strategic open pit mine planning course.pdf

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Toda la información contenida en este manual es de propiedad del Señor Kadri Dagdelen y cualquier reproducción parcial o total de la misma será sancionada legalmente.

Introduction to Mining Practices- Case Studies Open Pit Mining Terminology Pit Geometry and Slope Angles Open Pit Mine Planning Concepts - Circular Analysis Geologic Block Modeling Techniques Assay and Composite Sections and Block Modeling

Geostatistical Resource Estimation Techniques

Economic Definition of Ore Break-even Cutoff Grades and Stripping Ratio Analysis Economic Block Modeling, Cone and L&G Mining Analysis Final Pit Limits, Nested Pits and Mining Sequence Determination Cutoff Grade Policy, Scheduling and Stockpile Management

Mine Sequence, Cutoff Grade, Process Flow Determination

UNIT OPERATIONS AND EQUIPMENT SELECTION Drilling Fundamentals and Drill Selection Blasting Fundamentals Front End Loaders; Hydraulic Shovels and Cable Shovels Excavator Selection Considerations Equipment Cost Calculations Cat Handbook Truck Haulage and Cycle Times

Fleet Size Determination

Dispatch Systems In Pit Crushing and conveying systems

Mineral Processing

Mining Project Cash Flow Analysis Net Present Value Calculations

Mine Sequence, Cutoff grade and Process Flow NPV optimization

Papers by Kadri Dagdelen.

Bingham Canyon MinePorphyry Copper

Case Study

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General Information

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General Information

•World’s first low grade copper mine.

•5 billion tons of material and 13 million tons of copper produced since 1906.

•Overall stripping ratio is 0.4:1.

•Mine daily production is 111 Kton of ore and 99.2 Kton of waste. (40 and 36 Mton/year respectively).

•Reserves are at 1.0 Btons @ 0.5% Cu per ton which results in 25 years mine life.

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General Information

•210 Kton of copper; 350 oz of gold; 2.5 MM oz of silverand 6350 ton of moly per year.

•2.5 miles long; 0.5 miles deep.

•Truck haulage – haul road 150 ft wide; also 3 tunnels for ore and waste haulage.

•Mine operates three 8-hour shifts per day, 365 days per year.

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General Information

Layout

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General Information

Geology

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General Information

•Block model dimensions 100 x 100 x 50 ft. Each block is assigned a value of Cu, Au, Ag, and Mo using a geostatistical technique known as kriging.

•Development drilling on 400 by 600 ft centers.

•Density 2.58 t/m3 or equivalent tonnage factor of 12.38 ft3/ton.

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Mine Plan

•Pushbacks range from 100 ft to 200 ft in width and 50 ft in height.

•Five ore shovel production faces to meet average grade and metallurgical blending requirements.

•Five waste shovel production faces to meet long range stripping requirements.

•Operating interramp pit slope, including bench face angles and catch benches, is 34o; catch benches are 50 ft wide.

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nMine Plan

Typical Mining Sequence

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Mine Plan

•Ore is being mined in lower 900 ft of the pit and highest active waste stripping occurs 2000 ft higher elevation.

•In extreme cases, mining room must be brought down nearly 40 benches before new ore is exposed; this process can take as long as seven years.

•Slope angles for the ultimate pit limits are defined by subdividing the pit surface in 26 sectors.

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Mine Plan

•Slope angles for each of these sectors range from 29 to 50 degrees.

•Slope angles will be achieved by double benching or single benching and control blasting – “digging to hard”.

•Slope dewatering using near horizontal drains improves slope angles by 3 to 5 degrees in the ultimate slope.

•Mining plans are developed by defining the volume of ore and waste between series of pushbacks.

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Mine Plan

•The material in pushbacks sequentially mined by a computerized mining simulator algorithm. Highest relative profit margin ore is mined first.

•Haulage roads are added to the incremental pits.

•Mine plan is a series of annual plans for five-year followed by five year plans to the end of mine life.

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Drilling

•Drills operate 5 days per week and two 8-hour shifts per day.

•8 Bucyrus-Erie 60R track-mounted electric drills.

•They can drill 57 to 65 ft in a single pass by exerting 120 Klb thrust.

•Rotary tricone bits with carbide inserts are used to drill 12.25 in diameter holes.

•One drill can drill 12 holes per 8-hour shift.

•Two drilltech D75K track-mounted units; carbide insert bits 9.875 in diameter – 4 35-ft drill rods.

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Drilling

•D75K drills are used in resilient (hard) formations where closer patterns are necessary for proper fragmentation.

•One secondary drill uses 2.5-in and 12-ft drill rods to drill boulders. Also mine has rubber-tired rock breaker.

•Drill patterns vary with the rock types but range from 30 x 30 ft to 36 x 36 ft for 12.25-in holes. 25 x 25 ft to 30 x 30 ft for 9.875-in holes.

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Blasting

•Two ANFO trucks – blending of ammonium nitrate prills and fuel oil occurs when bulk delivery trucks deliver these material to the mine-site storage tanks.

•Commercial bulk emulsion-blend explosives are used in wet holes.

•Holes are primed with two 0.75-lb boosters placed near the bottom of the explosive column.

•A 200-ms delay is inserted into each booster and connected to individual 7.5-grain primaline down-lines.

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Blasting

•25 grain detonating cord is used for trunk lines and cross ties.

•Surface delays of 17 ms are used between holes and 100 ms between rows.

•A single strand of detonating cord extended from the pattern and initiated by a non-electric cap taped to the cord.

•Drill cuttings are used for stemming. Each hole produces 2.4 to 3.7 tons of cuttings. These cuttings are forced into loaded holes.

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Blasting

•Powder factor varies between 0.13 to 0.25 lbs of explosive per ton depending on rock type; average 0.16 lb per ton.

•Ground motion due to blasting is limited to 25 in/sec at the planned final pit slopes.

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Loading

•2 15-yd3 P&H2100; availability averages 78%; 10 Ktons per shovel shift.

•4 27-yd3 P&H2800 Mark II; availability averages 80%; 15 Ktons per shovel shift.

•3 30-yd3 P&H 2800 XP; availability averages 80%; 15 Ktons per shovel shift.

• 2 34-yd3 P&H 2800 XPA; availability averages 80%; 20 Ktons per shovel shift.

•2 8-yd3 International; 1 12-yd3 Clark; 2 12-yd3

Caterpillar rubber tired FEL’s.

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Loading

•Power is provided by 44-kva substations; radial lines are then fed to smaller substations with voltage reduced to 5500 V ac.

•Electric connections between the switch houses and shovels are made through trailing cables up 2000 ft for shovels and 3000 ft for the drills.

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Haulage

•Mainly trucks and some rail.

•Truck haulage utilizes a fleet of 44 trucks composed of 28 190-ton CAT-785 mechanical drive; 8 170-ton Unit Rig diesel electric; 8 170-ton Wabco diesel electric trucks.

•In 1990 34 truck-shifts/shift are scheduled with average availability of 94% for the new, larger trucks; 84% for the smaller, older trucks.

•All trucks are equipped with two-way radios to assist appropriate dispatching.

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In-Pit Crusher

•Movable, 60- by 109-in, 1000-hp Allis Chalmers gyratory crusher that has a capacity of 120,000 tons per day on continuous basis.

•Two trucks at a time at a dumping rate of one truck per minute.

•3 to 4 weeks are required to move the crusher.

•-10 in crushed rock is fed directly to a 72-in conveyor.

•The belt is 5 mile ling to Copperton concentrator and capable of carrying 10,000 tph at 900 ft/min speed.

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Road Maintenance

•28 miles of haulage roads and 40 miles of service roads.

•20 dozers (CAT D9H, D9L, D10L).

•11 graders (CAT 16G).

•2 scrappers (CAT 631).

•4 salt trucks (5.4 or 6 ton capacity).

•6 water trucks (converted 65-ton or 59-ton haulage trucks; 10,000 to 30,000 gallons capacity).

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Open Pit Mining Fundamentals

Dr. Kadri Dagdelen

Colorado School of Mines

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Terminology

• BENCH: Ledge that forms a single level of operation above which mineral or waste materials are mined from the bench face.

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Terminology (Cont.)

• BENCH HEIGHT: Vertical distance between the highest point on the bench (crest) and the lowest point or the bench (toe). It is influenced by size of the equipment, mining selectivity, government regulations and safety.

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Terminology (Cont.)

• BENCH SLOPE OR BANK ANGLE : Horizontal angle of the line connecting bench toe to the bench crest.

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Terminology (Cont.)

• BERM: Horizontal shelf or ledge within the ultimate pit wall slope left to enhance the stability of the a slope within the pit and improve the safety.Berm interval, berm width and berm slope angle are determined by the geotechnical investigation.

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Terminology (Cont.)

• OVERALL PIT SLOPE ANGLE: The angle measured from the bottom bench toe to the top bench crest. It is the angle at which the wall of an open pit stands and it is determined by: rock strength, geologic structures and water conditions.

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Terminology (Cont.)

• The overall pit slope angle is affected by the width and grade of the haul road.

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Terminology (Cont.)

• HAUL ROADS: During the life of the pit a haul road must be maintained for access.

• HAUL ROAD - SPIRAL SYSTEM: Haul road is arranged spirally along the perimeter walls of the pit.

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Terminology (Cont.)

• HAUL ROAD – SWITCH BACK SYSTEM: Zigzag pattern on one side of the pit.

• HAUL ROAD WIDTH: Function of capacity of the road and the size of the equipment. Haul road width must be considered in the overall pit design.

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Haul Road Effect on Pit Limits

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Terminology (Cont.)

• ANGLE OF REPOSE: Maximum slope of the broken material.

• SUBCROP OR ORE DEPTH: Depth of waste removed to reach initial ore.

• PRE-PRODUCTION STRIPPING: Stripping done to reach initial ore.

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Terminology (Cont.)

• ULTIMATE PIT LIMITS: Vertical and lateral extend of the economically mineable pit boundary. Determined on the basis of cost of removing overburden or waste material vs. the mineable value of the ore.

• PIT SCHEDULING: Material may be mined from the pit either in 1) sequential pushbacks 2) conventional pushbacks.

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Terminology (Cont.)

• STRIPPING RATIO: Expressed in tons of waste to tons of ore in hard rock open pit operations. Critical and important parameter in pit design and scheduling

• AVERAGE STRIP RATIO: Total waste divided by total ore within the ultimate pit.

• CUTOFF STRIPPING RATIO: Costs of mining a ton of ore and associated waste equals to net revenue from the ton of ore.

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Single Working Bench

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Shovel in Working Bench

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Two Working Benches

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Final Pit Limit

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Cresson Mine – Year 2001

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Pit Sequence (1)

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Pit Sequence (2)

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Pit Sequence (3)

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Pit Sequence (4)

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Section of Pit Sequence

Dr. Kadri Dagdelen


Source: Hustrulid and KuchtaOpen Pit Mine Planning and Design

Open Pit Mine Planning and Design: Fundamentals

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Geometrical Considerations

Parts of a bench

Cumulative frequencydistribution of measured

bench face angles (Call, 1986).

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Section through a working bench.Functioning of catch benches.

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Double benches at final pit limits. Catch bench geometry (Call, 1986).

Typical catch bench design dimensions (Call, 1986).Bench height Impact zone Berm height Berm width Minimum bench width

(m) (m) (m) (m) (m)15 3.5 1.5 4 7.530 4.5 2 5.5 1045 5 3 8 13S

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Safety berms at bench edge

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Height of reach as a function of bucket size.Sur

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Example orebody geometry.Ramp access for the example orebody.

Blast design for the ramp excavation.Sur

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Shovel Working Range

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Minimum width drop cutgeometry with shovelalternating from side to side.

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Minimum width drop cutgeometry with shovelalternating from side to side.

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Isometric view of the ramp in waste approaching the orebody.

Diagrammatic representation of the expanding mining front.

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Dropcut / ramp placement in ore. Expansion of the mining front.

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Plan view of an actual pit bottomShowing drop cut and miningExpansion (McWilliams, 1959).

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Extension of the currentRamp close to the pit wall(McWilliams, 1959).

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Creating initial access / benches.

Shovel cut sequence when initiatingbenching in a hilly terrain (Nichols, 1956).

Sidehill cut with a shovel.

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Detailed steps in the development of a new production level.Sur

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Parallel cut with drive by.Sur

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Parallel cut with the double spotting of trucks.Sur

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Parallel cut with the single spotting of trucks.Sur

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Time sequence showing shovelloading with single spotting.

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Time sequence showing shovelloading with double spotting.

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(Continued).

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Section and plan views through a working bench.

Simplified presentation of a safety berm.

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Initial geometry for the push back example.

Cut mining from bench 1.

Cut mining from bench 2.

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Overall slope angle.

Safety bench geometryshowing bench face angle.

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Overall slope angle with ramp included.

Interramp slope angles.

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Overall slope angle withWorking bench included.

Interramp angles associated withthe working bench.

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Overall slope angle withone working bench an a ramp section.

Interramp slope angles for a slope containinga working bench and a ramp.

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Overall slope angle for a slope containing two working benches.Sur

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Slopes for each working group.

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Final overall pit slope.Sur

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Advances in Pit Slope Management SystemsAdvances in Pit Slope Management Systems

Dr. Kadri DagdelenProfessor

Mining Engineering DepartmentColorado School of MinesGolden, Colorado 80401

Pit Slope Failure ProblemsPit Slope Failure Problems

l Continue to be the source of human and financial losses

l Recent examples from Wyoming coal mines and Grasberg pit in Indonesia point to additional research needs to be done in the area of pit slope management

l Pit slope monitoring research is undertaken at the Colorado School of Mines using Lidar Scanners with funding from Kennocott Energy and 3-DP

Plane FailurePlane Failure

l Failure plane must daylight in the slope face; i.e. its dip must be smaller than slope (S>P)

l Plane must strike parallel or nearly parallel (within 20o) to the slope face.

l Less common than other failure modes

Plane Failure in a Limestone Plane Failure in a Limestone QuarryQuarry

Wedge FailureWedge Failure

DAYLIGHTING WEDGE

NON-DAYLIGHTING WEDGE

• Most common mode of failure for rock slopes

• Line of intersection must daylight into slope face

• Often, failure is sudden

Circular FailureCircular Failure

l Soilsl Stock pilesl Reclamation pilesl Waste dumpsl Highly weathered overburden rocks

Toppling and StepToppling and Step--Path Path ModesModes

Toppling Mixed modes(e.g. Toppling & Step-Path)

Overall Slope DesignOverall Slope Design

l Identify geological sectors; their strength characteristics and possible mode of failures

l Determine maximum height and angle for inter-ramp design

l Determine bench geometryl Incorporate bench geometry into Inter-ramp

designl Overall slope design

Failure Modes in Different Failure Modes in Different Sectors Sectors

Pit Slope Monitoring Pit Slope Monitoring -- What to look for What to look for

l Overhang rockl New geological structuresl Swell and/or increased rock fall activity on highwalll Heavy precipitationl Signs of stressl Tension cracksl Movement (acceleration)l Increased water levels

Tension Crack Measurements Tension Crack Measurements l The formation of cracks behind slope is a sign of instability

(Safety Factor ˜ 1)l Monitoring changes in crack width and direction can provide

information on extent of unstable area

InclinometersInclinometers

l Inclinometers measure horizontal deflections of a borehole

l They can- Locate failure surface - Determine nature of failure surface

(rotational or planar)- Measure movement along failure

surface and determine if movement is accelerating

Borehole extensometerBorehole extensometer

l Consists of tensioned rods anchored at different points in a borehole.

l Measures changes in distance between anchors, as well as collar

l Provides displacement information across discontinuities.

New and Emerging TechnologiesNew and Emerging Technologiesl Automated Total Station Network (robots)

l Non-reflective Laser scanners (Lidar systems: Cyra, Riegl, I-Site)

l Radar Technologies

l GPS (Local sensors with multiple antenna)

l TDR (Time Domain Reflectometry)

l Digital photogrammetry

l Arial photography (Kodak)

Automated Total Station Network in Automated Total Station Network in Chuquicamata Mine, ChileChuquicamata Mine, Chile

• A network of automated total stations for geotechnical monitoring of pit slopes that operate continuously 24 hours a day, 7 days a week and during the 365 days a year.

• Provide a reliable and quantitative information in real time thatallows to establish with anticipation the behavior of the rock massand geologic structures on the pit slopes.

Completely Automated Electronic Completely Automated Electronic Station Network using Station Network using LeicaLeica TCA2003TCA2003

Motorized Station, Leica TCA2003

Characteristics• Reach with 1/3 prisms in average

atmospheric conditions : 2500/3500 mts.• Precision in distance : 1mm + 1 ppm• Angular precision : 0.3” (0.1 mgon)• Increase of lens : 30 x• Compartment for the insertedable

memory card PCMCIA.• Integrated application programs :

Reframing, orientation of horizontal circleand drag of levels, reseccion anddistance of connection between twopoints.

• Capture of information in modality ATR and DIST.

WirelessWireless CommunicationCommunication NetworkNetworkBridge

Bluebox

Switch

Energy

SHELTER 1

SHELTER 2

SHELTER 6

SHELTER 5

ARTURO OESTE

SHELTER 3

SHELTER 4

ARTURO ESTE

CONTROL ROOM ETHERNET NETWORK

SHELTER 1

SHELTER 2

SHELTER 6

SHELTER 5

ARTURO OESTE

SHELTER 3

SHELTER 4

ARTURO ESTE

CONTROL ROOMCONTROL ROOM

LocationLocation of Stations of Stations andand IntegrationIntegration of of InformationInformation

Software of Information Integration

• Have a Computational Software that allows to totally integrate and administer the acquisition of geotechnical data, procesingand analisis of the information in real time originating from therobotic system (TCA) intalled in each of the monitoring stations.

Total Station and Prism Locations in Total Station and Prism Locations in Chuquicamata Mine, ChileChuquicamata Mine, Chile

CasetaEste

CasetaOeste

GPS Surveyed Control Stations in GPS Surveyed Control Stations in Chuquicamata Mine, ChileChuquicamata Mine, Chile

Coordenadas de laEstación de MonitoreoAPS(N;E;Z)

ZONA-5 ZONA-6 ZONA-7

D1 D2 D3D4

“D” (PR-1)

“E1” (PR-2) Matus (PR-3)

GT-1 PR-4

Morgan (PR-5)

S4

S3

S5

S2

S1

D5

.

PILAR GT-1

APS-WEST. Norte : 2085.491Este : 3870.863Elev

Cota : 2846.745

Slope Stability Radar Technology Slope Stability Radar Technology from from GroundProbeGroundProbe of Australiaof Australia

Complete Pit Wall Coverage from Complete Pit Wall Coverage from Remote LocationsRemote Locations

Radar Scan Lines

Location and Time of Wall Location and Time of Wall MovementsMovements

18:13 8th October 2003




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Slip Area

Slope Stability Radar FeaturesSlope Stability Radar Features• High deformation precision (± 0.2 mm std. dev.)

• Broad area coverage (~1000’s pixels/scan)

• Continuous operation (~ 1’s min/scan, 24 hrs/day)

• 30-850m range

• All weather operation (incl. dust, fog)

• Rapid Deployment

• Remote Operation via radio link and internet

• High resolution CCD Camera

• Custom software with alarm settings

SSRViewerSSRViewer Images ScreenImages Screen

SSRViewerSSRViewer Figures ScreenFigures Screen

10mm movement over 45 hours in Region 1

0.0mm movement over 45 hours in Region 2

15mm movement over 45 hours in Region 3

Laser Scanning TechnologiesLaser Scanning TechnologiesThere are Many 3D Laser Scanners There are Many 3D Laser Scanners

Major Companies with Products are:Major Companies with Products are:

ll CyraxCyrax ((LeicaLeica) ) www.cyra.comwww.cyra.com (USA)(USA)ll OptechOptech ILRIS (Canada)ILRIS (Canada)ll II--site (site (MaptekMaptek) ) www.isite3d.comwww.isite3d.com (Australia)(Australia)ll LMS 3D Scanning systems (Riegl) LMS 3D Scanning systems (Riegl) www.riegl.co.at www.riegl.co.at

(Austria)(Austria)ll Z+F Laser Measuring Systems (Z+F Laser Measuring Systems (ZollerZoller+ + FröhlichFröhlich) )

www.zofre.dewww.zofre.de (Germany)(Germany)

CyraxCyrax 24002400

Other Application in Laser Technologies Other Application in Laser Technologies Riegl Z 210i Lidar Laser ScannerRiegl Z 210i Lidar Laser Scanner

•1200+ ft scan range•2.5cm accuracy @ 900 ft•5 cm accuracy > 900 ft•361 degrees x 80 degree scan•9000 Hz

SpecificationsSpecifications

Riegl LPM 800 HARiegl LPM 800 HA

•3000 ft scan range1cm accuracy @ 1250 ft2 cm accuracy > 1250 ft

•0.018 degrees step size•360 degrees of horizontal rotation•180 degrees of vertical rotation •1000 Hz


Riegl Z 420 Lidar Laser ScannerRiegl Z 420 Lidar Laser Scanner

•2400+ ft scan range•1cm accuracy in topo mode•6 mm accuracy in detail mode•0.01 degree step size•361 degrees x 90 degree scan window•8000 - 12000 Hz


High Wall Scan (Pre Blasting)High Wall Scan (Pre Blasting)

PostPost--Blast ScanBlast Scan

Pre Blast TrianglesPre Blast Triangles

Post Blast TrianglesPost Blast Triangles

Combined Combined –– Pre / PostPre / Post

Dynamic Cross SectionDynamic Cross Section

Complete Pit Scan using Complete Pit Scan using RieglRiegl

Pit Wall Scan Using Pit Wall Scan Using RieglRiegl

Pit Wall Failure Scan Pit Wall Failure Scan -- RiegleRiegle

NoModerate< 150 m~ hoursBroad Area

~ 1’s cmPhotogram-metry

YesDifficultn/a~ secsDiscrete Points

~ 1’s cmGPS

Extenso-meters

LIDAR SCANNER

Laser (Prisms)

SSR –GROUND PROBE

Technology

YesEasy850 m(1.4km)

~ minsBroad Area

± 0.2 mm

NoDifficult2 kmTwice Daily

Discrete Points

~ 1’s cm

NoEasy900 m~ secsBroad Area

~ 1’s cm

Difficult

Deployment

Yesn/a~ secsDiscrete Points

~ 1’s mm

All weather

RangeUpdate Rate

Wall Coverage

Precision

Slope Monitoring Systems

Slide Management OptionsSlide Management Optionsl Reduce slope anglel Dewater unstable areal Leave unstable areasl Continue miningl Unload slidel Partial clean upl Step-out

l Reduce slope height by segmenting the slope

l Support unstable groundl Contingency Planningl Blastingl Erosion control measures

(reclamation)- Geotextiles against erosion

and raveling- Vegetating and planting

Instability can be left alone if it is in

– an abandoned area,

– an inactive area,

– an area that can be avoided

Leave Unstable Areas untouchedLeave Unstable Areas untouched

Continue miningContinue miningIf the displacement rate is low and predictable, living with the displacement while continuing to mine may be the best action.

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t (cm

)

Time

1/4/02 5/4/02 11/4/02 16/4/02

50

100

150 May continue mining (displacement rate is constant)

Basic Principles of DrainageBasic Principles of Drainagel Prevent surface water from entering to the slope through

open tension cracks and fissuresl Reduce water pressure in the vicinity of the potential

failure surface l Providing for gravity flow of water is the most common

methodl Pumping is used on a temporary basis depending on the

urgency of the problem

Bench section view

Inclined bench for gravity flow

Slope crest

Bench face view

Benches sloped toward toe

Method of Slope DrainageMethod of Slope Drainage

POST

FLOWER PATCH

EXPL

ODI

NG

BLIND RODEO CREEK 1RODEO CREEK

GRAND JE

AN

AM

AN

DA

ANTI

POST

CH

RIS

TYS

DORM

ANT

JB

AN

FO

PA

TS

MIDNIGHT

60

60

60

50

85

80

60

55

50

25

60

60

75

N-00-B

EM

ILYS

LAST LAUGH78

RODEO CREEK

BLIND RODEO CREEK 1P

OW

ER

FUL

Horizontal Drain NetworkHorizontal Drain Network(303 drains/34 miles since 1999)(303 drains/34 miles since 1999)

Unload SideUnload Side

l Even though unloading has been a common response, in general it has been unsuccessful.

l In fact, there are situations involving high water pressure where unloading actually decreases stability.

Partial cleanPartial clean--upup

• Partial cleanup may be the best choice where a slide blocks a haul road or fails onto a working area

• Only that material necessary to get back into operation need be cleaned up

New (Flatter) Overall Slope Angle

Old Overall Slope Angle

Originally Planned Slope DesignNew Slope Design

Failure SurfaceStep out

StepStep--outoutl Increased highwall stability due

to shallower slope angle It locks up reserves

lAdvantages of leaving step out should be weighed against cleaning by considering ore lock up and having safer overall slope

Reduce slope height by Reduce slope height by segmenting slopesegmenting slope

Support unstable groundSupport unstable ground

Buttress

Rock Bolts

Anchors, Tiebacks, and Anchors, Tiebacks, and ShotcreteShotcrete

1. Reinforced concrete dowel to prevent loosening of slab at crest

2. Tensioned rock anchors to secure sliding failure along crest

3. Tieback wall to prevent sliding failure on fault zone

4. Shotcrete to prevent raveling of zone of fractured rock

5. Drain hole to reduce water pressure within slope

6. Concrete buttress to support rock above cavity

Mesh & BoltsMesh & Bolts

ButtressingButtressing

NE Wall Sept 2002NE Wall Sept 2002

2% ramp & buttress

mudslide

4880 buttress

unwting cut

N-00-B

4640

4280

NE Wall UnNE Wall Un--weighting Cutweighting Cut

Prism Data Feb 2002 to Feb 2003Prism Data Feb 2002 to Feb 2003PRISM DATA - All In Movement Area

-2.00

-1.80

-1.60

-1.40

-1.20

-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

2/1/02

2/15/0

23/1

/02

3/15/0

23/2

9/024/1

2/024/2

6/02

5/10/0

25/2

4/02

6/7/02

6/21/0

27/5

/02

7/19/0

28/2

/02

8/16/0

28/3

0/029/1

3/029/2

7/02

10/11

/02

10/25

/0211

/8/02

11/22

/0212/

6/02

12/20

/021/3

/03

1/17/0

31/3

1/032/1

4/032/2

8/03

DATE

MO

VE

ME

NT

IN (

INC

HE

S/D

AY

)

TN000084

TN000089

TN010095

TN010119

TN 80

TN 72

TN 97

TN 98

TN 101

TN 114

TN 115

TN 127

TN 144

TN 149

#3

#4

BlastingBlasting

Use of less charges next to toe

Linedrillholes

Productionholes Face

Pre-splitting Line drilling

SAFETY BERMCatch

Berm, ± 40 m. H13

BENCH

D5 BENCH

PUSHBACK

> 10 cm/dayStop push-back development

5 a 10 cm/dayOnly ore production stripping

2 a 5 cm/dayNormal

Displacement ratePUSHBACK DEVELOPMENT

Slide Management ExampleSlide Management Example

y = 63.213x - 2E+06

y = 16.016x - 597363

y = 8.7432x - 326060

y = 5.6082x - 209126

0

50

100

150

200

250

300

1/2/02 6/2/02 11/2/02 16/2/02 21/2/02

TIEMPO

DES

PLA

ZAM

IEN

TO (c

m)

Took outshovel

Access D5& H13 closed

Failure

Contingency PlanningContingency Planning

l Provide multiple access to production facesl Maintain double access to working benches,

whenever possiblel Stockpile ore/rockl Design to prevent noses in the plan geometryl Provide for failure costs in scheduling and budgetingl Add lag times in production schedulingl Plan step-outs

ConclusionsConclusions

l New Radar and Lidar based technologies applied to pit slope monitoring appears to be very promising in providing cost effective and accurate real time data .

l Accurate and reliable slope displacement information coupled with proper pit slope management practices has a potential to prevent unexpected catastrophic pit slope failures.

Haul Road Design

Dr. Kadri Dagdelen


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Haul Road Design

• HAUL ROADS: During the life of the pit a haul road must be maintained for access.

• HAUL ROAD - SPIRAL SYSTEM: Haul road is arranged spirally along the perimeter walls of the pit.

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Haul Road Design

• HAUL ROAD – SWITCH BACK SYSTEM: Zigzag pattern on one side of the pit.

• HAUL ROAD WIDTH: Function of capacity of the road and the size of the equipment. Haul road width must be considered in the overall pit design.

