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Page 1: REPORT MM 498

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TABLE OF CONTENTS LIST OF FIGURES ...................................................................................................................................... ii

DEFINITION OF TERMS .......................................................................................................................... iii

ABBREVIATIONS ..................................................................................................................................... iv

1.0 MINE BACKGROUND AND GENERAL INFORMATION ............................................................... 1

1.1 LOCATION AND ACCESSIBILITY: ............................................................................................... 1

1.2 GEOLOGY AND RESERVES. .......................................................................................................... 1

2.0 PROBLEM STATEMENT ..................................................................................................................... 3

2.1 MAIN OBJECTIVE ............................................................................................................................ 3

2.2 SPECIFIC OBJECTIVES ................................................................................................................... 3

2.3 SCOPE OF THE STUDY ................................................................................................................... 3

3.0 METHODOLOGY ................................................................................................................................. 4

4.0 LITERATURE REVIEW ................................................................................................................. 5

4.1 VOLUME SURVEYING ................................................................................................................... 5

4.1.1 PRINCIPLES OF VOLUME CALCULATION .......................................................................... 5

4.1.2 TRAPEZOIDAL METHOD ........................................................................................................ 6

4.1.3 SIMPSON METHOD ................................................................................................................. 7

4.1.4 DIGITAL CLOSE RANGE PHOTOGRAMMETRY ................................................................. 9

4.1.5 GPS SURVEYING .................................................................................................................... 13

4.1.6 DIGITAL TERRAIN MODEL ( DTM ) ................................................................................... 14

4.2 SHOVEL TRUCK PRODUCTION SYSTEM ................................................................................. 21

4.3 MINE FLEET DISPATCHING SYSTEM ....................................................................................... 23

4.3.1 BENEFITS OF FLEET DISPATCHING .................................................................................. 23

4.3.2 TRUCK DISPATCH SYSTEM ................................................................................................. 23

4.3.3 MANUAL DISPATCHING SYSTEM ...................................................................................... 25

4.4.4 SEMI-AUTOMATED DISPATCHING SYSTEM ................................................................... 25

4.4.5 FULL AUTOMATED DISPATCHING SYSTEM ................................................................... 26

5.0 POSSIBLE SOLUTIONS TO THE PROBLEM .................................................................................. 27

6.0 DATA COLLECTION PLAN .............................................................................................................. 28

7.0 REFERENCES ..................................................................................................................................... 29

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LIST OF FIGURES

FIGURE 1 : A map showing the location of Buzwagi mine. ........................................................ 1

FIGURE 2: Coordinate of object points (Pi) by triangulating bundles of observation rays from

different image planes (Li)............................................................................................................ 10

FIGURE 3: Conical Stockpile ...................................................................................................... 14

FIGURE 4: Triangles making up TIN that defines the ground model ......................................... 16

FIGURE 5: Thiessen-polygon ...................................................................................................... 19

FIGURE 6: Vonoroi-diagram, Delaunay-triangulation and the empty circle ............................... 20

FIGURE 7: Truck dispatch system ............................................................................................... 23

LIST OF TABLES

TABLE 1: Action plan .................................................................................................................. 28

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DEFINITION OF TERMS

Cycle time is a Time used by a machine to complete a single unit of operation.

Density is the ratio of the mass of a substance to its volume, and it can be calculated by dividing

the mass by the volume.

Digital imaging is a method of making images without the use of conventional photographic

film. Instead, a machine called scanner records visual information and converts it into a code of

ones and zeroes that a computer can read.

Fleet is a number of loading and hauling equipment working and managed as single unit

Mine dispatch is a center of information between the machines and equipment operation,

performance and mine production.

Payload is the quantity of load that a truck, or other vehicle that can carry, often expressed in

terms of weight or volume.

Software is a computer program; instructions that cause the hardware or the machines to do

work.

Stockpile is a collection and storage of large amounts of material.

Surveying is a mathematical science used to determine and delineate the form, extent, and

position of features on or beneath the surface of the earth for control purposes.

Swell factor is the percentage increase of material volume when are removed from in situ.

Terrain is a ground or a piece of land seen in terms of its surface features or general physical

character, especially for crossing it.

Truck factor is percentage of the rated capacity that a truck is assigned to carry at a particular

time and particular conditions.

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ABBREVIATIONS

3D – Three Dimension

BCM – Bank Cubic Meter

DEM – Digital Elevation Model

DGM – Digital Ground Model

DGPS – Differential Global Positioning System

DHM – Digital Height Model

DTEM – Digital Terrain Elevation Model

DTM – Digital Terrain Model

EDM – Electronic Digital Measurement

GCP – Ground Control Point

GNSS – Global navigation satellite system

GPS – Global Positioning System

HEX – Hydraulic excavator

ILRIS- Intelligent Laser Ranging & Imaging System

JDS – Jigsaw Dispatching System

KPI – Key Performance Indicator

LCD – Liquid Crystal Display

LCM – Loose Cubic Meter

MHz – Megahertz

OHT – Off- Highway Truck

SAE – Society of Automotive Engineers

TIN – Triangulated Irregular Network

UHF – Ultra High Frequency

VHF – Very high Frequency

WL – Wheel Loader

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1.0 MINE BACKGROUND AND GENERAL INFORMATION

1.1 LOCATION AND ACCESSIBILITY:

The Buzwagi Project is located in Kahama District, Shinyanga region, in northwest Tanzania.

