Chapter 15: Flyrock

Though an infrequent, if not rare event, flyrock deserves special attention in every blaster training and refresher course, and every blast design course, due to the high risks associated with its occurrence. Only a blaster can know the terrible dread and concern when a seemingly well planned event goes wrong and rock fragments are projected high into the air, with completely random trajectories. If they project beyond the blast perimeter and clearance zone, they can strike and destroy anything in their path. As a randomly thrown rock fragment comes to rest, it still represents risk to area, since two undeniable factors will always apply – the rock fragments which travel the greatest distances are large, and they travel silently at velocities high enough to penetrate any light structure or cover or stick in loose or cut earth. A fragment projected 400 meters (200 feet) from a quarry using 150 millimeters (6 inch) diameter boreholes will probably weigh at least 2 kilograms (4.5 pounds), and quite likely more than 10 kilograms (22 pounds); it will have a maximum projection velocity in the vicinity of 200 meters/second (450 miles/hour), and a maximum impact velocity of around 50 meters/second (110 miles/hour).

The two common objectives of rock blasting are to (1) break and displace rock (within a planned displacement zone) to promote muckpile looseness, and (2) facilitate its mechanical excavation. Rock fragments displaced beyond the planned displacement zone can be considered flyrock. By anticipating that blasting may produce rock fragments that travel outside the planned displacement zone, the blaster-in-charge must establish a safe clearance zone. The U.S. Mine Safety and Health Administration (MSHA) defines the area of expected blasted rock movement at the blast area.

Blast Area

The blast area is the area in which concussion (shock wave), flying material, or gases from an explosion may cause injury to persons.

In determining the blast area, the factors listed in table 15.1 shall be considered.

Table 15.1 - Factors to consider when determining the blast area. (MSHA)

The three objectives of this chapter are to (1) discuss the sources of flyrock, (2) explain the root causes of flyrock, and (3) provide a methodology to help the blaster-in-charge determine the maximum rock projection distance. This will enable the blaster-in-charge to establish a clearance zone to set a safe blast area perimeter.

Clearance Zone

The clearance zone is the zone around a blast beyond which there should be no risk to personnel from flying rock fragments, and beyond which the blaster must evacuate all personnel prior to firing the blast.

Flyrock

Rock fragments projected beyond the clearance zone are called flyrock.

It is incumbent on the blaster-in-charge to establish the clearance zone to (1) protect all people and property beyond this zone boundary, and (2) remove all equipment within or at the very least advise the mine or company of the risks of normal rock movement within the blast area.

Normal or planned rock displacements vary enormously according to the type and location of the blast. Many blasts are designed to produce minimal movement (e.g. so as to avoid dilution from inter-mixing of ore and waste materials within the blast volume), while others are designed to produce large displacement with either low muckpile profiles or high cast factors. Unless specifically designed to produce strong forward movement of the broken rock, the planned horizontal displacement from a blast fired in a free face is commonly around 4 to 10 times the height of the bench, depending on the powder factor being utilized.

It is essential that flyrock awareness be built into the blast design process, requiring an engineering approach to understand and control the outcomes and manage the associated risks. Since it is impossible to anticipate all the "unknown conditions" which might contribute to a flyrock event, it must be accepted that while risk levels can be made extremely low (much lower than many accurate accident statistics), in most situations the risk cannot actually be reduced to zero. Vigilance on behalf of the blaster-in-charge and the entire blasting crew during the loading of the charges remains one of the keys to controlling flyrock, though this alone will not suffice unless reliable guidelines relating maximum projection distances to charging conditions can also be adopted at the blast design stage.

Sources of Flyrock

Flyrock is generated close to air-rock interfaces – either from the free face of a bench blast or from the collar regions of the boreholes. Flyrock emanating from a vertical or sub-vertical free face will travel in a direction forward of the face and most likely in a direction more or less perpendicular to the bench face, and frequently at quite low trajectories. Roth (1979) reported that the breakout angle of material from a vertical face, in plan view, is generally around 90 degrees, i.e. ± 45° from a line drawn perpendicular to the free face in plan view. Flyrock fragments emanating from the borehole collar region have equal probability of being projected in all horizontal directions in plan view, and their trajectory angles are typically higher than those from a face. Roth (1979) also proposed a breakout angle in vertical section of around 90 degrees, i.e. ± 45 degrees from vertical. For these reasons, flyrock risk is generally considered to be greater from the collar region of boreholes than from the free face (Roth 1979, Lundborg 1975).

Figure 15.1 presents a schematic of the flyrock impact zones around a blast, where the maximum projection distances from each source are equal. Depending on the maximum burden and the minimum stemming length, maximum projection distances for either can be greater than the other.

Flyrock is commonly generated during the process of secondary blasting, where charges are either placed on top of boulders or in holes drilled into the boulders. As much as possible, secondary breakage with explosives should be avoided, since experience shows this requires the largest evacuation radius, has the largest degree of associated risk, and quantification of critical factors such as burden and boulder volume or weight is most difficult. Several non-explosive systems are available for this purpose, all of which require significantly smaller clearance zones and have lower risk profiles than explosives.

In summary, and a key element of flyrock control, that explosive charges must always have an appropriate degree of burial or confinement. Charge burial or confinement can be considered as the distance between the nearest element of the charge and a rock/air interface, and an appropriate distance will depend on the size of the charge (i.e. its diameter and its density) and the strength or resistance of the rock mass between the charge and the free surface. With insufficient burial or confinement of charges, flyrock can be eliminated.

Root Causes of Flyrock

Flyrock occurs when the rate of confinement of an explosive charge is insufficient for the applied excavation radius, resulting in an excess of energy for the required task, which causes projection of rock fragments beyond the clearance radius. It now remains to examine the conditions which might result in insufficient charge confinement or excess energy, of which there are three categories: (1) design faults, (2) deviations in implementation, or (3) unforeseen geological conditions.

