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Stiffness Ratio

Stiffness Ratio. Stiffness Ratio = B H / B where B H 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.

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Stiffness Ratio

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  1. 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

  2. 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

  3. 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

  4. 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

  5. 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

  6. 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)

  7. 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

  8. 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

  9. 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

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