A Methodology to Determine in Situ Rock Mass Failure

7/28/2019 A Methodology to Determine in Situ Rock Mass Failure

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i) SOCIETY FORR G Y A N Q ~ i 'MINING, METALLURGY,

AND EXPLORATION, INC.P.O. BOX 625002 LITTLETON, COLORADO 80162-5002

PREPRINTNUMBER

95-41

A METHODOLOGY TO DETERMINE IN SITU ROCK MASS FAILURE

K.Y. HaramyB.T. Brady

US Bureau of MinesDenver, CO

For presentation at the SME Annual MeetingDenver, Colorado - March 6-9, 1995Permission is hereby given to publish with appropriate acknowledgments, excerpts or

summaries 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 theEngineering Societies Library, 345 East 47th Street, New York, NY 10017 (212-705-7611).PREPRINT AVAILABILITY LIST IS PUBLISHED PERIODICALLY INMINING ENGINEERING


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ABSTRACT: A scale-invariant theory of the strength.and deformability of rock masses in static equilibriumand at incipient failure is proposed. The theory providesa rationale for designing structures in rock. This paperpresents results of experiments conducted by the U.S.Bureau of Mines and theoretical methods to determineand interpret in situ strength of rock masses using theborehole shear tester.

INTRODUCTIONAccurate determination of in situ rock strength isrequired for successful design of underground structures.Rock mechanics properties, such as strength anddeformability, are commonly determined from laboratorytriaxial compression tests (TCT) or direct shear tests oncore samples and from in situ measurements using theborehole shear tester (BST). Interpretation of therelationship between these two tests is at best ambiguous.This U.S. Bureau of Mines (USBM) publication presents

recent advancements in material failure criteria thatremove this ambiguity.Rock is distinct from other engineering materials, suchas concrete and metal. When dealing with reinforcedconcrete structures, the design engineer calculates theapplied loads to a specific strength required. Theoptimal geometry can then be determined with a highdegree of confidence. This is not the case whendesigning underground structures. Here, the appliedloads are not well defined and may vary significantlywith mining. Additionally, the stability of anunderground structure is highly dependent upon the rockmass physical properties and the geological conditions

within the rock mass. Except in rare instances, none ofthese requirements in rock are known with any degree ofconfidence. Successful design of engineering structuresin rock requires realistic mathematical models of rockmass strength and deformability.Developing realistic failure criteria for rock massesand methods to measure and interpret the stresses atfailure are difficult. The rock mass may range fromsmall intact segments to large heavily jointed segments,each of which can possess a different failure criterion.The design engineer must be concerned with all sizescales in this transition. The stability of rock in theimmediate vicinity of underground openings and the

behavior of rock bolts or other support structures arerelated to existing discontinuities and to fractures.Hence, structural stability depends upon the deformationand strength characteristics of the entire rock masssurrounding the excavation.The interrelations involved in determining the behavior

of rock surrounding an excavation or group ofexcavations are often so complex that they are notamenable to exact engineering analysis. In these cases,design decisions may have to consider previousexperience. To quantify this experience so that it may be

1extrapolated from one site to another, a number ofclas.sification schemes for rock masses have beendeveloped. These would include the rock mass rating(RMR) scheme developed by Bieniawski [l ] and the NGItunnelling quality index of Barton, et al. [2]. Theseclassification schemes seek to assign numerical values toproperties such as strength and deformability or featuresof the rock mass considered likely to influence itsbehavior and to combine these values into an overallrating for the rock mass. Rating values for the rockmass are determined and correlated with observed rockmass behavior. Hoek and Brown [3,4,5] and others havedeveloped empirical methods to use these techniques fordesigning excavations with considerable success.However, the development of rational techniques basedon physical behavior of rock remains elusive, and thegeneral applicability of empirical design procedures todesign in geotechnical materials is unknown.

