1 Introduction

The knowledge of vehicle loads plays a major role in the life cycle management of existing infrastructures and the design of smart transportation networks, considering the detrimental combination of material degradation and the occurrence of traffic overloads [1].

In view of structural safety checks, the traffic load models (TLMs) provided by Eurocode 1 (EC1)—Part 2 [2] were developed based on the traffic data obtained from several locations in Europe from 1980 to 1994 [3]. The recorded traffic data was associated with higher lorry flows during the particular measurement period, assuming the slow lane traffic measured in Auxerre, France, in May 1986 on the A6 Paris-Lyon motorway to be highly pertinent traffic data. The Auxerre motorway was considered one of the heaviest loaded infrastructures in Europe due to the high frequency of large axle weights among the 25 motorways available at that time [4]. The traffic data were recorded over a number of weeks, which was considered to be a sufficiently long timeframe [5]. However, the traffic composition, road-code provisions, and the frequency of heavy vehicles have changed considerably in recent years. Indeed, even though Directive 96/53/EC (1996) of the European Commission’s transport policy assumed that the limits for the total mass and length of the heavy goods vehicles (HGVs) are 44 t and 18.75 m, respectively, the European Union also allows the circulation of long and heavy vehicles (LHVs) with total mass and total length higher than 60 t and 25 m, respectively, following the equity and non-discrimination criteria [3]. Accordingly, several European countries are permitting the circulation of LHVs to reduce transportation costs, potentially inducing a significant increase in road traffic and maintenance costs. Previous studies thus evaluated the impact of heavy vehicles on the performance of the existing infrastructure [6,7,8], highlighting an 8% increase in lifetime maximum loading for European bridges subjected to vehicles in two same-direction lanes [9]. Nonetheless, the effects of traffic load variation and LHVs are not considered in TLMs provided by current codes and guidelines, delineating a major issue to be taken into account in future studies.

Considering the period of measurement and the change in the type of vehicles and traffic composition, current regulations should be updated and validated by the most recent traffic measurements obtained using the modern weigh-in-motion (WIM) systems [10]. Nowadays WIM systems are considered as the standard for traffic load measurements and semi-permanent monitoring. These advanced systems yield detailed traffic flow information and are highly useful for studying the vehicle loads on bridges [11]. The WIM systems are particularly useful for damage assessment, with special consideration to fatigue-induced damage. The installation of the WIM systems not only helps in recording the vehicle flow but also in the early detection of overload vehicles which results in avoiding adverse effects on critical structures [12]. The drastic change in the WIM measurement systems and technologies are reported in the recent literature significantly improving the quality of traffic data [13,14,15,16]. The available WIM information on the major parameters such as axle weights, inter-vehicle distance, vehicle length, and vehicle speed are particularly useful in the simulation of traffic-dependent phenomena. A proper calibration of the WIM systems and traffic monitoring guide (TMG) are necessary to avoid excessive errors associated with the vehicle weights and axle distances [17]. The unusual traffic data in the proximity of industrial and urban areas, which may be respectively subjected to heavy traffic and low-weight vehicle jams, indicates that a specific generalization of traffic is a complex task.

Studies on the vehicle load assessment from WIM data have attracted much attention in the last two decades [18,19,20,21,22,23,24]. Furthermore, understanding the variations in the statistical distribution of different vehicle classes plays a key role in relation to the probabilistic evaluation of the traffic effects on existing bridges and roads [25]. The statistical analysis of road traffic and development of simulated traffic loading for numerical analysis would increase the structural reliability of existing bridges, allowing large cost savings thanks to bridge safety assessment without proof-load traffic [26]. Recent studies also reported the comparative evaluation of the present-day traffic with EC1-conforming FLMs [3, 5, 27,28,29]. Other investigations focused on accurate computation of vehicle loads, providing live load factors for bridge design and estimates of future road traffic [30, 31]. With the help of suitable simulation methodologies to extract the vehicle load sequence from WIM data, structural design and assessment of infrastructures will become easier and more reliable.

The vehicle overload issue is more prevalent in recent days and studies using reliability-based methodologies to attain more reasonable vehicle weight limits are required. Actual traffic conditions from the WIM data aid in the establishment of stochastic traffic models for bridge assessment [32]. The damage detection method for highway bridges based on long-gauge strain time history under stochastic traffic flow was proven to be applicable for long-term monitoring of bridges under normal traffic conditions [15]. Followed by the development of vehicle load models, the WIM data are effectively being used in the structural health monitoring of bridges [14]. Specifically, the bridge weigh-in-motion (B-WIM) method in which the bridge is treated as a scale to measure the vehicle weight and the bridge response has become a promising technique in bridge maintenance [10, 16, 33]. Recent studies also reported the use of B-WIM systems for SHM using artificial neural networks and methodologies based on additional calculations such as the virtual axle concept [34,35,36].

After the collapse of the Polcevera bridge in 2018 [37], the Italian High Council of Public Works recently issued new guidelines for risk classification, safety checks, and SHM of existing bridges [38, 39]. Even if the Polcevera bridge was not collapsed under traffic overload, the new guidelines encouraged the possible implementation of WIM systems for a traffic-related hazard mitigation in case of safety–critical bridges. In addition, the guidelines assume novel TLMs according to the Italian road code [40] which provides different allowable vehicle classes with corresponding maximum gross vehicle weight (GVW). Nevertheless, those TLMs were developed when WIM data were not still available for the Italian road infrastructures. Based on the data collected by WIM systems installed on A3 Napoli-Salerno and A2 Salerno-Reggio Calabria highways in the South of Italy, this paper presents the following data and tools: (i) assessment of WIM effectiveness for enforcement of GVW restrictions; (ii) statistics and probabilistic distributions of traffic data; and (iii) traffic simulation methodology that could be used for several purposes, such as real-time damage detection and numerical predictions. After that the methodology of the study and main characteristics of the selected WIM systems are described, the paper presents the statistical analysis of traffic data with corresponding probabilistic distributions, followed by the proposal of a traffic simulation procedure.