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Haul Road Effect on Pit Limits

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Considerations for Haul Road Design

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• Visibility• Stopping distances• Vertical alignment• Horizontal alignment• Cross section• Runaway-vehicle safety

provisions

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Sight Distances and Stopping Distances

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• Vertical and horizontal curves designed considering sight distance and stopping distance

• Sight distance is the extent of peripheral area visible to the vehicle operator

• Sight distance must be sufficient to enable vehicle traveling at a given speed to stop before reaching a hazard

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Sight Distances and Stopping Distances

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• On vertical curves, road surface limits sight distance

• Unsafe conditions remedied by lengthening curve• On horizontal curves, sight distance limited by

adjacent berm dike, rock cuts, trees, etc; • Unsafe conditions remedied by laying back bank or

removing obstacles

8

Sight Distance Diagrams

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Sight distance diagrams for horizontal and vertical curves(Kaufman and Ault)

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Stopping Distances

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• Stopping distances depend on truck breaking capabilities, road slope and vehicle velocity

• Stopping distance curves can be derived based on SAE service break maximum stopping distances

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Stopping Distance Characteristics

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For example, stopping distance characteristics of vehicles of 200,000 to 400,000 pounds GVW

(Kaufman and Ault)

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Stopping Distances

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• Prior to final road layout, manufacturers of vehicles that will use the road should be contacted to verify the service brake performance capabilities

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Vertical Alignment

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• Establishment of grades and vertical curves that allow adequate stopping distances on all segments of the haul road• Maximum sustained grades

• Reduction in grade significantly increases vehicle uphill speed• Reduction in grade decreases cycle time, fuel consumption, stress

on mechanical components and operating costs• Reduction in grade increases safe descent speeds, increasing

cycle time• The benefits of low grades offset by construction costs associated

with low grades

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Vehicle Performance Chart

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Vehicle Retarder Chart

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Vertical Alignment

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• Maximum sustained grades• Some states limit maximum grades to 15 to 20% and

sustained grades of 10%• Most authorities suggest 10% as the maximum safe

sustained grade limitation• Manufacturer studies show 8% grades result in the

lowest cycle time exclusive of construction consideration

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Vertical Alignment

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• Maximum sustained grades• Property boundaries, geology, topography, climate

must be considered on a case by case basis. • Lower operating costs must be balanced against higher

capital costs of low grades.• Truck simulators and mine planning studies over the

life of mine should be used to make the determination of the appropriate grades

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Vertical Curves

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• Vertical curves smooth transitions from one grade to another

• Minimum vertical curve lengths are based on eye height, object height, and algebraic difference in grade

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Stopping Distance vs. Vertical Curve

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For example, vertical curve controls 9 ft eye height (usually minimum height for articulated haulage trucks of 200,000 to 400,000 pound of GVW)

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Horizontal Alignment

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• Deals primarily with design of curves and considers previously discussed radius, width, and sight distance in addition tosuperelevation

• Cross slopes also should be considered in the design

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Curves, Superelevation, and Speed Limits

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• Superelevation grade recommendations vary but should be limited to 10% or less because of traction limitations

• Depending on magnitude of the side friction forces at low speed, different values are suggested for small radius curves

• Kaufman and Ault suggest .04-.06 fpf(basically the normal cross slope)

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• CAT suggests higher slopes with traction cautions and 10% maximum caution

• Again, where ice, snow, and mud are a problem, there is a practical limit on the degree of superelevation

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Curve Superelevation

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(CAT)

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Recommended SuperelevationRates

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(Kaufman and Ault)

If superelevation is not used, speed limits should be set on curves.

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• Centrifugal forces of vehicles on curves are counteracted by friction between tire an road and vehicle weight as a result of superelevation

• Theoretically, with superelevation, side friction factors would be zero and centrifugal force is balanced by the vehicle weight component

• To reduce tire wear, superelevation or speed limits on curves are required

25

Combinations of Alignments

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• Avoid sharp horizontal curvature at or near the crest of a hill

• Avoid sharp horizontal curves near the bottom of sustained downgrades

• Avoid intersections near crest verticals and sharp horizontal curvatures

• Intersections should be made flat as possible• If passing allowed, grades should be constant and

long enough

26

Cross Section

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• A stable road base is very important• Sufficiently rigid bearing material should be

used beneath the surface• Define the bearing capacity of the material

using the California Bearing Ratio (CBR)

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California Bearing Ratio

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Subbase Construction

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Cross Slopes

• Cross slopes provide adequate drainage and range from ¼ to ½ inch drop per foot of width (approximately .02 to .04 foot per foot)

• Lower cross slopes used on smooth surfaces that dissipate water quickly and when ice or mud is a constant problem

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Cross Slopes

• Higher cross slopes permit rapid drainage, reduce puddles and saturated sub-base, and are used on rough surfaces (gravel and crushed rock) or where mud and snow are not a problem

• High cross slopes can be particularly problematic with ice or snow on high grades (+5%)

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Recommended Rate of Cross-Slope Change

(Kaufman and Ault)

Slope change should be gradual.

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Width

• On straight or tangent segments, width depends on• Vehicle width• Number of lanes• Recommended vehicle clearance, which ranges

from 44 to 50% of vehicle width

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Minimum Road Design Widths for Various Size Dump Trucks

(Couzens, SME Open Pit Planning and Design)

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Typical Design Haul Road Width

(Couzens, SME Open Pit Planning and Design)

Typical design haul-road width for two-way traffic using 77.11-t (85-st) trucks

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(Kaufman and Ault)

Typical Haulageway Sections

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Width

• Berm height and width as a function of vehicle size and material type

• Ditch(es) added to basic recommendations• Runaway provisions may also add to width• Road wider on curves because of overhang• Minimum turning radius considered on

curves (should be exceeded)

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Haulageway Widths on Curves

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Safety Provisions - Berms

• Triangular or trapezoidal made by using local material• Stands at natural angle of repose of construction

material• Redirects vehicle onto roadway• Minimum height at rolling radius of tire

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Berms

• Larger boulders backed with earthen material• Near vertical face deflects vehicle for slight

angles of incidence• Problems with damage and injury and

availability of boulders• Minimum height of boulder at height of tire

allowing chassis impact

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Runaway Provisions

• With adverse grades some safety provision should be integrated to prevent runaway vehicles

• Primary design consideration is required spacing between protective provisions

• Driver must reach a safety provision before truck traveling too fast to maneuver

• Maximum permissible speed depends on truck design conditions and operator

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Runaway Provisions

• Maximum permissible speed, equivalent downgrade, and speed at break failure determine distance between runaway truck safety provisions

• For example, at an equivalent downgrade of 5% and a maximum speed of 40 mph,

Speed at Failure 10 mph 20 mphProvision Spacing 1,000 ft 800 ft

(Kaufman and Ault)

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Runaway Precautions

(Atkinson SME Handbook)

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Median Runaway-Vehicle Provision Berms

• Vehicle straddles collision berm and rides vehicle to stop

• Made of unconsolidated-screened fines• Critical design aspects spacing between

berms and height of berm• Height governed by height of undercarriage

and wheel track governed by largest vehicle

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Median Runaway-Vehicle Provision Berms

• Requires maintenance in freezing conditions • Agitation to prevent damage to vehicle• May cover berm in high rainfall areas

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Escape Lanes

• Good tool for stopping runaway but expensive to construct

• Entrance from road is important; spacing, horizontal, vertical curve and superelevationare all considered in design

• Deceleration mainly by adverse grade and high rolling resistance material

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Escape Lanes

• Length a function of grade and speed at entrance and rolling resistance

• Stopping by level section median berm, sand or gravel or mud pits, road bumps or manual steering

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Escape Lanes

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Maintenance

• The road surface is deformed by the constant pounding of haulage vehicles.

• A good road maintenance program is necessary for safety and economics.

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Safety Considerations

• Dust, potholes, ruts, depressions, bumps, and other conditions can impede vehicular control.

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Economic Considerations

• The wear on every component is increased when a vehicle travels over a rough surface.

• If the vehicle brakes constantly, unnecessary lining wear occurs as well.

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Dust Control

• Dust may infiltrate brakes, air filters, hydraulic lifts, and other components of machinery.

• The abrasive effect of dust will result in costly cleaning or replacement of these items.

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Deterioration Factors

• Weather• Vehicles follow a

similar path• Spillage

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Motor Graders

• A motor grader should be used to maintain cross slopes, remove spills, and to fill and smooth surface depressions as they occur.

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Road Drainage

• To avoid overflow, roadside ditches and culverts should be periodically cleaned.

• Avoid erosion or saturation of subbase materials.

Haul Road Design

Open Pit Contour Maps

Dr. Kadri Dagdelen

Source: Hustrulid and Kuchta

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Example of Mapping Procedure

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Plan View of a Portion of the Open Pit

Crests denoted by dashed lines and toes by solid lines.

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Example of Mapping Procedure

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Midbench Elevation

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Plan View of Midbench Elevation

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Map Based on Midbench Contours

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Procedure to Convert Midbench to Toe and Crest Contours

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Representation of Crests and Toes

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Designing a Spiral Ramp Inside the Wall

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Completing the new crest lines

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Pit Layout Including Ramp

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Design of a Spiral Ramp Outside the Wall

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Design of a Switchback

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Example of Two Switchbacks

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Plan and Section Views of Pit Without Ramp

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Plan and Section Views of Pit With Ramp

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Road Volume in the Ramp

1

Block Modeling and Ore Reserves Estimation

Dr. Kadri Dagdelen

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Basic Block Model Information

• Topography Data • Drill Data• Sampling• Assays

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Topography Data

3D Display (Color Coded Elevations)

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Drill Data

Drill Hole Data Sources

•Collar Coordinates•Geologic Logs•Down Hole Surveys•Lab Tests

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Samplings

Sampling Data

•Rock Types•Alteration Types•Metal Grades•Attributes

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Samplings (Cont.)

Data Collections

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Assays

Assay Data for Cu and Mo

Multiple Cutoffs

Rock Types

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Geological Interpretation

Section View Showing Topography and Alteration Types

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Boundaries for rock types

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Color Filled Display for Alteration Types

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3D Geological View

3D Display of Alteration Type Solids

(With Drill Hole Piercing Points)

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Composites

Composited Grade Data with Corresponding Assay Interval Data

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3D Block Models

3D View of the Block Models

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Block Estimation

Kriging - Geological Interpolation Technique for Ore Reserve Estimation

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Block Values

Block by Block Profit Values in Association with Block Grade Data and Alteration Type Boundaries

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Block Models

Interpolated Grades from Drill Hole Data

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Ore Reserve Estimation

Interpolated Grades from Drill Hole Data

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Economic Pit Limits

Economic Pit Limits for Different Economic Scenarios

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3D View of Economic Pit Limits

3D View of Economic Pit Limits for Different Economic Scenarios

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Mine Planning Application(Open Pit Mine)

Yearly Maps for the Open Pit Mine Scheduling

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Geologic Resource Modeling Techniques

• Exploratory Data Analysis• Variogram Analysis• Search Strategies• Simple Kriging, Ordinary Kriging, Indicator

Kriging, Co-Kriging• Cross Validation• Uncertainty and Risk Evaluation

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Frequency and Cumulative Frequency Plots

•Classical Statistics•Data Posting and Display•Histograms •Cumulative Histograms•Probability Plots

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Inverse Distance Technique

• In general, ∑∑=

=

=n

iin

ip

i

pi v

d

dv

1

1

1

1

ˆ

• Inverse distance technique is the simplest interpolation method.

• Give more weight to the closest samples, and less to those that are farthest away.

∑=

= n

ipi

pi

i

d

dw

1

1

1

∑=

=n

iiivwv

1

ˆ 11

=∑=

n

iiwS

urfa

ce M

ine

Des

ign

24

Inverse Distance Technique (pg257)

v1

v2

d1

d244

1

1

1

34

1

1

1

24

1

1

1

14

1

1

1

2

24

2

23

2

22

2

21ˆ vvvvv

id

d

id

d

id

d

id

d

iiii∑∑∑∑

====

+++=

v̂ Inverse Distance Square

• We can make the weights inversely proportional to any power of the distance.

• If p=2, it is called Inverse Distance Square.

d3

d4

v3

v4

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Inverse Distance Square Example

V1=0.2

V2=0.3

d1=1d2=2

v̂

• Estimate the unknown point by using the Inverse Distance Square technique

d3=4

V3=0.5

v̂

v1= 0.2 d1 =1

v2= 0.3 d2 =2

v3= 0.5 d3 =4

?ˆ =v

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• First of all, calculate the weights w1, w2, w3

21161

1621

241

221

211

211

1 ==++

=w

214

162141

241

221

211

221

2 ==++

=w

211

1621161

241

221

211

241

3 ==++

=w Note:1321 =++ www

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• Then, calculate

233.05.0211

3.0214

2.02116ˆ =×+×+×=v

v̂

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Estimation Error

• Error estimation between estimation (Exploration data) and true value (Blasthole data).

Error = Estimated Grade – True Grade

e.g., Estimation Error for Block 1 = 0.463 – 0.433 = 0.031

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Histogram of Errors

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Scatter Graph

True grades agai n s t E s t i mated grades

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90True (%)

Est

imat

ed (

%)

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Surface Mine DesignMNGN312 - MNGN512

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Lecture 5September 14, 2004

InstructorDr. Kadri Dagdelen

2

Geologic Block Modeling

• Assume that a geologic model to be created by using 75ft by 75ft blocks from the exploration data set. Estimate the grade of these blocks using the inverse distance square (IDS) technique.

• Use rectangular search neighborhood of 37.5ft x 37.5ft.

• Assume that the center of the block represents the block grade.

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• Estimate the grade of the block (block size 75ft x 75ft) for exploration data set.

75ft

75ft

1̂v2v̂

Estimate the center point

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• Rectangular search neighborhood of 37.5ft x 37.5ft.75

ft 37.5ft

37.5ft 37.5ft

37.5ft

Use all the exploration holes within a given block (For this block, use 3 exploration samples)

75ft

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• In general,

∑∑=

=

=n

iin

ip

i

pi v

d

dv

1

1

1

1

ˆ

• Inverse distance technique is the simplest interpolation method.

• Give more weight to the closest samples, and less to those that are farthest away.

∑=

= n

ipi

pi

i

d

dw

1

1

1

∑=

=n

iiivwv

1

ˆ 11

=∑=

n

iiw

Unknown pointSampling points

Weights

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v1

v2

d1

d244

1

1

1

34

1

1

1

24

1

1

1

14

1

1

1

2

24

2

23

2

22

2

21ˆ vvvvv

id

d

id

d

id

d

id

d

iiii∑∑∑∑

====

+++=

v̂ Inverse Distance Square

• We can make the weights inversely proportional to any power of the distance.

• If p=2, it is called Inverse Distance Square (IDS).

d3

d4

v3

v4

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V1=0.2

V2=0.3

d1=1d2=2

v̂

• Estimate the unknown point by using the Inverse Distance Square technique

d3=4

V3=0.5

v̂

v1= 0.2 d1 =1

v2= 0.3 d2 =2

v3= 0.5 d3 =4

?ˆ =v

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• First of all, calculate the weights w1, w2, w3

21161

1621

241

221

211

211

1 ==++

=w

214

162141

241

221

211

221

2 ==++

=w

211

1621161

241

221

211

241

3 ==++

=w

Note:

121

1416321 =

++=++ www

• Then, calculate

233.05.0211

3.0214

2.02116ˆ =×+×+×=v

v̂

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9


25

25

g1

d1

36.352525 221 =+=d

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0032.00008.0

∑=

n

i id12

1

Block1 X Y vi x dist y dist di 1/di2 wi wi*viCentered on 12.5 12.5 0.42 25 25 35.35534 0.0008 0.25 0.105

(X=37.5, Y=37.5) 62.5 12.5 0.24 -25 25 35.35534 0.0008 0.25 0.0637.5 62.5 0.41 0 -25 25 0.0016 0.5 0.205

0.0032 1 0.37(Estimated Grade)

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• Using the estimated block values, one normally determines the overall estimated bench average grade of the copper ore at some cutoff, i.e, 0.7%Cu.

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Geologic Block ModelReconciliation

• Determine the average grade of 75ft by 75ft grid blocks for the blasthole data set (blasthole2004.txt) by averaging the grades of 9 blast holes that fall within each block.

Block 1 Grade

= (0.42+0.35+0.24+0.33+ … + 0.46) / 9

=0.35

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• Error estimation between estimation (Exploration data) and true value (Blasthole data).

Error = Estimated Grade – True Grade

e.g., Estimation Error for Block 1

= 0.37 – 0.35 = 0.02

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• Histogram of Error (Example of 100ft x 100ft estimation)

Histogram of Estimation Errors (Estimation - True)

0

0.5

1

1.5

2

2.5

3

3.5

-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 More

Bin

Fre

quen

cy

0.00%

10.00%

20.00%

30.00%

40.00%

50.00%

60.00%

70.00%

80.00%

90.00%

100.00%

Frequency

Cumulative %

Bin FrequencyCumulative %-0.2 0 0.00%

-0.15 0 0.00%-0.1 1 11.11%

-0.05 1 22.22%0 3 55.56%

0.05 3 88.89%0.1 0 88.89%

0.15 0 88.89%0.2 1 100.00%

0.25 0 100.00%More 0 100.00%

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• Scatter Graph (Example of 100ft x 100ft estimation)

True grades agai n s t E s t i mated grades

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90True (%)

Est

imat

ed (

%)

Draw a diagonal line (y=x) to show perfect estimation line.

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Univariate Distribution of Errors

• Error = Estimated Value - True Value• We also refer to these error as residuals.• If error is positive, then we have overestimated the true;

if error is negative, then we have underestimated the true.

If m=0, then Unbiased Estimates

Overestimates and underestimates are balanced.

We typically prefer to have a symmetric distribution.

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Univariate Distribution of Errors

• We would like to see the error distribution has small spread.

• Both distributions are centered on 0 and are symmetric.• The distribution shown in a), however, has error that span

a greater range.• Therefore, b) is better estimation than a).

a) b)

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Over and Under Estimation

• a) Negative mean: A general tendency towards the underestimation.

• b) Positive mean: A general tendency towards the overestimation.

a) b)

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Scatter Diagrams in EstimationE

stim

atio

n

True

Good Estimation

Est

imat

ion

True

Over Estimation at High Grade

Est

imat

ion

True

Under Estimation at Low Grade

Good Estimation: Falling closer to diagonal on which perfect estimates would plot.S

urfa

ce M

ine

Des

ign

20

Scatter Diagrams in EstimationE

stim

atio

n

True

Over Estimation at Low Grade

Est

imat

ion

True

Under Estimation at Low Grade

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Floating Cone Algorithm

Dr. Kadri Dagdelen

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Basic Procedure

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Top

-1 +1 -1 -1 -1

-1 -1 +3 -1 -1

BottomLeft Right

-1 -1

-1 -1 -1 -1

Heuristic procedure

3

Floating Cone Steps

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• The cone is floated from left to right along the top row of blocks in the section. If there is a positive block it is removed.

• Move to the second row. Start from the left and search for the first positive block. If the sum of all blocks falling within the cone is positive, the blocks are removed (mined).

• Follow the floating cone process moving from left to right and top to bottom of the section until no more blocks can be removed. Then go back to the top again and repeat the process for a second iteration. If during a given iteration no positive blocks can be mined, stop.

• The profitability of the mined area can be found by adding the values of the blocks that are to be removed.

• Overall stripping ration can be determined by dividing the number of positive blocks by the total number of negative blocks.

4

Example

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-1 -1 -1 -1 -1 +1 -1 Ore

-2 -2 +4 -2 -2

+7 +1 -3 Waste

Initial Block Model

5

Example

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-1 -1 -1 -1 -1 +1 -1 Ore

-2 -2 +4 -2 -2 Waste

+7 +1 -3 Mined

Step 1

6

Example

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-1 -1 -1 -1 -1 +1 -1 Ore

-2 -2 +4 -2 -2 Waste

+7 +1 -3 Mined

Step 2

7

Example

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-1 -1 -1 -1 -1 +1 -1 Ore

-2 -2 +4 -2 -2 Waste

+7 +1 -3 Mined

Step 3

8

Example

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-1

-2 -2

+1 -3

Final Pit

9

ShortcomingsMissing Combinations of Profitable Blocks

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-1 -1 -1 -1 -1 -1 -1 Ore

-2 -2 -2 -2 -2

+10 -3 +10 Waste

Initial Block Model

10

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Step 1

-1 -1 -1 -1 -1 -1 -1 Ore

-2 -2 -2 -2 -2 Waste

+10 -3 +10 Considered but rejected


11

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Step 2

-1 -1 -1 -1 -1 -1 -1 Ore

-2 -2 -2 -2 -2 Waste

+10 -3 +10 Considered but rejected

There are no blocks to be mined – wrong solution


12

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Correct solution

-1 -1 -1 -1 -1 -1 -1 Ore

-2 -2 -2 -2 -2 Waste

+10 -3 +10 Mined (Correct solution)

-3

Final Pit


13

ShortcomingsOver-mining

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-1 -1 -1 -1 -1 Ore

+5 -2 -2

+5 Waste

Initial Block Model

14


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First block analyzed

-1 -1 -1 -1 -1 Ore

+5 -2 -2 Waste

+5 Mined

The search process was started from bottom to top.

Everything is mined out.

15


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Correct solution

-1 -1 -1 -1 -1 Ore

+5 -2 -2 Waste

+5 Mined

-1 -1

-2 -2

+5

Final Pit

16

ShortcomingsCombination of problems

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-1 -1 -4 -1 -1 Ore

+5 -4 +5

+3 Waste

Initial Block Model

17


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First Step

-1 -1 -4 -1 -1 Ore

+5 -4 +5 Waste

+3 Considered but rejected

18


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Second Step

-1 -1 -4 -1 -1 Ore

+5 -4 +5 Waste

+3 Considered but rejected

19


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Wrong Solution

-1 -1 -4 -1 -1 Ore

+5 -4 +5 Waste

+3 Mined

Everything is mined out.

20


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Correct Solution

-1 -1 -4 -1 -1 Ore

+5 -4 +5 Waste

+3 Mined

-4

+3

Final Pit

21

ExampleInitial Data

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% recovery through mill and smelter 90.00%Value of recovered copper $1.00 per lbStripping and haulage to dump (level 1) $0.50 per tonMining and transportation to plant level $0.80 per tonHaulage cost increase per ton per bench $0.10 per ton/benchProcessing, smelting and refining $1.20 per tonGeneral overhead, administration, etc. $1.20 per tonUltimate Pit Slope 1:1

22

ExampleGeologic Model

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0.00 1.15 0.08 0.05 0.00 0.00 0.05

0.00 1.25 1.15 1.13 0.00

1.13 1.15 0.50

Copper Grades (%)

23

ExampleBlock Values

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P = Price

s = Sales Cost

c = Processing Cost

y = Recovery

m = Mining Cost

gB = Block Grade

BV = Block Value

mcygsPBV B −−−= **)(Ore Block:

Waste Block:

mBV −=

24

ExampleEconomic Model

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-0.50 17.50 -0.50 -0.50 -0.50 -0.50 -0.50

-0.60 19.20 17.40 17.04 -0.60

16.94 17.30 -0.70

Value per block ($/ton)

25


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-0.50 17.50 -0.50 -0.50 -0.50 -0.50 -0.50

-0.60 19.20 17.40 17.04 -0.60

16.94 17.30 -0.70


5.178.04.29.0*2000*100/15.1*)01( =−−−=BV

26


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-0.50 17.50 -0.50 -0.50 -0.50 -0.50 -0.50

-0.60 19.20 17.40 17.04 -0.60

16.94 17.30 -0.70


2.38.04.29.0*2000*100/0.0*)01()/($ −=−−−=tonBV If mined as ore

6.0)/($ −=tonBV If mined as waste

27


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Value per block ($/ton)Values rounded to the nearest $

-1 18 -1 -1 -1 -1 -1

-1 19 17 17 -1

17 17 -1

28

ExampleFloating Cone Algorithm

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1st Increment

-1 18 -1 -1 -1 -1 -1

-1 19 17 17 -1

17 17 -1

1

29


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2nd Increment

-1 18 -1 -1 -1 -1 -1

-1 19 17 17 -1

17 17 -1

1 22

2

30


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3rd Increment

-1 18 -1 -1 -1 -1 -1

-1 19 17 17 -1

17 17 -1

2 2

2

1 3

3

31


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4th Increment

-1 18 -1 -1 -1 -1 -1

-1 19 17 17 -1

17 17 -1

3

3

1 2 2

2

4

4

32


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5th Increment

-1 18 -1 -1 -1 -1 -1

-1 19 17 17 -1

17 17 -1

3

3

1 2 2

2

4

4

5

5

5

33


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6th Increment

-1 18 -1 -1 -1 -1 -1

-1 19 17 17 -1

17 17 -1

3

3

1 2 2

2

4

4

5

5

5 6

34


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Ultimate Pit Limit

-1

-1

-1

35

ExampleTotal Economic Value

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Value Per block considering:

Tonnage/block = 10,000 tons

-5,000 175,000 -5,000 -5,000 -5,000 -5,000

-6,000 192,000 174,000 170,400

169,400 173,000

36

ExamplePit Reserves

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Bench Ore tons Waste tons S.R. $

1 10,000 50,000 5.00 150,0002 30,000 10,000 0.33 530,4003 20,000 0 0.00 342,400

Total 60,000 60,000 1.00 1,022,800

1

Manual Pit Design

Dr. Kadri Dagdelen

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2

Manual Pit DesignStripping Ratio

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)/($)/($Pr)/($covRe).(.

tonCostStrippingtonCostoductionTotaltonValueeredBreakevenRS −=

)/($)/($)/($

tonCostStrippingtonCostMiningSurfacetonCostMiningUG

BreakevendUndergrounorSurface−

=

1:58.6)/66.0$

/70.0$/04.5$ =−=tonwaste

tonoretonoreBreakevendUndergrounorSurface

3

Manual Pit DesignExample

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Ore Grade (%Cu) 0.90 0.85 0.75 0.70 0.65 0.50 0.40

Conc. Recovery (%) 0.900 0.900 0.900 0.900 0.900 0.900 0.900Smelt. Recovery (%) 0.980 0.980 0.980 0.980 0.980 0.980 0.980Ref. Recovery (%) 0.990 0.990 0.990 0.990 0.990 0.990 0.990

Total Recovery (%) 0.873 0.873 0.873 0.873 0.873 0.873 0.873

Recovered Quantity (lb/ton) 15.7 14.8 13.1 12.2 11.3 8.7 7.0

Costs per ton

Finance 0.62 0.62 0.62 0.62 0.62 0.62 0.62Mining 0.70 0.70 0.70 0.70 0.70 0.70 0.70Concentration 2.68 2.68 2.68 2.68 2.68 2.68 2.68Smelter 1.70 1.48 1.38 1.29 1.21 1.19 1.18Refining 1.80 1.57 1.36 1.27 1.20 1.16 1.12

Total cost ($/ton) 7.50 7.05 6.74 6.56 6.41 6.35 6.30

Stripping cost ($/ton) 0.66 0.66 0.66 0.66 0.66 0.66 0.66

Breakeven stripping ratio

Copper Price ($/lb)0.90 10.07 9.56 7.65 6.73 5.70 2.29 -0.020.75 6.50 6.19 4.67 3.95 3.13 0.30 -1.610.70 5.31 5.06 3.68 3.03 2.27 -0.36 -2.140.65 4.12 3.94 2.69 2.10 1.42 -1.02 -2.67

07.10/66.0$

/5.7$/90.0$7.15=

−∗=

wasteoftonoreoftonlblbs

BESR

4

Manual Pit DesignStripping Ratio – Grade - Price

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S.R. - Ore Grades - Cu Prices

-4.00

-2.00

0.00

2.00

4.00

6.00

8.00

10.00

12.00

0.40 0.50 0.60 0.70 0.80 0.90

% Cu

Str

ipp

ing

Rat

io

0.90 $/lb0.75 $/lb0.70 $/lb0.65 $/lb

5

X'

SR =

A B

Y'Y

Topo

Orebody

X'Y'

SR = YX

X

Manual Pit DesignHypothetical Cross Section

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Manual Pit DesignS.R. in Section

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First

X’ = 30

Y’ = 5

S.R. = 6

G = 0.67%

Second

X’ = 39.6

Y’ = 6

S.R. = 6.6 (Breakeven)

G = 0.70%

First

X = 10

Y = 5

S.R. = 2

G = 0.48%

Second

X = 15

Y = 3

S.R. = 5

G = 0.70%

5 : 1 < 6.6 : 1 OK

Current Price = 0.90 $/lb

7

Manual Pit DesignRepeat for All Sections

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1

Cutoff Grade Optimization

Dr. Kadri Dagdelen

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2

Factors Influencing The Cutoff Grades

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• As the Cutoff Grade increases in a given operation cash flow also increases

• The ultimate adjustment of the dial is influenced by the available capacities in the mining system

• The Cutoff Grade is not only function of economic parameters but also capacities of the mining system with respect to mining,milling and the market (refining)

3

What Is Cutoff Grade

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1. Cutoff Grade is defined as the grade that is normally used to discriminate between ore and waste within a given deposit

2. Cutoff Grade is the dial that is used to adjust the cash flow coming from the mining operations in a given year

3. The Cutoff Grade policy allows a mining company to fine tune their operation with respect to a given financial objective

4. The Cutoff Grade dial also controls how much ore is available to the mill from a given bench and how much of final product to be produced in a given period

5. The overall influence of Cutoff Grade policy on the economics of an operation is profound

4

Economic Objectives And The Cutoff Grade

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• The cash costs related to mining, milling and refining along with the commodity price determines the lower limit to cutoff in a given period.

