Wear 302 (2013) 1426–1435

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0043-16

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Modeling of the connection road surface microtexture/waterdepth/friction

M.-T. Do n, V. Cerezo, Y. Beautru, M. Kane

IFSTTAR, Route de Bouaye, CS4, 44344 Bouguenais Cedex, France

a r t i c l e i n f o

Article history:

Received 7 August 2012

Received in revised form

9 January 2013

Accepted 11 January 2013Available online 23 January 2013

Keywords:

Water depth

Microtexture

Friction

Modeling

48/$ - see front matter & 2013 Elsevier B.V. A

x.doi.org/10.1016/j.wear.2013.01.031

esponding author. Tel.: þ33 2 40 84 57 95; fa

ail address: minh-tan.do@ifsttar.fr (M.-T. Do)

a b s t r a c t

The paper deals with the variation of tire/road friction with thin water depths and the effect of road surface

microtexture. Tests are performed in laboratory on slabs made of coarse aggregates mosaics embedded in a

resin matrix. Microtexture levels are simulated by sandblasting the mosaic surfaces. Aggregate profiles are

measured by means of high resolution sensor. Friction is measured at water depths ranging from 0 to 1 mm.

Stribeck curves are plotted from which a critical water depth is defined at the transition between boundary

and mixed lubrication regimes. Modeling of a rubber slider moving over a conical asperity is performed to

better understand experimental observations. Masking effect due to water is modeled simply by cutting

profiles at successive heights equal to the water depths. The slider is supported partly by emerging

asperities, which generate friction forces, and partly by the masking water film. Friction forces are composed

of three components: adhesion, hysteresis and hydrodynamic. The model is applied to aggregate profiles;

results are expressed in terms of friction coefficient/water depth plots. Comparisons to experimental

measurements are made and results are discussed.

& 2013 Elsevier B.V. All rights reserved.

1. Introduction

Accidents are more likely on just wet roads than on floodedones. Sabey says that ‘‘y about 60% of the wet road skiddingaccidents occur y when the road are wet but it is not raining’’ [1].This is due to the fact that thin water film traction can be very lowdespite the apparently safe aspect of the road; drivers can adoptinappropriate maneuvers (maintaining high speed for instance)with respect to available friction. Drivers are more familiar withthe concept of aquaplaning occurred on flooded road. Researcheshave been done extensively on the effect of thick water depths(41 mm) and have given place to the calculation of the so-calledhydroplaning speed (speed limit above which the driver can nomore act on his vehicle to control its trajectory) [1–3]. Less isknown about the effect of thin water depths and the tire/roadfriction loss referred to as viscoplaning (the term ‘‘visco’’ empha-sizes the viscous effect of thin water depths). Moreover, toproduce 1 mm of water depth, a rain intensity of 10 mm/hr(heavy rain) is required [1]. As heavy rain is a rather rare event,drivers would experience more often thin water film traction.

Moore [2] explains that only the road surface microtexture(surface asperities less than 0.2 mm in height and 0.5 mm inwidth [4]) is capable of mitigating the viscoplaning by providingenough pressure to break through the water film. Sabey [5]

ll rights reserved.

x: þ33 2 40 84 59 92.

.

conducts friction tests with spherical and conical single slidersand proves that there is a link between the calculated averagepressure exerted by the sliders (on an elastic plane) and themeasured wet friction coefficient (between the sliders and arubber plane). Greenwood and Tabor [6] use Sabey’s data in theirtheoretical works and prove that the measured friction coefficientis due to rubber deformation losses. As these pioneer works dealwith single sliders, other authors [7–9] investigate—by means oftheory [7,8] or combined theory/experiments [9]—multi-slidersurfaces and highlight, besides the shape, the effect of surfaceasperity height and density on delubrication mechanisms.

Thanks to the researches cited above, valuable knowledge hasbeen gained about the relationship between road surface micro-texture characteristics and friction. Nevertheless, less is knownabout the masking effect due to the water film and how itinteracts with the surface microtexture. Also, experimental evi-dence is still needed on the variation of friction coefficient withwater depth, mainly between dry and just wet states, on real roadsurfaces. The purpose of this paper is to report researchesconducted at IFSTTAR to fill these gaps.

