1 Introduction

Management and prevention of slip risk involves many factors. Some of these, related to the characteristics of the surfaces in contact, can be modified through a better design, a more accurate installation practice and the realization of non-slip surface finish [1]. The study of the slip** process starts with the selection of the parameters that can influence the interaction between the surfaces in contact during their mutual sliding. For the section, the correlation between friction and surface roughness is key.

In fact, looking at Fig. 1, it can be seen that friction is high both at low roughness levels, as the contact surface is high and at high roughness levels, since, here, large forces are required to overcome the high asperities. At intermediate roughness values, little influence on friction is observed (Fig. 1).

Fig. 1
figure 1

Roughness-friction force correlation

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From this qualitative analysis, it is clear that the value of the dynamic friction coefficient alone, or of the roughness alone, can not be the used to characterize the slip risk.

This research analyzes the correlation between some roughness parameters and the slip resistance of surfaces, as also done, e.g., in [2,3,4,5]. In this analysis it is important to consider that: (a) it is not correct to refer to a single value to define the anti-slip characteristic of a surface but, instead, it is essential to always refer to a range of values within which it is possible to define the "slip risk index" of a surface; (b) the definition of such ranges can be connected to high, moderate or low “slip risk indices” and needs to take into account the instrument and the measurement methodology adopted. It has been found that the evaluation of DCoF of a same surface can often give unreliable results due to differences in the adopted method and instrument to measure it [6, 7]. To overcome this possible limitation, in this study, DCoF measurements were performed always referring to a single measurement method, the "Pendulum Tester" [8,9,10]; (c) the DCoF is not a property of a material, but the result of the interaction between two materials in contact and of the ways of their sliding on each other; (d) the configurations of the surfaces in contact are important for phenomena correlated to slip**. Continuous and repeated contacts between surfaces can alter the initial roughness parameters and therefore modify their anti-slip characteristics; (e) the limitations in the knowledge of the properties relative to shoe-surfaces which, due to the multiplicity of interaction phenomena, are in fact “uncontrollable” variables. The definition of the risk of slip** is defined considering the controllable variables only and in relation to the conditions of the flooring surface before and during use.

To analyze the action of uncontrollable variables on the process (as, e.g., the chemical-physical characteristics of the materials in contact with the flooring, how they interact with the surface and how they change over time), the Pendulum Tester the large rubber cursor CEN # 46 is used, having a nominal hardness of 55 ± 5 IRHD (about 60 ÷ 65 Shore A). This is considered as the best approach to obtain a representative condition of the shoe-floor contact with a material having a hardness lower than the hardness of the various floors tested. The hardness of floors ranges between about 70 ÷ 80 Shore A, whereas the hardness of the slider was comparable to that of safety-shoe rubber (about 60 ÷ 70 Shore A). The new sliding-contact-factor ηsc is a parameter capable of providing information on the evaluation of the slip risk index of a surface and of its correlation with the DCoF, also taking into account how surfaces can be affected from a minimum pollution with water or by wear over time.

The manuscript is organized as follows: next Sect. 2 is devoted to the analysis of some roughness parameters used in the definition of the sliding-contact factor ηsc, which is presented in following Sect. 3 along with a description of its characteristics. Tests, experimental settings, and test equipment for data measurements on different kinds and morphologies of surfaces are reported in Sect. 4. Section 5 describes the obtained results and a discussion on the novel contribution of the proposed research. Some conclusions, possible future developments, and a discussion on the issues related to the assessment of the slip and fall risk are then proposed in Sect. 6.

2 Surface roughness parameters

The following parameters are analyzed:

  1. (a)

    Ra (μm), is the value of the arithmetic mean of the absolute distances with respect to the mean line, measured according to DIN EN ISO 4287—1998.

  2. (b)

    Rz (μm), is the average of the differences between the 5 highest peaks and the 5 deepest valleys. Defined as "10-point height parameter" and measured according to DIN EN ISO 4287—1998, the following applies:

z (pi) = height of the 5 highest peaks with respect to the midline in the measurement segment

z (vi) = height of the 5 deepest valleys, with respect to the median line, in the measurement segment (see Fig. 2).

  1. (c)

    Rk (μm), represents the amplitude, expressed in μm, of the core area of the roughness (core zone), i.e. the area between the peak zone the valley zone.

Fig. 2
figure 2

Roughness profile and reference system

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These zones are shown in Fig. 3, where Rpk is the surface part subject to immediate wearand Rvk is the area where substances accumulate. The "core" is, therefore, the part of the surface where frictional forces act, and where changes take place, over time, due to wear.

  1. (d)

    Rmr (adim) is the bearing length, measured according to EN ISO 4287: 1988, at the cut-off line, drawn at 5% less than the height (zmax), of the highest peak.

