George G. AndrE

—The pressure of a fluid is exerted equally in all directions; consequently the surrounding mass subjected to the force will yield, if it yield at all, in its weakest part, that is, the part which offers least resistance. The line along which the mass yields, or line of rupture, is called the “line of least resistance.” If the surrounding mass were perfectly homogeneous, it would always be a straight line, and it would be the shortest distance from the centre of the charge to the surface. Such, however, is never the case, and the line of rupture is, therefore, always a more or less irregular line, and often much longer than that from the centre direct to the surface. It will be obvious, on reflection, that the line of least resistance will be greatly dependent upon (1) the texture of the rock, which may vary from one point to another; (2) its structure, which renders it more easily cleavable in one direction than in another; (3) the position, direction, and number of the joints, which separate the rock into more or less detached portions; and (4) the number and relative position of the unsupported faces of the rock. All these circumstances must be ascertained, and the position and the direction of the bore-hole determined in accordance with them, in order to obtain the maximum effect from a given quantity of explosive. It must not be supposed, however, that this is a labour involving minute examination and long consideration. On the contrary, a glance is generally sufficient to enable the trained eye to estimate the value of those circumstances, and to determine accordingly the most effective position for the shot. In practice, the line of least resistance is taken as the shortest distance from the centre of the charge to the surface of the rock, unless the existence of joint planes, a difference of texture, or some other circumstance, shows it to lie in some other direction.

Force required to cause Disruption.

—When the line of least resistance is known, it remains to determine the quantity of the explosive compound required to overcome the resistance along that line. This matter is one of great importance, for not only is all excess waste, but this waste will be expended in doing mischief. In mining operations, the dislodged rock is violently projected, and the air is vitiated in an unnecessary degree; and in quarrying, stones are shattered which it is desirable to extract in a sound state. The evil effects of overcharging, in occasioning the formation of noxious gases, was pointed out in the last chapter. Of course it is not possible so to proportion a charge to the resistance that the rock shall be just lifted out, and no more; because neither the force developed by the charge, nor the value of the resistance can be known with precision. But a sufficient approximation may be easily arrived at to enable us to avoid the loud report that is indicative of wasted force.

Charges of an explosive compound of uniform strength produce effects that vary as the weight of those charges, that is, a double charge will move a double mass. And, as homogeneous masses vary as the cube of any similar line within them, the general rule is established that charges of powder capable of producing the same effects are to each other as the cubes of the lines of least resistance. Generally, the quantity of black blasting powder requisite to overcome the resistance will vary from ¹/₂₀ to ¹/₃₀ of the cube of the line of least resistance, the latter being measured in feet and the former in pounds. Thus, if the rock to be blasted be moderately strong limestone, for example, and the shortest distance from the centre of the charge to the surface of the rock be 3 feet, we shall have 3 × 3 × 3 = 27, the cube of the line, and ²⁷/₂₅ lb. = 1²/₂₅ lb., or about 1 lb. 1 oz., as the weight of the powder required. If dynamite be used, and we assume it to be four times as strong as common black powder, of course, only one-fourth of this quantity will be required. Also if gun-cotton, or cotton-powder, be used, and we assume its strength to be three times that of black powder, one-third only will be needed. Again, if Curtis’s and Harvey’s new extra-strong mining powder fired by a detonator be employed, we may assume it to be twice as strong as common black powder fired by the ordinary means, and consequently we shall need only one-half the quantity indicated by the formula.

It is neither practicable nor desirable that such calculations and measurements as these should be made for every blast; their practical value lies in this, namely, that if the principles involved in them be clearly understood, the blaster is enabled to proportion his charges by sight to the resistance to be overcome, with a sufficient degree of precision. A few experiments in various kinds of rock, followed by some practice, will enable a man to acquire this power.

As it is a common and a convenient practice to make use of the bore-hole as a measure of the quantity of explosive to be employed, we have calculated the following table:—

Diameter of the Hole.		Black Powder in 1 inch.	Gun- cotton in 1 inch.	Dynamite (or Tonite) in 1 inch.
ins.		ozs.	ozs.	ozs.
1		0·419	0·419	0·670
1	1/4	0·654	0·654	1·046
1	1/2	0·942	0·942	1·507
1	3/4	1·283	1·283	2·053
2		1·675	1·675	2·680
2	1/4	2·120	2·120	3·392
2	1/2	2·618	2·618	4·189
2	3/4	3·166	3·166	5·066
3		3·769	3·769	6·030

Fig. 40.

