1 Numerical Simulation of Rock Strength Testing

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NUMERICAL SIMULATION OF ROCK STRENGTH TESTING

A. J. BasuM. D. KuruppuWestern Australian School of MinesKalgoorlie, WA, Australia

For presentation at the SME Annual MeetingDenver, Colorado - February 24-27,1997Permission is hereby given to publish with appropriate acknowledgments. excerpts orsummaries not to exceed one-fourth of the entire text of the paper. Permission to print In moreextended form subsequent to publication by the Society for Mining. Metallurgy. and Exploration(SME). Inc. must be obtained from the Executive Director of the Society.If and when this paper is published by the SME. it may embody certain changes made byagreement between the Technical Publications Committee and the author so that the form inwhich it appears is not necessarily that in which it may be published later.Current year preprints are available for sale from the SME. Preprints. P.O. Box 625002.Littleton. CO 80162-5002 (303-973-9550). Prior year preprints may be obtained from the LindaHall Library. 5109 Cherry Street. Kansas City. MO 64110-2498 (8oo}662-1545.

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Abstract. Rock mass properties testing for determiningstrength parameters is an integral part of geomechanics.These tests are performed either in a laboratoryenvironment or in a field (in-situ). The authors share theirexperience in using numerical modelling in simulating thelaboratory test procedures. This approach helps studyingthe rock breakage and failure mechanism more efficientlyand provides a high degree of visualisation. Moreover,imperfections and discontinuities can be easily incorporatedin these models. This capability of providing arbitraryfractures and discontinuities facilitates in building a largeknowledgebase of rock strength and failure mechanisms.This knowledgebase may then be used to generateheuristics for determining rock strengths for rock masswith fractures and discontinuities.

Introduction And BackgroundNumerical simulation for rock strength determinationprovides a non destructive testing mode. The currentobjective is to develop a significant understanding ofmechanism of rock behaviour during its failure whileperforming standard laboratory testing for rock strengthdeterminations (Brown, 1981). Numerical simulation ofthe standard laboratory test procedures also helps inunderstanding the progressive failure mechanism.Moreover, the graphical interface and animation features ofthe finite element analysis software ANSYS (Basu andKuruppu, 1996) helps in visualising the failure mechanisms.

The research work by the authors has just started andprogress is relatively slow as there is no funding availablefor this work (authors priorities are currently with theexisting funded research projects). The authors expect thatthe research outcome in the proposed area will be theavailability of a tool to perform nondestructive testing toanalyse and determine rock strength parameters. A largenumber of rock testing scenarios including cracks,discontinuities can also be modelled very easily.Moreover, cost of expensive sample preparation can beavoided.

Numerical ModelThere are standard procedures available for rock

properties testing in a laboratory set up (Brown, 1981).These procedures provide testing guidelines and reportingprocedures. This paper does not include listing of theseprocedures. The presentation here is of demonstrativenature. The authors picked Indirect Tensile Testing(Brazilian Test) for modeling and analysing numerically.The obvious reason is in the simplicity in modeling.Therefore, the results obtained were analysed faster andalso checked by standard calculation. Moreover, a fracturemechanics test model was also developed and its resultswere derived using a hybrid finite element analysis andexperimental procedure.

1Model for Indirect Tensile Test

The tool used for this numerical simulation was a finiteelement analysis software ANSYS. The software selectionand features of ANSYS were addressed by the authorsearlier (Basu and Kuruppu, 1996). Figure 1 shows thetensile stress in the model after applying a point load of30 Kn. The maximum stress is approximately 10 Mpawhich is very close to the value obtained from laboratorytesting......n'!io.;JOCT 1 1 " 616: l l : f t' loOTIO. 1IIOOALIOt1l"TICI11' ' '=1lUI '"1fl"'-l"

