Multiple modes of shear failure In rock

Les differents modes de rupture par cisaillement dans les roches

Verschiedene Arten des Felsscherbruches

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by F. D. PATTON,Geologist and Foundation EngineerResearch Associate, Department of Civil Engineering, University of Illinois, Urbana, Illinois, U. S. A., (presently NATO Post-DoctoraFellow, LNEC, Lisbon, Portugal)

Summary

The mechanism of shear failure in rockwas investigated by studying over 300 rockslopes in the Rocky Mountains, makinglaboratory sliding friction tests on rocksamples and direct shear tests on simulatedrock surfaces, and reviewing the shearstrength literature. This paper describes theIabora tory shear tests used to provide atheoretical framework for interpreting theshear strength of intact or discontinuousrock having an irregular failure surface.Specimens made of plaster of Paris werecast with irregular surfaces and tested ina specially designed shearing device. Testvariables included the inclination, number,and strength of the specimen teeth, and thenormal loads applied. The following con-clusions were drawn: I) failure envelopesfor specimens with irregular failure surfacesare curved, 2) changes in the slope of afailure envelope reflect changes in the modeof failure, and 3) changes in the mode offailure are related to the physical proper-ties of the irregularities along the failureSurface. An application of these conclusionswas demonstrated by interpreting a seriesof laboratory shear tests on rock.

I. Introduction

Resume

On a etudie Ie mecanisme de rupture desroches par cisaillement, en observant plusde 300 pentes rocheuses dans les MontagnesRocheuses, en fa isant, au laboratoire, desessais de frottement sur des eprouvettes deroches et des essais de cisaillement directssur des modeles de surfaces rocheuses, eten passant en revue la literature sur la resis-tance au cisaillement, Dans la presentecommunication, on decrit les essais decisaillement executes au laboratoire qui ontservi II etablir un cadre theorique permettantl'interpretation de la resistance au cisaille-ment de roches intactes ou discontinuesayant une surface de rupture irreguliere.Dans un dispositif projete expressernent IIce but, on a fait des essais de cisaillementsur des echantillons en platre de Paris,rnoules avec des surfaces irregulieres, Lesvariables de J'essai comprenaient I'Inclinai-son, Ie nombre, et la resistance des redentsde l'echantillon et les charges normalesappliquees, On en a conclu que: I) lescourbes intrinseques de rupture des echan-tillons ayant des surfaces de rupture irre-gulieres ne sont pas droites; 2) des varia-tions dans I'inclinaison de la courbe in-trinseque traduisent des variations dans Iemode de rupture; et 3) les differents modesde rupture refietent les caracteristiques phy-siques des irregularites de la surface derupture. On a dernontre les conclusionsci-avant, en les appliquant II I'interpretationd'une serie d'essais de cisaillement de rochesexecutes au laboratoire.

Zusammenfassung

Durch Untersuchung von mehr als 300Felsboschungen in den «Rocky Mountains»,Rutschreibungsversuche von Gesteinsprobenund direkte Scherversuche von vorgetauschtenGesteinsoberfliichen im Labor, sowie Durch-sicht der einschliigigen Literatur, wurdeder Mechanismus des Felsscherbruches er-forscht. Dieses Referat beschreibt die La-borversuche die durchgefiihrt wurden, urnein theoretisches Gedankengebiiude zur Erk-larung der Scherfestigkeit ganzen oder di-skontinuierlichen Felsens entlang einer un-regelrnassigen Bruchfliiche zu schaffen. Eswurden Gipsproben mit unregelmiissigenOberfliichen geformt, und in einer speziellentworfenen Schereinrichtung geprUft. Unteranderem, wurde die Abhiingigkeit der Er-gebnisse von der Neigung, AnzahI und Fe-stigkeit der Probezahne, sowie von derNormallast untersucht. Es wurden folgendeErgebnisse erhalten: I) Die Mohrsche Urn-hullungskurve fur Proben mit unregelmiissigerBruchfliiche ist krummlinig. 2) Steilheitsan-derungen der Mohrschen UmhUlIungskurvezeigen Anderungen der Bruchart an. 3) An-derungen der Bruchart hiingen von den phy-sikalischen Eigenschaften der Unregelmiissig-keiten der Bruchfliiche abo Die Erkliirungeiner Reihe von Laborscherversuchen mitFelsen zeigt eine erfolgreiche Anwendungdieser Schliisse.

