ARMA-99-0415_Experimental Study on the Mechanical Behavior of Single Joint Under a Constant T-o...

8/12/2019 ARMA-99-0415_Experimental Study on the Mechanical Behavior of Single Joint Under a Constant T-o Loading Cond

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RockMechanicsor ndustrx,madei, ranz,Scott& Smeallieeds) 1999Balkema, otterdam,SBN90 5809052 3Experimentaltudy n hemechanicalehavior f singleointunderconstant/o loading onditionnd tsapplicationo mechanical odelingH.Yasuhara, . Kishida,H. Fujii & T.AdachiDepartment f Civil Engineering, yotoUniversity,apan

ABSTRACT:Althoughhe oint elementmethod anbe appliedo numerical nalyses f ointed ockmasses,the effort n datapreparationnvolvinghe oint parameters,he constitutiveaw, and he number f joints sincreased.o overcomehisdifficulty,he equivalent ontinuous odel s appliednstead f the oint elementmethod.n thisstudy, ocus s placedon he mechanicalarameters,ormalstiffness, andshear tiffness,.The relationship fk, andk, (Goodman 984) s measuredn this studyby constant /a loading ests.Then,the results reused o determinehe material onstantsf the equivalent ontinuous odel.l INTRODUCTIONRecently, he need for both rock and undergroundstructures, such as tunnels, dam foundations,undergroundowerhouses,ndundergroundavernsfor storingoil, gas,compressiveir, and radioactivewaste,hasbeen ncreasing. incehesestructuresreusually constructedn a jointed rock mass, themechanicalpropertiesof the jointed rock massshould e grasped recisely.n a discussionn themechanicalroperties f jointed ockmasses, neofthe most important tasks is to understand hemechanical ehaviorof the joints. The mechanicalproperties f rock oints cangenerally e describedand determinedby two mechanicalparameters,namely, ormalstiffness , andshear tiffness .The normal stiffness and the shear stiffness aredeterminedhroughuniaxialcompressiveestsanddirect shear tests on rock joints, respectively.Goodman1976), Barton 1976), Bandis 1980), andBandiset al. (1981) cardedoutuniaxialcompressivetests and direct shear tests on rock joints, andpresented ethodsor estimatinghe normaland heshear stiffness.

In this study, oading tests are conducted nconsiderationf the ointsand he loadingdirectionagainsthe joints.That is, by changinghe loadingdirection gainsthe oints, he mechanicalehaviorof the joints can be observed under variouscombinations of normal stress and shear stress onthe rock joints. It is thought, herefore, hat themechanical ehaviorof a jointedrock masscan bepracticallydiscussedn terms of excavationandconstruction.

In order o performexperimentsnd discussherelationship etween he joint stiffnessk and k)and the loadingdirection gainst he joints, a newtesting pparatusasbeendeveloped. constantloadingconditioncan be applied o the joints usingthisapparatus.hus, he estsdescribedn thispaperare calledconstant aloading conditionests.

2 CONSTANT r/a LOADING CONDITIONTESTS2.1 SpecimensIn order o investigatehe mechanical ehaviorofjoints, specimenshat containa single oint areemployedn the loading ests.The specimens sedin this researchare rectangular risms or whichthere s a cross ection f 42 x 42 mm anda heightof80 min.The specimensontain singleoint, whichis located at the center (lengthwise) of eachspecimenand is approximately ligned on thehorizontal plane, as shown in Figure 1. Thespecimens re made of mortar. The combinationratio of cement: sand: water is 1: 2: 0.65. Thecuring age in water is 28 days. Cylindricalspecimensare also prepared under the sameconditionsthe samecombinationatio and curingage) and are employedn the uniaxialcompressivetests oas o investigatehe mechanicalroperties fthe material.From the uniaxialcompressiveestsonthe cylindrical pecimens,he uniaxialcompressivestrength nd Young'smodulus re found o be 28.9MPa and .02x 10aM/a, espectively.In order to discuss the influence of the natural

