J. Cent. South Univ. (2018) 25: 159-168

DOI: https://doi.org/10.1007/s11771-018-3726-7

A landfill based approach to surface mine design

Yuksel Asli Sari, Mustafa Kumral

Department of Mining and Materials Engineering, McGill University,3450 University Street, Montreal, Quebec, Canada

Central South University Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Abstract: Surface mining operations extract a large quantity of waste material, which is generally disposed into a dump area. This waste can cause a series of environmental problems ranging from landscape deterioration to acidic water generation and water pollution. Therefore, mine waste management is a significant task in mining operations. As known, in strip mining, the overburden is not transported to waste dumps but disposed directly into adjacent strip which was mined out. This concept can be adapted for mine planning of relatively horizontal deposits through a mixed integer programming (MIP) model. The main idea behind this work is that, in one pit, production voids created in early year of mining are used for waste landfilling in late years of production. In other words, in addition to external dumping, a landfilling option within the same pit is proposed for mine design optimization. The problem is formulated as maximization of the net present value (NPV) of the mining project under the constraints of access, landfill waste handling, mining and processing capacities. A case study using a data set was carried out to see the performance of the proposed approach. The findings showed that this approach could be used in waste management incorporating a landfilling option into mine planning. As a result, material handling costs decrease, and environmental compliance increases due to less external waste quantity.

Key words: mine waste management; landfill; mine design; mineral industries; mine optimization

Cite this article as: Yuksel Asli Sari, Mustafa Kumral. A landfill based approach to surface mine design [J]. Journal of Central South University, 2018, 25(1): 159–168. DOI: https://doi.org/10.1007/s11771-018-3726-7.

1 Introduction

Surface mining operations are managed through various management units such as mine operation, geo-technique, planning, environment and maintenance units. Environmental management unit focuses on landscape and environmental protection, compliance and “social licence to operate”. These activities require measurement, analyzing, testing, monitoring, case studies, literature review and interview processes with the locals and authorities to succeed environmental objectives [1]. As a major part of environmental management, mine waste management deals with extraction, hauling, dumping, rehabilitation, analyzing and monitoring of waste materials. Essential engineering issues in mine waste handling are landscape degradation, accounting for ground conditions, closure and rehabilitation planning, possibility of acid water generation, and soil and water pollution. As such, mine waste management comprises of complex tasks and requires expertise in geology, hydrogeology, soil science, geotechnical, mining and environmental engineering. Therefore, reduction in waste quantities can directly facilitate mine waste management. Landfilling has a strong potential to lessen the magnitude of environmental problems and high costs associated with external dumping. Landfilling is used in environmental sciences to dispose various waste materials [2].Even though landfilling is long-known alternative in surface operations such as strip mining, it has not been mathematically formulated for mine planning practices where only one pit is operated. Horizontally extending deposits allow mine planner to use previously produced areas in the same pit for landfilling. This approach can be extended to the surface mining methods based on mechanical excavation. In this context, landfilling is investigated as a part of mine planning optimization.

In mining industry, the wastes can be classified into four groups [3]: 1) overburden of soil and/or rock that is extracted to access valuable material; 2) waste rock whose grade is below the cut-off grade (sub-grade material); 3) process tailing that is extracted in mineral concentration; and 4) the contaminated waste that is generated by heap or dump leaching. In general practice, the materials of the first two groups are directly disposed into dump areas.

Current mine waste handling approaches focus on treating waste rocks such that environmental effects are minimized. LI et al [4, 5] developed a model for the idea introduced by WILLIAMS et al [6] where the blocks having the potential to create acid water generation were encapsulated by safe, non-reactive blocks. They reported that the optimization models had an advantage in terms of solution time, truck utilization and cost saving.Although this method is a fair precaution, it is a much better approach to minimize the risk by reducing the quantity of waste rocks to be dumped as much as possible. Moreover, this may be combined with the above mentioned method for the best practice. Surface mining operations based on mechanical excavation with horizontally shaped deposits provide an opportunity to consider landfilling where waste rocks are disposed into previously emptied production areas of the pit. Landfilling has various advantages: 1) it alleviates environmental problems such as acid mine drainage which is treatable but costly and requires energy and chemicals that result in additional environmental impacts [7, 8]. Landfilling approaches this problem by reducing the external waste amount in the first place, solving the majority of the problem before its occurrence. 2) Transportation cost being almost half of total mining cost [9], makes landfilling option a reasonable approach, which is especially applicable to horizontal or multi- mine operations. 3) In addition to mitigation of environment problems, transportation, road maintenance and safety costs can be also reduced [10]. 4) Furthermore, mine closure and rehabilitation costs will also be reduced because mining voids are filled.

