Complete Stress-Strain Curve 1999

International Journal of Rock Mechanics and Mining Sciences 36 (1999) 279±289

0148-9062/99/$ - see front matter # 1999 Elsevier Science Ltd. All rights reserved.

PII: S0148-9062(99 )00006 -6

INTERNATIONAL SOCIETY FOR ROCK MECHANICSCOMMISSION ON TESTING METHODS

DRAFT ISRM SUGGESTED METHOD FOR THE COMPLETE STRESS±STRAIN

CURVE FOR INTACT ROCK IN UNIAXIAL COMPRESSION

CONTENTS

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281

2. Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282

3. Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282

4. Specimen preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285

5. Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286

6. Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286

7. Reporting of results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288

8. Additional interpretative comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288

Co-ordinators

C.E. Fairhurst (USA), J.A. Hudson (UK)

Draft ISRM suggested method for the complete stress±straincurve for intact rock in uniaxial compression

C.E. Fairhursta, J.A. Hudsonb

Accepted 15 January 1999

ISRM SUGGESTED METHODS (SMs): SECOND SERIES

A Second Series of Suggested Methods is being produced by the ISRM Commission on Testing Methods from 1998 onwards.

In this Second Series, for each SM two versions are published:

1. A Draft SM written by the Working Group Co-ordinator(s);2. A Final SM also produced by the Working Group Co-ordinator but with amendments resulting from the Draft SM review by

the Working Group Members and other comments received after publication of the Draft SM.

A suite of the new Suggested Methods is currently being published in this Journal. These started with an IndentationHardness Index SM written by T. Szwedzicki and published in June 1998. Several more will be published in 1999.

Please send written comments on this SM to thePresident of the ISRM Commission on Testing Methods:

Professor J A Hudson, 7 The Quadrangle,

Welwyn Garden City, Herts AL8 6SG, UK

1. Introduction

1.1 The subject of this suggested method is obtainingthe complete force-displacement curve for intact rockin a laboratory test. The terms `force' and `load' aresynonymous in this context, as are the terms `displace-ment' and `deformation'. Thus, a force-displacementcurve is the same as a load-deformation curve. Whenthe measured force is scaled by the original specimenarea and the measured displacement is scaled by theoriginal specimen length, a nominal stress±strain curvecan be plotted. The term `complete stress±strain curve'refers to the displacement of the specimen ends frominitial loading, through the linear elastic prepeak

region, through the onset of signi®cant cracking,through the compressive strength (when the stress±strain curve has zero gradient), into the postpeak fail-ure locus, and through to the residual strength.

1.2 The complete force-displacement curve of anintact rock specimen, whether tested in uniaxial com-pression or in a con®ned state, is useful in understand-ing the total process of specimen deformation,cracking and eventual disintegration, and can provideinsight into potential in situ rock mass behavior. Until1966, it was a paradox that rock specimens loaded inthe laboratory failed suddenly, but continuing rockfailure in situ often occurred gradually Ð even thoughthe rock had clearly been taken beyond the compres-sive strength. The key to obtaining the completestress±strain curve for rock in the laboratory is under-standing the role of the testing machine sti�ness.

1.3 The complete curve for rock has been obtainedsince 1966 [1,2]. Initially, the experimental techniquesinvolved increasing the testing machine sti�ness. Since,

aMTS Systems Corp., 14000 Technology Drive, Eden Prairie, MN,

USA.b T.H. Huxley School of Environment, Earth Sciences and

Engineering, Imperial College of Science, Technology and Medicine,

London SW7 2BP, UK.

C.E. Fairhurst, J.A. Hudson / International Journal of Rock Mechanics and Mining Sciences 36 (1999) 279±289 281

1969, however, servo-controlled testing machines havebeen used. During the initial development of the exper-imental techniques, it became evident that obtainingthe complete force-displacement curve in uniaxial com-pression for some rock types, e.g. high strength gran-ites, becomes at best di�cult and is sometimesimpossible without test optimization. Test optimizationincludes appropriate load frame sti�ness, choice offeedback signal and strain measurement transducers,specimen preparation techniques, etc. [3]. For speci-mens that exhibit brittle behavior when loaded in uni-axial compression, even using conventional axialstrain-controlled testing methods is often not su�cientto control the rate of failure of the specimen afterpeak strength. In this case, alternative control tech-niques, such as circumferential strain control or com-puted feed-back control, have been shown to greatlyimprove the experimental procedure for obtaining thecomplete force-displacement information.

