Consideration of sustainable development principles in ultimate pit limit design

Abstract

Sustainable development is a concept that was introduced almost at the end of the twentieth century and quickly entered the literature. In recent years, the concept of sustainability and sustainable development (SD) has been successfully extended to mineral resources, but there have been few attempts to consider this concept in the ultimate pit limit (UPL) design. The problem of UPL determination is the first step in the open pit mine design and planning process. There are several mathematical, heuristic and meta-heuristic algorithms to determine UPL. The objective function in these algorithms is the maximization of total profit. Few models integrated some aspects of mining reclamation benefit and cost in the UPL design. However, there is not any comprehensive method for UPL design based on SD considerations. This paper provides a model for UPL designing based on SD indicators. According to this model, it is possible to integrate the SD principles in UPL design. The proposed model is explained by a simple 2D example and applied in an iron mine as a case study. Generally, using SD principles in UPL design may lead to a larger UPL than traditional method (profit maximization). The suggested method is appropriate for those ore bodies with no underground option. In cases with the underground option, before applying the suggested method, the transition level from surface to underground shall be determined.

Appendix 1: detailed calculations of indicators values for UPL3

• (a) Waste production = [(Waste quantity +ore quantity × (1-average grade)]

  According to Fig. 7 the number of waste blocks in UPL₃ is 35 and the number of ore blocks in UPL₃ is 14. According to Fig. 2, the average grade of 14 ore blocks in UPL₃ is (0.56 × 1+0.27 × 1 + 0.29 × 1 + …  + 0.59 × 1)/14 = 0.38; Waste production = 35 + 14 × (1 − 0.38) = 44 ton.

• (b) Reclamation = ((pit wall surface) + (waste dump surface))

  • Pit wall surface in UPL₃: 27 m²;

  • Waste volume in UPL₃: 44 m³ (density is 1 ton/m³); It is assumed that waste dump shape is a cone with 45 degrees sides and all lateral needs reclamation. Therefore, the base circular radius of the cone (r) is equal to the cone height (h).

  • $$ {\text{Cone volume}}:V = \frac{1}{3}\pi r^{2} {\text{h }}\mathop \Rightarrow \limits^{r = h} \frac{1}{3}\pi r^{3} $$

    (10)
  • $$ {\text{Lateral surface area of the cone}}:S = \pi rl ,\;l = \sqrt {{\text{h}}^{2} + r^{2} } \mathop \Rightarrow \limits^{r = h} {\text{l}} = \sqrt 2 r $$

    (11)

  • Where, l is the slant height. Therefore: $43.74 = \frac{1}{3}\pi r^{3} \Rightarrow r = 3.47\,{\text{m}}; l = 4.91\,{\text{m}}; S = 53.47\,{\text{m}}^{2} ;$

  • Waste dump surface area for UPL₃ = S = 53.47 m², Reclamation of UPL₃ = (27 + 53.47) = 80.47. m²

• (c) Land use = ((Surface of natural land inside pit collar before pit opening + land area that is covered by waste dumps))

  According to Fig. 5, the surface of natural land inside the pit collar before pit opening for UPL₃ = 12 m²; Land area that is covered by waste dumps is equal to the A.

  $${\text{Base surface area of the cone}}:A = \pi r^{2}$$

  (12)

  $r = 3.47\,{\text{m}}$, A = 37.81 m²; Land use of UPL₃ = (12 + 37.81) = 50 m².

• (d) Energy Consumption = [f_m × ore + f_w × mine waste]

  Assumed f_m = 5 and f_w = 1; Energy Consumption = [5 × (14) + 1 × 35] = 105 energy unit

• (e) Job security = Life of mine = (ore in pit/ore production per year)

  Life of mine = 14/3 = 4.7 year

• (f) Safety = Depth of mine = (highest bench level − pit floor level)

  Safety = 7 − 0 = 7 m

• (g) Resource efficiency = (ore quantity in pit × average grade)/(orebody × average of orebody grade)

  Resource efficiency = (14 × 0.38)/(26 × 0.35) = 0.58 %

• (h) Number of employees = (ore and waste blocks in level 1 + ore and waste blocks in level 2 × 1.1 + …)/(life of mine)

  Number of employees = (13 + 11 × 1.1 + 9×1.2 + 7×1.3 + 5×1.4 + 3×1.5 + 1×1.6)/4.7 = 13 man

• (i) Profit = (sum of all blocks economic value in pit)

  Profit = (35 × (−4) +3+6 + 7+29 + 18 + 22 + 14 + 14 + 32 + 8+3 + 20 + 9+31) = 73 $

• (j) Post mining income = [reclaimed land × I_SL − land use × I_PL]

  Assumed I_pl = 0.01 $/m² and I_PL = 0.012 $/m², Post mining income = (80.47 × 0.1 − 50 × 0.12) = 1.9 $

• (k) Taxes generation = sum of all taxes

  Assumed tax on profit = 0.2, other taxes is 0.3$ per ton of excavated material (ore + waste), all customs duties = 0 Taxes generation = (73 × 0.2 + (14 + 35) × 0.3) = 29.23 $

• (l) Mining indirect benefit = sum of all mining indirect benefits.

  Assumed 20 % of mining costs spent in the local community. Mining indirect benefit = [(14 + 35) × 4$ + 14 × 12$] × 0.2 = 72.8 $