1. Jiangbi Hu, Transportation Research Center, Department of Civil Engineering,Beijing University of Technology, China 2011.5. A QUANTITATIVE MODEL OF ROAD-SURFACE SAFETY

2. Contents Introduction Safety factors in the interaction between vehicle and pavement Pavement performance and traffic safety Pavement safety model Model validation Conclusions

3. 1.INTRODUCTION Road traffic system is a dynamic and complicated system, which provides safe, comfortable and economic road condition for road customer Road(include its structures) condition is an important reason that causes the traffic accident and has caused accidents up to 30% along with driver interaction.

4. 1.INTRODUCTION Driver safety is associated with surface roughness and skid resistance. The friction is the basic parameter that limits vehicle speed, stability and effects traffic safety and driver comfort. In many countries standards, there are the minimum f value for new and maintained road.

5. 1.INTRODUCTION The minimum permissible f ranges from 0.6 in Belgium to 0.4 in France. Construction standards in the former SU f is determined by the expected traffic conditions and type of use. In dangerous sections: small- radius curves etc. f≥ 0.6; good conditions: f ≥ 0.45, ordinary conditions, f ≥ 0.3.

6. 1.INTRODUCTION In China, pavement skid resistance conditions research began in the 1980s, in 1996 SRV tested by a static pendulum skid-resistance tester was introduced. SRV limit an acceptable range, with no allowance for different pavement conditions. SRV of secondary roads is 47–50, with a SMTD of 0.4–0.6 mm.

7. 2.SAFETY FACTORS BETWEEN VEHICLE AND PAVEMENT Safe operation of a vehicle traveling on any road must be satisfied for equations (1) and (2): (1) Where: P is the vehicle traction force (kg) ； Z ω 、 Z ψ 、 Z j are the air, road, and inertia resistance (kg). P is limited to the friction between the tire and pavement: (2) Where:G K is the vehicle load; Ψ is the adhesion coefficient between the tire and pavement.

8. 2.SAFETY FACTORS BETWEEN VEHICLE AND PAVEMENT In a straight line, the braking resistance is parallel to the driving direction, longitudinal friction force F R is involved. The front wheels are turned at an angle to the driving direction, a transverse friction force F T occurs. F R and F T occur simultaneously, the integrated force should not exceed the maximum friction force F, as shown in equation(3). F 2 = F R 2 + F T 2 (3)

9. 2.SAFETY FACTORS BETWEEN VEHICLE AND PAVEMENT Figure 1: Friction between tire and pavement In Fig1, when Fmax is exceeded the vehicle will slide. Braking suddenly on a curve may cause the vehicle to exceed Fmax and accident.

10. 2.SAFETY FACTORS BETWEEN VEHICLE AND PAVEMENT Over speed is the major cause of accidents on curved sections. The low f, lack of superelevation on the curves of one national highway in China causes six sliding per year. Figure 2: Relationship between number of accidents and SFC.

11. 3. PAVEMENT PERFORMANCE AND TRAFFIC SAFETY If the normal reaction forces of the front wheels drop to zero, the wheels of the front axle may raise off the ground, resulting the car’s overturning. If the normal reaction forces of the rear wheels are at zero the traction force is lost base on the adhesion condition, and if the automobile is unable recover, it may slide. Figure 3:Accident rate versus SFC for rainless & rainy days

12. 3. PAVEMENT PERFORMANCE AND TRAFFIC SAFETY Figure 5 showing SFC changes in kilometers 0–48 of a certain highway in 3 years, opened in September 1993. Figure 5: SFC as a function of time and location for a certain expressway

13. 4.PAVEMENT SAFETY MODEL Adequate pavement friction is a necessary condition for vehicles to travel safety. According to conditions of the vehicle running force, f can be divided into: (1)longitudinal friction coefficient f R (2) transverse friction coefficient f T

14. 4.PAVEMENT SAFETY MODEL To keep the balance between the actual and expected values, some concepts are introduced : (1) maximum longitudinal friction coefficient f Tmax (2) allowable longitudinal friction coefficient f TA (allowed transit friction) (3)allowable transverse friction coefficient f SA (allowed side friction) (4) expected longitudinal friction coefficient f TR (required transit friction), and expected transverse friction coefficient f SR (required side friction).

