Determination of the Friction Coefficients of Icy Pavements Under Different Amounts of Snowfall

Summary

Here, we present a method for determining the friction coefficient of pavements with different ice thicknesses indoors. The complete procedure includes the preparation of the equipment, the calculation and analysis of the snowfall, equipment calibration, friction coefficient determination, and data analysis.

Abstract

Ice on road surfaces can lead to a significant decrease in the friction coefficient, thus endangering driving safety. However, there are still no studies that provide exact friction coefficient values for pavements covered in ice, which is detrimental to both road design and the selection of winter road maintenance measures. Therefore, this article presents an experimental method to determine the friction coefficient of icy road surfaces in the winter. A British portable tester (BPT), also known as a pendulum friction coefficient meter, was employed for the experiment. The experiment was divided into the following five steps: the preparation of the equipment, the calculation and analysis of the snowfall, equipment calibration, friction coefficient determination, and data analysis. The accuracy of the final experiment is directly affected by the equipment accuracy, which is described in detail. Moreover, this article suggests a method for calculating the ice thickness for corresponding amounts of snowfall. The results illustrate that even patchy ice formed by very light snowfall may lead to a significant decrease in the friction coefficient of the pavement, thus endangering driving safety. Additionally, the friction coefficient is at its peak when the ice thickness reaches 5 mm, meaning protection measures should be taken to avoid the formation of such ice.

Introduction

Pavement friction is defined as the grip between the vehicle tires and the underlying road surface¹. The index most commonly associated with pavement friction in road design is the pavement friction coefficient. Friction is one of the most important factors in road design and is second only to durability. There is a strong and clear correlation between pavement friction performance and accident risk². For example, there is a significant negative correlation between road accident rates and pavement skid resistance^3,4,5. Several factors may contribute to a decrease in pavement friction, and one of the most direct and influential of these factors is snowfall⁶. Specifically, snowfall causes ice to form on the pavement, thereby resulting in a significant reduction in the road friction coefficient^7,8. A study focusing on the factors that influence traffic accident rates in southern Finland noted that accident rates commonly peak on days with heavy snowfall and that more than 10 cm of snow can lead to a doubling of the accident rate⁹. Similar results have been found in studies performed both in Sweden and Canada^10,11. Therefore, studying the friction properties of snow-frozen pavements is crucial for improving road safety.

Determining the friction coefficient of icy pavements is a complex process because the friction coefficient may vary under different snowfall levels and pavement ice thicknesses. Furthermore, varying temperatures and tire characteristics may also affect the friction coefficient. In the past, numerous experiments have been conducted to study the friction characteristics of tires on ice¹². However, due to the differences in individual environments and tire characteristics, consistent results cannot be obtained and used as a basis for theoretical studies. Therefore, many researchers have attempted to develop theoretical models to analyze the friction of tires on ice. Hayhoe and Sahpley¹³ suggested the concept of wet friction heat exchange at the interface between tires and ice, while Peng et al.¹⁴ proposed an advanced data model to predict friction based on the above concept. In addition, Klapproth presented an innovative mathematical model for describing the friction of rough rubber on smooth ice¹⁵. However, the above models have been shown to have significant errors, mainly due to their inability to accurately and efficiently characterize the friction properties of tires on ice¹⁶.

To reduce the errors of theoretical models, a large amount of experimental data is needed. The Finnish Meteorological Agency developed a friction model for predicting icy pavement friction, and the formula for that model was primarily based on data obtained from road weather stations and through statistical analysis¹⁷. Furthermore, Ivanović et al. gathered a significant amount of experimental data by analyzing the friction characteristics of tires on ice and calculated the friction coefficient of ice by regression analysis¹⁸. Gao et al. also proposed a novel prediction model of tire-rubber-ice traction by combining the Levenberg-Marquardt (LM) optimization algorithm with a neural network to obtain the formula for the friction coefficient on ice¹⁹. All the above models have been either validated or applied in practice and are, thus, considered feasible.