2. Experiments

2.1. Specimens

Experiments are conducted in laboratory. Specimens aresquare slabs of 400 mm aside (Fig. 1b). Surfaces are mosaics

Nomenclature

m friction coefficientmdef deformation component of friction coefficientmadh adhesion component of friction coefficientmhyd hydrodynamic component of friction coefficientBL boundary lubricationML mixed lubricationEHL elastohydrodynamic lubrication

N total number of asperitiesNi number of contacting asperities (not submerged by

the water film)RMS profile height root-mean-squareWD water depth (ratio volume/wetted surface)WDcrit critical water depthWD* water depth trapped between the tire tread and the

road surface asperity summits

M.-T. Do et al. / Wear 302 (2013) 1426–1435 1427

composed of river coarse aggregates (fraction 7.2/10 mm); thistype of surface is close enough to that of actual road surface whileemphasizing the effect of surface microtexture. The fabricationsteps are the following:

-

place manually the aggregates in a single layer as closely aspossible, with their flattest faces lying on the bottom of themold (Fig. 1a);

-

fill the interstices between the particles with silica sand called‘‘Fontainebleau sand’’ (fraction 0.16/0.315 mm);

-

fill the mold with resin and remove any excess from the edgesof the mold;

Fig. 1. Fabrication of sla

Fig. 2. Sandblasting protocol ;(a) sandblasting machine and c

-

when the resin has completely set, remove the specimen fromthe mold. The bottom face of the slab, composed of flat faces ofthe aggregates, constitutes the test surface.

To study the effect of the surface microtexture, mosaics aresandblasted using corundum particles of different sizes (420–590–800 mm). Views of corundum particles, the sandblastingmachine and the sandblasting protocol are shown in Fig. 2.

Sandblasting is realized by sweeping the surface with thenozzle in X–Y directions (Fig. 2b). A complete sweeping is calleda passage. For each corundum particle size, the specimens aresubjected to respectively one, two and three passages. They arenumbered respectively S420-Ej, S590-Ej and S800-Ej, where

bs for friction tests.

orundum particles; (b) sandblasting sweeping directions.

M.-T. Do et al. / Wear 302 (2013) 1426–14351428

j (j¼0 to 3) represents the number of sandblasting passages. Intotal, nine microtextured surfaces are created in addition of thenaturally smooth microtexture of the river aggregates. This pointjustifies the use of aggregate mosaics, as it would be moredifficult to obtain really smooth surface using an ordinary asphaltconcrete.

Surface profiles are measured by means of laser sensor. Themeasurement area is located in the path of friction measuringpads (see 2.2). 15 profiles of 75 mm in length, sampled every0.01 mm and spaced every 0.5 mm, are collected per area.

2.2. Friction measuring machine

Friction tests are performed by means of the Dynamic FrictionTester (DFT) [10]. The machine is composed of a measuring unit(Fig. 3a) and a control unit. The measuring unit consists of ahorizontal fly wheel and disc which are driven by a motor(Fig. 3b). Three rubber sliders are attached to the disc by leafsprings. They are pressed on the test surface by the weight of thedevice and are loaded to 11.8 N each.

The main drawback related to the use of a commercialmachine like the DFT is that it is not possible to study the effectof rubber properties (friction pads provided by the manufacturer).

2.3. Wetting protocol

A spray is used to wet the surface (Fig. 4b). The amount ofwater sprayed on the test surface is known by weighing. Dividingthe volume of water by the wetted area, an average water depthcan be calculated. This water depth is called the ‘‘initial equiva-lent water depth’’ as it is the thickness of the water film beforefriction test is performed; in the rest of the text, symbol WD isused to refer to this water depth. The wetting protocol enables the

Fig. 3. Dynamic Friction T

Fig. 4. Wetting protocol ;(a) surfa

study of very thin water depths (few tenths of millimeters) forwhich no current sensor can measure.

The wetted area is a circle of 345 mm of diameter carved in aplastic plate and affixed to the specimen slab (Fig. 4a). To avoidwater from flowing from the test area, the edge of the circle isfilled with a sealant, and the slab is covered, except on its upperface, by a waterproof sheet. As soon as the surface is wetted,friction test is performed; it can be then said that the waterevaporation is negligible.

2.4. Friction tests

For each friction test, new sliders are used to ensure that sliderwear does not affect results. The test surface is leveled and free ofany contamination. The DFT is placed above the slab using visualmarkers to ensure that it is always placed at the same location.After a first friction measurement performed on a perfectly drysurface, the following procedure is repeated 12 times:

-

este

ce to

wetting of the slab surface by nine sprayings (E 7 g of waterin total);

-

friction measurement; - weighing of the spray.

3. Experimental results

3.1. Friction-water depth curve

Examples of friction/water depth plot are shown in Fig. 5 forspecimens S590-E0 and S590-E3 respectively. Specimen S590-E3shows a three-phase variation: the friction coefficient maintainsits ‘‘dry’’ value (phase 1) until a ‘‘critical’’ water depth is reached;

r (DFT) machine.

be wetted; (b) spraying.

