Crack Initiation

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    Identifying crack initiation and propagation

    thresholds in brittle rock

    E. Eberhardt, D. Stead, B. Stimpson, and R.S. Read

    Abstract: Recent work at the Underground Research Laboratory of Atomic Energy of Canada Limited in Pinawa, Manitoba,

    has shown that high compressive stresses near the tunnel face significantly contribute to the loss of strength, and eventual

    failure of the rock, through stress-induced brittle fracturing. A program of laboratory testing has been undertaken to

    investigate the effects of brittle fracture on the progressive degradation of rock mass strength. The work carried out in this

    study involves a detailed analysis of the crack initiation and propagation thresholds, two key components in the brittle-fracture

    process. This paper describes new techniques developed to enhance existing strain gauge and acoustic emission

    methodologies with respect to the detection of these thresholds and their effects on the degradation of material strength.

    Key words: tunnel, rock failure, brittle fracture, crack initiation, crack propagation.

    Rsum : Des travaux rcents au Underground Research Laboratory de lAECL Pinawa, Manitoba, ont dmontr que les

    fortes contraintes de compression prs de la face du tunnel contribuent de faon significative la perte de rsistance, et

    ventuellement la rupture de la roche, par suite de fractures fragiles induites par les contraintes. Un programme dessais enlaboratoire a t entrepris pour tudier les effets de la fracture fragile sur la dgradation progressive de la rsistance de masse

    de la roche. Le travail ralis dans cette tude comprend une analyse dtaille de linitiation de la fissure et des seuils de

    propagation, deux composantes cls dans le processus de la fracture fragile. Cet article dcrit de nouvelles techniques qui ont

    t dveloppes pour valoriser les mthodologies existantes de jauges de contraintes et dmission acoustique pour la

    dtection de ces seuils et de leurs effets sur la dgradation de la rsistance du matriau.

    Mots cls : tunnel, rupture de la roche, rupture fragile, initiation de fissures, propagation de fissures.

    [Traduit par la rdaction]

    Introduction

    The excavation of an underground opening in a stressed rockmass results in the deformation of the near-field rock due to aredistribution of stresses, resulting in induced stressconcentra-tions. This stressredistribution increasesstrainenergyin zones

    of increased compression. If the resulting imbalance in theenergy of the system is severe enough, it can result in theprogressive degradation of the rock mass strength throughfracturing. Thus it is important to establish the thresholds as-sociated with microscale and macroscale fracturing in thein situ rock mass.

    The deformation and fracture characteristics of brittle rockhave been studied by numerous researchers over the past30 years (Brace 1964; Bieniawski 1967a; Wawersik andFairhurst 1970; Lajtai and Lajtai 1974; Martin and Chandler

    1994). The general consensus of these studies has beenthat thefailure process can be broken down into a number of stagesbased largely upon the stressstrain characteristics displayedthrough axial and lateral deformation measurements recordedduring uniaxial and triaxial laboratory tests. Based on thestressstrain behaviour of a loaded material (Fig. 1), Brace

    (1964) and Bieniawski (1967a) defined these stages as being(1) crack closure, (2) linear elastic deformation, (3) crack in-itiation and stable crack growth, (4) critical energy release andunstable crack growth, and (5) failure and postpeak behaviour.

    Crack closure occurs during the initial stages of loading( < cc in Fig. 1, where is the total axial stress and cc isthe stress at crack closure) when preexisting cracks orientatedat an angle to the applied load close. During crack closure, thestressstrain response is nonlinear, exhibiting an increase inaxial stiffness (i.e., deformation modulus). The extent of thisnonlinear region is dependent on the initial crack density andgeometrical characteristics of the crack population. Once themajority of preexisting cracks have closed, linear elastic de-formation takes place. The elastic constants (Youngs modu-lus, Poissons ratio) of the rock are calculated from this linear

    portion of the stressstrain curve.Crack initiation (ci) represents the stress level where mi-

    crofracturing begins and is marked as the point where the lat-eral and volumetric strain curves depart from linearity. Crackpropagation can be considered as being either stable or unsta-ble. Under stable conditions, crack growth can be stopped bycontrolling the applied load. Unstable crack growth occurs atthe point of reversal in the volumetric strain curve and is alsoknown as the point of critical energy release or crack damage

    Can. Geotech. J. 35: 222233 (1998)

    Received July 24, 1998. Accepted December 2, 1997.

