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Introduction

Fall accidents resulting from slips and trips are one ofthe leading categories of non-traffic accidents in terms ofserious injuries and fatalities. They are a primary causeof workplace injury, as well as being one of the leadingcauses of injury related death for the elderly age 65 andover1, 2). There have thus been prolonged efforts to under-stand the vital causes of such accidents throughout theworld. It has been found that the most common precip-itating event leading to a fall is a loss of traction betweenthe shoe sole/heel and floor surface and its slip resistanceproperty is measured as a form of coefficient of friction(COF)37). Hence, knowledge about friction demand andthe friction available has been recognized as a primarykey factor for the slip safety evaluation. Since the COFmeasurements amongst the shoes, floors and environ-ments were adopted to determine whether a slip is tooccur, however, there has been ambiguity in the inter-pretation of the results. Importantly, its measurements

and interpretations have been misguided in manyresearches and practices for fall safety measures. That is,any slip resistance measurements have (1) specific characteristics to any combinations of the

shoes-floors-environments (dry and/or contaminatedwith different agents) and

(2) constant changes during entire service and/or test peri-ods.

Although the concept of friction is relatively simple andstraightforward, its measurement, analysis, and interpre-tation for solving real-world problems on slips and fallsare a quite challenging task. However, one of the mostimportant aspects to address is that the COF measure isnot a constant value because friction properties are intrin-sically noisy and continuously changed as a function ofa complex array of tribological phenomena between theshoes and floors4, 5). As a result, initial surface featuresand material characteristics of both the shoes and floorsare frequently and significantly modified from a firstmoment of contact by surface failures and wear evolu-tions. Surprisingly, however, there has been little analy-sis on how friction induced wear developments of the

Industrial Health 2008, 46, 6676 Original Article

Research on Slip Resistance MeasurementsA New Challenge

In-Ju KIM1* and Hisao NAGATA2

1University of Exeter, Heavitree Road, Exeter, Devon, EX1 2LU, United Kingdom2National Institute of Occupational Safety and Health, 146 Umezono, Kiyose, Tokyo 204-0024, Japan

Received August 2, 2007 and accepted November 30, 2007

Abstract: Slips, trips and falls are one of the most common causes of injuries and fatalities inthe general community and industry. The control of such incidents involves a complex array offactors including the characteristics of each individuals footwear and gait dynamics, walking andworking surfaces, and environmental conditions. Notwithstanding this complexity, slip resistanceproperties have been widely measured as a form of coefficient of friction (COF) index at the slid-ing interface between the shoes and floors. Since the COF measurements were commonly adopt-ed to evaluate slip potentials, it has been found that there were controversies in the interpreta-tion of COF measurement results. This study, therefore, was principally focused on broadeningthe knowledge base and developing new ideas on which improvements in the validity and relia-bility of slip resistance measurements might be made. To achieve this goal, crucial problems onthe current concept of slip resistance measurement were extensively analysed by a tribologicalpoint of view where principle understanding of the shoe-floor friction and wear phenomena couldbe made. Based on this approach, new theoretical models were suggested.

Key words: COF, Floors, Friction, Shoes, Slip Resistance, Tribology and Wear

*To whom correspondence should be addressed.

shoe heels and/or floor surfaces affect the slip resistanceproperties. In addition, slip resistance properties observedat the sliding interfaces between the shoe heels and floorsurfaces are diverse and combine various sub-mechanismsof friction and wear events4, 5, 8). Hence, it becomes clearthat a simple format of friction measurement does not pro-vide an accurate determination of intrinsic properties ofslip resistance between the shoes and floors and accord-ingly has obvious difficulty as an indicator for the fallsafety estimate.