As a main novelty of the present study, the effectiveness of WIM systems for the enforcement of traffic load limitations is shown by comparison of traffic data from two different locations in southern Italy, one of them including traffic load posting due to critical bridges. The present-day Italian road traffic is characterized by a detailed statistical analysis of WIM data obtained from the two highway locations. Further, a newly established simulation procedure for traffic load sampling was developed considering different traffic conditions: the validation of the procedure against available data ensures its usefulness for the performance assessment of road infrastructures.

2 Methodology and description of the selected WIM systems

This study relies upon a multi-objective methodology that consists of three main stages (Fig. 1): (1) traffic data assessment; (2) detailed statistical analysis and comparison; (3) traffic load simulation.

Fig. 1
figure 1

Methodology of the present study

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In the first stage, WIM data is collected from selected stations to assess the effectiveness of the system in enforcing GVW restrictions, allowing traffic characteristics to be compared to existing data available in the literature from European countries. WIM data sets were filtered in accordance with standard criteria and thresholds. The data filtering is mainly carried out to remove erroneous data from the WIM measurements. Then, the traffic parameters are initially analysed to assess the variation in traffic flow conditions throughout the measurement period, followed by the identification of the free flow, following flow, and traffic jams based on the time headway. The preliminary data assessment ends with a classification of vehicles at the selected locations, distinguishing between low-weight and heavy-weight vehicles. The heavy-weight vehicles are further classified based on the number of axles and axle distance.

The second stage of the methodology is aimed at the development of probabilistic models for various vehicle parameters, which are then used at the third stage for the development and implementation of a traffic load simulation procedure based on WIM data. Such a procedure was conceptualized by considering the requirement of different types of traffic load data during various stages of analysis and design of road infrastructure.

WIM data sets were collected from two stations with different traffic conditions, which are named ‘Fratte’ and ‘Pontecagnano’. Such WIM stations are located on two motorways in Southern Italy, which are a part of E45 European road. Specifically, Fratte and Pontecagnano WIM systems are located approximately 57 km and 72 km south of Naples, respectively. Even if only 15 km distant from each other, Fratte WIM system was installed in 2021 on A3 Napoli–Salerno motorway to prevent vehicles moving in the north direction and having total mass higher than 40 t passing on critical bridges located along a 10 km section (i.e. between Salerno Fratte and Cava de’ Tirreni toll stations). Those bridges were identified as safety critical since they were not conforming to the Italian building code safety provisions [41] and a reduced TLM with 440 kN GVW had to be adopted to provide adequate safety levels according to the new Italian guidelines [38, 39]. Salerno Fratte station is very close to the port of Salerno, so a high rate of heavy traffic would be expected at that location moving to the north direction. In contrast to Fratte, the Pontecagnano WIM system was installed 15 km south on A2 Salerno–Reggio Calabria motorway (also called ‘Mediterranean motorway’) where no limitations to traffic vehicles were imposed (i.e., allowable legal mass 44 t with a 5% tolerance according to the Italian road code [40]). It is worth mentioning that 44 t is the mass limit for legal vehicles in Italy unless a lower value is imposed or special permission is released by the road management agency. Along A3 motorway in the section between Salerno Fratte and Cava dè Tirreni toll stations, a special monitoring system was adopted to automatically track and divert vehicles with a total mass higher than 40 t (accounting for a 10% tolerance of the measurement system compared to the 440 kN TLM) within the framework of the ‘Monitoraggio Overload su Tratta’ project [42]. In case an overloaded vehicle (i.e. GVW > 40 t) is recorded by Fratte WIM station, the monitoring system enforces the police action automatically to stop and fine the driver, thus avoiding his passage on the highway bridges located a few kilometers ahead of the WIM station. Instead, in case an overloaded vehicle will cross Pontecagnano WIM station, no action will be enforced but only road signs will inform the driver about the restrictions along the A2 motorway. It can be noted that vehicles passing through Pontecagnano may also take a different direction before reaching A2 motorway; in that case, neither tracking nor derailment will be enforced.

The location of the WIM stations is shown in Figs. 2 and 3: three and two lanes were monitored through WIM stations at Pontecagnano and Fratte, respectively, corresponding to the total number of lanes on the carriageway. The traffic data was measured in the South-North direction over two weeks for all vehicles. It can be noted that when approaching both Pontecagnano and Fratte WIM stations, the road signs alert the drivers of the GVW restriction on the Salerno Fratte–Cava de’ Tirreni section along the A3 highway.

Fig. 2
figure 2

Google Maps view with location of the two WIM stations and traffic restrictions along A3 motorway

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Fig. 3
figure 3

Google Maps picture with road signs addressing 40 t load posting between Salerno Fratte and Cava de’ Tirreni in south-north direction: approaching Pontecagnano along A2 (a) and Fratte along A3 motorway (b)

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Therefore, the two WIM stations selected in this study allow both traffic assessment and simulation accounting for traffic restrictions with or w/o automatic derailment. Even though the data used in the study were obtained from two specific stations, the obtained data may represent the present data traffic on the Italian highways and provide useful information on the influence of automatic traffic derailment systems. Similar WIM systems were recently installed for traffic monitoring in other locations of Italian highways whose control panel is shown in Fig. 4 for a 5-axles sampled vehicle having GVW of 524 kN, i.e. 19.50% higher than the Italian legal limit of 440 kN [43].

Fig. 4
figure 4

Control panel of the WIM system considered in this study [43]

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The measurement period was selected in such a way to include the working days, weekends, and holidays to assess the variety of traffic conditions. The obtained data is considered to be enough to represent the traffic characteristics since previous studies observed that the results were not significantly affected by the use of a longer period of data [44].

3 Traffic data assessment

3.1 Main traffic characteristics and comparison with European countries

The WIM data at the selected locations contains the information on the vehicle crossing time, license plate number (for illegal vehicle tracking), vehicle acceleration, gross vehicle weight (GVW), vehicle speed (V), vehicle length (L), number of axles, axle weight, axle distance (d) and vehicle width. WIM measurements in the slow lane at the selected locations are considered in this study. Traffic data includes both low-weight vehicles and heavy-weight trucks. To avoid a hefty pool of data in the traffic load analysis, the traffic data was broadly classified into two categories based on GVW, where the vehicles with GVW less than 75 kN are considered low-weight vehicles. Based on this classification, the total number of low-weight vehicles recorded in the slow lane at Pontecagnano and Fratte were 100,656 and 162,966, respectively. The total number of heavy vehicles measured at Pontecagnano and Fratte were 1846 and 3472, respectively. The frequency of heavy trucks (GVW > 75 kN) was 1.80% and 2.10% of the low-weight vehicles measured in the slow lane at Pontecagnano and Fratte, respectively.

