Eurock '96, Barla (ed.)© 1996 Balkema, Rotterdam. ISBN 905410843 6

Shear behaviour of joint roughness with two types of asperitiesComportement au cisaiJlement de la rugosite des joints avec deux types differents

d' asperitesScherverhalten von Trennflachenrauhigkeit mit zwei Arten von Rauhigkeitsformen

H. Kusumi, K. Nishida & T. Suzuki - Department ojCivil Engineering, Kansai University. Osaka. Japan

ABSTRACT: It is considered that the surface profile of rock joint roughness considerably affectsthe shear behaviour of rock joints. Irregular joint surface consists of various asperity shapes andgradients, and it seems t hat the shear behaviour might be dominat e d by the large gradient a sp e ri t ie s,bUI the mechanism is not enough clarified. We made nine irregular triangular plaster specimenswh ichi n c lude two t y P e s 0 f t ria ngul a I' asp c ri tie san d subj ec I e d I h e m to di reel sh e a I' t e s t s. The res ult sshow that. when t h e asperities of the s p e c im e n s are not sheared. the shear behaviour depends onthe large gradient asperity. When the two phenomena of shearing and sliding are simultaneouslyobserved, the shear strength of the joint roughness depends on the number of the large gradienta sp e ri t ie s.

RESUME: On c o n s ide r e que l e profil s up erf ic ie! de la r ugo su e des joints ro c h eux un e influenceconsiderable sur Ie comportement de c i s a il le m c n t des joints. Lcs surfaces desjoints ir r e gul ier s so n t

fo rm e c s par des a sp e r i t e s avec d i If e r e n t s formes e t gradients. c t iI p a r a it que Ie comportment dec isa il le m e n t est do m i ne par les a sp e r i t e s avcc les plus grandsgradients, m a i s Ie mecanisme n 'est pascomplCtment c la rif ie . No us avons fait n e uf specimens triangulairs de p l a t r e , qui p r e s e m e nt deuxt yp e s d ta sp e ri t e s t r ia ngul a i r e s , e t nous les a v o n s so um it a des essais de c is a il lc m e n t . Lesresultantsm on t rcnt que. quand les a sp e r i t e s n e sont pas c is a il l e e s Ie comportement de c is a il le m e n t depend des'''1'0riI0s av c c plus !,'!"and gradient. Quandles deux phenomenes de c is a il l e m c n t et de g l is se rn e n t sont"b,crl0, s im u n a u e m e n r , la resistance au c i sa ii le m e n t de la r ugo si t e des joints depend du n o m bre(j'asperites avec grand gr a di en t .

ZUSAMMENFRASUNG: Es wird angenommcn, dal3 das Ob e r fl a c h e n pr o I'i l vonFc ist re n n f la c h e n ra uh igk e i t das Sc h e rv e rh a l t e n derselben betriichtlich beeinfluflt. U n r e gc lm a BigeFe l s tr e n n f lach cn besitzen unterschiedliche Rauhigkeitsformen und gradienten, und es scheit, dafldas Scherverhalten von den gr o Bc n Rallhigkeits!,'!"adienten be h e rr sc h t wird,wobeidieWirklUlgsweisej e do ch nichot geniigend ge k l a rt ist Es wurdcn neun un r e ge lm a lfige , dr cj cc k s f'o r m ige Gi p s mo de l leh c r gest e ll t , die z wi e Arten von dreieckigen Rauhigkeiten da r s t e l l e n , we l c he da ra uf'h in d i r e k t e nScherverhalten unterworfen wurden . Die erhaitenen Werte zeigen, dafl da s 'Sc h e rv e r h a lt e n von dengr o Be n Rauhigkeitsgradienten a bh a n gt , ralls die Ra uh igk e it e n del' Modelle n ic h t geschert sind.We n n die zwie Ph a n o m e ne des Scherens und Gleitens gleichzeit ig beobachtet we r den , dann h a n gtd e r Scherwiderstand del' T'r e n n f l a c h e n ra uh ig k e it von der Anzahl der grol3en Rauhigkeitsgradientenabo

