Volume:6
Issue:2
Year:
2007
Dr François Quirion1 and Patrice Poirier1
1 QI Recherche et Développement Technologique inc., Québec, Canada.
Correspondence: Dr François Quirion, QI Recherche et Développement Technologique inc., 2454 Vimont, Longueuil, Qc, Canada J4L 3Y1. Telephone: +1 450 6161733.
Abstract
Many slip and fall accidents occur on wet flooring. As the foot hits the wet floor, a liquid film may become trapped between the heel or the sole and the floor. If the threads on the heel or sole and the roughness and texture of the flooring allow the liquid to be evacuated rapidly, then there is a shoe-floor contact and friction dominates. If, however, the liquid cannot be evacuated rapidly, then the shoe slides over the squeezed liquid film without contact between the sole and the floor. This phenomenon is very similar to aquaplaning and its occurrence depends on the texture of the heel and sole material, the texture of the flooring and the thickness and viscosity of the liquid forming the squeezed film. We report a simple approach, the falling plate method, for the investigation of the slip resistance of wet flooring. A plate standing perpendicular to the wet flooring falls freely on it. As it hits the wet flooring, the plate slides over a distance that depends on the ability of the flooring to evacuate squeezed water. The minimum amount of water necessary for the plate to slide over a liquid film, t*, is called the aquaplaning threshold. It was determined by measuring the sliding distance of a smooth stainless steel plate as a function of the amount of water for nine floorings having a roughness, Ra, in the range 0.8μm < Ra < 11μm. We find that t* increases linearly with Ra being around 20μm for flooring with a Ra~1μm and increasing up to 63μm when Ra reaches 11μm. The aquaplaning threshold also correlates well with the wet friction determined with a Brungraber Mark II. These results suggest that the aquaplaning threshold provides valuable information on the slip resistance of wet flooring.
Key words: Aquaplaning; environmental health; falling plate; friction; slips, trips, falls; slip resistance; squeezed film; wet floor.
Introduction
It is well accepted that many slip and fall accidents occur on wet floors (Leclercq, 1999) and that slipping occurs mostly when the heel strikes the floor (Strandberg and Lanshammar, 1981). It is often suggested that during the slide, the heel is supported by a thin layer of water that allows little or even no contact with the flooring (Grönqvist et al, 2003). This raises the question of how much water is needed for the formation of a squeezed liquid film between a shoe heel or sole and the flooring. Intuitively, there should be a critical amount of liquid on a flooring under which the liquid film does not form and over which it forms and causes slipping. But what is that threshold and how does it vary from one flooring to another? Tribology (Rabinowicz, 1994) tells us that the apparent friction between two lubricated surfaces depends on many parameters including the relative velocity and the roughness of the two surfaces as well as the thickness and viscosity of the lubricant layer. It thus seems reasonable to assume that the threshold amount of water will depend on the heel material and its roughness, the flooring material and its roughness and the amount of water on the flooring.
Surprisingly, the investigation of the slip resistance of wet flooring seems to pay little attention to the amount and nature of the liquids used for the tests. The slipperiness of wet flooring is expressed as the friction coefficient measured with the same apparatus used for the determination of dry friction. Wet samples are often tested using an excess amount (Leclercq et al, 1994) or a fix amount (Chang, 1998) of liquid contaminant. It can be water, a detergent solution, mineral oil or a mixture of glycerol and water. For a review of these experimental methods, please see Chang et al (2001) and Cholet et al (2000).
In order to investigate the slipperiness caused by a squeezed film, the experimental method must be able to generate that filmby hitting the wet flooring with a rather flat object simulating the shoe heel or sole. One very simple approach consists in letting a flat plate fall and hit a wet flooring. Interestingly, the movement of the plate, as it falls to the floor, is quite similar to the movement of the foot simulated by Liu and Lockhart (2006) for typical slipping events. As for a slipping event, the sliding distance will be longer if there is a squeezed liquid film formed between the plate and the flooring.
