Rock join coe icien s and hei compu e ized classi ica ion
Tomáš Ficke
Facul y o Ci il Enginee ing, B no Uni e si y o Technology, 60200 B no, Czech Republic
a icle in o
A icle his o y:
Recei ed 24 July 2017
Recei ed in e ised o m 8 No embe 2017
Accep ed 8 July 2019
A ailable online 12 July 2019
Keywo ds:
Rock join s
Shea s eng h
Join ock coe icien s
Nume ical indica o s
Compu e ized assessmen
abs ac
A compu e ized me hod o de e mining ock join coe icien s is p esen ed. Two ela i e simila i y indi-
ca o s a e in oduced o classi y su ace mo phology o ock join s. The classi ica ion enables o compa e
in es iga ed and da abase ock join s. Such a compa ison aims a inding he couple o su aces ha a e
dis inguished by he highes dynamical con o mi y. The i s absolu e indica o esul s om he Fou ie
ma ix and e alua es wa y shapes o su aces. The second absolu e indica o quan i ies he heigh s o
su ace elie s and is de ined as he oo mean squa e heigh o he su ace ou line. Nume ical eliabili y
o hese indica o s is es ed wi hin he su ace analysis o a se ies o limes one specimens. Besides he
compu e ized assessmen , 25 people ha e pe o med isual assessmen o hese limes one specimens.
The esul s o isual assessmen s ha e been s a is ically p ocessed and compa ed o he esul s ecei ed
om he compu e ized p ocedu e. The newly in oduced absolu e indica o s ha e p o ed o be p ospec-
i e nume ical ools o e alua ing join ock coe icien s.
Ó2019 Published by Else ie B.V. on behal o China Uni e si y o Mining & Technology. This is an open
access a icle unde he CC BY-NC-ND license (h p://c ea i ecommons.o g/licenses/by-nc-nd/4.0/).
1. In oduc ion
Recen ly, a new me hod o oughness assessmen o ock join s
has been ou lined [1]. The me hod has been designed as a ully
compu e ized p ocedu e whose scena io esembled he isual
me hod published by Ba on and Choubey [2,3]. In ha compu e -
ized me hod, isual assessmen was eplaced by nume ical assess-
men ealized by wo simila i y indica o s. In ha me hod, bo h
he simila i y indica o s we e ep esen ed by he ela i e uni less
a ios ha howe e we e occasionally nume ically uns able and,
in addi ion, he used ela i e o ms p o ed o be concep ually
p oblema ic.
In he p esen con ibu ion, a new e sion o he compu e ized
me hod is de eloped. In his me hod, he absolu e simila i y indi-
ca o s a e employed ins ead o he ela i e ones. The absolu e indi-
ca o s p o ide a non-p oblema ic concep ual solu ion and show
be e nume ical s abili y. The p esen s udy illus a es unc ional-
i y o he new absolu e indica o s and desc ibes all necessa y s eps
ha p ecede, accompany and accomplish he new compu a ional
p ocedu e. The ha dwa e and so wa e o he new p ocedu e ha e
been modi ied o be capable o p ocessing la ge ock species,
whose linea dimensions equal hose implemen ed in he Ba on
and Choubey s anda d isual me hod [2,3].
The con inual in e es in oughness coe icien s o ock join s is
caused by he ac ha he su ace oughness o ock join s consid-
e ably in luences he mechanical s abili y o ock masses. Su icien
s abili y o ock masses is a p e equisi e o he mechanical s abil-
i y o la ge ci il enginee ing s uc u es, such as unnels, dams o
b idges si ua ed in egions whe e he ock masses con ain discon-
inui ies. Join s, aul s, shea zones, bedding su aces o olia ions
a e some o he discon inui ies ha may cause s uc u al weakness
o ock masses. In he majo i y o cases, he s ess le el due o g a -
i y loads is smalle han he comp essi e s eng h o ocks; hus,
he e is li le endency o in ac ocks o ac u e. Howe e , he
discon inui ies si ua ed wi hin s eep slopes show a endency o
sliding. Shea s eng h a he han comp essi e s eng h is he e-
o e decisi e o s abilizing ock masses. Fo his eason, he assess-
men o he shea s eng h o ock discon inui ies is c ucial. Se e al
ac o s in luence shea s eng h: geome y o discon inui ies, su -
ace i egula i ies, physical p ope ies o adjacen ocks, in illing
ma e ials, and g oundwa e a e some o hem. I is no i ial o
decide which one is mos impo an . The ac is ha he su ace
i egula i y o ock join s is one o he mos impo an ac o s. Rock
join s a e o en plana and mos ly o m a space ne wo k embedded
in o ock masses (Fig. 1).
