Chapter 9: Fragmentation and Heave Process

Rock fragmentation is the ultimate purpose of rock blasting, which allows extraction of rock from the earth by excavation equipment. The degree of fragmentation induced by blasting depends on many aspects of the blast including: (1) explosive properties such as Chapman-Jouget (C-J) pressure, detonation velocity, density, etc., (2) intact rock properties such as Young's modulus, Poisson's ratio, uniaxial compressive strength, density, porosity, etc., (3) rock fabric such as joint/fracture spacing and characteristics, and (4) blast pattern design such as borehole depth, borehole diameter, stemming length, burden and spacing.

Figure 9.1 – Borehole adjacent to rock bench face. (Courtesy: D. Preece)

The Single Borehole Model

An understanding of the rock breakage process can be enhanced by examination of a single borehole adjacent to a bench face such as that illustrated in figure 9.1. A horizontal cross-section through the middle of the explosive column is shown in figure 9.2. Computer simulations of the rock blasting process have progressed to the point that they can be used to understand transmission of the shock wave induced in the rock mass by the explosive and begin to understand how rock fragmentation occurs and important aspects such as crack propagation velocities and timing.

Figure 9.2 - Horizontal cross-section through borehole and bench face. (Courtesy: D. Preece)

Detonation

The configuration shown in figure 9.2 was analyzed using the computer code AUTODYN, which was developed for modeling impact and explosive events (ANSYS, 2007) (Preece and Chung, 2003). Figure 9.3 illustrates, on the two-dimensional cross-section plane, detonation of the explosives in the borehole and the transmission of the radial shock wave outward from the borehole in the rock.

Figure 9.3 – Explosive induced shock wave transmission sequence. (Courtesy: D. Preece)

Several characteristics of shock/stress wave transmission are evident in figure 9.3. The outward moving wave in figures 9.3a and 9.3b is compressive as designated by the positive pressures in the color/pressure scale. The second characteristic occurs in figures 9.3b and 9.3c, where the radial compressive shock wave encounters the bench face, which is sometimes referred to as a "free face". The compressive wave reflects from the free face as a tensile wave. Since the tensile strength of most rocks is approximately 1/10 the compressive strength, the rock is most likely to break in tension at the free face. This is a reason that rock requires less blasting and mining is easier on benches that allow exposure of two rock faces for reflection of compressive waves as tensile waves, which more readily break the rock. The damage pattern created during the outward movement of the shock wave is manifest as the pressure plots of figures 9.3c and 9.3d.

Shock/Stress Wave Cracking

Figure 9.4 illustrates the damage/cracking induced by the borehole at four different times. Damage immediately adjacent to the borehole as illustrated in figure 9.4a is a result of crushing of the borehole wall due to the extremely high pressures at the borehole created by the detonation. It also results from tensile hoop stress induced in the rock by the high pressure in the borehole that expands its size by pushing the walls out. The principal of hoop stress is shown in figure 9.5 and illustrates how radial expansion of the borehole wall induces radial cracks that emanate from the borehole for a limited distance as shown in figures 9.4a. Figure 9.4b demonstrates the start of cracking that is induced at the bench face by reflection of the compressive wave as a tensile wave (See figures 9.3b, 9.3c and 9.3d). That cracking develops into bench face spalling in figures 9.4c and 9.4d forming a triangular breakage region with one corner at the borehole and the other two on the bench face. Other, relatively fine cracking that can be seen in figures 9.4d, results from waves passing through that ground. These cracks behind the borehole are usually described as "backbreak" without a presplit line.