1.4 A complete stress±strain curve for rock is shownby the thick curve in Fig. 1. The prepeak portion isthe region OA. Wawersik [4] identi®ed two types ofcurve in terms of the characteristic of the postpeakregion: either the curve monotonically increases instrain or it does not. The former, the thick curve inFig. 1, is termed a class I curve; the latter, the thinnercurve in Fig. 1, is termed a class II curve. It is import-ant to understand these two types of curve in order tooptimize the control of rock failure [3,5]. Cylindricalspecimens that exhibit class I behavior tend to besomewhat ductile in nature when loaded axially;whereas specimens that exhibit class II behavior tendto respond in a brittle fashion to axial loading. A testconducted in axial strain control is generally su�cientto obtain the complete force-displacement curve ofspecimens exhibiting class I behavior. Alternative con-trol techniques are necessary when testing specimensthat exhibit class II behavior because the curve does

not monotonically increase in strain, and the shadedarea ABDCA is the surplus energy which would besupplied by a rigid machine with in®nite modulus,AD, or a servo-controlled machine with axial straincontrol, leading to uncontrolled failure.

1.5 The draft suggested method (SM) provided heredescribes recommended testing and control procedures,loading system hardware and specimen parameters forconducting laboratory tests on intact cylindrical rockspecimens for which complete force-displacement dataare desired. This SM complements the earlier ISRMSMs for determining the uniaxial compressive strengthand deformability of rock materials [6], and for deter-mining the strength of rock materials in triaxial com-pression [7]. It is hoped that the current SM, advisingon the complete force-displacement behavior of rockspecimens will allow comparison of data between ma-terials, laboratories and researchers, and contribute toa better understanding of rock failure.

2. Scope

2.1 The test methods described suggest methods forobtaining pre- and postpeak force-displacement (orstress-strain) data when testing rock specimens ofcylindrical geometry uniaxially loaded in compression(see Fig. 1).

2.2 The SM is intended for the characterization ofintact rock. However, certain extremely brittle speci-mens, even under the most favorable testing conditions(e.g. sti� testing frame, slow loading rate, circumferen-tial strain feed-back, low length/diameter ratio), mayfail abruptly or even explosively when tested withoutcon®nement. It is suggested that these specimens maynot be conducive to postpeak testing in a uniaxialmode, and should be tested in a con®ned state.

3. Apparatus

3.1 In the context of obtaining complete force-dis-placement data for rock specimens, a number of hard-ware elements can be optimized, as described below.

Loading system

3.2 When non-servo-controlled machines were usedin the 1960s to obtain the complete stress±strain curvefor rock, a high machine sti�ness was essential forcontrol. With a servo-controlled system, however, ahigh machine sti�ness is not essential, but it doesallow a faster response time and hence is preferablewith brittle rocks. A servo-controlled hydraulic testingmachine should preferably be used to axially load thespecimen. Loading frames with sti�nesses greater than

Fig. 1. Classi®cation of class I and class II behavior of rock failure

in uniaxial compression [4].

C.E. Fairhurst, J.A. Hudson / International Journal of Rock Mechanics and Mining Sciences 36 (1999) 279±289282

5 MN/mm are commonly available and are rec-ommended. The sti�ness of the entire load train (i.e.load frame, platens, spacers, load cell, etc.) should alsobe maximized. Replacing an in-line load cell (which bydesign is `soft') with a steel spacer, and measuringaxial load by an alternative method such as a di�eren-tial pressure transducer, will increase load train sti�-ness, but may compromise force readout accuracy,especially at relatively low loads. Moving the loadingpiston (or actuator) to the most retracted positionprior to testing also increases load train sti�ness byreducing the hydraulic ¯uid `spring' under the piston.The load frame capacity should exceed the estimate ofthe strongest specimen to be tested. The calibrations ofthe load frame transducers should be veri®ed at suit-able time intervals and should comply with acceptednational requirements such as prescribed in eitherASTM methods E4: veri®cation of testing machines orBritish standard 1610, grade A.

Hydraulics

3.3 A close-coupled hydraulic manifold (i.e.mounted to or located as close as possible to the load-ing piston) is recommended to minimize the response

time of hydraulic commands to the loading piston (seeFig. 2).

3.4 The hydraulic manifold should be ®tted with in-line accumulators (see Fig. 2). Accumulators providethe hydraulic ¯ow required for fast, short duration,movement of the piston, which is frequently necessaryto control the failure rate of brittle specimens.

