Assignment #5 Open Pit Assignment #5 Open Pit Stripping RatiosStripping Ratios

©Dr. B. C. Paul Summer 2003©Dr. B. C. Paul Summer 2003

Your AssignmentYour Assignment

• Produce a Spreadsheet that will calculate Produce a Spreadsheet that will calculate stripping ratios for Cone and Cylinder Shaped stripping ratios for Cone and Cylinder Shaped ore depositsore deposits

• Use it for the following Ore BodyUse it for the following Ore Body– Ore is a vertical standing cylinder 700 ft in Ore is a vertical standing cylinder 700 ft in

diameterdiameter• The cylinder starts at the surface and goes to indefinite The cylinder starts at the surface and goes to indefinite

depth (ie keeps on going)depth (ie keeps on going)

– The Pit is a circular cone that is flat on the bottom The Pit is a circular cone that is flat on the bottom (700 ft in diameter) – also called a frustum cone(700 ft in diameter) – also called a frustum cone

– The Pit Slopes back at 42 degrees from the The Pit Slopes back at 42 degrees from the horizontalhorizontal

Your Assignment Cont.Your Assignment Cont.

• Make the Pit 665 feet deep from the Make the Pit 665 feet deep from the surface to the flat bottom of the conesurface to the flat bottom of the cone– Find the Volumetric Stripping RatioFind the Volumetric Stripping Ratio

• Now Assume that Ore weighs 4700 Now Assume that Ore weighs 4700 lbs/cubic yard and Waste weights 4200 lbs/cubic yard and Waste weights 4200 lbs/cubic yardlbs/cubic yard– What is the weight based stripping ratio?What is the weight based stripping ratio?

• Change the Slope to 35 degreesChange the Slope to 35 degrees– What is the weight based stripping ratio now?What is the weight based stripping ratio now?

• Plot the stripping ratio as a function of pit Plot the stripping ratio as a function of pit slope in 1 degree increments from 35 slope in 1 degree increments from 35 degrees down to 21 degreesdegrees down to 21 degrees

Comments and TipsComments and Tips

• If you use a spreadsheet then the If you use a spreadsheet then the changes in cone angle will be instant. changes in cone angle will be instant. If you do it by hand it will be tedious If you do it by hand it will be tedious

• Most Spreadsheets calculate their Most Spreadsheets calculate their trig functions in radians while we trig functions in radians while we think in degreesthink in degrees– To convert degrees to radiansTo convert degrees to radians

•Deg * Deg * ΠΠ / 180 = Radians / 180 = Radians

More On CommentaryMore On Commentary

• You will need to calculate three shapesYou will need to calculate three shapes– A large Cone that starts at the surface and A large Cone that starts at the surface and

comes to point at the specified anglecomes to point at the specified angle– A small Cone that is 700 feet in diameter and A small Cone that is 700 feet in diameter and

slopes to a point at the specified angleslopes to a point at the specified angle– A cylinder 700 feet in diameter and 665 feet in A cylinder 700 feet in diameter and 665 feet in

heightheight• The large cone minus the small cone is the The large cone minus the small cone is the

total pit volumetotal pit volume• If you subtract the cylinder it will leave you If you subtract the cylinder it will leave you

with overburden volumewith overburden volume• The cylinder is your ore volumeThe cylinder is your ore volume

Some Geometry TipsSome Geometry TipsSizing the Small Cone

This Triangle Represents ½ the small cone

This side is ½ cone diameter or 350 ft

This angle is the slope angleThis is a right angle(meaning this is aRight triangle)

Height of cone can be found using the tangent function

Tan(θ) = Side Opposite (height we are after)/ Side adjacent(the 350 ft we know)

350 * Tan(θ) = Height of Triangle

VolumeHeight *350**3

1 2

More Geometry TipsMore Geometry TipsSizing the Big Cone

This side is Height of small cone plus 665 feet

This is the Slope Angle

This is a right triangle

Radius of Our Cone is

(Height of small cone + 650)/ Tan(θ) = Radius