Previous work by NEWLANDand ALLELY (1957), RIPLEYand LEE(1961), and WITHERS(1964) indicated that irregulari-ties along failure surfaces should play an important rolein the determination of shear strength characteristics ofrocks. With this in mind, a field and laboratory investigationinto the effect of surface irregularities was undertaken.

The effects of natural irregularities on the stabilityof rock slopes were studied on over 300 stable, unstable,and failed slopes in the Rocky Mountains (PATTON,1966).

By making corrections for the geometry of the rock discon-tinuities, the angle of frictional sliding resistance along arelatively flat plane was determined under field conditions.For sandstones and carbonate rocks this angle was foundto compare favorably with the angle of residual frictionalsliding resistance obtained from laboratory tests on wet,relatively flat, rough-sawn sandstone and carbonate rocksurfaces.

The field and laboratory study showed that irregularitieshave an appreciable influence upon the shearing resistanceof rock masses. Furthermore, it seemed apparent that

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different modes of shear failure take place along irregularrock surfaces. For example, failures of rock masses haveoccurred by sliding along rock surfaces having variousorientations, by shearing through intact rock, or both.A framework that would permit this multiple-mode failuremechanism to be better understood and allow an improvedinterpretation of the results of shear tests on rock wasrequired. The laboratory tests described in this paperwere devised to help provide such a framework.

D. Test specimens

The interpretation of the results of shear tests on realrocks is usual1y complicated by sample variability - evenwhen several samples are taken from the same block ofrock. To overcome this difficulty the laboratory specimenswere made from an artificial material so that the shape,size, and internal strength of the irregularities or «teeth»on the surface of the test specimens could be evaluated separa-tely.

Plaster of Paris was selected as the testing material asit had rock-like properties, fil1ers could be added to varyits strength, and the shape of the teeth could be accuratelyreproduced using molds. Two different fillers - crushedquartz sand and kaolinite - were used to decrease thestrength of the specimens. The properties and ingredientsof the specimens are outlined in Table t.

BBBB" •• Ill 011.55-

BBFig. 1 - Some of the Different Types of Plaster Specimens

Cylindrical samples, which were cast and cured witheach series of test specimens, were later tested for theirpoint-load tensile strength and their unconfined compressivestrength.

III. Test apparatus and procedure

A direct shear device was constructed to permit elec-tronic recording of the loads and the vertical and horizontal

Summary of Physical Properties of Plaster of Paris Specimens

Table 1

Filler

Ratio Filler: Plaster by weightWeight Mixing Water Ibs/IOO Ibs PlasterUnit weight at testing lbs/cu ft~, degrees (1)

Sand Sand Kaolinite Kaolinite

3: I 3:2 I: I I: 2148 85 127 9688.9 94.3 64.5 66.9

34-36 35-39 27-28 29-30

Tests on Cilinders

Av. unconfined comp, strength psiAv. point-load tensile strength psiAverage E, x 108 psi (I)

24853.65

12401201.15

60170.22

98890

.45

(I) Obtained from direct shear tests after large displacements(2) E1 is the tangent modulus of elasticity at Soo/u ultimate stren&tb

Five to eight identical specimens of 12 geometrical con-figurations were made for each of the four mixes. Fourtypes of inclined teeth with slopes of 25°, 35°, 45°, and 55°were formed. Two series of specimens - one with four teethand the other with two - were cast for each type of inclinedteeth. All the teeth had a height of 0.20 inches.

Both halves of each specimen were cast simultaneouslyin a brass mold the surfaces of which were machined towithin ± .005 inches. Similar specimens were cast withinone or two days of each other. The kaolinite-plaster speci-mens were cured at 70°F and 5C% relative humidity untiltesting ccrrmenced 45 to 50 days after casting. When bothhalves of the specimen were placed tcgether after casting,each specimen was 2.95 inches long, 1.75 inches wide,and 2.0 inches high. Figure 1 shows some of the differenttypes of specimens.