In this sense, a fresh insight would be required to sys-tematically search the friction and wear factors for betterfeaturing the slip resistance properties than a commonlypracticed mean or averaged COF value. New conceptu-al foundations for characterizing the slip resistance prop-erties should be based on thorough understanding of fun-damental mechanics and mechanisms of tribological char-acteristics between the shoes and floors. Because surfacetopographies of the shoes and floors are largely modifiedthroughout the course of repetitive contact-sliding frictionprocesses, this may considerably affect overall frictionand wear behaviours and be one of the most importantfactors on the slip resistance properties46, 817). Whilecontroversies around the friction measurement for slip-periness assessment still remain25), a tribological classifi-cation may provide an objective alternative to overcomethe current problems of slip resistance evaluations.Therefore, this study robustly discussed the limitations ofpresent concept on slip resistance measurements andanalysed the seriousness of misinterpretations on slipresistance properties that were mainly caused by over-simplified conceptions on friction phenomena between theshoe heels and floor surfaces. Based on those criticalanalyses, a new paradigm on friction and wear phenom-ena between the shoes and floors was proposed for futureresearches on the slip resistance measurements

Major IssuesDefinition of a COF

As well-known quantity, a friction coefficient (or coef-ficient of friction, COF) has long been used as a fall safe-ty indicator or index. It is easy to define, but hard tounderstand its overall characteristics. Conceptually, thedefinition of friction is a resistance to motion that occurswhenever one solid body slides over another. That is, aCOF is a property of the two interfacing and interactingsurfaces and serves as a measure of their micro- andmacro-roughness, inter- and intra-molecular forces ofattraction and repulsion, and their viscoelastic (polymerand/or elastomer deformation) properties18, 19). As such,surface topography of both the materials, areas of contact(nominal and real areas of contact), durations of contact

before movement (contact time), velocity of movement,pressure, material types, etc. are major contributing fac-tors to the COF results. The COF is also referred to aseither static or dynamic (or kinetic) friction coefficient(SFC and DFC) depending on whether it is a measure ofthe forces at the instant relative motion begins or afterthere is a continuous, uniform sliding motion, respective-ly15, 16).

Because of the nature of complexity and factorsinvolved, however, the measured COF quantities showinconsistencies even as the same shoe-floor combinationsare employed. This fact has been recognized as a greatconcern when different friction testers, sensors and/or pro-tocols are used worldwide8). However, variations of theCOF results under the same test environments have notreceived much attention in this research area. Despite ofthis fact, most slip safety researches have reported that aparticular shoe or floor surface resists the movement of aparticular floor surface or ones shoe sole across its sur-face. Wherein the co-equal contribution of the footwearor floor is either ignored or not even considered. Hence,it must be stressed that the COF is not a constant for anyparticular materials, but is typical of two materials slid-ing against each other under a given set of surface andenvironmental conditions. Therefore, what is the COFof this floor? or what is the COF of that shoe? has nomeaning at all. The question should be asked either whatkind of shoes were tested against what type of floor sur-faces? or what is the COF value between this shoe andthat floor surface?

It also should be noted that most slip resistance mea-surements in the literatures have been reported as a rou-tine format of measuring orders such as started from cleanand dry surface conditions and then moved into lubricat-ed ones without any specific analysis and/or considera-tions on friction and wear characteristics of the shoes andfloors. From those results, several vital issues could beraised. For example, surface conditions of the shoes andfloors tested would be substantially worn and damaged ina way during dry sliding friction. That is, the surfacesof both bodies would have significantly different condi-tions from their initial ones as the results of repetitiveabrasions and deformations. In this condition, the fol-lowing fundamental questions could be specifically chal-lenged:1) How will the modified surfaces of shoes and floors

affect further slip resistance properties in the clean anddry conditions?

2) How will the worn shoes and floors affect the slipresistance performances in lubricated conditions?

Although it is generally acknowledged that contami-nated floors and shoes are more potentially slip hazardous

NOVEL CONCEPTS ON FRICTION AND WEAR PHENOMENA BETWEEN THE SHOES AND FLOORS 67

than dry ones, traction mechanisms between both the sur-face conditions would be significantly different5, 6, 8). Inthe case of contaminated conditions, friction and wearmechanisms are much more complicated and combineseveral different regimes. Hence, slip resistance mea-surements and acceptable COF levels need to be sepa-rately assessed and determined between the dry and lubri-cated conditions.

