ARMA-99-0399_Rock Joints Behavior Under Cyclic Direct Shear Tests

8/12/2019 ARMA-99-0399_Rock Joints Behavior Under Cyclic Direct Shear Tests

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RockMechanicsor ndust Amadei,Kranz,Scott& Smeallie eds) 1999BalRema, otterdam,SBN 90 5809 052 3Rock ointsbehavior nder yclicdirectshear estsE Homand-Etienne,Lefevre,T.Belem& M. SouleyLaboratoire nvironnernentdorncaniquet Ouvrages, coleNationaleSupdrieure e Gologie,Vandoeuvre-lds-Nancy,rance

ABSTRACT: Cyclic directshear estswerecarriedout on undulated rtificial oints of mortar,accordingoconstantnormal stress CNS) and constantnormal stiffness CNK) loading conditions.The morpho-mechanical ehaviorwas analyzed n order to betterunderstandhe cyclic behaviorof these oints. Oneparameter as defined o quantify he degradationf the shearedoints. Two modelswere thenproposedopredict he degradationf the anisotropicoints accordingo the oading onditionsCNS or CNK) and heshearingmode monotonousr cyclic).The degradation odel or the CNK conditionwas generalizedorboth oading onditions nd hismodel s in agreement ith the undulatedoints est esults.1 INTRODUCTIONThe mechanicalpropertiesof rock massesarestrongly dependent on the presence ofdiscontinuitiesr oints.Thesediscontinuitiesffectthe stabilityof rock engineering tructurestunnels,mines, underground storages, open pits). Thereponse f a roughoint to shearoading ependsnits surfacepropertiesas well as the boundaryconditions hat are applied by surroundingockmass. These boundaryconditionscan exist in avarietyof formsandbetweenconstant ormalstress(CNS), in the caseof slopestabilityproblems earthe surface, to variable or constant normal stiffness(CNK) in the vicinityof undergroundxcavations.Most of studieson the anisotropicoints shearbehaviour howed hat degradation eemed o becontrolledmore by surfaceundulationshanby thedistribution f the asperities n this surface. heseobservationsanbe nterpreted hilebeingbased nthe conceptof primary and secondary sperities(Jinget al., 1993; Kant et al., 1996).The secondaryasperitiesare defined by the distributionof thesurface points, while the primary asperitiesaredefined y thesurface eometryundulations).Theseprimaryasperities etermine ndcontrol helocationof the possiblecontactareas (thus ofdegradation)f the oint wallsduringshearing. hedegradationf the oint wallscanbe approachednterm of direct quantification f wear, evolutionof

roughnessor evolution of the dilatancy angle(Plesha 1987; Hutson and Dowding 1990;Benjellounet al., 1990; Jing et al., 1993). To ourknowledge, except the ratio of the degradedasperities rea,definedby LadanyiandArchambault(1969), there does not exist in the literature aparameter of direct quantification of wear ordegradationf the oint wallsduringshearing.In thispaper,we study he nfluence f thecyclesof directshearon the degradationf an undulatedartificial oint of mortar.These estswerecarriedoutaccording o CNS and CNK conditionsundervarious levels of normal stress and normal stiffness.

The wear of the sheared oints is directlyquantified y thedegree f degradation,w, definedon the basis of the estimation of the actual surfaceareas before and after shear tests (Belem et al.1997). Basedon our experimentalesults, modelofdegradation prediction during shearing wasproposed. he model parameters re related o thejoint roughnessangularity ndanisotropy).2 EXPERIMENTAL PROCEDURES2.1 MaterialThe selectedoint surfacegeometry s an artificialregularly ndulated urfaceprimary sperities) ithan amplitudef 2 mm anda period f 25 min.The

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investigatedamples remade rom mouldsof 145 x150 mm dimensiony casting ith mortar. hemortar s a mixtureof very fine sand,cement,silicafume and water.The mortar s carefullyvibrated norder o get bubblefree amples nd after he settingtheyarecuredat 20C n waterduring28 days.2.2 Shear testsTwo series of cyclic direct shear tests wereconducted on several mortar undulated jointsaccording o the constant ormal stress CNS) andconstant normal stiffness (CNK) boundaryconditions. These tests have been carried out with anew computer-controlled D-shear apparatusprovidingconstantnormal load (CNL), constantnormal stress CNS) and constantnormal stiffness(CNK) shear ests.This shearapparatusun usingelectric micromotors. The shear motion is due to twosymmetrical nd oppositemovements f the twoshearboxes.The shearandnormal oadingcapacityis 120 kN.