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displacements. This allowed the complete load-displacementcurve to be obtained even with «brittle» materials.

The shearing device consisted of 1) a shear box in whicha horizontal shearing force was applied, 2) a motor, variable-speed transmission, and a worm gear-ram arrangementthat developed and transmitted the shearing force, 3) aloading frame and weights for applying the normal force,4) twin load cells to measure the shearing force in tension,and 5) three LVDT transducers to measure horizontal andvertical displacements. Shearing was at a constant rate ofdisplacement of .0624 inches per minute. Most of the resultswere plotted directly upon a Moseley x-y recorder.

After a series of tests on one type of specimen, thepeak and residual shear strengths were taken from theload-horizontal displacement graph made by the x-y recor-der and plotted on a shear strength diagram at the appro-

priate normal load. The results of several such tests werejoined by lines which formed two failure envelopes, onerepresenting maximum shear strength and the other residualshear strength.

IV. Definition of terms

~ is the angle of sliding or shearing resistance. It is usedwhere a more specific term does not seem warranted.

~I.l is the angle of frictional sliding resistance. Its valuechanges with the surface characteristics of the rock. Formost practical problems involving rocks, the appropriatevalue of ~I.l can apparently be obtained after large displace-ments have occurred along macroscopically smooth andflat but microscopically irregular (i. e., unpolished) wetsurfaces.

~r is the angle of residual shearing resistance of materialswhich initially were partly or completely intact. It is obtainedfrom the asymptotic minimum values of shear strengthfollowing large displacements. .

i is the angle of inclination of the failure surfaces withrespect to the direction of application of the shearing force.It is also used in a graphical sense as a particular angleon a shear strength diagram.

V. Resnlts

The results presented here are from the tests on speci-mens of kaolinite-plaster. Similar results were obtainedfrom tests on the sand-plaster specimens.

1) Specimens with fiat surfaces

Figure 2 shows a typical failure envelop , from a seriesof ,direct shear tests on relatively flat, unpolished, surfa7es.FaIlure envelopes from these specimens were straightlines passing through the origin and inclined at an angle~I.l from the horizontal. The angle ~I.l for the specimens ofthe stronger mix (kaolinite-plaster I :2) was 310. For theweaker mix ~I.l was 2710.

.•..c:..•..C'ICQI•...•..

(/)

01C•..eQI..c:.

(/)

Normal Load, N

Fig. 2 - Failure Envelope for Specimens with Flat Surfaces

2) Specimens with inclined teeth at low normal loads

Figure 3 shows two failure envelopes typical of thoseobtained from tests at low normal loads on specimens withinclined teeth. The maximum strengths recorded for a numberof specimens were used to form the maximum strength enve-lope (line A). The residual strengths remaining in these samespecimens after large displacements had occurred werethe basis for the residual strength envelope (line B).

The equation describing the maximum strength envelopeis S = N tan (~I.l+ i) where S is the total shearing strengthand N is the total normal load. The inclination of the resi-dual envelope is ~r and the envelope can be described by theequation S= N tan ~r' For the various plaster specimens,the angle ~r was always within 11° of ~I.l and the two wereoften identical.

Line A of Figure 3 represents two different types ofstrengths. It represents the value of the external frictionalresistance along the inclined planes, and it represents theinternal strength of the teeth at the point of failure. Whenfailure occurs these two strengths are equal.

It may be noted from line A that although intact materialwas sheared there was no cohesion intercept indicatedwhen the results were plotted. Yet the internal «cohesive»strength of the teeth still contributed to the total strengthby making possible the development of increased frictionalresistance along the surface of the teeth. The precise con-tribution of the internal «cohesive» strength of the teethat any given normal load is the difference in strengthsbetween the maximum and residual strength envelopes.A cohesion intercept would occur if the sum of ~I.l+i becameequal to or greater than 900.

3) Different inclinations of teeth

Results from three series of tests, each made on speci-mens with different inclinations of teeth, are shown inFigure 4. The failure envelope for specimens with i = 250is a straight line -line A. For specimens with i = 350and i = 45° the failure envelopes are curved but each envelopecan be approximated by two straight lines as are envelopesBand C, respectively. Line D is drawn through the residualshear strengths of aU three series of specimens.

