a new numerical method and ahp for mining method selection
TRANSCRIPT
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Shahriar / Bakhtavar / Akbarpour Shirazi: A New Numerical Method and AHP for Mining Method Selection 289
A New Numerical Method and AHP for Mining Method
Selection
K.Shahriar, E.Bakhtavar & Gh.Saeedi,
Amirkabir University of Technology, IR
M. Akbarpour Shirazi, Khajehnasir University of Technology, IR
ABSTRACT
Mining method selection decision is the most important phase which affects costs of project. In the
study for selecting suitable exploitation method, a new numerical Shahriar and Bakhtavar (Sh&B)
approach and the Analytic Hierarchy Process (AHP) were used. The method is a combined and
modified system of Nicholas, Modified Nicholas and UBC. Expert Choice software based on AHP
was utilized that it also allows users to specify the mining method considering specific relative
importance of each of governing factors. In the decision making process, the input data for the
software and the new system (Sh&B) were caught from information of Third Anomaly Gol-E-Gohar
Iron Ore Deposit located in Kerman province in south eastern of Iran. Finally according to the
achieved results of the software out put data and the new system, as well as comparison with results
of other numerical systems, open pit mining and sublevel caving were selected as the most suitable
mining methods.
ZUSAMMENFASSUNG
Die Auswahl des Abbauverfahrens hat den größten Einfluss auf die Kosten eines Projekts. In dieser
Studie wurden eine neuartiger numerischer Shahriar und Bakhtavar (Sh&B) Ansatz und das
Analytic Hierarchy Process (AHP) Verfahren benutzt. Die Methode ist eine Kombination und
Modifikation der Systeme von Nicholas, Modified Nicholas and UBC. Über auf AHP-gestützte
Expertensysteme können vom Benutzer bevorzugte Abbaumethoden gewichtet betrachtet werden.
Der Vergleich von AHP und des neuen (SH&B)-Systems wurde am Beispiel der Third Anomaly
Gol-E-Gohar Iron Ore Deposit in der Provinz Kerman im Süd-Osten des Irans getestet. Der
Vergleich der von AHP und (SH&B) erzeugten Ergebnisse mit den Ergebnissen anderer
numerischer Verfahren, führte zur Auswahl von Tagebau und Teilsohlen-Pfeilerbruchbau als das zweckmäßigste Verfahren.
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INTRODUCTION
In the past, selection of mining method for a new property was based primarily on operating
experience at similar type deposits and on methods already in use in the districts of the deposit.
Then, the chosen method was modified during the early years of mining as ground conditions and
ore character were better understood. Now a day, however, the large capital investment required to
open a new mine or change an existing mining system make it imperative that the mining methods
examined during the feasibility studies and the method actually selected have a high probability of
attaining the projected production rates [1,2]. Several methods have been developed to evaluate
suitable mining methods for an ore deposit based on physical characteristics of the deposit such as
shape, thickness, plunge, depth, grade distribution, and geo-mechanical properties of the rock. The
Nicholas method (1981) is one such procedure, which applies a numerical approach to rate different
mining methods based on the rankings of specific input parameters. The UBC Mining Method
Selection Algorithm is a modification to the Nicholas approach, which places more emphasis on
stoping methods, thus better representing typical Canadian mining design practices [3]. In 2002 the
MMS system was proposed based on The UBC Algorithm but provides the opportunity to describe
the parameters using fuzzy logic [4].
In the study for selecting suitable exploitation method, a new numerical named Shahriar and
Bakhtavar (Sh&B) approach and the Analytic Hierarchy Process (AHP) were used. The new
quantitative approach is a combined and modified system of Nicolas, Modified Nicolas and UBC
methods. Expert Choice software based on AHP was used that it also allows users to specify the
mining method considering specific relative importance of each of governing factors. In this paper
the input data for the software and the new system (Sh&B) were caught from information of third
anomaly Gol-E-Gohar iron ore deposit. Then according to the achieved results of the new system
and the software out put data, as well as comparison with results of some numerical approaches,
open pit mining and sub level caving were selected.
