The document discusses methods for estimating mineral reserves, specifically focusing on the triangular method. It defines mineral reserves and describes proven and probable reserves. It then explains the triangular method which involves calculating the area of the ore body using triangular sections, determining the average thickness, calculating the volume by multiplying area and thickness, and finally estimating reserves by multiplying volume by density. Examples are provided to demonstrate how to use the triangular method and calculate reserves using different techniques to determine average thickness.

1. MINERAL RESERVES
ESTIMATION BY USING
TRIANGULAR METHOD
BY
MD.NUMAN HOSSAIN
DEPT. OF PME ,SUST.

2. MINERAL RESERVES :
• A Mineral Reserve is the economically mineable part of a Measured and/or
Indicated Mineral Resource.
• It is described as total workable or probable working which depending on
thickness of deposit , it’s depth , quality , geological factors etc.
• In general mining practice , there are two types of mineral reserves .
• These are: (1) probable reserve & (2)proven reserves

3. :Proven Reserves Probable reserves
Proven reserves constitute mining assets with
greater confidence than any other mining assets
In other word , reserves in fully explored deposits
Probable reserves constitute mining assets with
lesser confidence than the proven reserves
In other word , reserves in estimated and fully
explored deposits
Mineral recovery :
 In mining , the process of valuable mineral extraction in known as mineral recovery
 It is the measure of mining or extraction efficiency
 For mineral recovery it is very essential to estimate ore reserves,know the mineable reserves ,
pit limits , cutoff grade etc .
 In this slide we will discuss only about different methods for estimating ore reserves.

4. Methods of ore reserves estimation
Triangular method
Polygonal methods
Method of sections (plans); longitudinal, transverse
Regular grid, random stratified grid
Inverse distance weighting (1/d, 1/d2, 1/d2.7, 1/d3, etc.)
Contouring methods
Here we only discuss about triangular method to estimate ore reserves.

5. Triangular method
By using triangular method, the area of the ore body is calculated
After that , this calculated area is multiplied with average thickness of the ore to
calculate the volume of the ore body
The average thickness can be calculated by
 Using known thickness of the ore body
 Using grade and the length of ore body
 Using weight age average thickness
After calculating volume , multiplying this value with ore density to estimate the
ore reserves.

7. • Here ,the area of the rectangle abcd = ( X3 – X2) (Y3 –Y1)
• Area of triangle A1 = ½ ( X2 - X1)(Y2-Y1)
• Area of triangle A2= ½ (X3 –X2) (Y3 –Y1)
• Area of triangle A3= ½ (X3 –X1)(Y3 –Y2)
• So the area of ore A = area of rectangle abcd – area of triangle (A1+A2+A3)

8. Calculate A for the following
Easting ( x )m northing (y) m
1100 1200
1500 1200
1100 800

9. Triangular method
• Using above equation
• The area of rectangle =(1100-1500)(800-1200)=160000 m2
• The area of triangle A1+A2+A3 = 1/2 (( 1500-1100)(1200-1200)+(1500-1100)(1200-
800)+(1100-1100)(800-1200)) =80000 m2
• The area of ore body ,A=160000-80000=80000 m2

10. Calculation of average thickness of the ore
body:
1. If thickness is givenC1= 3 m, C2=5 m,C3= 4 m , then ave. thickness =(C1+C2+C3)/3
=(3+5+4)/3 =4 m
2. If the length of the ore body (m) and the gradient(%) is given then the ave. thickness
is calculated by t(ave) = ∑tigi / ∑gi , for example we calculate ave thickness for
following case :
ymbol

11. The ave thickness , t(ave) =(0.6*0.59+1.4*0.48+1.4*0.6+1.4*0.56+1.3*0.32)/(0.59+0.48+0.6+0.56+0.32)
=0.503 m
3.calculation of reserves using weight age average thickness . For this case the following equ is used:
weight age ave. thickness, tw =( (t1Ѳ1+t2Ѳ2+t3Ѳ3)/60 )÷3 = (t1Ѳ1+t2Ѳ2+t3Ѳ3)/ 180 .an example
problem related with this is given bellow : where thickness t1=40 m, t2 =60 m ,t3 =50 m.
Length of the ore body (m) grade(%)
0.6 0.59
1.4 0.48
1.4 0.6
1.4 0.56
1.3 0.32

13. Now, ore volume calculation:
• Ore volume = area of the ore body * average thickness
• For , first case, t(ave)=4 m, so, ore volume = 80000*4 =320000 m3
• For , second case , using length of the ore body and grade, ave thickness = 0.503
So, for this ore volume = 80000*.503 =40240 m3
• For third case, weight age ave thickness , tw =50.77 m then ,
ore volume = 80000*50.77 =4061600 m3
N.B.here, I use one example problem for several ave thickness ,so don’t be confused with
evaluated ore volume .This indicates just calculation procedure . Here, the ave thickness
data had not been obtained from same ore reserve but I use here only to show the
evaluation procedure ,and so, ore volume can’t be obtained same for all time.

14. Ore reserve estimation:
• Ore reserve(in tons) =ore volume(m3) * density of ore (tons/m3)
• For example ,if the density of the ore = 1.35 tons/m3.
• Then ,for 1st case, ore reserves =320000*1.35 =432000 tons.
• For 2nd case, ore reserves = 40240*1.35 =54324 tons.
• For 3rd case, ore reserves =4061600*1.35 =5483160 tons.

15. Exercise Problem :
• For 1st fig the following parameters are given for a ore deposit :
• If the thickness for first layer C1=4 m, C2=8m ,C3=3m and for 2nd layer
C1=5m,C2=7m,C3=6m .And the density of the ore is 2.5 tons/m3 .Then estimate the
reserves for this ore deposit.
Easting (x) m Northing (y) m
300 700
600 300
100 0

16. Exercise Problem :
• Estimate the reserves by using triangular method for the following mineral
deposit(having density =1.024 tons/m3:
Length of ore body (m) grade (%)
.9 .62
1.2 .56
1.2 .61
1.8 .49
2.1 .68
2.8 .65
2.8 .61
2.5 .57
2.2 .52
1.9 .48
x (m) y(m)
3500 600
1365 450
350 46
N.B. use fig :1

17. Exercise Problem : Ѳ2
Ѳ1
Ѳ3
t3(800,1000)
t1(200,500)
t2(600,1500)
Calculate the reserve of the ore shown in above fig having density 2.65 tons/m3 by using the weight
average thickness , when t1=80 m, t2 = 125 m, t3 = 98 m.

18. Exercise Problem
• Calculate the reserve of the ore shown in above fig having density 2.65 tons/m3 by
using the weight average thickness where others information has give

21. References :
• Open Pit Mine Planning and Design,TwoVolume Set & CD-ROM Pack
-William A. Hustrulid, Mark Kuchta, Randall K. Martin
• Applied Mineral Inventory Estimation - ByAlastair J. Sinclair & Garston H.
Blackwell
• Internets & others

22. THAT’S ALL
THANKS……..