Fig. 41.

fault line

Fig. 42.

fault line

Fig. 43.

fault line

Conditions of Disruption.

—Having explained the law according to which the elastic gases evolved by an explosion act upon the surrounding rock, and shown how the force required to cause disruption may be calculated, it now remains to consider the conditions under which disruption may take place. Suppose a block of unfissured rock detached on all sides, as shown in plan, in Fig. 40, and a bore-hole placed in the centre of this block. If a charge be fired in this position, the lines of rupture will radiate from the centre towards any two, or towards all four of the unsupported faces of the block, because the forces developed will act equally in all directions, and the lines of rupture will be those of least resistance. Evidently this is the most favourable condition possible for the charge, since the rock offers an unsupported face on every side; and it is evident that the line of rupture must reach an unsupported face to allow of dislodgement taking place. Suppose, again, as shown in Fig. 41, the block to be unsupported on three sides only, and the charge placed at h. In this case, the lines of rupture may run to any two, or to all three, of the unsupported faces; and hence this will be the next most favourable condition for the action of the charge. The greatest useful effect, however, will be obtained in this case by placing the charge farther back at h', when the lines of rupture must necessarily run to the opposite faces b c, and, consequently, the whole of the block will be dislodged. Assume another case, in which the rock is unsupported upon only two sides, as shown in Fig. 42, and the charge placed at h. In this case, the lines of rupture must run to each of the unsupported faces a b. Thus, it is evident that this condition, though still a favourable one for the good effect of the charge, is inferior to the preceding. As rock is never homogeneous in composition nor uniform in texture, the lines of rupture, which, as before remarked, will be those of least resistance, may reach the faces at any point, as at m n, m' n', or any point intermediate between these. But it will be seen that the useful effect will be greatest when these lines, radiating from the charge, make an angle of 180°, or, in other words, run in directly contrary directions, and that the useful effect diminishes with the angle made by these lines of rupture. Suppose, again, the rock to be unsupported upon one side only, as shown in Fig. 43, and the charge placed at h. In this case, the lines of rupture must run to the face a, and the condition must therefore be considered as less favourable than the preceding. As in those cases, the useful effect will depend upon the angle made by the lines of rupture h m and h n, which angle may be very small, and which must necessarily be much less than 180°. A greater effect may be obtained, under this condition, by firing several charges simultaneously. If, for example, we have two charges placed, one at h, and the other at h', and fired successively, the lines of rupture will run in or near the directions h m, h n, h' m', h' n', and the portion of rock dislodged will be m h n h' n'. But if these two charges be fired simultaneously, the lines of rupture will be h m, h o, h' o, h' n', and the mass of rock dislodged will be m h h' n'. Simultaneous firing is in this way productive of a greatly increased useful effect in numerous cases, and the mining engineer, and the quarryman especially, will do well to direct their attention to this source of economy. There is yet another case to be considered, in which the conditions are still less favourable. Suppose two unsupported faces at right angles to each other, and the charge placed at h, as shown in Fig. 44. In this case, the lines of rupture will run to each of the two unsupported faces; but as these lines must necessarily make a very small angle with each other—for the length of the lines increases rapidly with the angle—the useful effect will be less than in the last case. It follows, therefore, that this is the most unfavourable condition possible, and as such it should be avoided in practice.

Fig. 44.

fault line

Fig. 45.

fault line

In the foregoing considerations, the holes have been assumed to be vertical, and for this reason the unsupported face which is perpendicular to the hole, that is, the face into which the hole is bored, has been neglected. For it is evident that, under the conditions assumed, the lines of rupture cannot reach this face, which, therefore, has practically no existence. Suppose, for example, a bore-hole placed at h, in Fig. 45, and the rock to be supported upon every side except that at right angles to the hole. The forces acting perpendicularly to the direction of the bore-hole are opposed on all sides by an infinite resistance. Hence, in this case, either the tamping will be blown out, or, if the forces developed are unequal to the work, no effect will be produced beyond a slight enlargement of the hole at the base. This, however, is a case of frequent occurrence in practice, and it becomes necessary to adopt measures for making this unsupported face available. Evidently this object can be attained only by so directing the bore-hole that a line perpendicular to it may reach the face; that is, the line of the bore-hole must make with the unsupported face an angle less than 90°. This direction of the bore-hole is shown in Fig. 46, which may be regarded as a sectional elevation of Fig. 45. In this case, the lines of rupture, which will run similarly to those produced in the case shown in Fig. 43, will reach the unsupported face at b, and the length of these lines, and consequently the depth of the excavation, for a given length of bore-hole, will depend upon the angle which the latter makes with the face. This mode of rendering a single exposed surface available is called “angling the holes,” and it is generally resorted to in shaft sinking and in driving headings. The conditions involved in “angling” are favourable to the action of strong explosives.

