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Coatings 2021, 11, 1254. https://doi.org/10.3390/coatings11101254 www.mdpi.com/journal/coatings
Article
Relationship between Friction Coefficient and Surface
Roughness of Stone and Ceramic Floors
Samsiya Khaday 1, Kai-Way Li 1, Lu Peng 2,* and Ching-Chung Chen 3,*
1 Ph.D. Program of Technology Management, Chung Hua University, Hsin-Chu 30012, Taiwan;
d10803014@chu.edu.tw (S.K.); kai@chu.edu.tw (K.-W.L.)
2 College of Information Management, Nanjing Agricultural University, Nanjing 210095, China
3 Department of Information Management, Hsing Wu University, New Taipei 24452, Taiwan
* Correspondence: lupeng942@njau.edu.cn (L.P.); 095165@mail.hwu.edu.tw (C.-C.C.)
Abstract: Slips and falls are common occupational incidents worldwide. The friction on a floor sur-
face is one of the critical environmental factors affecting the risk of a slip. In this research, we con-
ducted friction measurements on stone and ceramic floor tiles under dry, wet, and water–detergent
(WD) solution covered conditions using a horizontal pull slip meter (HPS). Our purposes were to
quantify the slip resistance of commonly used stone and ceramic floors under different surface con-
ditions and to validate the curvilinear relationship between the coefficient of friction (COF) and
surface roughness of the floors proposed in the literature. The COF data were analyzed together
with a surface profile parameter (Ra) of the floor samples. The results showed that the COFs of the
stone floors were significantly (p < 0.0001) higher than those of the ceramic floors. All the floors
under the dry conditions were slip resistant when adopting the ANSI 1264.2 criterion. Two and five
ceramic floors were not slip resistant under the wet and WD solution covered conditions, respec-
tively. Three polynomial regression equations were established to describe the relationship between
the COF and Ra. The curvilinear functions of these models indicate that the three-zone (initial
growth, steady-growth, and plateau) concept concerning the COF–Ra relationship in the literature
was valid when static COF values measured using an HPS were adopted. In addition, the three-
zone concept was valid not only on WD solution covered surfaces but also on dry and wet surfaces.
Keywords: slip; trip and fall; coefficient of friction; horizontal pull slipmeter; floor roughness
1. Introduction
Slips and falls create significant safety and health problems for workers worldwide
[1,2]. The official statistics in Taiwan indicate that there were 2,608 falls on the same level
and 566 falls from height at the workplace in 2018, which accounted for 23% and 5% of all
occupational incidents, respectively [3]. The national statistics in Singapore indicate that
slips, trips, and falls have accounted for 34.3% and 28.2% of all major and minor injuries
at the workplace, respectively [4]. The injuries statistics in Hong Kong indicated that same
level falls have accounted for 29.6% of all injuries at workplaces [5]. Similar statistics may
be found in other countries [6,7]. These statistics highlight the significance of slip and fall
issues in the safety and health of workers and the need for efforts in understanding the
mechanism and control of slips and falls.
A slip has been identified as the primary precedent event of a fall. Courtney et al. [8]
indicated that slip contributed to 40% to 50% of all fall-related injuries in the USA. It is
commonly accepted that people are more likely to slip when walking on slippery floor
surfaces. Friction has been adopted as one of the measures of floor slipperiness [9]. Slip
occurs because friction between the footwear and floor is inadequate to resist the move-
ment of the shoe sole on the floor, especially at the moment of the heel landing on the
floor. The friction between the footwear and floor may be quantified using the available
Citation: Khaday, S.; Li, K.-W.;
Peng, L.; Chen, C.-C. Relationship
between Friction Coefficient and
Surface Roughness of Stone and Ce-
ramic Floors. Coatings 2021, 11, 1254.
https://doi.org/10.3390/
coatings11101254
Academic Editor:
Diego Martinez-Martinez
Received: 4 September 2021
Accepted: 11 October 2021
Published: 15 October 2021
Publisher’s Note: MDPI stays neu-
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Copyright: © 2021 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and con-
ditions of the Creative Commons At-
tribution (CC BY) license (http://cre-
ativecommons.org/licenses/by/4.0/).
