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Contents lists available at ScienceDirect
Tribology International
journal homepage: www.elsevier.com/locate/triboint
Dynamic inter-particle friction of crushed limestone
surfaces
K. Senetakis⁎, C.S. Sandeep, M.C. Todisco
Department of Architecture and Civil Engineering, City
University of Hong Kong, Kowloon, Hong Kong Special Administrative
Region, China
A R T I C L E I N F O
Keywords:Sliding frictionFriction measurementCoefficient of
frictionSurface roughness
A B S T R A C T
The frictional characteristics of granular materials are of
major interest in research and practice in geotechnicaland
petroleum engineering. In this study, micromechanical sliding
experiments were conducted at the contactsof crushed limestone
grains in a range of vertical forces from 0.5 to 5.0 N capturing
the frictional responseduring a steady state sliding. This was
obtained after the completion of small shearing paths of about
100–300 µm. The results indicated that the dynamic coefficient of
friction was slightly lower than that of reportedvalues in the
literature on quartz grain contacts. These differences might be,
partly, due to the relatively smoothsurfaces of the grains of the
study. However there were not observed notable differences on the
frictionalresponse between surfaces tested in a fairly dry state
and surfaces immersed in oil.
1. Introduction
There has been a growing need in recent years to understand
thebasic mechanisms and quantify the frictional properties of
geologicalmaterials. Particularly in the fields of geotechnical
engineering, en-gineering geology and petroleum engineering, there
was much lessprogress over the past decades on the development of
proper experi-mental apparatus, capable to study and quantify the
load – deflectionand frictional response at the contacts of
naturally occurred orartificially created grains. Recent advances
in soil mechanics experi-mentation at the grain scale allowed the
development of apparatuscapable to quantify contact mechanics
properties of geological materi-als, for example the studies by
Cole and Peters [1,2], Cole et al. [3],Senetakis et al. [4,5] and
Yang et al. [6]. Particularly, Senetakis et al.[4,5,7,8] quantified
both sliding stiffness and friction at the contacts ofreal soil
grains which follow the general configuration of a sphere-sphere
type of contact. This type of contact may be more applicable
forsoil mechanics applications in comparison to the sphere-block
config-uration [9] or the block-block configuration with the latter
being morecommon in rock mechanics research and applications. This
is impor-tant, particularly in granular materials research and
applications, sinceduring the sliding of grains there is a
continuous change of the surfacesin contact on the macro-scale
point of view. On the other hand, inlaboratory configurations of a
sphere-block or block-block types ofcontacts, one of the two
surfaces in contact remains practically thesame during the shearing
process.
The grain contact properties of stiffness and friction allow
exploringand better understanding the mechanisms that take place at
the
contacts of geological material as well as provide invaluable
data tobe utilized in discrete element modeling (DEM) of granular
assemblies[10–13]. There are numerous notable works in the
literature exploringthe micromechanics of granular materials
[14–19] and there is a needfor laboratory test data to be produced
quantifying grain contactproperties.
The previous experimental works by Senetakis et al. [4]
andSenetakis and Coop [8] focused on the frictional response and
inter-particle sliding stiffness, respectively, at the contacts of
quartz surfaces.Senetakis et al. [5] presented a limited set of
micromechanicalexperiments with quantification of the sliding
stiffness and the overalltangential force – deflection response of
crushed limestone grains.These recent works highlighted that the
inter-particle coefficient offriction may be less in magnitude than
what would be previouslythought or, for example, what values are
commonly implemented inDEM analyses [15]. This is an important
outcome since, as DEMstudies have demonstrated [14,20], the
variation of the inter-particlecoefficient of friction plays a
major role in the mechanical behavior ofgranular materials
particularly when its overall magnitude is low,typically below 0.5.
This means that the sensitivity of soils to thecoefficient of
friction becomes more pronounced when the friction issmall.