• If the financial objective of the company is to maximize undiscounted profits, the cutoff grade should be lowered all theway down to process breakeven cutoff grade.

• Processing every ton of ore that pays for itself will maximize the undiscounted profits for the operation.

5

Economic Objectives And The Cutoff Grade (Cont.)

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• If the financial objective of the company is to maximize the discounted profits that is Net Present Value (NPV), the Cutoff Grade in a given period has to be adjusted upwards to pay for the opportunity cost of mining low grade ore now while the higher grades are still available.

• The mining rate, milling rate, the ultimate rate of production for the commodity being sold, and the production costs determine how far the cutoff grade has to be adjusted upwards to maximize the NPV.

6

Ultimate Pit Cutoff

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• Defined as the breakeven grade that equates cost of mining, milling and refining to the value of the block in terms of recovered metal and the selling price.

• Any administrative overhead expense which would stop if mining were stopped must be included in the cost calculations.

• Overhead costs should be divided between mining and processing.

7

Ultimate Pit Cutoff

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• Price (P) $400/oz• Sales Cost (s) $5 /oz• Processing Cost (c) $ 10/ ton ore• Recovery (y) 90 %• Mining Cost (m) $ 1.20/ ton• Overhead

(Included in c and m )

8

Ultimate Pit Cutoff

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gm covRe*)(Pr −+

=

tonozgm /0315.09.0*)5$400($

2.1$10$=

−+

=

9

Milling Cutoff

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• Defined as the breakeven grade that equates cost of milling and refining to the value of the block in terms of recovered metal and the selling price.

• Any administrative overhead expense which would stop if mining were stopped must be included in the cost calculations.

10

Milling Cutoff

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gc covRe*)(Pr −=

tonozgc /0281.09.0*)5$400($

10$=

−=

11

Block Value

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Block Grade = gB

if ggcc < < ggm <m < ggBB thenBlock Value = (P(P--S)* gS)* gBB * y * y –– c c –– mm

Else if ggBB < < ggm <m < ggcc thenBlock Value = Block Value = --mm

12

Block Value

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Block Grade = gB

if ggcc < < ggB B << ggmm thenBlock contains marginal ore.

• Marginal ore pays for processing cost but not for mining cost.

13

Block Value Calculation Example

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a) Ore BlockBlock grade = gB = 0.11 oz/tonggc c < < ggm < m < ggBB

0.0281 < 0.0315 < 0.11Block Value = (P(P--S)*S)* ggBB * y * y –– c c –– mm

Block Value = (400 - 5)*0.11*0.9 - 10 - 1.20= $27.9/ton of block

14

Block Value Calculation Example

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b) Waste BlockBlock Grade = gB = 0.01 oz/tonggB B < < ggc c << ggmm

0.01 < 0.0281 < 0.0315

therefore

Block Value = -- $1.20/ton$1.20/ton= Mining Cost

15

Mine Design Parameters For The Case Study

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• Price (P) $600/oz• Sales Cost (s) $5 /oz• Processing Cost (c) $ 19/ ton ore• Recovery (y) 90 %• Mining Cost (m) $ 1.20/ ton• Fixed Costs (fa) 8.35 M/year• Mining Capacity (M) Unlimited• Milling Capacity (C) 1.05 M• Capital Costs (CC) 105 M• Discount Rate (d) 15%

16

Calculation of Ultimate Pit Cutoff Grade

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gm covRe*)(Pr −+

=

tonozgm /038.09.0*)5$600($

2.1$19$=

−+

=

17

Calculation of Milling Cutoff Grade

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gc covRe*)(Pr −=

tonozgc /035.09.0*)5$600($

19$=

−=

18

Grade Tonnage Distribution

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Avg. IntervalGrade

0.000 - 0.020 70,000 0.01000.020 - 0.025 7,257 0.02250.025 - 0.030 6,319 0.02750.030 - 0.035 5,591 0.03250.035 - 0.040 4,598 0.03750.040 - 0.045 4,277 0.04250.045 - 0.050 3,465 0.04750.050 - 0.055 2,428 0.05250.055 - 0.060 2,307 0.05750.060 - 0.065 1,747 0.06250.065 - 0.070 1,640 0.06750.070 - 0.075 1,485 0.07250.075 - 0.080 1,227 0.07750.080 - 0.100 3,598 0.09000.100 - 0.358 9,576 0.2290

Cutoff Grade 0.035

KTonsGrade Interval KTons Grade

89,167

36,348

Waste

0.1023

Ore

Oz/ton

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Constant Cutoff Grades.Yearly Tons and Grade Schedules.

Table 3

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Year Cutoff Avg QM Qc Qr Profits Grade Grade $M/year

1 0.035 0.102 3.6 1.05 96.3 33.02 0.035 0.102 3.6 1.05 96.3 33.03 0.035 0.102 3.6 1.05 96.3 33.04 0.035 0.102 3.6 1.05 96.3 33.05 0.035 0.102 3.6 1.05 96.3 33.06 0.035 0.102 3.6 1.05 96.3 33.07 0.035 0.102 3.6 1.05 96.3 33.08 0.035 0.102 3.6 1.05 96.3 33.09 0.035 0.102 3.6 1.05 96.3 33.0

10 0.035 0.102 3.6 1.05 96.3 33.0For 11 to 34 0.035 0.102 3.6 1.05 96.3 33.0

35 0.035 0.102 3.4 1.00 91.7 31.4TOTAL 0.035 0.102 125.8 36.70 3365.9 1154.2

NPV $M 218.5

20

Profit

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Profits ($M) = (P Profits ($M) = (P –– s ) x s ) x QQrr –– QQcc x c x c –– QQmm x mx m

P – Price S – Sales CostQm – Total Material MinedQc – Ore Tonnage Processed By The MillQr – Recovered Ouncesc – Milling Costs ($/ton)m – Mining Costs ($/ton)

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Shortcomings of the traditional cutoff grades

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• They are established to satisfy the objective of maximizing the undiscounted profits from a given mining operation.

• They are constant unless the commodity price and the costs change during the life of mine AND

• They do not consider grade distribution of the deposit.

22

Traditional

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eryCostSalesiceofitMinimumonDepreciatiCostMilling

gc covRe*)(PrPr

−++

=

tonozgc /060.09.0*)5$600($

3$10$19$=

−++

=

23

Nontraditional ????????

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gc covRe*)(Pr −+

=

tonozgc /054.09.0*)5$600($

10$19$=

−+

=

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Constant Cutoff GradesYearly Tons and Grade Schedules

Table 4

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Year Cutoff Avg Qm Qc Qr Profits Grade Grade $M/year

1 0.060 0.153 6.90 1.05 144.60 57.82 0.060 0.153 6.90 1.05 144.60 57.83 0.060 0.153 6.90 1.05 144.60 57.84 0.060 0.153 6.90 1.05 144.60 57.85 0.060 0.153 6.90 1.05 144.60 57.86 0.054 0.141 6.00 1.05 132.80 51.97 0.054 0.141 6.00 1.05 132.80 51.98 0.054 0.141 6.00 1.05 132.80 51.99 0.054 0.141 6.00 1.05 132.80 51.9

10 0.054 0.141 6.00 1.05 132.80 51.9For 11 to 27 0.035 0.102 3.60 1.05 96.30 33.0

28 0.035 0.102 0.30 0.09 8.10 2.8TOTAL 0.035 0.102 125.80 28.44 3032.10 1112.7

NPV $M 355.7

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Declining Cutoff Grades

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eryCostSalesiceCostFixedonDepreciatiCostMilling

gc covRe*)(Pr −++

=

tonozgc /069.09.0*)5$600($95.7$10$19$

=−

++=

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gc covRe*)(Pr −+

=

tonozgc /050.09.0*)5$600($

95.7$19$=

−+

=

27


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eryCostSalesiceCostFixedofMinimumonDepreciatiCostMilling

gc covRe*)(Pr.Pr

−+++

=

tonozgc /075.09.0*)5$600($

95.7$3$10$19$=

−+++

=

28


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eryCostSalesiceCostMilling

gc covRe*)(Pr −=

tonozgc /035.09.0*)5$600($

19$=

−=

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Declining Cutoff GradesYearly Tons and Grade Schedules.

Table 5

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Year Cutoff Avg QM Qc Qr **Profits Grade Grade $M/year

1 0.075 0.182 9.2 1.05 171.6 62.82 0.075 0.182 9.2 1.05 171.6 62.83 0.075 0.182 9.2 1.05 171.6 62.84 0.075 0.182 9.2 1.05 171.6 62.85 0.075 0.182 9.2 1.05 171.6 62.86 0.069 0.169 8.2 1.05 160.0 57.17 0.069 0.169 8.2 1.05 160.0 57.18 0.069 0.169 8.2 1.05 160.0 57.19 0.069 0.169 8.2 1.05 160.0 57.1

10 0.069 0.169 8.2 1.05 160.0 57.1For 11 to 17 0.050 0.132 5.4 1.05 124.8 39.5

18 0.050 0.132 1.3 0.26 30.5 9.6

TOTAL 125.8 18.11 2562.5 885.6NPV $M 357.7

**Profits ($M)= (PProfits ($M)= (P--s) xs) x QrQr –– Qc x c Qc x c –– QmQm x m x m –– f af a

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Determination Of Optimum Cutoff Grades

When The MillIs Bottleneck

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Formula for Optimum Cutoff Grade

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ig ic *)(

)(−

++=

• Where FFii = d x NPV= d x NPVii /C/Cf = f = ffaa/C /C

and fa is annual fixed costs

32

Optimum Cutoff GradesYearly Tons and Grade Schedules

Table 6

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Year Cutoff Avg QM Qc Qr **Profits NPV Grade Grade $M $M

1 0.161 0.259 18.0 1.05 245.2 95.9 413.82 0.152 0.255 17.2 1.05 241.0 94.4 380.03 0.142 0.250 16.5 1.05 236.4 92.6 342.64 0.131 0.245 15.7 1.05 231.3 90.5 301.45 0.120 0.239 14.9 1.05 225.7 88.1 256.16 0.107 0.232 14.1 1.05 219.6 85.4 206.47 0.092 0.213 12.1 1.05 200.9 76.7 152.08 0.079 0.188 9.8 1.05 177.9 65.9 98.19 0.065 0.163 7.6 1.05 153.6 53.9 46.9

TOTAL 125.8 9.45 1931.4 743.4NPV $M 413.8

**Profits ($M)= (PProfits ($M)= (P--s) x s) x Qr Qr –– Qc x c Qc x c –– Qm Qm x m x m –– f af a

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Summary

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Avg Total Total Strip Profits NPV Life Undiscounted NPV Grade Amount Amount Ratio % Reduction % Increase

mined processed INC CUM INC CUMQm Qr $M $M yrs

Traditional 0.102 125.8 36.70 2.43 4453.4 218.5 35 n/a n/a n/a n/a

Heuristic 0.125 125.8 28.44 3.42 1127.4 355.7 28 3.6 3.6 63.0 63.0(Depr)

Heuristic 0.164 125.8 18.11 5.95 885.6 357.1 18 20.4 23.3 0.3 63.4(Depr and

Fixed Costs)

Lanes's 0.235 125.8 9.45 12.31 743.4 413.8 9 16.0 35.6 15.9 89.0Approach

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One Constraint Cutoff Grade

Optimization Algorithm

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Steps Of The Algorithm

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1. Start with Grade-Tonnage Curve.

2. Define: P - PriceC - Milling Capacity s - Marketing Costsm - Mining Costsc - Milling Costsfa - Fixed Costsd - Discount Rate

36

Steps Of The Algorithm (Cont.)

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3. Determine the cutoff grade gc for year (i).

ySPFfc

ig ic *)(

)(−

++=

• Where FFii = d x NPV= d x NPVii /C/Cf = f = ffaa/C /C

and fa is annual fixed costs

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4. For Cutoff Grade gmilling (i):

• Determine Ore Tonnage Tc and Grade gc

• Determine the Waste Tonnage Tw

• Stripping Ratio ((srsr) = ) = TTww//TTcc

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5. Set

QQcc = C = C if if TTcc > C> CQQcc = = TTcc if if TTcc < C< C

And

QQmm = Q= Qcc(1+(1+srsr))

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6. Determine the annual profit (Pi) by using the following equationPi =(PPi =(P--s) x Qc x s) x Qc x ggcc x y x y –– Qc x (c + f) Qc x (c + f) –– Qm Qm x mx m

P - Prices - Marketing Costs Qm - Total material minedQc - Ore tonnage processed by the millc - Milling Costs ($/ton)m - Mining Costs ($/ton)gc - Average Grade (Opt)y - Recoveryf - Fixed Cost ($/ton)

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7. Adjust the Grade-Tonnage Curve of the deposit for Qc and QQww = = Qm Qm –– QcQc .

8. If Qc < CQc < C in year (i) go to step 9 otherwise

Set i = i+1i = i+1 and go to Step 3.

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9. Calculate incremental NPV for each year (i)

∑=

+−+=

N

ijij

ji d

PNPV 1)1(

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10. If NPV1 for this iteration is not within some tolerance (say plusplus--minus $500K minus $500K ) on the NPV1 of the previous iteration go to Step 1otherwiseotherwiseStop the cutoff grade gc (i) for years i = 1i = 1, NN is Optimum Policy.

Open Pit Sequencing and Production Scheduling

Dr. Kadri Dagdelen

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Open pit production scheduling

• It is a timed sequence of extraction of the ore and waste within the ultimate pit limits from the initial condition of the deposit up to a predetermined stage that mat be referred to as an intermediate of final pit limit.

• It sets the relationship between quantity and quality of the material to be mined, time, geometry of the orebody, and the available resources.

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Time

Stri

ppin

gV

olum

e

Declining Stripping Ratio Method

1

2

3

4

5

67

1

2

76

5

4

3

1

2

3

4

5

67

Orebody

Waste

4

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Increasing Stripping Ratio Method

Orebody

Waste

5

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Constant Stripping Ratio Method

Orebody

Waste

6

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Long Term Production Scheduling

•Long term production scheduling is usually carried out from the initial condition of the deposit (i.e. initial topography) to the ultimate pit limit, in periods of at least one year.

•Its purpose is to determine ore reserves, stripping ratios, future investments, and to conserve and develop owned resources.

•Long term production scheduling takes into account capital availability, geometry and grade distribution of the orebody, metallurgical and physical properties of the material, as well as environmental and legal constraints.

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Short Term Production Scheduling

•Short term production scheduling is concerned with schedules on a daily, weekly or monthly basis.

•Its main objective is to furnish the requirements of the processing plant with ore of uniform quality to ensure operating efficiency.

•To accomplish this objective, short term production scheduling has to comply with restrictions imposed by the long term plan, equipment availability, blending of different materials from different sites within the mine, and the availability of exposed ore.

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Objectives in Open Pit Mine Planning

• To ensure the tonnage required by the processing plant in order to operate efficiently and to produce the expected amount of concentrate per mining period.

• To meet the grade specifications at the processing plant within a given range for each ore parameter that has an effect on the operating costs or the quality of the final product.

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Objectives in Open Pit Mine Planning (cont.)

• To minimize the pre-production stripping volume required to expose enough ore at the beginning of the mine life in order to ensure a continuous operation.

• To defer waste stripping as long as possible to maximize cash flow in the early years of the operation.

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• To ensure a feasible schedule in terms of mining practice. This implies mining exposed material sequentially, keeping appropriate mining widths, maintaining access to the mining areas, and maintaining stable pit walls.

• To ensure the schedule is compatible with the remaining periods. In other words, the present schedule must ensure the feasibility of the future extraction.

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• To mine the orebody in such a way that for each year the cost to produce a given kilogram of metal is at minimum.

• To develop an achievable start-up schedule with respect to manpower training, equipment deployment, infrastructure and logistical support in order to ensure positive cash flow as planned.

• To have enough exposed ore at the beginning of each scheduling period to offset any problem that could arise in the case of underestimation of ore tonnages and grades in the reserves model.

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Objectives in Open Pit Mine Planning (Cont.)

• To maximize design pit slope angles in response to adequate geotechnical investigations, and yet through careful planning minimize the adverse impacts of any slope instability, should itoccur.

• To properly examine the economic merits of alternative ore production rate and cutoff grade scenarios.

• To thoroughly subject the proposed mining strategy, equipment selection, and mine development plan to “what if” contingency planning, before a commitment to proceed is made.

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Pit Sequence Planning

• Orebodies are normally mined in stages, so as to defer waste stripping and maximize the net present value of the surface mining venture.

• These stages are commonly called sequences, expansions, phases, working pits, slices, or pushbacks.

• They are the basic building block on which more detailed time period planning is subsequently made.

• Phase planning should commence with mining that portion of the orebody which will yield the maximum cash flow and then proceed to mine other stages of lessening cash flow.

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Procedure to obtain the pushbacks

• Generate nested pits by increasing and/or decreasing the product price.

• According to the size of the deposit, pick a number of phases that allow enough operating room for the equipment.

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Example of how to obtain the pushbacks

•% Recovery through mill and smelter 90%

•Value of recovered copper $1.10/lb

•Stripping and haulage to dump (level 1) $0.50/ton

•Mining and transportation to plant level $0.80/ton

•Haulage costs increase per bench $0.10/ton

•Processing, smelting and refining $1.20/ton

•General overhead, administration, etc. (ore blocks only) $1.20/ton

•Ultimate pit slope 1 : 1

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Example of how to obtain the pushbacks (Cont.)

Block Model showing copper grades in %

Level1 0.00 0.10 0.15 0.08 0.05 0.00 0.00 0.05 0.03 0.00 0.05 0.05 0.05 0.05 0.05 0.052 0.00 0.22 0.08 0.25 0.15 0.13 0.10 0.13 0.45 0.20 0.20 0.32 0.10 0.15 0.24 0.213 0.05 0.05 0.12 0.13 0.02 0.14 0.11 0.08 0.22 0.09 0.08 0.15 0.22 0.20 0.14 0.054 0.04 0.15 0.12 0.45 0.08 0.09 0.25 0.20 0.29 0.14 0.15 0.04 0.24 0.05 0.02 0.045 0.05 0.08 0.15 0.12 0.30 0.21 0.09 0.79 0.10 0.45 0.32 0.23 0.01 0.01 0.01 0.016 0.08 0.10 0.08 0.01 0.05 0.34 0.45 0.02 0.01 0.04 0.38 0.00 0.00 0.00 0.01 0.15

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Economic Model showing block values in $/ton

Original copper price of $1.10/lb1 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.502 -0.60 1.06 -0.60 1.65 -0.60 -0.60 -0.60 -0.60 5.61 0.66 0.66 3.04 -0.60 -0.60 1.45 0.863 -0.70 -0.70 -0.70 -0.70 -0.70 -0.70 -0.70 -0.70 0.96 -0.70 -0.70 -0.70 0.96 0.56 -0.70 -0.704 -0.80 -0.80 -0.80 5.41 -0.80 -0.80 1.45 0.46 2.24 -0.80 -0.80 -0.80 1.25 -0.80 -0.80 -0.805 -0.90 -0.90 -0.90 -0.90 2.34 0.56 -0.90 12.04 -0.90 5.31 2.74 0.95 -0.90 -0.90 -0.90 -0.906 -1.00 -1.00 -1.00 -1.00 -1.00 3.03 5.21 -1.00 -1.00 -1.00 3.82 -1.00 -1.00 -1.00 -1.00 -1.00

mcygsPBV B −−−= **)(

mBV −=

For ore blocks:

For waste blocks:

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The floating cone algorithm was used to find the ultimate pit limit

Pit1 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 12 -0.60 1.06 -0.60 1.65 -0.60 -0.60 -0.60 -0.60 5.61 0.66 0.66 3.04 -0.60 -0.60 1.45 0.86 23 -0.70 -0.70 -0.70 -0.70 -0.70 -0.70 -0.70 -0.70 0.96 -0.70 -0.70 -0.70 0.96 0.56 -0.70 -0.70 34 -0.80 -0.80 -0.80 5.41 -0.80 -0.80 1.45 0.46 2.24 -0.80 -0.80 -0.80 1.25 -0.80 -0.80 -0.80 45 -0.90 -0.90 -0.90 -0.90 2.34 0.56 -0.90 12.04 -0.90 5.31 2.74 0.95 -0.90 -0.90 -0.90 -0.90 56 -1.00 -1.00 -1.00 -1.00 -1.00 3.03 5.21 -1.00 -1.00 -1.00 3.82 -1.00 -1.00 -1.00 -1.00 -1.00 6

7The ore block left at the right cannot be mined due to slope constraints. All ore blocks are mined in the first iteration. 8

91 102 113 124 135 146 15

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To find a smaller pit reduce the copper price to 0.60/lb Economic block model

1 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.502 -0.60 -0.60 -0.60 -0.60 -0.60 -0.60 -0.60 -0.60 1.56 -0.60 -0.60 0.16 -0.60 -0.60 -0.60 -0.603 -0.70 -0.70 -0.70 -0.70 -0.70 -0.70 -0.70 -0.70 -0.70 -0.70 -0.70 -0.70 -0.70 -0.70 -0.70 -0.704 -0.80 -0.80 -0.80 1.36 -0.80 -0.80 -0.80 -0.80 -0.80 -0.80 -0.80 -0.80 -0.80 -0.80 -0.80 -0.805 -0.90 -0.90 -0.90 -0.90 -0.90 -0.90 -0.90 4.93 -0.90 1.26 -0.90 -0.90 -0.90 -0.90 -0.90 -0.906 -1.00 -1.00 -1.00 -1.00 -1.00 -1.00 1.16 -1.00 -1.00 -1.00 0.40 -1.00 -1.00 -1.00 -1.00 -1.00

mcygsPBV B −−−= **)(

mBV −=

For ore blocks:

For waste blocks:

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The floating cone algorithm was used to find the limit of the pit at $0.60/lb

1 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.502 -0.60 -0.60 -0.60 -0.60 -0.60 -0.60 -0.60 -0.60 1.56 -0.60 -0.60 0.16 -0.60 -0.60 -0.60 -0.603 -0.70 -0.70 -0.70 -0.70 -0.70 -0.70 -0.70 -0.70 -0.70 -0.70 -0.70 -0.70 -0.70 -0.70 -0.70 -0.704 -0.80 -0.80 -0.80 1.36 -0.80 -0.80 -0.80 -0.80 -0.80 -0.80 -0.80 -0.80 -0.80 -0.80 -0.80 -0.805 -0.90 -0.90 -0.90 -0.90 -0.90 -0.90 -0.90 4.93 -0.90 1.26 -0.90 -0.90 -0.90 -0.90 -0.90 -0.906 -1.00 -1.00 -1.00 -1.00 -1.00 -1.00 1.16 -1.00 -1.00 -1.00 0.40 -1.00 -1.00 -1.00 -1.00 -1.00

123456

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To find an intermediate pit reduce the copper price to $0.86/lb Economic Block Model

1 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.502 -0.60 0.11 -0.60 0.57 -0.60 -0.60 -0.60 -0.60 3.67 -0.60 -0.60 1.65 -0.60 -0.60 0.42 -0.603 -0.70 -0.70 -0.70 -0.70 -0.70 -0.70 -0.70 -0.70 -0.70 -0.70 -0.70 -0.70 -0.70 -0.70 -0.70 -0.704 -0.80 -0.80 -0.80 3.47 -0.80 -0.80 0.37 -0.80 0.99 -0.80 -0.80 -0.80 0.22 -0.80 -0.80 -0.805 -0.90 -0.90 -0.90 -0.90 1.04 -0.90 -0.90 8.63 -0.90 3.37 1.35 -0.90 -0.90 -0.90 -0.90 -0.906 -1.00 -1.00 -1.00 -1.00 -1.00 1.56 3.27 -1.00 -1.00 -1.00 2.18 -1.00 -1.00 -1.00 -1.00 -1.00

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To find an intermediate pit reduce the copper price to $0.86/lb Economic Block Model

1 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 -0.50 Pit2 -0.60 0.11 -0.60 0.57 -0.60 -0.60 -0.60 -0.60 3.67 -0.60 -0.60 1.65 -0.60 -0.60 0.42 -0.60 13 -0.70 -0.70 -0.70 -0.70 -0.70 -0.70 -0.70 -0.70 -0.70 -0.70 -0.70 -0.70 -0.70 -0.70 -0.70 -0.70 24 -0.80 -0.80 -0.80 3.47 -0.80 -0.80 0.37 -0.80 0.99 -0.80 -0.80 -0.80 0.22 -0.80 -0.80 -0.80 35 -0.90 -0.90 -0.90 -0.90 1.04 -0.90 -0.90 8.63 -0.90 3.37 1.35 -0.90 -0.90 -0.90 -0.90 -0.906 -1.00 -1.00 -1.00 -1.00 -1.00 1.56 3.27 -1.00 -1.00 -1.00 2.18 -1.00 -1.00 -1.00 -1.00 -1.00

The ore block left at the right cannot be mined due to slope constraints. All ore blocks are mined in the first iteration.

123456

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The three pits shown in together

1 $0.60/lb23456

$1.10/lb$0.86/lb

24

ABCD

EF

Design Phase Limits Ultimate Pit

Ore

Rock Type I

Rock Type II

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Hypothetical Deposit and Pit Development Sequence

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Tonnage Inventory by Phase

Waste Ore Waste Ore Waste Ore5100 15,0005050 32,0005000 50,000 2,000 4,0004950 38,000 18,000 15,0004900 15,000 20,000 18,0004850 4,000 10,000 15,000 22,0004800 3,000 9,000 4,000 9,000 16,0004750 2,000 8,000 3,000 9,000 3,000 10,0004700 2,000 7,000 5,000 20,0004650 1,000 6,000 8,000 22,0004600 3,000 17,0004550 1,000 7,000

Total 159,000 27,000 65,000 31,000 95,000 76,000

Thousands of tonnes

Phase "A" Phase "B" Phase "C"Bench

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Summary by Phase

Waste above Waste on Ore Cumulativefirst ore ore Ore Life* ore lifebench benches (years) (years)

A 150,000 9,000 27,000 1.08 1.08B 55,000 10,000 31,000 1.24 2.32C 75,000 20,000 76,000 3.04 5.36D 128,000 38,000 125,000 5.00 10.36E 182,000 49,000 151,000 6.04 16.40F 220,000 45,000 130,000 5.20 21.60Total 810,000 171,000 540,000 21.60

*Assuming an annual milling rate 0f 25,000 tonnes

Phase

Thousands of tonnes

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Hypothetical Deposit and Pit Development Sequence

Time (Years)

10

ore deliveriesrequired to sustainMinimum waste stripping

Time (Years)Pre-production

(Mill

ions

of t

onne

s)C

umul

ativ

e St

ripp

ing

250

0

500

750

A

B

C

D

(Mill

ions

of t

onne

s)D

evel

oped

Ore

50

0

1000

100

150

BA

C

D

It requires 128 M tonnes strippingPhase "D" life = 5 yearsPhase "D" ore = 125 M tonnes

-10 -5

200

25050

F

200 M

25 M

75 M50 M

- Pre-production period

A proposed stripping

- Production period50 M tonnes / year

4 yrs. Yr 1

scheduleE

42-3

E

F

2015

stripping scheduledue to the proposedEarlier ore development

25

Period

-10 -5 0 5 10 15 20 25

schedule

4 yrs. Yr 1- Pre-production period

A proposed stripping50 M tonnes / year

- Production period

B

A

C

D

25 M50 M

200 M75 M4

2-3

0

500

250

-10 -5 0 51 2 3 42550

50

75

150

Pre-productionPeriod

200

BA

C

D

0

50

100

-10 -5 0 5

1.08

1.24

3.04

27 31

76

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10

ore deliveriesrequired to sustainMinimum waste stripping

Time (Years)

Pre-production

(Mill

ions

of

tonn

es)

Cum

ulat

ive

Stri

ppin

g

250

0

500

750

A

B

C

D

(Mill

ions

of t

onne

s)D

evel

oped

Ore

50

0

100

150

BA

C

D

It requires 128 M tonnes strippingPhase "D" life = 5 yearsPhase "D" ore = 125 M tonnes

-10 -5 50

200 M

25 M

75 M50 M

- Pre-production period

- Production period50 M tonnes / year

4 yrs. Yr 1

E

42-3

Estripping scheduledue to the proposedEarlier ore development

Period

-10 -5 0 5 101 2 3 4

75

505025

Cushion = 0.66 years



5.003.04

1.241.08

27 31

76

125

($374M)

Period 1$46M

Period 2$42M

Period 3$63M

Period 5$51M

Period 4$65M

Period 6$48M

Period 7 $43MPeriod 8 $16M

Period 1$81M

Period 2$72M

Period 3$63M

Period 5$37M

Period 6$32MPeriod 7

$43M

Period 8$9M

($398M)

Period 4$61M

Period 1$50M

Period 2$37M

Period 3 $60M

Period 4$50M

Period 5 $49M Period 6$50M

($366M)

Period 7 $52M

Period 8 $19M

($372M)

Period 1 $42MPeriod 7 $57MPeriod 8 $11M

Period 2$32M

Period 3$71M

Period 4 $51M

Period 5 $57MPeriod 6 $52M

Long Term Planning and Sequencing

Dr. Kadri Dagdelen


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• Objective is to determine the suitability of the limestone resource for the subsequent processing by the cement plant

• Life of mining and reclamation plans• Equipment Selection• Facility layout and Permitting

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• Create a geologic model• Define structural domains and stratigraphy• Chemistry• Long and short term variability

• Long term reserves and average chemistry• Estimate the block chemical values• Estimate possible raw mix requirements

• Quarry layout and operational plan yearly mine plans

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• Determine mineable resource boundaries• Haul road layout • Define long term reclamation needs

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Midlothian Cement Quarry:Case Study

• Current production 1.8 million tons of limestone• One 50ft to 60ft bench operation • In pit crushing - 1000 ton/per hour capacity• Expand the capacity to 3.6 million tons by bringing

the second bench into production• 50 percent of the production from first 50ft bench

and another 50 percent from the second bench.• %SO3 is not very good for the limestone coming

from the second bench. Blending of these two benches are necessary.

