The Concept of Specific Energy in Rock Drilling- Teale 1965

Int. J. Rock Mech. Mining ScL Vol. 2, pp. 57-73. Pergamon Press 1965. Printed in Great Britain.

THE CONCEPT OF SPECIFIC ENERGY IN ROCK DRILLING R. TEALE Mining Research Establishment, National Coal Board, Worton Hall, Isleworth, Middlesex (Received 5 July 1964)

Abstract--The fundamental problem in rock working is the breakage of fragments out of the face of a solid wall of rock. Mechanically this can be dorte only by forcing a tool into the rock surface, after the manner of an 'indenter' such as is commonly used for testing surface hardness. Since the process breaks rather than cuts solid rock into small fragments of assorted sizes it cart be regarded as essentially one of crushing. As in crushing processes generally, energy/volume relationships are therefore of interest. 'Specific energy', defined as the energy required to excavate unit volume of rock. is a useful parameter in this context and may also be taken as an index of the mechanical efficiency of a rock-working process. In drilling data from a number of sources its minimum value appears to be very roughly correlated with the crushing strength of the medium drilled in, for rotary, percussive-rotary and roller-bit drilling. The implications of this are discussed. INTRODUCTION ALL mining operations consist essentially of the excavation of various kinds of 'rock', the word here being used in its strict geological sense to mean all those solid substances which constitute the Earth's crust. When in place in that crust, however, rocks form a solid body with only one free face and excavation from such a body must be preceded by the breakage of small fragments out of its surface. Only when such small-scale breakage has been concentrated on a narrow front--as in drilling a shot-hole, for example--and a second free face has been created within the body of the rock, can excavation proper take place on a larger and more economical scale. Even as mining proceeds, the same situation recurs continually. If a heading is being driven, then at any time its face presents the same characteristic: it is the single free face of a solid body of rock into which further penetration has to be made. If this further penetration is effected by drilling a shot-hole into the face, then the pattern is repeated on a smaller scale at the bottom of the hole itself. This problem of penetration into the solid is fundamental to all rock-working, that is to all mining, processes. Since the body of rock is always large in relation to the entry which has to be made into it, the problem may be generalized as that of making an entry into a semi-infinite rock solid through its one and only free face. D R I L L I N G AS I N D E N T A T I O N If only mechanical methods of rock excavation are considered, penetration into the solid can be achieved only a fraction of an inch at a time, at the tip of some form of drilling tool. Since penetration is essentially measured normal to the original surface, it is unlikely to be greatly influenced by any lateral components of the force on the tool, whatever they may be. Thus fundamentally the action of a drilling tool resembles that of an indenter, such as is commonly used for measuring surface hardness, particularly of metals [1]. The indenter, 57