In geo echnics, he e is a long-las ing in e es in he su ace
mo phology and shea s eng h o ock join s. Se e al models o
calcula ing shea s eng h exis . These models ake in o accoun
aspe i ies as ele an ac o s in luencing shea s eng h. Pa on
[4] was p obably he i s who de eloped a shea s eng h model
o ough ock join s. His model was based on expe imen s ca ied
ou on saw- oo h iangula aspe i ies. La e on, Ladanyi and
A chambaul [5] succeeded in de eloping a model ha inco po-
h ps://doi.o g/10.1016/j.ijms .2019.07.002
2095-2686/Ó2019 Published by Else ie B.V. on behal o China Uni e si y o Mining & Technology.
This is an open access a icle unde he CC BY-NC-ND license (h p://c ea i ecommons.o g/licenses/by-nc-nd/4.0/).
E-mail add ess: [email p o ec ed]
In e na ional Jou nal o Mining Science and Technology 29 (2019) 701–709
Con en s lis s a ailable a ScienceDi ec
In e na ional Jou nal o Mining Science and Technology
jou nal homepage: www.else ie .com/loca e/ijms
a ed he mechanisms o sliding and shea ing o aspe i ies in o one
equa ion. Kula ilake e al. [6,7] published al e na i e peak shea
s eng h c i e ia o ock join s. Thei empi ical model o peak
shea s eng h is mul i-pa ame ic and akes in o accoun he
di ec ional dependence o he shea s eng h.
Ba on’s [2] model is one o he mos equen ly used models in
geo echnical p ac ice. Ba on and Choubey [3] showed expe imen-
ally ha he shea s eng h o ock join s
s
depends s ongly on
he aspe i ies o adjacen su aces, as ollows:
s
¼
n
g R
JRC
log
o
n

þU
b
 ð1Þ
whe e R
JRC
is he so-called join oughness coe icien (JRC),
n
he
no mal e ec i e s ess,
o
he e ec i e join wall comp essi e
s eng h (JCS) and
U
b
he basic ic ion angle (i.e. he ma e ial con-
s an ). The complexi y o e alua ing
s
consis s o he complexi y o
de e mining R
JRC
. The join oughness coe icien R
JRC
has no
assumed an exac analy ical exp ession ha would show accep able
pe o mance in all he cases whe e he join su aces may mani es
hemsel es. Ba on and Choubey [3] sugges ed calcula ing R
JRC
as
ollows:
R
JRC
¼
a c g
s
n

log
o
n
 ð2Þ
In addi ion, hey p oposed a sys em o 10 e e ence g aphical
su ace pa e ns oge he wi h he co esponding join oughness
coe icien s R
JRC
2(0, 20). These s anda d pa e ns o known R
JRC
alues enable isual assessmen o su ace i egula i ies o ock
join s. This isual assessmen may be a he subjec i e, bu is o en
used as a apid and app oxima e ool o de e mining R
JRC
alues.
A good o e iew o a ious me hods o measu ing and quan i-
ying he join oughness coe icien s in cu en geo echnical p ac-
ice has been published by Mo elli [8]. A comp ehensi e o e iew
o exis ing empi ical i ing pa e ns o JRC can be ound in he wo
ecen ly published pape s by Li and Zhang [9] and Li and Huang
[10]. In he i s pape Li and Zhang summa ize hose pa e ns
which employ a ious measu able opog aphic pa ame e s. The
second pape by Li and Huang summa izes exis ing empi ical i -
ing pa e ns o JRC ha a e based on he ac al dimensions D
o he measu ed p o iles o join ed su aces. O he wo pape s con-
ce ning beha iou o ock join s ha e appea ed only ecen ly
[11,12].
Besides he join oughness coe icien s, associa ed wi h he
Ba on isual me hod, he e a e a ious o he oughness coe i-
cien s ha can cha ac e ize su ace i egula i ies [13–17], bu he
join oughness coe icien s speci ied by Eq. (2) a e e y special
indica o s de i ed om expe imen al measu emen s o shea
s eng h de ined by Eq. (1). This makes hem op imally adap ed
o geo echnical pu poses.
Soon a e Ba on’s JRC concep [3] had been published, some
ollowe s appea ed who ied o exp ess he coe icien s R
JRC
in a -
ious analy ical o ms [18–21] using eg ession p ocedu es.
Al hough many o he sugges ed eg ession pa e ns 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 [2] employs
he measu ed oughness coe icien R
JRC
assigned o each s anda d
wo-dimensional (2D) da abase 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 wi h he s anda d
pa e ns seems o be a he p oblema ic. When se e al people pe -
o m isual compa isons, i can ha dly be expec ed ha hey all
will come o iden ical esul s. The esul s will be s a is ically sca -
e ed mo e o less a ound an a e age alue. To a ain a eliable
a e age alue o R
JRC
, i is desi able o ask mo e people o hei
judgmen s (i.e. o use a la ge s a is ical ensemble). Howe e , he e
a e o he possibili ies as o how o a oid subjec i i y in he isual
me hod. One o hese possibili ies is a compu e ized assessmen
based on image ecogni ion, which seems o be a p omising
solu ion.
