AO-A108 209 FOREIGN TECHNOLOGY DIV WRIGHT-PATTERSON API ON F/S 8/9PROFESSOR M. M. PROTOC' YAKONOY'S STRENGTH COEFFICIENT F OF ROCK--ECUNOV al M M PROTOO'YAKONOV

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FTD-ID(RS)T-1293-81

FOREIGN TECHNOLOGY DIVISION

PROFESSOR M. M. PROTODIYAKONOVS STRENGTHCOEFFICIENT f OF ROCKS

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M. M. Protod'yak-onov

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FTD-ID(RS)T-1293-81

EDITED TRANSLATION

FTD-ID(RS)T-1293-81 12 November 1981

MICRFICH NR:FTD-81-C-001026

PROFESSOR M. M. PROTODIYAKONOVIS STRENGTHCOEFFICIENT f OF ROCKS

By: M. M. Protod'yakonov

English pages: 37

Source: Voprosy Razrusheniya i DavleniyaGornykh Porod, Ugletekhizdat, Moscow,1955, pp. 42-55

Country of origin: USSRTranslated by: Gale M. WeisenbargerRequester: FTD/SDBFApproved for public release; distributionunlimited.

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FTD-D(RS)T129-81Date 12 Nov 19 81

-L-~~ ', ,* S -a

DOC = 1293 PAGE 1

1293,gw

PROFESSOR M. M. PROTOD'YAKONOVIS STRENGTH COEFFICIENT f OF ROCKS

M,. H. Protodlyakonov (Junior), Doctor of Technical Sciences.

Mining Institute of the Academy of Sciences USSR.

The mechanical propqrties cf rocks play a primary role in

mining; on them depend the selection of the extraction method, the

productivity of reans of extraction, the behavior of the roof, and so

forth.

Initially the mechanical rcperties of rocks were only evaluated

qualitatively. Prof. B. M. Protcd'yakonov, in one of his first wcrks

on this problem [1], claractexized the approaches to study of the

strength of rocks at the beginning of the XX century: "...in mining

science it has long been the custcm to determine not the absolute

valuns of strength of rock, but only to compare rocks with each

other, grouping them into kncwn classes of strength, in that sense in

which it is always understood, and to mike these classes so broad

DOC = 1293 PAGE 2

that it is easy to assign any given rock to one category or ancther.

The attempts of this classification, however, suffer from complete

lack of coordination because the authors, generally speaking, did not

have as a goal the comparison of the strength, for example, with

respect to drilling, with the strength with respect to settling cf

the surface and so forth and in addition the relationship between

classes is only rarely expressed numcrically and usually the authors

are satisfied simply with the terms:. "strong," "brittle" rocks and so

forth."

But the development of mining urgently demanded a quantitative

evaluation of the mechanical Ercperties of rocks.

A famous Russian sciontist, one of the founders of mining

science, Prof. M. M. Protcdayakcnov (1874-1930) was able for the

first time to generalize all of this uncoordinated data and to

establish objectively existing connectiins batween various indices of

mechanical properties cf rocks ard to establish the orderly study of

the strength of rocks. This study was one of the bases of the further

developmant of a number of very important divisions of mining

science.

Prof, M, M, Protod'yakcnov in his dissertation in 1907 [2], then

in a report at a conference cl scientists cn mining, metallurgy and

.M S l

DOC - 1293 FAGE 3

machine building in 1910 (1], in a number of other works, and finally

in a principal work in 1926 [3], established that the strength of

rocks in various respects (with various methods of breakdown) are

approximately identical and prcvided a general table of relative

coefficients of strength f of all rocks. He suggested making this

table the basis of calculating processes of recovering rocks and

supporting workings. The coefficients of strength of rocks f have

become widely known and have become firmly rooted in mining science

and production.

During the past almost half a century repeated attempts have

been made to refute the opinicns of M. M. Protod'yakonov, but his

teaching about the strength cf rccks has fcund increasingly wider

recognition and application in practice. Checking over a lcng period

of time has shown the viability cf the rock strength coefficients

which he proposed.

Rock strangth coEfficients f are important for many branchas of

mining science: the science ct tte pressure of rocks, the science of

the breakdown of rccks during their recovery, for technical

standardization and etc.

In mining literature we ercounter assertions that "strength" and

"crushing strength" are synca)rs and therefore it is necessary to use

-----------

DOC =1293 FAGI 4

the generil technical term "crushing strength" in mining. Such

assertions are incorrect and the suggesticn to exclude the term

lSstr--angth" is not acceiptable. In fact, let us analyze carefully the

contant and range of applicaticr of both terms.

