Question 7 of 7: Parametric Underground Mine Capital-Cost Estimating (O'Hara Method)

Question 7: Parametric Underground Mine Capital-Cost Estimating (O'Hara Method) (21 marks, one of three optional)

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.

7.1 — Who provides a same-day ±40% estimate

An experienced mining/cost engineer applying a published parametric (order-of-magnitude) cost model — exactly the O'Hara-type formulas used through the rest of this question — rather than an external engineering (EPCM) firm: a full EPCM scoping estimate takes weeks, while a parametric, capacity-and-depth-based model can be evaluated by one engineer, from a handful of inputs (tonnage, depth, stope width), inside a single day, at the ±35–40% accuracy such models are calibrated to deliver.

7.2 — The O'Hara capital-cost estimation method

A parametric (power-law, regression-based) cost-estimating method, published by T.P. O'Hara in the CIM Bulletin, February 1980, and subsequently updated and republished by Mular & Poulin as "CapCost" in CIM Special Volume 47 (1998). Rather than a detailed, bottom-up engineering estimate, it expresses each major mine capital-cost component (shaft sinking, hoist plant, mine development, mining equipment, compressor plant, etc.) as a simple function of a small number of easily known design variables — principally daily tonnage $T$, depth/hoisting distance $h$, and stope width $W$ — each regressed from a database of actual historical mine costs. It is the standard reference method for rapid, scoping-level (±35–40%) underground mine capital estimates, exactly the class of estimate identified in 7.1.

7.3 — Escalating to present-day and future-year costs

Each O'Hara/CapCost formula returns a cost in its own base publication year (1980 or 1998); to convert to a target year (2014, or a further projection to 2020), the base-year cost is multiplied by the ratio of a published cost index at the target year to the same index at the base year — exactly the escalation technique described for the Marshall & Swift M/M index in Question 1.7.1: $C_{target} = C_{base}\times(Index_{target}/Index_{base})$. Separate capital and operating cost indices should be used (they escalate at different rates — capital equipment/construction costs typically outpace labour-heavy operating costs, or vice versa depending on the period), and, since the O'Hara/CapCost formulas themselves are not re-derived here, the same index ratio is simply reapplied a second time to step from 2014 to a 2020 estimate once the relevant index values for those years are looked up.

7.4 — Shaft, hoist and development cost chain

Given. $T = 4500+1000 = 5500\ \text{mt/day}$ (total hoisted); $F=h=600\ \text{m}$; $W=10\ \text{m}$; $T_{ore}=4500\ \text{mt/day}$ (ore only, for $C_2$); $D_s=1.608\,T^{0.15}=5.85\ \text{m}$ and $d=3.976\ \text{m}$ as worked in the question statement.

Find. $C_{12}$, $L$, $S$, $H$ (motor power), $C_2$.

Approach. Substitute the given $T$, $F/h$, $W$ and the worked $D_s$, $d$ directly into each formula in turn, since $L$, $S$ and $H$ each depend on quantities already found earlier in the chain.

1. 7.4.1 — Shaft-sinking cost. $C_{12} = 314{,}838.7\,(5.85)^{0.5} + 3738.1\times600\times(5.85)^{0.7} = 314{,}838.7\times2.419 + 2{,}242{,}860\times3.171 \approx \boxed{\$8.49\ \text{M}}$.
2. 7.4.2 — Hoist drum diameter (given, restated for use below). $d = 3.976\ \text{m}$.
3. 7.4.3 — Head-frame height. $L = 3.0(3.976) + 0.1023(3.976)^3 + 1.983\,(5500)^{0.33} = 11.93 + 6.44 + 33.99 \approx \boxed{52.37\ \text{m}}$.
4. 7.4.4 — Hoisting speed. $S = 0.01486\,(600)^{0.5}(5500)^{0.4} = 0.01486\times24.49\times31.34 \approx \boxed{11.41\ \text{m/s}}$.
5. 7.4.5 — Hoist motor power. $H = 7.836\,(11.41)(3.976)^{2.4} = 7.836\times11.41\times27.42 \approx \boxed{2455\ \text{kW}}$.
6. 7.4.6 — Mine development cost. Using ore-only tonnage $T_{ore}=4500$: $C_2 = 37{,}033\,(4500)(10)^{-0.8} = 37{,}033\times4500\times0.1585 \approx \boxed{\$26.41\ \text{M}}$ — against a 9,000,000 mt development reserve (about 5½ years at 4500 mt/day ore), this is roughly USD 2.94/mt of reserve developed.

7.5 — Efficacy of the chosen parameters

Every formula in 7.4 is driven by only two or three easily known variables ($T$, $h$/$F$, $W$), which is exactly what makes the method usable for a same-day estimate (7.1) but also its central limitation: none of the formulas take rock strength, ground-support intensity, labour/regional cost differences, or the specific shaft-lining/headframe design as explicit inputs, even though the question itself states the rock is "relatively weak." The models capture the dominant, first-order economy-of-scale and depth trends correctly (cost rising with tonnage and depth in physically sensible ways, as seen in $C_{12}$ and $C_2$ above), but two mines with identical $T$, $h$ and $W$ yet very different ground conditions would receive the same cost estimate here — appropriate for a ±35–40% scoping estimate and options screening, but not a substitute for site-specific engineering once a project is far enough advanced to justify the cost of that engineering.