58

R. TEALE

penetrating the surface of a semi-infinite solid of brittle material under a normal thrust, is the basis of all mechanical rock-working processes. Existing types of drilling tool are very few. The simplest is the hand-held chisel which, repeatedly struck and turned to a new position, produces a circular hole. Orthodox percussive drilling is essentially a mechanized version of this crude process of 'percussive indentation'. Rotary drilling may be regarded as a combination of two distinct actions : 'indentation', by which the cutting edges of the bit are continuously pushed into the rock to give them a bite; 'cutting', by which the bit is given a lateral movement to break out fragments of rock. Though these actions are in practice virtually simultaneous, it is possible to conceive of them being applied separately and alternately. Percussive-rotary drilling adds percussive indentation to the static indentation and lateral 'cutting' of the pure rotary process, combining them in more or less arbitrarily determined proportions. The roller-bits used for oil-well drilling are essentially arrays of indenters, mounted in the form of teeth on rollers which run round on the rock surface under a thrust normal to it. They may have a slight scuffing or 'cutting' action, particularly if designed for soft rocks, but otherwise work almost entirely by a process of repeated indentation under static thrust. It is as well to point out here that the 'cutting' actions referred to above are not really cutting at all. In all cases the rock, being a brittle material, is broken into fragments of assorted sizes. Hence the 'cutting' action is essentially one of breakage, as is that of indentation. When a flat-ended, parallel-sided indenter is forced into a hard rock surface, broadly speaking two things happen: the indenter first penetrates by crushing and compacting the rock in front of it; subsequently, when it has penetrated some distance, fragments of rock break out from the bottom of the indenter hole, back to the original surface. This process repeats itself, 'penetration' being followed cyclically by 'breakage'. With a tapered indenter the process is similar. Indenters and drills--in brittle materials--have this in common: they all result in the breakage of an assortment of fragments, covering a wide range of sizes, out of the face of a semi-infinite solid. Indenters and drills may therefore be regarded as primary crushers; 'primary' because their product is broken from the solid and is not, as in other crushers, the result of reducing one existing size distribution to another. In the study of crushing generally, the applied energy is accepted as an important parameter and many attempts have been made to relate it to the properties of the material crushed and to the dimensions of the product [2]. To the author's knowledge, no work has been done on energy/size relationships in the sort of primary crushing which drilling and indentation represent, except that of WALKER and SHAW [3] referred to below. Nevertheless, such energy relationships must play an important part in the understanding of rockworking processes. In this present work, a start has been made by examining the energy balance of actual drilling operations. SPECIFIC E N E R G Y A useful parameter which can be defined in this field is 'specific energy'--the work done per unit volume excavated. (The quantity of rock broken is logically measured geometrically, by volume rather than by mass, since it is determined by a stress pattern which is itself geometrical.)

THE CONCEPT OF SPECIFIC ENERGY IN ROCK DRILLING

59

It is axiomatic that, to excavate a given volume of rock, a certain theoretically attainable minimum quantity of energy will be required. Its amount will depend entirely on the nature of the rock. Real mechanical processes might or might not approach this theoretical minimum: the difference between actual and theoretical requirements would be a measure of work dissipated in, for example, breaking the excavated rock into smaller fragments than necessary, in friction between tools and rock (which amounts perhaps to the same thing on a microscopic scale); or in mechanical losses quite outside the rock system. Breaking the debris into 'smaller fragments than necessary' may have a disproportionate effect on the energy needed to excavate the given volume. Not only do more particles have to be broken needlessly, but the specific energy itself increases considerably as the particle size is reduced. This effect is illustrated by WALKERand SHAW [3]. They measured the energy required to grind various sizes of both steel and rock from the solid and found, for example, that to grind marble to a particle size smaller than about 2.5 × 10 -5 in., the specific energy was 1,200,000 in. lb/in 3. It fell rapidly as the particle size increased and at the largest size produced, 1.5 x 10 -3 in., was only about 70,000 in. lb/in 3. The specific energy clearly cannot continue to fall indefinitely at this rate. It must level off at some finite value and decrease more slowly, possibly so slowly as to become virtually constant as the particle size increases indefinitely. This idea of constant specific energy carries important implications for the study of rock-working processes, for it sets the maximum mechanical efficiency it is possible to achieve. The mechanical efficiency of a rock-working process cannot be measured directly, since the minimum amount of work required to excavate a given volume of rock cannot be measured against any absolute standard. The volume of rock actually broken must therefore provide the index. The volume of rock broken per unit energy input is the reciprocal of specific energy as already defined, so that mechanical efficiency is a maximum when specific energy is a minimum. E N E R G Y IN R O T A R Y D R I L L I N G In rotary non-percussive drilling, work is done both by the thrust, F i b , say, and the torque, T l b in., say. If the rotation speed is Nrev/min, the area of the hole or excavation A in 2 and the penetration rate u in./min, the total work done in one minute is (Fu q- 2~'NT) in.lb. The volume of rock excavated in one minute is (Au) in 3. Putting e as the specific energy, dividing work by volume, gives

e ~ (A) + ( ~ ) ( N j ) in. lb/inZ.

(1)

Using subscripts t and r to denote the 'thrust' and 'rotary' components of e, et = ( F ) in. lb/in ~,

(2)

(2~r][NT] er = ~'1 \ ~-1

(3)

in. lb/in 3.