The most representative traffic parameters (such as GVW and V) at the selected locations are listed in Table 1. The ranges of vehicle speed do not show significant variations: the minimum vehicle speed of 3 km/hr was observed at the Fratte station during a traffic jam condition.

Table 1 Main traffic characteristics at Pontecagnano and Fratte
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The traffic characteristics at the selected locations were compared to those of previous European traffic measurements that were used in background studies of EC1—Part 2 [2] and the available data from the literature [3, 27, 45]. The important long-distance traffics considered in the development of EC1 was obtained from A61 motorway near the Brohltal bridge in Germany, A1 motorway between Paris and Roissy Airport in Garanor (France), A6 Paris-Lyon motorway in Auxerre (France) and additional five locations in A1 motorway in Italy (e.g. Fiano Romano, Piacenza, and Sasso Marconi). In addition, the Moerdijik traffic data from the Netherlands characterized by a high percentage of LHVs, as well as the Igualada traffic from A2 Madrid–Barcelona motorway representing the long-distance Spanish traffic, were also considered for the comparison [3]. The traffic characteristics such as the daily flow, mean and maximum GVW of the European traffic obtained from the literature, and the locations selected in the present study are listed in Table 2.

Table 2 Comparison between main traffic data collected in European countries
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The daily flow of heavy vehicles in the European traffic was considerably higher than that of the locations considered in the present study. This corresponds to the heavy traffic at the locations characterized by urban and industrial areas in the proximity, which makes the generalization of traffic data for comparison a rather difficult task. While comparing the mean GVW of the various locations, the value obtained from the heavy-weight vehicles at Pontecagnano station is close to the reported values on A1 motorway in Fiano Romano and Sasso Marconi in Italy, with a variation of 5.20% and − 4.00%, respectively, demonstrating to be representative of GVW peak value of the Italian roadways where no automatic derailment systems are implemented for overloaded vehicles, i.e. in case of unconditioned traffic load. The mean GVW of heavy trucks obtained from Fratte is close to that measured in 1984 on A1 motorway between Paris and Roissy Airport in Garanor, France, with a variation of − 6.40%. In the case of the maximum GVW, the value from the Pontecagnano station is close to the Garanor station. It is also important to note that the mean and maximum values of GVW at Fratte are the lowest out of all the stations considered in the comparison due to traffic limitations, thus confirming the effectiveness of the continuous monitoring and automatic system of penalties against traffic overloads.

The previous studies also reported that the GVW distribution of the Auxerre station follows a trimodal distribution with the mean values of their generating unimodal distributions at 30 kN, 250 kN and 440 kN. The Moerdijik and Igualada stations were characterized by bimodal distributions with the first mean value at 190 kN and the second mean value at 320 kN and 410 kN, respectively. Hence, the probability distributions of GVW of the low-weight and heavy-weight vehicles were identified for the comparison with existing European traffic. The vehicle parameter distributions tend to follow either unimodal or multimodal distributions. The GVW distribution of the vehicles recorded in the slow lane (including both low-weight and heavy-weight vehicles) were found to follow a trimodal distribution, which was derived according to assumptions and procedures described in detail in Sects. 4.1 and 4.2.

Similar to the Auxerre traffic, the GVW distribution of heavy trucks at the selected locations follows a trimodal distribution with mean values of unimodal distributions (assumed to be normal) generating the multimodal distribution of GVW at 99 kN, 198 kN, and 327 kN at Pontecagnano, and 128 kN, 183 kN, and 308 kN at Fratte. In case of low-weight vehicles, the mean values were 18.81 kN, 32.22 kN, and 98.36 kN at Pontecagnano, and 16.29 kN, 23.88 kN, and 70.54 kN at Fratte. The comparison of the GVW distribution of the vehicles at Pontecagnano and Fratte for the low-weight and heavy-weight vehicles is shown in Fig. 5. It can be noted that upper tails of GVW distributions for Pontecagnano are at the right of Fratte, reflecting the impact of traffic load restrictions.

Fig. 5
figure 5

GVW distribution at the WIM stations: a low-weight vehicles; b heavy-weight vehicles

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As seen from the traffic data, the maximum GVW measured at Pontecagnano is 9.80% larger than that at Fratte, i.e. 559 kN against 504 kN. At Fratte, 3.23% of total vehicles (i.e. 112) were found to be heavier than 40 t. In the case of Pontecagnano, 5.53% of recorded vehicles (i.e. 102) were found to be heavier than 44 t. In Maljaars the frequency of illegal vehicles (considering 500 kN maximum legal GVW in the Netherlands) was measured equal to 2.50% in 2018 with a maximum GVW of around 530 kN [5]. A significantly higher fraction of more weight vehicles had been measured in Auxerre in 1986, i.e. around 30%, with maximum GVW beyond 600 kN.

These results demonstrated that WIM systems can be effective in monitoring overloaded vehicles and—in case of enforced restrictions—higher confidence can be obtained by adopting automatic tracking of violation and derailment of illegal vehicles, thus allowing higher reliability when assessing structural safety of critical infrastructures.

3.2 WIM data filtering

Despite the calibrations, WIM devices may provide incorrect measurement data due to the uncertainties associated with electromagnetic interference and extreme weather conditions [13]. The WIM data obtained from the two stations was filtered as per the conditions listed below to improve the accuracy of the vehicle samples and the reliability of the analysis. The vehicles outside the range of parameters listed below were excluded from the analysis. The filter range and the conditions for the various parameters were fixed based on the literature review and the International Road Transport Union catalogue [44, 47]. Therefore, the WIM data was filtered and checked according to the following assumptions:

  1. 1.

    The minimum axle distance (\({d}_{i}\)) is 0.92 m, considering the minimum wheel diameter and spacing (i.e. \({d}_{i}\ge 0.92\text{ m}\)).

  2. 2.

