What is Digger

Isaaks & Co Specialists in Spatial Statistics

1042 Wilmington Way Emerald Hills CA 94062 Phone 650-369-7069

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September 7, 2015

What is Digger?

Digger is a C++ computer program for the design of constrained optimum

dig line design for open pit grade control. This document provides an

example using Digger. The example is based on a single blast of gold ore

containing approximately 135,000 tonnes of material. The blast contains

3,913 ore control model (OCM) blocks each measuring 2m x 2m x bench

flitch. Table 1 provides a sample of the input block model with a BlastID, block

coordinates, density, and gold grades. The BlastID variable is generally coded as

BlastID=1 if the block belongs to the current blast and BlastID=0 if the block is outside

of the current blast. The statistics of the ore control block model grades are given in

Figure 1.

A map showing 5 different ore types defined by au g/t cutoff grades is shown in Figure 2.

Note that waste is defined as containing less than 0.4 g/t au. However, the map in Figure

2 identifies high and low grade waste blocks by their light and darker grey colors. The

purpose of this distinction is to illustrate that where waste blocks are included in non-

waste dig lines, they are usually high grade waste blocks with grades just under the waste

cutoff grade (see Figure 4) thus minimizing dilution.

Table 1: An Example of the Input Ore Control Block Model

BlastID x y z Density Au

1 720051 7788935 1473.3325 2.59 0.4423137

1 720051 7788937 1473.3325 2.59 0.57111032

1 720051 7788939 1473.3325 2.59 0.71380657

1 720051 7788941 1473.3325 2.59 0.5656906

1 720051 7788943 1473.3325 2.59 0.53483204

1 720051 7788945 1473.3325 2.59 0.43616024

1 720051 7788947 1473.3325 2.59 0.30077431

Figure 1: Histogram and statistics of the ore control block model au grades in g/t for blast 456A. Note

there are 3,913 blocks in the blast which contains approximately 135,017 tonnes.



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Figure 2: A map showing the spatial patterns of ore types for blast 465A. The ore control model blocks

measure 2m x 2m x bench flitch.

Figure 3: This figure shows a set of dig lines designed at a minimum mining width of 6m in the mining

direction and 6 m perpendicular to the mining direction. The mining direction was set to an azimuth of 62

degrees which coincides with the directional trend seen in the pattern of mineralization.

As you can see, Digger enables the user to “rotate” the dig lines so that their design

coincides with either a digging direction or mineral trend or both. However, if you have

worked with rotated models, you know they can be confusing. Digger gets around this

by creating a new model rather than rotating the current ore control block model. Also

Digger generally re-sizes the blocks to 1/5 of the minimum mining width. For example,

for a 6 m minimum mining width, the original OCM blocks would be resized to 1.2 m.

Digger then proceeds to design dig lines on the new resized model. The new re-sized

OCM for blast 456A with dig lines is shown Figure 4.



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Figure 4: This figure shows the re-sized model built by Digger for dig line design. Note the blocks have

been reduced in size to 1/5 of the minimum width and rotated to the digging direction. Note that where the

dig line polygons include waste blocks, the waste blocks are generally “high grade” waste as indicated by

the dark grey color. For blast 465A, the dilution resulting from the inclusion of waste in non-waste

polygons is generally less than 2%.

Digger output is captured in 3 files;

A .csv txt file containing the dig line polygons. An example is shown in Table 2.

Note that this file is generally up loaded into the client grade control software

with a simple mouse click through a Python script.

A .csv txt file containing the resized OCM block model. The file contains the OCM and dig line ore type for each block as well as the gold grade etc. Each

OCM block is also identified by a polygon number. Thus, one can quickly

identify all blocks for any particular polygon for checking purposes. An example

of the output is given in Table 3.

A third .csv text file output by Digger is shown in Table 4. This file contains key statistics for evaluating a set of dig lines. For example, contents include;

o Date and time of run

o Input file names, and key control parameters.

o In situ tonnes and grade by ore type (before dig line design)

o Misclassification summary. This summary tells you the tonnes and grade

of each misclassified ore type within each of the dig line ore types.

o Dig line tonnes and grade by ore type (after dig line design)

o And finally we have ore loss, dilution and grade statistics. There are many

ways to quantify ore loss and dilution. Digger summaries are kept simple

so they are easier to understand. For example ore loss and dilution are

calculated as follows;

𝑑𝑖𝑙𝑢𝑡𝑖𝑜𝑛 /𝑜𝑟𝑒 𝑙𝑜𝑠𝑠 = total dig line tonnes / total in situ tonnes for each ore type.

