Evaluation of Rock Joint Coefficients

IOP Con e ence Se ies: Ma e ials Science and Enginee ing PAPER • OPEN ACCESS E alua ion o Rock Join Coe icien s To ci e his a icle: Ondej Audy and Tomáš Ficke 2017 IOP Con . Se .: Ma e . Sci. Eng. 245 032007 View he a icle online o upda es and enhancemen s. Rela ed con en Rock Join Coe icien s De i ed om he Th ee-Dimensional Fou ie Relie s Ondej Audy and Tomáš Ficke - NOVAE AS DISTANCE INDICATORS. S. an den Be gh and C. J. P i che - Moni o ing and e alua ion o ood alle gen labeling egula ion: a selec ion and anking model o compliance indica o s and espec i e me ics L F R C iollo, M F L Almeida and R F Calili - This con en was downloaded om IP add ess 147.229.6.155 on 06/12/2018 a 12:12 1 Con en om his wo k may be used unde he e ms o heC ea i eCommonsA ibu ion 3.0 licence. Any u he dis ibu ion o his wo k mus main ain a ibu ion o he au ho (s) and he i le o he wo k, jou nal ci a ion and DOI. Published unde licence by IOP Publishing L d 1234567890 WMCAUS IOP Publishing IOP Con . Se ies: Ma e ials Science and Enginee ing 245 (2017) 032007 doi:10.1088/1757-899X/245/3/032007 E alua ion o Rock Join Coe icien s Ondřej Audy 1, Tomáš Ficke 1 1 B no Uni e si y o Technology, Facul y o Ci il Enginee ing, Ve eří 95, CZ-602 00 B no, Czech Republic [email p o ec ed] Abs ac . A compu e me hod o e alua ion o ock join coe icien s is desc ibed and se e al applica ions a e p esen ed. The me hod is based on wo absolu e nume ical indica o s ha a e o med by means o he Fou ie eplicas o ock join p o iles. The i s indica o quan i ies he e ical dep h o p o iles and he second indica o classi ies wa y cha ac e o p o iles. The absolu e indica o s ha e eplaced he o me ly used ela i e indica o s ha showed some a i icial beha io in some cases. This con ibu ion is ocused on p ac ical compu a ions es ing he unc ionali y o he newly in oduced indica o s. 1. In oduc ion The concep o join ock coe icien s (JRC) was in oduced by Ba on and Choubey [1, 2] o y yea s ago. Ye , i has been used in geo echnical p ac ice up o p esen days. Soon a e in oducing his concep , many au ho s ied o exp ess he coe icien s JRC Rin a ious analy ical o ms. Thse and C uden [3] in es iga ed eigh di e en pa ame e s as po en ial candida es o JRC. These eigh pa ame e s include wo classical pa ame e s a R and q R aken om he a senal o oughness me ology o me allic su aces, and oo mean squa e alues 2 Z, 3 Z compu ed om he i s and second de i a i es o he measu ed p o iles, espec i ely. The eigh pa ame e s also include he pa ame e 4 Z ha ep esen s he pe cen age excess o he dis ance measu ed along he p o ile whe e he slope is posi i e o e he dis ance whe e he slope is nega i e; wo s a is ical pa ame e s called mean squa e alues (MSV) and he au oco ela ion unc ion (ACF); and, inally, he s uc u e unc ion (SF). Thse and C uden [3] compu ed all eigh pa ame e s om he measu ed wo-dimensional (2D) p o iles )(xy wi hin he leng h in e al (0, L) acco ding o he ollowing o mulae   L adxy L R 0 || 1 ,   L qdxy L R 0 2 1 ( oo mean squa e) (1)        Ldx dx dy L Z 0 2 2 1,          Ldx dx yd L Z 0 2 2 2 3 1,     nega i eiposi i ei xx L Z)()( 1 4 (2)   Ldxy L MSV 0 2 1,  Ldxxxyxy L ACF 0 )()( 1,  LdxxxyxySF 0 2 ])()([ (3) 2 1234567890 WMCAUS IOP Publishing IOP Con . Se ies: Ma e ials Science and Enginee ing 245 (2017) 032007 doi:10.1088/1757-899X/245/3/032007 Thse and C uden [3] ound ha only wo o he eigh pa ame e s, namely 2 Zand SF , a e s ongly co ela ed wi h Ba on’s join oughness coe icien JRC, and sugges ed he co esponding eg ession ela ions )log(47.322.32 2 ZJRC  , )log(58.1628.37 SFRJRC   (4) Mae z e al. [4] measu ed la ge a eas o join ock su aces using an in e es ing echnique called shadow p o ilome y and, as a desc ip o o he join oughness coe icien , p oposed he so-called oughness p o ile index p R ela ed o he so-called mic o-a e age angle i, de ined as an a e age o inclina ion angles j I be ween adjacen poin s along he sampling line           p n jjR I n i1 a ccos|| 1 1 (5) Mae z e al. [4] also sugges ed a eg ession pa e n )( pJRC RR in he ollowing o m )1(411   p RJRC (6) Hong e al. [5], [6] no iced ha he con en ional me hods o digi ized su ace p o iles usually unde es ima e he su ace oughness pa ame e s due o aliasing and he unde ec ed dead zones o su ace ex u e. Lee e al. [7] p oposed he ac al dimension as a ool o an objec i e quan i ica ion o oughness p o iles o ock discon inui ies. They compu ed dimension D om wo-dimensional p o iles by he ya d-s ick me hod, and sugges ed a eg ession equa ion as ollows: 2 015.0 1 9304.16 015.0 1 7844.3787804.0               DD JRC (7) Kula ilake e al. [8] used a spec al unc ion )( S D s K S 25 )(   (8) whe e is he spa ial equency o he wo-dimensional p o ile and s K is a cons an . They classi ied he oughness o join su aces by he h ee pa ame e s ( s KID ,, ); he symbol I ep esen ed he inclina ion angle o he aspe i ies. Al hough many o he sugges ed eg ession pa e ns men ioned abo e p o ide good esul s, he Ba on isual assessmen o join oughness coe icien s emains he mos equen ly used me hod in geo echnical p ac ice. The isual compa a i e me hod p oposed by Ba on [1] employs he measu ed oughness coe icien JRC assigned o each s anda d da abase 2D p o ile. The measu ed JRC alues ep esen one g ea ad an age o his me hod, since measu ed da a a e usually close o eali y han hose gene a ed by heo e ical models. Howe e , isual compa ison o su aces is a he subjec i e me hod. Fo his eason, i would be use ul o de elop a ully compu e ized objec i e p ocedu e ha 3 1234567890 WMCAUS IOP Publishing IOP Con . Se ies: Ma e ials Science and Enginee ing 245 (2017) 032007 doi:10.1088/1757-899X/245/3/032007 would eplace he subjec i e isual compa ison o he in es iga ed ock join p o iles wi h Ba on's s anda d p o iles. De eloping such a compu e ized p ocedu e is a goal o he p esen con ibu ion. 2. Compu e me hod The compu e me hod o assessing he ock join p o iles equi es he ock join p o iles o be digi ally scanned in he o m o a disc e e unc ion ),( ji yx . This disc e e unc ion can be i ed by he Fou ie pa ial sum ),( jiN yxF as ollows )sinsinsincos cossincoscos(),(),( 1 0, q yn p xk d q yn p xk c q yn p xk b q yn p xk ayxFyx j i kn j i kn j i kn N nk j i knknjiNji               (9) whe e )},(,),({ qqyppx        (10) dydx q yn p xk yx pq akn   coscos),( 1  (11) dydx q yn p xk yx pq bkn   cossin),( 1  (12) dydx q yn p xk yx pq ckn   sincos),( 1  (13) dydx q yn p xk yx pq dkn   sinsin),( 1  (14)               041 0,00,021 )0,0(1 nk nko nk nk kn  (15) The symbol N de ines he uppe bound )1(  N o he subsc ip s n, k, and es ic s he numbe o e ms in he Fou ie pa ial sum (9). To cha ac e ize wa y cha ac e o p o iles, he Fou ie ma ix ),( nkMN is in oduced along wi h wo indica o s )(NS and )(NH 2222 )()()()(),( knknknknknknknknN dcbankM   (16) 4 1234567890 WMCAUS IOP Publishing IOP Con . Se ies: Ma e ials Science and Enginee ing 245 (2017) 032007 doi:10.1088/1757-899X/245/3/032007       1 0 )( 1 0 |),(),(|)( N nN o N N k nkMnkMNS (simila i y indica o ) (17) |)()(|)( )( NRNRNH o (heigh indica o ) (18)      K i L jji low Nji yxFyx LK NR 11 2)( )],(),([ 1 )( (ho izon al p o ile wid h) (19) whe e LK  is a pixel esolu ion o he used digi al images c ea ed du ing scanning p ocedu e. Rock join s usually ha e a ce ain wa y base le el ),( )( ji low N yxF which is no a pa o hei inhe en su ace s uc u e and hus i should be emo ed om he scanned p o ile, i.e. ),(),(),( )()( ji co ji low Nji yx yxFyx  . So ha he Fou ie coe icien s (11) - (15) as well as he ma ix (16) a e compu ed om he co ec ed p o ile ),( )( ji co yx . Bo h he absolu e indica o s )(NS and )(NH we e discussed in ou sepa a e con e ence con ibu ion [9] and hus he es s conce ning hei capabili y o classi ying dynamical con o mi y o p o iles can be ound he e. 3. Resul s and discussions Eigh specimens o ock su aces ha e been ga he ed. Two o hem (Su ace 1 and Su ace 2) ha e been chosen as es ed su aces whe eas he emaining se en ha e se ed as da abase su aces. In he i s case, when Su ace 1 was es ed, he da abase su aces consis ed o su aces nos. 2 - 8. In he second