However, it is needed to be noticed that the
inter-particlecoefficient of friction may be strongly dependent on
the grain typeunder consideration, since different studies have
shown discrepancieswith respect to the inter-particle coefficient
of friction at a steady statesliding. For example, higher values of
inter-particle friction, incomparison to the reported data in [4,5]
were measured by Nardelliand Coop [21] for a carbonate sand, but it
is possible that the high
http://dx.doi.org/10.1016/j.triboint.2017.02.036Received 1
January 2017; Received in revised form 20 February 2017; Accepted
23 February 2017
⁎ Corresponding author.E-mail addresses: [email protected]
(K. Senetakis), [email protected] (C.S. Sandeep),
[email protected] (M.C. Todisco).
Tribology International 111 (2017) 1–8
Available online 24 February 20170301-679X/ © 2017 Published by
Elsevier Ltd.
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roughness of the grains tested by Nardelli and Coop [21] might
havecontributed to these observations.
On the other hand, Yang et al. [6] reported a notable
surfacedamage of the quartz grains they tested through SEM imaging,
but itwas noticed in their study that this damage, which was
attributed toplowing forces, was more evident for grains which had
been covered ontheir surfaces with water. Because of this, Yang et
al. [6] observeddifferent peak inter-particle friction values
between grain surfacestested in a dry state or immersed in water.
However, in their previousstudies, Senetakis et al. [4,5,7,8] did
not notice any notable effect of thesaturation state on the
mobilized inter-particle friction of quartz typegrains.
This paper reports on the dynamic inter-particle coefficient
offriction (μdyn) of crushed limestone surfaces through a
comprehensivedatabase of experiments developed by the authors. The
study com-prises part of an extensive laboratory study at the City
University ofHong Kong exploring the grain scale properties of
geological materialswith major interest to landslide problems and
other applications, forexample modeling the grain contact behavior
of granular materials. Inthis work, the crushed limestone grains
were used as a referencecrushable material in order to obtain some
basic understanding of theirfrictional response with respect to the
more thoroughly examinedquartz type grains. The frictional response
of crushed limestonesurfaces was explored, primarily, by conducting
micromechanicalsliding tests on grains in a fairly dry state, but
additional tests wereconducted on grains immersed in oil to explore
possible differences andany notable effect of the presence of a
lubricant on the frictionalresponse of the limestone surfaces.
Additionally, the paper discusses onthe inter-particle tangential
stiffness and for a limited number ofgrains, their surface
roughness was quantified before and after theconduction of
micromechanical sliding tests using the white lightinterferometry
technique. This analysis was carried out to obtain somefurther
insights into the micromechanics of geological materials at
thenano-scale, exploring possible changes of the surface
characteristics ofthe grains due to the coupled effect of the
application of the normalload and shearing to the grain
surfaces.
2. Equipment, materials and methods
2.1. Equipment used
The micromechanical sliding apparatus used in the study
wasdesigned and constructed by Senetakis and Coop [7] at the
CityUniversity of Hong Kong and later modified as described by
Nardelliet al. [21,22]. The apparatus has been designed in a way
that it allowsthe study of the frictional characteristics, the
tangential load –deflection and normal load – deflection
relationships at the contactsof a pair of grains of sand size,
typically between 0.5 and 5 mm.
An image of the apparatus is given in Fig. 1. The apparatus
usesthree linear micro-stepping motors which allow the conduction
ofsliding tests of a force or displacement controlled type, while
the grainsare confined in the vertical direction applying a load
which can beunder a target applied force (i.e. constant vertical
load) or targetdisplacement (i.e. the vertical force changes during
sliding to maintaina constant positioning of the upper grain). A
typical plot of verticalforce (Fv) – sliding displacement (s) on a
pair of grains where the Fv ismaintained in a force-controlled
manner is given in Fig. 2. Note thevery stable vertical force over
the total shearing path. In general, thisstable condition could be
achieved for tests with a vertical force greaterthan about 0.2 N,
but for applications of lower in magnitude verticalforces, the
system would have a less stable Fv value throughout theshearing
path.
In the out-of-plane direction, a third stepping motor is used
whichallows the control or monitoring of the response of the grains
duringsliding including the out of plane forces and displacements.