H. N. Protod'yakoriov [3] defined the concept of strength of

rocks as follows: "The strength cf rock and of any material is its

resistance to external forces.,'

The committee of technical terminology of the Academy of

sciences USSR (4] presently gives the fcllcwing definition to the

term "crush.ing strLngth": "crushing strength is the property of a

material under certain conditicre and within certain limits to

receive thost- cr other acticne without crushing.,,

As we spa, the term "crushing strength" refers oniy tc those

cases wh-an the material is not crushed. In the definition cf ths tcerm

"strength," however, there is nc such stipulation and therefore the

latter term is applicab~le both for characterizing rocks with respect

to their stability and with respcct to their resistance tc crushing

during recovery. Further, the term 1"strength" is applied for any type

of mechanical destruction, including such complex processes of

destruction as notching, boring, breaking down, blasting, crushing,

and so forth. The term lcxuscblrg strength," as a rule Is used in

DOC = 1293 PAGE 5

cases of determination of the teemporary resistances to elongation,

compression, bending, twisting, etc. Thus, by "crushing strength" we

normally understand the resistance of a material to the action of

only elementary stresses and nct to all actions.

H. M. Prot~d'yakornov I I] wrote: "Ia everyday use by the wor 4

"rock strength" we have in mind, generally speaking, varicus concepts

which in and of themselves are ccmplex. Thus it is possible to talk

about strength in the sense of greater or lesser ease of different

types of recovery, i.e., resistance during drilling, during blasting

or during direct recovery using those or other tools, for example a

pick, shovel, and so. forth. It is also possible to examine rocks with

respect to their stability, asc of a different type: when working,

concerning supports, safety tl.ocks, sinking of the day surface." "It

is already evident from this how varied the concept of the strength

of rock, and how dissimilar t.is concept is to those "elementary"

concepts of resistance to com~ressicn, shear, or elongaticn which

"structural mechanics" d'2als with.

- From what has baen presented above it follows that the content

of concepts embodied in the terms "str.ngth" and "crushing strength"

are not identical and that the term "crushing strength" is not

int.rchangeable with the term "strength."

wpm"

DOC = 1293 PAGE 6

As a measure of strength of rocks m. M. Protod'yakonov suggested

a coefficient of strength, i.e., a dimensicnless value indicating how

many times stronger one rock is than another which is taken for cne.

It is interesting to trace hou M. M. Protod'yakonov approached the

development of strength coefficients and his famous scale of strength

of rocks.

He first applied the coefficients of strength in 1907 for

characterizing the stability cf rocks and their pressure on mining

supports [2]. M. M. Protodyakonov considered that: "Rocks in mass

are far from a continuous elastic body, such as they are usually

considered in a course on the resistance of materials. A multitude of

cracks, from microcracks to large ones, divide the entire mass into

individual piecas and even there where a ccnnection remains, it is

significantly weaker than inisde cf the pieces themselves." In

addition he wrote: "It is obvious that the examined rocks also cannot

be considered as truly disccnnected (friable) bodies, because in the

latter there exists only fricticn and here there is also a certain

bond of the pieces with each. cther."

As is known, for characterizing friable bodies we use the

coeffic3ant of friction which is ogual to the tangent of the angle of

rest for these bodies. M. M. rctod'yakonov, by analogy, proposed for

characterizing the stability cf rocks that we use the apparant

mown"

DOC = 1293 PAGE 7

coefficient of friction (coefficient of strength) equal to the

tangent of the angle of rest ip cpen mine workings. It is apparaenr

because it took into account not only the force of friction but also

the force of adhesion of the pieces between each cther. Lat.r

research by P. M. TsimLarevict. skowed that the strength coefficients

of M. M. Protod'yakonova are equal to the tangents of angles of

internal resistance of the rccks, i.e. of angles at which the

greatest stressps arise in rocks and. at which cracks appear frcm the

action of destructive forces.

Analyzing the shortcomirgs cf the classifications of rock

strength proposed before him, M. M. Protod'yakonov wrot-: "Therefore

my problem is first of all to reduce the different "types of

strength" into a definite systea and second, to establish a more

rational classification and tc express the relationship between

classes in numbers" [ 1.

On the basis of theoretical considerations M. M. Protodlyakonov

came to the following conclusicn [1]: "Thus, if any rock is stronger

than another in the ratio f1:f in any one sense (in cur example,

during drilling) thrn in any cthgr (for example, supporting, sinking

of the surface, blasting, etc.) it wll be stronger in exactly tke

same ratio. Therefore the sale classification may be established for

all typcs of strength.

I.

I

DOC = 1293 PAGE E

However, the actual rocks are not ideal bodies. Therefore the

drawn conclusion can only he extended to them with a known error and

the questicn imwediately arises of its value; in other words it is

necessary to determine whether we are not risking obtaining clearly

inconsistent results."

Let us take characteristic rocks, place theDm in eight clsses and

for completeness let us add anctler extreme class, water.

