Texture characteristics of unpolished and polished aggregate surfaces

ARTICLE IN PRESS Tribology International 43 (2010) 188–196

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Texture characteristics of unpolished and polished aggregate surfaces Chengyi Huang  School of EME, Wuhan University of Science and Engineering, PR China

a r t i c l e in f o

a b s t r a c t

Article history: Received 3 July 2008 Received in revised form 29 January 2009 Accepted 11 May 2009 Available online 28 May 2009

In order to investigate evolution of polishing aggregate surfaces on an aggregate wear index (AWI) wear track specimen, experimental texture measurements and data dependent system (DDS) approach were utilized to model and analyze elevation profiles collected from unpolished and polished aggregate surfaces. It was found that the DDS approach was able to characterize the evolved macrotexture and microtexture. The polishing effect induced by the interaction between tire tread and aggregate surfaces was found to reduce the microtexture roughness significantly, but showed little influence on the macrotexture. This does not imply that the macrotexture plays little role in tire tread friction. It was also found that polishing effect presented a strong relationship with grain size existing on aggregate surfaces. & 2009 Elsevier Ltd. All rights reserved.

Keywords: Aggregate Surface texture Tire polishing Macrotexture and microtexture Data dependent system (DDS)

1. Introduction Pavement texture measurements, modeling and analysis are a great challenge and have attracted considerable interest over the past several decades. Pavement texture profiles generally present many of the statistical properties of random signals. It is very difficult to make a distinguishing between different surfaces using either experimental or theoretical methods. However, it is well recognized that pavement texture plays a vital role in the development of both pavement friction and tire wear. In general, pavement texture has traditionally been grouped into two classes, i.e., micro- and macrotexture. Based on ASTM E 867, the two textures can be characterized using characteristic dimension of wavelength and amplitude existing on pavement surfaces, for microtexture the characteristic value is defined less than 0.5 mm and for macrotexture it is defined larger than 0.5 mm. Pavement macrotexture has been found to play a substantial influence on the interaction between tire and road surfaces, especially at high speeds and in wet pavement conditions. Kokkalis [1] has shown a relationship between wet pavement accident rate and pavement macrotexture. As might be expected, the accident rate was shown to decrease as macrotexture increase. Gunaratne et al. [2] used an electro-mechanical profilometer to record the surface profiles of both asphalt and concrete pavements. The data were later modeled using auto regressive (AR) models, where a fast Fourier transform (FFT) technique was used to graphically regenerate the pavement surface. Since the order of the models used in the

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studies was very low (AR(3)), the models were only able to model macrotexture and could not capture the characteristics of microtexture. Fu¨lo¨p et al. [3] investigated the relationship between international friction index (IFI) and skid resistance, as well as the relationship of IFI with surface macrotexture. The hysteresis effect was found to result from macrotexture on the tire tread rubber. Hence, they concluded that macrotexture had a direct effect on skid resistance. Liu et al. [4] confirmed the direct effect of macrotexture on skid resistance by finding an optimum gap distance between aggregates at which skid resistance was at maximum. Due to advances in measurement technology, both micro- and macrotexture profile can now be obtained easily by setting a collecting step size using profilometer. Based on the apparent polishing phenomenon, more and more researchers have focused on the microtexture to search for friction contribution in terms of tire and road interaction. The investigations by Kokkalis [1] classified the microtexture and macrotexture as the first and second order of pavement surface irregularities, respectively. Rohde [5] developed a model to simulate a tread element descending on pavement microtexture. His model revealed the importance of microtexture pattern as well as the influence of its amplitude on the descent time of the tread element. Taneerananon and Yandell [6] developed a model to simulate a rigid tread element sinking onto portion of a road surface and studied the effect of microtexture roughness on braking force coefficient. They found that microtexture roughness became more important when the pavement surface was wet. Persson and Tosatti [7] presented a comprehensive treatment of the hysteric contribution to the friction for viscoelastic solids sliding on hard substrates with different types of (idealized) surface roughness. They discussed qualitatively how the resulting friction force depended on the

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nature of the surface roughness. When rubber was slowly sliding on the surface, at a velocity less than 1 cm/s (as in the case to ABS—braking of automotive tires), the rubber would deform and fill out the nanoscale cavities associated with the short-ranged surface roughness and this gave an additional contribution to the sliding friction. Recently, Luce et al. [8] utilized micro-Deval test and aggregate imaging system (AIMS) to investigate the influence of polishing on texture. But due to the influence of image noise, the AIMS texture analysis was just able to correlate skid friction with average aggregate texture. Slimane et al. [9] adopted the similar image technique to characterize microtexture of road surfaces and the maximum image resolution was about 50 mm. As part of a long-term effort to understand and improve pavement friction, the Michigan Department of Transportation (MDOT) has developed an aggregate wear track to quantify the tendency of individual coarse aggregate sources to polish under the action of traffic as shown in Fig. 1. The wear track consists of a pair of diametrically opposite rubber tire wheels attached to a common center pivot point. An electric motor is used to apply a driving force to the wheels through the center pivot point. Uniformly graded aggregates are used to make trapezoidal shaped test specimens for the wear track. To make the test specimens, aggregates are placed directly against a mold and then covered by Portland cement mortar. Placing 16 of the test specimen end to end forms a circular path about 2.13 m in diameter. The wear track specimens are subjected to four million wheel passes with the surface friction of each specimen measured at regular intervals. Based on these friction measurements, an aggregate wear index (AWI) (the AWI represents the average initial peak force measurement determined on duplicate test slabs after four million wheel passes of wear track polishing) is calculated for each aggregate source. Minimum required AWI values have been established by MDOT for coarse aggregates used in the wear courses of HMA pavements. To understand the generation mechanism of friction, it is necessary to establish a robust correlation between aggregate properties and laboratory measures of friction and texture. As the first research step, a methodology is developed to characterize texture on an AWI wear track specimen. Through the texture analysis, it is highly expected that mechanisms of pavement friction related to characteristics of surface texture could be essentially revealed, because tire tread friction has been recognized to mainly result from hysteresis effects generated by surface asperity [7,10]. Fig. 2 shows several polished aggregates from the specimen used in this study. The