Load cellsand displacement transducers of high resolution are used
to monitor
and control the experiments [7]. During the initial design and
first setsof experiments with this apparatus [4,5,7,8], it worked
as a two-dimensional system with a specially designed mechanical
system in theout of plane direction to constrain any deflections of
the systemlaterally during the sliding tests, allowing the
conduction of slidingtests following a stable shearing path. For
this initial design of theapparatus, linear variable differential
transformers (LVDTs) were usedas displacement sensors which were of
the free armature type [7].These LVDTs had a precision of 0.1 µm.
Later, the system was modified[21,22] allowing a stepping motor to
be placed in the out of planedirection which can work as a spring
controlling the lateral forces anddeflections or alternatively,
providing the adequate rigidity for thecompliance of the shearing
tests. Based on this modification, theapparatus uses non-contact
displacement sensors (eddy-current sen-sors) of precision equal to
0.01 µm. The load cells of the apparatus areof 100 N capacity and
they have a precision of 0.02 N, which providesadequate resolution
of the forces for the study of the micromechanicalbehavior of sand
grains at this scale.
Calibrations of the apparatus and the examination of its
repeat-ability in testing reference grains have been presented and
discussed in[7]. The apparatus utilizes bearing balls to allow the
conduction ofsliding tests with minimum friction as well as linear
bearings whichhave been presented in details by Senetakis and Coop
[7]. A pair ofgrains can be tested particularly with the lower
grain sliding over the
Fig. 1. Micromechanical sliding apparatus and close-up view
image with the grainsinside a small cell: (1) linear micro-stepping
motors (2) load cells (3) digital micro-camera (4) grains during
the set-up of test (5) frame of apparatus.
Fig. 2. Vertical force against sliding displacement during a
typical inter-particle slidingtest where Fv is maintained in a
force-controlled manner.
K. Senetakis et al. Tribology International 111 (2017) 1–8
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surface of the upper grain with the latter being constrained to
movehorizontally in the direction of shearing (sliding). A close-up
viewimage of the apparatus is also included in Fig. 1. It is
noticed that in thefigure a small cell is used which allows the
grains to be immersed in aliquid, typically water.
A software has been developed for the apparatus [7] which
allowsthe communication of the different electronic parts and the
conductionof experiments in a wide range of sliding velocities.
This softwareallows the performance of very slow sliding tests,
typically betweenabout 0.01–0.6 mm/h. Because of these slow
velocities, a large numberof data are recorded during the
experiments, which allows a precisemeasurement of the mobilized
friction and tangential stiffness at verysmall shearing paths,
which could not be the case, for example, for thesystem developed
by Yang et al. [6] which worked at much greatersliding velocities.
The greater velocities would allow the inter-particlefriction to be
measured at much greater displacements but withoutinformation of
the grain-contact stiffness.
2.2. Materials used
Crushed limestone (CLIM) grains with size between 1.18 and5.00
mm were used in the study. Previously, Senetakis et al.