The mine lies on the divide defined by boundaries of the Hindagi river watershed, which drains

toward Lake Victoria, and the Kagozi river watershed, which drains toward Lake Tanganyika.

The mine is located approximately 6 km east of Kahama town along the tarmac road, and

approximately 100 km west of the town of Shinyanga.

Figure 1 : A map showing the location of Buzwagi mine.

The Buzwagi open pit is located on land for which Pangea Mineral Limited (PML) acquired a

prospecting license in 1992. Between 1995 and 2000, this land was optioned to and explored by

Anmercosa Service (East Africa) Limited. In 2003, Pangea initiated its own exploration

program. Because of this exploration program, a design was made in 2004 to move the project

into development phase and in 2008 started the mining operations.

1.2 GEOLOGY AND RESERVES.

Buzwagi is hosted in the Nzega Belt, which consists of the lower portion of the Nyanzian

system. This belt is composed of basalts and intermediate volcanic intruded by granitoid masses.

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The regional structure elements are dominated by a deep seated structural trend referred to as the

Nzega shear. This shear comprises numerous second and third order structures in which the

Buzwagi deposit is likely hosted in one of these supplementary shears. Buzwagi mine operates a

single open pit mine; the size of the pit is approximately 0.9 km wide and 1.2 km length.

Production began in may 2009, expecting to generate 250 thousand to 260 thousand oz of gold

per year in its first full five years of operation. Proven and probable reserves at Buzwagi are 3.3

million oz of gold and 79 million kg (175 million lb) of copper. The expected mine life based

upon proven and probable reserves is about 15 years. With continued exploration indicating

additional reserves, it is anticipated that the life of mine may be extended.

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PROJECT TITLE:

A COMPARISON OF TONS MINED ON A MONTHLY BASIS MEASURED AGAINST

THE TONS REPORTED FROM SURVEY VOLUMES AT BUZWAGI GOLD MINE

2.0 PROBLEM STATEMENT

In mining industry, it is vital to get correct production figures as they are presented before

stakeholders and different shareholders. At Buzwagi mine, production figures are tracked and

recorded on daily basis by using a jigsaw dispatching system and at the end of the month are

compared to the monthly surveyed volumes.

A big difference has been noticed to exist between the production reports and the survey reports

whereas figures reported by dispatcher are higher than those reported by the surveyors.

2.1 MAIN OBJECTIVE

To investigate the causes of the variation and the best way to ensure the two reports are

presenting the same figures.

2.2 SPECIFIC OBJECTIVES

To determine the effectiveness of the jigsaw dispatching system

To review the material density and the swell factor

To review the truck factor

To review the volume computation by surveying methods

To compare the tons from production against surveyed volumes

2.3 SCOPE OF THE STUDY

The project will deal with blasted and mined material from the pit for the purpose of mine

production at Buzwagi mine.

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3.0 METHODOLOGY

1. Literature review

Literature review method includes reading books, journals, papers, past technical and

professional reports and searching the internet on selected items of concern to this

project. Notes taking technique of the important points from the literature review material

is applied to make the literature meaningful and clear to understand. The selected topics

in the literature review are outlined below;

Volume Surveying

Introduction to volume surveying

Principles of volume calculation

Volume computation methods

GPS surveying

Digital terrain modeling

Shovel truck production system

Mine fleet dispatching system

2. Data collection

Data will be collected on site from Geology, survey and production sections/departments.

Data collected will range from material density, stockpile volumes, truck factors and

production data.

3. Data analysis

Data collected will be analyzed to bring the meaningful interpretation. Tables, graphs,

variances, deviations and other statistical presentations of data will be applied.

4. Conclusion

Discussion and conclusion from the analysis of the data done above will be presented.

5. Recommendation

Recommendations will be given as solution to the problem of this project. The

recommendation will depend on the findings done while conducting this project through

the steps outlined above.

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4.0 LITERATURE REVIEW

4.1 VOLUME SURVEYING

Volume surveying is the process of gathering location and other information that can be used to

determine the volume of an object or area. Volume surveying may be used to determine the

amount of material that is available in a mound of Earth (such as in mining applications to

measure the volume of a mound of material). Calculation of excavation and filling volumes is an

important issue in many engineering and mining disciplines. Accurate 3D shape reconstruction

and volume estimation are important in applications of estimation of the ore removed from a

mine face. There are many surveying classical methods for volume computing. The trapezoidal

method (with rectangular or triangular prisms), cross sectioning (trapezoidal, Simpson, and

average formulae), and improved methods (Simpson-based, cubic spline, and cubic Hermite

formulae) are well known. Efficient high accuracy volume computation is an important question

both theoretically and practically.