Figure 1. Tensile stress distribution (Mpa) in the model.Please note that the solution method used was simplistic.The loading rate was not modelled. It was assumed that theentire load was applied at once. A more realistic solutionstep following the prescribed testing will be carried out infuture. Moreover, by incorporating a parametric languagemacro the progressive failure may be modelled. TheANSYS software has a birth and death feature (for

elements) available and it will be used to model theprogressive failure. The process will be written such thatall the elements exceeding certain stress level, (e.g., 9 Mpa)will be inactive and the model would assume a crack inplace of those elements exceeding the prescribed level andsolution will be continued and the process will be repeated.The authors are currently engaged in modeling thesefeatures and i f possible will be presented at the meeting.Figure 2 shows shear stress distribution (Mpa). Thepoints under applied loading and restraints experience highshear stress and it also confirms our existing knowledge

that we observe shear failure close to these points.


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Figure 2. Shear stress distribution (Mpa) in the model.Model for Fracture Toughness TestRock fracture mechanics deals with the crack initiation

and propagation in rock subjected to various types ofloading. Most rock are weak in tension and therefore thecrack opening mode of fracture is quite significant.Fracture toughness is a material property which is relatedto the critical level of he stress intensity factor, KI , in thecrack opening mode. It is used as a parameter forclassification of rock material, an index of fragmentationprocesses such as rock cutting and blasting, and as amaterial property in the modelling of rock fragmentationlike rock cutting, hydraulic fracturing and crater blasting(ISRM, 1988).Figure 3 shows finite element analysis model of the semicircular bend (SCB) test specimen (suggested by Chong

and Kuruppu, 1984) showing tensile stress distribution. ASCB test specimen was also used in laboratory fordetermining the fracture toughness of rock. InternationalSociety for Rock Mechanics (lSRM) committee on testingmethods has suggested methods for determining thefracture toughness of rock using the chevron bendspecimen (ISRM, 1988 and Ouchterlony, 1980) and theshort rod specimen (Barker, 1977). The SCB specimen is acore based, compact specimen which is tested under threepoint bending.

Figure 3. Tensile stress distribution in Semi-Circular Bend(SCB) test model.

2It is complimentary to other suggested methods and is

useful for the complete characterisation of transverselyisotropic, sedimentary rock such as oil shale due to thenecessity to determine the properties in orthogonaldirections using more than one specimen. It is particularlygood from the point of view of nonlinearity as compared tomany other specimens.The SCB specimen is analysed using the finite elementmethod to determine the elastic stress intensity factors. Thespecimen with straight crack through the thickness ismodelled using PLANE82 two-dimensional eight-nodedelements in ANSYS. One half of the specimen is modelledby taking advantage of the symmetry. Crack-tip singularityis represented using quarter-point isoparametric elementsaround the crack tip (Barsoum, 1976). ANSYS providesspecial routines named KSCON and KCALC for suchanalysis. Figure 4 shows non-dimensional stress intensityfactor versus crack length resulting from a number of finiteelement analyses. Fracture toughness can be roughlyevaluated based on the maximum load achieved duringtesting and the non-dimensional stress intensity factorshown in Figure 4 and the experimentally determinedfracture load are used to calculate the fracture toughness,K1C. A more precise determination requires the continuousmeasurement of both the load and the displacement(Ouchterlony, 1980). Table 1 gives the results of a recentstudy (Ngo, 1996) on the determination of he fracturetoughness of some commonly found rock types in theGoldfields region ofWestern Australia. These resultsrequire to be verified using the othe r ISRM suggestedmethods. However, they agree with some of he previousresults when the variation due to local inhomogeneities aretaken in to account (lSRM, 1988).

