Calculating Stripping Ratios Calculating Stripping Ratios for Area Strip Minesfor Area Strip Mines

Mnge 315Mnge 315

©Dr. B. C. Paul spring 2003 revised 2010©Dr. B. C. Paul spring 2003 revised 2010

Note – These notes contain information considered Note – These notes contain information considered common knowledge to those familiar with Strip common knowledge to those familiar with Strip

Mining. Books such asMining. Books such as

““Elements of Practical Coal Mining” and SME’s Elements of Practical Coal Mining” and SME’s “Surface Mining” were specifically referenced“Surface Mining” were specifically referenced

Stripping Ratio as a Stripping Ratio as a FundamentalFundamental• Ability to surface mine depends on the value Ability to surface mine depends on the value

of the ore being high enough to offset the of the ore being high enough to offset the cost of Overburden Removalcost of Overburden Removal– Stripping Ratio determines relative amounts of Stripping Ratio determines relative amounts of

each to be movedeach to be moved• If coal generates a $5/ton earning and If coal generates a $5/ton earning and

overburden costs 45 cents per cubic yard to overburden costs 45 cents per cubic yard to move – what is the maximum economic move – what is the maximum economic stripping ratiostripping ratio

• $5.00/ 0.45 = just over 11 cubic yards per $5.00/ 0.45 = just over 11 cubic yards per tonton

• Called a “Break Even Stripping Ratio”Called a “Break Even Stripping Ratio”

Complexities WarningComplexities Warning

• Units of Stripping Ratio depend on convenience Units of Stripping Ratio depend on convenience of the industryof the industry– Coal overburden is normally light and machines are Coal overburden is normally light and machines are

limited by volume in cubic yardslimited by volume in cubic yards– Coal is sold by the tonCoal is sold by the ton– Cubic Yards/ton makes senseCubic Yards/ton makes sense

• Hard Rock MetalHard Rock Metal– Both ore and overburden are truckedBoth ore and overburden are trucked– Both are heavy and trucks are usually weight limitedBoth are heavy and trucks are usually weight limited– Tons/ton makes sense (unit-less)Tons/ton makes sense (unit-less)

More WarningsMore Warnings

• Geometry problems usually measure Geometry problems usually measure volumes which convert to tons only if volumes which convert to tons only if density is the same for all materialsdensity is the same for all materials

• Material may be rehandledMaterial may be rehandled– Get operating and geologic stripping Get operating and geologic stripping

ratiosratios•Don’t use 40 cents per cubic yard to figure Don’t use 40 cents per cubic yard to figure

stripping ratio off of geometry if you have stripping ratio off of geometry if you have 10% rehandle10% rehandle

Fixed and Variable CostsFixed and Variable Costs

• Example of the CarExample of the Car– If you have a carIf you have a car

• InsuranceInsurance• Licensing FeesLicensing Fees• Storage or Parking SpaceStorage or Parking Space

– These Costs constant per unit of time regardless These Costs constant per unit of time regardless of use of carof use of car

• Variable CostsVariable Costs– GasGas– TiresTires– Oil ChangesOil Changes– Largely Dependent on mileage you driveLargely Dependent on mileage you drive

Fixed and Variable Costs in Fixed and Variable Costs in MiningMining

• Some mining costs are fixed (many Some mining costs are fixed (many administrative features for example)administrative features for example)

• Others are variable – direct materials Others are variable – direct materials handling costhandling cost

• What goes into Break Even Stripping RatioWhat goes into Break Even Stripping Ratio

• Direct materials costs go into Break EvenDirect materials costs go into Break Even

• Fixed Costs are charged to the average Fixed Costs are charged to the average stripping ratio you mine over the timestripping ratio you mine over the time

Simple Stripping RatiosSimple Stripping RatiosBottom of aStrip Mine

Top of a Strip Mine

For a pit 1 mile long and160 ft across, how significantlyDifferent is the length at the topAnd bottom of the pit?

Volumes are Length * Width * Height

Ratio is A/B

What happens if the length term inBoth A and B is the same number

It cancels – Long strip pits can beAnalyzed as 2D problems!!!Life is Good

The 2D Cross SectionThe 2D Cross Section

Overburden

Area = Base * Height

Interest Item – Slope AngleHas no effect

Base for both coal and the overburden is the sameThat means the base will cancel!

The problem is 1DOnly depends onThickness and density

The Coal Area Strip Mine The Coal Area Strip Mine FormulaFormula

• Strip Ratio = OB Thickness (in ft) * Strip Ratio = OB Thickness (in ft) * 11.11/ Coal thickness in inches11.11/ Coal thickness in inches– Assumes coal is 80 lbs/ft^3 (good for Assumes coal is 80 lbs/ft^3 (good for

bituminous)bituminous)– Area Strip Mine GeometryArea Strip Mine Geometry– Geologic Stripping Ratio – no accounting Geologic Stripping Ratio – no accounting

for rehandle or less than 100% coal for rehandle or less than 100% coal recoveryrecovery

Your TurnYour Turn

• Use What You Have Learned About Use What You Have Learned About Calculating Stripping Ratios for Strip Calculating Stripping Ratios for Strip Mines and Break Even Limits to Mines and Break Even Limits to Determine the Size of a Coal ReserveDetermine the Size of a Coal Reserve– Do Assignment #3Do Assignment #3

A Little ExplanationA Little ExplanationVery seldom is a coal seam the sameDistance from the surface always

Less overburden meansMore profit. Project worth is increased if you take the

Biggest profits first – thus strip mines startShallow and work into deeper stuff.

Is it possible that eventually the coalWill get deep enough to exceed the break-evenStripping ratio – of course!

In your homework you will look at a coal reserve – start shallow and work until it isDeep enough you can’t afford it anymore. Then you’ll tell me how far you could mine.