TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 12, No. 10, Octobe
r 20
14, pp. 7099
~ 710
7
DOI: 10.115
9
1
/telkomni
ka.
v
12i8.553
0
7099
Re
cei
v
ed
De
cem
ber 2
9
, 2013; Re
vi
sed
Jun
e
21, 201
4; Acce
pted July 15, 20
14
ANSYS Simulation Analysis of Stray Currents on
Subway Shield Tunnel
Guo Wa
ng*, Xiaoxiang Pei
Schoo
l of Auto
mation a
nd El
e
c
trical Eng
i
ne
e
r
ing, La
nzh
ou
Jiaoto
ng U
n
ive
r
sit
y
,
Lanz
ho
u, Gansu, Chin
a, 730
0
7
0
*Corres
p
o
ndi
n
g
author, e-ma
i
l
：
w
a
ng
gu
o20
0
5
@e
yo
u.com,
061
21
42@stu.l
z
jtu.edu.cn
A
b
st
r
a
ct
In ord
e
r to a
n
a
l
y
z
e
the
distri
b
u
tion
rul
e
a
nd
influ
ence
ran
g
e
of su
bw
ay s
h
iel
d
tu
nne
l i
n
differen
t
traction c
u
rrent
s, a thre
e-di
me
nsio
nal
ge
o
m
et
rical
mode
l an
d math
e
m
atica
l
mode
l of
sub
w
ay shiel
d
tu
n
nel
stray current field w
e
re bu
ilt
, and a finite
ele
m
ent
mod
e
l w
a
s devel
o
ped by Ansys
. Simul
a
ting f
o
r
ho
mo
gen
eo
us
and
stratifie
d
s
o
il
med
i
a w
e
r
e
ha
pp
ene
d
in t
he
metro stray
curre
nt fiel
d s
i
mu
lati
on, thr
o
u
g
h
different carry-
c
urrents of railway.
Sim
u
lation show that the potentia
l at
tenuation is
nonlinear from
the
subw
ay tunne
l
to the surroundi
ng un
der
gr
oun
d and a
l
o
n
g
far aw
ay rail loadi
ng curr
e
n
t of direction;
T
he
carry-current
is
differe
nt, the
potenti
a
l
of s
u
r
r
oun
din
g
medi
a is
differ
ent,
and
the
gr
eate
r
the c
u
rre
nt, the
greater the
ma
ximu
m pote
n
ti
al. Each po
int
s
stray curr
ent in situatio
n of surr
oun
din
g
soil
med
i
a su
b
w
ay
tunne
l shi
e
ld c
an b
e
an
aly
z
e
d
by the thre
e-
di
me
nsio
nal
fi
n
i
te ele
m
ent
mo
del, a
nd pr
ovid
e the bas
is for th
e
protectio
n
ran
g
e
of stray current and t
he pr
otection at a sp
e
c
ific locati
on.
Ke
y
w
ords
:
subw
ay shi
e
ld
tunne
l, stray current fiel
d,
ho
mo
gen
eo
u
s
soil
me
di
a, stratified so
il
me
di
a,
simulation analysis
Copy
right
©
2014 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
In sub
w
ay
DC tra
c
tion
po
wer sy
stems,
the ru
nnin
g
rails a
r
e
used
as th
e return
path of
the train’s
cu
rrent to the su
pply sou
r
ce. Due to
the rai
l
s have a po
o
r
insul
a
tion from the gro
u
n
d
,
a part of current leaves
ra
ils to the gro
und.
The
s
e l
eakage
cu
rre
nts are calle
d stray
curre
n
ts.
Stray curre
n
t cau
s
e
s
a
serie
s
of seri
ous
pro
b
lem
s
that ele
c
tri
c
al
corro
s
io
n
for bu
ried
metal
st
ru
ct
ur
es
[
1
-
2
]
.
