Daniel Arias

Variogram calculation is a fundamental tool for studying ore grade data in mineral deposits. It allows the discovery of hidden structures within the data and preferential directions of mineralization where the geological continuity is longer. The variogram allows us to classify samples and to define both the search radii for interpolation and the use of kriging as an interpolation and resource classification method. It is not difficult to use it in one dimension; complexity increases in two dimensions as the necessity to search for possible grade anisotropies in all directions arises. Three-dimensionally it is even more difficult to try to define the parameters of lag, bandwidth, and tolerances that define the data of the variogram calculation algorithm. There are rules of thumb to help in the development, but a trial-and-error approach is used in order to find enough sample pairs to allow the generation of variograms truly representative of the data. In this paper, two strategies are shown to help in variogram construction, the use of variogram maps and the graphical representation of the pair search areas (cones or pencils). The freeware tool RecMin Variograms has been developed and is freely available for download at its website; it is easy to learn and use. R code based on RGeostats libraries is used to check the operation and results of RecMin Variograms. Applying geostatistics to mineral deposits is essential to know the areas with the highest grades, thus allowing exact planning of future mining exploitation and minimizing mine footprint and environmental impact.

Three-dimensional block models are the most frequently used tool for estimating mineral resources and reserves within a mineral deposit. In open pit mining, the basis of mine design and the long term mining schedule is calculation of the ultimate pit limit. The ultimate pit limit is the pit with the highest profit value. Over the years, different algorithms have been developed that enable us to calculate the final pit: floating or mobile cone, floating cone II and its corrected forms, floating cone III, the Korobov algorithm and its corrected form, the Lerchs–Grossmann 2D algorithm (dynamic programming), and the Lerchs–Grossmann 3D algorithm (graph theory). All these algorithms have advantages and disadvantages. The floating cone method stands out for its simplicity, speed, and easy implementation, even for calculating a pit with a variable slope angle. The main drawback of this method is that it is unable to examine all possible combinations. For this reason, the algorithm does not consistently give optimal results, which is why it has required improvements over time. However, the improved methods still have some problems. To overcome these problems, a new algorithm called the floating cone IV method will be demonstrated in this paper.

The Touro volcanogenic massive sulfide (VMS) deposit is located in the NW of the Iberian Variscan massif in the Galicia-Trás-os-Montes Zone, an amalgamation of several allochthonous terrains. The Órdenes complex is the most extensive of the allochthone complexes, and amphibolites and paragneisses host the deposit, characterized as being massive or semimassive (stringers) sulfides, mostly made up of pyrrhotite and chalcopyrite. The total resources are 103 Mt, containing 0.41% copper. A 3D model of the different orebodies and host rocks was generated using data from 1090 drill core logs. The model revealed that the structure of the area is a N–S-trending antiform. The orebodies crop out in the limbs and in the hinge zone. The mineralized structures are mostly tabular, up to 100 m in thickness and subhorizontal. Based on the petrography, geochemistry and the 3D model, the Touro deposit is classified as a VMS of the mafic-siliciclastic type formed in an Ordovician back-arc setting, which was buried and metamorphosed in Middle Devonian.

In the framework of the largest urban-transit system ever built from scratch, the Riyadh Metro Project (6 lines totaling 176 km), a comprehensive investigation was carried out for karst detection, prevention and correction. This case study of the Metro Line 3 (41.6 km) seeks to show how the multi-technique geophysical survey (seismic refraction, electrical resistivity and ground penetration radar down to 40–50 m depth) was found to be a successful tool in detecting karst features. Preventive measures included systematic probing drilling to anticipate karst cavities below foundations (653 piers) and tunnel lining evaluation using 2D finite elements. Finally, this paper provides initial guidance of the corrective techniques used for each engineering challenge, such as cavity filling with grouting, geogrid reinforcement, etc.

This article exposes one of the main engineering problems in the design and construction of the upper reservoir of El Hierro hydro-wind plant, relative to the high settlement of the bottom in the southeast area. The high settlements measured during the construction phase are consequence of the geological-geotechnical settings of the site, a natural depression of a volcanic crater occupied by highly deformable soils derived from the weathering of volcanic materials. Ground improvement was carried out by partial preloading (mobile dune), preceded by the execution of a trial embankment in the southeast area of the reservoir, where the greatest thickness of deformable soils was identified.

In recent years, the introduction of specific software for the evaluation of geological resources and mineral reserves has increased significantly thanks to the use of block models capable of working with large databases and applicable to virtually all types of deposits. It is only in layered, tabular-shaped deposits where the use of block models poses certain drawbacks, not only in terms of visual representation but also during the process of interpolation. Other calculation methods for tabular bodies such as sections, polygons, and triangles work with 2D projections but not with 3D. The “Pentahedral” method described here is undoubtedly an innovative method that allows work to always be conducted in 3D, providing a fairly accurate representation of tabular bodies and making it possible to carry out calculations of resources and reserves using any interpolation method. It is demonstrated with figures and tables of the Carlés mineral deposit, a well-developed exoskarn gold deposit in northwestern Spain (Asturias) where the authors have worked extensively. The pentahedral method takes into account not only geological and stratigraphic data from the model interpolation, but also mining concepts such as “minimum thickness,” related to the minimum seam size that can be economically and technically mined, and “overbreak,” related to the dilution effect that appears during the mining process due to over-excavation.