24-MMP-A2 Underground Mining Methods and Design · December 2014
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
EGBC National Exam — Mining and Mineral Processing Engineering, 09-Mmp-A2 Underground Mining Methods and Design, 2014-Dec. 3 hours duration, closed book; only an approved Sharp or Casio calculator permitted, one hand-written 8.5×11 in. reference sheet allowed. Question 1 is compulsory (40 marks, all seven parts 1.1–1.7); a candidate then selects THREE of Questions 2–7 (each nominally 20 marks, Question 7 sub-totalling higher).
Reference texts: Hartman & Mutmansky (eds.), SME Mining Engineering Handbook, 3rd ed. (underground mining methods, rock support, mine ventilation, shaft hoisting design, headframes, backfill practice, mine cost estimation — the primary reference throughout this paper); Hustrulid & Bullock, Underground Mining Methods: Engineering Fundamentals and International Case Studies (room-and-pillar, vertical crater retreat and trackless mechanized stoping practice); O'Hara, T.P., "Quick Guides to the Evaluation of Orebodies," CIM Bulletin, February 1980, and Mular, A.L. & Poulin, R., CapCost – CIM Special Volume 47, 1998 (parametric underground mine capital-cost models used in Question 7); BC Ministry of Energy, Mines and Low Carbon Innovation, Health, Safety and Reclamation Code for Mines in British Columbia (Canadian regulatory context for hoisting-rope safety factors, overwind protection and shaft ventilation).
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.
Skip and vertical shaft. A vertical shaft is sunk (or an existing production shaft used) from surface to the mining horizon; ore is trammed to a skip-loading pocket at depth and hoisted vertically in a skip via a headframe-mounted sheave and winder (drum or friction hoist — Question 4). The shaft, headframe and hoist plant are large, fixed, single-purpose capital items sized once for the mine's peak production rate, moving rock the shortest possible (vertical) distance to surface.
Truck and decline. A graded spiral or switchback ramp (decline) is driven from surface (or from an upper level) down to the orebody, typically at about a 1:7 (~14–15%) grade to keep truck traction and braking within safe limits; diesel (or trolley/battery-electric) haul trucks drive the full ramp length from the loading face to a surface stockpile or crusher. The decline itself is reusable, extensible development rather than a single fixed structure, and the mobile truck fleet is added to incrementally as production grows, rather than being sized once for peak capacity up front.
| Component | Skip / vertical shaft | Truck / decline |
|---|---|---|
| Primary access development | Shaft sinking (illustrative USD 15,000–30,000+/m depending on diameter and ground — cf. Question 7's $C_{12}$ shaft-sinking model) | Decline development (illustrative USD 3,000–6,000/m, driven at production-heading size) |
| Fixed hoisting/haulage plant | Headframe, hoist (drum/motor), skip — large single fixed installation, several tens of USD millions for a major shaft (cf. $C_3$ hoist-plant total, Question 7.6) | Mobile haul-truck fleet, sized incrementally — typical large underground truck USD 1–3 million each |
| Ancillary/support plant | Compressed air, underground equipment and maintenance facility scaled to a single shaft-served production rate (cf. $C_4$, $C_5$, $C_6$, Question 7.7–7.8) | Ramp ventilation raises/fans, truck maintenance shop, road maintenance equipment |
| Scaling behaviour | Approximately fixed regardless of orebody geometry once depth and tonnage are set — a single large lump-sum capital item | Scales roughly linearly with decline length (hence with depth) and with fleet size (hence with tonnage), so capital can be committed incrementally as the mine develops |
| Component | Skip / vertical shaft | Truck / decline |
|---|---|---|
| Energy per tonne | Largely independent of haul distance beyond depth itself — hoist energy scales with static load and depth only (cf. Question 4.4's per-skip energy calculation), illustrative under USD 1/t at good utilisation | Scales with round-trip distance (haul distance × ~7 for a 1:7 decline) and diesel fuel/tyre/maintenance cost — illustrative USD 2–6/t-km, so total unit cost rises steeply with depth |
| Labour | Small, fixed hoist-operator crew regardless of tonnage moved | Truck-operator labour scales with fleet size (roughly linearly with tonnage) |
| Maintenance | Rope replacement (fatigue-life driven, Question 1.4.3), sheave/drum wear — low unit cost at high utilisation | Tyres, engine/drivetrain wear, road maintenance — a recurring, tonnage- and distance-driven cost |
| Sensitivity to rock strength / geometry | Largely insensitive once the shaft is sunk (fixed infrastructure) | Decline stability/ground support cost driven directly by rock strength along the ramp's full length; irregular orebody geometry (multiple zones) is easily accommodated by re-routing branch declines |
Deposit depth is the single strongest driver of the comparison: shaft capital is essentially a step cost paid once (largely independent of depth beyond the shaft-sinking linear-metre cost), whereas decline capital and, especially, operating cost both grow directly with depth because the round-trip haul distance on a fixed-grade ramp is roughly proportional to depth. Ore-body size (total tonnage) favours the shaft's high fixed-plant, low-marginal-cost structure at large scale, while a smaller or shorter-life deposit cannot amortise the shaft's large upfront capital and favours the decline's incrementally scaled fleet. Rock strength mainly affects the decline (ground support cost along its full length) more than the shaft (a single, once-off ground-support problem confined to the shaft collar and station areas).
Skip/shaft is favoured for deep (typically >500–800 m), high-tonnage, long-life operations: at depth, a fixed-grade decline's round-trip distance (roughly 7× the vertical depth at a 1:7 grade) makes trucking operating cost per tonne prohibitive, while the shaft's large but largely depth-insensitive capital is amortised over a high, sustained tonnage and a long mine life. Truck/decline is favoured for shallower or moderate-depth, shorter-life, or lower/uncertain-tonnage operations, or where orebody geometry is irregular/multi-zone and haulage flexibility (extending or re-routing the ramp without new shaft capital) matters more than achieving the lowest possible steady-state unit cost; the decline also defers the shaft/headframe/hoist-plant capital commitment, letting a smaller or earlier-stage operation begin production and generate cash flow sooner. A common real-world compromise, not asked for here but worth noting, is to start production via decline and later sink a shaft once tonnage and depth both justify the fixed investment.