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• Quarry currently operates 10 hours per shift, 5 days per week

• 1000 ton per hour Krubb In Pit Crusher• 2000 ft long main movable belt conveyor

with 500 ft long extension belt• Komatsu 14 and 10 cubic yard loaders

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• Determine next 50 years life of mine plans • Sequencing plan to come up with the right

blend limestone that meets the minimum of %1.3 SO3 requirements

• Determine equipment and capital investment needs for the next 10 years

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Quarry Development and Sequencing

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Holnam Quarry Mining Sequence: First Bench Development

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Second Bench Development During the First Three Years

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Holnam Quarry Mining Sequence: First and Second Bench Development

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Midlothian North Area Quarry Progress Contours Year1

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Midlothian North Area Quarry Progress Contours Year 2

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Midlothian Quarry Block Model Definition

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Midlothian Quarry Block Model Definition

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Midlothian Quarry Sequence: One Year Increments on Elevation 790

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Equipment Selection

Three Different Options were Evaluated:• One 15 yd3 Caterpillar 992G model loader working

with a 70 ton CAT 775D truck fleet.• One 15 yd3 Caterpillar 992G model loader working

with a 98 ton CAT 777D truck fleet.• One 11 yd3 Caterpillar 990series II model loader

working with a 70 ton CAT 775D truck fleet

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Loader - Truck Fleet Evaluation and Cost Analysis Year 1

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Loader - Truck Fleet Evaluation & Cost Analysis Haul Road Profile

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Loader - Truck Productivity Calculations

Assumptions• 90 % Loader and truck availability resulting

in 81 % fleet availability• 92 % Operator efficiency• 75 % bucket fill factor• 2400 scheduled hrs• 0.55 min. loader cycle time

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Loader - Truck Productivity Calculations

Assumptions (Cont.)• 0.1 min. first bucket dump time• 0.7 min. hauler exchange time• 2492 lbs/yd3 density• 14 ton/pass; 5 passes per truck• 2400 hours per year

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Equipment Productivity & Cost Estimation

• For CAT 992G Loader - 775D Trucks

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Option 1: Cat 992G Loader -775D Trucks

The truck cycle time for four different conditions:

• Year 1: 9.67 minutes• Year 2: 11.05 minutes• Year 3: 10.86 minutes• Year 7: 11.04 minutes

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Option 1: Cat 992G Loader - 775D Trucks Fleet Productivity in Tons

# of 775D's Year 1 Year 2 Year 3 Year 7 1 825,332 808,107 801,532 808,669 2 1,540,565 1,524,899 1,504,316 1,525,959 3 2,111,530 2,108,190 2,070,839 2,109,657 4 2,586,695 2,644,575 2,580,165 2,644,575

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The truck cycle time for four different conditions

• Year 1: 12.16 minutes• Year 2: 12.63 minutes• Year 3: 12.42 minutes• Year 7: 12.27 minutes

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# of 777's Year 1 Year 2 Year 3 Year 7 1 945,127 903,286 920,644 934,223 2 1,731,661 1,667,466 1,695,274 1,715,981 3 2,285,652 2,234,289 2,254,834 2,275,379 4 2,737,983 2,714,476 2,724,550 2,731,266

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Operating Cost for the Loader and Trucks

Model Operating CostCAT 992G $125/hrCAT 775 D $63/hrCAT 777 $82/hr

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Operating Cost for the Loader and Trucks

Model Operating CostCAT 992G $125/hrCAT 775 D $63/hrCAT 777 $82/hr

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Loader - Truck Capital Requirements

Model Purchase PriceCAT 992G $1,270,000CAT 775 D $740,000CAT 777 $1,060,000

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Loader - Truck Capital Requirements

• At the start of the production from bench two, $2.1 M is needed to purchase 1 Cat 992G Loader and 775D truck.

• In year 2, additional $1.5M is needed to purchase 2 more Cat 775D trucks.

• For the Cat 992G loader, Cat 777D truck combination, $2.35M and $2.12M would be needed at the start and beginning of year 2.

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Loaders and Shovels

Comparative Analysis

Dr. Kadri DagdelenColorado School of Mines

Source: J. Wiebmer, Caterpillar Incorporated

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Hydraulic Shovel Applications

• Hard Digging• Poorly shoot material• Selective loading• Wet, jagged floor• Pitching floor• Single face operation

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Hydraulic Shovel Selection Considerations

• Multiple loading fronts• Fast cycle time (25 to 30

seconds)• Low capital costs• Moderate mobility• Highly productive

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Hydraulic ShovelFavorable Site Conditions

• Single loading face• Tight digging materials• Face height equals to stick

length• Some will dig below and

above• Soft floors

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Hydraulic ShovelUnfavorable Site Conditions

• Requires clean-up support• Excessive tramming• High benches

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Wheel Loader Applications

• Mobility and versatility• Well blasted material• Low pile profile• Smooth, level floor• No clean-up support equipment• Short mine life

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Wheel LoaderSelection Considerations

• Highly mobile/versatile• High bucket fill factors• Low capital costs• No clean-up support

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Wheel LoaderFavorable Site Conditions

• Good loading materials• Lower face profile• Multi-face loading

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Wheel LoaderUnfavorable Site Conditions

• Poor underfooting (tire cost)• Soft floor• Tight load area

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Comparison Shovels vs. Loaders

Hydraulic Shovel Wheel Loader

% Operating Weight as bucket payload

8-11% 18-21%

Cost/CY of capacity ($1000)

100-120 60-80

Economic life (1000 hours)

30-60 30-60

Operating Cost/ton 0.07 - 0.12 0.07 - 0.12

Market Share (1980) 15% 85%

Market Share (1990) 30% 70%

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Mobility

0 200 400 600 800 1000 1200 1400

HydraulicShovel

Wheel Loader

Feet Traveled in One Minute

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Breakout Force

• For similar bucket capacities, a hydraulic shovel and a wheel loader will show approximately the same breakout force.

• However, because the difference in bucket shapes, the shovel can apply twice as much force.

• The shovel can apply the force over its reach of the face.

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Bucket Fill Factors

Hydraulic Front Shovels 80-85%

Hydraulic backhoes 100%

Caterpillar wheel loaders 100-115%

Other wheel loaders 85-95%

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Power and Fuel

• Hydraulic shovels burn less fuel per hour than wheel loaders.

• But considering tons moved per gallon burned, wheel loaders and hydraulic shovel compare very favorable to each other.

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Two-to-Three Minute Rule

• A truck does not make money when its tires are not running.

• Truck load times should be in the two to three minute range.

• Loading times are reduced by the use of the right loading tool, better rock fragmentation, operator training, and face supervision.

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Loading Tool Preferences

85% 15%

60% 40%

50% 50%

Region

North & South America

Europe, Africa, Middle East

Australia, Far East

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Hydraulic Shovel Production Range

Operating Weight (Tons)

Production Range (tons/hour)

140 800 - 1,100

230 1,100 - 1,800

340 1,600 - 2,400

620 3,000 - 4,000

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Wheel Loader Production Range

ModelProduction Range

(tons/hour)

Cat 994 2,700 - 3,100

Cat 992D 1,300 - 1,700

Cat 988B 700 - 900

Cat 980F 500 - 700

Cat 966F 300 - 500

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Conclusions

• No two pits are the same.

• There is a wide array of loading tools to meet operational needs.

• Analysis, not luck, will yield the winner for your operation

Types of Mobile Surface Mining Equipment

•Dozers

•Scrapers

•Trucks

•Front-end Loaders

•Hydraulic Excavators

•Electric Shovels

•Draglines

•Bucket Wheel Excavators

•Blast Hole Drills

Other Bulk Material Handling Systems

Surface and Underground Mining

•Belt Conveyors•Rail Haulage

Types of Underground Mining Equipment

•Blast Hole Drills•Roofbolters•Slushers•Overshot Loaders•Load-Haul-Dump Units (LHDs)•Trucks•Belt Conveyors•Rail Transportation•Hoisting Systems

Loading & Hauling EquipmentLoading Hauling Combination Loading Hauling Combination

Rubber WheelFront End

LoaderTrucks

Loader Scrapers

Front End Loader

TrucksLoad Haul

Dump Bulldozers

Back Hoe GradersOver Shot Loaders

CrawlerTrack

LoaderBulldozers

Track Loaders

Hydraulic Shovel

Bucket Wheel Excavator

Hydraulic Shovel s

Cable Shovel

Over Shot Loaders

Drag Line

Back Hoe

RailConventional

Rail Cars Over Shot Loaders

Mine Cars/ Locomotives

OtherWalking

Drag LinePneumatic/ Hydraulic

Pneumatic/ Hydraulic

Slusher

Dredge Conveyer Conveyers

Skips

SURFACE UNDERGROUND

Comparative Equipment Size

Transport Distances

(Source: Surface Mining Equipment, Martin, et. al., 1982)

Dozers

The dozer, or bulldozer is a crawler or wheel driven tractor with a

front mounted blade for digging and pushing material.

It is used to both excavate and transport material over short

distances.


Dozer Powered Functions


Typical Dozer Production Cycle


Applications


Land clearance: The dozer can be sized to provide sufficient power, and with proper operating techniques can move most obstacles in its path, including boulders, trees, etc. This makes it the primary tool in clearing land prior to mining. Special blades are available for this application.

Stripping overburden: Some mine plans utilize scrapers and dozers for overburden removal. The dozer, in these operations,moves a portion of the overburden by pushing it over the highwall.

Grading and leveling mining benches: Draglines, electric shovels and wheel excavators require a flat work surface free of boulders; dozers are commonly used in this clean-up operation.

Applications


Feeding a belt conveyor: The dozer can be effectively employed to push material into a "belt loader" which in turn feeds a belt conveyor.

Trapping for loaders: The efficiency of small to medium sized loading equipment can be improved by using a dozer to rip and position material to be loaded.

Reclamation: Dozers are a basic tool for leveling and recontouringmined out land. Special blades and special wheel models are available for this type of work.

Fait-Allis 41B with single shank ripper leveling dragline spoil piles.


CAT D11, Black Thunder Mine, Wyoming, Spring 2002

Scrapers

The scraper is a rather unique machine because of its ability to

excavate material in thin horizontal layers, transport the material a

considerable distance, and then discharge it in a spreading action.


Scrapers


Scraper Powered Functions


Scrapers


Applications


Topsoil removal: The scraper is broadly used in those activities which involve selective removal of horizontal horizons and transport to storage.

General reclamation: The scraper is applied in the rough leveling and contouring phase and for replacement of the upper horizons prior to revegetation.

Ore/Coal removal (with or without ripping): Scrapers are employed in cases where the seams are thin and other types of excavating equipment are inefficient.

Applications


Overburden removal (with or without prior ripping): These can be either initial cuts or prebenching operations for other excavating equipment, or complete overburden removal.

The latter case requires a well planned circular operational layout to minimize travel distances and utilize downgrade loading and dumping.

Typically, operations of this type use dozers for preshaping, supplementary material transport and push-pull scraperloading techniques.

x

Terex S-24B tandem scraper self loading overburden.(Source: Surface Mining Equipment, Martin, et. al., 1982)

Trucks

A truck is simply a mobile piece of equipment for hauling material.

It is often an integral part of the material handeling activities in the

mine for either transport of ore from the face to processing or

stockpile, or for transport of overburden to spoil.

Trucks


Truck Powered Functions


Applications


These trucks are used exclusively for material transport. The material can be just about anything but, in mining, the broad classifications are:

•Overburden•Ore/Coal

When trucks are used to haul overburden, the mine normally has an open pit or area mine plan with dumping off of spoil benches.

Trucks can be used to haul ore/coal to a hopper or stockpile, invirtually any surface mine plan.

Dumping to stockpile is generally done in shallow lifts.

Applications


Bottom dump units, driving over a grizzly, are used to feed a hopper.

A back-in hopper station is utilized with rear dumps.

In some cases the trucks carrying coal directly to a nearby power plant will on the return trip transport ash back into the pit for burial.

Large Haul Trucks, Cripple Creek –Victor, Colorado, Fall 2002

Large Haul Truck, Cripple Creek –Victor, Colorado, Fall 2002

Wabco 3200B, 250 ton, three axel rear dump.


Rimpull three axel bottom dump coal hauler.


(World Mining Equipment, September 2002)

(World Mining Equipment, March 2003)

Front-End Loaders (FEL)The front-end loader is a wheel or crawler mounted tractor with a

front mounted bucket and is utilized in excavating, loading, and

transporting material.

Because of its versatility, the front end loader is found in a wide

variety of mining applications.

FEL Powered Functions


Applications


The wheel loader is a competitive excavator, loader and transporter.

It competes with shovels, dozers and, over short transport distances, with scrapers and trucks.

Being quite fast, mobile, and versatile, it can be used in a number of mine applications.

Because the FEL has generally not been considered to have the digging ability of a shovel in consolidated digging faces, it finds many of its applications in softer formations, coal/ore andstockpile work.

The larger sizes are more rugged and powerful, and are proving themselves in difficult digging.

Applications


The primary mine applications are the following:

•Loading and/ or transporting topsoil

•Loading and/ or transporting coal/ ore from the digging face

•Loading and/or transporting coal/ore from stockpile

•Loading and/or transporting overburden and waste

In all of the above loading can be into trucks, hoppers, railroad cars, or belt loaders.

Transport can be for distances up to 1000 feet on the level or grades up to 12%.

CAT 994D loading a haul truck

Heavy Equipment, John Tipler, 2000

Hydraulic Excavators

Hydraulic shovels, primarily a European development, have

proven themselves on construction projects.

The have now reached a level of reliability and have increased in size to the point where units are common in surface mining applications.

Digging Profile


Hydraulic Excavator Powered Functions


ApplicationsHydraulic machines are employed in overburden removal, coal/ore loading or, in the smaller sizes, for utility work generally related to mine drainage systems.

The hydraulic shovel is primarily an excavating and loading device. While it can swing and/or propel to transport material short distances, it is used almost exclusively to load trucks or, in some cases, hoppers/crushers.

Hoes have similar uses to shovels. However, their below grade digging capability makes them particularly suited to tasks such as trenching or excavating under water.

Hoes are utilized in mining when floor conditions warrant keeping machines off the bottom of the pit.


Typical Hydraulic Shovel Production Cycle


Typical Hydraulic Hoe Production Cycle


Heavy Equipment, John Tipler, 2000

CAT 5230 hydraulic excavator loading a haul truck

Electric ShovelsThe shovel is one of the oldest types of excavating equipment.

With time, the machines grew in capacity , steam power was replaced by gas, then diesel fuel and finally, in the larger units used in mining today, by electricity.

In recent years, smaller shovels below 5 cubic yards in capacity are being replaced by front-end loaders and hydraulic machines.


Steam Shovel Mining Virginia Minnesota, circa 1910

Electric Shovels


Electric Shovel Powered Functions


Applications


Electric shovels generally have the same applications as hydraulic shovels although the electric units are considered to be particularly suited to more severe digging conditions.

They are available in larger sizes and have a proven service record in multi-shift mining operations. Electric shovels also tend to have longer range capabilities.

These shovels are applied in benching operations in either overburden or coal/ore.

Discharge is commonly into trucks but can also be into mobilehoppers.

The larger models and/or those equipped with long range front ends may be applied in direct spoiling overburden removal operations.

Loading Plans


The Bucyrus-Erie 1850-B Brutus with 90-yard dipper at Pittsburg and Midway Coal Mining Company in 1961.

This shovel is currently maintained by a preservation group.

Extreme Mining Machines, Keith Haddock, 2001

The last stripping shovel produced was this 105-yard Marion 5900, sold in 1971 to Amax Coal Company’s Leahy Mine in Illinois.


Draglines


Draglines

Through the years, the dragline has remained a unique excavating tool and has experienced a dramatic growth in maximum size.

With its long reach and ability to dig to substantial depths below itself, it has had broad applications on many irrigationprojects and, in more recent years, in surface mining.

The hydraulic hoe has, to some extent, replaced the smaller sized diesel draglines but the larger diesel and/ or electric machinesretain their popularity.

Draglines, along with the bucket wheel excavators, are the largest pieces of mobile equipment currently manufactured.

Draglines


Dragline Powered Functions


The world’s largest operating dragline (one of two), the Bucyrus2570-WS with 160 yard bucket at the Black Thunder Mine, WY.


The 100 yard Marion 8800 loading in Kentucky


Bucyrus International’s Big Muskie’s 220-yard bucket easily accommodates a high school band. Photo taken in 1969.


Bucket Wheel ExcavatorsWheel excavators dig with a rotating bucket wheel that discharges the material onto a belt conveyor.

The material is transported on this conveyor or a series of beltconveyors until it is discharged from the machine.


Bucket Wheel Excavators

Wheel excavators have been used, in limited numbers, for continuous excavation of unconsolidated materials starting back in the mid 1920's.

Interest in the machines has been much greater overseas with theGermans, in particular, performing extensive application studies and machine development.

Overall use within the United States has been very limited.


Bucket Wheel Excavator Powered Functions


Applications


There are currently very few bucket wheel excavators in service in the US. They have been used for:

•Overburden excavation with direct spoiling

•Overburden excavation with conveyor or truck loading, prestripping for a large dragline or stripping shovel

•Large earthmoving projects (medium size or small fixed wheels)

•Coal excavation with conveyor or truck loading(medium size or small fixed wheels)

•Topsoil removal and Reclamation leveling (small fixed wheels)

Rhineland Lignite Mine, Germanywww.mining- technology.com

World Mining Equipment, September 2002

Förderanlagen Magdenburg (FAM) bucket wheel excavator.

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Loading Equipment

Dr. Kadri Dagdelen


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Excavators

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Hydraulic Shovels Specifications

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Excavator Specifications

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Digging EnvelopesFront Shovels

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Curl and Crowd ForcesFront Shovels

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Digging EnvelopesExcavators

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Excavators Bucket

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Loaders

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Breakout ForceLoaders

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Breakout Force from RackbackLoaders

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Carry PositionLoaders

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900 Series II – Dimensions Loaders

14

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900 Series II – Dimensions Loaders

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SpecificationsLoaders

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SpecificationsLoaders

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Travel Time – LoadedLoaders

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Travel Time – EmptyLoaders

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Excavator Production Calculations

A standard formula for cyclic excavators can be employed:

O = B x BF x D x HS x J x A x 3,600 seconds(1+S) C hour

Bucket Load Buckets/Period

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Bucket Load

B x BF x D/(1 + S) < Recommended Operating Capacity

• With wheel loaders:50% of full turn static tipping load fora specific bucket type

• With front shovels:Maximum load

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Bucket Load

• Bucket weight depends on size, duty and ground engaging tools

• Bucket size depends on reach• Bucket size (B) based on 2:1 heap• Bucket fill (BF) decreases with increasing

material consolidation

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(CAT)

Wheel Loader Bucket Fill Factors

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Weight of Materials

(CAT)

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Bucket Load

• % Swell increases and load factor decreases with degree of consolidation

• In place density (D) important and should be a measured number

• Loose density (D/(1 + S)) important and should be a measures number

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Buckets/Period

• Average cycle time (C) based on standard cycle time adjusted for:• Material• Material fragmentation• Material size distribution• Pile configuration

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Buckets/Period

• Average cycle time (C) based on standard cycle time adjusted for:• Consistency of operation• Swing angle (Shovels)• Travel distance (Loaders)• Operator ability

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Wheel Loader Cycle Time

Average cycle time for truck loading increases with machine size

.60-.7015-21

.55-.607.5-11

.50-.555.0-7.5

.45-.501.7-4.5Cycle time (min)Loader Size (cy)

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Cycle Time

• Hours scheduled (HS) usually a given, based on management preferences and required output

• Longer shifts appear to be trend to minimize start-up, shut-down impact

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Cycle Time

• Job factor (J) depends on: • Truck assignment• Management issues• Job layout (Blending, etc.)

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Cycle Time

• Mechanical availability (A) depends on:• Material• Management/suppliers• Age of machine• Schedule

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Loading Methods

• Loading method impacts cycle time and job factor• Wheel loaders

• Y pattern used with machine digging point left to right• Truck spotting location important• With a limited truck fleet and excess loader capacity,

staggered and chain loading can be utilized

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Loading Methods

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Loading Methods

(Mining Magazine)

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Shovels:Double Back-Up

Options include • Double back-up• Single back-up• Drive-by• Modified drive-by

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• Trucks loaded on both sides• Average swing angle reduces• Clean-up allowed on one side while loading

continues• Moves required as shovel penetrates bank

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Requires balance of move time versus cycle time

(Oslund and Russell)

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Shovels:Single Back-Up

• Truck loaded on one side• Larger swing angle• Potential clean-up delays• Potential spotting delays depending on

excavator first cycle

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Shovels:Single Back-Up

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Shovels:Drive-By

• Used with tractor trailers• Large swing angles• Potential clean-up delays• Minimal amount of shovel moves• Blending problems

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Shovels:Drive-By

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Shovels:Modified Drive-By

• Truck backs in to reduce swing angle• Potential clean-up delays• Minimal amount of shovel moves• Blending problems• Depth of cut effects cycle time and move

time

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Shovels:Modified Drive-By

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Modified Drive-By:Optimum Width

Production Estimating of Material Movement With Earth Moving Equipment

There are five factors which need to be considered in preparing aproduction estimate of earthmoving equipment for any particular job.

These factors include:1. Earthmoving Cycle Components2. Job Efficiency Factors3. Material Weights & Swell Factors4. Vehicle Payloads5. Selection of Equipment

1. Earthmoving Cycle Components

The productivity cycle of any earthmoving job may be separatedinto six components:

1. load, 2. haul or push, 3. dump, 4. return, 5. spot,6. and delay.

Each of these components is responsible for a certain percentage of thetotal cycle time.

The factors affecting these components will determine the time eachcomponent will require.

Load Factors

• Performance ability of unit• Hauling distance• Haul road condition• Grades• Miscellaneous factors affecting haul speed

Haul/Push Factors

• Size and type of loading machine • Type & condition of material to be loaded• Capacity of unit • Skill of the loading operator

Dump Factors

• Performance ability of unit• Return distance• Haul road condition• Grades• Miscellaneous factors affecting return speed

Return Factors

• Destination of material -Hopper, Over Bank, Fill, Stockpile, etc.• Condition of dump area• Type & maneuverability of hauling unit• Type & condition of material

Spot Factors

• Time spent waiting on loading unit or pusher• Time spent waiting to dump –at crusher

Delay Factors

• Maneuverability of unit• Maneuver area available• Type of loading machine• Location of loading equipment

2. Job Efficiency FactorsAn estimate must indicate sustained, or average earthmoving production over a long period of time.

Overly optimistic hourly production estimates will result in failure to maintain forecasted production, and an insufficient number of unitsassigned to the job.

It is necessary to allow for the unavoidable delays encountered on all operations such as night operating, shovel moving, blasting, weather, traffic, shutdowns, or for factors such as management and supervisionefficiency, operator experience, proper balance of auxiliary equipment such as tamping roller, pusher or spreader bulldozers, proper crusher capacity, etc.

2. Job Efficiency FactorsThe maximum productivity of an earthmover should be derated to meet actual conditions. Typical deration factors are found in the following table:

3. Material Weights & Swell FactorsThe weight of material is most often expressed in pounds per cubic yard.

Undisturbed or “in place” material is called a bank cubic yard (BCY).

Material in a loose, broken, or blasted state is called a loose cubic yard (LCY).

3. Material Weights & Swell FactorsThe relationship between bank and loose cubic yards is established by the swell factor or percent swell.

For example, the percent swell of shale is 33% indicating that one bank cubic yard of shale will swell to 1.33 cubic yards in the loosestate.

Shale weighs 2800 pounds per bank cubic yard. At a swell factor of 0.75 (inverse of 1.33) the weight of one loose cubic yard of shale is 2100 pounds (2800 pounds * 0.75).

Note: Earthfill projects employ mechanical means such as rolling, tamping and adding water to compress the deposited loose cubic yard back to the state it was in the bank. This compaction may reduce the volume of the bank cubic yard by as much as 15%.

4. Vehicle PayloadsThe rated payload of hauling units is given on the specification sheets in pounds, struck (water level) capacities and SAE capacities.

For haulers the SAE heaped capacity is for a load at a 2: 1 slope. For scrapers the SAE heaped capacity is for a load at a 1: 1 slope.

For estimating purposes, the payload in pounds should not be exceeded.

Vehicle Payloads Should Not Be Exceeded

4. Vehicle PayloadsLoaders, scrapers and haulers all carry material in the loose condition.

To assure adequate volumetric capacity, the pounds payload should be divided by the weight per loose cubic yard and compared to the heaped capacity as shown below:

5. Selection of Equipment

After the estimator has examined the job requirements and operating conditions and decided to investigate earthmoving equipment, a tentative equipment selection will be made.

The final decision will, of course, depend on which method offers the lowest cost per yard or ton.

In some cases, methods such as draglines, belt conveyors, etc. will also be considered.

Example

Rock density: 11 cubic feet per short tonSwell factor: 1.6

ShovelBucket capacity: 18.8 cubic yardsDigging cycle time: 30 seconds per passBucket fill factor: 0.92

TruckLoad capacity: 62 cubic yards struck

88 cubic yards at 2:1 SAE140 tons payload capacity

a) Calculate the number of passes to load the truck.b) Calculate the total time required to load a truck.

Loading and HaulingFleet Productivity

Dr. Kadri Dagdelen

Source : Hrebar – Lafarge 2000 Presentation

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Truck Selection

• Number and type of trucks selected should be based on overall system economics

• Lowest cost fleet selected considering operating and capital coats

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Truck Selection

• Production requirement and operating schedule

• Material characteristics• Density in place and loose, swell• General size distribution, particularly maximum

and minimum sizes and percentage of total• Hardness and texture• Ease of handling

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Truck Selection

• Physical and climatic conditions• Effect of altitude on engine efficiency• Effect of ambient temperature on engine cooling, tire

performance, and use of lubricants• Effect of rainfall, frost, snow, fog, etc. on road conditions

and travel

• Haul road characteristics• Length, grade, and surface condition of

segment

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Truck Selection

• Loading• Space and ground conditions at loading point• Type and size of loading equipment• Total availability of loading equipment

• Dumping• Dumping arrangements: rear dump into hopper, drive

over hopper, edge of spoil, windrow, etc.• Space and ground condition at dump point• Total availability of down stream equipment

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Truck Selection:Rear Dump

• High horsepower to weight ratio• Deep pits, high grades, maneuverability required

high impact and rough in pit conditions. • Can be used with any type of material ( e.g.,

blocky, free flowing, etc. )• Used for dumping into hoppers or over bank or fill• Economic distance limited

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Truck Selection:Bottom Dump

• Low HP/weight ratio• Free flowing material• Dumping over hopper or in windrow• Operational advantages: Dump on the move,

More favorable tire and axle loading, high speed hauling on level hauls

• Moderate grade and long distance hauls

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Production Calculations

• The prime mover delivers a force that propels the haulage vehicle plus the load

• The force the drive wheels deliver to the ground is referred to as rimpull

• This force is a function of: the torque developed by the engine, the ratio of the gears, and the size of the wheels

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Production Calculations

• Maximum velocity is reached when rimpullis equal to resisting forces of gravity, rolling resistance. etc.

Horsepower x 375 x EfficiencyAvailable Rimpull =

Speed in MPH

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Rimpull vs. Velocity

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Rolling Resistance

• Measure of the force required to overcome internal bearing friction and the retarding effect between the tires and the ground (i.e., tire penetration and tire flexing).

