24-MMP-A5 Surface Mining Methods and Design · May 2015
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, 2015-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 FOUR of Questions 2–7 (each worth 20 marks).
Reference texts: Hartman & Mutmansky (eds.), SME Mining Engineering Handbook, 3rd ed. (equipment availability/utilization, dragline stripping systems, truck-shovel productivity, mine dewatering, mine cost estimation); 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, discounted cash-flow 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; O’Hara, T.A. (1980), CIM Bulletin (Feb. 1980), and Mular, A.L. & Poulin, R. (1998), CapCosts: A Handbook for Estimating Mining and Mineral Processing Equipment Costs, CIM Special Volume 47 (parametric capital-cost formulae used in Question 6); Theis, C.V. (1935) and Cooper & Jacob (1946) aquifer-test methods (standard hydrogeology references, Question 3.2).
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.
1.5.1 – Moving/floating cone rule base (2-D section). Working on a single vertical cross-section of block-model cash flows (revenue for ore blocks, cost for waste blocks): (1) starting from the highest-value block, provisionally place an inverted cone (a symmetric wedge in 2-D) whose sides honour the maximum stable wall slope, apex at that block, opening upward to surface; (2) sum the cash flow of every block inside the cone; (3) if the total is positive, accept the apex block and every block above it within the cone – the waste is "paid for" by the ore at the apex; (4) if negative, reject that cone and move to the next-highest-value untested block; (5) repeat for every ore block, re-testing a previously rejected cone once neighbouring cones have added stripping capacity nearby; (6) stop when no remaining block yields a positive cone – the union of accepted cones is the floating-cone pit outline. This is exactly the block-by-block logic mechanised by the depth-profile dynamic program used in Question 5.2.
1.5.2 – Deficiencies the Lerchs–Grossmann algorithm fixed. The floating-cone method (a) is not guaranteed to find the true global optimum – each cone is tested only against the CURRENT partial outline, so the accepted pit depends on test order, and a genuinely optimal pair of adjacent, individually-negative cones (whose UNION is positive once shared waste is counted once) can be missed; (b) double-counts shared waste when two overlapping cones are each accepted separately; and (c) has no rigorous proof of optimality – it is a heuristic. Lerchs & Grossmann reformulated the block model as a directed graph (each block a node, slope-constraint precedence arcs) and applied max-flow/min-cut (graph closure) theory, guaranteeing the mathematically optimal ultimate pit in one pass, independent of test order.
1.5.3 – Why Lerchs–Grossmann is still not "optimal" for a 10–20 year mine. LG optimizes a SINGLE, static block-value model – the best ultimate shape if every block were mined and sold today, at today's prices/costs/discount rate. A 10–20 year mine life exposes at least three gaps it cannot resolve: (i) it ignores the TIME VALUE of money – it says whether a block is inside the ultimate pit, not WHEN it is mined, so the NPV-optimal outline (Question 1.2.3: discounting front-loads value) can differ from the tonnage-optimal LG outline; (ii) it assumes one fixed price/cost/slope scenario, whereas price, cost and even achievable slope angle change over a 10–20 year horizon, so the real answer is a family of nested pit envelopes scheduled through time, not one static outline; (iii) it ignores fleet, mill and blending constraints that govern the achievable MINING SEQUENCE – exactly what pushback/phase design (Question 2's Phase 1/Phase 2 sequencing) adds on top of the LG outline.