Fig. 3
figure 3

Roughness parameter Rk (core of roughness) (μm)

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Three values of this parameter can be measured: Rmr(1), Rmr(2), Rmr(3), respectively at (− 1 μm), (− 2 μm), and (− 3 μm), below the cut-off line to 5% (see Fig. 4).

Fig. 4
figure 4

Abbot curve of the roughness parameter Rmr (contact line) (%)

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3 Definition of the sliding-contact factor ηsc

The goal of the research is to identify a parameter capable of providing information on the evaluation and classification of the "slip risk index" of a surface through the correlation of specific roughness parameters with the dynamic coefficient of friction DCoF, measured with the Pendulum Tester.

The "sliding-contact factor" ηsc is defined as follows:

$${{\varvec{\upeta}}}_{{{\mathbf{sc}}}} {\text{ (sliding - contact factor )}} = \frac{Rk \times 100}{{Rmr\left( 1 \right) \times L}}\% .$$
(1)

The sliding-contact factor, ηsc, provides indications on the tribology of the surface. We identified specific ranges of values for the sliding-contact factor ηsc which allow to:

  • evaluate the “slip risk index” (high, moderate, low) of the dry or wet surface;

  • evaluate how the use has changed the “slip risk index” over time, by comparison with the initial value, before the use of the flooring, or, in any case, prior to the time of measurement;

  • evaluate, where a "high slip risk index" is found, how to restore a low or moderate slip risk index, by applying any finishing layers or through surface abrasive treatments;

  • have a "theoretical" indication of the DCoF of the surface, dry or wet with water, with only data of the ηsc, calculated by means of roughness measurements performed with an easy to use handheld instrument (Portable Surface Roughness Measuring Instrument).

The following additional two relationships are also defined:

$$\varvec{\rho}_1=\frac{\varvec{R}\varvec{k}\varvec{\times}{\bf 100}}{\varvec{R}\varvec{m}\varvec{r}\left({\bf 2}\right)\times \varvec{L}} \varvec{\%} \qquad\varvec{\rho}_2=\frac{\varvec{R}\varvec{k}\varvec{\times}{\bf 100}}{\varvec{R}\varvec{m}\varvec{r}\left({\bf 3}\right)\times \varvec{L}} {\%}.$$

Even if the sliding-contact factor is defined only considering the value Rmr(1),the other two quantities, ρ1 and ρ2, determined using Rmr(2) and Rmr(3) can be also correlated to the DCoF (see Fig. 5). This allowed a more accurate evaluation of the experimental relationship between ηsc and DCoF.

Fig. 5
figure 5

Correlation between the sliding-contact factors ηsc, ρ1, ρ2, and DCoF

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4 Experimental

Various tests are carried out on different morphologies and/or surface finishes with different types of coverings. For each sample roughness parameters and the dynamic friction coefficient on dry and wet surfaces are measured. All data collected in the various measurements are analyzed and correlated with the dynamic friction coefficient, measured with the Pendulum Tester. This allows to identify ranges of values of the sliding-contact factor, within which it is possible to define the slip risk index of the surface.

Samples are identified by reference to the particular surface texture or surface finish applied.

Floor samples in polyurethane and epoxy resin are considered, since this kind of floor allows the realization of different surface textures by means of surface abrasion, or also through the application of finishes with different no-slip characteristics. Floor surfaces typical of civil and industrial applications are also analysed, such as stoneware, ceramic, terracotta floor, parquet, marble. For each sample, ten measurements on dry surfaces and ten measurements on water polluted surfaces are performed, measuring the roughness parameters and the dynamic friction coefficient. For textures with an anisotropic response, five measurements in the longitudinal direction and five measurements in the transversal direction are performed. The mean values of the various measurements are reported in Table 1 along with the characteristics of the considered surfaces. However, the real measured data, and not the mean values, are actually used in the present work.

Table 1 Surface characteristics and textures of the analysed samples
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Roughness parameters are determined with the Mahr Group Mod. “Marsurf PS1” palm-sized tester, whereas the DCoF values are determined with the Controls Srl “ Skid resistance and friction tester Mod. 48PV0190/A” Pendulum Tester.

After the first measurement of roughness parameters and of the DCoF, the same surfaces are subjected to accelerated wear, by means of abrasive cycles with a rotating tool and abrasive paper with # 150 grit:

  1. (a)

    Abrasion cycle 1–750 rpm and 1,250 kg load and 1 min abrasion time.

  2. (b)

    Abrasion cycle 2–1,500 rpm and 1,250 kg load and 1 min abrasion time.

The data collected during the tests performed are processed and, by means of Eq. (1), the values of the sliding-contact factor are computed and then correlated with the DCoF, (see Fig. 6).

