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Optimal blast fragmentation.

Good optimisation and control of blast fragmentation is of major importance for any mining operation.

What is good fragmentation? Frequently good fragmentation is described as that which produces rock fragments that are easy to dig and which will not require secondary blasting. However, recovery of valuable mineral does not stop with digging - fragmentation affects production in many other ways.

The cost and efficiency of crushing and grinding operations are seriously influenced by the outcome of blasting. The efficiency of heap leaching, for example, is influenced by the size distribution and mechanical properties of the ore on the leach pad. In quarrying, the quality of the final product is partly determined by the way which blasting is conducted. It is thus possible to define good blast fragmentation as that which will be most instrumental for increased profitability of the entire mining process.

One aspect of an industry-funded research programme, currently being undertaken by the Julius Kruttschnitt Mineral Research Centre (JKMRC) at the University of Queensland in Australia, has been the development of a software tool for the selection of blast design parameters that will produce a targeted optimal fragment size distribution.

Mechanisms of Blast Fragmentation

Whilst the degree of fragmentation is governed by the natural discontinuities within the rock mass, the properties of the rock matrix, the properties of the explosive and by the blast design, two other factors contributing to blast induced fragmentation need to be considered. First is the dynamic stress wave action, lasting several milliseconds, and which emanates from the detonating blasthole. Second is the quasi-static action of the high pressure gases generated during blasting.

Immediately after detonation the blast hole is filled with gaseous detonation products under very high pressure (several giga pascals) at high temperature. In the immediate vicinity of the blasthole, the pressure of these gases is sufficient to generate compressive stress in the rock generally higher than the compressive strength of the rock itself. This causes an annulus of rock surrounding the charge to be crushed and typically reduced to millimetre-size fragments.

Further from the blasthole, however, the propagating stress wave induces tensile stresses in the rock matrix, causing the propagation and coalescence of any naturally-occurring pores and cracks. This particular fragmentation process is further advanced by the action of the high pressure blast gases which penetrate into these cracks and further extend them. This so-called macroscopic blast fragmentation is assisted by the reflection of the stress wave from free surfaces within the rock mass.

Fragment size distribution is thus controlled by the extent of fracture propagation, coalescence and interaction of the propagating stress wave with any free surfaces, as well as the physical properties of the rock matrix. This inter-dependence is very complex and to date there is no complete theoretical solution for this problem. This is a primary reason for the popularity of less accurate, but, nonetheless, still useful, empirical models for prediction of blast size distribution. The most commonly used is the Kuz-Ram model (Kuznetsov, Cunningham, Lilly).

Kuz-Ram model of blast fragmentation

The Kuz-Ram model combines two semi-empirical formulas in order to predict fragment size distributions of blasted rock. A formula developed by Kuznetsov (1973) was used to predict the mean fragment size of the blasted rock, based on the use of TNT as the explosive. It was not until 1982 that Cunningham developed a more general formulation of the Kuznetsov equation suitable for other commercial explosives. Later, in 1987, Cunningham this model further to incorporate Lilly's concept, put forward the previous year, of blastibility index as a measure of the suitability of rock to be fragmented by blasting.

According to the Kuz-Ram model, the mean fragment size can be calculated by equation (1):

X = A x [(V/Q).sup.0.8] x [Q.sup.0.167] x [(E/115).sup.-0.633 (1)


X mean fragment size (cm)

A rock factor (an empirical constant deter mined from the rock density, strength and jointing)

V volume of the blasted rock ([m.sup.3])

Q mass of explosive per hole (kg)

E relative weight strength of explosive (ANFO = 100)

An estimate of the fragment size distribution is given by the Rosin-Rammler equation, which is a negative exponential function, in the form:

[R.sub.(x)] = 1 - exp (-[(X/[X.sub.C]).sup.n]) (2)


R proportion of the material passing screen of size X

X screen size (cm)

[X.sub.C] characteristic size (cm), (calculated from the mean size)

n index of uniformity

The index of uniformity is determined by the blast design and bench height, through equation (3), which includes hole diameter, burden, spacing, charge length, drilling accuracy and bench height:

n = (2.2 - (14 x (B/d)) x (1-(W/B)) x ([(1 + (R-1)/2).sup.0.5]) x (L/H) (3)


d Charge diameter (mm)

B Burden (m)

W Standard deviation of drilling accuracy (m)

R Spacing/burden ratio

H Bench height (m)

L Charge length (m)

An increasing coefficient of uniformity indicates a more homogenised fragment size distribution, with reducing volumes of oversize and fines fractions. Values of uniformity coefficient usually vary between 0.8 and 2.0.

Fragment size distribution is presented as a Rosin-Rammler function, of a form which is very similar to the equations describing the length of the intact blocks in the rock mass (Priest and Hudson, 1981). The probability of an intact length of rock being less than a specified size is given by equation (4):

[F.sub.(X)] = 1 - exp (-aX) (4)


a mean fracture density

X distance between cracks (m)

This equation indicates that the form of the Kuz-Ram fragmentation distribution curve is governed by the distribution of pre-existing fractures and discontinuities in the rock mass. Hence, the underlying mechanism of blast fragmentation, assumed within the Kuz-Ram model, is one of extension and coalescence of the pre-existing fractures due to the tensile stress field generated away from the blasthole.