Design Faults

Design faults relate to an inappropriate choice of the burden for the planned charging configuration or an inappropriate charge concentration for an already-drilled burden, or an inappropriate length of stemming for a given borehole diameter, density, and the applied excavation radius. This, in turn, supposes the burden – i.e. the distance between the explosive charge in the borehole for which a free face is available – instrumentalization and software tools are readily available for blasters to know the minimum burden at any location along the length of the borehole. An appropriate safety factor (i.e. a value greater than one) should be applied to the minimum burden when choosing the charge diameter, type, and density appropriate to the blast. Designing a trench blasting within 50 meters (100 feet) of occupied housing will be quite different from that for quarry blasting conducted at 500 meters (1,000 feet) from occupied housing, even if the hole diameter and burden are similar. Design aspects affecting flyrock are covered in chapter 33.

Deviations in Implementation

Deviations in implementation can occur during borehole charging, such that the actual stemming length or the minimum front row burden for a borehole becomes significantly different from design intent. Charging and deviations that use materials and further stemming lengths are now from the borehole open ore can easily be per the dosing or detlectors. If a flyrock incident occurs as a result of a deviation in a human failure, and the failure is not that a deviation was made during charging, but rather that the operator failed to detect the condition and apply appropriate site procedures. A vigilant blast crew who, through regular quality control checks, how much variability must be expected for each blasting site, and this variability will be recorded in a determining a safe clearance distance and a safe blast design. Deviations resulting in greater than expected variability will be noted and reported, the risks will be reevaluated, and appropriate mitigation measures applied.

Unforeseen Geological Conditions

Unknown geological conditions make it impossible to ever achieve a zero level of risk from flyrock. Anything that reduces the ability of the rock in the stemming zone or in the face in front of the borehole to confine the high-pressure gasses can become a release valve, allowing high-pressure gas to escape and project rock fragments at high velocities. Factors such as cavities, clay seams and layers of unconsolidated material can act to increase the probability of flyrock generation. In the stemming zone, accurate drill logs will assist in identifying the depth of weak or unconsolidated material overlying competent rock, and inspection of free faces will assist in identifying the depth, size, and character of weak seams.

Maximum Projection Range

During a series of well monitored and documented field studies, Swedish workers (Lundborg et al, 1975) established maximum flyrock range as a function of charge diameter, as given by equations 15.1 and 15.2 (modified from the authors' original equation to express diameter in millimeters and feet/inches, for consistency of units).

$$Range = 30 \times d_e^{0.667}$$ Equation 15.1

Where:

• Range = Flyrock range (meters)
• $d_e$ = Charge diameter (millimeters)

In the U.S. system equation 15.1 appears as equation 15.2.

$$Range = 853 \times d_e^{0.667}$$ Equation 15.2

Where:

• Range = Flyrock range (feet)
• $d_e$ = Charge diameter (inches)

This equation was developed from measurements made during crater blasting operations, in which explosive charges were inserted into shallow holes, and produced a maximum flyrock range of 260 meters (850 feet) for a 25 millimeter (1 inch) diameter borehole, approximately 650 meters (2,100 feet) for a 100 millimeter (4 inch) diameter charge, and approximately 1,400 meters (4,500 feet) for a 311 millimeter (12¼ inch) diameter charge. These should be considered to be near the maximum likely range of projection of flyrock, but not typical distances from normal bench blasting operations. The authors noted that normal bench blasting, with a greater degree of burial of the charge, produced maximum projection distances generally around one sixth (1/6) of those produced in crater blasting. They also finally noted that once the depth of burial of a charge exceeds approximately 40 times the charge diameter, little or no disruption occurred around the borehole collar, and the fragment projection distance could be considered to be zero.

Caution

Equations 15.1 and 15.2 do not imply that rock fragments will always be projected this distance, but do indicate the greatest distance that fragments could be projected, under worst-case conditions.

EXAMPLE 15.1

Calculate the worst-case flyrock projection distance for poorly confined charges for a borehole diameter of 140 millimeters using equation 15.1.

$Range = 30 \times d_e^{0.667}$

$Range = 30 \times 140^{0.667}$

$Range = 810$

The maximum flyrock range is 810 meters.

EXAMPLE 15.2

Calculate the worst-case flyrock projection distance for poorly confined charges for a borehole diameter of 5.5 inches using equation 15.2.

$Range = 853 \times d_e^{0.667}$

$Range = 853 \times 5.5^{0.667}$

$Range = 2,659$

The maximum flyrock distance is 2,659 feet.

The following sections in this chapter present a way to estimate maximum projection distances as a function of blast design, for conditions ranging from complete burial of the charge to Lundborg's crater blasting configuration.

Factors Affecting Maximum Projection Distance

The factors controlling the maximum flyrock range are the four factors listed in table 15.2, over which the blaster has control of only one – the initial launch velocity of the particle, the size of the fragment particle, the shape of the fragment particle, and the angle and the horizontal(s) at which the fragment particle(s) is projected. The blaster has no ability to control the size or shape of the fragments likely to be ejected, or the angle of projection (these are all random factors) but does have a strong ability to control the launch velocity by controlling the depth of burial or degree of confinement of the charge.

Table 15.2 - Factors affecting maximum flyrock distance.

Intuitively, factors having a strong effect on the velocity of ejection of rock fragments include the dimensions and weight of the explosive charge and the depth to which it has been buried or confined within the rock mass. A well known term which incorporates all these factors is the scaled depth of burial (SDOB), which can be applied both to the vertical burial below a horizontal drilling surface, and to a horizontal burial from a vertical free face.

