Open-Pit Cutoff Grade & Stripping Ratio Formula

Never confuse in-pit Marginal Milling Cutoff with Ultimate-Pit Mining Cutoff Grade!

In Kenneth Lane’s (1988) open-pit mine optimization, engineers separate two distinct Cutoff Grades for ore grade g (e.g., % Cu or g/t Au, where Net Payable Price per unit of recovered metal is P_net = P_mkt - C_ref and Mill Recovery is Rec): (1) Once a shovel has ALREADY blasted and loaded rock inside the pit, Mining Cost C_mine ($/t) is sunk vs dumping at the waste dump, so rock goes to the concentrator whenever recoverable revenue exceeds Processing + G&A Cost (C_proc + C_ga): Marginal Milling Cutoff Grade g_mill = (C_proc + C_ga) / (P_net * Rec)! (2) Conversely, expanding the ultimate Lerchs-Grossmann pit shell outward must pay Mining Ore Cost C_mine_ore PLUS SR * C_mine_waste for Waste-to-Ore Stripping Ratio SR (tonnes waste / tonne ore): Breakeven Stripping Ratio at ore grade g is SR_max = (g * P_net * Rec - (C_mine_ore + C_proc + C_ga)) / C_mine_waste!

Verify on a gold open pit with Net_Gold_Price P_net = $80.00/gram (~$2,488/troy oz net of refining, B2), Mill_Recovery Rec = 0.90 (90.0%, B3 -> $72.00 revenue per g/t!), Ore_Mining_Cost C_mine_ore = $3.60/t (B4), Waste_Mining_Cost C_mine_waste = $3.00/t (B5), Mill_plus_GA_Cost C_proc = $18.00/t (B6), and Block_Head_Grade g = 0.75 g/t Au (B7): Marginal In-Pit Milling Cutoff is 18.00 / 72.00 = 0.2500 g/t (E2); Zero-Strip Pit Cutoff Grade is (3.60 + 18.00) / 72.00 = 0.3000 g/t (E3); Recoverable Block Net Value before stripping is 0.75 * $72.00 - $21.60 = $32.40/t (E4); and Maximum Breakeven Stripping Ratio is 32.40 / 3.00 = 10.8000 tonnes waste per tonne ore (E5)! Drop grade g to 0.28 g/t: SR_max is negative (-0.48 -> rock cannot justify pit-wall pushback, yet inside an existing bench 0.28 > 0.25 g_mill still pays to mill rather than dump as waste)!

Maximum Breakeven Stripping Ratio (SR_max) Formula

Validate P_net > 0, 0 < Rec <= 1, positive mining/milling costs, and g >= 0!

=LET(p_nt, B2, rc_m, B3, c_mo, B4, c_mw, B5, c_pr, B6, gr_o, B7, IF(OR(p_nt <= 0, rc_m <= 0, rc_m > 1, c_mo <= 0, c_mw <= 0, c_pr <= 0, gr_o < 0), "Invalid Pit Economics", ROUND((gr_o * p_nt * rc_m - (c_mo + c_pr)) / c_mw, 4)))

Marginal Milling vs Full Mining Cutoff Grade Formula

Stockpiling low-grade halo rock between 0.25 g/t and 0.30 g/t is standard Kenneth Lane mine scheduling practice!

=IF(ISTEXT(E5), E5, ROUND((B4 + B6) / (B2 * B3), 4))

Further reading

• Arte Sheets Lesson — Hotelling Exhaustible Resource Scarcity Rent Rule Formula
• Arte Sheets Lesson — Bulk Carrier Stowage Factor & Full-and-Down Formula