Indonesian J
ournal of Ele
c
trical Engin
eering and
Computer Sci
e
nce
Vol. 1, No. 2,
February 20
1
6
, pp. 349 ~
353
DOI: 10.115
9
1
/ijeecs.v1.i2.pp34
9-3
5
3
349
Re
cei
v
ed O
c
t
ober 7, 20
15;
Revi
se
d De
cem
ber 26, 20
15; Accepted
Jan
uary 12, 2
016
Resear
ch on the Surface Fractal Characteristic of the
Rock with Rockburst Proneness
Li Mo-xiao
1
*,
Zhang Gua
n
g
1
, Chen Jin
g
-xi
2
1
School of Res
ource a
nd Env
i
ronme
n
t Engi
n
eeri
ng,
W
uha
n Univers
i
t
y
of
T
e
chn
o
lo
g
y
, W
uhan, Ch
in
a
2
School of T
r
ansportati
on, W
uha
n Univ
ersit
y
of T
e
chnolo
g
y
, W
uha
n, Chi
n
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: ma
y
s
h
i
n
e
-19
88@
163.com
Ab
stra
ct
In order to strength
en the
pr
ed
iction of r
o
ckburst an
d inq
u
ire the re
l
a
tions
hip b
e
tw
een the
rockburst pron
eness of rock and its surfa
c
e fractal c
haracteristic, the
surface fractal
of
the rock
w
a
s
studie
d
by fractal meth
od an
d uniax
ial co
mpressi
on tes
t.
T
he chan
ge ru
les of surface fractal of different
types of rock
w
e
re compar
e
d
by calc
ulati
n
g its fr
actal di
me
nsi
on of ro
ck before ex
p
e
ri
ment a
nd
after
exper
iment. Ba
sed on this, w
e
found that the
di
me
nsio
n afte
r test is bigger
than bef
ore tes
t
for four kinds of
rocks. The roc
k
w
i
th stronger
rockburst pr
on
eness
has
mo
r
e
inte
nse fa
ilur
e
in th
e l
oad
in
g proc
ess a
nd
its
crack m
o
r
p
hology is more com
p
lex.
Ke
y
w
ords
:
Fractal, Rockbur
st, Rockburst
prone
ness, Uni
a
xial co
mpressi
on
Copy
right
©
2016 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
With the g
r
eat pro
g
ress of so
cial a
nd e
c
on
omic, more a
n
d
more
und
e
r
groun
d
engin
eeri
ng
grad
ually d
e
velope
d d
eep
er.
Ro
ckbur
st
is i
n
crea
sin
g
l
y becoming
one
of the
m
a
jor
geolo
g
ical
di
sa
sters in th
e develo
p
me
nt of
unde
rg
round engi
ne
ering. Ro
ckb
u
rst
i
s
a nonl
inear
dynamic
phe
nomen
on tha
t
rock ma
ss along th
e i
n
ternatio
nal
airpo
r
t of ex
cavation
su
rface
relea
s
e
ene
rg
y [1]. It is a complicated p
r
oblem a
nd th
ere i
s
n
e
ither
a set
of matu
re the
o
ry in
u
s
e
of pre
d
ictio
n
in n
o
r
syst
ematic
and
comp
re
hen
si
ve und
erstan
ding it
s rea
s
ons be
ca
use
o
f
compli
cate
d
probl
em
s exi
s
ting in
the
rockbu
rst
and
different the
o
r
ies of g
r
adi
n
g
. Many sch
o
lars
con
s
id
er th
e
rockbu
rst
a
s
a
uniq
ue
pro
p
e
r
ty of ro
ck
it
self [2]. Frac
tal geometry
was
int
r
oduc
e
d t
o
analysi
s
the
rock
dam
age
and f
r
a
c
ture
by Xie
Hepi
ng, an
d it in
dicate
s
a ne
w d
e
velopm
e
n
t
dire
ction fo
r ro
ckburst
[3]. Rece
nt
rese
arch
e
s
sh
owe
d
that the fra
c
tal p
henom
eno
n
is
rema
rkable
d
u
ring th
e bre
a
kin
g
pr
ocess of ro
ck fra
c
ture. The
di
st
ribution and geomet
ry
of
th
e
fractu
re
hav
e fra
c
tal
structure [4].
