This paper discusses a complex investigation to determine the microcrack closure and opening, with four different triaxial tests of a homogeneous isotropic limestone. Two of the researches

were under drained conditions (deviatoric triaxial test and triaxial test with constantly increasing stress) and two of them were under undrained conditions (triaxial test connected with decreasing confining pressure and triaxial test with constantly increasing stress). During the tests the uniaxial and the confining pressure, the pore-fluid pressure, and the axial and the lateral strains were

measured continuousl

Deli, Árpád

Vásárhelyi, Balázs

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611Bestimmung der Schließung und Öffnungvon Mikrospalten mit auf verschiedenen Belastungswegenausgeführten triaxialen VersuchenDetermining the Microcracks Closureand Opening with Different Loading Paths Triaxial TestsTeach. Ass. Vásárhelyi, Balázs – Technical University of Budapest, Budapest, HungaryAss. Prof. Deli, Árpád – Technical University of Budapest, Budapest, HungaryABSTRACT: This paper discusses a complex investigation to determine the microcrack closure andopening, with four different triaxial tests of a homogeneous isotropic limestone. Two of the researcheswere under drained conditions (deviatoric triaxial test and triaxial test with constantly increasingstress) and two of them were under undrained conditions (triaxial test connected with decreasingconfining pressure and triaxial test with constantly increasing stress). During the tests the uniaxialand the confining pressure, the pore-fluid pressure, and the axial and the lateral strains weremeasured continuously.ZUSAMMENGFASSUNG: In diesem Artikel wird eine komplexe Experimentenserie zur Bestimnungder Schliessung und Öffnung von Mikrospalten dargestellt, die aus vier verschiedenent aufhomogenem isotropem Kalkstein ausgeführten triaxialen Untersauchungen besteht. Zwei von diesenExperimenten waren drainiert (erstens eine deviatorisch-triaxiale Unterschuchung, zweitens einetriaxiale Untersuchung mit ständig wachsender Spannung), undzwei waren undrainiert (eine triaxialeUntersuchung in Bezug auf abnehmenden Seitendruck und eine triaxiale Untersuchung mit ständigwachsender Spannung). Während der Experimenten wurden der uniaxiale und der Seitendruck, derPorenflüssigkeitsdruck und die axialen und lateralen Deformationen stets gemessen.1. IntroductionThe failure process of brittle rock has beeninvestigated by several researchers (e.g.: 1-7,etc.) with uniaxial compression tests. Using thestress-strain diagrams, the stages of crackdevelopments and measuring the axial andlateral strains the crack volume strains can becalculated (6).Between the crack closure and the yieldstress, the axial stress-strain curve behaveselastically and its slope (the axial stiffness)should define the elastic modulus (E). Elasticconditions prevail at low stress, before the crackinitiation point. Cook (8) proved that thevolumetric strain of a sample measured bysurface strain gauges was a pervasive volumetricproperty of the rock and not a superficialphenomenon. For a cylindrical sample subjectedto axial loading, with or without a confiningstress, and under small strains, the volumetricstrain from the axial strain (ea) and the lateralstrain (e1) curve is given byev = VVD @ 2 el + ea (1)Fig. 1. Convention of the signs.The pore volumetric strain is the excess ofthe measured entered or departed fluid (DVP)(the conventions according to Fig. 1) divided bythe pore volume (VP) which is reached by thefluid during the saturation:612Q  = PPVVD(2)If the saturation of the rock is perfect, thusthere are not closed pore in the sample, thechanging of the pore volumetric strain is in ratioof the crack volumetric strain.The goal of this paper is to present a complexinvestigation to determine the microcrackclosure and opening with four different triaxialtests. The examined limestone was saturated andthe different tests were carried out under drainedand undrained conditions. The