Chapter 36 . . ' .

A SERIES OF COMPREHENSIVE OPTIMIZATION MODELS FOR SURFACE MINE LONG-TERM PLANNING

Zhang Youdi Li Kemin Shang Tab . .

Department of Mining Engineering China Institute of Mining and Technology

Xuzhou, Jiangsu, China

ABSTRACT

According to general guidelines, deposits suitable for surface mining can be divided into two basic cate- gories: horizontal or flat-bedded deposits and inclined or dip-buried deposits. A series of mathematical models for surface mine long-term planning (SMLTP) has been deve- loped and can be used for any kind of deposit. The basic theory and methodology of the models are oriented- graph simulation which combines graph and network theory with a systems simulation technique to form a new approach. From the viewpoint of surface mining and long-term plan modeling, the main differences between the two categories of deposits are analyzed, an important algorithm is put forward, and the structure of the models and some results of applications are introduced. Dynamic and comprehensive optimizations have been completed by the SMLTP model series. Combining different OR branches, the new approach has been proved to be a powerful tool to solve the strategic problems of surface mine planning.

O.R. IN LONG-TERM PLAYING

The main task of mine long-term planning is to solve the strategic

problems of a mining-project. Once a decision on long-term planning (e.g., on the mining sequence or haulage system) has been carried out, it is very difficult to change the sequential short-range.planning and operations stage of the mine.

Some O.R. methods have been employed in surface mine long-term planning. For instance, graph theory, dynamic programming and moving-cone simulation have been used in pit limit analysis (1,3,5); dynamic programming has also been used to optimize the scheduling of stripping and mining work (6) or cutoff grade and production rate (2).

. . In-many cases, however, the :

application of a single O.R. approach has its limitations, especially for the rigorous optimization methods (4) '

which usually ask for strict constraints and obtain a single optimization solution. The limitation of methodol-ogy has been an obstacle to the study of mine planning. In recent years there is a tendency to combine two or more different O.R. methods,together to solve complicated mining problems.

A new approach, oriented-graph simulation, which combines graph and network theory with a systems

376 21st APCOM PROCEEDINGS

simulation technique,' has been developed for surface mine long-term planning: (7). Actually it is a method of network simulation with a 3-D spatiality consideration.

BASICS OF A MINING-ORIENTED GRAPH

Mining areas at any location and any mining stage can be simulated and defined as an oriented.graph --- FIGURE 1. Mining-oriented graph. defined here as a cycle with clockwise direction. The basic parameters off an ,

oriented graph are as follows (see The spatial-oriented graph Fig. 1): system can be developed from the

bottom-oriented graph, as shown in i is the number of a node Fig. 2.

or a side, (xi, yi, zi) are the

three-dimensional coordinates oftnode i,

i - is the phase angle of

side is

Oi' is the .phase angle of the extension direction

, of side i, and (Ai, Bi, Ci), is the characteristic

label of side i -.

The-characteristics labels are defined as: . . ..r

0,. if i is an old side (mined border)

1, if i is a new side (mined border)

( 0, final b.nk 'slope of rock 1, working slope of rock 2, final loose material slope

. of rock 3,,re-stripping final slope of

rock . . . 4-7, for soil slope , , correspondingly ,,

1, located in the direction of top-wall +

2, located in the direction of f oo t-wall

3, located in the direction of , pit end 1

4, located in the direction of pit end 2

b

n Bottom ~rienied Graph Level. Oridnted Graphs

FIGURE 2. Spatial-oriented graph . system.

It has been found that this- approach is a powerful tool to' describe the development of the open pit as time goes on.

'MINING CHA~CTERIS~TICS~ OF DIFFERENT DEPOSITS ' ' . ,

According to mining technology, the characteristics of deposits suitable for surface mining can be divided into two basic categories:

(A) horizontal or flat-bedded deposits, and

(B) inclined or d'ip-buried' .deposits.