• Expressed in terms of lb/ton vehicle weight or % vehicle weight

• Haul Road Resistance can be estimated by:RR = 2%+1.5% per inch of tire penetration

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Rolling Resistance FactorsTYPICAL ROLLING RESISTANCE FACTORS

Various tire sizes and inflation pressures will greatly reduce or increase the rolling resistance. The values in this table are approximate, particularly for the track and track+ tire machines. These values can be used for estimating purposes when specific performance information on particular equipment and given soil conditions is not available See Mining and Earthmoving Section for more detail:

ROLLING RESISTANCE, PERCENT ̀ Tires Track Track

UNDERFOOTING Bias Radial ** +Tires A very hard, smooth roadway, concrete, cold asphalt or dirt surface, no penetration or flexing 1.5%* 1.2% 0% 1.0% A hard; smooth, stabilized surfaced roadway without penetration under load; watered; maintained 2.0% 1.7% 0% 1.2% A firm, smooth, rolling roadway with dirt or light surfacing, flexing slightly under load or undulating, maintained fairly regularly, watered 3.0% 2.5% 0% 1.8% A dirt roadway, rutted or flexing under load; little maintenance, no water, 25 mm (1”) tire penetration or flexing 4.0% 4.0% 0% 2.4% A dirt roadway; rutted or flexing under load; little maintenance, no water, 50 mm (2”) tire penetration or flexing 5.0% 5.0% 0% 3.0% Rutted dirt roadway, soft under travel, no maintenance, no stabilization 100 mm (4”) tire penetration or flexing 8.0% 8.0% 0% 4.8% Loose sand or gravel 10.0% 10:0% 2% 7.0% Rutted dirt roadway, soft under travel, no maintenance, no stabilization, 200 mm (8”) tire penetration and flexing 14.0% 14.0% 5% 10:0% Very soft, muddy, rutted roadway, 300 mm (12”) tire penetration, no flexing 20.0% 20.0% 8% 15% *Percent of combined machine weight. **Assumes drag load has been subtracted. to give Drawbar Pull for good to moderate conditions. Some resistance added for soft conditions. (CAT)

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Grade Resistance

• Force required to overcome gravity when moving vehicle uphill. Expressed in % vehicle weight (adds power to vehicle downhill).

• Percent Grade = Vertical rise or drop (ft) x 100Horizontal Distance (ft)

e.g., 60 ft rise in 1,000 ft, Grade = 60/ 1,000 x 100 = 6%Horizontal Distance =

(Horizontal distance2 + vertical distance2)1/2

e.g., (1,0002 +602)1/2 = 1,001.8 ft

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Weights and Traction

• Weights: determines the force required to propel vehicle.• Function of vehicle weight, rated capacity (CY), and

density of material hauled, number of passes of excavator

• Traction: force deliverable can be limited by traction conditions• Usable rimpull is a function of road surface and weight

on the drive wheelsUsable Rimpull =

Coefficient of Traction x Weight on Drive Wheels

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Coefficient of Traction Factors

(CAT)

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(CAT)

Altitude Deration

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Speed Limits

• Speed Limits: limits on curves, in pit, and on main haul roads• Curves based on radius and super elevation• In pit, ramp, and main haul roads, the speed limit

depends on haul road width and conditions

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Acceleration, Deceleration, Operator

• Speeds obtained from performance curves indicate maximum velocity under optimum conditions on a given profile.

• These speeds must be corrected for acceleration, deceleration, and operator performance to yield reasonable haul and return times.• F=Ma Simulation utilized to account for acceleration and

deceleration • Time studies indicate that simulated haul times are less

than actual haul times

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Tires

• Limit capability of machine to perform by limiting load and speed

• Ton-mile-per-hour ratings should not be exceeded and depend on:• Weight (Flex/revolution)• Speed (Flexes/period)• Ambient Temperature• Road Surface Temperature

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Tires

TMPH = Average Tire Load x Average Speed for Shift

Average Tire Load = Empty Tire Load + Loaded Tire Load (tons)2

Average Speed = Round Trip (mi) x Trips/ShiftTotal Hours (hr)

Limits by tire type and limits may also include maximumspeed

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Ton-MPH Data

(CAT)

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Estimating Cycle Time

• Limiting factors are considered in developing an estimate of the cycle time. The cycle time consists of variable or travel time (haul and return time) plus the fixed time (load, dump, and spot times).

• Travel time (haul and return times) is a function of payload, vehicle weight, HP/weight ratio, haul road segment lengths, rolling and grade resistance, speed limits, etc.

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Estimating Cycle Time

• Loading time is a function bucket size, fill factor, excavator cycle time, loose material density, and truck capacity

• Other fixed times depend on loading method and dump configuration• Spot and maneuver in loading area (typically .6-.8 min)• Dumping (typically 1-1.2 min)

• Unit production calculated considering truck payload, truck cycle time, hours per shift, and operating efficiencyS

urfa

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ine

Des

ign

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Unit Production

• Unit Production (Tons/shift)• Truck payload / Truck cycle time x Operating

efficiency x Hours/shift• Units required are a function of total shift tonnage

requirements and unit production and mechanical availability

• Units Required Operating• Tons required/shift / Unit truck production/shift

(Usually rounded up)

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Unit Production

• Units Required Purchased• Units Required Operating (Not rounded) /

Mechanical availability

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Match Factor and System

• Production of the excavator truck system dependent on the number of trucks assigned to the excavator

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Allocations based on at least two approaches:• Number of trucks = Truck cycle time / Load time

(excluding first pass)This calculation approach reduces excavator delays

• Number of trucks = Truck cycle time

Load time (excluding first pass) + Truck exchange time

Match Factor and System

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Match Factor Approach

• Match factor approach reduces truck delays compared to first method. For example:L o a d e r c y c l e t i m e . 5 m i nN o . o f p a s s e s 7E f f e c t i v e l o a d i n g t i m e ( 7 - 1 ) x . 5 3 . 0 0 m i nT r u c k s p o t t i m e ( e x c h a n g e t i m e ) 1 . 3 0 m i nH a u l , d u m p a n d r e t u r n 1 2 . 7 1 m i nT r u c k c y c l e t i m e 1 7 . 0 1 m i n

N o . T r u c k s ( 1 7 . 0 1 / 3 . 0 0 ) 5 . 6 7N o . T r u c k s ( 1 7 . 0 1 / ( 3 . 0 0 + 1 . 3 0 ) ) 3 . 9 6

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System Production

• System production must consider number of trucks, unit production and excavator availability.

• System production• Number of truck/shift x Unit production (Tons/shift)

x Excavator availability

• Complexity of calculations and variability of times leads to use of fleet production simulators such as FPC and TALPAC

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The End

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TRUCK SELECTION AND PRODUCTION CALCULATIONS

Dr. Kadri Dagdelen

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Wheel Loader Production Calculations

• Example:Calculate the output in tons/hr of a 990 Wheel Loader with a 11cy bucket with .55 min. cycle time and 95% bucket fill factor loading material with 3100 lbs. per LCY. Assume 85% mechanical availability and 83.3% job factor.

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Wheel Loader Production Calculations (Cont.)

• Equation to estimate the production per hour:

O = BC*BF*D*MA*JF*3,600sec(1+SF)*CT hour

Where,O =Production, tons/hrBC =Bucket Size, CY (Usually heaped at 2:1)BF =Bucket Fill Factor, %D =In Place Density, tons/CYMA=Mechanical Availability, %JF =Job Factor, %SF =Material Swell, %100CT =Average cycle time, seconds

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Wheel Loader Production Calculations (Cont.)

• Solution:

O = 11*0.95*1.55*0.85*0.833*3,600sec33sec

= 1252 tons/hr

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Loader-Truck Production Calculations

• Example:CAT775 truck (65ton) is loaded with a 11.0CY 990 loader with 0.55min cycle time with 95% fill factor.For truck cycle time, use the following table. Determine the number of trucks needed for the loader and the total production per hour.

0.6minSpot

1.8minReturn

1.0minDump

3.8minHaul

Truck cycle time

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Loader-Truck Production Calculations (Cont.)

Tons / cycle = 11CY/cycle * 0.95*3100lb/cy / 2000lb= 16.2T/cycle

# of cycles/truck = 65T / truck / 1 cycle/16.2T= 4 cycles

Loading time = (4-1) cycles * 0.55min / cycle = 1.65 min

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Cycle time

1.7minLoad

0.6minSpot

1.8minReturn

1.0minDump

3.8minHaul

Total Cycle time 8.9min

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• Number of Trucks/ Loader

No. of Trucks = Truck cycle time / Load time= 8.9 min / 1.65 min= 5.4 trucks(Assume 6 trucks)

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• Total ProductionAssume – 50 min / hour, and 85% availability

65T/cycle*1cycle/8.9min*50min/hr*0.85/unit = 312T/hr

Total Production = No. of trucks * tons/hr – unit= 5.4 trucks * 312T/hr per truck= 1685 tons/ hr

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Loader-Truck Production Calculations

• Example:

A quarry works with CAT769D flat floor trucks (Max payload 41T, Engine+-450hp) that is loaded by 8cy loader.

The material density is 2800lb/LCY and the quarry is located at the sea level, sending material at 260tons/ hour to the crusher.Calculate truck loading time, productivity, and number or trucks required.

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• Example (Cont.):Loader data:

Capacity: 8cyFill factor: 80%Cycle time: 0.5 min/passMechanical availability: 88%

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• Example (Cont.):Truck cycle time data:

Spot time: 0.8 minDump time:1.5min

Truck mechanical availability: 85%

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• Example (Cont.):Road profile:

4

2

4

Rolling resistance (%)

0

8

0

Grade (%)

45

20

45

Speed limit (km/hr)

1523

7622

1221

Length (m)Segment

Road condition: Firm

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Tons / cycle = 8CY/cycle * 0.8*2800lb/cy / 2000lb= 9T/cycle

# of cycles/truck = 41T / truck / 1 cycle / 9T= 4.6 cycles (5 cycles)

Loading time = (5-1) cycles * 0.5min / cycle = 2.0 min

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Haul Speed:Segment1

Total Resistance = 4%Max speed = 42km/h

< Speed limit (45km/hr)

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Conversion of Max Speed to Average Speed

Weights to HP ratio: 75050kg = 165456lb165456lb / 450hp = 368lb/hp

Haul load length: 122m = 401ft

Conversion factor = 0.51

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Haul Speed :Segment2



Conversion factor = 1Avg speed = 16km/hr

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Haul Speed :Segment3



Conversion factor = 0.68Avg speed

= 42km/hr*0.68=28.6km/hr

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Haul Time:Segment1:

0.122km / 21.4km/hr * 60min = 0.34 min

Segment2: 0.762km / 16km/hr * 60min = 2.86 min

Segment3: 0.152km / 28.6km/hr * 60min = 0.32 min

Total Haul Time:0.34+2.86+0.32 = 3.52 min

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Return Speed:Segment1


> Speed limit (45km/hr)So, choose 45km/hr

Avg speed = 45km/hr*0.68=30.6km/hr

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Return Speed :Segment2

Total Resistance = -8%+2% = -6%Max speed = 69km/h> Speed limit (20km/h)

Choose 20km/hr

Avg speed = 20*0.95= 19km/h

69

6%

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Return Speed :Segment3


> Speed limit (45km/hr)So, choose 45km/hr

Avg speed = 45km/hr*0.54=24.3km/hr

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Return Time:Segment1:

0.122km / 30.6km/hr * 60min = 0.24 min

Segment2: 0.762km / 19km/hr * 60min = 2.41 min

Segment3: 0.152km / 24.3km/hr * 60min = 0.38 min

Total Return Time:0.24+2.41+0.38 = 3.02 min

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Haul and Return Time Summary:

0.3824.30.5445734401523

2.41190.952069-62-87622

0.2430.60.6845734401221

time (min)Avg. Speed

(km/hr)ConversionLimit

(km/hr)Speed (km/hr)

Total Resistance (%)RR (%)Grade(%)

Length(m)Segment

Return

0.3228.560.6845424401523

2.86161201610287622

0.3421.420.5145424401221

time (min)Avg. Speed

(km/hr)ConversionLimit

(km/hr)Speed (km/hr)

Total Resistance (%)RR (%)Grade(%)

Length(m)Segment

Haul

Total time = 3.52min(haul)+3.02(return)=6.54 min

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Truck cycle time (min)

0.8minSpot

3.0minReturn

1.5minDump

3.5minHaul

2.0 minLoad

Total 10.8min

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• Slip condition check (Segment2):

Available Rimpull=(Grade resistance + Rolling resistance)

* Gross Vehicle Weight = (8% + 2%) * (34050kg + 41000kg)= 10%*75050kg= 7505kg

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Usable Rimpull: Function of road surface and weight on the drive wheels

Usable Rimpull = Coefficient of Traction * Weight on Wheel

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Typical Coefficient of Traction

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Weight of Wheel:

769D: Rear 66.7%, Front 33.3% Distribution (by CAT Performance Book)

Weight on Rear Tire is 75050kg * 0.667 = 50058kg

Then, Usable Rimpull is 0.6*50058kg*Cos(8%) = 29939kg

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• CONDITION CHECK

Usable Rimpull > Available Rimpull

There is no slip condition.

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• Unit Production

Assuming 50min / hour

Productivity:41T/cycle*1cycle/10.8min*50min/hr*0.85 = 161T/hr

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• Number of Trucks/ Loader

For maximum productivity: 10.8min / 2.0min = 5.4 (6trucks)

To achieve 260T/hr: 260 / 161 = 1.61 (2 trucks)

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Fleet Size Determination Using Binomial Distribution

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Example

Consider the following fleet:

One loader, 80% mechanical availability and an estimated productivity of 9,000 tons per operating shift.

Three haul trucks, 70 percent mechanical availability and an estimated productivity 0f 4,000 tons per operating shift.

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Example

Assume that the fleet is scheduled 100% of the time and will only be inoperative if either the loader or all the trucks are down for repairs.

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Wrong Assumption

One could incorrectly assume that the average loader production would be 80% of 9,000 tons per shift, or 7,200 tons per shift.

However, since the loader production is dependent on available haul trucks, the truck downtime distribution must be considered.

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Binomial Distribution

xnx ppxnx

n −−⋅−

)1()!(!

!

This formula gives the fraction of time x units are available out of a fleet of n units with a given availability of p.

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Binomial Distribution for Trucks

42.0)7.01(7.0)!12(!1

!2 121 =−⋅−

−

Availability = 70%

0 1 2 3 4 5 6

1 0.30 0.70

2 0.09 0.42 0.49

3 0.03 0.19 0.44 0.34

4 0.01 0.08 0.26 0.41 0.24

5 0.00 0.03 0.13 0.31 0.36 0.17

6 0.00 0.01 0.06 0.19 0.32 0.30 0.12

Fleet Size (n)

Number of Units Available (x)

Fraction of the time that 1 truck out of a fleet of 2 will be operating

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Fleet Capacity

The fleet capacity can be stated as follows:

The loader operates 80% of the time and during this time, 34% will be at 9,000 tons per shift, 44% will be at 8,000 tons per shift, and 19% will be at only 4,000 tons per shift.

0.80 x 0.34 x 9,000 = 2,448 tons

0.80 x 0.44 x 8,000 = 2,816 tons

0.80 x 0.19 x 4,000 = 608 tons

TOTAL = 5,872 tons

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Fleet Capacity

From this example, it can be seen that production from the loader would be 18% short of the initial estimate of 7,200 tons per shift that was determined without consideration of the haul fleet.

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Haul Truck Requirement Determination

Annual target objective 1,800,000 tons

Shifts scheduled 250 shifts

Tonnage requirements per shift 7,200 tons

Average truck productivity 4,000 tons per shift

Need 1.80 operating trucks per shift

3 trucks at 70% availability will average 2.1 shifts

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It could be incorrectly assumed that 3 trucks would be sufficient.

However, if the loading fleet contains only 1 loader , then 20% of the time the haul fleet would be idle waiting for the loader to be repaired.

It is also known that the loader could not keep up with three trucks and production would be limited to 9,000 tons per shift, not the 12,000 tons indicated by the haulage capacity.

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250 shifts x 0.80 x 0.34 x 9,000 tons = 612,000 tons



TOTAL = 1,468,000 tons per year

The solution in this case would be to purchase another loader or work more shifts.

Estimating Owning and Operating Costs

by

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Hourly owning and operating cost estimate

AnalystDate

1 2Machine Designation Track-type Tractor Wheel LoaderEstimated Ownership Period (Years) 7 5Estimated Usage (Hours/Year) 1200 1500Ownership Usage (Total Hours) 8400 7500

1. a. Delivered Price (including attachments) 135,000 1,200,000 b. Less Tire Replacement Cost if Desired 4,000 c. Delivered Price Less Tires 135,000 1,196,000

2. a. Residual Value - % of original deliverd price 35% 48%b. Less Residual Value at replacement 47,250 574,080

3. a. Value to be recovered through work 87,750 621,920 b. Cost per hour 10.45 82.92

4. a. Interest rate 16% 16%b. Interest costs 10.29 76.54

5. a. Insurance rate 1% 1%b. Insurance Costs 0.64 4.78

6. a. Tax rate 1% 1%b. Property tax 0.64 4.78

7. Total hourly owning cost 22.02 169.03

Antonio Peralta11/7/2005

Owning Costs

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Hourly owning and operating cost estimate

8. a. Fuel unit price 2.20 2.20 b. Fuel consumption 5 4 c. Fuel cost 11.00 8.80

9. Lube oils, filters, grease 0.46 0.43 10. a. Life of tires (Hours) 3,500

b. Tires replacement cost 1.14 c. Impact factor 0.20 d. Abrasiveness factor 0.20 e. Z factor 0.30 f. Basic factor 6.20 g. Under carriage 4.34

11. a. Extended use multiplier for repair reserve 1.00 1.00 b. Basic repair factor for repair service 4.50 4.00 c. Repair reserve 4.50 4.00

12. a. Special wear items 1.32 0.60

13. Total hourly operating cost 21.62 14.97

14. Maching Owning plus operating 43.64 184.01

15. Operator's hourly wage (include fringes) 30.00 30.00

16. TOTAL OWNING AND OPERATING COST 73.64 214.01

Operating Costs

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9A. Lube Oils, Filters, Grease

Unit Price Consumption Cost/Hour Unit Price Consumption Cost/HourEngineTransmissionFinal DrivesHydraulicsGreaseFilters

Total 0 Total 0

Track-type tractor Wheel Loader

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12A. Special Wear Items

# Cost Life $/Hour Cost Life $/Hour1 105 150 0.70 50 165 0.302 165 450 0.37 80 450 0.183 125 500 0.25 70 600 0.12456

Total 1.32 Total 0.60

Track-type tractor Wheel Loader

Drilling

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Drilling Methods

• Top hammer drilling

Hydraulic self-contained drills

Pneumatic drills with portable air compressors

• Down-the-hole (DTH) drilling

Pneumatically operated carriers with portable air compressors

Hydraulically operated self-contained carriers

• Rotary drilling

Drills for rotary crushing

Drills for rotary cutting

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Surface Drilling Methods and Applications

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Components of Surface Drilling Methods

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Top Hammer Drilling

• Soft to hard rock

• Diameter from 7/8” to 10”

• Top hammer drills can be classified according to their size and principle of operation:

Hydraulic or pneumatic handheld drills

Light hydraulic drills mounted on feeds for mechanized drilling in different types of boom applications

Pneumatic crawler drills operated by a separate portable air compressor

Hydraulic crawler or wheel-based drills operated by a powerpack onboard

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Principle of Top Hammer Drilling

• It can be hydraulic or pneumatic

• It combines four functions

Percussion

Feed

Rotation

Flushing

• Parameters that affect the penetration rate:

Impact energy, impact frequency, rotation speed, feed force, andflushing of the hole

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Relative Penetration Rate as a Function of Percussion Pressure

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The Optimal Adjustment of Drilling Parameters Means Maximum Penetration

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Flushing

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Flushing

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Penetration Rates Between Pneumatic and Hydraulic Top Hammer Drilling

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Bench Drilling Rig

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Bench Drilling Rig

A modern surface crawler drill should fulfill the following requirements, to make the operation economical:

• High penetration rate

• Short cycle times

• High quality holes

• High availability

• Low operating cost

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Choice of Bit Type

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Application Range of Tube Drill Steels

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DTH Drilling

• It is more efficient than top hammer drilling

• A DTH hammer follows immediately behind the bit

• Good drilling accuracy

• DTH drills are used in bench drilling of 3½” to 6½” holes on benches up to 150 feet

• DTH hammer life is dependent on:

Hammer size, operating pressure, rock abrasiveness, and rock drillability

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Principle of DTH Drilling

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A Typical DTH Hammer

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Features of DTH Hammer

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Truck Mounted DTH Drill

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DTH Bit Designs

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Rotary Drilling

• It is used in most major open pit mining operations

• Diameter from 4” to 17½”, depth up to 150 feet

• The key elements in rotary drilling are:

Sufficient torque to turn the bit in any strata encountered

Sufficiently high bit loading capability (pulldown force) for optimum penetration

Sufficient flushing air volume to remove the cuttings during penetration, as well as to provide cool air to the drill bit bearings

Selection of the proper type of bit for the material being drilled

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Principle Rotary Drilling

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Rotary Drills

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Rotary Drills

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Principles of Rotation

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Rotary Power versus Hole Diameter

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Pull Down versus Hole Diameter

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Principles of Feed Systems

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Thrust and Pulldown Force

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Flushing Air Compressor Size

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Carrousel Type Pipe Changer

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Rotary Drilling Accessories

• Drill bits

• Drill pipes

• Shock subs

• Stabilizers

• Saver subs

• Bit subs

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Rotary Drill Bit Components

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Rotary Bit Selection Parameters

Type of ground Tooth or insert spacing Tooth depth Cutting actionSoft formations with low compressive strengths and high drillability: shales, unconsolitaded sands, calcites

HighLarge: Inserts extended chisel shaped

Mostly gouging and scraping by skew cone action, with little chipping and crushing

Medium Formations: harder shales, limestone, sandstones, dolomites

Medium, closeMedium: Inserts short or blunt chisel shaped

Partly by gouging and scraping but with significant chipping and crushing action especially at harder end of type

Hard formations: siliceous limestones, hard sandstones, porphyry copper ores

Close with low intermeshLow: Inserts spherical or conical

Mostly by chipping and crushing by cutter rolling action

Very hard formations: taconites, quartzites

Very close with low intermesh

Very low: Insert hemispherical conical or ovoid

Nearly all excavation by true rolling action of cutters

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Bit Selection for Rotary Drilling

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Insert Shapes for Tricone Bits

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Penetration Rate versus Bit Load

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Principles of Rotary Cutting

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Penetration Rate

300)log2861( 10

rpmWScP ⋅⋅−=

φ

Where:

P = penetration rate (ft/hr)

Sc = uniaxial compressive strength, in thousands of psi

W/F = Weight per inch of bit diameter, in thousands of pounds

rpm = revolutions of drill pipe per minute

Bauer and Calder, 1967 (Surface Mining Handbook)

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Horse Power

5.15.2 WDrpmKhp ⋅⋅⋅=Where:

D = bit diameter (in.)

W = weight on the bit in thousands of pounds

K = constant that varies with rock type.

As material strength decreases, the value of K increases. This caters for the greater teeth penetration experienced in soft rocks. Values vary from 14 x 10-5 for soft rocks down to 4 x 10-5 for high-strength materials.

Surface Mining Handbook

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Balancing Air Velocity

2/12/1264 dpUm ⋅=Where:

Um =

2420 fpm for 13 mm (1/2 in.) diameter platelets with a density of 2.7 g/cc

d = diameter of the chip in inches

p = density of the chip in lb/ft3

Surface Mining Handbook

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Bailing Velocities

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Bailing Velocities

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Air Requirements Chart

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Optimal Bit Load

5DC

LoadOptimumBit×

=

Where:

C = Rock compressive strength

D = bit diameter in inches

Source: R. Baker, Tamrock

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Total Work

TNRWWTWorkTotal ××××= π2)(

Where:

W = bit load (lbs)

R = penetration rate (feet/min)

N = bit rotation speed

T = torque (foot lbs)


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Rotary Horsepower

CWRD

hpPowerHorse6.1)1000/(95.4

)(×××=

Where:

hp = rotary horsepower

R = bit rotational speed

D = bit diameter (inches)

W = optimum bit load (lbs)

C = rock compressive strength


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Maximum Bit RPM

6.1)1000/(95.4)(

WDChp

RRPMBitMaximum××

×=

Where:

hp = rotary horsepower

R = bit rotational speed



C = rock compressive strength


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Volume CFM

×+×

×=

14425.0

14425.0 22 D

PSFD

PCFMVolumeππ

Where:

P = penetration rate


SF = swell factor (0.6 sedimentary or 0.4 Igneous/metamorphic)


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Air Velocity

22

183dD

CFMVelocityAir

−×

=

Where:

d = pipe diameter (inches)


CFM = effective compressor volume (CFM)


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Compressive Strength

9.0)10000/1(2.018.2

)(DP

RWCStrengtheCompressiv

×××××

=

Where:

P = average pure penetration rate (feet/hour)

W = average bit load (lbs)

R = average bit rotation



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Pure Penetration

)10000/(2.018.2

)(9.0 CDC

RWPnPenetratioPure

×××××

=

Where:

P = average pure penetration rate (feet/hour)


R = optimum bit rotation speed


C = average compressive strength


Explosives

Definitions

Explosive -A chemical mixture that releases gasses and heat at high velocity, causing very high pressures.

Explosion –Thermochemical process in which mixtures of gasses, solids, or liquids react with almost instantaneous formation of gaseous pressures and heat release.

Detonation – Supersonic explosive reaction which creates a high pressure shock wave, heat, and gasses.

Theory of Blasting

The rock is affected by a detonating explosive in three principal stages.

In the first stage, starting from the initiation point, the blastholeexpands by crushing the blasthole walls. This is due to the high pressure upon detonation.

In the second stage, compressive stress waves emanate in all directions from the blasthole with a velocity equal to the sonic wave velocity in the rock. When these compressive stress waves reflect against a free rock face, they cause tensile stresses in the rock mass between the blasthole and the free face. If the tensile strength of the rock is exceeded, the rock breaks in the burden area, which is the case in a correctly designed blast.

Mechanics of Detonation

Compressive Shock Waves

Tensile Shock Waves

Mechanics of Detonation

In the third stage, the released gas volume "enters" the crackformation under high pressure, expanding the cracks.

If the distance between theblasthole and the free face iscorrectly calculated, the rockmass between the blastholeand the free face will yield andbe thrown forward.

Bench Blast

(Atlas Copco)

History of Explosives Development

1000 -Black Powder•Discovered in China around 1000 A.D.

•Mixture of potassium nitrate (saltpeter), sulfur and charcoal.

•The combustion of charcoal (C) and sulfur (S) is the fuel, and oxygen is contained within the nitrate ion (NO3).

•Marco Polo brought it to Europe where it was originally used for military purposes.

•The first blasting application was in Hungary in 1627 and by the end of the 17th century most of the European miners used black powder to loosen rock.

•The first black powder mills were established in America around the year 1775.


1831-Safety Fuse•William Bickford, an Englishman, patented the “Miners Safety Fuse”, in 1831.

•Safety fuse gave blasters a safe and reliable means of initiating black powder.

1846 -Nitroglycerin•In 1846, Ascanio Sobrero, an Italian, discovered nitroglycerin (C3H5N3O9), but he considered it too unpredictable and hazardous for anyone to use.


1867 -Blasting Caps

•The main problem with nitroglycerin was to get it to shoot consistently.

•Alfred Nobel, a Swede, solved this problem with the invention of the fulminate of mercury blasting cap in 1867.

•Use together with safety fuse, the blasting cap provided an excellent initiating system for nitroglycerin.


1866 –Dynamite

•In his efforts to make nitroglycerin safer to handle, Alfred Nobel in 1866 discovered that Kieselguhr (a diatomaceous earth) not only absorbed three times its own weight of nitroglycerin, but also rendered it less sensitive to shock.

•After kneading and shaping it into a cartridge, it was wrapped in paper and the Dynamite was invented.


1894-PETN•The explosive PETN (C5H8N4O12) was discovered in 1894.

•It was not widely used until the 1940’s and today it is the primary explosive compound in modern initiators and boosters.

1922-Electric Blasting Caps•In the beginning of the 20th century the electric initiation wasintroduced, and by 1922 the first electric delay detonator (with1 sec. delay) came into practical use.

•The introduction of the short delay detonator 10-100 milliseconds) in the late 1940's has had the greatest importancein the development of modern blasting techniques.


1956 –ANFO

•In 1956, ANFO (Ammonium Nitrate and Fuel Oil) was introduced to the U.S. market.

•The success of the ANFO in U.S.A. is indisputable, from a consumption rate of almost nil in 1956, the consumption had increased to over 1,000,000 tons by 1975, the consumption of dynamites has, during the same time, declined from 340,000 tons to 135,000 tons.

History of Explosives Development1960’s -Water gels and slurries

•In the 1960's, we have seen the development of water gels, also called slurries.

•A slurry explosive is a high density aqueous explosive containing ammonium nitrate which is an oxidizer.

•Water gels contain 10 to 30 percent water and are sensitized by carbonaceous fuels, TNT, aluminum, or certain organiccompounds like methylamin nitrate.