In addition to theoretical methods, many practical methods have been developed for measuring the friction coefficient of pavements in snowy and frozen areas. Due to the particularities of the weather, these methods have been widely used in Nordic countries such as Sweden, Norway, and Finland²⁰. In Sweden, the following three main types of friction measuring devices are used: the BV11, SFT, and BV14. The BV14, a dual friction tester developed specifically for winter maintenance assessments, is directly connected to the measuring vehicle and measures the dry friction on both wheel paths simultaneously²⁰. In Finland, the friction measuring vehicle (TIE 475) is used for winter road maintenance assessments, while in Norway, the ROAR friction measuring device (without water) is a commonly used piece of equipment². Most of the winter friction measurements carried out in Sweden, Norway, and Finland have been performed using ordinary passenger cars with ABS and instruments measuring deceleration under braking^2,20. The advantage of this method is that it is simple and relatively inexpensive, and the main disadvantage is that the accuracy of the method is very low.

The studies described above provide methods for predicting and detecting friction coefficients on ice. However, a uniform method and a specific value to guide road designers have still not been provided. Moreover, for winter roads, the friction coefficient between the tires and ice may vary with respect to different ice thicknesses, and different disposal measures should also be implemented²¹. Therefore, this paper aims to determine the friction coefficient of icy roads under different amounts of snowfall.

Internationally, the British portable tester (BPT) and the Swedish Road and Transport Research Institute portable friction tester (VTI PFT) are currently the most commonly used instruments for measuring the friction coefficient^22,23. The PFT is a portable friction tester developed by VTI, and it allows the operator to take measurements in an upright position and save the data on the computer²². The PFT can measure most contoured road markings, but the number of instruments currently available is still very small². The BPT is a pendulum friction coefficient tester that was developed by the British Road Research Laboratory (RRL, now TRL). The instrument is a dynamic pendulum impact-type tester used to measure the energy loss in cases when a rubber slider edge is propelled over a test surface. The results are reported as British Pendulum Numbers (BPNs) to emphasize that they are specific to this tester and not directly equivalent to those from other devices²⁴. The instrument has been shown to be useful for the determination of friction coefficients in the experimental pavement field²³. This experiment uses the BPT for the determination of friction coefficients.

The present study describes the experimental procedure for measuring the friction coefficient of icy pavements corresponding to different snowfall amounts indoors. The problems to be noted in the experiments, such as experimental calibration, experimental implementation, and the methods of data analysis, are explained in detail. The present experimental procedures can be summarized by the following five steps: 1) the preparation of the equipment, 2) the calculation and analysis of the snowfall, 3) equipment calibration, 4) friction coefficient determination, and 5) data analysis.

Protocol

1. Preparation of the equipment

1. BPT
   1. Ensure that the BPT (Figure 1) is within its service life and that the surface is clean and undamaged.
      NOTE: The components of the BPT are the base, leveling spiral, leveling bubble, pointer, pendulum, lifting spiral, fastening spiral, handle, and dial.
2. Asphalt slabs
   1. Ensure that the asphalt mixture sample size used for the experiment is 30 cm x 30 cm x 5 cm.
3. Freezing equipment
   1. Ensure that the freezing equipment used can freely regulate the temperature between -20 °C and 0 °C.
4. Prepare other equipment used in the experiment: a tripod, a measuring cylinder, a rubber sheet, a pavement thermometer, a sliding length ruler, and a brush.
   NOTE: The size of the rubber sheet used in the experiment was 6.35 mm x 25.4 mm x 76.2 mm, and it should meet the quality requirements given in Table 1²⁴.
   1. Ensure that the rubber sheet does not have any of the following defects: 1) oil stains; 2) widthways edge wear greater than 3.2 mm; or 3) lengthways wear greater than 1.6 mm.
   2. Before using a new rubber sheet, ensure that the rubber sheet is measured 10 times using a BPT on a dry surface before using it for official testing.

2. Calculation and analysis of the snowfall

NOTE: Table 2 provides the snowfall class classification. Considering extreme cases, the equipment requires 24 h of snowfall to conduct the study.

