MECHANICS OF ROCK BREAKAGE

Confined Charges in Boreholes

Three basic mechanisms contribute to rock breakage with charges confined in boreholes. The first and least significant mechanism of breakage is caused by the shock wave. At most, the shock wave causes microfractures to form on the borehole walls and initiates microfractures at discontinuities in the burden. This transient pressure pulse quickly diminishes with distance from the borehole and since the propagation velocity of the pulse is approximately 2.5 to 5 times the maximum crack propagation velocity, the pulse quickly outruns the fracture propagation.

After that, 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 pressure 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 pressure vessel. In the case of frozen water pipes, a longitudinal split occurs parallel to the axis of the pipe (Figure 1).

Figure 1: Fracture of Frozen Water Pipe

The same phenomenon occurs in other cylindrical pressure vessels due to the generation of hoop stresses. If a borehole is considered a pressure vessel, one would expect fractures to orient themselves parallel to the axis of the borehole. 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 in many locations. 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 2).

 Figure 2: Radial Cracking in Plexiglass

Direction and extent of the radial crack system can be controlled by the selection of the proper distance from the borehole to the face (burden) (Figure 3).

Figure 3: Influence of Distance to Face on Radial Crack System

The second major breakage mechanism occurs after the radial cracking has been completed. There is a time lag before the second breakage mechanism goes into play. The second mechanism influences the breakage perpendicular to the axis of the charge.

Before the second breakage mechanism is discussed, form a mental picture of what has happened during the radial cracking process. Stress wave energy (shock) has caused minor cracking or microfracturing on the borehole walls and at discontinuities throughout the burden. The sustained gas pressure, which follows the shock pressure, puts the borehole walls into tension due to hoop stresses generated and causes the existing microfractures to grow. The high pressure gases extend fractures throughout the burden. The burden in massive 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 fixed bench height, it has been severely weakened due to the fact that its slenderness ratio has increased.

The work process has not yet been completed since the expanding borehole still contains very high pressure gases. These gases subject the wedges to forces acting perpendicular to the axis of the hole. One can say they are pushing towards relief or towards 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.

Bench Stiffness

In most blasting operations, the first visible movement occurs when the face bows outward near the center. In other words, the center portion of the face is moving faster than the top or bottom of the burden (Figure 4).

Figure 4: Axisymmetric Bending Diagram

 Figure 5: Cantilever Bending Diagram

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 (Figure 5).

In either of these cases, the differential movement causes the burden to break in the third dimension. This breakage mechanism has been called flexural rupture or flexural failure. To properly discuss flexural failure, one must realize that these 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 one discusses beam loading, the stiffness ratio is significant. The stiffness ration relates the thickness of the beam to its length. The effect of the stiffness can be explained by using, as an example, a full-length pencil. It is quite easy to break a pencil with the force exerted with one's fingers. However, if the same force is exerted on a two-inch 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.

Two general modes of flexural failure of the burden exist. In one case, the burden bends outward or bulges in the center more quickly than it does on the top or bottom. In the second case, the top or the bottom of the burden moves at a higher rate than the center. When the burden rock bulges at its center, tensile stresses result at the face and compression results near the charge. Under this type of bending condition, the rock will break from the face back toward the hole (Figure 4). This mode of failure generally leads to desirable breakage.

In the second case, the rock is cantilevered outward (Figure 5) and the face is put into compression and the borehole walls are in tension.

This second case is undesirable. This mechanism occurs when cracks between blastholes link before the burden is broken and is normally caused by insufficient blasthole spacings. 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.

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. 

Effect of Blasthole Length

The rock breakage process occurs in four distinctive steps. As the explosives detonates, a stress wave moves through the rock uniformly in all directions around the charge. Radial cracks then propagate predominantly towards the free face. After the radial cracking process is finished, high pressure gases penetrate into the cracks approximately 2/3 of the distance from the hole to the face throughout the radial crack system. Only after the gas has time to penetrate into the crack system are the stresses on the face of sufficient magnitude, to cause the face to move outward. Before the face begins to move and bend outward, fractures are created in the third dimension as a result of the flexural failure or bending.