0.0

0.2

0.4

0.6

0.8

1.0

0.00 0.40 0.80 1.20 1.60water depth (mm)

frict

ion

coef

ficie

nt

CE1

Fig. 6. Measurements performed on IFSTTAR test track.

0.0

0.5

1.0

1.5

0.0 0.2 0.4 0.6 0.8 1.0water depth (mm)

frict

ion

coef

ficie

nt

S590-E0

S590-E3

fitting E0

fitting E3

Fig. 5. Variation of friction coefficient versus water depth.

M.-T. Do et al. / Wear 302 (2013) 1426–1435 1429

then it decreases rapidly for increasing water depths (phase 2)before stabilizing again at a ‘‘final’’ value. For specimen S590-E0,only phases 2 and 3 are observed.

Graphs in Fig. 5 can be treated as Stribeck curves in whichthe water depth (WD) replaces the usual ZV/p term, where: Z isthe lubricant viscosity, V is the relative sliding speed, and p is theaverage contact pressure. Even if the use of (ZV/p) term is popularin the literature, (WD) is preferred as water depth is the mainissue of this research. It can be then said that tire/wet roadcontact experiences the same lubrication regimes—boundary(BL), mixed lubrication (ML) and elastohydrodynamic (EHL)—asother lubricated contacts.

To make sure of the representativeness of results presented inthe rest of the text, with respect to the test surfaces and thetesting machine, measurements are performed on actual roadsurfaces using friction measuring vehicles. Tests are performed onIFSTTAR test track. Surfaces represent in majority actual traffickedroads, as those shown in Fig. 6, and some special surfaces likeepoxy, painted surfaces, etc. The ADHERA vehicle [11] is used inFrance for monitoring and safety diagnosis purposes. The frictioncoefficient is obtained by locking the measuring wheel (pure

sliding mode). Water depths are obtained by adjusting the waterflow. No dry test is performed as the dry test conditions on road(wheel sliding on a distance of 20 m) are more severe than inlaboratory. Results for two test boards (C: fine surface dressing;E1: bituminous asphalt concrete) are shown in Fig. 6. It can beseen that the friction-water depth curves are similar to thoseshown in Fig. 5: both curves exhibit boundary and mixedlubrication regimes. The combination test speed (90 km/h)/waterdepth (1.5 mm) is probably not severe enough to reach thehydrodynamic regime.

It can reasonably be said that, with respect to the study of themicrotexture effect, surfaces composed of aggregate mosaics canbe used and results should reflect actual road tendencies.

Two observations can already made from Fig. 5:

-

the dry value of friction coefficient is higher for specimenS590-E0, compared with specimen S590-E3. It can beexplained by the fact that dry friction depends mainly oncontact area, which is greater for a smooth surface (S590-E0);

-

there is no phase 1 for specimen S590-E0. Again, the expectedlow microtexture level of this surface, compared with speci-men S590-E3, can explain the fact that the friction coefficientdrops immediately as soon as the surface is wetted.

Previous works used to show that the friction coefficientdecreases as the water depth increases [1,3,12]. The differencebetween the tendency shown by specimen S590-E3 in Fig. 5 andliterature results can be attributed to the water quantity sprayedon the dry test surface to obtain the first wet state. Actually, if toomuch water is sprayed (as is the case of previous studies), thetransition from ‘‘dry’’ to ‘‘wet’’ can be missed.

Fig. 7 shows friction-water depth variations for differentspeeds (20–40–60 km/h). Examples are shown for specimensS590-E0 and S590-E3. The speed dependency is similar for bothspecimens: at any water depth, friction coefficient decreases withspeed. Friction coefficients at 20 km/h and 40 km/h are similarand are higher than that at 60 km/h. The speed dependency issignificant for water depths belonging to BL and ML regimes (upto0.3 mm and 0.5 mm respectively for E0 and E3 specimens). In theEHL regime, the speed dependency is negligible.

3.2. Critical water depth

Observations made in section 3.1 show that even the surfaceaspect remains unchanged (damp aspect), the friction coefficientcan vary in the meantime significantly. This result explains partlywhy drivers cannot always be aware of slippery risks. Attemptsare made in this section to define indicators allowing the predic-tion of viscoplaning situations. For contact between machinecomponents, the situation of interest is the transition from EHLregime to ML regime where some grips can occur. The friction-water depth variation presented in Figs. 5 and 6 shows that thecritical moment for car driver would rather be the one at whichfriction drops drastically, i.e., at the transition between BL and MLregimes. A so-called ‘‘critical’’ water depth is then defined as afirst step towards the prediction of viscoplaning.