The
cha
nge
of fra
c
tal
dimen
s
ion
of
ro
ck du
ring
its
deform
a
tion
p
r
ocess
wa
s i
n
co
ncer
t
with its
stre
ss state, mech
an
ical p
r
o
pertie
s
, phy
sical
a
n
d
chemi
c
al
p
r
o
pertie
s
afte
r
many researche
s
[5]. In
this p
ape
r,
we
sel
e
cte
d
marbl
e
, grani
te,
hornfel
s an
d
skarn to
carry out uniaxial comp
re
ssi
on
experime
n
t. We stu
d
y the
chan
ge rule
o
f
rock’
s
su
rface fra
c
tal dim
ensi
on by
col
l
ecting
and
a
nalyzin
g the
surfa
c
e
cha
r
acteri
stic of rock
before
an
d
after te
st. Base
d o
n
thi
s
, we
study
the relation
ship b
e
twe
e
n
su
rfa
c
e fra
c
tal
dimen
s
ion a
n
d
the ro
ckb
urst pron
ene
ss.
2. Experimenta
l
2.1.
Mecha
n
ics Experiment o
n
Rock
burs
t
Pronene
ss
In order to st
udy the characteri
stics of surfa
c
e fracta
l of di
f
f
erent rocks, the exp
e
rime
nt
sele
cts m
a
rbl
e
, granite, h
o
r
nfels
and
skarn to
con
d
u
c
t uniaxial
co
mpre
ssion te
st. Our
sam
p
l
e
s
are conventio
nal stan
dard cy
linde
r with
a size of
Φ
50mm×100mm.
In this experi
m
ent we use
burst ene
rgy
i
ndex and elastic defo
r
ma
tion energy i
ndex to
measure the stren
g
th of
ro
ckburst prone
ness [6, 7].
Uiaxial
comp
ression te
st u
s
ed
MTS81
5
.04-
t
y
pe
ro
ck
mech
ani
cs t
e
st
sy
st
e
m
de
v
e
lope
d
by W
uha
n Institute of Rock
and Soil Me
chani
cs, Chine
s
e
Academy
of Sciences.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 25
02-4
752
IJEECS
Vol.
1, No. 2, February 201
6 : 349 – 353
350
I
Figure 1. MTS815.04
-type
ro
ck me
cha
n
i
cs te
st syste
m
The value of
each
ro
ckbu
rst p
r
one
ne
ss index
of e
a
ch
ro
ck
wa
s calcul
ated
by using
MA
TLAB.
The result is given in
T
a
ble.1.
From th
e tab
l
e we
can
se
e that granit
e
had
a
stro
ng tend
en
cy to ro
ckburst
and the
rockb
u
rst pro
nene
ss of horn
s
tone a
n
d
ska
rn were
relatively weak, the ma
rble’
s
ro
ckbu
rst
pron
ene
ss
was wea
k
e
s
t.
The stren
g
th of
ro
ckburst
p
r
one
ne
ss of three
ro
cks arrang
e in
ord
e
r
of:
granite
> ho
rn
stone
> ska
r
n
>ma
r
ble.
Table 1. The
result of burst energy ind
e
x and el
a
s
tic d
e
formatio
n en
ergy index of each ro
ck
sample
uniaxial compressive strength
（
Mp
a
）
burst energ
y
ind
e
x
elastic deformation energ
y
inde
x
DH4
54.74
1.50
-
DH5
53.15
1.32
-
DH8
54.84
1.06
-
DH6
92.32
-
1.91
DH9
83.62
-
1.72
HB1 1
17.18
2.31
-
HB2 31
1.24
3.00
-
HB4 189.20
1.71
-
HB6 151.34
-
6.15
HB7 245.60
-
6.17
J
Y
3
109.86
1.10
-
J
Y
4
84.18
2.00
-
J
Y
8
125.61
-
5.21
X3 97.38
-
2.16
X4 1
13.99
1.22
-
X6 98.26
-
2.17
X8 146.95
1.42
-
X10 85.98
1.37
-
3. Resul
t
s
and
Disscu
sion
3.1.
The Extr
acti
on of the Su
rfac
e Cha
r
ac
teristic
s of
Rock
W
e
have to take pi
ctures
of
four ro
cks before a
nd af
ter test. In order to obtain
surfa
c
e
feature
s
of rock befo
r
e and
after the
test as far
as possible we mu
st use
the profession
al digital
came
ra.
T
r
y to make
su
re
the picture h
a
ve
the high
image definiti
on and u
n
iform brightn
e
ss in
ca
se of a large area of the sha
d
o
w
.