    The maximum axle weight (\({w}_{i}\)) is 392 kN (corresponding to 40 t), i.e. \({w}_{i}\le 392\text{ kN}\). Axle weights greater than 40 t are not considered [47].

  3. 3.

    The maximum legal vehicle length (\(L\)) in Italy is 18.75 m (i.e. \(L\le 18.75\text{ m}\)) and is herein assumed to be the sum of the axle distances of each vehicle.

  4. 4.

    The maximum GVW according to the carrying capacity of combined vehicles with five axles or more is set \(\le 1500\text{ kN}\).

  5. 5.

    The GVW must be equal to the sum of axle weights with 10% margin of error (i.e. \(0.90\sum {w}_{i}\le \text{GVW}\le 1.10\sum {w}_{i}\)).

  6. 6.

    The sum of the axle distances must be less than the vehicle length (i.e. \(\sum {d}_{i}\le L\)).

  7. 7.

    The vehicle speed must be less than 170 km/hr (i.e. \(V<170\text{ km}/\text{hr}\)).

  8. 8.

    The number of axles must vary from 2 to 7.

  9. 9.

    Weight measurement accuracy ± 10%.

The WIM data filtering was mainly carried out to remove the erroneous vehicle records with formatting mistakes and other errors [48]. The WIM systems may have errors in the vehicle information and one of the possible errors could be a consideration of the two closely passing vehicles as a single super long vehicle with large number of axles. Hence, filtering in the pre-processing stage of WIM data is highly essential to improve the reliability of the analysis through the potential elimination of false vehicle data [14, 19]. In Fratte, the 10% tolerance in weight measurement required a legal limit of GVW equal to 400 kN lower than the design load of 440 kN (i.e. 400 × 1.10) established as the allowable limit according to the Italian guidelines for safety assessment of existing bridges.

3.3 Traffic flow assessment

The traffic flow is usually described in terms of daily traffic and hourly traffic measured at each station corresponding to the number of vehicle crossings recorded per day and per hour, respectively. According to the above assumptions, the overall profiles of the daily traffic flow at Pontecagnano and Fratte are shown in Fig. 6a. The number of vehicles recorded at Fratte is higher than that of Pontecagnano due to vehicles leaving the port of Salerno and moving to Naples or to the north direction. The number of vehicle crossings during the working days are comparatively higher than that of the weekends and holidays. In week 1, a smaller number of vehicles were observed on Friday, Saturday, and Sunday at both locations. Similarly, a smaller number of vehicle crossings were seen on Thursday, Saturday, and Sunday during the second week. While assessing the hourly traffic flow, the traffic flow had shown a regular pattern during the working days with peaks around 13:00 and 18:00. Furthermore, the frequency of the vehicles during the day hours from 07:00 to 22:00 is comparatively larger than the night hours every day of the week. An hourly traffic flow during week 1 at Pontecagnano is shown in Fig. 6b. The weekends and holidays are marked in dashed line, clearly indicating a reduced frequency of vehicles compared to that of the working days.

Fig. 6
figure 6

Traffic flow: a daily traffic at Pontecagnano and Fratte; b hourly traffic at Pontecagnano during week 1

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Based on the frequency of vehicles observed from the hourly traffic flow, the traffic data from the stations were classified into free flow, following flow, and traffic jam conditions. The inter-vehicle distances and the time interval between the successive vehicles were examined separately for the different traffic conditions. The consideration of the different traffic flow conditions is required to perform a separate simulation of traffic loads for several purposes, such as structural health monitoring, near real-time damage detection, and quantitative risk assessment of roads and bridges.

While considering the traffic jam conditions at the selected sites, the A2 and A3 motorways tend to have traffic jams due to accidents, road repairs or maintenance operations. Hence, the vehicle speed variation at Fratte and Pontecagnano was studied every day to identify the vehicles showing signs of traffic jams. From the available data, traffic jam conditions were identified at Fratte during a working day from 16:00 to 19:00. The minimum value of vehicle speed observed during the traffic jam condition was 3 km/h. The traffic jam window is shown in Fig. 7. Similarly, another traffic condition was observed in Fratte station in two-time intervals for about 7 h, during which the vehicle speed dropped to 7 km/h. The third identified traffic jam condition lasted about 2 h with a minimum vehicle speed of 3 km/h. From the WIM data recorded for two weeks, traffic jam was observed for a total duration of 12 h on working days. Based on this observation, the probability of occurrence of traffic jam was identified as 0.04 for 2 weeks corresponding to 0.003 per day. Furthermore, the reason for the traffic jam in the A2 motorway might be due to some unforeseen events such as road accidents or repair works which does not have a significant influence on the particular time window of any day.

Fig. 7
figure 7

Traffic jam time window identified at Fratte

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Regarding bridges, even though the effect of traffic jams on fatigue damage can be assumed to be negligible as confirmed by earlier studies [5], the assessment of traffic jam load conditions is of paramount importance to identify more severe load effects approaching the ultimate limit state. It is also noteworthy that traffic jams should also be considered when simulating traffic loads for SHM purposes and probabilistic risk assessment.

3.4 Vehicle classification

The low-weight vehicles measured in the slow lane at the selected locations were considered separately in the present study. Even though low-weight vehicles are usually excluded from traffic load analysis due to negligible impact, such traffic is considered in the present study to identify the maximum load effect during traffic jam conditions and the recurrence of frequent vehicles in traffic load simulations. The low-weight vehicles at Pontecagnano and Fratte were 98.20% and 97.90% of the total vehicle traffic. The average GVW of the low-weight vehicles at Pontecagnano and Fratte was 25.04 kN and 18.82 kN and their average speed was 92.74 km/h and 74.84 km/h, respectively.

Following data filtering and traffic flow assessment, the different types of vehicles at the selected locations were identified to reflect the exact traffic conditions over the whole timeframe of interest. It is a common practice to classify the vehicle groups into different categories based on the number of axles and axle distances. Based on the standard vehicle classification groups reported in the literature [27], the vehicles at the selected locations were classified into nine vehicle classes as listed in Table 3. The most frequent vehicle classes with a frequency greater than 20% at both stations were found out to be 2A and 5F. The vehicle classes 2A, 3B, 4D, and 5F constitute about 94% and 92% of total vehicles at Pontecagnano and Fratte, respectively. Average GVW values at Fratte are comparatively lower than those measured at Pontecagnano for all vehicle classes, further remarking on the effects of traffic restrictions. In the same trend, the average speed range of vehicles at Pontecagnano was found to be [82.60 km/h, 88.30 km/h], which is higher than at Fratte (i.e. [55.60 km/h, 73.20 km/h]) due to influence of urban traffic and port area in the latter case.