Let us now examine whether this table leads to any

inconsistencies if we use it fcr all types of strength." Further M.

M, Protcd'yakonov writes: "o..various perscns, each for his own

purposes, completely individually, established a classification of

rocks with respect to strength; one for drilling, another for

blasting operations, a third for sinking of the surface, a fourth for

supporting, and so forth. nc ce had in mind comparing these tables.

But it turns out that if we dc this we obtain a fully explicit

identity of classifications.,

Then M. m, Protodlyakonov procassel thG data of a number of

authors by replacing specific mames of indices with dimensionless

coefficients and all of the figures obtained in this manner he

ii

|'I

DOC= 1293 PAGE 5

reduced t3 a single common tatle, dividing the rocks into similar

classes of strength:

"Now it remains to reduce the obtained figures of relative

strength in such a variety of serses into cne table."

11i'l - ~ h~mi- N a, a.. ....p. .. ...... . ..'*,l,,, ,

#J $ j) ......... . . ..-'ll -lXOKIW11~~? .11 t p.I I p

vpi) u p . i p C j idhJ U

II I~~lieliM!' I jjieiiil 1 II I ll: 'lail, . .16)J t

]\' Cp¢.iicii KpcllIU'7il I(l'¢ih~iIik I.III If.It.~liV IlloC.1;111¢1, m m I'K1 i I#0

,j~n~ti.iio C.UI5,c., d ,II~ tliicl i u.IL tfl~t)

yroab 30b) .2 '00 - NICJor,' L.ja6wjd l,)J)ohi a) I.ilia, Cwipol ii c'ol .1C -C I

VII Cun -'itil IO1,0.LI A) Cyxo ne , ounwi -) 0,7 J10M.ITIib;e e)

VIII lni y ) 11.16B)'11 .).. .- bii

IX o0 , 1A .. . . ...... 0 b ""

Table. KEY: I. No. of classes; 2. name of classes; 3.

characteristic rocks; 4. ultimate resistance to compression kg/m 2 ; 5.

nota; I - a. quite strcng; t. quartzite; c. blasting; II - a. strong;

b. granite and graywackA; III - a. rather strong; b. solid sandstone

and limestone; IV - a. average strength; b. solid clay slate, soft

sandstona, hard coal; V - a. rather weak; soft slate, soft coal; c.

pick work; VI - a. weak rocks; b. clay, wt sand; VII - friable

rocks; b. dry sand, talus; c. skovel work; VIII - a. running; b.

-... , . : . , . . ,. ... . ... . * .

DOC = 1293 PAGE 10

quicksand; c. dredging; IX- a. water.

2) wiyp~a I I W Ci UAMX ')1,C 1 W")C. I " ' ' ..I ,. ... .......... .

1 3000 20 20 - 18 -- 13.3 - -I I 15u0 I0 II !0 12 12 10,7 10 10

fli 90o 6 7 7 6 6 6,7 6 6iV 60o 4 4,8 4 - 4 4 4 4V 300 2 1,7 2 - - 2 2 2

VI 1 1.1 I - - - I IVI -1 0.7 0,6 0,5 - - 0.7 - 0.7V! I 0,1-0,3 .- - - 0,1-0,3

S 0 -. . . .. 0

Table. KEY: 1. classes off strength; 2. kg/cm 2 ; 3. recovery; 4. Rzhikha;5. Dolezhalek' 6. drilling of blastholes; 7. blasting; 8. Shalon;9. sinking of surface; 10. support and pillars; 11. author.

It is easy to see that the data of various authors and for

diffar.nt concvpts of str.ngth are closa to each other, almost to the

point of complete identity, which cannot be explained by chance and

one must see the confirmaticn cf the correctness of our conclusions

conc3rning the possibility of a single, rational classification with

respect to the strengt ccefficient."

From the excerpts given atcve it is evident that even in his

first works, in the area cf study of rock strength M. M.

Prctod'yakoncv Irew all of the Lasic conclusion$ concerning this

problem: 1) he showed that vazicus indices of relative strength of

rocks practically do nct differ from each cther; 2) provided a

measure of relative strength cf rocks - the strength coefficient; 3)

divided all rocks Ao several classes with respect tc the value cf

the strength coefficients.

DOC = 1293 PAGE 11

In subsequent works M. M. Protod'yakonov supplemented, expanded

and refined the work performed in this area. Thus, he increased the

number of classes from eight tc ten and for some classes introduced

an additional subclassificaticn which considerably expanded the

quantity of comparable data shabing the practical identity of various

classifications.

In proportion to the accumulation of data he refined several

times the relationship between the ultimate resistance of rock to

uniaxial compression and the strength coefficient.

The generally known version of the tatle of rock strength

coefficients and its more cozylete bases are given in the book by M.