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THE SHAHRIAR&BAKHTAVAR METHOD
Introduction
In order to combine and modify rankings of the previous quantitative approach named Nicholas,Modified Nicholas, and UBC and suggested weighting rates in Modified Nicholas, a new numerical
approach was improved. The new method was named Sh&B (Shahriar and Bakhtavar are names of
authors). The authors believe the new method in mining method selection process for all deposits
can be most effect than other privious methods. Such as the previous numerical methods, a finite
number of methods are considered in the Sh&B approach. It is recognized that certain mining
methods, for example Square Set Stoping, are no longer in common use. No attempt has been made
in this paper to update these mining methods to be considered.
Mining Method Selection in Sh&B Approach
Except the “Grade Quantity” which added, all input parameters of the new approach and UBC are
the same. This parameter was added to the effective input parameters collection because of its
significant in deposit evaluation. The selection process proceeds in the same fashion as modified
Nicolas and UBC. However, most of rankings and numbering system as well as range of input
parameters are different. The Sh&B method uses the input parameters to rate the various mining
methods and arrive at an appropriate mining method (as shown in table 1).
Deposit Geometry Rock Mechanics
Ore Thickness Rock Mass Rating of Ore
Ore Plunge Rock Mass Rating of Hanging Wall
General shape Rock Mass Rating of Foot Wall
Grade Distribution Rock Substance Strength of Ore
Grade Quantity Rock Substance Strength of Hanging Wall
Depth Rock Substance Strength of Foot Wall
Table 1: Input parameters for Sh&B approach
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Ore Thickness
In the Sh&B Method the ore thickness category of the UBC approach to recognize that many mines
may work ores less than 10 meters in width was applied. It includes a “Very Narrow” category to
consider ore thickness between 0 and 3 meters. Table 2 shows the categories and input value ranges
for ore thickness.
Description Range in Values
Very Narrow < 3 metres
Narrow 3-10 metres
Intermediate 10-30 metres
Thick 30-100 metres
Very Thick > 100 metres
Table 2: Ore Thickness
Ore plunge
The plunge of a deposit is important parameter to consider as it influences the mining method
directly, the location of development and hence overall mining costs. Furthermore, certain deposit
geometries are more applicable to certain mining methods than others. The Sh&B Method modifiesthe deposit plunge categories of Nicholas and UBC approach to increase accuracy degree in the
mining method selection process. Table 3 summarizes the categories and input value ranges for
deposit plunge.
Description Range in Values
Flat < 15 degree
Low dip 15-30 degree
Intermediate 30-45 degree
Rarely steep 45-60 degree
steep > 60 degree
Table 3: Ore Plunge
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General shape
The Sh&B Method utilizes the same categories as Nicholas and UBC for general shape of a deposit.
These factors are important parameters to consider as they directly influence development
requirements and equipment selection. Furthermore, certain deposit geometries are more applicable
to certain mining methods than are others. The table 4 shows the categories for general shape.
General Shape Description
Massive All dimensions are on the same order of magnitude
Platy-tabular Two dimensions are many times thickness, which does not usually exceed 35m
Irregular Dimensions vary over short distances
Table 4: General Deposit Shape
Grade distribution
The New Method also uses the same categories as the Nicholas and UBC for grade distribution to
influence the selected method (table 5). For example, deposits having an erratic grade distribution,
with ore grade changing over short intervals, are more faverably mined using more expensive, but
more selective techniques, such as Cut&Fill Stoping. However, lower tonnage rates can be expected
utilizing the more selective methods.
General Shape Description
UniformThe grade at any point in the deposit does not vary
significantly from the mean grade for that deposit
GradationalGrade values have zonal characteristics, and grades
change gradually from one to another
ErraticGrade values change radically over short distances and
do not exhibit any discernible pattern in their changes
Table 5: Grade Distribution
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Deposit Depth
The Nicolas Method does not explicitly account for the depth of mining during development of the
mining method rankings, but uses it to later modify the rankings. The UBC Method utilizes the
depth of mining to eliminate or restrict the use of open pit mining. In some instances, the Nicholas
approach may give erroneous results leading to selection of open pit mining as a preferred method
even for deep deposits. The Sh&B Method modifies (with increasing depth because of systems and
machines development in mining technology especially about open pit) the deposit depth categories
of UBC approach to increase accuracy degree in the mining method selection process. Table 6
summarizes the categories and input value ranges for deposit depth.