Several direct shear tests were carried out under(i) constant ormalstressesangedbetween0.5 and6 MPa for CNS condition, and (ii) constantnormalstiffnesses anged between 1.0 and 3.0 MPa/mmwith different initial normal stresses for CNKcondition. Each test consistedof ten cycles offorward and reverse shear directions. All shear testswereperformed ntil a 10 mm sheardisplacementsachieved.2.3 Topography ata acquisitionIn order o quantify he degradation f the shearedjoints, topographicmeasurements ere carded outbefore and after the shear tests with a laserprofilometer Sabbadini et al. 1995; Hornand-Etienne et al. 1995; Belem et al. 1997). Thisequipmentallows three-dimensional easurementsof the oint wall surfaces. he measurementystemuses he aser riangulation rinciple etween laserplaneand a CCD camera hiftedwith respect o thelaserplane (the laser plane unit and video camerabeing indeformable). The topographic profilecorrespondso the crossing f the laserbeamwiththe sample urface.The laserprofilometers madeup mainly of anopticalsensor quippedwith a CCD cameraof a 50Ixm resolutionand with a He-Ne laser of 670 nmwavelength.The design eaturesof the laser beamare: 40 mm length; 50 Ixm thickness; 0 Ixm ofvertical resolution (z axis); 73 Ixm of horizontalresolution x or y axis according o the sensor

position); grn of standard eviationof the errorofthe white noise due to the mechanical vibration.Beforecomputinghe oint surfacedegradation,herow data must be processedo obtain regularlyspaced nddetrended ata.3 RESULTS OF CNS SHEAR TESTS3.1 CyclicshearbehaviorFigure 1 showscurvesof CNS cyclic shear estsperformed on the undulated oints under normalstressesof 1 and 4 MPa (Figure la and lb,respectively). his figure ncludes he shearstrength(a ) and normal displacementCU,) vs sheardisplacementW). For the two normalstressevels,the shearstrength-shearisplacementurvesshowan increase f a as a function f cycleswhile hedilatancyU,) decreases.This behavior s exactly the oppositeof thatobserved by Hutson and Dowding (1990) onundulated rtificialgraniteoints.The analysis f allthe carriedout tests eadsus to think that the figurela is representativef the response f the undulatedjoint for testscarriedout at an < 2 MPa while thefigure lb is representative f the undulatedointresponseor tests arried ut at n > 2 MPa. Beyond5 MPa, surfaces resent ignificant egradationsueto the failure of the mortar. The observation ofsheared surfaces indicates:

for an < 5 MPa, a main effectof morphology(undulations); for an > 5 MPa, a main effect of material(mortar).Because the material is not a natural rock, thedominating ffect of morphology n shearbehaviorhasbeenprioritized.n order o studymorepreciselythe evolution of the shear curves, each curve wassubdividednto 5 partsand resultswere discussedbasedon the average aluescalculated n eachpart.Thus, for eachcycle the average riction coefficientPm at/an)and he average ngleof dilatancym (o)are calculatedn each part b, c, d and e (Figure 2)and or the first parta of the shear urves.Figure 3 shows he variationof average rictionangle/.tinor eachnormalstressevel after hecycles1 (top) and7 Coottom)n the partsb, c, d ande.The analysisof all the curvesshows hat eevolutionof /.tin at cycle 1 (Figure 3, top) isrepresentativef thatobserved ntil thesixthcycle.

