parameters. Based on this, a scholastic traffic flow model for heavy vehicles was established using the R-vine Copula model with an improved LHS method. The applicability and superiority of the method were verified. This method provides a reference for vehicle load modeling and load design limit optimization.