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1 YPICAL ROUGHNESS PROfiLES J RC

I f I 0. 4

2 f- I 2 . 8

3 I -j

5 . 8

4 I - - - - - 1 6. 7

5 ~ 9 . 5

6 ~ 10. 8

7 ~ 12. 8

8 I--~ 14. 5

9 ~ 16. 7

\0 ~ 18. 7

0 5 10I , J cm SC1l.LE

Fi gur e 1. Typi cal r oughness pr of i l es andt he J RC val ues ( Bar t on &Choubey, 1977) .

T=shear st r ess

0n=normal st r essb=f r i cti on angl e of sur f ace wi t hout

r oughnessJ CS=j oi nt wal l compr ess i ve st r engt h

Bart on &Choubey( 1977) conduct ed sheart es t s of 10 di f f er ent r oc k j oi nt s anddet er mi ned t he val ue of J RC f or each j oi ntf r om back- cal cul at i on usi ng Eq. ( l ) . Thet ypi cal pr of i l es and t he J RC val ues ( r e -f er r ed t o her e as B- C pr o f i l es and B- C J RC

val ues, r especti vel y) shown i n Fi g. 1 ar eadopt ed i n t he suggest ed met hods f or t hequant i t at i ve descri pt i on of di scont i nui t i esi n r ock masses ( I SRM, 1978) . I n order t odet er mi ne t he J RC val ue of a pr of i l e i nquest i on, t he pr of i l e must be vi sual l ycompar ed wi t h t he B- C pr of i l es. As a r esul t

t he esti mat e t ends t o be subj ecti ve. Fort hi s r eason, many r esear cher s have i nvest i -gat ed t he cor r el at i on bet ween t he B- C J RC

val ues and st at i st i cal par amet er s ( Tse &Cr uden, 1979; Reeves, 1985; Yu &Vayssade,1891) or f r actal di mensi ons ( Tur k et al . ,

1987; Lee et al . , 1990; Xi e &Par i s eau,1992) of t he B- C pr of i l es. However , t he B- C

J RC val ues t hemsel ves i ncl udes a f ew pr ob-

l ems; ( 1) A j oi nt sur f ace ext ends i n t wodi mensi ons, and t he r oughness changes not

onl y al ong a pr of i l e but al so acr oss t he

pr o f i l e. The t es t r es ul t s us ed t o c al c ul at e

t he B- C J RC val ues do not r ef l ec t t he B- Cpr of i l es al one. ( 2) The degr ee of mat chi ngof bot h sur f aces i s not cl ear l y descr i bed

i n t hei r paper . When one hal f has a pr o-f i l e, t he ot her hal f does not necessar i l y

have t he same pr of i l e. ( 3) Si nce t he shearst r engt h of a j oi nt depends on t he shear i ng

di r ect i on ( Aydan &Kawamot o, 1990; Huang &Doong, 1990) , each of t he B- C pr of i l es may

have t wo di f f er ent J RC val ues.I n t hi s st udy, f i r st l y, 10 al umi num

speci mens i ncl udi ng t he B- C pr of i l es i n t heshear i ng di r ecti on but no r oughness i n t he

per pendi cul ar di r ect i on were made wi t h anumeri cal l y cont r ol l ed cut t i ng t echni que,and pl ast er speci mens wer e made by cast i ngi nt o t he al umi num speci mens. Secondl y, push

t est s wer e per f ormed under a l ow nor mal

str ess gener ate d by t he sel f - wei ght of t heupper hal f usi ng t he al umi num speci mens,and shear t est s under nor mal st r esses

r angi ng f r om 0. 1 MPa t o 4 MPa usi ng t hepl ast er speci mens. Fi nal l y, t he cor r el a-

t i ons of s t a t i s t i c al par a met er s of t he B- Cpr of i l es wi t h t he push t est r e sul t s wer e

exami ned t o char acteri ze t he j oi nt pr o-

f i l es.

