PROPAGATION OF UHF RADIO WAVES 

IN LIMESTONE ROOM AND PILLAR MINES 

Robert L. Lagace, Task Leader 

Alfred 6. Emslie 

prepared for 

UNITED STATES 

DEPARTMENT OF THE INTERIOR 

BUREAU OF MINES 

ARTHUR D. LITTLE, INC. 

CAMBRIDGE. MASSACHUSETTS 

summary report 

JANUARY 

TASK 

50377065 

UNDER 

ORDER 

BASIC 

1979 

NO. 

AGREEMENT 

50387217 7 

Arthur D Little, Inc 
The views and conclusions contained in this document are thou, 

of the authors and should not be interpreted as necessarily 

representing the official policies or recommendations of the 

Interior Department's Bureau of Mines or of the U.S. Government. 
4. Title md Subtitle I. Pepon Date 

PROPAGATION OF UHF RADIO WAVES IN LIMESTONE January 1979 

ROOM AND PILLAR MINES 6. 

1. Author(%) 8. Performing Org.aiutian Rcpon No. 

Robert L. Lagace, Task Leader ADL-81863 

Alfred 6. Emslie 

I. Performing Orgmizrcion Name and Addrns ( 10. Pmjrcc/T.rk/WocL Uair No. 

Arthur D. Little, Inc. 

25 Acorn Park 11. Contrm oiGrnnr No. 

Cambridge, Massachusetts 02140 Task Order 50387217 

13. Type d Report 

12 Sponsorens O~gnnnrrr#on Nsmc and Address 

Office of the Assistant Director - Mining Summary 

Bureau of Mines April 1978 - January 1979 

Department of the Interior - 

Washington, D. C. 20241 14. 

15. Supplementary Natcr 

This report presents a mathematical model for the propagation of UHF radio waves 

in the large cross-section tunnels of a room and pillar limestone mine, and 

describes the analysis of a small amount of propagation data obtained in a limestone 

mine. The model and analysis is based on the waveguide mode theory developed 

earlier for the transmission of UHF waves in coal mine tunnels, with allowance for 

propagation losses due to refraction into the tunnel walls, to scattering by wall 

roughness, and to long range random tilt of the walls. Propagation around 

corners and through pillars is also examined based on a ray theory approach, 

together with the beneficial effects of placing reflectors at intersections to 

significantly reduce corner losses. The theory is found to be in fair agreement 

with the data; however, additional in-mine measurements are needed to provide a 

more conclusive test of the model. 

17. Orzgmnator's Key Words 18. Av.ilability Statement 

Radio Propagation--UHF, Tunnels 

Tunnel Communications 

Mines--Radio Communication 

Mine Communication--Wireless 

Mines--Limestone, Coal 

19. C.S. Securdty Classif. of #he Report 20. U.S. kurity Classif. d Thin Pale 21. No. of Pagn 22. Price 

42 
PROPAGATION OF UHF RADIO WAVES 

IN LIMESTONE ROOM AND PILLAR MINES 

Robert L. Lagace - Task Leader 

Alfred G. Emslie 

ARTHUR D. LITTLE, INC. 

Cambridge, Massachusetts 02140 

C-81863 

The views and conclusions contained in this document are 

those of the authors and should not be interpreted as 

necessarily representing the official policies or 

recommendations of the Interior Department's Bureau of 

Mines or of the U. S. Government. 

SUMMARY REPORT 

USBM TASK ORDER NO. 30387217 

Under Basic Agreement 50377065 

JANUARY 1979 

UNITED STATES 

DEPARTMENT OF THE INTERIOR 

BUREAU OF MINES 

Arthur D Littlelnc 
FOREWORD 

This report was prepared by Arthur D. Little, Inc., Cambridge, 

Massachusetts, under USBM Task Order No. 50387217 under Basic Agreement 50377065. The contract was initiated under the Coal Mine Health 

and Safety Program. It was administered under the technical direction 

of the Pittsburgh Mining and Safety Research Center with Mr. Harry 

Dobroski acting as the technical project officer. Mr. Joseph Gilchrist 

was the contract administrator for the Bureau of Mines. 

This report is a summary of the work recently completed as part 

of this contract during the period April 1978 to January 1979. This 

report was submitted by the authors in January 1979. 

No inventions or patents were developed, and no applications for 

inventions or patents are pending. 

iii 

Arthur D Little, Inc 
TABLE OF CONTENTS 

List of Tables 

List of Figures 

I. INTRODUCTION 

11. MODEL FOR HAULAGEWAY TUNNH. WITH BELT CONVEYOR 

A. REFRACTION LOSS 

B. ROUGHNESS LOSS 

C. TILT LOSS 

D. COMPARISON OF THEORY WITH HAULAGE TUNNEL DATA 

E. MODE CONVERSION 

111. APPLICATION TO TUNNELS IN ROOM AND PILLAR AREAS 17 

A. COMPARISON OF THEORETICAL AND EXPERIMENTAL 17 

RESULTS 

B. PREDICTED VARIATION IN ATTENUATION RATE OF (1,l) 27 

MODES WITH FREQUENCY 

IV. COMMENTS ON PROPAGATION IN A COAL MINE TUNNEL 29 

V. PROPAGATION AROUND A CORNER AND THROUGH A PILLAR 31 

A. RAY PATH REFRACTION AND REFLECTION 31 

B. EVANESCENT WAVES 

C. ATTENUATION RATE IN LIMESTONE 

VI. REFERENCES 36 

Arthur D Little Inc 
LIST OF TABLES 

I. 

11. 

111. 

IV. 

v. 

VI. 

VII. 

VIII. 

