24-MMP-A5 Surface Mining Methods and Design · December 2016
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Surface Mining Methods and Design (09-MMP-A5) — December 2016 National Exam. Compulsory Question 1 (six sub-questions) plus all five optional Questions 2–6 are answered in full below (candidates select only three of Questions 2–6 in the real exam; all are solved here as a complete study resource).
Reference texts: Hustrulid, Kuchta & Martin, Open Pit Mine Planning and Design (3rd ed.) — pit optimization, Lerchs–Grossmann, floating cone, dragline stripping geometry; SME Mining Engineering Handbook (3rd ed.); BC Health, Safety and Reclamation Code for Mines; Newnan, Eschenbach & Lavelle, Engineering Economic Analysis — sinking funds and future-worth factors.
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.
Starting from the highest-value block in the section, an inverted cone (in 2-D, a triangle) is expanded downward at the pit's design wall-slope angle; the algorithm sums the value of every block inside that cone. If the cone's net value is positive, all blocks in it are marked "mine"; the process is then repeated, scanning for the next-highest remaining positive-value block and floating a new cone from it, until no positive-value cone can be found anywhere in the section — at which point the union of every accepted cone is taken as the (heuristic) final pit outline. This exact "process every positive block from a deep, high-grade seed, one block at a time" logic is what was applied to columns A/B/D of the Q6 expansion, by hand, as a sanity check against the L-G-equivalent DP.
The moving cone is a greedy, sequential heuristic: which block is picked as the NEXT seed, and in what order overlapping cones are evaluated, can change the final outline, so it is not guaranteed to find the true value-maximising envelope, can double-count or omit blocks where cones overlap, and requires ad-hoc tie-breaking rules that different practitioners applied inconsistently. Lerchs & Grossmann re-cast the same problem as a maximum-closure problem on a directed graph (blocks as nodes, slope-precedence arcs) and proved that graph-theory max-flow/min-cut methods find the single, unique, MATHEMATICALLY OPTIMAL 3-D pit outline for a given block model and slope constraint — removing the order-dependence and heuristic tie-breaking of the cone method entirely (the 1-D envelope DP used in Question 6 below is the exact 2-D specialisation of this same graph closure).
Lerchs–Grossmann finds the single BEST ULTIMATE pit outline for one fixed set of block values (one price/cost/grade scenario, evaluated all at once with no time value of money). It does not sequence WHEN each block is mined, does not discount later-mined blocks' cash flow, and does not re-optimise as commodity prices, costs or geological knowledge change through a 10–20-year life — a genuinely optimal LIFE-OF-MINE plan requires nesting many L–G pits at different revenue factors and then scheduling/discounting between them (e.g. via Whittle-style nested-envelope optimisation and NPV-based push-back sequencing), which L–G by itself does not provide.