It will be noted that the thrust component, (F/A), is equivalent to the mean 'pressure' exerted by the thrust over the cross-sectional area of the hole. Specific energy is, in fact, dimensionally identical with pressure or stress, since (in. lb/in a) is equivalent to (lb/in2). (Physically this arises from the fact that if a force F acting on and normal to a surface of area A moves it through a distance ds, the increment of work done, d W say, is equal to

60

R. TEALE

Fds. The volume change effected by the movement, dV say, is Ads. If e is the specific energy at any point, then e = d W/d V ~- F/A ~ P, the pressure at that point.) For a given size of excavation, A is constant so that et is directly proportional to F. It is always small in comparison with et, sometimes negligible. For given A and N, er is proportional to (T/u). Now the torque/penetration-rate curves for rotary drilling, over a fairly wide working range, approximate to straight lines through the origin. Thus (T/u), which would be the slope of such a line, is also approximately constant. It follows that for given A and N, er and therefore e itself should not vary a great deal over the working range referred to. This is consistent with the suggested constant value of specific energy at large particle sizes. It is of interest, however, to study the extent of the variation, its relationship to other variables and whether or not it exhibits a minimum value. Another approach to the above is to put p as the penetration per revolution (p ~ u/N in./rev). Then from equation (3) er =

'~4

Pin.

lb/in a.

(4)

T is the torque required to remove a layer of rock of depth p in one revolution. Since the amount of energy required to break brittle materials like rock is not much affected by the rate at which it is applied, the relationship between T and p may not be significantly affected by changes in rotation speed. The ratio (T/p) may therefore be a useful index of specific energy. Considering the application of the above to measurements made on an actual drilling machine, it is apparent that specific energy will reach very high values at low thrusts. Below a certain value, the thrust will be inadequate to effect penetration of the bit. The volume excavated will then be zero but a finite amount of work will still be done,against friction. The specific energy, as has been seen, will increase of itself as the particles broken become smaller. Together, these effects will cause specific energy to tend towards infinity at zero thrust. As the thrust increases, the size of particle broken will also increase; the work lost in friction will constitute a rapidly decreasing percentage of the total work done. Together, these effects will contribute to a fall in specific energy. However, this fall will not continue indefinitely; a stage may be reached when the tool is pushed so heavily into the rock that it becomes overloaded and clogs. The reduction in efficiency at this stage will cause the specific energy to rise again until the drill stalls. For a practical drilling tool, then, operating at a fixed rotation speed in a particular rock, it is to be expected that the specific energy at low thrust will be high. It will fall fairly rapidly, as the thrust increases, until it reaches a value beyond which it either will continue to decrease so slowly as to remain virtually constant or will actually start to rise again. The lowest value attained is a measure of the maximum mechanical efficiency of the particular tool in the particular operating conditions. It enables comparison to be made with any other type of tool operating in the same rock. Its characteristics--whether it occurs as a sharp turning point at one particular thrust, or remains constant over a range of thrusts--are of considerable interest. Finally, it offers a possibility of relating the drilling process to some parameter of rock strength. PRACTICAL M E A S U R E M E N T S OF SPECIFIC E N E R G Y Experimental data relating to rock drilling from a number of sources have been examined.

THE CONCEPT OF SPECIFIC ENERGY IN ROCK DRILLING

61

In all cases where it has been possible to calculate specific energy at different thrusts it has behaved much as predicted. The fall to a minimum is always apparent, though the ensuing rise again occurs only i n certain types of drilling. An interesting point which has arisen is that the minimum energy in all cases is of the order of the quoted compressive strength of the material drilled. The correlation, based as it is on a variety of results in very variable materials, is not precise but since, as noted above, the units in which specific energy is expressed are dimensionally identical with those of stress in which compressive strength is expressed, it is perhaps not altogether surprising that a relationship of some kind should exist. Tri-cone roller bits The first evidence [4] relates to a few tests made with a 'Security M3' and a 'Hughes W7R' roller bit, both of 12½ in. dia. The tests were made in Pennant sandstone and in a concrete with an aggregate of Darley Dale sandstone. The rotation speed was 24 rev/min in all cases. It will be seen from Fig. 1 that the measured specific energy does behave as predicted. (Only the rotary component is shown; the thrust component is negligible in comparison.)