We (Quirion and Poirier, 2005 and 2006) presented preliminary results using the falling plate method to identify the aquaplaning threshold of various flooring. The purpose of this investigation is to present the method in more detail and to confirm that the aquaplaning threshold gives valuable information on the slip resistance of various flooring in wet conditions.
The falling plate method
The falling plate method measures the sliding distance of a plate as a function of the amount of water on the flooring. Experimentally (see Figure 1.0), the base of a thin rectangular plate is placed against a holder while its length forms an angle _ with the flooring.
Figure 1.0 In the falling plate method, a plate, leaning on a holder, stands at an angle with the flooring (A). When released, it falls flat on the flooring and slides (B) until it stops (C). The sliding distance is measured and analysed in term of the apparent friction of the plate on the flooring.
When the plate strikes the wet flooring, it is projected forward and parallel to the flooring. The sliding distance, d, depends on its horizontal kinetic energy and the amplitude of the forces acting against it. This approach was used for many years to determine the speed of cars from the length of the skidmarks (Adamson, 1976) assuming that the friction coefficient was known. In this investigation, we use the sliding distance to evaluate the friction of a plate on a flooring.
As the plate falls, its potential energy, EP, is transformed into kinetic energy. Upon impact with the flooring, a fraction, _, of that energy is transformed into horizontal kinetic energy, EK,H, so that the plate has an initial horizontal velocity, vH (Equations 1 and 2). The horizontal kinetic energy is dissipated into friction energy, EF, where g is the gravitational acceleration and m the mass of the plate (Equation 3). For simplicity, it is assumed that all the forces acting against the horizontal motion generate an apparent dynamic friction coefficient, μK,app (Equation 4).
The apparent dynamic friction coefficient increases with the reciprocal of the sliding distance of the plate on the flooring. However, to obtain the absolute value of the apparent dynamic friction coefficient, one must determine the parameter _. In order to keep the method as simple as possible, we chose to eliminate _ by expressing the apparent dynamic friction coefficient of the wet flooring, μK,app,wet, relative to that of the dry flooring, μK,app,dry. It is also assumed that _wet = _dry. The friction ratio, μR, becomes a very simple function of the sliding distance under dry, ddry, and wet, dwet, conditions (Equation 5).
When the sliding distance of a given plate-flooring combination is measured as a function of the amount of water, then ddry is a constant and the trend of the friction ratio is that of the apparent dynamic friction coefficient of the plate on the wet flooring. If the amount of water on the flooring is too low to form a liquid film between the plate and the flooring, then the sliding distance is rather small with a friction ratio close to one. Conversely, when the amount of water is large enough to form a liquid film under the plate, the sliding distance is high with a low friction ratio.
The critical amount of water necessary to form a liquid film between the plate and the flooring can be determined through the analysis of the sliding distance of the plate as a function of the amount of water on the flooring. We chose to express the amount of water in termof the apparent water thickness, t, using the volume of water, VW, spread on the geometrical area of the flooring, AW (Equation 6). For instance, an apparent thickness of 100μmof water corresponds to 100millilitre of water per square metre of flooring.
A typical example is shown in Figure 2.0 for a smooth stainless steel plate sliding on a finished vinyl composition tile. The sliding distance remains almost constant until the apparent water thickness is around 30μm. At higher water thickness, the sliding distance increases steeply and finally reaches a plateau. Using Equation 5, the sliding distances were converted into a μR vs. t data set. The friction ratio, which reflects the apparent dynamic friction coefficient of the wet flooring, drops steeply at a thickness of water around 30μm.
To eliminate the subjectivity of a graphical interpretation, all the μR vs. t data sets were fitted to the same empirical model (Equation 7) with μR,i and μR,f the initial and final friction ratio, t*, the aquaplaning threshold and a, the steepness of the friction drop. For most data sets, μR,i = 1 and μR,f is the friction ratio at high values of t. The data can then be fitted with only two variables, a and t*.