Table 3 Classification of vehicles at Pontecagnano and Fratte
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3.5 Comparison with TLMs in European standards

Available TLMs from standard regulations were based on the traffic data collected at specific sites years ago. According to modern reliability analysis methods, a relevant difference is established between dominant vehicles, i.e. to be adopted for fatigue safety checks, and very rare vehicles exceeding a given percentile of the load variable distribution, i.e. to be adopted for design and assessment at ultimate limit states. Modern structural codes provide design loads in terms of notional vehicles aimed at reproducing equivalent load effects thus not corresponding to any standard vehicle. Hence, the obtained traffic data can only be compared with the fatigue load models provided by the most relevant standards in Europe.

Fatigue load model 2 (FLM2) in EC1 [2] was represented by a set of idealized “frequent” lorries, where the vehicles were defined by the number of axles, axle distance, and frequent load of each axle. The vehicle classes 2A, 3B, 4D and 5F considered in the present study are similar to the first four frequent lorries mentioned in FLM2. The comparison of mean axle distance and axle loads of the most frequent vehicle classes is given in Table 4. Only a slight variation in the axle distance was observed between traffic data considered in the present study and FLM2 recommended values, however, considerable differences arise in terms of axle loads for all vehicle classes.

Table 4 Comparison of traffic data with FLM2 [2]
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The comparison of the traffic data at both WIM stations with the fatigue load model 4 (FLM4 [2]) with the traffic percentage values corresponding to medium traffic confirms a significant variation, addressing the need of site-specific traffic load models for fatigue assessment of existing bridges in future studies.

Since the 440 kN TLM in the new Italian guidelines was calibrated on a real 5-axles vehicle as per Italian road code [40], the comparison with the geometry of vehicle class 5F may suggest any refinement of the silhouette. The 95th percentile level in the upper tail (i.e. assumed to be representative of the characteristic value) of the GVW (GVW0.95) of the vehicle class 5F at Pontecagnano (452.8 kN) is close to the 440 kN TLM suggested by the Italian guidelines with a variation of + 2.82% which is also within 5% tolerance to maximum legal value. The GVW0.95 and axle weights of the most frequent heavy vehicle class 5F are listed in Table 5 and compared to the 440 kN TLM. The axle weights of vehicle class 5F at Pontecagnano and Fratte vary from − 6.6% to 53.71% compared with that of the standard vehicle with a larger variation in case of the front axle w1 at both the stations, suggesting the possibility of adopting different axle weight distributions in the 440 kN TLM.

Table 5 Comparison of GVW0.95 (kN) and axle weights (kN) of vehicle class 5F (percentage variation in brackets)
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4 Detailed statistical analysis of traffic data

4.1 Assumptions and procedure for derivation of probabilistic models

A common practice followed in traffic simulation and calibration of TLMs is the generation of the traffic arrays from probabilistic distributions of the axle weights, axle distances, and GVW of the standardized heavy vehicles obtained from real-time measurements [5, 18]. A detailed statistical analysis of traffic data was thus carried out to study the different load conditions and dependency upon traffic restrictions at the selected locations. Probabilistic models were then fitted to data to support the simulation of traffic flows consistently with actual measurements. The vehicle parameters may follow unimodal, bimodal, or multimodal distributions due to the composition of different types of vehicles varying with respect to the carrying load [7, 11, 48,49,50]. Further, the distribution of each vehicle parameter—which was assumed to be a random variable (RV)—varies according to the vehicle type. Hence, every RV associated with the vehicle class was analysed to identify the suitable probability distribution. The comparison was made using various statistical models, namely normal (N), lognormal (Logn), logistic (Log), loglogistic (Loglog), kernel (K), and Weibull (W), using maximum likelihood estimation to estimate model parameters in case of unimodal distributions.

Previous studies have shown that the GVW and axle weight distributions, specifically, tend to follow multimodal distributions due to the variation in the loading conditions of the vehicles [49, 51]. The probability density function \(p\left(x\right)\) of the multimodal distribution adopted in the present study is described in Eq. (1):

$$p\left(x\right)=\sum_{i=1}^{n}{r}_{i}{p}_{i}\left(x\right)$$
(1)

where \(x\) is the RV, \(n\) is the number of distribution components, \({p}_{i}\left(x\right)\) is the \(i\)th unimodal probability distribution, and \({r}_{i}\) is the proportion of the \(i\)th distribution. In the present study, \({p}_{i}\left(x\right)\) in the multimodal distribution is considered to follow normal distribution. Hence, the multimodal distribution can also be represented as a finite mixture distribution. The model parameters were estimated using the expected maximum (EM) algorithm which is one of the most frequently used methods for the estimation of model parameters with required accuracy [52]. The validation of the unimodal and multimodal distributions was carried out using Kolmogorov–Smirnov (K-S) hypothesis test with a significance level of 0.05. The distributions were mainly developed for the most relevant traffic parameters of the different vehicle classes for simulating traffic loads using the marginal distributions.

4.2 Probabilistic models for gross vehicle weight and vehicle speed

To compare GVW and V for the different vehicle classes, the probability distributions were fitted to data and the results are listed in Table 6 (see Appendix). The variables are defined in terms of mean value and standard variation of the statistical distributions. The multimodal distributions are listed with the proportion of the single distributions along with corresponding statistical parameters (mean, standard deviation).