Limitations of a COF indexWhat does slip resistance mean? The answer seems to

generally depend upon who is asked and what measuringdevices are used. For those concerned with the defini-tion as it applies to slip resistance between the footwearand floor surfaces, there are many definitions from whichto choose. However, all those definitions are simple. Ifa floor surface meets a static friction coefficient (SFC)and/or dynamic friction coefficient (DFC) value of 0.3 or0.4 or greater as measured by various types of testers, theflooring product can be classified as very slip resistant.With this classifying guideline, however, the minimumvalue of 0.3 or 0.4 actually varies considerably from timeto time, causing a great deal of confusion as a safetythreshold for manufacturers and consumers. Here is thestart of the problem and confusion. Since the 0.4 refer-ence value was established, many different types of testersfor the slip resistance measurements have been developedto claim the measure of SFC as well as DFC. Several ofthese devices reference the 0.4 value as their safety thresh-old. However, what is an important point to note is thatnot all the testers will give the same result and should notbe used as a basis of comparison by other test devices.Because each tester and/or apparatus has different theo-retical and mechanical principles, it seems unreasonableto adopt the reference value without any reference to theinstrument used for slip resistance measurements. Thismeans that there is still great uncertainty about what asafe value for the COF between the footwear and under-foot surfaces should be. This matter may benefit from areview of the definition of friction from a fresh point ofview.

It is also considered that COF values or indices are pri-marily intended for scientific research, more sophisticat-ed users and for evaluating brand new products18). Thatis, most of the measuring references established are usedto focus on brand new products (both shoes and flooringmaterials) rather than considering real world service sit-uations. Those situations should include surface degra-dation of both the footwear and floors caused by normalwear proceedings such as surface failures and materialembeddings from the shoe sole into the floor surface andvice versa, maintenance factors and surrounding environ-ments. In particular, there is no existing source of defin-

itive and quantified wear data during slip resistance mea-sures against which test devices can be correlated. Manyround-robin comparisons of different instruments havebeen carried out, but there are still no reliable referencedata to point towards the tester that most closely predictsreal world performances. Therefore, this matter alsoshould be fully explored for the development of furtheruseful concepts in future.

Average or mean COFA question rose from the slip resistance measurements

is not only a simple matter of friction measurement butalso a matter of the primary issues of friction and wearmechanics and mechanisms between the shoes and floors.Therefore, an average or mean COF measure is a quitecontroversial issue to confine the slip resistance propertyand seems to oversimplify the whole nature of tribologi-cal phenomena observed at the sliding interfaces amongstthe shoes, floors and environments.

Figure 1 shows a brief example of measurement resultsof slip resistance between three shoes and a smooth vinylsurface as a function of test time under dry surface con-ditions. DFCs of the Polyurethane and Nitrile Rubbershoes against the floor counterface were graduallydecreased whilst the DFCs of the PVC shoe were steadi-ly increased. For a detailed investigation, the DFC resultsbetween the three shoes and the vinyl surface were divid-ed into three stages. Each stage was counted on the basisof ten times of rubbings. When compared the DFC resultsbetween the stage I and stage III, there were clear dif-ferences in their slip resistance performances.

Statistic comparisons of the average DFC readings werefully compared in Table 1. In spite of the limited amountof rubbings, the overall DFC values were clearly changed.Amongst the various statistical results, the mean, correla-tion coefficient, and r-square values showed evident com-parisons. Although the three shoes were simply testedagainst the flooring specimen, their slip resistance prop-erties showed quite distinctive and unique results. If thefriction tests were extended further and applied to othertypes of flooring materials, however, the DFC resultsamongst them would be much larger so that this resultcould lead to total misinterpreting of the slip resistanceproperties.

