Big Dog Mining

Surface Bench Blast Pattern

Burden, spacing, stemming, subdrill and explosive per hole from your hole diameter and bench height. Two published methods, worked side by side, because where they disagree is worth knowing before you drill 200 holes.
Surface bench blasting only: vertical holes to a free face. Underground ring, drift and stope rounds work differently and are not what this calculates.
Once you have a pattern, Surface Blasthole Drill Productivity tells you what it costs to drill it.

Step 1: The hole and the bench

Everything downstream scales off these two numbers.

Units ?

Source equations are imperial. Metric is converted.

Blasthole diameter ?in

Drilled diameter, not the bit size you meant to use.

Bench height ?ft

Floor to crest. Hole depth is deeper by the subdrill.

Drill pattern ?

Sets the spacing-to-burden ratio.

Rock being blasted ?

Fills the bank density below. Override it for your own rock.

Bank density auto ?lb/yd³

Weight in the ground, before the shot.

Step 2: The explosive

Choosing a product fills in density, detonation velocity and energy.

Product ?

Density auto ?g/cc

As loaded in the hole.

Explosive energy class auto ?

For the Ash burden ratio. Our suggestion, not the book's.

Rock hardness ?

Pairs with energy class to set the Ash burden ratio.

Powder factor ?

The design target. Pick your ground or enter your own.

Powder factor value auto ?lb/yd³

Explosive per unit volume of rock broken.

burden

spacing

explosive per hole

Step	Value	Where it comes from

Bench section: one hole, to scale

Plan view: the pattern

Stemming and scaled depth of burial

Stemming is what holds the gas in the hole. How well it does that is measured as scaled depth of burial: how deep the charge sits, divided by the cube root of its weight, in ft/lb^1/3, the same units as cube-root scaled distance. The figure below is for the pattern above, worked with Wiss's equation for stemming shorter than the powder column, as the US Bureau of Mines published it.

scaled depth of burial

Stemming shorter than the powder column	B_s = D_cg ÷ W^1/3	USBM RI 8485, p. 77
Stemming longer than the powder column	not computed here	p. 77 prints B_s = 3/2 × S^2/3 ÷ W^1/3, which is not in ft/lb^1/3 and does not meet the first equation where stemming equals the column; the errata sheet does not correct it
D_cg, depth to the charge's center of gravity, ft	stemming + half the powder column	definition p. 76; the half column is ours, for an evenly loaded vertical hole
S, stemming length, ft; W, charge weight, lb	from the working above	Eq. 11.2 and Eq. 11.5, SME MRH p. 280

2.3 ft/lb^1/3	20 dB less airblast (1/10)	Wiss, via USBM RI 8485, p. 77
4.6 ft/lb^1/3	40 dB less airblast (1/100)	Wiss, via USBM RI 8485, p. 77
6.8 ft/lb^1/3	60 dB less airblast (1/1000)	Wiss, via USBM RI 8485, p. 77

Worked case, the values this page loads with: 12.0 ft of stemming over a 22.0 ft powder column holding 218 lb. Stemming is the shorter, so D_cg = 12.0 + 11.0 = 23.0 ft, W^1/3 = 6.02, and B_s = 23.0 ÷ 6.02 = 3.82 ft/lb^1/3 (1.52 m/kg^1/3): past the 2.3 step, short of 4.6.

Wiss measured those steps on 9 to 12 inch holes up to 120 ft long, so on a smaller hole read them as a guide, not a limit. The same report treats a scaled depth of burial above 1.4 m/kg^1/3 (about 3.5 ft/lb^1/3) as properly confined, "a condition usually met in typical mine blasts" (p. 97). And the reason it matters past the noise: "improper stemming or insufficient burden often leads to high air blast, which is usually accompanied by flyrock" (SME Mining Engineering Handbook, 3rd ed., p. 458).

Commercial explosive characteristics

Type	Grade	Density, g/cc	Detonation velocity, ft/s	Energy, RBS	Water resistance
Straight dynamite	50% ditching dynamite	1.32	17,400	n/a	Good
Ammonia dynamite	40%	1.30-1.32	9,800-12,500	146	Fair
Ammonia dynamite	60%	1.28-1.30	12,470-15,300	152	Very good
Semi-gelatin	n/a	1.29	13,100	n/a	Very good
Semi-gelatin	n/a	1.16	12,600	n/a	Very good
Semi-gelatin	n/a	1.26	17,500	149	Very good
Semi-gelatin	n/a	0.94	11,300	n/a	Good
Straight gelatin	80%	1.35-1.43	18,700-22,000	201	Excellent
Ammonia gelatin	40%	1.30-1.50	11,000-18,500	146-171	Excellent
Ammonia gelatin	60%	1.34-1.43	17,400-18,900	164	Excellent
Ammonia gelatin	80%	1.34	20,200	199	Excellent
Water gel	Packaged 2-9 in. diameter	1.18-1.52	13,230-19,000	128-183	Very good
Emulsion	Bulk	0.95-1.28	13,100-19,000	103-156	Excellent
Emulsion	Package HE	1.10-1.20	13,500-17,000	102-167	Excellent
ANFO	Poured	0.77-0.85	9,100-15,100	100	None
ANFO	Pneumatic loading	0.85-1.10	9,000-11,000	100-122	None
ANFO/Emulsion mix	20:80	1.05	16,400	138	Poor
ANFO/Emulsion mix	30:70	1.20	17,400	166	Fair
ANFO/Emulsion mix	40:60	1.30	18,100	185	Good
ANFO/Emulsion mix	50:50	1.30	17,900	179	Excellent
ANFO/Emulsion mix	60:40	1.30	17,500	175	Excellent
ANFO/Emulsion mix	70:30	1.30	17,100	169	Excellent
ANFO/Emulsion mix	80:20	1.30	16,700	165	Excellent

SME Mining Reference Handbook, 2nd ed., p. 279. RBS is relative bulk strength with ANFO as 100. Water resistance matters more than the energy figure on a wet hole: ANFO has none at all.