However, this model does not take account of the mechanism of fragmentation caused by the compressive/shear failure of the rock matrix in the immediate vicinity of the blasthole. This is primarily the reason why Kuz-Ram model in its classical form, generally underestimates the proportion of fines (fragment sizes less than 10-20 mm) generated during blasting. For relatively hard rock, this introduced error is insignificant as the actual zone of rock compression during a blast is relatively small (one blast hole diameter or less), so the Kuz-Ram model performs well. However, for softer rock, where the extent of the compressive zone around the blast hole is much greater, it becomes necessary to-exercise caution when interpreting the results of fragmentation estimates, and to develop separate models for fines prediction.

The actual volume of fines produced is governed by the interaction between the mechanical properties of the rock matrix (UCS, Young's modulus, density) and the properties of the explosive. Fines are generated mainly close to the blasthole through the effect of the outgoing stress waves on the rock. This means that the form of the fines size distribution is not necessarily described mathematically by a negative exponential, but perhaps one that resembles the decay of the dynamic stress with distance, or one that correlates stress intensity with the spatial/temporal concentration of explosive energy or its derivatives.

As part of its ongoing work, the JKMRC is currently developing a blast fragmentation model which will take into account the compressive/shear mechanism of blast fragmentation, and will be able to predict the entire fragment distribution curve more accurately, irrespective of the mechanical properties of the rock matrix.

Optimal Blast Fragmentation

In order to design a blast that will deliver optimal fragmentation of the rock, it is necessary to consider blast fragmentation as the first element in the rock size reduction process. The products of blast fragmentation in a mining operation, after digging and hauling, will usually be fed to a primary crusher, followed by a secondary and tertiary crusher. Therefore, the optimal blast fragmentation, from the point of view the crushing circuit, will be that which will maximise throughput and minimise power consumption.

But, for some ore types, the optimal fragmentation distribution does not just rely on maximising throughput - the particle size distribution resulting from a blast can have serious implications for the market value of the final product. It is well known, for example, that iron ore fines (fragments smaller than 6.35 mm) are a less valued product than lump ore (fragments with size between 6.35 mm and 31.75 mm).

At the same time blasting needs to be conducted in a way which will minimise its negative side effects. In gold mining, for example, the extent of ore dilution is critical and blasting needs to be carried out in such a way that the mixing of ore and waste is minimised. Another important consideration is blast damage and its effect on rock stability - slope instability due to blast damage, for example, will clearly have an adverse affect on overall ore recovery. Therefore, any potential reduction in crushing and grinding costs may be more than offset by the increased costs associated with lower recovery or dilution.

Depending on the desired characteristics of the blast fragmentation and the type of ore, an optimal blast design could consume more or less explosive than is currently used in a particular mine or quarry. Thus, an optimal blast design could easily mean a more expensive blast per tonne of rock.

At this point, it is worth highlighting the range of costs involved in the fragmentation process. In a typical, well run, open pit gold mine the approximate costs are shown below:

Drilling and blasting                 A$0.3 - 0.4/t

Digging and hauling                   A$0.4 - 0.5/t

Crushing (primary, secondary,
SAG & ball mills)                     A$6.0 - 8.0/t

Thus, in a large open pit gold mine, the cost of rock fragmentation associated with blasting (drilling + blasting + digging + hauling) represents just 10-15% of the cost of fragmentation that occurs within the crushing plant. Clearly, even a significant increase in blasting costs associated with delivering an optimal feed to the crushing plant could be very easily justified by only a modest increase in the productivity of the crushing circuit.

Selection of the optimal blast design

Selection of the blast design parameters frequently starts with some 'rules of thumb', followed by fine tuning through a trial and error approach. The main parameters of blast design are bench height, blast hole diameter, burden between rows, spacing between blastholes along the row, subgrade, stemming and explosive properties. Bench height and blast hole diameter are generally predetermined by the local ground condition and available equipment.

Burden in front of a row can vary in the range 25 - 40 blast hole diameters. Spacing between holes could be between 1 - 2 burdens (25 - 80 blast hole diameters). Subgrade is typically in the range 8 - 12 blast hole diameters. Stemming is typically in the range 20 - 30 blast hole diameters.

Selection of explosive, meanwhile, is largely influenced by ground conditions. For dry ground, the explosive density (which strongly influences its blasting strength) can vary from 800 to 1,300 kg/[m.sup.3]. In wet ground, meanwhile, the density of available explosives typically varies from 1,100 to 1,300 kg/[m.sup.3]. Developments in explosives technology makes it possible to choose any explosives density within the given ranges.

