2.2.1. Qualitative assessment

An early blastability classification was proposed by Aleksandrov et al. (1963) which was presented in Mosinets et al. (1967). This qualitative assessment scheme was developed based on field inspections and qualitative assessments of several blasting outcomes at the Kal'makyr mine, in the former Soviet Union. Kal'makyr mine is located in the east of Uzbekistan, in Tashkent Province, and is among the largest copper reserves in the world. The blasts, considered in the development of this classification, aimed at obtaining good rock breaking to achieve continuous operation. Aleksandrov’s blastability classification is also known as the Central Research Institute’s (CRI) classification. According to the CRI classification, rock masses may be classified into:

Category I: Easily blasted: small blocks, strongly fractured, with average discontinuity spacing around 0.15 m. This can be interpreted as providing a finer fragmentation for a given specific charge or requiring a smaller specific charge to obtain the desired fragmentation.

Category II: Medium ease of blasting: medium size blocks with average discontinuity spacing around 0.5 m. This may also be interpreted as providing a medium fragmentation for a given specific charge or requiring a medium-specific charge to obtain the desired fragmentation.

Category III: Difficult blasting: Large blocks of rocks with average discontinuity spacing over 0.5 m. This can also be considered as resulting in a coarse fragmentation for a given specific charge or requiring a considerably large specific charge to obtain the desired fragmentation.

However, this qualitative classification suffers from a few drawbacks, e.g., soft sedimentary rocks, like potash without discontinuities or hard jointed igneous rocks may result in different fragmentation when identical blast set up is used. The behaviour of rocks in blasting may not simply be classified based on the spacing of discontinuities. The classification approach is also subjective to personal judgment and the interpretation of the distance between discontinuities in a rock mass. The joint network can form blocks with different sizes with a specific particle size distribution, (PSD), which is also known as the in-situ block size distribution (IBSD). Additionally, this approach is only applicable to areas where rock discontinues are visible. Differentiation between the blast-induced cracks, caused by the firing of the previous rounds of blasting, and the natural discontinuities may also not be straightforward. In other words, the pre-conditioning of the rock mass by the previous blast rounds should be identified and considered.

2.2.2. Quantification using powder factor and energy

Sukhanov (1947) proposed using the powder factor, q (kg/m3), as a qualitative characterisation of the blastability of a rock mass for fragmentation design and developed a series of standard test conditions for this purpose (Sukhanov, 1947; Sukhanov and Kutuzov, 1967). Rocks were divided into sixteen classes according to the powder factor, that is needed to achieve the desired fragmentation, and a few other blast design factors. If the powder factor is high, the rock is more difficult to fragment, otherwise it is easy to blast. A series of correction factors were proposed to adjust the powder factor for non-standard conditions; however, these have proved cumbersome to use in practice. The classification also involves considerable levels of personal interpretation. Gokhale (2010) also reported on the work performed by researchers in the Soviet Union, e.g., Kutuzov (1979), to improve these qualitative categorisation schemes by including factors like the intact rock strength, rock density, and average joint spacing, Sj-av in (m). Typical examples of the powder factors needed to fragment the rocks for different rock types have been tabulated in

The complexities of defining blastability in terms of a powder factor without understanding the fragmentation outcomes are indicated by the very different suggested powder factors for the same compressive strength between data for surface coal mines in Turkey (Muftuoglu et al., 1991) and the powder factors predicted by Mohamed et al. (2015) (see Fig. 1) and Table 3 (Gokhale, 2010).

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Fig. 1

Table 3. Powder factor estimation based on rock strength, rock density, and joint spacing (Gokhale, 2010).

Powder factor (kg/m3)		Sj-av (m)	σc (MPa)	ρr (kg/m3)
Range	Average
0.12–0.18	0.150	<0.1	10–30	1400–1800
0.18–0.27	0.225	0.10–0.25	20–45	1750–2350
0.27–0.38	0.320	0.20–0.50	30–65	2250–2550
0.38–0.52	0.450	0.45–0.75	50–90	2500–2800
0.52–0.68	0.600	0.70–1.00	70–120	2750–2900
0.68–0.88	0.780	0.95–1.25	110–160	2850–3000
0.88–1.10	0.990	1.20–1.50	145–205	2950–3200
1.10–1.37	1.235	1.45–1.70	195–250	3150–3400
1.37–1.68	1.525	1.65–1.90	235–300	3350–3600
1.68–2.03	1.855	>1.85	>285	>3550

To expand the range of parameters considered in estimating the powder factor, Lilly (1986) proposed a linear relationship between the powder factor needed to fragment iron ore rocks and a blastability index (BI). The blastability index depends on the characteristics of the discontinuities in the rock mass, the strength, and the density of the intact blocks of rocks. The powder factor, q, (kg/m3), can be estimated by:$q=a_1\times \mathit{BI}+b_1$where a1 and b1 are empirical coefficients depending on the diameter of the blast hole and the bench height.

