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8/9/2019 Empirical Approach to Calculate Rock Loads in Coal Mine Roadways
1/8
EMPIRICAL APPROACE TO
CALCULATB
ROCK LOADS
IN C O U NINE ROADWAYS
by
Dr.Erda1 Unal
Assistant Professor of Mining Engineering
Middle East Technical University
Ankara Turkey
BSTR CT
In order to define the suppart parameters, by uee
of empirical approaches, it is particularly important
to analyze the rock-load height that should be
controlled by supports. The controling mechanism.
however, depends on the type of support used there-
fore, the rock loads should be treated differently.
In this paper, an empirical equation is intro-
duced which relates the rock-load height (ht) to a
quantitative rock quality index REIR) , and roof span
(B) as fallows:
The above equation has been developed based on
the following:
(i) the roof-fall records obtained from various
coal mines;
(it1 the roof-fall
case bistorieg published in
literature;
(iii) a data point obtained from field imestiga-
tions carried out, by Rafia (I), in a coal
mine in West
Virgina:
(iv) a comparision of the empirically calculated
rock-load heights with:
a
the results (caving heights) of field
investigations and finite element analy-
sis carried out by Peng and Okuho(2).
b. the failure heights obtained from a
series of sensitivity analyses carried
out by utilizing the Boundary Element
program presented by Hnek and Brown
3 ) .
c. the estimates of other empirical methods,
iS*Tetzaghi
4 )
and Barton et.al. 5 ) ,
d. the estimates of the Diatinct Element
Method u t i l l a e d by Veo~ele(6).
The d e v e l o ~ t f the empirical equation is
presented in the paper and practical implementation
is stated.
The particular factor which is of interest during
the preliminary design stage of empirical approaches
is the rock load for which a tunnel or roadwayshould
be designed. he rack-load criteria developed hy
Terzaghi
(4)
w s mostly based on experience in civil
engineering tunnels supported by steel arches with
wooden blocking. This criteria, have been used
extensively for constructing rock tunnels w e r the
pest 50 pears. It is unlikely however that the
Terzaghi's original or rpdified methods developed
for steel arches suitable for tunnelling methods
utilizing reek bolts and shotcrete. In addition,
the rock-mass classification systems suggested by
Terzaghi and various other reserchers are to general
to permit an objective evaluation of the rockquality
and strata behavior and that they provide no quanti-
tative information on praperties of rock mass and
other parameters effecting the stability.
In order to utilize the empirical approaches in
design of coal-mine roadnays, it is particularly
important to express the rock load height that should
be controled by rock bolts in terms of quantitativ-
ely defined parameters, to clarify the mechanism
upon vhich the rock bolts provide support, and to
calculate the rock bolt parameters (i.e., length,
diameter, spacing. and capacity). The other two
stages of the design proeess, namely, the under-
ground observations and measurements: andmthe feed
hack cycleware also required to complete the design
process.
DEVEWPBWT
OP ROCK-LOAD
BEIEHT
EQUATION
The rock-load height in this study is defined as
the height of potential instability zone, above the
roof line, which will eventually fall if not
supported (see Figure 1).
The rock-load height can be determined either by
analizing the roof fall eases, or by making use of
various approaches. The roof-fall cases can be
obtained from the mine records (i.e. Mine Accident
Injury
nd
Illiness
Report
NW-Form
or rw actual
observations of the falls. If such a record does net
exist, or if the desi~n hould be made for a new
mine, then the fallowing equation is suggested in
estimating, the roek-load heihht:
8/9/2019 Empirical Approach to Calculate Rock Loads in Coal Mine Roadways
2/8
a.
In
the case of mine roadways Whittaker
and
Pye showed by underground obsemations
that the height of the relaxed zone above the
crown was equal to the width of the opening.
b. In the U.S. coal mines, the vast majority of
the roof-fall heights, obtained from the roo
fall records of the five mines visited in
Pennsylvania and West Virgina and the case
histories indicated in literature, were less
than the roof span.
(3) The rock load betWeen the upper (h -B) and the
lower (h 0 limits changes linea ly. This
assumptisn is based on the following:
Figure 1. Representation of the Kysi ca l Meaning of
the
Roek-Load Leight Concept As Used in
the Current Study.
where, ht is the rock-load height,
RKR
is the rock
mass rat- suggested by Ceolaechsnics Classification
7),
andBistheroof
spm Formineentriestheroofapw
is asawed to be equal to the entry width (B) and
for four-way
intersections
to the diagonal distance
(B') between the pillars. Ths plots 05 the mck -
load height as a function of roof span and RKR is
presented in Figure 2.