Fig. 1. AWI circular wear track assembly (the wheel tire is 578 mm in diameter and rotates around the center pivot point at a speed of 25 rpm).

189

Fig. 2. Aggregates on polished AWI wear track surface.

limestone aggregates are around 10 mm in size. A laser sensor was used to collect elevation profiles from unpolished aggregate surfaces and polished aggregate surfaces with four million wheel passes separately. The significantly different surfaces might have made it easier to investigate the evolution process of tire polish. Data dependent systems (DDS) methodology [11] was employed to model the elevation profiles. This approach models the trends in the data to capture the dominant frequencies (or wavelengths), their damping characteristics quantifying the regularity with which they repeat, and their contributions to variance quantifying the roughness magnitude, so that the surfaces could be distinguishingly characterized in both directions of length and height.

2. Surface texture measurements Under interaction of tire and pavement surface, the mechanism of pavement texture to generate friction remains unclear. As described in the introduction, it is generally accepted that macrotexture and microtexture play a significant role in generation of tire–road friction. Persson et al. [10] considered that rubber friction was mainly induced by surface roughness that generated pulsating forces on rubber surface. They used power spectrum of surface texture to calculate the hysteric friction. Limited by the texture region they studied (1 cm order of length), it seemed to be impossible to consider the effect of macrotexture on the hysteric friction. In 1980s, Spectral techniques were introduced into pavement roughness analysis, a series of spectral functions describing power spectral density (PSD) of pavement profiles were developed [12–15]. It has been found that various pavement profiles have shown many similarities in spectral characteristics and a single parameter known as the roughness index can shift the PSD level up or down, depending on the roughness [14]. Some authors even suggested dividing the PSD curves into two families, one used for rigid pavements and the other one used for flexible pavements. Because pavement profiles usually appear in random signals and present stochastically statistical properties, it seems to be difficult to distinguish different pavement profiles using spectral techniques. The purpose of this paper is to characterize the macrotexture and the microtexture presented on both the unpolished and polished wear track aggregate surfaces as an effort to explain the influence of the aggregate texture on generated friction. A high resolution laser profilometer was used to collect the elevation profiles on the surfaces. The laser sensor of the profilometer has a maximum 1 mm resolution. Due to a restriction on the number of data points that can be effectively used in the subsequent DDS

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analysis, a maximum of 1024 points were collected for each scan length. Therefore, higher resolution scans were used for shorter scan lengths. For example, if 1 mm step size is adopted to scan a surface, then the maximum scan length allowed is around one millimeter, which represents 1024 data points. Since the optimum step size for a given pavement is not known a priori, a number of step sizes (from 1 mm in [16] to 20 mm in [17]) have been adopted arbitrarily to measure road surface irregularities depending on the purpose of microtexture or macrotexture measurement. Most of texture measurements were characterized using the mean texture depth (MTD) [2] or the root mean square (RMS) of the texture profile [3]. As an effort to explore the effects of collecting step size on characteristics of aggregate surface, three step sizes, 1, 30 and 45 mm, were chosen to scan both the unpolished and polished regions of aggregate surfaces spanning 1, 7 and 46 mm, respectively. The 1 and 30 mm step size scans were limited to individual aggregate surfaces and turned out that they could provide only information about the microtexture presented on those aggregates. The 45 mm step size scans sampled several aggregates including the spaces between them and can therefore capture both the macrotextural and microtextural features of the aggregate surface. Total 10 scans were collected for each step size, five from unpolished surfaces and five from polished surfaces. Each scan data was imported into a DDS program so that parameters of the modeling model such as frequency (wavelength), damping ratio and variance contribution could be determined. Comparisons of the model parameters from the unpolished and polished scans can distinguish the differences between them caused by the polishing action of tires, so that the friction mechanism related to surface texture can be further revealed.