    E. Eberhardt.1 Department of Geological Sciences, Universityof Saskatchewan, Saskatoon, SK S7N 5E2, Canada.D. Stead. Camborne School of Mines, University of Exeter,Redruth, Cornwall TR15 3SE, England.B. Stimpson. Department of Civil and Geological Engineering,The University of Manitoba, Winnipeg, MB R3T 5V6, Canada.R.S. Read.2 Whiteshell Laboratories, Atomic Energy of CanadaLimited, Pinawa, MB R0E 1L0, Canada.

    1 Present address: Engineering Geology, ETH H`nggerberg,8093 Zhrich, Switzerland.

    2 Present address: KlohnCrippen Consultants Ltd., Calgary,AB T2E 7H7, Canada.

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    stressthreshold cd (Martin 1993). Bieniawski (1967a) definesunstable crack propagation as the condition which occurswhen the relationship between the applied stress and the cracklength ceases to exist and other parameters, such as the crack

    growth velocity, take control of the propagation process. Un-der such conditions, crack growth would continue even if theapplied load were kept constant.

    Unstable crack growth continues to the point where the nu-merous microcracks have coalesced and the rock can no longersupport an increase in load. Martin (1993) notes that the peakstrength of granite (including the uniaxial compressive strengthin unconfined tests) is not a unique material property but is de-pendent on loading conditions such as the loading rate. The crackinitiation and crack damage stresses were found to be more char-acteristic, essentially independent of loading conditions.

    Work at the Atomic Energy of Canada Limited (AECL)Underground Research Laboratory (URL) has concentrated onusing the crack initiation (ci) and crack damage (cd) stressthresholds to better quantify rock damage. The detection ofthese thresholds, however, has proven difficult especially with

    respect to crack initiation. A series of uniaxial tests were sub-sequently performed to refine existing analysis techniques fordetermining the crack initiation stress threshold of intact rock.These techniques involve the use of stressstrain data andacoustic emission monitoring. New methods of data analy-sis were also introduced to help substantiate the interpreta-tion of the data with respect to crack initiation and growth.These methods include the application of a moving pointregression technique to the stressstrain data and an exami-

    nation of the changes in the acoustic event properties withloading. Testing wasperformedon cylindrical samples of Lacdu Bonnet granite obtained from the URL 130 Level (130 mbelow ground surface). This paper examines the effects of

    crack initiation and damage in the degradation of materialstrength, emphasizing the underlying mechanismsand char-acterization methods.

    Detection of crack development in brittlerock

    A number of techniques have been developed to detect andstudy crack growth in brittle materials. The most common ofthese involves the use of electric resistance strain gauges tomeasure slight changes in sample deformation that can be re-lated to the closing and opening of cracks (Brace et al. 1966;Bieniawski 1967b). To a lesser extent, acoustic emissionmonitoring has been used to correlate the number of acousticevents to various strain gauge responses (Scholz 1968; Ohnakaand Mogi 1982; Khair 1984). Other techniques have involved

    the use of photoelastics, optical diffraction patterns, scanningelectron microscopes, laser speckle interferometry, ultrasonicprobing, and electrical resistivity.

    Stressstrain dataStrain gauge measurements have provided the most insightinto delineating the stages of crack development in rock.The use of strain gauges in past studies, however, has beensomewhat limited by data sampling, computing, and storage

    Fig. 1. Stressstrain diagram showing the elements of crack development (after Martin 1993). Note that only the axial (axial) and lateral (lateral)

    strains are measured; the volumetric strain and crack volume are calculated. axial, axial stress; ucs, peak strength; V, change in volume; V,

    initial volume.

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    capabilities. Recent work by the Rock Mechanics ResearchGroup at the University of Saskatchewan has been directedtowards using more powerful computers with larger data stor-age capabilities in conjunction with faster data logging sys-tems. These capabilities have allowed for tests to be conductedin which the sampling rate has been increased five to ten timesthat allowable with older testing systems (i.e., capable of fivemeasurements per second). Thus more data points along theaxial and lateral stressstrain curves can be collected and ex-amined for indications of crack growth. In essence, higherresolution of sample deformation relating to crack initiationand growth is achieved.

