hand method

8/13/2019 Hand Method

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Ben jamin C. KoskiniemiA M A X A r iz o n a I nc .

Benjamin C. Koskiniemi s currently the manager ofmining and geology for AMAX Arizona Inc. Hegraduated from Michigan College of Min ing andTechnology with a B.S. i n mining engineering and aB.S. in engineering administration. He has occupiedthe following positions: mining engineer for Kenne-cott Copper Corp. in Salt Lake City mine evaluationengineer of AMAX in Denver and mining engineerand later chief mine engineer of ANAMAX Min ing Co.


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Introduction SURFACEhen evaluating any ore body, one of the first ques- OVERBURDENtions concerns the ore reserves. In the case of a n open TOP OF ROCKplt mine, thls 1s not possible to answer reliably untilthe ultimate final) pit limits have been established.

Techniques used in designing an ultimate pit are classed WASTE R O C Kas 1 ) manual , 2 ) computer, and 3 ) com b~nedmanual-computer. This chapter will describe howmanual techniques can be ut~lized n designing an ultl-mate pit Certaln econom ic and deslgn criteria mustbe established before the actual design begins In orderto be g ~ n esigning an ultimate pit, it wlll be assumedthat the engineer already has the following data avail-able 1 vertlcal sections, 2 ) horizontal sections foreach level, 3 ) stripping curve, 4) bench height, 5 )bank slope angle between levels, 6 ) level berm width, ORE BLOCKS YLEVEL WITH7 ) roadway width, 8) pit slope angles at ultimate GRADE ( Ipit 11mits estimated average including roads and rampsand between roads and ramps), and 9 ) mlnimumwidth of pit bottom. Fig 2 Vertical sectionw h ~ c h onsist of cross, longitudinal, and rad ial sectionsDesign as illustrated in Flg. 1. These sections should includeHand methods of ultimate pit design usually begin the mineral block inventory and surface topography aswith vertical sections Soderberg and Rausch, 1968 ) minimum requirements. An exam ple of a vertical sec-he pit limits are first located on the vertical sections, tion 1s presented in Fig. 2. If the re are materials ofsignificantly different specific gravity, these area s shou ldLONGITUDINAL SECTION also be identified. This is especially imp ortan t whenthe stripping ratio is on a tonnage basis, metric tonswaste:metric tons ore short tons waste:short tons or e) .

The pit slope angles to be used when working withthe vertical sections are the average angles, which in-clude allowances for haul roads and ramps. Theseangles see Fig. 3) a re approximated, based on pre-

HAUL ROAD

AVERAGE PITSLOPE ANGL

ORE LINE PIT SLOPE ANGLE ABETWEEN ROADSFig 1 Plan of ore body Fig 3 Pit slope angles


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190 Open Pit Mine Planning and Design

O R E G R D E CuFig. 4. Stripping curve.

Itminary estimates of anticipated p ~ t imensions, roadand ramp requirements, and pit slope stability studiesThe p ~ timits are located on each section so the oregrade along the pit limit line supports a stripping ratiocorresponding to the break-even or allowable strippingratio. Illustrated In Fig. is the stripping curve used toevaluate the typlcal sections. Break-even strippingratio signifies that the costs used include all directcosts. Depreciation is usually also included Allow-able stripping ratio usually signifies use of a profit factorin addition to direct costs and depreciation Erick son,196 8) An illustration from Halls 19 70 ) that depictsthe pit limits based o n use of th ese different cost a s-sumptions is shown in Fig. 5. The design methodsdescribed apply to any of the cost assumptions. If th estripping curve includes depreciation and profit, it maybe prudent to at least locate the surface intercept forthe direct cost pit to ensure that permanent plant facili-ties and waste dumps are not planned within theselimitsLocatlng the pit limit on each vertical section is atrial and error process usually requiring a number ofapproxim ations. Considerable judgment is required onthe part of the engineer durin g each phase of the designprocess. By visually observing the ore grad e distribu-tion on the sections and relating these to the break-evenstripping ratios, a first pit limit approximation is arbi-trarily made . T he grade of the ore along the pit limitintercept selected is calculated, and the break-even

