Empirical Approach to Calculate Rock Loads in Coal Mine Roadways

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:


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.


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,


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).


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


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


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


8/8

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.

Empirical Approach to Calculate Rock Loads in Coal Mine Roadways

Documents

Transcript of Empirical Approach to Calculate Rock Loads in Coal Mine Roadways