The accuracy of volume depends on the way the land surface is presented. The total number of

X,Y,Z coordinate points, the distributions of these points and the interpolation methods are also

important. Without doubt, a sufficient number of properly distributed points provide better

representation of the land surface. However, extra points mean more time and cost. Sometimes

obtaining geodetic points can be risky if not impossible. For this reason, the surface of land in

most cases cannot be represented correctly.

4.1.1 PRINCIPLES OF VOLUME CALCULATION

Several methods can be used to calculate a volume. Every method has its own advantages and

disadvantages depending on the shape of the object. Those can be differed in two groups: linear

and surface objects. Streets, railways, dams, tunnel etc are seen as linear objects whereas surface

objects are landfills, shaft pits, dumps etc. For linear objects, the common used method is the

cross sectioning method. The volume of a surface object can be computed with the trapezoidal

method ( rectangular or triangular prisms ), classical cross sectioning ( trapezoidal, Simpson, and

average formula ) and improved methods ( Simpson-based, cubic spline, and cubic Hermite

formula ).

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4.1.2 TRAPEZOIDAL METHOD

Two ways are possible to calculate the volume with the trapezoidal method: rectangular or

triangular prisms. The advantage of the rectangular method is the regularity of the modelling.

However, extreme shapes of the terrain cannot be depicted. The triangular structure fits optimal

to the terrain. The volume can be determined by the multiplication of the medial height with the

area.

Formula for triangular prisms

……………………………………………………………………Equation 1

….………………………………………………………………………………………Equation 2

………………………………………………….……………………….Equation 3

i = name of one triangle

n = number of all triangles

hi1, hi2, hi3 = height of each vertex of one triangle

hmi = medial height of one triangle

V = volume of the object

Vi = volume of one triangle

Fi = area of one triangle

Formula for rectangular prisms

……………………………………………………………………….Equation 4

……………………………………………………………………………………..Equation 5

Here is:

hm = medial height of all vertices

gi = number of the on the vertex adjoining rectangles

hi = height of the vertex

n = number of the all rectangles

V = volume of the whole object

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F = surface of the whole object

h0 = height of the horizontal reference face

This is the formula for an area with many rectangles. One rectangle can be calculated like the

triangle, but then there are four heights and four divides the sum. The volume can also be

determined with the product of area and the medial height. However, if there are many rectangles

it is easier with this formula. The volume can be calculated between the object ( e.g. a DTM )

and a reference plane or between two objects. If the calculation is done in the second way, it is

better to compute first the volume between the object and a reference plane. Then the difference

of both results can be taken. If one object is not horizontal but if it is sloped, there can be errors.

(Bettina Pflipsen pp 9-10)

4.1.3 SIMPSON METHOD

A basic approximation formula for definite integrals which states that the integral of a real-

valued function ƒ on an interval [a,b] is approximated by h[ƒ(a) + 4ƒ(g + h) + ƒ(b)]/3,

where h = (b - a)/2; this is the area under a parabola which coincides with the graph of ƒ at the

abscissas a, a + h, and b.

A method of approximating a definite integral over an interval which is equivalent to dividing

the interval into equal subintervals and applying the formula in the first definition to each

subinterval. The rule is used in the calculation of volume of material using the contour lines from

a geological map. Specifically, it is the following approximation:

…………………………Equation 6

Composite simpson's rule

When the function we are trying to integrate is not smooth over the interval, means that either the

function is highly oscillatory, or it lacks derivatives at certain points then the interval [a,b] is

broken into a number of small subintervals.

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Simpson's rule is then applied to each subinterval, with the results being summed to produce an

approximation for the integral over the entire interval. This sort of approach is termed the

composite Simpson's rule.

…………………..Equation 7

where xj = a + jh for j = 0,1,...,n − 1,n with h = (b − a) / n; in particular, x0 = a and xn = b. The

above formula can also be written as

…….…Equation 8

Alternative extended simpson's rule

This is another formulation of a composite Simpson's rule: instead of applying Simpson's rule to

disjoint segments of the integral to be approximated, Simpson's rule is applied to overlapping

segments, yielding:

..Equation 9

Simpson's 3/8 rule

Simpson's 3/8 rule is another method for numerical integration proposed by Thomas Simpson. It

is based upon a cubic interpolation rather than a quadratic interpolation. Simpson's 3/8 rule is as

follows:

……Equation 10

The 3/8 rule is about twice as accurate as the standard method, but it uses one more function

value. (http//www.answers.com/simpson rule)

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4.1.4 DIGITAL CLOSE RANGE PHOTOGRAMMETRY

Digital close range photogrammetry is a technique for accurately measuring objects directly from

photographs or digital images captured with a camera at close range. Photogrammetry is a

computer based process that performs 3-D measurement from digital photographs. The software

conducts 3-D measurements from stereo images – two images taken from different angles to the

left and a right – of the object of measurement. The resulting model 3-D surface is accurate often

on a sub-centimetre level which makes it ideal for field mapping.