Employmen o he Fou ie o malism o classi ying su ace
shapes is no a new idea in he ield o geo echnics. Fou ie shape
desc ip o s ha e been used o classi ying mo phological ea u es
o g anula ma e ials o se e al decades [22–27]. In pa icula ,
sedimen ologis s ha e de eloped a ious me hods o he assess-
men o su ace mo phology o mic oscopic g ains. An in e es ing
applica ion o he Fou ie analysis o digi al imaging o pa icle
shapes has been published by We imuny and Penumady [26].
So a , he g ea majo i y o s udies ha e conce ned mic oscopic
single g ains in es iga ed p e alen ly in 2D egimes. To he bes o
ou knowledge, he e is a lack o Fou ie shape s udies conce ning
mac oscopic 3D su ace elie s o la ge ock specimens. Since Ba -
on’s isual me hod is based on he shape compa ison be ween la -
ge ock su aces, i s compu e ized coun e pa should also be
capable o p ocessing la ge species. This s udy aims a op imizing
such a me hod. P ope nume ical indica o s o su ace simila i ies
should be he co e o ha me hod. Finding such indica o s is no a
s aigh o wa d ma e , and equi es ho ough es s ha a e
desc ibed he e.
Fig. 1. Ne wo ks o ock join s si ua ed in he o me lime qua y ‘Hády’ nea he ci y o B no in he Czech Republic.
702 T. Ficke / In e na ional Jou nal o Mining Science and Technology 29 (2019) 701–709
2. Scanning 3D su aces
As has been men ioned, he shape classi ica ion o 3D objec s
equi es hei scanning and con e sion in o digi al o ms. To scan
digi ally 3D elie s o la ge ock samples (10 cm 6.67 cm), a spe-
cial pho og aphic echnique has been employed. I uses ho izon al
op ical sec ions made by he came a, mo able in he e ical di ec-
ion, abo e he in es iga ed su ace (see Fig. 2). To copy he su -
ace, i is necessa y o eco d many op ical sec ions (i.e. digi al
images aken in disc e e e ical posi ions). A ypical numbe o
sec ions amoun s o abou 200 images. Op ical sec ions se e as
inpu da a o he special so wa e ha o ms he disc e e 3D elie
(x
i
,y
i
). To supp ess he possible da a nonlinea i y and nons a ion-
a i y, p e-p ocessing p ocedu es ha e been inco po a ed in o he
so wa e like polynomial i ing and sub ac ing he global end
om he p o ile da a along wi h emo ing noise by means o a e -
aging he mul iplica i ely aken snapsho s.
One may ask a ques ion as o whe he he used sec ional econ-
s uc ion me hod shows a quali y compa able wi h o he digi al
me hods, e.g. wi h he scanning lase sys ems. A de ailed s udy
compa ing he sec ional me hod wi h he scanning lase sys em
has been ecen ly epo ed [27,28]. This s udy documen ed ha
he esul s o he sec ional me hod we e compa able wi h hose
o he lase scanning sys em. One o he many 3D elie s o med
by he sec ional me hod is shown in Fig. 3.
The ha dwa e used o cap u ing op ical sec ions consis s o he
pho og aphic came a Canon EOS 600D augmen ed by he objec i e
EF 100 mm /2.8 Mac o USM (Fig. 2). This objec i e possesses a su -
icien ly small dep h o op ical ield when i is se o /2.8. The pho-
og aphic came a is moun ed on a ough aluminum s and wi h a
s epping mo o , enabling disc e e mo emen in he e ical di ec-
ion. The mo emen consis s o equidis an posi ions a which he
came a akes snaps o he su ace. The dis ance be ween wo posi-
ions has o be se so ha i may no exceed he dep h o he op ical
ield o he objec i e. The dep h o he op ical ield should be a
leas se e al imes smalle han he a e age heigh o he su ace
p o usions, o he a e age dep h o he su ace dep essions.
The de eloped ha dwa e is usable no only in labo a o ies bu
also in ou doo e ain. The pho og aphic came a moun ed on an
assembly o wo ipods and equipped wi h a p ope s epping
mechanism may ake snaps o la ge pa s o ock elie s di ec ly
in ou doo spaces as shown in Figs. 4 and 5.