Description Range in Values
Shallow 0-200 metres
Intermediate 200-500 metres
Rarely Deep 500-800 metres
Deep > 800 metres
Table 6: Deposit Depth
Deposit Grade ValueThe Nicolas and UBC Methods do not explicitly account for the deposit grade value of the mining
method rankings. The Sh&B Method utilizes the grade value of the deposit in title of cost
alternative and because of this factor influence on mining method selection process. Table 7 shows
the categories for deposit grade value. It is differ in various minerals and their prices of market, for
example Iron with average deposit grade less than 30% take place in Low Grade category.
General Shape Description
Low Grade Depends on kind of mineral and its market price
Medium Depends on kind of mineral and its market price
High Grade Depends on kind of mineral and its market price
Table 7: Average deposit Grade Value
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Rock Mass Rating
Parameters of Uni-axial Compressive Strength (UCS) of the intact rock, Rock Quality Designation
(RQD), Discontinuities Spacing, Surface Condition of Discontinuities, and Groundwater Conditions
are used to classify the ore zone, hanging wall and foot wall rock mass rating. The final adjusted
RMR value is rated into one of 5 classes, which describes the relative quality of rock mass (table 8).
Description Range in Values
Very Poor (0-20)%
Poor (20-40)%
Fair (40-60)%
Good (60-80)%
Very Good (80-100)%
Table 8: Rock Mass Rating
Rock Substance Strength (RSS)
The parameters such as UCS, Vertical Stress various with depth, and Ratio of Horizontal to Vertical
Stress are applied to define the Rock Substance Strength (RSS). With respect to the UBS Method,
RSS is a dimentionless parameter defined as the ratio the UCS of rock mass to the maximum in situ
stress at the depth of mining in the new approach too. Table 9 summarizes the categories and input
value ranges for RSS.
Description Range in Values
Very Weak < 5
Weak 5-10
Moderate 10-15
Strong > 15
Table 9: Rock Substance Strength
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Rating the Mining Methods in Sh&B Method
The mining methods are ranked according to table 10-13. The resulting rankings are summed to
arrive at a rating for each method based on the input parameters. In the tables these abbreviations
were applied: (OP-Open Pit; BC-Block Caving; SLS-Sublevel Stoping; SLC-Sublevel Caving; LW-
Long Wall; RP-Room&Pillar; SHK-Shirinkage; CF-Cut&Fill; TS-Top Sclicing; SS-Square Set)
MM Ore Thickness Ore Plunge
< 3 3-10 10-30 30-100 > 100 < 15 15-30 30-45 45-60 > 60
OP 1 2 3 4 4 4 4 4 4 4
BC -50 -50 0 3 4 -10 0 1 3 4
SLS -10 2 4 3 2 -10 0 2 4 4
SLC -50 -10 3 4 4 -10 0 1 3 4
LW 4 2 -10 -50 -50 4 3 1 -50 -50
RP 4 2 -10 -50 -50 4 2 -10 -50 -50
SHK 4 4 3 -10 -50 -50 -10 1 4 4
CF 3 4 4 1 -10 1 1 3 4 4
TS 1 0 0 2 1 3 4 2 0 0
SS 4 3 2 0 0 1 2 3 4 4
Table 10: Ranking of Thickness and Plunge of Ore
M M General Shape Grade Distribution Grade Value Depth
MA T/P IR U G E L M H SH I RD D
OP 4 3 3 3.8 2.85 1.9 1.6 1.6 1.6 2.4 0.6 -25 -50
BC 4 2 0 2.85 1.9 1.9 1.6 0.8 0.4 0.6 1.2 1.8 2.4
SLS 3 4 1 3.8 3.8 2.85 0.4 1.6 0.8 1.2 1.8 2.4 2.4
SLC 3 4 1 2.85 1.9 1.9 0.4 1.6 0.8 1.2 1.8 1.8 2.4
LW -50 4 -50 3.8 0.95 0 0.4 1.6 0.8 0.6 1.2 1.8 2.4
RP 0 4 2 3.8 2.85 0 0.4 1.6 0.8 1.8 2.4 1.2 0.6
SHK 1 4 2 3.8 1.9 1.9 0 0.8 1.6 1.8 1.8 1.8 0.6
CF 1 4 4 2.85 3.8 3.8 0.4 1.2 1.6 0.6 1.2 2.4 2.4
TS 1 2 0 1.9 0.95 0.95 0.4 1.2 1.2 1.2 1.2 0.6 0.6