3. Data dependent system methodology

l2n  j1 l2n1  j2 l2n2      j2n ¼ 0

1  y1 B  y2 B2      y2n1 B2n1 at ð1  l1 BÞð1  l2 BÞ    ð1  li1 BÞð1  li BÞð1  liþ1 BÞ    ð1  l2n BÞ 1 X ¼ Gj atj (3)

Xt ¼

j¼0

where j

j

j

Gj ¼ g 1 l1 þ g 2 l2 þ    þ g 2n l2n

where the variable Xt denotes the ‘‘state’’ of a system at time t, i.e., the profile height in this analysis. The adequacy of the model implies that a single state Xt completely characterizes the behavior of the system by expressing the dependence of the present state, i.e., the current profile height Xt on past states Xt1, Xt2,y, Xt2n and this relation is usually called as the autoregressive equation. The remainder at’s are independent or uncorrelated random variables with zero mean and are often referred to as white noise to represent the stochastic process existing in the profile. The relation of at’s is usually called as moving average equation. The order n is increased until an adequate model is found, as explained later. In Eq. (1), the ji’s are autoregressive parameters and the yi’s are moving average parameters.

(4)

is called Green’s function. Its coefficients gi can be calculated in terms of the root li and are given by gi ¼

2n2 l2n1  y1 li      y2n1 i ðli  l1 Þðli  l2 Þ    ðli  li1 Þðli  liþ1 Þ    ðli  l2n Þ

i ¼ 1; 2; 3; . . . ; 2n

(5)

The gi terms simply scale the magnitude of the response from the ith mode and can also introduce a phase shift when that mode is complex. To better clarify the role of complex conjugate pairs of  roots, each li, li and associated gi, g i can be expressed in the sinusoidal form, that is j

(1)

(2)

where a real root provides a decaying exponential dynamic mode and a complex conjugate pair of roots provide a decaying (damped or undamped) sinusoidal mode with certain decay rate and frequency or wavelength. Substituting the backshift operator BXt ¼ Xt1 into Eq. (1), then decomposing the autoregressive equation in terms of the characteristic roots li solved by Eq. (2), Eq. (1) can be rewritten as

j

g i li þ g i li ¼ 2jg i jjli jj cosðoi j þ bi Þ

DDS approach is commonly used for time series analysis of sequentially sampled data. The methodology provides an effective approach to model such series in a statistically optimal manner. The elevation profiles collected by the laser profilometer at a constant step size represent a uniformly sampled time series or space series data. The DDS modeling of the surface texture is aimed at a complete frequency or wavelength decomposition of the surface characteristics. The DDS approach for modeling the elevation profiles utilizes the autoregressive moving average model, represented as ARMA(2n,2n1). Pandit and Wu [11] depicted the detailed procedure of DDS modeling in their monograph. The autoregressive moving average model is given by X t ¼ j1 X t1 þ j2 X t2 þ    þ j2n X t2n þ at  y1 at1  y2 at2      y2n1 at2nþ1

Based on the autoregressive equation, if the ARMA(2n, 2n1) model is adequate, the roots li (i ¼ 1,2,3,y,2n) can be found from its characteristic equation of the autoregressive equation by using the definition of backshift operator BXt ¼ Xt1

(6)

where the damped frequency oi and phase shift bi come from the root li and the corresponding scaling factor gi, respectively [11]. The damped frequency can be further expressed in terms of the damping ratio z and natural frequency on as qffiffiffiffiffiffiffiffiffiffiffiffiffiffi Reðli Þ (7) oi ¼ on 1  z2 ¼ cos1 jli j where the damped angular frequency oi and the natural frequency on are expressed as angle per sampling interval, and can be converted into cycles/s (Hz) by division of 2p or can be converted into wavelength by using the constant speed of the profilometer. For a real root, the break or pseudo-frequency is defined by the half power point in the spectral domain. Once the model has been fitted to the corresponding measured elevation profile data, the variance can be written in terms of the roots as

g0 ¼ VarianceðX t Þ ¼ EðX 2t Þ ¼ d1 þ d2 þ    þ d2n

(8)

where di ¼ s2a

2n X j¼1

gi gj ; 1  li lj

i ¼ 1; 2; . . . ; 2n

(9)

Thus, the power of a particular root, that is its contribution to the variance g0, is represented by the corresponding di for real li, and by di+di+1 for a complex conjugate pair li, li+1; these di or di+di+1 are refered to as variance components. The choice ARMA(2n,2n1) sequence is mainly based on the configuration of the characteristic roots li. Since the autoregressive parameters ji’s are always real, the complex roots can occur only in conjugate pairs. For example, for an ARMA(2,1)

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191

model, we have

j1 ¼ l1 þ l2 ;

j2 ¼ l1 l2

(10)

If j21 þ 4j2 o0, then the roots l1 and l2 must be a complex conjugate pair. Therefore, if we increase the order by one, allowing odd autoregressive orders, one of the roots will be forced to be real. Another reason for increasing the autoregressive order in steps of two is that it is computationally more economical than in steps of one. A step increase of two requires fitting only half the number of models compared to the increase by steps of one. Using the above formulation, the experimentally obtained elevation profiles for each scan were modeled. The critical issue in modeling is to identify the correct model order 2n, that completely captures the trends (or correlations) existing in the elevation profile data. To achieve this, the model order is continuously increased until the adequate order of the model is determined based on three criteria [11]: (1) verify the independence of the residuals (the at’s) of the fitted model by using the autocorrelations of the residuals, i.e., the chosen model is deemed to completely charaterize the data if the unified correlations (sample correlation divided by its standard deviation) are less than two which corresponds to a 95% probability in a normal distribution; (2) once the data have been characterized completely, the residual sum of squares (RSS) is made as low as possible by introducing an F-test parameter that relates the RSS from the current model order 2n to the previous model order (2n1) in the computer program. The chosen model is considered adequat if the F-test parameter value is smaller than the one from an F-table corresponding to a statistically insignificant reduction in RSS; and (3) in addition to the above two criteria, if there exists an obviously known physical wavelength in elevation profiles, the adequate model should capture the physical wavelength, such as the one corresponding to the size of aggregate or spacing between the aggregates on the surface.