ATTENUATION COEFFICIENTS (EXPERIMENTAL VALUES) FOR 

THE HAULAGEWAY TUNNEL 

COMPARISON OF THEORETICAL arefraction WITH EXPERIMENTAL atotal FOR HAULAGE TUNNEL 

COMPARISON OF THEORETICAL atotal FOR Eh,l,l MODE 

WITH EXPERIMENTAL atotal FOR HAULAGE TUNNEL 

THEORETICAL ATTENUATION RATES OF LOWEST AND HIGHER 

ORDER MODES AT 450 MHz FOR TUNNEL IN ROOM AND 

PILLAR AREA 

VARIATION OF THEORETICAL ATTENUATION RATES WITH 

FREQUENCY FOR TUNNEL IN A ROOM AND PILLAR AREA 

VARIATION OF THEORETICAL ATTENUATION RATES WITH 

FREQUENCY FOR THE Eh,l,l MODE IN A COAL MINE 

TUNNEL 

EVANESCENT WAVE DECAY RATE 

ATTENUATION RATE IN LIMESTONE 

Arthur D Littlelnc 
LIST OF FIGURES 

Figure 

No. 

Sections of a Plan View Mine Map of a Room 

and Pillar Limestone Mine 

Comparison of Free Space Loss and Measured 

Total Path Loss at 466 and 812 MHz in Belt 

Haulageway of Black River Limestone Mine 

Photograph of Haulageway Tunnel with Belt 

Conveyor in Limestone Mine 

Close-Up Photograph Illustrating Roughness of 

a Side Wall 

Signal Strength Versus Distance Around a 

Corner Having No Reflector -- f = 466 MHz -- 

Geometry A 

Signal Strength Versus Distance Around a 

Corner Having a Reflector -- f = 466 MHz -- 

Geometry B 

Signal Strength Versus Distance Around a 

Corner with a Reflector at 450 MHz and 850 

MHz -- Geometry C 

Signal Strength Versus Distance Around a 

Corner without a Reflector at 450 and 850 

MHz -- Geometry C 

Signal Strength Versus Distance Around a 

Corner with a Reflector at 450 and 850 MHz -- 

Geometry D 

Signal Strength Versus Distance Around a 

Corner without a Reflector at 450 and 850 MHz - 

Geometry E 

Metal Reflectors Mounted Near the Roof in an 

Intersection of Two Tunnels in a Limestone 

Mine 

Ray Diagram for Propagation Around and Through 

a Pillar 

Arthur D Little,lnc 
I. INTRODUCTION 

This report presents a mathematicalmodel for the propagation 

of UHF radio waves in the tunnels of a room and pillar limestone mine, 

and describes the analysis of a small amount of propagation data 

obtained by R. L. Chufo and R. A. Isberg (1'2'3) in the Black River 

limestone mine in Kentucky. The model and analysis is based on the 

waveguide mode theory(4) developed earlier for the transmission of 

UHF waves in coal mine tunnels, with allowance for propagation losses 

due to refraction into the tunnel walls, to scattering by wall roughness, and to long range random tilt of the walls. 

Two types of tunnel in the limestone mine are considered. One is 

a haulageway, containing a belt conveyor but no crosscuts, and having 

cross-sectional dimensions of about 20 ft. x 9 ft., which are comparable 

with the dimensions of the high-coal tunnels previously studied. The 

other kind of limestone tunnel occurs in a room and pillar area and 

has much larger cross-sectional dimensions, namely, 40 ft. wide by 

35 ft. high. Each side wall of this large tunnel has an average open 

area of more than 50% owing to the presence of intersecting cross-cuts. 

A sample of the room and pillar geometry is shown in Figure 1, a plan 

view of a section of the mine. 

The basic elements of the model are developed in the discussion 

of the haulageway tunnel, and then applied to the analysis of first 

the haulageway tunnel data and second the room and pillar area data. 

Propagation around corners and through pillars is also examined based 

on a ray theory approach, together with the beneficial effects of 

placing reflectors at intersections to significantly reduce corner 

losses. The theory is found to be in fair agreement with the data; 

however, additional in-mine measurements are needed to provide a more 

conclusive test of the model. 

Arthur D Little, lnc 
Source: Reference 1. 

FIGURE 1 SECTIONS OF A PLAN VIEW MlNE MAP OF A ROOM 

AND PILLAR LIMESTONE MlNE 
11. MODEL FOR HAULAGEWAY TUNNEL WITH BELT CONVEYOR 

Figure 2 shows experimental data taken by Chufo and 1sberg'l) of 

total signal attenuation in dB experienced along a small cross-section 

haulage tunnel at the two UHF frequencies of 466 MHz and 812 MHz. 

Figure 3 is a photograph depicting the actual tunnel environment. The 

total path attenuation is normalized with respect to isotropic transmitting and receiving antennas. Also shown for comparison are calculated 

free-space attenuation curves for the same frequencies. It is seen 

that the experimental data agree with the free-space curves at small 

ranges, but decay more rapidly at larger ranges. Beyond about 300 feet, 

however, the average trend is linear, which means that the electric 

field falls off exponentially with range in this region, rather than 

according to the free-space law. 