    Moving point regression technique

    Improvements can also be made in the way strain gauge dataare analyzed. Stressstrain data analysis has traditionally con-centrated on picking noticeable slope changes in the plottedstressstrain curves (axial, lateral, and calculated volumetric)which may then be correlated to several of the theoreticalstages in crack development. However, a high degree of errorand subjectivity is incorporated into this analysis procedure

    when one considers the combined use of poor data resolutionand the manual picking of points. Bearing in mind that certaininflections, some of which may be undetectable to the unaidedeye, in the stressstrain curves are of key interest, a movingpoint regression technique, which uses the first derivative ofthe curves to highlight any slope or rate changes in the curves,was developed.

    The moving point regression technique uses a sliding win-dow approach to move through an x, y data set, fitting astraight line over a user-defined interval. The slope at eachpoint is calculated over the interval and recorded, the processbeing repeated at successive points (Fig. 2). When plottedagainst the parameter of interest, inflections in the original x,

    y data curve are highlighted. For example, using an axial stressversus axial strain curve, the technique produces a moving

    point average of the changes in the Youngs modulus through-out loading (Fig. 3). This is referred to as the average axialstiffness, therefore avoiding problems in terminology whencalculating the slope outside the range of linear elastic behav-iour. In regards to the sensitivity of the method to the user-defined regression interval, it was found that the general shapeof the stiffness curve remained the same with increasing inter-val sizes, but small-scale fluctuations in the measured defor-mation response were filtered out when extremely largeregression intervals were used. Analysis results indicate thatthe size of the regression interval should be approximately 5%of the total number of x, y data pairs.

    Acoustic emission response in rockAcoustic emission (AE) in polycrystalline rock originates as aresult of dislocations, grain boundary movement, or initiation

    and propagation of fractures through and between mineralgrains. The sudden release of stored elastic strain energy ac-companying these processes generates an elastic stress wavewhich travels from the point of origin within the material to aboundary where it is observed as an acoustic event (Hardy1977). AE techniques have been used with some success inidentifying microfracturing in brittle materials. Scholz (1968)found that characteristic AE patterns in rock correlate closelywith stressstrain behaviour. However, most of the success in

    correlating AE activity to microfracturing has involved thelater stages of crack development. This is due to the fact thatthe majority of AE events occur just prior to failure. The lackof significant AE activity in the initial stages of loading makesit more difficult to distinguish backgroundnoise from fracture-related acoustic events. A balance must be struck between set-ting event threshold limits high enough to filter out themajority of the background noise, yet low enough to pick upthe beginning of the microfracturing process.

    Characteristics of an acoustic eventIn addition to recording the number of acoustic events and

    correlating this number to the measured deformation responsein the rock, it is also possible to record certain properties of theAE waveforms. The signal waveform of an acoustic event isaffected by the characteristics of the source, the path takenfrom the source to the sensor, the sensor characteristics, andthe recording system. Generally, these waveforms are complexand using them to characterize the source can be difficult. Dueto these complexities, AE waveform analysis can range fromsimple parameter measurements to more complex pattern rec-ognition. However, relatively little work has been done in thearea of waveform analysis with respect to rock mechanics andthe progressive degradationfailure process in rock.

    The event threshold serves as a reference for several of thesimple waveform parameters (Fig. 4). These AE event proper-ties are defined in Table 1. The characteristics of an acousticevent may also be used to approximate the release of kinetic

    energy through the AE event. The true energy is directly pro-portional to the area under the acoustic emission waveformwhich in turn can be measured by digitizing and integratingthe waveform signal. However, this can be both difficult andtime consuming. As a simplification, the event energy can beapproximated as the square of the peak amplitude (Spanneret al. 1987; Lockner et al. 1991) or the square of the peakamplitude multiplied by the event duration (Beattie 1983;Mansurov 1994). The resulting values are actually more

    Fig. 2. Moving point regression technique.

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    representative of the event power (the units are given in dBand dBs, respectively), but are commonly referred to as en-ergy calculations in the literature due to their approximatelylinear relationship with energy. This type of energy analysishelps in accentuating AE events with abnormally large ampli-tudes or durations.