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U.(mm)2 T ,,[;-'TIm1.5

-10 -5 0 5 10

ot (Ml'a) 53

I ;5 lWxram),,-10 -5 0 5 10

Figure1. TypicalundulatedointsCNS shearestcurvesa) an = 1 MPa and b) an = 4 MPa.m 1.1 0.9

0.7)I I i ': ": 0.5

0.3 c d2

0.90.7

-2 2 4 6 8 10 0.3 partsFigure2. Locationof the studiedpartson the shearstresstop) anddilatancy bottom) urves.Indeed,Figure3 shows hat from the part b (justafter the peak) the average riction coefficientdecreasesraduallyn the partsc, d ande.In the sameway, the evolutionof /tin at cycle 7(Figure3, bottom) s representativef that observeduntil the tenth cycle. This figure especiallyhighlightsa perfectelastoplastic ehaviorof thejoint from cycle 7. To support hese assertionsconcerninghe behaviorof the undulatedoint, wealso analyzed he dilatancycurves n the samewaythat hoseof the tangential tress.

b c d e

'- on=0.5Pa n=lPaO n=2Pa-X - on=3 MPa o--4 MPa 1- - on=5 MPaFigure3. Average rictioncoefficient/a for eachpartaftercycle1 (top)andcycle7 (bottom).Figure 4 presents he evolutionof the averagedilatancyangle, ra, with respect o the cyclesofshear or the testcarriedout at an = 4 MPa and oreachpart.For the first cycles 1 to 6), figure4 showsthat the average ilatancy ngle m decreasesn thepartb while t increaseslightly n theparts , d ande.

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1412lO

8

1 2 3 4 5 6 7 8 9 10Figure 4. Variation n the averagedilatancyanglewith cycles er = 4 MPa).

1.21.00.8

0.60.4

[1m

--on=3 MPa on=2 MPacyclesI I I I I I : : :

2 3 4 5 6 7 8 9 10

Figure5. Variation n frictioncoefficient ycles orCNS shear est n part c.This observation an be explainedby the fact thatinitially, the slight ncreasen the average ilatancyangle m of the partsc, d and e is produced y thewear materialsdue to the surfacesdegradationncontact,which are distributed long the undulation.Moreover, his degradationmpliesa significantallin im in the part b which is explainedby thecumulated effect of the wear and the accumulationof the wearmaterials ue o the shear ycles.In the last cycles 7 to 10), the averagedilatancyangles m (o) are nearly dentical or all the studiedpartsim_b im_c-' m__d--ra_e)ndcorrespondo theresidual behavior.

The very close valuesof the averagedilatancyanglesof all the studiedparts mean that undulatedmorphologywas transformednto a surface lmostin saw teeth. Following these observationsweconsider hat figure 4 is representative f the testscarried utat ern 2 MPa because t ern 1 MPa weestimate that the undulations have undergone amoderate egradation.The part c (Figure 5) is representativef /haevolution n all the studied arts or the testsat ern2 MPa.

Indeed, n the part c, the average rictioncoefficientincreases lobally rom one cycle o another or allnormal stress evels except ern= 5 MPa where aslight eductionn/ha is observed way rom cycle5. The ncreasen/ha is associatedith the ncreasein contact areas. However, from cycle 7, /tmincreases ery slightly or doesnot vary any more.This also conesponds o the residual behaviorhighlighted y thecycles.3.2 Failure criterionFigure 6 shows hat the values of peak strength,*.a, for cycle7 are well fittedby the Molar-Coulombriterionitha friction ngle,P,eak,f 48degrees. ssuminghat the undulatedoints failurecriterion is a Molar-Coulomb riterion, figure 7illustrates he evolutionof the peak and residualfrictionangleswith respecto the cycles.From ycle to cycle thepeakriction ngleP,eakincreases ith the numberof cycles between 3 and48 as previously uggestedy the analysis f theshearand dilatancycurves.From the seventh ycle,

' I I I I Io 1 2 3 4 5

Figure6. Molar-Coulombailurecriterion or thecycle 7.