A mathematical model is first developed to fit the shape of thefriction-water depth curve derived from the experiments:

m¼Dm e½�ðWD=WD0Þa� þmF ð1Þ

where m¼friction coefficient; WD¼water depth; mF¼final frictioncoefficient; Dm¼difference between m at WD¼0 and mF; and WD0,a¼constants.

The model (1) is similar to that proposed by Kulakowski andHarwood [12] but can simulate other shapes than the exponentialone (for which a¼1). The dotted line in Fig. 5 shows how well the

0.0

0.5

1.0

1.5

0.0 0.2 0.4 0.6 0.8 1.0water depth (mm)

frict

ion

coef

ficie

nt

critical0.0

0.5

1.0

1.5

0.0 0.2 0.4 0.6 0.8 1.0

S590-E3

BL ML EHL

critical

Fig. 8. Definition of critical water depth.

0.0

0.5

1.0

1.5

0.0 0.2 0.4 0.6 0.8 1.0water depth (mm)

frict

ion

coef

ficie

nt

S590-E0S590-E1S590-E2S590-E3

Fig. 9. Effect of surface microtexture on friction-water depth curve.

0.0

0.5

1.0

1.5

0.0 0.2 0.4 0.6 0.8 1.0water depth (mm)

frict

ion

coef

ficie

nt

20km/h40km/h60km/h

Fig. 7. Speed effect on friction-water depth curve; (a) sample S590-E0; (b) sample

S590-E3.

M.-T. Do et al. / Wear 302 (2013) 1426–14351430

model (1) fits experimental data. The critical water depth isdetermined from the intersection of two lines (Fig. 8):

-

the first line is horizontal and defines the BL friction coefficient(mBL). (mBL) is calculated as the average of measured frictioncoefficients which do not differ from the dry value more than0.04 (precision of the DFT machine);

-

the second line defines friction decay in ML regime. The slopeof this line is defined as the one determined locally at theinflection point (zero second derivative of formula (1)).

For the example shown in Fig. 8, the critical water depth (WDcrit)is about 0.21 mm (specimen S590-E3; speed 40 km/h). Analysesshow that WDcrit is roughly the same at 20 km/h and 40 km/h, thendecreases at 60 km/h (WDcrit¼0.11 mm for specimen S590-E3). Thisresult not only confirms the danger due very thin water film on theroad surface, but also emphasizes the combined risk with increasingspeed (the friction drop occurs earlier).

3.3. Effect of the surface microtexture

Graphs in previous sections highlight the effect of the roadsurface microtexture. Fig. 9 shows this effect by comparing S590specimens at different states: smooth (E0) and respectively one(E1), two (E2) and three (E3) sandblasting passages.

Plots for (E0) and (E3) are already shown in Fig. 5. Plots for (E1)and (E2) confirm the first observations: i) dry friction coefficientis higher for smooth surface, ii) microtexture preserves the BLregime, and iii) friction coefficient is higher for microtexturedsurfaces. These observations corroborate those made by Moore in[13] on smooth and rough spheres. Some more observations canbe made from Fig. 9:

-

the microtexture effect depends on the water depth: thedifference between the four specimens increases with waterdepth in ML regime and remains stable in EHL regime. Thefinal friction coefficient (mF) is the same respectively for (E2)and (E3), and for (E0) and (E1);

-

the transition BL/ML point does not seem to be the same forthe three sandblasted specimens.

0.0

0.4

0.8

1.2

0.0 0.2 0.4 0.6 0.8 1.0water depth (mm)

frict

ion

coef

ficie

nt

S590-E1 S590-E2 S590-E3

Fig. 10. Effect of surface microtexture on critical water depth.

M.-T. Do et al. / Wear 302 (2013) 1426–1435 1431

Fig. 10 clearly shows the effect of microtexture on the transi-tion BL/ML. Curves are derived from formula (1) for specimens E1,E2 and E3. It can be seen that the BL/ML transition point movesrightward (increasing values) while the friction-water depthcurve moves upward. As an example, values of (WDcrit) at40 km/h for specimens E1, E2 and E3 are respectively 0.06 mm,0.12 mm and 0.21 mm. Increasing microtexture allows thendelaying friction drop.