Multiple, overlapping, images taken from different perspectives, make possible measurements

that can be used to create accurate 3D models of objects.

The Ground Control Points (GCPs) in the photogrammetric method are used to calculate the

position and orientation of each camera in a stereo pair of photographs. In many cases the

placement cannot be made because of inaccessibility or safety restrictions. In this case,

correction points on objects can be used as GCPs. In addition, an accurate automatic orientation

procedure can be used to obtain the relative orientation of the whole set of images. One of the

basic problems in photogrammetry is the correspondence problem, which is to identify 2D points

in two images that are projections of the same 3D point in the real world. From corresponding

points within the image sequences the relative orientation and the 3D positions of the

corresponding points can be estimated. Usually, two persons are needed for the classical

measurement. Photogrammetric processing itself can be done by one person. Only GCPs have to

be measured on the terrain by classical methods.

However, it requires fewer points compared to evaluation of all points or lines in a quarry or a

mine. Therefore, photogrammetric methods are used more and more often in this case. 3D

models obtained from stereo images are used in many applications. Many different algorithms

are employed to evaluate these images. Dense surface measurements and dense matching

methods are the two techniques frequently used to obtain object surfaces. Automatic image

matching techniques take shorter time in processing.

The multi-image matching approach was originally developed for the processing of satellite and

aerial images and it has been extended to a certain extent to process close-range images.

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Photogrammetry techniques allow conversion of images of an object into a 3D model. Using a

digital camera with known characteristics (lens focal length, imager size, and number of pixels),

one needs a minimum of two pictures of an object.

If the same three object points in the two images can be identified and a known dimension

indicated, then one can determine other 3D points on the images.

The photogrammetric 3D coordinate determination is based on the co-linearity equation which

states that object point, camera projective centre and image point lay on a straight line. The

determination of the 3D coordinates from a definite point is achieved through the intersection of

two or more straight lines.

Therefore, each point of interest should appear in at least two photographs. Later, coordinates are

measured from the 3D model which is constructed by photogrammetric software.

L2

L3

L1

P5 L4

P6

P4

P1

P2 p3

FIGURE 2: Coordinate of object points (Pi) by triangulating bundles of observation rays from different

image planes (Li) (Source; H. Murat Yilmaz,The Arabian Journal for Science and Engineering, Volume 33, Number

1A)

Compared to classical surveying methods, digital close range photogrammetry is efficient and

rapid, significantly reducing the time required to collect data in the field. Measurements

collected in less than three days in the field would have taken 10 days in a conventional survey.

Secondly, it is considerably safer. All surveyors are able to obtain precise measurements without

physically accessing any of the measurement points.

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Finally, the process produces a comprehensive visual record of existing site conditions from

which any identifiable features can be measured or geometrically assessed at a later date.

Digital close range photogrammetric methods have been successfully applied to projects in

archaeology, architecture, automotive and aerospace engineering, and civil and mining

engineering.

The same process can be used to obtain dimensional measurements efficiently on inaccessible

structures such as tunnels and dams, and large or complex facilities such as refineries or water

treatment plants.

Digital close range photogrammetric measurements can be integrated with 3D modeling and

reverse engineering processes. The acquired data can be very extensive and the cost savings

substantial.

Volume computation in close range photogrammetry

Current methods used for estimating the volume assume that the ground profile between the grid

points is linear (based on the trapezoidal rule), or nonlinear (based on Simpson’s 1/3 and 3/8

formulas). Generally speaking, the nonlinear profile formulas provide better accuracy than the

linear profile formulas. However, all the methods mentioned have a common drawback: the

joints (grid points) of any two straight lines (the trapezoidal rule), quadratic polynomials

(Simpson’s 1/3 formula), or cubic polynomials (Simpson’s 3/8 formula) form sharp corners.

Geodetic instruments have been used to survey point coordinates in classical methods. But in the

photogrammetric method point coordinates can be obtained from the 3D model of the object.

Simpson equations are been used in volume calculation

……………………Equation 11

here:

Fi…n = cross section area,

Li…n = distance between cross sections.

In the case of rectangular and triangular prisms on the object surface, during the volume

calculation of the excavation area, by means of trapezoidal methods, volume calculation is made

using the equation

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…………………….…………………..Equation 12

In this formula F is base areas, H is average height.

Volume values are obtained from the differences between pre- and post surfaces in the

excavation area. Volume under the f(x,y) function can be determined with double integrals:

V =

……………………………...…………………..Equation 13

In the softwares, this integral can be computed by the trapezoidal rule:

…………….……………….Equation 14

………………………..………….Equation 15

For coefficients (1,,2,,2,,2,……,2,2,1);

By an Extended Simpson Rule:

………………………..Equation 16

……………………………Equation 17

For coefficients (1,4,2,4,2,4,2,……,4,2,1);

Or by the extended Simpson 3/8 Rule:

……..…………….Equation

18

……...…………………………Equation

19

For coefficients (1,3,3,2,3,3,2,…,3,3,2,1).

