Calculating Stripping Ratios for
Simple Open Pits
Mnge 315
©Dr. B. C. Paul spring 2003
Open Pit on Pipe Shaped
Disseminated Deposit
Cone
1/3*Base*Height
Cylinder
Base * Height
You’ve seen these
Formulas derived in
Your calculus classes
Getting Our Cone
Our Frustum Cone =
The Big Cone we Imagine -
The Little Cone
We are missing
Getting Our Overburden
The Frustum Cone
we just calculated -
The Part of that
Volume that is
PAY DIRT!
Calculating Stripping Ratio
Just One Catch
Calculation we just did
Was based on Volumes
Stripping Ratio = Overburden / Ore
We assumed no material
Was rehandled and all
Ore was recovered
Called a Geologic Volumetric
Stripping Ratio
The Problem with Volumetric
Stripping Ratios
• Most Open Pit materials are weight limited
in the trucks
– The economics are driven by weights not
volumes
• Easy to Fix
– Overburden Tons =OB Volume * Tons/unit vol
– Ore Tons = Ore Volume * Tons/unit vol
• Make sure you don’t mess up your units
• Divide again to get Weight based SR
Interesting Observation
What happens if we
Change the slope
Angle?
What just happened to the overburden volume?
What just happened to our stripping ratio?
Conclusion – Pit Slope Makes a Big
Difference in Open Pits
Comments on Generality
• 1/3rd base * height really works on cones of any base
•
•
•
•
•
shape
Base * Height works on “Cones” of any base shape
Formulas work on ellipse and oval bases
Formulas work even if the “pipe” shaped ore body is not
vertical
Formulas work for irregular shaped bases (provided you
can get the area)
Conclusion – importance of Pit Slope on Open Pit
Economics is a general truth not restricted to circular
cones, frustums, and cylinders
Your Assignment
• Produce a Spreadsheet that will calculate
•
stripping ratios for Cone and Cylinder Shaped
ore deposits
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 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
– Find the Volumetric Stripping Ratio
• 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
– 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
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
• Most Spreadsheets calculate their trig
functions in radians while we think in
degrees
– To convert degrees to radians
• Deg * Π / 180 = Radians
More On Commentary
• 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
If you subtract the cylinder it will leave you with
overburden volume
The cylinder is your ore volume
Some Geometry Tips
Sizing the Small Cone
1
*  * 350 2 * Height  Volume
3
This side is ½ cone diameter or 350 ft
This is a right angle
(meaning this is a
Right triangle)
This angle is the slope angle
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
This Triangle Represents ½ the small cone
More Geometry Tips
Sizing the Big Cone
This is a right triangle
This is the Slope Angle
Radius of Our Cone is
(Height of small cone + 650)/ Tan(θ) = Radius
This side is Height of small cone plus 665 feet