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2 = 42mm1 = 42mm

h = 80 m

Figure 1. Specimen.Table I The value of JRC and the order of the loadingangles.Specimen JRC 0 degree 15derees 30 derees 45 dereesA 12.61 0 0 0 0B 13.07 0 0 0 0C 16.68 0 0 0 0joint surface oughness,hreekindsof naturalointsurface oughnessre chosenhrough ecovered oresamples.Aer choosing he natural oint surfaceroughness,mpressions re made of them. Usingthese mpressions,eproducedmortarspecimensrethen created.The impressionsre made of Siliconrubber (TSE350, made by Toshiba Silicon).Variationsn joint surface oughnessontainedn thesamplesmade t possibleo carryout many ypesofconstant /loading conditionests.Beforeperforminghe tests,measurementsf thejoint surface oughnessre takenwith a non-contacttype of laser-scanmicrometerwhich is situatedon athree-dimensionaltage,a 3-D Roughness rofiler(Tanimotoand Kishida, 1995). Data acquisitionsfully automatedby a computer,and each jointsurface oughnesss measured t 0.5 mm intervals.A bird's-eye view of the measuredoint surfaceroughnesss shown n Figure2. Basedon the digitaldataof joint surface oughness, arton's RC (JointRoughnessCoefficient) (Barton, 1973) in eachspecimen is calculated using the relationship

betweenJRC and Z2 (Tse and Cruden, 1979). Thecalculated RC value for eachspecimens presentedin Table 1.The relationshipbetween he loading directionand he oint of eachspecimens shown n Figure2The value of 0 formed where the joint inclinationand the loadingdirectioncrosseachother,and it is

definedas the loadingangle in this paper.Thesethree specimens ave been previouslyset up invariousdegrees f loadingangle0, and hen he testshave been started.The order of the loadinganglesused n this research ork is alsopresentedn Table1.2.2 Testing pparatus nd an outlineof the testsThe testing apparatuss shown n Figure 3. Eachspecimens separatednto upperand ower partsbythe rock oint. The upperpart s completelyixed tothe loading frame, while the lower part can movefreely in both verticaland horizontaldirections. helinear-value displacement ransducer LVDT) fixedon the loading rame measureshe vertical and thehorizontal isplacementsf eachspecimenv andh,respectively), nd he strainof the intact ock parts smeasured y the straingauge.Since he strainof theintact rock is measured t the lower and the upperparts a and b, respectively),he total displacementof intact ock u,,, canbe calculated sing his stressCompressiveoadP is worked hrough he load cell.Figure 4 illustrates the image of the specimendeformationand the measuringparameters.Sincecompressiveoad P canbe brokendown nto normaland sheardirections n the rock oint, the testsareassumed to be a kind of direct shear test under aconstant /crloadingcondition.As mentioned above, the upper part of thespecimen s completely ixed and the lower part ofthe specimencan move freely in both vertical andhorizontaldirectionsn the devicedevelopedn thisresearchwork. Thus, the main purpose s to applythe load to the rock joint under various loadingangles. In other words, the influence of therelationship etween he loadingdirectionand the

(a) SpecimenA (b) Specimen (c) SpecimenFigure2. Bird's-eye iew of the naturaloint surface oughness.

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i?-%'.. LVDTI .157''{...vertical)

LUST

I -'.::..2:2:22:2:2:2:2;2'22:2'.i.:i.:.:.:.:.2:2:2:2:2:2:2:'.:2.2:i4.2,i '"::oadelFige 3. Testingappams.

P

leJoint P(Load

Figme . e relationhipemeene jolt inclinationde loadingdkecfionjoint inclination an be discussed,nd themechanicalroperties f the rock oint of eachspecimenanbe determinednder ariousoadingdirections.