In order to quantify the effect of surface microtexture, theroot-mean-square (RMS) is calculated on profiles extracted fromthe aggregate summits. The profile extraction procedure is illu-strated in Fig. 11:

-

the measured profiles (in black) are first approximated usingthe moving average method (Fig. 11a). The red profiles(obtained by the moving average method) are assumed torepresent the aggregate curvature (Fig. 11b);

-

each measured profile and its approximation are cut at 1 mmdepth from the highest point. This upper part is assumed to bein touch with the tire (or friction pads in this study);

-

Fig. 11. Extraction of microtexture profiles; (a) measured and approximated

profiles, (b) close view of an aggregate summit and (c) microtexture profile.

by subtracting the red profile from the black profile, oneobtains the microtexture profile on which the RMS is calcu-lated (Fig. 11c).

Due to the extraction method, the profile length on which theRMS is calculated varies from one aggregate to another. For asurface, the RMS is calculated on all extracted profiles and theaverage is calculated.

In Fig. 12, specimens S590 are replaced by values of the profileRMS, which are 4.22 mm, 5.33 mm, 5.93 mm and 6.01 mm forrespectively E0, E1, E2 and E3 specimens. Values of frictioncoefficient at different water depths (0.3–0.5–1 mm in Fig. 12)are then plotted against RMS.

Variation of friction coefficient with RMS depends on the dry/wet difference. At dry state, friction coefficient (due mostly toadhesion forces) decreases with increasing RMS. It is well knownthat rough surfaces offer less contact area than smooth surfaces; theresult in Fig. 12 corroborates then the explanation provided insection 3.1. At wet state, friction coefficient (due mostly tohysteretic forces) increases with increasing RMS. However, theincrease rate depends on the water depth: for high water depths(1 mm), the increase rate is stable; for low water depths, theincrease rate is sharper as water depth approaches the criticalvalue. Explanation can be provided assuming a masking effect: athigh water depth, most of surface asperities are submerged and an

increase of microtexture height has little effect on friction; whereas atlow water depth, a slight increase of microtexture height can changesignificantly the number of asperities in touch with the tire – called

M.-T. Do et al. / Wear 302 (2013) 1426–14351432

‘‘contacting asperities’’ in the rest of the text—and, consequently, canimprove friction.

It might seem to be surprising that roughness of a few microns inheight has a significant effect on surfaces covered by a water film ofa few millimeters in depth. Actually, as mentioned in 2.3 (Wettingprotocol), the water depth value used in the graphs represents anequivalent value. For a smooth surface, this value is the same at anyplace of the surface. For road surfaces, there is more water in thetroughs (between the aggregates) and much less at the top of theaggregates—few ten microns in depth after [2,,7]—where the RMS iscalculated. The order of magnitude of RMS and its effect ondelubrication mechanisms appear then consistent when one con-siders the water depth at the top of the aggregates.

We are aware that RMS is not the most appropriate parameterto characterize surface roughness; other presentations suchas the power spectra would provide more information. However,the RMS has been used by previous authors ([7] for example)as a delubrication criteria (RMS4minimum film thickness). Graphin Fig. 12 proves that the RMS, despite its simplicity,can already help to better see the masking effect of the water film.Nevertheless, the analysis shown in Fig. 12 should be considered asa first attempt and improvements can be done in the future.

4. Modeling

4.1. Model formulation

Even if formula (1) fits well experimental data, a more compre-hensive model is needed: (i) to better understand how surfacemicrotexture asperities generate friction while being partly masked

0.0

0.5

1.0

1.5

4.0 5.0 6.0 7.0RMS (µm)

frict

ion

coef

ficie

nt

dry0.3mm0.5mm1mm

Fig. 12. Effect of surface microtexture height on friction-water depth curve.

Fig. 13. Rubber slider moving

by the water film, (ii) to better understand the concept of criticalwater depth defined macroscopically in section 3.2, and (iii) to movetoward a definition of viscoplaning criteria.

The model presented in this section refers to two mechanisms:

-

ov

friction generation;

- water masking.

Modeling of friction generation is based on an existing modeldeveloped by Do [14]. The model considers a rubber slidermoving over a conical asperity with an angle 2a at the summit(Fig. 13). Considering the equilibrium of the slider (Fx

!þFz!¼ R!