    Laboratory testing of Lac du Bonnetgranite

    Laboratory uniaxial testing was performed on 20 samples of

    pink Lac du Bonnet granite from the 130 Level of the URL.The pink granite is medium to coarse grained, with an averagegrain size between 3 and 4 mm. Based on work by Jackson andLau (1990), 61 mm diameter cores were chosen to minimizesize effects. Jackson and Lau found that samples of Lac duBonnet granite with smaller diameters were more sensitive tosample disturbance, thereby influencing the observed me-chanical behaviour of the rock samples during testing.

    Samples were prepared for testing according to AmericanSociety for Testing and Materials standards (designationASTM D4543-85) with length to diameter ratios of approxi-mately 2.25. Considerable care was taken in minimizing theinfluence of end effects on strain gauge and AE transducerreadings. This entailed the use of a specially constructed framethat allowed for the sample ends to be highly polished. Meas-urements of end surface flatness and perpendicularity five

    times lower than those recommended by ASTM standardswere attained. Each sample was instrumented with six Micro-Measurement electric resistance precision strain gauges (threeaxial and three lateral at 60 intervals, 12.7 mm in length, witha 5% strain limit) to record sample deformation and four175 kHz piezoelectric transducers to record acoustic emis-sions. Strain gauges were epoxied directly to the cleaned sam-ple surface to ensure a solid bond, whereas the AE transducerswere mounted onto wave guides, which were in turn epoxied

    to the sample surface. Acoustic emissions were recorded withan AET 5500 logging system using a gain of 40 dB and athreshold value of 0.1 V.

    Prior to uniaxial testing, P- and S-wave traveltimes wererecorded for each sample (Table 2). Results from these meas-urements indicate a significant increase (4050%) in both P-and S-wave velocities when compared with previously testedgranite and granodiorite samples from the 420 Level of the

    URL (Eberhardt et al. 1996). With maximum in situ stressesincreasing from approximately 15 MPa at 130 m depth to60 MPa at 420 m depth (Martin 1990), considerable damagethrough stress-induced microcracking would be expected insamples from the 420 Level. Static elastic properties were de-termined from the stressstrain data following ASTM stand-ards (designation D3148-93) and include Poissons ratio,average Youngs modulus, and secant Youngs modulus (Ta-ble 3).The difference between the average and secant modulus

    Fig. 3. Moving point regression analysis of axial stressstrain data showing the changes in axial stiffness throughout loading for a 130 Level

    pink granite. Eavg, average Youngs modulus.

    Fig. 4. Definition of simple acoustic emission waveform

    parameters.

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    (which would include any nonlinearity due to preexistingcracking) for the 130 Level samples is relatively small(5 GPa), indicating that initial sample damage is relativelylow.

    Interpretation of crack development in Lacdu Bonnet granite

    It is generally accepted that the first fractures in a uniaxiallyloaded brittle material are tensile microcracks (Lajtai and La-

    jtai 1974). The growth of these cracks has been shown to occurin the direction of the major principal stress ( 1), where cracksnot aligned with 1 grow along a curved path to align them-selves with 1 (Fig. 5). This phenomenon has been observed ina number of materials including glass (Brace and Bombolakis1963; Hoek and Bieniawski 1965), hard plastics (Nemat-Nasser and Horii 1982; Cannon et al. 1990), plaster (Lajtai1971), ice (Schulson et al. 1991), and rock (Wawersik andFairhurst 1970; Peng and Johnson 1972; Huang et al. 1993).The opening of crack faces parallel to the applied load and theclosure of crack faces perpendicular to the load cause certain

    changes in the relative lateral and axial deformations, respec-tively. These changes appear as inflections in the stressstraincurves which, in turn, can be used to identify the differentstages of rock deformation and failure.

    Test results were analyzed to define the stages of rockdeformation and failure as defined by Brace (1964) andBieniawski (1967a). The following discussion highlights someof the key observations. Results from this analysis are summa-rized in Table 4.

    Crack closure

    The crack closure stress level (cc in Fig. 1) indicates the loadat which a significant number of preexisting cracks haveclosed and near-linear elastic behaviour begins. This point isapproximated by determining the point on the stressstraincurve where the initial axial strain appears to change fromnonlinear to linear behaviour. Crack closure stresses (cc) werepicked for each test using the moving point regression analysis(Fig. 3). As was expected, a rapid increase in axial stiffnesswas observed before values levelled off and behaved in a rela-tively linear manner.This pattern andthe corresponding valueswere consistent for each test (Table 4).