•Both cap sensitive and non-cap sensitive water gel explosives are available


1970’s-Nonel•In the late 1970's we saw new non-electrical initiating systems like Nonel being developed.

1970’s -Emulsions•1970's the development of emulsion explosives.

•Emulsion explosives are composed of separate, very small drops of ammonium nitrate solution and other oxidizers, densely dispersed in a continuous phase, which is composed of oil and wax.

•The oil/wax mixture, which is the fuel, is in this way given a very large contact surface to the oxidizer, the ammonium nitratesolution .

Properties of Explosives

In the ideal conditions of dry blastholes a simple explosive can be used, while under wet conditions, more sophisticated products are called for .

The most important characteristics of an explosive are:•velocity of detonation (VOD)•strength•detonation stability•sensitiveness (propagation ability)•density•water resistance•sensitivity•safety in handling•resistance to freezing•oxygen balance•shelf life

Classification of Explosives

The explosives used in civil engineering and mining can nowadaysbe classified as:

•High explosives•Blasting agents

High explosives are characterized by high velocity of detonation (VOD), high pressure shock wave, high density and by being cap sensitive.

Blasting agents are mixtures consisting of a fuel and oxidizer system, where none of the ingredients are classified as an explosive and when unconfined cannot be detonated by means of a #8 test blasting cap (1.0 grams of high explosives). Blasting agents have to be initiated by a primer. ANFO is a typical blasting agent.

Firing Devices

Firing methods can be divided into two main groups:

Non-electric•Safety Fuse and Blasting Cap•Detonating Cord•Nonel system

Electric•Electronic Blasting Caps

Safety Fuse and Blasting Cap

The safety fuse consists of a black powder core that is tightly wrapped with coverings of textile and waterproofing materials.

Safety fuse has a steady well controlled burning speed, usually around 40 seconds per foot.

Safety Fuse and Blasting Cap

To initiate the explosive, a plain detonator has to be attached to the safety fuse.

Detonators of different strengths expressed as a number are available, currently #6 or #8 caps.

The #8 detonator contains approximately 1.0 grams of high explosives, and the #6 about 0.8 grams.

Detonating Cord

Detonating cord consists of a PETN core which is wrapped in coverings of textiles and waterproofing materials.

Detonating cord may be initiated with a #6 detonator and detonates along its entire length at about 7000 meters/second.

It initiates most explosives.

Does not work well with ANFO in small to medium sized blastholes, (incomplete detonation).

Firing pattern for detonating cord blast.

Electric Blasting Caps

Electric detonators can be divided into three different classes according to their timing properties:

•instantaneous•millisecond delays•half second delays

The millisecond delay detonator has a built-in millisecond delay element. Delays are usually available in 25 ms delay intervals.


Electric detonators may be connected in series or parallel depending on the number of detonators in the round, and the current available in the blasting machine.

Parallel series circuit.


The testing instruments for blasting circuits have to be specially designed for their purpose and be approved by the authorities concerned.

An Ohm-meter is used to control the resistance of single electric detonators, detonators in series and in parallel-series and for the final check before firing.

Electric Blasting CapsThe series are connected in parallel and subsequently measured.

The resistance of the parallel connection is in accordance with Kirckhoffs law:

As the difference in resistance between the series must not exceed ± 5 percent, the resistance of the parallel connection will be:

series ofNumber /seriesResistance

R =

Rn1

...R1

R1

R1

21

+++=

ExampleAssume a blast of 250 V A-detonators with a resistance of 3.6 Ohms each. (The resistance is always 3.6 Ohms independent of legwire length.) The firing cable has a resistance of 5 Ohms and a CID 330 V A blasting machine is used.

In accordance with the instructions on the blasting machine, the round may be connected in 5 parallel series.

Number of detonators in each series: 50.

Resistance per series: 50x3.6=180 Ohms.

Resistance after parallel connection :

Resistance at the firing point is the resistance of the parallel-series connection plus the resistance of the firing cable.36 + 5 = 41 Ohms.

Ohms 365

180series ofNumber

/seriesResistanceR ===

Possible errors during measuring:Resistance too high:

* Larger number of detonators than calculated.* Sub-division into series wrongly carried out.* Poor contact ill some connection or detonator .

Resistance too low:* All detonators are not connected into the circuit.* Sub-division into series wrongly carried out.* Some part of the round not connected into the circuit.

Infinite resistance:* Interruption in series through incomplete connection.* Faulty detonator (usually torn off legwire).


Blasting machines of various types are used to fire the rounds.

Shown is the model CI 50 which is designed for firing a maximum of 50 conventional detonators.

Nonel systemThe NONEL detonator functions as an electric delay detonator, but the legwires and the fuse head have been replaced by a plastic tube through which a shock wave is transmitted.

The endsplit of of the shockwave from the plastic tube initiates the delay element in the detonator.

The 3mm diameter plastic tube is coated on the inside with a thin layer of reactive material which transmits the shockwave with a velocity of about 2000 meters per second.

Non-Electric vs. Electric

Tubing Air Space

Shell

Non Electric Cap

Electric Cap

CrimpsPlug

IgnitionCharge Fuse

Powder

FuseElement

PrimingCharge

BaseCharge

ClosureBridgeWire

Nonel systemA connector with a strength of 1/3 a #8 cap is used to connect and initiate the detonators.

Nonel system

NONEL connected for bench blasting.

Nonel system

NONEL detonators may also be connected to a detonating cord using a specially designed clip if noise is not a problem.

Nonel system

A NONEL round may be fired using a plain detonator and safety fuse, or by using a specially designed NONEL system blasting machine.

Bench BlastingBench blasting is the most common kind of blasting work.

It can be defined as blasting of vertical or nearly vertical blastholes in one or more rows towards a free surface.

The blastholes can have free breakage of fixed bottom.

Free breakageFixed bottom

Bench Blasting

The tensile, compressive and shearing strengths of a rock mass vary with different kinds of rock and may vary within the same blast.

As the rock's tensile strength has to be exceeded in order to break therock, its geological properties will affect its blastability.

Faults and dirt-seams may change the effect of the explosive in the blast.

Faulty rock containing voids, where the gases penetrate without giving full effect, may be difficult to blast even though the rock may have a relatively low tensile strength.

Bench BlastingThe requisite specific charge, (kg/m3 ) provides a first-rate measure of the blastability of the rock.

By using the specific charge as a basis for the calculation, it is possible to calculate the charge which is suitable for the rock concerned.

The distribution of the explosives in the rock is of the utmost importance. A closely spaced round with small diameter blastholes gives much better fragmentation of the rock than a round of widely spaced large diameter blastholes, provided that the same specific charge is used.

Burden -the distance between the drill hole and the nearest parallel free face.

Spacing - the distance between holes along rows that are parallel to the face.

Stemming -non-explosive material that is placed in the bore hole to confine the explosives (usually placed near the collar of the hole).

Sub-drilling is the amount of hole that is drilled below the intended new bench level.

Basic Definitions

Blasting Theory

When hole depth equals the bench height masses of rock are oftenleft at the toe of the bench because of lack of reflected tension energy from the free face. The solution for this is either sub-drilling or inclined holes.

Partial Reflected

WaveUn-reflectedCompression

Wave

Leaves Un-fractured Toe

Bef

ore

Bla

stin

g

Aft

er B

last

ing

Blasting Theory

Inclined holes cause total reflective tensile waves at the toe of the bench. This causes a flat lower bench and is a more efficient use of explosives.

Total ReflectedTensile Waves

Vertical Holes vs. Inclined Holes

Vertical Holes• Easier to drill• Avoids difficulties in

fractured rock

Inclined Holes• Commonly drilled between 10 &

15 degrees• Causes more productive

reflected shock wave in toe of bench

Bench Height Factors

Research indicates that bore hole length should

be approximately 3 times the burden

distance.-Ash & Smith, Society of

Explosives Engineers, 1976

Bench Height is a function of both hole diameter and burden distance.

Zone of optimal fragmentation

Burden Spacing Equations

Burden Spacing EquationsAndersonB = K(d*L)**2

Pearse B = K*d*(P/T)**2

AshB = K*d/12

Fraenkel (meters & mm)((R*L)**0.3)*(l**0.3)*(d**0.8)

B =50 B burden distance (inches)

d hole diameter (inches)L hole length (feet)T ultimate tensile strength of rock (pounds per square inch)P stability pressure of explosive (pounds per square inch)K constants (empirically determined)

Rock characteristics are difficulty to mathematically model since rock is never really homogeneous.

Burden Spacing Equations

S/B*f*cs*p

33d

Bmax =

Langefors/Kihlström

Bmax = maximum burden (m)d = diameter in the bottom of the blasthole (mm)p = packing degree (loading density) (kg/liter or g/c3 )s = weight strength of the explosive (ANFO = 1)c = rock constant, 0.3 to 0.5c = c + 0.05 for Bmax between 1.4 and 15.0 metersf = degree of fixation, 1.0 for vertical holes

and 0:95 for holes with inclination 3:1S/B = ratio of spacing to burden

Terminology

Charge Calculations

The maximum burden in the bottom of the blasthole depends on:

•weight strength of the actual explosive (s)•charge concentration (lb)•rock constant (c)•constriction of the blasthole (R1)

Table 1a.

Kadri DagdelenFuat Bilgin

Mining Engineering DepartmentColorado Shool of MInes

RECENT DEVELOPMENTS IN VEHICLE PROXIMITY WARNING AND COLLISION AVOIDANCE SYSTEMS

USING GPS AND WIRELESS NETWORKS

10/29/2006

COLORADO SCHOOL OF MINES

2

OUTLINE

INTRODUCTION

PREVIOS WORK

CURRENT WORK

FUTURE WORK

CONCLUSIONS

MAIN

10/29/2006


3

INTRODUCTION Surface Mining Safety Research Program

• Safety Issues• Truck Proximity Warning• Collision Avoidance

• Global Positioning System (GPS)• Wireless Network Technology

10/29/2006


4

EE--Mail Requesting Help Mail Requesting Help

Jim:Jim:

You may or may not be aware that at couple of You may or may not be aware that at couple of weeks ago El Abra suffered a fatal accident weeks ago El Abra suffered a fatal accident when a truck driver backed through the berm. when a truck driver backed through the berm. Shortly after that happened, I was asked by Shortly after that happened, I was asked by Dennis Barlett and Hunter White to lead a team Dennis Barlett and Hunter White to lead a team of representatives from North American of representatives from North American operations to make sure that this was the last operations to make sure that this was the last accident of this type that we had to suffer. ….accident of this type that we had to suffer. ….

…………..…………..

Thanks,Thanks,

FerolFerol

The Problem We Face

10/29/2006


5

CONCEPTUALIZED SYSTEM

• Software for dump edge recognition

• Trimble GPS

• Trimble 900 MHz radios

• Introduction to 802.11b

10/29/2006


6

Field Tests at the Morenci Field Tests at the Morenci Copper Mine Copper Mine -- ArizonaArizona

MORENCI TEST PREVIOUS WORK

10/29/2006


7

CURRENT WORK

• LAFARGE QUARRY IMPLEMENTATIONOptiTrack

• Real Time

• Design of the System

• Hardware Development

• Software Development

• Robustness of the System

10/29/2006


8

OptiTrack SYSTEM CURRENT WORK

10/29/2006


9

Description of the System (Infrastructure)

GPS Differential Correction Service

Data, DTM

GPS data

GPS Differential

GPS

Control Base

OptiTrack Network at Lafarge Quarry

Wireless CommunicationTransmitting Truck Position

Wireless Communication Between Lafarge Quarry and CSM

DTM

10/29/2006


10

OptiTrack (Lafarge) CURRENT WORK

• Mobile Clients• Haul Trucks• Manager Trucks• PDAs

• Central Points• Repeaters• Trailer

10/29/2006


11

OptiTrack Mobile Clients CURRENT WORK

10/29/2006


12

OptiTrack Haul Trucks CURRENT WORK

DC Injector N-Female N-Female

Amplifier 1wt WAF2400-1000

N-Female N -Female

Barrel Adapter N-Male N -Male

Lighting Arrestor WRLA-1.2/1.8 N-Female N -Female

Jumper Cable

N-Male RPTNC-Female

LMR600

N-Male N-Male

Omni Antenna

RS 232

GPS SatellitesGPS Device & Antenna

Wireless PCMCI Card Cisco LMC 352

10/29/2006


13

OptiTrack Central Points CURRENT WORK

• Repeater at Mechanic House

• Repeater on the Trailer

10/29/2006


14

OptiTrack Repeater CURRENT WORK

10/29/2006


15

OptiTrack Trailer CURRENT WORK

10/29/2006


16

OptiTrack Trailer CURRENT WORK

10/29/2006


17

Schematic Representation of OptiTrack TrailerCURRENT WORK

Power Supplies Solar Panels

Cisco AP 350


Amplifier 1wt WAF2400-1000

N-Female N-Female

Barrel Adapter N-Male N-Male

Lighting Arrestor WRLA-1.2/1.8 N-Female N-Female

Jumper Cable

N-Male RPTNC-Female

LMR600

N-Male N-Male

Coax Cable

LMR600 N-Male N-Male

Coax Cable


Coax Cable LMR600

N-Male N-Male

Directional Antennas WRPA2400 11-AM

V Pol N-Male

Point to Point Antenna WR2400-24M H Pol

N-Female

RPTNC-male

10/29/2006


18

OptiTrack (CSM) CURRENT WORK

OptiTrack at CSM GPS Laboratory

Server

10/29/2006


19

OptiTrack Antenna CURRENT WORK

Point to Point Antenna (Brown Building)

10/29/2006


20

Schematic Representation of OptiTrack (CSM)CURRENT WORK

Cisco AP 350

RPTNC-male

Jumper Cable N-Male RPTNC-Female



Amplifier 1wt WAF2400-1000 N-Female N-Female

Barrel Adapter N-Male N-Male

Lighting Arrestor WRLA-1.2/1.8 N-Female N-Female

RF Coax Cable N-Male N-Male

Antenna on the roof of Brown Building

10/29/2006


21

OptiTrack Software CURRENT WORK

10/29/2006


22

Future Work

• New Mobile Clients• PDAs• Sensors

• Radar Implementation

• Mobile Adhoc Network(MANET)

10/29/2006


23

Description of the System (Ad Hoc)

GPS Differential Correction Service

Data, DTM

GPS data

GPS Differential

GPS

Control Base

OptiTrack Network at Lafarge Quarry

Wireless CommunicationTransmitting Truck Position

Wireless Communication Between Lafarge Quarry and CSM

DTM

10/29/2006


24

Broadcast Protocols Future Work

Existing Protocols• Flooding• Adaptive-SBA• AHBP-EX

OptiTrack Protocols• Naive Bayes• Adaptive Boosting (AdaBoost)

10/29/2006


25

Existing Protocols Future Work

10/29/2006


26

Machine Learning Approach Future Work

Classification

Rebroadcast

Discard

Incoming Packet

10/29/2006


27

OptiTrack Protocols Future Work

10/29/2006


28

Simulation Comparison Future Work

95 %Confidence Interval

10Number of Trials

100 secondsSimulation Time

50Node Max. IFQ Length

64 bytes payloadData Packet Size

100 meterNode Tx Distance

350 x 350 meterNetwork Area

NS-2 (1b7a)Simulator

ValueSimulation Parameter

8060402010Pkt. Src. Rate (pkts/sec)

20151051Average Speed (m/sec)

9070605040Number of Nodes

54321Trial

10/29/2006


29

Delivery Ratio of the Protocols

Delivery Ratio

60

65

70

75

80

85

90

95

100

1 2 3 4 5

Trial

Deliver

y R

atio

Adaptive SBA

AHBP-EX

Flooding

AdaBoost

Naive Bayes

Future Work

10/29/2006


30

Number of Retransmitting Nodes

Number of Retransmitting Nodes

0

10

20

30

40

50

60

1 2 3 4 5

Trial

Num

ber

of R

etra

nsm

ittin

g N

odes

Adaptive SBA

AHBP-EX

Flooding

AdaBoost

Naive Bayes

Future Work

10/29/2006


31

End-to-End Delay Future Work

End-to-End Delay

0

0,5

1

1,5

2

2,5

3

1 2 3 4 5

Trial

End-to

-End D

elay Adaptive SBA

AHBP-EX

Flooding

AdaBoost

Naive Bayes

10/29/2006


32

ADHOC & INFRASTRUCTURE Future Work

ADHOC

Infrastructure

10/29/2006


33

1.1. The tests that are being carried out at CSM as well The tests that are being carried out at CSM as well as in Lafarge Quarry indicate that as in Lafarge Quarry indicate that ““OptiTrackOptiTrack”” softsoftware system can be used as a proximity warning dware system can be used as a proximity warning device to avoid collisions between off highway truckevice to avoid collisions between off highway trucks and the other vehicles as well as to monitor truck s and the other vehicles as well as to monitor truck positions with respect to dump edge on a 3positions with respect to dump edge on a 3--D topoD topography map.graphy map.

2.2. Integration of the developed GPS based system witIntegration of the developed GPS based system with other systems based on concepts such as RFID, rh other systems based on concepts such as RFID, radar, and video cameras need to be pursued to havadar, and video cameras need to be pursued to have a complete and reliable collision avoidance systee a complete and reliable collision avoidance system.m.

Conclusions

Surface Mine Design Surface Mine Design –– MNGN312/512MNGN312/512

Sustainability Issues in Mining

Antonio Peralta

by

Source: Rozgonyi and Ramirez, January 2003


What is Sustainable Development?Sustainable development is:

• A concept of needs;

• Idea of limitations;

• Future oriented paradigm, and;

• A process of change.

This concept reflects a compromise between the world’s tripartite aspirations:

• ECONOMICAL: Promoting economic betterment but preserving of options for future generations.

• ECOLOGICAL: Protecting, maintaining and restoring of environmental quality.

• SOCIAL: Promoting and improving social and community stability and values.

SUSTAINABLEDEVELOPMENT

ECONOMICAL

ECOLOGICALSOCIAL

SUSTAINABLEDEVELOPMENT

ECONOMICAL

ECOLOGICALSOCIAL


Sustainable Development in Mining

§ Applying the concepts of sustainable development and sustainable natural resource management to energy and mineral resources is not an oxymoron.

§ Energy and mineral resources are mostly not renewable; sustaining any given deposit or mine is not possible. However, SD involves designing, developing and managing resources in a way that is conducive to long-term wealth creation. Minerals are a form of natural capital and thus of endowed wealth.

§ Therefore, mining projects can serve sustainability objectives if they are designed and implemented in ways that build viable long-term capacities, strengthen communities and rehabilitate damaged ecosystems.


Global Mining and Mineral Industry Trends

• International mergers, and globalization,

• Shifts in supply availability and recycling,

• Consumer demand (responsibility for the whole life cycle of the minerals, metals),

• Political restructuring,

• Economic transformations,

• Social and cultural developments,

• Public attitudes about mining and minerals,

• The new paradigm of “sustainable development”,

• An era of increasing regulations affecting all phases of activity from exploration and extraction to processing and products.


Principal Mining and Environmental Actions During Each Phase of Mine Development

Environmental assessment

Rehabilitation planExploration permit application

Exploration road construction

Rock core drillingGeochemical analysisGeostatistical analysisOrebody evaluation

Exploration

Comprehensive EIA and reviewMitigation planningReclamation and closure planningConceptual design for closureReclamation and closure costing

Closure fund design

Plan of operationsTechnology selection

Conceptual to final designsCosting and cost benefit analysisInvestment brokerage

Feasibility study

Environmental baseline studyEnvironmental assessment“Fatal Flaw” analysis

Initiation of permitting process

Initial mine and minerals process planningFacilities sitingSchedulingEconometric analysisInitial technology selection

Pre-feasibility study

PRINCIPAL ENVIRONMENTAL MANAGEMENT ACTION

PRINCIPAL MINE PLANNING ACTIONPHASE IN MINE PROJECT DEVELOPMENT


Principal Mining and Environmental Actions During Each Phase of Mine Development (cont.)

Implementation of closure planSite cleanupFinal reclamationFinal impact assessmentPost closure planning

Facilities decommissioningDismantlingDecontaminationBurialRemovalAsset recoveryRecycling

Closure

Installation of pollution control facilitiesGeneral environmental management (air,

water, land)Construction phase reclamation and

closure

Access and haul road developmentSite clearing and grubbingEarth moving and surface water managementMine dewateringUtilities installationBuilding and infrastructure construction

Construction

TreatmentMaintenanceMonitoringFinal bond release

Post closure

General environmental managementPerformance assessment/auditMonitoringConcurrent reclamationFinal closure designPartial closurePartial bond release

Ore extractionSize reductionMinerals processingSmelting and refiningMaintenance and upgrade

Production

PRINCIPAL ENVIRONMENTAL MANAGEMENT ACTION

PRINCIPAL MINE PLANNING ACTIONPHASE IN MINE PROJECT DEVELOPMENT


Elements of Environmental Planning

A). INITIAL PROJECT EVALUATION

B). THE STRATEGIC PLAN

C). THE ENVIRONMENTAL PLANNING TEAM


Environmental Planning Procedures (EPP)A). INITIAL PROJECT EVALUATION:

1. Prepare a detailed outline of the proposed action.

2. Identify permit requirements.

3. Identify major environmental concerns.

4. Evaluate the opportunity for and likelihood of public participation in the decision making process.

5. Consider the amount and effect of delay possibly resulting from public participation during each stage of the project.

6. Evaluate the organization and effectiveness of local citizens groups.

7. Determine the attitudes and experiences of governmental agencies.

8. Consider previous industry experience in the area.

9. Consider recent experience of other companies.

10. Identify possible local consultants and evaluate their ability and experience.

11. Consider having a local consultant check the conclusions of the initial evaluation.


Environmental Planning Procedures (EPP) (cont.)

B). THE STRATEGIC PLAN:

1. Outline of technical information needed to obtain permits and to address legitimate environmental, land use and socio-economic concerns. Permitting process is quite long and complex.

2. Categorically assign responsibilities for the acquisition of the technical information and hire necessary consultants.

3. Prepare a schedule for obtaining information and data and for submitting permit applications to the appropriate agencies.

4. Select local legal, technical and public relations consultants.

5. Avoid hostile confrontations with environmental groups.

6. Develop a consistent program for the generation of credible factual information.

7. Perform risk assessment.

8. Perform cost analysis.

9. Prepare mine reclamation plan.


Environmental Planning Procedures (EPP) (cont.)

C). THE ENVIRONMENTAL PLANNING TEAM

The team shall be multidisciplinary:

Ø Mining engineers

Ø Metallurgical engineers

Ø Biologists

Ø Environmentalists

Ø Toxicologists

Ø etc.


Risk Assessment

1. Data collection and hazard evaluation.

2. Toxicity assessment.

3. Exposure assessment.

4. Risk characterization.

a). Non carcinogenic risks.

b). Carcinogenic risks.

5. Risk assessment / management by considering:

a). What types of problems or failures could occur, and what is the probability that each one will occur?

b). What types of environmental impacts could result?

c). What types of compliance-related retrofits or remediation methods could be required?

d). What are the possible fines or remediation costs?


Cost Analysis

By considering:

Ø Capital costs

Ø Operating costs

Ø Closure costs

Ø Potential costs for retrofits associated with regulatory compliance

Ø Potential cost for remediation

Ø Life-cycle environmental costs


Mine Reclamation

i. Surface and groundwater management

ii. Mine waste management

iii. Tailings management

iv. Cyanide heap and vat leach systems

v. Acid Mine Drainage Control

vi. Landform reclamation

vii. Revegetation

viii. Site stability

ix. Subsurface stabilization

x. Erosion prevention


Location of the McLaughlin Mine in California


Facilities map of the McLaughlin Mine


Mine waste management

1) 2)

3) 4)

M

c

L

a

u

g

h

l

i

n

Early stage for waste disposal & AMD control facilities Advance of the waste disposal works

Final limit of the waste dump Erosion control by revegetating is started


5) 6)

7) 8)

Mine waste management (cont.)

M

c

L

a

u

g

h

l

i

n

Advance on the erosion control & and pit backfilling

South pit is backfilled & west dump is almost covered

East waste dump is completely covered

Waste dumps encapsulation is finished

06/14/ 98

05/04/ 92 05/04/ 93

05/10/ 93


Acid Mine Drainage Control

AMD control facilities at the west waste dump


Revegetation

Supervising the revegetation works on the west waste dump

(notice the AMD control facilities on the right side)


Minimizing AMD in open pit mining through mine planning

Antonio Peralta

by

Acid Mine Drainage (AMD)Acid Mine Drainage (AMD)

q It encompasses all issues associated with the environmental effects of sulphide oxidation resulting from mining activities.

q Its significant potential for long-term environmental degradation makes it one of the biggest environmental issues facing the mining industry.

Acid Mine Drainage ExamplesAcid Mine Drainage Examples

Contributing FactorsContributing Factors

q Primary factors are directly involved in the generation of sulphide oxidation products.

q Secondary factors consume or alter those products.

q Tertiary factors are the physical conditions that influence the process.

Problems for Mine OperatorsProblems for Mine Operators

q Impact on mine water quality.

q Impact on aquatic ecosystems.

q Impact on riparian communities.

q Impact on groundwater quality.

q Impairment of the use of waterways.

q Revegetating and stabilizing mine wastes.

q Long term liability.

Acid Mine Drainage ControlAcid Mine Drainage Control

q There is a number of well established principles for minimizing AMD.

q Mine planning to minimize AMD is the most cost effective and desirable solution to the problem.

q Treatment is less desirable due to the long term nature of AMD and associated high treatment costs.

Principles to Prevent Acid Mine DrainagePrinciples to Prevent Acid Mine Drainage

q Exclusion of oxygen from wastes.

q Control of water flux within wastes.

q Minimize transport of oxidation products.

q Neutralization of AMD with alkaline materials.

q Monitoring to determine the effectiveness of remediation measures.

11stst Step Step –– Characterization of Rock TypesCharacterization of Rock Types

q Geological assessment.

q Geochemical tests, classified as static and kinetic tests.

q Static testing evaluates the acid generating and acid neutralizing processes.

q Kinetic testing evaluates the rate of sulphide oxidation, AMD characteristics, and assess potential management techniques.

Geological Assessment Geological Assessment –– Information SourcesInformation Sources

q Acid generation characteristics of similar ore bodies and host rocks.

q Relevant information should be logged and recorded from drill core during the exploration stage.

q Core samples must be retained for further testing.

Geological Assessment Geological Assessment –– SamplingSampling

q Sampling should be representative, based on accepted statistical procedures.

q Representative profiles of all geological units should be sampled.

q The number of samples will depend on geological variability, complexity of rock types, and level of confidence required.

Geological Assessment Geological Assessment –– Handling of SamplesHandling of Samples

q Samples should be stored in a cool, dry environment to minimize sulphide oxidation prior to testing.

q Static tests may require as little as 2 grams of sample.

q Kinetic tests require a minimum of 500 grams of sample.

Geological Assessment Geological Assessment –– InterpretationInterpretation

q Topography and drillholes


q Cross section of the drillholes


q Interpretation of rock types


q 3D view of two interpreted sections

Geochemical Tests Geochemical Tests –– Static TestsStatic Tests

q Acid base accounting or net acid producing potential (NAPP) test.

q Net acid generation (NAG) test.

q Saturated paste pH and conductivity (EC).

q Total and soluble metal analysis

Net Acid Producing PotentialNet Acid Producing Potential

q NAPP is determined by subtracting the estimated acid neutralizing capacity of a sample from the estimated potential acidity of the sample.

q It has three components:Maximum potential acidity (MPA)Acid neutralizing capacity (ANC)Sample classification.

Net Acid Generation TestNet Acid Generation Test

q NAG comprises the addition of a strong oxidizing agent such hydrogen peroxide to a prepared sample and the measurement of the solution pH and acidity after the oxidation reaction is complete.

q This test can provide and indication of sulphide reactivity and available neutralizing potential within 24 hours.

Saturated paste pH and conductivitySaturated paste pH and conductivity

q The test gives a preliminary indication of the in situpH and the reactivity of the materials present in the sample.

q A crushed sample (<1 mm) is saturated to create a paste and the pH and EC is determined after a period of equilibration.

Total and soluble metal analysisTotal and soluble metal analysis

q Initial screening should compare metal concentration in the solids with that of the background soils and country rocks in the area.

q Statistical methods are available to determine whether any enrichment is significant.

Geochemical Tests Geochemical Tests –– Kinetic TestsKinetic Tests

q They simulate weathering and oxidation of rock over time under exposure to moisture and air.

q They provide an indication of the oxidation rate and time periods for onset of acid generation (lag time).

q Columns and humidity cells are the most used kinetic test techniques.

Rock ClassificationRock Classification

q Acid Generating (AG)

q Potentially acid generating (PAG)

q Potentially acid consuming (PAC)

q Potentially neutral (PN)

Classification for regulatory and permitting purposes.

22ndnd Step Step –– Quantifying the Materials to be disposedQuantifying the Materials to be disposed

q AMD waste materials includes overburden, waste rock, pit walls, pit floor and tailings.

q A database of the AMD parameters determined in the tests is required.

q A predictive AMD block model should be created using the information available in the database.