3. Fou ie 3D elie s o ock join s
Fo he mo phology analyses o ock join s, he Fou ie scheme
is p oposed. P o ided ha a 3D su ace elie is a ailable in a dis-
c e e scanned o m (x
i
,y
i
), i can be i ed by he Fou ie pa ial
sum:
ðx
i
;y
j
ÞF
N
ðx
i
;y
j
Þ
¼X
N1
k;n¼0
s
kn
a
kn
cos k
p
x
i
pcos n
p
y
j
qþb
kn
sin k
p
x
i
pcos n
p
y
j
q

þc
kn
cos k
p
x
i
psin n
p
y
j
qþd
kn
sin k
p
x
i
psin n
p
y
j
qð3Þ
whe e,
X¼ x2ðp;þpÞ;y2ðq;þqÞg ð4Þ
a
kn
¼1
pq ZZ
X
ðx;yÞcos k
p
x
pcos n
p
y
qdxdy ð5Þ
b
kn
¼1
pq ZZ
X
ðx;yÞsin k
p
x
pcos n
p
y
qdxdy ð6Þ
c
kn
¼1
pq ZZ
X
ðx;yÞcos k
p
x
psin n
p
y
qdxdy ð7Þ
d
kn
¼1
pq ZZ
X
ðx;yÞsin k
p
x
psin n
p
y
qdxdy ð8Þ
s
kn
¼
1k>0;n>0
1=2k¼0;n>0o k >0;n¼0
1=4k¼n¼0
8
>
<
>
:
9
>
=
>
;
ð9Þ
The symbol Nde ines he uppe bound (N-1) o he subsc ip s
n,k, and es ic s he numbe o e ms in he Fou ie pa ial sum
speci ied by Eq. (3).
Fig. 4. A modi ied op ical de ice adap ed o e ain scanning.
Fig. 2. A labo a o y scanning de ice o cap u ing 3D su ace elie s.
Fig. 3. A scanned elie o limes one su ace 10 cm 6.67 cm wi h a esolu ion o
720 pixels 480 pixels.
T. Ficke / In e na ional Jou nal o Mining Science and Technology 29 (2019) 701–709 703
To de elop a co esponding ma hema ical basis o he Fou ie
indica o s o 3D elie s, i is con enien o ew i e Eq. (3) as
ollows:
ðx
i
;y
j
Þ X
N1
k;n¼0
a
k
cos k
p
x
i
pþb
k
sin k
p
x
i
p


c
n
cos n
p
y
j
qþd
n
sin n
p
y
j
q

ð10Þ
whe e,
a
k
c
n
¼
s
kn
a
kn
b
k
c
n
¼
s
kn
b
kn
a
k
d
n
¼
s
kn
c
kn
b
k
d
n
¼
s
kn
d
kn
8
>
>
>
<
>
>
>
:
ð11Þ
Eq. (10) con ains a p oduc o wo e ms in b acke s. These
e ms ep esen ha monic wa es wi h cha ac e is ic wa eleng hs
k
x
=2p/kand k
y
=2q/n(in pixels). The unc ional p oduc s speci ied
by Eq. (10) ep esen 2D wa e modes possessing indices (k,n) and
wa eleng hs (k
x
,k
y
). A squa e ma ix M
N
o he Fou ie indica o s
D
N
(k,n) may be in oduced as ollows:
M
N
¼
D
N
ð0;0ÞD
N
ð0;1Þ:::::::::: D
N
ð0;N1Þ
D
N
ð1;0ÞD
N
ð1;1Þ:::::::::: D
N
ð1;N1Þ
::::::::::
::::::::::
D
N
ðN1;0ÞD
N
ðN1;1Þ:::::::::: D
N
ðN1;N1Þ
0
B
B
B
B
B
B
@
1
C
C
C
C
C
C
A
ð12Þ
D
N
ðk;nÞ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ð
s
kn
a
kn
Þ
2
þð
s
kn
b
kn
Þ
2
þð
s
kn
c
kn
Þ
2
þð
s
kn
d
kn
Þ
2
qð13Þ
Some o he ma ix elemen s ha e special meanings. Fo exam-
ple, he i s elemen D
N
(0,0) = a
0,0
/4 is associa ed wi h an in ini-
i ely la ge wa eleng h and ep esen s a basic heigh o he
ho izon al le el. I s alue will be he la ges compa ed o all o he
ma ix elemen s. F om he iewpoin o he shape (wa e) analysis,
his i s diagonal elemen is i ele an and will be se o ze o. I
will no be aken in o accoun in u he conside a ion. The ma ix
M
N
is a cha ac e is ic ma ix and con ains all ele an wa e modes
o su ace elie s. One example o his ma ix plo ed in g aphical
o m as a unc ion o wo a iables k,nis p esen ed in Fig. 6.
Na u ally, i would be possible o s udy each pa icula indica-
o D
N
(k,n) o g oups o indica o s, and o e eal hei unc ionali y
associa ed wi h local mo phological ea u es o 3D elie s.
Undoub edly, he indica o s o lowe o de s (k,n< 10) bea in o -
ma ion on a global wa y shape o he elie , since hey co espond
o spa ial wa es o la ge wa eleng hs (i.e. small equencies). The
indica o s o highe o de s (k,n> 10) would undoub edly quan i y
a ine s uc u e o 3D elie s. All hese p ope ies can be obse ed
on he g aphical plo o he ma ix M
N
in Fig. 6, whe e he indica-
o s o lowe o de s mani es la ge alues (peak alues), whe eas
he indica o s o highe o de s quickly lose hei magni udes. How-
e e , a de ailed analysis o his kind would no be p ac ical. One-
alued indica o s enabling quick o ien a ion and a apid decision
a e needed. To each his goal, e o mula ing he ma ix M
N
is nec-
essa y. This ask is accomplished in he nex sec ion.