I INTRODUCT ION for many years and indeed numerous shearmodels have been proposed(e.g. Patton 1966;Ladanyi and Archambault 1970; Jaegar 1971;Barton and Choubey, Kodikara and Johnston1994). In these joint model, Ko di ka r a andJohnston carried out the direct shear test withthe artificial specimens of irregular triangularrough joint, and tried to the s im ula t ions of the

The characterizations of rock joint's surfaceprofile affect the shear strength and t h e shearbc h a v io ur of rock joint. However, it is notclarificd which factors of the joint roughnessuc p c nd o n t h e shearstrcngth of rock joint. Thisproblem has been t he subject of invest igat ion

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stress- strain cur v e an d the dilatancy behaviour.However, because these investigations weredo n e for the be t wee n I' 0 c k surf ac e and con ere t esurface, this simulation can not be applied tot he pure rock joint.

In this paper, the effects of asperity angleandof the number of large gradient asperitiescomposed of rock joint surface on the peak andresidual shear strength of rock joint arediscussed. The rock joint specimens are makingfrom the plaster and combine two typestriangular asperity, and nine i rre gul a rtriangular and three regular triangularspecimens arc applied to the direct shear testunder three different normal stresses. As theresults of these experiments,it is recognizedthat the shear behaviour of the joint roughnessconsisted of combined two t y p e s a sp e ri t ie s canbe distributed into three modes which is basedon the sheared condition of asperities and thedilatancy behaviour, and t hat when theshearing and sliding of a sp e ri t ics issimultaneously observed during direct sheartest, the increase of the number of largegradient asperities bring about the higher peakshear strength.

2 SPECIMEN

T he specimens us in g t h e experiment make fromthe m a t e ri a l which mixed plaster.fine grainsand and water, these weight are in the ratios1.1 :0.6. After pouring this material into themold, these specimens are curing for two weeksunder 20 ° temperature and 20% lesshumidity conditions. The shapes of specimenscan be classified into four types, from withinthese, two are intact and saw cut specimen.The shape of other specimens show Figure 1and Fig ure 2. Fig u re lin d ica t est h e s hap e 0 fregular triangular joint model(it is named byRi-5), and the gradient of triangular i isI 0 0 ,20 o and 30 c res p ec t i vel y, and e a c hspccimen calls RI 0-5, R20-5 and R30-5. Table1 shows the dimensions of regular triangularspecimens. Figure 2 indicates the shape ofirregular triangular specimens, these consist ofdifferent two triangulars, and these jointprofiles are determined by the number of largegradient asperities. For example, the jointprofile which haven pieces(n=J-3) ofi,,=30°1 ria ngul a r and (5-n) pieces of i,=20° triangularis named R20-30-n. In general, each specimencan be named by "Ri,-ib-n" where i, < ib.

Therefore, in case of the ir r e gul a r triangular

-

00

u

'"

o

n

",-

I. l." 100.0 ~IFig.1 Dimension of regular triangular specimen

0~.'"

0~.",- i" "/0

'0

~"0

0;<:j.'"

in < ill

~I." 100,0 ~I

unil

Fig.2 Dimension of irregular triangular specimen.

Table I. Hcight and length for asperity of each

regular triangular specimen.

Height lengthspecimen h (mm) f (111m)

R10-5 1.76 21l.0R20-5 3.64 20.aR30-5 5.77 20.0

specimen, the joint profile which is applied tothis experiment are RIO-20-n,RI0-30-n andR2 0-30-n (n= 1-3 ).T he tot a I0 f these specimensare nine.