4. Analysis of unpolished and polished aggregate surface profiles 4.1. One micron step size scans Figs. 3a and b present two typical elevation profiles collected at 1 m step size from unpolished and polished surfaces of the AWI wear track specimen, respectively. Comparison of the vertical scale in these two plots shows that the variation in magnitudes of the elevations is apparently different, and hence it brings about that the variance (mean squared deviation from the mean) would be higher for the unpolished surface compared to that of the polished surface. This variance will be referred to as scan variance. The each scan data from the unpolished and polished surfaces was imported into the DDS program. The starting model order for every scan was ARMA(2,1) and the model order was increased in steps of 2, until the adequate model that satisfies the three criteria mentioned above was found. Tables 1 and 2 present the modeling results for the two scans in Figs. 2a and b, with adequate models ARMA(22,21) (for 011 unpolished profile) and ARMA(12,11) (for 01a polished profile), respectively. In these tables, the frequency refers to number of cycles/mm. The wavelength is the inverse of this spatial frequency. The damping ratio indicates how well a given wavelength component of the profile repeats at that frequency in the scan. For example, a damping ratio of zero

011

4.1

4

3.9 5

5.25

5.5 5.75 6 Scan Length (mm)

6.25

6.5

6.1 01a Height (mm)

and

Height (mm)

4.2

ð1  j1 B  j2 B2 Þ ¼ ð1  l1 BÞð1  l2 BÞ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi j21 þ 4j2 j1  l1 ; l2 ¼ 2 2

6

5.9

5.8 5

5.25

5.5

5.75

6

6.25

Scan Length (mm) Fig. 3. (a) Typical 1 mm step size scan from unpolished aggregate surface and (b) typical 1 mm step size scan from polished aggregate surface.

Table 1 DDS modeling results of a 1 mm step size (011) of an unpolished aggregate. Frequency (cycles/ Wavelength mm) (mm)

Damping ratio VC (mm2) (%)

2.69 7.02 93.2 97.2 112 193 217 270 322 367 415 466

100 72.2 100 6.77 27.7 5.63 5.49 4.75 0.51 1.18 2.37 0.34

0.372024 0.14245 0.010725 0.010288 0.008947 0.005195 0.004615 0.003711 0.003102 0.002727 0.002410 0.002146

Scan variance (mm2)

1.42E03 1.04E03 3.80E04 1.16E06 9.44E08 3.30E07 2.63E08 2.73E08 3.52E09 2.49E10 1.69E08 3.83E08 1.51E08

Note: VC means variance component.

Table 2 DDS modeling results of a 1 mm step size (01a) of a polished aggregate. Frequency (cycles/ Wavelength mm) (mm)

Damping ratio VC (mm2) (%)

2.31 9.94 168 250 294 434 500

100 33.3 2.40 31.9 4.49 3.09 100

0.433839 0.100563 0.005956 0.004006 0.003403 0.002306 0.002

Scan variance (mm2)

2.01E04 2.25E04 2.37E05 1.04E08 4.77E07 5.18E08 2.48E08 9.90E08

would indicate a perfect sinusoidal wave extending for infinite length. The maximum damping ratio tending to 100% would imply that the wavelength component does not exist or repeat at

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Table 3 (a) Unpolished surface dominant characteristics (1 mm) and (b) polished surface dominant characteristics (1 mm). Scan ID

Scan variance (mm2)

Dominant wavelength (mm)

Dominant variance component (mm2)

(a) 011 012 013 014 015

1.04E3 2.75E3 7.86E4 5.42E4 1.41E3

0.3720238 0.1228199 0.2457606 0.307031 0.4299226

1.42E3 2.73E3 7.83E4 8.67E4 2.72E3

(b) 01a 01b 01c 01d 01e

2.25E4 7.24E5 1.14E4 2.66E4 4.65E5

0.4338395 0.1930502 0.2016536 0.2810568 0.2644803

2.01E4 6.40E5 1.13E4 2.65E4 4.47E5

Fig. 4. Microstructure of limestone aggregates revealing bright crystal and dark algae region.