For example, fitting the μR vs. t data presented in Figure 2.0 with Equation 7 gave μR,i = 1.0 (fixed), μR,F = 0.26 (from experimental data), a = 6.5 and t* = 29μm. The rather high value of the exponent a indicates a steep change in the friction of the wet flooring relative to the dry flooring. The change occurs at the aquaplaning threshold, t*, and the model imposes that the friction ratio at the threshold is μR* (Equation 8).
In the example of Figure 2.0, the threshold friction ratio corresponds to _R0.53, i.e. that the risk of aquaplaning would increase when the apparent friction drops suddenly to 53% of the dry friction. This is an empirical definition of the aquaplaning threshold and it only has the advantage of being objective. Our concern is not to determine the absolute value of the aquaplaning threshold and of the threshold friction ratio. We are mostly interested in their evolution for different types of flooring.
In this investigation, we wish to emphasise the contribution of the flooring to slip resistance in wet conditions. To do so, we used a smooth stainless steel plate as the slider. It is known that hard materials with little roughness are very slippery in wet conditions. For instance, the evaluation of the slip resistance of whole shoes is sometimes performed on smooth stainless steel plates (Leclercq et al, 1995) to emphasise the intrinsic contribution of the shoe to slip resistance. The reverse should also be valid, i.e. using a smooth stainless steel plate as the heel (sole) material in order to emphasise the contribution of the flooring to slip resistance in wet conditions.
Figure 2.0 Typical data set for the sliding distance, d, and the friction ratio, μR, of a stainless steel plate (mass = 76g, width = 41mm and length = 64mm) on a finished vinyl composition tile (VCTF) against the apparent water thickness (t). Solid line is the best fit using Equation 7 with μR,i = 1.0, μR,F = 0.26, a = 6.5 and t* = 29μm.
Note that the falling plate method is not limited to stainless steel and to smooth plates. We have also obtained good results using a Neolite slider (Quirion and Poirier, 2005). Rougher or even patterned plates could be used as well as rougher and patterned flooring materials.
Methodology
This section describes briefly the experimental procedures that were used to obtain the sliding distance, the average roughness and the wet friction of the flooring. The flooring tested consisted of commercial flooring cut to a width of 75mm and a length between 150 and 200mm.
Sliding distance, friction ratio and aquaplaning threshold
This investigation presents μR vs. t data sets obtained with a stainless steel plate of width 41mm and length 64mm weighing 76g. Before each series of measurements on a given flooring (typically 15 to 20 measurements), the plate was sanded (orbital sander) with 220 grit paper and cleaned with acetone. The average roughness, Ra, of the stainless steel was 0.15μm.
The sliding distance was always measured in the same way. As shown in Figure 1.0, the plate was placed against the holder. Unless otherwise specified, the drop angle was 90° so that the plate initially stood perpendicular to the flooring. The fall was initiated by pushing the top of the plate very slowly until it fell freely under the action of gravity. When the plate reached a stop, the sliding distance was measured. In this investigation, the maximum sliding distance is limited by the length of the flooring sample (either 150 or 200mm), the length of the sliding plate (64mm) and the thickness of the holder (12mm). It is thus either 82 or 124mm depending on the length of the flooring sample. In some conditions, the plate slid past the edge of the flooring sample. These data were rejected because there is no way to find out just how far it would have gone.
The sliding distance on the dry flooring, ddry, can be obtained at any moment. The only requirement being that the flooring is completely dry. The sliding distance on the wet flooring, dwet, was determined by spraying water homogeneously over the tile using an airbrush applicator. After weighing the mass of water on the tile, the sliding distance was measured as described above. After each measurement, water was wiped off from the flooring and the procedure was repeated for the determination of the sliding distance at a new water thickness. The sliding distances on the wet and dry flooring were used to calculate the μR vs. t data sets with Equation 5 and the aquaplaning threshold, t*, was obtained by fitting the μR vs. t data sets with Equation 7.
Average roughness (Ra)
The average roughness of the flooring was determined at the beginning of the investigation using a DekTak 3030 (radius of curvature of the tip = 12μm, Force = 0.05 N, scan length = 5mm). Each scan provided a value for the average roughness, Ra, and the values reported in this investigation are the average of at least four scans at different locations of the flooring.