Frictional forceA frictional force component in the COF measurement

is likely to be a highly dependent variable and signifi-cantly affected by friction processes. Although a basicconcept for computing the COF quantity is that a fric-tional force increase proportionally to a normal forceholding contacting surfaces together, this may not be trueunder some circumstances20). In order to investigate this

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Industrial Health 2008, 46, 6676

matter in-depth, it would be necessary to study how thefrictional forces are generated when there is an attemptto slide one of the surfaces relative to the other. Figure 2suggests a contact-sliding model between a shoe heel andfloor surface as a microscopic form. As shown in Fig.2, the highest asperities of the floor surface penetrate intothe heel area and make real areas of contact. If the shoeslides on the floor surface, frictional forces would be pro-duced between the two interfacing surfaces. During repet-itive sliding friction, contact areas of the heel surface

would be ruptured, deformed and increased by wedge-shaped asperities of the floor surface. As a result, thiswill significantly affect a basic mechanism of frictionalforce generation and consequently slip resistance results.This feature indicates that the frictional force would belargely changed during cycled sliding friction even thoughall the conditions such as same shoes, floors and verticalload are kept constant. Therefore, it is believed that fric-tional events at the shoe-floor sliding interface would besignificantly depended upon the surface topography of


Fig. 1. A result of slip resistance measurements between three shoes(Polyurethane, Nitrile Rubber, and PVC) and a smooth vinyl surface as afunction of test runs.

Table 1. Summary of statistic results of the DFC readings according to the order of test stage

Stage No.

StatisticsVariables Polyurethane Shoe Nitrile Rubber Shoe PVC Shoe

I Min. Value 1.325 1.258 1.024Max. Value 1.403 1.278 1.056

Mean 1.374 1.269 1.044Std. Dev. 0.024 0.007 0.008

Corr. Coeff. 0.762 0.928 0.870R-Square 0.580 0.861 0.758

II Min. Value 1.299 1.211 1.059Max. Value 1.368 1.249 1.078

Mean 1.340 1.227 1.066Std . Dev. 0.017 0.014 0.006


III Min. Value 1.319 1.156 1.076Max. Value 1.349 1.189 1.097

Mean 1.332 1.174 1.086Std. Dev. 0.009 0.010 0.006


both the bodies.

Theory Developments

A tribological system between the shoe and floorFriction behaviours are the results of extremely com-

plex interactions between the surface and near-surfaceregions of two materials in contact. Physical, chemical,and mechanical properties in the surface and near-surfaceregions may well differ from the corresponding bulk prop-erties of parent materials. In addition, these surface andnear-surface regions could change radically as a result ofinteractions of the surface molecules with their environ-ments and with each other throughout the course of repet-itive friction processes. As a result, slip resistance prop-erties caused by repetitive rubbings are neither a constantnor an intrinsic character of any particular material com-positions, but change constantly.

However, one of the most important aspects on slipresistance properties seems to be a matter of relativity.That is, one flooring material could be more slip resistantthan another under one set of conditions, but less slipresistant under another ones. This could be due not onlyto the shoe material types and changes of surface geom-etry caused by wear, but also to the surface contaminants.Hence, all the possible forms of tribological characteris-tics should be analysed in any given walking environ-ments. Both quantities of friction and wear behaviours,e.g. COF and wear rate, should be considered at the samemanner because they would be significantly dependedupon the following basic groups of parameters:1) key tribological systems, i.e. material properties of the

shoes and floors and relevant tribo-physical and -chem-ical properties of the systems components (adhesionand deformation)

2) operating variables such as normal load, frictional load,

kinematics and kinetics, velocity, operating duration,and contact angle

3) tribological interactions between the shoes and floorssuch as wear developments and wear induced surfacefailures and material transfers

Figure 3 suggests a tribological system between a shoeheel and floor surface during sliding friction events. Asshown in Fig. 3, there are many factors involved in thesliding interfaces between the shoes and floors.Therefore, any slip resistance measurements should bebased on fundamental understanding and thorough inves-tigation of friction and wear phenomena between theshoes and floors.

Primary aspects of wear phenomenaOne of the most important characteristics in the shoe-

floor tribology system would be a material property ofthe shoes, where the surface topography rapidly changesand continuously produces wear particles during everysingle sliding. Wear development of the heel surfaceseems to be a major concern and considerably affect theslip resistance property. Because elastic modulus of theshoe soles/heels is considerably lower than that of floor-ing materials, it could be assumed that wear behavioursmostly occur at the heel contact areas caused by protu-berances on the floor surface. In this situation, the pro-tuberances could be defined as follows:(1) asperities on a floor surface arising from its topogra-

phy, and/or (2) particles of harder materials from the floor surface

partially embedded into a heel surface, and/or(3) possibly lumps of elastomeric or polymeric debris

transferred to the floor surface.