In mine planning practice, firstly, a 3D block model is created, and each block is estimated or simulated through an appropriate geostatistical technique. A block containing sufficient valuable metal is then classified as ore and otherwise it is classified as waste. This classification is made on the basis of a cut-off grade reflecting minimum metal to be extracted in such a way as to pay-off operation costs of a block. In traditional approach, there are two possible destinations: if the grade of a mining block is above the cut-off grade (ore), it will be sent to the processing plant, and if not (waste), it will be sent to an external waste dump. In this work, landfilling is added to mine production scheduling as a new destination. This addition inevitably increases the problem complexity from decision- making point of view. Mine planning can be divided into two decision making problems: 1) cut- off grade determination or ore–waste discrimination (where to send the blocks to be produced) and 2) block sequencing (when to produce these blocks) [11]. The division of mine planning optimization into two sub-problems increases computational efficiency. However, this may reduce the value of project because 1) cut-off (ore–waste discrimination) cannot be independent of time and 2) capacity utilization may be reduced due to idle capacity [12]. Identifying blocks as ore or waste in advance of the optimization may delay or prevent the access from the rich areas of a deposit due to capacity constraints whereas simultaneous optimization of ore–waste discrimination and block sequencing enhances the search space such that a more effective search may be carried out with an increased number of decision variables. In scenarios where there are multiple waste options, it is not meaningful to use a cut-off grade which discriminates ore and waste. Therefore, a priori cut- off grade in the traditional approach is not used in this research. Ore–waste discrimination is also incorporated into the optimization process. In other words, block destinations are formulated as decision variables to be solved by MIP. Furthermore, landfilling is restricted by void availability at the time of dumping whereas external dumping has more flexible dumping conditions. Dumping location and capacity requirements of external dumping are not as restrictive as void availability of landfilling. Void availability for landfilling increases the complexity in such a way as to grow the number of decision variables and constraints. To be able to place a block to a landfill location, underling nine blocks of that location, where slope angles are 45^o, should be filled previously. In this research, there are two critical assumptions that 1) the produced material is fully landfilled to the previously created void. In other words, it is assumed that swelling is negligible. In practice, when material is excavated, its in-situ volume expands. Depending upon material characteristics, swelling factor associated with volume expansion ranges in 10%–60%. In hard rocks, this factor is 30%–45% [13]. This is a reasonable assumption because mining equipment can compress the material. The other assumption is that 2) bottom of a landfilled area cannot be mined at a later period. Because of this, mining operation will not be extended beyond ultimate pit limits. Therefore, mine management should be certain about mine life and extensions.

Solid waste management regarding surface mining was discussed by DESHPANDE and SHEKDAR [14] and DENG et al [15]. The effects of contaminants were detailed and improvement strategies were given. ZAITSEVA et al [16] explored the applicability of internal disposal for flat-dipping and inclined bedded deposits from points of geometry and dip view. ZUCKERBERG et al [17] proposed an approach to use internal dumping for multiple pit operations. This research allows internal disposal to implement for even one pit as long as the pit extension is horizontal. In this approach, when the production in a pit is completed, this pit serves as dumping location for the material coming from other pit. PANOV et al [18] focused on geotechnical and slope stability aspects of internal disposal. SAKANTSEV and CHESKIDOV [19] addressed internal disposal in steep and deep deposits. They investigated relationship between access road and associated costs. KALANTARI et al [20] investigated the relationship between long-term mine plans and the final composite tailings produced downstream such that random parameters were incorporated. LU and CAI [21] reviewed the management of solid wastes in mining and recommended new utilization strategies. PIMENTEL et al [22] provided a comprehensive review of mining and environment interaction including mine waste management. QUE et al [23] investigated 16 project characteristics to assess socio-political risks affecting stakeholder and community engagements on mining projects on the basis of six demographic factors. ADIBI and ATAEE-POUR [24] addressed to incorporate sustainability into ultimate pit limit problem as a part of mine planning optimization.