15. (1) Quantitative safety model for the longitudinal friction coefficient The longitudinal friction coefficient can be calculated by (7) (7) Where: f T —— the longitudinal friction coefficient F T —— the longitudinal friction Q —— the gravity.

16. (1) Quantitative safety model for the longitudinal friction coefficient f TA is a reliably safe and determined by the pavement friction-coefficient standard. f Tmax is the maximum value under special limiting conditions f TR is under the expected operating speed. In practice, there is probably a certain standard deviation Δf T between f TA and f TR, which is calculated by(8) (8)

17. (1) Quantitative safety model for the longitudinal friction coefficient When f TA ≤ f TR, while Δf T ≤ 0, the pavement safety performance is “good.” When Δf T > 0 but less than a certain “critical value,” the pavement safety performance is “relatively good.” When Δf T > 0 and also more than a “critical value,” the pavement safety has hidden danger

18. (2) Quantitative safety model for the transverse friction coefficient The transverse friction coefficient value deviation Δf S between f SA and f SR, can be calculated by (12) (12) When Δf S ≤ 0, the pavement safety performance is “good.” When Δf S > 0 but less than a certain “critical value,” the safety performance is “relatively good.” When Δf S > 0 and greater than a “critical value,” the pavement is “dangerous.”,

19. 5. Model validation A certain road in China was divided into three sections according to pavement age: 16 years, 4 years, and new reconstruction completed in September 2003. In the three sections, the accident-prone portions and those with skidding accidents are chose as shown in Table 3.

20. 5. Model validation In tested sections, five representative points about 5–10 m apart along the left wheel path in the driving direction tested by the pendulum apparatus in table 4. Pavement structure type: 3-cm asphalt concrete, 10-cm bituminous penetration, 20-cm gradation of sand–gravel-doped lime soil.

21. 5. Model validation Table 4: Measured pavement friction coefficients Serial number Location route characteristic surface age of pavement F B20 11205.800–1206.800curve smooth, intact, and level with ruts in pavement 16 years32.8 21210.000–1421.000 straight-line segment smooth, intact, and level with ruts in the pavement 16 years33.8 31223.448–1224.448curve cracks and ruts in the pavement 16 years31.5 41364.300–1365.300 straight-line segment pavement intact4 years42.28 51361.000–1362.000 straight-line segment pavement intact3 months57.2 According to pavement design standard, f TA = 47. Equation (8) for the quantitative model gave Δf T values of 14.2, 13.2, 15.48, 4.72, and -10.2 Taking the Δf T =Min(14.2,13.2,15.48)=13.2 as the critical value, we obtain F B20 ≥ 47 (Δf S ≤ 0)

22. 5. Model validation serial number kilometer numberroute characteristic age of pavement F B20 safety 11205.800–1206.800curve16 years32.8 dangero us 21210.000–1421.000straight-line segment16 years33.8 dangero us 31223.448–1224.448curve16 years31.5 dangero us 41364.300–1365.300straight-line segment4 years42.28 good 51361.000–1362.000straight-line segment3 months57.2 safe Effects of appraise

23. 6. CONCLUSIONS The road system must meet the following equation: Safety: Δf T ≤ 0, Δf S ≤ 0,(ΔfT=f TA -f TR, Δf S =f SA -f SR ) good: 0<Δf S ≤min(Δf Si ), 0<Δf T ≤min(Δf Ti ), Dangerous: Δf S >min(Δf Si ), Δf T >min(Δf Ti ) The minimum f for penetration-type asphalt pavement allowable standards is too low and can easily contribute to skidding accidents in China.

24. Thank you for your attentions!