Seriou
sly affects
t
he no
rmal ope
ratio
n
of
urb
an
rai
l
tran
sit. Th
erefore,
co
untri
es
arou
nd the
worl
d attach
great impo
rtance to th
e
protectio
n
a
nd influen
ce
of stray current
probl
em. Pre
s
ently, the st
udy dirction
s are mai
n
ly
the followi
ng
asp
e
ct
s: the model of return
circuit syste
m
at subway; influenc
es a
nd distri
butio
n of stray cu
rrent; the mon
i
toring sy
ste
m
of
s
t
r
a
y curr
ent.
The mod
e
l o
f
return
circu
i
t system at
sub
w
ay: W.
V.Baeckamn
n had e
s
tabl
ishe
d a
model of
stray curre
n
t field un
der th
e ideal
con
d
i
t
ions, re
sp
ect
i
vely for vari
able
with tra
c
tion
power
cu
rren
t and th
e resi
stan
ce
of rail
and th
e resi
st
ance of track-to-ea
r
th [2].
On thi
s
b
a
si
s,
a
track-to
-ea
r
th
model of
sta
y
current
with
drain
age
net
wa
s e
s
tabli
s
hed by M
ou
Long
hua
and
Liu
Yan [3-4]. An electri
c
field whi
c
h can solve un
derg
r
o
und el
ectri
c
field distrib
u
tion
wa
s
establi
s
h
ed b
y
Ade ogu
nsola an
d Pan
g
Yuanbi
ng,
th
ereby,
curre
n
t
which le
ave
s
bu
rie
d
met
a
l
stru
ctru
es
was de
rived,
and ultimatel
y
imputed
to
corro
s
ion
q
uantity as st
anda
rd
whi
c
h to
as
se
ss t
he h
a
za
rd
s of
st
r
a
y
cur
r
ent
[
5
-
7
]
.
Mult
iple
interval cal
c
ula
t
ion prog
ram
wa
s written b
y
Ardizzo
n
for the model of
return ci
rcuit system [8].
Influence an
d dist
ribution
of stray
cu
rrent:
M.T.So
ylemeze
sim
u
lated the
effects of
traction
volta
ge of DC1
5
0
0
V and
DC75
0V on rail pot
ential an
d st
ray cu
rre
nt, a
nd indi
cate
d that
increa
sing th
e voltage level can effe
ctively reduc
e p
o
tential and stray current [9]; C-H.Le
e,Kinh
D an
d Zh
ang
Xiaoyu thou
ght that the
mainly fact
o
r
of that is th
e dista
n
ce b
e
twee
n adj
acent
traction
su
bstation and ra
il resi
stan
ce;
Mou Lon
gh
ua studi
ed the effect of overall tra
c
k bed
reinfo
rced strcture
on
rail potential and
stray cu
rrent. Un
der DC p
a
ram
e
ters, it
has no
effect
on
rail
p
o
tential and obital cu
rre
nt.
But
the
stray
cu
rre
n
t lea
k
age
is mainly
com
posed
of ste
e
l
stru
cture of
circulatio
n, redu
cing th
e
damag
e to t
he out
side
[1
0-12]. T
he ef
fects
of ea
rthing
strategi
es on
rail p
o
tential
and
stray
currents in
DC
transit rail
way were studie
d
by
J.G.Yu,
a
n
d
the feature
s
and ap
plications
of these
were poi
nted
out [13]. B.Y.Ku and Li
We
i had sho
w
n t
hat
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ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 10, Octobe
r 2014: 709
9
– 7107
7100
diode
-g
roun
d
ed sy
stem m
a
y re
sult in hi
gh rail
potenti
a
l
and stray current
of d
r
ai
nage
net at the
s
a
me time, even if, it
may
reduc
e
s
t
ray
c
u
rrent c
o
rros
ion [1, 14].
There is a
differen
c
e b
e
tween the
re
sults of
these mo
dels a
nd a
c
tu
al values. T
h
e major
rea
s
on
is th
a
t
these m
ode
ls were e
s
tab
lishe
d
an
d si
mulated
und
er the i
deal
condition
s, it can
only macroscopically and qualitatively analyze the e
ffects of different facto
r
s on stray current.
These m
odel
s
can
not be
accu
rately
simulated
fo
r
compl
e
x st
ru
cture
of
sub
w
ay tun
nel a
n
d
geolo
g
ical co
ndition
s.