Figure 2. The Rock Load Reight Versus Boof S p m
Relationship as Defined By Equation 1.
Equation 1 was derived based on the folloving
assumptions:
(1) For a competent rock (i.e.. RNR-100) the rock-
load height is
zero
(ht-0). This is the 1-r
limit of the rock-load height.
(2) For an incompetent rock (i.e, RKR
0
the rock-
load height is equal to the roof span (ht B)
This assumption for the upper limit of ht is
baaed on the follwing informtion:
a. a data point obtained from underground
investigations, carried out in a mine in West
Virgina, coincides with the linear line
obtain from Equation 1,
b. the underground investigations, on roof
fall cases, and the associated finite-elcment
analysis carried out by Peng and Okuba 2)
have shown that there is a linear relation-
ship between the height of roof fall and width
of entry,
e. the results obtained from boundary-element
analysis indicated that, the relationship
between the
l xirmm
height of failure zone,
a h m e the opening, and the roof span iaal mst
linear,
d. Teraghi
(4)
suggested a linear relationship,
between the rock-load height and dimensions
e. The rock-load heights, as calculated by Eqna-
tion
l,
appeared to provide realistic rock-
load es Cht ion s for the entry widths
typicalzy osed in coal mining when compared
with the other enpirical ~ t h o d s .
Field Data
One of the
t ein
objectives in developing the
rock-load height cqnation was to obtain data points
fros aftus d sr 8r ou nd observations. b g he
quite a t e ~ c l v e ata collected for Geenechanics
Classification studies, only w field case prwided
the required inforpatian. that is, the thr ee, pra p
eters (bt. BXE and
B)
required were deteoiued, all
together, ae one Location only.
The following data Presented in Table 1 was
collected during the underground investigations
carried out in a coal mine in Rest Virginia
(1):
Using,thevaluesof Band 81 8 as 5.941~ 19.5ft) and
44 respectively,in Equation 1,the rock-load height
can be calculated as 3.3 (10.92ft).
The ahare result indicates an encauraging agree-
ment between the calculated (3.33~~) nd observed
(3.35m) values of the rock-load height; however, it
is statistically not significant. Therefore, more
investigations to obtain additional data are highly
desirable.
8/9/2019 Empirical Approach to Calculate Rock Loads in Coal Mine Roadways
3/8
Table 1. Suormary of the Field Data Collected
by Raf a.
Field Data and Finite Element Analysis
l.ocaico~?
f
rhe noof Fa1
Data and Method of Analysis-- Feng and Okubo 2)
colIected field data of roof falls at the raadmv
intersections in an unaerground coal mine 180m
(592ft) below surface. The coal aeam was Pittsburgh
Seam with an average thickness of 2.4mC8 ft). The
entry width was
6.0m (20ft). A rota1 of 22 roof
falls were observed during the data collection
period. The height of the roof fells ranged from
1.2 to
3.3
m 4 to 11 ft) with an average value
of 2.5m (8.45 ft) A 5uprmarg of the field data
collected by Feng and Okubo is presented in Tahle 2
U i m n a ~ o n f
Cllc
Rani rail. m . i t l
Tahle 2. Summary of the Field Data Collected by
Peng and Okubrr
Boor Span Bock uecr
Rottng
B m(~t) RMRI
Haxinwm Iheisllr o
t l l c
ohrmrvod
Roar ILI 3 . 9 . (11 It1
u r r a ~ e ri? ht
or the
lnnl F a l l 2.dSm 4 .LSfr )
Roof
Spnmr
t ilsr
tnlerrerlinn (il ):
8 4 h (28.2RTtI
Peng and Okubo used the criterion that the
contour linea = 0.1
u
defines the boundaries of
the arch zonePabove thx intersection that has more
or less loasened up and requires support. In the
above shown relationship
o
is the vertical stress
on the horizontal plane atPmid-height of the coal
seam and a
is the overburden stress. Peng and
Okub alsoVdetermined the arch zone ahove the inter-
sections of various roadway widths, as shown in
Figure
3
both by underground observations and by
using a finite-element program. Based on the ealcu-
lated results,
they concluded that an arching zone
was farmed ahove a four-way intersection and a
region of vertical stress was developed over a short
distance into the roof. He also indicated that the
analysis of field data combined with the calculated
results show that the roof falls occur within the
region
where
Q
0.1
p
P
V
Rock Load Heishthts
and Cavinp Heights--
Using
Equation 1,
for intersections,and the data
presented
in Tahle 2, the RMR values were hack
calculated from Equation 2 as fcllows:
Figure
3
Computer Arching Zones and the Average
Fall Shape At an Intersection (After Peng
and Okubo (2)
For the m i n i m roof-fall height, R R 86
For the m ximum raof-fall height. RMR 61
For the average roof-fall height, R R
=
70
The result
RMR
=
70 indicated the average quality
rating of the coal-mine roof. Using this value the
expected rock-load heights were calculated for
tlifferent roof spans and considering the plots
presented earlier in Figure 3 a comparison was
made.between the rock-load heights as calculated by
the current study and by the finite-element results
obtained by Peng and Okub
Table
3
shows the
results obtained from the two methods. As can be
seen from the table the rock-load heights predicted
by both methods are very close to eaeh other.