Example of a Heading.

—To show how these principles are applied in practice, we will take a typical case of a heading, 7 feet by 9 feet, as shown in Fig. 47. In this case, we have at starting only one exposed face, which is perpendicular to the direction of the driving. Hence it is evident that we shall have to proceed by angling the holes. We might begin in any part of the exposed face; but, as it will hereafter appear, the most favourable position is the centre. We therefore begin at this point by boring a series of holes, numbered 1 on the drawing. These holes are angled towards each other; that is, the two sets of three holes vertically above each other converge in the direction of their lower ends, as shown in the sectional plan, Fig. 48. In this instance, we have assumed six holes as necessary and sufficient. But it is obvious that the number of holes, as well as their distance apart horizontally, will be determined by their depth, the tenacity of the rock, and the strength of the explosive used. When these holes are fired, a wedge-shaped portion of the rock will be forced out, and this result will be more effectually and certainly obtained if the charges be[116]
[117] fired simultaneously. The removal of this portion of the rock is called “taking out the key.” The effect of removing this key is to leave the surrounding rock unsupported on the side towards the centre; that is, another face is formed perpendicular to the first.

Having thus unkeyed the rock by the removal of this portion from the centre, it will evidently be unnecessary, except for convenience or increased effect, to angle any more of the shot-holes. The second series therefore, numbered 2 in the drawing, may be bored perpendicularly to the face of the heading. When this series is fired, the lines of rupture will all run to the unsupported face in the centre—and from hole to hole, if the shots be fired simultaneously—and the annular portion of rock included between the dotted lines 1 and 2 will be removed. If the shots be fired successively, the first will act under the condition of one unsupported face, as illustrated in Fig. 43; but as another unsupported face will be formed by the removal of the rock in front of this charge, the succeeding shots will be subject to the more favourable condition represented in Fig. 42. The firing of this second series of shots still leaves the surrounding rock unsupported towards the centre, and consequently the same conditions will exist for the third series, numbered 3 on the drawing, the firing of which series will complete the excavation. Fig. 49 shows the appearance of Fig. 48 after the firing of the central holes.

It may be remarked here that, owing to the want of homogeneity in the rock, and to the existence of joints and fissures, the outer line of rupture will not, in practice, run so regularly as indicated, in this assumed case, by the dotted lines. This circumstance will influence the position of the holes, or the quantity of explosive, in the next series, and furnish an opportunity for the exercise of judgment on the part of the blaster.

There exist also other circumstances which will influence the position and the number of the holes in a very important degree, and which therefore must be taken fully into account at every advance. One of these is the irregularity of the face of the excavation. Instead of forming an unbroken plane at right angles to the direction of the heading, or of the shaft, this face is broken up by projecting bosses and more or less deep depressions. Obviously these protuberances and cavities will influence, in no inconsiderable degree, the lines of least resistance; the latter being lengthened or shortened, or changed in direction, by the presence of the former, which give existence to unsupported faces to which the lines may radiate. These conditions must, in every case, be taken into account when determining the best position for the bore-hole. Of yet greater importance, is the existence of joint planes and bedding planes. A bed of rock may be, and frequently is, cut up by these planes into detached blocks of greater or less dimensions, according to the more or less perfect development of the different sets. Hence it becomes necessary, in determining a suitable position for blasting the charge, to consider such planes as unsupported faces, and to ascertain the direction and length of the lines of resistance under such conditions. If a charge be placed in close proximity to one of these planes, not only may the lines of rupture run in unforeseen directions, but the greater part of the force of the explosion will be lost by the escape of the gases along the plane. The same loss of force may be occasioned by the presence of a cavity, such as are of frequent occurrence in cellular or vughy rock. When the joint planes are fully developed, their existence can be ascertained by inspection; but when their development is imperfect, there may be considerable difficulty in discovering them. In such cases, the rock should be carefully inspected, and sounded with a hammer or pick. When a cavity is bored into, it may be rammed full of clay, and the boring continued through the clay; or if sufficient depth has been obtained, the charge may be placed upon the clay, which will prevent the wasteful dissipation of the gases. As none of the aforementioned circumstances occur under precisely similar conditions, no general rule of much service can be laid down; they are matters upon which the blaster must be left to use his own judgment, and to do this effectively, it is necessary that he possess some knowledge of the materials with which he deals.