We interpret this behavior in terms of excitation of the waveguide 

modes of the tunnel in the following way. The transmitting antenna 

excites a large number of these modes which decay exponentially with 

range at greatly different rates, depending on the horizontal and 

vertical mode number components n and n Theory shows(4) that the 1 2' 2 loss rate in dB1100 ft. is proportional to a linear combination of nl, 

2 and n2. Theory also shows that, if the width of the tunnel is greater 

than its height, as inthe present haulageway case, the mode of smallest 

attenuation rate is the (1,l) mode with horizontal polarization, which 

we designate as E h,l,l. We therefore postulate that, beyond a distance 

of about 300 feet, the only surviving mode is Eh,l,l' 

A further postulate is necessary since the actual transmitting 

antenna, rather than being isotropic, is a vertical dipole. Such an 

antenna would not excite the 

Eh,l,l 

mode of a smooth-walled tunnel. It 

has been found(5) experimentally, however, that at large ranges the 

polarization is predominantly horizontal no matter what the orientation 

of the transmitting antenna may be. We therefore assume that the tunnel 

walls are not ideally flat and smooth but have enough roughness and 

tilt to cause mode conversion from the initial vertically-polarized 

Arthur D Littlelnc 
Source: Reference 1 

FIGURE 2 COMPARISON OF FREE SPACE LOSS AND MEASURED TOTAL PATH 

AT 466 AND 812 MHz IN BELT HAULAGEWAY OF BLACK RIVER LIM
Source: U.S. Bureau of Mines. 

FlGURE 3 PHOTOGRAPH OF HAULAGEWAY TUNNEL WITH 

BELT CONVEYOR IN LIMESTONE MINE 

Arthur D Little, Inc 
E mode to the horizontally-polarized # mode, within a distance v,l,l ,131 

of the order of 300 feet. 

The first step in analyzing the data in Figure 2 is to determine 

the attenuation rate of the Eh mode. To do this we fit a least- ,191 

square straight line to the data from 300 to 2200 feet for each 

frequency. The two straight lines are shown in Figure 2. Table I 

gives the values of the attenuation coefficient a in dB1100 ft. 

TABLE I 

ATTENUATION COEFFICIENTS (EXPERIMENTAL VALUES) 

FOR THE HAULAGEWAY TUNNEL 

Next we compare these experimental values of a with theoretical 

values for the %l,l 

mode. Three kinds of loss contribute to a: 

refraction loss, scattering loss due to wall roughness, and scattering 

loss due to random long range wall tilt relative to the mean planes of 

the four walls. In calculating these losses we use a combination of 

wave theory and ray theory. 

A. REFRACTION LOSS 

Each tunnel waveguide mode can be described, from the ray theory 

point of view, as a bundle of parallel rays which are reflected successively by all four walls of the tunnel. The grazing angles of 

reflection (in radians) are given by the expressions: 

Arthur D Little,lnc 
where the subscript 1 refers to the side walls and the subscript 2 refers 

to the roof and floor. Thus nl, n2 are the horizontal and vertical 

mode numbers respectively; dl and d are the horizontal and vertical 2 

tunnel dimensions; and X is the free space wavelength. Expressions 

(1) and (2) are the conditions for phase coherence of the multiply 

reflected rays with each other. 

The power gain for a distance z can be written as 

where g is the gain for side wall reflections and g2 for roof and 1 

floor reflections. In reality, the gains are less than unity, and 

thereby correspond to power losses per reflection. In general, for 

either the haulage tunnel or the room-and-pillar tunnels, 

F is the effective fraction of reflecting surface on the side walls, 

allowing for cross-cuts orothernonreflecting areas. N1 and N are 2 

the number of bounces of a ray in a distance z, given by 

Lastly, the power reflectances R1 and R are given by the Fresnel 2 

formulas 

Arthur DLittlelnc 
where K is the dielectric constant of the wall material and the subscripts h and v signify horizontal and vertical polarization, respectively. These are approximate expressions which are certainly valid 

for the small values of and $2 that pertain to the dominant modes. 

Therefore the attenuation rate arefraction is given by 

10 lotiOg 

a refraction = -10 ) (12) 

a 

n2A 

~o~~~(FR~) + 7 log (R ) refraction 

2d2 

10 2] 

where A, dl, and d are expressed in feet, and a 2 refraction in d~I100 ft. 

B. ROUGHNESS LOSS 

We assume as in Ref. 4, that the walls of the tunnelarerough, 

as illustrated in the close-up photograph of a sidewall in Figure 4, 

with a Gaussian amplitude distribution about the mean surface described 

by a root mean square value of h. The power loss factors per reflection 

are then given by 

Arthur D Littlelnc 
Source: U.S. Bureau of Mines. 

FIGURE 4 CLOSE-UP PHOTOGRAPH ILLUSTRATING ROUGHNESS 

OF A SIDE WALL 

Arthur 6) L~ttlt. Pnc, 
Again taking + and +2 as small angles, we find, from (I), (2), (3), 1 

(6), and (7) that the attenuation rate due to roughness is 

r3 roughness 

where all lengths are in feet and aroughness is in dBf100 ft. 

C. TILT LOSS 

Instead of calculating the tilt loss for a fixed tilt angle Bo, 

as in Ref. 4, we now consider the long range tilt to have a Gaussian 

distribution with a root mean square value B0 (radians). For a particular reflection at a part of a side-wall where the tilt angle is 0, 

the reflected beam is inclined at an angle Q1+ 20 with respect to the 

wall. The electric field of this beam therefore has the form 

whereas the field of the mode is 

where k = 2nlX. 

0 

The power coupling factor of E' back into the mode E is given by 

the normalized overlap integral 

where the integrations are taken over the cross-section of the tunnel. 

For small 6 and Q (17) reduces to 1 

Arthur El Little,lnc 
and likewise, 

sin k 0d 2 

We now introduce the statistics by using the Gaussian weighting 

factor 

Then m 

In order to avoid numerical integration, we use the approximation 

and obtain for (21) and (22) the closed form expressions: 

Arthur D Little, Inc 
Then from (I), (2), and (3), the tilt loss rate becomes: 

= - I L a tilt 2 l0g10g1 - 2 loglog2 d, d, 

where all lengths are in feet and a tilt in dB1100 ft . 

