PAPERS OF GENERAL INTEREST

 

A model to calculate blasting costs using hole diameter, uniaxial compressive strength, and joint set orientation

 

 

A. Ghanizadeh Zarghami^I; K. Shahriar^II; K. Goshtasbi^III; A. Akbari^IV

^IDepartment of Mining Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
^IIDepartment of Mining Engineering, Islamic Azad University of Tehran Central, Iran
^IIIDepartment of Mining and Metallurgy Engineering, Amir Kabir University, Iran
^IVDepartment of Mining Engineering, Faculty of Engineering, Tarbiat Modares University, Iran

 

 

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SYNOPSIS

Calculation of the blasting costs plays a significant role in blast pattern design and reduction of the final extraction cost of minerals. Blasting costs include drilling costs, blasting materials costs, and additional costs of blasting operations. We assessed information from three copper mines in Iran, and found that there is a significant relationship between blasting costs and hole diameter. A relationship was derived to calculate blasting costs per cubic metre as a function of hole diameter, bench height, uniaxial compressive strength, joint set orientation, the cost of drilling, and the unit cost of explosives. This model will enable engineers to estimate blasting costs prior to designing the blast pattern. Based on the model, an increase in the rock strength and the angle between the bench face and the main joint set will increase the blasting cost. On the other hand, the costs will decrease when the hole diameter increases for every range of uniaxial compressive strength.

Keywords: Blasting cost, hole diameter, uniaxial compressive strength, joint set, Iran copper mines.

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Introduction

Reduction of the operating costs is of great importance with respect to the final costs of the product. The ability to estimate blasting costs before designing blast patterns enables design engineers to choose suitable blast-hole diameters and other crucial parameters of the blast design (Ghanizadeh Zarghami, 2005). Specific charge and specific drilling are two substantial factors concerning blast pattern design that influence blasting costs (Ghanizadeh Zarghami et al., 2017). The hole diameter is generally regarded as a crucial parameter in designing blast patterns (Ostovar, 2013). In the same vein, this study, proposes several models to estimate blasting costs as a function of hole diameter and other parameters, including uniaxial compressive strength (UCS).

 

Research objective

Blasting models have been formulated by applying technical and economic information on blasting operations at three large copper mines in Iran, namely Sungun, Miduk, and Chah-Firouzeh (Figure 1), After determining the hole diameter and rock uniaxial compressive strength, it will be possible to calculate blasting costs for these three mines and similar operations.

 

 

Various investigations have been conducted with the aim of reducing blast operation costs. Afum and Temeng (2014) explored various parameters affecting drilling cost and blast optimization in a gold mine in Ghana. At this mine, blasting was done in three different blocks. The blasting and crushing costs were affected by parameters such as the ground conditions and blast pattern. The model was employed in order to regulate the costs by testing suggested patterns. The results indicated a decrease of between 5.3 and 12.2% in ore costs and between 2.9 and 14.8% for waste costs.

Adebayo and Akande (2015) investigated the effects of drilling in terms of blast-hole deviation and muck-pile loading costs for six scenarios at Hwange Colliery, Zimbabwe. The study showed that the drilling and operational costs were in the range of US$0.13-7.53 per m3. Ancillary costs of drilling increased from US$1.7 to US$4.2 per m3 with an increase in blast-hole deviation from 7% gradient to 21%.

Adebayo and Mutandwa (2015) evaluated the relationship between blast-hole deviation, fragment size, and fragmentation cost. The use of ANFO, heavy ANFO, and emulsion explosives in holes 191 mm and 311 mm in diameter was compared using six scenarios. The results showed that as blast-hole deviation increases the mean fragment size decreases and the cost of drilling and blasting increases. Increasing the hole diameter from 191 mm to 311 mm increased the blast fragmentation.

Nenuw and Jimoh (2014) designed and optimized the blasting parameters to reduce the damaging effects and blasting costs by using Langfors and other common blast formulae. In this study, which was conducted at four mines, parameters such as burden, spacing, bench height, hole diameter, the number of holes, bottom charge, and total charge per hole were examined and the planned and actual costs calculated. The actual costs of blasting material were higher than the calculated cost, which required modification and revision.

Cunningham (2013) investigated four key parameters that determine the ability to design an effective blast in terms of delay timing and cost. These parameters included heave control and monitoring, hole diameter, and explosive type.

Strelec, Gazdek, and Mesec (2011) designed an optimized blast pattern to reduce drilling costs. The blast fragmentation was optimized by applying the calibration factors in the Kuz-Ram model.

Eloranta (1995) showed, by comparing the loading costs of materials to the blasting costs, that due to the increase in specific explosive charge in large-diameter holes, the blasting costs have a strong inverse correlation with the specific explosives charge. Increasing the specific explosives charge by 15% increased the shovel and crusher efficiencies by 5%, resulting in an overall reduction in operating costs.