128

Fig.3 Testing apparatus

3 TESTING MACHINE AND PROCEDURE

Figure 3 shows the direct shear machinedeveloped for testing triangular specimens.The shear box consists of moving box (lefthand) and fixed box (right hand ). and twoboxes separat in g on shear zone. Fur t her. theinner box exists in each sh e a r b o x , andafterthespecimen puts into inner bo x .th e shear test canbestarted. The shear and normal load areapplied on vertical and horizontal directionrespectively. The direct shear test is done byi h c strain control method under the normal'tress of I 0.5.0 and 10.Okgf/cm1. t h e shearspeed beingO.1 mm/% for the all of specimens.

4 SHEAR CHARACTERIZATION OF EACHSPECIMEN

Figure 4 shows the relationships between shearst re ss.n o r m a l displacement and sheardisplacement for R20-30-1 specimen undere a c h norm a1st I' e ss. In cas e 0 I' f1 ,,~ I . 0 k gf / c m 'shear stress - shear displacement curve is like aplastic deformation. This behaviour occursonly the sliding of asperity because thedilatancy angle v is measured to almost 30·which equal to the inclinat ion of large gradientasperity, and this shear behaviour call to typeI Incaseof a ,,~5.0kgf/cm1,thedilatancy

angle v takes at bet ween 20 and

r,50E~ 4001/

""~ 30t.,

:;; 200)

OJ

~ 10"0).c

VI

4 52 3

Shear Displ.tccmcut LJ (nun)

:: 2S> 1.5Cu~~.• 05~is 0

a~kg~

a ~/=,2

~--ro<=§ -0.5Z 0 2

Shear Displaccrncm u (nun)

FigA Shear displacemcn u versus shear stress T andnormal displacement for R20-30-1.

30 U ,t h e rc f o re it is considerd that twophenomena simaluteniously o c c ur t h a t are bothof the shearing of large gr a di cn t asperity andthe S iIi di n g a Ion g I he sm a II gr a d i en t asp e ri t y ,and this shearbehaviourcallsto type 0 .l n caseof a " ~I 0.Okgf/cm1, the initial peak of shearst ress is o bse rv e d at a shear displacement of0.7mm. and subscn que n t l y , the maximum shearstrength is obtained at a sheardisplacement of2 . 7 m m. Its e ems t hat t his be h a v i0 uri s c a used bythe shearing of two different asperities. Thein it ial peak c o m c s out from the shear of largegradient asperity. the maximum shear strengthis given by t he failure of all the asperit ies, andthis shear behaviour calls to type ill It isrecognized that the shear behaviour of otherspecimens can be classified into the abovethreetypes in the region of the normal stress underthis experimental condition.

Figure 5 shows the idealized relationshipsbet ween shear st ress, normal displacement andshear displacement of three shear behaviourtype. The dilatancy angle v of each shearbehaviour can be presented by as follows;

Type I V=7lb

Type IJ ia~v<ib

Type ill: v< i,The shear behaviour types of each irregular

129

0II U 0 0

"I IIII u u

(a) (a) (a)

v v v

VI' -a,

r r

o oII u

(b)

Type

r

oII II II u

(b) (b)

Type 2 Type 3

Fig.5 Idealized relationships between shear stress r normal displacement v and shear displacement ufor each shear behaviour type.

Table 2. Shear behaviour type of irregulartriangular specimen under each normal stress.

normal stress a " (kgf/cm'lspecimen 1.0 5.0 10.nRI0-20-1 I [] f]R 10-20-2 I [] IJR J 0-20-3 I [] f]R 10-30-1 I IJ []R 10-30-2 I IJ []

R 10-30-3 I f] IJR20-30-1 I f] IIIR20-30-2 I IJ IIIR20-30-3 I [] III

triangular specimen under each normal st resswhich is classified in t o the shear typcs arcsummarized in Table 2 In this t abl e, the shearbehaviour of all the specimens under (J u

= I.Okgf/cm2 belong to type I ,and in condit ionof (J ,,=5.0kgrlcm2, the behaviour of all thespecimens indicate type IJ . When the i rr e gul a rt riangul a r specimen applied to the direct scarr e s: tinder (J ,,=IO.Okgf/cm2, the sh e ar Y

behaviour of both type Il and type ill arcobserved. and I he specimens presented Iype illare only R20-30-n under (J n =1 O.Okgf/cm2

Therefore, when the surface conditions ofspecimen which the garadient of asperity i, iscomparatively large, and high normal stress isloaded on the specimen, the type of shearbehaviour is becoming 10 ill. It is recognizedthat the classification of shear behaviour typedepends on the m a gn it tide 0 f asperit y gr a di cn tand of normal st ress.