D. COMPARISON OF THEORY WITH HAULAGE TUNNEL DATA 

The haulage tunnel has nominal dimensions of 20 ft. in width and 

9.5 ft. in height. However, Figure 2 and the photograph of Figure 3 

indicate that the conveyor belt system occupies about 5 ft. of the 

width and contains equipment and debris that would trap incident UHF 

waves. We therefore assume that the effective dimensions of the tunnel are d = 15 ft. and d2 = 9.5 ft., and that only a fraction 213 of 1 

the area of the wall on the conveyor-belt side is reflecting. This 

meansthat the geometric mean of the reflecting fractions of the two 

side walls is F = (213 x 1)'12 = 0.816. The wavelengths corresponding 

to the frequencies of 466 MHz and 812 MHz usedinthe experiments are 

A = 2.11 ft. and 1.21 ft., respectively. The dielectric constant K of 

limestone is assumed to be 5. Moderateerrors in this assumed value 

are tolerable, since calculations show that the final results are very 

insensitive to K. 

For these values of the physical constants Eq (13) gives the 

values of a refraction shown in Table 11, for both the Eh and 

.1,1 

E v,l,l modes. 

TABLE I1 

COMPARISON OF THEORETICAL arefraction 

WITH EXPERIMENTAL atotal FOR HAULAGE TUNNEL 

12 

Arthur DLittleInc 

f 

(MHz) 

466, 

812 

Theoretical 

a a h,refr. v,refr. 

(d~1100 I ) (d~I100~) 

3.60 7.12 

1.43 2.57 

Experimental 

a total 

(d~lloo') 

4.02 

2.03 
It is seen that the Eh,l.l values for a refraction are comparable with 

the experimentally determined a total results, although somewhat lower. 

This is reasonable since roughness and tilt losses have not yet been 

included. The E values are definitely higher than the experimental v,l,l 

values, in accord with the idea that the horizontally polarized (1,l) 

mode always dominates at large distances for tunnels of this shape. 

If we now include the roughness and tilt effects, we find from a 

series of trial calculations, using Eq (16) and (28), that roughness 

and tilt values h = 0.2 ft. and 0 = 0.0122 radian = 0.7', give good 0 

agreement between theory and experiment as shown in Table 111. 

TABLE 111 

E. MODE CONVERSION 

COMPARISON OF THEORETICAL [Xtotal FOR Eh,l 1 MODE 

WITH EXPERIMENTAL atotal FOR HAULAGE ~NNEL 

FOR h = 0.2 FT. AND Oo = 0.122 RADIAN = 0.7' 

Since the transmitting antenna in the haulage tunnel is a vertical 

dipole, whereas the received signal at large distances is mainly the 

E 

h,l,l mode, the structure of the tunnel walls must be such as to cause 

mode conversion from the E and higher order vertically polarized v.1.1 

a 

exp t 

(d~1100') 

4.02 

2.03 

f 

(MHz) 

466 

812 

, , 

modes to the Eh,l,l 

mode. ,This conversion process clearly requires 

a a a a refr. roughness tilt total 

(d~/100') (d~/100') (d~/100') (d~/100') 

3.60 0.051 0.377 4.03 

1.43 0.029 0.589 2.05 

that portions of the tunnel walls are tilted about the longitudinal 

z-axis of the tunnel, or that conductors with this kind of tilt are 

present in the tunnel. The support structure of the conveyor belt 

indeed contains metal struts and other members oriented in this way 

as shown in Figure 3. 

Arthur D Littlelnc 
The vertically-polarized mode having, by far, the greatest 

coupling to the Eh mode is the E mode. The reason is that 

,191 v,l,l 

these two modes have exactly the same spatial structure, of the form 

cos(nx/d )cos(ry/d2), whereas higher modes are orthogonal to the 1 Eh,l,l 

mode. We therefore consider only the interaction between the two (1,l) 

modes, which can be described by means of the following coupled differential equations: 

- dlv - - a1 -a I +ah% 

d z vv vhv v 

where I I are the intensities of the two waves, and a are the h' v v 

power attenuation coefficients, and avh, ahv are the power coupling 

constants of the waves. From the reciprocity principle it follows 

that 

Equations (29) and(30)can be written in the more compact form 

where 

"1 = % + %v (34) 

a2 = av + %v (35) 

- a12 - %v (36) 

The solution of (32) and (33) for the boundary conditions % = 0, 

I =I atz=O,is v 0 

Arthur D Little, Inc 
where 

From (39), (40), (34), and (35), 

2 2 \ - = )av - a,,) + 4avh 

If we make the reasonable assumption that a is small compared with vh 

a - ah, Eq (37) becomes 

v 

This shows that Ih reaches a maximum at the distance 

From Table I1 we find, on considering only the refraction losses 

-1 and converting from dB/100 ft. to (ft.) , that ah and av have the 

-1 values .0083 ft. and .0164 ft.-' at 466 MHz, and the values .0033 ft. -1 

and .0059 ft.-' at 812 MHz, respectively. Therefore, upon substitution 

of these a and a,, values into (43), we get z = 84 ft. at 466 MHz and 

v m 

223 ft. at 812 MHz. These results are consistent with the point on 

Figure 2 at about 300 ft. beyond which exponential decay takes over. 

Inclusion of roughness and tilt losses would reduce zm somewhat. 

Arthur D Little,lnc 
For large values of z, (37) and (38) reduce to the approximate 

forms: 

In these equations ah and a can be calculated at each frequency from 

v 

the roughness and tilt parameters determined above. Also Ih versus 

z is known for large z from the experimental data. However, I versup. v 

z at large z is not known experimentally from the measurements to date 

in the belt haulageway. Therefore Eq (45) does not provide any useful 

information for analyzing the current set of data. This means that 

we have two unknown quantities, namely, I and a and only one 

o vh 

equation, i.e., Eq (44). There is therefore not enough information in 

the present set of data to determine the mode conversion parameter avh. 