Recently a scale-invariant theory of the strength anddeformability of a rock mass in static equilibrium andnear incipient failure has been proposed by the USBM.This model provides a rationale for designing structuresin rock. In this paper, this theory is applied tointerpreting in situ BST and laboratory TCT data todetermine the rock mass failure criteria. Failure criteriaare determined and compared for various rock types insitu using the BST data and in the laboratory using theconventional TCT data. The application of criticalphenomena physics to fracture has shown that at failure(neglecting time-dependent effects of fracture), rockswith a wide range of strengths satisfy the followingequation:

where 't and (J are the shear and normal stress along thefailure plane, to is the tensile strength of the rock mass(tension is positive), 213 is a universal constant equal to0.684 small correctional terms, and A is a materialconstant. Average values for A determined from BSTand TCT reported in this paper are approximately 2.466and 3.018, respectively; values are comparable to Adetermined using Hoek and Brown material constants forfailure of undisturbed and disturbed rock masses [3].

UNIVERSALITY OF ROCK MASS STRENGTHAT INCIPIENT FAILURE

Rational structural design in rock is based on rockmass behavior at incipient brittle failure. Application ofa reasonable safety factor, that is, design the structure tofail and then backing off, to the design provides a safeworking environment. This observation provides therationale for solving the scale problem in geotechnicalengineering.Based on extensive experimental evidence (6), brittlefracture or structural failure will be modeled as a three-


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phase system that includes solid material, microcracksUoints, faults) in the solid matrix, and finally, themacro crack that represents the final stage of the fractureprocess. The macrocrack denotes coalescence of themicrocracks. Formation of the macrocrack and itsgrowth leads to fault formation. In this article, brittlefracture is formulated as a continuous phase change thatexhibits the characteristics of a thermodynamic system atits critical point (7). The phase transition ischaracterized by separation of the solid into two pieces.In general, each microcrack that forms in the solid matrixlocally breaks the translational and rotational symmetryof the system (solid), and if each microcrack is a phasechange, then one must view the fracture problem as atrue polycritical or N-critical system and the local tensilestress at which a given microcrack forms as the criticalpoint for that microcrack. Ordinary and tricritical pointsare the simplest cases of polycritical points. However,for ease of argument, we shall assume all microcrackscan be grouped into one classification class. Thus, thesystem we -shall deal with is the tricritical system. Inthis context, the application of a shearing stress (strain)to an otherwise undistorted lattice can be viewed asbreaking the original symmetry of the lattice. For thetricritical system, this breaking of a symmetry ismeasured by a quantity called an order parameter. Inthis paper, the order parameter will be chosen to be theshear stress.

A scale-invariant theory of the strength anddeformability of a rock mass in static equilibrium andnear incipient failure has been developed by the USBM(7). In this theory, brittle fracture of geotechnicalmaterials is shown to be treatable as a generalized phasechange occurring within the rock mass. Here theformation of a fracture in a material is taken to be of aphase change, in this case from a solid phase to a voidphase. The following equations are found to exhibit allthe characteristics of a thermodynamic system near itscritical point. Here the tensile strength, to' of the rockmass and the normal stress at failure, a, across what willbe the fracture surface, play the role of the criticaltemperature, Tc' and system temperature, T, respectively.Symbolically,

(1)where, &r = (1 - T/Tc) is defined as the reducedtemperature of the thermodynamic system and, lOa = (1 -alto) the reduced normal stress acting on the rock mass

at incipient failure. In this paper, tensile stresses arepositive.The full power of the theory of critical phenomena canthen be applied to the brittle fracture of rock masses. A

simple result of this approach is that the shear strengthof the rock mass can then be written in the followingform:

~ = A ( 1 - ~ i ~ , (2)to towhere, A and are the material and universal constants

2on the order of Acorre.ctional terms. 2.00 and 28 0.684 small

One of the most powerful observations in criticalphenomena is that physical and chemical systems of thesame universality class near their respective criticalpoints [8,9] have identical (or nearly so) criticalexponents, such as in equation 2. Properties ofapparently diverse systems of the same universality classhave identical critical exponents and, further, thecoexistence phases along the phase transition line can besuperimposed by simple scalings of the importantvariables. The properly scaled data for differentthermodynamic systems (fluid-gas and magnetic) arefound to "collapse" onto a common curve. A primarygoal of the critical phenomena theory is to explain howsystems that have different microphysics continue toexhibit data collapse and yield the same criticalexponents. For there is a paradox here; the interatomicforces responsible for the existence of a phase transitioncannot play any role in determining the criticalexponents, since those stay the same when the atoms andthe forces change.