(/)..s:•..encQI•..•..

(/)

enc•..tlQIs:(/)

Normal Load" N

Fig. 3 - Failure Envelopes for Specimens with Irregular Surfaces

511

~o MAll VALU[~ 'Oft , TE(IH6 MAll VAlU(~'()III 2 fEtfH

. It(SIQUAl VALUn 'Olt 1I0THr"PC5 or ~"[CIM[N~

o KAOllNlf[ ,PLAST!1t ll21.,.4S"

6 I<AOlINl1[ "lASTEoII 1l.11,;'U"

" 1t[5'OUAL VAlUeS 11:21 SP[CIM[N5

• It[SIDUAL VALUES II II SPECIMENS

.. "'"~llOAO,H 1M.

KAOLINIT[ PLAST[lt 11.11

100 200 3001'0011I"''''' lOAO. N 1M.

Fig. 4 - Failure Envelopes for Specimenswith Different Inclinations of Teeth

Fig. 5 - Failure Envelopes for Specimenswith Different Numbers of Teeth

Fig. 6 - Failure Envelopes for Specimenswith Different Internal Strengths

The inclinations of the lower or primary portions oflines A , B, and C are equal to, or within one degree of,«i11+i. The inclinations of the upper or secondary portionsof lines Band C are very close to the 'value «i,. The abruptchanges in the slopes of lines Band C are related to changesin the mode of failure. Below the changes in slope the maxi-mum shearing strength is related to the frictional resistancealong the inclined surfaces. Above the transition in slopethe maximum strength is unrelated to the increased surfacefriction due to the inclination of the teeth.

The cross-sectional area of the intact material at thebase of the 350 teeth is greater than for the 450 teeth. Thisexplains why the transition in the mode of failure for thetwo inclinations of teeth occurred at different normalloads. Line A is straight because the range of normal loadsused was not high enough to reach the transition for thespecimens with 250 teeth.

4) Varying the number of teeth

Figure 5 shows the effect of doubling the number ofteeth from two to four and keeping the specimens identicalin other respects. Each maximum strength failure envelope,although curved, is approximately described by two straightlines. The secondary portion of the failure envelope forspecimens with four teeth '(line A) is about twice as farabove the residual envelope' (line C) as the envelope forspecimens with two teech (line B).

The steeply sloping primary portions of the failureenvelopes are approximately equal to ~11+ i , The inclina-tions of the secondary portions of the failure envelopesare approximately «i,. The change in slope again is relatedto a change in the mode of failure associated with the initialdisplacements.

The effect of having additional teeth is to move theabrupt change in slope of the failure envelope to a highernormal load and to move the secondary portion of thefailure envelope about twice as far above the residual enve-lope as the failure envelope for two teeth.

This diagram illustrates the difficulties encountered inattaching any real meaning to the average shearing stressescomputed for tests on real rocks. In rocks the number,size, and shape of the irregularities are unknown; hence thereal shearing and normal stresses are also unknown.

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From tests made on higher strength specimens it wasfound that specimens with four teeth often gave failureenvelopes that were only slightly greater than the envelopesfor specimens with two teeth. This was interpreted as evi-dence of progressive failure.

5) Varying the strength of the teeth

Figure 6 shows the results of tests on two series of spe-cimens with identical surface configurations but differentinternal strengths. Line A is the failure envelope for thestronger specimens and line B for the weaker specimens.Lines C and D are their respective residual strength envelopes.

Slopes of the primary and secondary portions of thefailure envelopes are slightly different for each series oftests. These differences reflect a change in ~11 and ~, forthe two strengths of specimens. The change in mode offailure occurs at a higher normal stress for the strongerspecimens than for the weaker ones. Thus, increasing thestrength of the specimen teeth has an effect similar to thatof increasing the number of teeth.

VI. Conclusions

Three general conclusions can be drawn from the resultsof the tests on plaster specimens: 1) failure envelopes forspecimens with irregular failure surfaces are curved, 2)changes in the slope of the failure envelope reflect changesin the mode of failure, and 3) changes in the mode of failureare related to the physical properties of the irregularitiesalong the failure surface.

