The Effect of Vehicle and Road Conditions on Rollover of Commercial Heavy Vehicles during Cornering: A Simulation Approach

Heavy vehicles make up a relatively small percentage of traffic volume on Malaysian roads compared to other vehicle types. However, heavy vehicles have been reported to be involved in 30,000–40,000 accidents yearly and caused significantly more fatalities. Rollover accidents may also incur cargo damages and cause environmental or human disasters for vehicles that carry hazardous cargos if these contents are spilled. Thus, in this paper, a comprehensive study was conducted to investigate the effects of vehicle and road conditions on rollover of commercial heavy vehicles during cornering at curved road sections. Vehicle conditions include the heavy vehicle class (based on the axle number and vehicle type), speed and gross vehicle weight, while road conditions include the cornering radius and coefficient of friction values. In order to reduce the risks involved in usage of actual heavy vehicles in crash experiments, a simulation approach using a multi-body vehicle dynamic software was applied in this study, where the verified virtual heavy vehicle model was simulated and the output results were extracted and analyzed. The results showed that a maximum of 40% and a minimum of 23% from the total number of simulations resulted in an unsafe condition (indicated as failed) during the simulations. From the unsafe conditions, two types of rollover accidents could be identified, which were un-tripped and tripped rollovers. The heavy vehicle speed was also found to have a strong correlation to the lateral acceleration (to cause a rollover), followed by gross vehicle weight, coefficient of friction and cornering radius, respectively.