T
o
be su
re t
he
came
ra le
ns i
s
pe
rpe
ndicul
a
r to the su
rf
ace
in ca
se imag
e deform
a
tion
. In order to e
n
su
re the con
s
iste
ncy of the image befo
r
e and afte
r the
test we
sh
oul
d pla
c
ed th
e
spe
c
ime
n
s i
n
the sa
me po
sition [8]. W
e
sele
cted th
e
same
po
sitio
n
of
the sp
ecim
en
as far
as
po
ssi
ble to a
nal
ysis the
su
rfa
c
e fra
c
tal feat
ure a
nd the
p
i
cture
after te
st
contai
ns at least one crack.
Then we used MA
TL
AB software to further manipul
a
t
ion the chosen
picture.
The
whol
e process is:
choo
se t
he su
rfa
c
e i
m
age of rock
→
co
nvert the
image to bin
a
ry
image
→
edg
e
detection
→
the cal
c
ul
atio
n
of fractal
dimen
s
ion.
T
he analy
s
is
pro
c
e
s
ses
of a
sampl
e
ch
osen from ma
rb
le are a
s
follo
ws.
The surfa
c
e i
m
age of rock wa
s sel
e
cte
d
by
usin
g a
64 x 64 pix
e
l block.
Th
e
spe
c
ific
operation
s
are as follo
ws.
Evaluation Warning : The document was created with Spire.PDF for Python.
IJEECS
ISSN:
2502-4
752
Re
sea
r
ch on
the Surface F
r
actal
Cha
r
a
c
teristic
of the Ro
ck
with Ro
ckburst… (Li Mo-xiao
)
351
before te
st
after tes
t
Figure 2. The
sele
cted po
si
tion of surfa
c
e
feature bef
ore an
d after
test of marble
before te
st
after tes
t
Figure 3. The
image of su
rface featu
r
e
b
e
fore an
d after test of marble
In the Figu
re
2, the re
d blo
ck i
s
th
e pa
rt
of
su
rface fea
t
ure
we
sele
cted.
The im
ag
e after
extraction i
s
show in Fig
u
re
3.
The image in the Figure 3 wa
s pro
c
e
s
se
d by our own image–
proce
ssi
ng pro
g
ra
m which
prog
ram
m
ed
by MA
TLAB8
.0.
The imag
e noi
se redu
ction i
s
the fi
rst
step of p
r
oce
s
sing.
Th
e
surfa
c
e featu
r
e of ro
ck i
s
more di
stin
ct after this
step so it is faci
litat
e to the next step of the
work.
The p
r
o
c
e
s
sed imag
e is sh
ow in F
i
gure 4.
before te
st
after tes
t
Figure 4.
The
processe
d image of su
rfa
c
e featu
r
e bef
ore an
d after
test of marble
(step1
)
The next step is conve
r
ting the denoi
sed ima
ge into binary image so the fracta
l
dimen
s
ion
ca
n be cal
c
ul
ated by MA
TLA
B
8.0.
The bin
a
ry image i
s
sho
w
in Figu
re 5.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 25
02-4
752
IJEECS
Vol.
1, No. 2, February 201
6 : 349 – 353
352
before te
st
after tes
t
Figure 5. The
binary imag
e
of surfa
c
e fe
atur
e befo
r
e
and after te
st of marble (ste
p2)
3.2.
The Calc
ulation of Frac
ta
l Dime
nsion of Ro
ck be
fo
re and after
T
e
s
t
The image i
n
Figure 5 is
divided by 2x
2 pixels
bl
ock, 3x3 pixels b
l
ock,…, 64x6
4
pixels
block. W i
s
th
e numb
e
r of
non em
pty sq
uare
parti
tion
in the gra
ph
and r i
s
mea
s
ureme
n
t sca
l
e
(the scale
of block).
Th
e di
mensi
on can
be determi
ne
d
by the
linea
r reg
r
e
s
sion o
f
the W and r
in
the dou
ble lo
garithmi
c
coo
r
dinate.
T
he
value of di
me
nsio
n is th
e a
b
sol
u
te value
of the slo
pe
of
the line fitting.
The result of calculating i
s
sho
w
in Figu
re 6.
before te
st
after tes
t
Figure 6. The
result of calculati
ng of fractal dimensi
o
n
of marble
The Figure 6 sho
w
s that the correlati
on co
ef
ficient
of surfa
c
e fractal dime
nsi
on fitting
cha
r
t of granite are more than 0.98.
The fitting
result
means that the surfa
c
e of
rock sho
w
s the
fractal
cha
r
a
c
teristics. Rep
eat the abov
e step
s
to ca
lculate the
di
mensi
on of o
t
hers
ro
cks a
n
d
the result is show in
T
abl
e 2.