390

i

i

residual'peak ', Cteles.: : : :', : : , .2 3 4 5 6 7 8 9 10

Figure 7. Relationshipbetween Mohr-Coulombfrictionangleandcyclesof shear

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2.0 lkoni=3Pa1.0 []oni=2PaO oni=l MPa0.0 I

0 1 Kn (MPa/mm) 21.2 - slope1MP.80.60.4 []oni=2Pa.2 O oni=l MPa

0 I 0 5 O1es 10

Figure 10. (top) Valuesof slopes for CNK testsatcycle5; Coottom) lopevariation sshear ycles.aniCoottomanel).On this igure, he estat Yh= 3MPa/mm was not taken into account because of themortar failure. It can be noted on the Figure 10Coottomanel) hat from cycle4, the slopes emainconstant.Other investigations re currently inprogresso overcomehe analysis f CNK tests.5 DEGRADATION OF JOINT SURFACES5.1 Definitionof the degradation egree

In order to quantify the degradation f jointbetween its initial state (prior to shear) and itsultimate state after shear),Belem et al. (1997) havedefined he degreeof degradation f shearedointsurfaces w. This degradationarameters definedfrom calculation f the actualareasof joint wallswhich were estimated from roughnessprofilingbefore and after shearing. According to theseauthors,he degree r percentagef degradationoran nitially roughsurfaces definedas:D,,,(%)00t*At, At*A .- 100A - A -2A.' (4)0_


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T / I 6060 rpho1 40i0 0.0 0.2 0.4 0.6 0.8 1.00.0 0.2 0.4 0.6 0.8 1.0

Figure 11. Predicteddegradation s normalizednomal stress.

./Mo_rpho2 Iorpho

//j..."'.,.orpho0.0 0.1 o'n/oe 0.2

IoTsts-MorphoTsts-MorphoB2Tsts-MorphoFigure 12. Comparison etweenmodel and CNSdata.

Figure 13. Degradation s initial normal stressCrnipredictive urves or differentK nvalues.

10' .-'.v- Oni/Oc, ,0.00 0.04 0.08 0.12

&KnMPa/mmKnMPa/mmKn = 3 MPa/mm CNS (Kn = 0)Figure 14. Comparisonbetween model and CNKdata.

specific contacts which will result in highdegradationsith thecycles.Figure12 compareshe calculated aluesof D w withthosepredictedby the model (equation5) for thetwo morphologiesMorphoA and B). Let us recallthat or MorphoB 1, W,= 20 ramand or MorphoA2and B2, W, = 400 min. This figure shows hat themodel rather well predicted he degradation f theundulatedoint than the degradation f the naturaljoint replica.* CNK degradationmodelFortheCNK condition,n variesinearlywithKnasa functionof dilatancy:an = ani+aan = ani+Kn aUn (7)During one cycle of shear,we approximate Un bytheproductfpeak ilatancyate,an(ipeak, and herelative angentialdisplacement f the first part ofthecycleLcy/4).n addition,he esultshowhattan(ipeakdecaysxponentialyith hecyclesnd

tends to tan(Os)after 10 shear cycles.We thusassumehat for eachcycle:AU = tan(Os)W = tan(Os)cy/4 (8)$By combiningequations 7) and (8), equation 6)becomes:=( a/2TWt o,.Knan0,L(9)The CNK degradationmodel s then:

andwasexpressed ith regard o rrniandnot to thenormalstress stimatedrom Art , becausehe termw takes nto accountheCNK condition.Figure 13 presents he prediction curves obtainedwith the equation 10) for the artificial undulatedjoint with threevalues f normalstiffnessI = 1, 2,3 MPa/mm) and W, = 400 mm. The modelparametersre:T = 25 mm,L, = 100mm, O = 10.3.

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Figure14 compareshe calculated aluesof Dw tothose predictedby the model (equation 10) forvariousYh. The CNS model is integrated n thediagram Ith = 0). The model well predicts hedegradation f the undulated oint and shows heinfluence of the normal stiffness.