(H. Murat Yilmaz and Murat Yakar, pp 66-67)

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4.1.5 GPS SURVEYING

GPS data collected can be combined to assist in survey volume calculations.

The most mining GPS systems are implemented as Differential GPS (DGPS). These systems

require a reference station that acts as a base for the entire GPS network at the mine site. The

corrections calculated are from the GPS coordinates compared to the known coordinates of the

references station and are transmitted by the radio network to the rovers in the field.

When the rovers receive the corrections from the reference station, the corrections are applied to

the position determined from the rovers GPS. In turn this enables the precise position to be

known, all in real-time. One reference station can support unlimited rovers. To maintain

communication between the reference station and the rovers a radio network is required at all

times. If radio communication is required over long distances, radio repeaters can be installed

around the site to relay the data corrections between the reference station to the rovers or onto

another radio repeater in the network.

Most radios used in GPS fall in one of the following frequency ranges: 150 – 174 MHz (VHF);

406 –512 MHz (UHF) and 902 – 928 MHz (spread spectrum).

The GPS surveying rover pack is designed to be more lightweight and user friendly for survey

personnel using the equipment on foot and walking over uneven ground. The basic pieces of

Equipment required for GPS surveying are: GPS receiver, GPS antenna, radio and radio antenna,

lightweight batteries for power, cables, backpack, handheld data collector.

The distinct advantage of using GPS for surveying in open pit mining is that only a single

surveyor is required to operate a GPS rover, compared to the traditional two-man crew when

utilizing a total station (theodolite) method of surveying.

When the volume of a pile of stock material has to be calculated, a common method is to have an

individual with a GPS unit walk around the perimeter of the pile to establish GPS ground

reference points for calculating the base area. Then the GPS operator has to climb the pile in order

to get height reference points. This approach, however, has several risks. First, it is potentially

hazardous as it exposes workers to injuries caused by falling debris, or collapsing into unstable

material.

Second, it is time consuming; third, it is often inaccurate once the number of satellites available

for signal transmission is not adequate.

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Figure (3) shows how the surface area of a cone- shaped stockpile is estimated based on three

GPS points at the base of the pile and one at the top. Using the equation below the volume can be

calculated based on the cone’s geometry.

FIGURE 3: Conical Stockpile

h

…………..Equation 20

rr

(Optech field notes, pp1)

4.1.6 DIGITAL TERRAIN MODEL ( DTM )

Different countries have different names for one thing: digital terrain model. There are also

descriptions like digital elevation model (DEM), digital height model (DHM), digital terrain

elevation model (DTEM), digital ground model (DGM), etc. All this names describe the same

subject. Only the basis for the calculation is different.

Definition: The digital terrain model (DTM) is simply a statistical representation of the

continuous surface of the ground by a large number of selected points with known X, Y, Z

coordinates in an arbitrary field. The aim is to describe a terrain model on a mathematical basis

in this way that it could be handled and read by a computer.

How models are formed in DTM

A digital ground or terrain model (DGM/DTM) is created on computer from three dimensional

data sets consisting of easting, northing and height.

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The data sets are often generated from field observations and recordings to total station (EDM)

or Global Positioning Systems (GPS or GNSS). This is only possible when work has been

carried out. When a volume is to be computed at tender stage then it is necessary to extract the

3D data from the contract documents, usually the setting out drawings. The data will then be

manually input to the computer. In some instances when the proposed works have been designed

on a 3D computer model then this can be imported into the system. Most software use some form

of Triangulated Irregular Network (TIN) process to create the model.

With this, triangular planes are formed between points surveyed and the shape is controlled by

break lines linking up lines of detail and topographic features such as the top and bottom of an

excavation or sudden changes in gradient. The method has its limitations in that plane rather than

curved surfaces are formed but practical use over many years has proved the method. Figure (4)

shows a screen grab with the triangles that make up the TIN.

In forming a model it is important for the field surveyor or site engineer to pick up as much

detail as possible particularly the break lines. When recording data prior to work commencing

such as with an original ground level survey this is not a problem as the whole site is available

and visible. However once work has commenced it is often, if not always, the case that the areas

to be surveyed are exposed for short periods of time. There is no period when, for example, the

whole site is soil stripped, because as it is stripped the reduced dig is being undertaken. It is in

this instance that the surveying of break lines is made more difficult. It is also the case that the

soil strip survey for example is built up over a number of days or weeks from a number of

different surveys. It is worth making a special note that when it is necessary to create a ground

model to define an element that is yet to be constructed it is usually necessary to rely on the

setting out drawings. These drawings are often of a poor standard, typical problems are a lack of

easting and northing co-ordinates or co-ordinates that have no height to define them and levels

which are sporadic, only indicative of the actual position, falls that do not tie up with levels etc.

To overcome this it is necessary to interpolate levels to co-ordinates and vice-versa.