If the unknown intensity I. is eliminated from (44) and (45), we 

obtain the simple relation 

for the equilibrium ratio of the two (1,l) modes at large distances. 

This ratio could easily be determined by means of a dipole receiving 

antenna that could be oriented first vertically and then horizontally. 

Then (46) would permit the determination of avh. 

Arthur D Littlelnc 
111. APPLICATION TO TUNNELS IN ROOM AND PILLAR AREAS 

A. COMPARISON OF THEORETICAL AND EXPERIMENTAL RESULTS 

Figures 5 - 10 show the results of experiments on propagation 

around corners in a room and pillar area, with and without the help 

of a metal reflector having two perpendicular 4 ft. x 4 ft. panels 

mounted in an intersection near the roof and inclined at 45' to the 

two intersecting cross-cuts as shown in Figure 11. In each graph the 

vertical scale represents the received signal in dB relative to 1 uV. 

Also included in each figure is a diagram showing the relative positions 

of the fixed receiver, the corner, and the movable transmitter. 

Figures 5 and 6 show that a marked decrease in signal loss rate 

occurs beyond the corner when the reflector is located at the intersection of the two tunnels containing the transmitter and receiver. 

In discussing theresult it is convenient to consider the transmitter 

and receiver to be interchanged, which makes no difference to the signal, according to the reciprocity principle. Then the TX dipole now 

replacing the RX dipole at the bottom of the diagram in Figure 5 

excites many modes of the tunnel which attenuate at very different 

rates depending on the mode numbers nl and n2. By the time the waves 

reach the corner, 1300 feet away, only the two (1.1) modes have 

appreciable amplitude. These modes are very well collimated since the 

grazing mode angles and g2 are of the order of lo. The portion of 

the wave that enters the aperture of the cross tunnel is therefore 

very small, and furthermore is nearly pependicular to the cross-tunnel 

side walls. The modes excited in the cross tunnel are therefore highorder modes which decay rapidly, in agreement with Figure 5. On the 

other hand when a reflector is present at the corner, a substantial 

fraction of each incident (1,l) mode is re-directed down the cross 

tunnel, and preferentially excites low order modes in the cross 

tunnel, which decay at a lower rate, as in Figure 6. 

In order to check these arguments we show on Figures 5 and 6 the 

theoretical decay rate of the E,, mode calculated for K = 5 and the ,131 

17 

Arthur D Littlelnc 
I I I I I I I I I I I I I I I I 

3$~i~a~ Intercept Point Arbitrarily Chosen 

-. -------_._ 

I. - - 

- 28F ... . -- . Eh 7 7 Theoretic, . r _ ----.--_ 0 

-

26- 

I 

24k 

I 

22 - 

20 - 150' 1 

Received I 

Signal 18- F 

m indB re 1 pV " 

16; 

L----

- 

1 r 

I 

141 i 

I 1300'/ 

12L0 

I *!% 

6 8k 0 

IL-.-LA I 

4t7k- 200 

I I I I I 

2 300 400 500 600 700 

Distance r of TX Beyond Corner in Feet 

Source: Reference 1, Figure 7. 

FIGURE 5 SIGNAL STRENGTH VERSUS DISTANCE AROUND A 

HAVING NO REFLECTOR - f =466 MHz -GEOMETR
3% I I I I I I I I I I I I I I I 

Point Arbitrarily 

26 - Chosen 

24 

22 

20 

Received 

Signal 18 

in dB re 1 pV 16 

14 

12 

10 

8 

6 

4 

0 100 200 300 400 500 600 700 

Distance r of TX Beyond Corner in Feet 

Source: Reference 1, Figure 7. 

FIGURE 6 SIGNAL STRENGTH VERSUS DISTANCE AROUND A 

HAVING A REFLECTOR - f = 466 MHz -GEOMETRY 

- 

TX 

- -- 

r - 12

- 

- 

1450' 

- 

- 

- 

- I . RX 

- 

- 

I I I I I I I I I I I I 1 1 I 
40 I I I I I I I I I I I I I I 1 

- 

Vertical Intercepts Arbitrarily Chosen 

n O 

5 Eh,l,~ Mode Theoretical (450) 

Eh,l,l Mode Theoretical (850) 

10- 

Received 

0 

- a a I3 0 

0 

Signal N 

o in dB re 1 pV 

-10 

-20 

-30. 

- Frequency 

o 450 MHz 

0- 

13 850 MHz 

- 

- 

- 

- 

I I I I I I I I I I I I I I I 

0 100 200 300 400 500 600 700 

Distance r of TX Beyond Corner in Feet 

Source: Reference 4. 

FIGURE 7 SIGNAL STRENGTH VERSUS DISTANCE AROUND A 

WITH A REFLECTOR AT 450 MHz AND 850 MHz -GE
40 

30 

Distance r of TX Beyond Corner in Feet 

Source: Reference 3. 

FIGURE 8 SIGNAL STRENGTH VERSUS DISTANCE AROUND A 

A REFLECTOR AT 450 AND 850 MHz -GEOMETRY 

I I I I I I I I I I I I I I 

- 

- 

0 

1 

0 

20 

10 

Received 

Signal 

indBre1pV 0 

-10 

-20 

-30 

- 

- 

- 

- 

Frequency 

- 0 450 MHz 

- El 850 MHz 

- 

- 

I I I I I I I I I I I I I I 

0 100 200 300 400 500 600 700 
40 

I I I I I I I I I I I I I I I 

a - 

I3 

30 

0 

0 0 0 0 

0 

0 a 

a a 

0 

Received 0 

Signal 0 

in dB re 1 pV 

Frequency 

0 450 MHz 

-10 13 850 MHz 

0 100 200 300 400 500 600 700 

Distance r of TX Beyond Corner in Feet 

Source: Reference 3. 