Boundary Element Analysis
The Method and Typical Results-- In order to
determine the x ten t of the f ilure
zones
developin
around rectangular openings, a two-dimensional
houndary-element program, prepared by Drs. Bray,
Hockin , Eissa and Hammet
was
utilized. A detailed
information on the computer pragram have been
presented by Hoek and Brown
3 ) . The
effects of a
number
of
parameters (i.e.. rock class. roof span,
8/9/2019 Empirical Approach to Calculate Rock Loads in Coal Mine Roadways
4/8
Table 3 Comparison of Bock-Load Eeights Calculated
by Peng and Okub
2)
and Geomechanics
Classification
and horizontal-to-vertical stress ratio) to the
extent of failure height were analyzed. The rock-
load heights, estimated by the Geomechanics
Classification, were compared to the failure heights
determined from the analysis of boundary-element
method. A detailed discussion on the mining con-
ditions considered, rock material and rock mass
properties assumed and the ranges of variable
parameters used has been given by itnal (8). In order
to determine the effects
of
the variable parameters
on
the failure heights,
a total of 96 computer runs
were analyzed. The variable paraweters used include
the following: rock-ss rating W),oof span
(B), and horizontal-to-vertical stress ratio (K).
In Figure 4, the effect of K an the behavior of
a 6.1- wide roof excavated in a fair rock
(BMR-45) is illustrated. In this figure, the effect
of on the mode of failure (shear and tensile) and
the extent of the failure zones can be clearlv seen.
S P A N - 6 l m R L I R 4 S m
0 2 , =OW
K 01
Figure 4. Ettect oi horlzontal-to-vertlcal btress
Ratio(K1 on the Extent of the Failorezone
and the Modes of Failure +
ndicates
Tensile
Failure and
9
indicates ShearFailurei
m
and s Vabes Indicate the-terial Cmstant
as Defined byHoek and Brown, (3)).
Figure 5 illustrates the effect of the increasing
rockloass quality in the same stress field (K is
constant). It is obvious from this figure that the
extent of failure zone is decreasing with the
increasing quality of the rock mass.
Rock Load Eeights and Failure Heights- During
the analyses, the failure heights (hf), the
maximum extent of the failure zone above the roof
line of a rectangular opening,
were
compared with
the rock load heights (h
.
Although it is sometimes
t
sensible to compare the analytical solutions with
emperical rules and with the performance of existing
roadways, combined results could provide valid basis
for sensitivitv analvsis. The results could also
.
reflect the effectsof various assumption made. The
typical plot obtained from the analysis of empirical
and analytical results are shown in Figure 6. In
this figure the symbols ht and hf are named as
caving height and they were plotted as a function
of various roof spans and of vertical-to-horizontal
stress ratios. The dotted lines in the figure
represent the cases where stress ratio, K. is less
than the unity. The solid lines indicate the situa-
tions where K is equal or greater than one. The
solid line which incorporates the symbol RMR
represents the results of the empirically calculated
rock-load heights.
The results of the boundary element analysis
indicate that in the majority of the eases (i.e.
0.3 < K < .5, a d 5 W < 5) the rock-load height
envelope obtained
rom
the predictions of the
empirical equation forms an upper limit to the
failure-height envelopes determined from the
boundary-elent analyses.