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FIGURE 4: Triangles making up TIN that defines the ground model

(source; Kemp Engineering)

The more points are registered the better will be the model. However, the more points are

recorded the more expensive the model will be. The skill of the terrain modeling consists in the

registration of the exact shape of the terrain with a minimum of data.

(Kemp Engineering, pp 1-3)

For the modeling and calculation of the DTM, there are four approaches:

1. point-based modeling

2. triangle-based modeling

3. grid-based modeling

4. A hybrid approach combining any two of the above three item

The most used are the grid-based and the triangle-based modeling. In most of the programs, the

user can choose which one he wants to take. There are some differences in the result because of

the different basis.

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Because the points are normally not measured in a regular grid, the heights have to be

interpolated for the grid-based modeling. For that reason with this method, there is created an

artificial model without direct measured points.

However, if there are two horizons it is easier to make a cut and compare it or to calculate a

difference model.

The only thing the user can choose is the distance between the lines of the grid. The smaller the

distance is, the more data have to be computed and the longer time is taken for calculation. In

contrast to this, triangles are more flexible.

Thus, they can better incorporate break lines etc. and the approach to the terrain is more accurate.

The model is created of the original points; each point is a vertex of a triangle.

There are three requirements for a TIN:

1. For a given set of data points, the resulting TIN should be unique if the same algorithm is

used, although one may start from different places, for example, the geometric centre,

upper-left corner, lower-left corner or other points.

2. The geometric shapes of resultant triangles are optimum, that is, each triangle is nearly

equilateral, if there are no specific conditions.

3. Each triangle is formed with nearest neighbor points, that is, the sum of the three edges of

the triangle is minimum

All these requirements are fulfilled in the Delaunay-triangulation. There are different methods to

create a triangulation. Each method has its own basis criterion.

Shorter diagonal: in a quadrangle these diagonal - of the two diagonals – is taken, which

is shorter.

triangulation with minimal weight: the sum of the triangle side gets minimal; between n

points there are n rectilinear connections; these are ordered of the length and all the lines

which cut a shorter are eliminated ( n is the number of measured points ).

max-min-angle criterion: triangles are created, which smallest angle is as big as possible

The last criterion is one of the conditions for a Delaunay-triangulation. That is also the most used

triangulation. In all used software that is the basis of the creation of a DTM.

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However, with all criterions something should not be forgotten: a DTM is an approach to the

surface; it will never show the exact shape of the terrain. Some influences are important for the

quality of the model. First the devices and the methods of surveying influences the accuracy and

certainty. Things like the density of the points and the kind of the terrain are also important. At

last, the method of working in post processing – e.g. grid-based or triangle-based modeling –

influences the quality of the result.

Delaunay triangulation

A Delaunay triangulation has attributes, which are important for a DTM. Triangles in the

network are linked but not overlapping and there are no blanks between them. If a

circumscribing circle is drawn around a triangle, it does not include any other points. Therefore,

the triangulation is definite. Break lines are identical with the sides of the triangles. The principle

of the Delaunay-Triangulation consists of three steps:

( 1 ) The closest points Pj around a point Pi, so-called natural neighbours, are connected to Pi. At

the middle on the lines between these neighbours and Pi the perpendicular is drawn. The

perpendiculars form a closed polygon. That is named a ―Thiessen‖-polygon.

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2

1

3 4

5

6 7 8

11

9 10

12

FIGURE 5: Thiessen-polygon

(Source; Bettina Pflipsen)

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FIGURE 6: Vonoroi-diagram, Delaunay-triangulation and the empty circle

(Source; Bettina Pflipsen)

1. If this ―Thiessen‖-polygon is constructed around all points of a point set, it is acquired

―Voronoi‖ — diagram.

2. The points inside of neighboured ―Thiessen‖-polygons are connected. The result is the

Delaunay-triangulation. (Bettina Pflipsen, pp 11-14)

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4.2 SHOVEL TRUCK PRODUCTION SYSTEM

Shovel-truck systems are a prevalent loading and hauling system in surface mining operations.

The loading units are typically wheel loaders (WL), hydraulic excavators (HEX) or rope

excavators. The trucks can be off-highway trucks (OHT), articulated dump trucks or coal haulers

as in coal mining. Generally truck fleet sizes increase with progressive mining or when

expansion projects are envisaged. Haulage distances invariably increase with increasing pit depth

as mining progresses, consequently reducing individual truck productivity and demanding more

trucks to maintain the same level of production.

Off-highway truck manufactures provide specifications of importance to the truck operator

(user). These specifications frequently are determined in accordance with procedures established

by the Society of Automotive Engineers (SAE) or other organizations.

The following definitions apply in truck productivity;

Actual production is the current performance of a hauler from the pit to the dumping place and

back again considering the distance and the average cycle time.

Target production is the performance of trucks without any disturbances occurring while

working.

Loss production is the difference of target payload and the truck load (these are fragments that

are supposed to be loaded by the excavator to achieve the percentage of the established truck

factor of the hauler).