REVENUE COVERS COSTSAND DEPRECIATION

REVENUE COVERS COSTONLY . DOES NOT PROVIDE ACONTRlBUTlON TOWARDSDEPRECIATIONFig. 5. Economic pit limits Halls, 1970 .stripping ratio is determined from the stripping curve.The lengths of ore and waste along the pit limits aremeasured, and the stripping ratio W:O) is calculatedon the basis of these measurem ents adju sting, whennecessary, for changes in specific gra vity ). Th e calcu-lated stripping ratio is compared to the break-evenstripping ratio for the grade calculated and if the calcu-lated ratio is less than break-even, the pit limits areexpanded; but, if the calculated ratio is greater, the pitlimits are reduced in size. These approx imations con-tinue until the pit limit is found that conforms to thestripping curve.Each ore body and each section within an ore bodyusually presents a different set of conditions In Fig. 6,the pit bottom is in waste; therefore, only the ore grade

SURFACE

Fig. 6. Pit limits, bottom in waste.


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Hand Methods 191and ore waste intercepts along the slope lines are usedIn determining the break-even strrpping ratios andlocatlng the final plt limits. Eac h slope is evaluated~ndependently.On the right side, the grade is estimatedat 0 8 Cu, and thls supports a break-even strippingratio of 6: waste:ore) as determined from the strip-ping curve in Fig. 4. Assuming that this grade wlll bethe same along any slope llne in this area, the line isfound that gives a 6:l ratio at the designed averagefinal plt slope angle:

leng th of X Y wastelength of Y Z ore 1On the left side, the estimated 0 6 Cu grade sup-ports a 3.2.1.0 break-even stripping ratio, and theslope line meeting this condition is located. If the oregrade changes as the slope llne is moved, the requiredbreak-even stripping ratio is also changed.In Fig 7, the ore extends to depth, and therefore,the plt bottom w ~ ll e In ore. Th e pit bottom IS de-signed at ~ t s inimum width, and the ore along thebottom is also used to calculate the break-even strip-

pin ratios. Eac h slope is assumed to be ~nfluen cedby one-half of the ore exposed along the pit bottomFrom Fig. 4, a grade of 0.52 Cu has a break-evenstr~pp ing atio of 2.1, nd the ul t~ ma te it slope meet-Ing this condition 1s located :

length of X Y waste -leng th of Y Z 2 oreIn Fig. 8, the ore extends to depth on an incline

wlth the pit bottom and one slope completely In ore.SURFACE

WASTE

Fig. 8 Pit limits bottom and slope in ore.The pit bottom is designed at its minimum width, andthe ore along the entire bottom IS used to calculate thebreak-even stripping ratio for the slope in waste.Equating pit limit distances directly is acceptablewhen working with parallel sections, but it can be veryInaccurate when dealing with rad ial sections. Fig. 9

Fig. 7 Pit limits bottom in ore. Fig.9 Radial section area of influence.


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192 Open Pit Mine Planning and Designillustrates, in plan, why it IS not feaslble to locate thefinal pit limlt on a vertical radial section simply bydlvldlng the waste dlstance by the ore dlstance whendetermining the break-even strlpplng ratlo. On thebasis of simple geometrlc shapes, the stripping ratio inplan is approximately 7.5: 1, if the waste length XYIS twlce the ore length Y Z Th e stripplng ratlo on thevertical sectlon would actually be measu red at 2. 1. Ifthe surface Intercept was at X with X Y being equal toYZ, the stripplng ratio in plan is 3 : 1. On the verticalsectlon, ~t would measu re a t 1 :1. This means that thebreak-even strlpping ratio as determined from thestrlpping curve must be adjusted before being appliedto a vertical radial sectlon. In this example, Flg. 1 0illustrates the correction factors required to measuredistances directly In loca ting the pit llmits on the radlalsectlons.When the ultlmate plt limits have been located oneach of the vertical sections, a preliminary ore reservecan be estimated from the sectlons Flrst, the plt 11mlton each section must be compared to the adjolnlngsections to see that a logical relationship exlsts inregard to mlnabillty of the ore body. When calcu latingtonnages, parallel sectlons usually do not present aproblem, and the area of influence is taken as halfwaybetween adjolnlng sections In the case of radial sec-tions, the tonnages can be calculated by methods dls-cussed by Popoff (1966) or by the sector methodsfirst discussed by Soderberg (1 95 9) .

