Assignment #5 Open Pit Stripping Ratios ©Dr. B. C. Paul Summer 2003

Your Assignment Produce a Spreadsheet that will calculate stripping ratios for Cone and Cylinder Shaped ore deposits Produce a Spreadsheet that will calculate stripping ratios for Cone and Cylinder Shaped ore deposits Use it for the following Ore Body Use it for the following Ore Body –Ore is a vertical standing cylinder 700 ft in diameter The cylinder starts at the surface and goes to indefinite depth (ie keeps on going) The cylinder starts at the surface and goes to indefinite depth (ie keeps on going) –The Pit is a circular cone that is flat on the bottom (700 ft in diameter) – also called a frustum cone –The Pit Slopes back at 42 degrees from the horizontal

Your Assignment Cont. Make the Pit 665 feet deep from the surface to the flat bottom of the cone Make the Pit 665 feet deep from the surface to the flat bottom of the cone –Find the Volumetric Stripping Ratio Now Assume that Ore weighs 4700 lbs/cubic yard and Waste weights 4200 lbs/cubic yard Now Assume that Ore weighs 4700 lbs/cubic yard and Waste weights 4200 lbs/cubic yard –What is the weight based stripping ratio? Change the Slope to 35 degrees Change the Slope to 35 degrees –What is the weight based stripping ratio now? Plot the stripping ratio as a function of pit slope in 1 degree increments from 35 degrees down to 21 degrees Plot the stripping ratio as a function of pit slope in 1 degree increments from 35 degrees down to 21 degrees

Comments and Tips If you use a spreadsheet then the changes in cone angle will be instant. If you do it by hand it will be tedious If you use a spreadsheet then the changes in cone angle will be instant. If you do it by hand it will be tedious Most Spreadsheets calculate their trig functions in radians while we think in degrees Most Spreadsheets calculate their trig functions in radians while we think in degrees –To convert degrees to radians Deg * Π / 180 = Radians Deg * Π / 180 = Radians

More On Commentary You will need to calculate three shapes You will need to calculate three shapes –A large Cone that starts at the surface and comes to point at the specified angle –A small Cone that is 700 feet in diameter and slopes to a point at the specified angle –A cylinder 700 feet in diameter and 665 feet in height The large cone minus the small cone is the total pit volume The large cone minus the small cone is the total pit volume If you subtract the cylinder it will leave you with overburden volume If you subtract the cylinder it will leave you with overburden volume The cylinder is your ore volume The cylinder is your ore volume

Some Geometry Tips Sizing the Small Cone This Triangle Represents ½ the small cone This side is ½ cone diameter or 350 ft This angle is the slope angle This is a right angle (meaning this is a Right 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

More Geometry Tips Sizing 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