The concept of the scaled depth of burial of a charge was defined during cratering experiments, and has been well described by Chiappetta et al (1997), as with it is clear that as the depth of burial of a charge is reduced (from right to left in figure 15.2), the velocity of projection of ejected rock fragments increases, the range of projected material increases, and the probability of flyrock increases. The scaled depth of burial is defined as the length of stemming plus half the length of charge contributing to the cratering effect, divided by the cube root of the weight of explosive contained within the portion of charge contributing to the crater effect. It is calculated in either metric units (SDOB_m) or U.S. units (SDOB_U.S.) by the equations 15.3 and 15.4.

$$SDOB_m = \frac{l_s + 0.0005 \times m \times d}{0.00923 \times (m \times d^3 \times \rho_e)^{0.333}}$$ Equation 15.3

Where:

• $SDOB_m$ = Metric scaled depth of burial (meters/kilogram^(1/3))
• $l_s$ = Stemming length (meters)
• $d$ = Borehole diameter (millimeters)
• $m$ = Contributing charge length factor (See equation 15.5)
• $\rho_e$ = Explosive density (grams/centimeter³)

$$SDOB_{U.S.} = \frac{l_s + 0.0005 \times m \times d}{0.00923 \times (m \times d^3 \times \rho_e)^{0.333}}$$ Equation 15.4

Where:

• $SDOB_{U.S.}$ = U.S. scaled depth of burial (feet/pound^(1/3))
• $l_s$ = Stemming length (feet)
• $d$ = Borehole diameter (inches)
• $m$ = Contributing charge length factor (See equation 15.6)
• $\rho_e$ = Explosive density (grams/centimeter³)

Charge Length

In equations 15.3 and 15.2, the value of "m" is the ratio of charge length to borehole diameter (contributing charge length factor), which gives charge length as a multiple of the borehole diameter as equations 15.5 and 15.6 for metric and U.S. respectively. The maximum value of "m" used is based on the borehole diameter as stated in the following Rule. So equations 15.5 and 15.6 to calculate "m".

Maximum Value of "m" Rule

"m" has a maximum value of 8 for borehole diameters less than 100 millimeters (4 inches), and a maximum value of 10 for a borehole diameter greater than or equal to 100 millimeters (4 inches).

$$m_m = \frac{l_c \times 1,000}{d}$$ Equation 15.5

Where:

• $m_m$ = Contributing charge length factor (borehole diameters)
• $l_c$ = Charge length (meters)
• $d$ = Borehole diameter (millimeters)

$$m_{U.S.} = \frac{l_c \times 12}{d}$$ Equation 15.6

Where:

• $m_{U.S.}$ = Contributing charge length factor (borehole diameters)
• $l_c$ = Charge length (feet)
• $d$ = Borehole diameter (inches)

The term "m" therefore defines the length of buried charge contributing to the cratering effect, and says that for projections from the collar region, only the topmost portion of the explosive column (to a maximum length of 10 borehole diameters) contributes to flyrock. Long charges therefore have no greater propensity to eject flyrock than short charges once the charge becomes longer than 10 times the diameter of the borehole.

Example 15.3

Calculate the SDOB for an ANFO charge (density = 0.8 grams/centimeter³) that is 10 meters long in a borehole 140 millimeters in diameter and a 3 meter stemming length.

Step 1 Calculate the value of the contributing charge length factor "m" using equation 15.5.

$m_m = \frac{l_c \times 1,000}{d}$

$m_m = \frac{10 \times 1,000}{140}$

$m_m = 71.4$

Since the borehole diameter is greater than 100 millimeters the value of "m" is the smaller of 10 and the calculated value 71.4.

Therefore, the value of "m" is 10.

Step 2 Calculate the SDOB using the value of "m" in step 1 and equation 15.3.

$SDOB_m = \frac{l_s + 0.0005 \times m \times d}{0.00923 \times (m \times d^3 \times \rho_e)^{0.333}}$

$SDOB_m = \frac{3 + 0.0005 \times 10 \times 140}{0.00923 \times (10 \times 140^3 \times 0.8)^{0.333}}$

$SDOB_m = \frac{3 + 0.7}{0.00923 \times 318.7}$

$SDOB_m = 1.44$

The SDOB is 1.44 meters/kilogram^(1/3).

EXAMPLE 15.4

Calculate the SDOB for an ANFO charge (density = 0.8 grams/centimeter³) that is 2 feet long in a borehole 5½ inches in diameter with a 10 foot stemming length.

Step 1 Calculate the value of the contributing charge length factor "m" using equation 15.6.

$m_{U.S.} = \frac{12 \times l_c}{d}$

$m_{U.S.} = \frac{12 \times 2}{5.5}$

$m_{U.S.} = 4.4$

Since the borehole diameter is greater than 4 inches the value of "m" is the smaller of 10 and the calculated value 4.4.

The value of "m" is 4.4.

Step 2 Calculate the SDOB using the value of "m" in step 1 and equation 15.4.

$SDOB_{U.S.} = \frac{l_s + 0.042 \times m \times d}{0.0923 \times (m \times d^3 \times \rho_e)^{0.333}}$

$SDOB_{U.S.} = \frac{10 + 0.042 \times 4.4 \times 5.5}{0.0923 \times (4.4 \times 5.5^3 \times 0.8)^{0.333}}$

$SDOB_{U.S.} = \frac{10 + 1.01}{0.0923 \times 5.315}$

$SDOB_{U.S.} = \frac{5.535}{1.281}$

$SDOB_{U.S.} = 4.33$

The SDOB is 4.33 feet/pound^(1/3).

Clearly, the SDOB can be increased by reducing the weight of explosive in the top 8 to 10 borehole diameters of the charge (by decreasing borehole diameter or explosive density) or by increasing the stemming length. When blasting close to a sensitive target, blasters should design for a SDOB in the range of 1.4 meters/kilogram^(1/3) to 2.3 meters/kilogram^(1/3) (3.5 feet/pound^(1/3) to 5.8 feet/pound^(1/3)). As the distance to sensitive receivers increases, the SDOB can be reduced, but should not fall below approximately 1 meter/kilogram^(1/3) (2.5 feet/pound^(1/3)).

Caution

Do not assume that flyrock cannot occur if there is an air deck anywhere in the borehole, even if the air deck is at the top of the column and longer than 8 to 10 times the borehole diameter.

In air decking situations, the effective density of the charge used in the SDOB calculations should be adjusted. Since air is compressible, assume the charge is evenly distributed over the combined charge plus air deck length. Calculate the effective density with equation 15.7.

If there is a water-filled gap between the top of charge and the base of the collar stemming, the density used in calculating the SDOB should be the actual, unadjusted product density, since water does not compress and transmits pressure very efficiently from the charge column to the base of the stemming column.

$$\rho_{eff} = \rho_e \times \left(\frac{l_c}{l_{air}}\right)$$ Equation 15.7

Where:

• $\rho_{eff}$ = Effective explosive density (grams/centimeter³)
• $\rho_e$ = Explosives density (grams/centimeter³)
• $l_c$ = Length of explosive charge (meters) (feet)
• $l_{air}$ = Length of explosive charge + air deck (meters) (feet)

EXAMPLE 15.5

Calculate the effective density of a charge of ANFO 6 meters long (density = 0.8 grams/centimeter³) and an air deck 2 meters long using equation 15.7.