The mathematical reasoning used in fluid! gas andmagnetic thermodynamic systems in the vicinity of theirrespective critical points has been applied to the problemof brittle fracture [8]. When the shear strength of abrittle material is chosen as the order parameter 1,equation 2 results. In the derivation of equation 2, twoassumptions are made; firstly, spatial homogeneity withinthe material (vt=o), and secondly, stationarity of theorder parameter (ch/at=o). Both assumptions can bereadily relaxed to take into account anisotropy and timedependent effects.

Tables 1 and 2 illustrate the applicability of equation2 to Hoek and Brown [4,5] data on shear strength ofundisturbed and disturbed rock as a function of rock typeand RMR. Several important conclusions result fromthese tables and equation 2. Rock mass behavior near incipient failure, isindependent of the physical characteristics and thechemical makeup of the rock mass. This observationshows universality and that the law of correspondingstates is satisfied in the immediate vicinity of thephase change (fracture) boundary. The law ofcorresponding states is the result of observation that

data, properly nomalized (scaled) fall on one and thesame curve [8].

IThe existence of a quantity which is nonzero belowthe critical temperature and zero above is found to be acommon feature associated with critical points of a widevariety of physical systems. Thus to distinguish betweentwo phases, one defines an order parameter beingnonzero in the ordered low temperature phase and zeroin the disordered or high temperature phase.


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Table I.-Strength of Intact and Jointed Undisturbed Rock Masses(Modified from Hoek and Brown 1980, 1988) (to is the tensile strength of the rock mass)-

R O C K T Y P E \ ~ Fine. Grained Po1:i!!!ineralic Coarse Grained Poll!!!im:ralie Cllfbonate Rocks wi!!J Well Arenaceous Rocks with Strong and l..ilhlfjedA!llil!aoeousRo::1csROCK MASS QUALITY IQ!eousCmtalineRoc:ks I ~ e o u s .and Metamo!l!hie Cmtaline ~ e 1 o ~ Cn:stal Cleavage (Dolomite, P o o r l ~ Devel22i! COOta.l CJeav!!l:C (Mudstone, Siltsume. Shale. and SIat.e)(Andesite, Dolaite, Diabase, and Rhyolite) ~ (Amphibolite, Gabbro. Gneiss. Ume!;!one, and Marble) (Sandstone and Quanzite)Granite. Norile and Quartz Diorite)Intact RockSIlmI![csLaboratory Size Rock [ )'6% [ roo [ r' " : ' . 2 . 4 ( l ( ) [ 1 - ~ )'.692 ..:. 01.937 [1- JM77;'=2572 2.=3,155 ": '=1598Specimens Free From 10 to to to to 10 to 10 to toStroc:ruralDefects(RMR= 100)High Q!!alin: Rock MassTIghtly Interlocking [ roo [ )"'" . [ [ rm " : ' = 2 . 1 3 1 [ I _ ~ ) ' . 6 9 2;'a2.846 2. =3.495 1- . ! ":'=.1.754 l-.! ":'=2.664Undisturbed Rock with to to to to to to 10 10 to toUnweathered JointsSpaced at 3m.(RMR::-85)Good Q!!alitt Rock MassFresh to Slightly [ )'6% [ [ " : ' = 2 . ' 6 0 [ I - ~ )"69S " : ' = 2 . 0 4 6 [ 1 - ~ Jo.68l.:." 2.743 1 - . ! 2. =3.354 1- . ! ":'=1.685 1 - . !Weathered Rock. Slightly to to to 10 to to to to lolaDisturbed with JointsSpaced at 13m.eRMR= 65)Fair S2!:!!litl Rock MassSevera.lSwof [ r' [ roo [ t' " : ' = 2 . 4 3 6 [ 1 - ~ )'''' " : " 1 . 9 1 3 [ 1 - ~ r 67S..:: =2.612 ..::. ",,3.221 ..:: :1.595ModeratelyWeathered to to to to to (0 to to to toJoints Spaced at 0.3 -1m.(RMR.44)Poor 2l!!!!!I Rock MassNurncrousWe&lheted [ r' [ rOM ..:. 1.796 [1- )"'" " : " 2 . 6 1 6 [ 1 - ~ )"'" ..:..2.125[ JM5S::'''''2.838 "::'=3,461Joints Spaced at 3().. [0 to to to to to to 10 to to500mm withSome Gouge Filling/ClcanRock Wasil:. (RMR "" 23)