Thereby, this paper
simul
a
ted the act
ual m
odel of
sub
w
ay tunnel with FEM [15-18].
Becau
s
e the
type of subway tunnel
in driving ra
nge
is shied tun
nels, so this pape
r ch
ose the
shie
d tunnel
as sim
u
lation
model. Un
de
r the multif
ario
us conditio
n
s
of non uniform track-to
-ea
r
th
resi
stan
ce, soil resi
stan
ce
, rail resi
stan
ce and in ho
mogen
eou
s
soil medi
a and stratified
soil
media, the simulation wa
s develo
ped
by ansys
,
and the di
stribution of stray current was
analyzed. To
further a
naly
z
e the effe
cts of tractio
n
curre
n
t on st
ray cu
rrent field, different
rail
curre
n
ts were
loaded.
2. Stra
y
Current Field Mo
del in Sub
w
a
y
2.1. Geometr
i
cal model
Based
on
ap
paratu
s
[1
9], a thre
e-di
me
nsio
nal m
ode
l of stray
cu
rrent field
com
putional
domain in
su
bway shield tunnel was b
u
ilt accordi
n
g
to the actual size. The
section
a
l view of
comp
utional
domain
of su
bway stray current
field,
a
s
sho
w
n
in Fi
gure
1. Fi
gure 1 illu
strates that
the g
r
ou
nd
was
mod
e
led
with a
len
g
th
of 100
m, a
h
e
ight of
60m
and
a
width
o
f
1000
m
cub
o
id.
The top
of th
is tunn
el i
s
lo
cated
at a d
e
p
th
of 10m
measured fro
m
the
road
surface. Figu
re 2
sho
w
s
the
structure of
sub
w
ay shiel
d
tu
nnel and
ra
il
way. the
tunn
el ha
s a
circu
l
ar
cross sect
ion
with a
n
inte
rn
al diam
eter o
f
2.6m, and
a
out
si
de
diam
eter of
2.75m
. There a
r
e
0
.
05m bet
wee
n
them. To
sim
p
lify calculati
on, two
rail
s
were e
quival
ed to two cu
boid
s
, which
are
se
pa
rat
e
d
from 1.435m,
with a length
of 0.15m,
a height of 0.176
m and a widt
h of 1000m.
Figure 1. Sectional View of
Computio
nal
Domain of S
ubway Stray Curre
n
t Field
5.5
5.
2
Figure 2. Structure of Sub
w
ay
Shield Tun
nel and
Railway
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TELKOM
NIKA
ISSN:
2302-4
046
ANSYS Sim
u
lation Analysi
s
of Stray Current
s on Subway Shield T
unnel (Guo
Wang)
7101
2.2 Mathemat
ical mod
e
l
Take
any clo
s
ed su
rfa
c
e
s
from a
spa
c
e
condu
ctor wh
o
s
e volu
me
cu
rre
nt den
sity is
j
,
according to t
he la
w of con
s
ervatio
n
of charg
e
, t
he el
ectri
c
qu
antity that flows o
u
t of the clo
s
ed
surfa
c
e
p
e
r u
n
it time, mu
st
be
eq
ual to
t
he a
m
ou
nt of
ch
arge th
at v
o
lume
V
whi
c
h is
surro
und
e
d
by the
clo
s
ed
su
rfa
c
e S
de
cre
a
sed
in
un
it time,
then t
he
cu
rre
nt co
ntinuity equ
ation i
s
give
d a
s
formula (1):
sv
q
j
ds
dv
tt
(1)
The cu
rrent continuity equ
ation in integral fo
rm is calcualted from th
e followin
g
Equation
(2):
sv
j
ds
dv
t
(2)
Whe
r
e
mean
s the ch
arg
e
den
sity (C/m
3).