Design payload or tonnage capacity specified is the weight the truck is designed to carry with

manufacturer’s standard equipment. If optional equipment substantially increases truck weight,

the design payload must be reduced by a corresponding weight.

Actual payload is the actual weight of material loaded, which depends on material density,

loading equipment, and operating conditions and varies from load to load. Average actual

payload should be as near as practical to and never exceed 110% of the design payload.

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Volumetric capacity of the truck body is based on SAE struck and heaped 2:1 capacities. Neither

of these capacities represents the volume of material that can be loaded into and hauled by the

truck. Experience indicates that actual capacities are about 105% to 130% of SAE struck

capacity with the highest percentage for the largest trucks with wide bodies and top extensions.

The productivity of a hauler/loader operation can be estimated by the stages below:

Calculate the hauler and loader cycle times

Determine the number of haulers to be used to maximize production

Use the loader cycle time to calculate the possible loader production.

Use the hauler cycle time to calculate the hauler production

Use the material density to calculating the tones of material loaded/ hauled

Use the established truck factor to approximate the amount of material carried by the

hauler for each cycle made.

Truck production, assuming 100% availability and/or utilization can be calculated by

……………………………………………………………………………..Equation 21

where

Pt is the truck production rate based on actual active-operating time, t/h (short ton per hour)

Lt is the truck actual payload , t(ton)

ttc is the truck total cycle time, minute

Trips per hour made by a truck, T, can be calculated by

…………………………………………….……………………….………..Equation 22

Thus, truck production rate can be calculated by

………………………………………………...…………………………..Equation 23

Truck fleet production, …………………………………………… ….Equation 24

Where K are the available trucks in the fleet at a specific time.

(http//books.smenet.org)

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4.3 MINE FLEET DISPATCHING SYSTEM

This is a system for monitoring equipment location and status which gives the supervisors the

information to make decisions without delays. Added with the GPS technology advantage the

system can provide one with Real Time Location of vehicles.

The Real Time fleet monitoring and information system has been designed for those mines that

require accurate production statistics and information on their fleet-trucks, loading equipment,

and all auxiliary equipment.

4.3.1 BENEFITS OF FLEET DISPATCHING

Loading tonnage analysis

Full task/activity management and reporting

KPI and production displays

Maximize production with Real Time Monitoring displaying equipment location and

status which gives supervisors the information to make decisions without delay. This

production monitoring system allows operators to update pattern progress on the fly.

4.3.2 TRUCK DISPATCH SYSTEM

FIGURE 7: Truck dispatch system

(Source; Karim Mleli)

HAULER

INPUTS

CENTRAL

DISPATCHING

FORMULA

DISPATCHING

DATA BASE

ON

BOARD

HAULER

OUTPUT

EXCEPTION

REPORTING

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Hauler inputs

This includes the information that assists in computation of the desired output information. It

includes

Material density

Swell factor of material

Truck factor

Truck payload

Swell factor of material

The swell factor of materials is a variable which is dependent upon the type and compaction of

the undisturbed (bank run) material. The variability in swell is affected by moisture, clay and

other mineral content.

Central dispatching formula

This includes the mathematical formulas that use the truck input information to provide the

desired answers/ information

Dispatching data base

This is a collection of data organized for storage in a computer memory and designed for easy

access by authorized users. The data may be in the form of text, numbers, or encoded graphics.

Exception reporting

This is a generation of a report with only the required or programmed information to be

produced.

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On board hauler output

This may include

Total tones hauled by a truck

Number of cycles made by a truck

Total amount of materials hauled by a number of trucks over a given time.

4.3.3 MANUAL DISPATCHING SYSTEM

This is the standard practice of truck assignment. The trucks are assigned to a particular

shovel and dump point at the beginning of the shift, changing the circuit according to the

dispatcher’s best judgment of the situation based on production requirements, shovel

locations, fleet availability, etc. in this system, the decision making requires a dispatcher

located at a strategic point in the pit to oversee the operation and keep track of the equipment

status and location. The effectiveness of the system relies heavily on the use of radio-

transmitted information and therefore both shovels and trucks are equipped with two-way

radio to allow communication. The system is recommended for small mines having up to 10

operating trucks.

4.4.4 SEMI-AUTOMATED DISPATCHING SYSTEM

In semi-automated system, the computer is programmed to aid the dispatcher in the decision

making process for assigning the trucks. A digital computer is used to record the status of

equipment and the location of trucks which make up the haulage fleet. The computer is also

used to assist the dispatcher to assign the trucks to shovels according to the dispatching

strategy applied. The system is called semi-automated since the computer does not have

direct contact with the equipment and the dispatcher is necessary to communicate all

instructions.

The dispatcher collates this information with the actual position of equipment in the pit and

takes an independent decision which may or may not agree with the computer suggested

assignment. The dispatcher relays information manually by radio or visually.

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The main advantage of this dispatching system is that it facilitates recording of events,

generating production reports and reduction of equipment waiting times. Using this system

the maximum achievable production will be a function of the dispatching policy applied.

