.,Shear strength and stiffnesses of rock joints

Resistance au cisaillement et raideur de joints rocheux. Scherfestigkeit. und Steifigkeit von Felskluften . ""J ;

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',' ".R. KUMAR & A. K. DHAWAN, Central Soil and Materials Research Station, New Delhi, India

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ABSTRACT:' Engineers are more concerned with the properties of jointed rock mass than intact rock or rock joints. Their interest inintact rock and rock joints is basically to derive the properties of the jointed rock mass from those of intact rock and rock joints for aknown joint fabric. It is stiffnesses of rock joints which is required for assessing the deformability and strength of the jointed rockmass to predict the settlement or collapse of rock structures. For the numerical analysis, the stiffnesses of rock joints are requiredwhich can be found out from the laboratory tests or in-situ tests, The failure criterion of a rock discontinuity is usually non-linear.The angle of shearing resistance decreases as the level of normal effective stresses increases. Empirical strength criteria in the form ofpower or logarithmic relationship have been reported in literature. The main shortcoming of these proposals is the validity in the lim-ited stress range and the lack of physical meaning. In this paper, it has been shown that the same or similar failure law can be derivedfor rock discontinuities from in-situ shear tests on rock joints with non-rigid asperities and also the stiffnesses of rock joints are pre-sented, 1

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RESUME ,: Le genie est pIus s'interesse aux qualites du materiel du rocher joint quele rocher intact ou les joints du rocher. Leur,interet dans Ie rocher intact et les joints du rocher est au fond a deriver les qualites du materiel du rocher joint du rocher intact et desjoints du rocher pour une etoffe jointe deja connue. C'est la rigidite des joints du rocher qui est recquise pour faire I'asessement dela defcrmabilite et la resistence du materiel du rocher joint de manier a poedire l'etablissement ou lecroullement des structures durocher. Pour I'analyse numerique, la rigidite des joints du rocher sont recquises qui peuvent se rouver dans les epreuves laboratoriesou dans les epreuves en situ. Le critere pour Ie manque de la discontinuite d'un rocher est general non lineaire, L'angle dereesistence de la tonte effective normale diminue quand Ie niveau dune tension' s'augmente. Le critere'de la force empirique dans lafovme de la force de la capacite ou la relation logarithmique est comple rendu en litterature, L'erreur principal de ces propositions estla validite dans Ie rayon de la tension limite et Ie manque d'une signification physique. Dans ce chapitue, cela montre Ie mame ou laloi similaire du manque peut ~tre derivee pour les discontinuites du rocher des epreunes de sa toute en situ sur les joints du rocheravec les apretes non-rigid et aussi la rigidite des joints du rocher sont presentes.

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ZUSAMMENFASSUNG: Die Ingenieure beschaftigen sich ~ehr mit der Eigenschaft der vollstandigen Gesteinrnalle als intaktGesteins oder Gesteingelenks. Sie interessieren sich ffir die Eigenschaft des intakt Gesteins und Gesteingelenks, weil sie hilft die Ei-genschaft der vollsandigen Gesteinmafle -zu herleiten und ein wissend einigen Fabrik zu bauen. Es braucht die Steifheit desGesteingelenks die Deformierung fahigkeit und starke der vollstandiger Gesteinmatlen festzusetzen, die Vereinbarung oder der Ein-sturz der Gesteinstruktur wird gebracht ffir die zahlenmapig Analyse, die wird uns - labor od "in situ" Kalkuliert. DieVersaurnnisbedingung in ein Gestein ist meistens nicht linear. Der winked des schere Keristanz vermindertals wird. Level des no-malweises Effektiv Druck Vermchrt. Emperische Stark Kritierium im Formen des Starks oder logarithmische Beziehungen wird imLiteratur gezogen. Aber diese Vortragen wird nicht akzeptiert, weil es geht gut nur in ein beschrankt Druck (Strejl) Reihe, (range)und Mangel der phyrische Bedeutung. Diese Papiere zeigt, dal3die gleiche oder ahnliche Versaumengesetz kann man von unterbre-chenden gestein beurteilen, Es ist MOglich in "in situ" schere Probe urn Gesteingelenken mit nicht-starr Eigenschaften, also die steif-heit des Gesteingelenken prasentiert. :

