Mining & Mineral Economics

Mine Size, Life & Optimum Cut-off Grade

Taylor's rule for optimum mine life and the break-even cut-off grade that separates ore from waste.

PART 1

Topic Breakdown & Traps

The Engineering Principle

Two linked decisions size a mine: how fast to mine (production rate / life) and what to call ore (cut-off grade). Taylor's rule is the classic empirical guide to optimum mine life from the tonnage of reserves — bigger deposits justify proportionally longer (but not linearly longer) lives, and the optimum daily rate follows. The break-even cut-off grade is the grade at which the revenue from a tonne of ore just equals the cost of mining, processing and selling it; material above cut-off is ore, below is waste. Raising the cut-off lifts the average grade fed to the plant but shrinks the reserve — the central economic trade-off in planning.

The Core Formula Matrix

Taylor's rule (optimum life):

Life (years) \approx 0.2 \times 4 ExpReserves (tonnes)

(±20%)

Daily rate:

Rate = \frac{Reserves}{Life \times operating days/yr}

Break-even cut-off grade:

g_{co} = \frac{Cost per tonne}{Price \times Recovery}

Cut-off in metal terms: above

g_{co}

a tonne pays its way; below it loses money.

The ‘IIT Traps’

⚠
Taylor's rule uses the fourth root of tonnage, not a linear scaling — doubling reserves does not double life.
⚠
Match units in the cut-off formula. Price per unit metal and cost per tonne ore must be consistent; include recovery.
⚠
**Recovery sits in the denominator of $g_{co}$ .** Ignoring it underestimates the grade needed to break even.
⚠
Higher cut-off = higher head grade but lower tonnage. It is a trade-off, not a free improvement.

PART 2

Progressive 3-Tier Question Suite

Q1BASIC1 Mark · MCQ

Material whose grade lies below the break-even cut-off grade is classified as:

Q2MEDIUM2 Marks · NAT

Mining + processing + selling cost is

\

p er t o nn eo f or e . T h e m e t a l se l l s f or

2000

per tonne and process recovery is

75%

. The break-even cut-off grade is ______ % metal. (Round off to two decimal places.)

Q3HARD2 Marks · NAT

By Taylor's rule, the optimum life of a mine with expected reserves of

50

million tonnes is approximately

0.2 \times 4 tonnes

years. The optimum life is ______ years. (Round to the nearest whole number.)

years