SERIES OF COMPREHENSIVE OPTIMIZATION MODELS

A series of mathematical models specified mining alternative, the for surface mine long-term planning vertical extending direction is (SMLTP) has been developed. The defined as shown in Fig. 3. corresponding models f o; different category of deposits are:

SMLTPl --- for category A and SMLTPZ --- for category B.

SMLTPl is associated with a 2-D ore deposit model, while SMLTP2 is associated with a 3-D ore deposit.

From the viewpoint of mining engineering, there are significant differences between the two categories of deposits, such as:

--- The overburden can be dumped into the mined out area for a horizontal or flat-bedded deposit, while few possibilities to do so exist for an inclined or dip-buried deposit.

--- In addition to the horizontal advance of the mining front in the plan, the vertical extension work of the open pit for an inclined or dip-buried deposit always exists as the mine advances.

--- The open pit has a rather large final pit limit in plan but is usually rather small in depth for a horizontal or flat-bedded deposit, while a rather large depth may exist for an inclined or dip-buried deposit.

--- Accordingly, .the mining sequence and the haulage development system are different in the two categories of deposits as well.

A few comments on the algorithm of long-term planning for inclined or dip-buried deposits will be briefly represented as follows.

VERTICAL EXTENSION OF AN OPEN CUT . , It is well-known that the

sequential extension of mining and stripping work in the vertical direction is an important link for inclined ore body mining. For a

u Characterized l e v e l s

L,r Other l e v e l s

, Angle o f v e r t i c a l extensiom . .,

FIGURE 3. Mining section showing the vertical extension.

Instead of giving the location and size of the box cut (working trench) at each mining level, we can only input the oriented-graph' parameters of a few characterized mining levels as shown in Fig. 3, while the other oriented graphs of the box cut at each level are developed by'means of a special interpolation subroutine. The. developed oriented graphs between two characterized drop levels are shoyn in Fig. 4.

FIGURE 4. Perspective drawing of developing oriented graphs by interpolation.

-..378 . .. 21st APCOM PROCEEDINGS

MINING QUANTITY AND ORE QUALITY

Based on the bottom-oriented graph at a specified box cut level as well as the open pit mining parameters, a frustum can be developed and the associated oriented graphs at each of the above.levels can be defined.

Because of the continuous vertical extension of the open pit, a frustum of the last mining step might be overlapped, even wholly involved, by the frustum of the following mining step at some lower location (Fig. 5). To obtain the exact mining and stripping volumes as well as the ore quality values at each level of each mining step, the mining topography has to be dynamically lowered to the mined-out boundary after the oriented graphs at each level have been scanned. As shown in Fig 5, after "mining" the frustum above level 7, the topography .is lowered from AEFC

to A'E'F'C'. The typical scanning area of an oriented graph at a level is also shown in Fig. 5.

VERIFICATION OF MINE PRODUCTION

A reasonable mine production is a very important factor in mining design work. Other than the consideration of market and economic factors, what is the maximum possible productivity of a surface mine according to the equipment selected and located in the open pit? It is quite convenient to solve this problem by means of a SMLTP model.

An actual production in units of t/a of a surface mine at any mining step is decided by the following formula :

where: Ai is the actual annual production of the mine .at mining step i, t/a, .

AP. is the annual mine

H - M

FIGURE 5. Volume scanning for a dip-buried deposit.

productivity limited by mining front advance intensity at mining step i, tla,

AW; is annual OB productivity limited by stripping front advance intensity at mining s.tep i, m3/a, ,

n is the stripping ratio at mining step i, m3/t,

AH is the annual mine productivity limited by the vertical extension rate at mining step i, t/a, and

AD is the planning mine production at mining stgp A i, t/a.

In the above formula, AP and AW can be derived from the mining an4 stripping front lengths by searching the oriented-graph side characteristic labels level by level, as well as the corresponding possibly allocated loading machines and their productivities (reference 8).

SERIES OF COMPREHENSIVE OPTIMIZATION MODELS

3-Dimonsiomal Final pit ore deposit limit

I ' Mining and stripping scheduling optimization 1

+ +

' 1 program I

Investment estimation dnd ecbaomic effect evaluation program

Optimization program for mini ng-by-stage

Program oP vertical The maim program of extension rate surface mine opti mizat i on long term planning

. . FIGURE 7. Macro Structure of SMLTPZ.