    Examination of the lateral stiffness curve (Fig. 6) over thisregion reveals relatively high stiffness values when the load isfirst applied to the sample (the lateral stiffness term, although

    somewhat unconventional, represents the change in the lateralstrain rate with axial loading). Artificially high values of thisterm during the initial stages of loading represent a point in theload history where there is not a continuous transmission ofstresses due to the presence of open microcracks, therefore thelateral and axial strain responses are not fully coupled. Theseinitially high values are followed by a marked reduction (35%)during the first 25 MPa of loading. The initial stages of crackclosure appear to predominantly involve the simple movementof preferentially aligned crack walls towards one another,parallel to the direction of applied load. This would have asignificant effect on the axial strain but little effect on thelateral strain, since the displacement would be in the axialdirection. With increasing load, values of lateral stiffness be-gin to rapidly decrease, possibly signifying shear or sliding

    movement between the faces of closing or closed cracks. Thisbehaviour has been observed in glass plates by Bieniawski(1967b) who noted that the sliding deformation demonstratedby single closed cracks continues even during linear elasticbehaviour.

    Linear elastic behaviour

    Figure 3 shows that after crack closure is reached, a period ofrelatively linear axial strain occurs. The average Youngs

    AE event property Description

    Ring-down count The number of times a signal crosses a preset threshold datum; in general, large events require more cycles to ring

    down to the threshold level and will produce more counts than a smaller event; provides a measure of the intensity of

    the acoustic emission event

    Peak amplitude Related to the intensity of the source in the material producing an AE event; measurements are generally recorded in

    logarithmic units (decibels dB) to provide accurate measurement of both large and small signals

    Event duration When an acoustic event first crosses the preset threshold, an event detector measures the time that the waveform

    amplitude remains above the threshold, thereby giving the event duration

    Rise time Measures the time it takes to reach the peak amplitude of an event; provides an account of the positive-changing AE

    signal envelope

    Table 1. Definition of acoustic emission (AE) event properties (as shown in Fig. 4).

    Location rock t ype Densit y (g/ cm3) P wave (m/s) S wave (m/s)

    130 Level pink granite 2.62 (0.01) 4890 (190) 3030 (120)

    420 Level grey granite 2.61 (0.02) 3220 (100) 2160 (60)

    Note: Standard deviation is given in parentheses.

    Table 2. Average acoustic velocities of URL granites.

    Prope rty 130 m Level Pink Granite

    Average modulus, Eavg (GPa) 66.1 (2.5)

    Secant modulus, ES (GPa) 61.0 (2.9)

    Poissons ratio, 0.31 (0.04)

    Note: Standard deviation is given in parentheses.

    Table 3. Average static elastic moduli for URL pink granite atthe 130 Level.

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    modulus was taken as a least squares fit along this region. Interms of lateral stiffness, linear behaviour is never trulyreached. Instead, the lateral stiffness continuously decreasesfrom values of approximately 300 GPa to values less than20 GPa prior to failure (Fig. 6). This would seem to indicatethat a number of processes may be contributing towards the

    gradual but continual loss of lateral stiffness in the specimenstested. These mayinclude sliding (shear) between faces of clos-ingcracks,tensile opening of cracks duringcrackinitiation, andpossibly further shear movement related to crack coales-cence columnar buckling during the latter stages of rock de-formation. Following ASTM standards, Poissons ratio wascalculated using a least squares fit over the same interval asthat used in calculating the average Youngs modulus (i.e., lin-ear region of the axial stressstrain curve). It will be shownlater that this may not be the most appropriate interval overwhich to calculate Poissons ratio.