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I l N PENNANT SANDSTONE

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"} I N DAP,LEY DALE SAN DSTONE

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l 60~000

DRILLING THRU.(;T, F ~

FIG. I. Specific energy for two roller bits in two media. The reported crushing strengths of the rock and concrete used are also indicated in Fig. 1. Except for the M3 bit in Pennant sandstone, there is a close correspondence between these values and the minimum specific energies attained. The discrepancy in the case of the M3 bit may be due to its being designed for softer rocks, that is, it has fewer teeth and greater scuffing action than the W7R. It drills faster than this bit in Pennant sandstone, but presumably at the expense of greater wear. The 'excess' specific energy is taken to be associated with this greater scuffing action. Figure 2 shows the relationship between thrust and penetration per revolution. In Pennant sandstone they are approximately linear even at the highest thrusts. In the Darley Dale concrete, however, the curves tend to become concave downwards above a penetration per revolution of about 0.15 in. This may be explained by a 'bedding in' of the bits in the

62

R. TEALE

softer medium, so that they work less effectively. The departure is most marked for the W7R, which has more closely spaced teeth and therefore tends to spread its load more quickly. Figure 3 confirms that for both bits the torque is proportional to the penetration per revolution, except in Darley Dale concrete. Even here, however, the departure from

./

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FIG. 2. Penetration per revolution for t w o roller bits in two media.

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PENETRATION PER P,EVOLUTION.Cin.~ FIG. 3. Torque characteristics o f two roller bits in two media.

THE CONCEPT OF SPECIFIC ENERGY IN ROCK DRILLING

63

linearity occurs only above a penetration per revolution of 0.15 in., which has already been noted as marking the onset of less efficient working in this rock. The straight line portions of Fig. 3 intercept the torque-axis above the origin. The intercepts represent work lost, presumably in friction, at zero thrust. This lost work may be eliminated by ignoring the intercepts and using the slopes of the straight line portions to give values of (T/p) for equation (4). er =

-~

in. lb/in 8.

The values obtained are given in Table 1. TABLE I Specific energy (in. lb/ina.) Bit Pennant Sandstone

Darley Dale Concrete

M3 W7R

18,700 13,300

6400 5870

Crushing Strength

13,780

7210

(Specific energies calculated from torque/penetration-per-revolution graphs)

They agree quite well with, though they are somewhat lower than, the minimum values of Fig. 1. This suggests that the 'true' specific energy is constant over the wide range in which the torque/penetration per revolution relationships are linear. It follows that over this range either the size of particle broken does not increase or, if it does, the reduction in specific energy which theoretically such increase might be expected to produce is not significant. The high specific energy at low thrusts can be accounted for almost entirely by the work lost at zero thrust. OPOLSKI [9] has used a similar method to assess a 'drillability' index for the rotary drilling of coal. This will be referred to later. Roller-cutter tests The results of a number of roller-cutter tests are available [5]. In these, a variety of cutters was used to cut grooves about 4 in. wide, up to 6 in. deep, in a ring of concrete segments. They operated over a fair range of thrusts and rotation speeds. The resultsare subject to wide scatter, and in many of the earlier tests the instrumentation had not been perfected. Nevertheless, the results of 212 of them, plotted in Fig. 4, show specific energy decreasing from high values at low thrust, to values which lie reasonably well within the range (6730 to 10,790 lb/in 2) of measurements of the crushing strength of the concrete used. Russian tunnelling machine LOCHANIN [6], describing the PPK-1 tunnelling machine, gives the power consumption R.M.--E

64

~. TEALE

as 14 to 24 kWh/m a of rock---equivalent to overall specific energies between 7300 and 13,000 in. lb/in 3. The rocks drilled are described as sandy shale and sandstone with strengths on the Protodyakonov f-scale of 6--8 and 10 respectively. These correspond to crushing strengths of about 8500-11,300 and 14,200 lb/in 2 respectively (see Appendix) so that the rough correlation between specific energy and crushing strength is again apparent in this machine.