Height (mm)

5.9

30_1

5.7 5.5 5.3 5.1 5

6

7

8

9

10

11

12

13

11

12

13

Scan Length (mm) 5.9

Height (mm)

all. Fig. 3a shows a dominant peak at half shape of a wave crest at the right end. Generally, the dominant peak has the largest height and the largest wavelength compared to other wave crests or wave troughs and may not repeat in the same elevation profile. In DDS analysis, the dominant peak will be solved as a real root or an imaginary root with high damping ratio. The dominant wavelengths are indicated by bold in the Tables of DDS scan modeling. In Table 2, the dominant wavelength is 0.434 mm and the corresponding variance component is 2.01 104 mm2, which is less than the dominant contribution of 1.42  103 mm2 from the unpolished scan in Table 1. This result exactly agrees with the comparison of the vertical scale in Figs. 3a and b. All other wavelengths given in these tables are significantly smaller with low variance component and typically have much smaller damping ratios indicating that these wavelengths repeat more frequently over the length of the scan. Thus, the 1 mm step size scans can be effectively used to capture the microtextural features. Tables 3a and b present the dominant characteristics of 10 scans, five from unpolished and five from polished surfaces. It is clear that both the scan variances and the dominant variance components for polished surfaces are consistently lower than those of the unpolished surfaces. In comparison of the dominant wavelengths in Table 3, the unpolished wavelengths seem to be a little bit larger than the polished dominant wavelengths. Through a petrographic investigation of the aggregate, it can be found that the grain size of the aggregate has a strong relationship with the dominant wavelengths. The grain size of the aggregate is measured in the range of 20–500 mm and this seems to agree well with the dominant wavelengths shown in Tables 3a and b. Fig. 4 presents a thin section of the aggregate revealing its microtexture. The dark area is composed of algae lumps and they have a very fine particle size around of 2–10 mm, while the white area is composed of calcite crystals with grain size around 20–500 mm. Therefore, the dominant wavelengths found in 1 mm step size scans can be effectively correlated to the characterization of the aggregate grain size and the change in the variance components of these dominant wavelengths indicates a reduction of roughness due to polishing. The variance reduction based on the dominant wavelength can be used to distinguish the difference between the unpolished and the polished aggregate surfaces in 1 mm step size scans and it may be possible to search for an application in other step size scan. The analysis of 1 mm step size scans appears to correlate the microtexture of unpolished with that of polished aggregate surfaces and the correlation of the macrotexture has to be explored continuously.

30_a

5.7 5.5 5.3 5.1 5

6

7

8 9 10 Scan Length (mm)

Fig. 5. (a) Typical 30 mm step size scan from unpolished aggregate surface and (b) typical 30 mm step size scan from polished aggregate surface.

4.2. Thirty micron step size scans The impact to determine step size on texture characterization of aggregate surfaces is another important issue related to surface texture analysis. The exploration of collecting step size will be helpful to reveal the interaction effect of tire and aggregate on larger wavelengths existing on aggregate surface. A 30 mm step size scans were collected from unpolished and polished aggregate (five different scans from each). Because of limited size of individual aggregates, the 30 mm step size scans were composed of only 234 sampling points extending over 7.02 mm in length to ensure the scans collected on one aggregate surface. Figs. 5a and b present typical elevation profiles collected from unpolished and polished surfaces, respectively. Tables 4 and 5 present the

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Table 4 DDS modeling results of an unpolished aggregate using 30 mm step size (301). Frequency (cycles/ mm)

Wavelength Damping VC (mm2) (mm) ratio (%)

0.012 0.773 1.96 4.10 5.09 7.04 9.44 11.4 12.7 14.1 15.0

82.44 1.293 0.510 0.244 0.196 0.142 0.105 0.087 0.079 0.071 0.067

100 100 23.9 0.83 6.11 6.54 0.94 8.60 0.8 23.6 0.38

UVCP (mm2)

UVCT (mm2)

Scan variance (mm2)

6.83E02 1.80E4 6.85E2 6.56E05 3.15E05 1.24E04 1.24E04 2.89E05 2.89E05 3.09E05 3.09E05 1.84E08 1.84E08 4.38E06 4.38E06 3.47E07 3.47E07 1.26E05 5.70E07 5.70E07

193

Table 6 (a) Unpolished surface characteristics (30 mm) and (b) polished surface characteristics (30 mm). Scan ID Scan variance (mm2) Microtexture wavelength range (mm) UVCT (mm2) (a) 301 302 303 304 305

6.85E02 9.82E03 2.24E03 1.84E02 1.77E02

0.07–0.24 0.07–0.76 0.07–0.66 0.07–0.23 0.07–0.4

1.80E04 1.05E04 1.60E04 1.54E04 1.34E04

(b) 30a 30b 30c 30d 30e

8.48E04 2.66E03 1.21E03 2.17E03 4.58E04

0.08–0.18 0.07–0.16 0.09 0.08 0.15

1.01E05 1.70E05 3.62E07 2.80E06 1.21E05

Note: UVCP means undamped variance component; UVCT denotes undamped variance contribution.

