lerchs grossman method

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LERCHS-GROSSMAN METHOD
A Computer Assisted Method of Designing Optimum Pit on a Vertical Section
Designing Open Pits
Manual
Method
Computer Method
Computer-Assisted
Automated
LERCHS-GROSSMAN
Lerchs-Grossman
ADVANTAGES
it eliminates trial-and-error process of manually designing the pit in each section
it is convenient for computer processing
DISADVANTAGE
ultimate pit resulting from the smoothing of all the vertical sections is probably not optimal
Figure 1. Vertical section showing the net value* of each block.
*net value if the block is mined and processed independently
1
2
3
4
5
6
7
8
9
10
11
1
-$2
-$2
-$4
-$2
-$2
-$1
-$2
-$3
-$4
-$4
-$3
2
-$5
-$4
-$6
-$3
-$2
-$2
-$3
-$2
-$4
-$5
-$5
3
-$6
-$5
-$7
$6
$13
-$2
-$5
-$4
-$7
-$4
-$6
4
-$6
-$6
-$8
-$8
$17
$8
$5
-$6
-$8
-$9
-$7
5
-$7
-$7
-$8
-$8
$6
$21
$5
-$8
-$8
-$9
-$7
6
-$7
-$9
-$9
-$8
-$5
$22
-$8
-$8
-$8
-$9
-$8
7
-$8
-$9
-$9
-$9
-$8
$10
-$9
-$9
-$9
-$9
-$9
0
1
2
3
4
5
6
7
8
9
10
11
1
-$2
-$2
-$4
-$2
-$2
-$1
-$2
-$3
-$4
-$4
-$3
2
-$5
-$4
-$6
-$3
-$2
-$2
-$3
-$2
-$4
-$5
-$5
3
-$6
-$5
-$7
$6
$13
-$2
-$5
-$4
-$7
-$4
-$6
4
-$6
-$6
-$8
-$8
$17
$8
$5
-$6
-$8
-$9
-$7
5
-$7
-$7
-$8
-$8
$6
$21
$5
-$8
-$8
-$9
-$7
6
-$7
-$9
-$9
-$8
-$5
$22
-$8
-$8
-$8
-$9
-$8
7
-$8
-$9
-$9
-$9
-$8
$10
-$9
-$9
-$9
-$9
-$9
-7
-13
-19
-26
-33
-41
-2
-6
-11
-17
-2
-24
-33
-42
STEP 1: Add the values down each column of blocks.
The upper value in each block represents the cumulative value of the material from each block to the surface.
STEP 2: From the top block in the left column and working down each column, put an arrow pointing to the left-adjacent block with the highest bottom value.
-4
-2
3
-4
-2
3
-4
-2
3
0
0
0
0
0
0
0
0
0
0
0
0
x
-2
-2
-4
-2
-2
-1
-2
-3
-4
-4
-3
x
-7
-6
-10
-5
-4
-3
-5
-5
-8
-9
-8
x
-13
-11
-17
1
9
-5
-10
-9
-15
-13
-14
x
-19
-17
-25
-7
26
3
-5
-15
-23
-22
-21
x
-26
-24
-33
-15
32
24
0
-23
-31
-31
-28
x
-33
-33
-42
-23
27
46
-8
-31
-39
-40
-36
x
-41
-42
-51
-32
19
56
-17
-40
-48
-49
-45
The bottom value in each block represents the total net value of (1) material from the block, (2) the blocks in the column and (3) the blocks in the pit profile to the left of the block.
 
= -2
+
0
= -2
-2
Bottom Value =
Upper Value of the block
+
Bottom Value of the block pointed by the arrow
-2
-8
STEP 2: From the top block in the left column and working down each column, put an arrow pointing to the left-adjacent block with the highest bottom value.
0
0
0
0
0
0
0
0
0
0
0
0
x
-2
-2
-4
-2
-2
-1
-2
-3
-4
-4
-3
x
-7
-6
-10
-5
-4
-3
-5
-5
-8
-9
-8
x
-13
-11
-17
1
9
-5
-10
-9
-15
-13
-14
x
-19
-17
-25
-7
26
3
-5
-15
-23
-22
-21
x
-26
-24
-33
-15
32
24
0
-23
-31
-31
-28
x
-33
-33
-42
-23
27
46
-8
-31
-39
-40
-36
x
-41
-42
-51
-32
19
56
-17
-40
-48
-49
-45
STEP 3: Trace the arrows back to get the outline of the pit starting from the top row block with the maximum total value.
-2
-8
-2
-4
-12
-25
-2
-9
-11
-32
-6
0
15
0
10
18
39
46
5
8
34
46
2
3
25
31
-1
17
16
13
8
10
-2
-1
-2
-3
The optimal pit for this example is $13.
0
1
2
3
4
5
6
7
8
9
10
11
1
-$2
-$2
-$4
-$2
-$2
-$1
-$2
-$3
-$4
-$4
-$3
2
-$5
-$4
-$6
-$3
-$2
-$2
-$3
-$2
-$4
-$5
-$5
3
-$6
-$5
-$7
$6
$13
-$2
-$5
-$4
-$7
-$4
-$6
4
-$6
-$6
-$8
-$8
$17
$8
$5
-$6
-$8
-$9
-$7
5
-$7
-$7
-$8
-$8
$6
$21
$5
-$8
-$8
-$9
-$7
6
-$7
-$9
-$9
-$8
-$5
$22
-$8
-$8
-$8
-$9
-$8
7
-$8
-$9
-$9
-$9
-$8
$10
-$9
-$9
-$9
-$9
-$9
These steps are repeated to all the vertical sections.
Smoothing, or fitting together of all the vertical sections is done manually by the engineer.
End of Lecture