    Crack initiationThe crack initiation stress threshold, as determined throughlaboratory testing, has been defined as the point where thelateral strain curve departs from linearity (Brace et al. 1966;

    Bieniawski 1967a; Lajtai and Lajtai 1974). Examination of thelateral strain curve (Fig. 6) revealsthat the identification of thispoint can be very subjective. This is clear from analysis of thelateral stiffness curve which indicates that at no time is thelateral stressstrain curve truly linear. Noting the difficulty inusing lateral strain gauge data, especially in highly damagedsamples, Martin (1993) suggested using the calculated crackvolumetric strain to identify crack initiation. For a cylindricalsample loaded uniaxially, crack volume is determined by sub-

    tracting the linear elastic component of the volumetric strain,given by

    [1] Velastic =1 2

    Eaxial

    where E and are the elastic constants and axial is the axialstress level, from the volumetric strain calculated from themeasured axial (axial) and lateral (lateral) strains, given by

    [2] V = axial + 2lateral

    The remaining volumetric strain is attributed to axial cracking,i.e.,

    [3] Vcrack = V elastic

    Martin (1993) defines crack initiation as the stress level atwhich dilation (crack volume increase) begins in the crackvolume plot (Fig. 1).

    This method is limited, however, because of its dependenceon the use of the elastic constants E and . Although theYoungs modulus E can be determined with a reasonably highdegree of confidence and consistency, the nonlinearity of thelateral strain response complicates the measure of Poissonsratio. The resulting value is the ratio of lateral to axial strainmagnitudes based on the linear elastic axial strain behaviourand the best approximation of a straight line through a non-

    linear region of lateral strain over the same stress interval.Table 5 lists the respective Poissons ratio values calculatedover the same stress interval as the average Youngs modulus(as per ASTM standards) and over the stress interval betweencrack closure and crack initiation as determinedusingthe mov-ing point regression analysis. This variability introduces alarge degree of uncertainty into the crack volume calculationused to determine crack initiation. Figure 7 demonstrates thesensitivity of crack initiation valuesto changes in the Poissonsratio using crack volumereversal as the indicator (for example,a change of 0.05 in the Poissons ratio results in a 40%change in the ci value).The crack volume stiffnessplot shownin Fig. 7 is calculated as the change in slope of the crack vol-ume strain curve, the reversal of which is noted by the changefrom a positive to a negative slope.

    Using an approach that involved the combined use of the

    moving point regression analysis and acoustic emission re-sponse, it was found that that the crack initiation stress thresh-old could be more accurately determined. From the straingauge data, it was found that, although the lateral strain isnonlinear, rate changes do occur and can be correlated to thegrowth of cracks in the sample. These rate changes are mostevident when analyzing the volumetric strain and stiffnesscurves (Fig. 8). The volumetric stiffness curve is based on thestress-dependent rate of change in the volumetric strain. Volu-

    Fig. 5. Model of internal crack extension towards the major

    principal stress. t, major principal stress; , shear stress.

    Property Stress threshold (MPa)

    Crack closure, cc 47.5 (2.9)

    Crack initiation, ci 81.5 (3.7)

    Crack coalescence, cs 104.0 (3.8)

    Crack damage, cd 157.3 (9.9)

    Peak strength, ucs 206.5 (10.0)

    Note: Standard deviation is given in parentheses.

    Table 4. Average strength parameters for URL pinkgranite.

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    metric strain is defined in eq. [2]. The volumetric stiffness iscalculated as the slope of the volumetric strain versus axialstress curve. The rate at which the volumetric strain curvechanges is dependent on the rate of change in the measuredaxial and lateral strain.

    Examination of the volumetric stiffness curve indicated aseries of characteristic patterns (Fig. 8) that recur in each of

    the uniaxial tests performed. During the initial stages of load-ing, the axial strain controls the shape of the volumetric straincurve. The nonlinear behaviour of the axial strain during crackclosure distinguishes itself as an irregular region along thevolumetric stiffness curve (Fig. 9). This irregular region is fol-lowed by a linear region marked by a small break in slopesignifying a rate change. This break in slope represents thetransition from crack closure to near-linear elastic behaviour.This linear region also marks the stress interval in which the

    lateral strain achieves its most linear behaviour (i.e., the Pois-sons ratio should be calculated in this region as shown inTable 5). The volumetric stiffness curve then makes a transi-tion to a less regular region without any discernible break inslope at approximately 80 MPa. Throughout this region theaxial strain rate maintains a near-constant level, therefore anychange can be attributed to a change in the lateral strain rate.