4. Classi ying su ace mo phology
P io o selec ing simila i y indica o s, i mus be clea which
su ace ea u es should be compa ed and wha should ac ually be
unde s ood unde he no ion o ‘su ace simila i y’. Only su ace
ea u es ha a e decisi e o he shea s eng h o ock join s ha e
o be p e e ably aken in o accoun . Ba on and Choubey [2,3]
di ided su aces o ock join s in o 10 ca ego ies acco ding o hei
Fig. 6. An example o he g aphical ou pu o he Fou ie ma ix M
N
(k,n).
Fig. 5. Rock elie scanned in e ain (A e [28,29]).
704 T. Ficke / In e na ional Jou nal o Mining Science and Technology 29 (2019) 701–709
mo phologies, s a ing om plana and smoo h su aces up o
wa y and ough su aces. Likewise, Bandis [30] desc ibed a se o
su aces acco ding o hei mo phologies, and men ioned h ee
basic shape ca ego ies, namely plana , undula ing and s epped su -
aces. He di ided each ca ego y in o h ee heigh subca ego ies,
namely he subca ego ies ha he e med as slickensided, smoo h
and ough. These ca ego ies and subca ego ies a e mu ually inde-
penden and may be combined in o nine di e en mo phological
pa e ns. Na u ally, his is a simpli ied classi ica ion and, in eali y,
u he a ian s o su ace p o iles may appea . Howe e , e en
om his simplis ic dis ibu ion, i is clea ha he shape and
heigh o he su ace p o iles a e wo ele an su ace ea u es ha
a e decisi e in he assessmen o he shea s eng h o ock join s.
These cha ac e is ics also play an impo an ole in e alua ing he
simila i y o ock join su aces.
Howe e , unde he e m ‘simila i y’ canno be unde s ood a
simple geome ical simila i y since join ed su aces show speci ic
dynamical p ope ies esul ed in shea s eng h ha is di ec ion-
ally dependen . Consequen ly, he co esponding shape indica o
should be sensi i e o he di ec ion o shea ing, i.e., i should be
o a ionally sensi i e. Such an indica o is capable o classi ying
he so called ‘dynamical simila i y’ o join ed su aces. On he o he
hand, he global heigh s o 3D p o iles a e independen o di ec-
ions and hus he co esponding heigh indica o should be in a i-
an o o a ions. I is necessa y o ind a leas wo independen
indica o s, one o which will classi y shape (plana i y, wa iness,
s epped shape, e c.) and will be o a ionally sensi i e whe eas
he second will classi y p o ile heigh and will show in a iance o
o a ion. The ma ix M
N
seems o be a good s a ing poin o o m-
ing a one- alued shape indica o , since his ma ix con ains ‘signa-
u es’ o all cha ac e is ic wa e modes o he su aces. As a heigh
indica o , he so-called oo mean squa e (RMS) pa ame e R
q
migh be con enien , since i e alua es global heigh s o su ace
p o iles. This global indica o is equen ly used when analyses o
su ace oughness a e pe o med [13–17].
Fo he pu pose o compa ison o join ed su aces, he ollowing
wo absolu e nume ical indica o s S, and Hwill be employed. The
i s indica o Sis de i ed om he elemen s D
N
(k,n) o he Fou ie
ma ix M
N
as a ue indica o o dynamical simila i y; and he sec-
ond indica o Hquan i ies he global in a ian heigh s o 3D su -
ace p o iles:
SðNÞ¼X
N1
k¼0
X
N1
n¼0
jD
ð0Þ
N
ðk;nÞD
N
ðk;nÞj ð14Þ
HðNÞ¼jR
ðoÞ
q
ðNÞR
q
ðNÞj ð15Þ
R
q
ðNÞ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1
KLX
K
i¼1
X
L
j¼1
ðx
i
;y
j
ÞF
ðlowÞ
N
ðx
i
;y
j
Þ
hi
2
u
u
ð16Þ
whe e (x
i
,y
j
) is he scanned elie and F
ðlowÞ
N
ðx
i
;y
j
Þ ep esen s he
Fou ie elie , which se es as a basis o compu ing heigh di e -
ences. The auxilia y quan i ies R
q
ðNÞand R
ðoÞ
q
ðNÞa e RMS alues
ela ed o he es ed su ace and he da abase su ace, espec i ely.
The symbols D
N
(k,n) and D
ðoÞ
N
ðk;nÞin Eq. (14) a e associa ed wi h
he es ed su ace and he da abase su ace, espec i ely. The p o-
duc K·Lis a pixel esolu ion o he used digi al images o su aces.
In ou case K·L=720 pixels 480 pixels ( he colo pixel as e o he
CMOS senso o he came a), which co esponds o he a ea
10 cm 6.67 cm (measu ed on he samples). The symbol (x
i
,y
j
)
in Eq. (16) ep esen s he scanned elie .