- -

380 21st APCOM PROCEEDINGS

* AH can be obtained in units of i

The programs with marked in t/a by: Fig. 6 and Fig. 7 might be optional in

a given case.

I AH = Pi * V /h i i i

where Pi is the ore tonnage mined out at step i, t,

Vi is the vertical extension rate of mining work at step i, m/a, and

hi is the increment of mining depth at step i, m:

Here V is derived by a special i program in which PERT & CPM methods

are used.to figure out the minimum circular time for developing and preparing a new bench completely under certain conditions of equipment allocation and mining 'extension . . . sequence.

. .

STRUCTURE OF THE MODELS

The macro-structure of model SMLTPl is shown in Fig. 6. It is applicable for horizontal or flat-bedded deposits.

m i n i n ~ and strippinu. scheduling optimization

. . ..

and economic effect evaluation program

FIGURE 6. Macro structure of SMLTP 1.

final pit limit program

2-D ore depo- sit program

APPLICATION OF THE MODELS

1 + I main program of surface. mine l o n ~ term planning -

- 3 .

The model has been applied to a number of coal and iron ore open pits for optimizing different mining alternatives, with the total number of applications reaching nearly a hundred.

The models can be used for either single-factor optimization or comprehensive optimization.

Some case studies of single factor optimization are as follows.

Mining Technology Selection

In a flat-bedded coal mine, two mining alternatives have been tested with the same pit limit and about the same mining sequence. The difference

. between the two mining alternatives is mainly concerned with the in-pit haulage system --- one is railway haulage and another is truck haulage. The corresponding annual production rate: for railway haulage --- 7/Mt/a, for truck haulage --- 21/Mt/a.

Thhumulated net present values vs. the mine's age for the two different mining alternatives derived from,~SMLTPl are shown in Fig. 8. Compared with railway haulage, it is faster to obtain the same net present value for the truck alternative because it has a higher mining intensity. However, the final net present value for the two mining alternatives are not significant (7.67%).

For inclined or dip-buried deposits, the model SMLTPZ can be selected, the macro-structure of' which is illustrated in Fig. 7.

SERIES OF COMPREHENSIVE OPTIMIZATION MODELS

cl Truck haulage 2 = Liai lway haulage

4. 0,

).

1.

I a

0 - 20 So 60 60 I # , ?

- I. Mine's age, years

-1.

FIGURE 8. Cumulated net present values for the two haulage alternatives.

Taking the different mine productions into account, we use another index to evaluate the economic effect:

where: P is the unit net present value, Yuan/t ,.

CNPV is the cumulated NPV, Yuan, and , .

T is the ccinulated tonnage of mined ore, t.

The unit net present values vs. the mine's age are shown in Fig. 9. In the early years, it is more profitable for the railway haulage alternative because it has a rather low mining cost. But this advantage diminishes as the mine life increases.

Mine's aRe, yo

FIGURE 9. Unit net present values as a'. function, of the two haulage alternatives.

Mine'construction volume and duration can be easily obtained via this model. A shorter construction period (1 to 2 years) has resulted from the truck alternative compared with the railway alternative in this case.

Pit Length Analysis

In the above mine, comparison among mining alternatives with different pit lengths has been made to find the optimal pit length with a truck haulage system.

The parameters of different mining alternatives as well as,the technical and economical results coming from SMLTPl are shown in Table 1.

Two factors --- the-stripping ratio and the overburden haulage distance --- have an opposite influence on the economic result, along with an increase of the pit length. Within the range of this study, the overburden haulage distance from the stripping face to the mined-out area appears to have a stronger impact on ,the mining cost. So the optimized mining alternative A with a short pit length of 1.2 km is derived.

TABLE 1. Comparison among alternatives with different pit lengths.

Mining Alter- native No.