M. Protcd'yakonov (3], the first chapter of which is given in the

first section of this collecticr.

Among the supporters and followers of M. M. Protodlyakonov there

exists a rather widespread, altbough simplfied interpretation of the

values cf the strength coefficient. They usually consider that the

* strength coefficient f is cre btndredth of the ultimate resistance of

rock to uniaxial compression aqd forget co'wp]etely about its other

connections. This definition is correct but at the same time it is

- -*

DOC 1293 PAGE 12

incomplete and imprecise. N. N. Protod'yakcnov considered that the

strength coefficient of rock is the average relative strength of rock

det.rmined by saveral differcnt methods.

Thus, he wrote [31: "Varicus methods are suitable for

determination of the strength coefficient of rock. From what has been

said it is evident that for tlIs we may use the values of any

ultimate resistance, or what is even better, the averages of various

ultimate resistances. We may a]sc use the quantity of expended labor

during various mining operaticns, the required quantity of explosive,

prassure produced by one cr ancther rock, and so forth."

making a salection from P. N. Protod'yakonov's table [3] for one

class of strong rocks we obtain:

-J Method of Destruction; Strength Coefficient

uniaxial compression of cutes in a press; 9.4-10.0

recovery using the Rzhikha metI.cd; 10.0

recovery using the Dolezhalek method; 10.0

manual drilling according to the descripticn of the Donets basin; |0.'

DOC = 1293 PAGE 13

drilling with pneumatic hammers; 11.2

pressure on timbering according to Protod'yakonov; 10.0

sinking of the surface according to Rzhikha; 10. 0

dressing of stones according to the Urochnyy position; 10.0-12.2

drilling with pneumatic hammers according to the description of the

Donets basin; 10.7-11.2

Average; 10.0

From these data it is possible to confirm that M. M.

Protod'yakonov considered: if a rock is stronger than the standard in

one ratio by 9.4 times and in another ratio by 10 times, and in a

third by 11.2 times, etc. then in general it is stronger than the

standard by approximately 10 tiaes. He used this number 10 as the

strength coafficient which was ccmmon for the entire given group of

* rocks.

-A*

DOC =1293 PAGE 141

4 In Fig. I the axis of the abscissa shows the average values ofthe sttength coefficient f which were emplcyed by M. M.

Protod'yakonov, and oa the axis cf ordinates the values of the same

toefficients obtained by him ty Frocessing data of a number of

tesearchers with the varicus methods of destruczion mentioned above.

Wya fthnected all points fcr each method of destruction with each

Otherb Asi we see, all lines intertwine closely together and move in a

bingle common bundle. The line of average valuas of the strangth

C66effcient passes exactly tkrc ugh the middle of this bundle.

DOC = 1293 PAGE 15

Ii __ , // -/

--- " - ,,

Ii i I '

10 5

Fig. 1. Relatioasips of iLdividual and average values of strength

* coefficients according to the data of Prof. M. M. Protod'yakonova.,. -- V

DOC = 129J PAGE 16

Taking the avcraga values instead of the individual values of

strength coefficients M. M. Erctod'yakonov replaced tha entire bunch

with a single straight line. Let us try to evaluate the deviations of

individual values of strength coefficients from their common average

values. For this we select linits of fluctuations of the strength

coefficients with respect tc vazious methods of destruction and

calculate the values of coefficients of a variation for each class of

strength of rocks. As a result se obtain:

wpa.,igj I Iu II'- o- i.,.,'im im,..t

- o,2 -

,7- i,.s U,8 14

2.04-- J,2 3,0 "12o8. -I,4 9

,5 7, , 152,o- .,' ,o 12

: l, b -, 4,11 9,8- ,, 5,0 19

Al- j" II lII -

8,U 7loh t - I ' :' l i t i ) 8

2 j)- I .t1,.1 12I P+L )--'r t ) 2tlI o )

KEY: 1. f according to various methods; 2. f according to

Protod'yakonov; 3. coafficient cf variation; 4. averaga.

As we see, thL deviations are estimated by coefficients of

variation from 7 to 26 0/0 and cm the averagg comprise 140/a. A

4 similar difference does not exceed the difference from heterogeaeity

+,4 ' " " * ** , + . ° . 4 v c. " . A.-+

DOC = 1293 PAGE 17

of rock in one and the same stcF-, [5]. In this case it is also

necessary to consider that M. H. Protod' yakonov compared data from

published works of various authcrs. Rocks of the same kind tested by

differert authors did not necessarily have precisely identical

properties. But even under tt.ese conditions the deviations had a

permissible value. Therefore, if different methods of breakdown for

determining the strength coefficients were actually employed on the

same rocks then the deviaticrs %culd.be even less. M. N.

Protodlyakonov was able tc note the connection between various

classifications because he tcck a sufficiertly wide range of change

of the strength of rocks and a large volume of oata.