Figure 9.4 - Explosive induced damage/cracking sequence. (Courtesy: D. Preece)

Figure 9.5 – Circumferential (hoop) tensile stress induced by radial borehole expansion. (Courtesy: D. Preece)

Crack Propagation

An important concept that has a very substantial impact on blast timing, is that the development of blasting-induced fracturing and damage has a significant time lag behind the stress wave. The following four (4) key items lend support to this concept: (1) Timing of fracturing and damage is limited by the crack tip velocity in rock; (2) Crack tip velocity is theoretically limited to 38% of the compressive sound wave velocity, or 0.38Vc (Mott, 1945). However, empirical measurement of crack tip velocity indicates a maximum of approximately 0.27Vc (Curran and Ellis, 1998), that would be approximately 1,000 meters/second (3,281 feet/second for Sandstone); (3) By definition the shock velocity is faster than Vc, so development of damage and fragmentation will have a significant time lag relative to the shock wave, and (4) The shock wave dissipates in stress waves relatively close to the borehole and will then propagate at a velocity of approximately Vc. The waves can either shock or stress waves depending on how far they have traveled from the borehole and will be generally referred to as stress waves. Also, for independent reasons the velocity of explosive gases in cracks is less than about 1,000 meters/second (3,281 feet/second) (Vogg and Blake, 1987).

When figures 9.3 and 9.4 are compared frame by frame it can be seen that the development of cracks and damage has a significant time lag behind the shock wave. This principal is very important in relation to the effect of electronic detonators on fragmentation patterns and optimizing timing.

The RHT damage model illustrated in figures 9.3 and 9.4, correctly simulates the crack propagation velocity as a percentage of the stress wave velocity (Riedel et al. 1999) for prediction of crack and damage development in the model. Damage induced in the rock mass also results in a reduction of the modulus of the material and can reduce or retard the stress wave. When a pure compressive stress wave meets damaged material the impedance mismatch causes a portion of the wave to reflect while a compressive portion continues to transit the damaged material at a slower velocity. Depending on the level of the impedance mismatch the reflected wave can be tensile. These features will be demonstrated in the following section.

3-D Computer Simulations of Shock Wave Transmission, Damage and Fragmentation

Figure 9.6 illustrates the geometry of a realistic scenario from a surface coal mine bench blast where two adjacent boreholes are modeled in 3-D with several different delay times between the boreholes. Figure 9.7 shows the 3-D Lagrangian model used for the simulations. Blast design parameters are: (1) burden = 9.9 meters (32.5 feet); (2) spacing = 14.63 meters (48 feet); (3) borehole diameter = 304.8 millimeters (12 inches); (4) explosive: emulsion; (5) rock: shale with unconfined compressive strength (UCS) = 5.52 megapascals (800 pounds/inch²); (3) borehole

Figure 9.6 – Surface coal mine blast geometry illustrating the portion of the bench treated in a 3-D Detonation/Fragmentation Simulation. (Courtesy: D. Preece)

Figure 9.7 – Surface coal mine blast geometry illustrating the portion of the bench treated in the 3-D Detonation/Fragmentation Simulations. (Courtesy: D. Preece)

3-D Bench Blast Simulations With Delay Timing

A 3-D simulation of the model from figure 9.7 with a 2 millisecond delay between borehole detonations is illustrated in figure 9.8 showing the pressure (stress wave) at four different times (Preece and Lownds, 2008). This calculation requires approximately 6 hours to execute out to 20 milliseconds on a 3.2 gigahertz desktop computer. The 3-D model is visually displayed as a translucent block of rock. Interaction of the stress waves generated by the two boreholes and the resulting stress and strain fields are a very complex analogy of the process that occurs during blasting. An explosively generated compressive stress wave reflects from the bench face as a tensile wave. This process is more difficult to visualize in 3-D because the cone-shaped wave front, seen in figure 9.8, dynamically interacts at the free face and contacts a volume of rock close to the face that is in a tensile stress state. Thus in a dynamic process where the tensile volume expands and contracts over a few milliseconds and it is this tensile volume, as well as its duration, that contributes to breaking rock close to the bench face.

Figure 9.8 – Translucent color representation of explosive-induced pressure from 2 boreholes with a 2 millisecond delay. Dark blue volumes adjacent to the bench face and ground surface represent rock at a tensile stress of at least 700 kilopascals (100 pounds/inch²). (Courtesy: D. Preece)

Figure 9.9 – Translucent color representation of explosive-induced pressure from 2 boreholes with an 8 ms delay. Dark blue volumes adjacent to the bench face and ground surface represent rock at a tensile stress of at least 700 kilopascals (100 pounds/inch²). (Courtesy: D. Preece)