 

Blasting blocks information

More than 4600 records of blasting operations at Sungun, Miduk, and Chah-Firouzeh from 2012 to 2014 were collected. Incorrect and unreliable records were deleted and finally, 2414 blasts with limited back break, air blast, ground vibration, oversize, and destructive effects were selected. Basic information on the blasting operations, including drilling costs, blasting material, and blast block geometry for the three mines is shown in Table I (Ghanizadeh Zarghami, 2017).

 

 

In Table I, the mines are categorized according to rock strength. The drilling cost per metre is considered according to the contractor price, and the cost for ANFO is based on the purchase price, transport, and delivery to the mine. The types of rocks blasted are shown in Table II.

 

 

The choice of effective parameters

The large number of factors and the complicated iterations make it impossible to determine the theoretical consumption of explosives at the present level of development in blasting theory. Thus, recourse is made either to practical data or to empirical formulae that generalize blasting practice in application to drifting (Pokrovsky, 1980). In the present research, four important parameters: hole diameter, UCS, joint set orientation, and bench height were selected for calculating blasting cost. These parameters could be easily calculated by the engineers and ultimately aid in estimating the blasting costs.

 

Blasting pattern and cost calculations

The correct ratios between the geometric parameters of blasting patterns and hole diameter in the UCS range between 10 and 250 MPa and for the angle between the bench face and main joint set (y) <90° and >90° were extracted from the blasting databases at the respective mines. These ratios are presented in Tables III and IV. In the same UCS range, more energy is required when y is greater than 90° because the joint set dips in the opposite direction to the free face direction. Therefore, the specific charge and specific drilling, and blasting costs are higher for y>90° than for y<90° (Ghanizadeh Zarghami, 2017).

According to the rules of block theory, the angle between the bench face and the main joint set is important. This angle is located between the two normal vectors of the planes. In other words, y is the same angle between the two planes and it is a necessary factor for writing the equation of plane, dip, and dip direction of the plane. The dip and dip direction of the main joint set and bench face are of importance to present the equation of their plane. Equation [1] demonstrates the plane equation and Equation [2] represents the coordinates of normal vector through dip and dip direction (Dehghan, 2001). Figure 2 shows the layout of the angles and plane.

 

 

In Equation [2], a indicates the dip and ß represents dip direction relative to north. Equation [3] is used to measure the angle between the two planes (y).

 

 

All blasting costs were modelled in the Comfar technical and economic analysis software and the cost per cubic metre broken was calculated. As presented in Table V, 87% of the blasting operation costs depends on the cost of ANFO and drilling costs. Equation [4] shows the cost of blasting operations according to specific drilling, specific charge, the price per kilogram of ANFO, and drilling cost per metre (Ghanizadeh Zarghami, 2017).

In Equation [4], parameter C₁represents ANFO cost, C₂ represents drilling cost, BC represents blasting cost per cubic metre, P_Athe price of ANFO per kilogram, P_Dthe price of drilling per metre, SC the specific charge (kg/m3), and SD the specific drilling (m/m3).

Tables VI to IX show the burden, spacing, stemming, and sub-drilling considering the rock strength with y<90° and y>90°. At the studied mines, hole diameters of 6 to 6.5 inches are used. The burden parameter, spacing, stemming, and sub-drilling in zone classification of UCS were calculated according to joint set orientation with a hole diameter of 6 inches (152.4 mm).

 

Discussion and review

Factors in the blasting operation costs include blasting material costs and auxiliary costs such as staff wages, transportation, storage, and overhead costs. The bulk of the costs includes the blasting costs and consists of the drilling costs and the cost of ANFO. Finally, considering the contractor costs, the blast side cost was equal to 15% of the total cost.

The cost of drilling operations and consumed specific costs were calculated through burden, spacing, stemming, and sub-drilling. Parameter calculations and the operational costs in rocks with UCS of 10 to 70 MPa and hole diameters of 2 to 16 inches are presented in Table X, for y<90°.

According to Table VI, for y>90°, the same calculations were carried out based on Table X, the results of which, along with the results of calculations for y<90°, are shown in Figure 3.

For other rock strengths in the three mines, the tables of calculated blast parameters and diagrams are presented together. Table XI lists the parameters and blasting costs in rock with a strength of 70-120 MPa and with hole diameters of 2 to 16 inches.

According to Table VII, for y>90°, the same calculations were carried out based on Table XI, the results of which, along with the results of calculations for y<90°, are shown in Figure 4.

Table XII shows the parameters and blasting costs in rock with the strength of 120 to 180 MPa and hole diameters of 2 to 16 inches.

According to Table VIII, for y>90°, the same calculations were carried out based on Table XII, the results of which, along with the results of calculations for y<90°, are shown in Figure 5.

Table XIII shows calculations of parameters and blasting costs in rock with strength between 180 to 250 MPa and hole diameters of 2 to 16 inches.

According to Table IX, for y>90°, the same calculations were carried out based on Table XIII, the results of which, along with the results of calculations for y<90°, are shown in Figure 6.

 

Results of reviews

According to the research and the proposed models shown in the previous section, the relationship between the hole diameter and specific charge, specific drilling, and blasting costs for bench heights of 15 m in y<90° and y>90° are determined. The results are presented in Table XIV for the range of UCS considered.