Table 5 DDS modeling results of a polished aggregate using 30 mm step size (30a). 2

Frequency Wavelength Damping VC (mm ) (cycles/ (mm) ratio (%) mm) 0.597 2.10 5.54 8.70 10.8 12.0 16.7

1.674 0.477 0.181 0.115 0.093 0.084 0.060

100 28.4 0.69 3.49 36.4 1.84 100

UVCP (mm2)

UVCT (mm2)

Scan variance (mm2)

5.28E04 1.013E5 8.48E4 2.60E04 1.10E05 1.10E05 1.17E06 1.17E06 1.44E05 3.30E07 3.30E07 3.60E05

corresponding DDS analysis results. Similar to the 1 mm step size scans, the vertical scale in Figs. 5a and b shows a significant difference of the elevation magnitudes and hence the scan variance of the unpolished surface would be expected to be larger than that of the polished surface. However, in contrast with Figs. 3 and 5 shows the much more complicated scan profiles and the analysis appears to be unable to become simpler. A naturally occurring aggregate surface is not a flat plane, even on the polished surfaces there exist some areas where the tire rubber could neither contact the aggregate surface entirely nor polish it to reduce the height of irregularities. Fig. 5b presents the situation where there are two large wave troughs that are hardly affected by the tire polishing action. These kinds of troughs may become the dominant wavelengths and affect the scan variance of elevation profiles significantly in DDS analysis. The dominant wavelength of 1.674 mm in Table 5 seems to correspond to one of the troughs. Another surface feature that affects the value of variance component comes from the slope of an elevation profile. For instance, in Table 4, the dominant wavelength is 82.44 mm which is 11.7 times the scan length. This indicates that there is a slope in the overall elevation profile (Fig. 5a) and the dominant wavelength reflects the entire wave profile corresponding to the slope. Therefore, the dominant wavelength may result from the overall surface shape, rather than its texture and the surface shape can dramatically affect the value of total variance. Based on the above analyses, using the dominant variance to serve as a criterion to distinguish between unpolished and polished surfaces may lead to a wrong physical comparison in 30 m step size scan. And this can also be confirmed by the scan variance values shown for the separate scans in Tables 6a and b, where the variances seem to be of comparable order between unpolished and polished aggregate surfaces. Therefore, the dominant variance criterion used in the

1 mm step size scans is not applicable to 30 mm step size scans to distinguish between unpolished and polished scans. Typically, if the damping ratio z is less than 10%, Eq. (7) shows that the frequency is nearly undamped and the wavelength component repeats regularly. Its resulting variance component to the variance is given by Eq. (8) as di for a real root li and di+di+1 for a complex conjugate pair li, li+1. Since a 30 mm step size scan is around 7 times the scan length of a 1 mm step size scan, it is possible that the dominant wavelength in the 1 mm step size scan may also appear several times in 30 mm step size scans. Therefore, a new criterion based on damping ratio is introduced into the 30 mm step size analyses. First of all, take a look at the variance components with damping ratio larger than 10%, an inverse trend can be found between the unpolished and polished surfaces in Tables 4 and 5. The variance components from all the wavelengths that have a damping ratio less than 10%, (see the column ‘‘UVCP’’ (undamped variance component) in Tables 4 and 5) are summed up to obtain a Undamped Variance Contribution (see the column ‘‘UVCT’’ in Tables 4 and 5). Table 6 presents those undamped variance contributions obtained from 10 such scans, as well as the corresponding wavelength ranges. Since most of the wavelengths are less than 0.5 mm, the texture can be considered as ‘‘microtexture’’ and the associated UVCT physically describes a measure of the averaged squared microtexture roughness. In Table 6b, there are two ‘‘negative’’ UVCT; the negative signs imply that these undamped variance contributions have a phase opposite to those with a positive contribution. Comparison of the UVCT between the unpolished and polished surfaces clearly indicates that polished aggregate line scans have significantly lower UVCT than those on the unpolished scans. This reduction, shown in Fig. 6, would indicate that the polishing action of rubber tires wears away the micro-roughness present on the original unpolished aggregate surfaces. It is also interesting to note that the microtexture wavelengths satisfying the damping ratio criterion in the 30 mm step size scans are close to the dominant wavelengths obtained in the 1 mm step size scans. Thus, only the microtextural features under polishing action appear to be captured effectively in both 1 and 30 mm step size scans, in other words that the interaction of tire and aggregate surface appears to influence the surface microtexture significantly. Another interesting feature that can be seen in the results presented in Table 6 is that the microtexture wavelengths are smaller in the surface texture of the polished surfaces. The larger wavelength features appear to have been removed due to the polishing action of repeated tire passes.

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30 µm Step Size Undamped Variance Contribution Undamped Variance Contribution

2.0E-004 1.5E-004 1.0E-004 5.0E-005 0.0E+000 1 -5.0E-005

2

3 4 Unpolished

5

6

7

8 9 Polished

10

11

Fig. 6. Comparison of undamped variance contributions for 30 mm step size scan.