In this work, internal waste option is incorporated into mine planning optimization problem. Landfilling is well known in strip mining systems. However, the proposed approach takes a further step and landfilling is formulated as a part of mathematical optimization model. After the description of the problem and literature review are presented in Section 1, the optimization model as a MIP (mixed integer programming) problem is developed in Section 2. A case study is demonstrated, and the findings and discussion are provided in Section 3. Finally, conclusions and future work recommendations are given in Section 4.

2 Model development

In this research, waste management through landfilling is integrated into mine planning problem such that material handling costs are reduced. In inclined or vertical deposits, this option will have a limited manoeuvring room. For a block to be produced, in our formulation, there are three possible destinations: a mineral processing plant, an external dump or landfill. Since landfilling is less costly than external dumping, the produced waste blocks are forced by the model to destine to internal disposal as long as landfill constraints are met. This formulation raises the number of decision variables. A more challenging issue is the upsurge of the number of constraints. As known, slope constraint is the condition that overlying nine blocks should be produced to access the block located at the apex of upward cone. Slope angle is governed by changing block sizes in orebody modelling stage.Similar to slope (predecessor or access) constraint used to access a block, there is a landfilling constraint for each waste block. The landfilling constraint is to landfill a block and underlying nine blocks should be either within ultimate pit limits or landfilled in the current/previous periods. The landfilling constraint is basically the inverse of the slope (access) constraint. Figure 1 shows these constraints. To produce the block located at the apex of the cone in this figure, a downward cone is created and all the blocks within this cone should be produced earlier. To landfill the same location, an upward cone is created and all the blocks within this cone should be either landfilled earlier or be within the ultimate pit limits.

Figure 1 Illustration of access and landfill constraints

The formulation is solved using MIP, which is an exact method that is utilized in various applications [25]. The notation used in this formulation, the parameter values in the case study, the indexes and variables are given in Tables 1, 2 and 3.

Maximize:

                    (1)

where A=r×m×p; B=C_m×m; C=D_i×m; D=D_e×m; E=Cp×m; g_i is the grade of block i.

Subject to:

1) Time and location constraints:

a) A block can only be extracted once.

Table 1 Parameters and their values for case study

Table 2 Indices and sets

Table 3 Binary decision variables

                               (2)

b) A location can be disposed landfill only once.

                               (3)

c) If a block is extracted, it should be sent to one of the following destinations: mill, landfill or external dump.

    (4)

d) In order to use landfill option, the void should have been previously created by extraction of the block in this location.

                      (5)

2) Capacity constraints:

e) Mined block mass should be below mining capacity per period. Mining capacity should be compatible with equipment fleet.

                          (6)

f) Mined block mass should be above minimum mine production limit per period.

                          (7)

g) Block mass sent to mill should be below mineral processing capacity per period. Since these capacities are installed before, the ore to be produced cannot exceed.

                          (8)

h) Block mass sent to mill should be above minimum mineral process feed per period.

                          (9)

3) Access constraints:

i) Blocks at the mine boundary cannot be extracted because it is assumed that the boundaries cannot be extended.

                              (10)

j) All overlying blocks must be extracted at the present or earlier periods to allow mining at the current block.

                  (11)

k) One of the two conditions should be true in order to be able to landfill for each underlying block: 1) the underlying should also have been landfilled previously or in the same period, or 2) the underlying should not be extracted during mine life.

       (12)

Expressing conditional constraints is not possible directly in linear programming and the problem is solved using the big M method [26] which defines a very large number M and a new binary variable p(i) such that feasibility and optimality are combined. In the end, the above constraint is converted to following constraints:

                (13)

                (14)

            (15)

     (16)

4) Binary constraints:

l) The decision variables can take the value of either 0 or 1.