Fig. 6
figure 6

Correlation between the sliding-contact factor and the dynamic coefficient of friction

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Data of the sliding-contact factor can be used to interpret the interaction between surfaces in contact, aiming to the definition of the slip index of various floor types. It is known that such index is strongly related to friction, and thus to the roughness and to the specific conditions of the floor surface. The parameter usually used for the definition of the slip-risk of a surface is the dynamic friction coefficient DCoF. As previously discussed, the interaction between two surfaces in contact and in reciprocal motion cannot be fully determined by the measurement of the dynamic friction coefficient only [4, 9]. Moreover, the DCoF of a surface can be altered (increased or reduced) as a consequence of a variety of factors related to the operating conditions, wear, aging, or to the presence of filming substances (water, oils, dust, solids).

A possible correlation between the sliding-contact factor, linked to surface roughness, and the DCoF is here obtained, allowing to define the slip-risk index and its evolution in time. A sliding-contact experimental model is now presented, allowing to speculate on the evolution of the interaction between surfaces in reciprocal motion, on the effects of roughness and of plastic deformation of the surface with minor hardness, and on how relevant the actual contact area is for the generation of friction forces and of their evolution in time due to wear of the weaker material.

The sliding-contact model is defined through a fitting of the data, obtaining a good agreement with an analytical representation of the sliding contact model as a second order polynomial with respect to ηsc, for wet surfaces with water (2):

$${\text{DCoF }} = {\mathbf{a}} \, ({{\varvec{\upeta}}}_{{{\mathbf{sc}}}} )^{{\mathbf{2}}} + \, {\mathbf{b}} \, ({{\varvec{\upeta}}}_{{{\mathbf{sc}}}} ) \, + \, {\mathbf{c}}$$
(2)

where the values of the parameters a, b, c is the following:

$$\begin{aligned} {\mathbf{a}} & = \, - 151,77 \\ {\mathbf{b}} & = \, 13, \, 836 \\ {\mathbf{c}} & = \, 0,2349 \\ \end{aligned}$$

with 0,85% < ηsc < 8,25%

The relative gap (ΔDCoF %) between the values of DCoF computed by means of Eq. (2) and those measured on the samples with the Pendulum Tester is, in general, ± 20% (see Fig. 7).

Fig. 7
figure 7

Variations of ∆DCoF %

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This gap can create uncertainty only in the range of ηsc values related to the transition zone between medium sliding risk index, and high sliding risk index.

The relative gap (ΔDCoF %) is defined as:

$$\Delta {\text{DCoF }}\% = \frac{{{\text{DCoFm}} - {\text{ DCoFv}}}}{{{\text{DCoFm}}}}\%$$

where

DCoFm = dynamic friction coefficient measured with the Pendulum Tester.

DCoFv = dynamic friction coefficient calculated with (2).

It can be observed that, when the value of the sliding-contact factor is greater than 8.0%, the frictional forces between surfaces in contact are influenced by the difference in hardness between the two materials. The closer the hardness of the materials is, the higher the risk of slip**, being this latter linked only to the structural bridges between the asperities, resulting in a reduced contact surface. The difference in hardness increases the frictional forces generated between the surfaces, due to plastic deformations in the less hard material.

The correlation between the sliding-contact factor and the dynamic friction coefficient also highlights how the friction force between two surfaces can be of the same entity even if surface roughness can be different.

Data analysis also shows that a same DCoF can correspond to two different values of the roughness parameter Rz.

For example a DCoF = 0.36, is measured when Rz = 12.2 μm (point A) is measured and when Rz = 99.1 μm (point B). The same is obtained with the proposed model between the sliding-contact factor and the dynamic friction coefficient giving also information on the nature of the contact between the two surfaces, as described below.

Looking at Fig. 6, indeed, it can be noted that at points A and B the contact conditions between the two surfaces are different:

  • Point A: ηsc ≈ 0.3% the frictional forces are essentially due to the contact area between the surfaces with the contribution of the weak structural bridges that are established between the limited deformations of the less hard material due to its low roughness.

  • Point B: ηsc ≈ 8.4%, it is the presence of higher asperities that determine strong structural bridges within the less hard material.

In both situations, the friction is practically the same, but the interactions between surfaces are different. In the first situation (point A) a minimum surface pollution (for example water) can cause the risk of slip** and possibly falls. In the second situation (point B) the variation of the slip risk index is much less influenced by any possible pollution, in fact conditions of slip hazard only arise when the saturation of the spaces between valleys and ridges surface roughness occurs.

5 Results and discussion

The limitations made in the previous paragraph regarding the definition of the slip** risk, require that the ranges of values of the reference parameters, within which a potentially non-slippery surface can be defined, are representative of the real conditions that arise during the contact and reciprocal sliding between shoe and flooring, a phenomenon that is difficult to study due to the many variables involved and not always explicitly known.

Ranges of sliding-contact factor ηsc values have been identified for the definition of slip** risk indices. These ranges of ηsc values have been highlighted in Fig. 8 and reported in Table 2.