fracture processhas been investigated using the same triaxialtests with saturated sandstone (9, 10).2. Material Description, SpecimenPreparation and Test EquipmentA homogeneous, isotropic Jurassic limestone(from Lavoux, France) was examined. Table 1and 2 show the measured petrophysicalconstants and the minerals with their volumepercentage, respectively. There are not poresinside the minerals.The diameter and the length of eachcylindrical test specimen was 38 mm and 76 mmlong, respectively and each sample was driedduring   72  hours  in   60 °C  before   they   wereequipped with two axial and two lateral straingauges that were attached to the middle third ofthe specimen to avoid end effects. Recording theaxial (ea) and lateral (el) strains in a sample as itis loaded with or without confining stress wascarried out according to the standard (11).Petrophysical constants Unit ResultDensity (dried), rd kg/m3 2119Density (saturated), rw kg/m3 2334Grain density, rs kg/m3 2700Apparent porosity, nw % 21.28Total porosity, nt % 21.51Secondary micro-poreporosity, nw0% -Micro-cracks closingpressure, PfMPa -Table 1: Measured pertophysical constant of theexamined limestone.PetrographicconstituentsV%Grain size(mm)Min. Aver. max.Microoncoids 39.0 0.025 0.27 0.65Bioclastics 32.0 0.05 0.55 0.20Cement (micrit) 26.5 0.001 0.005 0.10Limonite 0.5 - - -Porosity 2.5 < 0.005 0.075 0.37Table 2: Petrographic constituents of theinvestigated rock.Fig. 2: Schematic diagram of the test arrangement. Tap 1: open position: drained / closed position:undrained condition. Taps 2-5: for oil and air regulate.613The saturation was carried out after thedrying: firstly the specimens were saturated withwater for 24 hours in a glass vessel with thin air,afterwards the samples were in water for 48hours long under atmospheric pressure. Finallyall the samples were covered with a rubberjacket to protect them from the oil during thetriaxial tests.Fig. 2 shows schematically the arrangementof the test equipment. The capacity of thetriaxial cell was 100 MPa and it was connectedwith two Gilson-305 type pumps (capacity: 60MPa) which were used to regulate both theconfining pressure (Pc) and the injection for thepore-fluid pressure. The measurement sensitivityof both the pore water-pressure and theconfining pressure (Pc) was 0.01 MPa.Capillaries with different diameters were used todetermine the volume of the pore water. Thedeformation was measured with two LVTD.At room-temperature (22 °C) the sampleswere saturated with methanol. Therefore thepore water pressure (Pi = 1 MPa) chosen waslower than the starting point of the hydrostaticpressure (s1 = s3 = Pc = 2 MPa) in the Gilson-pump used for producing the required pore fluidpressure (Fig. 2) and the tap for draining wasopen thus the air of the pores was mixing withthe methanol and getting out across the tap.After 15-17 hours the saturation was complete.Since quasi-static loading rates were intendedto make thus the strain rate (e&) was 10-6/sec incase of undrained deviatoric triaxial tests and theconstant stress rate (s& ) was 5×10-3 MPa/sec incase of the other investigations.3. Applied Loading PathsThe researches were carried out with thefollowing triaxial tests:a) drained condition: deviatoric triaxial test andtriaxial test with constantly increasing stress;b) undrained condition: triaxial test connectedwith decreasing confining pressure andtriaxial test with constantly increasing stress.3.1 Undrained, Deviatoric Triaxial TestFig. 