)on the ascending and descending faces of the asperity andprojecting the vectors respectively on these faces, the followingformulae can be written [14]:

Fxa ¼Fzaðcosaþm0sinaÞ

sina�m0cosa ð2Þ

Fxd ¼Fzdðm0sina�cosaÞ

sinaþm0cosað3Þ

m¼ Fx

Fz¼

FxaþFxd

Fz¼ h

cos aþm0sinasina�m0cosa

� 1�hð Þm0sina�cosasinaþm0cosa

ð4Þ

h¼Fza

Fzð5Þ

where Fx, Fz¼horizontal and vertical forces respectively; Fxa,Fxd¼components of Fx on ascending and descending faces respec-tively; Fza, Fzd¼components of Fz on ascending and descendingfaces respectively; m¼friction coefficient; 2a¼angle at the asper-ity summit; h¼factor defining the distribution of Fz on theasperity; and m0¼FT/FN the friction coefficient encountered bythe slider on the asperity ascending and descending faces (assum-ing that both faces have the same friction coefficient).

The ‘‘h’’ factor is equal to 0.5 if the slider is elastic (symme-trical deformation); in this case, formula (4) is similar to Tabor’smodel cited in [15]. The viscoelastic behavior of rubber creates anasymmetrical deformation with an overload on the ascendingface. The factor (h) depends then on rubber properties; a value ofh¼0.83 was adopted in [14] and is used for the present study. It isassumed that the rubber slider is deformed not only by theconical asperity but also by smaller ones–not visible–located onits two faces (ascending and descending). Those tiny asperitiesgenerate friction forces that give place to m0. Assuming thatroughness scales separated by a factor of 10 cannot be seentogether, as microtexture profiles are sampled every 0.01 mm, itcan be said that m0 represents friction forces generated byasperities smaller than 10 mm in width. Previous studies [14]showed that the friction contribution of aggregate asperitiessmaller than 10 mm is independent of the aggregate type and isequal to 0.3; this value is adopted for m0 in the present study.

er a conical asperity.

Fig. 14. Example of aggregate profile (m: asperity summit; K: asperity valley;

dotted line: water depth).

0.0

0.2

0.4

0.6

0.8

0.00 0.01 0.02 0.03 0.04 0.05water depth WD* (mm)

frict

ion

coef

ficie

nt

S590-E0 S590-E3

Fig. 15. Theoretical friction-water depth curves.

M.-T. Do et al. / Wear 302 (2013) 1426–1435 1433

Application of the friction model to the measured aggregateprofiles (see 2.1) requires the detection of profile asperities, eachbeing composed of a summit and its two neighbor valleys.Summits and valleys are respectively local maxima and minima.Fig. 14 shows an example of aggregate profile and the detectedsummits and valleys.

Modeling of the masking mechanism is quite simple at thisstage: the water film is represented by a horizontal line (dottedline in Fig. 14) moving upward as the water depth increases. Thewater depth is defined as the height difference between thedotted line and the profile troughs (mean value of the profileminima). The friction force calculation takes into account the factthat, as the water depth increases, the normal load is supportedby both the water film (where asperities are submerged) and theprofile asperities. However, the model neglects the shear stress ofthe water film. Equations used to calculate a water depth-dependent friction coefficient are the following:

Fx,def ¼X

Ni

Fxi ¼X

Ni

miFzi ð6Þ

Fzi ¼Fz

Nð7Þ

Fx,def ¼Fz

N

X

Ni

mi ð8Þ

mdef ¼Fx,def

Fz¼

1

N

X

Ni

mi ð9Þ

where mdef¼deformation component of friction coefficient;Fx¼total friction force; Fz¼total load; Fxi, Fzi, mi¼respectivelyfriction force, load carried and friction coefficient at contactingasperity (i); N¼total number of asperities; and Ni¼number ofcontacting asperities (not submerged by the water film).

Eq. (7) reflects the fact that, at dry state, the total load isuniformly distributed over all asperities (N in total). With increas-ing water depth, only (Ni, NioN) asperities are in contact with therubber slider. The model assumes that each contacting asperitystill supports the same load Fzi as at the dry state, and part of Fz

that is no longer supported by asperities is supported by thewater film. The resulting friction coefficient is then simplyexpressed by eq. (9), the friction coefficient (mi) being providedby formula (4).

The present model does not claim to be as comprehensive asthose of the literature (for example in [16]). It simply assumesthat the calculated friction coefficient depends intimately on thenumber of contacting asperities: as long as the water film fillsonly the troughs, the number of contacting asperities remains

constant and also is the friction coefficient; there is a momentwhere the number of contacting asperities is no longer enoughand the friction coefficient starts to decrease.

The variation of friction coefficient with water depth aspredicted by the model is shown in Fig. 15. It should be notedthat the water depth WD in Figs. 5 and 7 is due to water sprayedon the surface before friction measurements, whereas the waterdepth in Fig. 15 - denoted WDn–is due to water trapped betweenthe tire tread and the road surface asperity summits (see alsodiscussions in 3.3 about the effect of the profile RMS). At themoment, arbitrary values of WDn are used to construct the graphsin Fig. 15. Modeling works are underway to estimate WDn fromthe consideration the contact conditions and the asperity geome-try; these works deserve a separate future paper.