In order to better understand the rock breakage process, a finite element model was created to closely resemble the radial crack network before burden movement occurs. The model was unique in that it allowed the study of redial cracks which were partially pressurized. An interim technique was used to recalculate and update the borehole pressures as borehole volume increased. The model was designed to study the important aspects of bench blasting. 

>>>Blasting Parameters

In order to compare the model's behavior with that of actual field results, parameters were chosen so that actual burden movement could be predicted. The model consisted of a single hole, four inches in diameter.The burden was fixed at ten feet, stemming and subdrilling were eight feet and four feet respectively and the bench height was varied from twelve to one hundred feet. Therefore, the stiffness ration (bench height divided by burden) changed from 1.2 to 10. The explosive parameters used in the model were those of ammonium nitrate and fuel oil. The borehole was initially pressurized with explosive gases to 425,000 psi.

>>>Stiffness Analysis

The burden was held constant at 10 feet throughout the analysis, therefore, changes in the stiffness (L/B) ratio resulted from varying the bench height. As the L/B ratio increased from 1.2 to 10, the bench height increased from 12 to 100 feet. Fourteen different models were used for the displacement analysis. Displacements and outer fiber stresses were calculated for nodes, which were located on the face, in the middle of the bench and in the direction of the burden face.

For discussion purposes, four different L/B ratios, 1.2, 2.4, 3.6, and 4.0 will be considered. With an L/B ratio of 1.2, there was no displacement on the face of the shot, instead local crushing occurred around the hole. As the bench height increased and the L/B ration became 2.4, less local crushing occurred and the model indicated a maximum displacement on the face of the 43 inches. For an L/B ratio of 3.6, the model indicated a displacement of 186 inches and at L/B ratio of 4.0 and the displacement was 279 inches or 23.2 feet. Figure 6 shows the deformed geometry configuration of this model and Figure 7 shows scaled displacements.

Figure 6: XZ-View of The Deformed Geometry Configuration as L/B Ratio Changes from 1.2 to 4.0

Figure 7: Actual Displacements for XZ-View as L/B Changes from 1.2 to 4.0

Further analysis was conducted applying beam bending theory in an effort to quantitatively explain the behavior of burden rock subjected to explosive gas pressure loads. A rectangular cross section was selected having a depth of 120 inches and a width of 1 inch. The beam length would be equivalent to the bench height. The deflection at the middle of the beams were calculated and compered to the results of the finite element model. A close correlation between the finite element model and the rectangular cross section was observed as shown in Figure 8.

 Figure 8: Comparison Between Calculated Finite Element Displacements and Rectangular Cross Section Deflection

The graph of L/B ratio vs. displacement for both the finite element model and the rectangular cross sectional model produce a better understanding of why this ratio is so important in bench blasting. The graph shows that the displacement increased at a slow rate when L/B ratio varied between 1 and 3.5. At 3.5, there was a distinct change in slope of the curve, which indicated that for the same gas pressure there was additional displacement. When the L/B ratio was greater than 6, there were significant increases in displacement with small changes in the L/B ratio.

Research conducted by Konya in 1967 and empirical data from the field indicate that a practical upper limit for L/B ratio is approximately 4. Above 4, the effects of stiffness are minimal and are no longer considered in field work. In this finite element analysis, the curve made two slope changes, one at approximately 3.5 and the other at 6. In both of these transitional zones, there was a significant increase in displacement for small changes in the L/B ratio.

The results of these analysis further confirm the hypothesis that rock breaks as a result of the gas pressure moving into the radial fractures and causing a burden displacement, and breakage as a result of flexural failure. 

Source: 
1) Rock Blasting and Overbreak Control (U.S Department of Transportation)
2) Book 2 
3) Book 3