.',.STIFFNESSES OF ROCK' JOINT

\ '"The pattern of joints, shear zones and faults in a rock mass re-duces the~effective shear strength to' a value much below the in-tact rock strength, at least in directions parallel to these disconti-nuities, Where the direction of loading is parallel or sub-parallelto the structural features, the shear strength is governed by theshearing resistance along the rock surfaces of the discontinuityand will generally be 'much lower. I: ,

I .~ ",In-situ shear tests have been conducted as per Indian Standard

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(IS 7746-1975) on the rock mass to assess its shear strength andjoint stiffness, In this test,ia block of rock cut from the parentrock, is sheared along the rock"surfaces of the discontinuity by

, ! t J t ."'1' 1 't: 1 _ "

r'the horizontal jack, whilst a second jack simultaneously exerts aperpendicular load. This test gives an estimate of the cohesionand angle of shearing resistance of the rock and also the normaland shear stiffnesses of the joint. The block has usually a planarea of approximately 4900 cm2, bti't larger area may be consid-ered [Serafim (1964»). r},,

(I)

It is assumed that Coulomb's laws applies, i.e.•.

t = C + an tan. ,• " f ''';. • '"

where t is shearing resistance, c is cohesion, an is the stressnormal to shearing surface (effective) 'and. is the angle ofshearing resistance. From these. tests, performed. with yarious

-' ..,. ,., .,..

normal loads, an estimate of the effective values of c and • maybe made. The normal and shear stiffne;ses are measured fromthe tangent of the plot of normal stress Vs verti~al deformationand shear stress Vs horizontal deformation and can be calculat~dby the following relationship:K = /)..Un -,

n /)..8n

K = /)..,J /)..8

J

Where Kn and Ks are normal and shear stiffnesses, AGn and ATare increments of normal and shear stresses and ASn and ASs areincrements of vertical and horizontal deformations of the rockjoint respectively.- i

For each in-situ shear tests on rock joints, graphs of shear stressVs horizontal displacement and normal stress Vs vertical dis-placement are plotted to show the nominal normal stress and anychanges in normal stress during shearing., '. r-

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The normal and shear stiffnesses are evaluated from the graphbetween normal stress Vs vertical deformations and shear stressVs horizontal deformations and can be calculated by usingequations (2) and (3). The normal stiffness is the initial tangentof the plot and the shear stiffness is the tangent at peak of load-• t • • 1 ~109 cycle or unloading cycle. ' . f ,

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Ll « Results and Discussions of Stiffnesses l~

The. ~e~~ltsof normal and she~ stiffnesses are calculated fro~the in-situ shear test results -of Omkareshwar H. E: Project (MP),Parvati H. E. Project (HP) Stage III, Teesta H. E. Project (Sik-kim) Stage VI and Nathpa Jhakri H. E. Project (HP). The projectsites are located in northern, central and north-eastern part of In~dia, The results of stiffnesses for different interfaces depend onthe condition and infillings of joints. Fig. I shows the variationof normal and shear stiffnesses of Omkareshwar H. E. Project(MP). Similarly the results of other projects have been studied.,

300 ..- _ .... ---- .-.

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200,

250 .

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,-"50

100

50

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" Number of tests . r.· t.!. - r ';

A' !..Fig. 1 Variation of Normal and Shear Stiffnesses

2 SHEAR STRENGTH OF ROCK JOINTS" ;. -

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The failure criterion of a rock discontinuity is usually non-linear. The angle of shearing resistance decreases as the level ofnormal effective stresses increases. At low normal stresses, mo-tion takes place by climbing up the ridges and asperities whichcompose the rough face of the discontinuity. The result is a highapparent frictional resistance due to this effect of dilatancy. Athigher normal stresses failure occurs in a very complex mannerby ploughing, by shearing through the ridges and fracturing ofthe rock material adjacent to the contact. The contribution ofdilatancy to the total shearing strength gradually decreases bythe rise of stress level. If the normal effective stress is largeenough, all dilatancy would be suppressed and the rock discon-tinuity would shear at nearly a constant volume.

(2)

(3)

Empirical strength criteria in the form of power or logarithmicrelationship have been reported in literature. The main short-'coming of these proposals is the validity in the limited stressrange and the lack of physical meaning. As per the research pa-pers (Maksimovic [1979], [1988], [1989 a, b, cD, the function ofhyperbolic type offers excellent possibilities for range of stressesfrom zero to practical infinity for most non-cemented soils. Inthis paper, it will be shown tha\ the same or similar failure law

• can be derived for rock discontinuities from in-situ shear tests onrock joints with non-rigid asperities.