Economical Considerations.

—Besides the important economical considerations involved in the foregoing, there are others which claim attention. Foremost among these is the question whether, for a given effect, it be better to augment or to diminish the individual importance of the shots; that is, whether it be better to diminish the number of the holes and to increase their diameter, or to diminish their diameter and increase their number; or, again, to diminish their diameter and to increase their depth, or to increase their diameter and to diminish their number and their depth. It may be readily shown mathematically, and the results are confirmed by experience, that there is an important gain in reducing the diameter of the shot-holes to the lowest limit allowed by the strength and the gravimetric density of the explosive, and increasing their depth. The gain is mainly in the direction of a saving of labour, and it is especially remarkable in the case of machine boring. Here again we perceive the advantage of strength in the explosive agent employed.

The simultaneous firing of the shots offers several important advantages. It has already been shown how one charge aids another, under such a condition, and in what way the line of rupture is affected by it. When the shots are fired successively, each one has to tear out the portion of rock allotted to it; but when they are fired simultaneously, their collective force is brought to bear upon the whole mass to be dislodged. This is seen in the diagram, Fig. 43. When deep holes are used, the greater useful effect caused by simultaneous firing becomes very marked. Hence electricity associates itself naturally with machine drills and strong explosives.

Tamping.

—To “tamp” a shot-hole is to fill it up above the charge of explosive with some material, which, when so applied, is called the “tamping.” The object of tamping is to oppose a resistance to the escape of the gases in the direction of the bore-hole. Hence a primary condition is that the materials used shall be of a strongly resisting character. A second determining condition is that these materials shall be of easy application. This condition precludes the use of all such devices as plugs, wedges, and forms of a similar character, which have been from time to time proposed.

The only material that, in practice, has been found to satisfactorily fulfil the requirements, is rock in a broken, pulverulent, or plastic state. As, however, all rock is not equally suitable, either from the point of view of its resisting character, or from that of convenience of handling, it becomes necessary to consider which satisfies the two conditions in the most complete manner.

Though it is not easy to assign a perfectly satisfactory reason why one kind of rock substance opposes a greater resistance to motion in a bore-hole than another, yet it is certain that this resistance is mainly due to the friction among the particles of that substance. If a column of solid, hard rock, of the same diameter as the bore-hole, be driven down upon the charge, the resistance opposed by the column to the imprisoned gases will be, neglecting the weight of the former, that of the friction between the sides of the column and those of the hole. But if disintegrated rock be used, not only is an absolute motion imparted to the particles, but, on account of the varying resistances, a relative motion also. Consequently, friction occurs amongst the particles, and as the number of these is immense, the sum of the slight friction of one particle against another, and of the great friction of the outside particles against the sides of the hole, amounts to a much greater value than that of the outside particles of the solid column against the sides of the bore-hole. If this view of the facts alone be taken, it follows that dry sand is the most resistant material, and that the finer the grains, the greater will be the resistance which it offers. In practice, however, it has been found that though the resistance offered by sand tamping is very great, and though also the foregoing inference is true when the tamping is lifted by the pressure of a solid against it from below, this substance is notably inferior to some others when acted upon by an explosion of gases. The explanation of this apparent anomaly is that the gases, under the enormous tension to which they are subjected in the bore-hole, insinuate themselves between the particles, and so prevent the friction which would otherwise take place. When the readiness with which water, through the influence of gravity alone, permeates even closely compacted sand, is borne in mind, there will be no difficulty in conceiving a similar action on the part of more subtile gases in a state of extreme tension. Under such conditions as these, there is no resistance whatever due to friction, and the only resistance opposed to the escape of the gases is that proceeding from the inertia of the mass. How this resistance may be very great, we have shown in the case of air tamping. Hence, it becomes necessary to have recourse to some other material of a composition less liable to be thus acted upon, or to seek means of remedying the defect which renders such action possible.