Coatings 2021, 11, 1254 2 of 13
coefficient of friction (COF) [10]. The friction required to resist the movement of the shoe
sole on the floor, on the other hand, may be quantified using the required COF [11].
Measurements of both the required and available COF are complicated. The former
requires the recruitment of human participants and the use of one or more force platforms
so as to analyze the ground reaction force of the foot on the floor [12,13]. The latter, on the
other hand, requires the use of a friction measurement device, also called a tribometer or
a slipmeter, to measure the COF of the floor under certain footwear and floor conditions
[9,14]. The required friction depends on the gait pattern of a walker and is dependent on
human factors [11,15,16]. The available COF is influenced not only by the characteristics
of the footwear and floor but also by the friction measurement device adopted [9,17,18].
Measurements of the available COF have been reported both in the field and in the
laboratory. Field measurements were normally conducted to assess the risk of slip and fall
in certain workplaces, such as restaurants and other jobs in public places [19–21]. Such
assessments might be performed to compare the friction measurement results with the
perceived floor slipperiness of human participants [22]. The friction measurements con-
ducted in the laboratory were normally performed to explore the mechanisms of slipping
of the shoe sole on the floor. Studies testing the effects of the floor, footwear, floor inclined
angle, and floor surface contaminations on slipperiness have been reported [14,18,23–32].
There were also studies comparing the testing parameters, test methods, reliability, and
validity of friction measurement devices [13,17,32–35].
There is a general awareness that rough floors are more slip resistant than the smooth
ones. Floor roughness was found to be positively correlated with the COF of the floor
[26,35,36]. The surface profile characteristics of the floor predominantly contribute to the
friction at the footwear–floor interface in two aspects. The first one is that asperities on the
floor surface could interlock with the tread on the shoe sole and, hence, impede the shoe
sole from sliding on the floor. The second one is that floor roughness provides void space
for drainage when the floor is covered by liquid, which allows faster contact of the shoe
sole and the floor [26,36].
Many surface roughness parameters have been defined to depict the surface profiles
of a floor surface. The correlations between more than 20 of these parameters and the slip
resistance of floors have been discussed [37]. The parameter Ra, also known as the center
line average of surface heights (CLA), is one of the most commonly used roughness pa-
rameters in discussing friction on the floor [38]. Li et al. [38] measured the Ra and subjec-
tive rating of floor slipperiness on their floor samples. They found these two measures
were highly correlated (ρ = 0.79, p < 0.0001) with each other. They concluded that Ra may
be adopted as one of the predictors of the perceived floor slipperiness of human partici-
pants. Grönqvist et al. [39] measured the dynamic COF of floor samples with varying floor
roughness. The COF and Ra of their floor samples were highly correlated (r = 0.87, p <
0.001) with each other. They recommended Ra values of 7–9 μm and 16–22 μm for adequate
(dynamic COF = 0.2) and very slip resistant (dynamic COF = 0.3) floors, respectively, on
glycerol contaminated surfaces. Kim et al. [26] claimed that an Ra higher than 17 μm might
be sufficient for proper slip resistance (dynamic COF = 0.4) on soapsuds contaminated
floors. Chen et al. [36] reported that, when the floor was contaminated by viscous (38 mPa·s
or higher) liquid, the frictions on all the floors they tested were extremely low (almost
zero). When the viscosity of the liquid on the floor was low (2 mPa·s or less), the floor may
still be slip resistant (static COF = 0.5) if the Ra of the floor surface was 40 μm or higher.
The COF values in the above-mentioned studies were measured using different devices
and protocols. The recommended floor roughness levels in those studies are, therefore,
not comparable.