Dry friction (μK,dry)
The friction experienced by the plate as it slides on the Dr François Quirion and Patrice Poirier dry flooring is very similar to the friction obtained by a horizontal pullmethod. In this investigation, the dynamic friction coefficient was measured by pulling the stainless steel plate at a velocity of 25 mm.sec -1 on the dry flooring. For each run, the pulling force was sampled (Shimpo, FGV-1 force gauge) at 10 hertz for two seconds after the initial movement of the plate. The dynamic friction coefficient on the dry plates was then calculated by dividing the average pulling force by the weight of the plate. In this investigation, the values of μK,dry correspond to the average of at least 4 runs. The standard deviation on μK,dry was always between 1 and 2 % except for the QTM where it was 10%.
Wet friction (μK,wet)
The wet friction of the flooring was determined using a Brungraber Mark II apparatus. Instead of using the recommended Neolite or leather skates, we fitted the stainless steel plate used for the falling plate experiments to the Mark II holder. Before each drop, the back of the slidere was tilted so that it touches the flooring. Measurements were made on wet flooring at a water thickness around 100μm (100 ml.m-2).
Results and discussion
The flooring tested in this investigation were cut from commercial flooring having no definite patterns and a relatively low average roughness (Ra). Their origin and Ra are reported in Table 1. Sample QTF was prepared from a new QTM tile that was worn and fouled with fat according to a procedure developed in our laboratory (Massicotte and Quirion, 2002).
Table 1.0 Origin, average roughness, dry friction, fraction of potential energy converted into kinetic energy, sliding distance and critical water thickness of the nine floorings tested.
The resulting QTF is very similar to the tiles found in many commercial (Underwood, 1992) and institutional kitchens (Massicotte and Quirion, 2002). VCTF is the same vinyl composition tile as VCT with two coats of acrylic finish (ShureShine, Tarkett).
The average roughness of the stainless steel slider was 0.15 μm, i.e. much less than any of the floorings tested. The average roughness of the flooring tested did not change by more than 10% from the beginning to the end of the investigation.
Sliding distance on dry flooring (ddry)
The sliding distance, ddry, and the dynamic friction coefficient, μK,dry, of the stainless steel plate over the nine flooring tested are reported in Table 1. There seems to be no correlation between either ddry and μK,dry. However, Figure 3.0 shows that ddry is higher for the smoother tiles and decreases to a plateau value as Ra increases.
The longer sliding distances on the smoother tiles could be the result of the formation of an air cushion between the plate and the tile. This is similar to a paper sheet sliding over a smooth table top or a wood panel sliding over long distances on a smooth concrete floor. In such conditions, the apparent friction on the dry flooring would be lower than the real friction, μK,app, dry < μK,dry and Equation 4 tells us that the ddry would be longer than expected. Equation 4 also tells us that the longer sliding distance could be the result of a higher energy transfer to the plate, _dry, for smoother flooring. At this point, it is difficult to discriminate between the two effects (lower apparent friction and higher energy transfer). Using Equation 4, the value of _dry was calculated with by replacing μK,app, dry with μK,dry and it is reported in Table 1.
Figure 3.0 Evolution of the sliding distance, ddry, of a stainless steel slider (width = 41mm, length = 64mm) as a function of the average roughness, Ra, of the dry floorings.
The assumption that μK,app, dry ~ μK,dry is realistic for the rougher flooring where the air cushion is less likely to form under the plate. For these flooring (QTM, Q01, F75 and F77) the average roughness increases from 5 to 11μm with very little change in the value of _dry which remains almost constant at ~7%. If one assumes that the energy transfer is not correlated to the roughness, than the longer sliding distance for the smoother flooring would be the consequence of a low apparent friction coefficient, possibly due to the formation of an air cushion.
Testing the method on wet tiles
The simplicity of Equation 5 suggests that the friction ratio, μR, is not a function of the drop angle, _, so that the sliding distances obtained at different values of _ should all fall on a master curve when they are expressed in terms of their friction ratio, μR.