Fig. 8
figure 8

Classification of slip** risk indices in relation to the sliding factor—contact ηsc

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Table 2 Classification of slip** risk indices
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The areas of values with “MODERATE” slip potential represent “dubious” situations, in the sense that the anti-slip characteristics vary from “low” to “high” slip risk. In this scenario, to avoid possible confusions or errors, the “MODERATE” slip risk classification has been integrated with the words “safe with reserve”.

Two extremal values of the sliding-contact factor ηsc = 0.85% and ηsc = 8.25%, delimit the range within which the sliding risk is low or moderate, while values below ηsc = 0,85% and greater than ηsc = 8.25%, certainly represent conditions of high risk of slip** (areas indicated in Fig. 8 with vertical lines).

The classification of the slip-risk on the basis of sliding-contact factor ηsc is shown in Table 2

The main idea at the basis of the present work is to provide a way to evaluate the slip-risk related to a surface by means of an intrinsic characteristic of the specific surface. The aeasy measurement methodology proposed, with a portable palm-sized instrument, also allows for a continuous monitoring of surface morphology changes due to wear or of the effects of pollutants on the slip-risk index. The sliding-contact factor ηsc thus, can be used as a reference parameter for the slip-risk assessment, next to the dynamic friction coefficient. Further, the sliding-contact factor ηsc can be correlated to the DCoF, as an additional validation of the data.

The DcoF is evaluated with the Pendulum Tester, considering as acceptable the repeatability and the reliability of the measures obtained by such tool, as also verified by other authors [4, 11]. Some roughness parameters are also considered in other works [12, 13]. The main difference of the proposed approach from these other works lies in the fact that here roughness parameters are not considered one by one, but a new parameter is introduced derived from a combination of two roughness parameters:

  • Rk (μm), measuring the depth of roughness core, which is key to determine the evolution in time of surface characteristics:

  • Rmr, (adim), representing the percentage of the contact length with respect to the evaluation length L.

In this way the sliding—contact factor ηsc can provide a more complete set of information:

  • the interactions between surfaces is known, i.e. how friction and roughness interact: if there is a large contact surface, or high asperities and large deformations are present in the less hard material, or, still, intermediate situations in which friction is due to both the contact surface and the presence of asperities.

  • the evolution in time of the initial conditions due to wear can be predicted.

  • the application of anti-slip layers or abrasive treatments of the surface can be programmed to reduce the slip risk index.

Table 3 reports, for comparison purposes, some of the most used classifications of the slip-risk related to the dynamic friction coefficient alone [14, 15].

Table 3 Comparison between different classifications of slip** risk indices
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6 Conclusions

In this study, the sliding—contact factor ηsc, is identified as a new measurement tool allowing a more in-depth analysis of the non-slip characteristics of a surface. By determining the value of the sliding-contact factor combined with surface roughness parameters, using a simple calculation program, it is possible to define the risk index of sliding of the surface in both dry and wet (with water) conditions, and the correlated dynamic coefficient of friction, DCoF. The sliding-contact factor ηsc provides information on the nature of the contact between the two surfaces in reciprocal sliding, giving indications on which surface characteristics mainly determine the frictional forces between the surfaces in contact and how they could be influenced by any pollution with water and by changes over time due to wear.

For values of ηsc ≤ 2% the friction forces are strongly influenced by a large contact surface, while for values ηsc ≥ 7% the friction forces are mainly affected by the difference in hardness between the two contact materials. For intermediate sliding-contact factor ηsc values between 2% < ηsc < 7% the friction forces are poorly affected by surface roughness.

The sliding contact factor ηsc also allows to characterize the functionality of a surface in relation to wear over time and to evaluate the variation over time of the bearing fraction of the surface. The sliding conditions are related to the characteristics of the surfaces of the materials in contact and the way in which they interact with each other during the activity of walking. The shear stresses and therefore the values of the frictional forces vary over time in relation to surface wear of one or both surfaces. Normally one of the two materials is less hard than the other, leading on one hand to its plastic deformation with a consequent increase in the contact surface and on the other hand to its increased wear due to the breaking of the crests of the thinner asperities.

In conclusion the presented sliding-contact factor ηsc can provide information on:

  • the morphology of the profile;

  • how this profile changes with wear;

  • the contact surface and how it can be affected by liquid pollution (water).

Particular attention is however needed in the definition of the various involved variables related to the nature and the characteristics of the shoe surfaces that are in contact with a certain floor surface, and also to the nature of possibly present polluting substances [16, 17]. This study, e. g., only takes into account water as a possible pollutant.

Finally, given the importance ofto surface roughness, the present work also aims at providing a first basis for the development of deeper analyses and investigations and for the definition of a international standard [18, 19] for the classification and evaluation of the slip-risk, thus also improving safety in work and life environments.