I 2.1 Model for Non-linear Failure Envelope,f to. l r. ,f ; J Jl t. !

The expression, originally proposed for granular materials byNewland and Allely (1957), and for rock discontinuities byPatton (1966) and Goldstein et. al. (1966), for relating the angle

. of shearing resistance, 'dilatancy and friction at the discontinuity. between two planes with'surface irregularities may be written as, . .

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¢= ¢B +rp. , (4)1 .

where +B is a .physical friction or basic angle of friction and cpthe angle of dilatancy, or the angle between displacement vectorand the shearing plane. '"

The mechanical analog model of dilatancy proposed by (Mak-simovic [199~D.is sho~n in Fig. 2. . I r I

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The mechanism in the zone of the discontinuity consists of theelement unit, of the unit size, the simulated surface of the asper-ity linked to the dash pot governed by the Boyle's law. A modelequation for the angle of the shearing resistance is:

and the shearing strength of the rock discontinuity is

t'. . \ . '.

!::..¢Tf = a; ~ ¢B + ( J

1 a;+-• • I. PN

The meaning of each parameter is shown in Fig. 3.

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Af

T

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1I-----1---IPH

N.ORMAL STRESS

1."M- -r

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Fig. 3 Definition of parameters of the non-linear failureenvelop

~B is the basic angle of friction, the angle of the shearing re-sistance mobilized at high normal stress levels at which all dila-tancy effects are suppressed, as all the asperities are sheared off

forming the smooth shearing plane. This angle could be ap-proximately equal to the angle of the physical friction betweenmineral grains.

(5)

6~ is the joint roughness angle, reflects the surface roughnessof the discontinuity. The associated dilatancy effects at zerostress level and it can be described as the angle of maximumdilatancy which occurs on undamaged rugged surface.

PN median angle pressure is equal to the level of the normalstress at which the contribution of dilation is equal to one half ofthe angle of dilatancy for the zero normal stress. It mainly re-flects the deformability and the resistance of the asperitiesagainst crushing .

(6) 2.2 Examples and Justifications

2.2.1 Example 1. Data by Barla et al. (1985) and Nilsen (1985)

.'The results of the direct shear tests on sandstone discontinuityare evaluated by Barla et al. (1985). Six data points are proc-essed, using the least square fit for the Eq. (5) with the methoddescribed, and a very good approximation with the proposedfailure law was obtained. To compare the proposed failure crite-ria with the power law, an example of interpretation of test re-sults obtained on foliation joints in mica schist, with a portableshear machine were presented by Nilsen (1985). The failure lawwas described by power law 1:f= 0.87 anO.7. Applying the re-gression analysis for a proposed hyperbolic variation of the an-gle of shearing resistance using six points computed from theabove given expression, taking' = arctan (1:fIan), failure enve-lope and parameters are obtained. As can be seen in the paper byNilsen (1985), the agreement is remarkable.

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2.2.2 Example 2. Data of Different Projects in IndiaT I.

The above failure criteria was interpreted for the laboratory tests.The above failure' criteria has been utilised for in-situ tests con-ducted at'different projects in different parts of India. The resultsinterpreted are from Omkareshwar H. E. Project (MP), Teesta H.E. Project (Sikkim) Stage VI, Parvati H. E. Project (HP) StageIII and Nathpa Jhakri H. E. Project (HP). The shear tests havebeen conducted on different interfaces. The proposed failurecriteria was compared with the power law, the examples of in-terpretation of field test results obtained on different interfaces!joint condition have shown a good agreement: The proposed hy-perbolic variation of the angle of shearing resistance using fiveto six points in each set computed from the field test results,failure envelopes and parameters were obtained and a goodagreement was obtained. .0. "< ;

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3 CONCLUSIONS.Xt,.~"1.JQ-'

In-situ tests on the rock mass, as distinct from laboratory tests onsamples of the rock materials, are an important and oft~n eS;5en-• ~~., • ._. U L

tial requirement as a basis for sound design. The geometry of therock mass is generally so complex and the basic material prop-erties so far divergent from the idealized ones necessarily as-

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Teesta H. E. Project (Sikkim) Stage VI80.00 . ,

75.00

'ln70.ooCIJCIJ...0-~ 65.00'-'~g'60.00 ~" , I-c

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55.00

50.0010

Normal Stress (Kg/sq. em)

Fig. 4 Semi log plot, Secant angle Vs Normal stress !;

"., , < ! J "..- •.J • •• ~ It. r t.sumed for ease of analysis that the design of rational and con-sistent test procedures is not possible., Nevertheless, g~engineering practice has always taken into. account, factorswhich can not be analysed by exercising judgement on ~heirpos-sible effects when making final decision. The theoretical analy-sis, together with empirical data and intuitive appraisal of intan-gible factors, are all components entering into solution of thetechnicall?robl~m. . " .'

