Sánchez, LK, Emery, XM & Séguret, SA 2021, 'Improving the geostatistical modelling of geotechnical 
variables considering directional dependence', in PM Dight (ed.), SSIM 2021: Second International Slope Stability in Mining, Australian Centre for Geomechanics, Perth, pp. 401-412, https://doi.org/10.36487/ACG_repo/2135_25
(https://papers.acg.uwa.edu.au/p/2135_25_Sanchez/)
Abstract: Together with geological and geometallurgical modelling, geotechnical modelling is one of the essential components for the planning and development of open pit and underground mining projects. A particular characteristic of many geotechnical variables is to be direction-dependent, i.e. the measurement of a core sample not only depends on the geographical position of this sample, but also its orientation. To account for this characteristic, it is proposed to regionalise such variables in a five-dimensional space corresponding to the product on the three-dimensional geographical space and the two-dimensional sphere, so that each measurement is indexed by its easting, northing, elevation, azimuth, and dip. Instead of making predictions and simulations conditioned to a particular direction, this new paradigm allows geotechnical variables to be interpolated at any place in the geographical space, for any direction. The spatial correlation structure can be inferred and modelled by using separable covariances or combinations of separable covariances, under an assumption of stationarity in the geographical space and isotropy on the sphere. Also, conditional simulation can be performed by turning bands or spectral methods, based on products of basic stationary random fields in the geographical space and isotropic random fields on the sphere. The proposed methodology is illustrated with the modelling of the linear discontinuity frequency (P10) and the rock quality designation in two copper deposits.

Keywords: geotechnical modelling, directionality, geostatistics