stiffness ratio stiffness ratio = b h / b where b h is bench height b is the burden target stiffness...
TRANSCRIPT
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