Mechanics of Rock Breakage

There are four basic effects of the detonation of explosives used for rock excavation: (1) rock fragmentation, (2) rock displacement, (3) ground vibration and (4) air overpressure. These effects are controlled by the confinement of the explosive and also the two basic forms of energy that are released when high explosives detonate: (1) shock energy and (2) gas energy. Explosives can be detonated in an unconfined or confined manner. An example of a confined application is when explosives are used in a borehole with stemming material and surrounded by rock.

Although both types of energy are released during the detonation process, the blaster can select explosives with different proportions of shock or gas energy to suit a particular application. If explosives are used in an unconfined manner, such as mud capping boulders or for shearing structural members in demolition, the selection of an explosive with high shock energy is advantageous. On the other hand, if explosives are used in boreholes and confined by the use of stemming materials, an explosive with a high gas energy output is beneficial.

To help form a mental picture of the difference between the two types of energy, compare the difference in reaction of a low and high explosives. Low explosives, such as black powder, are those that deflagrate, or burn, very rapidly. These explosives may have reaction velocities of 2000 to 5000 ft. per second and produce no shock energy. They produce work only from gas expansion. High explosives, such as dynamite, detonate and produce not only gas pressure, but also shock pressure.

Figure 9 shows these differences with a diagram of reacting cartridges of low explosive and a high explosive. For a low explosive, if the reaction is stopped when the cartridge has been partially consumed and the pressure profile is examined, one can see a steady rise in pressure due to the reaction until the maximum pressure is reached. Low explosives produce only gas pressure during the combustion process. A high explosive detonates and exhibits a different pressure profile producing shock energy at the reaction front followed by the gas pressure.

This shock energy produced by the high explosive normally results in a higher pressure than gas expansion produces. After the shock energy passes, gas energy is released. The gas energy in high explosives is much greater than the gas energy released in low explosives. The shock pressure is a transient pressure that travels at the explosives rate of detonation. This pressure is estimated to account for only 10% to 15% of the total available useful work energy in the explosion. The gas pressure accounts for 85% to 90% of the useful work energy and follows the shock energy. However, unlike the transient shock energy, the gas energy produces a force that is constantly maintained until the confining vessel, usually the borehole, ruptures. This causes fracturing in the rock that is continued until this pressure is relieved. In an ideal model, a homogeneous rock mass, the shock energy will propagate outward, out running the growing fracture tips at the edges of the rupture, much like the ripples on a pond. This energy will attenuate proportional to the square of the distance from the blast and in relation to the elastic properties of the rock. While this picture is more complicated when taken from the ideal of homogeneous rock and applied in a rock mass where the reaction will be modified by the presence of inhomogeneities and discontinuities it is useful to understand how this energy will move through and idealized rock before adding the complicating factors of more site specific rock mass.

The shock energy is commonly believed to result from the detonation pressure of the explosion. The detonation pressure, a form of kinetic energy, is a function of the explosive density times the explosion detonation velocity squared. Determination of the detonation pressure is very complex, but an estimate of the detonation pressure can be calculated with:

The detonation pressure or shock energy can be considered similar to kinetic energy; it is at its maximum in the direction of travel. This means the detonation pressure will be highest in the end of the explosive cartridge opposite where the initiation occurs. This property explains why when mudcapping boulders, it is more effective to place the cartridge with the bottom directed toward the boulder, rather than placed sideways on the boulder (Figure 10). Therefore, to maximize the use of the detonation pressure, the explosive should be in good contact with the rock to be blasted. An explosive with high density and high detonation velocity will result in a high detonation pressure.

Explosion pressure results from the amount of gases liberated per unit weight of explosive and the amount of heat liberated during the reaction. The higher the temperature produced, the higher the gas pressure. If more gas volume is liberated at the same temperature, the pressure will also increase. For a quick approximation, it is often assumed that explosion pressure is approximately one-half of the detonation pressure. The nomograph pictured in Figure 11 shows explosive density, explosion pressure, detonation pressure, and detonation velocity.

Confinement of the charge also has a significant effect on the amount of energy that is directed toward the rock fragmentation as opposed to air overpressure or air blast. Figure 10 demonstrates, with the older mechanism of mudcapping, that the mud placed on top of an unconfined explosive charge in either configuration provides almost no confinement for an explosive. Unconfined charges placed on boulders and subsequently detonated produce shock energy that will be transmitted into the boulder at the point of contact between the charge and the boulder. Since most of the charge is not in contact with the boulder, the majority of the useful explosive energy travels out into space and is wasted. This wasted energy manifests itself in excessive air blast overpressure. Gas pressure can never build since the charge is essentially unconfined; therefore, gas energy does little work. The mud does couple the explosive to the rock and acts as a wave trap that reflects some of the escaping shock energy downward toward the boulder (Figure 12). Ultimately, if a borehole charge was used instead of placing the charge on top of the boulder considerably less explosive can be used as it will harness both the shock and the gas energy.