$\rho_{eff} = \rho_e \times \left(\frac{l_c}{l_{air}}\right)$

$\rho_{eff} = 0.8 \times \left(\frac{6}{6 + 2}\right)$

$\rho_{eff} = 0.6$

The effective density of the charge is 0.6 grams/centimeter³.

EXAMPLE 15.6

Calculate the effective density of a charge of ANFO 20 feet long (density = 0.8 grams/centimeter³) and an air deck 6½ feet long using equation 15.7.

$\rho_{eff} = \rho_e \times \left(\frac{l_c}{l_{air}}\right)$

$\rho_{eff} = \rho_e \times \left(\frac{20}{20 + 6.5}\right)$

$\rho_{eff} = 0.8 \times (0.75)$

$\rho_{eff} = 0.6$

The effective density of the charge is 0.6 grams/centimeter³.

Caution

When using a decoupled cartridged explosive charge the effective explosive density used is adjusted by the coupling ratio in equation 15.8, to appear as equation 15.9.

See chapter 14 for a discussion of the coupling ratio in equation 15.8.

$$K_c = \left(\frac{d_e}{d_b}\right)^2$$ Equation 15.8

Where:

• $K_c$ = Coupling ratio (dimensionless)
• $d_e$ = Diameter of explosive (millimeters) (inches)
• $d_b$ = Diameter of borehole (millimeters) (inches)

$$\rho_{eff} = K_c \times \rho_e$$ Equation 15.9

Where:

• $\rho_{eff}$ = Effective explosives density (grams/centimeter³)
• $K_c$ = Coupling ratio (dimensionless)
• $\rho_e$ = Explosives density (grams/centimeter³)

Caution

The diameters must be the same units of measure.

EXAMPLE 15.7

Calculate the effective density for a decoupled 2 inch diameter cartridge explosive (density = 1.1 grams/centimeter³) in a 3 inch diameter borehole using equation 15.8.

$K_c = \left(\frac{d_e}{d_b}\right)^2$

$K_c = \left(\frac{2}{3}\right)^2$

$K_c = 0.44$

$\rho_{eff} = K_c \times \rho_e$

$\rho_{eff} = 0.44 \times 1.1$

$\rho_{eff} = 0.48$

The effective density is 0.48 grams/centimeter³.

Roth (1979) reported that rock type significantly affects flyrock velocities and flyrock range based on field observations. Interestingly, his maximum range equations suggest that softer rocks (sandstone and limestone) are likely to be projected greater distances than granite, though other graphs in his report show higher projection velocities for granite than for sandstone for the same charge burial conditions. Despite the observations, no quantitative adjustments to flyrock range have been proposed as a function of any mechanical rock property, so that the conservative approach is to consider the maximum projections range to be independent of rock type.

Roth (1979) also examined the propensity of different products to generate flyrock. In his field trials he noted that watergel products' explosive(s) tended to eject water gel and slurry products generate higher projection velocities and increased maximum projection distances than ANFO. Interestingly, Roth suggests that while increasing VOD for a fixed explosive type (e.g. by increasing hole diameter) tends to increase projection velocity, the reason that "slurry" explosives produce greater projection distances is due to their increased density, not their increased velocities of detonation relative to ANFO.

The effect of delay timing on flyrock range has not been studied closely, and no quantitative relationships are known to relate the two factors. The scaled depth of burial makes no allowance for delay timing, and arguments could be made along the lines that long delay times provide time for charges to disrupt and weaken the stemming zone or burden in adjacent holes, thereby increasing the risk of flyrock. However, if there is an influence of delay timing, it appears more likely that short delay times will promote flyrock rather than long delay times. Figure 15.3 shows a photograph taken from a movie of a blast, which contains different surface delay timing on each side of the control line. The control row for this blast in figure 15.3 contained 25 millisecond delays running down a center line of holes away from the camera. Initiations commenced at a center hole near to the camera (shown by arrow). Delay times extending out from the control line to the left were 65 milliseconds and 42 milliseconds to the right side of the control line. All holes contained the same charge configuration, and the image was taken close to the point of maximum surface expression. The image suggests that flyrock is likely to have a higher probability of appearance from the section of the blast where the shorter delay times were used than in the section with longer delays. It may be that delay timing affects more the probability of a flyrock incident than the actual projection velocities and maximum projection distances.

Roth (1979) also questioned the influence of delay timing, and even mis-timing, on the likelihood of producing flyrock. He also concluded that flyrock range is likely to be the same from multi-borehole blasts as it is from single borehole blasts, from which it can be concluded that shot size is not likely to have a strong influence over flyrock range. It would be prudent to consider every borehole in a shot as an independent, potential source of flyrock.

Importantly, powder factor is not always a reliable indicator of flyrock range or the probability of flyrock, as demonstrated by Roth (1979). The correlation reported by Lundborg (1975) must be viewed in the context of his cratering studies. In bench blasting, a high powder factor can still be achieved with a high degree of charge confinement, especially with respect to flyrock emanating from borehole collars. Reducing front row burden will certainly increase projection velocities from the vertical free face, though front row burden can be maintained relatively large while the burdens in subsequent rows are decreased in order to control this effect.

Estimating Maximum Projection Distance

While Figure 15.2 (Chiappetta et al 1997) provides a clear guide to the role of stemming length in controlling collar ejection velocities, it does not provide a quantitative relationship, since it does not relate velocity to scaled depth of burial. Gustafsson (1973) proposed an empirical equation for estimating maximum flyrock range as a function of charge diameter, as given by equation 15.10.

$$V_o = v_i \times \left(\frac{d}{n}\right) \times \left(\frac{d^2 \rho_e}{n^3}\right)^{0.105}$$ Equation 15.10

Where:

• $V_o$ = Initial projection velocity (meters/second)
• $d$ = Borehole diameter (inches)
• $n$ = Fragment size (meters)
• $\rho_e$ = Rock density (kilograms/meter³)

From equation 15.10 it is clear that the projection velocity is inversely proportional to the fragment size, i.e. small particles have a very high projection velocity and large particles have a relatively small velocity. Further, as rock density increases, the projection velocity decreases for a fixed particle size.