SS 0 2 4 0.95 1.9 2.85 0 0.4 4 0.6 0.6 1.2 2.4
Table 11: Ranking of Shape, Grade Distribution and Value, and Depth of Ore
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In the table 11: (MA-Massive, T/P-Tabular/Platy, IR-Irregular, U-Uniform, G-Gradational,
E-Erratic, L-Low, M-Medium, H-High, SH-Shallow, I-Intermediate, RD-Rarely Deep, D-Deep)
MM Ore Hanging Wall Foot Wall
< 5 5-10 10-15 > 15 < 5 5-10 10-15 > 15 < 5 5-10 10-15 > 15
OP 2.63 3.5 3.5 3.5 2.1 2.1 2.8 2.8 1.32 1.32 1.76 1.76
BC 3.5 2.63 1.75 0 2.8 2.1 1.4 0 1.76 1.32 0.88 0.44
SLS 0 0.88 3.5 3.5 0 0.7 2.8 3.5 0 0.44 0.88 1.32
SLC 0.88 2.63 2.63 1.75 2.8 2.1 1.4 0.7 0.44 0.88 0.88 0.88
LW 5.25 4.38 1.75 0.88 4.2 3.5 2.1 0.7 0 0.44 0.88 0.88
RP 0 0 2.63 5.25 -7 0 1.4 4.2 0 0 0.44 1.32
SHK 0 0.88 2.63 3.5 0 0.7 2.1 2.8 0 0.88 1.32 1.32
CF 0 0.88 2.63 2.63 2.1 3.5 2.8 1.4 0.44 1.32 0.88 0.88
TS 2.63 1.75 0.88 0 2.1 1.4 1.4 1.4 0.88 0.88 0.44 0.44
SS 3.5 2.63 0.88 0 2.8 2.1 0.7 0 1.32 0.88 0 0
Table 12: Ranking of Rock Substance Strength
MM Ore Hanging Wall Foot Wall
VP P F G VG VP P F G VG VP P F G VG
OP 2.63 2.63 2.63 2.63 2.63 1.4 2.1 2.8 2.8 2.8 0.88 1.32 1.76 1.76 1.76
BC 3.5 2.63 1.75 0 -50 2.1 2.1 2.1 1.4 1.4 1.32 1.32 1.32 0.88 0.88
SLS 0.88 2.63 3.5 3.5 3.5 -50 0 2.1 2.8 2.8 0 0 0.88 1.32 1.32
SLC 2.63 3.5 2.63 0.88 0 2.8 2.8 2.1 1.4 1.4 0.44 1.32 1.32 1.32 1.32
LW 5.25 5.25 3.5 1.75 1.75 4.2 3.5 2.8 2.1 2.1 1.32 1.76 1.32 0.88 0.44
RP -50 0 2.63 4.38 5.25 -50 0 2.1 3.5 4.2 1.32 1.32 0.88 0.44 0
SHK 0 0.88 2.63 2.63 2.63 0 0 1.4 2.8 2.8 0 0 0.88 1.32 1.32
CF 0 0.88 1.75 0.88 2.63 2.1 3.5 2.8 2.1 2.1 1.32 1.32 1.32 0.88 0.88
TS 2.63 1.75 0.88 0 0 0 0 1.4 2.1 2.1 0 0 0.44 0.88 0.88
SS 3.5 3.5 0.88 3.5 0 2.8 2.8 0.7 0 0 1.32 0.44 0 0 0
VP-Very Poor P-Poor F-Fair G-Good VG-Very Good
Table 13: Ranking of Rock Mass Rating
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ANALYTIC HIERARCHY PROCESS (AHP)
Overview
Multiple Attribute Decision Making (MADM) deals with the problem of choosing an alternativefrom a set of alternatives which are characterised in terms of their attributes. Usually MADM
consists of a single goal, but this may be of two different types. The first is where the goal is to
select an alternative from a set of scored ones based on the values and importance of the attributes
of each alternative. The second type of goal is to classify alternatives, using a kind of role model or
similar cases. MADM is a qualitative approach due to the existence of criteria subjectivity [5]. The
decision maker might express or define a ranking for the criteria as importance/weights. There are
many forms for expressing these weights, but the most common are: Utility Performance Function,
Analytical Hierarchy Process [6,7], and Fuzzy Version of the classical linear weighted average
[8,9]. AHP is a multi-criteria decision method that uses hierarchical structures to solve complicated,
unstructured decision problems, especially in situations where there are important qualitative
aspects that must be considered in conjunction with various measurable quantitative factors. The
AHP is based on four main axioms [10]:
1) Given any two alternatives (or sub-criterion), the decision-maker is able to provide a pairwise
comparison of these alternatives under any criterion on a ratio scale which is reciprocal.2) When comparing two alternatives, the decision-maker never judges one two be infinitely better
than another under any criterion.