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CTHE HORIZONTAL LINES SHOW THE LIMITS OF CRUSHING STRENGTH OF THE"PENNANT CONC~ETF_~sUSED IN THE TESTS AS DETERMINED FROM 6in. CUT CUBES AND 4in. AND 6in. B,S. CAST CUBES~,)

FIG. 4. Specificenergy in tests on roller cutters.

OTHER TYPES OF D R I L L I N G Intuitively, the idea that minimum specific energy may be correlated with crushing strength can be extended to all methods of rock drilling. They are all forms of crushing, producing fragments of much the same order of size, and the minimum energy which can achieve a given effect must be the same whatever the mechanical process used.

Small-hole rotary drilling Some of the experimental data on orthodox rotary small-hole drilling, previously reported by FIsH and BARKER[7, 8] have been re-examined. A similar pattern emerges. Referring to a set of experiments in which holes 1t~ in. dia. were drilled in a single block of Darley Dale sandstone using orthodox two-winged carbide-tipped rotary

THE CONCEPTOF SPECIFICENERGYIN ROCK DRILLING

65

bits with neutral, negative and positive rakes, Fig. 5 shows how torque is a reasonably linear function of penetration per revolution. Figure 6 shows that the specific energy in these tests fell to a value of the order of 6000 in. lb/in 8. This is also the order of the crushing strength of this rock, though unfortunately no record of the actual strength of the particular specimen used is now available. Calculating specific energy from the slope of the (T/p) line as drawn in Fig. 5 yields a value of 6250 in. lb/in a.

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FIG. 5. Torque and penetration per revolution for rotary drilling in Dazley Dale sandstone. Figures 7 and 8 show similar results of experiments in 'Chislet shale' (a mudstone from Chislet Colliery, Kent), using the same types of bit. The results are more scattered, no doubt due to the presence of zones of weakness in the less homogeneous shale. Figure 8 shows specific energies, and also the crushing strengths of four 2½ in. cubes cut from the particular specimen drilled in. Since the cubes tested must have represented only the stronger, more homogeneous parts of the specimen (those containing major weaknesses would disintegrate in preparation) the correlation seems reasonable. The specific energy calculated from the slope of the line in Fig. 7 is 5900 in. Ib/in3. Other results which have been examined, for both the sandstone and the shale, show similar patterns. As previously mentioned, OPOLSKI [9] has calculated a 'drillability index' for coal. This is obtained from the slope of the power-consumption/penetration-rate curve and gives an index of r Wsec/cm3. (This is akin to calculating specific energy from the torque/ penetration-per-revolution graph.) Values both of r and of strength (on the Protodyakonov

66

R . TEALE

BIT TYPES i -NEUT P,A L RAKE NEGATIVE P,~KE POSITIVE PAKE

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FIG. 6. Specific energy and penetration per revolution for rotary drilling in Darley Dale sandstone

67

THE CONCEPT OF SPECIFIC ENERGY IN ROCK DRILLING

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68

R. TEALE TYPE

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Fro. 8. Specific energy and penetration per revolution for rotary drilling in shale.

f-scale) are given for only two coals, but bearing in mind the crudity of the f-scale for coal (see Appendix), it can at least be said that the values are once more of the same order: Coal 1 : f = 1.5 = 2100 lb/inL r ---- 8"96 Wsec/cu cm = 1300 in. lb/in 3. Coal 2: f = 2.0 = 2900 lb/inL r = 20 Wsec/cu cm = 2900 in. lb/in 3.

Percussive-rotary drilling The results of a number of percussive-rotary drilling experiments were, at the author's suggestion, examined from the point of view of specific energy [10]. Figure 9 shows total specific energy plotted against penetration per revolution in Pennant sandstone. The percussive-rotary values shown represent three rotation speeds and two levels o f percussive energy input, one twice the other. N o significant differences can be detected for the different levels of these variables. Also shown are a few points for rotary drilling in the same rock. Those representing pure rotary drilling with a percussive-rotary bit fall to a minimum which is on the same level as that obtained with this type o f bit when percussion was used, whereas those representing rotary drilling with a rotary bit proper are rather lower. This suggests that the minimum specific energy attained by a particular bit is determined by its geometry. With or without