3.5 A high-speed, high-frequency response servo-valve should be used to reduce servovalve spool open-ing time and improve system response time.

Spherically seated platen and specimen platen

3.6 A spherically seated upper loading platen shouldbe used, which reduces the e�ect of specimen non-par-allelism on test results. The radius of the spherical pla-ten should be equal to or greater than the specimenradius, and the center point of the spherical seatshould coincide with the top surface of the specimeneven if an intermediate platen is used. The matingspherical surfaces should not be lubricated, since thespherical joint is intended only to accommodate initialspecimen alignment, and is not expected to move orrotate during testing. (If necessary, a thin ®lm of min-eral oil is acceptable to reduce corrosion). The radial

Fig. 2. Example of servo-controlled, closed-loop testing system.


Fig. 3. Example of simultaneous mounting of one circumferential and two axial extensometers.


center of the spherical surface should coincide with thecenter of the top end of the specimen, to within 1 mm.

3.7 Specimen platens in the form of discs and havinga Rockwell hardness of not less than Rc 58 should beplaced at the specimen ends. The diameter of the pla-tens shall be between D and D+2 mm, where D is thediameter of the specimen. The thickness of the platensshall be at least 15 mm or D/3 (whichever is greater).Surfaces of the disc platens should be ground andtheir ¯atness should be better than 0.005 mm.

3.8 The specimen, the platens and the spherical seatshall be accurately centered with respect to oneanother and to the loading machine. Etched circles onthe lower platen are recommended to facilitate speci-men centering. Specimen platens with machined center-ing grooves should not be used, because the groovescan restrict lateral displacement of the specimen duringthe test.

Control system

3.9 A closed-loop, servo-hydraulic, control system,capable of operation in axial force, axial strain andradial strain control should be used (see Fig. 2).Control systems with high loop-closure rates (1 kHz orgreater, real-time) are recommended, as are controlsystems that allow closed-loop control based on acomputed feedback signal [8,9].

Strain measurement transducers

3.10 Measurement of axial and circumferential ordiametrical displacement by means of direct contactextensometers is recommended. Both axial and circum-ferential strains shall be determined within an accuracyof 1% of the reading and a precision of 0.2% of fullscale. The overall possible physical travel of the extens-ometers should exceed the maximum expected speci-men displacements. Two axial extensometers arerecommended and should be attached to the specimen1808 apart, and contact the specimen at approximately25 and 75% of the axial dimension (see Fig. 3). Theoutput of the two extensometers should be acquiredseparately, but averaged for the test report. If axialmeasurement is made between the upper and lowerplatens, care should be taken to determine and correctfor any platen de¯ection. The circumferential or dia-metrical extensometer should be located at the speci-men mid-height. Pay particular attention to datareduction for the circumferential transducer where thetransducer is measuring a change in chord lengthrather than a direct change in circumference. Electricalresistance strain gauges, linear variable di�erentialtransformers (LVDTs), or other suitable measuringdevices can also be used to measure axial and lateral

specimen strain. The devices should be robust andstable, with strain sensitivity of the order of 5�10ÿ6.3.11 If electrical resistance strain gauges are used,

the length of the gauges over which axial and circum-ferential strains are determined shall be at least tengrain diameters (of the rock microstructure) in magni-tude and the gauges should not encroach within D/2of the specimen ends, where D is the diameter of thespecimen.

3.12 If LVDTs are used for measuring axial and lat-eral displacement due to loading, these devices shouldbe accurate to within 0.002 mm in any 0.02 mm rangeand within 0.005 mm in any 0.25 mm range. It may bemore di�cult to control a complete force-displacementtest on a specimen that exhibits class II behavior usingconventional LVDTs, due to the inherent time delayof LVDTs and alternating current conditioning elec-tronics, which can have a detrimental e�ect on thecontrol loop closure rate. If di�culty is experienced, itis recommended that digital transducers be used. TheLVDTs should not encroach within D/2 of the speci-men ends.

3.13 With some strain measurement transducers, itmay be useful to surround the specimen with a ¯exiblemembrane in order to prevent spalling chips of rockfrom interfering with the transducers. If such a mem-brane is used, ensure that the membrane does notover-constrain the lateral expansion of the specimen.Also, e�ects of the membrane-specimen interfaceshould be considered.

Data acquisition

3.14 A personal computer system for acquiring andstoring data should be used. Data should be acquiredas frequently as once/second, or as a function ofchange in force or change in axial or radial displace-ment.