If the calculated ratio above is greater than 1.0, it indicates dilution. If it is less than 1.0,

then we have ore loss. The logic is simple. There are X number of in situ tonnes of each

ore type available for mining before dig line design. However, the actual number of



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tonnes that can be mined given the minimum mining width constraint may be more

(dilution) or less (ore loss) following dig line design.

Grade statistics follow the same logic. Before dig line design, Digger calculates the

average grade of each in situ ore type. Then following dig line design, Digger calculates

the average grade of each dig line ore type. The dig line average ore type grades will be

delivered to the mill, stockpile, leach pad etc. given an efficient mining method and

minimum unplanned dilution. Thus, ideally, we would like to see the ratio of the in situ

and dig line grades as close to 1.0 as possible.

Table 2: An example of the Digger output

dig line polygon file in .csv format.

x y z N Oretype

720049.7 7788937.4 1473.3 1 W

720049.2 7788937.2 1473.3 2 W

720049.5 7788936.6 1473.3 3 W

720050.0 7788935.6 1473.3 4 W

720050.6 7788934.5 1473.3 5 W

720051.1 7788933.5 1473.3 6 W

720051.4 7788932.9 1473.3 7 W

720052.0 7788933.2 1473.3 8 W

720053.0 7788933.8 1473.3 9 W

720053.5 7788934.1 1473.3 10 W

Table 3: An example of the resized and rotated block model output by Digger

BLPLY x y z au ocm-ot dig-ot sg PolyNo

1 720049.98 7788936.91 1473.33 0.571 LG W 2.558 2

1 720050.55 7788935.85 1473.33 0.442 LG W 2.558 2

1 720051.11 7788934.79 1473.33 0.442 LG W 2.558 2

1 720051.67 7788933.73 1473.33 0.442 LG W 2.558 2

1 720049.92 7788939.6 1473.33 0.714 MG LG 2.558 10

1 720050.48 7788938.54 1473.33 0.714 MG LG 2.558 10

1 720051.04 7788937.48 1473.33 0.571 LG LG 2.558 10

1 720051.61 7788936.42 1473.33 0.571 LG LG 2.558 10

1 720052.17 7788935.36 1473.33 0.389 W W 2.558 2

1 720052.73 7788934.3 1473.33 0.389 W W 2.558 2



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Table 4: DIGGER SUMMARY INFORMATION FOR DIG-LINES 465A

DIGGER Version August 20 2015 11:00AM

Date and time ==> Mon Sep 07 13:32:10 2015

Working with OCM file C:\Users\ed\Google Drive\AhafoDigger2015\Digger\Digger\465A.csv

Working with Digger Control File AhafoControls.txt

Azimuth of Digging Direction ==> 62.0 or 152.0

The effective selective mining unit is 6.0 by 6.0 by 3.3 m or 120 cubic m

Read 11004 1.2 by 1.2 OCM Blocks,

---In situ OCM ore type tonnages---

Tonnes W ==> 63196

Tonnes LG ==> 22240

Tonnes MG ==> 11181

Tonnes HG ==> 7401

Tonnes VHG ==> 31040

Grand Total In situ Tonnes ==> 135057

---Average In situ Au Grade (g/t) per OCM Ore Type---

Average W Grade ==> 0.210

Average LG Grade ==> 0.484

Average MG Grade ==> 0.699

Average HG Grade ==> 0.899

Average VHG Grade ==> 2.234

Output block file is C:\Users\ed\Google Drive\AhafoDigger2015\Digger\Digger\465A_blks.csv

Output file with polygon points is C:\Users\ed\Google Drive\AhafoDigger2015\Digger\Digger\465A_poly.csv

---Misclassification Summary---

55390.3 tonnes W at 0.196 g/t au in W dig lines

2687.9 tonnes LG at 0.467 g/t au in W dig lines

822.3 tonnes MG at 0.669 g/t au in W dig lines

196.4 tonnes HG at 0.849 g/t au in W dig lines

196.4 tonnes VHG at 1.436 g/t au in W dig lines

4504.4 tonnes W at 0.337 g/t au in LG dig lines

15305.0 tonnes LG at 0.480 g/t au in LG dig lines

1436.0 tonnes MG at 0.669 g/t au in LG dig lines

454.1 tonnes HG at 0.895 g/t au in LG dig lines

319.1 tonnes VHG at 1.145 g/t au in LG dig lines

1755.1 tonnes W at 0.281 g/t au in MG dig lines

2295.1 tonnes LG at 0.508 g/t au in MG dig lines

4406.2 tonnes MG at 0.700 g/t au in MG dig lines

1656.9 tonnes HG at 0.886 g/t au in MG dig lines

1313.3 tonnes VHG at 1.334 g/t au in MG dig lines

1227.3 tonnes W at 0.275 g/t au in HG dig lines

1301.0 tonnes LG at 0.508 g/t au in HG dig lines

2540.6 tonnes MG at 0.707 g/t au in HG dig lines

2872.0 tonnes HG at 0.904 g/t au in HG dig lines

3866.1 tonnes VHG at 1.332 g/t au in HG dig lines

319.1 tonnes W at 0.257 g/t au in VHG dig lines

650.5 tonnes LG at 0.512 g/t au in VHG dig lines

1976.0 tonnes MG at 0.719 g/t au in VHG dig lines



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2221.5 tonnes HG at 0.907 g/t au in VHG dig lines 25344.8 tonnes VHG at 2.438 g/t au in VHG dig lines