7.6 — Hoist plant cost

1. Hoist equipment. $C_{31} = 134{,}261.5\,(2455)^{0.2}(3.976)^{1.4} \approx \boxed{\$4.42\ \text{M}}$.
2. Hoist installation. $C_{32} = 65{,}437\,(3.976)^{1.8} \approx \boxed{\$0.785\ \text{M}}$.
3. Hoist room. $C_{33} = 25{,}956\,(3.976)^{3.2} \approx \boxed{\$2.15\ \text{M}}$.
4. Head-frame complex. $C_{34} = 719.67\,(52.37)^{1.8}(3.976)^{1.2} \approx \boxed{\$4.69\ \text{M}}$.
5. Total hoist plant. $C_3 = C_{31}+C_{32}+C_{33}+C_{34} = 4.42+0.785+2.15+4.69 \approx \boxed{\$12.04\ \text{M}}$.

Comment. The head-frame complex ($C_{34}$, driven by $L^{1.8}$) and the hoist equipment itself ($C_{31}$) together dominate the total, while the hoist-room cost ($C_{33}$) is disproportionately sensitive to drum diameter through its steep $d^{3.2}$ exponent — a modest error in the drum-diameter calculation (7.4.2) would be amplified roughly three-and-a-half-fold in $C_{33}$ alone. Reliability would improve by adding the winder type (drum vs. friction) and drive type (DC vs. modern AC/VFD, Question 4.2) as explicit inputs, since these materially change both $C_{31}$ and installation labour cost, and by using a location-specific structural-steel cost factor for the head-frame ($C_{34}$) rather than a single national-average coefficient.

7.7 — Compressor plant cost

1. Compressed-air requirement. $Q = 0.0957\,(5500)^{0.46} \approx \boxed{5.03\ \text{m}^3/\text{s}}$.
2. Compressor equipment and installation. $C_{41} = 369{,}938\,(5.03)^{0.8} \approx \boxed{\$1.35\ \text{M}}$; $C_{42} = 81{,}382\,(5.03)^{0.7} \approx \boxed{\$0.252\ \text{M}}$.
3. Total compressor plant. $C_4 = C_{41}+C_{42} \approx \boxed{\$1.60\ \text{M}}$.

Comment. A computed $Q$ of about 5 m³/s falls within the range typically seen at mines of this scale (broadly 2–8 m³/s depending on how much of the underground fleet is pneumatically powered), but the single power-law-in-$T$ form is a coarse proxy: it says nothing about how much of the fleet is pneumatic (rock drills, pneumatic loaders) versus electric or electro-hydraulic. A mine that has already converted most of its fleet away from compressed air — as most modern trackless operations have (Question 2.3) — would find $C_4$ from this formula a conservative upper bound rather than a close estimate.

7.8 — Underground equipment and maintenance facility cost

1. Underground mining equipment. $C_5 = 27{,}963\,(10)^{-0.3}(5500)^{0.8} \approx \boxed{\$13.77\ \text{M}}$.
2. Underground maintenance facility. $C_6 = 31{,}945\,(5500)^{0.5} \approx \boxed{\$2.37\ \text{M}}$.

7.9 — Underground-only power, water, services, access and town-site

These items are governed almost entirely by location (grid-connection distance, water source/dewatering needs, existing road access) and by the milling/processing complex, so a full estimate for $C_7$ is intentionally excluded here and would be developed alongside the mill/surface-infrastructure package. For underground-only purposes: electrical power distribution (transformers/substations feeding the hoist, ventilation and pumping loads) is typically already partly embedded in $C_3$/$C_5$ above rather than separately itemised; underground water supply/dewatering pumping infrastructure typically runs a few percent of total underground fixed capital; general plant services (compressed-air/power reticulation, communications) are a similarly small incremental fraction once the major systems above are costed; and access, town-site and housing costs are the most site-specific of all — negligible for a mine with existing road/rail/town access, but potentially very large (new access road, fly-in/fly-out camp, or a purpose-built town-site) for a remote greenfield operation.

7.10 — Reliability and applicability of this methodology

The O'Hara/CapCost parametric method is appropriate, and reliable to its stated ±35–40% band, for early-stage scoping and prefeasibility-level estimates and for screening multiple project options against each other quickly and consistently — exactly the "quick estimate within a day" use case of 7.1. It is not a substitute for a detailed, bottom-up engineering estimate (±10–15%) once a project advances to feasibility study, and, as noted in 7.5, it is most reliable when the tonnage/depth/width inputs fall within the range of mines used to originally calibrate the regressions — extrapolating well outside that range (a much deeper or much smaller operation than the database) degrades the stated accuracy. Any estimate from the method should be escalated with a current, published cost index (7.3) and, wherever possible, sanity-checked against recent comparable-project actual costs before being used for investment decisions.