4. Specimen preparation

4.1 Test specimens shall be right circular cylindershaving a height-to-diameter ratio of between 2.0 and3.0 and a diameter preferably of not less than approxi-mately 50 mm. The diameter of the specimen shall beat least 20 times the largest grain in the rock micro-structure.

4.2 The ends of the specimen shall be ¯at to 20.01mm and shall not depart from the perpendicular to thelongitudinal axis of the specimen by more than 0.001rad (about 3.5 mm) or 0.05 in 50 mm.

4.3 The sides of the specimen shall be smooth andstraight to within 0.3 mm over the full length of thespecimen.


4.4 The use of capping materials or end surfacetreatments other than machining is not permitted.

4.5 The diameter of the test specimen shall bemeasured to the nearest 0.1 mm by averaging two di-ameters measured at right angles to each other close tothe top, the mid-height and the bottom of the speci-men. The average diameter shall be used for calculat-ing the cross-sectional area. The height of thespecimen shall be determined to the nearest 1.0 mm.

4.6 Specimens shall be stored for no longer than 30days, and in such a way as to preserve, as much aspossible, the natural water content. The moisture con-dition shall be reported in accordance with ISRM SMfor determination of the water content of a rocksample [10].

4.7 The number of specimens tested under a speci-®ed set of conditions should be su�cient to adequatelyrepresent the rock sample, and should be a function ofthe intrinsic variability of the rock. A minimum of ®vespecimens per set of testing conditions is rec-ommended.

5. Procedure

5.1 Personnel conducting the tests should be su�-ciently trained in the use of servo-hydraulic testing sys-tems, closed-loop control concepts and brittle rocktesting, so that testing is performed safely.

5.2 Attach the strain or displacement measurementtransducers to the specimen and install the assemblyonto the lower platen in the load frame.

5.3 Apply a small preload to the specimen in forcecontrol. This helps `seat' the specimen to the loadingplatens and the upper loading platen to the sphericallyseated platen. When applying preload to the specimen,the system should be in force control (i.e. using theoutput of the axial force cell as feedback). Since rockhas a relatively high modulus, applying preload inaxial strain control is not recommended, because asmall amount of axial strain could correspond to anaxial force above the maximum load bearing capacityof the specimen. Also, it should be noted that, if usinga di�erential pressure transducer in place of a load cellfor force measurement and control, applying small pre-loads is di�cult due to the piston friction at low loads.

Specimens that generally exhibit ductile behavior(gentle, large strain failure behavior)

5.4 Switch the control mode to axial strain control,and load the specimen at an axial strain rate of 0.001mm/mm/s. until reaching approximately 70% ofexpected peak force. At 70% of peak force, switch theaxial strain rate to 0.000001 mm/mm/s until theapplied force falls to 50% of peak force. Then switch

the axial strain rate to 0.001 mm/mm/s until a com-plete force-displacement curve is obtained. The force-displacement curve can be considered to be completein the testing context when the load carrying capacityof the specimen declines to less than approximately30±40% of peak load carrying capacity.

Specimens that generally exhibit brittle behavior(severe, small strain failure behavior)

5.5 Switch the control mode to axial strain control,and load the specimen at an axial strain rate of 0.001mm/mm/s. until reaching approximately 70% ofexpected peak force. At 70% of peak force, switch thecontrol mode to circumferential control, at a rate of0.0001 mm/mm/s, until the applied force falls to 50%of peak force. Then switch back to an axial strain rateof 0.001 mm/mm/s until a complete force-displacementcurve is obtained. If the test is unsuccessful due toabrupt specimen failure, alternative control modes maybe considered, such as a computed channel feedbackloop [8,9].

5.6 Force and axial and circumferential strains ordisplacements shall be recorded at a frequency of 1Hz.

6. Calculations

6.1 The force will be obtained from the built-in loadcell information. Axial strain and diametric strain maybe recorded directly from strain indicating equipmentor may be calculated from displacement readingsdepending upon the type of instrumentation used.

6.2 The compressive stress, s, is calculated as,

s � P=A0,

where, P is the compressive force on the specimen, andA0 is the initial cross-sectional area, and in this testprocedure, compressive stresses and strains are con-sidered positive.

6.3 Axial strain, ea, is calculated as

ea � Dl=l0,

where Dl is the change in measured axial length (posi-tive for a decrease in axial length) and l0 the axiallength of specimen prior to loading.