The cu
rrent continuity equ
ation in differ
ential form is
gived as form
ula (3
):
j
t
(3)
In a ste
ady
electri
c
fiel
d, elect
r
ic fiel
d
and
cha
r
g
e
do not
ch
ang
e with time,
unde
r a
steady
ele
c
tric field,
the
curre
n
t conti
nuity equ
atio
n in
integ
r
al
form
is calcualted f
r
om
the
following Equation (4):
0
s
jd
s
(4)
the curre
n
t co
ntinuity equat
ion in differen
t
ial form is gived as fo
rmula
(5):
0
j
(5)
Acco
rdi
ng to Ohm'
s law, th
e curre
n
t den
sity compo
n
e
n
ts of three
-
di
mensi
onal
steady
curre
n
t field are form
ula (6
):
z
γ
j
y
γ
j
x
γ
j
z
z
y
y
x
x
(6)
Whe
r
e jx
，
jy and
z
j
rep
r
e
s
ent
current de
nsi
t
y compone
nt in the directi
on of x,y and
z and
x
，
y
and
z
represen
t condu
ctivity
in
the dire
ctio
n of x,y and z
；
representspotential(V
)
.
Acco
rdi
ng to equatio
ns(5
), the curre
n
t co
ntinuity equat
ion in the dire
ction of x
，
y and z
will be as follow (7):
0
xy
z
j
jj
xy
z
(7)
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ISSN: 23
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046
TELKOM
NI
KA
Vol. 12, No. 10, Octobe
r 2014: 709
9
– 7107
7102
Acco
rdi
ng to Equation (5)
and (6
), we
can get
the pot
ential ba
sic e
quation
s
of the stray
curre
n
t of the three-dimen
s
ional sub
w
ay sheil
d
tunnel,
a
s sho
w
n formula (8
):
()
(
)
(
)
0
xy
z
xx
y
y
z
z
(8)
For a co
nsta
nt current field, only the bounda
ry con
d
itions a
r
e nee
d
ed to list. The model
sho
w
n i
n
fig
u
re 1 i
s
sym
m
etrical to y axis, el
e
c
tric
field line
s
pa
ssi
ng throug
h the y axis
are
perp
endi
cul
a
r to y axis. T
he rate of po
tential va
riati
on the axis o
f
symmetry in the x direct
ion
wa
s 0, so tha
t
the boun
da
ry conditio
n
s
a
r
e alo
ng to
Neuman
n bo
un
dary
conditio
n
s. Equ
a
tion
(9)
gives the defi
n
ite con
d
ition
s
of Equation
(8).
0
0
n
下表
面
(9)
3.Simulation Results and
Discuss
tion
of Stra
y
Current Field
Since th
e a
c
tual bou
nda
ry shap
e of t
he st
ray
current field
co
mputional
do
main in
sub
w
ay i
s
co
mplex an
d
chang
eable,
a
nd the
ge
olo
g
ical
conditio
n
is diverse,
the st
ructu
r
e
can
be cla
ssified
as a small u
n
it
by
the
fini
te
eleme
n
t m
e
thod. Th
us,
it is e
a
sy to
simulate
vari
ous
stru
ctures
of irre
gula
r
shap
e. It
can ha
nd
le all types
of boun
dary
con
d
itions. Also,
it can
simulat
e
stru
cture of varieties m
a
terial [15]. Therefo
r
e,
due
to the distribution of stray current field
analyzed by ansy
s
with the method of finite elemen
t, it can better reflect any ca
se on real tun
nel
surro
undi
ngs.
This pa
per a
nalyze
s
a
nd
simulate
s t
h
e
distri
bution
o
f
stray
curre
n
t
field with FE
M
method in ho
mogen
eou
s soil media an
d
stratified soil media sepa
ra
tely.
3.1. Anal
y
s
is
of Stra
y
Current in Hom
ogeneous Soil Media
Figure 1
sho
w
s that me
di
a 1-4 a
r
e
the
sam
e
m
edia
in h
o
mog
e
n
eou
s
soil m
e
dia. The
para
m
eters o
f
calcul
ation a
r
e sh
own as
Table 1.