    Changes in the lateral strain rate result in slight slope changesin the volumetric strain curve. However, because the axialstrain rate still dominates in controlling the shape of the volu-metric strain curve, no noticeable slope change occurs in thevolumetric stiffness curve. Although these changes in the lat-eral strain ratedo notcontribute to the overallvolumetric strainenough to cause a major change in the slope of the volumetricstiffness curve, they do contribute enough to cause irregulari-ties in it. These changes in the lateral strain rate, and conse-

    Fig. 7. Variability of crack volume strain reversal with Poissons ratio for a 130 Level pink granite.

    Fig. 6. Plots of lateral strain and lateral stiffness against axial stress for a 130 Level pink granite.

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    quently the volumetric stiffness curve, signify crack initiationat approximately 80 MPa.

    Correlation between the behaviour of the volumetric stiff-ness curve and crack initiation can also be validated throughacoustic emission analysis.The average response from the fourAE transducers shows that the majority of activity occurs to-wards the end of the test. Although AE activity occurs con-

    tinuously throughout the test, the logarithmic plot in Fig. 10shows that the beginning of significant AE activity is at ap-proximately 80 MPa. This coincides with the crack initiationstress threshold (ci) of 80 MPa as determined using the volu-metric stiffness curve in Fig. 9. AE activity prior to this pointcan be attributed to movement along crack faces during crackclosure, as recognized in the lateral strain rate and previouslydiscussed. It is also likely that small cracks may form duringlow stresses in areasalready weakened by stress-reliefcracking.

    Fig. 8. Plots of volumetric strain and volumetric stiffness against axial stress for a 130 Level pink granite.

    Fig. 9. Breakdown and correlation of volumetric stiffness with the stages in the compressive failure process of rock for a 130 Level pink granite.

    Method of calculation

    ASTMa 0.31 (0.04)

    cc cib 0.24 (0.03)

    Note: Standard deviation is given inparentheses.a Calculated according to ASTM standards.b Calculated over the stress interval between

    crack closure and crack initiation as

    determined through the moving point

    regression analysis.

    Table 5. Average Poissons ratio forURL pink granite at the 130 Level.

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    In addition to the acoustic emission response, the propertiesof the acoustic events themselves are markedly different be-fore and after crack initiation. Figures 11 and 12 contain plotsof the maximum event duration and ring down counts. Fromthese plots it can be seen that a marked increase in their re-spective magnitudes occurs at approximately 80 MPa, coin-ciding with crack initiation. Larger event durations and ringdown counts both signify larger acoustic events. Although

    acoustic activity occurs prior to this point,the size of the eventsis relatively small (in terms of event duration, these events are70% shorter in duration than those occurring above 80 MPa).This may indicate that the acoustic events generated throughcrack closure are much smaller than those generated throughstress-induced tensile cracking. Calculations of the acousticevent energy based on the peak amplitude andevent durationof the event waveform (hereinreferred to as the elastic impulseenergy so as not to confuse it with the true energy) also rein-

    forces these observations. Plots of the elastic impulse energyand its stress-dependent rate change (Fig. 13) show that thesize of the events in terms of energy dramatically increasesshortly after crack initiation begins.

    Crack coalescence and crack damageIn defining the various stages of crack behaviour, stable crackgrowth is interpreted as one stage bounded at the lower end by

    the crack initiation stress threshold (ci) and at the upper endby the crack damage stress threshold (cd). Analysis of labora-tory data, however, indicates that this region may consist oftwo stages distinguished by a major change in the volumetricstrain rate. Analysis of both the axial and lateral stiffnesscurves indicates that a large rate change occurs in strain wellbefore unstable crack propagation (i.e., cd). During stablecrack growth, rate changes are believed to occur solely interms of lateral strain, since crack growth is predominantly in

    Fig. 10. Plot of log acoustic emission event count vs. axial stress for a 130 Level pink granite.

    Fig. 11. Plot of event duration vs. axial stress for a 130 Level pink granite.