Introduction
Many developing countries including Malaysia have shown rapid growth in the past decades, particularly in the industrial sectors and infrastructure developments. Parallel to this, Malaysia has seen remarkable a period of economic expansion and growth in terms of its population, industrialization and motorization. According to the Malaysian Automotive Association [1], an average of 60,000 new vehicles are registered in Malaysia every year, with the total number of new vehicles of 604,287 in 2019. These include various types of land vehicles, ranging from passenger cars to commercial vehicles, such as trucks, prime movers, pick-ups, panel vans and buses. This in turn adds up to the traffic composition on Malaysian roads, where 24.57% of traffic was contributed by heavy vehicles, such as light lorries (14.21%), medium lorries (6.29%) and heavy lorries (4.07%) [2].
Heavy vehicles have been reported to be involved in 30,000-40,000 accidents yearly and caused significantly more fatalities than cars [2]. The study by Karim et al. revealed that more than 10% of the fatalities occurred in accidents involving heavy vehicles were caused vehicle model is replicating the actual heavy vehicle as accurately as it can, in terms of its performance and dynamic behavior (Figure 1), as we have reported previously [25]. The virtual model was found to closely represent the actual heavy vehicle and this was further validated by multiple performance indices. As shown in Table 1, the root mean square error (RMSE) of lateral acceleration was very close to 0, indicating a good correlation was obtained between both experimental and simulation data. The lateral acceleration mean absolute error (MAE) was also very close to 0, implying that the simulation model accurately represents the experimental data. The regression coefficient (R) for lateral acceleration was also observed to be close to 1, indicating that the simulation model has explained the majority of the variances observed.
Sustainability 2021, 13, x FOR PEER REVIEW 3 o Validation of the virtual heavy vehicle model with the actual heavy vehicle is portant when a simulation approach is employed. This is to ensure that the virtual he vehicle model is replicating the actual heavy vehicle as accurately as it can, in terms o performance and dynamic behavior (Figure 1), as we have reported previously [25]. virtual model was found to closely represent the actual heavy vehicle and this was furt validated by multiple performance indices. As shown in Table 1, the root mean squ error (RMSE) of lateral acceleration was very close to 0, indicating a good correlation obtained between both experimental and simulation data. The lateral acceleration m absolute error (MAE) was also very close to 0, implying that the simulation mo accurately represents the experimental data. The regression coefficient (R) for lat acceleration was also observed to be close to 1, indicating that the simulation model explained the majority of the variances observed.  Thus, in this paper, several classes of verified heavy vehicles with various indepe ent parameters were simulated. These independent parameters were divided into sev categories as outlined in Table 2, while Figure 2 shows the flowchart describing the s ulation process that had been conducted using the IPG TruckMaker(R) software. The a ysis took into consideration the common single unit trucks (SUT) and single truck-trai (STT) that are commonly used in Malaysia, which are SUTs with two, three and four a and SSTs with four and five axles. Figure 3 shows the SUTs and STTs used in the sim tions conducted in this study.   Thus, in this paper, several classes of verified heavy vehicles with various independent parameters were simulated. These independent parameters were divided into several categories as outlined in Table 2, while Figure 2 shows the flowchart describing the simulation process that had been conducted using the IPG TruckMaker(R) software. The analysis took into consideration the common single unit trucks (SUT) and single truck-trailers (STT) that are commonly used in Malaysia, which are SUTs with two, three and four axles and SSTs with four and five axles. Figure 3 shows the SUTs and STTs used in the simulations conducted in this study. It has been reported that GVW, speed and road condition were among the contributing factors in a rollover accident [5,9,10,[26][27][28][29][30][31]. Thus, in this study, the simulation of the heavy vehicles was conducted using various speed values, gross vehicle weights (GVW), coefficient of friction and cornering radius. Additionally, Karim et al. [32] have analyzed and reported the prevalence and degree of GVW and speed violations in selected areas in Malaysia; these data were used as the reference value and input data for the simulation settings in this study. Karim et al. [32] have also reported that 2-axle vehicles recorded the highest percentage of GVW violation, with 120% from its permissible GVW, followed by 3-axle (101%), 4-axle (83.9%) and 5 axle ones (51.9%). It was also reported that 46% of the total heavy vehicles weighing more than 20t violated the permissible speed (driving at more than 90 km/h) [32]. However, heavy vehicles driven at very low speeds (below 40 km/h) were also recorded. Table 3 shows the summary of heavy vehicle settings for speed and GVW used in the simulation.  It has been reported that GVW, speed and road condition were among the contributing factors in a rollover accident [5,9,10,[26][27][28][29][30][31]. Thus, in this study, the simulation of the heavy vehicles was conducted using various speed values, gross vehicle weights (GVW), coefficient of friction and cornering radius. Additionally, Karim et al. [32] have analyzed   It has been reported that GVW, speed and road condition were among the contributing factors in a rollover accident [5,9,10,[26][27][28][29][30][31]. Thus, in this study, the simulation of the heavy vehicles was conducted using various speed values, gross vehicle weights (GVW), coefficient of friction and cornering radius. Additionally, Karim et al. [32] have analyzed  In order to precisely determine the vehicle stability, the location of the vehicle center of gravity should be considered [10]. However, in this study, the location of the center of gravity (CoG) for each of the different heavy vehicle types was established by the IPG Truck Maker(R) software, where the volume and the height of the load was assumed to be uniform, regardless of the load weight (GVW) applied. According to Elischer and Prem, even though homogeneous loading does not fully represent the actual situation, it can be used to represent the "worst case" loading configuration, when used to determine the stability and safety of the heavy vehicle [33].
Jones and Childers defined the coefficient of friction of wet condition as 0.4 and 0.9 for dry condition [34]. Meanwhile, Kordani et al. mentioned the coefficient of friction of the roads used in his study is between 0.18 (icy) to 0.9 (dry) [29]. In addition, several studies have also reported on coefficients of friction that ranged from as low as 0.17 to 0.7 [35,36]. Thus, five values of road coefficient were also used to represent the real condition of Malaysian roads, which were 0.3 (wet condition), 0.4 and 0.5 (normal conditions) and 0.6 and 0.7 (dry conditions). In the simulation, the road segmented geometry was designed to have a cornering section that started and continued with a straight lane. This road was purposely designed in order to observe the effect of the vehicle stability and safety when maneuvering on the curved section of the road with different coefficients of friction and cornering radius values. Three values of cornering radius, which were 150 m, 200 m and 250 m, calculated 90 degrees of turning from its center, were selected. Figure 4 shows the road geometry generated using the IPG TruckMaker(R). Each cornering radius was designed to follow the superelevation value and the left side was set as the drive lane, in accordance with the Malaysian law. IPG TruckMaker(R) also offered the driving and maneuvering mode features to accurately replicate the driving experience, which were the corner cutting value and driving mode. The corner cutting value was set to "1", which indicated that the heavy vehicle was only allowed to drive on the driving lane area for the entire simulation, while the driving mode was set as "normal"; this was to indicate that the driver was in a calm condition while driving through the simulation. This normal driving mode was rated by a maximum value of the longitudinal and lateral acceleration (known as G-G diagram) of 3.0 ms −2 or approximately 0.31 g while cornering. Other driving modes available in the software were "defensive" and "agressive" conditions with different maximum G-G diagram value [37].
There are several parameters that can be used to measure the roll stability of a vehicle, such as through lateral load transfer (LTR), vehicle roll angle and lateral acceleration [10,38,39]. In this study, lateral acceleration was chosen as dependent parameter as it is commonly used to determine the roll stability and rollover propensity [15,17].  There are several parameters that can be used to measure the roll stability of a vehicle, such as through lateral load transfer (LTR), vehicle roll angle and lateral acceleration [10,38,39]. In this study, lateral acceleration was chosen as dependent parameter as it is commonly used to determine the roll stability and rollover propensity [15,17].