THE CONCEPT OF SPECIFIC ENERGY IN R O C K D R I L L I N G

69

percussion, specific energy for the percussive-rotary bit remains much the same for a given penetration per revolution, although of course the thrust required to attain a particular penetration per revolution is much higher when percussion is not used. The compressive strengths of the rock specimens drilled in may, in the light of previous experience, reasonably be expected to lie in the range 16,000 to 22,000 lb/in 2.

l

(/"ROTARY DRILLING WITH PERCUS~LVE-) ~,ROTA~Y BIT :¢ .~- 176)OOO

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• PE]RCUSSIVEENERG'Y 4 0 0 , BOO in.ll, lmin X PERCUSSIVEENERGY I,O06.COO[n.lb/min[ ROTARY DRILLING AT 2 0 0 roy/rain WITH PECUSSWE - ROTARy BIT O WITH PURE ROTARY BIT

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FIG. 9. Specificenergy and penetration per revolution for percussive-rotaryand rotary drilling in Pennant sandstone. Figure I0 shows a similar pattern of results in Darley Dale sandstone, the compressive strength of which lies between 6000 and 9000 lb/in 2. Since the above results were obtained, those of PFLEIDERand LACAaANNE[11] have been examined. Figure 11, taken from their paper, shows very similar results for rotary and percussive-rotary drilling in 'Shiely Blue Limestone', using a 1 ~ in. dia. percussiverotary bit in a laboratory rig. The minimum specific energy is about 2400 ft lb, or 28,000 in. lb/in 8. The mean compressive strength of the rock is given as 23,710 lb/in ~ perpendicular to the bedding, this result being based on two measurements with a standard deviation of 18.6 per cent; 21,680 lb/in 2 parallel to the bedding, four measurements giving a standard deviation of 2 per cent. DISCUSSION AND CONCLUSIONS The experimental evidence which has been presented arises from scattered sources. The accuracy both of the measurements from which specific energy has been calculated and of the determinations of crushing strength is not known. Rocks themselves vary, so

70

R. TEALE ALL BITS II'/16 DIAMETER. PERCUSSIVE- ROTARyDRILLING AT lOO,200 AND 300 rtv/m~n • PERCUSSIVE ENERGY400;800 in. lb/rn;n X PERCUS5IVE ENEP,GY 728~ 400 in.lb/min ROTARY DRILLINGAT 200 rcv/m;n WITH PERCU~C.,IVE--ROTARYBLT O WITH PURE ROTARy BiT

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FIG. I0. Specific energy and penetration per revolution for percussive-rotary drilling in Darley Dale sandstone.

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ROTARY PERCUSSIVE ROTARY

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FIG. 11. Work required to drill one cubic inch of 'Shiely Blue Limestone' (after PrLEmER and LACABANNE) 1 ~ in. diameter percussive-rotary bit.