Table 1. Simulation Para
meters of Ho
mogen
eou
s
Soil Media
Material Name
Ralative permittivity
Resistivity
(
Ω
·m)
Element
Tunnel
6.4
150
SOLID23
1
PLAN
E230
Rail 1×10
7
2.1×10
-7
Soil 30
100
Figure 3. Electri
c
Potential
Contou
rs in
Homo
gen
eou
s Soil Media (10A)
Figure 4. Electri
c
Potential
Contou
rs of
Neig
hbo
ring Tunnel
in Ho
mogen
eou
s Soil
Media (10A)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
ANSYS Sim
u
lation Analysi
s
of Stray Current
s on Subway Shield T
unnel (Guo
Wang)
7103
In orde
r to a
nalyze th
e ef
fects of diffe
rent
value
s
of
traction
current on di
strib
u
tion of
stray
cu
rre
nt field in
hom
ogen
eou
s
so
il media, t
h
e
value
s
of traction
curren
t of 20A, 20
0A,
1000A, 200
0
A
were
cal
c
ul
ated se
parately. The mod
e
l simulate
d two rail
s, and
the values of
rail
curre
n
t of 10A, 100A, 500A, 1000A we
re load
ed
se
parately on
o
ne end of e
a
c
h rail. Figure 3
displ
a
ys that
the elect
r
ic p
o
tential co
nto
u
rs
i
n
hom
og
eneo
us soil media when the
value
of
rail
curre
n
t is 10
A, and Figure
4 sho
w
s the
neigh
bori
ng tunnel in the
same situatio
n
.
Different loa
d
i
ng cu
rre
nts
have the sa
me c
onto
u
rs.
The only differen
c
e
s
are potential
value of cont
ours, as
sho
w
n in Tabl
e 2
.
Table 2. Co
ntour Potential
Value Co
rr
espondi
ng to the Different Lo
ading
Current
Traction
c
u
rrent(A
)
A(V) B(V)
C(V)
D(V)
E(V)
F(V)
G
(
V)
H(V) I(V)
10 0.795148
2.38544
3.97574
5.56604
7.15633
8.74663
10.33669
11.9274
13.5175
100
7.95148
23.8544
39. 7574
55. 6604
71. 5633
87. 4663
103. 3669
119. 274
135.175
500
39.7574
119.272
198.787
278.302
357.817
437.332
516.846
596.361
675.876
1000
79.5148
238.098
397.574
556.604
715.633
874.663
1033.669
1192.74
1351.75
In orde
r to a
nalyze the di
stributio
n of stray
curre
n
t from the rail to
the surrou
nd
ing, the
longitudinal
section was i
n
stalled
t
h
rough
the center of
rail on
the
l
e
ft, as
shown in
profile 1-1 of
Figure 3. Fig
u
re 5
sh
ows
that the
pote
n
tial cu
rve of
different de
p
t
hs in the lo
n
g
itudinal
se
ction.
The
cro
s
s se
ction
wa
s in
stalled thro
ug
h the bottom
of
rail, a
s
sh
own i
n
profile
2-2
of Figu
re 3
.
Figure 6 sh
o
w
s that the
potential
curve of different location
s i
n
the cross
se
ction. Figu
re 7
sho
w
s that th
e Potential
curve of
rail
wa
y in hom
ogen
eou
s
soil m
e
dia. On th
e di
agra
m
, 0 i
s
t
he
positio
n of cu
rre
nt-carrying
.
Figure 5. Potential Cu
rve of 1-1 in
Homo
gen
eou
s Soil Media
Figure 6 Potential Curve of
2-2 in
Homo
gen
eou
s Soil Media
Figure 7. Potential Cu
rve of Ra
ilway in Homo
gen
eou
s Soil Media
Figure 5-7
sh
ow that the di
stri
butio
n of stray current from the rail to the surro
undi
ng with
the different value
s
of tracti
on cu
rrent, as sho
w
n in Ta
ble 3.