3) One can formulate the decision problem as a hierarchy.
4) All criterion and alternatives which impact a decision-problem are represented in the hierarchy.
The above axioms describe the two basic tasks in the AHP: formulating and solving problem as a
hierarchy, and eliciting judgements in the form of pairwise comparison.
Saaty (1980) has been developed the mathematics necessary to combine the results of the pairwise
comparisons made at different levels in order to final priority value for each of the alternatives at
the bottom of hierarchy [10].
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Figure 1: AHP Hierarchy [10]
Expert Choice Software
Expert Choice (EC) software is a multi-objective decision support tool based on the Analytic
Hierarchy Process. A mathematical theory first developed at the Wharton school of the
Pennsylvania University by one of Expert Choice's founders, Thomas L. Saaty. The AHP is a powerful and comprehensive methodology designed to facilitate sound decision making by using
both empirical data as well as subjective judgments of the decision-maker [11].
CASE STUDY
Introduction
The Sh&B Method has been validated utilizing input data of the Third Anomaly of Gol-E-Gohar
Iron Ore Deposit. This deposit located in Kerman province in south eastern of Iran. The length of
the deposit is about 2200 meters (north-south) with an average width of 1800 meters (east-west).
The main Iron ore is Magnetite with hanging and foot wall of Schist and Shale respectively. The
input parameters of the anomaly for Mining Method Selection (MMS) process are given in table 14.
Goal
Criteria 1 Criteria 2 Criteria 3
Alternative A Alternative B Alternative CAlternative A Alternative B Alternative CAlternative A Alternative B Alternative C
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Input Parameters Description
Ore Thickness 40 meters
Ore Plunge 20 degrees
General Deposit Shape Platy
Grade Distribution Gradational
Grade Value High
Depth 350 meters
RQD 75%
Joint ConditionFilled with talk strength less than
rock substance strength
Rock Substance Strength 8.7
Rock Mass Rating 63.5
Ore
Zone
Uniaxial Compressive Strength 128 MPa
RQD 38%
Joint Condition Clean joint with a smooth surface
Rock Substance Strength 4.9
Rock Mass Rating 50
Hinging
Wall
Uniaxial Compressive Strength 46 MPa
RQD 38%
Joint Condition Clean joint with a smooth surface
Rock Substance Strength 4.9
Rock Mass Rating 50
Foot
Wall
Uniaxial Compressive Strength 46 MPa
Table 14: Input parameters of third anomaly of Gol-E-Gohar for MMS Systems
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Mining Method Selection
Note that the final outcome will depend on which category is chosen. Using Nicholas, UBC, and
SH&B Methods the total values are shown in table 15.
