24-MMP-A5 Surface Mining Methods and Design · May 2014
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
EGBC National Exam — Mining and Mineral Processing Engineering, 09-MMP-A5 Surface Mining Methods and Design, 2014-May. 3 hours duration, closed book; one hand-written 8.5×11 inch reference sheet and an approved Casio or Sharp calculator permitted. Question 1 is compulsory (40 marks, all six parts 1.1–1.6); a candidate then selects THREE of Questions 2–6 (each worth 20 marks).
Reference texts: Hartman & Mutmansky (eds.), SME Mining Engineering Handbook, 3rd ed. (dragline stripping systems, truck-shovel productivity, mine cost estimation — the primary reference throughout this paper); Hustrulid, Kuchta & Martin, Open Pit Mine Planning and Design, 3rd ed. (block-model economics, floating/moving-cone algorithm, the Lerchs–Grossmann graph-theoretic pit-optimization method, annual push-back scheduling); Kennedy, B.A. (ed.), Surface Mining, 2nd ed., SME (dragline range-diagram geometry, stripping methods); Lerchs, H. & Grossmann, I.F. (1965), “Optimum Design of Open-Pit Mines,” CIM Bulletin, 58, 47–54.
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
Given. Per-bench ore/waste tabulation (17 benches, 1600–1360 m elevation, 15 m bench height, matching the 15 m block size of Question 6), pit totals 89.59 Mt (59.98 Mt ore, 29.61 Mt waste); Year 1 mine capacity 15 Mt; Years 2–6+ mine capacity 20 Mt/yr, mill-rated ore feed 10 Mt/yr; mining rules 4.a–4.c above.
Find. The bench-by-bench annual ore and waste schedule, the annual production table, and the overall stripping ratio.
Approach. Because the source gives only PER-BENCH totals (not a plan-view block breakdown), the schedule is built as a top-down, bench-sequential cascade — the only allocation consistent with rule 4.a using the data actually given — splitting a bench’s ore and waste proportionally across a year boundary whenever an annual cap (mine total or mill ore) is hit mid-bench. This directly respects 4.a (strictly top-down) and approximates 4.b/4.c (ore and waste in the same bench are extracted together as that bench is reached, so waste is never more than the current bench ahead of ore).
| Bench elev. (m) | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | Year 6 | Year 7 |
|---|---|---|---|---|---|---|---|
| 1600 | 0.00 / 0.25 / 0.25 | – | – | – | – | – | – |
| 1585 | 0.00 / 0.83 / 0.83 | – | – | – | – | – | – |
| 1570 | 0.67 / 1.00 / 1.67 | – | – | – | – | – | – |
| 1555 | 1.70 / 2.43 / 4.13 | – | – | – | – | – | – |
| 1540 | 3.85 / 3.85 / 7.70 | – | – | – | – | – | – |
| 1525 | 0.23 / 0.19 / 0.42 | 5.19 / 4.19 / 9.38 | – | – | – | – | – |
| 1510 | – | 4.81 / 2.66 / 7.47 | 2.14 / 1.18 / 3.32 | – | – | – | – |
| 1495 | – | – | 6.63 / 4.04 / 10.67 | – | – | – | – |
| 1480 | – | – | 1.23 / 0.56 / 1.79 | 5.23 / 2.36 / 7.59 | – | – | – |
| 1465 | – | – | – | 4.77 / 1.92 / 6.69 | 0.99 / 0.40 / 1.39 | – | – |
| 1450 | – | – | – | – | 5.26 / 1.61 / 6.87 | – | – |
| 1435 | – | – | – | – | 3.75 / 0.82 / 4.58 | 0.90 / 0.20 / 1.09 | – |
| 1420 | – | – | – | – | – | 3.97 / 0.53 / 4.50 | – |
| 1405 | – | – | – | – | – | 3.27 / 0.31 / 3.58 | – |
| 1390 | – | – | – | – | – | 1.86 / 0.13 / 1.99 | 0.60 / 0.04 / 0.64 |
| 1375 | – | – | – | – | – | – | 1.78 / 0.09 / 1.87 |
| 1360 | – | – | – | – | – | – | 1.15 / 0.02 / 1.17 |
| Annual total | 6.45 / 8.55 / 15.00 | 10.00 / 6.85 / 16.85 | 10.00 / 5.78 / 15.78 | 10.00 / 4.29 / 14.29 | 10.00 / 2.83 / 12.83 | 10.00 / 1.17 / 11.17 | 3.53 / 0.15 / 3.68 |
4.2.2 — Overall stripping ratio. $$SR = \frac{\text{total waste}}{\text{total ore}} = \frac{29.61}{59.98} = \boxed{0.494 : 1}$$ (about one tonne of waste for every two tonnes of ore) — a notably low ratio for an open pit, consistent with a thick, shallow, high-grade zone.