Figure 9.9 shows a simulation with this same model but with the delay time between the boreholes set at 8 milliseconds. This delay allows the first hole to complete detonation approximately 4 milliseconds before the second begins detonation. Stress waves from the second borehole are traversing ground that has already been traversed by stress waves from the first borehole and the ground is beginning to crack and fragment. A variable called "damage" that ranges from 0.0 to 1.0 and represents the cracking/fragmentation induced in the rock that can be correlated with rock sieve analysis and it means that the rock mass is totally rubblized. Figure 9.10 displays the damage for the 8 millisecond delay simulation at the same time as the pressure is shown in figure 9.9'. What is immediately obvious is that damage accumulation significantly lags behind the primary stress wave at least, as discussed previously. The orderly set of 6's to 's' to 10's for 60% because it has been demonstrated to be the damage level at which individual rock fragments will form (Thomas et al, 1998); (Griffini 1 clearly shows that rock damage was likely broken by the blast-induced movement rather than by the shock wave. It is also interesting to note that significantly more damage is predicted in the side of the borehole in the over-burden case 2.94 meters (9.63 feet) than in the optimal burden case.

The damage field for the zero (0) millisecond delay simulation the effects of the stress wave reflection from the free face and from the collision of the stress waves halfway between the two boreholes. Damage fields from the 2 millisecond delay simulation indicate that damage is skewed toward the second borehole because the stress waves from the first borehole arrive at the second just as it is detonating. The two stress waves collide and produce significant damage but the first stress wave has been depleted in strength after traveling through the rock mass and it is overwhelmed by the more powerful stress wave that has traveled only a short distance. The stress wave from the second borehole inhibits the velocity, shear, tension, cracked and damaged zone created by the stress wave from the first borehole while it is evolving (See figure 9.8 3 milliseconds). This occurs because damage (crack propagation) has a significant time lag behind the stress wave (See figures 9.8 and 9.9) and the compressive stress wave from the second borehole stifles tensile or shear stresses necessary to propagate cracks. For the case of the 8 millisecond delay, the stress wave from the first borehole has passed and much of the damage has been induced before passage of the second stress waves through the rock. However, the damage in this case is not complete and is reduced by more delay time as shown in the state of damage at 15 milliseconds. The optimum delay-time depends on the mechanical properties of the rock and the geometry of the blasting scenario.

Figure 9.10 – Translucent color representation of explosive-induced damage from 2 boreholes with an 8 millisecond delay. Red volumes encompass rock with a damage between 0.7 and 1.0. A damage of 0.7 has been shown to be the fragmentation threshold. (Courtesy: D. Preece)

Figure 9.11 – Color representation, on a slice-plane, of explosive-induced damage at 20 milliseconds from 2 boreholes with delays of 0, 2, 8 and 15 milliseconds. Damage range: 0 (blue) to 0.7 (red). (Courtesy: D. Preece)

Gas Pressure

Explosive detonation leaves behind an expanded borehole lined with rock and filled with high-pressure gaseous explosive detonation products that have a density almost equal to the original density of the explosive and also at very high temperature. Due to the high pressure, the gaseous detonation products will begin to flow through penetrating cracks and/or radial cracks produced by the hoop stress (See figure 9.5). Gas flow as cracks can widen the cracks and assist in driving the crack tip forward to enhance fragmentation. The debate over the primary cause of fragmentation being gas induced shock wave have endured has gone on for decades. A general consensus now is that gas is an important component in the total fragmentation close to the borehole (within a few borehole diameters). It also contributes to extending shock-induced radial cracks that emanate from the borehole and often curve slightly to intersect with other radial cracks (See figure 9.4).

Rock Movement

A distinct but short time delay occurs between detonation of the borehole and the initial detectable movement of the bench face or top surface. This time is defined in g by. Blasting induced rock movement is often called "heave" and is an additional benefit of blasting. However, if the blast is designed with too little burden or stemming and/or too high of a powder factor, premature movement of the rock can consume explosive energy in the form of ej=ting gases. This only converts explosive energy to gas into air blast and equipment are thrown and also has two consequences: safety is compromised and (2) less explosive energy goes into breaking and moving rock. Blast design guidelines such as timing, air blast, spacing and stemming height should be followed and adjusted as incurrents to prevent these types of problems and optimize the application of explosive energy.

