24-MMP-A5 Surface 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-A5 Surface Mining Methods and Design, 2014-Dec. 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 seven parts 1.1–1.7); a candidate then selects THREE of Questions 2–7 (each worth 20 marks).
Reference texts: Hartman & Mutmansky (eds.), SME Mining Engineering Handbook, 3rd ed. (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); 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; Mular, A.L. & Poulin, R. (1998), CapCosts: A Handbook for Estimating Mining and Mineral Processing Equipment Costs, CIM Special Volume 47 (parametric open-pit capital-cost formulae used throughout Question 7).
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.
1.7.1 – Marshall and Swift Mine/Mill index. The M&S M/M index is a composite escalation index specific to mining and milling capital projects, published annually and tracked against a fixed base year; it is the index Mular & Poulin's 1998-dollar capital-cost formulae (Question 7) are pegged to, and it is used the same way as any cost index (Question 1.3): $\text{Cost}_{now}=\text{Cost}_{1998}\times(\text{Index}_{now}/\text{Index}_{1998})$, letting an estimator escalate a historical parametric cost model to a current-year figure without re-deriving the underlying equipment/labour basket from scratch.
1.7.2 – The six-tenths rule. Also called the capacity-exponent or power-sizing rule (Williams' Law), it scales the cost of a piece of equipment or plant with its CAPACITY rather than assuming a 1:1 linear cost-capacity relationship: $$C_2=C_1\left(\dfrac{Q_2}{Q_1}\right)^{n}$$ with $n\approx0.6$ (hence “six tenths”) for many types of process equipment, because cost tends to scale with surface area or material volume while THROUGHPUT capacity scales with a higher power of the equipment's linear dimension – larger units are cheaper per unit of capacity. The exponent is not universal: it genuinely varies by equipment type from roughly 0.5 to 0.85, which is exactly why the rule is quoted under different names (“six-tenths”, “two-thirds”, “0.7 rule”) depending on the practitioner's own field of equipment – the shovel/truck/drill sizing formulae used throughout Question 7 (exponents of 0.4, 0.73, 0.85 for different cost centres) are all instances of this same family of relationship, each calibrated to its own equipment class.
1.7.3 – Cost centres. The M&S M/M (and comparable mining capital-cost) indices are built up from cost centres such as: mine pre-production/site preparation, mining equipment (shovels, trucks, drills), mine infrastructure (maintenance facilities, access roads), milling/processing equipment, tailings and water management, and general/administrative and engineering overhead – the same category structure Question 7's own cost buildup ($C_{12}$ site prep, $C_{21}/C_{22}$ pre-production stripping, $C_{31}$-$C_{33}$ mine equipment, $C_4$ maintenance, plus engineering/administration percentages) follows directly.
