Title:Effects of cross section of mine tunnel on the propagation characteristics ofUHF radio waveSuggested area: B8 (Tunnel Propagation)Author: Zhang changsen Mao Yan

Post. 454003 . . . . o *e o e e o **o **2010.1..****** .... * * .

Telephone * * * 13103999885 0391-3987715 * O -

email: zhangchangsenkhpu.edu.cn

1

Effects of cross section of mine tunnel on the propagation

characteristics of UHF radio waveZhang changsen Mao Yan2

1 School of computer science and technology, 2 School civil engineering,

Hean polytechnic university, Jiaozuo city, Henan province, 454003 *Email: zhangchangsenWhpu.edu.cn

Abstract: The paper studies the propagation

characteristics of UHF radio wave in circular tunnels,

rectangular tunnels, arched tunnels, ellipse tunnels,

trapezium tunnels and semi -circle tunnels. A conclusion

is made that trapezium tunnels and semi-circle tunnels

can equivalent with circular tunnels with the same area

of cross sections; these tunnels have a same formulation

of attenuation rate though their cross section is different.

The larger the area of cross sections is, the lower

attenuation rate is, and the shape of cross sections affects

on attenuation rate too. When the diameter or the larger

side is larger than about fifteen times the free-space

wavelength, attenuation rate is very low and hardlyrelated to the shape of cross sections, and doesn't

severely depend on area of cross sections of tunnel any

more, and the wave can be looked upon transmitting at

free space.

Key words: cross sections of tunnel; circular tunnel;

rectangular tunnel; arched tunnel; trapezium tunnels;

UHF

1 Preface

To optimize the design of communication of system,

the transmission mechanism of the wireless electric wave

must be mastered. The communication system in the

tunnel usually uses leaking feeder source. in the earlier

period, the leaking system works in the 450 MHz, it uses

800 or 900 MHz at present. technically, leaking system

can be worked in 2 GHz, the transmitting loss of wireless

electric wave will not lead much at so high frequency, in

this way, for the short tunnel the wireless communication

based on free promulgation can be used in the leaking

communication; for the long tunnel, the small area

structure cellular can be used it reported that, the UHF

wave range has low point-blank transmission loss, tiny

influence of electromagnetic interference, and its rolling

shoot characteristic probably makes its field strengthbehind the block attained higher level than the

receiver required. So the UHF wireless electric wave,

especially the frequency range from 1 GHz to 2 GHz

becomes the best window for transmission wireless

electric wave underground. This paper studies the effects

of mine tunnel's cross section on the propagation

characteristic ofUHF electromagnetic wave.

2 Circular tunnels

When analyzing the tunnel electromagnetic wave

propagation, the most representative tunnel model is the

circular tunnel, on the assumption that the circular tunnel

is a kind of loss medium, the diameter is d, the internal

electricity parameter is (e g0 ), the exterior magnetic

conductivity rate is PJ , relative dielectric constant is Er'

and the electric conductivity rate is 0 . Building the

cylinder reference frame, making use of the continuity of

the field variable's slice vector to acquire characteristic

equation, the second kind Hankel function and its

differential coefficient to acquire the E. attenuation

constant's approximation, fir the base model Eh1, the

attenuation rate (dB/m) is:

h-y= 5.092r h+ g\ j(I)

In the formula, w is the max of the circular tunnel

width, h is the max of the height, w=h=d.

2

3 Rectangle tunnels

Emslie had studied the propagation characteristic of

the electromagnetic wave in the rectangle tunnel whose

cross section's dimension is much larger than the

electromagnetic wave length. Supposed that there are

rectangle tunnel with four not- ideal conductor walls, the

width is w, height is h, relative dielectric constant of the

two sides is Er1 relative dielectric constant of the crest

and the bottom both is 8r2' the electricity parameter of

the air in the tunnel is (£ 0Uo), the rectangle tunnel

with four rectangle sides can load two molds, the

horizontal polarization E h and vertical polarization

EBv (if the direction z upright the outside of thepaper), acquiring the attenuation rate by using the slice

variable continuous boundary condition on the

electromagnetic field, but it only can be approximatelysatisfied. Besides the horizontal electromagnetic field,existing electromagnetic variable on the axis z whose

value is much less than the value of the horizontal, so the

boundary condition only can be approximately satisfied,

the attenuation rate expression of the horizontal BA

wave mold is I'l:

lh -j = 4343 K r3(£ - 1) /2 h3 (E 221)