A

B

C

, - . , , J

Mining Sequence Selection Comprehensive Optimization. . . In'an iron ore open pit with a A great number of mining

dip-buried ore body, different mining alternatives can be comprehensively sequence options have been studied. considered, compared and optimized via

the model series. Fig. 10 show the different

alternatives which a21 possess the In the feasibility study of a same final pit limit. The locations large surface coal mine, 24 mining of the intermediate pit limit(s) for alternatives have been put forward. alternative (c) and (d) are optimized They are different from each other, by a special program. being characterized by the following

technical factors: The results are shown in Table

2. Compared with 'the-normal mining PIT LIMIT; methods, a lower stripping ratio in EQUIPMENT SIZE: The bucket the early period can be achieved for capacity of the shovel ranges from 8 the bench group mining method. If to 27 m3; the options of mining by stages with intermediate pit limit(s) were HAULAGE SYSTEM, including truck, selected, further benefit would be railway or combined haulage system; obtained.

MINE PRODUCTION, ranging from 6 .0 to 24.0 mil. tons per year;

Parameters

Pit Mine Mine Lonxth, Produc- Life, km tion, years

~ t / a

1.2 12.0 31.83

1.6 16.8 32.79

2.4 21.0 36.03

Output Results

Aver. Haulage Stripping Dist. CNPV , p, Ratio, of OD, mil. Yuan yuan/t m3/t km

*

2.87 1.67 551.6 1.549 -1.95

2.76 1.98 580.8 1.149 -2.47

2.82 2.18 5?1,7 0.770 -2.70

A

SERIES OF COMPREHENSIVE OPTIMIZATION MODELS 383

(a) Normal 'Mining (b) Bench Group Mining

(c) Mining by Two Stages (d) Mining by Three Stages

@ : working slope angle y : f i n a l slope angle

FIGURE 10. Mining sequence options.

TABLE 2 . Comparison among al ternat ives with di f ferent mining sequences.

I Mining Sequence Alternative

Stripping Ratio in 1 2 . 6 3 2 . 5 6 2.08 1.80 The 1st Period, t/t

Running Results

Total NPV, mi 1. Yuan ( 1754.7 1758.3 1933.0 1977.3

(a) (b) (c, (a') Norma 1 Bench M i n i n ~ Mining Mining Group b y by

Mining 2 Stages 3 Stages

Unit NPV, ~uan/t 3.53 3.54 3.89 3.98

384 21st APCOM PRO-CEEDINGS

PIT LENGTH, ranging from 1.2 to It is also possible to use the 2.4 km; factor K as a main evaluation index

for mining alternatives with quite MINING ADVANCE DIRECTION; large differences among their

investment amounts, and to take LOCATION OF PREPARATION PLANT AM) factor P as the secondary evaluation

DUMPING AREA. index in this case.

The results are shown in Table 3.

Other than the.NPV of unit tonnage of mined coal (P), another factor for evaluation of economic effect has been taken,as:

. . K = CNPV/CNPI

where K is the NPV of-unit net present investment,

CNPV is the cumulated net present value, and

CNPI is the cumulated, net present investment.

From Table 3, it is easy to see that if there were no limitation to the annual mine production, alternative 7 or alternative 21 should have been selected to obtain the largest NPV from unit investment. However, when an annual production of no less than 10 Mt/a is required, the best options turn out to be alternative 14 or ilternative 2.

In this study, it takes 1 to 2 minutes of CPU time to run a comprehensive mining alternative on

mining a1 t e r - n a t i r e No.

TABLE 3. Results for comprehensive optimization.