Kim et al. [26] introduced a concept of surface roughness zones in the mechanism of
friction at the footwear–floor interface. They demonstrated that the slip resistance in-
creases slowly with the increase of floor roughness when the surface roughness is low. In
this “initial low-grow zone”, multiple friction mechanisms are involved between the shoe
sole and floor while interlocking effects are not present. In the “steady-growth zone,” the
Coatings 2021, 11, 1254 3 of 13
interlocking of the floor asperities with the shoe sole dominating the friction and linear
relationship between the floor roughness and COF is likely. In the “plateau zone,” the
interlocking mechanisms become exhausted and increasing the floor roughness made no
further benefits in increasing the COF of the floor. Based on a dynamic COF of 0.4, they
recommended using Ra values of 17 and 50 μm as the lower and upper bounds of the
steady-growth zone. They indicated that finding the floor roughness range in such a zone
is critical in establishing a slip resistant floor environment. The study of Kim et al. [26]
was performed using a pendulum-type friction tester, and they used a dynamic COF of
0.4 as a criterion of slip resistance. It is well known that the theoretical bases of using static
and dynamic friction in assessing the risk of slip and fall are different. It has also been
shown that the COF readings on a floor sample may be dependent on the friction meas-
urement device [9]. Whether the concept of surface roughness zones will be valid or not
is not clear when using both a different friction measurements device and a static COF in
the criterion of slip resistance.
The main objective of the current study was to validate the three-zone concept of Kim
et al. [26] using a different friction measurement device and criterion of slip resistance.
Establishing regression models to predict the COF on the tested floors using their Ra val-
ues was also one of the objectives of this study. These models provide quantitative evi-
dence to show the relationship between the COF and Ra. In addition, both stone and ce-
ramic floorings are commonly used both indoors and outdoors. Friction measurements
for these floors are essential to quantify the risk of slipping on these floors. Our third ob-
jective was to quantify the slip resistance of the commonly used stone and ceramic floors
under different surface conditions.
2. Method
A friction measurement experiment was performed in the laboratory.
2.1. Friction Measurement Device
A horizontal pull slip meter (HPS, S.C.S Forces, Agawam, MA, USA) was used (see
Figure 1). This slip meter encompasses a power unit and a weight unit. There are three
circular footwear pads (Neolite, Akron, OH, USA, Ø12.7 mm) on the bottom of the weight
unit. The Neolite footwear pads had an averaged specific gravity of 1.27 ± 0.02 and a Shore
A hardness of 94. The total contact area of the footwear pad on the floor is approximately
3.8 cm2. The contact pressure between the footwear pads and floor surface is approximately
70.2 kPa. There is a motor inside the box of the power unit. This motor rotates to generate
a horizontal pull force to drag the weight unit (2700 ± 34 g). The reading on the meter at
the moment when the weight unit starts to move is the slip index [40]. This slip index is
ten times the static COF at the footwear–floor interface. The rationale of the HPS is to
determine the coefficient of friction by dividing the horizontal pull force by the gravity of
the weight unit. This is similar to that of the sliding friction tester in the literature [41].
Coatings 2021, 11, 1254 4 of 13
(a)
(b)
Figure 1. Horizontal pull slip meter: (a) power and weight units, (b) footwear sample on the bot-
tom of the weight unit.
2.2. Floor Tiles
Twelve floor tiles were tested, including six ceramic and six stone floors. These floors
are commonly used both indoors and outdoors. Table 1 shows these floors. The stone
floors included four sandstones (S1, S2, S4, and S6) and two unpolished granites (S3 and
S5). The Ra values of all the floor samples were measured using a Mitutoyo S301 pro-
filometer [42] (Mitutoyo Inc., Sakado, Japan). This device uses a detector stylus tracing the
surface of the floor sample. The direction of the stylus movement was parallel to that of
friction measurement. The lengths of cut-off and measurement were 2.5 and 12.5 mm, re-
spectively [38]. The Ra was determined based on the movements of the stylus. The litera-
ture has shown that friction correlates well with bandpass filtered profile parameters [43].
The Gaussian filter was adopted in processing the stylus tracing data [42]. On each floor,
nine Ra readings were collected, each from one location. The average of these readings
was used. The Ra of the ceramic and stone floors ranged from 8.9 to 30.4 μm and from 29.0
to 65.1 μm, respectively.
Coatings 2021, 11, 1254 5 of 13
Table 1. Floor samples.