J' - 'I t . l "... 1 •••

In a. semi-logarithmic plot (Fig...4), it can be .~o~edthat verygood 'approximation could also be obtained by using the linearrelationship in the rather wide interval. Extrapolation of thecurve to small stress range would overestimate and extrapolationin the very high stress range would underestimate the angle ofthe shearing resistance.

The. power law in the form Tf = A aB described the non-linearfailure envelope with parameters that depend on units and haveno physical meaning. This law defines a vertical tangent to thefailure envelope in the origin, suggests the angle +0 = 900,which makes it unusable in dealing with dilatancy at zero stresslevel. It lacks a reasonable asymptote and is therefore unable todefine.the'basic angle of friction.' s , s.r '; "J > 'I" ~ _

a ,, ... I, ,

All the examples presented above, which could be described bya logarithmic and power law, show excellent conformity withthe simple fonnof the variation of the shearing resistance anglederived from the analog model. The proposed model has signifi-cant advantages; parameters have the mathematical point ofview, as it has only a few divisions and additions.

4 REFERENCES

Barla, G.: Forlati, F. and' Zanin~tti, A: (1985). Sh~ar behaviourof filled discontinuities. 'Proc:' 'of In~.•Symp. on Fiindamentals of

• r • " j

Rock Joints, Bjorkliden, Centek Publ., Lulea, pp. 163-J72.· I

~l :. ~ ~ J f t'l V• it

Goldstein, M., Goosev, B., Pyrogorsky, N., Tulinov, R. and Tu-rovskaya, A. (1966). Investigation of mechanical properties ofcracked rock. Proc., t lst Int. Congrs of Int. Soc. Rock Mech.,Lisbon, Vol. I, 1'1'.521-524. . } i

IS:7746 - 1975. Indian Standard code of practice for in-situshear tests on rock.

Maksimovic, M. (1979). Limit equilibrium for non-linear failureenvelope and arbitrary slip surface. 3rd Int. Conf NumericalMethods in Geomechanics, Aachen, PI'; 76~-777.

Maksirnovic, M. (1988). General Slope Stability Software pack-age for micro-computers. 6th Int. Conf Numerical Methods inGeomechanics, Aachen, pp. 769-777.

','ft.-' " ,l

Maksimovic, M. (1989a). Non-linear failure envelope for soils.Jour. Geotech. Engg., Vol. 115,'No. 3, Innsbruck, pp, 2145-2150.

Maksimovic, M. (1989b). On the residual shearing strength ofclays. Geotechnique, Vol. 39, No.2, Pl'. 581-586.

~Maksimovic, M. (1989c). Non-linear failure envelope forcourse-grained soils. 12th Int. Co"'"J.S/lrfFE, Rio de Janeiro: Vol.

. '\I, Pl'. 731-734. \.•••... ~ ",

Maksimovic, M. (1992). New Description of the Shear Strengthfor Rock Joints. Rock Mech. and Rock Engg., Vol. 25, No.4, Pl'.

/'\ .275-284. • ". I

Newland, P. L. and Allely, B. H. (1957). Volume, changes ~drained triaxial tests on granular materials. Geotechnique, Vol.7, Pl'. 17-34.

,Nilsen, B. (1985). Shear strength of rock joints at low normalstresses - a key parameter 'for evaluating rock slope stability.Proc. of Int. Symp. on Fundamentals of Rock joints, Bjorkliden,Centek Publ., Lulea, pp. 487-494.

Patton, F. D. (1966). Multiple modes of shear failure in ~ock.Proc. of 1st Int. Congrs Rock Mech., Lisbon, Vol.' I, pp, ,509-513.

Serafim, 1. L~(1964). Rock mechanics considerations in the de-sign of concrete dams. Paper 14, Intern. Con! State of Stress inthe Earth's Crust (Ed. W. R. Judd), Elsevier, New York.

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