Confined charges have four basic mechanisms that contribute to rock breakage: (1) shock wave, which can initiate microfractures on the borehole wall and moves through the rock uniformly in all directions around the charge causing initial radial microfractures, (2) sustained gas pressure, which penetrates and extends the radial microfractures toward the face, (3) the face begins to bend outward due to the expanding gases, and (4) fractures are created in the third dimension as a result of this flexural failure or bending.

The first occurrence in time, but the least significant mechanism of breakage, is caused by the shock wave or stress wave. At most, the shock wave causes radial microfractures to form on the borehole walls and may initiate microfractures at major discontinuities in the burden. This transient pressure pulse quickly diminishes with distance from the borehole. Since the propagation velocity of the pulse is approximately 2.5 to 5 times the maximum crack propagation velocity, the pulse quickly outruns the crack propagation or fracture propagation.

The more important mechanism is the sustained gas pressure. When the solid explosive is transformed into a gas during the detonation process, the borehole acts similar to a cylindrical pressure vessel. Failures in pressure vessels, such as water pipes or hydraulic lines, offer an analogy to this mechanism of rock breakage. When the vessel is over pressurized, the pressure exerted perpendicular to the confining vessel’s walls will cause a fracture to occur at the weakest point. In the case of frozen water pipes, a longitudinal split occurs parallel to the axis of the pipe (Figure 13).The major difference between pressurizing a borehole and pressurizing a water pipe is rate of loading. A borehole is over pressurized almost instantaneously and therefore does not fail at one weakest point along the borehole wall. Instead, it will simultaneously fail in many locations in a geometric pattern. Each resulting fracture will be oriented parallel to the axis of the borehole. Failure by this mechanism has been recognized for many years and is commonly called radial cracking. Figure 14 shows this same radial fracturing in rock at the bottom of a borehole after rock has been removed.

The third mechanism is relief of the sustained gas pressure by the free face and movement of the cracked rock mass. There is a time lag in the rock mass from the formation of the initial radial cracking and the extension of that radial cracking toward the relief face. The distance of that face influences the formation of the radial crack system. Here the burden in the rock is transformed from a solid rock mass into one that is broken by the radial cracks in many wedge-shaped or pie-shaped pieces. These wedges function as columns, supporting the burden weight. Columns become weaker if their length-to-diameter ratio or slenderness ratio increases. Therefore, once the massive burden is transformed into pie-shaped pieces with a fixed bench height, it has been severely weakened due to the fact that its slenderness ratio has increased.

The high-pressure gases subject the wedges to forces acting perpendicular to the axis of the hole that push toward relief or toward the line of least resistance.

This concept of relief perpendicular to the axis of the hole has been known for well over a hundred years. Relief must be available perpendicular to the axis of the hole for borehole charges to function properly. If relief is not available, only radial cracks will form. As a result, boreholes will crater, or the stemming will be blown out. In either case, the fragmentation suffers and environmental problems result. The direction and extent of the radial cracking system is controlled by the selection of proper burden from the borehole to the face (Figure 15).

Finally, the flexure of the entire mass ensures cracking in the third dimension so that the rock is displaced outward from the face. This is the second major breakage mechanism called “flexural failure.” In most blasting operations, the first visible movement occurs when the face bows outward near the center (Figure 2-8a). In other words, the center portion of the face is moving faster than the top or bottom of the burden. This type of bowing or bending action does not always occur. One can find cases where instead of the center bowing outward, the top or bottom portion of the burden is cantilevering outward. These other two cases cause problems in blasting. The blast design controls the mechanism of “flexural failure.” Figure 16 shows the three mechanisms often seen in rock blasting.

In the second case, the top or the bottom of the burden moves at a higher rate than the center (Figure 16 b,c) so the rock is cantilevered outward. The face is put into compression and the borehole walls are in tension. This mechanism occurs when cracks between blastholes link before the burden is broken; it is normally caused by insufficient blasthole spacing. When the cracks between holes reach the surface, gases can be prematurely vented before they have accomplished all potential work. Air blast and flyrock can result along with potential bottom problems.

For all three cases, this breakage mechanism is called flexural rupture or flexural failure. The individual pie-shaped columns of rock caused by the radial cracking will also be influenced by a force perpendicular to the length of the column. This would be similar to beam loading conditions. When discussing beam loading, the stiffness ratio is significant. The stiffness ratio relates the thickness of the beam to its length. The effect of the stiffness can be explained by using, for example, a full-length pencil. It is quite easy to break a full-length pencil by grasping the pencil on either end. However, if the same force is exerted on a much shorter, for example 2 in long pencil, it becomes more difficult to break. The pencil’s diameter has not changed; the only thing that has changed is its length. A similar stiffness phenomenon also occurs in blasting. The burden rock is more difficult to break by flexural failure when bench heights approach the burden dimension in length. When bench heights are many times the burden in length, the burden rock is more easily broken.

The bending mechanism or flexural failure is controlled by selecting the proper blasthole spacing and initiation time of adjacent holes. When blasthole timing results in charges being delayed from one another along a row of holes, the spacing must be less than that required if all the holes in a row were fired simultaneously. The selection of the proper spacing is further complicated by the stiffness ratio. As bench heights are reduced compared to the burden, one must also reduce the spacing between holes to overcome the problems of stiffness.