In thisstudy,ests reperformed ith four ypesof loading ngles, amely, , 15,30, and45 degrees,asdescribedn Table1. The45-degreeoading ngleis the maximumbecauseof the limit for this testingapparatus. ive steps of cyclic loading andunloadingre performed nder he stress ontrolmethod, s shown n Figure 5. The loading evelincreases,tepby step,and he maximumoad oreach teps determinedntil henormal tress n herock joint reaches2, 4, 6, 8, and 10 MPa,respectively.he loading elocity n the verticaldirection is 2.0 MPa/min.

8

6' 4

z 2

0 2 6 12 20 30Time [mitt ]

Figure5. Loadingpattern3 RESULTS OF THE CONSTANT r/or LOADINGCONDITION TESTS3.1 Deformation f intact ockpartsIn thissection,he deformation f intact ock parts sdiscussedhroughhe constant/crloading onditiontests. As mentioned above, uniaxial compresslyetestswere performedusing cylindricalspecimens,and the results were describedsuch that Young'smodulus and Poisson's ratio were 1.39 x 104 MPaand0.174, respectively.On the other hand, Young's modulusobtainedthrough he constant /or oadingcondition ests smeasuredo be 1.59, 1.70,2.25, and 1.82x 104MPaon the 0, 15, 30, and 45-degree oadingangles orSpecimen . It is confirmedhat Young'smodulus,obtainedhrough he constant /or oadingconditiontests, s arger han hatobtainedhroughhe uniaxialcompresslyeests. The same tendenciescan beconfirmed for SpecimensB and C. Since thespecimensn the constantr/or loading tests arecoveredwith steeland are laterally ixed, as shownin Figures3 and 4, Young'smodulus ields argermeasurements. hen applying Young's modulusobtainedhroughhe constant/crloadingests o thenumerical simulation of a jointed rock mass,therefore, his trend must be considered.3.2 Deformation f therock ointsIn performing he constantder loadingconditiontests, both the vertical and the horizontaldisplacements along the testing device can bemeasuredhrough VDT. And, the vertical oad canbe measuredhrough he load cell. The purpose fthe tests s to clarify he mechanical ehaviorof therock oints hrough hesedata.Then, he oad and hevertical and the horizontal displacements aretransformed into normal and shear directions on therock oints,and he mechanical ehaviorof the rock

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Uintact a + b

Figure6. Measuring arameters.joints s discussed.irst of all, the calculatinglowof the stress nd he displacementsn he rock ointsare describedn the following.The displacements f the rock joints aredescribedsingnormal ndshear isplacementsjnandu, respectively,sshownn Figure , and heyarecalculatedy the ollowing quations:uj,= vcosO- sinO-Uintact (1)ujs vsinO+ cosO (2)where v and h are the vertical and the horizontaldisplacementseasuringIT, respectively,nd 0is the loadingangle.On the otherhand, he normaland the shearstresson the rock oints (rr and r,respectively) an be calculatedby the followingequations:

PcosOa- (3)PsinOr- (4)

where P is the applying oad and A is the jointcontactarea. The relationship,which is formedbetweenheEquations3) and 4), is r/rris equal otanO. n thisstudy,herefore,he ests re carried utundera constant /rr loadingcondition n the rockjoint of eachspecimen.Since he joint contactarea changes ith theperformancef the tests, he areacanbe calculatedas he ollowing quation:A = l,(l: - (5)

where and 12are the lengthsof the specimensshownn Figure1. The stress displacementurvesof both the normal and the shear directions on therock oint aredescribedn Figure7.4 MECHANICAL BEHAVIOR OF TI-[E ROCKJOINTSBased on the resultsof the constantdrr loadingconditionests, he mechanicalropertiesf therockjoints are discussed. onsideringhe mechanicalproperties f the rock joints, the normal and theshearstiffnessmust be determined. n this section,therefore, he normal and the shearstiffness f thejointsare determined,nd he mechanical ropertiesof the rock oints and the relationship etween henormaland he shearbehaviorof the rock oints arediscussed.4.1 Estimation f thenormalstiffnessFirst of all, the determination f normalstiffness nis introduced. igure7(a) showshe results f the 0-degreeoading ngle est.Since he loading ngle sequal o 0 degrees, nly the normalstress normaldisplacementurveon he rock oint canbe obtained.The traditional method for determiningnormalstiffness n closely esembleshe normal stressnormaldisplacementurve to a function.And, thetangentialgradientof the approximateunction scalculated o as o determinehe normalstiffness n.In order o calculate he value of kn, therefore, heapproximateunctions f the normalstress jointnormaldisplacementre described. andis 1980)andBrown& Scholz 1986) presented,espectively,the following mpirical quations:

