First Step is Selection of Burden

• B = 0.67 * De * (E/Sgr)0.33

– De is hole diameter in inches

– Sgr is the specific gravity of rock where water = 1

– E is the relative weight strength of the explosive as measured by bubble test

• ANFO = 100• TNT = 115

– Burden is delivered in feet

Burden Corrections for Local Conditions

• Confinement near rear of the shot– Bc = B * 0.9

• Bedding Dips into Pit and Aides Toppling

• Bt = B * 1.18

Burden Corrections

• Bedding Dipping Into Face and Holding Material Back– Bf = B * 0.95

• Heavy Cracked and Degraded Rock– Bd = B * 1.3

• Thin Layers and Tight Joints– Bl = B * 1.1

More Burden Adjustments

• Massive Intact Rock– Bm = B * 0.95

• Sometimes Need to Apply Several Adjustments at Once

• Example Pick Burden for Back Row of A Shot in Hard Massive Limestone Using ANFO in 3 inch Hole– 0.95 * 0.9 * 0.67 * 3 * (100/2.6) 0.33 = 5.73 ft– Round and call it 5 ft 9 inches

Controlling Cratering

• Cratering is where material is blasted upward rather than to the side

• Cratering results from lighter free face to surface than into pit - characterized in a stiffness ratio

Stiffness Ratio

• Stiffness Ratio = BH/ B

– where BH is Bench Height

– B is the Burden

• Target Stiffness Ratios– 3 to 4 is normal range– > 4 does not improve fragmentation (may risk

cut-offs much above 6)– 2 - redesign if you can– < 2 - Get someone you don’t like near shot

Stiffness Ratio Example

• What is the Stiffness Ratio for a 40 foot bench with 6.5 feet of burden on each hole– 40 / 6.5 = 6.15

• Shot won’t crater• No real advantage to such a high bench

and small hole• May need to watch for cut-off problems in

later practice or other equations

The Problem of Interrelationships

• Burden is a function of Hole Size and explosive

• Acceptable Bench Height is a function of burden and thus hole size and explosive

• Hole Size is a function of drilling equipment - but so is bench height

• Solution is usually to find what parameter is fixed and work out from there

Suppose Bench Height is Fixed

• In a quarry thickness of rock layers may set• May have been set in a previous mine plan• May be fixed by grade control constraints in

metal mine– need to be able to selectively mine– can’t scramble ore face with explosives

• Working Height of Equipment may Set

Solving for Maximum Allowable Hole Size on a Fixed Bench

• Combining the Burden and Stiffness Ratio formulas and backsolving hole size– For SR = 2 , L = Bench Height = 40, E = 100,

Sgr = 2.6

– L / (2 * { E/ Sgr } 0.33) = 6 inches

• Holes larger than 6 inches will likely cause cratering - smaller size is desirable

Solving with a Fixed Hole Size

• Can Occur for Fixed Drilling Equipment• Can Determine a minimum acceptable bench

height with an approximation - Rule of 5– Lmin = 5 * De

– If De = 3 inch hole then Lmin = 15 ft

• Check– 15 / 6.37 = 2.35 ft (6.37 from burden formula with

ANFO and 2.6 Sgr)

What if I have no constraints and I’m Lost

• Most Real Problems Have Hidden Constraints

• Equipment may fix– A Truck size usually constrains loader and

loaders have digging height that may fix the bench

– A given type of drill can only drill holes of specific size range

– Hole loading technique may limit bench height

Finding Hidden Constraints

• Geology may Constrain– Need to mine certain intervals

• quarry rock quality control• toxic or substitute topsoil rock in coal mine

– Grade Control• height of bench averages out high and low grades

and may limit selective mining

– Need to Manipulate Problem Layers• hard layer on top won’t fragment in stemming zone• In middle may cause cut-offs

Finding Constraints

• Performance may constrain– May require certain fragmentation characteristics

or costs• fragmentation usually more uniform with smaller holes

and benches• fragmentation usually cheaper with larger holes and

benches

• Regulations may constrain– Some localities limit bench height for safety– Blast Vibration may limit charge length

Picking Stemming Length

• Stemming is the inert material places at the top of hole to constrain fly rock and noise

• T = 0.7 to 1 * B– where T is stemming in feet– use 0.7 for river gravel (digs into side of

hole and holds better)– use 1 for drill cuttings

Problems with River Gravel

• Gravel must be size to tightly fill the hole and not get hung-up (leaving void space where inert fill was required)

• Hole Diameter should be 20 times hole for good fill and no hang-ups– Sz = 0.05 * De

• Where Sz is the size in inches for gravel• If lot of gravel is finer it is probably drill cuttings and

won’t dig into side of hole

Get Subgrade

• Subgrade is length of drilling below level of next bench needed to pull the toe and keep a level bench surface