Code
Stone Floor
Ra (μm)
Code
Ceramic Tile
Ra (μm)
S1
31.5
C1
8.9
S2
29.0
C2
18.9
S3
56.8
C3
20.3
S4
38.4
C4
27.2
S5
33.6
C5
27.5
S6
65.1
C6
30.4
2.3. Surface Conditions
The surface conditions included dry, wet, and water–detergent (WD) covered condi-
tions. For dry condition, dry and clean surface of the floor sample was measured. For wet
measurements, all the stone floors were immersed in a container full of tap water for 24 h
so that the floors were fully moisturized before measurement. For measurements of wa-
ter–detergent (WD) solution covered condition, all the stone floors were immersed in WD
solution also for 24 h before testing. This solution included 30 mL dishwashing detergent
(purchased from a local market) mixed with 2 L tap water. For the friction measurement
of each of the two liquid contaminated conditions, we poured a small cup (10 mL) of liquid
on each of the three footwear pad contact points of the HPS on the floor sample.
2.4. Measurement Procedure
All the friction measurements were performed by the same operator. Prior to meas-
urement, the operator wiped the floor samples with a 3% ammonium hydroxide (NH4OH)
solution and dried them with a clean cloth. The floor sample was sanded using a No. 60
grit abrasive paper. After this, the sample was sanded again using a No. 400 abrasive pa-
per. The operator then brushed the surface to remove loose particles. This procedure fol-
lowed those in the ASTM [40].
On each floor sample, four locations were selected for friction measurements. These
locations were evenly distributed on the floor samples. In other words, each of them was
at a distance approximately one quarter of the way to the two adjacent sides of the floor
sample. On each location, 6 measurements were performed. On each measurement, the
units of the power and weight of the HPS were on the same level. The operator aligned
Coatings 2021, 11, 1254 6 of 13
the pulley on the power unit with the hook on the weight unit and then connected the
string of the power unit to the hook on the weight unit. The string was parallel with the
test surface and was in line with the pulley on the power unit. The operator pushed down
the power unit to prevent its moving and then pressed the switch. When the weight unit
started to move, the switch was turned off. The reading on the meter was the slip index.
The COF was the slip index divided by 10.
2.5. Statistical Analysis
The order of friction measurements on each floor sample was randomized among the
three surface conditions. There were a total of 864 COF readings (12 floors × 3 surface
conditions × 4 locations × 6 repetitions). The normality of these data were ensured by
checking the normal probability plot. Descriptive statistics and analysis of variance
(ANOVA) were performed for the measured COF values. Duncan’s multiple range tests
were performed to compare the differences between any two treatments in a factor if the
main effects of the factor reached the α = 0.05 significance level. This test is powerful and
is very effective at detecting differences between means when real differences do exist
[44]. Regression analyses were performed to establish regression models showing the re-
lationship between the COF and Ra using the readings of three out of the six repetitions
on the same location of each floor and surface condition. In other words, half of the data
were used in establishing the regression models. A mean absolute deviation (MAD) (see
Equation (1)) was calculated to determine the prediction errors of the COF values for each
of the floor, surface condition, and location. The measured COF values in Equation (1)
were the COF readings not used in establishing the regression models. The statistical anal-
yses were performed using the SPSS version 20 software (IBM®, Armonk, NY, USA).
MAD =
1
n |predicted COF − measured COF|
(1)
where n is the number of pairs of predicted and measured COF values used.
3. Results
3.1. ANOVA Results
Figure 2 shows the means and standard deviations of the COF of all the floor samples.
The ANOVA results indicated that both the floor material and the surface condition sig-
nificantly (p < 0.0001) affected the COF. The Duncan’s multiple range test results showed
that the COF of the stone floors (0.71 ± 0.09) was significantly higher than that of the ce-
ramic floors (0.53 ± 0.12). The COF on the dry surface (0.69 ± 0.11) was significantly (p <
0.05) higher than those of the wet (0.61 ± 0.13) and WD solution covered surfaces (0.55 ±
0.15). Duncan’s multiple range tests were also performed separately to compare the COFs
of the three surface conditions for each of the stone and ceramic floors. For the stone floors,
the COF on the dry surface (0.74 ± 0.08) was significantly (p < 0.05) higher than those of
the wet (0.71 ± 0.07) and WD solution covered (0.67 ± 0.09) conditions. The COF of the wet
condition was significantly (p < 0.05) higher than that of the WD solution covered condi-
tion. For the ceramic floors, the COF on the dry surface (0.63 ± 0.09) was significantly (p <
0.05) higher than those of the wet (0.52 ± 0.09) and WD solution covered (0.44 ± 0.09) con-
ditions. The COF of the wet condition was also significantly (p < 0.05) higher than that of
the WD solution covered condition.