Figure 4.0 Impact of the drop angle (_ = 90° (*), 70° ( ), 60° ( ), 50° (Δ), 40° (X)) on a) the sliding distance, d, and b) the friction ratio, μR, for a stainless steel plate falling on wet ceramic tiles (CER). t is the apparent water thickness.
Figure 5.0 Evolution of the friction ratio, μR, of the stainless steel plate on eight different floorings as a function of the apparent water thickness, t. The different symbols represent different data sets.
This was checked by measuring the sliding distance, d, of the stainless steel slider on ceramic tiles (CER) as a function of the apparent water thickness, t, at five drop angles (_ = 90, 70, 60, 50 and 40°). Figure 4.0a shows that, on the dry ceramic tiles (t = 0), the sliding distance increases with the drop angle in accordance with Equation 4 (ddry _ sin(_)). This is also true at any given value of t, confirming that Equation 4 holds for both dry and wet conditions.
At a given drop angle, the sliding distance increases with the apparent water thickness and the trend is the same for the five drop angles tested. When the sliding distances obtained at a drop angle are reduced to the friction ratio, μR, with the corresponding sliding distances on the dry tiles, all μR vs. t data sets fall on a master curve (Figure 4.0b) in accordance with Equation 5.
The aquaplaning threshold (t*)
When the plate hits the wet flooring, water has to be evacuated rapidly to prevent the formation of a squeezed liquid film that will reduce drastically the friction. If there is too much water, the plate will slide over the liquid film resulting in a low apparent friction coefficient, and a small friction ratio. As observed in Figure 4.0b, the friction ratio remains close to one at low water thickness and then decreases sharply when the apparent thickness reaches a threshold value. In this investigation, we refer to that transition as the aquaplaning threshold, t*, and we define it as a critical thickness of liquid (in μm) over which the risk of aquaplaning becomes important.
Figure 5.0 presents the μR vs. t data sets obtained for eight of the nine floorings (for VCTF see Figure 2.0). All the data sets obtained on a given flooring are plotted together with different symbols to emphasise the good reproducibility. The trend of the μR vs. t data sets is not always the same from one flooring to another. Sometimes there is a small plateau at low apparent water thickness (CER, F77 and QTM) and sometimes the friction ratio drops rapidly at very low water thickness (POR, VCT, F75). In most cases, the friction ratio reaches a plateau at high water thickness, suggesting that the addition of more water does not change the apparent friction of the plate with the flooring. This is in accordance with the formation of a liquid film between the plate and the flooring. Once the plate slides on the liquid film, adding more water should have little impact on the apparent friction.
Figure 6.0 Evolution of the critical water thickness, t*, with the average roughness, Ra, of the floorings tested. The solid line is the best linear fit with slope = 4.24, ordinate = 17.2μm and r2 = 0.91.
All μR vs. t data sets were fitted independently to Equation 7 to get the aquaplaning threshold. The different values of t* obtained for a given flooring were averaged and they are presented in Table 1.0 together with their standard deviation.
Intuitively, the ability of a plate-flooring combination to generate a squeezed liquid film should decrease as the roughness of the flooring increases. In other words, the aquaplaning threshold should increase with the average roughness of the flooring. This is shown in Figure 6.0 where the aquaplaning threshold, t*, increases linearly with the average roughness, Ra, of the flooring tested. It has been suggested that the roughness of a flooring gives information on its slip resistance in wet conditions (Chang, 1999). So, the good correlation of the aquaplaning threshold with the average roughness of the flooring indicates that the aquaplaning threshold also gives valuable information on the slip resistance of these flooring under wet conditions.
Interestingly, t* does not extrapolate to zero. This suggests that it would take a minimum amount of water to induce aquaplaning on a perfectly smooth flooring. This makes sense when we consider the empirical definition of the aquaplaning threshold imposed by Equation 7. Since, by definition, the risk of aquaplaning occurs when the friction ratio reaches the value of μR* (Equation 8), then it seems reasonable to assume that it will take a minimum amount of liquid on the surface of any flooring for the friction to drop from 1 to μR*.