(17)

3 Case study

To demonstrate the performance of the proposed model, a case study was carried out on a deposit extending horizontally. The data were based on an old copper mine, which was mined out long time ago. The operation was implemented in one pit throughout mine life. Using drill-hole data of this deposit, a block model was created and estimated through ordinary kriging. Figure 2 shows the 3D shape framing of the orebody. This extension facilitates the use of landfilling. The voids created in early years of the production can be filled in subsequent years of the production. The total number of the blocks is 25000 (100 (EW)×25 (NS)×10 (Vertical)). All parameter values used in this case study have been given in Table 4.

For the optimization model given in Section 2, the objective function and constraints were created and this model was then submitted to an optimization tool to generate the solution. The outputs of the optimization have been thoroughly tested and verified that all constraints are satisfied. The number of decision variables is 1875000 and the number of constraints is 2932314. As can be seen, the number of constraints is much larger than the number of decision variables because slope and landfill constraints lead to swift increase in the problem size.

Figure 2 Extension of mineral deposit

Table 4 Parameter values for case study

Figures 3–6 demonstrate the results of the case study where each colour corresponds to a year of the operation. Figure 3 illustrates the landfill feasibility on a randomly selected cross-section. As can be observed from the cross-section, according to the optimized model, although landfilling takes place each year after the first year, the voids created by producing the east side of the orebody are filled massively (876 out of 910) in Year 5. If the horizontal extension of the orebody was greater, massive backfill may have started in earlier periods. Slope and landfill angle is 45°. For different angles, block size should be changed accordingly. Slope angle also affects the feasibility of approach. As slope angle decreases, possibility for horizontal extension grows.

Figure 4 shows randomly selected cross- sections of the production plan taken in x- and y-direction.

The annual present values are provided in Table 5. Total project life is 6 years (5 operations and one investment year). Initial investment of the project is $2.0×10⁹. In this case, the NPV of the project becomes (48.434016765–2.0)×10⁹= $2.8434016765×10⁹. Throughout the project, a total of 14328 blocks are produced. 7500, 5918 and 910 blocks are sent to mineral processing plant, external dump and landfill, respectively. As can be seen from the parameters, processing capacity is 7.5× 10⁶ t per year and each block mass is 5000 t. A summary of production plan in annual base is given in Table 5. Therefore, the maximum number of blocks to be produced in a given year is 7500000/5000=1500 blocks. Given that total number of blocks produced during the project is 7500 and project production life is 5 years, the production rate in upper bound is fulfilled (7500/5=1500). The difference between the costs of landfill and external dumping is $2.5; when projected to the present case, the gain from using landfilling is $7.82×10⁶, which is an approximately 7% decrease in the transportation costs.

For the case study, the optimization matrix is created in ZIMPL (Zuse Institut Mathematical Programming Language [27]) and the problem is then solved using IBM ILOG CPLEX Optimization Studio. A Dell Precision T3610 with IntelXeonCPU E5-1620 v2 and 16.0 GB RAM was used and running time was 29.4 h. The gap for optimality is 0.01%.

Figure 5 provides a randomly selected 3D view of the production plan generated by the optimization process to give an idea about the evolution of the mining operation.

Figure 6 shows the production scheduling plan for a randomly selected cross-section in terms of block destinations and the production periods. In Figure 6(a), the blocks to be sent to mineral processing with production periods are shown. Each colour of the legend represents a period. Figure 6(b) illustrates the blocks to be sent to external waste dump. As can be seen from Figures 6(a) and (b), as mining advances to deeper zones, the number of blocks to be sent to external waste dump decreases. There are two reasons for this: 1) more valuable blocks are located in deeper areas, thus the number of blocks sent to processing increase and 2) waste blocks are dumped internally because the voids are available for landfilling. Figures 6(c) and (d) show the landfilling from two perspectives on various cross-sections. In Figure 6(c), the blocks to be removed for landfilling and in Figure 6(d), the blocks to be located for landfilling are shown. As can be recognized, landfilling is realized towards the end of project. All figures providing the views of the production plan are generated using SGeMS (Stanford Geostatistical Modeling Software).

