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Tribology International

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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: ksenetak@cityu.edu.hk (K. Senetakis), sschitta2-c@my.cityu.edu.hk (C.S. Sandeep), ctodisco2-c@my.cityu.edu.hk (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.

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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.

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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.

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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.

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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.

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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.

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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