5 EFFCT OF LARGE GRADIENT ASPERJTY

The factors of joint asperity which affect theshear behaviour are gradient, height and thenumber of the similar sh a p e a sp e r i t y ifthejoinlis constituted by h o m o ge n io us material. In thispaper, I he relationshipe bet ween large gr a di en t

of asperity and peak and residual strength ofrock joint and large gradient asperity whoseproportion occupied on joint surface arediscussed.

130

0.6"," 0.4

0.2

0

2 3 4 5 60

11

0.8

0.6v,"- 0.4

0.2

00

RIO-20-11RIO-30-11R20-30-11

a/::;o . "\~""

. ..~....•.... ; : .i:,.t/..Q...,.

11

Fig.6 ~,versus n for type 1 (" ,,= I.Okgllcm ').

0.8 a/::;

RIO-20-11RIO-30-11

0.6v,"-

0.4

0.2

oo

Fig.R ~,versus n for typc IT (" ,,=IO.Okgf/cm').

5.1 Peak shear strength

Figure 6 shows the ralationship between Sp andthe number of largegradient asperity n , andthespecimens included in this figurc belong toshcar behaviour type I ,and the condit ion ofnormal stress"" is 1.0 kgf/cm' Where thcnotation .,At. and. present Sp of RI0-5,R20-5 and R30-5 respectively, and Sp can beObtaincd by the follows equation;

Sp = (TI'-T,,,,)

«., - Tmr)

(I)

where r p the peak shear strength of eachirregural triangular specimenr 'm: the maximum shear strength of saw-cut

specimenr ,m: the maximum shear strength of intact

SpecimenIn this figure, Sp values of RI0-30-n and ofR20-30-n indicate almost the sa m e throughn=I-3 because the da i lat a n c y behaviour of type1 is only sliding up along the inclination ih =

30' for the large gradient asperity. Further,increaseing t he number of large gradient

0.8

0.6"," 0.4

0.2

06 0

a RIO-20-11/::; RIO-30-11o 1120-30-11

••. j .

·············.R3ii~5

Cb§..... ®........ ~..... ·····.jiI(j~

62II

Fig.7 ~,versus n for type IT (" ,,=5.0kgflcm').

0.8 I 0

2 3 5 64II

Fig.9 ~,versus n for type III (" ,,=IO.Okgf/cm').

asperity n , Sp of the both specimens have atendency to increae. RI0-20-n specimen'sSp isalmost constant as the number of largegradientasperity n increases, and it's constant value isnearly eqaul to Sp of R20-5 The shearbehaviour type of R20-5 under "=1.Okgf/cm' belongs to type I , therefore theSp of RI0-20-n and R20-5 is almost equalbecause the dailatancy behaviour induced byonly sliding of asperity is owing to the sameasperity inclination 20' The Sp of R30-5 isdiffrent behaviour compared with those ofRIO-30-n and R20-30-n, because the shearbehaviour of R30-5 under" ,,=I.Okgf/cm' isnot type I and is di s t r ibut e d to type IT Asthese results, it is recognized that the shearbehaviour of irregular triangular specimenswhich indicate type I is subject to themagnitude of inclination for large gradientasp e ri t y and ii's n umber.

Figure 7 and 8 show the relationship betweenSp and n of which the specimens present typeIT behaviour under a ,,=5.0 and 10.0kgf/cm'respectively. On the figure 7, the both Sp ofRl0-20-n and RIO-30-n which have smallgr a d ien t asp c ri t y con s is ted 0 f i, = lOt a k e a Imostthe same value throuth n=l, 2 and 3. Because,it isconsideredthat the largegradient asperities

131

2.5RIO-20-11RIII-10-1l/1211-111-11

a/:}o2

1.5 ..............................