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    the direction of uniaxial loading (i.e., 1). Volumetric strainreversal then occurs as a result of increases in the lateral strainrate surpassing the constant axial strain rate as the dominantcomponent in the volumetric strain calculation. This results ina reversal of the volumetric strain curve defining the crackdamage threshold. Analysis indicates, however, that the axialstiffness is not constant but decreases well before cd at160 MPa (Fig. 3). Analysis confirms that the lateral strain ratechange does eventually exceed the rate change in axial strainthereby causing the reversal in the volumetric strain curve.These changes can be seen in the volumetric stiffness curve,where large increases in the lateral strain rate combined withchanges in the axial strain rate cause large irregularities as the

    volumetric strain curve approaches reversal (Fig. 14).The unexpected departure from linear behaviour seen in theaxial strain response prior to the crack damage threshold maybe explained through the coalescence of propagating cracks ina loaded sample. At the beginning of crack initiation, smalltensile cracks begin to grow parallel to the applied load. Thesecracks originate from small flaws preferentially aligned to theloading direction so as to induce cracking through high tensilestress concentrations. The cracks are assumed to appear ran-domly throughout the sample and, for the most part, are iso-lated from one another. They have very little effect indecreasing the overall competency of the rock. As the load isincreased additional cracks begin to grow as their individualstrengths are exceeded, incrementally contributing to the deg-radation of the inherent rock strength (i.e., cohesion). This isevident in the acoustic emission data which show increasing

    bursts of AE activity leading up to cd (Fig. 10).As cracks increase, both in number and size, they eventu-

    ally begin to interact with one another. Crack interaction thenbecomes extremely complex as stress shadows overlap. Thishas been demonstrated using a numerical modelling study ofthe process (Eberhardt et al. 1998). Eventually cracks will be-gin to step out and coalesce (i.e., develop en echelon (Lajtaiet al. 1994)). This coalescence of cracks would involve somecrack growth at oblique angles to the loading direction and

    perhaps an element of shearing, thereby contributing to achange in the axial strain rate. Thus, the changes seen in theaxial and volumetric stiffness curves may be attributed to astage of crack coalescence (cs) prior to the crack damagestress threshold.

    Following crack coalescence, determination of the crackdamage stress threshold (cd) is relatively straightforward. Al-though a certain degree of subjectivity may be introduced bypicking the point of volumetric strain reversal directly off thevolumetric strain curve, the point stands out very clearly in aplot of volumetric stiffness versus axial stress (Fig. 14). Thecrack damage threshold could represent the intermediate-termstrength of the sample, since beyond this point failure will even-tually occur through unstable cracking (Martin 1993). Values ofcs and cd for the tested samples are given in Table 4.

    Conclusions

    The deformation and fracture characteristics of brittle rock arean important consideration in assessing its long-term strength.The initiation, propagation, and interaction of stress-inducedcracks are closely linked but extremely complicated. Throughthe combined use of strain gauge analysis and acoustic emis-sion monitoring, techniques were developed to aid in the iden-tification and characterization of mechanisms leading to brittlefailure.

    The following observations were made with respect touniaxial testing performed on samples of pink Lac du Bonnetgranite:

    (1)Crack closure involved both axial andlateral strain com-ponents.

    (2) Near-linear elastic behaviour was seen only in axialstrain measurements. Lateral strain followed a nonlinear trendthroughout the entire test, as depicted through continuouslydecreasing values of lateral stiffness.

    (3) The combined use of moving point regression analysis(performed on the axial, lateral, and volumetric stressstraincurves) and acoustic emission response (including the event

    Fig. 12. Plot of ring down counts vs. axial stress for a 130 Level pink granite.

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    Fig. 13. Plot of cumulative elastic impulse energy vs. axial stress and the stress-dependent energy rate vs. axial stress for a 130 Level pink granite.

    Fig. 14. Plot of average volumetric stiffness vs. axial stress, indicating the occurrence of major strain rate changes between crack initiation and

    crack damage for a 130 Level pink granite. cs, crack coalescence stress threshold.

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    properties and energy calculations) provided the most accurateand reliable means of identifying crack initiation (ci).

    (4) Analysis of both the axial and lateral stiffness curvesindicates that a significant rate change in strain occurs prior tothe crack damage threshold, possibly marking the small-scalecoalescence of cracks.

    Acknowledgments

    Parts of the work have been supported by Atomic Energy ofCanada Limited and a Natural Sciences and Engineering Re-search Council of Canada operating grant. The authors wish tothank Dr. Derek Martin and Zig Szczepanik for their sugges-tions and contributions to this work. Special thanks are ex-tended to Dr.EmeryLajtaifor his insights into the initial stagesof this work.

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