It can be seen that the theoretical curves have the shape ofStribeck curves. The assumption based on the close link betweenfriction and contacting asperities seems then relevant. However,all theoretical curves show the existence of a boundary lubrica-tion regime whereas Fig. 9 shows that only microtexturedsurfaces dispose of this regime. Also, the fact the friction coeffi-cient decreases continuously until reaching zero whereas mea-surements show a ‘‘final’’ value (see Fig. 9 for example), meansthat a minimum number of contacting asperities always remains(thanks to water runoff or squeezing action of the rubber slider).Finally, the difference between theoretical curves of respectivelyS590-E0 and S590-E3 specimens is not as flagrant as the experi-mentally observed difference.

To explain the last observation mentioned above, it is thoughtthat the model does not take into account another frictioncomponent called abusively ‘‘adhesion’’. Actually, this componentmakes use of the available contact area. Attempts are then madeto introduce an adhesion component into the model. The follow-ing equations are used:

Fx,adh ¼X

Ni

Fxi,adh ¼X

Ni

tiai ð10Þ

ai ¼ prizi ð11Þ

1

ri¼

zx�Dx,i�2zx,iþzxþDx,i

Dx2ð12Þ

where Fx,adh¼total friction force due to adhesion; Fxi,adh, ti, ai, ri,zi¼respectively friction force due to adhesion, shear stress, con-tact area, curvature radius at the summit and deformation depthat contacting asperity (i); zx,i¼height of asperity (i) located atabscissa (x); and Dx¼profile sampling interval.

M.-T. Do et al. / Wear 302 (2013) 1426–14351434

Expression of (ai) is derived from reference [16]. Values of (ri)are calculated from profile heights and sampling interval usingformula (12). Values of (zi) are deduced from Hertz theory. It issupposed furthermore that (ti) is constant (the (t) symbol is usedin place without the index i). The following equations can then bewritten:

Fx,adh ¼ ptX

Ni

rizi ð13Þ

madh ¼Fx,adh

Fz¼ptFz

X

Ni

rizi ð14Þ

where madh¼friction coefficient due to adhesion.For numerical applications, the factor (pt/Fz) is assumed to be

equal to 1 (meaning that tffi3.75 MPa, as Fz¼11.8N after 2.2).The new theoretical m-WDn curves (m is the sum of mdef (9) andmadh (14)) are plotted in Fig. 16 and compared to the former ones(without consideration of adhesion component).

Some improvements can be seen:

-

Figadh

the difference between S590-E0 and S590-E3 specimens aremore significant and logical (E3 curve above E0 curve);

-

values of friction coefficient are closer to experimental values(see Fig. 5, same specimens), even if the values in the EHLregime still converge to zero. The friction gain due to theadhesion component is more important for the microtexturedsurface (0.2) than for the smooth one (0.05). This result is dueto the fact that the number of contacting aspe rities (Ni) ismore important for the microtextured surface irrespective ofthe water depth.

To take into account the existence of a non-zero value offriction coefficient in the EHL regime, a third friction componentis added, meaning that:

m¼ mdef þmadhþmhyd ð15Þ

where: mhyd¼hydrodynamic friction component, determinedexperimentally for the moment.

Comparison between prediction and measurement can now bemade by means of two transformations:

1.

convert WD* in WD using, at this stage, the formulaWD¼l.WD*, l being adjusted by trial and error.

2.

match mhyd with friction measurements at high water depths.

0.0

0.2

0.4

0.6

0.8

0.00 0.01 0.02 0.03 0.04 0.05water depth WD* (mm)

frict

ion

coef

ficie

nt

S590-E0 S590-E3 E0 with adhesion E3 with adhesion

. 16. Theoretical friction-water depth curves with/without consideration of an

esion component.

For specimen S590-E3, values of (l) and mhyd are respectively15 and 0.4. Fig. 17 shows the transformed theoretical curvetogether with measurements at different speeds. It can be seenthat, despite the very crude transformations proposed above, thecomparison is rather satisfactory. Predictions match observationsat 20 km/h and 40 km/h and overestimate friction values at60 km/h (this result is more or less expected since one of themodel’s weakness is the description of the boundary lubricationregime). The most interesting point to highlight is that the frictiondecay rate in the mixed lubrication regime is well described bythe model.