Clay, dried either in the sun, or, preferably, by a fire, appears to fulfil the requirements of a tamping material in the fullest degree. This substance is composed of exceedingly minute grains of silicious matters, bound together by an aluminous and calcareous or ferruginous cement. Thus constituted, there are no voids between the particles, as in porous substances, and, consequently, there is no passage for the gases, the substance being impervious alike to water and gas. Hence, when this material is employed as tamping, the forces act only upon the lower surface, friction takes place among the particles, and the requisite degree of resistance is produced. By reason of its possession of this property, clay is generally used as the tamping material.

In rock blasting, it is usual to prepare the clay beforehand, and this practice is conducive both to effective results and to rapidity of tamping. The latter consideration is an important one, inasmuch as the operation, as commonly performed, requires a good deal of time. To prepare the pellets of clay, a lump is taken and rolled between the palms of the hands until it has assumed the form of a sausage, from three to four inches in length, and of the diameter of the bore-hole. These pellets are then baked until they are thoroughly dry, when they are ready for use. In making them up to the requisite diameter, a little excess should be allowed for shrinkage, since it is essential that they fit tightly into the hole. When the charge has been put in, and covered with a wad of hay, or a handful of sand or rubbish, one of these pellets is inserted and pushed home with a wooden rammer. Considerable pressure should be applied to make the clay fill the hole completely, but blows should be avoided. A second pellet is then pushed down in the same way, and the operations are repeated until the whole of the hole is tamped. To consolidate the whole, light blows may be applied to the outer pellet. It will be found advantageous to place an undried pellet immediately above the charge, because the plasticity of such a pellet enables it to fill all the irregularities of the sides of the hole, and to securely seal the passage between the sides and the tamping, along which the gases might otherwise force their way. In coal blasting, soft shale is always used for tamping, because it is ready at hand, and heavy shots are not required.

Broken brick constitutes a fairly good tamping material, especially when tempered with a little moisture; but as it is not readily procurable, its application is necessarily limited. The dust and chippings of the excavated rock are largely employed as tamping in quarries. This material, however, has but little to recommend it for the purpose beyond its readiness to hand.

It now remains to consider what means are available for remedying the defect inherent in sand as a tamping material. This constitutes a very important practical question, because if the defect can be removed, sand will constitute by far the most suitable material whenever the bore-hole has a downward direction. It can be everywhere obtained at a low cost; it may be poured into the hole as readily as water; and its application gives rise to no danger. Obviously the difficulty will be overcome if we can find suitable means for preventing the gases from penetrating the sand.

The end proposed may be successfully attained by means of the plastic clay pellet applied in the following manner. Immediately above the charge, place a handful of perfectly dry and very fine sand. This may be obtained by sifting, if not otherwise procurable. Upon this sand, force firmly down with a wooden rammer, so as to fill every irregularity, a plastic clay pellet, about four inches in length, and of the same diameter as the bore-hole, prepared by rolling between the hands in the manner already described. Above this pellet, fill the hole with dry sand. The impervious nature of the clay prevents the gases from reaching the sand, except along the line of junction of the clay with the sides of the hole. Tamped in this way, a resistance is obtained scarcely, if at all, inferior to that opposed by the most carefully placed dried clay.

By the employment of a detonator, the defect due to the porous character of sand is not removed, but its influence is greatly diminished. When detonation is produced in an explosive compound, the full force of the elastic gases is developed instantaneously; and it has already been shown that, under such conditions, the resistance occasioned by the presence of any substance in the bore-hole, even the air alone, in the case of nitro-glycerine, is sufficient to throw the chief portion of the force upon the sides of the hole. Loose sand, therefore, may be successfully employed as tamping under these conditions, since its inertia will oppose a sufficient resistance to the escape of the gases. But though the rock may be dislodged when light tampings are used with detonation, there can be no doubt that a considerable proportion of the force of the explosion is lost; and hence it will always be advantageous to tamp securely by means of the clay pellet, as already described. The highest degree of economy is to be obtained by detonating the charge, and tamping in this manner.