Coatings 2021, 11, 1254 7 of 13
Figure 2. COF values of the floor samples.
Duncan’s multiple range tests were also performed separately for the wet and WD
solution covered conditions to compare the COF values between any two floor samples.
The results are shown in Table 2.
Table 2. Duncan’s multiple range test results for floors under wet and WD solution covered conditions.
Floor
Ra (μm)
Wet
Mean COF
Grouping*
WD Solution
Mean COF
Grouping*
S2
29.0
0.78
A
0.77
A
S1
31.5
0.77
AB
0.76
A
S6
65.1
0.74
B
0.70
B
S5
33.6
0.68
C
0.63
C
S3
56.8
0.63
D
0.58
D
S4
38.4
0.63
D
0.57
D
C3
20.3
0.62
D
0.55
D
C6
30.4
0.60
D
0.49
E
C4
27.2
0.52
E
0.45
F
C5
27.5
0.52
E
0.41
G
C2
18.9
0.47
F
0.40
G
C1
8.9
0.42
G
0.30
H
*Duncan grouping; different letters indicate they are significantly different (p < 0.05).
3.2. Correlation Analyses & Regression Modeling
The Pearson’s correlation coefficients between Ra and COF under dry, wet, and WD
solution covered conditions were 0.63, 0.62, and 0.66, and all of them were statistically
significant (p < 0.0001).
To establish the relationship between the COF and Ra under a surface condition, a
regression analysis was performed using the COF as the dependent variable and the floor
roughness parameter Ra and surface condition as the independent variables. It was as-
sumed that the measured COF is a function of Ra under surface conditions, or alterna-
tively:
COF = f(Ra/surface condition)
(2)
Coatings 2021, 11, 1254 8 of 13
Initially, a simple linear regression model was fitted to predict the COF using Ra.
However, it was found that the curvilinear model may be more appropriate. A polynomial
regression model was then fitted (see Equation (3)):
COF = ß0 + ß1 Ra + ß2 Ra2+ ß3 Ra3
(3)
where ßi is the regression coefficient, i = 0, 1, 2, 3. The unit of Ra is μm.
The results of the regression analysis are shown in Table 3. The t-test results of the
regression coefficients showed that all the regression coefficients were statistically signif-
icant at p < 0.0001.
Table 3. Results of regression modeling.
Surface
ß0
ß1
ß2
ß3
R2
√MSE
dry
0.508
−4.1 × 10−3
5 × 10−4
−6 × 10−6
0.96
0.022
wet
0.393
−2.5 × 10−3
5 × 10−4
−6 × 10−6
0.94
0.033
WD solution
0.297
−4.4 × 10−3
6 × 10−4
−7 × 10−6
0.93
0.044
The polynomial regression models and measured COF values of the dry, wet, and
WD solution covered conditions are shown in Figure 3. The measured COF values are the
means of the three readings not used in establishing the regression models. The MADs for
the dry, wet, and WD solution covered surfaces were 0.014, 0.021, and 0.025, respectively.
Figure 3. Regression model and measured COF (dot): the curves from top to bottom are for dry,
wet, and WD solution covered conditions. The dotted lines indicate the boundaries of the three
zones recommended by Kim et al. [26].
The polynomial regression models in Figure 3 support the zones of initial low
growth, steady-growth, and plateau concept of Kim et al. [26].
Coatings 2021, 11, 1254 9 of 13
4. Discussion
Friction measurement is one of the major approaches to assess the risk of slip and
fall. The result of such a measurement is the available COF. Numerous friction measure-
ment devices have been developed. However, none of them have been accepted univer-
sally as a perfect one. All of them have pros and cons. Different friction measurement
devices may report different readings. The readings on different devices may, therefore,
not be directly comparable. The HPS is one of the friction measurement devices recom-
mended by the ASTM [40] to measure the COF of floor samples. It is not sensitive to op-
erator variability and is easy to use [9,45,46]. These were the reasons why we adopted this
device. Due to its drag mechanism design, the HPS is proposed to be used primarily for
dry measurement. However, the significance of the surface conditions on the COF in the
current study indicates that this device is capable of differentiating the slip resistances
among the dry, wet, and WD solution covered surfaces.