These conclusions, together with the fact that ~ does notvary throughout a wide range of normal loads (although~+i does vary), have many practical applications. In par-ticular, they facilitate the interpretation of curved failureenvelopes.

VII. Interpretation of tests on real rocks

From the results of shear tests on real rocks one wouldexpect to obtain a superposition of the effects of the separatevariables investigated for the plaster specimens. For example,in the same sample of rock the irregularities along the failuresurface would have different sizes, inclinations, internal

300

SUMMARYill: 29~41°

APPARENT COHESION INTERCEPT: 10- 50 psi

VIQ.

IIIIIIWIt: 200•..III

00 100 200 300AVERAGE NORMAL STRESS, psi

a) STRAIGHT· LI NE FAILURE ENVELOPES

300

SUMMARY

ill~-4lr:33°

COHESION INTERCEPT: 0

200

100

100 200 300AVERAGE NORMAL STRESS. psi

b) CURVED FAILURE ENVELOPES REFLECTINGMULTIPLE MODES OF fAILURE

Fig. 7 - Two Interpretations of Direct Shear Tests on Ruck Samples with Irregular Surfaces

strengths, and coefficients of friction. Thus, failure envelopesfor rocks would not reflect a simple change in the modeof failure but changes in the «intensities» of different modesof failure occurring simultaneously.

. Figure 7 illustrates two interpretations that can begiven to four series of tests (A , B , C , and D) on differentsurfaces of the same rock. Figure 70 shows the shear testresults interpreted as forming straight-line failure envelopes.This is equivalent to saying that only one mode of failureo~urred during the tests at different stress levels. FromF!gure 70 it would also appear that the value of ~ wasdIfferent for each series of tests and was not a relativelyc~nstant property of the material. In addition, the straight-line envelopes could lead some designers to conclude thatan appreciable amount of cohesive strength exists at zeronor mal load. These errors are avoided in Figure 7b in whichthe same data is used to form curved failure envelopes.

The curved failure envelopes in Figure 7b also providemore information on the geometry and effectiveness of thesurface irregularities than is offered in' Figure 70. Forexample, at a given normal stress the vertical distancebetween a point on any maximum strength failure envelopeand the residual envelope (line E) gives the internal strengthcontributed by the irregularities. This strength is the strengththat is lost when significant displacements occur along thefailure plane.. From Figure 7b the rocks of the test series outlined by

~me A can be interpreted as having small relatively steepIrregularities which were effective between a normal stressof 0 to 40 psi. Above 40 psi these small irregularities failedbefore displacements could occur along them. Between a

normal load of 120 and 270 psi some larger irregularitieswhich had inclinations of 10° (43° minus 33°) became effec-tive. Above 270 psi these larger irregularities began to failbefore displacements could occur.

For some engineering design purposes straight-linefailure envelopes are adequate. But to facilitate an under-standing of the failure mechanisms curved failure envelopesreflecting the multiple modes of shear failure appear to bea necessity.

VIII. Acknowledgments

This paper is based upon a thesis submitted in partialfulfillment of the requirements for a Ph. D. in Geology atthe University of Illinois. The thesis was completed underthe direction of Dr. D. U. Deere, professor of civil engineer-ing and geology, who made many valuable contributionsto the study.

References

NEWLAND. P.· L., and B. H. ALLELY - 1957, Volume changes in drai-ned triaxial tests on granular materials, Geotechnique, Vol. VD,pp. 17-34.

PATTON, F. D. - 1966, Multiple Modes of Shear Failure in Rockand Related Materials, Ph. D. Thesis, Univ. of Illinois, 282 pp.

RIPLEY, C. F., and K. L. LEE - 1961, Sliding friction tests on sedi-mentary rock specimens, Communication 8, 7th Congress ofLarge Dams, Vol. IV, pp. 657-671.

WITHERS, J. H. - 1964, Sliding Resistance Along Discontinuities InRock Massi'S. Ph. D. Thesis. Univ. of Illinois. 124 pp.

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