Lilly’s blastability index was initially developed to classify all the rock mass types present in the iron ore mines of the Pilbara area in northwest Western Australia. The index has a maximum value of 100 which reflects the characteristics of the heavily massive and hard, iron-rich cap rocks, in the area with a specific gravity of about 4.0 (tonne/m3). The blastability index could also successfully classify the soft friable shales with indices around 20 or less in the area (Lilly, 1986).

The hardness parameter, Hr, incorporates the effect of strength using (Lilly, 1992):$H_r=0.05\times {\sigma }_c$where σc is the uniaxial compressive strength of rocks (MPa).

It is also noteworthy that the BI factors are highly weighted towards the nature and orientation of the widely spaced joint planes. The index attempts to account for the directional effects though the JPO factor, though in highly jointed rock masses it can be challenging to determine which joint set forms the major plane of weakness. A further complication is the large, discrete change in BI for a small change in the parameters of a rock mass. A typical example could be two separate jointed rock masses with identical strength and density. The joint spacing in the first one is 1.0 m while in the second it is 1.1 m. The parameter JPS changes sharply from 20 to 50 which consequently results in a significant difference between the blastability of these two rock masses.

Lilly (1992) also produced a series of design charts (e.g., see Fig. 2 an example of these charts) for estimating the blast patterns (Burden × Spacing) and powder factors for various blasthole diameters. The design charts are for three different bench heights of 5 m, 8 m, and 10 m. The blasthole diameters are also assumed to be 76 mm, 89 mm, 102 mm and 114 mm. It is also assumed that the fragmentation is predictable based on Kuz-Ram model (see Section 2.2.3 and Eq. 9) and %95 of materials shall pass an 800 mm grizzly. It is also assumed that blastholes are vertical, and blasts are drilled in a triangular pattern with (S = 1.16×B), sub-drilling is also assumed to be 8 times the blasthole diameter, and stemming is set to burden size. Anfo was also considered as the charge for the blastholes and it is expected that the initial sequence can provide adequate burden relief and material movement.

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Fig. 2

Similarly, Fig. 3 also shows the application of Bickers et al. (2002) modified BI (see Section 3.3.2 and Fig. 16) to predict the holes standoff and linear charge concentration kg/m in the wall to limit damage from trim blasts in an open-pit iron ore mine in Australia.

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Fig. 3

A proper characterisation of rock mass blastability is needed to use the controllable factor in a way to minimise the undesirable consequences of blasting, such as the ground vibration due to blasting or fly rock (Müller (1997). This means that achieving a good fragmentation and minimising the ground vibration and flyrock are not independent objectives. High ground vibrations can be related to the blastability in terms of the acoustic impedance of the rocks, Ir (kg/m2sec), and this is compounded by the excessive volume of the blast generated gases (see Fig. 13, Fig. 4). Instead of the powder factor, an empirical parameter known as the specific blasting effect, Sg, which is linked to the impulse per unit blast volume (Ns/m3) was proposed, which is defined as (Hohlfeld and Muller, 1999):$S_g=\sqrt{\frac{Q_e{R}_v{Q}_{\mathit{eh}}{\rho }_e{A}_b{R}_f}{I_r{A}_r{A}_f{t}_b}}$where Qe is the total mass of the charge (kg), Rv is the ratio of the explosive volume to the borehole volume, Qeh is the heat of the explosion (J/kg), ρe is the density of the explosive (kg/m3), Ab is the surface under stress in the total blast installation (m2). Additionally, Rf denotes the fragmentation ratio, and Ar is the remaining face surface of the total blast installation (m2). Furthermore, Af shows the free surface of the total blast installation (m2), and tb indicates the delay time of the total blast installation (s).

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Fig. 4

The complete description of these parameters can be found in (Hohlfeld and Muller, 1999; Müller, 1997; Müller and Hohlfeld, 1997). The correlations between the specific charge effect, fracture frequency, loosening and fragmentation of rocks, and ground vibration are shown in Fig. 4.