Replicement of the individual values of the strength

coefficients by averages enabled N. M. Protod'yakonov to establish

the common, typical, and main differences cf rocks from each other.

Disragarding tha individual, secondary differences of mechanical

properties of rocks which cnly cicuded the general picture and made

understanding of the problem difficult, he significantly simplified

matters.

Precisely the significance and the simplicity of the strength

coefficients proposed by N. M. Protod'yikonov have made them so

widely used in practice.

DOC = 1293 PAGE 18

m. m. Protod'yekonov wrote (3]: "Numbers, expressirg the

relative strength of rcck will be "strength coefficients" and their

most important property is that they make it possible to compare

rocks with each other without kncwing what stresses there are in thcm

and how they are brought abcut." Consequently, strength, as

understood by M. M. Protod'yakcncv is an objective property of rock

which depends only on itself zrd does not depend cn the process of

destruction in which it is manifested.

This thougLt is y~esv-. ted most cIparly in another part of the

same wozk (3]: "If a rock is strcnger than another by a certain

number of times in some respect, for example during drilling, then it

will be the same number of tines strcnger in any other respect, for

example during blasting, with respect to the pressure on timber, and

so forth*" M. M. Protod'yakcncv noted repeatedly that the equality of

strengths is approximate.

After M. M. Protod'yakcncv's death attempts were made to refute

his strength coefficients and the scale of rock strengths. Prof. A.

F. Sukhanov citpd such arguments as the fact that clay is easy to

drill but difficult to blast hbile granite is equally difficult to

drill and blast. Por the two classes of rocks the differenca in the

expenditure of explosives is mct proportional to the dificrence In

the quantity of blastholes per unit Cf volume.

I -J&

DOC 1293 PAGE 19

The~ effpct of raplacemsnt of steel drills by Pobedit ones is not

identical in the two rocks.

on the basis of theste exauFles A. F. Sukhanov concluded that the

coefficients of drillability and blastability are not equal and are

nct proportional to each other and therefore the strength

coefficients of M. M. Erotodlyakonovarb not founded and contradict

reality. He reccmmended proceedirg to establish individual

classif2zations: borabiliAty, tiastability, separation, and so forth

and rejecting the concept of strength [6].

In essence this conclusicn sugg-ists returning to the position in

the evaluation of rock strength which existed before M. M.

Protod *yak onov.

For checkitig the conclusicns of A. F. Sukharhov let us use thG

classification of rocks with respect to borability and blastability

which hp' suggestcd. At the end of his work (6] A. F. Sukhanov gives a

consoliditcea table (32) of varicus indicas of mechanical properties

of rocks.

The coefficient of relative strength of rocks in this table is

DOC = 1293 PAGE 2C

equal to

fl;O.01 H1

where H, is the ultimate resistarce of rock to uniaxial compression

in kg/cm 2 .

Calculation of the cceff3cients.of strength of rocks on the

basis of production indices cf their drillability and blastability

using the final formulas cf M. M. Protod'yakonov was not possible

since the current indices ottained by A. F. Sukhanov refer to new

types of drilling hammers with a differp.nt operation of the hammer

and to new types of drills reinfcrced with cermet hard alloys, and to

new types of explosives which did not yet exist when N. M.

Protod'yakonov was working.

However, following the path of M. K. Protod'yakonov it is easy

to find new empirical formulas %hich have the same structure and

differ only by numerical coefficients. For example, graphically

comparing thA drilling time of klastholus using reinforced bits

(min/m) with N. M. Protod'yakcncv's strength coefficients given in

the same table (6, Table 32] it is possible to find that they are

practically equal to each other:

A -. ..-

DOC - 1293 PAGE 21

In the same manner we find the following empirical formulas:

f,3O. 15113;

f **4 H4 ,

where H2 - drilling time for 1 a of blasthola with reinforced bits,

mina;

H3 -specific work of drillirg klastholes, kg/cM3;

H4 specific expenditure cf ammonite No. 2, kg/rn3.

In view of the fact that the ratio between the strcngth

coefficient and the specific exlenditura of bits, according to MI. M.

4 Protod'yakonev. has an exponential form, we also find this dependence

graphically, but not in the ccnventional system of coordinates but on

a double logarithmic grid. TIhen we obtain

S2,8hZ

where Z -specific expenditure cf reinforced bits, pieces/a.

DOC =1293 PAGE 22

Let us designate by f the ceefficients of strength of M. m.

Proto'dyikonov, which are given in the table by A. F. Sukhanov.