2 TEST PROCEDURES

2. 1 Push t est s usi ng al umi num speci mens

To pr epar e t he speci f i c speci mens, t he B- Cpr of i l es shown i n Fi g. l wer e enl ar ged f our

t i mes wi t h a copy machi ne. Roughness dhei ght s of t he enl ar ged pr of i l es wer e r eaout usi ng a di gi t i zer , at 1 mm i nt er val sal ong t he pr of i l es. As a r esul t , sampl i ng

i nt er v al s f or t he or i gi nal pr o f i l es ar e0. 25 mm, and t he number of data i s about400 f or each pr of i l e. L i near t r ends wer e

excl uded f r om the pr of i l es by r egr essi on

anal ysi s. Thi s modi f i cat i on may make a

sl i ght di f f er ence bet ween t he pr esentpr o f i l es and t he B- C pr o f i l es , but i t i s

necessar y f or exami ni ng t he ef f ect ofshear i ng di r ect i on on t he st r engt h. usi ngkst he di gi t i zed pr of i l e data, al umi num bl oC( 10 cm l ong by 3cm wi de by 8 cm hi gh) wer e

cut at t he mi d- hei ght , wi t h a numer i cal l Ycont r ol l ed machi ne havi ng a wi r e saw of adi amet er of 0. 25 mm. Fi gur e 2 shows t he

al umi num speci men composed of t wo hal vesl eswhose sur f aces have one of t he B- C pr of 1 ' ni n t he l engt h di r ect i on but no r oughneSS 1

t he wi dt h di r ect i on.

Push t est s wer e per f or med usi ng t heal umi num speci mens, wher e t he upper hal f

was hor i zont al l y moved par al l el t o t he _ j oi nt sur f ace unt i l a hor i zont al di s pl ace

ment of 10 mm was r eached at a const ant

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Fi gur e 2. The speci men used i n push t est s.

r at e of 0. 01 mm/ sec. Then, f r i cti on f or ces

between t he upper and l ower hal ves weremeasur ed at i nt er val s of 1 second usi ng aSmal l l oad cel l at t ached t o a push r od. Thenor mal st r ess of 1. 06 kPa was gener at ed byt he s el f - wei ght of t he upper hal f . A c on-Vent i onal di spl acement meter such as an

LVOT is unsui t abl e t o measur e t he di l at i onof t he upper hal f because t he r eacti on

f or c e is not negl i gi bl e compared wi t h t hewei ght of t he upper hal f . Hence, a l aserdi spl acement met er of non- cont act t ype wasuSed f or measur i ng t he di l at i on. The pusht est s wer e per f or med i n t wo di f f er ent

Shear i ng di r ect i ons. When t he upper hal f ismOVed t o t he l ef t , i t is r ef er r ed t o her eas t he l ef t t es t ( L - t es t ) , and when t heuPPer hal f is moved t o t he r i ght , i t is

r ef er r ed t o as t he r i ght t es t ( R- t es t ) . I naddi t i on, f or exampl e, t he l ef t t es t and

t he r i ght t es t us i ng t he No. 5 B- C pro f i l especi men are t er med L5 and R5, r espect i ve-l y .

2. 2 Shear t est s usi ng pl ast er speci mens

~he mat er i al used f or shear t est s is pl as-er . The pl as t er: wat er r at i o is 1: 0. 4 by

Wei ght , and t he uni axi al compr essi ve

~t r engt h of t he model mater i al is 21. 5 MFa." ' Odel . . h

1 J O~nt s wer e made by c as t i ng t ep ast er mat er i al i nt o t he al umi num speci -mens ( whose j oi nt sur f ace i s 10 cm by 8 emand w' dt ~ er t han t he one us ed i n t he pusht ~st S) havi ng t he No. 2, No. 5 and No. 8 of

e B- C pr of i l es.

f Lef t

shear t est s wer e per f or med under~ve c t 1 MFo ons ant nor mal s t r es ses of O. a,

d:4

l 1Pa, 1 MPa, 2 MPa and 4 MPa, usi ng a

a~r ect shear t est i ng appar at us ( Esaki etsh ' 1991) . The pl ast er speci mens wereU ear ed at a const ant r at e of 0. 025 mm/ sect ~ t o a di spl acement of 10 mm. Four conven-

~onal di spl acement t r ansducer s wer e set at

t h e c or n er s of t h e upper s hear box t o

measur e di l ati on and r otat i on.