KI


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3Table 1. Fracture toughness (laboratory testing results) oflocal rock samples.Rock typeQuartz-feldsparporphyryHigh magnesiumbasaltUltramafic schistDolerite

Future Research Plan, Methods AndTechniques

The parameter most widely used in engineering design isUniaxial Compressive Strength (UCS). The UCS is oftenquoted as a major design parameter in mining and civilengineering. The other tests used for strength prediction ofa rock mass are direct and indirect tensile tests, direct shearand triaxial tests. Numerical models of the standardlaboratory procedures for detennining rock strengthparameters (e.g., uniaxial compressive testing, indirect anddirect tensile testing, direct shear and triaxial testing) willbe built.A numerical model of the stiff testing instrument may alsobe created to help simulate the laboratory testingprocedure. Loading will be applied at the specified ratesfor each testing procedure. A parallel set oflaboratorytests will also be carried out and the results will be used tovalidate the numerical models.The initial numerical models will be free from anyimperfections. Progressive failure mechanism underloading will be studied. A visual record can also be madeusing the animation feature ofthe numerical analysis toolANSYS. The models will then be modified to containcracks and discontinuities and results will be obtained forthese models. These results can then be compared with theearlier results with ideal conditions. This comparison willfacilitate to quantity a scaling factor for converting strengthparameters for intact rock sample to its corresponding in-situ condition.

ConclusionsThe mechanical behaviour of rocks during progressivefailure plays a predominant role in the geotechnical design.Laboratory testing ofrock mass samples is the onlyavailable practice to predict the rock strength properties.This practice is not always adequate to model in-situcondition and may prove very expensive. Currently rockstrength parameters obtained from standard laboratorytesting procedures are scaled down for use in design (totake care of in-situ conditions, cracks, and discontinuities)using a scaling factor (Cunha, 1990). This scaling factor isarbitrary and has no supporting analysis. Numerical

analysis will allow creating an ideal sample as well as

K1C (MN/m312)1.44 0.081.61 0.100.68 + 0.121.75+0.13

sample with imperfections. The results from these analysiswill lead to establish design guidelines in using a scalingfactor for adjustment to in-situ strength parameters.Moreover, a numerical model for a rock properties testingprocedure may help in increasing confidence on the initialresults obtained from a standard laboratory test.

AcknowledgmentsThe software has been leased through the funding by theWASM Education Fund. The authors also acknowledgethe technical support and help provided by Mr. JosephCorvetti of Worley Limited.

ReferencesBarker, L. M., 1977, "A Simplified Method for MeasuringPlane Strain Fracture Toughness", Eng. Fracture Mech.,

Vol. 9, pp. 361-369.Barsoum, R. S., 1976, "On the Use ofIsoparametric FiniteElements in Linear Fracture Mechanics", Int. J. forNum. Meths. in Engrg., Vol. 10, pp 25-37.Basu, A. J. and Kuruppu, M., 1996, "Numerical Modellingin Mining Geomechanics", SME Annual Meeting,March, Phoenix, AZ, USA.Brown, E. T. (ed.), 1981, Rock Characterisation Testingand Monitoring - ISRM Suggested Methods.Pergamon Press, Oxford.Chong, K. P. and Kuruppu, M. D., 1984, "New Specimenfor Fracture Toughness Detennination ofRock andOther Materials", lnt. J. Fracture, Vol. 26, pp.R59-R62.Cunha, A.P., 1990, "Scale Effects in Rock Mechanics",Proceedings, Conference on Scale Effects in RockMasses, Balkema.ISRM, 1988, " Suggested Methods for Detennining theFracture Toughness ofRock", F. Ouchterlony, ed.,Int. J. Rock Mech. Min. Sci. & Geomech. Abstr.,

Vol. 25, pp 71-96.


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Ngo, B.T., 1996, "Mode I Fracture ToughnessDetennination ofRockMaterials using SCBSpecimen", Projec t Thesis, WA School ofMines,Cutin Univ., Western Australia.

OuchterIony, F., 1980, "A New Core Specimen for theFracture Toughness Testing ofRock", SwedishDetonic Research Foundation, SveDefo Report DS1980: 17, Stockholm.

Lim, 1. L., Johnson, 1. W., Choi, S. K., and Boland, 1. N.,1994, "Fracture Testing of a Soft Rock with SemiCircular Specimens under Three Point Bending. Pa rt 1-Mode I ", Int. Journal of Rock Mechanics, MiningScience and Geomechanics Absstr., Vol. 31,pp 185-197.

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1 Numerical Simulation of Rock Strength Testing

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