[5]presented preliminary results on this material investigating the
tan-gential load – deflection relationship and tangential stiffness
throughexperiments of a force-controlled type. This general type of
material ofbiogenic origin is of major interest in the oil and gas
industry sincemany oil platforms, subsea infrastructure and other
facilities may befound on fresh deposits of biogenic origin. In
this study, an attempt wasmade to investigate the inter-particle
coefficient of friction of pairs ofgrains under different
saturation conditions, particularly investigatingtheir response in
a fairly dry state and immersed grains in oil applyingvariable
normal forces. Immersion of the grains in oil might give rise toa
lubrication of the surfaces in contact, which thereafter could have
aneffect on the frictional characteristics of the biogenic
sand.Characterization of the grains was based on white light
interferometryand the quantification of the amplitude of the
surface roughness bymeans of the mean root square roughness (Sq)
flattening the surfacesduring the imaging process [4,5,23]. The
CLIM grains previously testedby Senetakis et al. [5] were
relatively rough with an average Sq value ofabout 1 µm. A typical
image taken during the white light interferometrytesting is given
in Fig. 3 (after Senetakis et al. [5]). This imagecorresponded to a
grain prior to the conduction of inter-particle sliding
test. For the purpose of this study, a total set of ten grains
wasexamined in the interferometer, prior to the inter-particle
sliding tests,and the resultant Sq values are summarized in Fig. 3
by means ofhistograms. Note the relatively scattered values of the
measuredsurface roughness amplitude which was due the relatively
inconsistentand of high variability surface characteristics and
morphology of theCLIM grains which is opposite to the highly
consistent surfacecharacteristics of Leighton Buzzard sand quartz
grains tested in[4,5,7,8]. For this set of CLIM grains, the Sq
values ranged from about0.138–0.543 µm, with an average value and a
standard deviation of Sq,over the set of ten grains, to be equal to
0.307 and 0.142 µm,respectively. In general, the values of Sq for
the CLIM grains may beconsidered relatively lower than the
corresponding values of quartzgrains [5] or carbonate sand grains
[21] from previous studies. It isnoticed that due to the low
reflectivity of the material of the CLIMgrains, it was technically
difficult to obtain systematically interferom-eter images for all
the grains included in the study. This limited theinvestigation of
their surface roughness to a small number of grains aswell as to a
representative set of tests investigating surface damage ofthe
grains due to the shearing tests, as will be discussed throughout
thispaper.
2.3. Testing program and sample details
In the study, a set of thirty tests was conducted on CLIM
grains,each test on a different pair of grains. The testing program
and detailsof the experiments are given in Table 1. Three tests
were conductedunder a sliding of a force-controlled type and
twenty-seven tests wereconducted with a sliding of a
displacement-controlled type. In Table 1,the loading rate of the
different types of tests is given in terms of N/hand mm/h for the
force-controlled and the displacement-controlledtests,
respectively. The applied vertical force (Fv) during a given
slidingtest was kept constant and the values of Fv ranged from 0.5
to 5 Nthroughout the total set of tests. All the tests were
conducted followinga monotonic sliding path, typically within a
range of 100–300 µm. Thisshearing path was efficient to observe a
steady-state sliding during theexperiments. Note that the
application of vertical forces in this range ofmagnitudes is
aligned with DEM studies which have reported that fortypical
geotechnical engineering applications and pressures
underconsideration, the normal forces developed at the contacts of
real soilgrains are of very small magnitude, in general below 5 N
[24]. Thus, theintention in this study was to apply forces in that
range that representsbetter the potential developed inter-particle
forces of geologicalmaterials for soil mechanics applications. It
is also noted that theparticular apparatus developed by Senetakis
and Coop [7] is in realitymore capable to work in the range of
relatively small forces, betweenabout 0.2–10 N and to test
relatively small size grains, which is moreapplicable for soil
mechanics purposes.
Additionally, for two pairs of grains with code names of the
tests asCLIM24 and CLIM30, repeating shearing tests were conducted
ata given applied vertical load. One of these pairs of grains was
tested atFv =2 N and the second one was tested at Fv =5 N. For
these tests, afterthe completion of a given shearing test, the
grains were placed at theirinitial position, and the shearing test
was repeated three more timesfollowing the same shearing path.
These tests were conducted toexplore any possible measurable change
of the frictional response atthe contacts of the grains due to the
repetition of the shearing test.
3. Results and discussion
3.1. Typical tangential force – displacement and tangential
stiffness –displacement plots
Typical plots of tangential force – sliding displacement of two
pairsof CLIM grains tested at 1 and 2 N of vertical force,
respectively, aregiven in Fig. 4. Within a path in a range of
80–120 µm, a steady state
Fig. 3. Mean root square roughness (Sq) measured on
representative grains from whitelight interferometry and typical
flattened surface of CLIM grain.
K. Senetakis et al. Tribology International 111 (2017) 1–8
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sliding was observed and beyond that sliding level, the
tangential forceremained constant under an increasing sliding
displacement. In thestudy, the dynamic coefficient of friction
(μdyn) was defined within thissteady-state sliding. Note that μdyn
corresponds to the ratio FT/FN,where FT is the tangential force and
FN is the normal force at thecontact of the grains. In reality, the
tangential and normal axes to thesliding direction continuously
rotate during the tests with respect to thehorizontal and vertical
axes, due to the geometry of the grains(approximated by spheres).
