Mining & Mineral Economics

Ultimate Pit & Stope Planning

Stripping ratio, the break-even stripping ratio (BESR) and the Lerchs–Grossmann idea behind the ultimate pit limit.

PART 1

Topic Breakdown & Traps

The Engineering Principle

For a surface mine, the ultimate pit limit is the economically optimal final shape — mined only while each extra increment of ore pays for the waste removed to reach it. The key ratio is the stripping ratio

S R

= tonnes (or volume) of waste per tonne of ore. The break-even stripping ratio (BESR) is the maximum waste a tonne of ore can carry before mining it loses money. The classic optimisation is the Lerchs–Grossmann algorithm, which finds the maximum-value pit on a block model subject to pull-back slope (wall) angle constraints. Underground, the analogous decision is stope boundary planning — choosing which blocks to stope so that each pays for its own development and support.

The Core Formula Matrix

Stripping ratio:

S R = \frac{waste mined}{ore mined}

(t/t or m³/t)

Break-even SR:

B E S R = \frac{( Price - Production cost ) per t ore}{Cost of removing one tonne of waste}

Mine while

S R \leq B E S R

; stop extending the pit when

S R = B E S R

.

Pit value (block model):

\sum (block value)

maximised subject to slope-angle precedence (Lerchs–Grossmann).

The ‘IIT Traps’

⚠
BESR uses the *net* value of ore (price − production cost) over the waste-removal cost — not price alone.
⚠
**Mine only while $S R \leq B E S R$ .** Extending the pit where $S R > B E S R$ destroys value.
⚠
Stripping ratio can be mass or volume based — state which; rock densities differ between ore and waste.
⚠
Slope-angle constraints drive waste. Flatter walls (weaker rock) force more stripping for the same ore.

PART 2

Progressive 3-Tier Question Suite

Q1BASIC1 Mark · MCQ

The stripping ratio of an open-pit mine is the ratio of:

Q2MEDIUM2 Marks · NAT

A tonne of ore returns a net value (price minus production cost) of

\

. R e m o v in g a t o nn eo f w a s t ecos t s

3

. The break-even stripping ratio is ______ (tonnes waste per tonne ore). (Round to the nearest whole number.)

Q3HARD2 Marks · NAT

A pushback exposes

200, 000 t

of ore and requires removing

1, 400, 000 t

of waste. If the break-even stripping ratio is

8 : 1

, the actual stripping ratio is ______, so the pushback is (economic / uneconomic). Give the numerical stripping ratio. (Round off to one decimal place.)