V m : P o o r ~ ! l :~ . " : " 1 . 6 2 6 [ I - ~ r ' " " : " 2 . 2 0 4 [ 1 - ~ J.... " : " O . 7 9 4 [ 1 - ~ r'" " : " V ' 6 7 [ 1 - ~ r 684 ":"1.05'[ J....urn.erousbeavily to to to to to to to to to toweathered spac.ed lessthan 50mm widt gougefilling/wasll:.rodc:wilhfumes (RMR=3).xponent IS bken to be the mem of exp:lI\enLS Cor all rocl: types and ro


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The theory predicts that a universal scalinghypothesis is applicable to all materials, includingbrittle fracture, belonging to the same universalityclass.'. The subject matter of critical phenomena and itspowerful mathematical apparatus can be brought to

bear to the subject of brittle fracture with theprovision that one can view to as the critical pointfor the rock mass phase change. The classical Griffith theory of fracture correspondsexactly with the classical Landau mean field theory

of critical point thermodynamic systems with 2B =0.50. In particular, the empirical Hoek-Brown theoryof failure for geological materials results using thecommonly measured critical exponent of 28 = 0.684 0.10.

According to Tables 1 and 2, the equations for theshear strength of undisturbed and disturbed rock massesare statistically identical within a confidence interval of95% and independent of material type and rock massquality, that is

undisturbed, (3a)

disturbed, (3b)

where Aud = 2.466 0.58, Ad = 3.018 0.88, 28 =0.684 0.017, and to refers to the tensile strength of therock mass. Experience gained by using the empiricalHoek and Brown failure criterion (1) showed that theestimated rock mass strengths for undergroundexcavations were reasonable. However, when thecriterion is applied for slope stability studies where therock mass is disturbed by stress relaxation resulting fromexcavation, the estimated rock mass strengths aregenerally low.

There is no compelling reason in critical phenomenatheory as to why there should be a difference in thedisturbed and undisturbed values of A in equations 3aand 3b. In fact, it is a simple matter to show that thedisturbed effect can be subsumed readily by making asimple reduction in the disturbed rock mass tensilestrength by a factor of approximately 27% over itsundisturbed value. Thus, equation 3 becomes

"t = 2.466 ( l _ ~ ) O . 6 8 4 ,to to (4)

where to refers to the tensile strength of the rock mass,disturbed or undisturbed. In the following sections, thishypothesis is applied to explain the observed differencesin BST and TCT values of rock mass strength.

