Open pit mine ultimate limit
Open pit or cavity mining is an excavation method through opening a large pit and gradual expansion of the pit on the group. The pit expansion is continued until ultimate pit limit (UPL) is achieved. Determining UPL has been one of the major challenges for mine planners over the past years [1]. Optimization of UPL design is based on economic-technical concerns and indices. The most common indices used for the optimization are maximum net value, maximum metal content, and optimum mine life. That is, a UPL determined based technical concerns ensures the highest not-discounted value . This limit actually represents the final shape of the mine and it is used to determine mine reserve, stripping volume, and the location of waste dump and other facilities [2]. Different methods are available for UPL design and on general they are categorized as computerized and manual methods [2]. Over the past fifteen years, several computer methods have been introduced for UPL design. These methods are based on exact mathematical algorithms, approximation mathematical algorithms, fusion algorithms based on math and heuristic methods, and meta-heuristic algorithms. Some examples are Learch-Grosman classic algorithms [3], floating cone [4], and Korbove’s algorithm [5]. These classic algorithms are based different approaches like graph theories, grid maximum flow (حداکثر جریان شبکه) techniques, linear programming, dynamic programming, and parameterizing techniques. According to Kim, optimum design methods are categorized as rigid (سخت) and non-deductive (غیر استدلالی) techniques. He used the term “rigid” for the methods that rely on mathematical proof like graph theory, linear mathematical programming, and dynamic programming. The term “non-deductive” is used for the algorithms that yield a proper answer in almost all cases, while they do not have a rigid mathematical proof. Different versions of floating cone methods are the examples of such algorithms.
In the simplest way, open-pit mine UPL problem can be solved as a classic linear mathematical programming. In fact, linear programing models are the simplest and most accurate methods for UPL design [6]. A block is the smallest element in mine design and it is defined based on economic factors (e.g. price and costs), parameters of geology simple block model, and orebody economic block model [7]. According to economic block model, each block, whether waste or minerals, is assigned with an economic value. In addition, each block is taken as an integer and the set of maximum profit blocks is selected through expressing the problem as a linear mathematical programming model, defining an objective function to achieve (e.g. maximum operational profit), and observing technical concerns. Given the load and complexity of computations in these models, they are not easy to use in orebodies with a large number of blocks. This is were approximation methods become an alternative.
Most of the non-mathematical and non-deductive models lose their efficiency in the realm of uncertainty so that in the best scenario, they can be used for sensitivity analysis. Linear programming model; however, keeps their efficiency even with uncertainty provided that meta-heuristic analyzers are used to solve large models. With regard to uncertainty programming, different methods like random-probability programming, fuzzy programming, robust optimization and programming, and some of fusion methods are among the options.