Af t er t e st i ng, t he j oi nt s ur f ac es wer el i ght l y br ushed t o r emove t he pl ast erpowder ed by shear i ng and one hal f of t hespeci men was pl aced on an aut omat i c st age.

Pr of i l e hei ght s of t he sur f ace wer e meas-ur ed at 0. 05 mm i nt er val s al ong a scanl i neat t he mi d- wi dt h of t he speci men, usi ng al aser di spl acement met er. The ot her hal fwas al so measur ed. Thi s syst em wi t h a l aser

di spl acement met er makes speedy and pr eci semeasur ement s of j oi nt r oughness ( Lee &J uang, 1990) .

3 TEST RESULTS

3. 1 Push t est s usi ng al umi num speci mens

Fi gur es 3( a) and 3( bl show t he shearst r ess- shear di spl acement cur ves ( sol i dl i ne) and di l at i on- shear di spl acement

cur ves ( br oken l i ne) whi ch wer e obt ai nedf r om t he L4 and L8 t es t s . Wi t h i nc reas i ngt he shear di spl acement , t he shear st r essi ncreases and r eaches i t s maxi mum val ue

enen

wC l::

tiO.s

jIen

(a)3~EE

2~0;:::

, : 5is

10 a

6

(b)5

4S

3z0;:::

2~

2.0

0

iLS

3en

en

wg : : 1.0en

C l::

l 5I

e n o .s

2 4 6 8 10 0

SH EAR D I SPLAC EM EN T (mm)

Fi gur e 3. Shear st r ess- shear di spl acement( sol i d l i ne) and di l at i on- shear di spl ace-

ment ( bro ken l i ne) c ur ves f or t he L4 t es t

( a) and t he L8 t est ( b) usi ng t he al umi numspeci mens. Ci r cl es and t r i angl es show t hes hear s t r es s and di l at i on c al c ul at ed f r omt he di gi t i zed pr of i l es, r especti vel y.

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i mmedi atel y af t er t he begi nni ng of shear-

i ng. Ther eaf t er , t he s hear s t r es s i r r egu-

l arl y changes havi ng smal l peaks, andsomet i mes dr ops t o near l y zer o i n t he L4t est . Roughl y speaki ng, di l ati on monoto-

nousl y i ncreases wi t h t he shear di spl ace-ment . Thi s di l at i on f i nal l y r eaches a

const ant val ue when t he J RC i s smal l .The shear st r engt h of a r ock j oi nt i s

r el at ed t o t he f r i c t i on angl e of t he s moot hsur f ace and t wo addi t i onal wor ks necessar y

f or shear i ng t he asper i t i es and f or r i di ngup on each ot her . Damage t o asper i t i es

dur i ng shear i ng i s negl i gi bl e because t hepush t est s wer e per f or med under an extr eme-

l y l ow nor mal st r ess usi ng t he al umi numspeci mens. Hence, t he r el at i on i s expr essedas

F( u) =W ( dv/ du) +W t an b ( 2)

wher eF(u) =shear f or ce

u=shear di spl acementv=di l at i onW=wei ght of t he upper hal f

I f changes i n di l at i on wi t h t he shear

di spl acement are known, we can est i mate t heshear f or ce by usi ng Eq. ( 2) . Tr i angl es i nFi g. 3 show t he di l at i on cal cul at ed usi ngt he di gi t i zed pr of i l es. Al t hough t he di l a-

t i on f r om t he push t ests i s smal l er t han

t hat f r om t he cal cul at i on, t hey have asi mi l ar t endency. Subst i t ut i ng t he cal cu-l at ed di l at i on i nt o Eq. ( 2) gi ves t he shearst r ess mar ked wi t h ci r cl es i n Fi g. 3. Theest i mat ed peak shear st r ess appear s at ashear di spl acement of 0. 25 mm, whi ch i s t hef i r st i ncr ement of t he shear di spl acement

i n t he si mul at i on, and i s hi gher t han t hatf r om t he exper i ment . Af t er t he peak str ess,t he changes i n t he est i mat ed shear st r essesagr ee wi t h t hose f r om t he exper i ment .