4EXPERIMENTAL PROCEDURE

The BST was used to obtain the in situ shear strengthof coal and sedimentary rocks in several undergroundmines. The BST is hydraulically operated, portable, andprovides routine and rapid test measurement in a 76-mmdiam hole up to 12 m in length for all inclinations[ l0,11]. The BST performs a direct shear test inside theborehole (figure 1). A pair of diametrically opposedloading plates are expanded against the borehole wallwhile the normal force is maintained. The unit isretracted until a segment of rock, about 2 mm thick incontact with each plate is sheared parallel to the boreholeaxis. Each plate has a cylindrical surface (-25 mmcircumferentially and 20 mm axially) to fit the boreholewall. Current load capacities of the device areapproximately 35 MPa and 45 MPa for normal andshearing pressures, respectively [10]. At failure, both thenormal and shearing gauge pressures are recorded andconverted to normal (0) and shear ("t) stresses. Detailedtest procedure and data analysis are described elsewhere[12]. The peak value of"t as a function of 0 is obtainedby repeating the test at several locations in the boreholewhile altering the normal applied pressure. Tests wereperformed using the BST in boreholes at differentunderground mines at 0.6-m intervals in each hole withthe outer 3 m being excluded to avoid edge effects.Cores were also obtained from the same boreholes fortriaxial laboratory testing. However, test data (TCT,BST) do not necessarily report the same location withinthe borehole.

Pulling jack

Normal stress0= FnApShearing stress't = .!'L2A

Figure 1. Borehole Shear Tester force schematic.Tests using the BST and TCT are reported for the fourrock types, two coals, one sedimentary rock, and onemetasedimentary rock. NX-sized cores with length-todiameter ratio of 2.0 were prepared to ASTM standardsfor all TCT experiments. Mean shear stress and meannormal stress were used to approximate the Mohr failureenvelopes from the TCT tests. Selection of data was


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limited to rock materials for which the EST and TCTwere performed on the same material. At least 10samples were tested for each rock type.RESULTS: Mohr failure envelopes for two coal rocks,a metasediment and sandstone rock, were developedusing BST and TCT data. The relationship between theshear stress versus normal stress at failure for each rocktype was developed. The plots and the best fittingequations to each data set are shown in figure 2. Valuesof A and to for the BST and the TCT were determinedby fitting these data to equation 2, using the average2/3 = 0.684 (determined from tables 1 and 2).Remarkably, values of A for the EST and TCT werefound to fit closely to the undisturbed and disturbedvalues, respectively (equations 3a and 3b). The valuesfor the tensile strength of each rock determined by thisprocedure are listed in table 3. For all rocks, the TCTexperiments consistently gave higher values by anaverage of 27% for tensile strength than for the BST tovalues.

Using data from both tests, the reduced shear strengthCr/to) versus reduced normal stress at failure ( = 1 -alto) for each rock type were plotted on a log-log scaleand are shown in figure 3. As discussed earlier, thesedata support the contention that the BST provides ameasurement of the undisturbed shear strength of the insitu rock mass with an RMR value of 100, whereas theTCT provides a measurement of the disturbed intact rockmass. Thus, the shear strength of the undisturbed in siturock mass can be written:

60

5

10(85T)=0.192 MPa Coal 11 o(TCT) =0.374 MPa40

TCT

20

ctI 0..:::i: 60P

A4 AAA Metasediment40

20

Table 3.-Comparison of tensile strengths of coal andcoal.measure rocks using EST and TCT data(modified from Panek, 1979.)to' MPa to' MPa

Rock Type BST TCTCoal 1 . . . . . . . . . . . . . 0.192 0.374Coal 2 ............. 0.350 0.363Metasediment ........ 0.785 0.810

. Sandstone . . . . . . . . . . . 0.286 0.652

~ = 2 . 4 6 6 ( l - ~ ) O . 6 8 4 ,to to (5)where to is the tensile strength of the undisturbed rockmass (measured by the EST). Using Hoek and Brown's[1] relationship between the m and s values as a functionof the RMR,

wheres = e

1 o(BST) =0.350 MPa1 o(TCT) = 0.363 MPa

TCTBST

TCT

(RMR-100)9

Coal 2

Sandstone

(6a)

(6b)

O' - - - - ' - - - ' - - - - - ' - - - ' - - - ' - - -L- - - - ' - - - - "-80 -60 -40 20 o -80a,MPa

-60

Figure 2. Mohr failure envelopes.

