Bench Blasting Burden, Stemming & Powder Factor Formula

Why subdrilling J adds explosive cost below grade while stemming T subtracts charge—yet Bank Volume stays strictly B * S * H!

Open-pit copper/gold mine and aggregate quarry blast engineers balance drill-and-blast cost against primary crusher/SAG-mill fragmentation! Each rotary blasthole of diameter D_h (mm) drilled on Burden B (m to free face) by Spacing S (m along row) across Bench Height H (m) breaks Bank In-Situ Volume V_bank = B * S * H (m³—subdrilling below floor grade NEVER counts toward payable bank volume, even though drilling J ~ 0.3*B below floor prevents hard toe humps!). Meanwhile, inert crushed-rock Stemming T (m at hole collar, ~0.7*B to prevent violent airblast/flyrock) leaves Charged Explosive Column Length L_charge = H + J - T (m), holding Bulk Explosive Mass W_exp = (PI() / 4) * ((D_h / 1,000)^2) * L_charge * (rho_exp * 1,000) kg, defining Volumetric Powder Factor PF_vol = W_exp / V_bank (kg/m³) and Tonnage Powder Factor PF_mass = PF_vol / rho_rock (kg/t)!

Verify on a 12.0 m Hard-Granite Quarry Production Bench—Hole_Diameter D_h = 165.0 mm (B2), Burden B = 4.50 m (B3), Spacing S = 5.20 m (B4), Bench_Height H = 12.00 m (B5 -> Bank Volume = 280.80 m³ in E2), Subdrilling J = 1.20 m (B6), Collar_Stemming T = 3.40 m (B7 -> Charge Column = 9.80 m), Pumped_Emulsion_Density rho_exp = 1.18 g/cm³ (B8), and Rock_Specific_Gravity rho_rock = 2.65 t/m³ (B9): Explosive Charge Mass per Hole equals 247.27 kg (E3), Volumetric Powder Factor hits 0.881 kg/m³ (E4), and Tonnage Powder Factor lands at 0.332 kg/t (E5)!

Open-Pit Bench Blasting Charge Column & Powder Factor Formula

Validate Hole_Diameter > 25 mm, Burden > 0, Spacing > 0, Bench_Height > 0, Subdrilling >= 0, Stemming > 0, positive Charge_Length (H + J - T > 0!), Explosive_Density in [0.60, 1.60] g/cm³, and Rock_Density in [1.50, 4.50] t/m³!

=LET(dm_h, B2, br_m, B3, sp_m, B4, bh_m, B5, sb_m, B6, st_m, B7, re_g, B8, rr_t, B9, IF(OR(dm_h <= 25, br_m <= 0, sp_m <= 0, bh_m <= 0, sb_m < 0, st_m <= 0, bh_m + sb_m <= st_m, re_g < 0.6, re_g > 1.6, rr_t < 1.5, rr_t > 4.5), "Invalid Blast Pattern", LET(vb_k, br_m * sp_m * bh_m, lc_h, bh_m + sb_m - st_m, ch_k, (PI() / 4) * ((dm_h / 1000) ^ 2) * lc_h * (re_g * 1000), ROUND(ch_k / (vb_k * rr_t), 3))))

Dry-Season Prilled ANFO Switch & Tightened Pattern Check (Set B = 4.0, S = 4.6, rho_exp = 0.82)

Switch dry summer blastholes from heavy pumped emulsion (1.18 g/cm³) to low-cost prilled ANFO (B8 = 0.82 g/cm³) while tightening Burden x Spacing to 4.00 m x 4.60 m (B3 = 4.0, B4 = 4.6): Bank Volume E2 tightens to 220.80 m³, Charge per Hole E3 drops to 171.83 kg, Volumetric Powder Factor E4 settles at 0.778 kg/m³, and Tonnage Powder Factor E5 lands at 0.294 kg/t!

=IF(ISTEXT(E5), E5, LET(vb_k, B3 * B4 * B5, lc_h, B5 + B6 - B7, ch_k, (PI() / 4) * ((B2 / 1000) ^ 2) * lc_h * (B8 * 1000), ROUND(ch_k / vb_k, 3)))

Further reading

• Arte Sheets Lesson — Two-Product Mineral Froth Flotation Recovery Formula
• Arte Sheets Lesson — Tumbling SAG & Ball Mill Critical Centrifuging Speed