The final ore reserve estlrnates are calculated fromlevel plans (horizontal sections) wlth the plt limits foreach level determined from a composite mlne plan m ap.The mine plan map IS constructed from the verticalsections. As the first step In prep ring the composite,the locations of the pit bottom and the surface mter-cepts of the plt l~ m its re transferred from the vertlcalsectlons to the plan m ap. If a vertical section does nothave a single continuous slope llne from the pit bottomto the surface intercept, any changes are also trans-ferred to the plan map. Th e ore Intercepts can also belocated, if desired.The actual designing of the composite plan generallybegins with the pit bottom. The points from the sec-tions usually present a very irregular pattern, bothvertically and horizontally. In smooth~ ng hese anddesigning the bottom bench, the engineer has severalthings to keep in mind. ( 1 ) averaging the break-evenstripping ratios for adjoining sections, (2) use of simplegeometrlc patterns for ease of design, 3 ) location oframp to pit bottom, and (4) watching for patterns thatmlght lead to slope stability problems.

It should be remembered that the design is Intendedto optimize ore recovery and maximize profits; there-fore, the design configuration must follow the ore, butbecause thls is usually a cut and try method, the simplerthe geometric shape of the bottom level, the easier it isto deslgn the remainde r of the plt.Th e llne plotted for each level on the composite planis generally the median line, which is the contour eleva-tion midway between the level elevation and the eleva-tion of the next higher level, as shown in Flg. 11. Thefinal pit limit dewgn will also usually include any roadsthat wlll be in the final pit slope. In prellmlnary de-signs, the roads sometimes are not shown, and theX DENOTES LOCATIO N OFLEVEL MEDIAN LINES

nap~~flANGLELEVEL BERMlDTH

FINAL PIT LIMIT

M E A S U R E D S T R I P P I N G R A T I O BENCH HEIGHTON RADIAL SECTION Fig. 11 Location of median lines section

Fig. 10 Stripping curve for radial section. A-A of Fig. 12.


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Hand Methods 93medlan llnes will be based on the flatter average overallpit slope.Once the bottom level has been established, the p ~ tdeslgn progresses toward th e surface. Polnts for thelevel median lrnes are located on the plan map, andthese are usually uniformly spaced and are dependenton the angles of the final plt slopes. Th e poin ts for eachlevel are connected to complete the design, as shown InFig. 12. Care must be exercised, especlally if dlfferentarea s of th e pit have dlfferent slope angles.It S also Important that condltlons that can lead toslope fallures are not incorporated Into the pit deslgn.An example of thls would be an area that bulges Intothe plt, especlally in a potentially unstable area

When the composlte ultlmate plt plan IS completed,the plt l l m~ ts re transferred to the lndlv~ dual evelplans see Flg. 13 . The plt can then be dlvlded Intosectors to determine whether the break-even strippingratlo requirements have been achieved. Th ls can bedone by measuring the lengths of ore and waste oneach level at the pit llm~twlthin a glven sector Thiswlll provide the data for calculating the actual strlpplngratio along the plt limit intercept. Th e or e grade iscalculated by me suring the lengths of the dlfferent orezones exposed in the sector and gettlng a weighted

EDIAN L I N E

WASTE BLOCK ASSAYS ( jFig 13. Level plan with ultimate p it limitaverage grade. Th e strlpplng curve IS checked to deter-mine what break-even strlpplng ratlo goes with thecalculated grade, and thls ratio is compared to thecalculated stripplng ratlo. If there are any anomal oussectors, the plan can be revlewed to see how ~t m ~ gh tbe affected ~ ~t were shlfted In a given direction.