Post-Processing and Correlation Analysis
A number of simulations were run with various parameters, thus generating numerous sets of simulation files in spreadsheet format. Each file consisted of thousands of output data (lateral acceleration). The exhaustive list of data values was then screened to reveal the data of interest, i.e., the values for maximum lateral acceleration that occurred during vehicle cornering. For this purpose, a computer program language software, MATLAB was used. Through the use of custom-generated coding, the maximum values of lateral acceleration were sorted and transferred into a dedicated file. The flow of the screening process using MATLAB is as shown in Figure 5. The data collected were then tabulated and entered into a statistical analysis software, SPSS. A multivariate Pearson coefficient correlation analysis was employed to investigate the significance and degree of relationships between the independent and dependent variables. The correlation analysis was essential to determine which and whether the independent variables played a significant role in the occurrence of rollovers.

Post-Processing and Correlation Analysis
A number of simulations were run with various parameters, thus generating numerous sets of simulation files in spreadsheet format. Each file consisted of thousands of output data (lateral acceleration). The exhaustive list of data values was then screened to reveal the data of interest, i.e., the values for maximum lateral acceleration that occurred during vehicle cornering. For this purpose, a computer program language software, MATLAB was used. Through the use of custom-generated coding, the maximum values of lateral acceleration were sorted and transferred into a dedicated file. The flow of the screening process using MATLAB is as shown in Figure 5.  There are several parameters that can be used to measure the roll stability of a vehicle, such as through lateral load transfer (LTR), vehicle roll angle and lateral acceleration [10,38,39]. In this study, lateral acceleration was chosen as dependent parameter as it is commonly used to determine the roll stability and rollover propensity [15,17].

Post-Processing and Correlation Analysis
A number of simulations were run with various parameters, thus generating numerous sets of simulation files in spreadsheet format. Each file consisted of thousands of output data (lateral acceleration). The exhaustive list of data values was then screened to reveal the data of interest, i.e., the values for maximum lateral acceleration that occurred during vehicle cornering. For this purpose, a computer program language software, MATLAB was used. Through the use of custom-generated coding, the maximum values of lateral acceleration were sorted and transferred into a dedicated file. The flow of the screening process using MATLAB is as shown in Figure 5. The data collected were then tabulated and entered into a statistical analysis software, SPSS. A multivariate Pearson coefficient correlation analysis was employed to investigate the significance and degree of relationships between the independent and dependent variables. The correlation analysis was essential to determine which and whether the independent variables played a significant role in the occurrence of rollovers. The data collected were then tabulated and entered into a statistical analysis software, SPSS. A multivariate Pearson coefficient correlation analysis was employed to investigate the significance and degree of relationships between the independent and dependent variables. The correlation analysis was essential to determine which and whether the independent variables played a significant role in the occurrence of rollovers.

Simulation of Virtual Heavy Vehicle Models
The simulation files for the results obtained from IPG TruckMaker(R) were exported into spreadsheet format (Microsoft Excel) using an IPG TruckMaker(R) feature called IPG Control. This enabled the data to be screened and thoroughly analyzed. In total, there were 8235 simulation files that had been generated, with 1080 files from two-axle SUTs, 1485 files from three-axle SUTs, 1755 files from four-axle SUTs, 1755 files from four-axle STTs and 2160 files from five-axle STTs. Different types of heavy vehicles generated a different amount of simulation data due to the different maximum number of GVW sets (see Figure 2), as, the higher the maximum GVW, the more simulation data would be generated for the same speed, coefficient of friction and cornering radius. After all data had been successfully screened and sorted, they were then imported into a statistical analysis software (SPSS) to be further analyzed.