Figure 4 suggests a flow chart for overall wear cycles

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Fig. 2. A schematic illustration of a contact-sliding model between a shoe heeland floor surface.


Fig. 4. A flow chart for overall wear cycle between a shoe heel and floor surface during slip resistance mea-surements.

Fig. 3. A tribological system of the sliding interface between a shoe heel and floor surface.

between a shoe heel and floor surface during repetitivesliding occurrences. As shown in Fig. 4, it could be pre-sumed that the heel surface would be involved into animmediate wear cycle from an initial contact to particleformations during sliding events. Since the surfacechanges leading to wear outcomes seem to be mainlycaused by forces acting on real areas of contact (RCA),macroscopic operating conditions such as tread patternsand shoe material types could not define the process bythemselves. On the other hand, a particular micro-geom-etry of the heel surface may determine the real contactconditions between the two surfaces under a range ofwalking conditions. The actual forces working on theRCAs then establish the subsurface stress fields and straindistributions, which could result in the accumulation ofdamages eventually leading to the removal of wear par-ticles. An important point in this process is that the for-mation of wear particles seems to be accompanied bygradual and/or abrupt changes of geometry in the heel sur-face. As a result, a feedback loop as shown in Fig. 4would be considered during the repetitive sliding friction.The worn heel surfaces will affect the contact sliding con-ditions and the slip resistance results. Hence, the micro-geometry is not a given property, but constantly generat-ed throughout the course of wear evolutions. This seemsto cause wide differences in the wear rates often experi-enced under macroscopically similar type of shoes.

Surface Analyses

Importance of surface analysisRecent studies have shown that surface roughness have

substantial effects on the slip resistance performancebetween the shoes and floors under various types of walk-ing environments46, 8, 9, 12, 14, 21, 22). Surface roughnessprovides necessary drainage spaces to avoid squeeze filmformations in contaminated conditions. Proper tread pat-terns on the heel surface improve traction properties byproviding more void spaces for the removal of contami-nants and lead to an increase in direct contact with thefloor counterface. Hence, any specific macro-roughnessor tread patterns have been designed into the heel areasbut this would be inadequate in some cases, especiallyafter worn. On the other hand, geometric characteristicsof the floor surface could rather drastically enhance thetraction performances more than the shoe cases. That is,the floor surface may provide tougher, taller, and sharp-er asperities, enough to extend upward through lubricat-ing films sufficiently to engage with the bottom areas ofheel surfaces in a manner like sandpapers. Hence, sur-face roughness of the footwear and floor coverings shouldbe fully observed with friction measurements whenanalysing the slip resistance property.

However, one of the greatest obstacles is that surfacetopography of both the bodies constantly changes in cer-tain ways during friction measurements. Kim et al.6)examined this aspect from a wear point of view and foundthat changes in the DFC results were largely caused bywear developments of the heel surfaces. Manning et al.14)also showed an interesting result that extended wear onsmooth floors could cause polishing and a considerablefall in COF results. In this sense, if the surface charac-teristics of shoe soles/heels and floors and their interac-tions could be quantitatively measured and analysed, thenour understanding on this complex issue of friction andwear mechanics and mechanisms would be considerablyenhanced. Although key theories and model develop-ments, which could be quantitatively possible to predictthe slip resistance property from known surface charac-teristics, for the shoe-floor sliding friction have notreached a perfect stage yet, this approach may not onlyprovide a sound theoretical foundation for the under-standing of both the frictional and wear mechanisms butalso enhance the reliability of slip resistance measuresbetween the shoes and floor surfaces. On a broader scale,this may also assist the improvement of design aspects ofthe footwear and floor surfaces that consequently lead toreduction in fall accidents.