EXAMPLE 15.8

Calculate the worst case velocity of projection of a 2 inch size fragment from a 5 inch diameter borehole for a rock of density 2.11 tons/yard³. This worst case velocity only occurs for very poor charge confinement, corresponding to crater blasting and a metric SDOB at approximately 0.6 meters/kilogram^(1/3).

Step 1 Convert the fragment size in inches to meters by multiplying its size by 0.0254 as follows.

$n = 2 \times 0.0254$

$n = 0.051$

The fragment size is 0.051 meters.

Step 2 Convert rock density in tons/yard³ to kilograms/meter³.

$\rho_{(kg/m^3)} = \rho_{(tons/yd^3)} \times 1,187$

$\rho_{(kg/m^3)} = 2.11 \times 1,187$

$\rho_{(kg/m^3)} = 2,504.6$

The rock density is about 2,500 kilograms/meter³.

Step 3 Calculate the worst-case velocity of projection using equation 15.9.

$V_o = v_i \times \left(\frac{d}{n}\right) \times \left(\frac{d^2 \rho_e}{n^3}\right)^{0.105}$

$V_o = \frac{2,406}{1,211} \times \frac{2,500}{0.051}$

$V_o = 1,020$

The worst-case velocity of projection is 1,020 meters/second.

This velocity can be converted to velocity in miles/hour by multiplying by 2.24.

Although the initial velocity is extremely high, air resistance is also extremely high for small particles so that the velocity is quickly reduced.

McKenzie (2009) determined appropriate velocity coefficients for each of Lundborg's field observations for crater blasting, bench blasting, and projection velocities when stemming length approaches 40 times the hole diameter, and replaced Lundborg's maximum range equation 15.13 by a more general and fully metric equation which estimated the maximum range of flyrock for any degree of charge confinement as presented in equation 15.11.

$$Range_m = 11 \times SDOB_m^{-2.167} \times d^{0.667}$$ Equation 15.11

Where:

• $Range_m$ = Maximum flyrock range (meters)
• $SDOB_m$ = Metric scaled depth of burial (meters/kilogram^(1/3))
• $d$ = Borehole diameter (millimeters)

EXAMPLE 15.9

Calculate the maximum flyrock range for a 5 inch diameter borehole charged with a stemming length of 8 feet and a column of 30 feet of bulk explosive of density 1.2 grams/centimeter³.

Step 1

Convert stemming length to meters, borehole diameter to millimeters, and charge length, to meters as follows:

Stemming length conversion

$l_{meters} = l_{feet} \times 0.3048$

$l_{meters} = 8_{feet} \times 0.3048$

$l_{meters} = 2.4$

The stemming length is 2.4 meters

Borehole diameter conversion

$d_{mm} = d_{in.} \times 25.4$

$d_{mm} = 5. \times 25.4$

$d_{mm} = 127$

The borehole diameter is 127 millimeters.

Charge length conversion

$l_{meters} = l_{feet} \times 0.3048$

$l_{meters} = 30 \times 0.3048$

$l_{meters} = 9.1$

The charge length is 9.1 meters.

Since the charge length is greater than 10 times the borehole diameter, and the borehole diameter is greater than 100 millimeters (4 inches), then "m" = 10.

Step 2 Calculate the metric scaled depth of burial using equation 15.3.

$SDOB_m = \frac{l_s + 0.0005 \times m \times d}{0.00923 \times (m \times d^3 \times \rho_e)^{0.333}}$

$SDOB_m = \frac{2.4 + 0.0005 \times 10 \times 127}{0.00923 \times (10 \times 127^3 \times 1.2)^{0.333}}$

$SDOB_m = \frac{2.4 + 0.635}{0.00923 \times 289}$

$SDOB_m = \frac{3.035}{2.667}$

$SDOB_m = 1.14$

The SDOB is 1.14 meters/kilogram^(1/3).

Step 3 Calculate the maximum flyrock range for the charge configuration using equation 15.11.

$Range_m = 11 \times SDOB_m^{-2.167} \times d^{0.667}$

$Range_m = 11 \times 1.14^{-2.167} \times 127^{0.667}$

$Range_m = 210$

the maximum flyrock range is 210 meters.

This range is converted to feet by multiplying by 3.28.

Caution

Equation 15.11 does not imply that a blast will produce flyrock. Rather, it estimates the maximum range of flyrock if it occurs.

McKenzie (2009) showed that equation 15.11 reproduces all of Lundborg's observations and equations, providing Lundborg's crater tests could be described reasonably as having a scaled depth of burial of 0.6 meters/kilogram^(1/3) (1.5 feet/pound^(1/3)), and providing that what Lundborg described as "normal bench blasting" could be described reasonably as having a scaled depth of burial of 1.4 meters/kilogram^(1/3) (3.5 feet/pound^(1/3)). McKenzie (2009) further developed the general and fully metric equation provided for reference (So equation 15.12) to estimate the size of fragment, which would travel the maximum distance (assuming optimum projection angle).

$$n_o = 1.83 \times SDOB_m^{-1.63} \times d^{0.67}$$ Equation 15.12

Where:

• $n_o$ = Fragment size (millimeters)
• $SDOB_m$ = Metric scaled depth of burial (meters/kilogram^(1/3))
• $d$ = Borehole diameter (millimeters)

According to Chernigovskiy (1985), the weight of this fragment, $W_o$, is given by equation 15.13 for reference.

$$W_o = \frac{4}{3} \times n_o^3 \times \rho_r$$ Equation 15.13

Where:

• $W_o$ = Fragment weight (kilograms)
• $n_o$ = Fragment size (millimeters)
• $\rho_r$ = Rock density (grams/centimeter³)

Estimating Trajectories of Motion

There is a tendency within technical literature to use simple kinematic equations of motion (based on particle motion in a vacuum, or ignoring air drag effects) to describe the trajectories of flyrock fragments. It is a simple matter to demonstrate that rock fragments, which are projected more than a hundred meters or so, must have a launch velocity in excess of 50 meters/ second. McKenzie (2009) shows that even at modest flyrock launch velocities like 70 meters/second, the predicted maximum range when using kinematic equations of motion can be in error by a factor of at least 2, and by much greater factors for higher launch velocities. Furthermore, kinematic equations take no account of particle size (and therefore wind resistance), so that such models can give no insight as to the size and shape of fragments which might travel long distances. For these reasons, it is not recommended to use such models to predict flyrock trajectories, despite their classical known link to air drag, and which have been known to science for many decades. The same approach was adopted by St George & Gibson (2001), McKenzie (2009), and Little & Blair (2009).