Summarizing all of the results in Table 1, we find:

i 3.7"1 35,i! 1) A0 :37.0 8$3 3.,0 1., 28 I

70) 7 17,7 1. -1, (1,3 17 18,0 J,.80 0.8 JI jj1 1.3 l3 1.1) :,,31 12:) 1 108 11

904,

800 .11 ,U 1) T 7, 2,0 8,o u,() 7 .() i~t

60 . . : 35*2 5, 1.. . . . . . . . . . . . . . . .0 t

DOC = 1293 PAGE 23

LI

Plotting fl, fz, f3, f4, fs, f, and f on a graph (Fig. 2) we

obtain a narrower bunch of lines which interweave more closely than

in Fig. 1.

f - -

I iI I ' I

__0__ -

m -.

___, _/1 _

0 K0 20 30fcp

! "il

DOC - 1293 PAGE 24

Fig. 2. Relatioaship of individual- and average values of strength

coefficients according to the data of A. F. Sukhanov.

Calculating the limits cf fluctuations of f and the variation

coefficienrs v (w/), we find

1,0 P.i - 1,3 " I 9.iI 9- 1(1 __ _ __ _

1,4 1,1- " i12 f--I12IM .5-2,1 17 I. 13-- 82.4 .) .- I,, I ,o 17 -- Is 33.2 3,0 -3.5 -I -.- I,0 2o-21 34,-0 112 1- 27 55.0 5- 9 3-1,0 28-37 Io0.0 5- -6NO( 7'-8 ) t'' II v" v 1e 0

KEY: 1. average.

As we see the difference tetween the strength f, determined with

various mcthods of destruction (Vep 100,/, vaKc=240 /o), turned out to

be less than for H. M. Protod,)akonov and less than that obtained

when repeating the tests usinS the same method in a stope (due to

heterogEneity cf the rocks).

Thus, the data of A. F, Sukhanov not only did not refute, but

rather, brilliantly ccnfirmed t e view of M. M. Protod'yakonov

DOC 1293 PAGE 25

concorning the unity of strcngth coefficients with various processes

of breakdown.

In concentrating his attention on individual deviations from a

general law, Prof. A. F. Sukhapcv did not notice the law itself.

Supporters of the individual independent technological indices

(cuttability, drillability, klastability), A. F. Sukhanov, Ye. M.

Montlevich, and others made a number of errors in attempts to refute

the views of M. M. Pxotod'yakcncv experimentally.

Thus, for example, in ccmparing cuttatility and drillability of

two seams of coal and having discovered that the layer which was

difficult to cut was easier to drill, and vice versa, the laye: which

was easy to cut was difficult tc drill, they concluded that in

general there is not, and there cannot be, any kind of connection. In

this case they lost sight of the fact that cutting is don* in the

base of the seam and the drilling of blast holes is done through its

thickness, i.e., with resrict to different benches of the seam.

Meanwhile it has become kncwn tItat the strength of various benches of

one and the same seam mayAquite different. In one seam the cutting

zone may be stronger than the bench in which blastholes are being

drilled, and in the other vice versa. Therefcre researchers comparing

two different methods of determining strength made a gross error in

?1 I.

DOC - 1293 PAG E 26

assuming identical strength of all benches of a single seam. In

essence, they compared indices under completely different,

inccmparable conditions.

An3ther error which Js often made by these researchers is that

they compare two methods cf detexmining the strength of only two

rocks, which differ little in strength and with a limited volume of

data. At the same time they did not go beyond the zone of data spread

brought about by heterogeneity cf the rocks, where in general it is

impossible to establish any kind of law.

Using the lata of Table 1 let us compare the indices of

borability f3 and f, in two adjacent classes of rocks, for example in

rocks of classes I and II acccrding to A. F. Sukhanov. Then we

obtain:

Raw K 0opol I, 14

1 37 33II 26 '.

KEY: 1. class of rocks.

As we see, for rock cf class I the drillability is greater than

blastability by 1.12 times and for rock of class II, vice versa, it

is less by 0,96 times.

DOC = 1293 PAGE 27

If we limit ourselves to this data only (which some researchers

usually Aid) one can come to the incorrect conclusion that these two

*methods of determinaticn cf strength are nct comparable (drillability

and blastability of rock).

But if instead of two adjacent classes of rocks, differing from

each othar only by 1.2-1.4 times, we take the entire gamut of locks

differing in strength by 28-34 times and plot the value.s f3 and f, on

a diagram (Fig. 2) then we notice the presence of a fully defined

correlation between both indices. In this case it becomes clear that

in the entire wide range of change of the strength of rock, which

exc;-eds by s.veral times the spr'zad of data, there exists a practical

equality of f3 and f,. ThE grEater the number of experimental points

and the broader the range of tested rocks, the clearer the connection

of various indicEs with each cther. The 3rror of tha researchers

mentioned above consists in the fact that they try to find a

functional - precise connecticr, where there actually exists only an

approximate correlation ccnnection.