FIGURE 9 SIGNAL STRENGTH VERSUS DISTANCE AROUND A CO

REFLECTOR AT 450 AND 850 MHz - GEOMETRY D 
40- 

35 

( 

30 

25 

20 

15- 

Received 10- 

Signal 

indBrelpV 

h, 

W 

0 

-5 

-10- 

-15 

-20 

-25 

-30 

I I I I I I I I I I I I I I I 

-E 

E! 0 I TX - I 

0 I 

I 

- 

#, 

%J 

0 - 

- 0 

E 

a El 

0 

I3 

5- I3 

0 

- 

- 

Frequency 

0 450 MHz 

- 13 850 MHz 

- 

- 

I I I I I I I I I I I I I 

0 100 200 300 400 500 600 700 

Distance r of TX Beyond Corner in Feet 

Source: Reference 3. 

FIGURE 10 SIGNAL STRENGTH VERSUS DISTANCE AROUND A CO

A REFLECTOR AT 450 AND 850 MHz -GEOMETRY E 
Source: U.S. Bureau of Mines 

FIGURE 11 METAL REFLECTORS MOUNTED NEAR THE RrjCJF 

IN AN INTERSECTION OF TWO TUNNELS 1N A 

LIMESTONE MINE 
same roughness and tilt values, h = 0.2 ft. and 0 = 0.0122 radian = 0 

0.7' found for the haulage tunnel. However, we use tunnel dimensions 

of dl = 40 ft. and d2 = 35 ft., and a value F = 0.467 which corresponds 

to the 35 to 40 ratio of reflecting area to open area on the side walls 

of the tunnel in the room and pillar area. For these parameters, the 

theory gives loss rates of 0.53 dB/100 ft. for the # mode and ,191 

0.56 dB/100 ft. for the EvalSl mode, at 466 MHz. The near equality , . of the two loss rates is due to the almost square cross-section of the 

tunnel. The vertical positions of the 

Eh,l,l 

theoretical curves in 

Figures 5 and 6 are arbitrarily chosen. It is seen that the slope of 

the line agrees fairly well with the experimental points in Figure 6. 

In addition, the period of the oscillatory character of the experimental 

points suggests interference between the %,l,l and modes, which ~9191 

are close in amplitude and phase velocity. However, it is not clear 

how a vertical receiving antenna would sense this. 

In Figure 7 (with-reflector) the calculated theoretical % ,191 

curves for 450 and 850 MHz do not agree very well with most of the 

experimental points at these frequencies. In Figure 8 (without 

reflector) the experimental decay rates are greater than those in 

Figure 7, but not as markedly different as in the cases of Figures 

5 and 6. The reason for this is not very clear. In Figure 9, with a 

reflector at the corner, the experimental decay rates show signs of 

interference, but the rates seem to be much greater than the theoretical 

#,l,l and rates. Figure 10, with no reflector at the corner, ~3191 

shows experimental decay rates considerably greater than in Figure 9, 

as expected. 

The reason for the high experimental attenuation rates relative 

to the calculated Eh,l,l 

values may be that the higher modes have not 

completely died out in distances of the order of 1000 feet around the 

corner. Table IV gives calculated values of the attenuation constants 

a and av for a number of higher modes at 450 MHz, for the same para- h 

meters as before. It is seen that for a 1000 foot distance the total 

attenuation is about 7 dB for the (1,l) modes, 16 dB for the (2,2) 

Arthur D Little Inc 
TABLE IV 

THEORETICAL ATTENUATION RATES OF LOWEST AND HIGHER ORDER MODES 

AT 450 MHz FOR TUNNEL IN ROOM AND PILLAR AREA 

FOR dl = 40 FT., d2 = 35 FT., F = 0.467, 

K = 5, h = 0.2 FT. 8 = 0.0122 RADIAN = 0.7' 

0 

Arthur D Littlelnc 

Mode No. 's 

n 1 "2 

1 1 

1 2 

2 1 

2 2 

1 3 

3 1 

2 3 

3 2 

3 3 

1 4 

4 1 

2 4 

4 2 

3 4 

4 3 

4 4 

Refraction 

"h a 

v 

(d~1100') (d~/ioo~) 

0.399 0.430 

0.765 1.088 

0.644 0.479 

1.009 1.136 

1.178 1.997 

1.057 0.560 

1.423 2.046 

1.423 1.217 

1.836 2.127 

1.640 3.175 

1.646 0.673 

1.885 3.223 

2.012 1.331 

2.298 3.304 

2.425 2.240 

2.887 3.418 

Total 

a h a 

v 

(d~1100') (d~1100') 

0.658 0.689 

1.160 1.483 

1.028 0.863 

1.558 1.656 

1.713 2.532 

1.568 1.071 

2.083 2.706 

2.071 1.865 

2.623 2.914 

2.318 3.853 

2.287 1.314 

2.688 4.026 

2.789 2.108 

3.228 4.234 

3.341 2.272 

3.947 4.478 

Roughness 

%' "v 

(d~/ioo') 

0.0004 

.0021 

.0014 

.0032 

.0068 

.004 2 

.0079 

.0059 

.0106 

-01 60 

.0096 

.0170 

.0113 

.0198 

.0160 

.0252 

Tilt 

"h' "v 

(d~/100') 

.259 

.393 

.383 

.517 

.528 

.507 

.652 

.642 

.776 

.662 

.631 

.786 

.766 

.910 

.900 

1.035 
modes, and 28 dB for the (3,3) modes. Thus the higher modes do die out 

fairly rapidly compared with the (1,l) modes. However, beats between 

the two (1,l) modes will persist for quite large distances. 