Senetakis and Coop [7] have described indetails the process to
analyze the forces FT and FN based on themeasured, in a
straightforward way, horizontal force Fh and verticalforce Fv,
utilizing the recorded vertical and horizontal deflections. Inthe
present study, due to the apex-to-apex setting of the grains prior
tothe sliding tests as well as the relatively small sliding paths,
a reason-able approximation was that FT=Fh and FN=Fv. As described
by
Senetakis and Coop [7], this initial alignment as apex-to-apex
forsphere-sphere type of contacts was the key in the development of
thisapparatus. This was achieved by designing the apparatus with
very highstiffness which allowed revealing meaningful
micro-quantities at verysmall sliding paths.
Fig. 5 gives a plot of the mobilized coefficient of friction
against thesliding displacement for the pairs of grains described
in Fig. 4. The datashow that the mobilized friction, particularly
at early stages of theshearing, may reach values above about
0.4–0.6, but at the steady statesliding, the coefficient of
friction is of low magnitude, lower than 0.2 forthese sets of
grains. Note that for these two pairs of grains described inFigs. 4
and 5, there was a notable difference with respect tothe mobilized
inter-particle coefficient of friction prior to the steady-state
sliding is reached. Particularly, it is shown in Fig. 5 that the
test at
Table 1Inter-particle sliding tests on crushed limestone
grains.
Code of test FV (N) State Loading rate forforce-controlled
tests (N/h)
Loading rate fordisplacement-controlled
tests (mm/h)
µdyn
CLIM-01 2 Dry 10 – 0.175CLIM-02 2 Dry 10 – 0.120CLIM-03 3 Dry 10
– 0.123CLIM-04 1.5 Dry – 0.6 0.140CLIM-05 2 Dry – 1.4 0.124CLIM-06
2 Dry – 0.9 0.122CLIM-07 1 Dry – 0.6 0.080CLIM-08 0.5 Dry – 0.6
0.090CLIM-09 0.5 Dry – 0.6 0.152CLIM-10 1.5 Dry – 0.6 0.070CLIM-11
1.5 Dry – 0.6 0.076CLIM-12 3 Dry – 0.6 0.113CLIM-13 3 Dry – 0.6
0.089CLIM-14 3 Dry – 0.9 0.107CLIM-15 3 Dry – 0.9 0.092CLIM-16 1
Dry – 0.9 0.050CLIM-17 1 Dry – 0.9 0.041CLIM-18 5 Dry – 0.9
0.062CLIM-19 5 Dry – 0.9 0.084CLIM-20 0.6 Dry – 1.6 0.205CLIM-21
0.6 Dry – 1.2 0.080CLIM-22 1 Dry – 0.06 0.145CLIM-23 2 Dry – 0.06
0.176CLIM-24 2 Dry – 0.06 0.160CLIM-25 1 Immersed – 0.9
0.070CLIM-26 1 Immersed – 0.9 0.130CLIM-27 3 Immersed – 0.9
0.205CLIM-28 3 Immersed – 0.9 0.160CLIM-29 2 Dry – 0.06
0.210CLIM-30 5 Dry – 0.06 0.250
Fig. 4. Typical plots of tangential force – sliding displacement
at different vertical forces.Fig. 5. Typical plots of mobilized
inter-particle friction – sliding displacement atdifferent vertical
forces showing some effect of the vertical force on the mobilized
friction.