THE CONCEPT OF SPECIFIC ENERGY IN ROCK DRILLING

71

that their strength cannot be truly represented by a single number. In spite of this, all the results show a remarkable correlation between specific energy and crushing strength. Nowhere, in fact, does the ratio specific energy/crushing strength rise above 1.6 or fall below 0.8. It cannot be said, of course, that lower values will never be attained; on the other hand, the agreement between the separate values of specific energy measured in Pennant sandstone seems significant. BARKER obtained a minimum value of 14,000 in. lb/in a while GUPPY, drilling a small hole by pure rotary drilling, obtained a minimum value of 15,000 in. lb/in 8. This agreement between different workers may indicate that their results are in fact close to a real minimum; this is significant, whether the suggested correlation with crushing strength stands the test of further investigation or not. The correlation does, however, serve as a useful basis for further work and thought and it is apparent that the further investigation is called for. The first point which calls for comment is that 'crushing strength' is in no sense an absolute measure of rock strength. It is dependent on the experimental technique used to measure it--the size and shape of the specimens, the flatness and parallelism of their ends and the arrangements for applying the load to them--and unless the technique, the number of specimens tested and the scatter of results about the quoted mean are all specified, it remains a somewhat vague term. Such information is not available for most of the results quoted in this report. Even when all the required information is available, the load under which artificially prepared specimens of special shape fail when loaded in an arbitrarily standardized way remains, at least until a better understanding of the mechanism of fracture is achieved, very much an empirical measure of strength. The principal virtue is convenience of measurem e n t - - a virtue which, when hedged about with the restrictions enumerated above, is much reduced. It has no obvious physical similarity to the rock-working process; the most that can be said is that since compressive strength and specific energy are both functions of rock strength, there must be some kind of relationship between them. The fact that in this first appraisal the relationship appears to be the simple and convenient one of numerical equality, or near equality, must not, however, be allowed to mask the further fact that compressive strength is only one, and not necessarily the best, measure of strength. It is desirable to devise some other index which is more directly related to the process of excavating fragments out of the solid; one, furthermore, which will help towards an understanding of the process itself. Indentation may provide such a measurement; it is certainly more closely related to the drilling process. Moreover, EVANS and MURRELL [12] have shown that the resistance of a semi-infinite block of coal to penetration by a wedge-shaped indenter up to a depth of 0.15 in. can, to a first approximation, be regarded as a uniform pressure of the order of the compressive strength of the coal, q lb/in 2, say. On this basis the specific energy required to displace a volume v in a would be (q. v)/v or simply q in. lb/in 3. The correlation is, very crudely, immediately apparent, though in practice chipping may occur so that the volume of an indentation is much greater than the volume actually displaced by the indenter itself. Further work on energy-breakage relationships in the indentation or 'primary crushing' of brittle materials is indicated. It may be noted that the effects of indenters need not necessarily be limited to local damage immediately around the tool. It may be possible, by using suitable arrays of indenters, to cause the stresses they induce to link up, so resulting in the breakage of larger fragments from the surface.

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R. TEALE

As regards the practical problems of rock working, there must be a minimum attainable specific energy for a particular tool in a particular rock. An understanding of the way specific energy is governed by other variables, principally thrust and rotation speed, is necessary if tools are to be designed and used most effectively. There is some evidence, from the percussive-rotary drilling results, that specific energy is governed mainly by geometry--the shape of the bit and its penetration per revolution--and not much influenced either by rotation speed or the manner in which the energy is applied. It appears that for most rocks the minimum specific energy for primary crushing by simple indentation is readily attainable with existing tools. It will have been noted, however, particularly for roller bits in soft rocks, that minimum specific energy--maximum mechanical efficiency--sometimes occurs at a relatively low thrust, and at a correspondingly low penetration rate which is well below the best the tool can give. The problem of obtaining improved performance thus becomes one not so much of designing tools which have a higher mechanical efficiency in breaking rock as of devising means of transmitting more power into a given face area of rock while maintaining mechanical efficiency at its maximum attainable level. This has already been recognized; for example, PENNINGTON[13] concluded that the power a roller bit can transmit is limited and that the only way to obtain significant increases in energy transmission (for oil-well drilling) is by percussion. It is emphasized once again that rock-working processes should be studied as mechanical systems for breaking rock into fragments and suggested that in this context the work done per unit volume broken is the basic factor which relates the process to physical properties of the rock and against which the behaviour of all other variables should be set. Finally, it is interesting to speculate whether, on physical grounds, any process of breaking rock from the face of a semi-infinite solid can be conceived which would require a lower specific energy than do the mechanical methods now available. Acknowledgements--The author wishes to thank Messrs. B. G. FISH,J. S. BARKERand G. A. GUPPYfor unpublished data on work carried out by them.

REFERENCES I. 2. 3. 4. 5. 6.

TABOR D. The Hardness of Metals. Oxford University Press, London (1951). D.S.I.R. Crushing and Grinding; a Bibliography. H.M.S.O., London (1958). WALKER D. R. and SHAW M.C. Mining Engng 6, 313-20 0954). BARKER J. S. N.C.B., M.R.E., Private communication. National Coal Board. Unpublished report. LOCrtANIN K. A. Ugol, Moscow, pp. 30-34 (May 1955).