Cratering Mechanisms

Crater blasting exhibits a different, more constrained, response to explosive-induced rock fragmentation. Figure 9.12 illustrates a typical crater blasting environment where the only free surface is the ground surface.

Cratering, or explosive results in transient stress wave propagation and rock motion. Rock breakage and definition of the crater is caused by the transient stress wave propagation along with the stresses induced in the rock by the high-pressure gases. Rock in the crater is broken, moved, dilated and (for optional cratering) usually heaved into a pile over the boreholes. A series of frames from a crater blast may be observed in figure 9.13 (material is observed in figure 9.13. The final excavated crater is shown in figure 9.14 and consists of the crater surfaces defined below and a flat crater floor.

Figure 9.12 – Typical crater blast configuration with explosives, stemming and a single free surface. (Courtesy: D. Preece)

Excavation of the crater, typically using a backhoe, reveals the center as defined by the boundary between broken and unbroken rock. A photograph of an excavated crater in layered shale is shown in figure 9.14. A surveyed cross-section of this excavated crater, along with the charge configuration, is illustrated in figure 9.15 (Schmidt, et al, 1990).

Both of these different mechanisms work together to break the rock and form a crater. Explosive events such as crater blasting occur so quickly that direct observation is difficult. Computer hydro-code simulations can shed light on the mechanisms involved in explosive events by allowing us to see into the intricate details and mechanisms involved. Figures 9.16c and 9.16b show that the computer-calculated pressure wave induced by the detonation as it propagates outward from the borehole as a compressive wave (ANSYS, 2007). Figures 9.16c and 9.16d illustrate reflection of the compressive wave from the surface of the ground as a tensile wave and the propagation of that cone-shaped tensile region back toward the borehole. In figures 9.16c and 9.16d the compressive wave continues propagating outward while the tensile wave propagates downward. High-pressure gas remains in the expanded borehole having an effect on the stress state and breakage of the rock mass.

Figure 9.13 – Four frames extracted from high-speed film of a crater blast in shale. (Courtesy: D. Preece)

Figure 9.14 – Photograph of the excavated crater treated in these analyses. Please note that this photo was taken in 1987 during a joint test program between Sandia National Laboratories and Atlas Powder Company. Safety standards at that time did not reflect current accepted procedures, that would include proper fall protection, working around highlife, emergency extraction from a confined space, approved ladders and the use of proper PPE. (Courtesy: D. Preece)

Figure 9.15 - Typical surveyed excavated crater resulting from a single charge, optimal DoB crater blast. Charge details: Diameter = 142 millimeters (5.6 inches); DoB = 2 meters (6.56 feet); charge length = 1 meter (3.28 feet); Explosive = Emulsion; Rock = layered shale. (Courtesy: D. Preece)

Figure 9.16 - Explosive induced pressure waves at four different subsequent times induced in the rock during a crater blast. Pressure range: Red = 2.0x10⁴ kilopascals (2900 pounds/inch²) and greater, compression; Blue = 800 kilopascals (116 pounds/inch²) and less, tensile (ANSYS, 2007). Crater blast details are given in figure 9.15. (Courtesy: D. Preece)

Figure 9.17 – Explosive induced damage/fragmentation at four different subsequent times induced in the rock during a crater blast. Damage: Blue = 0, intact rock. Red = 1.0, or rubblized rock. (ANSYS, 2007). Crater blast details are given in figure 9.15. (Courtesy: D. Preece)

This gas will begin to percolate outward from the borehole into the rock mass and will also have some impact on rock breakage. Explosive gas pressure remaining after detonation has the most impact on rock velocity and movement with a small portion of the induced velocity coming from the peak particle velocities imparted by the shock wave. Gas venting can be seen in frame 2 of figure 9.13.

Figure 9.17 shows the evolution of damage as predicted by a hydro-code (ANSYS, 2007). Further details of the damage model were presented earlier in this chapter. As explained in the earlier section on Crack Propagation, the fragmentation/damage and damage field should be dealt from its physical limitations on the crack propagation speed. This is evident when comparing the pressure field and damage at different times in figures 9.16 and 9.17.