SPAN
s
6.1 m
R M R 2 3
5 P A N . 6 1 m
m . 5 0
R M R
8 5
Z O I
I, FAIII1HL
] i.03
.
Figure
5
The Effect of Rock-Uass Rating on the ex-
tent of a Failure Zone (Roof apan. B-6.lm;
Horizontal-to-Vertical Stress Ratio.
K 0.3).
8/9/2019 Empirical Approach to Calculate Rock Loads in Coal Mine Roadways
5/8
ROOF
SPA* 1
Figure 6. Comparison of Uock load Heights Predicted by Geomechanics Classification System and Bock
Failure Heights Found by Using Boundary Element Method.
Comparison of U ~ o k oad Heights With the Estimates
of Other Empirical Methods
The particular factor which is of interest in
majority of design approaches is the rock load for
which the tunnel support should he designed.
The empirical methods which utilize the rock loads
are the folloaing:
(4) Modified Terzaahi bv Deere et al.(l
(1) Bierbaumer (1913)
2)
Terzaghi (1946)
3 ) Stini (1950)
)69,1970)
(5) Cording et al.; (19j1,
1972)
(6) Cording and Mahar (1974)
1)
7) Barton et al. (1971
A detailed information on the comparison of the
roek-load heights suggested by various empirical
methods has been presented elsevhere (8). In this
paper, only the methods suggested by Terzaghi and
by Barton will be considered.
In Figure 7. the plots of the total rack-load
height as a function of roof span as estimated by
Terraghi's Xathod and Geomechanics Classification
are Presented. In this figure three of the Terzaghi
rock-classes (3.4 and 5) and all of the Geomechanics
Classification rock classes (very good to very pood
are included. As oan be seen from the figure, the
rocx-lad he ig hw in th e upper portion
ef
elaas 9
(very blocky and seamy) are nuch higher than that
of the
maximum
rock load, associated with very
poor rack (RMR
8/9/2019 Empirical Approach to Calculate Rock Loads in Coal Mine Roadways
6/8
ROOF SPAN B .
- 1 ROOF
SPAN. B.
m )
Figure
7.
Su m~ ar y f Rock-Load Beights Estimated by Method of Terzaghi and
Calculated by the Geoslechanics Classification.
(1)
A
number of values, representing different
rock classes, were selected,
2)
For eech
RM
value selected, the corresponding
00
S M I S ~ I O E O ~
Q value was calculated using Equation 4
proposed by Bieniawski(7):
RM 9 1nQ 44
(Eq.4)
(3)
For each Q value calculated, the corresponding
support-pressure ranges were determined by
utilizing Equation 4.
4)
number of roof spans including the full range
of the widths (entry and intersection) con-
sidered in
U.S.
coal mines, were selected.
(5) The rock loads were calculated using Equation
5,
shown below:
I
4
The suronary of the support pressures and the rock
loads as calculated respectively by Q-System and
Geomecbanics Classification are presented in
Figure
8
It is readily apparent that for all of the rock
classes the upper limits of the constant support
pressures suggested by Barton et al. s method are
significantly higher than the rock loads predicted
by Geomechanies Classification, but the lower limits
are comparable for poor and fair rock classes.
For
very good and ~ o o d ocks, and within the roof-span
ranges utilized in mining, the rock-laad
Figure
8 Sumery
of the Support Pressures Caleula-
red
by
the
9
and the BMR System.
predictions of the Geomechanics Classification are
in betweeo the laver and the upper limits of the
support prersures as sugpented by Barton et al..but
closer to the lover limits.
Cornparision af Rock Loads With the Estimates of
Distinct-Element Method
Figure 9 presents s sumary of the required
support force as s function of span for those r w k
lnlsses considered by the Geomec11;micsClassificstion
8/9/2019 Empirical Approach to Calculate Rock Loads in Coal Mine Roadways
7/8
and investigated by the Distinct Element Method.
The dotted lines indicating the trend of the
Distinct Element data which was calculated by
Voegele (6) using Equation 6
shown below:
ah tan
B P 4
Y
where B is the roof span, oh is the horizontal
stress, is the friction angle of joints and y is
the unit weight of the rock.
The solid lines shown in Figure 9 are various
PMR envelopes representing different rock classes.