The GVW distribution of the vehicle classes associated with heavy-weight vehicles tends to follow loglogistic, lognormal, and multimodal distributions. The majority of statistical distributions of vehicle speed were found to be logistic and loglogistic distributions. The comparison of the probability density functions of GVW of the most frequent vehicle classes 2A and 5F at Pontecagnano and Fratte are shown in Fig. 8. The GVW distribution of the vehicle class 2A exhibits loglogistic distributions with the mean weight of 128 kN and 116 kN at Pontecagnano and Fratte, respectively. GVW distribution of vehicle class 5F follows loglogistic distribution with the mean weight of 268 kN at Pontecagnano and the multimodal distribution with the mean values of 167 kN and 285 kN at Fratte. The probability density functions of V for the same vehicle classes are shown in Fig. 9. Both GVW and V measured at Pontecagnano tend to be larger than those at Fratte. A similar trend was confirmed by other vehicle classes.

Fig. 8
figure 8

Probability density functions of GVW for two vehicle classes: a 2A; b 5F

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Fig. 9
figure 9

Probability density functions of V for two vehicle classes: a 2A; b 5F

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In the case of low-weight vehicles, GVW can be described by trimodal distributions at both WIM stations. The comparison of the GVW distributions at Pontecagnano and Fratte is shown in Fig. 5a. Similar to heavy-weight vehicles, the mean GVW at Pontecagnano was found to be comparatively larger than that related to Fratte. Vehicle speed of low-weight vehicles follows loglogistic distribution with mean value around 92.76 km/h and 73.70 km/h at Pontecagnano and Fratte, respectively.

4.3 Probabilistic models for axle weight

Under each vehicle class of heavy-weight vehicles, the statistical distributions of axle weights and axle distances were identified, and the distribution types are listed in Table 7 (see Appendix). The axle weight was represented as \({w}_{i}\), where the subscript denotes the number of the axle from front to rear. The axle distance was represented as \({d}_{ij}\), where the subscript denotes the number of the axles between which the distance was measured. The distributions for vehicle class 7I were not derived due to the least number of vehicle data.

The axle weight in most of the vehicle classes follows the normal and loglogistic distributions. Few axle weight distributions from Fratte stations were found to follow bimodal distribution. In the case of axle distances, the vehicle classes follow loglogistic and multimodal distributions predominantly. The probability distributions of the axle weights of the vehicle classes 2A and 5F are shown in Figs. 10 and 11. While comparing the axle weight distributions of all the vehicle classes, the average axle weight recorded in Pontecagnano is larger than in Fratte for all the axle weights.

Fig. 10
figure 10

Probability density functions of axle weight of vehicle class 2A: a \({w}_{1}\); b \({w}_{2}\)

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Fig. 11
figure 11

Probability density functions of axle weight of vehicle class 5F: a \({w}_{1}\); b \({w}_{2}\); c \({w}_{3}\); d \({w}_{4}\); e \({w}_{5}\)

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The comparison of the axle weight distributions of low-weight vehicles are shown in Fig. 12. The axle weight follows a trimodal distribution at both WIM stations with the major proportion of the axle weight around 9.38 kN and 8.16 kN at Pontecagnano and Fratte, respectively.

Fig. 12
figure 12

Probability density functions of axle weight (\({w}_{1}\)) of low-weight vehicles

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4.4 Probabilistic models for axle distance

The axle distance is essential data for traffic load simulation and statistical distributions of the different vehicle classes are listed in Table 7. For the various vehicle classes of heavy-weight vehicles, the axle distance distribution tends to follow normal, logistic, loglogistic, and bimodal distributions. The probability density functions of the axle distance \({d}_{23}\) of vehicle class 2A and axle distance \({d}_{23}\) of vehicle class 5F are shown in Fig. 13a and b, respectively.

Fig. 13
figure 13

Probability density functions of axle distance: a \({d}_{12}\) of vehicle class 2A; b \({d}_{23}\) of vehicle class 5F

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The comparison of probability density functions of the low-weight 2-axle vehicles at Pontecagnano and Fratte is shown in Fig. 14. The axle distance was found to follow a trimodal distribution at both locations. The major proportion of the axle distance at Pontecagnano was concentrated at 1.70 m and 1.72 m. In the case of Fratte, the axle distances of 1.78 m and 2.16 m constitute the major proportion of the recorded vehicles.

Fig. 14
figure 14

Probability density functions of axle distance of low-weight vehicles

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4.5 Probabilistic models for relative axle weights

A relative axle weight (\(\text{RW}\)) distribution was also assessed in the present study to clarify the relative weight of the different axles in comparison with the total GVW. \(\text{RW}\) is defined for the ith axle as the ratio of the axle weight (\({w}_{i}\)) to GVW for every vehicle class, as mentioned in Eq. (2):

$${\text{RW}}_{i}=\frac{{w}_{i}}{\text{GVW}}$$
(2)

The \(\text{RW}\) distributions were assessed at both the selected locations, as shown in Fig. 15 for vehicle class 2A. The \(\text{RW}\) distribution at Pontecagnano follows loglogistic and logistic distributions with the mean value around 0.4 and 0.6 for axle 1 and axle 2, respectively. In the case of Fratte, the \(\text{RW}\) distribution was found to be multimodal with the mean value of the largest distributions at 0.39 and 0.61 for axle 1 and axle 2, respectively. Despite the different statistical distributions, the mean value of \(\text{RW}\) tends to be similar at both locations for both axles.

Fig. 15
figure 15

Probability density function of relative axle weights (\({\text{RW}}_{\text{i}}\)) of vehicle class 2A at a Pontecagnano and b Fratte

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The \(\text{RW}\) distributions of the vehicle class 5F are shown in Fig. 16. The statistical distributions tend to follow unimodal and multimodal distributions. The mean \(\text{RW}\) of axles 3, 4, and 5 were found to be close to each other at both locations, with the mean \(\text{RW}\) value varying between 0.16 and 0.17. While comparing the distribution of \({\text{RW}}_{1}\) between Pontecagnano and Fratte, the mean values of the multimodal distribution were almost similar with a slight variation in the standard deviation and the proportions. In case of \({\text{RW}}_{2}\), the mean values of the multimodal distribution were found to be between 0.26 and 0.28 at both stations. The cumulative probability functions of the relative axle weights of vehicle classes 2A and 5F are shown in Fig. 17 with higher dispersion of the former class in comparison with the latter.