In he i s phase o he mo phology esea ch o join ed su -
aces, we ied o ind nume ical indica o s independen o mea-
su ing echniques in o de he esul s coming om di e en
labo a o ies could be compa able. F om his iewpoin , he ela-
i e indica o s in oduced as ac ions in which he nume a o s
had absolu e o ms (see Eqs. (14) and (16)) whe eas he denom-
ina o s con ained he da abase e ms D
ðoÞ
N
ðk;nÞand R
ðoÞ
q
ðNÞ, espec-
i ely, seemed o be con enien [1]. Howe e , u he esea ch
showed ha ela i e indica o s a e no as nume ical s able as
he absolu e indica o s speci ied by Eqs. (14) and (16) and, in
addi ion, he denomina o s may occasionally change he igh
p edic ions o absolu e nume a o s. In o he wo ds, he ela i e
indica o s a e no as eliable as he absolu e indica o s. Fo his
eason, we ha e abandoned he ela i e indica o o ms in he
p esen pape and in oduced he absolu e indica o s de ined by
Eqs. (14) and (16) as con enien pa ame e s ha a e capable o
e ealing dynamical simila i ies o join ed su aces mo e eliably.
Fu he de ailed discussion conce ning unc ional beha iou o
he absolu e nume ical indica o s and hei p ope ies can be
ound elsewhe e [31].
I should be highligh ed ha he join ed su aces acqui ed by
d illing he e ain slopes usually show some a i icial base ha
is o en inclined o bended. This addi ional unwan ed pa s o
join s ep esen unc ional ends which a e no inhe en pa s
o join s and ha e o be emo ed. These unc ional ends can
be i ed by he Fou ie p o iles wi h su icien ly low N- alues,
i.e. F
ðlowÞ
N
ðx
i
;y
j
Þo by he wo-dimensional polynomials. These i -
ed disc e e unc ions se e as e e ence le els and a e employed
o co ec ing he scanned p o iles ( elie s) (x
i
,y
j
) as shown in
Eq. (16).
When compu ing he Fou ie ma ix speci ied by Eq. (12), he
co ec ed scanned p o ile has o be used as well, i.e.
Fig. 7. Eigh limes one species o a ious su ace ex u es selec ed o simila i y es s.
T. Ficke / In e na ional Jou nal o Mining Science and Technology 29 (2019) 701–709 705

½ ðx
i
;y
j
ÞF
ðlowÞ
N
ðx
i
;y
j
Þ !
ðco ec edÞ
ðx
i
;y
j
Þ. This co ec ed scanned
unc ion is hen used o compu ing he accu a e ma ix D
N
(k,n),
bu his ime i is necessa y o pe o m he Fou ie expansion wi h
a su icien ly high N- alue o ai h ully desc ibe all he su ace
i egula i ies including wa y shapes and aspe i y s uc u es.
Since he oo -mean-squa e heigh indica o His calcula ed
acco ding o Eqs. (15) and (16) as a di e ence be ween he e -
e ence le el F
ðlowÞ
N
ðx
i
;y
j
Þand he scanned elie (x
i
,y
j
), i.e. as a
wo-le el di e ence, he indica o His independen o o a ion.
The equi ed sensi i i y o he indica o S o he ope a ions o
o a ion dese es a de ailed discussion and can be ound in
Re . [31]. Bo h he indica o s Sand H ul ill he necessa y p op-
e ies o co ec assessing he dynamical con o mi y o h ee-
dimensional elie s.
Eqs. (14)–(16) should be capable o iden i ying such a da abase
elie ha shows he highes dynamical con o mi y wi h he elie
unde in es iga ion. When wo iden ical elie s a e compa ed, a ull
con o mi y (dynamical simila i y) mus be indica ed, and he wo
indica o s ha e o show ze o alues (S=0,H= 0). Such a si ua ion
can only a ely occu in p ac ice when wo independen elie s
a e compa ed. In he g ea majo i y o si ua ions, only incomple e
dynamical simila i y will be ound, which will be indica ed by some
minimum posi i e alues o shape and heigh indica o s, i.e. 0 < S,
0<H. In addi ion, heigh and geome ical shape a e wo mo e o
less independen p ope ies and may show a a ie y o combina-
ions. Acco dingly, he indica o s Sand Hmay show di e en
esul s in some si ua ions and in his case he esul associa ed wi h
a smalle alue o JRC should be accep ed since his alue is a he
side o highe sa e y. An analogous p oblem may a ise when a g oup
o people pe o ms isual assessmen s o ock join s.
The es s in he ollowing sec ion a e aimed a he unc ionali y
o he indica o s Sand H.
5. Tes o simila i y indica o s
Eigh agmen s aken om he o me limes one qua y ‘Hády’
nea he ci y o B no in he Czech Republic (Fig. 1) ha e been ga h-
e ed. Thei su aces (Fig. 7) ha e di e se mo phologies s a ing
om e y coa se (No. 3 in Fig. 7) up o e y ine (No. 6 in Fig. 7).