Effects of surface roughness on slip resistance propertiesAlmost all surfaces are rough on a microscopic scale

and comprise an aggregation of micro- and macro-asper-ities. That is, most of the solid surfaces have surfaceroughness and the variations in surface profile can be rep-resented by a random arrangement of peaks and valleys.When two such surfaces are in contact, they touch onlyat tiny discrete areas where their highest asperities are incontact23, 24, 26). The local pressure at the contact regionsis then high enough to cause plastic deformation of theasperities even at the lightest load. If at least one of twosliding surfaces is of a viscoelastic material such as theshoe-floor sliding system, the variation of COF with thenormal pressure could have practical consequences. Thismeans that a contact-sliding system between the shoe heeland floor surface would be an elasto-plastic state and havean interlocking mechanism. The interlocking mechanismwould be governed by a number of factors such as asper-ity shape, size and distributions of the shoe heels and floorsurface, surface properties, normal load, surface condi-tions (dry and/or lubricated), and sliding speeds underwhich the contacts occur. During repeated rubbings, topo-graphic characteristics of both the mating surfaces will becontinuously changed by friction and wear processes.That is, as the shoe heel frequently slides over the floorsurface, changes in the surface topography may occur atthe same place and/or at different positions according to

72 I-J KIM et al.


their surface profile structures. Recently, Kim et al.6) examined the progressive wear

and surface changes of three shoe surfaces during slipresistance measurements. They showed that variations inthe surface geometry of the shoe heels had a major effecton the slip resistance properties. Kim and Smith4, 5) alsoanalysed the topography changes of floor surfaces beforeand after the slip resistance measurements. They foundthat embedding of the polymeric materials from shoeheels into the valley areas of floor surfaces was a majorcause of the changes of floor surface geometry. Otherstudies also showed that surface roughness parameterswere well correlated with the standard deviation of peakheights and the changes in the surface roughness withinthe contact areas, as well as the comparative facing oftwo surfaces between the shoe heels and floor specimensduring the dynamic friction tests8, 9).

All these studies clearly identified that surface topog-raphy of the shoes and floors underwent noticeablechanges during the slip resistance measurements. As aresult, surface changes of the shoes and floors through-out the course of repeated friction and wear developmentshad a major effect on the slip resistance results. Thosestudies also found that wear and wear-induced surfacealterations and failures were more severe than expectedand occurred at a very early stage of sliding friction. Thatis, slip resistance properties between the shoes and floorsdepend not just on the friction when a slip starts, but alsoon how the friction changes as a slip progresses.Therefore, it becomes evident that surface geometry ofboth the shoe heels and floor surfaces should be thor-oughly analysed with the measurements of slip resistanceproperties.

Model Development

Major hypothesesFollowings are major assumptions on the development

of contact-sliding models between the shoe heel and floorsurface: (1) Contact mechanism between the shoe heel and floor

surface would be elasto-plastic deformations.Deformations are assumed to be primarily concen-trated on the heel surface, whose elasto-plastic mod-ulus is ten times or more less than that of the floorsurface.

(2) Tribological behaviors of the shoe-floor pair would besignificantly influenced by surface topographies of thefloor surface. This concept could be idealized as acontact-sliding model. That is, a soft shoe heel slidesover an array of wedge-shaped hard asperities of thefloor surface. As the shoe heel touches the floor, highasperities of the floor surface will penetrate into the

heel areas and make real areas of contact. If the shoeslides on the floor surface, the surface of the shoe heelwill be ruptured and deformed by wedge-shapedasperities of the floor surface. From this model, itcould be considered that density of the peak height(denseness of peak asperity within the assessmentlength) of the floor surfaces profile would be a majorfactor to affecting wear development of the heel sur-face. In this process, asperity angles of the wedgeswill play an important role in the configuration of shoeheel deformations.