K. Senetakis et al. Tribology International 111 (2017) 1–8
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Fv =1 N, gave much greater values of the mobilized friction
incomparison to the test at Fv =2 N with respect to the range of
slidingdisplacements prior to the steady state is reached. It is
believed thatthese discrepancies might be due to the morphology of
the grains. Atearly stages of shearing, there is a continuous
increase of the tangentialforce necessary to trigger sliding at the
interface of the grains. Duringthe shearing tests, a steady state
sliding is typically reached, but priorto this, the shape of the
tangential force – displacement curve as well asthe absolute
magnitude of the mobilized inter-particle friction might beaffected
by the morphology of the grains. In Fig. 6, additional test dataon
different pairs of CLIM grains tested at a vertical force of 2 and
5 Nare presented in terms of inter-particle coefficient of friction
againstsliding displacement (s). For these two tests, the shape of
the tangentialforce – displacement curves was found different than
the testspresented in Figs. 4 and 5, with a peak tangential force
that took placeat a sliding displacement of about 15 µm, followed
by a slight drop ofFT reaching gradually the steady state. Within
the shearing paths of thetests shown in Fig. 6, there was not
observed any notable effect of theapplied vertical load on the
mobilized inter-particle coefficient offriction, apart from
slightly different magnitudes of μdyn (coefficientof inter-particle
friction at the steady state sliding). It is possible thatthe
different morphologies of the grains resulted in these
discrepancieswith respect to the shape of the tangential force –
displacement curves,but within the scatter of the data, there was
not observed any notableeffect of Fv on the dynamic coefficient of
friction.
Differentiating the tangential force with respect to the
slidingdisplacement, allows the quantification of the tangential
stiffness (KT)at the contacts of the grains as well as its
degradation against thesliding displacement (s). Plots of (KT) –
(s) for the pairs of grainsdescribed in Figs. 4 and 5, are given in
Fig. 7 along with a typical imagetaken from a digital micro-camera
during the sliding tests. As also
reported by Senetakis et al. [5], the inter-particle tangential
stiffnessdegrades rapidly which mirrors the highly non-linear
response at thecontacts of geological materials. This observation
is aligned with pastand recent research works reported in the
literature [3,21]. Within asliding path of less than 10 µm, KT
reaches zero, which was observed inmost experiments of the study.
Note that the tangential stiffness forthis limited set of tests had
values close to 100–120 N/mm forhorizontal displacements between
2×10−1 and 5×10−1 microns for thisrange of normal forces between 1
and 2 N. It is also noted that for thetest at FN=1 N, the
tangential stiffness degraded faster in comparisonto the test at
FN=2 N. For quartz type surfaces, Senetakis and Coop [8]quantified
the tangential stiffness over a range of normal forces fromabout
0.5–5 N and reported that a straight line envelope couldapproximate
the tangential stiffness – normal force relationship. Thatenvelope
would predict values for KT equal to 116 and 232 N/mm at FNequal to
1 and 2 N, respectively. As also reported by Senetakis et al.
[5],the inter-particle tangential stiffness might be controlled,
majorly, bythe hardness of the surfaces in contact.
One of the major advantages of the micromechanical
slidingapparatus developed at the City University of Hong
Kong[4,5,7,8,21,22] is that, due to its high stiffness and high
resolution offorces and displacements, it allows the quantification
of both frictionand stiffness at the contacts of geological
materials. Other apparatus,for example the newly developed system
by Yang et al. [6], could allowonly friction measurements at the
contacts of sand grains. This isperhaps, due to the lower
resolution of forces and displacements duringthe early stages of
sliding as well as the relatively high speed of thesliding tests as
also mentioned previously. In addition, this capability ismajorly
because of the initial configuration of the grains in an
apex-to-apex manner. This allows a straightforward measurement of
the forcesand displacements in the tangential and normal to the
sliding direc-tions, thus the measurement of stiffness is feasible,
without theoccurrence of stick-slip [25].
3.2. Repeating shearing tests for a given pair of grains
andquantification of grain surface damage
The repeating shearing tests for the tests with codes CLIM-24
andCLIM-30, are given in Figs. 8 and 9, respectively, in terms of
tangentialforce against sliding displacement. Note that there was
observed aslight decrease of the dynamic inter-particle friction
from about 0.165to 0.135 for the test with code CLIM24 test and
from about 0.250 to0.200 for the test with code CLIM30, throughout
this process ofrepeating shearing tests, considering that μdyn
corresponded to theratio FT/FN and that FT corresponded to the
steady state sliding. Thus,the observed reduction of μdyn from the
first to the fourth shearing wasof the order of about 20%.