3 shows the applied stress path, where0: hydrostatic starting point, where Pc = 01s  = 2MPa;0A: drained hydrostatic loading till Pc = s1 = 30MPa (e&= 10-6/sec). During this period tap 1was open, i.e. Pi = 0 MPa;A: Setting the starting value of the pore fluidpressure ( 0iP = 1 MPa). Tap 1 was closed.Starting from point A Pc was constant (30 MPa)and deviatoric stress was applied underundrained condition (e&= 10-6/sec).Fig. 3: Loading path of the undrained deviatorictriaxial test ( axe& =10-6/sec)3.2 Undrained Triaxial Test with ConstantlyIncreasing StressThe applied stress path can be seen in Fig. 4. Incase of the undrained test tap 1 was closed.0: Hydrostatic starting point ( 0cP  = 01s = 1 MPa)and setting the starting value of the pore fluidpressure ( 0iP =1 MPa);0-A-B… : Applying Ds1 and Ds3 axial andlateral stresses with increasing rate with k = 10and k = 20 values (k = Ds1/ Ds3). The loadingrate ( 1s& ) was 5×10-3 MPa/sec and Ds3 = 0.1MPa.Fig. 4: Applied loading path for undrained,constant stress increasing triaxial test( axs& =5×10-3 MPa/sec)6143.3 Drained Triaxial Test, Connected withDecreasing Confining PressureFig. 5 presents the applied loading path. Tap 1was open (drained test).0: hydrostatic starting point with Pc = 01s  = 2MPa;0A: drained hydrostatic loading;Starting at A: drained unloading in the lateraldirection; decreasing the confining stress (Pc)manually with tap 3. The axial stress (s1) wasconstant: 60 MPa.Fig. 5: Applied loading path of drained triaxialtest connected with decreasing confiningpressure (s&=5×10-3 MPa/sec)3.4 Drained Triaxial Test with ConstantlyIncreasing StressThe test was carried out according to the loadingpath presented in Fig. 6. During the test tap 1was open (drained test).Fig. 6: Loading path of drained triaxial test withconstantly increasing stress( axs& = 5×10-3 MPa/sec).0: hydrostatic starting point with Pc = 01s  = 1MPa;0-A-B… : Applying Ds1 and Ds3 axial andlateral stresses with increasing rates k = 10 andk = 20 values (k = Ds1/ Ds3). The loading ( 1s& )rate is 5×10-3 MPa/sec and Ds3 = 0.1 MPa.4. Results and Discussion4.1 Results of Undrained, Deviatoric TriaxialTest (Pc = 30 MPa)The deviatoric stress (sdev) in the function ofthe strains (e1, e3, ev) is shown in Fig. 7. Due tothe plastic behaviour of the rock the measurablemaximal deviatoric stress in case of e3 is higherthan e1 or ev. The non-linearity of the curve isstarting at low stress level.According to Fig. 8, there is an “S-pattern”between the microcrack threshold and the pore-fluid pressure changing (9). Determining themaximum value of Pi from Fig. 8 the stresses arethe same level as the microcrack opening limitin Fig. 7. Since the microcracks are opened afterthis point the pore fluid pressure decreases dueto the increasing pore volume. This deviatoricstress is approximately half (54 %) of the failurestress.Fig. 7: Deviatoric stress versus strains in case ofundrained triaxial test (Pc = 30 MPa).Fig. 8: The relation between the deviatoricpressure and the pore fluid pressure in case ofundrained deviatoric test – the “S-pattern”(Pc = 30 MP).6154.2 Results of the Undrained Triaxial Test withConstantly Increasing Stress (k = 10 and k = 20)The characteristic of the curves are the sameas in Figs. 7-8. There are not closing parts of thes1- ev curves thus the porosity from themicrocracks are neglectable. The maximum ofthe pore fluid pressure is also at the dilationlimit. Because of the increasing volume of themicro-crack system the pore fluid pressure isdecreasing after the maximal stress. The strengthand the pore fluid pressure are higher if k issmaller. The failure stress is among 75-80 % ofthe s3 for the maximal pore fluid pressure andno depend on k.4.3 Results of the Drained Triaxial Test,Connected with Decreasing Confining PressureTill Pc = 20-22 MPa the Q  is zero ornegative, i.e. fluid entering the sample, thus themicrocracks developed during the hydrostaticstress and strain (see Fig. 9).Fig. 9: Changing of the relative pore volume indrained hydrostatic pressure and after lateralload decreasing.Analysing the shydr-e curves (Fig. 10) afterthe linear part till 30-35 MPa e3 startingdecreasing (i.e. the diameter of the sampleconsidering e3  increases, although the volume ofthe sample decreases). It means that during thelinear part the pore system and the bond amongthe minerals do not change significantly. Duringthe second part of the curve (after 30-35 MPa)the damage of the pore system is more and moresignificant.Fig. 11 presents a measured hydrostatic stress– relative pore volume changing (shydr -Q ) curve.Due to hydrostatic pressure the pore volume,which indicated the small value of the Q  at thefirst part, decreases.Fig. 10: Drained hydrostatic pressure versusstrains.Fig. 11: Confining pressure versus strains fordrained triaxial tests with decreasing lateral load.4.4 Results of the Drained Triaxial Test withConstantly Increasing Stress (k = 10 and 20)Figs. 12-13 present the measured stressversus strain and relative pore volume changeversus pressure curves, respectively, in case of k= 20. The stress of microcracks openingdecreases with increasing k (from 40 % to 30 %)but the pattern of the curves are same.Fig. 12: Stress-strains diagram for the drainedtriaxial test in case of constantly increasing axialstress (k = 20).616According to Fig. 13 the fluid is absorbedbecause in case of k ¹ 1 (when there is nohydrostatic pressure) the deformation of grainsis not dominant although the closed pores (insideand among the grains) are open and create a newmicro-crack system with increased pore volume.Fig. 13: Changing of the relative pore fluidvolume in case of drained triaxial test (k = 20).5. ConclusionFour different triaxial tests were carried outduring the research with saturated limestone.Two of them were under drained conditions andtwo of them were under undrained conditions. Inundrained conditions the determine microcrackpropagation from the deviatoric stress-straincurves is equal to the maximal value of the porefluid pressure. With decreasing the lateral loadunder undrained conditions (k = 10 and k = 20)the maximum value of the pore water pressure isin ratio of the dilation limit of the s1 - ev curveand this ratio is inverse to k.Under drained conditions the grains and thebonds were linearly deformed. During thedrained triaxial tests with constantly increasingstress (k = 10 and 20) the fluid was absorbedbecause in case of k ¹  1 the deformation ofgrains was not dominant although the closedpores were open and create a new microcracksystem with increased pore volume.Acknowledgements: The authors are indebted toProf. F. Homand for her expert help inperforming the experiments. The work has beenmade possible through a grant by the FrenchGovernment Scholarship (BGF) and theNational Scientific Research Foundation ofHungary (OTKA F022620).References1. Brace, W. F., 1964, Brittle Fracture of Rocks.In.: State of stresses in Earth’s crust: Proc. Int.Conf., Santa Monica, 110-178.2. Bieniawski, Z. T., 1967, Mechanism of BrittleFracture of Rock. CSIR Report, Pretoria, SouthAfrica.3. Eberhardt, E., Stimson, B. & Stead, D., 1999,Effects of Grain Size on the Initiation andPropagation Thresholds of Stress-InducedBrittle Fractures. Rock Mech. Rock Engng.32(2), 81-99.4. Lajtai, E. Z. & Lajtai, V. N., 1974, TheEvolution of Brittle Fracture in Rocks. J.Geological Sci. 130(1), 1-18.5. Lajtai, E. Z., 1998, Microscopic FractureProcesses in a Granite. Rock Mech. RockEngng. 31(4), 237-250.6. Martin, C. D. & Chandler, N. A., 1994, TheProgressive Fracture of Lac du Bonnet Granite.Int. J. Rock Mech. Min. Sci. & Geomech.Abstr. 31(6), 643-659.7. Wawersik, W. R. & Fairhurst, C., 1970, AStudy of Brittle Rock Fracture in LaboratoryCompression Experiments. Int. J. Rock Mech.Min. Sci. & Geomech. Abstr. 7(5), 561-575.8. Cook, N. G. W., 1970, An ExperimentalProving that Dilatancy is a PervasiveVolumetric Property of Brittle Rocks Loadedto Failure. Rock Mech. Rock Engng. 2(3), 181-188.9. Deli, Á., 1991, Essais Triaxiaux sur un Greset un Calcaire. Diplom Etude d’Approfondiesde Genie Civil et Miner, Laboratoire deGéomécanique, INPL, ENSG-Nancy.10. Deli, Á. & Vásárhelyi, B., 2000,Investigation of the Fracture Process withDifferent Loading Paths Triaxial Tests onSaturated Sandstone. Bull. Engng. Geol. Env.59(3), 184-193.11. ISRM, 1981, Rock Characterization Testingand Monitoring, ISRM Suggested Methods,Edited: Brown, E. T., Pergamon Press, Oxford,107-127.

Determining the Microcracks Closure and Opening with Different Loading Paths Triaxial Tests

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