4.2. Summary and discussions

The modeling of the connection road surface microtexture/water depth/friction is not straightforward. The development ofthe model was made in three steps:

1.

the first modeling attempt – giving mdef (9) – assuming thatfriction forces come uniquely from rubber deformation under-estimates the resulting friction coefficient and does not differsurfaces with/without microtexture.

2.

adding a so-called adhesion component (to make a better useof the contact area provided by the contacting asperities) –madh (14) – gives place to a better consideration of thehierarchy with/without microtexture. However, some weak-nesses of the model still remain: the predicted boundarylubrication regime for smooth surfaces is still too largecompared with experimental observations, and the predictedfriction coefficient in the EHL regime is zero whereas a low butnot null friction coefficient is measured even at high waterdepths.

3.

it was perceived that adding a third friction component – mhyd

– equal to the measured friction coefficient at high waterdepth provides a reasonable comparison between predictionsand measurements.

Despite its simplicity and the use of many assumptions, themodel helps to understand the primary importance of the numberof contacting asperities: the friction decay due to increasing waterdepths can be attributed essentially to a masking effect whichsubmerges these asperities. We also perceive that some adhesionand hydrodynamic components should be taken into account;this observation emphasizes the need to link thin/thick water

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.00 0.20 0.40 0.60 0.80 1.00water depth WD (mm)

frict

ion

coef

ficie

nt

S590-E3 calc S590-E3 20km/h S590-E3 40km/h S590-E3 60km/h

Fig. 17. Comparison of calculated/measured friction-water depth plots.

M.-T. Do et al. / Wear 302 (2013) 1426–1435 1435

depth researches. At its present state, the model represents asignificant progress toward the understanding of thin water filmtraction and the prediction of viscoplaning. However, manyimprovements can be expected and even more comprehensiveapproaches based for example on Persson’s theory [17,18] can bedeployed to integrate the multi-scales nature of road surfaceprofiles and the rubber properties.

5. Conclusions

In this paper, works are presented on the measurement andthe modeling of tire/road friction variation with thin water depths(o 1 mm). Tests are performed in laboratory on slabs made ofcoarse aggregate mosaics embedded in a resin matrix; this type ofsurface is close enough to that of actual road surface whileemphasizing the effect of surface microtexture. Friction is mea-sured at water depths ranging from 0 to 1 mm. The friction-waterdepth plot is treated as a Stribeck curve from which a criticalwater depth is defined as the transition between the boundaryand mixed lubrication regimes. The effect of surface microtextureis clearly seen through friction-water depth variation: withoutmicrotexture, friction drops as soon as the surface is wetted,whereas the presence of microtexture maintains friction at anearly constant value until the critical water depth is reached.Observations also show that an increase of microtexture heightimplies an increase of critical water depth.

Modeling is carried out to better understand how the waterfilm affects the contact between the road surface asperities andthe tire. Equilibrium of a rubber slider moving over a conicalasperity is considered. The calculated friction coefficient takesinto account viscoelastic properties of the rubber and a frictioncoefficient induced by small roughness scales. The masking effectdue to water is modeled simply by cutting aggregate profiles atsuccessive heights equal to the water depths. The slider issupported partly by emerging asperities, which generate frictionforces, and partly by the masking water film. It was perceived thatconsideration of the rubber deformation alone cannot differenti-ate surfaces with and without microtexture. Adding an adhesioncomponent, to make use of the available contact area provided bycontacting asperities, and a hydrodynamic component gives placeto a better comparison between predictions and observations. Themodel helps to understand that there is a critical number ofcontacting asperities under which, irrespective of the asperityshape, road surface skid resistance cannot be maintained at anacceptable level.

The major contribution of this work, compared with previousresearches such as those published in the 50’s in [5,6], in the 70’sin [1] and more recently in [17], is that it provides experimentalevidence into the way friction varies with water depth (from dryto just wet state, which is likely to cause accidents) and the effectof road surface microtexture. The strong link between friction andthe number of contacting road asperities, which implies thewater-depth dependency of friction, is highlighted. The concept

of critical water depth is introduced – in a more physical waythan previous works [12]—to define the moment at which frictiondrops drastically (while the road surface still displays a safeaspect). Analysis of experimental data shows that the number ofcontacting asperities and their height are primordial when thewater depth is near its critical value. Previous authors talkedabout the importance of the microtexture height, shape anddensity without providing the way these parameters interact; itis hoped that the results presented in this paper could help to fillthis gap.

Acknowledgment

This study was carried in the context of the project: EnhancedDriver Safety due to Improved Skid Resistance (SKIDSAFE)financed by the European Union 7th Framework Program, Theme:Safety and Security by Design.

References

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