Figure 9.18 compares the measured crater (Schmidt, et al, 1990) with that predicted by the computer code and presented in figure 9.174. Comparison of predicted and measured craters is remarkably good and lends some validity to this type of computer modeling. These types of comparisons will always be influenced by differences in geology and by limitations of the modeling software. A current software limitation is the ability to treat layered (jointed) media, which was characteristic of the rock where this crater blast occurred.

Figure 9.19 compares the measured crater (Schmidt, et al, 1990) with the final damage predicted by a hydro-code simulation where the depth of burial 2.94 meters (9.63 feet) is greater than optimal 2 meters (6.56 feet) and, as expected, produces a smaller crater. Damage/fragmentation predicted is relatively good, in terms of the crater outline, but implies that damage in crater was likely broken by the blast-induced movement rather than by the shock wave. It is also interesting to note that significantly more damage is predicted in the side of the borehole in the over-burden case 2.94 meters (9.65 feet) than in the optimal buried case.

Figure 9.18 – Comparison of surveyed crater (Schmidt, et al, 1990) with predicted final damage from crater blast hydro-code modeling presented in figure 9.17d. (Courtesy: D. Preece)

Figure 9.19 – Comparison of surveyed crater (Schmidt, et al, 1990) with predicted final damage from crater blast hydro-code modeling. This crater blast is identical to that described in figure 9.15 except that the depth-of-burial is 2.94 meters (9.65 feet). (Courtesy: D. Preece)

The reason is that the added confinement prevents explosive energy from being channeled to the ground surface so it does more damage at a greater range around the borehole. An attempt was made at the time of this test program to determine if blast-induced fracturing existed to the side of over-buried charges. Boreholes to extract core were drilled a few feet from the experimental boreholes and geological fracture analyses were performed on the core. It was discovered that substantial blasting-induced cracking did exist in the cores and correlated well with the damage prediction shown in figure 9.19 (Falgun, 1998).

Blasting Induced Rock Movement

Fragmentation and rock movement are both important results of rock blasting. Rock movement is usually a favorable result since the same blast that fragmented the rock can also provide the energy to move it to its final location. It is certainly more economical to move rock with explosives than with mechanical equipment. Systems such as cast blasting are designed to maximize rock displacement. Rock movement during blasting is also referred to as "heave" or "throw".

Figure 9.13 illustrates the sequential vertical rock movement induced by a crater charge. However, crater charges are a relatively inefficient explosive method for moving rock. A much more efficient method for both fragmentation and movement is the bench blast that is often employed in surface quarries and coal mines.

Rock Quarry Bench Blast

A typical rock quarry bench blast is illustrated in figure 9.20. Many of the controllable bench blast design parameters have an impact on the rock movement induced by the blast. These parameters are listed in table 9.1.

Quarry Bench Design Parameters

Table 9.1 – Quarry bench design parameters.

These design parameters influence rock movement at the moment of initiation and thus through the remainder of the blast until the muck settles into place.

Figure 9.20 – Typical bench blast configuration employed in a rock quarry. (Courtesy: D. Preece)

To illustrate this point, sequential photos from a rock quarry blast are shown in figure 9.21. Blast design parameters for this blast are provided in table 9.2. An outcome desired from this particular blast was controlling rock movement to preserve the rock type layering in the muck pile. To do this, three explosive decks were created in each borehole with stemming separating the decks and a precise (electronic) delay detonator in each deck. Detonation time for each explosive deck in each borehole, starting at the bottom, was 6, 13 and 34 milliseconds. Thus, corresponding explosive decks in each of the five boreholes were detonated simultaneously. This procedure maintained rock type segregation in the muck pile as illustrated during excavation in figure 9.22.

Blast Design Parameters For Example Rock Quarry Blast

Table 9.2 – Blast design parameters for example rock quarry blast.

Figure 9.21 – Quarry blast designed to preserve rock layer segregation in the muckpile. (Courtesy: S. Chung)

A usual goal of rock movement during quarry blasting is to spread the blasted rock on the quarry floor to enhance diggability and to customize the muck pile for optimal digging with the excavation equipment available at a quarry. Rock that has limited blast induced movement is usually tight and hard to dig even though the fragmentation is adequate. Blast designs that will cause substantial rock movement will have higher powder factors than that needed just for fragmentation.