Fi gur e 4 shows t he r el at i onshi p bet weent he B- C J RC val ues and t he f r i cti on angl es,

, obt ai ned f r o m t he pus h t es t s . I t s houl dbe not ed t hat t he f r i c t i on angl es f r o m t heL- t es t and t he R- t es t f or t he s ame pr o f i l ear e di f f er e nt . Par t i c ul ar l y i n t he No. 9pr of i l e, t hi s di f f er e nce i s 20 degr e es.Accor d i ng t o Eq. ( l ) , t he r e l at i on shown i n

Fi g. 4 shoul d be expr essed as a l i near onebecause t he J CS and t he nor mal st r ess ar ehel d const ant i n t he pr esent exper i ment .

The r esul t s of t he L- t est s gi ve a bet t erl i near i t y t han t hos e of t he R- t es t s . I t i spr esumed t hat Bart on and Choubey sheared

t he upper hal ves of t hei r speci mens t o t he

l ef t . The s t r ai ght l i ne pl ot t ed i n Fi g. 4 i sobt ai ned f r om l i near r egr essi on anal ysi sf or t he r es ul t s of t he L- t es t s , except t heLl and L2 t es t s , and i s expr es sed as

80

o Left

6 Right

5 2010JR C

Fi gur e 4. The r el at i onshi p bet ween t he J RCval ues and t he f r i ct i on angl es obt ai nedf r o m t he pus h t es t s .

15

=3. 2 J RC+8 (3 )

( The r e ason f or excl udi ng t he t wo t ests i st hat t he r el at i ve er r or i nc l uded i n adi gi t i zed pr of i l e i s l ar ge i n such pl anarpr of i l es as t he No. 1 and No. 2. ) The i nt er -

cept of 8 degr ees i n Eq. ( 3) i s det er mi ned

f r om a push t est usi ng t he speci men havi nga smoot h ( no r oughness) pr of i l e. Even i nt he L -t est s, some of t he B- C J RC val ues ar e

i nappr opr i at e f or t he B- C pr of i l es. Ther e ason i s t hat t he B- C J RC val ue r e f l ects

t he whol e of a j oi nt sur f ace, whi l e t hef r i cti on angl e obt ai ned f r om the pr e' sent

exper i ment r ef l ects t he pr of i l e i n onedi mensi on. I n t he next chapt er , a newcoef f i ci ent J RC* i s used, whi ch i s gi ven bY

s ubs t i t ut i ng t he f r i c t i on angl e f r o m t hepush t est i nt o Eq. ( 3) and has t wo val uesf or each B- C pr of i l e, f or char acter i zi ng

t he pr of i l es.

3. 2 Shear t est s usi ng pl aster speci mens

The shear st r ess - shear di s pl acement cur veS

and di l ati on- shear di spl acement cur vesobt ai ned f r om t he shear t est s under con-st ant nor mal st r esses f r om 0. 1 MPa t o 4 MPa

f or t he No. 8 pr of i l e ar e shown i n Fi g.5Whi l e t he maxi mum shear st r ess i ncr eases

wi t h t he nor mal str ess, such a shar p peak

at t he begi nni ng of shear i ng as seen i n

Fi g. 3( b) i s not obser ved. Di l at i on, undert he nor mal st r ess of 0. 1 MPa, i s near l yequal t o t hat obt ai ned f r om t he push t est ,but i t becomes t o be st r ongl y suppr essed

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Normol stress

4 M P o

2 M P o

l MPo

O.4MPo

O.IMPo

2 4 6 8 10S H E A R D I S PL A C E M E N T (mm)

2 4 6 8S H E A R D I S PL A C E M E N T (mm)

10

F'~gur e 5. Shear st r ess- shear di spl acement

and di l ati on- shear di spl acement cur vesunder di f f er ent nor mal st r esses usi ng t hepl ast er speci men of t he No. 8 pr of i l e.

wi t h i ncreases i n t he nor mal st r ess.

