2. 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

3. 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

4. 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

5. 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

6. 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, S gr = 2.6 L / (2 * { E/ S gr } 0.33 ) = 6 inches Holes larger than 6 inches will likely cause cratering - smaller size is desirable

7. 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 L min = 5 * D e If D e = 3 inch hole then L min = 15 ft Check 15 / 6.37 = 2.35 ft (6.37 from burden formula with ANFO and 2.6 S gr )

8. 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

9. 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

10. 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