Data Screening and Processing
Each simulation file for each vehicle class produced a data set which consisted of the distance travelled, vehicle speed, GVW, CoF, curve radius and lateral acceleration. The maximum value of lateral acceleration was screened from each data set by using a customized programming language on MATLAB. The selected screened data for two-axle SUTs maneuvered at cornering radius of 150 m, CoF of 0.3 and GVW of 10,000 kg and 15,000 kg are shown in Table 4.  Table 5 shows a summary of vehicle safety conditions generated through the simulations. The vehicle was categorized to be in either safe or unsafe (rollover) conditions based on a large number of simulations. Two-axle SUTs recorded the highest percentage of unsafe conditions (40%), followed by three-axle SUTs (32%), four-axle SUTs (27%), five-axle STTs (25%) and four-axle STTs (23%), out of the total number of simulations. These different percentage values of unsafe conditions could be due to the number of axles on the heavy vehicle. For example, for simulations computed using the same GVW, vehicle speed and road conditions, the three-axle SUT was likely to be more stable than the two-axle SUT, since three-axle SUTs would have more tire contact patches on the road to hold the lateral force and slide slip, compared to the two-axle SUT. However, four-axle STTs recorded 4% less unsafe conditions compared to four-axle SUTs, even though similar GVW, speed and road condition settings were used in the simulation. This was due to the fact that four-axle SUTs have a shorter wheelbase than four-axle STTs, thus generating more lateral force during cornering. In addition, Figure 6 shows the number of unsafe conditions when arranged according to the heavy vehicle speed, coefficient of friction and cornering radius. Based on Figure 6, it can be observed that speed has a positive correlation with the occurrence of unsafe conditions, whereby as the vehicle speed increased, the number of unsafe conditions also increased. This observation obeys the principle of circular motion where the increase of lateral acceleration value is directly proportional to the speed of the vehicle, when the cornering radius is constant. In contrast, as the CoF and cornering radius increased, the number of unsafe conditions were observed to decrease, due to the better road grip during vehicle maneuvering.  The unsafe conditions in these simulation cases can be divided into two types, which are tripped rollover and un-tripped rollover [19]. The tripped rollover occurred when the heavy vehicle left the driving lane, tripped to the curb and rolled over (Figure 7). Meanwhile, an un-tripped rollover occurred when the heavy vehicle started to roll over on the driving lane due to overspeeding and excessive GVW. The road coefficient of friction (CoF) was found to be the main contributing factor that resulted in the occurrence of either The unsafe conditions in these simulation cases can be divided into two types, which are tripped rollover and un-tripped rollover [19]. The tripped rollover occurred when the heavy vehicle left the driving lane, tripped to the curb and rolled over (Figure 7). Meanwhile, an un-tripped rollover occurred when the heavy vehicle started to roll over on the driving lane due to overspeeding and excessive GVW. The road coefficient of friction (CoF) was found to be the main contributing factor that resulted in the occurrence of either tripped or un-tripped rollovers. For instance, when the same vehicle type, GVW, speed and cornering radius were used during the simulation, a lower CoF would result in a tripped rollover, while a higher CoF would result in an un-tripped rollover. Table 6 shows the percentage of tripped and un-tripped rollovers from the unsafe conditions of the different heavy vehicle classes.