---Total Tons per Dig line Ore Type---

Total tonnes W ==> 59293

Total tonnes LG ==> 22019

Total tonnes MG ==> 11427

Total tonnes HG ==> 11807

Total tonnes VHG ==> 30512

Grand Total Tonnes ==> 135062

---Average Au Grade (g/t) per Dig Line Ore Type---

Average W Grade ==> 0.221

Average LG Grade ==> 0.482

Average MG Grade ==> 0.697

Average HG Grade ==> 0.893

Average VHG Grade ==> 2.152

---Dilution, Ore Loss and Grade Statistics---

Dig Line Ore Type W

Dig Line/In Situ Tonnes 93.83%

Dig Line/In Situ Grade 105.14%

Dig Line Ore Type LG



Dig Line Ore Type MG



Dig Line Ore Type HG



Dig Line Ore Type VHG



Although Digger output may suggest a very complex program, all of the complexity is

taken care of internally with clever algorithms and clean C++ code. From the users

perspective, it couldn’t be simpler. For example for blast 465A, all of the control

parameters are given in Table 5. Very simple stuff – input fields, ore type names, cutoff

grades, minimum mining widths, dig direction and a maximum proportion of waste

blocks in non-waste dig line polygons (If the maximum proportion is exceeded, the dig

line polygon contents are re-classified as waste).

Digger is very fast. For example, Digger completed processing 465A.csv in 80 seconds.

One of my clients is particularly thrilled with Digger. Prior to Digger he was required to

manually design dig lines daily for an extremely complex deposit. Manual design

generally required an hour or so, but with Digger, he could complete dig line design in 5

minutes. Now he has more time for other tasks.

But the key advantage of Diggers speed and versatility is the ease with which grade

control engineers can adapt dig line design to local conditions. For example as mining



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progresses through a deposit, mineralogy and mineralization patterns often change.

Digger enables the grade control engineer to determine the most profitable set of local dig

lines by testing various control parameter values such as the minimum mining width, dig

direction, and cutoff grade. Given Diggers speed and the detailed summary statistics

shown in Table 4, grade control engineers are in a position to significantly reduce

dilution and ore loss as mining progresses through the deposit.

As an example consider the HG ore type shown in red in Figures 3 and 4. There are only

7401 tonnes of in situ HG ore type which is approximately 5.5% of the total tonnage in

the blast. Now with a careful examination of Figures 3 and 4 you will notice that the red

HG blocks are scattered throughout the blast. And given this sparse scattered pattern, it’s

not hard to imagine that given a 6 m minimum mining width, the HG dig line polygons

are going to suffer from significant dilution. And if you check the dilution and ore loss

statistics at the end of Table 4, you will see the dilution ratio is 159%. Or looking at it

another way, 37% of the material contained by the HG dig line polygons is non-HG. But,

look at the dig line HG average grade! It is within 99.34% of the in situ HG grade before

dig line design. In fact, if you review the tonnage and grade ratios for the remaining ore

types, you will see most of them are within 2% of the ideal. FYI, it’s generally accepted

that dilution is often in the order of 10% in mines with moderately complex

mineralization patterns similar to 465A.

For those of you who work with more complex ore deposits and multifarious ore types, I

have good news for you. Digger is now able to design constrained optimum dig lines for

deposits which define dozens of ore types. For example, in a recent study constrained

optimum dig lines were successfully designed for the case where 29 ore types are defined

by various combinations and threshold values of 7 different block model variables. The

key is a new optimization algorithm based on geometric shapes and fuzzy matrices. The

objective function remains the same as that of Diggers initial revenue based optimization

algorithm and that is to minimize the number of blocks misclassified by dig lines for a

given minimum mining width. However, Digger is no longer limited by complex ore type

definitions. If the ore types can be defined by a set of “Rules” or if-then-else statements,

Digger can design constrained optimum dig lines no matter how many ore types are

defined. As an example, Table 6 shows a moderately complex set of rules that define 7

ore types given 8 block model variables.

