# A Novel Safety Assessment Framework for Pavement Friction Evolution Due to Traffic on Horizontal Curves

^{1}

^{2}

^{3}

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## Abstract

**:**

_{HGV}). The results show that the AADT and AADT

_{HGV}have a considerable impact on the road risk level. When the truck traffic volume is less than 1000 veh/d, the risk of horizontal curves changes less as road operational time goes. The research results can provide a reference for the road maintenance department to determine the timing of road maintenance.

## 1. Introduction

## 2. Methodology

#### 2.1. Single-Vehicle Risk Assessment Model

#### 2.1.1. Evolution of Friction Supply

_{HGV}) to establish the friction evolution model of the SMA asphalt pavement, expressed by Equation (1):

#### 2.1.2. Skidding Limit State Function

^{2}), $v$ is the driving speed (m/s), $f$ is the side fraction factor, and $e$ is the superelevation. The anti-skid friction demand ${f}_{p-demand}$ of the mass point model is shown in Equation (8):

#### 2.2. Reliability Theory

#### 2.3. Multi-Vehicle Risk Index

## 3. Numerical Study

#### 3.1. Basic Model Parameters

#### 3.1.1. Speed

_{1}and Z

_{1}for the car. The counterparts of HGV are 78.56 and 9.38, utilized in model Z

_{1}and Z

_{1}for HGV. The Kolmogorov–Smirnov test results of the speed data are shown in Table 2. The two-tailed asymptotic significance value is 0.2, which is greater than 0.05. Therefore, it could be considered that the speeds of cars and HGV have a normal distribution in a statistical significance. This finding was consistent with Sil, et al. [30] and Himes [31].

#### 3.1.2. Mean Profile Depth (MPD)

#### 3.1.3. Vehicle Parameters

#### 3.2. Parametric Study Results

#### 3.2.1. Influence of Traffic Characteristics on Friction Coefficient

_{HGV}). In the early stage of road operation (e.g., CTV = 30 million vehicles or less), the friction coefficient drops dramatically as the CTV increases. After that, the rate of decrease of the friction coefficient slows down with the increase of CTV. This evolution trend of friction coefficient is consistent with Kane, et al. [32].

_{HGV}on friction coefficient is more substantial for a higher CTV (e.g., CTV over 40 million vehicles). When CTV exceeds 20 million vehicles, most of the curves tend to be parallel. Pavement friction coefficient in these curves with AADT

_{HGV}= 5000 veh/d is only 80% of AADT

_{HGV}= 1000 veh/d for a certain value of CTV. This result verifies the point that the friction coefficient of the road is significantly affected by the truck [1,32]. Therefore, freeways with numerous truck volumes need more road maintenance work to ensure that the road can provide sufficient friction coefficient for vehicles.

#### 3.2.2. Model Comparison

_{1}and the suspension vehicle model Z

_{2}under different CTV where AADT

_{HGV}equals to 2000 veh/d. It can be seen that the reliability of model Z

_{2}is lower than that of model Z

_{1}for car. Therefore, the skidding probability of model Z

_{2}is higher than model Z

_{1}. This result indicates that the car’s suspension system reduces the safety when turning, which is consistent with You, Sun, and Gu [15]. A similar finding is obtained for HGV.

_{2}) is very small (close to 0). However, compared to the HGV, the suspension system substantially affects the safety for car. This result illustrates that the mass point model adopted by current road design theory has less impact for skidding failure probability of HGV, but has strong influence for the car. The reason may be that the driving speed of HGV is too low in contrast with the cars’ speed, leading to a reduced skidding risk.

_{1}and Car-Z

_{2}becomes more and more significant as the road operation time goes. When the CTV is equal to 100 million vehicles, the skidding probability for Car-Z

_{2}is about 22 times that of the Car-Z

_{1}. It not only demonstrates that traditional road design theory underestimates the risk of cars, but also that the hidden dangers caused by such underestimation will be magnified over time.