Fi gur e 6 s hows t he pr of i l es of t he upper~nd l ower sur f aces measur ed af t er shear i ngf he No. 5 pl ast er speci men. For dr awi ng t hi sh~gur e, t he upper and l ower pr of i l es, whi ch

~ve no damage and ar e i dent i cal , ar e f i r st~haced at t he same posi t i on. Af t er t hat ,t he upper pr of i l e al one i s moved l a mm t od.e l ef t and t h en r o t at ed ac cor d i ng t o t he

~l at i on measur ed at t he f r ont and r earends of t he upper shear box. Fi nal l y, t he

uPPer prof i l e i s moved ( about 2. 1 mm)uPwar d unt i l t he bot h pr of i l es are i n

Cont act at a poi nt . The hat ched par t s

~epr esent t he asperi t i es damaged by shear -~ngr , and t he bl ack ones t he gouge mat er i al

ber na~ned on t he sur f ace i n spi t e of l i ghtr Ush'

and ~ng .The l ef t end of l ower pr of i l es

a t h e r ~ght one of upper pr o f i l es f ai l i nt e '1I t ns~ e mode r at her t han i n a shear mode.d s houl d be not e d t h at as per i t i es ar e

aar naged at hi gh and negati ve sl opes. Thesper ' t

0. 1 ~ Y. damage under t he nor mal st r ess ofas MPa ~s s l i ght , s o t hat di l at i on oc cur st i mUch as t hat of t he pus h t e st . I n addi -

no~~' t he r ot at i on of t he upper hal f i sst ~ceabl e. Wi t h i ncr easi ng t he normal

dur ~ss, t he ar ea of asper i t i es damaged1 r ~ng sheari ng becomes l ar ger and t hi s

F~ad t o decreased di l at i on. The ar r ows i n9. 6 i nd'and ~c at e t he pl ac es wher e t he upper

l ower s ur f ac es were i n c ont ac t at t he

Fi gur e 6. Asper i t i es damaged by shear i ngunder di f f er ent nor mal st r esses ( No. 5pr of i l e)

shear di spl acement of l a mm. The r ati o oft he s urf ac e i n c ont ac t i nc reas es wi t h t henor mal s t r es s , but i t i s about 20 % even att he nor mal st r ess of 4 MFa.

Fi gur e 7 shows t he r el at i onshi p bet weent he nor mal st r ess and t he ar ea of damagedasper i t i es f or t he No. 2, No. 5 and No. 8pro f i l es , where t he bot h ends of t he pr o-f i l es ar e excl uded. Whi l e t he t hr ee pr o-f i l es have qui t e di f f er ent r oughnes s , t he

ar ea of damaged asper i t i es i s r el at i vel y

si mi l ar t o each ot her . I n t he No. 2 pr of i l e,however , i t seems t hat a l i mi t of damagedar e a i s r e ac hed at a nor mal s t r es s of 2MPa. The maxi mum ar ea of asperi t i es pr onet o be damaged dur i ng shear i ng i n a pr of i l e

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- - -NE 50. . s

(f)

wf=4Da : : :wa,(f)

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*~

20 o dx=0.25 mm6dx=l mm

20 ~ 60 80

arctan Sm (degrees)

Fi gur e 9. The r el at i onshi p bet ween ar ct anSm and J RC*.

