Transcript Stiffness Ratio - Supplemental Teaching Resources

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