Fig. 16
figure 16

Probability density functions of relative axle weights (\({\text{RW}}_{\text{i}}\)) of vehicle class 5F at a Pontecagnano and b Fratte

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Fig. 17
figure 17

Cumulative probability functions of the relative axle weights (\({\text{RW}}_{\text{i}}\)) of a vehicle class 2A and b vehicle class 5F

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4.6 Probabilistic models for headway

The time headway, which is the time difference between two consecutive vehicles, is calculated from the vehicle arrival time and vehicle speed information from the WIM data [47, 53]. Similar to other traffic parameters, the headway distribution was identified at both stations. Considering the variation in the traffic characteristics of the free flow, following flow traffic, and traffic jams, the headway of the vehicles was identified separately. As mentioned earlier in the assessment of the hourly traffic at the selected locations, the free flow occurs during the night and early morning hours (i.e., 00:00–08:00 and 18:00–24:00) and the following flow occurs during the daytime (08:00–18:00).

The sample of time headway distributions of the heavy-weight vehicles following flow and free flow traffic at Pontecagnano are shown in Fig. 18. At Pontecagnano, the time headway was found to follow the loglogistic distribution with the mean value for the following flow and free flow around 178 s and 433 s, respectively. In the case of Fratte, the mean value of time headways was found to be 96 s and 276 s for the following flow and free flow, respectively.

Fig. 18
figure 18

Time headway distributions of heavy-weight vehicles: a following flow; b free flow

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In the case of low-weight vehicles (as shown in Fig. 19), the mean values of the time headway distributions were found to be lower due to the higher frequency of such vehicles. The mean value of the following flow traffic at Pontecagnano and Fratte were found to be around 6 s and 4 s, respectively. The free flow traffic had shown mean values of the distributions around 15 s and 10 s.

Fig. 19
figure 19

Time headway distributions of low-weight vehicles: a following flow; b free flow

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5 Traffic load simulation based on WIM data

An automated procedure was developed to carry out traffic load simulations based on traffic data collected by WIM systems, using the probability distributions and statistics of different vehicle parameters presented in Sect. 4. The traffic models are usually adopted in Monte Carlo simulation, which facilitates the unobserved traffic at the selected site while following the appropriate statistical distributions [54]. In the case of road infrastructures, the procedure can provide useful data to inform artificial neural networks and develop surrogate models for damage detection and fatigue analysis. Infrastructure-dependent traffic modelling allows for accurate risk analysis of existing bridges through structural fragility analysis and direct calculation of conditional failure probability [55, 56].

In the present study, a specific methodology for sampling of traffic load sequence is developed according to collected WIM data. The traffic arrays were simulated considering the distribution of the axle weights and axle distances of the different vehicle classes reported earlier. The inter-vehicle distances were calculated based on the distributions of the vehicle speed, the time stamp of each vehicle crossing, and the frequency of the different vehicle classes. The traffic characteristics can be selected as free flow, following flow, and traffic jams based on the vehicle movement. The movement of the vehicle is said to be following flow when the vehicle flow is affected by the vehicle moving in the front, otherwise, it is mentioned as free flow. Simulations are carried out for both the free-flow traffic and the following flow. Studies state that the flowing traffic is usually considered for the fatigue load models, due to the smaller contribution of traffic jams to fatigue damage [5]. To avoid complexity, the axle loads and relative spacing are considered as independent of each other. The traffic load simulation is carried out using MATLAB computer program [57].

The advantages of the simulation procedure include the following: (i) the procedure is general and can be suitably applied to data from different locations, (ii) the wide range of load simulation parameters at the initial stages ensures the simulation of different types of traffic load data for future analysis (single traffic or accumulation traffic, lightweight and heavyweight), (iii) the traffic characteristics are defined in the procedure through simple statistical distributions that can be easily accomplished, and (iv) the procedure is straightforward and numerically efficient. Even if the procedure was calibrated with WIM data from specific locations it can be used for future applications through proper definition of statistical distributions of the different vehicle parameters.

The steps involved in the simulation of random traffic flow are shown in Fig. 20 and the three main simulation steps are described in detail in the following sections.

Fig. 20
figure 20

Flowchart of random traffic simulation

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5.1 Selection of WIM station and traffic flow conditions

Based on the site-specific traffic data at Pontecagnano and Fratte, the traffic load samples simulated for the two stations can show a significant variation. In this regard, the initial step of the simulation methodology is the selection of the WIM station, followed by the total duration (td) of the traffic load sample required (one day, one year, etc.).

The traffic flow conditions of the required traffic load sample are initially selected. The specification of the time window or the probability of the various traffic flow conditions can be set for the simulation, through the time duration of different types of flows—i.e., free flow (tfr), following flow (tfo), and traffic jam (ttj)—having total duration td.

5.2 Vehicle classification and identification of statistical distributions

The classification of the vehicles at the WIM stations and the identification of the statistical distribution of the traffic parameters such as GVW, axle weight, and axle distance of the different vehicle classes is the first step in the simulation of the random traffic. As mentioned earlier, the description of the vehicle parameters through statistical distributions facilitates the consideration of several vehicle types within the distribution, which were not exclusively recorded during the measurement period. The statistical distribution data of the GVW, axle weights, and axle distances of the different vehicle classes presented in Sect. 4 were programmed in different function files for the simulation.

5.3 Traffic load sampling

The traffic load simulation starts with initializing the number of axle weights (n = 1) and the vehicles (N = 1), which gets updated during the sampling process. During the simulation, the vehicle class for the selected duration (td) will be selected using a random number generator, calculated based on the vehicle frequency identified from the WIM data of the stations. Then, the axle weight and distance sequences for the selected vehicle class (with the number of axles = na) will be generated from the identified statistical distributions. The headway distance will then be generated from the statistical distribution of the selected traffic condition (following flow, free flow, or traffic jam), through which the starting point of the following vehicle will be identified. The total distance of the generated sample will be identified from the vehicle axle distance sequence and headway distance. Then, the duration of the simulated sample will be identified using the identified velocity distribution of the vehicles. The calculation of the distance and duration of the developed sample at every step facilitates the output traffic load sample with respect to both distance and time. These sampling steps will be continued until the duration of the simulated sample (t) reaches the required total duration (td). After every step, the number of vehicles (N) and the number of axle weigh points (n) will be updated by 1 and na, respectively. Finally, the simulated sample's accuracy has been checked by comparing the vehicle class frequencies and GVW distribution of the simulated traffic against the original WIM data.