The stripplng ratlos at the plt llmlts can also bedetermlned for each sector by overlaying the composlteplan on the individual level plans and marking the orecontacts on the composlte plan and planlmeterlng theore and waste zones. Th e stripping r at ~ o s an also becompared by transferring the plt limits from the ulti-mate plt plan to the vertlcal sectlonsIt should be kept in mind that the break-even andallowable strlpplng ratlos are the ratlos at the final pltsurface and do not reflect the overall stripplng ratlofor a sectlon, sector, or the entire ore body.The final ore reserves and overall strlpplng ratios aredetermlned from the level maps. Th e ore tons andgrade, and the waste tons wlthln the ultlmate plt I lm~ ts,are determined for each level, and these are accumu-lated to arrive at the mlne totals. Ore 1s considered tobe that material within the pit limits havlng a gradeequal to or greater than the grade from the strippingFig 12. composite ultimate pit plan curve at a break -even strippin g ratlo of zero . Th ls 1s


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94 Open Pit Mine Planning and esigngenerally called the ore reserve cutoff grade. In Fig. 4,the cutoff grade is 0. 3% Dividing the total mine wastetons by the total ore tons results in the overall averages t r~ppi ngatio for the o re body.

Open pit vs. underground mlnlng is also a considera-t l on when h~ghstrlpplng ratlos are involved. Glll

1966), al though not mentlonlng underground mlnlng,states, high waste to ore ratios shou ld not be avoidedi there 1s enough grade, or value, to mine the materlalat a sui table profit . Pan a and Davey (1 97 3) statefur ther that, The dlstinctlon can best be made by de-terminlng which minlng method generates the largestnet profit.Conclusions

The ultimate (final) plt limits must be determinedbefore the ore reserves can be est imated. Ha nd meth-ods are still widely used, and although they are grad-ually being replaced by computer methods, it is surelynot becomlng a lost ar t . Even w ~ t hhe computer, someamount of hand de s~ gn s required In the prel lm ~narystages of evaluation an d as a check o n the final projectIn fact, there is probably no b et ter way for an englneerto get to know the ore body he IS worklng wlth than by

dolng some hand deslgn. T h ls s h o ul d giv e h ~ m o r econfidence in the results obtalned from computer tech-niques, if that IS his primary method of deslgn.ReferencesEnckson, J D 1968 Long-Range Open Pit Plannlng,Mining Engrneerrtlg Apr~ l , p . 75-78G111, D. K. 1966 Open Pit Plannlng, Mrtling CongressJournal July, pp. 48-51Halls, J L., 1970 The Bas~cEconomics of Open PltMinlng, Proceedrngs Symp os~um on the TheoreticalBackground to the Plannlng of Open Pit Mlnes w~thSpecla1 Reference to Slope Stabdlty, South Afrlcan In-s t~tute f Mlnlng and Metallurgy, JohannesburgPana, M T , and Davey, R K 1973 Pit Plannlng andDes~gn, SME Minrng Engrneerrng Handbook A. B.Cummins and Gwen, I A , eds., AIME, New York, pp10-17 17-19.Popoff, D. C 1966 Comput~ngReserves of Mlneral De-posits Prlnc~plesand Conventional Methods, Infor-

mation Clrcular 8283 US Bureau of MlnesSoderberg, A , 1959 Elements of Long-Range Open PltPlann~ng, M i r l ~ t ~ gongress Jorlrnal Aprll, pp. 54-58.62.Soderberg, A , and Rausch, D. O., 1968 Plt Plannlng andLayout, Surface Min ing E P. Pflelder, ed., AIM E,New York, pp. 141-165

hand method

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