6.4 Diametric strain is determined either by measur-ing the changes in specimen diameter or by measuringthe circumferential strain. In the case of measuring thechanges in diameter, the diametric strain, ed, is calcu-lated as

ed � Dd=d0,

where Dd is the change in diameter (negative for an


increase in diameter) and d0 the diameter of the speci-men prior to loading.

In the case of measuring the circumferential strained, the circumference is C=pd, and so the change incircumference is DC=pDd. The circumferential strain,ec, is

ec � DC=Co � DC=pd0,

where Co is the original specimen circumference.The circumferential strain, ec, is therefore equal to

the diametric strain, ed, because

ec � DC=pd0 � pDd=pd0 � Dd=d0 � ed:

6.5 The Young's modulus, E, of the rock is de®nedas the ratio of the change in axial stress to the changein axial strain Ð as caused by the axial strain.Young's modulus is usually associated with the pre-peak portion of the complete stress±strain curve, but itcan also be determined in the postpeak region. In theprepeak and postpeak regions, the modulus may be

calculated using any one of several methods employed

in accepted engineering practice, as described below.

In the postpeak region, the specimen has to be

unloaded from any postpeak location, and then

reloaded to generate a further subsidiary complete

stress±strain curve (see Fig. 4). The Young's modulus

is then the positive slope of the ascending portion of

this new curve, and is not the slope of the original

stress±strain curve at the postpeak location (where the

slope is generally negative).

The most common methods of establishing the

Young's modulus value are as follows:

1. Tangent Young's modulus, Et, is measured at a

stress level which is some ®xed percentage of ulti-

mate strength. It is generally taken at a stress level

equal to 50% of the uniaxial compressive strength.

The compressive strength is the peak stress sus-

tained by the specimen.

2. Average Young's modulus, Eav, is determined from

Fig. 4. Complete stress±strain curve for a rock specimen showing the prepeak Young's modulus, compressive strength and postpeak Young's

modulus.


the average slopes of the more-or-less straight lineportion of the axial stress±axial strain curve.

3. Secant Young's modulus, Es, is usually measuredfrom zero stress to some ®xed percentage of thecompressive strength, generally at 50%.

Axial Young's modulus E is expressed in units ofstress, i.e. Pascal (Pa) but the most appropriate mul-tiple unit is the gigapascal (GPa=109 Pa).

6.6 Poisson's ratio, n, is calculated as

n � ÿ�slope of axial stressÿ strain curve=slope of

diametric stress±strain curve�,

n � ÿE=�slope of diametric curve�,where the slope of the diametric curve is calculated inthe same manner for either of the three ways discussedfor Young's modulus above. Note that Poisson's ratioin this equation has a positive value, since the slope ofthe diametric curve is negative by the conventions usedin this procedure.

6.7 The volumetric strain, ev, for a given stress level,is

ev � ea � 2ec:

7. Reporting of results

The testing report should include the following.

Rock sample information (note that the term`sample' refers to the block of rock obtained in thesite investigation; the term `specimen' refers to thespeci®c piece of rock prepared and tested).

(a) A lithologic description of the rock, includinggrain size.(b) Orientation of the axis of loading with respectto rock anisotropy, e.g. bedding planes, foliation.(c) Source of the sample, including: geographiclocation, depth and orientations, dates andmethod of sampling, storage history and environ-ment.(d) Number of specimens obtained from a givenrock sample.

Specimen information (for each specimen tested)(e) Specimen diameter and height.(f) Water content and degree of saturation of thespecimen at the time of testing.(g) Date of testing and test duration.(h) Values of applied force, stress and strain astabulated results or as recorded on a chart.(i) Prepeak Young's modulus and Poisson's ratio,expressed to three signi®cant ®gures.

(j) A plot of the complete force-displacementcurve, indicating the location of the peak force.(k) Mode of failure: axial splitting or shearfailure.(l) Any other observation or available physicaldata such as speci®c gravity, porosity and per-meability, citing the method of determination foreach.

General information(m) Number of specimens tested.(n) Description of testing machine type.(o) Method of determination of prepeak Young'smodulus and at what axial stress level or strainlevel determined.(p) Method of determination of postpeakYoung's modulus and at what axial stress levelor strain level determined.(q) Average result (if appropriate) of prepeakYoung's modulus and Poisson's ratio, expressedto three signi®cant ®gures for all specimens inthe sample.