The agmen s do no ep esen eal ock join s, bu hei su ace
mo phologies co e almos he en i e ange o Ba on’s s anda d
p o iles [2]. These eigh su aces ha e been subjec ed o simila i y
es s. A pa icula su ace has been compa ed o he emaining
se en su aces ha play he ole o da abase su aces. This p oce-
du e was epea ed eigh imes, i.e., each su ace was compa ed o
he es o he o he da abase su aces. The compa a i e p ocedu e
Table 1
Visual and compu e assessmen s.
In es iga ed
su ace
Visual assessmen Compu e
assessmen
The mos simila
da abase su aces
The mos simila
da abase su aces
SH
14 44
2 3 and 8 8 8
32 22
41 11
58 88
67 77
76 66
8 5 and 2 5 5
Fig. 8. Values o S-indica o s compu ed o couples o su aces. The S-indica o s ha e o show ze o alues when wo iden ical su aces a e compa ed. The couples o iden ical
su aces a e as ollows: 1–1, 2–2, 3–3, 4–4, 5–5, 6–6, 7–7, and 8–8. These simple es s illus a e he co ec unc ionali y o he so wa e used.
706 T. Ficke / In e na ional Jou nal o Mining Science and Technology 29 (2019) 701–709
was pe o med bo h isually (subjec i ely) and au oma ically
(objec i ely) on he compu e .
Simila i y compa isons o su aces a e p oblema ic, since he e
a e no ools enabling a decision wi h absolu e ce ain y. Fo his
eason, we pe o med a double compa ison (i.e. isual and compu -
e ized) in o de ha he esul s may be con on ed.
5.1. Visual assessmen
To ob ain s a is ically ele an esul s, we asked 25 people o
classi y he su aces acco ding o he s anda d p o iles o Ba on
[2,3]. In his way, he co esponding JRC- alues ha e been asc ibed
o su aces and he couples o he mos dynamically simila su -
aces ha e been speci ied. Na u ally, hese indi idual decisions
we e no uni ied bu a he dispe sed. Since i was ha dly possible
o weigh s a is ically each decision, we calcula ed common a i h-
me ic a e ages o JRC alues and he couples o he mos simila
su aces ha e been sa ed in Table 1.
I should be highligh ed ha he isual assessmen s o ock su -
aces based on human judgmen s a e a he p oblema ic, since he
esul s a e a ec ed by s a is ical a iabili y caused by indi idual
human di e ences.
5.2. Compu e assessmen
The second ype o simila i y compa ison has been pe o med
on he compu e by using indica o s Sand H. Scanned su aces
No. 1-No. 8 (Fig. 7) we e con e ed in o he co ec ed Fou ie
elie s, om which he desc ip o ma ices M
N
(Eqs. (12) and
(13)) we e de i ed, and a e wa ds he alues o he global shape
indica o Sand he heigh indica o Hwe e e alua ed.
To e i y he unc ionali y o he so wa e, a simple es was
ca ied ou . The es was based on compa isons be ween one cho-
sen su ace and he eigh ‘da abase’ su aces among which he cho-
sen su ace was also p esen . Wi hin such a compa ison, whe e
wo iden ical su aces can be me , he simila i y indica o s Sand
Hha e o show ull dynamical simila i y (ze o alues). Figs. 8
and 9 show he esul s o such es s. The g aphs in hese plo s con-
i m ha he so wa e co ec ly iden i ied all eigh couples o iden-
ical su aces.
The main es s a e, howe e , ocused on simila i y compa isons
o non-iden ical su aces. An in es iga ed su ace was compa ed o
he emaining se en da abase su aces. The e a e eigh such
a angemen s: (i) su ace No. 1 e sus Nos. 2–8, (ii) su ace No. 2
e sus Nos. 1 and 3–8, (iii) su ace No. 3 e sus Nos. 1, 2 and 4–
8, (i ) su ace No. 4 e sus Nos. 1–3 and 5–8, ( ) su ace No. 5 e -
sus Nos. 1–4 and 6–8, ( i) su ace No. 6 e sus Nos. 1–5 and 7, 8,
( ii) su ace No. 7 e sus Nos. 1–6 and 8, ( iii) su ace No. 8 e sus
Nos. 1–7. All hese nume ical compa isons we e accomplished, and
he co esponding g aphs a e p esen ed in Figs. 10 and 11. In hese
g aphs, he co esponding mos simila da abase su aces a e indi-
ca ed by bold a ows.
