Application of Numerical Algorithms in Mining

Author: George Pacheco


Most numerical algorithms have been invented long before the widespread use of computers. Algorithms were designed to speed up human computation, therefore constructed to minimize the number of operations to be carried out. The advent of object-oriented type programming provided the channel for code reuse , which in principle also include concepts of inheritance, polymorphism, and data encapsulation. While not particularly concerned with the internal workings of object orientation one must be aware of the capability these concepts render. Take for instance the ability to mix through inheritance a common set of methods, making implementation of numerical algorithms intelligible and effortless. Minimizing the number of operations is paramount to speed up code execution.

In mining, as in any other industry, handling volumes of data bundled in large databases are commonplace. Consider area selection which is a crucial step in professional mineral exploration. Area selection is based on applying theories behind ore genesis, the knowledge of known ore occurrences and the method of their formation to determine potential areas where a particular class of ore deposit being sought may exist. It usually requires some form of geophysics such as down-hole probing of drill holes in order to geophysically delineate ore body continuity within the ground.

The use of polynomials in this area is quite important because they are often used in approximating functions determined by experimental measurements like drill holes. For example, polynomial least-square fit numerical algorithms can provide a representation of body continuity as defined by the set of core samples taken. Additional benefits come from linear optimization often applied to mineral extraction, where the objective function may consist of minimizing the total cost of operation based on constraint parameters like grade of ore, transportation costs, manpower and others. Linear optimization algorithms like Simplex Algorithm, Powell’s Algorithm and Hill-Climbing Algorithm are widely used.

Numerical algorithms are representations of proven mathematical theory. Real world numerical algorithm applications are coded statements strictly following accepted hypothesis. Specialty areas of function evaluation, interpolation, iterative algorithms, series, linear algebra, statistical analysis, optimization, linear and nonlinear systems are heavily used mining applications. Consider the use of differential equations: most problems in engineering, mining included, are governed by either high-order equations or coupled differential equation systems where Euler and Runge-Kutta numerical methods, which are actually a general class of algorithms, provide reasonable generalizations for numerical implementation in mineral applications.

Many commercial mineral algorithms are available, however, one size does not necessarily fit all. Large companies can afford customization to fit their operations. Smaller outfits tend to write their own provided they have the expertise in house. Assistance is always accessible through internet inquiry or other specialized software houses.

Numerical algorithms in mining provide fast, accurate and reliable results. The scope of applications is as diverse as resource type evaluation tasks like quantifying the grade and tonnage of a mineral occurrence, to everyday complexity encountered in open pit mining or underground shaft sinking, block caving, cave mining , cut and fill, or similar extraction operations. Added benefits incorporate code reusability and ease of use.

Practical samples and further interesting discussions on mineral engineering can be found at


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