Block Modeling Block Modeling

q A block model is a three-dimensional spatial representation of an ore body.

q It is used to quantify the geology an economics of the deposit.

q It is developed by dividing the ore body and the host rock into regularly shaped blocks representing the smallest mineable unit.

Information in the Block Model Information in the Block Model

q Ore grades.

q Contaminants.

q Metallurgical recoveries.

q Physical parameters of the ore.

q Economic parameters.

q Environmental parameters.

Steps to create a block modelSteps to create a block model

q Produce a detailed geologic interpretation.

q Create drill hole composites per material type.

q Perform statistical analysis.

q Perform spatial analysis if sufficient data exist.

q Interpolate a value into each block, for each of the required variables.

Complete Block ModelComplete Block Model

q Block model includes waste and ore blocks.

Constrained Block ModelConstrained Block Model

q Block model includes only ore blocks.

Block Model and Mine DesignBlock Model and Mine Design

q Blocks inside and outside the final pit limit.

33rdrd Step Step -- Mining DevelopmentMining Development

q Site potential and reserves

éExpected pit development

q Development phasing

éPeriod of development

éAreas of extractionby phase

2005

2035

2020

2050

Maps for different time periodsMaps for different time periods

Coordination with ReclamationCoordination with Reclamation

q Clearing / Vegetation removal

q Topsoil management

q Overburden / Waste rockmanagement

q Grading principles

q Erosion control

q Revegetation

Isolation Strategy Isolation Strategy

q The objective is to isolate reactive wastes for selective disposal either separately or within non-reactive materials.

q In some cases, it may be preferable to segregate highly reactive wastes within a separate facility to permit intensive treatment and control strategies.

Waste EncapsulationWaste Encapsulation

q AMD waste is selectively handled and surrounded with non-acid producing materials to limit flow of air and water into waste and AMD flow out.

q A cell structure is formed. The surface is covered with compacted benign material, usually clay.

InIn--Pit DisposalPit Disposal

q Similar in concept to encapsulation. Method is useful where a mined out pit of sufficient size is available.

q With effective mine planning an early closure of one of a series of mined pits allows for in-pit disposal of AMD wastes.

CoCo--disposal and Blending of Wastedisposal and Blending of Waste

q Involves the blending/mixing and co-disposal of AMD wastes with benign non-acid producing materials or even acid neutralizing materials.

q Small cells within a waste dump are rapidly filled and covered to reduce AMD generation and water ingress.

CoversCovers

q A low permeability cover is constructed over an existing waste dump, mainly using locally available borrow or benign waste, to reduce the infiltration of surface water and infusion of air into the dump.

Recovery and TreatmentRecovery and Treatment

q Option for marginal acid producing wastes where subsequent acid drainage is recovered and treated downstream.

q Collection/recovery systems can include catchment ponds, drains, trenches and groundwater bores.

ConclusionsConclusions

qMine planning can be a cost effective method to control AMD in open pit mines.

q There are three basic steps to achieve AMD control: characterize the rock types, quantify the amount and content of the rocks, and develop a mine plan according to the previous steps.

q The mine plan should include waste management strategies to minimize AMD: isolation, encapsulation, in-pit disposal, co-disposal, blending, covers, and treatment.

q A combination of these strategies could be highly effective to control AMD.

Questions and comments???????Questions and comments???????

Summitville, ColoradoSummitville, Colorado

Summitville, ColoradoSummitville, Colorado

According to the United States Environmental Protection Agency (US EPA), mining generates twice as much waste as all other American industries put together.

So-called "hard rock" mining wastes are acidic and contaminated with toxic heavy metals which have poisoned more than 12,000 miles of streams and rivers and 180,000 acres of lakes.

EPA estimates the public cost to clean up the more than 550,000 abandoned mines in America at between $32-72 billion.

The very scale of today's massive open-pit mining operations means that sometimes cleanup costs will outstrip the value of the metals pulled out of the ground, as happened with the $232 million cleanup of the Summitville mine in southern Colorado.

Examples, ColoradoExamples, Colorado

At Eagle mine, a zinc, copper and silver operation, ten million tons of mine waste and mine tailings were left along the banks of theEagle River in Gilman Colorado.

Cleanup costs exceeded $55 million which totaled more than $5.50per ton of mine waste.

A zinc, lead and silver mine at Smuggler Mountain in PitkinColorado. The estimated cost for environmental recovery is $7.2 million. This equals $2.40 per ton of waste.

Feasibility StudiesThe formal feasibility study includes an economic analysis of the rate of return that can be expected from the mine at a certain rate of production.

Some of the factors considered during such an economic analysis are:

Tons in the depositGrade of the mine productMill recoverySale price of the metal or mineralCost of mining per tonCost of milling per tonRoyaltiesCapital cost of the mine

Capital Cost of the millExploration and development costMining rate, tons per dayDepreciation method usedDepletion allowanceWorking capital necessaryMiscellaneous costs of operationTax rate

Risk

Mining is a very risky business.

The most serious risks in any mining project are those associated with:

•Geology: the actual size and grade of the minable portion of the deposit,

•metallurgical factors: how much of the orebody can be recovered, and

•Economics: metal markets, interest rates, mining, processing,ect.

Return on Investment

In order to compensate for risk, a mining organization will require a minimum acceptable rate of return on investment.

The cost of borrowing capital for the mine or of generating the needed capital internally within the company must be considered.

If a company has a number of attractive investment opportunities, the rate of return from the proposed mine venture may be compared with the rate expected on a different mining venture elsewhere, or with some other business opportunity unrelated to mining.

Management has an obligation to its stockholders or investors toselect projects with the best rate of return.

As a general rule of thumb, a project must have better than a 15-percent rate of return to be considered by a major company.

An individual commonly expects a 30- to 50 percent rate of return to consider investing in a mining venture.

Among other uses of the cash flow generated by the mine, these funds must finance:

•continuing exploration elsewhere, •pay for past failures, and •contribute to the mine's portion of main office and general overhead.

Time Value of MoneyMoney has a time value. The future value of an investment can be calculated by:

where:P = Present value of investmentF = Future value of investmenti = interest rateN = number of years

For example $100 invested at 10% interest for 1, 2, and 3 years would yield:

F = 100(1 + .10)1 = $110.00F = 100(1 + .10)2 = $121.00F = 100(1 + .10)3 = $133.10

Ni)P(1F +=

Time Value of MoneyConversely money received in the future is not as valuable as money received today. If money is received in the future:

Using the same example:

P = 110.00/(1 + .10)1 = $100.00P = 121.00/(1 + .10)2 = $100.00P = 133.10/(1 + .10)3 = $100.00

Ni)(1/FP +=

DCF-ROR

The criterion most commonly employed in the minerals industry when evaluating the rate of return on an investment proposal is called the discounted cash flow rate of return (DCF-ROR).

The term is a special version of the more generic term, internal rate of return (IRR).

The internal rate of return is defined a that interest rate which equates the sum of the present value in cash inflows with the sum of the present value of cash outflows for a project:

ΣPV cash inflows = ΣPV cash outflows (3)

DCF-RORThe DCF-ROR can be calculated by:

(4)

where:CFn = Amount of cash in or out in a given yearn = YearN = Project lifei = DCF-ROR

Once the cash flows for a project have been determined, the interest rate i can be solved for using an iterative process, i.e. guess at an initial value for i and then solve Equation 4 until a result of 0 is obtained.

0i)(1

CFN

0nn

n =+∑

=

Steps Involved in Cash Flow Analysis

The evaluation of a mining project is usually an iterative process using the following steps:

1. Select a mining method2. Select a production rate3. Calculate Capital and Operating Costs4. Select cutoff grade and tonnage5. Calculate cash flow and return

Change steps 4, 2, and 1 and select the alternative that gives thehighest return.

Steps Involved in Cash Flow AnalysisIn a feasibility study, attempt to quantify all geologic, technical,marketing, environmental, political, etc. factors. Many of thesevariables are dependent on each other. A feasibility study are usually divided into the pre-production, production, and post-production phases:

1. Preproduction PeriodExploration

Water and land acquisitionMine and mill capital

Working capital, etc2. Production Period

Revenue less costsCalculation Of Annual Cash Flow

3. Postproduction PeriodEquipment salvage

Working capital liquidation

Steps Involved in Cash Flow Analysis

DepletionOne of the features that distinguish a mining enterprise from many other businesses is that during production, the company’s assets, i.e. the ore, is consumed.

The percentage depletion allowance is based on the idea that as minerals are extracted, the mine is worth less.

The percentage depletion allowance permits mining companies to deduct a certain percentage from their gross income to reflect the mine's reduced value over time.

DepreciationDepreciation is an allowable deduction when computing taxable income that represents the exhaustion, wear, and tear of property used in a trade or business, or of property held for the production of income.

The purpose of the depreciation deduction is to provide a means by which a business or trade can recapture the capital needed to keep itself in business.

Therefore depreciation allowances for capital assets are deducted from taxable income in an orderly manner such that the property owner has deducted the initial investment in the asset by the time it wears out or becomes exhausted.

Having recaptured the initial asset cost from the annual tax deductions, the owner can, in theory, replace the worn-out piece of equipment with a new one and keep himself in business.

Case StudyThe calculation of the cash flow and DCF-ROR is illustrated using a bedded zinc deposit, producing 6000 tons per day, with total reserves of 22.5 MM Tons @ 14% zinc.

Simplifying and other assumptions:1. No royalty2. No investment tax credits3. Straight line depreciation and depreciation life equal to life of property4. Federal, state, and local taxes equal to 40% net after depletion5. No replacement or additional equipment requirements 6. No start-up costs or learning curve 7. Uniform grade mined over mine life 8. Uniform production rate over mine life 9. Operating costs constant over mine life 10. Mine would be division of large profitable corporation with 100% of exploration

and development expensed11. No consideration of cost depletion12. Price/cost differential constant over life of mine with no consideration of escalation

and inflation

Cash Flow Calculations

Pre-Production PeriodYear 1 2 3 4 5 6 7 TotalExploration *1 2,000 4000 4000 0 0 0 0 10,000Development *2 0 0 0 4000 8000 8000 0 20,000Mine/Mill 0 0 0 15000 36000 36000 0 87,000Working Capital 0 0 0 0 0 2600 9,300 11,900Total Investment (2,000) (4,000) (4,000) (19,000) (44,000) (46,600) (9,300) (128,900)Tax Savings *3 800 1600 1600 1600 3200 3200 0 12,000Net Cash Flow (1,200) (2,400) (2,400) (17,400) (40,800) (43,400) (9,300) (116,900)

*1 Expensed under Section 617 of IRS Code*2 Expensed*3 Assume federal, state, and local tax rate = 40% of net after depletion

Cash Flow Calculations ($1,000)

Zinc Smelter Schedule

PaymentsSilver: Deduct 2 Troy oz., pay for 80% of remainder at

Handy & Harman quotation for refined silver inMetals Week, averaged for the calendar monthfollowing delivery, less $.055 per oz.

Lead: No payment.

zinc: Pay for 85% of zinc content at delivery price for prime western zinc published in Metals Week, averaged for the calendar month following delivery,less $.015 per pound.

Zinc Smelter Schedule

DeductionsSmelter Charge:

$170/dry ton

Price Adjustment: Increase by $3.00 per ton for each $.01 that the zincquotation exceeds $.40 per pound. Fractions in proportion.

Decrease by $2.00 per ton for each $.01 that the zinc quotation decreases below $.40 per pound. Fractions in proportion.

Smelter Schedule CalculationsConcentrate Grade = 55%zinc Price = $0.47/lb

Payments:2,000 lb/ton * 0.55 * 0.85 * $(0.47- 0.015)/lb = $425.43/ton

Deductions:Base Charge 170.00Price Adjustment(47- 40)c * $3.00/c = 21.00Total Deductions: (191.00)

Freight:Truck 5.00Rail 15.00Total Freight: (20.00)

Net Smelter Return/Ton Concentrate (NSR/T) $214.43/ton

Revenue and Operating CalculationsRevenue/year = Tons/year Concentrate * NSR/ton

Tons/year Concentrate = (Tons/year Ore * Grade * Mill Recovery)/(Conc. Grade)Mine Schedule = 250 Days/yearMill Recovery = 90%

Tons/year Concentrate = 6,000 T/D * 250 D/Y * 0.14 * 0.9/0.55 = 343,636 Tons/year Concentrate .

Revenue/year ($1,000) = 343,636 T/Y * $214.43/1,000 = $73,684/Year

Direct Operating cost/Year = Tons/year Ore * Operating Costs/Ton OreDirect Operating Costs

Mining $15.00 /Ton OreMilling 5.00Overhead 3.00

Total 23.00 /Ton Ore

Operating Cost/Year ($1,000) = 6,000 T/D * 250 D/Y * $23.00/T/1,000 = $34,500/Year

Production PeriodYear 7 8 9 10 11 12-21Revenues 73,684 73,684 73,684 73,684 73,684 73,684Operating Costs (34,500) (34,500) (34,500) (34,500) (34,500) (34,500)Net Before D & D 39,184 39,184 39,184 39,184 39,184 39,184Depreciation (5,800) (5,800) (5,800) (5,800) (5,800) (5,800)Net After Depr. 33,384 33,384 33,384 33,384 33,384 33,384Depletion (6,211) (16,211) (16,211) (16,211) (16,211) (16,211)Taxable Income 27,173 17,173 17,173 17,173 17,173 17,173Tax @ 40% (10,869) (6,869) (6,869) (6,869) (6,869) (6,869)Net After Tax 16,304 10,304 10,304 10,304 10,304 10,304Depreciation 5,800 5,800 5,800 5,800 5,800 5,800Depletion 6,211 16,211 16,211 16,211 16,211 16,211Cash Flow 28,315 32,315 32,315 32,315 32,315 32,315Working Capital (9,300) 0 0 0 0 0Net Cash Flow 19,015 32,315 32,315 32,315 32,315 32,315

Depletion Calculation: 7 8 9 10 11 12-21Initial Recapture 10,00022% Revenue 16,211 16,211 16,211 16,211 16,211 16,21150% Net After Depr. 16,692 16,692 16,692 16,692 16,692 16,692Depletion Earned 16,211 16,211 16,211 16,211 16,211 16,211Depletion Recaptured 10,000 0 0 0 0 0Recapture Balance 0 0 0 0 0 0Depletion Claimed 6,211 16,211 16,211 16,211 16,211 16,211

Depreciation and Depletion

Depreciation/Year = (Mine & Mill capital)/Mine Life

Mine Life = Reserves/Annual Production= 22,500,000 Tons/(6,000 T/D * 250 D/Y) = 15 years

Depreciation/Year ($1,000) = $87,000,000/15 Yr/1,000 = $5,800/Year

Depletion ($1,000):

Statutory % * Revenue or 50% Net after Depreciation, Select Smaller

zinc Depletion Rate = 22%

22% * $73,684 = $16,211 <=== Select SmallerOR

50% * $33,384 = $16,692

Production PeriodYear 7 8 9 10 11 12-21Revenues 73,684 73,684 73,684 73,684 73,684 73,684Operating Costs (34,500) (34,500) (34,500) (34,500) (34,500) (34,500)Net Before D & D 39,184 39,184 39,184 39,184 39,184 39,184Depreciation (5,800) (5,800) (5,800) (5,800) (5,800) (5,800)Net After Depr. 33,384 33,384 33,384 33,384 33,384 33,384Depletion (6,211) (16,211) (16,211) (16,211) (16,211) (16,211)Taxable Income 27,173 17,173 17,173 17,173 17,173 17,173Tax @ 40% (10,869) (6,869) (6,869) (6,869) (6,869) (6,869)Net After Tax 16,304 10,304 10,304 10,304 10,304 10,304Depreciation 5,800 5,800 5,800 5,800 5,800 5,800Depletion 6,211 16,211 16,211 16,211 16,211 16,211Cash Flow 28,315 32,315 32,315 32,315 32,315 32,315Working Capital (9,300) 0 0 0 0 0Net Cash Flow 19,015 32,315 32,315 32,315 32,315 32,315

Depletion Calculation: 7 8 9 10 11 12-21Initial Recapture 10,00022% Revenue 16,211 16,211 16,211 16,211 16,211 16,21150% Net After Depr. 16,692 16,692 16,692 16,692 16,692 16,692Depletion Earned 16,211 16,211 16,211 16,211 16,211 16,211Depletion Recaptured 10,000 0 0 0 0 0Recapture Balance 0 0 0 0 0 0Depletion Claimed 6,211 16,211 16,211 16,211 16,211 16,211

Post-Production PeriodYear 22Working Capital 11,900After-Tax Reclam. -8,000Net Cash Flow 3,900

DCF-ROR or Internal Rate of ReturnPresent Value Present Value Present Value

Year (j) Net CF 1/(1+.20)^j CF @ 20% 1/(1+.25)^j CF @ 25% 0.21509 CF @ 21.509%1 (1,200) 0.833 (1,000) 0.800 (960) 0.823 (988)2 (2,400) 0.694 (1,667) 0.640 (1,536) 0.677 (1,626)3 (2,400) 0.579 (1,389) 0.512 (1,229) 0.557 (1,338)4 (17,400) 0.482 (8,391) 0.410 (7,127) 0.459 (7,982)5 (40,800) 0.402 (16,397) 0.328 (13,369) 0.378 (15,403)6 (43,400) 0.335 (14,535) 0.262 (11,377) 0.311 (13,485)7 19,015 0.279 5,307 0.210 3,988 0.256 4,8628 32,315 0.233 7,515 0.168 5,422 0.210 6,8009 32,315 0.194 6,263 0.134 4,337 0.173 5,597

10 32,315 0.162 5,219 0.107 3,470 0.143 4,60611 32,315 0.135 4,349 0.086 2,776 0.117 3,79112 32,315 0.112 3,624 0.069 2,221 0.097 3,12013 32,315 0.093 3,020 0.055 1,777 0.079 2,56714 32,315 0.078 2,517 0.044 1,421 0.065 2,11315 32,315 0.065 2,097 0.035 1,137 0.054 1,73916 32,315 0.054 1,748 0.028 910 0.044 1,43117 32,315 0.045 1,457 0.023 728 0.036 1,17818 32,315 0.038 1,214 0.018 582 0.030 96919 32,315 0.031 1,011 0.014 466 0.025 79820 32,315 0.026 843 0.012 373 0.020 65721 32,315 0.022 702 0.009 298 0.017 54022 3,900 0.018 71 0.007 29 0.014 54

367,726 3,580 (5,666) 0

By Linear Interpolation

DCF-ROR = 20% + 3580/(3580+5666)*(25-20)% = 21.9%

Exact Solution 21.5090%

Present Value of Cash Flows at 21.5% Discount Rate

(20,000)

(15,000)

(10,000)

(5,000)

0

5,000

10,000

1 3 5 7 9 11 13 15 17 19 21

Year

$ *1

000

Projected Cash Flows For Bedded Zinc Deposit

-50000-40000-30000-20000-10000

010000200003000040000

1 3 5 7 9 11 13 15 17 19 21

Year

$ *1

000

Definitions of troy ounce on the Web:

ounce: a unit of apothecary weight equal to 480 grains or one twelfth of a pound

he traditional unit of weight for gold is the troy ounce, named, it is thought, after a weight used at the annual fair at Troyes in France in the Middle Ages.

Although the metric system is used increasingly in mining and the gold business, the troy ounce remains the basic unit in which the price of 995 gold is quoted.

One troy ounce = 31.1034807 grams, 32.15 troy ounces = 1 kilogram, 1 troy ounce = 480 grains,

Mine Production Scheduling Mine Production Scheduling OptimizationOptimization

-- The State of Art The State of Art --

K. Dagdelen

ProfessorMining Engineering Department

Colorado School of MinesGolden, Colorado 80401

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OPEN PIT OPTIMIZATIONOPEN PIT OPTIMIZATION

For Each Block in The For Each Block in The ModelModel

ll If a given block of If a given block of material should be material should be mined?mined?

ll When it Should be When it Should be mined?mined?

ll Once it is mined what to Once it is mined what to do with the block of do with the block of MaterialMaterial

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OPEN PIT OPTIMIZATIONOPEN PIT OPTIMIZATIONStart

Physical Capacities

Ultimate pit

Design Of Cuts

Cutoff Grade

Steps of Traditional Planning by Circular Analysis

ExtractionScheduling

ProductionCosts

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OPEN PIT OPTIMIZATIONOPEN PIT OPTIMIZATIONULTIMATE PIT LIMITS

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l Identifies What blocks should be mined and which ones should be left in the ground.

l Defines the lateral and vertical extent to which a given deposit can economically be mined to

l 3-D Breakeven Analysis l Moving Cone algorithm gives sub-optimum resultsl Lerchs and Grossmann algorithm gives true

breakeven pit that maximizes the undiscounted profits

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The Lerchs and Grossmann Algorithml Only finds the maximum profit pit boundary l No time value of money is consideredl The pit that maximizes discounted profits (NPV) by

taking into account time value of money is much smaller than the ultimate pit found by this technique

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l Common practice is to apply Lerchs and Grossmann’s algorithm to the economic block model that is generated to discounted block values

l Economic block model is generated by discounting block values based on a rough initial production schedule

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l If the schedule is not defined by identifying effect of waste stripping on the overall cash flows then the ultimate pit limit may not be correct

l NPV analysis on the last incremental pushbacksalways results in elimination of non-contributing incremental pits

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Physical Capacities

Ultimate pit

Design Of Cuts

Cutoff Grade



ProductionCosts

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OPEN PIT OPTIMIZATIONOPEN PIT OPTIMIZATIONDESIGN OF PUSHBACKS

Economic block models are developed by varying eitherl Metal Price l Cutoff Grade l Minimum profits required per ton of orel Some ratio in block evaluation equationl As these variables change the pit outline also changesl Each outline is then used as pushbacks

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PHASE 2

PHASE 1

PHASE 3

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l The concept is based on mining “next best ore” without considering impact of stripping to be done ahead of time

l First incremental pit contains the ore that has the highest average overall value per ton. The subsequent pits have lower and lower average value per ton of ore

l The push back designs do not take into account effect of timing of waste stripping on the NPV

l Blending requirements can not be taken into account

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Physical Capacities

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Design Of Cuts

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ProductionCosts

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OPEN PIT OPTIMIZATIONOPEN PIT OPTIMIZATIONCUTOFF GRADES

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Cutoff GradesCutoff Gradesl A cutoff grade is the grade that is used to

differentiate between ore and waste in a given mining environment. Although the definition of cutoff grade is straight forward, the determination of it is not.

l To determine if a block of material should be milled or taken to the waste dump, breakeven mill cutoff may be used.

Milling cutoff grade

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McLaughlin Gold MineMcLaughlin Gold MineCalifornia, USACalifornia, USA

Waste dumps

Autoclave Mill

Pit

Waste Ore and waste discrimination

Cutoff grade

Stockpiles

Ore

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Round Mountain Gold MineRound Mountain Gold Mine

Waste dumps

Leach Pads

Stockpiles

Low grade stockpiles

Crusher

WasteOxide

Sulfide

CIP Mill

Ore

Breakeven Mill Cutoff GradeBreakeven Mill Cutoff Grade

l The lowest economic grade where mining, milling, and administration cost are equal to revenues obtained from the metal produced.

Breakeven cutoff grade = Milling Cost

(Price – Refining Cost - Sales Cost) * Recovery

l Traditionally, this breakeven cutoff grade has been widely used in a production scheduling.

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l The economic and operational parameters:

Price (P) 600 $/oz

Sales Cost (s) 5 $/oz

Processing Cost (c) 19 $/ton ore

Recovery (y) 0.9

Mining Cost (m) 1.2 $/ton

Fixed Cost (fa) 8.35M $/year

Mining Capacity (M) Unlimited

Processing Capacity (C) 1.05M tons

Discount Rate (d) 15 %

Production Scheduling By Production Scheduling By Breakeven Cutoff Grade (Case1)Breakeven Cutoff Grade (Case1)

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l If one uses breakeven cutoff grade for a production scheduling:

$19/ton

($600/oz - $5.0/oz) * 0.90Breakeven cutoff grade =

= 0.035 oz/ton

l All the materials above 0.035oz/ton goes to process, and below goes to waste dump.

McLaughlin Case StudyMcLaughlin Case Study20

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l Consider a case study from McLaughlin Mine in California where an epithermal gold deposit was mined by an open pit.

l The grade distribution within the ultimate pit limit is:

Grade CategoryFrom To midpoint Ktons

0 0.02 0.0100 70,0000.02 0.025 0.0225 7,257

0.025 0.03 0.0275 6,3190.03 0.035 0.0325 5,591

0.035 0.04 0.0375 4,5980.04 0.045 0.0425 4,277

0.045 0.05 0.0475 3,4650.05 0.055 0.0525 2,428

0.055 0.06 0.0575 2,3070.06 0.065 0.0625 1,747

0.065 0.07 0.0675 1,6400.07 0.075 0.0725 1,485

0.075 0.08 0.0775 1,2270.08 0.1 0.0900 3,5980.1 0.358 0.2290 9,576

125,515

Ton

s

Grade intervals36,346 [email protected]/ton

89,167 tons

SR=2.45

COG

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l Assuming the deposit is homogeneously distributed, yearly mining rate is given as follows:

l Yearly ore tons: 1.05Mtons (Limited by process capacity)l Yearly ounces recovered: 1.05Mtons x 0.102 oz/ton x 0.9

= 96.3kozl Yearly waste tons: 1.05Mtons x 2.45 (SR) = 2.58Mtonsl Yearly mining rates: 1.05M + 2.58M = 3.62Mtons

Yearly Schedules by Breakeven Yearly Schedules by Breakeven Cutoff Grade (Cont.)Cutoff Grade (Cont.)

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l Mining the deposit with breakeven cutoff grade of 0.035oz/ton at 1.05M tons process capacity:

Avg Qm Qc Qr Profits

Year (i) COG Ore Grade (Mtons) (Mtons) (ktons) ($M)

1 0.035 0.102 3.6 1.05 96.3 33.0

2 0.035 0.102 3.6 1.05 96.3 33.0

3 0.035 0.102 3.6 1.05 96.3 33.0

4 0.035 0.102 3.6 1.05 96.3 33.0

5 0.035 0.102 3.6 1.05 96.3 33.0

6 0.035 0.102 3.6 1.05 96.3 33.0

7 0.035 0.102 3.6 1.05 96.3 33.0

8 0.035 0.102 3.6 1.05 96.3 33.0

9 0.035 0.102 3.6 1.05 96.3 33.0

10 0.035 0.102 3.6 1.05 96.3 33.0

11 to 34 0.035 0.102 3.6 1.05 96.3 33.0

35 0.035 0.102 3.4 1.00 91.7 31.4

Total 125.8 36.7 3,365.9 1,154.2

(NPV@15%)

$218.5

Shortcomings of the Traditional Shortcomings of the Traditional Cutoff GradesCutoff Grades

l They are established to maximizing the undiscounted profits from a given mining operation.

l They are constant unless the commodity price and the costs change during the life of the mine.

l They do not consider grade distribution of the deposit.

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l Many open pit mines are still designed and operated using cutoff grades based on breakeven economic analysis which maximizes undiscounted profits

l The cutoff grades should be set to much higher levels than the breakeven cutoff during the initial years of the operation

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l The heuristic algorithm to define optimum declining cutoff grades that maximize the NPV of a given project was developed by Kenneth Lane in 1965

l Applying this method to a given project results in higher NPV for a project specially if capacities are not in harmony with the grade distribution of the deposit

Declining Cutoff GradeDeclining Cutoff Grade20

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l Traditional cutoff grade (constant cutoff grade) does not maximize the NPV.

l Many approaches have been suggested to improve NPV of the project.

l K. F Lane in 1964 suggested an heuristic algorithm to obtain cutoff grades higher than breakeven grades during the early years that maximize the Net Present Value (NPV) of a project

Optimum Cutoff Grades by Lane’s Optimum Cutoff Grades by Lane’s Algorithm Algorithm

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l Lane’s approach considers the mining operation to be constrained by the capacities of mine, mill, and refinery.

l The cutoff grades are optimized by considering the grade distribution of the deposit in providing highest quality of ore to the mill subject to three capacity constraints.

l This approach has been successfully used in the mining industry for many years.

Optimum Cutoff Grades by OptiPit Optimum Cutoff Grades by OptiPit ®®20

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l Linear Programming (LP) based algorithm and software is being developed to optimize cutoff grades under complex mining and process constraints.

l Mathematical programming approach is very powerful and provides complete flexibility in modeling complex operating environments.

l This approach will be described and demonstrated using four case studies coming from gold mines in Western United States.

Round Mountain Gold MineRound Mountain Gold Mine

Waste dumps

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Stockpiles

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Crusher

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CIP Mill

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COMPLICATED PROCESSES AND COMPLICATED PROCESSES AND CAPACITIESCAPACITIES

Dump

ROM Leach

Cr Leach

Cr

Flot.