(2)

4 Arch tunnels

The arch tunnel radius is a, its boundary is divided

into two parts, the arc part (0 < Ip| < 11) and straight

line part (Ip < 0) , the internal free space electricity

parameter is ( o,/I0 ), the exterior tunnel magnetic

conductivity rate is /to, relative dielectric constant is

Er' the electric conductivity rate is 7 . Because the

boundary is symmetries to the x axis, based on the

boundary condition, in the scope of 0- p, along the

boundary looking for the matching point, that is the

matching method, the paper[2] studied the arch tunnel byusing matching point method, for Ehl 1, there is the

approximate expression(the attenuation rate unit is

dB/m):

5.132N! - + i](3)oh-g =5 I32 h3

In the expression, w is the max width of the arch

tunnel (w=2a), h is the max height (h = a(l + cos 0)).

5. Oval tunnels

The longer axis of the oval is 2a, the shorter axis is

2b, and the axis z is ellipsoid's axis. The internal

electricity parameter is (£ g0 ), the exterior magnetic

conductivity rate is o0, relative dielectric constant is Er I

the electric conductivity rate is 0 . Adopted the oval

reference frame, the characteristic equation can be

gained. The paper[3] studied on the oval tunnel, for the

Eh1l , it has obtained the approximate expression as

follows:(the attenuation rate unit dB/m)

4.457 2! r r1 j4(h-t =4X52 3 h

In the formula, w is the max width of the oval tunnel

(w=2a), h is the max height (h=2b).6 Trapezoids and semicircle arch tunnels

Based on that the power flow of the tiny interfere

method is equal to the power absorbed by the wall, we

can attain the attenuation constant of the trapezoid and

the semicircle arch tunnel by limited method[4]:Although adopted the limited unit method can

discover the electromagnetic wave's propagationcharacteristic in the trapezoid tunnel and the semicircle

3

arch tunnel, it is quit complicate in practice, according to

the common used mineral well tunnel model['5], equaled

the trapezoid tunnel and the semicircle arch tunnel to the

circular tunnel, through lots of calculation, the

electromagnetic wave that above the UHF can be

regarded as the circular tunnel with the same area, their

attenuation rate error will less than 10%.

7. The general form of the attenuation constant in

tunnels

Generally speaking, the tunnel attenuation rate is

related to the tunnel size, wave-length, polarized wave

model and the function of the tunnel wall medium. When

the work frequency is placed in the UHF frequency

segment, because the frequency is so high, the electric

conductivity rate of the tunnel wall medium is quite

low, so the imaginary part in the complex capacitance

rate EeI= e /e£ -je /C#oO is very small so it can

be omitted. Referenced to the expression of the wave

mold attenuation rate of circular tunnel, rectangle tunnel,

arch tunnel, oval tunnel and the conclusion of the

semicircle arch tunnel, the general expression of the

attenuation constant in tunnels can be written by:

x 2 Er[et hX2+ 3~ (6)

W is the max of the oval tunnel width, h is the max

of the height. X is a coefficient, its value varies by the

different shape of the tunnel ,to the circular x=5.09, to

the rectangle tunnel x=4.343, to the arch tunnel x=5.13,

to oval tunnel x=4.45,to the trapezoid and the semicircle

arch tunnel ,it can equal to the same area circular tunnel

to calculate.

8 The effect of the tunnel radius divides the wave

length on attenuation rate

Based on the expression (6) which studied on the

proportional relation between the tunnel radius and the

wave-length, while the ratio of the tunnel radius and the

wave-length is bigger than 10(that is (d /A) > 20 ), it

can be divided into two cases.