20 6 0

o dx=0.25 mm6dx=l mm

6 0

60

1560 ill

90 0

*6 00:: 6 0- - ,

10 ~ 0

6 060

6o 6 05 6 0

6 hi) 0

6 0

, , ,

5 10 15arctan So (degrees)

20

Fi gur e 10. The r el at i onshi p bet ween ar ct anSa and J RC*.

~~gd~r e 0. 25 mm. Wi t h i ncr eases i n dx, t her aa ~ent s ar e di st r i but ed i n nar r oweri snges. and t he peaks become hi gher. There

an ~ S~gni f i c ant di f f er enc e i n t he f r i c t i ont h

ges f r om t he L- t es t and t he R- t es t on

eN09 fiLgr ad' p~o ~ e, as s een i n Fi g. 4. TheSUch~ent d~st r i but i ons i n Fi g. S( b) pr esent

s t a char act er i s t i c of t he s hearr engt h. For dx=O 25 mm and 1 mm gr adi -

ent s hi - : 'negat . gher t han 40 degr ees appear i n t heal t h ~ve s l opes r el at ed t o t he L- t es t s ,

Ough t he f r equency is l ow. Such hi gh

0. 4

> -

~OJ

EwO.2>

~"'0.1

Normal eb-ese

G---O 0.1 MPa

- l:> 1 MPa0 0 4MPa

o

Fi gur e 11. The gr adi ent di st r i but i ons f ort he No. 5 pr of i l e shear ed under di f f er entnor mal st r esses ( dx=l mm) .

gr adi ent s do not exi st i n t he posi t i ves l opes rel at ed t o t he R- t es t s .

Consi der i ng t hat t he uni t of J RC* is t heangl e ( i n degree) , i ns t ead of Sm ( c ons i s t -i ng of SmP and Smn) , ar ct an Sm is correl at-ed wi t h t he J RC* ( Fi g. 9) . The cor r el at i on

coef f i ci ent s ar e 0. 97 f or dx=0. 25 mm and0. 95 f or dx=l mm. The r egr essi on equat i ons

ar e expr essed as

J RC*=- 3. 74+0. 36 ar ct an Smf or dx=0. 25 mm ( S a)

J RC*=- 1. 05+0. 41 ar ct an Smf or dx=l . O mm ( Sb)

I f damage t o asperi t i es is negl i gi bl edur i ng shear i ng, ; he r el at i onshi p bet weenar ctan Sm and J RC can be expr essed as

J RC*=1/ 3. 2 ar ct an Sm (9)

wher e t he val ue of 3. 2 is t he s l ope of t her egr essi on l i ne pl ot t ed i n Fi g. 4. Equat i on( 9) is pl ot t ed i n Fi g. 9. Al t hough t hepar amet er of ar ctan Sm has a st r ong cor r e-l at i on wi t h J RC* as ment i oned above,Eqs. ( Sa) and ( Sb) do not compl et el y agr eewi t h Eq. ( 9) . I t appears t hat Eq. ( 9) is

s ui t abl e t o hi gher val ues of ar c t an Sm f ordx=0. 25 mm and l ower ones f or dx=l mm. Thi ss ugges t s t hat t he s t at e of c ont ac t bet weent wo s urf ac es , gover ni ng t he f ri c t i on angl eor di l at i on, var i es wi t h t he J RC val ues.

The r el at i onshi p bet ween t he J RC* andarct an Sa f or dx=0. 25 mm and dx=l mm is

shown Fi g. 10, wher e Sa consi st s of SaP andSan. The cor r el at i on coef f i ci ent s ar e 0. 93f or dx=0. 25 mm and 0. 92 f or dx=l mm, andar e sl i ght l y l ower t han t hose of ar ctan Sm.

However , si nce t he par amet er of Sa is anaver age gr adi ent of posi t i ve or negat i ve

sl opes i n a pr of i l e, i t may be mor e pr acti -cal t han Sm bei ng t he maxi mum of t he

sl opes.Fi nal l y, t he f r equenc y of gr adi ent s , f or

dx=l mm, of t he No. 5 pr of i l e measur ed af t er

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