Ash burden ratios, K_b

Explosive energy	Soft rock	Average	Hard rock
Low	30	25	20
Average	35	30	25
High	40	35	30

SME Mining Reference Handbook, 2nd ed., Table 11.2, p. 281, after Ash 1963. Burden is then K_b × hole diameter ÷ 12. The same table appears identically in the 1st edition on p. 207, which is a useful independent check on the transcription.

Published powder factors

Source	Condition	lb/yd³
General surface blasting	Low difficulty	0.25-0.40
General surface blasting	Medium difficulty	0.40-0.75
General surface blasting	High difficulty	0.75-1.25
General surface blasting	Very high difficulty	1.25-2.50
Surface metal, by seismic velocity	Weathered limestone, 1,000-2,000 ft/s	0.20
Surface metal, by seismic velocity	Weathered porphyry, 2,000-3,000 ft/s	0.60
Surface metal, by seismic velocity	Rhyolite breccia, 3,000-4,000 ft/s	0.75
Surface metal, by seismic velocity	Monzonite porphyry, 4,000-5,000 ft/s	1.00
Surface metal, by seismic velocity	Quartz sericite porphyry, 5,000-6,000 ft/s	1.00
Surface metal, by seismic velocity	Fresh limestone, 5,000-6,000 ft/s	1.00
Surface metal, by seismic velocity	Massive jasperoid, 6,000-12,000 ft/s	1.30
Surface coal	Large dragline, shale	0.50-0.80
Surface coal	Large dragline, sandstone	0.70-1.00
Surface coal	Shovel, shale	0.60-0.90
Surface coal	Shovel, sandstone	0.70-1.20
Surface coal	Front-end loader, shale	0.70-1.10
Surface coal	Front-end loader, sandstone	0.80-1.30
Surface coal	Cast blasting, shale	0.90-1.30
Surface coal	Cast blasting, sandstone	1.10-1.80

Materials not in the handbooks. Rock salt appears nowhere in any of the 22 references behind these tools: not in Table 10.4-1, not in the Caterpillar weight-of-materials table, and nowhere in the full text. Its row is kept separately, shown under its own heading in the picker, and labeled on screen every time it is used. Bank density 2.16 t/m³ is the density of pure NaCl, the figure used for Avery Island domal salt (Oak Ridge, Thermal Properties of Rock Salt); swell 1.49 is the 49% Church (1981) gives for well-blasted rock, via the NRC report Bulking Factor of Rock for Underground Openings. Potash and trona are deliberately absent: the same treatment needs a source per material, and inventing two more rows to round out a list is how a table stops being trustworthy.

Worth saying plainly: salt is mined underground, room and pillar, not from a surface bench. That is very likely why no bench-blasting table carries it. The row is here for its density if you want tonnage, but the pattern this page works out is a surface pattern, and an underground round is a different calculation.

General surface blasting and the seismic-velocity table: SME Mining Reference Handbook, 2nd ed., pp. 284-285. Surface coal and surface metal mines: SME Mining Reference Handbook, 1st ed., p. 209.

These are first approximations. The source says so in as many words: the empirical methods here give a starting pattern that needs adjustment to meet field conditions. Structure, water, free faces, timing and what the last shot actually did all move these numbers, and none of that is in the equations. Shoot it, look at the muck pile and the back, and adjust.

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Worked example

Worked with the values this page loads with, so the method can be checked against the cited source without entering anything. Change any input above and the calculator recomputes; the numbers below stay as a fixed reference case.

15.1 ft
22.6 ft
218 lb

Load factor	9.91 lb/ft	Eq. 11.1: 0.34 × 0.810 × (6.00 in)², p. 280
Stemming	12.0 ft	Eq. 11.2: 24 hole diameters, p. 280
Subdrill	4.0 ft	Eq. 11.3: one third of stemming, p. 280
Bench height	30.0 ft	your input
= drilled hole depth	34.0 ft	bench + subdrill
= powder column	22.0 ft	Eq. 11.4: bench + subdrill − stemming, p. 280
= explosive per hole	218 lb	Eq. 11.5: powder column × load factor, p. 280
÷ powder factor	0.57 lb/yd³	published table
= rock broken per hole	379 yd³	Eq. 11.6, p. 280
Burden	15.1 ft	Eq. 11.7, p. 281
Spacing	22.6 ft	Eq. 11.8: 1.5 × burden, p. 281
Ash burden ratio K	25	Low energy, Average rock, Table 11.2 p. 281
Ash burden	12.5 ft	Eq. 11.12: K × 6.00 in ÷ 12, p. 281
Ash powder factor	0.84 lb/yd³	same charge over the Ash pattern
Bank density	4,000 lb/yd³	Shales, Table 10.4-1 p. 933
Rock per hole	759 short tons	rock broken × bank density
Powder factor by weight	0.287 lb/ton	explosive per hole ÷ rock per hole

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Estimating aid only. This is not an engineering design and not a substitute for the judgment of a competent or qualified person. Verify every result against the cited source and your own site conditions. Full terms and disclaimer.