7. Flsrt B. G. and BARKERJ. S. Comparative studies of tools for rotary drilling in rock, Trans. lnstn Mining Engrs 116, 389-401 (1956-7). 8. FISH B. G. and BARKER J. S. The design of rotary drilling tools, Coll. Engng. 34, 513-8 (1957) 9. OPOLSKI T. Speed of advance and power consumption in rotary drilling, Bergbautechnik, No. 12, 654-8 (1956). (N.C.B. Trans. A1277.) 10. GuPPY G. A. N.C.B., M.R.E. Private communication. 11. PFLEIDER E. P. and LACABANNE W. D. Research in rotary-percussive drilling. Bull. Univ. Missouri, School of Mines and Metallurgy, No. 94, pp. 46-66 (1957). 12. EVANS I. and MURRELL S.A.F. The Forces Required to Penetrate a Brittle Material with a WedgeShaped Tool. Mechanical Properties of Non-Metallic Brittle Materials. (Walton W. H. Ed.) Pergamon Press, London, 1958, pp. 432-9. 13. PENNINGTON J. V. Rock failure in percussion. Petrol. Engrs, Section B, 26, B76-B88 (1954).

APPENDIX The Protodyakonov Scale The Protodyakonov scale is used to denote the strength of rocks : it assigns a series of numbers, f = 1 to

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ca.20, in ascending order of strength. The translation of the scale into British units is not always clearly understood. The following is a quotation from the earliest known reference to the scale [A1] 'The coefficients of strength of coals and rocks f proposed by Professor M. M. PROTODYAKONOVare widely known among mining experts. However, to determine these coefficients by the temporary resistance of cubes to uniaxial compression requires complex laboratory e q u i p m e n t . . . ' The paper then goes on to say how two simpler methods of estimating f w e r e set up: (a) by crushing a sample of coal fragments, contained in a cylinder, by five blows of a drop hammer and (b) from the quarterly consumption of drilling bits in a particular seam, in relation to the output. It thus appears that the original scale of f was related to the crushing strength of cubes and that the two methods above are proposed as empirical, on-the-spot methods for estimating f w h e n laboratory facilities for preparing and crushing cubes are not available. Clues to the interpretation of the original Protodyakonov scale are contained in two other papers. WASILEWSK][A2] notes that: 'Protodyakonov's scale covers the full range of coals and rocks, the unit factor being equivalent to 100 kg/cm~'. He also states that: 'the compressive strength of coal, normal to the bedding varies from 50 to 300 kg/cm 2'. In another Polish paper, OPOLSKI[A3] remarks that ' . . . for the classification of c o a l . . , the (Protodyakonov) factor lies within a range of 0"4 to 3'0'. At 100 kg/cm ~ per unit, this corresponds closely with the quoted strengths of 50-300 kg/cm 2. It appears that Protodyakonov's f is simply a measure of the compressive strength of cubes, expressed in units of 100 kg/cm 2, and may be converted into lb/in 2 on this basis. Howevec, if the index has been estimated by either of the empirical methods (a) or (b) above, the conversion is likely to give only a crude approximation to compressive strength as usually measured. POMEROY[A4], investigating method (a), found that: ' . . . as it is described it exhibits several obvious faults that can give rise to unreliability in the results'. Conversions of f f o r coal must therefore be treated with reserve unless the method by which it has been measured is specified. This is not usually the case. The reservation may not apply to rocks, to which the empirical methods are presumably not applied. REFERENCES A1. PROTODVAKO~qOVM. M. The Determination of Strength of Coal in Mines. Ugol, Moscow, Yr 25, pp. 20-24 (Sept. 1950). (N.C.B. Trans. A347.) A.2. WASILEWSKYK. Critical Comparison of Workability Methods. Prace Instytutu Mechanisju Gornictwa, No. 7 (1954). A3. OPOLSKI T. Speed of Advance and Power Consumption in Rotary Drilling, Bergbautechnik, No. 12, pp. 654--658 (1956). (N.C.B. Trans. A1277.) A4. POMEROYC. D. Simple methods for the assessment of coal strength, J. Inst. Fuel 30, 50-54 (1957).