bUjn - + C ( a, b,c:constant (6)a+&Ujn a + ptnrr ( a, ,8: constant (7)Equations6) and 7) are henapplied o the resultsandnormalstiffness , is determined.n Figure7(a),a permanent eformation anbe confirmedor eachloading and unloading cycle. The permanentdeformationor the irst oading ndunloading ycleis larger han that of the other cycles.This is thereasonwhy the influence of the contacting ointsurface oughness nder he initial conditionoccursin the first oading ndunloading ycle. n the othercycles, each permanent deformation is almostconstant and each tangential gradient of theunloading curves is almost equal. The normalstiffnesss representedy the elastic ehavior f thenormaldeformationof eachrock oint. Therefore,

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8 4

2

0.1 0.2 0.3 0.4 0.5 0.6Jointdisplacementmm]

(a) The oading ngle; degree

Normaldirection .:.10 - - .......Shearirection

4

2

0.1 0.2 0.3 0.4 0.5 0.6Jointdisplacementmm]

(b) The oading ngle;15 degrees

.,/ /////...,Z.. ' 5...::i::'>q:",.,z0.2 0.4 0.6 0.8

JointDisplacementmm](c) The loading ngle; 0 degrees

8

2

: [ ........hearirection"" ). :.....--'?3' O..'.......... ,..."5;5'.0.2 0.4 0.6 0.8 1

JointDisplacementmm](d) The oading ngle; 5 degrees

Figure7. The stress displacementurves f both henormaland he shear irections n therock oint (Specimen )the normal stiffness s determinedusing theunloading urve n the final loadingand unloadingcycle. n the caseof the approximationf Equation(7), a highercorrelation oefficient R = 0.998) canbe obtained.When Equation 7) is applied o theresults, the normal displacements row to anunlimited alue f thenormal tress ecomesnfinity.However, this behavior is not realistic because henormaldisplacementf a rock oint is actually initeand a maximum oint closure xists. n the caseofthe approximationof Equation (6), a highercorrelationcoefficient R = 0.999) can also beobtained. f the normal stressbecomes nfinity,Equation 6) convergeshe value (b + c) and themaximumoint closurecan be obtained. herefore,it is thought hatEquation 6) is moreaccuratehanEquation 7) in resembling he normal stressnormal isplacementurve. n Equation8), normalstiffnesskn is determined n order to calculate hetangentialgradientof the normal stress normaldisplacementurveon the rock oint usingEquation(6).k.- act a or) (8)d ttjna.b

8

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35Jointnormaldisplacementmm]

Figure 8. The normal stress normal oint displacement

Equation (8) shows that normal stiffnessk, is afunction of the normal stress o:Figure 8 presents he normal stress normaldisplacementcurves for a rock joint in the finalunloading ycle.The curves re obtainedhroughO-degree oading angle test. Since he curvesaresimilar to eachother, he difference n specimens,namely, he difference n joint surface oughness,snot clearly shown. It is thought that the normaldeformation f the rock oint and/ornormalstiffnesskn doesnot dependon the shapeof joint surfaceroughness. omesamples f the normalstiffness n,

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LoadingangledelFee)a0 2.0215 1.6030 1.9345 2.93

Table . Thenormal tressata = 2.0MPa) and hevalues fa by ndSpecimenA Specimen Specimenb c (x104Pa) a b c (x104Pa) a b c0.163 0.132 4.74 1.43 0.340 0.147 2.80 1.97 0.144 0.164