(3) During repetitive sliding friction, topographies of thefloor surface also could be affected by several rea-sons. Amongst various possible causes, deposition ofabraded polymer particles from the shoe heel into thecervices of asperities on the floor surface could be oneof the most important considerations. This means thatvalley areas of the floor surface will be one of thevital parameters. Hence, this factor requires thoroughinvestigations and continuous monitoring. Therefore,contact-sliding mechanisms between the shoe heel andfloor surface would be significantly depended uponthe surface topography of the floor counterface.

Based on the above assumptions, the followings sug-gest friction and wear models between the shoe and floorsurface during slip resistance measurements.

Friction modelWhen a shoe heel is first loaded against a floor sur-

face, initial contact would be made at the peaks of a rel-atively small number of asperities. Because elastic mod-ulus of the floor surface would be so much greater thanthat of the shoe heel, peak asperities of the floor surfacewould penetrate into the heel surface. In this condition,it would be assumed that initial surfaces of both the heeland floor possess Gaussian distributions of asperityheights, respectively. Figure 5 shows a schematic dia-gram of a contact model between a shoe heel and floorsurface with asperity height distributions.

Mutual effects between the two surfaces could be con-sidered as a manner of normal and frictional loading.When gross sliding occurs, the heel surface would beunderwent both normal and horizontal displacements.This could be explained by assuming that when the heelsurface is displaced from rest it must climb up and passthe forward of asperity slopes. From this condition, fol-lowing two key components are considered separately.(1) Normal loading

When two rough Gaussian surfaces of the shoe heeland floor are brought into contact, there would be gaps(d) between their reference planes and asperities withheights originally greater than d would be in contacteach other (see Fig. 5) In this topographical situation,


the load carried by an individual asperity would be a func-tion of its compression:

Wi = fp(zid) Eqn 1where Wi is the normal load carried by individual asper-ities, fp is a function of compression and zi is the separa-tion of the mean planes of the surfaces.

The number of asperities with heights between z andz + dz is AnDa(z)dz, and the total load for a separationd thus becomes:

W = AnDa fp(zid)(z)dz Eqn 2where W is the total load, An is nominal contact areasand Da is the density of contour.(2) Frictional (or tangential) loading

The normally loaded contact would be subsequentlysubjected to a tangential load, applied by moving the shoeheel surface horizontally a distance (d) (see Fig. 6). Anindividual asperity could behave in two different waysdepending on its original height. An asperity lower thana limiting height zL would slip and therefore contribute tothe total frictional (or tangential) force with Fi = Wi. Anasperity higher than zL may exhibit partial slip, but hassome part of its contact area that is sticking, and is car-rying a tangential force that could be a function of theglobal tangential displacement and the normal compres-sion:

Fi = f(d, zid) Eqn 3which is valid for loads less than the limiting friction, thatis, Fi Wi.

When gross sliding occurs, the upper heel surface willudergo both normal and horizontal displacements. Thiswould be explained by assuming that when the shoe heel

surface is displaced from rest it must climb up and passthe forward of asperity slopes. That is, the total frictionalforce is given by

F = Fadhesion + Fdeformation Eqn 4

Wear modelOne of the most important aspects for a model devel-

opment of the shoe-floor wear mechanism would be thattwo materials have totally different material characteris-tics such as hardness. When two such materials areloaded together, two opposed asperities involved in con-tact-sliding events must be loaded, and therefore stressedto the same level. If the hardness levels of both materi-als are significantly different, the softer material willdeform plastically, but the deformation of the harder onemust remain at least nominally elastic. As the load isincreased, plastically deforming materials may be work

74 I-J KIM et al.


Fig. 5. A schematic diagram of contact model between a shoe heel anda floor surface with Gaussian height distributions.

Fig. 6. A schematic diagram of an asperity height distributionwith region of slip and stick.

harden. But as long as its current hardness is lower thanthat of the opposing surface, the harder asperity willremain nominally elastic. Therefore, the softer bodycould cause subsurface plastic deformation in the harderone. Thus, tribological behaviors during sliding frictionwould be significantly dependent on the differences inhardness between the two materials.