NPV of NPV o f aver. mine m i n i n g cost, NPV I unit unit

Slt, produc- ~uan/t mil. Yuan tonnage investmen ml/t tiom, cotzl, ~ u a n / Y u a n

Mt/a ~ u n n / t

2.78 12.0 8.44---12.84 551.64 1.55 0.563 2.78 18.0 8.44---12.84 832.10 2.34 0.61 1 2.78 24.0 8.44---12.81 1037.40 2.91 0.595, 3.48 12.0 10.03---17.93 247.17 0.38 0.102 2.76 16.8 9.84---12.88 580.88 1.15 0.501 2.91 7 .0 5.57---6.72 433.80 2.15 * 0.581 2.80 7.0 5.93---6.27 519.60 2.12 0.712 2.80 6.0 5.93---6.27 448.44 ' 53 . 0.659 3.14 10.5 10.89---15-70 11.63 r . 34 40.011 3.14 '6.0 10.89---15.70 -9.43 -0.03 -0.013 3.14 10.5 10.89---15.70 203.97 0 .70 0.212 3.14 10.5 10.89---15-70 97.78 0.34 0.092 3.15 10.5 11.89---17.60 213.52 0.72 0.205 2.78 12.0 8.44---12.84 534.49 1.50 0.631 2.78 10.5 8.44---12.84 479.83 1.35 0.6?8 3.48 10.5 10.03---13.93 117.77 0.29 0.117 2.82 21.0 10.34---13.20 521.76 0.73 0.331 2.83 7 .0 5.84---8.18 484.59 ' 0.68 0.706 4.42 7 .0 8.44---11.53 277.83 0.79 0.263 4.24 10.5 13.20---18.80 -36.18 -0.15 -0.035 3.87 7 .0 6.07---11.49 530.58 0.75 0.71 8 3.87 6 .0 6.07---11.49 453.81 0.64 0.661 2.83 7 .0 6.00---6.31 331.05 1.34 0.476 2.58 17.0 9.30---12.88 461.70 0.85 - .

SERIES OF COMPREHENSIVE OPTIMIZATION MODELS 385

the IBM-4341 computer. It took only 2. Dowd, P., 1976, "Application of one month to complete the Dynamic and Stochastic above-mentioned work for the Programming to Optimize Cutoff feasibility study, including all Grades and Production Rates," preparation work. This is a significant saving of labor and time, yet the results are more accurate and reliable.

CONCLUSIONS

Combining different O.R. approaches, the new method has been proven as a powerful tool to simulate the time-and-space varying development of open pit mine engineering. Taking the main program of SMLTP as the central model, a number of subprograms with various functions by means of different O.R. approaches might be involved in the model. Further extension can be conveniently made, if necessary.

Traditional models related to surface mine long-term planning are usually based on a single objective and a static form. Among them the typical ones are existing pit limit , optimization models' which look for an optimum final pit limit not taking the time factor of value into account. In adaition to the functions of the traditional form, dynamic and comprehensive optimization for surface mine long-term planning can be completed by the SMLTP model series.

Further widespread applications of the SMLTP model series for surface mine long-term planning are anticipated.

REFERENCES

1. 'Crawford, J. T., and Davey, R. K., 1979, "Case Study in Open-pit Limit Analysis,"

York.

Transactions/Section A of IMM, Vol. 85.

3. Johnson, T. B., 1973, "A Comparative Study of Methods for Determining the Ultimate Open Pit Mining Limit," Proceedings, 11th Annual Symposium on Computer ~pplications in the Mineral Industry, Tucson, Arizona.

4. Kim, Y. C., 1979, "Open-Pit Limit Analysis, Technical Overview,"

5. Lerchs, H., and Grossman, I. F., 1965, "Optimum Design'of O~en- it ~ines." Canadian . . . Institute of Mining Bulletin, Vol. 58.

6. Zhang, Y. G., Yun, Q. X., Gui, E. Y., and Xu, L. J., 1986, "A New Approach for Production Scheduling in Open-pit Mines," Proceedings, 19th International Symposium on Application of Computers and Operations Research'in the Mineral Industry, SME, Littleton, Colorado.

7. Zhang, You-di, Li Ke-min and. Shang Tao, 1986, "Oriented-Graph Simulation For Long-Range Surface Mine . Planning," Proceedings, .19th International Symposium on Application of Computers and Operations Research in the Mineral Industry, SME,' Littleton, Colorado.

8. zhang Youdi, Li Kemin and Shang Tao, 1987, "System Simulation for Open Pit Planning," Mining Science and Technology, Trans Tech Publications, Clausthal-Zellerfeld.