4.3. Forty-five micron step size scans

7

w45

Height (mm)

6 5 4 3 2 10

0

20 30 40 Scan Length (mm)

7

50

60

50

60

c45

6 Height (mm)

In using 1 and 30 mm step sizes, the scans were limited on the surface of individual aggregates and only the microtextural features appear to be captured. As a result, the scan length might not be enough to capture the macrotexture caused by the aggregates protruding from the surface. In order to capture macrotextural characteristics, a longer scan length was investigated using a 45 mm step size and a total scan length of 46 mm. These longer scans encompassed several aggregates and reflected part of macrotextural profile on the wear track. Figs. 7a and b present two typical elevation profiles collected at 45 mm step size from unpolished and polished surfaces, respectively. It is clear that there are several aggregate profiles in the two plots with an average size of around 10 mm lengths and their vertical scale does not appear to be significantly different. As previously mentioned, due to the inherent irregularities present on any aggregate, all areas of an aggregate surface do not get polished uniformly. Hence even a scan of polished areas will include some areas of unpolished surface and these areas have to be excluded in DDS analysis. Tables 7 and 8 present the modeling results corresponding to the scans shown in Figs. 7a and b, respectively. The dominant variance components shown in bold corresponding to the largest wavelengths are 6.64 and 10.4 mm, respectively, resulting from real roots. These two wavelengths indicate physically the average size of the aggregates appearing in Fig. 7. The corresponding dominant variance does not make any sense comparing the unpolished and polished scans. It implies that the polishing action has little influence on the macrotexture of the wear track. The wavelengths shown in Tables 7 and 8, other than the dominant wavelengths are in the range of microtexture varying between 0.09 and 0.47 mm. It can be seen that the polished aggregate surface has a relatively smaller range of microtexture wavelengths than the unpolished aggregate surface. To determinate the contribution to variance resulting from features with low damping characteristics, the same damping criterion applied in the 30 mm step size scans was again used. It can be found from Tables 7 and 8, when the value of ‘‘damping ratio’’ is less than 10%, the corresponding wavelengths are always less than 0.5 mm. Once again, these wavelengths agree well with the dominant wavelengths found in the 1 mm step size scans and correspond to the grain sizes appearing on the aggregate surfaces. The corresponding UVCTs provide an encouraging comparison of the microtexture roughness. In comparison of Tables 7 with 8, it is clear that the polished surface has smaller UVCT (of the order of around 107) than the unpolished one (of the order of around 104). Therefore, the 45 mm step size scans effectively capture not

5 4 3 2 1 0

10

20 30 40 Scan Length (mm)

Fig. 7. (a) Typical 45 mm step size scan from unpolished aggregate surfaces and (b) typical 45 mm step size scan from polished aggregate surfaces.

Table 7 DDS modeling results of an unpolished aggregate scan using 45 mm step size (W45). Frequency (cycles/ mm)

Wavelength Damping VC (mm2) (mm) ratio (%)

0.15 2.12 2.98 3.81 5.89 7.57 9.86 11.1 11.1

6.64 0.47 0.34 0.26 0.17 0.13 0.10 0.09 0.09

47.4 2.76 4.78 3.84 0.19 2.34 0.36 100 100

UVCP (mm2)

UVCT (mm2)

Scan variance (mm2)

6.36E01 8.143E04 0.636 2.05E04 2.05E04 4.21E04 4.21E04 1.86E04 1.86E04 9.08E06 9.08E06 9.83E06 9.83E06 2.04E06 2.04E06 2.34E06 7.55E04

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only the characteristics of macrotexture, but also the features of microtexture using low damping ratio criterion, i.e., UVCP. Table 9 summarizes the macrotextural and microtextural characteristics from 10 scans using the 45 mm step size. From the table, the variance does not show any trend between unpolished and polished surfaces, but the dominant wavelength seems to represent the average aggregate size. Since the scale of aggregate height is much larger than the scale of microtexture roughness, the large characteristics completely mask the minor variance components. This phenomenon is reflected in a manner that the dominant variance in 45 mm step size scan is equal to the scan variance as shown in Tables 7 and 8. However, similar to the situation in 30 mm step size, the UVCT due only to features that satisfy the 10% damping ratio criterion reveal a clear difference between unpolished and polished surfaces as shown in Fig. 8. The

Table 8 DDS modeling results of a polished aggregate using 45 mm step size (C45). Frequency (cycles/ mm)

Wavelength Damping VC (mm2) (mm) ratio (%)

0.0961 5.31 6.56 11.1

10.4 0.188 0.153 0.09

44.0 100 3.25 100

UVCP (mm2)

UVCT (mm2)

Scan variance (mm2)

1.46 5.32E07 1.46 4.96E03 5.35E07 5.35E07 1.67E05

Table 9 (a) Unpolished surfaces characteristics (45 mm) and (b) polished surfaces characteristics (45 mm). Scan Scan variance ID (mm2)

Dominant wavelength (mm)

UVCT (mm2)

Microtexture wavelength range (mm)

(a) V45 W45 Y45 Z45

0.463 0.723 1.55 0.999

6.14 7.53 5.68 9.41

5.44E4 5.37E4 2.40E3 7.02E4

0.1–0.27 0.1–0.47 0.1–0.37 0.1–0.32

(b) A45 B45 C45 D45 E45

0.336 2.03 1.46 0.247 0.099

4.7 5.26 10.4 15.74 3.9

9.23E6 1.3E4 5.35E7 1.26E5 4.65E5

0.153 0.1–0.22 0.1–0.14 0.1–0.23 0.1–0.13

195

range of microtexture wavelengths as well as their roughness contributions are significantly smaller on the polished surfaces indicating that the effects due to tire polishing on this type of aggregate is to either chip away the large particles (or grains) or break them into smaller fragments.