Figure 9.22 – Muck pile resulting from a rock quarry blast where the blast design and delay timing were defined to preserve rock layer segregation. Notice the horizontal banding in the muckpile. (Courtesy: S. Chung)

Surface Coal Mine Cast Blast

Prior to the 1950s explosives were used in surface coal mines to fragment the rock, which was then excavated with mechanical equipment. It was discovered at that time that explosives could move massive amounts of overburden to its final location and the "cast blasting" revolution began in surface coal mining. Presently delay detonators were a developed innovation that gave cast blasting possible since it depends on relatively accurate detonation delay timing to control the blast. Long delay detonators allowed all of the detonators in a blast to be energized but to then delay their timing before the first borehole detonated. This precision and cut off of the delay timing signals and gives high assurance that all of the boreholes will detonate.

The key significant difference between quarry bench blasting, discussed previously, and surface coal cast blasting are: (1) the coal seam sits at the bottom of the bench is usually weaker than the rock above it and a nearly sheared (a mild damaged) coal (blasting); (2) a balance is sought between maximizing rock throw and minimizing coal damage as well as controlling the overburden and blast pattern. Quarry blasts are in more granite type of rock, includes sedimentary, metamorphous and igneous, where coal mine cast blasting is always in a sedimentary environment and often thinner beds rocks; and (4) cast blasts attempt to shape the muck pile for optimal operations and excavation by a dragline.

A typical surface coal mine cast blast is shown in figure 9.23 through 9.26. Figure 9.23 illustrates the preblast bench. Four frames from a high-speed digital camera are shown in figure 9.24. overall rock movement is illustrated in figure 9.25 and the post blast muck pile is displayed in figure 9.26. As discussed earlier in the fragmentation section, these blasts are designed with a detonation delay between boreholes parallel to the bench face and between rows of boreholes progressively deeper from the free face. Design parameters for this blast are given in table 9.3. This mine site subsects the bench height (depth to coal), rock types and coal thickness. The other parameters are developed to maximize rock movement without damaging the coal.

Design Parameters For Example Cast Blast

Table 9.3 – Design parameters for example cast blast.

Figure 9.23 – Surface coal cast blast, preblast bench. Blast design parameters given in table 9.3. (Courtesy: D. Preece)

Figure 9.24 – Four frames from a high-speed video of a coal mine cast blast illustrating early explosively induced rock movement. Blast initiation is progressing toward the camera. (Courtesy: D. Preece)

Figure 9.25 – Overall view of a cast blast in progress. (Courtesy: D. Preece)

Figure 9.26 – Final muck pile produced by cast blast. (Courtesy: D. Preece)

Following a cast blast the muck pile (See figure 9.26) is excavated using combinations of bulldozers, trucks, shovels and draglines to uncover the coal.

Percent Cast and Center-of-Gravity Movement

Both quarries and surface coalines compare the effectiveness of different blast designs and measure the efficiency of explosively induced rock movement with the concepts of "percent cast" and "center-of-gravity (CG) movement."

In surface coal mining percent cast is a measure of the amount of overburden that is placed in its final location by the blast and does not require any further handling. A definition of percent cast is described at a cross-section of a quarry blast as shown in figure 9.27 and as a surface coal mine in figure 9.28. An important point is that surveying of the preblast bench and post blast muck pile is necessary for calculating percent cast. The major difference on the percent cast calculation for quarries or surface coal is exclusion of the coal seam from the full muck area. This highlights the point that the percent cast is normally customized to each mining operation depending on the geometry they are dealing with. For example, surface coal mines blasting personnel may move the arc line anchor point from the toe to the mid-height or top of the coal or change the angle. Quarries do not have nearly as much waste or spoil rock and they also are not moving rock into a final location so they tend use the percent cast to compare rock movement induced by different blast designs. Thus, the cast line may be at lower altitudes of 0° or 45° or 60°.