It is noticed that for these two tests, the grains were not
examined
Fig. 6. Typical plots of mobilized inter-particle friction –
sliding displacement atdifferent vertical forces without any
notable effect of the vertical force on the mobilizedfriction.
Fig. 7. Typical plots of tangential stiffness – sliding
displacement at different verticalforces and close-up image of CLIM
grains in contact during an experiment.
Fig. 8. Repeating shearing tests at the contact of a given pair
of CLIM grains at a verticalforce of 2 N.
K. Senetakis et al. Tribology International 111 (2017) 1–8
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in the interferometer after the shearing tests to quantify
possibledamage of their surface, but the authors examined the
possible changesof the surface characteristics of the CLIM grains
for another pair ofgrains, similar to the procedure described by
Senetakis et al. [5].Particularly, specially designed markers were
placed on the brassmounts which were used as a guide to provide
reference positioningof the grains, as shown in Figs. 10 and 11.
This allowed thequantification of the position of the apex of the
grains with respect toa Cartesian system to be used during the
interferometry analysis. Asreference position, a cross-hair point
of one marker was used, shown inFig. 12, which point could be
identified easily during the interferometeranalysis. Based on the
known relative position of the apex of the grainswith respect to
the reference point, the system grain – brass mountcould be placed
on the interferometer base in a way that any othermarked point
could be thereafter identified. This made it feasible toidentify
the surface of the grains which are in contact and capture
theshearing path prior to and after the conduction of the sliding
tests.Through white light interferometry analysis, the surface
roughness ofthe grains was quantified in this way before and after
the conduction ofsliding tests and these results are given in Fig.
13 in terms of cross-sections of the grains throughout the shearing
path as also described bySenetakis et al. [5]. Note that in Fig.
13, the horizontal axis has size of141.5 µm. Quantifying the Sq
value from these two cross sections, itwas revealed that the
surface roughness of the grains was reducedalmost 25% after the
conduction of the shearing test. This observationis aligned with
the study by Senetakis et al. [5], where a reduction of Sqbetween
about 13% and 62% was found for quartz sand grains. It isalso
interesting to notice that there was observed a removal of
sharpasperities of the grains, which might be due to the coupled
effect of theapplication of the vertical load and the shearing of
the grains. Note thatthis examination as well as the interferometry
analyses by Senetakiset al. [5] were conducted on grain surfaces
after the performance ofsliding tests on pairs of grains tested in
a fairly dry state.
3.3. Dynamic inter-particle friction test results
A summary of all the test data for the CLIM grains in terms of
μdynagainst FN is given in Fig. 14. In the same figure, the mean
value of thedynamic coefficient of friction as well as a range of
one standarddeviation are depicted along with the mean value of
correspondingexperiments on quartz grains (Leighton Buzzard sand)
reported in [4].For the CLIM, the mean μdyn value was found equal
to 0.109, which islower in magnitude than the corresponding mean
value for quartzgrains (=0.166). These differences might be
attributed, partly, to thelower amplitude of surface roughness of
the CLIM grains in compar-ison to the quartz grains tested by
Senetakis et al. [4]. The aforemen-tioned results corresponded to
grains tested in a fairly dry condition.
Fig. 9. Repeating shearing tests at the contact of a given pair
of CLIM grains at a verticalforce of 5 N.
Fig. 10. Sketch of the system grain – brass mount with
markers.
Fig. 11. Plan of the system grain – brass mount with markers
with Cartesian system onthe base of the interferometer.
Fig. 12. Identification of the coordinates of the marker in
order to capture the shearingpath of a grain after the conduction
of sliding test.