5. Discussions As mentioned in the introduction, most of the previous publications in the literature have focused on obtaining a single number, such as MTD or RMS, to characterize surface texture. Although the use of a single value is clearly desirable for simplicity, it cannot provide an in-depth description of the microas well as macrotextural features that is characteristic of any polishing process. Moreover, comprehensive descriptions of the evolving wavelengths are desirable for more precise correlations with measurements of friction. A more complete characterization of the evolving surface texture is also desirable for identification of the effects of aggregate type, traffic level, mix-design, pavement age, or weather conditions over a period of time. In this paper, the 1, 30 and 45 mm step size scans were adopted to capture the induced micro- as well as the macrotextural features on aggregate surfaces due to tire polishing. The DDS methodology characterized the aggregate surfaces with texture wavelengths and texture roughness, so that a characteristic comparison could be made between unpolished and polished aggregate surfaces. The 1 mm step size scans collected from individual aggregates, provide the dominant wavelengths consistent in size with the grain structure of aggregate. The variance component from these dominant wavelengths provides a measure to distinguish the microtexture features on unpolished and polished surfaces. The scans from the polished aggregate surfaces had much lower values of dominant variance component than unpolished aggregate surfaces (the reduction rate of the average dominant variance component over five scans is 12.4 times in terms of Tables 3a and b). This reduction in variance component can be considered as the effects of tire polishing and it results in a considerable decline in tire friction based on the friction tests conducted by MDOT. However, the dominant wavelengths obtained from the analysis in the 30 mm step size scans may lead to a wrong physical comparison because these scans are sometimes dominated by the effects of an overall slope of the sampled surface or by the macrotexture, which is impossibly touched by polishing. The use of a maximum damping ratio of 10% has been proved to be

45 µm Step Size Undamped Variance Contribution

Undamped Variance Contribution

2.5E-003 2.0E-003 1.5E-003 1.0E-003 5.0E-004 0.0E+000 1 -5.0E-004

2

3 4 Unpolished

5

6

7

8 9 polished

10

Fig. 8. Comparison of undamped variance contributions for 45 mm step size scan.

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an effective criterion to distinguish the unpolished and polished aggregate surfaces and the results agree well with the analysis of 1 mm step size scans. The 45 mm step size scan was found to capture both the macrotexture and the microtexture characteristics. For the macrotexture, it captured the aggregate profiles and for the microtexture, it captured the evolution of the microtextural irregularities due to polishing action. Based on DDS analysis, the polishing effects under traffic action is to reduce the microtexture roughness of aggregate surfaces as well as the corresponding wavelengths of microtexture, but the macrotexture is influenced little. In comparison of the unpolished microtexture roughness with the polished one, the reduction rates of the average UVCTs are 17.3 times for 30 mm step size scans (Tables 6a and b) and 25.1 times for 45 mm step size scans (Tables 9a and b), respectively, and these values agree with the reduction rate calculated by the average dominant variance component for the 1 mm step size scans. It indicates that the 30 and 45 mm step size scans can both effectively capture the microtexture features on aggregate surfaces. On the other hand, tire polishing seems to primarily influence surface microtexture, the microtexture might play a dominant role in generation of friction. However, the present analysis dose not imply that macrotexture has little influence on the interaction of tire and aggregate surface. MDOT once conducted a series of AWI wear track tests using the specimens composed of different aggregate sizes. The different levels of friction were obtained. The similar friction tests conducted by Liu et al. [4] also confirmed the significant effects of macrotexture on the interaction of tire and aggregate surface. Surface texture has been recognized to play an enormous role on tire–road friction which includes both adhesive (surface) and hysteretic (bulk) components [10,18]. The adhesive component is generated from the attractive binding forces between rubber surface and the substrate. And its friction level is determined by the contact area at the tire–road interface through weak attractive van der Waals interactions. Increasing with roughness of the substrate, the adhesive friction will become much smaller because of the considerable reduction of contact area and the hysteretic friction mechanism is believed to prevail. Because the effects of tire polishing influence macrotexture little, it can be assumed that macrotexture has the same influence on the interaction of tire and aggregate surface on both unpolished and polished aggregate surfaces. The reduced tire friction due to the tire polishing will mainly result from the reduction of microtexture roughness on aggregate surfaces. The fact related to the reduction of tire friction on polished aggregate surfaces is in itself an indication that the adhesive contribution to rubber friction on aggregate surfaces is unimportant, since the adhesive friction should increase when the surface becomes smoother. Therefore, the hysteretic component generated by the texture roughness (including both micro- and macrotexture) should be the primary contribution to tire friction.

6. Conclusions This paper introduced the DDS methodology into aggregate surface texture analysis. The DDS methodology can be effectively used to capture the induced micro- as well as the macrotextural features on aggregate surfaces due to tire polishing. Experimental surface texture measurements were collected by a laser sensor and were modeled and analyzed. Through the exploration of the three different step size scans, it is found that polishing action influences microtexture significantly, but it affects macrotexture little.

Acknowledgments The author would like to thank Dr. Karl Peterson for supplying with the images of AWI wear track and also acknowledge the financial support from Michigan Department of Transportation and the Transportation Materials Research Center at Michigan Technological University.

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