Table 5: The Digger Control File

!!---DIGGER CONTROL PARAMETERS -- August 20 2015---

!!--Comment lines begin with double exclamation mark

!!---INPUT FIELDS(columns) for variables blastID,x,y,z,au(g/t) in input file

1,2,3,4,6

!!---INPUT FIELD(column) for density or SG in input file

5

!!---Default Density---

2.59

!!---ore types by name----



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W,LG,MG,HG,VHG !!---cutoff grades (order W/LG, LG/MG, MG/HG, HG/VHG)---

0.40,0.6,0.8,1.0

!!---OCM block dimensions (DX,DY,DZ)---

2.0,2.0,3.332

!!---MMW_x and MMW_y---

6,6

!!---Digging Direction (Azimuth)---

62.0

!!---Maximum proportion of OCM waste blocks in dig line polygon---

1.0

Table 6: A snippet of C++ code showing the “Rules”

function which defines 7 ore types given 8 block grades.

The ore type is returned as a character string in *ot.

int Rules(struct point *ocm, char *ot ){

//---BLPLY,x,y,z,cu,au,eqcu,nag,pb,zn,mtyp,ortyp,sg—

float au,cu,eqcu,nag,pb,zn,mtyp,ortyp;

cu = ocm->grade[1];

au = ocm->grade[2];

eqcu = ocm->grade[3];

nag = ocm->grade[4];

pb = ocm->grade[5];

zn = ocm->grade[6];

mtyp = ocm->grade[7];

ortyp = ocm->grade[8];

if( eqcu < cutff[1] || cu < cutff[4] || pb > cutff[6] || zn > cutff[5] ) {

if( mtyp > cutff[7] ){

//---Green ore type---

strcpy(ot,"Grn");

} else if( nag < cutff[8] ){

//---blue ore type---

strcpy(ot,"Blu");

} else if( nag >= cutff[8] ){

//---red ore type---

strcpy(ot,"Red");

} else {

strcpy(ot,"Blu");

}

} else if( ortyp > cutff[9] ){

//---problematic ore type---

strcpy(ot,"Prob");

} else if( eqcu < cutff[2] )

//---Medium ore type---

strcpy(ot,"Med");

else if( eqcu < cutff[3] )

//---High grade ore type---

strcpy(ot,"High");

else if( eqcu < 100.0 )

//---Super high grade ore type---

strcpy(ot,"Super");

else {

strcpy(ot,"Blu");

}

return(0);

}



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Why Digger?

Revenue Increase! Dig line misclassification errors are usually very costly.

For example, given 35 dollar rock, the loss of a single 600 tonne OCM block

sent to the dump exceeds 20 thousand dollars. Similarly waste blocks may be

classified as mill feed and so on. In fact, given N ore types in a single blast, the number

of possible misclassification types is N2-N. For example, given 4 ore types, there are 12

different ways blocks may be misclassified by dig lines in a single blast. And the bad

news is that none of these misclassification errors cancel one another. The total dollars

lost simply accumulate with each misclassified block. For instance, at 35 dollar rock the

dollars lost by a dozen or more 600 tonne mill feed blocks located within a few waste dig

line polygons exceeds a quarter million dollars! Over the course of a single year,

misclassification losses may exceed several million dollars! Digger minimizes these

losses.

Digger is currently being used by Newmont Mining Corp, Barrick Gold, Freeport

McMoRan, MMG, and IAM Gold. I am very proud of the latest installation of Digger

which is at Grasberg. Test cases and demonstrations at these properties show in situ net

revenue increases ranging between 2% and 7%.

Comments from Industry

“We implemented Digger in 2008 and it has been an integral part of our operation since.

The added efficiency and confidence in ore delineation Digger offers has helped us

remain productive in a challenging mining environment. We are excited to see what

benefits will emerge from Digger 2015”. Senior Mine Geologist, Bald Mountain, Nevada,

Barrick Gold Corporation.

“Scoping studies of a combined LAK and Digger ore control system for two of

Yanacocha’s oxide ore bodies showed a 5 – 7.5% increase in net revenue by addressing

ore loss and dilution relative to the conventional Ordinary Kriged and manually defined

polygon system that it replaced in 2010”. Yanacocha Ore Control Group, Peru,

Newmont Mining Corp.

“Approximately 1 year ago, we implemented Digger and it has become the main tool for

defining ore polygons. For each bench, we define polygons manually and with Digger.

When we make the comparison between both methods, it’s very exciting to notice that the

Digger polygons earn an average of 5% more ounces than manual method. The result is

2,500 ounces Au gained per 1.8 ha of bench”. Essakane Mine, Burkina Faso,

IAMGOLD.

Digger is a new product, but interest within the industry is growing. Imagine a 2% to 7%

increase in revenue with no additional sampling, employees, or equipment, just a simple

computer program. Call today 650-369-7069 or email [email protected] and take

advantage of an introductory offer.

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