Chernigovskiy (1985) published the following three equations of motion to describe particle trajectories through air at high velocities (provided for reference).

$$z = \left(\frac{V_o^2}{g}\right) \times \delta(t) \times V_x V_z$$

$$x = \left(\frac{V_o^2}{g}\right) \times \delta(t) \times V_x V_z$$

$$y = \left(\frac{V_o^2}{g}\right) \times \delta(t) \times V_x V_z$$

Where:

• $V_o$ = Projection velocity (meters/second)
• $t$ = Time after launch of the fragment (seconds)
• $g$ = Acceleration due to gravity (9.81 meters/second²)
• $n_o$ = Fragment size (meters)
• $\rho_r$ = Rock density (kilograms/meter³)
• $x$ = Distance measured along the line of the initial projection angle (meters)
• $y$ = Vertical distance measured from the line of initial projection (meters)

With numerical methods are required to solve these three simultaneous equations, the solution can be implemented in spreadsheets to construct the trajectories for any size of particle, for any projection velocity, and for any launch angle. Special search procedures are then required to find the particle size and launch angle, which produce the maximum fragment trajectory. At low projection velocity and relatively large fragment size (i.e. conditions of negligible air drag), the trajectories become the same as those calculated from simple kinematic equations.

Establishing a Safe Blast Area

Establishing a safe blast area involves evacuation of personnel to a distance beyond the maximum fragment projection distance. Lundborg et al (1975) were absolutely correct when they stated, "People must be protected against flyrock, no matter what the cost." Since reported flyrock projection distances have exceeded 1,000 meters (3,300 feet), the selection of a clearance distance must be carefully undertaken with full knowledge of the particular blasting application, recognizing that borehole charge configurations can change quite significantly in different parts of the blast. The use of a conservative distance to satisfy appropriate clearance distance for a fixed blasting practice (e.g. many mining operations), but will sometimes mean establishing a safe clearance zone that will sometimes involve evacuation to distance greater than what the scaled depth of burial says is needed (1.2 or greater) in relation to achieving an optimum blast.

Wherever operations have the flexibility to adjust clearance distances (e.g. blasting close to established housing or public passageways) the recommended procedure is to use the protection of the maximum projection range as the basis for determining maximum clearance distance. Clearly, this estimate must be conducted with full knowledge of the length of stemming and actual charge configurations in every borehole, and distance determined according to the particular charge configuration with the largest estimated projection distance. This is where blaster vigilance, and education and training of all shot crew, become particularly important.

Once the maximum projection distance has been calculated, an appropriate factor of safety must be applied. The need for a factor of safety is highlighted by Chernigovskiy (1985) in his "Caution" statement that the margin of fragment cannot be calculated with better than 20% accuracy below within the extent of initial velocity of projection if known that data(s) is rarely to be known. A minimum value for the factor of safety is therefore considered to be 150%, i.e. the clearance distance should be at least 1.5 times the calculated maximum fragment projection distance. The US Office of Surface Mining (Dick et al. 1989) prohibits facturing flyrock from their zone-half line distance to the nearest dwelling occupied structure regardless of direction, effectively demanding that a minimum Factor of Safety of 2 be used in the United States. Equation 15.14, a modified form of equation 15.11, is recommended for this application.

$$Clearance ; Dist = FoS \times 11 \times SDOB_m^{-2.167} \times d^{0.667}$$ Equation 15.14

Where:

• Clearance Dist = Minimum personnel clearance distance (meters)
• $SDOB_m$ = Metric scaled depth of burial (meters/kilogram^(1/3))
• $FoS$ = Dimensionless factor of safety (for which Dick et al. (1989) recommend a minimum value of 2.0).
• $d$ = Borehole diameter (millimeters)

The metric scaled depth of burial ($SDOB_m$) should be calculated for the borehole with the shortest stemming length.

EXAMPLE 15.10

Calculate the minimum personnel clearance distance for a blast containing boreholes of 5 inch diameter charged with a stemming length of 8 feet and 30 feet of bulk explosive of density 1.2 grams/centimeter³.

Step 1 Convert stemming length to meters, borehole diameter to millimeters, and charge length to meters as follows:

Stemming length conversion

$l_{meters} = l_{feet} \times 0.3048$

$l_{meters} = 8 \times 0.3048$

$l_{meters} = 2.4$

Stemming length is 2.4 meters.

Borehole diameter conversion

$d_{mm} = d_{in.} \times 25.4$

$d_{mm} = 5 \times 25.4$

$d = 127$

The borehole diameter is 127 millimeters.

Charge length conversion

$l_{meters} = l_{feet} \times 0.3048$

$l_{meters} = 30 \times 0.3048$

$l_{meters} = 9.1$

The charge length is 9.1 meters.

Since the charge length is greater than 10 times the borehole diameter, and the borehole diameter is greater than 100 millimeters (4 inches), then "m" = 10

Step 2 Calculate the metric scaled depth of burial using equation 15.3. Since the charge length is greater than 10 times the borehole diameter, and the borehole diameter is greater than 100 millimeters (4 inches), then "m" = 10

$SDOB_m = \frac{l_s + 0.0005 \times m \times d}{0.00923 \times (m \times d^3 \times \rho_e)^{0.333}}$

$SDOB_m = \frac{2.4 + (0.0005 \times 10 \times 127)}{0.00923 \times (10 \times 127^3 \times 1.2)^{0.333}}$

$SDOB_m = \frac{2.4 + 0.635}{0.00923 \times 289}$

$SDOB_m = 1.14$

The SDOB is 1.14 meters/kilogram^(1/3).