One of the cases is the tunnel radius is a constant

that equals 2 m, the tunnel cut off frequency is about 75

MHz at this time(the cut off wave-length is 4 m),while

the wave-length gradually decreases to 0.2 m the

attenuation rate decreases gradually, too, the change

process illustrated in figure 1. Another case,

wave-length is a constant that equals 4 ms,

electromagnetic wave work frequency is 75 MHz, the

radius gradually increase form 2 m , the attenuation rate

decreases gradually, the change process illustrated in

figure 2.

It can be seen from figure. 1 that while

(w/X) >15 the work frequency of the

electromagnetic wave above 1200 MHz, the attenuation

rate of the electromagnetic wave is quite small in the

UHF frequency segment, the attenuation rate of the 1

Km long tunnel is less than 5 dB; it can be seen from

figure 2 that even the frequency is not high, when the

tunnel radius increases the attenuation rate decreases

quickly, while (w / A) > 1 5 ,the attenuation rate lower

than 5dB,then the electromagnetic wave can be

approximately propagated in the freedom space without

wastage.

100 -

10 -

1-

dB/km

1 w=h=d=4m

2:w=h=d=6m

I-

5 10 15 20 25 30 35 40WLA

Figure 1 Relation between attenuation andw / X while

diameter is a constant

4

need (w / A) > 15 , at this time the fade of the

0.1

1:)==1 m

2:9=4m

5 10 15 20 25 30 35 40WI)

Figure 2 Relation between attenuation rate w / X while

wave-length is a constant

In the rectangle tunnel or the arch tunnel, the value

of w/h is no longer 1, when this value changes, the

attenuation rate will also change. Actually[8],in the

rectangle tunnel: the value of W/h varies form 1.2 to

1.8,the relative change of the attenuation rate is

approximately 13%;Arch tunnel: while the value of

w/h varied between 1.3-1.6(0 is 600 800),x has a

little bit change, the attenuation rate is approximately

12%.While (w / A) > 1 5 ,the attenuation rate of the 1

Km long tunnel is about a few dB, the effect of the

tunnel shape brings less than 1 dB, it is so little that can

be omitted.

While (w / X) > 15, along with the increase of the

tunnel radius or the frequency, the attenuation rate also

continuing decrease, but at this time the absolute

attenuation rate is quite small, only a few dB. Generallyspeaking, the radius of the actual tunnel are less than

several meters, while the electromagnetic wave work

frequency above 1200 MHz, meet the

electromagnetic wave is only a few dB, its attenuation

rate is almost irrelevant to the shape of the tunnel cross

section, and its dependence on the area of the tunnel

cross section also becomes weak, approximately regardas transmitted in the free space.

8 Conclusions

While studying the propagation characteristic of the

electromagnetic wave in tunnels, the trapezoid and the

semicircle arch tunnel can equal to the circular tunnel

with the same area and different tunnel shape have the

likeness attenuation rate formula. Tunnel cross section

has effect on the inherent electromagnetic wave

propagation, while the tunnel diameter or the longer side

is 15 times as long as the wave-length, the attenuation

rate almost irrelevant to the tunnel cross section shape,and the dependence on the tunnel cross section area also

becomes weak, it can regard as transmitted in the free

space.

Reference

[1]. Emslie, A. G., Lagace, R. L. and Strong, P. F.

Theory of Propagation of UHF Radio Waves in

Coal Mine Tunnels. IEEE Transactions on Antennas

and Propagation, 1975, 23(2):192 205

[2]. Yamaguchi, Y., Abe, T., Sekiguchi, T. Attenuation

Constants of UHF Radio Waves in Arches

Tunnels[J]. IEEE Transactions on EMC, 1989,

31(1):87 91

[3]. Yamaguchi, T., Sekiguchi and Y., Abe. Propagation

characteristics of the dominant mode in tunnels

with elliptical cross section. Trans. IECE of Japan,

1981, 64(9):1632 1638

[4]. *. . . . . . . . . J].. .

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dB/km

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