.•. R20-5...,......R30"

0.5

oo

/I

Fig.IO 8,. versus n for type I (()',,=1.0kgf/cm~)

2.5

2 a RIII-20-11'" RIO-10-1I

1.5",. j ~ ~ . ..............· ; 8 ..............................•R}O:5

Gl • IUO-............... ~.. : .0.5

.•. R20-5o o 5

/I

Fig.12 8, versus n for type U «()' ,,=IOOkgf/cm~).

are sh e a rd a s t he dailataney angle vex isis in theregion of ia~ v'< ib. In case of figure R, therelationship between Sp and n indicates almostthe same to figurc 7, and in detail. these Sp ofRI 0-30-2 and RI 0-30-3 exceed those of RI 0-20-2 and RI0-20-3 by a few Further, theincreasing tendency of this relation is markedco m p are d tot hat of figurc 7. It is consideredt h a t the shear characterization for type IJdc p c nd s on the magnitude of normal stress, andthat thc factor of joint asperity producedpeak shear strength is not large gradienta s p c ri t y but small gradient asperity in.

Figure 9 represents the relationship betweenSp and n for the specimens which the shearbehaviour indicates type ill, the normal strcssunder this shear type is I 0 Gk gfvc m ". As thecharacterization of dailatancy on type illsat isfies the condit io n m e n t io n e d previously, itseems that t he all a sp e ri t ie s of one specimenare sh e a rd, and this phnomenon can beconfirmed by t h c dailataney curve during sheartest and the observation of joint surface ofspecimen after shear test. On this figure, it isrecognized that the Sp value of sp e c im e n s arealmost constant regardless of the n value. Thisshear behaviour is like a oneofintaet specimen

2.5

2a/:}o

RIO-20-11RIO-10-1IR20-10-11

1.5",.

. ";'R20-

~. ~·"O.~~ ~~5

...0. , , , ..6

6

0.5

o o 6/I

Fig.11 8, versus n for typc IJ «()' ,,=5.0kgf/cnl~).

2.5

2 I 01.5 .............................

.........:.~~g:5............P , , , .

i R20-5

op,

0,5

6o

o 65/I

Fig.13 S, versus n for type 111 «()' ,,= I O.Okgf/cm ~)

as the both asperities are sh e a rd, but the peakshear st rength of irregular triangular specimenin d i ea ted t y P e ill is lowe I' t han t hat of in tactspecimen.

5 . 2 Res i du a Ish e a I' s t I' eng t h

Figure 10-13 showthe relationship between Srand n under the same shear behaviour type andthe same normal stress. Sr is given by thefollows equation.

where r r c s idua l shear st rengt h ofirregular triangular specimen

r." residual shear strength of saw-cut specimen

r" residual shearstrength of intactspecimen.In case of Sr for each shear behaviour type,increasing the number of large gradienta sp e ri t ie s , the Sr of almost specimens exceptedRIO-20-n of type I increase. It is considerdthat the increase of number of large gradient

132

a'pnit ics brings about higher residual shearst rcngt h under t he constant normal st ressbecause t he joint surface of i r r e gul a r triangularspecimens inregion of t he residual shearcondition are bccoming to be more rough.Espccially, the r e s idua l shear strengths for theall specimcnsofn=3 cxcepted Rl 0-20-3 e x c e edthat of intact specimen. Thcreforc it isrccognized that t h e rcsidual strength of jointwhich arc constituted by two types triaugularaspcritics depend on the number of largcb'radient asperity On RI0-20-n reprcscntedFlgurc lOt he r e la t io n s h ip bet we e n SI and n IScompletely diffent against the o t h e r sp e c im e n s ,and Sr of this specimen undcr the condition offigure 10 indcates the low v a l ue in comparisonwith that of intact specimen. Undcr IT ,,=1.0kgf/cm', the maximum gradient of asperity onintact sp c c ime n aftcr shear t e st is over 20

0

thcreforc it s e e m s that this shear behaviour iscauscd which the gradient of a sp e ri t y on shearSurface of intact specimen after d ir e ct s h e a rt c st is bigger than that of large gr a di en t

aspcrity of RI0-20-n undcr (J ,,=1.0 k gf'/c m '.