1. To ensure the ease of the experiment, carry out the corresponding calculation and analysis using the upper limit for each level of snowfall.
   ​NOTE: The different levels of the snowfall depth and the corresponding water volume of the samples after calculation are provided in Table 3. The experiment did not consider the influence of extraordinary snowstorms, and the categories of very light snow to large blizzards were numbered from 1 to 6.

3. Equipment calibration

1. Leveling and zero adjustment
   1. Place the BPT in a suitable position.
      NOTE: A suitable position means that the ground is flat and free of potholes.
   2. Rotate the leveling spiral on the base of the BPT to ensure that the leveling bubble remains in the middle position.
   3. Loosen the fastening spiral, rotate the lifting spiral to make the pendulum lift and swing freely, and then tighten the fastening spiral.
   4. Place the pendulum arm on the right cantilever of the pendulum table, keeping the arm in the horizontal position while rotating the pointer to the right side flush with the arm.
   5. Press the release button to let the pendulum arm swing freely. When the pendulum crosses the lowest point to reach the highest point, hold it by hand.
      NOTE: If it is accurate, the pointer should indicate zero at this time.
   6. If the pointer does not show the zero point, loosen or tighten the zeroing nut, and repeat step 3.1.4 and step 3.1.5 until the pointer indicates the zero point.
2. Calibration of the sliding length
   1. Place the asphalt slab directly under the pendulum while loosening the fastening spiral so that the lowest edge of the rubber sheet touches the surface of the asphalt slab.
   2. Prepare the sliding length ruler, and bring it close to the rubber sheet.
   3. Lift the carrying handle so that the left scale mark of the sliding length ruler is flush with the lowest edge of the rubber sheet.
   4. Lift the carrying handle, and move the pendulum to the right so that the lowest edge of the rubber sheet just touches the surface of the asphalt slab.
   5. Observe whether the sliding length ruler is leveled with the edge of the rubber sheet. If it is, the sliding length meets the requirement of 126 mm. Otherwise, continue the following operations.
   6. Turn the lifting spiral to adjust the height of the pendulum, and repeat steps 3.2.3-3.2.5 to adjust the sliding length so that it meets the requirements.
   7. When fine-tuning is needed, twist the leveling spiral on the base.
      ​NOTE: The leveling bubble needs to remain in the center during the adjustment.

4. Friction coefficient determination

1. Select seven asphalt slab pieces, clean them with a brush, and dry them naturally at room temperature.
2. Number the asphalt slabs in the order of 1-7.
3. Place the asphalt slabs into molds, and simultaneously cool and freeze them with a water layer.
   NOTE: In this experiment, the seven samples were placed into the freezer at a controlled temperature of -10 °C for 24 h. The different samples with the corresponding water volumes are shown in Figure 2.
   1. Sample 1: To simulate very light snow, pour 9 cm³ of water onto the asphalt sample. Fill the asphalt slab surface void with water, and level the raised part. The ice layer is not expected to completely cover the sample surface asphalt particles. Therefore, some particles will be exposed, and this phenomenon is known as patchy ice.
   2. Sample 2: To simulate light snow, pour 216 cm³ of water onto the asphalt sample using a measuring cylinder. The expected icing thickness is 2.17 mm. In this case, the water layer completely covers the surface of the sample. It should be completely frozen after icing.
   3. Sample 3: To simulate medium snow, pour 441 cm³ of water onto the asphalt sample using a measuring cylinder. The expected ice thickness is 5.4 mm.
   4. Sample 4: To simulate heavy snow, pour 891 cm³ of water onto the asphalt sample using a measuring cylinder. The expected ice thickness is 11 mm.
   5. Sample 5: To simulate a blizzard, pour 1,791 cm³ of water onto the asphalt sample using a measuring cylinder. The expected ice thickness is 22.1 mm.
   6. Sample 6: To simulate a large blizzard, pour 2,691 cm³ of water onto the asphalt sample using a measuring cylinder. The expected ice thickness is 33.2 mm.
   7. Sample 7: Directly place the sample into the freezer for cooling without adding water as a dry frozen sample for comparison.
4. After freezing, remove the samples from the freezer; in turn, remove the molds, and place them onto the BPT centers, which were previously leveled and zeroed.
5. Use the pavement thermometer to measure the surface temperature of the sample and record it.
6. Perform sliding length calibration to ensure a sliding distance of 126 mm.
7. Press the pendulum arm release switch. When the pendulum arm crosses the lowest point and swings to the highest one, hold it by hand, and read and record the result.
8. Restore both the pendulum arm and the pointer to the zero and horizontal positions, respectively.
   NOTE: The sliding length should be recalibrated each time a new sample is tested.
9. Repeat the steps a total of 10 times, and measure seven samples in sequence.
   ​NOTE: Each sample has 10 measurement readouts, and both the minimum and the maximum value differences should be less than 3.