Another measurement of the effectiveness of a blast is the movement of the center-of-gravity of the rock mass. Figure 9.29 illustrates this concept. The center-of-gravity of the pre- and post-blast cross-sectional areas are computed using survey methods and compared for different blast designs. It is usually the horizontal component that is of most interest.

Figure 9.27 Definition of percent cast on the surveyed cross-section of a quarry blasting scenario. Survey techniques are employed for area calculations. (Courtesy: D. Preece)

Figure 9.28 – Definition of percent cast on the surveyed cross-section of a surface coal blasting scenario. Survey techniques are employed for area calculations. (Courtesy: D. Preece)

Figure 9.29 – Definition of center-of-gravity (CG) movement on the surveyed cross-section of a surface coal blasting scenario. The initial CG is that of the preblast bench and the final CG is that of the muck. Survey techniques are employed comparing the CG of the preblast bench as well as the post blast muck. (Courtesy: D. Preece)

Most blast designs parameters that increase the percent cast will also increase the horizontal component of the CG movement. Parameters causing more movement are those that increase the powder factor such as a higher density explosive with more energy, decreasing the stemming or decreasing the burden and/or the spacing.

Dynamic Free Surfaces

A bench blast begins with a free face on the ground surface and the face of the bench. As discussed earlier, in the fragmentation section, free surfaces enhance fragmentation because the compressive shock and stress waves reflect from the free surface as tensile waves that are more efficient at breaking rock than compressive waves. An important aspect of delay timing, particularly row-to-row, is allowing enough time between rows for the burden rock to move and create a gap in front of the next row to fire. This gap generates a new free face from which compressive waves created by the next row of boreholes can reflect as tensile waves. Because this happens on a millisecond time scale during the blast these are called dynamic free surfaces. Row-to-row delays must be necessary to create effective dynamic free surfaces depend very much on the rock type and geometry of the blast. They are usually on the order of tens of milliseconds and can be as high as several hundred milliseconds.

Since all of this occurs inside the blast and on a very short time scale, no videos of this process exist for production blasting. Distinct element computer modeling of the blasting process allows clear visualization of what happens inside a blast. Figure 9.30 shows a 2-D (or thin cross-section) distinct element computer model (Cevrana and Bonet, 2004), a few hundred milliseconds following initiation of the front row. The delay time between the first and second row is 200 ms to allow the first row to move out of the way and then 100 ms between subsequent rows. This figure demonstrates the concept of a gap opening between rows where a dynamic free surface is created immediately in front of the next row to detonate.

Figure 9.30 – Distinct element computer simulation of a bench blast, on a 2D cross-section, illustrating the concept of row delay timing producing dynamic free faces within the blast. This simulation was produced by the computer code Soft (Son of Blanca) which employs rectangular discrete elements (Minchinton and Dare-Bryan, 2005).

Predicting Rock Movement During Blasting

Blasting induced rock heave is a complex process, and, as such, has eluded efforts to quantify it with simple equations.

A number of methods have been developed for predicting rock movement during blasting. Eversten (1983) started an early effort to quantify the velocities and trajectories of fragmented rock during a blast in two dimensions. Another early method employed explosive/rock interaction equations to predict the launch trajectory for discrete blocks of rock in a bench. That trajectory then located the particle in the muck pile according to some rules that regarded arrival order and post-landing movement (Harries, 1987). Yang and Katerski (1990) took a similar but more advanced approach and expanded it to three dimensions. Due to the spatial distributions of explosive energy these methods all required a computer to do the book keeping for each block of rock.

A logical approach for computer modeling of rock heave is the distinct element method. Preece et al (1993) employed spherical distinct elements to model rock particles and coupled that with a gas flow method to accurately treat rock movement during blasting. DMC (Distinct Motion Code) is the computer program developed from that effort and continues to be improved and used today. Four frames from a DMC simulation of a bench blast are shown in figure 9.31. As discussed in figure 9.30, SoB is a computer program that employs rectangular distinct elements to predict blast heave.

Figure 9.31 – Four frames from a DMC surface coal bench blast simulation illustrating the blasting induced rock movement of three overburden rock layers and the underlying coal seam. (Courtesy: D. Preece)

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