Fig. 10 shows he esul s o simila i y compa isons pe o med
by means o he S-indica o s. Fo example, he chosen su ace
No. 1 is compa ed o he da abase su aces Nos. 2–8; i s da abase
coun e pa No. 4 was ound as i s mos simila pa ne among
he emaining da abase su aces. Acco dingly, in Fig. 10, he bold
a ow poin s o he da abase su ace No. 4. Since he compa isons
a e no pe o med be ween iden ical su aces, he alues o he
Fig. 9. Values o H-indica o s compu ed o couples o su aces. The H-indica o s ha e o show ze o alues when wo iden ical su aces a e compa ed. The couples o iden ical
su aces a e as ollows: 1–1, 2–2, 3–3, 4–4, 5–5, 6–6, 7–7, and 8–8. These simple es s illus a e he co ec unc ionali y o he so wa e used.
T. Ficke / In e na ional Jou nal o Mining Science and Technology 29 (2019) 701–709 707
Fig. 11. Compu e ized simila i y es s o non-iden ical su aces. Values o H-indica o s a e compu ed o he ollowing couples: 1 e sus 2–8; 2 s. 1, 3–8; 3 s. 1, 2, 4–8; 4 s.
1–3, 5–8; 5 s. 1–4, 6–8; 6 s. 1–5, 7, 8; 7 s. 1–6, 8; 8 s. 1–7. The a ows poin o he mos simila da abase su aces.
Fig. 10. Compu e ized simila i y es s o non-iden ical su aces. Values o S-indica o s a e compu ed o he ollowing couples: 1 e sus 2–8; 2 s. 1, 3–8; 3 s. 1, 2, 4–8; 4 s.
1–3, 5–8; 5 s. 1–4, 6–8; 6 s. 1–5, 7, 8; 7 s. 1–6, 8; 8 s. 1–7. The a ows poin o he mos simila da abase su aces.
708 T. Ficke / In e na ional Jou nal o Mining Science and Technology 29 (2019) 701–709
S-indica o s canno be equal o ze o, bu hey show small posi i e
non-ze o alues, which ep esen he o al minima o he S-g aphs.
The o he in es iga ed su aces (Nos. 2–8) we e ea ed
analogously.
Fig. 11 o e s esul s achie ed by means o he heigh
H-indica o s. The a angemen is he same as in Fig. 10, and he
bold a ows again poin o he mos simila da abase su aces. All
he esul s o he H-indica o s shown in Fig. 11 ag ee wi h hose
o he S-indica o s p esen ed in Fig. 10. The esul s o he simila i y
assessmen s achie ed by he wo indica o s Sand Ha e collec ed in
Table 1.
5.3. Compa ing isual and compu e assessmen s
Table 1 con ains he esul s o bo h he isual and compu e
assessmen s. Bo h hese assessmen s a e in good ag eemen . The
absolu e indica o s Sand Hseem o be con enien o he compu -
e ized simila i y assessmen s o ock join s. They cons i u e p inci-
pal ools in he de eloped so wa e code. Al hough hei p edic i e
esul s ha e been iden ical in all ou p esen ed es s and in many
o he s so a no published, i should be epea edly s essed ha
hese wo indica o s may some imes sligh ly di e in hei p edic-
ions especially when heigh and shape p ope ies o su ace elie s
a e no su icien ly co ela ed. In such cases he smalle JRC alue
should be p e e ably accep ed as a pa ame e ha gua an ees
highe sa e y.
The pe o med es s ha e shown ha he absolu e o ms o he
indica o s Sand Hha e succeeded in hei ole o simila i y indica-
o s inding ock join coe icien s associa ed wi h he da abase
elie s. The modi ied ha dwa e and so wa e we e capable o co -
ec ly p ocessing la ge ock su aces whose linea sizes we e ully
compa able o hose o he Ba on s anda d JRC p o iles.
6. Conclusions
The isual assessmen o he oughness o ock join s, o en used
in geo echnical enginee ing, may be eplaced by he ully compu -
e ized p ocedu e based on he absolu e heigh Hand shape Sindi-
ca o s. The absolu e unc ional o ms o hese indica o s ha e
p o ed o be nume ically mo e s able compa ed o he ela i e indi-
ca o s used p e iously. The compu e ized p ocedu e based on com-
pa ison wi h he da abase su aces o known JRC yields wo kinds o
he ock join coe icien s, namely JRC
H
and JRC
S
, which a e e med
acco ding o he indica o s Hand S. The alues JRC
H
and JRC
S
a e
usually iden ical, especially when he e is a highe co ela ion
be ween he heigh and wa y shapes o he su ace p o iles. Ne e -
heless, a weake co ela ion may cause a sligh di e ence be ween
hese wo coe icien s. In such a case, he weigh ed o simple a e -
age (JRC
H
+JRC
S
)/2 may be used bu he sa es solu ion is o accep
he smalle alue o hese wo magni udes.
The de eloped compu e ized compa a i e me hod is applicable
no only o he ock join s in geo echnics, bu also o o he ields o
science and echnology whe e su ace mo phology plays an impo -
an ole. The me hod is capable o p ocessing bo h he mic oscopic
and mac oscopic specimens and his makes he me hod e y
uni e sal.
Acknowledgmen s
This wo k was suppo ed by he G an Agency o he Czech
Republic unde con ac No. 13-03403S.
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