10M tons/yr

limited by crusher

5M tons/yr

1.05M tons/yr

2M tons/yr

Proc 1

Proc 2

Proc 3

Proc 4

Tailings

80%

20%

Autoclave

Mine

Phase1

Phase2

Mining Capacity: 12M tons/yr

Refining Capacity: 350 koz/yr

Stockpile available

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l Linear Programming (LP) based algorithm and software is being developed to optimize cutoff grades under complex mining and process constraints.

l Mathematical programming approach is very powerful and provides complete flexibility in modeling complex operating environments.

CUTOFF GRADE FORMULATION CUTOFF GRADE FORMULATION

McLaughlin mine

Mine

Dump MillCutoff Grade

Index i

Index g

Index d

Index t: YearsT

ons

Grade intervals

igdtX

l Decision variables:

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OPEN PIT OPTIMIZATIONOPEN PIT OPTIMIZATIONFUTURE

l NO scheduler in the market that incorporates shortcomings discussed

l There are efforts to develop methods that will overcome these shortcomings

l The advancements in hardware and software technology in recent years is providing an unique opportunity to solve this problem by way of “Linear –Integer Programming” techniques

l In the mean time, the use of computer programs that optimizes sub-problems will give you higher NPV for a given project if not the optimum.

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Push Backs or Phases

• Defines how the pit will evolve with time.

• Defines ore tons and its quality for different time periods.

• Defines waste tons for removal schedules.

• Defines the cash flows and overall project economics.

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Push Backs or Phases Example

Phase 1 Phase 2

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Push Backs or Phases Example (Cont.)

Phase 3 Phase 4

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Push Backs or Phases Example (Cont.)

Cross Section

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Cutoff Grade

• Minimum grade of the material for processing.

• Normally used to discriminate between ore and waste within a given orebody.

• Cutoff grade is Dynamic.

Read “Cutoff Grade Optimization” by Dr. Dagdelen

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Breakeven Cutoff Grade

• The lowest economic grade where mining, milling, and administration cost are equal to revenues obtained from the metal produced.

• Cutoff grades in the pit are normally much higher than the breakeven cutoff grade.

• Cutoff grades decline as the mine matures, and approaches the breakeven cutoff.

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Hypothetical Case Study

• Consider a hypothetical case study where an epithermal gold deposit will be mined by an open pit.

• The grade distribution within the ultimate pit limit is:Grade Category

From To midpoint Ktons0 0.02 0.0100 70,000

0.02 0.025 0.0225 7,2570.025 0.03 0.0275 6,3190.03 0.035 0.0325 5,591

0.035 0.04 0.0375 4,5980.04 0.045 0.0425 4,277

0.045 0.05 0.0475 3,4650.05 0.055 0.0525 2,428

0.055 0.06 0.0575 2,3070.06 0.065 0.0625 1,747

0.065 0.07 0.0675 1,6400.07 0.075 0.0725 1,485

0.075 0.08 0.0775 1,2270.08 0.1 0.0900 3,5980.1 0.358 0.2290 9,576

125,515

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Mine Design Parameters

• Capacities and Costs are:

Price (P) 600 $/oz

Sales Cost (s) 5.00 $/oz

Processing Cost (c) 19.0 $/ton ore

Recovery (y) 90 %

Mining Cost (m) 1.2 $/ton

Fixed Costs (fa) 8.35 $M/yr

Mining Capacity (M) Unlimited

Milling Capacity (C) 1.05 M

Capital Costs (CC) 105 $M

Discount Rate (d) 15 %

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Traditional Cutoff Grades

• Traditionally, a cutoff grade is used to determine if a block of material should be mined or not.

• And, another cutoff is used to determine whether or not it should be milled or taken to the waste dump.

Ultimate pit cutoff grade

Milling cutoff grade

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Ultimate Pit Cutoff Grade

• Ultimate pit cutoff grade is defined as the breakeven grade that equates cost of mining, milling, refining and marketingto the value of the block in terms of recovering metal and the selling price.

Ultimate pit cutoff grade = Milling Cost + Mining Cost


$19/ton + $1.2/ton

($600/oz - $5.0/oz) * 0.90Ultimate pit cutoff grade =

= 0.038 oz/ton

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Milling Cutoff Grade

• Milling cutoff grade is defined as the breakeven grade that equates cost of milling, refining and marketing to the value of the block in terms of recovering metal and the selling price.

Milling cutoff grade = Milling Cost


$19/ton

($600/oz - $5.0/oz) * 0.90Milling cutoff grade =

= 0.035 oz/ton

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Milling Cutoff Grade (Cont.)

• In the milling cutoff grade, no mining cost is included since this cutoff is basically applied to those blocks that are already selected for mining.

• The depreciation costs, general and administrative costs (G & A) and the opportunity costs are not included in the cutoff grade.

• The basic assumption is that all of these costs including fixed costs defined as G & A will be paid by the material whose grade is much higher than the established cutoff grades.

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Summary of the Traditional Cutoff Grades

• The ultimate pit limit cutoff is used to ensure that no material (unless they are in the way of other high grade blocks) is taken out of the ground unless all of the direct costs associated with gaining the metal can be recovered. (This assurance is automatically built into the ultimate pit limit determination algorithms like Learchs – Grossmann and Moving Cone)

• The milling cutoff is used to ensure that any material that provides positive contribution beyond the direct milling, refining and marketing costs will be milled.

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Shortcomings of the Traditional Cutoff Grades

• They are established to satisfy the objective of maximizing the undiscounted profits from given mining operation.

• They are constant unless the commodity price and the costs change during the life of the mine.

• They do not consider grade distribution of the deposit.

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Yearly Tons and Grades Schedules by Constant Cutoff Grades

• Define:Qm: Amount of total material mined in a given year (Mtons)

Qc: The ore tonnage processed by the mill (Mtons)

Qr: The recovered gold (koz)

• The annual cash flows:

Profits ($M) = (P - s) * Qr – Qc * c – Qm * m

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Yearly Tons and Grade Schedules by Constant Cutoff Grades

• Mining the deposit with traditional milling cutoff grade of 0.035oz/ton at 1.05M tons milling capacity (Table3):



1 0.035 0.102 3.6 1.05 96.3 33.0

2 0.035 0.102 3.6 1.05 96.3 33.0

3 0.035 0.102 3.6 1.05 96.3 33.0

4 0.035 0.102 3.6 1.05 96.3 33.0

5 0.035 0.102 3.6 1.05 96.3 33.0

6 0.035 0.102 3.6 1.05 96.3 33.0

7 0.035 0.102 3.6 1.05 96.3 33.0

8 0.035 0.102 3.6 1.05 96.3 33.0

9 0.035 0.102 3.6 1.05 96.3 33.0

10 0.035 0.102 3.6 1.05 96.3 33.0

11 to 34 0.035 0.102 3.6 1.05 96.3 33.0

35 0.035 0.102 3.4 1.00 91.7 31.4

Total 125.8 36.7 3,365.9 1,154.2

(NPV@15%)

$218.5

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Yearly Tons and Grades Schedules by Constant Cutoff Grades (NPV Calculation)

• NPV of the project:

NPV = 33.0(1 + 0.15)1

33.0(1 + 0.15)2

+ 33.0(1 + 0.15)3

+

33.0(1 + 0.15)4

+ 33.0(1 + 0.15)5

+ …

33.0(1 + 0.15)34

+

= $218.5M

31.4(1 + 0.15)35

+

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Summary of Constant Cutoff Grade

• Total 28.44M tons is mined (Avg. grade 0.102 oz/ton)

• Overall stripping ratio: 1: 2.42

• Mine life: 35 years

• Undiscounted profits: $1154.2M

• NPV: $218.5M

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Declining Cutoff Grade

• Traditional cutoff grade (constant cutoff grade) does not maximize the NPV.

• Many approaches have been suggested such that NPV is improved.

• Using cutoff grade higher than breakeven grades during the early years for a faster recovery of capital investments and using breakeven grades during the later stages has been practiced in the industry.

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Heuristic Cutoff Grade

• The traditional cutoff grade is modified so that they include depreciation, fixed costs and minimum profit per ton required for a period of time to obtain a much higher cutoff grade during the early years.

• After the end of the initial period, minimum profit requirement is removed from the equation to lower the cutoff grades further until the plant is paid off.

• At that point, the depreciation charges are also removed.

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Concept of Heuristic Cutoff Grade

• The concept is demonstrated pictorially as follows:

Idealized cross section of a series of pits for various cutoff grades

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Capital Cost

• Assume:

Capital Cost: $105M (Depreciated during the first 10 years)

• Depreciation cost per year

$105M / 10 yrs = $10.5M / yr

• Depreciation cost per ton

$10.5M / 1.05M tons = $10 / ton of ore

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Minimum Profit

• Assume:

Minimum profit of $3.0 per ton will be imposed to increase the cash flows further during the first five years

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Heuristic Cutoff Grade Calculation

• The milling cutoff grades will be:

g milling = Milling Cost + Depreciation + Minimum Prof.


$19/ton + $10/ton + $3/ton


= 0.060 oz/ton

Yr 1 to 5

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Heuristic Cutoff Grade Calculation (Cont.)

g milling = Milling Cost + Depreciation


$19/ton + $10/ton


= 0.054 oz/ton

Yr 6 to 10

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Heuristic Cutoff Grade Calculation (Cont.)

g milling = Milling Cost


$19/ton


= 0.035 oz/ton

Yr 11 to Depletion

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Yearly Tons and Grade Schedules

• The year by year tons and grade schedule obtained modified cutoff grade policy (Table4):



1 0.060 0.153 6.9 1.05 144.6 57.8

2 0.060 0.153 6.9 1.05 144.6 57.8

3 0.060 0.153 6.9 1.05 144.6 57.8

4 0.060 0.153 6.9 1.05 144.6 57.8

5 0.060 0.153 6.9 1.05 144.6 57.8

6 0.054 0.141 6.0 1.05 132.8 51.9

7 0.054 0.141 6.0 1.05 132.8 51.9

8 0.054 0.141 6.0 1.05 132.8 51.9

9 0.054 0.141 6.0 1.05 132.8 51.9

10 0.054 0.141 6.0 1.05 132.8 51.9

11 to 27 0.035 0.102 3.6 1.05 96.3 33.0

28 0.035 0.102 0.3 0.09 8.1 2.8

Total 125.8 28.44 3,032.1 1,112.7

(NPV@15%)

$355.7

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Summary of Modified Cutoff Grade

• Again, a total 28.44M tons is mined (Avg. grade 0.106 oz/ton)

• Overall stripping ratio: 1: 3.88

• Mine life: 25 years

• Undiscounted profits: $1112.7M (3.6% reduction from Table3)

• NPV: $355.7M (63% increase from Table3)

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Heuristic Cutoff Grade (Including G & A)

• Assume:

Fixed Costs per year: $8.35M / year

Fixed Costs per ton: ($8.35M/year) / (1.05Mtons/year)

= $7.95 / ton

• In the previous calculations, the G & A costs were not included in the cutoff grade and profit calculations.

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Heuristic Cutoff Grade Calculation (With G & A)

• The milling cutoff grades will be:

g milling = Milling Cost + Depreciation + Minimum Prof. + Fixed cost


$19/ton + $10/ton + $3/ton + $7.95/ton


= 0.075 oz/ton

Yr 1 to 5

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Heuristic Cutoff Grade Calculation (With G & A) (Cont.)

g milling = Milling Cost + Depreciation + Fixed cost


$19/ton + $10/ton + $7.95/ton


= 0.069 oz/ton

Yr 6 to 10

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Heuristic Cutoff Grade Calculation (With G & A) (Cont.)

g milling = Milling Cost + Fixed cost


$19/ton + $7.95/ton


= 0.050 oz/ton

Yr 11 to Depletion

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Yearly Tons and Grades Schedules

• The year by year tons and grade schedule obtained modified cutoff grade policy that includes fixed costs (Table5):



1 0.075 0.182 9.2 1.05 171.6 62.8

2 0.075 0.182 9.2 1.05 171.6 62.8

3 0.075 0.182 9.2 1.05 171.6 62.8

4 0.075 0.182 9.2 1.05 171.6 62.8

5 0.075 0.182 9.2 1.05 171.6 62.8

6 0.069 0.169 8.2 1.05 160.0 57.1

7 0.069 0.169 8.2 1.05 160.0 57.1

8 0.069 0.169 8.2 1.05 160.0 57.1

9 0.069 0.169 8.2 1.05 160.0 57.1

10 0.069 0.169 8.2 1.05 160.0 57.1

11 to 17 0.050 0.132 5.4 1.05 124.8 39.5

18 0.050 0.132 1.3 0.26 30.5 9.6

Total 125.8 18.11 2,562.5 885.6

(NPV@15%)

$357.1

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Summary of Modified Cutoff Grade with Fixed Cost Included

• The policy of declining cutoff grades calculated with depreciation, minimum profit, and the G & A cost further improved the NPV of the deposit by 1% ($355.7M vs. $357.5M)

• Overall undiscounted profits were adversely reduced by 20% ($1112.7M vs. $885.6M)

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Lane’s Approach

• Declining cutoff grades throughout the mine life gives higher NPV.

• The question is, “How should the cutoff grades be determined to obtain the highest NPV?”

• K. F. Lane discussed the theoretical background, a general formulation, and a solution algorithm.

Read “Choosing the Optimum Cutoff Grade” by K.F. Lane

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Lane’s Approach (Cont.)

• Lane showed that cutoff grade calculations that maximize NPV have to include the fixed costs associated with not receiving the future cash flow quicker due to the cutoff grade decision taken now.

• Underlying philosophy in inclusion of the opportunity cost is that every deposit has a given NPV associated with it at a given point in time and that every ton of material processed by the mill during a given year should pay for the cost of not receiving the future cash flows by one year sooner.

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Cutoff Grade Equation for Lane’s Approach

• The cutoff grade equation that maximizes the NPV of the deposit constrained by the mill capacity is:

g milling (i) = c + f + Fi

(P - s) * y

Where i = 1, …, N (mine life), gmilling(i) is the cutoff grade to be used in Year i.

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Cutoff Grade Equation for Lane’s Approach (Cont.)

• Fi is the opportunity cost per ton of ore in Year i and it is defined as:

Fi = d * NPVi / C

• f is defined as:f = fa / C

Where d is the discount rate; NPVi is the NPV of the future cash flows of the years (i) to the endof mine life;fa is the annual fixed costs

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Yearly Tons and Grades Schedules

• The year by year tons and grade schedule resulted from Lane’s approach (Table6):

Avg Qm Qc Qr Profits NPV

Year (i) COG Ore Grade (Mtons) (Mtons) (ktons) ($M) ($M)

1 0.161 0.259 18.0 1.05 245.2 95.9 413.8

2 0.152 0.255 17.2 1.05 241.0 94.4 380.0

3 0.142 0.25 16.5 1.05 236.4 92.6 342.6

4 0.131 0.245 15.7 1.05 231.3 90.5 301.4

5 0.120 0.239 14.9 1.05 225.7 88.1 256.1

6 0.107 0.232 14.1 1.05 219.6 85.4 206.4

7 0.092 0.213 12.1 1.05 200.9 76.7 152.0

8 0.079 0.188 9.8 1.05 177.9 65.9 98.1

9 0.065 0.163 7.6 1.05 153.6 53.9 46.9

Total 125.8 9.45 1,931.4 743.4

(NPV@15%)

$413.8

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Steps to Obtain Table 6 (1st Iteration)

Avg Waste Ore SR Qm Qc Qr Profits NPV Year (i) NPVi Cog Ore Grade (Mtons) (Mtons) (Mtons) (Mtons) (ktons) ($M) ($M)

1 0 0.050 0.133 101.5 24.0 4.2 5.5 1.05 125.7 39.9 $255.02 0 0.050 0.133 97.1 23.0 4.2 5.5 1.05 125.7 39.9 $253.43 0 0.050 0.133 92.6 21.9 4.2 5.5 1.05 125.7 39.9 $251.54 0 0.050 0.133 88.2 20.9 4.2 5.5 1.05 125.7 39.9 $249.35 0 0.050 0.133 83.7 19.8 4.2 5.5 1.05 125.7 39.9 $246.86 0 0.050 0.133 79.3 18.8 4.2 5.5 1.05 125.7 39.9 $243.97 0 0.050 0.133 74.9 17.7 4.2 5.5 1.05 125.7 39.9 $240.6…21 0 0.050 0.133 12.7 3.0 4.2 5.5 1.05 125.7 39.9 $86.622 0 0.050 0.133 8.3 2.0 4.2 5.5 1.05 125.7 39.9 $59.723 0 0.050 0.133 3.8 0.9 4.2 5.1 0.91 108.9 33.1 $28.7

Total 125.8 24.0 2,874.0 910.8 (NPV@15%)

$255.0

Year 1: Cog= 19+8.35/1.05+(0*0.15)/1.05 = 0.050(600-5)*0.9

Year 2: Cog= 19+8.35/1.05+(0*0.15)/1.05 = 0.050(600-5)*0.9

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Steps to Obtain Table 6 (2nd Iteration)

2nd iterationAvg Waste Ore SR Qm Qc Qr Profits NPV

Year (i) NPVi Cog Ore Grade (Mtons) (Mtons) (Mtons) (Mtons) (ktons) ($M) ($M)1 $255.0 0.118 0.238 116.6 8.9 13.1 14.8 1.05 224.9 87.8 $399.52 $253.4 0.118 0.238 102.9 7.9 13.1 14.8 1.05 224.9 87.8 $371.73 $251.5 0.117 0.236 89.1 6.8 13.1 14.8 1.05 223.0 86.6 $339.74 $249.3 0.117 0.236 74.5 5.7 13.1 14.8 1.05 223.0 86.7 $304.05 $246.8 0.116 0.236 61.6 4.8 12.9 14.6 1.05 223.0 86.8 $262.96 $243.9 0.115 0.236 48.2 3.8 12.9 14.5 1.05 223.0 86.9 $215.57 $240.6 0.115 0.236 34.8 2.7 12.9 14.6 1.05 223.0 86.9 $160.98 $236.8 0.114 0.235 20.0 1.6 12.9 14.6 1.05 222.1 86.3 $98.29 $232.4 0.112 0.234 7.0 0.5 15.6 7.5 0.45 94.8 30.5 $26.6

Total 125.0 8.9 1,881.8 726.4 (NPV@15%)

$399.5

Year 1: Cog= 19+8.35/1.05+(255*0.15)/1.05 = 0.118(600-5)*0.9

Year 2: Cog= 19+8.35/1.05+(253.4*0.15)/1.05 = 0.118(600-5)*0.9

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Steps to Obtain Table 6 (3rd Iteration)

3rd iterationAvg Waste Ore SR Qm Qc Qr Profits NPV


Total 125.8 9.5 1,925.0 739.7 (NPV@15%)

$411.81

Year 1: Cog= 19+8.35/1.05+(399.5*0.15)/1.05 = 0.157(600-5)*0.9

Year 2: Cog= 19+8.35/1.05+(371.7*0.15)/1.05 = 0.149(600-5)*0.9

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Steps to Obtain Table 6 (4th Iteration)

4th iterationAvg Waste Ore SR Qm Qc Qr Profits NPV


Total 125.8 9.5 1,922.1 738.0 (NPV@15%)

$412.30

Year 1: Cog= 19+8.35/1.05+(411.8*0.15)/1.05 = 0.160(600-5)*0.9

Year 2: Cog= 19+8.35/1.05+(378.7*0.15)/1.05 = 0.151(600-5)*0.9

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Table 6

Table 6Avg Waste Ore SR Qm Qc Qr Profits NPV

Year (i) NPVi Cog Ore Grade (Mtons) (Mtons) (Mtons) (Mtons) (ktons) ($M) ($M)1 $413.8 0.161 0.259 18.0 1.05 244.8 95.7 $413.82 $380.0 0.152 0.255 17.2 1.05 241.0 94.4 $380.23 $342.6 0.142 0.250 16.5 1.05 236.3 92.5 $342.84 $301.4 0.131 0.245 15.7 1.05 231.5 90.6 $301.75 $256.1 0.119 0.239 14.9 1.05 225.9 88.2 $256.36 $206.4 0.105 0.232 14.1 1.05 219.2 85.2 $206.67 $152.0 0.091 0.2131 12.1 1.05 201.4 77.0 $152.38 $98.1 0.077 0.188 9.8 1.05 177.7 65.7 $98.29 $46.9 0.063 0.163 7.6 1.05 154.0 54.3 $47.2

Total 125.8 9.5 1,931.7 743.7 (NPV@15%)

$413.82

Year 1: Cog= 19+8.35/1.05+(413.8*0.15)/1.05 = 0.161(600-5)*0.9

Year 2: Cog= 19+8.35/1.05+(380.0*0.15)/1.05 = 0.152(600-5)*0.9

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Summary of Lane’s Approach

• Lane’s approach gives 90% higher NPV and 35% lower undiscounted profits than constant cutoff grade (Table3).

• Total tons mined are the same.

• Tons milled is lower (36.7Mtons vs. 9.45Mtons)

• Ounces of gold recovered is lower (3.37Moz vs. 1.93Moz)

• Mine life is significantly shorter (36yrs vs. 10yrs)

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Cutoff Grade Optimization 2

• How to determine a cutoff grade policy where

Mining capacity, milling capacity, and refining capacity may be limited,AndMaximizing NPV of the projects

Read “An NPV Maximization Algorithm For Open PitMine Design” by Dr. Dagdelen

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Definition of the Problem

• The problem is to maximize the NPV subject to production constraints:Maximize ∑

=+

=N

id iiprofitNPV

1)1(

1*)(

Subject to MiQm ≤)( for i = 1,…N

CiQc ≤)( for i = 1,…N

RiQr ≤)( for i = 1,…N Where

i: Year indicator

N: Mine life in yearsQm: Amount of total metal mined in a given year (Ore + Waste)

Qc: Ore tonnage processed in a given year

Qr: Recovered metal (in tons) in a given year

M: Annual mining capacity in tonsC: Annual milling capacity in tonsR: Annual refinery capacity in tons

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Derivation of Opportunity Costs of Mining Low Grades

• Define:

V: Maximum possible present value of future profits (cash flows) from the operation (NPV of total operation)

Profits ($M): Profits (Cash flow) from mining Qm amount of material

Vq: Maximum possible present value of future profits (cash flows) after the next Qm amount of material has been mined

v=V-Vq: Marginal increase in present value to be achieved by mining next Qm of material

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Derivation of Opportunity Costs of Mining Low Grades (Cont.)

TdVqMprofits

V)1(

))($(+

+=

))($()1(* VqMprofitsdV T +=+

If i is relatively small, then )*1()1( Tdd i +=+

VqMprofitsTdV +=+ )($)*1(*

VqMprofitsTdVV +=+ )($**

TdVMprofitsVqV **)($ −=−

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Derivation of Opportunity Costs of Mining Low Grades (Cont.)

Let v=V-Vq then

TVdMprofitsv **)($ −=

The opportunity cost of taking low grades now when higher grades are still available

We need to set cutoff grade so that we do not delay high grade

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Basic Present Value Expression

• Annual profits can be calculated as follows:

TVdTfQmQcQsrPv mcr ******)( −−−−−−=

WhereP: Metal price per ton of productr: Marketing cost per ton of product

c: Processing cost per ton of orem: Mining cost per ton of ore

f: Annual fixed administrative costs

s: Sales cost per ton of product

T: Number of time periods that will take to mine, concentrate and refine Qm amount of material from the pit (i.e. years)

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Mine Limiting Case

• When the mining capacity is the bottleneck in the system:

MQ

T m=

mcrm QM

VdfmQcQsrPv *

)*(**)(

+

+−−−−=

COG

vm

vm is a function of cutoff grades

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COG of Mine Limiting Case

• Cutoff grade of mine limiting case is:

ysrPc

gm *)( −−=

where

y: Metallurgical recovery

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Concentrator Limiting Case

• When the concentrator capacity is the bottleneck in the system:

CQ

T c=

mcrc QmQC

VdfcQsrPv **

)*(*)( −

+

+−−−=

• Cutoff grade of concentrator limiting case is:

ysrPC

Vdfc

gc *)(

)*(

−−

++

=

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Refinery Limiting Case

• When the refinery capacity is the bottleneck in the system:

RQ

T r=

mcrr QmQcQR

VdfsrPv ***)

)*(( −−

+−−−=

• Cutoff grade of refinery limiting case is:

yR

VdfsrP

cg r

*)*(

+−−−

=

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Balancing Cutoff Grade (Cont.) Mine - Mill

C/M

g mc

12

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Balancing Cutoff Grade (Cont.)Mine - Refinery

R/M

g mr

13

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Balancing Cutoff Grade (Cont.)Mill - Refinery

R/C

g rc

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Open Pit Copper Case StudyDeposit Reserves

(Mtons)(%Cu)

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First Year Production Reserves

(Mtons)(%Cu)

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Open Pit Copper Case Study Unit of mining: ton

Price (P): $25/ 1%Cu of one unit of mining

(=$25/1%Cu*1ton = $25/0.01tonCu = $25/20lbsCu

= $1.25/lbCu)

Mining Cost (m): $1/ one unit of mining = $1/ton

Concentrator Cost (c): $2/ one unit of mining = $2/ton

Refinery Cost (s): $5/ 1%Cu of one unit of mining

Fixed Cost (f): $300M /yr

Mine capacity (M): 100M one unit of mining /yr = 100Mtons/yr

Concentrator capacity (C): 50M one unit of mining /yr = 50Mtons/yr

Refinery capacity (R): 40M of 1%Cu of one unit of mining /yr

(=40M*0.01tonCu /yr = 400k tons Cu /yr)

Recovery (y): 100%

Discount rate (d): 15%

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Mine Limited Case

(V=0) (V=1174)

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Concentrator Limited Case

(V=0) (V=1174)

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Refinery Limited Case

(V=0) (V=1174)

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Balancing Cutoff Grade

Balancing Cutoff Grades (V=0)

-300

-200

-100

0

100

200

300

400

500

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

COG

Pro

fit vm

vc

vr

gm gr

gc

Gopt

Feasible Region

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Balancing Cutoff Grade

Balancing Cutoff Grades (V=1174)

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

COG

Pro

fit vm

vc

vr

Gopt

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Limiting Economic Cutoff Grades

CuCutonCu

tonysP

cg m %10.0%

1*)525(2

1*)1*%1/)($525()/($2

*)(=

−=

−=

−=

• Cutoff grade of mine limiting case is (V=0):

• Cutoff grade of concentrator limiting case is (V=0):

CuCutonCu

yrtonMyrM

ton

ysPC

Vdfc

g c %40.0%1*)525(

50300

2

1*)1*%1/)($525()/(50)/($300

)/($2

*)(

)*(

=−

+=

−

+=

−

++

=

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Limiting Economic Cutoff Grades (Cont.)

• Cutoff grade of refinery limiting case is (V=0):

( ) 1*))/1*%1(40

)/($300)1*%1/($525

)/($2

*)*(

−−

=

+

−−=

yrtonCuMyrM

tonCu

ton

yR

VdfsP

cg r

CuCu %16.0%1*

40300

525

2=

−−

=

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Grade – Tonnage Curve

25

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Average Grade Above Cutoff

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Ore : Material Ratio

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Product : Material Ratio

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Product : Ore Ratio

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Grade – Tonnage Relationship

Cutoff Quantity Tons Below Tons Above Avg Grade Cu Produced Ore to Product to Product to Ore to(%Cu) (Mtons) Cutoff Cutoff Above Cutoff (%Cu of Material Material Ore Waste

(Mtons) (Mtons) (%Cu) 1ton of Material) Ratio Ratio Ratio Ratio(C ) ( R) (C/M) (R/M) (R/C)

0.00 100 0 1000 0.500 500 1.0 0.500 0.500 0.00

0.10 100 100 900 0.550 495 0.9 0.495 0.550 0.11

0.20 100 200 800 0.600 480 0.8 0.480 0.600 0.25

0.30 100 300 700 0.650 455 0.7 0.455 0.650 0.43

0.40 100 400 600 0.700 420 0.6 0.420 0.700 0.67

0.50 100 500 500 0.750 375 0.5 0.375 0.750 1.00

0.60 100 600 400 0.800 320 0.4 0.320 0.800 1.50

0.70 100 700 300 0.850 255 0.3 0.255 0.850 2.33

0.80 100 800 200 0.900 180 0.2 0.180 0.900 4.00

0.90 100 900 100 0.950 95 0.1 0.095 0.950 9.00

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Balancing Economic Cutoffs

gmc: Ore : Material = C:M = 50M/100M =0.5

Then, from the table above gmc= 0.50 %Cu

gmr: Product : Material = R:M = 40M/100M =0.4

Then, from the table above gmr= 0.45 %Cu

grc: Product : Ore = R:C = 40M/50M =0.8

Then, from the table above grc= 0.60 %Cu

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Choosing Optimum Cutoff Grade

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Choosing Optimum Cutoff Grade

Gmc = 0.40%Cu Grc = 0.40%Cu Gmr = 0.16%Cu Then, Gopt = 0.40%Cu

strategic open pit mine planning course.pdf

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