Mine Cost Estimation — Camm (1989) Parametric Shaft and Block-Caving Models, Escalated to 2008: 24-MMP-A2 Underground Mining Methods and Design, December 2016, Q4

Question 4: Mine Cost Estimation — Camm (1989) Parametric Shaft and Block-Caving Models, Escalated to 2008 (20 marks)

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.

NOTE: Table 4.1's shaft cost model (371X + 180D·X^0.404 capital; 2343/X + 0.44D/X + 0.00163D operating) and Table 4.2's block-caving mine cost model (64,800X^0.759 capital; 48.4X^-0.217 operating) are the Camm (1989) cost tables, evaluated at X=20,000 st/d, D=2,000 ft design basis. Table 4.3 supplies the escalation indices (56.9→98.7 capital, 91.1→141.9 operating, 1989 to 2008).

Given.

Design basis and Table 4.1 / 4.2 model parameters (Camm, USBM, 1989)
Quantity	Symbol	Value
Mine capacity	X	20,000 short tons/day
Nominal shaft depth	D	2,000 ft
Table 4.1 total shaft capital cost model (USD)	—	371X + 180D·X^0.404
Table 4.1 total shaft operating cost model (USD/st)	—	2343/X + 0.44D/X + 0.00163D
Table 4.2 total mining capital cost model (USD)	—	64,800·X^0.759
Table 4.2 total mining operating cost model (USD/st)	—	48.4·X^-0.217
Capital cost index, 1989 / 2008 (Table 4.3)	—	56.9 / 98.7
Operating cost index, 1989 / 2008 (Table 4.3)	—	91.1 / 141.9

Find. The component and total 1989 shaft capital/operating costs (4.1), the component and total 1989 block-caving mining capital/operating costs excluding the shaft (4.2), and the total shaft-plus-mining capital and operating costs escalated to 2008 (4.3), with commentary on model adequacy throughout.

Approach. Substitute X = 20,000 and D = 2,000 into every component formula of Table 4.1 (shaft) and Table 4.2 (block-caving mine) to get the 1989 component and "Total" line costs, cross-checking the sum of components against the independently regressed Total line each time; then multiply the 1989 shaft and mining totals by the ratio of the 2008 to 1989 capital and operating indices from Table 4.3.

Part 4.1 — shaft capital cost components, 1989. Each Table 4.1 capital term is evaluated at X=20,000, D=2,000 (Lumber, Fuel and Tires are marked "NAp" for a shaft and contribute nothing):

Table 4.1 shaft capital cost, 1989 (USD)
Category	Formula	Cost (USD)
Labor	75D·X^0.399	7,801,900
Equipment	350X + 65D·X^0.386	12,944,900
Steel	25D·X^0.373	2,010,300
Lube	6D·X^0.342	354,900
Explosives	5D·X^0.389	471,100
Construction material	9D·X^0.522	3,165,300
Electricity	4D·X^0.230	78,000
Sum of components	—	26,826,400
Total (Table 4.1 formula)	371X + 180D·X^0.404	27,095,200

Equipment (about 48% of the component sum) and Labor dominate, consistent with a mechanised shaft-sinking crew and a permanent hoisting/guide/service installation; the independently regressed "Total" formula comes out about 1% above the arithmetic sum of components, close enough to treat the model as internally consistent for a screening-level estimate.

Part 4.1 — shaft operating cost components, 1989.

Table 4.1 shaft operating cost, 1989 (USD/short ton)
Category	Formula	Cost (USD/st)
Labor	2010/X	0.1005
Equipment	0.325D/X	0.0325
Steel	0.00014D	0.2800
Lube	0.090D/X	0.0090
Construction material	200/X	0.0100
Electricity	0.0014D	2.8000
Sum of components	—	3.2320
Total (Table 4.1 formula)	2343/X + 0.44D/X + 0.00163D	3.4212

At 20,000 st/d × 365 d/yr this is an annual shaft operating cost of about USD 24.97 million. The Electricity term (2.80/st, over 80% of the operating total) is disproportionately large for what is normally a modest hoisting/pumping/ventilation power draw at a single shaft — worth flagging as a possible scaling artefact in the underlying regression and sanity-checking against an independent kWh-based estimate before it is used in a real feasibility budget.

Part 4.2 — block-caving mining capital cost components, 1989 (excluding shaft). All ten Table 4.2 categories are pure functions of X alone (no depth term, since these are mining costs excluding the shaft):

Table 4.2 block-caving mining capital cost, 1989 (USD)
Category	Formula	Cost (USD)
Labor	27,900X^0.646	16,752,100
Equipment	25,600X^0.812	79,556,600
Steel	4,410X^0.685	3,896,200
Lumber	149X^0.902	1,129,100
Fuel	10.6X^0.897	76,400
Lube	4.54X^0.897	32,700
Explosives	1,040X^0.737	1,537,800
Tires	1.87X^0.946	21,900
Construction material	31,100X^0.591	10,831,000
Electricity	50.4X^0.748	83,100
Sum of components	—	113,917,000
Total (Table 4.2 formula)	64,800X^0.759	119,139,800

Equipment again dominates (about 70% of the component sum), consistent with the mechanised LHD/crusher/conveying fleet a block-caving operation of this scale requires; the Total-formula result runs about 4.6% above the component sum — expected since the mining Total was regressed across a broad capacity range (4,000–40,000 st/d) rather than summed directly — and both figures should be carried forward with the difference treated as part of the estimate's inherent uncertainty band.

Part 4.2 — block-caving mining operating cost components, 1989 (excluding shaft).