#### 3.2.3. Safety Assessment for Different Traffic Characteristics

_{HGV}= 2000 veh/d) to analysis the impact of AADT for safety on the horizontal curve over time. Figure 6 exhibits the multi-vehicle risk index of the varying AADT changes over the years. It is found that the safety on the horizontal curve is very sensitive to the AADT. Among these five traffic characteristics, the AADT with a value of 10,000 veh/d has the least threat to vehicle accident risk. Although for a curve with a heavy traffic volume (e.g., AADT over 30,000 veh/d), the multi-vehicle risk index (MRI) rises rapidly to 100% after four years, indicating that the road has not be maintained during this period, the probability that one or more cars skid will reach to 100%. Therefore, this result suggests that the freeway with heavy traffic flow need to be frequently maintained.

_{HGV}= 1000 veh/d) will rise much slower. This result indicates that the large truck traffic volume not only leads to lower friction coefficient, but also causes higher hidden slippery risk.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgements

## Conflicts of Interest

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**Figure 5.**Risk comparison of different models (AADT

_{HGV}= 2000 veh/d). POF, probability of failure; HGV, heavy goods vehicle.

Radius (m) | Design Speed (km/h) | Posted Speed(km/h) | Lane | Length (m) | Gradient (%) | Superelevation (%) |
---|---|---|---|---|---|---|

1000 | 100 | 100 | 4 | 574 | 2.84 | 5 |

Vehicles | Sample Size | Normal Parameters | Most Extreme Differences | Asymp.sig. (2-Tailed) | Kolmogorov- Smirnov Z | |||
---|---|---|---|---|---|---|---|---|

Mean | Std.Deviation | Absolute | Positive | Negative | ||||

Car | 117 | 103.27 | 11.17 | 0.06 | 0.06 | -0.04 | 0.06 | 0.20 |

HGV | 79 | 78.56 | 9.38 | 0.09 | 0.09 | -0.07 | 0.09 | 0.20 |

Section | Geometrical Design | CTV (veh) | Initial MPD (mm) | Recent MPD (mm) |
---|---|---|---|---|

A1 | Straight/relatively straight alignment and slope less than 3% | 22 × 107 | 1.02 | 1.04 |

A2 | 22 × 107 | 1.02 | 1.04 | |

A3 | 22 × 107 | 1.08 | 1.15 | |

A4 | 21.7 × 107 | 1.16 | 1.22 | |

A5 | 34.2 × 107 | 1.1 | 1.14 | |

A6 | 33.6 × 107 | 1.17 | 1.16 | |

B1 | Straight/relatively straight alignment and slope less than 3% | 9.16 × 107 | 1.26 | 1.31 |

B2 | 5.31 × 107 | 1.26 | 1.43 | |

B3 | 9.47 × 107 | 1.42 | 1.66 | |

B4 | 5.07 × 107 | 1.27 | 1.61 | |

B5 | 3.58 × 107 | 1.19 | 1.26 | |

C1 | Higher curvature and maximum slope 3–6% | 17 × 107 | 1.59 | 1.69 |

C2 | 18.5 × 107 | 1.55 | 1.73 | |

C3 | 8 × 107 | 1.34 | 1.5 | |

C4 | 8.41 × 107 | 1.27 | 1.46 |

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**MDPI and ACS Style**

Xu, G.; Xu, J.; Gao, C.; Sun, R.; Shan, H.; Ma, Y.; Ran, J.
A Novel Safety Assessment Framework for Pavement Friction Evolution Due to Traffic on Horizontal Curves. *Sustainability* **2022**, *14*, 10714.
https://doi.org/10.3390/su141710714

**AMA Style**

Xu G, Xu J, Gao C, Sun R, Shan H, Ma Y, Ran J.
A Novel Safety Assessment Framework for Pavement Friction Evolution Due to Traffic on Horizontal Curves. *Sustainability*. 2022; 14(17):10714.
https://doi.org/10.3390/su141710714

**Chicago/Turabian Style**

Xu, Guilong, Jinliang Xu, Chao Gao, Rishuang Sun, Huagang Shan, Yongji Ma, and Jinsong Ran.
2022. "A Novel Safety Assessment Framework for Pavement Friction Evolution Due to Traffic on Horizontal Curves" *Sustainability* 14, no. 17: 10714.
https://doi.org/10.3390/su141710714