-40 20 o


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6100 ~ - - ' - ' - r T T T r r T - - - ' - ' I - I " I " o u "

Coal 1

10 TCTBST

1 1 10 100 1( J1 - to

Coal 2

Sandstone

TCT

BST

10 100

Figure 3. Nonnalized shear strength versus reduced nonnalstress for various rock materials.

(RMR-100)28 (6c)

An RMR value of 100 refers to intact material. Forvalues of slm 1, equation 6a can be simplified to

or simply

3-mto(RMR) = toes 2_0 )m(7a)

to(RMR)loge = O.13(RMR -100) , (7b)towhere to is the tensile strength of the intact in situ rockmass (BST) and to(RMR) is the tensile strength of the insitu rock mass for RMR


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DISCUSSIONAn important result of this investigation is that the in

situ intact strength of rock mass can be reasonablydetermined using the borehole shear test device. TheBST does not provide a measure of the undisturbed insitu rock mass strength, where undisturbed is used in thesense given by Hoek and Brown [1]. After calculatingthe tensile strength of the rock as a function of its RMRvalue (equations 3a and 8), the normalized equation forshear strength (equation 2) can be used to determine thein situ strength of a rock mass.

Application of this model of the strength anddeformability of rock masses requires a determination ofthe tensile strength of the rock mass. Laboratorymeasurement of to on small test samples using, say, theBrazilian test, and extrapolating this value to the largescale by using appropriate values of "m" and "s" inequation 8, provides one estimate of the rock masstensile strength. Another method consists of measuringthe compressive strength of the rock in the laboratory,relating this to its tensile strength, and extrapolating thevalue to the large scale as discussed earlier. Thisprocedure will be discussed in a future USBMpublication.

REFERENCES1. Bieniawski, Z. T., Geomechanics Classification of

Rock Masses and Its Application in Tunnelling,Proc. 3rd Congr. Int. Soc. Rock Mech., vol. 2, partA, pp. 27-32, 1974.

2. Barton, N. R., R. Lien, and J. Lunde, EngineeringClassification of Rock Masses for the Design ofTunnel Support, Rock Mech., vol. 6 no. 4, pp. 189-239, 1974.

73. Hoek, E. and E. T. Brown, The Hoek-Brown Failure': t;::riterion - A 1988 Update, Proc. 15th CanadianRock Mechanics Symposium, pp. 31-38, 1988.

4. Hoek, E. and E. T. Brown, Underground Excavations in Rock, London Instm. Min. Metal!., 140 pp.,1980.

5. Brady, B. H. G. and E. T. Brown, Rock Mechanicsfor Underground Mining, London: George Allen andUnwin, 527 pp., 1985.

6. Stanley, E., Introduction to Phase Transitions andCritical Phenomena, Oxford University Press, NewYork, 308 pp., 1971.7: Binney, J. J., N. J. Dowrick, A. J. Fisher, and M. E.J. Newman, The Theory of Critical Phenomena: AnIntroduction to the Renormalization Group, OxfordUniversity Press, New York, 464 pp., 1992.8. Handy, R. L., J. M. Pitt, L. E. Engle, and D. E.Klockow, Rock Borehole Shear Test, Proc. 17th U.S.Rock Mech. Symposium, 11 pp., 1976.

9. Panek, L. A., Criterion of Failure for Design of RockMass Structures as Determined by Borehole ShearTests, Proc. 4th Congress. Intemat. Soc. Rock Mech,Montreau, Switzerland, vo1.2, pp. 509-515, 1979.

10. Haramy, K.Y., Borehole Shear Tester: Equipmentand Technique, BuMines IC 8867, 19p 1981.11. Paterson, M.S., Experimental Rock Deformation-TheBrittle Field, Springer-Verlag, New York, 308p,

1971.12. Brady, B.T., A Thermodynamic Basis for Static andDynamic Scaling Laws in the Design of Structuresin Rock, Proceedings of First North American RockMechanics Symposium, Balkema, pp. 481-487, 1994.

A Methodology to Determine in Situ Rock Mass Failure

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