Equation [5] shows the general equation of blasting cost, which is derived to calculate the blasting cost according to the hole diameter. In this equation, coefficients 'a' and 'b' are functions of bench height, UCS, join set orientation, the cost of drilling per metre, and the cost of ANFO.

BC_e in Table XIV is the estimated blasting cost during 2017. If the price of ANFO and drilling cost are fixed, blasting engineers can use BC_ein Table XIV; otherwise, they can use BC for calculating blasting cost, which excludes a time-frame. However, they should determine P_A and P_D for every year.

According to Table XIV, blasting cost was calculated using the UCS, hole diameter, and joint set orientation for Sungun, Miduk, and Chah-Firouzeh. In this model the blasting cost was calculated for each blast block, which includes drilling cost, the cost of ANFO, and auxiliary charges for the blasting operation. It should be mentioned that the blasting cost will increase with increasing rock strength and y, and decrease with increasing hole diameter in all ranges of UCS.

 

Conclusion

Investigation of the blasting cost at Sungun, Miduk, and Chah-Firouzeh copper mines revealed that there is a relationship between hole diameter and blasting cost.

Generally, the relationship can be expressed as BC = a(Dh)~^b, where Dh is the hole diameter in inches, BC is blasting cost in US dollars per cubic metre, and coefficients 'a' and 'b' are a function of bench height, UCS, joint set orientation, drilling cost per metre, and ANFO cost per kilogram. The bench height considered was 15 m. The values of coefficients 'a' and 'b' for various UCS ranges and values of y (the angle between plane of the bench face and the plane of the main joint set) less than or greater than 90° are as follows.

 

 

This relationship shows that blasting costs will increase with increasing rock strength and y value, but will decrease with increasing hole diameter in every range of UCS.

 

Acknowledgments

The authors would like to express their thanks to the anonymous reviewer for his/her useful comments and constructive suggestions. The authors are also grateful to National Iranian Copper Industries Company and Zaminkavan-e-Gharn Company for providing information.

 

References

Adebayo, B. and Akande, J.M. 2015. Effects of blast-hole deviation on drilling and muck-pile loading cost. International Journal of Scientific Research and Innovative Technology, vol. 2. no. 6. pp. 64-73.         [ Links ]

Adebayo, B. and Mutandwa, B. 2015. Correlation of blast-hole deviation and area of block with fragment size and fragmentation cost. International Research Journal of Engineering and Technology (IRJET), vol. 2. pp. 402-406.         [ Links ]

Afum, B.O. and Temeng, V.A. 2014. Reducing drill and blast cost through blast optimization: a case study. Proceedings of the 3rd UMaT Biennial International Mining and Mineral Conference. Ghana Mining Journal, vol. 15. no. 2. pp.137-145.         [ Links ]

Cunningham, C. 2013. Blasting for construction some critical aspects. Civil Engineering, vol. 21. July 2013. pp.11-21.         [ Links ]

Dehghan, M. 2001. Block Theory and Its Application to Rock Engineering, 1st edn. Shahrood University of Technology. 100 pp.         [ Links ]

Eloranta, J. 1995. Selection of powder factor in large-diameter blast holes. Proceedings of the 21st Annual Conference on Explosives and Blasting Techniques, Nashville, TN. International Society of Explosives Engineers. Vol. 1. http://elorantaassoc.com/download/Papers/E&A_Powder_Selection_Factor_in _Large_Diameter_Blast_Holes.pdf        [ Links ]

Ghanizadeh Zarghami, A. 2017. A model for calculating ANFO specific charge regarding the economic and geo mechanical parameters of copper mines in Iran. Science and Research Branch, Islamic Azad University, Tehran.         [ Links ]

Ghanizadeh Zarghami, A., Shahriar, K., Goshtasbi, K. and Akbari, A. 2017. Assessing the most important economic parameters of surface mine blasting using ANP method. Proceedings of the 4th National Open Pit Mining Conference. Kerman, iran, 14-17 May 2017. iranian Society of Mining Engineering. pp. 9-19.         [ Links ]

Ghanizadeh Zarghami, A. 2005. A Collection of Mining Engineering Software. 1st edn. Dibagaran Tehran, Tehran. 474 pp.         [ Links ]

Nenuwa, O.B. and Jimoh, B.O. 2014. Cost implication of explosive consumption in selected quarries in Ondo and Ekiti State. International Journal of Engineering and Technology, vol. 4. no. 7. pp. 402-409        [ Links ]

Ostovar, R. 2013. Blasting In Mines. 9th edn. Vol. 1-3. Jihad Amirkabir University, Tehran. pp. 800.         [ Links ]

Pokrovsky, M. 1980. Underground Structure and Mines Construction Practices. Chapter 1, Blasting Parameters. 13 pp.         [ Links ]

Strelec, S., Gazdek, M,, AND Mesec, J. 2011. Blasting design for obtaining desired fragmentation. Technical Gazette. vol.18. pp. 79-86.         [ Links ] ♦

 

 

Paper received Mar. 2018
revised paper received Apr. 2018