Method OP BC SLS SLC LW RP SHK CF TS SS
Nicholas 39 32 -29 33 -19 -28 35 37 34 35
UBC 33 26 31 29 -25 -32 -29 29 18 14
Sh&B 30.16 20.11 19.76 22.67 -25.6 -37.59 -44.91 10.02 16.92 21.45
Table 15: Evaluted total values of the Mining Method Selection Systems
According to the evaluated total value of the Nicholas Method, Open Pit, Cut&Fill, and Shirinkagemining methods were selected respectively. But the results of UBC Method show that Open Pit,
Sublevel Stoping, Sublevel Caving and Cut&Fill are most suitable respectively. Based on the
calculated rankings in the Sh&B Method, the most effective and fitness mining methods for the
third anomaly of Gol-E-Gohar Iron Deposit are: 1- Open Pit; 2- Sublevel Caving; 3- Square Set.
For choosing a most suitable mining method from these three alternative ( emphasis on the results
of the Sh&B Mining Method Selection approaches), the Expert Choice Code based on AHP Method
was used.
In first step, it is necessary to create an Expert Choice Model from the problem with Goal, Criteria
(Objectives), and alternatives (figure 2). The number of objectives must be limited to four. In the
next step, judgments/pairwise comparisons with the goal and working down to the alternatives (top-
down) have to started.
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Figure 2: AHP Model for Mining Method Selection of Gol-E-Gohar Deposit
In this way, decision alternatives are evaluated by pair wise comparisons, thus allowing more
accurate judgements than the simple weighted product model. Figure 3 and 4 show the weighting
results of pair wise comparison between Geometry and Geotechnical parameters respectively.
Figure 3: Weighting results of pair wise comparison between Geometry parameters
Figure 4: Weighting results of pair wise comparison between Geotechnical parameters
Mining Method Selection
GEOTECHNICAL PARAMETERS GEOMETRY PARAMETERS
Ore Thickness
Ore Plunge
Ore Shape
Grade Distribution
Grade Value
Deposit Depth
RSS of Ore
RSS of Hanging Wall
RSS of Foot Wall
RMR of Ore
RMR of HangingWall
RMR of Foot Wall
Sublevel
Caving
Square
Set
Open Pit
Alternatives
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According to Experts judgments, pair wise comparisons of the alternatives based on sub-criteria
were implemented. The alternatives characteristics based on all sub-criteria (for example mining
methods comparison with emphesis on Ore Plunge, Ore Depth, RMR of Hanging Wall, and RSS of
Foot Wall are shown in Figures 5 to 9 respectively) and the total weight of criteria were evaluated.
Figure 5: Mining Methods Comparison with emphesis on Ore PLunge
Figure 6: Mining Methods Comparison with emphesis on Ore Depth
Figure 7: Mining Methods Comparison with emphesis on RMR of Hanging Wall
Figure 8: Mining Methods Comparison with emphesis on RSS of Foot Wall
Figure 9: Importance Degree based on Geometry and Geomechanical Parameters
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Finally the weight of each alternative was determined. Table 16 shows the achieved results of the
applied software.
Parameters Weight Open Pit Sublevel Caving Square Set
Geometry 0.454 0.451 0.293 0.257
Geomechanical 0.455 0.416 0.3 0.283
Total Weight 0.435 0.296 0.269
Table 16: Final weight of alternatives
In respect to the out put data of the Expert Choice for the Third Anomaly of Gol-E-Gohar Iron Ore
Deposit, Open Pit was selected as the most suitable mining method [11,12].
CONCLUSION
Generally, systems applied to choose potential mining methods basis on a finite number of defined
input parameters. Due to the evaluated total value of the Nicholas Method, Open Pit, Cut&Fill, and
Shirinkage mining methods were selected respectively. But the results of UBC Method show that
Open Pit, Sublevel Stoping, Sublevel Caving and Cut&Fill are most suitable respectively. Based on
the calculated rankings in the Sh&B Method, the most effective and fitness mining methods for the
Third Anomaly of Gol-E-Gohar Iron Deposit are: Open Pit, Sublevel Caving, and Square Set. Due
to the output results of the Expert Choice Code, Open Pit method was selected for the Third
Anomaly of Gol-E-Gohar Iron Ore Deposit as the most suitable mining method.
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LITERATURE
[1] Nicholas, D. E: Method Selection-A Numerical Approach, Design and Operation of Caving
and Sublevel Stoping Mines, 1981, 39-51
[2] Miller-Tait, R. et al: UBC Mining Method Selection, Mine Planning and Equipment
Selection, 1995, 163-168
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