Using the above-mentioned traffic simulation methodology, the traffic load can be generated for various time periods based on the requirement. Further, the free flow and following flow traffic loads can also be separately generated for use in different types of analysis. The samples of free flow and following flow traffic load at Pontecagnano simulated for one hour are shown in Fig. 21a and b, respectively. The number of vehicles crossing in the free flow and following flow traffic are 9 and 22, respectively.

Fig. 21
figure 21

Traffic load at Pontecagnano: a free flow; b following flow; c traffic jam

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The traffic load for the traffic jam can be generated considering the minimum inter-vehicle distance (equal to 3.0 m) along with the low-weight vehicles in the slow lane. The traffic jam load sample for a length of 30 m is shown in Fig. 21c. The length of 30 m was chosen considering the mean span of existing simply-supported bridges in Italy [55]. The simulated traffic jam load sample resulted in ten two-axle vehicles.

During the simulation of the traffic load sample, the free flow and following flow conditions are considered for the respective time windows. In the case of traffic jams, the probability of occurrence of traffic is considered for the inclusion of the traffic jams and the assessment of duration of traffic jams.

A sample of one-day traffic simulation of heavyweight vehicles only is shown in Fig. 22. The number of simulated vehicles considering the free flow and following flow conditions is 197. The comparison of the frequency of different vehicle classes is shown in Fig. 23a, which shows a minor variation in the frequency of the various vehicle classes. Furthermore, the comparison of the GVW distribution of the most frequent vehicle classes 2A and 5F are shown in Fig. 23b and c, respectively. The simulated GVW distribution of vehicle classes was found to follow a loglogistic distribution similar to that of the recorded traffic. The mean GVW of the vehicle classes 2A and 5F of the recorded traffic were 134.71 kN and 285.54 kN, respectively. In case of the simulated traffic, the mean GVW was 168.72 kN and 250.767 kN for the vehicle classes 2A and 5F, respectively. The variation in the mean values was found to be less than 20%. Similar to GVW, less variation has been observed in the vehicle parameters of other vehicle classes.

Fig. 22
figure 22

One-day random traffic load sample at Pontecagnano (N = 197)

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Fig. 23
figure 23

Comparison of the recorded and simulated traffic at Pontecagnano: a vehicle frequency; b GVW of vehicle class 2A; c GVW of vehicle class 5F

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The simulated one-day traffic load sample at Fratte in the slow lane (including both low-weight and heavy-weight vehicles) considering the different flow conditions is shown in Fig. 24. The traffic jam traffic load was simulated for 4 h during the time interval of 18:00–22:00 h. In the case of traffic jam conditions, a simultaneous occurrence of 3 vehicles was observed.

Fig. 24
figure 24

One day random traffic load sample at Fratte (N = 9890)

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6 Conclusions

This study presented the statistical evaluation of the traffic characteristics of present-day Italian traffic and the impact of WIM systems on the enforcement of traffic restrictions for critical infrastructures. The WIM data were obtained from two stations (namely Pontecagnano and Fratte) on the E45 European highway close to Naples, Italy, over a period of two weeks as per previous studies.

The initial GVW assessment of the present-day traffic with the existing European traffic data had shown considerable variations, with the maximum GVW measured at Fratte being the lowest among the stations due to enforced traffic load limitations. The traffic flow assessment at the WIM stations had shown a larger number of vehicle crossings during the working days than on the weekends and holidays. The daily traffic had shown a peak around 10:00 and 16:00 h during the day. The average GVW of the various vehicle classes measured at Pontecagnano was found to be larger than that obtained at Fratte. A very limited number of overloaded vehicles were recorded at Fratte, demonstrating the drivers’ sensitivity to enforced weight restrictions to a maximum GVW of 400 kN. As far as Pontecagnano is concerned, measured GVW was comparatively higher than at Fratte and in line with available data from past measurements along different Italian highways.

In the second part of the paper, a detailed statistical assessment was performed after WIM data had been properly filtered to remove the erroneous data. The vehicles were classified according to the number of axles and axle spacing configuration into nine different vehicle classes. Based on the results, the two-axle vehicle class 2A and five-axle vehicle class 5F were identified as the most frequent vehicles with a frequency greater than 20% at both stations. The statistical distributions of major vehicle parameters, such as axle weight, axle distance, GVW, vehicle speed, and relative axle weight, were then identified. The vehicle parameters tend to follow unimodal and multimodal distributions. The unimodal distribution parameters were identified using the maximum likelihood estimation method and the results were validated using Kolmogorov–Smirnov (K-S) test with a significance level of 0.05. In the case of multimodal distributions, the model parameters were identified using the expected maximum algorithm and validated using the K-S test. The statistical distributions of the vehicle parameters of the different vehicle classes measured at both stations were presented. Further, the probability density functions of the most frequent vehicle classes were also provided and compared.

In the last section of the paper, a methodology for traffic simulation using probabilistic models derived from WIM data has been presented to inform future studies on damage detection and probabilistic risk analysis of roadway infrastructures subjected to traffic loads. A generic procedure considering the various types of traffic conditions, duration of traffic, WIM stations, and vehicle weights was developed. The simulated traffic loads were found to exhibit similar probability distributions to recorded traffic, indicating the usefulness of the simulation methodology and accuracy of the probabilistic models presented in this study.

The major lessons learned from the present study include the following:

  • From the observed GVW data at the stations, the traffic limitations enforced at Fratte are found to be effective due to the continuous monitoring and automated system of penalties against overload. This in turn also ensures the safety of the road critical infrastructure.

  • WIM data filtering is an important step in the data assessment process, due to the inherent uncertainties associated with row data.

  • In addition to free flow and following flow traffic conditions, the simulation of traffic jam conditions is highly important for the evaluation of annual maxima in the safety assessment of bridges.

  • The vehicle categories and the most frequent type of vehicle in a particular location may vary significantly compared to the standard vehicles described in the common design standards. This notable variation demands a remark about the present-day traffic conditions and continuously changing load patterns in the design standards.

  • The automated procedure developed in the present study can be easily applied to simulate the traffic load at different locations even considering different probabilistic models for damage detection and fatigue analysis of road infrastructures.