Step 3 Calculate the minimum personnel clearance distance for the charge configuration using 2.0 as per OSM requirements (Dick et al. 1989) using equation 15.14.

$Clearance ; Dist = FoS \times 11 \times SDOB_m^{-2.167} \times d^{0.667}$

$Clearance ; Dist = 2 \times 11 \times 1.14^{-2.167} \times 127^{0.667}$

$Clearance ; Dist = 420$

The personnel clearance distance is 420 meters. Note: To convert to feet, multiply by 3.28.

The clearance distance equations 15.14 applies only for the case where the sensitive target and the borehole collar are at the same, or similar elevations. The equations of motion can, however, be quite easily solved for the case where there is a significant positive or negative difference in elevations, or where a barrier of known height exists between the borehole collars and the sensitive target.

Where operations have limited ability to adjust clearance distances (e.g. blasting close to established housing or public passageways) the recommended procedure is to adjust the Scaled Depth of Burial until the maximum flyrock projection distance is less than the distance to the nearest sensitive target. Once again, an appropriate factor of safety should be applied to the stemming length or front row burden so that fragments cannot travel more than half (or less than) of the distance to the nearest sensitive receiver. McKenzie (2009) derived equation 15.15 for this purpose.

$$l_{s(min)} = 0.028 \times \frac{(m \times \rho_e)^{0.37} \times d^{1.208}}{\left(\frac{Dist}{FoS}\right)^{0.46}} - 0.0005 \times m \times d$$ Equation 15.15

Where:

• $l_{s(min)}$ = Minimum stemming length (meters)
• $d$ = Borehole diameter (millimeters)
• $Dist$ = Minimum distance to a sensitive receiver for any hole in the pattern (meters)
• $\rho_e$ = Effective explosive density (grams/centimeter³)
• $FoS$ = Dimensionless factor of safety (minimum value is, 2, as previously outlined)
• $m$ = Ratio of charge length to borehole diameter but has a maximum value of 8 for boreholes of diameter less than 100 millimeters (4 inches), and 10 for boreholes of diameter greater than or equal to 100 millimeters (4 inches)

Example 15.11

Calculate the minimum stemming length required to ensure that flyrock does not travel more than half of the distance to the nearest protected structure under the following conditions. A blast with 5 inch diameter boreholes and a 50 foot bench height is being conducted 600 feet from a house. The charge configuration used in each of the boreholes consists of a bulk loaded heavy ANFO charge of density 1.2 grams/centimeter³.

Step 1 Convert the borehole diameter to millimeters and the distance to the nearest protected structure to meters as follows:

$d_{mm} = d_{in.} \times 25.4$

$d_{mm} = 5 \times 25.4$

$d_{mm} = 127$

The borehole diameter is 127 millimeters.

$Dist_m = Dist_{ft.} \times 0.3048$

$Dist_m = 600 \times 0.3048$

$Dist_m = 183$

The distance to the nearest structure is 183 meters.

Step 2 Calculate the minimum stemming length for for the charge configuration by using a factor of safety of 2.0 as per OSM requirements (Dick et al. 1989), and substitute into equation 15.15.

$l_{s(min)} = 0.028 \times \frac{(m \times \rho_e)^{0.37} \times d^{1.208}}{\left(\frac{Dist}{FoS}\right)^{0.46}} - 0.0005 \times m \times d$

$l_{s(min)} = 0.028 \times \frac{(10 \times 1.2)^{0.33} \times 127^{1.208}}{\left(\frac{183}{2}\right)^{0.46}} - 0.0005 \times 10 \times 127$

$l_{s(min)} = \frac{35.9}{7.985} - 0.64$

$l_{s(min)} = 3.9$

The minimum stemming length is 3.9 meters. (Note: To convert to feet, multiply by 3.28).

With respect to the measurement of stemming length, various authors (Chiappetta, 1997, Stiemer, 2003) have suggested that soft soil or overburden in the collar region should not be included in the measurement of stemming length. The length of stemming used to calculate the scaled depth of burial should therefore be the length in rock of reasonable competence. Hence, if the top 0.9 meters (3 feet) of a borehole is in soft overburden material, and the blast design requires a stemming length of 2.4 meters (8 feet), then the depth measured from the borehole collar to the top of explosive should be 3.3 meters (11 feet).

The Human Factor

As in most processes, the Human Factor is often the weak link in the process of controlling flyrock. The main area in which human error can foil an otherwise good blasting outcome is in the quality control of charging, i.e. the design implementation. Quality control during charging becomes increasingly important the closer blasts are to sensitive structures. In such circumstances, it is not sufficient to simply count boreholes to list the sensitive receivers are located behind the free face. Stemming lengths (including any zone of unconsolidated soil or overburden) play a critical role in avoiding flyrock, requiring constant focus on the issues listed in table 15.3.

Table 15.3 - Flyrock control issues.

A simple statistical analysis of normal charging operations (e.g. measurement of stemming column length for a hundred or more boreholes) will always reveal error and variability in the length of stemming columns. Assuming a normal distribution of such errors, stemming lengths should be considered to have a mean value, $l_{avg}$ (hopefully close to the design value), as well as a standard deviation, $\sigma_l$. When estimating a nominal clearance distance, it is prudent to allow for normal levels of error in stemming lengths. Therefore, when calculating scaled depth of burial (See equation 15.16 provided for reference) in the above equations, users should use at least a 95 % value of the stemming length, $l_{95}$, which is exceeded by 98% of boreholes in the pattern.

$$l_{95} = l_{avg} - 1.64 \times \sigma_l$$ Equation 15.16

Where:

• $SDOB_m$ = Metric scaled depth of burial (meters/kilogram^(1/3))
• $l_{95}$ = 95th percentile of all the stemming lengths in the pattern (See below)
• $l_{avg}$ = Average stemming length (meters)
• $m$ = Ratio of charge diameter to charge length (as discussed above)
• $d$ = Borehole diameter (millimeters)
• $\rho_{eff}$ = Effective density of explosive (grams/centimeter³)
• $\sigma_l$ = Standard deviation of stemming lengths (meters)

A normal degree of variability in stemming length would be around 10%, i.e. if the design stemming length was 5 meters, the standard deviation of the errors in length is probably around 0.5 meters, and the value of stemming length used in calculating SDOB should therefore be approximately (5 - 1.64 × 0.5) = 4.2 meters, or 84% of the designed stemming length. This approach, combined with a minimum Factor of Safety of 1.5 applied to the calculated maximum projection distance, should permit calculation of an appropriate clearance distance, which guarantees the safety of all in the vicinity of the blast.