5. Data analysis

1. Record the data in Figure 3 in a table, and average the measurement results to obtain the final result (Table 4).
2. Temperature correction for pendulum values
   1. Input the temperature value measurements into the following equation to obtain the temperature-compensated BPN value:
      
      NOTE: The temperature unit used in the original equation is the Kelvin, while the experimental temperatures are all in centigrade, so a temperature conversion has to be carried out. The two temperature units are converted as follows:
      T (K) = 273.15 + T (^oC)
   2. Subtract the compensated BPN value from the average BPN value in Table 4 to obtain the final temperature-compensated BPN value.
   3. Plot the final BPN values in Table 4 as a bar graph for more intuitive results (Figure 4).

Representative Results

Sample 7 in Table 4 is the dry sample control group, while the remaining samples 1-6 correspond to ice thicknesses ranging from very light snow to a large blizzard.

When comparing sample 7 and the other six groups, ice formation was observed to significantly reduce the friction coefficient of the pavement. Furthermore, the pavement friction coefficient decreased with increasing ice thickness, and the ice thickness tended to stabilize at 5 mm, which corresponds to medium snow. The final ice friction coefficient was approximately 25% of the surface friction coefficient of the dry and wet samples.

Based on sample 1, very light snowfall was noted to have a strong impact on the road friction coefficient. Furthermore, even with a very thin ice layer, the icing of the road surface caused by trace snowfall still reduced the road friction coefficient by approximately 50% compared to the control sample 7. For sample 4, sample 5, and sample 6, the final average BPN values were identical. This indicates that the road friction coefficient of the ice layer tends to stabilize and that the measurement of a thicker ice layer is not necessary.

With respect to sample 2, sample 3, and sample 4, the surface friction coefficient was observed to gradually decrease. The above samples correspond to ice thicknesses of 2 mm, 5 mm, and 11 mm, respectively. In theory, the friction coefficient of these samples should be consistent, whereas the actual measurement of the friction coefficient was greater for the 2 mm ice layer. The analysis suggests two reasons for this. First, at an ice thickness of 2 mm, the microstructure of the sample surface particles in the ice layer has a certain impact. Even if the ice surface of the sample is placed horizontally, with natural icing, it is not smooth at the microscopic level. Second, the pendulum arm contacts the ice during the experiment. The ice is compacted and deformed from the friction of the pendulum arm due to the thinness of the ice and the pressure exerted on it. The rubber block friction process undulates the surface particles of the test piece, resulting in a greater friction coefficient.