Figure 3 Illustration of landfill feasibility on a cross-section (on the 7th slice of y-direction)

Figure 4 Randomly selected sections in different directions of production plan:

Figure 5 3D image of production schedule (x=52, y=13 and z=3)

Figure 6 Destination map of ore and waste blocks on various cross-sections of y-direction (each colour represents production or landfill periods):

Table 5 Summary of production scheduling

In addition to cost reduction effect of landfilling associated with shorter transportation distance, mine closure costs will also be reduced. Therefore, the contribution of landfilling is beyond the financial contribution illustrated herein. Furthermore, environmental risk such as acid water generation, and mine rehabilitation and closure costs may be also lowered. As the amount of external dumping is reduced, the area to be rehabilitated will be also smaller. Likewise, landfilling will reduce the size of void created by mining. These, to some extent, it will facilitate mine closure and rehabilitation at the end of mining operation. In addition, since waste material will be disposed into its host area in landfilling, and the possibility of acid water generation will be low because rock characteristics and hydrogeology do not allow this previously.

4 Conclusions and future works

As stringent environmental regulations put pressure on mining operations, innovative production methods need to be found. The paper proposes a mining production approach that production and landfilling can be carried out in a same pit. It presents an environmental friendly waste management optimization approach to be used in surface mining operations based on mechanical excavation. Landfill option is used in strip mining and the proposed approach makes it more mathematical and formal. The proposed approach will reduce mine closure time and costs as well as increasing environmental compliance. Furthermore, in cases where 1) external dumping costs are high, 2) the distance between pit and external dump is long, 3) the capacity of external dump is limited and 4) the deposits are more extended horizontally, landfilling will contribute to increase the NPV of the project. The main challenge in the optimization process is the increase in the problem size. Since this formulation requires additional decision variables, the number of decision variables increases significantly. The number of constraints also grows significantly due to newly introduced landfilling constraint. The approach is tested on a case study where during the project life, a total of 4.55×10⁶ t waste is disposed inside the pit. In other words, almost 13% of a total of 6828 (910/(5918+910)) blocks are dumped inside the pit. This reduces waste management and transportation costs. The study showed that optimization based waste management model recommended in this paper can be used to increase the project’s NPV and has a potential to enhance operation efficiency in terms of sustainability. Apart from lowering the transportation costs, potential environmental risks are also reduced. As mine life and mine size increase, the contribution of landfilling in cost reduction will also increase. In the future, the research will be extended such that the effect of swelling factor will be incorporated. The approaches that increase computational efficiency associated with the number of decision variables and constraints should be explored. For this reason, various aggregate-disaggregate, decomposition and clustering approaches will be investigated. The contaminant restrictions can be added to the optimization process through encapsulation of pollutant blocks. Finally, the research can be extended to probabilistic optimization model that considers random characteristics of parameters.

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(Edited by YANG Hua)

中文导读

一种废弃物填埋纳入露天开采设计的方法

摘要: 露天采矿作业会剥离出大量的废弃物，通常排置于排土场中。这些废弃物会造成一系列的环境问题，从景观恶化到酸性水的生成以及水污染等。因此，矿山废弃物管理是采矿作业的一项重要任务。在露天采矿中，上覆岩土层并非运输至排土场，而是直接排置于已开采完毕的相邻采坑中。利用混合整数规划（MIP）模型，可将此想法应用到较平缓矿床的矿山设计规划。本项工作的主要思路为：在一个采坑中，初期因采矿产生的采空区可被用于后期生产所需的废弃物填埋。除了将废弃物排置于外部的排土场，本文提出了一种同采坑中的填埋可选方案用于矿山设计优化。该方案的提出，是为了在运输条件、废弃物填埋处理、以及采矿和选矿能力的限制下，实现采矿工程净现值（NPV）的最大化。为了验证所提出方法的效果，利用采集的数据开展一个案例分析。研究结果表明，此方法可用于将废弃物填埋可选方案纳入矿山规划的废弃物管理之中。因此，由于废弃物的数量减少，降低了废弃物处理成本，也提升了环保合符规定的程度。

关键词: 矿山废弃物管理; 填埋场; 矿山设计; 矿物产业; 矿山优化

Received date: 2016-12-23; Accepted date: 2017-12-01

Corresponding author: Mustafa Kumral, PhD, Associate Professor; Tel: +1–514–3983224; E-mail: mustafa.kumral@mcgill.ca; ORCID: 0000-0003-1370-7446