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Vol. 12, No. 10, Octobe
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9
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7104
Table 3. Poe
n
tial Distri
buti
on of the Rail
way to the Surro
ngdi
ng Un
derg
r
o
und En
vironme
n
t
Curre
nt(A)
Profile 1-1potenti
a
l(V)
Profile
2-2potenti
a
l(V) Rail
potential(V)
Max
i
mum
value
Minimum
value
Max
i
mum
value
Minimum
value
Max
i
mum
value
Minimum
value
10 14.3127
0
14.3127
2.5272
14.313
14.154
100 143.127
0
143.127
25.272
143.13
141.54
500 715.633
0
715.633
126.36
715.63
707.7
1000
1431.27
0
1431.27
252.72
1431.3
1415.4
Figure 3-7 an
d Table
3 sh
ow that the
p
o
tentia
l atten
uation i
s
nonl
inear f
r
om th
e rail to
the surro
undi
ng unde
rg
rou
nd. The farth
e
r from t
he rail and the more g
ently the cu
rve is, the
smalle
r the stray curre
n
t stren
g
th it has. The
di
stri
bution rul
e
o
f
potential so
lved by FEM in
homog
ene
ou
s soil medi
a
is con
s
iste
nt with t
he
theoreti
c
al result
s proj
ected unde
r ideal
con
d
ition
s
in appa
ratu
s [20
]
.
From th
e a
n
a
lysis, in
p
r
o
f
ile 1-1, th
e
value of m
a
ximum pot
ential incre
a
ses
with the
increa
sing traction curren
t. The value
of minimum
potential is 0
.
In profile 2-2, the value of
maximum po
tential and m
i
nimum pote
n
tial also in
crea
se
with the increa
sing
traction
cu
rre
n
t.
The value of rail potential
incre
a
ses wi
th the increa
sing tra
c
tion
curre
n
t, but
decli
ned by less
extent. Simulation re
sult
s sho
w
that the
potentia
l on
each point from the rail to
the surro
und
ing
unde
rg
roun
d
has o
b
taine
d
, and providin
g the basi
s
fo
r the prote
c
ti
on ra
nge of stray curre
n
t and
the specific location.
3.2. Anal
y
s
is
of Stra
y
Current in Stratified Soil Media
In stratified
soil me
dia, Fig
u
re
1
sh
ows t
hat
me
dia
1-4 is the
different me
dia
s
.
The type
of eleme
n
t
and
paramet
ers of tu
nne
l and
rail
chosen
are
n
o
t ch
angi
ng.
The
Rsi
s
tivity
Paramete
rs o
f
each Soil, as sh
own in Table 4.
Table 4. Rsist
i
vity Parameters of e
a
ch S
o
il
Number
Name
Ralative
permittivity
Resistivity
(
Ω
·m)
Media 1
Cla
y
(
w
et)
8
10
Media 2
Soft soil
30
100
Media 3
Cla
y
la
y
e
r
40
500
Media 4
gravel
6
1000
In stratified
soil medi
a, si
milarly, the v
a
lue
s
of
rail
curre
n
t of 1
0
A, 100A, 50
0
A
, 1000A
were loa
ded
sep
a
rately o
n
one e
nd of
each rail.
Fi
gure
8 di
spla
ys that the e
l
ectri
c
pote
n
tial
conto
u
rs in
stratified soil
media
whe
n
the value of
rail current i
s
10A. Fig
u
re 9 sho
w
s t
he
neigh
bori
ng tunnel in the
same situatio
n
.
Figure 8. Electri
c
Potential
Contou
rs in
Stratified Soil Media (1
0A)
Figure 9. Electri
c
Potential
Contou
rs of
Neig
hbo
ring
Tunnel in Stratified Soil Media
(10A)
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TELKOM
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ANSYS Sim
u
lation Analysi
s
of Stray Current
s on Subway Shield T
unnel (Guo
Wang)
7105
Different loa
d
i
ng cu
rre
nts
have the sa
me c
onto
u
rs.
The only differen
c
e
s
are potential
value of cont
ours, as
sho
w
n in Tabl
e 2
.