B. PREDICTED VARIATION OF ATTENUATION RATE OF (1,l) MODES WITH 

FREQUENCY 

Table V shows how the attenuation rates of the (1,l) modes vary 

with frequency, again for the same parameters. As expected for tunnels 

having nearly equal vertical and cross-sectional dimensions, the vertical and horizontal attenuation rates are also close in value. The 

total attenuation rates are seen to fall steadily with increasing 

frequency, which suggests that microwave frequencies would be worth 

trying, especially since reflectors at the tunnel intersections would 

have much sharper reflected main beam patterns, and would therefore 

couple much more efficiently into the (1,l) modes of the cross-cut. 

Should this beam sharpening introduce a reflector alignment accuracy 

requirement at say X-band wavelengths, simply reducing the size of the 

reflector will broaden the beam to more tolerable widths. It is to be 

noted that roughness loss becomes negligible at high frequencies. An 

interesting prediction of the theory is that the tilt loss should at 

first increase with frequency, reach a broad maximum at about 1000 MHz, 

and then steadily decrease. 

Arthur D Little.1~. 
TABLE V 

VARIATION OF THEORETICAL ATTENUATION RATES 

WITH FREQUENCY FOR TUNNEL IN A ROOM AND PILLAR AREA 

FOR nl = n2 = 1, dl 2 40 FT., d2 = 35 FT. F = 0.467 

K = 5, h = 0.2 FT., 8, = 0.0122 RADIAN = 0.7' 

Arthur D Littlelnc 

Frequency 

f 

(MHz) 

500 

1,000 

1,500 

2,000 

3,000 

5,000 

10,000 

Tilt 

a h' "v 

(d~/100') 

.269 

.289 

.267 

.242 

.201 

.I52 

.097 

Ref ac tion 

a a h v 

(dB/10O1) (dBI100') 

.349 .375 

.I53 .I60 

,098 .lo0 

.071 .073 

.046 .047 

.027 .028 

.013 .013 

Total 

% a 

v 

(dB/lOO1) (d~1100') 

.618 .642 

.442 .449 

.365 .367 

.313 .315 

.247 .248 

.I79 .I80 

.I10 .I10 

Roughness 

a a h' v 

(dB/100') 

.00035 

.00018 

.00012 

.00009 

.00006 

.00004 

.00002 
IV. COMMENTS ON PROPAGATION IN A COAL MINE TUNNEL 

Table VI shows calculated attenuation rates for the coal mine 

tunnel investigated in Reference 4, including revised values of the 

attenuation rate due to tilt, based on the improved tilt theory given 

in the present report. It is seen that, although a tilt has a flat 

maximum at about 3000 MHz, a total decreases steadily with increasing 

frequency, instead of falling to a minimum and then increasing as in 

Reference 4. It turns out, however, that the rms tilt angle 8 = 1' 

0 

used in the present calculation gives as good a fit to the original 

experimental data as the constant-8 value of lo used in Reference 4. 

The results in Table VI suggest that even higher frequencies than 

1000 MHz may be usable in coal mines as well as in limestone mines. 

However, one must keep in mind that the attenuation rates in tunnels 

havirg large scale undulations (like in some coal seams) that obstruct 

the line of sight will be more severely affected at the higher 

frequencies. 

Although portable and mobile equipment are not commercially 

available above 1000 MHz, fixed point to point mine communication 

applications may arise that are suited to the use of available fixed 

station equipment at these higher frequencies. The use of small, 

compact, low power police radar equipment may be well suited to performing simple in-mine experiments to test the validity of the theoretically predicted behavior at X-band frequencies. 

Arthur D Littlelnc 
TABLE VI 

VARIATION OF THEORETICAL ATTENUATION RATES WITH FREQUENCY 

FOR THE Eh,l 1 MODE IN A COAL MINE TUNNEL 

FORdl = 12 FT., d2 = 7 FT., F = 1.0 

K = 10, h = 4 IN., eo = lo 

Arthur D Littlelnc 

Frequency 

MHz 

200 

500 

1,000 

1,500 

2,000 

3,000 

4,000 

5,000 

7,000 

10,000 

Tilt 

CY tilt 

(dB/lOOf) 

.35 

.79 

1.27 

1.50 

1.60 

1.62 

1.55 

1.46 

1.29 

1.09 

Refraction 

CY ref 

(d~/100' ) 

25.50 

3.72 

.92 

.41 

.23 

.10 

.06 

.04 

.02 

.01 

Total 

C( total 

(d~I100') 

26.89 

4.93 

2.40 

2.05 

1.94 

1.79 

1.66 

1.54 

1.34 

1.12 

Roughness 

CY rough 

(d~I100') 

1.05 

.42 

.21 

.14 

.ll 

.07 

.05 

.04 

.03 

.02 
V, PROPAGATION AROUND A CORNER AND THROUGH A PILLAR 

A. RAY PATH REFRACTION AND REFLECTION 

Figure 12 shows what happens to a pair of parallel rays A and B, 

belonging to a low-order mode in a North-South tunnel, whentheyencounter 

two pillars. Ray A misses the first pillar and enters an East-West 

intersecting tunnel where it zig-zags between the two pillars at steep 

angles, corrsponding, on the wave picture, to a superposition of high 

order modes of the East-West tunnel. These modes attenuate rapidly by 

refraction, roughness, and tilt losses. 

Ray B strikes the West wall of the first pillar where it is partly 

reflected and partly refracted into the pillar. The reflected ray 

remains in the original low-order mode since the grazing angle $ is 

unchanged after reflection. Note that the grazing angle has been 

exaggerated in Figure 12 to better illustrate the principles involved. 