The above consideration could be applied to the con-tact-sliding interface between the shoe heel and floor sur-face. That is, surface topography of the shoe heel wouldbe continuously changed and produced wear particles dur-ing every single sliding. Relative sliding would requirehard asperities of the floor surface to plough grooves inthe surface areas of the shoe heel. In addition, wear phe-nomena would be severer and unpredictable in the caseof new shoes than used ones. Hence, wear growth of theshoe heel would be a major concern and considerablyaffects the slip resistance property.

Based on those assumptions, a wear model for the shoe-floor sliding friction is suggested to the followings:(1) Adhesive wear

Adhesive wear will take place when relative move-ments between the shoe and floor induce breakagesof the junction inside the shoe heel rather than at theinterface. Adhesive wear will affect only upper lay-ers of the surface, where the tops of asperities breakoff.

(2) Abrasive wearAbrasive wear could be considered as events by dis-

placement of polymeric materials from the shoe heelin relative sliding motion caused by ploughing effectsof hard protuberances on the floor surface, such aspeak asperities and/or embedded hard particles.Abrasive wear will affect both the upper and lowerlayers of the heel surface because polymeric materi-als can be removed from the valley areas as well asfrom the peak ones.

(3) PloughingPloughing could take place when abrasion does not

include any material removals from the heel surfacebut only relocation of material. Ploughing will affectboth the upper and lower layers of the heel surfacebecause polymeric materials will be moved on the sur-face, forming peaks and leaving valleys.

(4) Fatigue wearFatigue wear could be occurred when the heel sur-

face has been exposed to a large number of alternat-ing tensile and compressive stresses, which are typi-cal modes for heel striking and sliding for walkingphase. That is, as the floor surface has blunt rathersharp projections, the heel surface will undergo cyclicdeformations, and surface failures due to fatigue weareventually will occur. Fatigue wear would affect only

the lower layers of the surface because cracks willstart from the valleys and form more valley areas.Fatigue wear may differ from the above wear mech-anisms being characterized by the formation of largecracks after a critical number of repetitive loadings.Prior to this critical point, only minor or negligiblewear would be taken place.

It also would be anticipated that the floor surfaces willbe experienced certain types of wear and surface alter-ations during the repetitive sliding friction. For example,film depositions or transferring of abraded polymer par-ticles from the shoe heel into the floor surface would beone possibility. In this case, material pick-ups would beadded to the wear mechanisms. The material pick-upswill prevalently affect the upper layer of the floor surfacebecause deposits of polymeric materials will be added tothe peak heights. Hence, wear observation should beextended to surface topography of the floors with the mea-suring of their bearing areas.

From the above wear model, it seems clear that wearbehaviors are directly related to the state of progressivewear and surface alterations of both the bodies. Surfacechanges could be identified by various ways such as visu-al inspections of vertical cross-sections through abrasionpatterns and numerical measurements in terms of changesin the surface topography.

Conclusion

In order to prevent accidents from slips and falls, anadequate level of slip resistance between the footwear andunderfoot surface should be provided. As clearly dis-cussed in the main context, however, a simple format offriction measurement could misrepresent the nature of slipresistance properties between the shoes and floors.Facilitated routine friction measurements from laboratoryenvironments could also oversimplify the intrinsic fea-tures of slip resistance properties. Although there hasbeen considerable progress on the understanding of slipresistance properties, it would be probably true to men-tion that none of the COF measurements reported to datecould be regarded as final objective values for any cho-sen shoe-floor-contaminant combinations.

As long as the controversies around the friction mea-surement as a format of COF index remains, improve-ments in the principal concepts and methodologies on slipresistance properties and measurements are urgentlyrequired. This should be based on thorough understand-ing on the nature of tribological phenomena at the slid-ing interfaces between the shoes and floors and their inter-actions during slip resistance measures. In this context,therefore, this study was focused on broadening the


knowledge base and developing new notions for charac-terizing the slip resistance properties from a tribologicalpoint of view on which improvements in the validity andreliability of the slip resistance measurement might bemade. It is wished that suggestions from this study willnot only provide a sound theoretical foundation for theunderstanding of both frictional and wear phenomenabetween the footwear and underfoot surfaces but alsoenhance the creditability of overall pedestrian safety.

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