In connection with the assertion of M. M. Protod'yakonov

concerning the fact that: "If any rock is stronger than another a

certain numbgr of times in ene respect, for example during drilling,

- ~ *L ~h *

DOC = 1293 PAGE 2E

then it will be the same number of times stronger in any other

respect, for example during blasting, with respect to pressure or.

timber, and so forth," we shculd not conclude that in ganeral LetwS3n

all indices of mechanical prcperties of coals and rocks there must be

a direct proportionality.

In the opposite case, without having established a direct

proportionality between any tbc indices of mechanical properties of

rocks one may conclude the absence of any connections between these

indices, which refutes the ccrcept of M. M. Protod'yaKonov about the

unity of strength coefficients cf rocks during various processes of

their distr uction.

However, from the works cf . . Protod'yakonov it follows that

to the strength coefficient are directly proportional not all, but

~only those indices which in cre cr another form represent thei specific work of destruction (under constant conditions of

destruction). For example, Ac~dices of the specific expenditure of the

tool are proportional to the strength coefficient in the second

' power, tha indices of intensity of the processes of breakdown are

inversely proportional to the strength coefficient f, Prof, M. M.

Protod'yakonov nowhere speaks cf proportionality of all constants to

each other, but speaks of equality cf the strength coefficients

during various processes of breakdown.

DOC = 1293 PAGE 29

Let us explain this with an example. According to the data cf

Table I let us take the vdlues cf Z and f5 for various classes of

rocks:

K.Iacc IoP ,A, ZW

1 1,00 28Xi 0,03 5

KEY: 1. class of rock.

and let us take the ratio of these indices to each other. For rock of

strength class I the ratic will be equal tc 28: 1=28, and for rock of

class XI 5:0.03=167, i.e., six times greater.

This is quite understandatle and does not require explanation

because the ratio of squarcs cf the two valucs is not equal to the

ratio of their first powers at all. At ths same time the strength

coefficients fs, calculated on the basis of the specific expenditure

of bits Z according tc the emtirical formula given above:

,-.'2,," I A, turn out to be practically the same as the strength

coefficients obtained ty anotler method.

Let us repeat that the rcsition of M. H. Protodlyakonov spiaks

not about the direct propcrticality of all indices to each oth-r but

te

DOC = 1293 PAG E 30

about tha correlation connecticn of all indices of mechanical

properties of rocks with eaci: ether.

The form of such a ccnnecticn for each specific process of

destruction and strength indei may be easily established graphically

in the pressence of data for a wide rangz of rocks with respact tc

strength, Using the obtained SraFhs cr empirical formulas it is

possible to find an approximate value of the strength coefficient

with respect tc any characteristic of mechanical propirties of rccks

during any process of treakdcur. The strength coefficients found in

this manner during various Erccesses of breakdown are practically

equal to each cxher in spitq cf the absence of a direct

proportionality between scre cf the initial indices. Th~z differe~nce

between the strength coefficients determined by various methods does

not exc~ed the differbnce during repetition of the tests with the

same method.

It is necessary to note cases when, in fact, thv strength

coefficients of rock ottained during differ; nt processes of breakdown

differ considerably.

Prof. M. M,. Protod'yakoncv wrote: "**sit is necessary to ke very

careful with the detervinaticr cf f In certain cases and its value

may not be identical in various respects. Example. Let a given

DOC 1293 PAGE 31

granite, being strong (f=10) te broken by strong cleavage. For

drilling blast hOcls this is not significant and tberesfore the value

of f must be accepted as indicated. But it is obvious that during

blasting such granite easily breaks into pieces and a small guantity

of explosive is required and therefore in this case f should be taken

smaller, for example 8 or 6, depending on the circumstances."

Subsequently M. M. Protod'yakonov emphasized that in individual

cases there may he deviatiors fzcm the general law,

Summing up what has been said on the problem of the strength of

rocks we may note the following:

1. Errors of researchers, c~ponents of M. H. Protod'yakonov,

consisrd in the fact that in ccparing indices they overlooked the

difference in the strength of various banches of one and the same

seams and sought functional ccnnecticns there where correlation

conLections existed, and sought to find a direct proportionality

there where there existed other types of dependence; they

concentrated their attention cn specific, secondary differences

instead of on basic, general features and connections.

2. Graphic comparison cf the data of supporters of independent

technological indices of mechanical properties of rocks leads ta the

-. . ..-. . . .o -

DOC - 1293 PAGE 32

conclusion of the presence of correlation connections between thesc

indices, which cornfirms the viebroint cf M. m. Protod'yakonov. Using

equations of these connections it is possible to move from any index

of mechanical Froperties of rccks to strength coefficients and vice

versa.