The refracted ray is strongly bent, as shown, and proceeds in the limestone pillar at an angle with respect to the normal to the N-S wall 

that is slightly less than the critical angle C, which for K = 5 is 

26.6'. The ray then strikes the E-W wall of the pillar at 63.4' with 

respect to its normal, which is well beyond the critical angle of 26.6' 

for the E-W wall. Total internal reflection therefore occurs, and no 

refracted ray enters the E-W cross tunnel. The ray next strikes a N-S 

wall at slightly less than the critical angle. Therefore refraction 

occurs and part of the ray enters the parallel N-S tunnel and travels 

southward at the correct mode angle in this tunnel. Thereisalso an 

internally reflected ray which undergoes further reflections and 

refractions. It is to be noted, however, that refractions occur only 

at the N-S walls of the pillar. No rays enter the E-W tunnels from 

within the pillar. 

The main effect of propagation through and around the pillars is, 

therefore, that the original low-order mode in a tunnel, produced by a 

distant transmitter, can be transferred to parallel tunnels, provided 

that attenuation in the limestone is not too large. No direct transfer 

of the low-order mode into 90' intersecting tunnels takes place. 

Arthur U Little. lnc 
FIGURE 12 RAY DIAGRAM FOR PROPAGATION AROUND 

AND THROUGH A PILLAR 

Arthur D Little,Inc 
B. EVANESCENT WAVES 

When total internal reflection occurs as shown in Figure 12, an 

evanescent wave exists in the cross tunnel just outside the E-W wall 

of the pillar. The electric field of this wave 'falls off with distance 

x from the wall according to the relation 

where 

Here X is the free-space wavelength, K is the dielectric constant of 

the limestone, and J, is the internal angle of incidence at the wall. 

For the case illustrated in Figure 12, J, 2 90' - C. Therefore, 

and (47) becomes 

Table VII shows values of a for K = 5, at the wavelengths of 

interest. 

TABLE VII 

EVANESCENT WAVE DECAY RATE 

It is seen that the evanescent wave is of negligible amplitude at a 

distance of 1 foot from the wall. However, this conclusion is strictly 

valid only in the case of a perfectly smooth wall. If the wall is 

rough, the evanescent wave undergoes diffuse scattering to an extent 

3 3 

Arthur D Little, Inc 
that depends on the magnitude of the ratio h/X of the rms roughness to 

the wavelength. However, since the diffuse radiation is almost isotropic, it does not significantly excite the desirable low-order modes 

of the E-W tunnel which are concentrated at small grazing angles. 

C. ATTENUATION RATE IN LIMESTONE 

The efficiency of transfer of a low-ordermode from one tunnel to 

a parallel tunnel by transmission through pillars, as illustrated in 

Figure 12, depends on the electrical conductivity of the limestone. 

The attenuation and phase constants,aL and BL, for propagation in the 

limestone are given by the real and imaginary parts of the equation 

where p , eo are the magnetic and electric permittivities of free 

0 

space, K is the dielectric constant of limestone, and a is the conductivity of limestone. 

Table VIII shows how aL depends on frequency and conductivity. 

TABLE VIII 

ATTENUATION RATE IN LIMESTONE 

It is seen that a depends very slightly on frequency, but varies L 

almost linearly with conductivity. Since the pillar cross-sectional 

dimensions are 35 ft. x 35 ft., the shortest path of a ray from the 

left-hand to the right-hand tunnel is about 42 ft. The minimum 

Arthur D Littlelnc 
attenuations are therefore 880 dB, 94 dB, and 9 dB, respectively, for 

conductivities of 10-l~ lo-', and Mho/m. If values of limestone conductivity(6) are more likely to be in the vicinity of lo-' 

than lom3 Mholm, it appears that mode transfer to a parallel tunnel 

will not be significant in most cases. However, in those cases where 

the conductivity is close to Mho/m, a usable amount of coupling 

to the parallel tunnel will occur. Furthermore, qualitative data taken 

by Chufo and 1sberg(') in parallel tunnels at the Black River limestone 

mine appear to support the existence of this behavior at this mine. 

Arthur D Littlelnc 
VI. REFERENCES 

1. R. L. Chufo and R. A. Isberg, "Passive Reflectors as a Means for 

Extending UHF Signals Down Intersecting Crosscuts in Mines or Large 

Corridors," Conference Record, Twenty Eighth IEEE Vehicular Technology Conference, Denver, Colorado, IEEE Cat. No. 78CH1297-lVT, 

pp 267-272, March 22-24, 1978. 

2. R. A. Isberg, "UHF Radio System Tests in Black River Mine," Collection of Informal Field Test Reports to U. S. Bureau of Mines, 

Nov. 14-18, 1977. 

3. R. Chufo, Graphs of Data Taken at Black River Limestone Mine, 

Informal Communication, 1978. 

4. A. G. Emslie, R. L. Lagace, and P. F. Strong, "Theory of the Propagation of UHF Radio Waves in Coal Mine Tunnels," IEEE Trans. on 

Antennas and Propagation, Vol. AP-23, No. 2, pp 192-205, March 1975. 

5. J. V. Nickel and L. Burkett, "800 MHz Radio Communications for 

Underground Mining," Proceedings of the Fourth WW Conference on 

Coal Mine Electrotechnology, pp 26-1 to 11, August 2-4, 1978. 

6. E. I. Parkomenko, "Average Electrical Properties of Large Masses 

of Rock," Figure 8, p. 294 in Supplementary Guide to the Literature 

on Electrical Properties of Rocks and Minerals by G. V. Keller, 

Electrical Properties of Rocks, Edited by G. V. Keller, 314 pp, 

Plenum Press, New York, 1967. 

Arthur D Little, Inc 
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