Analysis of Simulation Results
Data analysis revealed that there is a relationship between the maximum lateral acceleration and the heavy vehicle speed (Table 4), where the maximum lateral acceleration increases with increasing heavy vehicle speed, at any coefficient of friction values. In other words, the faster the heavy vehicle is, the higher is the maximum lateral acceleration that would be generated during cornering, thus increasing the risks of unsafe conditions and rollover propensity. To understand these in detail, the graphs generated by a two-axle SUT when maneuvering a 150 m, 200 m and 250 m cornering radius are shown in Figures  8-10. The heavy vehicle rollover incidences were indicated by the red-colored line in the graphs. The maximum lateral acceleration values that were beyond the right section of the red-colored lines were the lateral acceleration values at which an impending rollover would occur.
The graphs show that, at the same speed and CoF, the maximum lateral acceleration increased when GVW increased. However, these can be seen clearly at the speed of 60 km/h and above, since speeds of 40 km/h and 50 km/h showed a very minimal change of maximum lateral acceleration value when GVW increased. Hence, it can be concluded that the heavier the load carried by the heavy vehicle is, the higher are the risks of rollover during cornering [27,28]. Furthermore, as the CoF increased, the maximum lateral acceleration also increased. This was due to the road surface becoming rougher as the CoF values increased, resulting in a better tire contact patch on the road (more grip), hence more lateral acceleration was required for a rollover and unsafe condition to occur [29].

Analysis of Simulation Results
Data analysis revealed that there is a relationship between the maximum lateral acceleration and the heavy vehicle speed (Table 4), where the maximum lateral acceleration increases with increasing heavy vehicle speed, at any coefficient of friction values. In other words, the faster the heavy vehicle is, the higher is the maximum lateral acceleration that would be generated during cornering, thus increasing the risks of unsafe conditions and rollover propensity. To understand these in detail, the graphs generated by a twoaxle SUT when maneuvering a 150 m, 200 m and 250 m cornering radius are shown in Figures 8-10. The heavy vehicle rollover incidences were indicated by the red-colored line in the graphs. The maximum lateral acceleration values that were beyond the right section of the red-colored lines were the lateral acceleration values at which an impending rollover would occur.
The graphs show that, at the same speed and CoF, the maximum lateral acceleration increased when GVW increased. However, these can be seen clearly at the speed of 60 km/h and above, since speeds of 40 km/h and 50 km/h showed a very minimal change of maximum lateral acceleration value when GVW increased. Hence, it can be concluded that the heavier the load carried by the heavy vehicle is, the higher are the risks of rollover during cornering [27,28]. Furthermore, as the CoF increased, the maximum lateral acceleration also increased. This was due to the road surface becoming rougher as the CoF values increased, resulting in a better tire contact patch on the road (more grip), hence more lateral acceleration was required for a rollover and unsafe condition to occur [29]. Data analysis conducted on three-axle SUTs, four-axle SUTs, four-axle STTs and five-axle STTs also showed similar trends (graphs not shown). Data analysis conducted on three-axle SUTs, four-axle SUTs, four-axle STTs and five-axle STTs also showed similar trends (graphs not shown).   For every heavy vehicle type, the maximum lateral acceleration values resulting from the different GVW (at the same speed, CoF and cornering radius) were tabulated and used to determine the mean maximum lateral acceleration. Table 7 shows an example of the calculated mean maximum lateral acceleration of a two-axle SUT driven at 40 km/h, with CoF of 0.3 and cornering radius of 150 m. The relationship between the mean maximum For every heavy vehicle type, the maximum lateral acceleration values resulting from the different GVW (at the same speed, CoF and cornering radius) were tabulated and used to determine the mean maximum lateral acceleration. Table 7 shows an example of the calculated mean maximum lateral acceleration of a two-axle SUT driven at 40 km/h, with CoF of 0.3 and cornering radius of 150 m. The relationship between the mean maximum lateral acceleration and vehicle speeds (at various cornering radius) of other heavy vehicle classes were also analyzed and these are shown in Figure 11, for other SUTs, and Figure 12 for STTs. For two-axle SUTs, the trends observed for cornering radii of 200 m and 250 m were similar to those for 150 m, as explained in previous paragraphs. Data analysis also revealed that the mean maximum lateral acceleration increased when vehicle speed was increased (for all heavy vehicle classes). On the other hand, the mean maximum lateral acceleration increased when the CoF increased. lateral acceleration and vehicle speeds (at various cornering radius) of other heavy vehicle classes were also analyzed and these are shown in Figure 11, for other SUTs, and Figure  12 for STTs. For two-axle SUTs, the trends observed for cornering radii of 200 m and 250 m were similar to those for 150 m, as explained in previous paragraphs. Data analysis also revealed that the mean maximum lateral acceleration increased when vehicle speed was increased (for all heavy vehicle classes). On the other hand, the mean maximum lateral acceleration increased when the CoF increased.