Different slip resistance criteria considering pedestrian safety have been used in dif-
ferent countries. Some of the slip resistance criteria pertain to a certain type of friction
measurement methodology or device. For example, the Australian and New Zealand
Standard [47] adopted a dynamic COF of 0.4 based on a pendulum tester. The Health and
Safety Executive of the UK [48] recommended values of slip potential, instead of slip re-
sistance, based on the pendulum test value (PTV). The slip potential is low for a PTV of
36 or higher. Static COF has been adopted to assess the slip resistance more often in the
USA than in many other countries. A static COF of 0.5 was adopted as a safety criterion
for pedestrian walkways by both the American National Standards Institute (ANSI) [49]
and the U.S. Occupational Safety and Health Administration (OSHA) [50]. The Americans
with Disabilities Act (ADA) requires the static COF being 0.6 and 0.8 or above for level
surfaces and ramps, respectively [51].
Stone floors are widely used in public spaces. Unless they have been ground and
polishing processed, stone floors normally have a rough surface and are believed to have
proper slip resistance for walking. The COF of these floors was significantly (p < 0.0001)
higher than that of the ceramic floors. Such results were not surprising and were con-
sistent with the findings in the literature [52]. All the floor samples we tested under the
dry condition met the requirement of ANSI [49]. Even on wet surfaces, all the stone floors
and four of the ceramic floors had mean COF values higher than 0.5. On the WD solution
contaminated conditions, all the ceramic floors except C3 had mean COF values lower
than 0.5. This implies that most (five of six) of the ceramic floors we tested are risky under
the WD solution contaminated condition.
In tribology, the transmission of friction, as a function of normal load, along a sliding
surface depends, at least partially, on the topography of the surface [49,53,54]. The Ra val-
ues of the floor samples were adopted in this study to represent the surface profiles of
these samples because this parameter is the one that has been used most commonly in slip
and fall research [26,37,38]. The estimates of the regression coefficients and corresponding
statistics in Table 3 demonstrate the significance of Ra on the COF under the three surface
conditions tested. The polynomial regression models of the COF indicate that Ra affected
COF in a nonlinear fashion. There are discrepancies between our study and that of Kim et
al. [26] in developing the regression models. The first one is that our COFs were static
while the COFs in theirs were dynamic. Secondly, we tested only the Neolite footwear
sample while they tested one PVC and two Nitrile Rubber soles from three commercially
available shoes. Finally, our models considered the dry, wet, and WD solution covered
conditions while the cubic function in theirs considered only their soapsuds covered con-
dition. Even with these discrepancies, the curvilinear relationship between the COF and
Ra in our models still supports the three-zone concept of Kim et al. [26].
In Figure 3, all three curves reach their peaks at an Ra of approximately 54–55 μm for
the three surface conditions. These peaks imply that a further increase of the surface
roughness (Ra) provided no extra help in improving the slip resistance (COF). The begin-
ning of the plateau, or, alternatively, the upper bound of the steady-growth zone, should
Coatings 2021, 11, 1254 10 of 13
be somewhere before the Ra has reached those peak values. This implies that the upper
bound of the steady-growth zone proposed by Kim et al. [26] (Ra = 50 μm) was supported.
In the zone of steady growth, the COF increases almost linearly with Ra. A COF of
0.5 [48] of the safety criterion was adopted to determine the lower bound of the steady-
growth zone. Ra values of 19 and 27 μm were obtained for the wet and WD solution cov-
ered conditions, respectively. Table 4 summarizes the Ra values of the current study and
those in the literature. Our Ra values are slightly higher than that recommended by Kim
et al. [26] but are lower than that of Chen et al. [36].
Table 4. Comparison of the lower bound Ra values in different studies.