An excellent practice for blasters to introduce into everyday activities is that of video recording every blast, and carefully reviewing each blast from the perspective of retention of high-pressure gases. The ideal blast is one where no rock fragments are projected beyond the mass of moving and broken material, either from the collar regions or the free face. In areas where strict control over flyrock is critical, signs of localized energetic rock response should be treated as signals to review the Scaled Depth of Burial of the charge, review the quality control procedures during borehole charging, and increase stemming lengths or front row burden accordingly.

It must be remembered that if one borehole in a pattern is badly loaded, the safety of all in the vicinity is compromised. The failure in a blast which produces flyrock is set so much the error in charging which produced the flyrock, but the lack of awareness and failure to respond appropriately to the error by those in charge of loading and initiating the blast.

Flyrock Risk for Equipment

It is quite common that mining equipment or other valuable machinery is left inside the personnel clearance radius, and even inside the maximum flyrock projection zone. Large electric shovels and draglines, for example, are very slow to evacuate, and the time lost in moving to and from the working face can represent a significant loss in daily production. As a result, it is common to see personnel evacuation distances of the order of 500 meters, but equipment withdrawal distances of only 100 meters or 150 meters. Under these conditions, it is useful to have a tool by which the risk from flyrock can be quantified, and maintained constant for any type of blast. McKenzie (2009) proposed the concept of a "flyrock footprint" which can be a useful way to quantify risk. The "flyrock footprint" is formed by determining the maximum projection distance for all sizes of particles, for any specific charging configuration. The family of curves published by Lundborg et al (1975) proposed a family of footprints for crater blasting with different hole diameters, and an example is presented in figure 15.6 for a large scale mining operation using 311 millimeters (12¼ inch) diameter boreholes in very hard rock. The very hard rock has forced the mine operators to reduce stemming lengths to a minimum, so that maximum projection distances are quite large (450 meters or 1500 feet). The electric shovel, however, is only moved a maximum clearance distance of 200 meters, so that there is clearly a risk that fragments will strike the shovel. The boomerang shaped curve in Figure 15.6 shows the maximum projection distance for all sizes of rock fragments from 1 millimeter to 2 meters. No rock fragments can be above this curve. The dashed horizontal line represents the distance to which the shovel has been retracted.

Only fragments of size between S₁ and S₂ are capable of reaching the shovel, and of these, only the ones that also have the right trajectory. A measure of risk therefore becomes the ratio of the area bounded by the flyrock footprint and the horizontal equipment retraction line, to the total area of the flyrock footprint. While this does not represent the probability that the shovel will be hit, it is an indicator of that probability. Without knowledge of the number of rock fragments projected from each borehole collar, or the probability that a blast will produce flyrock, it is not possible to estimate the probability correctly.

Operations can therefore adjust equipment withdrawal distances according to different blast designs, while maintaining the flyrock risk factor constant. In the hard rock areas of the mine, it may be necessary to move the shovel 200 meters, but in the softer rock environments, where stemming volumes can be increased, it may be necessary to move the shovel only 100 meters, thereby reducing lost production time. In the context of risk to equipment inside the maximum projection radius, flyrock and its effect on excavation productivity becomes simply another blast design variable to be adjusted and optimized according to local conditions – which requires a reasonably sophisticated engineering-based model.

Technology Gaps

Unfortunately, the science associated with flyrock prediction is not well advanced. This places further emphasis on the blaster to be conservative, prudent, and to monitor carefully all blasts using a video camera with as high a resolution as possible. The influence of Deviations from Lundborg's limited trials in the 1970s is still not well understood or modelled.

Table 15.4 - Technology gaps in flyrock understanding.

References

Chernigovskiy, A.A. 1985. Applications of directional blasting in mining and civil engineering, chapter 4 Movement of flyrock subject to air drag. pp 91-100.

Chiappetta, R.F. and T. Treleven.1997. Expansion of the Panama Canal: Blasting Analysis International, Inc. (BAI) Proceedings of the 7th High-Tech Blasting Seminar: State-Of-the-Art Blasting Technology Instrumentation and Applications. July 1 – July 3, 1997. BAI, Allentown, PA.

Dick, R.A., L. R. Fletcher, D.V. and D'Andrea. 1989. Explosives and Blasting Procedures Manual, chapter 5, Environmental Effects of Blasting. USBM IC 8925; p. 14.

Gustafsson, R., 1973. Swedish Blasting Technique. SPI, Gothenberg Sweden.

Lundborg, N., PA. Persson, A. Ladegaard-Pedersen and R. Holmberg. 1975. Keeping the lid on flyrock in open-pit blasting. Engineering and Mining Journal, 31: pp 95-100. E & MJ, Jacksonville, FL.

McKenzie, C.K. 2009. Flyrock range and fragment size prediction, International Society of Explosives Engineers (ISEE) Proceedings of the 35th Annual Conference on Explosives and Blasting Techniques, February 8 – 11, Denver. CO. ISEE, Denver, CO.

Mine Safety and Health Administration (MSHA). Code of Federal Regulations, Title 30, MSHA, Washington, D.C.

Roth, J. 1979. A model for the determination of flyrock range as a function of shot conditions, United States Department of the Interior, Contract No. JO387242; OFR. pp 77-81.

Stiemer, V. A., 2003. Trench blasting patterns and pitfalls. Blasters' Training Seminar, February 1 – 2, Nashville, TN. International Society of Explosives Engineers, Cleveland, OH.

St. George, J.D., and M.F.J. Gibson. 2001. Estimation of flyrock travel distances: A Probabilistic Approach, Australasian Institute of Mining and Metallurgy (AusIMM) EXPLO 2001 Conference, pp. 409 – 415, Hunter Valley.