The modelsuchas it is defined equations -10)is the generalized eakstrength riterion or both heCNS andCNK loading onditions.ndeed, Yni 0 &K. 0 correspondo a CNK condition nd ni 0 &K. = 0 correspondo a CNS path.6 CONCLUSIONSMany cyclic direct shear estswere carriedout onartificialundulatedoints of mortar.These estswereperformed according to CNS and CNK loadingconditions.The morpho-mechanical ehavior wasanalyzedon the shearand dilatancycurves or theCNS tests t an > 2 MPa and heresults howedhat:

for a given cycle: basedon the shearcurves,we observe i) a clear peakfrom cycle 1 to cycle 6(ii) a perfectelastoplasficehavior rom cycle 7 tocycle 10; from the dilatancy urves ndaccordingothepartsb, c, d ande, we observehat i) fromcycle1 to cycle : averageilatancynglesm_c im_dim_e t im_b im_cdeii) fromcycle to cycle10:im_b im_cdend he undulationsre practicallytransformed into saw teeth.

From cycle n-l) to cyclen: basedon the shearcurves,we observe i) from cycle 1 to cycle 6, theshear strength ncreases ue to an increase n thecontactareas, ii) at cycle 7, the residualstresssreached; rom the dilatancycurvesand accordingotheparts,we note i) fromcycle1 to cycle6: ira_decreasesnd m_cdelightlyncreasesn relationoan increase n the contactareas ii) from cycle 7 tocycle10: ra_ = ira_ = im_d im_e.A parameter was defined to quantify thepercentage f degradation f shearedoints. Twomodels were then proposed to predict thedegradationof the anisotropic oints accordingloadingconditionsCNS or CNK) and the shearingmode (monotonousor cyclic). The degradationmodel or CNS conditions thengeneralizedor thetwo loadingconditions,his modelwell predicts hedegradationf theundulatedoints.

Belem T. (1997). Morphologieet comportementmcanique esdiscontinuitsocheuses.hsedeDoctorat NPL, Nancy, 220p.Belem T., Hornand-Etienne . & SouleyM. (1997).Fractalanalysis f shear oint roughness.nt. J.Rock Mech. & Min. $ci., 34:3-4, paperNo. 130,10p.Benjelloun .H., BoulonM. & Billaux D. (1990).Experimentalndnumericalnvestigationn rockjoints.Rock oints,Barton& Stephanssoneds),Balkema,Rotterdam, p. 171-178.Hornand-Etienne ., Belem T., SabbadiniS., ShtukaA. & RoyerJ.-J. 1995). Analysis f the evolutionof rock joints morphology with 2Dautocorrelationvariomaps). roc. 7th Int. Conf.on Appl. Stat. & Proba, Paris,Lemaire,Favre &Mebarki (eds), Balkema, Rotterdam,pp. 1229-1236.HutsonR.W. & DowdingC.H. (1990).Jointasperitydegradation uring cyclic shear. nt. J. RockMech. Min. Sci. & Geomech. Abstr., 27, No. 2,pp. 109-119.Jing L., NordlundE. & Stephansson. (1993).Study of rock joints under cyclic loadingconditions.Rock Mech. Rock Engng.,26, No. 3,pp. 215-232.Kana D.D., Fox D.J. & Hisiung S.M. (1996).Interlock/friction model for dynamic shearresponsen natural ointed rock. Int. J. RockMech. Min. $ci. & Geornech.Abstr., 33, No. 4,pp. 371-386.LadanyiB. & Archambault (1969).Simulation fthe shearbehaviour f a jointedrock mass.Proc.11tht Syrup.on Rock Mech., Berkeley,pp. 105-125.

Lefvre F. (1999). Comportementmcanique etmorphologiqueesdiscontinuit6sn cisaillement.Thdse e Doctorat NPL, Nancy. h paratre)PattonF.D. (1966). Multiple modesof shear ailureJn rock. Proc. 1st. Congr. nt. Soc.RockMech.,Lisbon,pp. 509-513.PleshaM.E. (1987). Consfitufivemodels or rockdiscontinuities with dilatancy and surfacedegradation.nt. J. for Num. & Anal. Meth. inGeom.,Vol. 11, pp. 345-362.Sabbadini S., Hornand-Etienne F. & Belem T.(1995).Fractalandgeostafisficalnalysis f rockjoints roughness efore and after shear ests.Proc. 2nd Int Conf. on Mech. of Jointed &Faulted Rocks, Vienna, Rossmanith (ed),Balkema,Rotterdam, p. 535-541.

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ARMA-99-0399_Rock Joints Behavior Under Cyclic Direct Shear Tests