Therefore, the models developed for semi-automated systems must be as flexible as possible

to allow changes in operating policies according to the prevailing conditions at any particular

time. The system is applicable to medium-sized mines, say up to 20 operating trucks.

4.4.5 FULL AUTOMATED DISPATCHING SYSTEM

The fundamental problem with both manual and semi-automated dispatching systems is the

limited ability of human dispatcher to store and transfer large amounts of information over a

long time span in a very short processing time. This was the main reason for the development

of full automated dispatching systems and they are the most emphasized. Automated

dispatching systems enable the computer to make the necessary decisions for dispatching

trucks without any intervention by a human dispatcher. Truck locations are detected by

sensors and sent to the computer, which calculate the destination for truck allocations using

the chosen dispatching strategy applied as in semi-automated dispatching systems.

The assignments are sent to trucks directly and appear on LCD displays mounted in truck’s

cabin or in a central location where trucks go by.

The advantage of such systems is that the dispatcher does no longer need to communicate

instructions to the trucks or to keep track of the truck status. Automated dispatching systems

have been reported to decrease truck haulage requirements from 5 to 35 percent. The benefits

vary depending on type of material handling fleet, haulage network configuration and

specific dispatching procedures. They provide precise and timely production reports and

increase efficiency of the haulage equipments. The only drawback with this system is the

high installation cost involved due to monitoring and transmission equipment required.

(karim Mleli, pp 4-6)

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5.0 POSSIBLE SOLUTIONS TO THE PROBLEM

Re-checking material density each time grade control is done. Also avoiding averaging of

the material density over the entire pit since the pit covers a large area hence there is a

possibility of large variation density between different locations with different rock types

and lithologies within the pit.

Checking the effectiveness of surveying practices and use of surveying instruments with

advanced accuracies. Literature has shown that a combination of methods and software

can result into a more accurate volume computation of stockpiles. An example of the use

of Polywork software which merges two data sets; georeferenced GPS points and ILRIS-

3D range data. (www.optech.ca/www.ilris-3d.com)

Reviewing the factors used in truck factors establishment.

Reviewing the data inputs and the central dispatching formula as it can lead to wrong

data outputs and hence reporting wrong data.

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6.0 DATA COLLECTION PLAN

The plan of collecting data together with description of tasks, resources and how the tasks will be

done and organized is summarized in the table below.

Table 1; Action plan

Task to be done

(what will be done)

Resource

funding/people/materials

How to do the task Time

(when)

1.Field work

Collecting rocks

sample for density

and swell measuring

Collecting

information on

surveying operations

and techniques used

at Buzwagi mine

Collecting stockpile

volumes data and

production data

Geologists,

Buzwagi geology

laboratory

Surveying section

Survey section and

dispatch

Dispatch Engineer

Studying the

geology of

Buzwagi

Getting along

with the survey

crew,

interviewing and

asking them basic

questions

Recording the

data from the

available database

and from field

17th April to

23rd

April

2011

2.Data analysis

Collected data and

the Literature

Using formula

and principles

Semester 2

(Week 1-17)

3. Discussion of the Results

Results of data

Analysis

Using formula

and principles

4. Conclusion

5. Recommendation

6. Presentation

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7.0 REFERENCES

Bettina pflipsen, volume computation, a comparison of total station versus laser scanner

and different software, A master’s thesis, 2006, University of Gavle, Switzerland.

H. Murat Yilmaz and Murat Yakar, computing of volume of excavation areas by digital

close range photogrammetry, The Arabian Journal for Science and Engineering, Volume

33, Number 1A, Aksaray University, Engineering Faculty Geodesy and Photogrammetry

Department, Aksaray, Turkey.

http//books.smenet.org/Surf_Min_2ndEd/sm-ch06-sc05-ss02-bod.cfm

http//www.answers.com/

JC Najor and PC Hagan, Mine production scheduling within capacity constraints, The

University of New South Wales (UNSW), Sydney

Karim Mleli, Fleet management study using Jigsaw dispatching system at Buzwagi gold

mine with the aim of improving productivity and operating performance, Field report,

2010, Buzwagi Gold Mine, Tanzania.

Kemp-Engineering survey and setting out services-page 1,

www.kempengineeringsurvey.co.uk

M. A. R. Cooper and S. Robson, "Theory of Close Range Photogrammetry", Close Range

Photogrammetry and Machine Vision, 1996, p. 9.

Modular Mining Systems. 2003, whttp://www.mmsi.com/modular/news, Company

News, Arizona,USA.

Osanloo, M. , Gholamnejad, J. and Karimi, B.(2008) 'Long-term open pit mine

production planning: a review of models and algorithms', International Journal of Mining,

Reclamation and Environment, 22: 1, 3 — 35, First published on: 02 July 2007

Wenco International Mining Systems. 2003, http://www.wencomine.com/products. asp,

Product Overview, Vancouver, Canada.

www.optech.ca/www.ilris-3d.com

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