Correlation Analysis
A Pearson correlation analysis was performed to determine the degree and strength of the relationships between the dependent and independent variables. This exercise was also done to ensure that any change (in value) of the independent variables would correlate and result in a significant change to the dependent variables. Otherwise, the independent variables could be deemed as not important and thus neglected.
In the case of two-axle SUTs (Table 8), a significantly strong correlation was observed between the speed of the two-axle SUT and maximum lateral acceleration (r = 0.873, p < 0.01). A significant correlation was also observed between the two-axle SUT GVW and the maximum lateral acceleration, but this correlation was observed to be low (r = 0.352, p < 0.01). Meanwhile, a significant correlation was found between the two-axle SUT CoF and the maximum lateral acceleration (r = 0.346, p < 0.01), indicating that the maximum lateral acceleration increased when CoF values increased. In contrast, a very weak and negligible correlation (albeit significant) was observed between the two-axle SUT cornering radius and the maximum lateral acceleration (r = −0.214, p < 0.01).
Similar observations were also recorded when a Pearson correlation analysis was conducted for all classes of heavy vehicles (Table 9). These findings further confirmed that vehicle speed, GVW and CoF are significant factors that influenced the maximum lateral acceleration that can cause a heavy vehicle to roll over, in parallel with findings in previous reports [27][28][29]. These results are consistent with those reported in previous studies, where vehicle speed and road conditions (CoF) have been shown to significantly influence lateral acceleration [40][41][42]. In parallel with our results, Ryu et al. [43] also stated that vehicles with a heavy load often have a higher center of gravity, thus increasing the risk to roll over in an accident. However, in this study, the location of the center of gravity (CoG) for each of the different heavy vehicle types was established by the IPG Truck Maker(R) software, where the volume and the height of the load were assumed to be uniform, regardless of the load weight (GVW) applied. Even though homogeneous loading does not fully represent the actual situation, we postulate that this configuration would represent the "worst case" scenario that could happen, when a particular heavy vehicle with high GVW (with high loading) maneuvers a curved section of the road.

Correlation Analysis
A Pearson correlation analysis was performed to determine the degree and strength of the relationships between the dependent and independent variables. This exercise was also done to ensure that any change (in value) of the independent variables would correlate and result in a significant change to the dependent variables. Otherwise, the independent variables could be deemed as not important and thus neglected.
In the case of two-axle SUTs (Table 8), a significantly strong correlation was observed between the speed of the two-axle SUT and maximum lateral acceleration (r = 0.873, p < 0.01). A significant correlation was also observed between the two-axle SUT GVW and the maximum lateral acceleration, but this correlation was observed to be low (r = 0.352, p < 0.01). Meanwhile, a significant correlation was found between the two-axle SUT CoF and the maximum lateral acceleration (r = 0.346, p < 0.01), indicating that the maximum lateral acceleration increased when CoF values increased. In contrast, a very weak and negligible correlation (albeit significant) was observed between the two-axle SUT cornering radius and the maximum lateral acceleration (r = −0.214, p < 0.01).
Similar observations were also recorded when a Pearson correlation analysis was conducted for all classes of heavy vehicles (Table 9). These findings further confirmed that vehicle speed, GVW and CoF are significant factors that influenced the maximum lateral acceleration that can cause a heavy vehicle to roll over, in parallel with findings in previous reports [27][28][29]. These results are consistent with those reported in previous studies, where vehicle speed and road conditions (CoF) have been shown to significantly influence lateral acceleration [40][41][42]. In parallel with our results, Ryu et al. [43] also stated that vehicles with a heavy load often have a higher center of gravity, thus increasing the risk to roll over in an accident. However, in this study, the location of the center of gravity (CoG) for each of the different heavy vehicle types was established by the IPG Truck Maker(R) software, where the volume and the height of the load were assumed to be uniform, regardless of the load weight (GVW) applied. Even though homogeneous loading does not fully represent the actual situation, we postulate that this configuration would represent the "worst case" scenario that could happen, when a particular heavy vehicle with high GVW (with high loading) maneuvers a curved section of the road.