Table 4.2 block-caving mining operating cost, 1989 (USD/short ton)
Category	Formula	Cost (USD/st)
Labor	60.0X^-0.305	2.9264
Equipment	4.40X^-0.230	0.4510
Steel	0.217X^0.0	0.2170
Lumber	0.310X^0.0	0.3100
Fuel	0.894X^-0.239	0.0838
Lube	0.545X^-0.253	0.0445
Explosives	0.183X^0.0	0.1830
Tires	0.412X^-0.151	0.0924
Construction material	2.83X^-0.182	0.4667
Electricity	1.36X^-0.060	0.7507
Sum of components	—	5.5255
Total (Table 4.2 formula)	48.4X^-0.217	5.6432

Labor is the single largest term (about 53% of the component sum), the pattern expected of an underground block-caving labour force; the negative exponent on every category reflects the economy of scale the model is built to represent (unit cost falls as capacity X rises) — a positive exponent giving a rising unit cost with capacity would itself be a useful adequacy red flag, which none of the ten terms shows.

Part 4.3 — escalation factors, 1989→2008 (Table 4.3). $$\text{capital factor} = \dfrac{98.7}{56.9} = 1.7346, \qquad \text{operating factor} = \dfrac{141.9}{91.1} = 1.5576$$ The capital index roughly doubled over the period while the operating index rose by about 56% — a markedly steep capital escalation, consistent with the well-documented 2000s commodity/construction capital-cost boom outpacing wage-driven operating cost inflation.

Part 4.3 — total shaft and mining costs escalated to 2008. Applying the 2008 factors to the Table-formula 1989 totals from Steps 1–4:

2008 escalated totals (USD, using the Table 4.1/4.2 "Total" formulas)
Item	1989	× factor	2008
Shaft capital	27,095,200	1.7346	46,999,900
Shaft operating (/st)	3.4212	1.5576	5.3289
Mining capital	119,139,800	1.7346	206,662,500
Mining operating (/st)	5.6432	1.5576	8.7899

$$\boxed{C_{cap,2008} = 47.00\text{M} + 206.66\text{M} = 253.66\text{M USD}}$$ $$\boxed{c_{op,2008} = 5.329 + 8.790 = 14.12\ \text{USD/st}\ \ (\times 20{,}000 \times 365 \approx 103.1\text{M USD/yr})}$$

Part 4.3 — adequacy of the 2008 estimate. A single scalar escalation factor applies the SAME multiplier to every cost category regardless of how that category's own inputs actually moved between 1989 and 2008 — a Labor-heavy line item and a Steel/Equipment-heavy line item (which tracked the 2000s commodity/construction boom far more steeply than site labour rates) did not escalate at the same rate in reality, so the blended-index result understates the true dispersion across categories even though the overall total is a reasonable order-of-magnitude figure. The estimate is further weakened by extrapolating a regression fitted to 1989 data forward nineteen years, and for the shaft model, by applying it at a capacity/depth combination near the edge of the sample the original Camm dataset was built from. Both models remain adequate for pre-feasibility/screening-level comparison between design options — exactly the use the question poses — but should never substitute for vendor-quote-based estimates once a project reaches a bankable feasibility study.

Question 4 — final numeric results (2008 USD unless noted)
Item	Result
4.1 Shaft capital, 1989	27.10M USD (component sum 26.83M)
4.1 Shaft operating, 1989	3.42 USD/st (24.97M USD/yr)
4.2 Mining capital, 1989 (excl. shaft)	119.14M USD (component sum 113.92M)
4.2 Mining operating, 1989 (excl. shaft)	5.64 USD/st (41.20M USD/yr)
4.3 Escalation factors, 1989→2008	capital ×1.7346, operating ×1.5576
4.3 Shaft capital, 2008	47.00M USD
4.3 Shaft operating, 2008	5.33 USD/st
4.3 Mining capital, 2008	206.66M USD
4.3 Mining operating, 2008	8.79 USD/st
4.3 TOTAL capital (shaft+mining), 2008	253.66M USD
4.3 TOTAL operating (shaft+mining), 2008	14.12 USD/st (103.1M USD/yr)

Topic. Parametric (power-law) capital and operating cost models for shaft sinking and block-caving mining, and time-escalation of a base-year estimate via a published cost index.

Key relations. Component cost $C_i = a_i X^{b_i}$ (and, for the shaft, $a_i D X^{b_i}$); index escalation $C_{year2} = C_{year1} \times (\text{Index}_{year2}/\text{Index}_{year1})$; six-tenths-rule family of exponents (Question 1.4.2).

Why this works. Each cost category is independently regressed against a historical database of comparable mines, so summing categories and comparing to the model's own directly-regressed "Total" line is itself a built-in consistency check; escalating with a published index converts the whole 1989 estimate to current dollars without re-deriving the underlying engineering quantities.

Common pitfall. Applying the capital escalation factor to an operating cost (or vice versa) — the two indices move differently and are not interchangeable; and treating a decades-extrapolated parametric model as more precise than the ±30–50% typically implied by an order-of-magnitude/pre-feasibility estimate.

Source. Camm, T.W. (1989), Simplified Cost Models for Prefeasibility Mineral Evaluations, US Bureau of Mines IC 9298; Hartman & Mutmansky, SME Mining Engineering Handbook, cost-estimation chapter.

Question 4 of 6: Mine Cost Estimation — Camm (1989) Parametric Shaft and Block-Caving Models, Escalated to 2008

Question 4: Mine Cost Estimation — Camm (1989) Parametric Shaft and Block-Caving Models, Escalated to 2008 (20 marks)