Table 5. Co
ntour Potential
Value Co
rr
espondi
ng to the Different Lo
ading
Current
Traction curre
nt(
A
)
A(V)
B(V) C(V)
D(V)
E(V)
F(V) G
(
V)
H(V)
I(V)
I
=10A
2.2046
6.6138
11.023
15.4322
19.8414
24.2506
28.6598
33.069
37.4782
I
=10A
22.046
66.138
110.23
154.322
198.414
242.506
286.598
330.69
374.782
I
=500 A
110.23
330.69
551.15
771.61
992.07
1212.53
1432.99
1653.45
1873.91
I
=1000A
220.46
661.38
1102.3
1543.22
1984.14
2425.06
2865.98
3306.9
3747.82
From the ab
o
v
e datas
sh
o
w
that the distribution rul
e
of
potential in stratified soil
media
is co
nsi
s
tent
with the hom
ogen
eou
s soi
l
media.
Figure 10. Potential Curve
of 1-1 in Strat
i
fied
Soil Media
Figure 11. Potential Curve
of 2-2 in Strat
i
fied
Soil Media
Figure 12. Potential Curve
of Ra
ilway in Stratified Soil Media
Figure 8
-
12
a
nd Ta
ble 5
show th
at the
potentia
l atte
nuation i
s
n
o
n
linea
r fro
m
the rail to
the surro
undi
ng unde
rg
rou
nd. The farth
e
r from t
he rail and the more g
ently the cu
rve is, the
smalle
r the stray curre
n
t stren
g
th it has. The
di
stri
bution rul
e
o
f
potential so
lved by FEM in
homog
ene
ou
s soil medi
a
is con
s
iste
nt with t
he
theoreti
c
al result
s proj
ected unde
r ideal
con
d
ition
s
in appa
ratu
s [20
]
.
Figure 10
-12
sho
w
that the
distrib
u
tion o
f
stra
y cu
rren
t from the rail
to the su
rro
u
nding
unde
r environ
ment with the
different values
of tra
c
tion
curre
n
t, as sh
own in Ta
ble
6.
Table 6. Pote
ntial Distri
buti
on of the Rail
way to the Surro
undi
ng Un
derg
r
o
und En
vironme
n
t
Curre
nt(A)
Profile 1-1potenti
a
l(V)
Profile
2-2potenti
a
l(V) Rail
potential(V)
Max
i
mum
value
Minimum
value
Max
i
mum
value
Minimum
value
Max
i
mum
value
Minimum
value
10
39.6828
0 39.6828
27.299
39.682
39.524
100
396.828
0 396.828
272.99
396.82
395.24
500 1984.14
0
1984.1
1364.9
1984.1
1976.2
1000
3968.28
0 3968.28
2729.9
3968.2
3952.4
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TELKOM
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Vol. 12, No. 10, Octobe
r 2014: 709
9
– 7107
7106
Wheth
e
r it is
homog
ene
ou
s or
stratified
soil
me
dia, th
e potential att
enuatio
n is n
online
a
r
from the
rail
to the
su
rro
un
ding u
nde
r
e
n
vironm
ent. In the
sam
e
v
a
lue of t
r
a
c
tio
n
current, I=1
0
A,
the Com
p
a
r
ison of ho
mog
eneo
us
soil
media a
nd
stratified soil m
edia, a
s
sho
w
n in
Table
7
and
in Table 8.
Table 7. Co
m
pari
s
on of Ho
mogen
eou
s
Soil Media an
d Stratified Soil Media
Profile 1-1
y
=54m
potentia (V)
y
=60m
potentia (V)
Voltage
drop(V
)
y
=30m
potentia (V)
y
=40m
potentia (V)
Voltage
drop (V
)
Homogeneo
us soil media
4.57
4.47
0.1
3.42
5.63
2.21
Stratified soil media
28.58
28.55
0.03
25.42
31.42
6
As can
clea
rl
y be seen i
n
Table
7, th
e voltage
drop in
homo
g
eneo
us
soil
media i
s
obviou
s
ly larger than the
voltage dro
p
in stratified
soil media in 5
0
-60
m
are
a
of the profile 1-1.
On the cont
rary, the voltage dro
p
in homoge
neo
us soil media i
s
obviou
s
ly smaller than t
h
e
voltage drop
in stratified
soil media in
30-4
0
m a
r
ea
of
the profile
1-1. Th
e mai
n
rea
s
o
n
is t
hat
the voltage drop is mainly concentrate
d
in the area
s of
high re
sistivi
y
(
1
234
).