0.390 0.108 2.52 3.54 0.368 0.168 2.36 2.10 0.452 0.1250.487 0.091 1.18 3.58 0.358 0.176 2.43 4.38 0.347 0.2610.239 0.108 3.46 0.943 0.107 0.005 3.74 1.63 0.180 0.030

10MPa)4.802.152.674.48

Table . Theshear tiffnessf the ockoints.degrees 30 degrees 45 degrees Direct shear estSpecimenlx5103Pa) (x103Pa) (x103Pa) x103Pa).4 9.65 6.85 6.13 3.52B 9.46 7.84 4.65 4.12C 3.64 4.98 3.28 3.42

( x 10)3.5 ''' I''-I'-'i'"'"": - - 4S-degree ...."1 ' ..:4

............0 ', ,,, i,,, ,,, ,,2 4 6 8 10

Jointno strossMPa]Figure9. The normalstifflless f each oading ngle.

determinedy Equation 8), are presentedn Table2.In this case, he conditionof the determinations setat or= 2.0 MPa. Table2 alsopresentshe values ora, b, andc in Equation6).Next, the results of the constantz'/cr oadingcondition ests on a 15-degree oading angle areshown n Figure 7(b). Both the normal stressnormal oint displacement nd the shearstressshear oint displacementurvesare shownby thesolid ine and he broken ine, respectively. pplyingEquation 6) to the resultsof the normal stressshearoint displacementurves, highercorrelationcoefficientR = 0.999) canalsobe obtained.n thiscase, he valuesof a, b, andc are different han hosedeterminedn the O-degreeoadingangle est. t isconfirmedhat the loadingangleaffects he normaldeformation f the rock oint. And, it is thought hatthe shear behavior contributes to the poorcorrelation.

In the caseof the 30 and45-degreeoadingangletests, he stressjoint displacementurves f boththe normaland he sheardirections n the rock ointare shown in Figures 7(c) and (d), respectively.Applying Equation (6) to the unloadingnormalstress normaloint displacementurvesn the finalcycle,a highercorrelation oefficientR = 0.999;30degreesnd0.998;45 degrees) analsobe obtained.And, different alues or a, b, andc are calculatedneachcase.As mentioned bove, t is also confirmed

that he oading ngles ffect he normaldeformationof the rock oint.The normal joint stiffness - normal stressrelations or each oadingangle est are shown nFigure 9. It is easily confumed hat the normalstiffness epends n the normalstress nd increaseswith increments n the normal stress.And, it can benoticed that the normal stiffness decreases withincrementsn the oading ngles, xcept or the caseof the 45-degreeoading ngle.Based on the results, normal stiffness k,decreasesith incrementsn the loading ngle.Withincrements n the loading angle, shear behavioroccurs nd he contact ondition f the oint surfaceroughness ecomesunstable.That is, since theaspertiesof the joint surface oughness o notengage smoothly, he limited allowanceof thedeformation n the normal direction is clearlyappeared.On the other hand,k, on the 45-degreeloading ngle ncreasesompared ith k on the 30-degree oadingangle. n the caseof the 45-degreeloading angle, the dilation occurswith the shearbehavior,parts of the normal deformation n therock joint divide the dilation, and the normalstiffnessncreases. he turningpoint is when thedilationbegins o affect he normaldeformation nthe rock joint, and this phenomenon annotbegraspedn detailwith thisapparatus.4.2 Estimation f theshearstiffnessThe broken ines n Figures7(b), (c), and (d) showthe shear tress shearoint displacementurvesoreach oading ngle.The permanent eformation fthe shear deformation is larger than that of thenormaldeformation.Shearstiffness s s determinedusing hese urves. irst of all, the oading urvesnthe nitialcyclic oading reextracted ntil he shearstress reaches 2.0 MPa, and the straight line isestimatedy the east-squaresethod. inally,shearstiffness ks, which is the gradient of anapproximatelystraight ine, can be determined.Table3 shows hear tiffnesss. t is generallyoundthat shear stiffness ksvaries inversely with.the

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