K. Senetakis et al. Tribology International 111 (2017) 1–8
6
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Fig. 14 depicts also the μdyn values from experiments on
grainsimmersed in oil. Within the scatter of the data, there was
not observedany particular effect of the immersion of the grains in
oil with respect totheir frictional response in terms of dynamic
inter-particle coefficientof friction as well as shape of the
tangential force – sliding displace-ment. In their study, Yang et
al. [6] reported a more pronouncedplowing effect when the quartz
grains they tested had water at theirinterface which resulted in
greater values of friction in comparison tograins tested in a dry
state in terms of peak values. These plowingeffects might be not
the case when oil is used as the lubricant becausethe same
frictional response between grains tested in a dry state orgrains
tested as immersed in oil, was found throughout the experi-ments of
this study. It is noticed however that the authors did notexamine
for these tests, where the grains were immersed in oil,
theirsurface characteristics after the conduction of the sliding
tests. It isbelieved that since the immersion in oil did not result
in anymeasurable effect on the force – displacement and friction
responsesof the tests, that the immersion in oil might not
differentiate notablythe friction mechanism between tests in a dry
state or tests with grainsimmersed in a liquid for the CLIM grains.
This may be in contrast tothe observed trends by Yang et al. [6].
However, it is noticed that first,Yang et al. [6] examined the
effect of water as the lubricant and that intheir study, they
applied high speeds of shearing, whereas in thepresent study the
whole set of experiments was conducted at relativelylow sliding
velocities. It could be possible that the influence of a
lubricant might have a relation to the speed of a sliding test,
but thiswould need further systematic investigation to be figured
out.
4. Conclusions
Experimental micromechanical test results were reported
withrespect to the frictional characteristics of crushed limestone
surfacesconducting sliding tests on small size grains at low
confining forces.The inter-particle coefficient of friction was
quantified during a steadystate sliding and the results were
compared with reported data onquartz sand grains. Differences in
hardness as well as grain morphologyby means of surface roughness
amplitude may have played animportant role to the differences
between the crushed limestone grainsof the study and literature
data on quartz (LBS) grains. The presentwork mostly focused on
reporting data with respect to the frictionalcharacteristics at the
contacts of geological materials exploring someranges of values
rather than de-coupling possible different factors thatcontrol the
inter-particle sliding behavior. Overall, the results showedthat
the inter-particle coefficient of friction at a steady state was
lowerin comparison to reported data in the literature for quartz
type grains.It is possible that the morphological characteristics
of the surfaces ofthe crushed limestone grains might affected the
shape of the tangentialforce – displacement curve. Interferometry
analysis indicated a notabledamage of the surfaces of the grains
which was attributed to thecoupled effect of the application of the
normal load and shearing.However, notable differences on the
frictional response between grainstested in a dry state and grains
immersed in oil were not observed.Perhaps, the slow velocities of
the tests could have affected these trendsand it is believed that
further systematic work is necessary in thisdirection since the
effect of a lubricant could be related to the slidingvelocity in
conducting a shearing test.
Acknowledgements
The study was supported by the Theme-based research
projectScheme (TRS) “Understanding Debris Flow Mechanisms
andMitigating Risks for a Sustainable Hong Kong” (Project No.
8779012,RGC). Dr Sergio LOURENÇO from the University of Hong Kong
isacknowledged for kindly permitting use of the interferometer.
Theanonymous reviewers are acknowledged for their constructive
com-ments that helped us to improve the quality of the
manuscript.
Fig. 13. Cross-sections of grain along the shearing path
quantifying surface damage and alteration of the surface roughness
due to the coupled effect of the application of normal loadand
shearing.
Fig. 14. Summary of results of the study with mean value +/- one
standard deviationequal to 0.109 ± 0.042 and corresponding mean
value for quartz grains by Senetakis et al.(2013a) equal to
0.166.
K. Senetakis et al. Tribology International 111 (2017) 1–8
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Dynamic inter-particle friction of crushed limestone
surfacesIntroductionEquipment, materials and methodsEquipment
usedMaterials usedTesting program and sample details
Results and discussionTypical tangential force – displacement
and tangential stiffness – displacement plotsRepeating shearing
tests for a given pair of grains and quantification of grain
surface damageDynamic inter-particle friction test results
ConclusionsAcknowledgementsReferences