case, when Su ace 2 was es ed, he da abase su aces consis ed o su aces nos. 1, 3 - 8. The esul ed alues o bo h he indica o s S and H ha e been plo ed g aphically in igu e 1. The bold a ows in his igu e ma ks he o al minima o he g aphs. The minima indica e couples o he mos simila p o iles (in es iga ed su ace e sus da abase su ace). Fo example, he minimum o S indica o associa ed wi h Su ace 1 is loca ed a he da abase no. 4 which means ha Su ace 1 and da abase su ace 4 ep esen he wo mos simila su aces among all he possible couples o su aces con aining Su ace 1. Figu e 1. Resul ed alues o he simila i y and heigh indica o s ela ed o selec ed wo p o iles (Su ace 1, Su ace 2) and da abase p o iles (1 - 8) 5 1234567890 WMCAUS IOP Publishing IOP Con . Se ies: Ma e ials Science and Enginee ing 245 (2017) 032007 doi:10.1088/1757-899X/245/3/032007 As seen om igu e 1, bo h he indica o s S and H de e mines he same couples o he mos simila su aces, namely Su ace 1 e sus da abase su ace no. 4 and Su ace 2 e sus da abase su ace no. 8. By expec ing isually all possible couples o su aces, we came o he same conclusions. This ac migh suppo he unc ionali y o bo h he indica o s. Howe e , he iden ical esul s o hese indica o s is no a qui e na u al ma e . Occasionally, di e en esul s may appea . This is unde s andable since su ace p ope ies ela ed o p o ile heigh s and p o ile shapes a e no igh ly co ela ed and hus hei a ious combina ions may occu . Fo example, wo p o iles may ha e compa able heigh s bu qui e di e en wa y shapes. In such a case he indica o s H and S will ine i ably de e mine di e en couples o he mos simila su aces. The ques ion is how such a si ua ion should be sol ed. The answe is easy. Since he compa ison is done be ween an in es iga ed specimen and he s anda d da abase p o iles, whose JRC a e known, he ele an couple will be ha associa ed wi h he smalle da abase JRC. Such a solu ion will always be a he side o highe sa e y. 4. Conclusions The compu e ized compa ison o ock join p o iles wi h s anda d da abase p o ile is an objec i e p ocedu e based on nume ical indica o s. In his con ibu ion, wo indica o s o wa y shape and p o ile heigh ha e been in oduced and subjec ed o p elimina y es s o e i y hei unc ionali y. These p elimina y es s ha e indica ed ha employmen o he wo indica o s could be p ospec i e bu a u he es s a e necessa y o a inal decision. Acknowledgmen Suppo o his p ojec was p o ided by he G an Agency o he Czech Republic (p ojec no. 13- 03403S). The Fou ie compu a ions we e pe o med by he so wa e w i en by Assoc. P o . D. Ma išek, PhD. Re e ences [1] N. Ba on, Re iew o a new shea -s eng h c i e ion o ock join s. Enginee ing Geology, ol. 7, pp. 287-332, 1973. [2] N. Ba on and V. Choubey, "The shea s eng h o ock join s in heo y and p ac ice", Rock Mechanics, ol. 10, pp. 1–65, 1971. [3] R. Thse and D. M. C uden, "Es ima ing join oughness coe icien s", In . J. Rock Mech. Min. Sci. & Geomech. Abs ., ol. 16, pp. 303–307, 1979. [4] N. H. Mae z, J. A. F anklin and C. P. Benne , "Join oughness measu emen using shadow p o ilome y", In . J. Rock Mech. Min. Sci. & Geomech. Abs ., ol. 27, pp. 329–343, 1990. [5] E. S. Hong, I. M. Lee and J. S. Lee, "Measu emen o ock join oughness by 3D scanne ", Geo ech. Tes ing J., ol. 29, pp. 1–8, 2006. [6] E. S. Hong, I. M. Lee and J. S. Lee, "Unde es ima ion o oughness in ough ock join s", In . J. Nume . Anal. Me h. Geomech., ol. 32, pp. 1385–1403, 2008. [7] Y. H. Lee, J. R. Ca , D. J. Ba and C. J. Haas, "The ac al dimension as a measu e o he oughness o ock discon inui y p o iles", In . J. Rock Mech. Min. Sci. & Geomech. Abs ., ol. 27, pp. 453–464, 1990. [8] P. H. S W. Kula ilake, G. Shou, T. H. Huang and R. M. Mo gan, "New peak shea s eng h c i e ia o aniso opic ock join s", In . J. Rock Mech. Min. Sci. & Geomech. Abs ., ol. 32, pp. 673–697, 1995. [9] O. Audy and T. Ficke , "Rock join coe icien s de i ed om he h ee-dimensional Fou ie elie s", Wo ld Mul idisciplina y Ci il Enginee ing-A chi ec u e-U ban Planning Symposium- WMCAUS, 12 -16 June, 2017, P ague.