| Quantity | Result |
|---|---|
| Mine life (at stated annual caps) | ~6.4 years (Years 1–6 full, Year 7 partial, 3.68 Mt) |
| Year 1 ore / waste / total | 6.45 / 8.55 / 15.00 Mt |
| Years 2–6 ore / total (each) | 10.00 Mt ore (mill-capped); total falls from 16.85 to 11.17 Mt as waste thins with depth |
| 4.2.2 Overall stripping ratio | 0.494 : 1 (waste:ore) |
4.3 — If the rules cannot be achieved. If the 4.a–4.c geometry cannot physically be honoured with the available equipment/schedule (e.g. a bench cannot be depleted before the next must start, or waste would have to lead ore by more than one bench to keep the mill fed), the recommended action is to RELAX THE ANNUAL PRODUCTION TARGET rather than the slope/sequencing rules themselves — i.e. accept a temporary shortfall in mill ore feed (blend in lower-grade stockpile material, Question 4.5.2) or add a second working face/pushback so more than one bench can be active at once, rather than violate the no-undercut wall-stability rule, which is a geotechnical safety constraint, not a scheduling preference.
4.4 — Releasing shovels. Each shovel handles 7 Mt/yr, so 3 shovels together can move up to 21 Mt/yr — comfortably above the 20 Mt/yr peak this schedule ever requires (Year 2, 16.85 Mt) and far above the ≤12.83 Mt/yr needed by Year 5. From Year 5 onward (total ≤12.83 Mt/yr, i.e. under 2 shovels’ combined 14 Mt/yr capacity) one shovel is no longer needed on this pit and can be PERMANENTLY released to begin stripping the next pushback; by Year 6 (11.17 Mt/yr, under one shovel’s own 7–14 Mt range with a second held in reserve) a second shovel could similarly be freed, leaving only enough capacity on this pit to finish the Year 7 tail.
4.5.1 — Justifying full-capacity purchase immediately. Buying the full equipment fleet up front lets the mine hit its 20 Mt/yr and 10 Mt/yr mill-ore targets from Year 1 rather than the 6.45 Mt ramp-up this schedule actually delivers — the extra ore recovered in the early years is worth more in present-value terms (time value of money) than the same tonnes recovered later, and avoids the mill running below its rated capacity (idle capital) in Year 1. This is justified when the deposit and price outlook are well enough understood that the capital risk of buying ahead of need is low, and financing costs are favourable.
4.5.2 — Justifying staged purchase. Staging equipment purchases (buying only what Year 1’s achievable 15 Mt actually requires, then adding fleet as the schedule ramps to 20 Mt/yr) defers capital outlay, reduces exposure if the price forecast or reserve estimate proves optimistic, and matches spending to the mine’s own demonstrated cash flow rather than borrowing against a forecast. The cost is accepting lower-grade/blended mill feed in the early years (as this schedule’s Year 1 6.45 Mt ore shortfall already shows) and a longer ramp-up to full mill utilization. This is the more conservative choice when price/reserve risk is high or financing is constrained.