Currently used trial and error approaches are largely influenced by the lack of technical communication between the engineer responsible for the blasting operation and the metallurgist responsible for the crushing plant. Assuming that information about the optimal fragment size distribution is available to the mining engineer, it is then possible to optimise a blast design that will produce a fragment size distribution as close as possible to a pre-determined target. Selection of the blast design is based on application of the Kuz-Ram model and minimisation of the error function, defined as the absolute difference between the targeted fragment size distribution curve and the modelled size distribution curve [ILLUSTRATION FOR FIGURE 1 OMITTED]. The modelled fragment size distribution curve is developed from values of blast design parameters and their inter-relationships, which are within the framework of normal blasting practice.

In this way, it is possible to eliminate the costly trial and error approach to blast design and to almost instantaneously predict an optimal blast design that will give a targeted fragment size distribution. Some fine tuning of the design may still be necessary, however, in terms of avoiding any side effects of the blast, such as design of the optimal initiation sequence which will be the most effective for prevention of dilution and negative environmental effects.
Table 1: Blasting parameters for a hypothetical iron ore mine

Size distribution

Size                        %
(cm)                     passing

6                           20
9                           40
15                          50
20                          60
40                          80

Rock characteristics

Young's Modulus          20 GPa
UCS                      30 MPa
Rock density             3,200 kg/[m.sup.3]
Jointing                 massive rock
Ground condition         Dry

Bench height             10 m
Blast hole diameter      229 mm

Hypothetical scenarios

When mining iron ore, the single most significant source of fines (material less than 6.35 mm in size) is blasting. For reasons of market value, as outlined above, it becomes very desirable, therefore, to minimise the amount of this size fraction in the final product.

Assuming that an optimal blast should produce a fragment size distribution as described in Table 1, based upon the rock characteristics shown, the model predicts that optimal fragmentation, closest to that targeted, can be achieved with the following blast design:
Table 1A

Bench height                      10.0 m
Stemming                           2.3 m
Burden                             2.9 m
Subdrill                           0.9 m

Drilling pattern               staggered
Spacing                            7.8 m
Blastholes diameter               152 mm

Explosive density     1,280 kg/[m.sup.3]
Powder factor          2.16 kg/[m.sup.3]

Explosive per hole              198.7 kg

Targeted and predicted fragment size distributions are shown in Figure 2.
Table 2A

Bench height                      10.0 m
Stemming                           5.7 m
Burden                             7.1 m
Subdrill                           2.1 m

Drilling pattern               staggered
Spacing                            7.8 m
Blastholes diameter               229 mm

Explosive density       840 kg/[m.sup.3]
Powder factor         0.403 kg/[m.sup.3]

Explosive per hole                223 kg

In contrast to the preceding example for a hypothetical iron ore blast, the optimal fragment size distribution when blasting gold ore should have a large of small fragments (less than 20 mm in size) in order to maximise the productivity of the crushing plant.

Under the conditions defined in Table 2, the predicted distribution will be produced by the blast designshown in Table 2A.


Blasting is not a self serving exercise, but an integral part of the process which produces a marketable product. Although blasting is the cheapest method of rock fragmentation, and crushing and grinding among the most expensive, substantial improvements in profitability of a mine can be achieved by tuning blasting designs to produce a fragment size distribution as close as possible to the optimal for downstream processing. Therefore, blasting objectives and benchmarks should be set by a team consisting of people responsible for both mining and mineral processing.
Table 2: Blasting parameters for a hypothetical gold mine

Size distribution

Size                        %
(cm)                      passing

2                           20
6                           40
8                           50
10                          60
15                          80

Rock parameters

Young's Modulus        100 GPa
UCS                    120 MPa
Rock density           2,750 kg/[m.sup.3]
Jointing               massive rock
Ground condition       Dry

Bench height           10 m
Blast hole diameter    152 mm

The developed fragmentation model and methodology, although far from perfect, are sufficiently good to design a blast that will fragment the rock in a way more suitable for downstream processing. It should be noted, however, that whilst the cost of blasting and digging may increase in some instances relative to the current practice, the total cost of production of the milled product will be lower.


Cunningham C.V.B. The Kuz-Ram model for the prediction of fragmentation by blasting. 1st International Symposium on Rock Fragmentation by Blasting, Lulea, Sweden, 1983, 439-454.

Cunningham C.V.B. Fragmentation estimations and the Kuz-Ram model - four years on. 2nd International Symposium on Rock Fragmentation in Blasting., Keystone, Colorado, USA, 1987, 475-487.

Priest S.D. & Hudson J.A. Estimation of discontinuity spacing and trace length using scanline surveys. International Journal of Rock Mechanics, Science & Geomechanical Abstracts, Vol. 18. 1981, 183-197.

Kuznetsov V.M. The mean diameter of the fragments formed by blasting rock. Soviet Mining Science, 1973, V9, 144-148.

Lilly P.A. An empirical method of assessing rock mass blastability. The Aus. IMM/IE Aust. Newman Combine Group, Large Open Pit Mining Conference, 1986.

JKMRC Mine-to-Mill Research Group. Optimisation of mine fragmentation for downstream processing. First progress report. Submitted to Australian Mineral Industries Research Association, 1997.
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Author:Djordjevic, Nenad
Publication:Mining Magazine
Date:Feb 1, 1998
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