Should it be necessary in some instances to test spe-cimens that do not comply with the above speci®ca-tions, these facts shall be noted in the test report.

8. Additional interpretative comments

8.1 It is helpful to have a good conceptual under-standing of the complete stress±strain curve when con-ducting the tests. This understanding should be basedon the control variable.

8.2 Axial force cannot be used as the control vari-able to obtain the complete stress±strain curve. If theaxial force is programmed to linearly increase withtime, the inevitable result is uncontrolled failure at thecompressive strength when the machine attempts toincrease the force on the rock specimen Ð which can-not sustain more force.

8.3 Axial displacement is the most widely used con-trol variable. This means that axial displacement is theindependent (or control) variable and axial force is thedependent (or response) variable. Note that when theforce and displacement are scaled to nominal stressand strain as described in this Suggested Method, thestress±strain curve is plotted with the independentvalue on the x-axis and the dependent variable on they-axis, as is conventional in science.

8.4 If, however, the complete force-displacementcurve does not monotonically increase in axial displa-cement (the class II curve in Fig. 1), then axial displa-cement is not suitable as the control variable. Oftencircumferential displacement has been used becausethis does monotonically increase even if the axial dis-placement does not. In this latter case, the circumfer-


ential displacement is the independent (or control)variable, and both the axial force and axial displace-ment are dependent (or response) variables.

8.5 In fact, the choice of control variable is wide.For example, the control variable could be the energybeing input to the specimen or the rate of acousticemission, and others are possible. We have concen-trated here on the `conventional' methods of obtainingthe complete stress±strain curve.

8.6 There has been debate over the years concerningthe validity of the scaled force-displacement curve as atrue stress±strain curve. This relates to the stress beingdetermined through scaling the force by the originalarea, rather than by a continuously reducing area asthe rock is progressively fractured. It has beensuggested that the true stress±strain curve is elastic-plastic, i.e. an ascending portion followed by a con-stant stress portion. This debate is beyond the scope ofthe SM. However, the `engineering' complete stress±strain curve as determined by the method describedhere will always be useful because it represents thestructural collapse of a specimen of rock, and, apartfrom size and scale e�ects, describes the potentialbehavior of a similar block of rock in the ®eld.

Acknowledgements

The authors are grateful to F.A. Bezat (USA) forhelp provided during the preparation of this suggestedmethod draft.

References

[1] Cook NGW. The failure of rock. Int J Rock Mech Min Sci

1965;2(4):389±404.

[2] Cook NGW, Hojem JPM. A rigid 50-ton compression and ten-

sion testing machine. S Afr Mech Eng 1966;16:89±92.

[3] Hudson JA, Crouch SL, Fairhurst C. Soft, sti� and servo con-

trolled testing machines: a review with reference to rock failure.

Eng Geology 1972:155±87.

[4] Wawersik WR. Detailed analysis of rock failure in laboratory

compression tests. Ph.D. thesis, University of Minnesota, 1968.

p. 165.

[5] Hudson JA, Brown ET, Fairhurst C. Optimizing the control of

rock failure in servo-controlled laboratory tests. Rock Mech

1971;3:217±24.

[6] Brown ET. Suggested methods for determining the uniaxial

compressive strength and deformability of rock materials. In:

Brown ET, editor. Rock characterization, testing and monitor-

ing Ð ISRM suggested methods. Oxford: Pergamon Press,

1981. p. 113±6.

[7] Brown ET. Suggested methods for determining the strength of

rock materials in triaxial compression. In: Brown ET, editor.

Rock characterization, testing and monitoring Ð ISRM

suggested methods. Oxford: Pergamon Press, 1981. p. 125±7.

[8] Okubo S, Nishimatsu Y. Uniaxial compression testing using a

linear combination of stress and strain as the control variable.

Int J Rock Mech Min Sci Geomech Abstr 1985;22:323±30.

[9] Okubo S, Nishimatsu Y, He C. Technical note: loading rate

dependence of class II rock behavior in uniaxial and triaxial

compression tests: an application of a proposed new control

method. Int J Rock Mech Min Sci Geomech Abstr

1990;27:559±62.

[10] Brown ET. Suggested methods for determining water content,

porosity, density, absorption and related properties and swelling

and slake-durability index properties. In: Brown ET, editor.

Rock characterization, testing and monitoring Ð ISRM

suggested methods. Oxford: Pergamon Press, 1981. p. 81±94.


Complete Stress-Strain Curve 1999

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