The dotted lines were obtained by Voegele using
Equation
6
These lines
are
also a function of
aspect ratio (ratio of block thickness ta block
width) of the blocks formed by the jointings. It is
not
hedia tely clear that there should be a corre-
lation between RQD and aspect ratio of blocks 6 ) ;
however, these two parameters are included, directly
or indirectly, in the
calculation of
R R
values.
Figure 9. Summary of the Geomechanics Classifica-
tion and Distinct Element Method Calcula-
ted Rock Loads; Also Illustrated are the
Various Aspect Ratios (a,b.c and d) Con-
sidered in Distinct Element
Method.
CONCLUSIONS
In this paper, an empirical equation is intro-
duced and the development of this equation is
presented. The major conclusions drawn from this
study ara the f~llpwins:
the entry widths typically used in coal
mining:
(2) the caving heights determined, by Peng and
Okuba
2 )
based on field inveatigations and
finite-element analysis; and the rock-load
heights calculated hased on the same field
data and using the empirical equation, pre-
sented in this paper, are almost identical;
3) The parametric studies carried out in the
study by using Boundary Element Method, have
shown that the in-situ stress field,
the rac
quality, and the roof span have a significa
effect on the extent of the failure nones. I
majority of the cases, the rock-load height
envelope8 determined fromthe predictions of
the empirical equation,
forms
an upper limit
to the failure-height emrelopest' obtained
from numerical analyses
(BEM) For the cases
wbere horizontal-to-vertical stress ratio i
0.3, and for a wide range of RM values, the
ratio of the failure-height to rock-load
height is close to imity, that is, the
numerical and the empirical approaches pre-
dict the
same
height;
4)
The results of the investigations indicated
that a resonable estimate of the upper limi
to the amount of load, to be controlled by
support Systems, can he calculated in terms
of RM and B and
the undue conservation of
the other empirical methods can be eliminat
considerably;
(5) Once the rock-load height is calculated the
specifications of the rock bolts can he
determined.
Determination of the rock-bolt specifications will
be a topic of another paper in which the theories
and the aesumptions associated with the following
equations will be discussed:
(i)
Bolt Length
L)
Mechanical Bolts L 0.65 ht
Resin Bolts
where, ht is the rock-load height, B is the
roof span, and
is the horizontal stress
h
acting on the roof.
(ii) Bolt Spacing (S),
where. C is the holt capacity and
T
is the
uait weibt of the rock.
(1) the equation presented in this paper can be
incorporated with the Geomechanics Classifi-
cation System, and provides more realistic
rock load-estimations when compared with
the other empirical methods
especially for
8/9/2019 Empirical Approach to Calculate Rock Loads in Coal Mine Roadways
8/8
The study presented in this paper is based on a
part of a research project carried out by the
writer for his doctoral studies at the Pennsylvania
State University. The writer wishes to express his
gratitute to Professor Dick Bieniawski for his
contribution
and
encouragement throughout the entire
project.
REFERENCES
1. Raf a, F., (1980),
An
Assessment of Room-and-
Pillar Coal Mine Roof Conditions by Means of
Engineering Rock Mass Classifications , M.S.
Thesis, PSU, 123 pp.
2.
Peng, S.S. and Okuho, S., (1978). Roof Bolting
Patterns at the Four-Way Entry Intersections ,
A paper presented at the 1978 NM Anuual
Meeting, Denver, Colorado, 24 pp.
3 Boek, E. and Brown, E.T., (1980), Underground
Excavation in Rock, Inst. Min. and Metall.,
London. England, 527 pp.
4.
Terraghi,
K.,
(1946). Writing in Rock Tunneling
With Steel Supports, by R.V. Proctor and
T.L. White, Colnnercial Shearing and Stamping
Co., Ohio, 296 pp.
5. Barton, N.R., Lien, R. and Lunde,
J.,
(1974).
Engineering Classification of Rock Masses for
the Design of Tunnel Support , Rock Mechanics,
Vo1.6, No.4.
6 Voegele. M.D.. (1975) Rational Design of Tunnel
Support, Technical Report GL-79-15, September
516 pp.
7. Bieniawski, Z.T., (1979). The Ge~mechanics
Classification in Rock Engineering Applica-
tions, Proc.4th.Int.Cong. on Rock Mech.,
Montreux, Switzerland, Vol.11, pp.4148.
8 Unal,
E.,
(1983). Development of Design
Guideline8 and Roof Control Standards for
Coal-Mine Roofs ,
Ph.D.
Thesis, Penn.Smte
Univ.,
355
pp.