Figure 7.0 Aquaplaning threshold, t*, obtained with the falling plate method using a stainless slider as a function of the wet friction determined with the Brungraber Mark II. For these experiments, the Mark II was equipped with the stainless steel plate used for the falling plate method and the measurements were performed at a water thickness around 100μm (100 ml.m-2).
The average value of μR* for the 32 data sets analysed in this investigation was 0.48 ± 0.03. But is 17.2μm a reasonable value for the aquaplaning threshold of a perfectly smooth flooring? The value seems too high. Another contribution would be the roughness of the plate itself. Although it is very small, it can accommodate some water. We have considered that the plate and the flooring tested were perfectly flat. It is possible that both surfaces present small deformations that would allow some liquid to remain trapped, thus overestimating the aquaplaning threshold. But at this moment, it is not possible to quantify these contributions.
If, as suggested by Chang (1999), the roughness is correlated with the wet friction, and if the aquaplaning threshold is correlated with the roughness, than the aquaplaning threshold should be correlated with the wet friction. To check this, the wet friction of the stainless steel plate on the nine floorings tested was determined at an apparent water thickness of t ~ 100μmwith a Brungraber Mark II. This experimental method allows water to be trapped under the plate as it hits the surface of the wet flooring. The aquaplaning threshold is plotted against the wet friction of the flooring tested in Figure 7.0.
There is indeed a good correlation between the two parameters. It is not clear if the aquaplaning threshold extrapolates to zero at very low wet friction or if it reaches a plateau. More experimental work is required to answer that question.
The results of this investigation strongly suggest that the aquaplaning threshold could be used to compare the risk of aquaplaning on different types of flooring. For example, the risk of aquaplaning would be similar for the smoother flooring (QTF, CER, VCTF, POR and VCT) with an average aquaplaning threshold of 24 ± 4μm. The new and rougher quarry tiles (QTM, Q01) would be able to accommodate about 70%more water than the smoother tiles before the risk of aquaplaning appears. This amount would increase to 100%for F77 and 160%for F75.
The results of Table 1 also indicate that the aquaplaning threshold of newly installed flooring of quarry tiles (QTM = 43μm) would drop significantly as the tiles would wear and become fouled (QTF = 20μm) in accordance with observations made during a field investigation (Massicotte and Quirion, 2002).
Conclusions
The falling plate method was developed to investigate the aquaplaning resistance of wet flooring. The experimentalmethod is very simple to use and the theory behind it is quite easy to understand. A flat plate falls freely on a flooring covered with different amount of a liquid. The sliding distance on the wet and dry tiles are used to calculate the friction ratio between wet and dry conditions. The evolution of the friction with the apparent water thickness is then analysed with an empirical model to obtain the aquaplaning threshold for the plate on the flooring. This investigation confirms that: _ The falling plate method is easy to use and it generates reproducible data sets from which the aquaplaning threshold can be extracted.
- The theoretical background is respected, for instance that data obtained at different drop angle all provide the same results.
- The use of a smooth stainless steel plate emphasises the contribution of the flooring to the aquaplaning resistance.
- For flooring without texture and a relatively small average roughness (0.8 < Ra < 11μm), the aquaplaning threshold increases linearly with the average roughness.
- The aquaplaning threshold increases with the wet friction of flooring.
In this investigation, the falling plate was a rather light and smooth stainless steel plate but other types of plate could also be used to investigate the impact of the nature of heel or sole the material and texture on the resistance to aquaplaning. Although the results are promising, there is still much to do to come up with a method that would reproduce a typical heel(sole)-floor interaction. Nevertheless, the aquaplaning threshold can be used to compare the aquaplaning resistance of different flooring.
Table 2.0 List of symbols
Acknowledgements
This investigation received financial support from the Institut de recherche Robert-Sauvé en santé et en sécurité du travail (IRSST) under grant No 99-079. Plain vinyl composition tiles were provided by Tarkett and Traction Step vinyl sheeting were provided by Forbo. The Brungraber Mark II was lent to us by Tarkett.
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