As shown in Figure 4, the ice friction coefficient tended to rapidly decrease as both the snowfall and thickness of the ice layer increased. Furthermore, it tended to stabilize when the ice thickness corresponding to medium snow was reached. Sample 1 represents very light snow adhered to the pavement surface after icing; this resulted in a reduction in the pavement friction coefficient, and its BPN value decreased by approximately 43% compared to the dry sample. Sample 2, sample 3, and sample 4 correspond to light, medium, and heavy snow, respectively, and the ice layer thicknesses of the three samples were different after icing. Among them, the BPN value of the medium snow was only one-half that of the light snow because the thickness of the ice layer corresponding to little snow was only 2 mm. Therefore, the microstructure of the sample surface still affects the friction coefficient value. When the ice layer reached the medium and heavy snow thicknesses, the microstructure of the sample no longer affected the friction coefficient. The slight difference between the two BPNs is due to the differing extrusion of the rubber sheet on the different ice thicknesses, which leads to ice deformation. The BPNs of the heavy snow, blizzard, and large blizzard samples were the same, meaning that when the ice thickness reached 11 mm, the rubber sheet no longer deformed the ice layer by compacting it, and the BPNs and friction coefficient values remained unchanged.

Temperature	Environmental temperature (°C)
	0	10	20	30	40
Flexibility	43-49	58-65	66-73	71-77	74-79
Hardness	55 ± 5

Table 1: Technical index requirements for the rubber sheet. This refers to natural rubber in particular.

Level	12h snowfall	24h snowfall
Very Light Snow	< 0.1	< 0.1
Little Snow	0.1 – 0.9	0.1 – 2.4
Medium Snow	1.0 – 2.9	2.5 – 4.9
Heavy Snow	3.0 – 5.9	5.0 – 9.9
Blizzard	6.0 – 9.9	10.0 – 19.9
Large Blizzard	10.0 – 14.9	20.0 – 29.9
Extraordinary Snowstorm	≥15.0	≥30.0

Table 2: Snowfall level classification. The unit of data in the table is millimeters (mm).

Level	24h snowfall (mm)	Snowfall depth (mm)	Corresponding to the volume of water on the sample (cm3)	Corresponding to the thickness of ice on the sample (mm)
Very Light Snow	< 0.1	< 0.8	< 9	0.1
Little Snow	2.4	19.2	216	2.6
Medium Snow	4.9	39.2	441	5.4
Heavy Snow	9.9	79.2	891	10.9
Bilzzard	19.9	159.2	1791	21.9
Large Bilzzard	29.9	239.2	2691	32.9
Extraordinary Snowstorm	≥30.0	≥240	≥2700	33

Table 3: Different snowfall levels corresponding to the volume of water on the sample. The densities of water and ice are 1g/cm³ and 0.92g/cm³, respectively.

Sample number	Pendulum value     Temperature: -1°C										Average value	Temper- ature corrected pendulum value
	1	2	3	4	5	6	7	8	9	10
	51	50	50	48	51	49	50	48	51	48	50	45
	31	33	32	33	33	34	34	33	32	31	33	28
	19	18	20	20	21	21	20	19	20	19	19	14
	17	18	20	19	18	18	19	19	18	18	18	13
	18	19	18	17	16	18	19	18	17	18	18	13
	18	17	18	17	16	18	19	18	17	18	18	13
	83	82	85	83	83	84	85	82	83	82	83	78

Table 4: Results for the friction coefficients of the ice-covered asphalt samples.

Figure 1: The BPT used in the experiment. Please click here to view a larger version of this figure.

Figure 2: Different samples with the corresponding water volumes. Please click here to view a larger version of this figure.

Figure 3: Experimental recording results (BPN). Please click here to view a larger version of this figure.

Figure 4: Friction coefficients of pavement ice under different snowfall levels. Please click here to view a larger version of this figure.

Discussion

The present paper examines the procedure for testing the friction coefficient of icy pavement using a BPT. Several points need to be comprehensively analyzed and are discussed in detail here. First, in terms of the preparation of the asphalt mixture samples, one should try to use road petroleum asphalt to prepare the samples, but this is not a requirement. The preparation of the asphalt mixture samples should be performed in strict accordance with the ASTM (D6926-20) experimental protocols, as this affects the accuracy of the final results²⁵. If the friction coefficient of the final sample is too large or too small as a result of poor mix grading, the sample must be re-prepared and tested once more. The prepared asphalt slabs should be maintained in accordance with the requirements.