As can be seen in Fig. 4, low levels of loosening and fracturing often occur in smooth blasting which has a small specific blasting effect. By increasing the distribution of charge, the disintegration and fragmentation of the rock mass as well as the specific blasting effects increase. If the specific blasting effects exceed a threshold, which is around 50 Ns/m3, the risks of flyrock increase and must be considered in the blast design. The interrelationships between blast design, site characteristics, and the rock fragmentation, ground vibration, and flyrock could be very complex. Interestingly enough, Müller (1997) mentioned that an increase in the specific blast effect is associated with a decrease in ground vibration. He stated that overcharged blasts with Sg > 50 Ns/m3 yield a smaller vibration effect but impose a much higher risk of flyrock (Müller, 1997).

2.2.3. Fragmentation size prediction

If it is possible to predict the fragmentation caused by a certain set of controllable blast inputs as per Eq. 1, then an inversion will enable the designer to identify the correct design for the desired blast fragmentation size or distribution. Numerous investigations were undertaken by Protodyakonov in the former Soviet Union, over 100 years ago (1909 to 1926), to develop a quantitative approach to analyse the strengths of rocks for different mining applications (Protodyakonov, 1962a, Protodyakonov, 1962b) (See Section 3.1.1). Kutuzov et al. (1974) also reported on some of the old research performed by Protodyakonov for estimating the powder factor based on rock strength/hardness. Since Protodyakonov’s test estimates the amount of fines for a given impact, the approach was also applied by Kuznetsov (1973) to estimate the mean size of the fragmentation generated by the firing of a blasthole. The mean fragment size (cm) is linearly related to the rock factor, AK, and can be estimated as:$x_m=A_K{\left(\frac{V}{Q_e}\right)}^{4/5}{Q}_e^{1/6}$where AK is the rock mass blastability, Qe is the mass of the explosives (kg), and V is the volume of the rock mass (m3). Fragmentation prediction was developed further in the Kuz-Ram approach by including the particle size distribution, Rx, in the form of an adapted Rosin-Rammler (Rosin and Rammler, 1933) equation (Cunningham, 1983, Cunningham, 2005) so that:$x_m=A_{K-R}{q}^{-0.8}{Q}_e^{1/6}{\left(\frac{\mathit{RWS}}{115}\right)}^{-19/30},R_x=\mathit{exp}\left(-0.693{\left(\frac{x}{x_m}\right)}^n\right)$where AK-R is the Kuz-Ram rock factor, RWS is the relative weight strength of the explosive with respect to ANFO (in percent). Rx is the mass fraction retained on the screen opening x, xm was defined as the mean fragment size (cm) and n is the uniformity index (ranging between 0.7 and 2). Notably, the Rosin-Rammler uniformity coefficient, n, depends on burden B (m), spacing S (m), bench height H (m), hole diameter (mm), standard deviation of drilling precision W (m), charge length L (m), bottom (BCL) and column (CCL) charge lengths (m) and is independent of the rock mass factor.

Later, a modified version of Lilly’s blastability factor BI (see Eq. 4) was included by Cunningham (1987) to replace the Kuznetsov index AK so the Kuz-Ram rock factor AK-R is 0.12BI. The model has been updated and modified many times (e.g., by Cunningham (2005) and Gheibie et al. (2009)). Reviews of these modifications can be found elsewhere (Ouchterlony and Sanchidrián, 2019; Sanchidrián and Ouchterlony, 2017a). However, for this review, it is important to note that Cunningham (2005) added a blastability calibration factor C(A) that varied between 0.5 and 2.0. A variation between -50 % and +100 % implies that the index does not quantitatively predict the contribution of the rock mass. Additionally, Cunningham (2005) modified the uniformity by a factor to produce a more uniform fragmentation in harder rocks with AK-R > 6. Therefore, the rock factor and the uniformity index in the Kuz-Ram model (see Eq. 9) were amended as:$A{\prime }_{K-R}=A_{K-R}C\left(A\right),n\prime =n\left(B,S,H,d,W,L,\mathit{BCL},\mathit{CCL}\right){\left(A_{K-R}/6\right)}^{0.3}$where B, S, H, d, W, L, BCL, and CCL refer to burden (m), spacing (m), bench height (m), hole diameter (mm), the standard deviation of drilling precision (-), charge length (m), bottom charge length (m), and column charge length (m), respectively. An alternative and convenient, blastability index was developed for copper and gold mines and proved to be valid for iron ores in Australia (Scott, 1996, Scott, 2017; Scott et al., 2006) using a multiplicative approach where the blastability is modified by a series of factors. The equivalent Kuz-Ram rock factor, AK-R, can be estimated (Scott and Onederra, 2015a) as:$A_{K-R}=11.5\times \left(\text{Strength Factor}\times \text{Structure Factor}\times \text{Density Factor}\right)-1$

The strength factor, density factor, and structure factor are shown in Fig. 5 and Eqs (16), (20), (31).