6 FAILURE CURVE

Figure 14 shows the failure curves of R20-30-n , RI0-5, R20-5 and R30-5. Thc shearbchaviour of R20-30-n include t h e all sheartypes under each normal stress, and as isobvious from Table 2, the shear behaviour typeundcr e a c h normal st ress is

IT ,,= Lu k gf'/c m ' :Typc IIT ,,= 5.0kgf/cm2 :Type ITIT ,,=IO.Okgf/cm' :Type illIn this figure, it is rccognized that the failurccurvcs of each regular triangular sp e c im e n arercmarkable difference in accordance with theinclination of asperity. When the shearbehaviour indicates type (undcr (J

=1.Okgf/cm2), the peak shear strengths of

Irregular triangular sp e c im e n s crows near thatof R30-5. When t h e shear behaviour indicatestype IT (under (J ,,=5.0kgf/cm'), those peakshcarstrengths gather around that of R20-5.lncase of type ill (under (J ,,=10.Okgf/cm2), thepeak shear st r e ngt hs 0 f these spec irn e n s sca t ter,and those exists between thc peak shearstrength of R20-5 and that of R30-5. It isclarified that from these failure curves, theeach shear be h a v io ur type in di ca t e srell1arkably the differcnt characterization.

___ RIO-S

50 -----.- R20-S---r- R30-SR20-30-1R20-30-2~ 40 0 R20-30-3

l"'IE0

U:-- 30on 6::s

20... 10

8 10 12lkgt/cm2)

Fig.14 Relationshipe between randp(J for R20-30-n and R.-5.

n I

7 CONCLUSIONS

The shear behaviour of rough rock jointconsisted of two triangular asperities can bedistributed in t h r e e types, and the firstbehaviour type is the sliding along theinclination of large gradient a sp e ri t y , thesecond p r e s en t s t h e both o f the sliding alongthe inclinat ion of small gradient asperity andthe shcaring of the largc gradient asperity, thcthird is the shearing of all asperities. Thc peakshcar strength of joint in accordance with eachshear behaviour represents its own t e n den c y ,especially, it is recognized that the secondbehaviour typc has the correlation be t wee n thepeak shear strength and the number of largegradient asperit ics.

REFERENCES

Barton,N.R. and Ch o ube y , V.: Shearstrength ofrock joints in theory and practice, RockMechanics, Vol. 10, pp.I-54, 1977.Dight, P.M. and Chiu, H. K.: Predict ion of shearbehaviour of joints using profiles, Int.J.RockMech.M in. Sci. &Geomcch. Abst r. ,Vo I. 18,pp.369-386,1981.Huang,S.L. and Oelfke,S.M.: Applicability offractal characterization and modcling to rockjoint profilc, Int.J.Rock Mech.Min.Sci.&Geomcch.Abst r.,VoI.29,pp.89-98, 1992.H aberfield,C. M andJoh n st on, I.W.: A me c h an i st ically-based model for rough rock joints,Int.J. Rock Mech.M in. Sc i.&Geomech .Abst r.VoUl ,pp.279-292, 1994.Kodikara,J. K.andJohnston,I.W. :Shearbehaviour of ir r e gul a r triangular rock-concrete

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JO in is.: n t.J. Rock Mech. M in. Sci &Geo me c h ,Abst r.,Vol.3 1,pp.313-322, 1994.Ladanyi,B. and Archambault,G.: Simulation ofshear behaviour of a jointed rock mass,Proc.11 thSymp.RockMech.,AIME.pp.105-125,1970.

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