Study
Friction Measurement Device
Surface Covered by
Safety Criterion
Ra (μm)
Gronqvist et al. (1990)
dynamic step simulator
glycerol
DCOF = 0.2
7–9
glycerol
DCOF = 0.3
16–22
Kim et al. (2013)
pendulum-type
hydraulic dynamic friction tester
soapsuds
DCOF = 0.4
17
Chen et al. (2015)
Brungraber Mark II
water, soda
SCOF = 0.5
28
Liquids: 2 mPa·s < Viscosity < 38 mPa·s
SCOF = 0.5
40
Current study
HPS
Water
SCOF = 0.5
19
WD solution
SCOF = 0.5
27
The positive correlation between the Ra and the COF values in our study was con-
sistent with the findings in Chang et al. [9] but was only partially consistent with those in
Kim et al. [26]. The Pearson’s correlation coefficients between the Ra and the COF for the
dry, wet, and WD solution conditions in the current study were approximately the same
(0.62–0.66, p < 0.0001). This was inconsistent with the results in Kim et al. [26] where they
found Ra was significantly correlated with their dynamic COF on soapsuds covered sur-
faces, but the correlation was insignificant on their dry surfaces. A possible reason for this
inconsistency may be that the static COF in our experiment is less sensitive to the varia-
tions on the surface profile represented by Ra. The inconsistency could also be attributed
to the different footwear and floor samples in the two studies.
A limitation of this study was that only one footwear material (Neolite) was tested.
This material has been adopted in many friction measurement studies because of its ho-
mogeneity and reliability in physical characteristics [18,19,24,36]. Our results could be dif-
ferent if other footwear materials were used. Another limitation was that most of the floor
samples we tested were rougher than the common floors found indoors. Almost all the
floor samples (eleven of twelve) had an Ra higher than 9 μm. Our results may, therefore,
not be applicable to floors with an Ra less than this level.
5. Conclusions
A friction measurement study was performed on six stone and six ceramic floor sam-
ples under dry, wet, and WD solution covered conditions. The COF values of the stone
floors were significantly higher than those of the ceramic floors. All the stone floors under
all the surface conditions tested had mean COF values higher than 0.5, a safety criterion
recommended by the ANSI [49]. Two and five ceramic floors tested under the wet and
WD solution covered conditions, respectively, had mean COFs lower than 0.5. Three pol-
ynomial regression equations between the COF and Ra were developed. These equations
confirmed that the three-zone concept proposed by Kim et al. [26] is valid when static
COF values measured using an HPS were adopted. In addition, the concept is valid not
only on the WD solution (soapsuds) covered surface but also on dry and wet surfaces. The
upper bound Ra values in the steady-growth zone in the current study were equivalent to
those in the literature [26]. The lower bound Ra values under our wet and WD solution
covered conditions were slightly higher than that proposed in the literature. The findings
Coatings 2021, 11, 1254 11 of 13
of the current study can provide insightful implications for the prevention of floor slip-
periness and can thus help in reducing slip and fall incidences. Future research may be
considered to test commonly used footwear materials not tested in our study, such as
blown rubber and ethylene vinyl acetate, to validate the applicability of the three-zone
concept on those materials.
Author Contributions: Conceptualization, S.K. and K.-W.L.; methodology, K.-W.L.; validation,
L.P., K.-W.L.; formal analysis, S.K. and K.-W.L.; investigation, S.K.; resources, K.-W.L.; data cura-
tion, S.K.; writing—original draft preparation, S.K. and K.-W.L.; writing—review and editing, K.-
W.L. and L.P.; visualization, C.-C.C.; supervision, K.-W.L.; project administration, C.-C.C.; funding
acquisition, K.-W.L. and L.P. All authors have read and agreed to the published version of the man-
uscript.
Funding: This research was financially supported by research funding from the Ministry of Science
and Technology of Taiwan (MOST110-2221-E-216-004), General Project of Philosophy and Social
Science Research in Universities of Jiangsu China(2021SJA0060), and Humanity and Social Science
Funding of Fundamental Research Expenses of Central Government Higher Education of Nanjing
Agricultural University (SKYC2021024).
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: Not applicable.
Conflicts of Interest: The authors declare no conflict of interest.
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