Table 8. Co
m
pari
s
on of Ho
mogen
eou
s
Soil Media an
d Stratified Soil Media
Profile 2-2
Minimum potential (V)
Maximum poten
tial
(V)
Voltage drop
(V)
Homogeneo
us soil media
27.30
39.68
12.38
Stratified soil media
2.53
14.31
11.78
Table 8 sh
ows that the voltage drop in h
o
m
oge
neo
us
soil medi
a is clo
s
e to the voltage
drop i
n
st
rati
fied soil m
e
dia in the
profile 2-
2. T
h
i
s
re
ason i
s
con
s
i
s
tent wi
th the above-
mentione
d. Similarly, Tabl
e 3 and
Tabl
e 6 s
how th
e
minimum p
o
t
ential maxim
u
m potential
of
rails a
nd the
voltage dro
p
is no differe
nce.
The greater t
he Re
si
stivity is,
the faster the spee
d it has, the less stray curre
n
t leaks
surro
undi
ng soil can g
e
t. But both of the rails, an
d tun
nel nea
r pote
n
tial become
greate
r
.
4. Conclusio
n
In this
pap
er the di
strib
u
tion rule
and
influn
ce
ran
ge of
su
bwa
y
sheil
d
tun
n
e
l stray
curre
n
t in
different
tra
c
tion
cu
rrents hav
e be
en
ca
rri
e
d
out
by a
n
sys. Analyzi
n
g
the
simul
a
tio
n
results
can b
e
noted that:
(1) With th
e i
n
crea
singly v
a
lue of
cu
rre
n
t-
ca
rryin
g, the rail p
o
tent
ial of the
su
rroundi
ng
media a
nd le
aka
ge
current
raise comsta
ntly. The
grea
ter the resi
sti
v
ity of the surroun
ding m
e
d
i
a
is, the less stray current it has.
(2) T
he two typical p
r
ofile
s sho
w
that th
e
the potenti
a
l attenuation
is nonli
nea
r from the
rail to the su
rroundi
ng und
e
r
groun
d. Increasi
ng re
si
stivity of rail and tunnel of su
rro
undi
ng me
dia
can effe
ctively reduce the effe
cts range
of stray cu
rre
n
ts.
(3) An
alyzin
g
the simul
a
tion re
sult
s can
be
kn
own, Wheth
e
r i
t
is homo
g
e
neou
s o
r
stratified
soil
media, the vo
ltage drop tre
nd from
the
rail to the su
rroundi
ng un
de
r enviro
n
me
nt is
sho
w
in
g no
differen
c
e. T
he
spe
ed of
voltage
dro
p
is rel
a
ted
to re
sist
ivity. The
greater the
Re
sistivity is, the faster th
e spe
ed it ha
s, t
he less st
ray cu
rrent le
aks su
rroun
di
ng soil
can g
e
t.
But both of the rails, an
d tunnel ne
ar pot
ential be
com
e
greate
r
.
(4) T
he thre
e-dimen
s
ion
a
l finite element
model
can an
alyze every p
o
ints st
ray cu
rre
nt in
situation of surroun
ding
soil media
sub
w
ay tunnel
shield. Beca
use of this, pro
v
ide the basi
s
for
the prote
c
tion
range of
stra
y current and
the prot
e
c
tion
of specifi
c
lo
cation
can b
e
inferre
d.
Ackn
o
w
l
e
dg
ements
This work is supp
orted b
y
natural sci
ence fund of GanSu prov
ince (121
2RJZA064),
basi
c
scie
ntific re
se
arch speci
a
l fund o
f
GanSu insti
t
ution of high
er edu
catio
n
，
and the Yo
ung
Schola
r
s Scie
nce Fo
und
ation of Lan
zh
o
u
Jiaoto
ng University (2
01
1042
).
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
ANSYS Sim
u
lation Analysi
s
of Stray Current
s on Subway Shield T
unnel (Guo
Wang)
7107
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