3. Unity of the strength ccefficients f during various processes

of breakdcwn is a basic law estatlished by numerous experimants in a

wide range of strength cf rccks. The difference in the strength

coefficients during various Frccesses of breakdown is a deviation

from the basic law. It bears a partial, seccndary charactcr and is

manifested in a narrow range cf change of strength.

4. Use of single coefficients of strength f rakes it possible to

compare and to generalize data cn various types of breakdown. When

usirg a number of irdcpsndznt indices scientific ganeralizations are

not possible. At the same time the use of cne index, the coefficient

of strength f, in practice is ccnsiderably simpler than several

indepandent indices.

Analysis of the structure cf numerous empirical formulas

obtained by N. M, Protod'yakcrcv by processing mine data [3] makes it

possible to joiti the overwhelmirg majority of them into three basic

groups:

DOC = 1293 PAGE 33

() k1 II;

(2 ) 1 2.

(3)

where f - copfficient of strer.gth;

H - specific work of breakdcwn;

V - productivity of the means cf breakdown;

Z - specific expenditure cf tcols;

kL, k2 , k3 - numerical coefficients cf proportionality.

The values entering intc the fcrmulas, which wo're expressed by

Kt. K. Protod'yakonova often are not in the names indicated above but

their physical sense is the same as that givan by us above.

For examplp, value H may be exFressed not only by kg/m a , but

also by the nurber of man/shifts expended or breaking down 1 ton of

-SE. K

DOC = 1293 PAGE 34

coal or rock, the expenditure cf coirpressed air for drilling 1

running meter of blast hole, the spe-cific consumption of explosives

in kg/t, and so forth. In this case only the numerical values of the

coefficient k will change.

Value V with a constant pqwer of the means of breakdown is

expresseI through values of the rate of passage or drilling, the

productivity of excavation wcrkers (t/h or t/shift) the rate of feed

of machines, etc.

Designating:

V - power of the means of breakdcwn;

T - time of breakdown;

U - broken down volume;

A - expended labor;

* - expenditure of tools, we cktain

H=-; V=-; Z=1; AWT.

Substituting values, wc find that the threa formulas given above

DOC =1293 PAGE 35

may be reduced to two formulas:

(4) U1 '

1(5). k

Expressionis (4) and (5) are valid with various processe-s of

breaking Jown rocks (cutting, kreaking, drilling, blasting, etc.),

* ie.,they reflect certain objective gene~ral laws of processes of

* break down.

Consequently, applying these exrressicns during the study of new

processes and me~ans of breakdcwn which were not investigated by &. M.

Protodlyakonov, it is possible t1o- expect to obtain corr.act r.asults.

Actually, thc basic laws, estat]ished for the first time by M. m.

Protod'yakonov, were later ccipstantly used in various moclificaticnis

by many researchers.

From formula (4) it follcus that with a constant power of the

* means of breakdown W, the coefficient of stre~ngth f is directly

* proportional to the specific erelgy cf breai~down H=A/U. i~t turned out

* that the indices of strength cf ccals (suggested by the Institute of

Mlining of the Acadcmy of Sciences, USSR and BUGI) , based on the

measurement Of the specific tEergy cf breakdown, are directly

DOC 1293 PAGE 36

proportional to thE coefficients of strangth of M. M. Protod'yakcLCV.

It is known that not a single process of breakdcwn may occur

without the expenditure of energy, and consequently the specific

energy is a universal physical index, characteriziLg tha mechanical

properties of rocks under constant conditicns of breakdown. The

presence of a direct prcpcrticnality be.twaen relative and

dimensionless coefficients of strength of M. N. Protod'yakonov and

the specific energy of breakdcwn is a quite important factor which

explains why thi coefficients of strength f reflect so well the

various mechanical properties of rocks during breakdcwn and are

firmly rooted in the practice of mining.

LITERATJRE

1. M. M. Protodlyakonov. Strength of rocks from the viewpoint of

mining science. Works of the corference of scientists in mining,

metallurgy, and machine building. Y¥katsrinoslav, 1911.

2. M. M. Protod'yakoncv. Fressure of rocks on mine timber. (Theory

of mine timbering). Yekaterincslav, 1907.

3. Mikhail Protod'yakonov, Frcf. Materials for a fixed position of

mining operations, Part I. Minirc operaticns. Publication of the TsK

I!

O

DOC = 1293 PAGE 37

of miners. 1926.

4. Terminology Df tha theory of ilasticity, tests, and mechanical

properties of materials and strtctural mechanics. Committee of

technical termitiology, Issue 14. Pub. House AS USSR, 1953.

5. M. M. Protod'yakonov (Junicr). The problem of a unified method

for determination of the strength of coal. Bullatin of the Academy of

Sciences USSR, Department of technical sciences, 1953, NO. 2.

6. A. F. Sukharov. The problem of a single classification of rocks.

Uglete khizdat, 1947.

Jil