• J = 0.3 * B– where J is subgrade in ft

• Example– 0.3 * 6.5 = 2 ft of subgrade

Hole Spacing

• Depends on Stiffness Ratio and the Delay Timing on the Shot

• If SR < 4 and entire row is on single delay (no delay between holes)– S = ( L + 2*B) /3

• where S is the spacing

– Example - 15 foot bench with 6.5 ft burden• (15 + 13) /3 = 9 ft 4 inches

• Spacing to Burden Ratio (9.333/ 6.5 ) = 1.44

More Hole Spacing

• If SR < 4 but interhole delay is practiced

• S = ( L + 7*B) / 8

• Example– ( 15 + 7 * 6.5 )/8 = 7.562 ft

• Checking Spacing to Burden Ratio– 7.562 / 6.5 = 1.163

Additional Hole Spacings

• If SR > 4 and row is instantly fired– S = 2 * B

• If SR > 4 and row uses interhole delay– S = 1.4 * B

Observations about Hole Spacing

• Note that instantaneous delays require greater hole spacing– problem is bridging between holes - bridge

crater and loose forward throw– inner hole delay reduces problem– also gives us a clue on how to pre-split

• Lower SR allows holes closer– Lower SR comes from larger holes with less

powder and less tendency to bridge

Choosing a Primer Position

• Bottom Prime is Standard– Primer overdrives explosive and bottom of hole

and better kicks out toe– Kicks out bottom and collapses top for better

collected muckpile near face

• Top Prime– May overdrive explosive below stemming zone

and improve caprock break-up– Topples rock away from face to spread out

muck pile

Other Primer Placement Strategies

• Place Extra Boosters just below hard rock intervals– Overdrives the explosive for breaking up

rock

• Double Prime hole if powder column is too long or one zone produces cut-offs

• May have multiple explosive decks with inner deck stemming in single hole

The Cut-Off Risk Problem

• Cut-off involves a break in the detonation continuity of a powder column– Effects fragmentation performance– Can be a hazard to later mining operations

• Control is based on crack propagation from one hole to the next or to the face– Assume that cracks propagate at 20% of the

velocity of the p wave through rock

Cut-Off Formula

• Pcmax = 5 * B * Ve/ Vp + J

– Ve = velocity of detonation of explosive

– Vp = p wave velocity in rock

– Pcmax = longest powder column that can reliably detonate without risk of cut-offs

• Note that this will tend to form an upper limit on bench height for a given hole size - while cratering will form a lower limit

Review that 3 inch hole on a 40 ft bench where SR was > 6

• 5 * 6.5 * 11,000/ 12,000 + 2 = 31.79 ft

• But the powder column on a 40 foot bench is 37.5 feet!

• This bench is prone to cut-offs

• If can’t shorten bench or increase holes size then may want to consider double priming

Calculate Delay Timing

• Delays between rows in blast– Chosen based on avoiding backbreak,

vibration and cut-offs and creating the desired muck-pile shape

• Must be > 2 ms/ ft of burden– will backbreak from inadequate time for rock

movement if less

• 3 ms/ ft will cause pile high and close to the face

Timing Between Rows

• 4 ms/ft gives an average muck pile distribution and is usually safe from cut-offs

• 6 ms/ft gives a spread out muck pile with some cut-off risk– material starts out fast and slows - later rows

pile up into material blast front and are held back

– long delay times get front out of way of later material

Long Timing Between Rows

• 7 to 14 ms/ft is the range used for cast blasting– warning above 8 ms/ft the cut-off risk rises

rapidly

• 10 to 20 ms/ft is used on deep back rows to allow material in front to move and avoid backbreak without alteration of the drilling pattern

Inner Hole Delay Timing

• Timing between holes in the same row is controlled by material being blasted

• Sands, Loams, Coal (soft and spongy) use 1.8 to 2.1 ms/ft

• Limestone, Shale and Salt (medium grade sedimentary) use 1.5 to 1.8 ms/ft

• Quartzite, Basalt, Gneiss 1.2 to 1.5

• Diabase, Magnetite, Mica Shist, Compact Gneiss 0.9 to 1.2

Regulatory Constraints

• The more powder that blows on one delay the greater the vibration

• Regulations normally limit maximum vibration and thus charge that can be fired on one delay

• Charges detonating within 8 ms of each other are considered to be on the same delay

Supply Constraints

• Delays come in only specific delay times– in ms series the lower delays are every 25

ms up to 200 and every 50 up to about 500

• Can extend options with sequential blasting machines that send separate pulses at a fixed or now computer selected interval

• Delays on big patterns are harder than you think.

Du Pont Millisecond Delay Series Blasting Caps

Coal Mining Delay Sequence Caps