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Fig. 5

Subsequently, a substantial number of similar models have been presented in attempts to accurately predict the fragmentation of rocks after blasting. In particular, Ouchterlony and his teams at the Lulea University of Technology in Sweden and the University of Leoben in Austria; and Sanchidrián and co-workers at the Polytechnic University of Madrid, in Spain, have devoted considerable efforts to developing methods for the reliable estimation of blast-induced particle size distributions. The development of the Swebrec model (also known as the KCO model) (Ouchterlony, 2005; Ouchterlony et al., 2006), the fragmentation-energy fan, FEF, model (Ouchterlony et al., 2017; Segarra et al., 2018), and the distribution-free, DF, (also known as xp-Frag) model (Sanchidrián and Ouchterlony, 2017a, Sanchidrián and Ouchterlony, 2017b) are among the main achievements of these investigations. Further information on the various fragmentation prediction models can also be found in relevant reviews (Ouchterlony and Sanchidrián, 2019; Sanchidrián et al., 2012; Sanchidrián et al., 2014). Here, the scope of this study is not to review all the fragmentation prediction models but to identify the key geological and geotechnical factors controlling the mechanisms of rock fragmentation. The applicability of the existing blastability assessment approaches, for the development of 3D distribution of blastability models for differential blasting input to Grade Engineering, is also investigated.

3.1.1. Protodyakonov’s impact hardness/strength index

Protodyakonov and his son (Protodyakonov, 1962a, Protodyakonov, 1962b) developed a blastability assessment known as the rock sturdiness or crushing strength method, which is often referred to as Protodyakonov’s hardness or strength index f (which is shown by fp in this study) (Protodyakonov, 1981). The index is defined as the volume of -0.5 mm fines in a specific container produced by a given number of blows of a known weight and uses units of cm-3. The details of the experimental method can be found in the relevant literature (Brook and Misra, 1970; Protodyakonov, 1962b). Protodyakonov’s strength index has been widely used in rock mechanics and mining applications (Aldorf and Exner, 1986) and has been applied to the assessment of the blastability of rock masses (Protodyakonov, 1981; Zou, 2017).

The values of the blastability parameter AK-R vary, from 7 for rock of medium hardness (fp = 8 to 10), though 10 for hard fissured rock (fp = 10 to 14), and up to 13 for hard and slightly fissured rock (fp = 12 to 16) (Faddeenkov, 1974; Kuznetsov, 1973). Although some efforts were made to explore the applications of Protodyakonov’s method during the 1970s (Brook, 1977; Brook and Misra, 1970), the method was mainly employed in Russia, Eastern Europe, and the countries that used to be a part of the Soviet Union. For example, Baron (1968) tried to relate the size of the crater developed around a blast hole to fp. Additionally, Makhin and Karchevskii (1965) showed that the specific expenditure of explosives, which is defined as the mass (kg) of explosives needed to generate one square meter of the new fracture surface, is directly proportional to the Protodyakonov’s rock strength index. Several revised applications of Protodyakonov’s rock strength index in blast design have also recently been proposed in (Eremenko, 2017; Zairov et al., 2018).

3.1.2. Specific surface energy index

Michik and Dolgov (1966) preferred the specific energy of rock samples after blasting, Es, as being better related to the amount of fracturing energy per unit area of newly formed surfaces. A calorimetric technique was used to determine the surface energy, Es (kg.m), which was defined as (Michik and Dolgov, 1966):$E_s=E_b-E_c$where Eb is the whole energy emitted during the blast, Ec is the proportion of the explosive energy passing to the calorimeter in the form of heat. It is also noted that, in these tests, Michik and Dolgov (1966) used spherical charges of PETN weighing 0.70 or 1.20 gr, and the heat emission capacity of the PETN, was recorded to be around 6.276 MJ/kg. The cylindrical rock samples prepared for the tests had 21 cm3 volume and a central hole was embedded in the middle of the samples for the insertion of charges.

The specific surface energy, SEs (kg.m/m2) is then defined as:${\mathit{SE}}_s=E_s/A_{\mathit{fr}}$

The surfaces area of the freshly created fragmented particles, Afr (m2), can simply be estimated as:$A_{\mathit{fr}}=\frac{6V_{\mathit{fr}}}{x_m}$where Vfr is the volume of the broken rocks (m3) and xm is the mean size of the rock fragments (m) (Michik and Dolgov, 1966).