Another critical step is the calculation of the snowfall. Snow accumulation is a result of precipitation. According to research conducted by the Meteorological Bureau of the People's Republic of China, snowfall may be measured by the following method: a standard container is used to melt the snow, collected in 12 h or 24 h, into water, and the value obtained with a measuring cup is measured in millimeters (mm), with 1 mm of snowfall representing a snow depth of approximately 8 mm²⁶. The sample size of the experimental prefabricated asphalt mixture is 30 cm x 30 cm x 5 cm, and 1 mm of precipitation on the asphalt slab has a water volume of 30 cm x 30 x cm 0.1 cm = 90 cm³. According to this calculation method, the required water volumecan be derived from the corresponding sample with an ice layer thickness of 1.1 mm.

Furthermore, the determination of the freezing temperature and time are also important. In the experiment, the temperature range is set to −5 °C to −10 °C. All the samples should be frozen for at least 24 h. The time can be obtained by test freezing the samples before the experiment. Notably, the time obtained by different equipment with different freezing effects may vary.

Next, when calibrating the sliding length of the rubber sheet, the lowest edge of the rubber sheet should touch the surface of the asphalt slab. It should not slide forward with the inertia of the swinging arm, as this would cause the sliding length to differ from the 126 mm requirement.

Finally, a temperature correction method must be used. Previous studies have indicated that BPNs are related to both the temperature and rubber sheet material²⁷. The ASTM (E303-93) specification requires the use of synthetic rubber with low sensitivity to temperature, meaning there are no temperature conversions involved^24,28. However, most current experiments use BPT for the indoor determination of the friction coefficient for natural rubber. The BPNs obtained from these experiments at different temperatures must be converted to values at standard temperatures²⁹. Numerous studies have provided an array of methods for BPN temperature conversion³⁰. The present paper employs the method of Bazlamit et al., as they provided formulas for the conversion of BPNs at any temperature to values at standard temperatures³¹.

The future engineering applications of this method primarily relate to road design and winter road maintenance. First, when designing roads in snowy and frozen areas, designers should understand the local snowfall level, consider the possible ice thickness during road operation, and use the most favorable friction coefficient for the road design. The friction coefficients corresponding to different ice thicknesses may affect the cross-slope values as well as the superelevation values in road design, which, in turn, may affect the radius of the road's circular curve. Second, our experiments may aid in improving the efficiency of pavement maintenance in winter, as solutions for ensuring appropriate friction coefficients of pavements at different icing thicknesses may be further developed. According to the results of the paper, the impact on vehicle driving remains the same once the ice thickness on the road surface becomes greater than 5 mm. This work provides a reference for road management in winter, suggesting that certain measures should be implemented before the ice thickness reaches 5 mm. In addition, the present study shows that the negative impact on road safety can be significant even with trace amounts of light snow, as such snow is more likely to freeze and cause a significant decrease in the road friction coefficient in a very short period.

Further, the method presented in the paper has some limitations as well. Follow-up experiments should be combined with actual road data to verify the experimental results. In addition, the medium snow range should be further divided to determine the exact value when the friction coefficient no longer depends on the ice thickness. The limitations of the protocol mainly relate to the inability to obtain uniform ice surfaces on the samples, which in some cases, leads to large experimental errors.

Materials

Name	Company	Catalog Number	Comments
Brush	Shenzhen Huarui Brush Industry Co., LTD	L-31
Freezing equipment	Haier Group	BC/BD-251HD
Measuring cylinder	Zhaoqing High-tech Zone Qianghong Plastic Mould Co., LTD	lb1
Pavement thermometer	Fluke Electronic Insrtument Company	F62MAX
Pendulum Friction Cofficient Meter	Muyang County Highway Instrument Co., LTD	/
Rubber sheet	Jiangsu Muyang Xinchen Highway Instrument Co., LTD	785120123500
Sliding length ruler	Jiangsu Muyang Xinchen Highway Instrument Co., LTD	785120123500
Tripod	Hangzhou Ruiqi Trading Co., LTD	TRGC1169