T
abl
e 2. Re
su
lt of surface fr
actal dime
nsi
on of each ro
ck
t
y
pe
Nu-mbe
r
dimension before
test
dimension after t
e
st
change of dimen
s
ion.
dimensi-
on
ave-rage
dimen-
sion
ave-rage
mar-bl
e
DH5
1.6391
1.6380
1.6357
1.6450
0.0070
DH6
1.6538
1.6986
DH8
1.5998
1.5896
DH9
1.6590
1.6560
gran-ite
HB6 1.6190
1.6231
1.661
1
1.6552
0.0321
HB7 1.6271
1.6492
hornstone
J
Y
4
1.6759
1.6587
1.6540
1.6664
0.0077
J
Y
8
1.6414
1.6787
skar
n
X3 1.5756
1.6272
1.6091
1.6470
0.0198
X6 1.6305
1.6058
X10 1.6756
1.6945
Evaluation Warning : The document was created with Spire.PDF for Python.
IJEECS
ISSN:
2502-4
752
Re
sea
r
ch on
the Surface F
r
actal
Cha
r
a
c
teristic
of the Ro
ck
with Ro
ckburst… (Li Mo-xiao
)
353
In the
T
a
ble 2
it sho
w
s th
at the su
rface frac
tal dime
nsions of
four rocks have
in
crea
sed.
The amplifi
c
ation of gran
ite is about 2% and
the amplificatio
n of ska
rn is
about 1%.
The
amplificatio
n of
marble an
d
hornsto
ne are
b
o
th
belo
w
1%.
The
strength
of ro
ckbu
rst p
r
on
e
ness
of three ro
cks arrang
e in orde
r of: gra
n
ite> ho
rn
sto
ne> ska
r
n >marbl
e.
Acco
rding to the result
the ro
ck
of strong
er
ro
ckb
u
rst p
r
on
ene
ss
have
big
g
e
r chan
ge of
dimen
s
ion
be
tween b
e
fore
an
after test.
Th
e dime
nsio
n
after test i
s
bigge
r than
before
test f
o
r fou
r
kind
s of ro
cks.
Th
at is
becau
se the surfa
c
e
s
of rock cra
c
ked
after
test and have more
complex features.
The m
o
re
compl
e
x surf
ace ha
s a big
ger dime
nsi
o
n.
The rock with strong
er rockbu
rst pron
ene
ss ha
s m
o
re
intense failure in the loadi
ng pro
c
e
s
s a
nd its cr
ack
morp
holo
g
y is more com
p
l
e
x. So its change
of dimen
s
ion
durin
g the t
e
st is
bigge
r
.
Given all th
at, the cha
n
ge of dime
n
s
ion
duri
ng t
h
e
uniaxial comp
ressio
n ca
n b
e
use
d
to jud
ge the strengt
h of rockbu
rst prone
ne
ss of
rock.
4. Conclu
sion
Cal
c
ulate
d
four
kind
s o
f
rock’
s
su
rface fra
c
tal
dimen
s
ion
durin
g the
uniaxial
comp
re
ssion
and foun
d that the dimension after test
is bigg
er than
before te
st for four
kind
s
of
rocks.
The rock with
stro
nger
ro
ckbu
rst pro
nen
ess has mo
re i
n
tense failure in the loa
d
ing
pro
c
e
ss
and
its cra
c
k m
o
rph
o
logy is more
co
mpl
e
x.
The cha
nge of dime
nsio
n du
ring
the
uniaxial com
p
re
ssi
on ca
n be use
d
to judge the stren
g
th of rockb
u
r
st pro
nen
ess of rock. In th
is
pape
r
,
wh
en the ch
ang
e of dimen
s
ion ov
er 0.03 the ro
ck h
a
ve stron
ger rockb
u
rst pron
ene
ss.
Ackn
o
w
l
e
dg
ements
This work was suppo
rted
in part by the
Speci
a
lize
d
Resea
r
ch Fund for the
doctoral
colle
ge (NO.2
0120
143
1
1
0
0
05).
Referen
ces
[1]
He Manc
hao,
Miao Jin
li, Li
Deji
an, W
a
n
g
Chu
ngu
an
g.
Chin
ese Jour
na
l
of Rock Mechan
ics an
d
Engi
neer
in
g
. 2007; 26(
5).
[2]
Cook N G W
SAIMM. 1966; 66(1).
[3]
Xi
e HP
. Proc.
2nd Int. S
y
mp.
On Min. Sci. &
T
e
ch. (CUMT
)
. 1991.
[4]
Y
i
Shu
n
min,
T
a
ng Hu
imin
g. Earth Scienc
e. 1
995; 20(
1).
[5]
Guangm
ing
Y
,
Ai
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