ORIGINAL PAPER Development of a 2D and 3D computational algorithm for discontinuity structural geometry identification by artificial intelligence based on image processing techniques Mohammad Azarafza 1 & Akbar Ghazifard 1 & Haluk Akgün 2 & Ebrahim Asghari-Kaljahi 3 Received: 3 January 2018 /Accepted: 28 April 2018 # Springer-Verlag GmbH Germany, part of Springer Nature 2018 Abstract Block geometry is commonly the most important feature determining the behaviour of a rock mass and directly controls the structural instability in underground openings or surface cuttings. Various methods are used to estimate block geometry and to perform a block survey, and these are standardly divided into empirical-based methods (e.g. spot mapping, linear mapping, areal mapping) and computer-based methods (e.g. laser scanning, image processing, digital image mapping). Empirical approaches are associated with effective features as well as with a number of errors; however, the latter can be covered by artificial intelligence (AI) techniques. The combination of image processing and areal mapping have led to geometric block estimation in two-dimensional (2D) and three-dimensional (3D) spaces; these approaches can be widely used in stability analysis, dimension stone extraction, excavations, open pit mining design and the delineation of blasting patterns for dimension stone extraction. Therefore, the application of an approach that allows both the modelling and production of rock blocks based on their actual status with qualified accuracy and speed are both worthwhile and necessary. In this study, to estimate the shape and block dimension utilized, we used the algorithm based on the AI image processing technique for rock mass structural detection and for rock block definition in 2D and 3D space obtained with the Mathematica software package. The algorithm, by categorizing the discontinuities in two groups (opened and closed), which represents the main and the secondary discontinuities, can identify the emplacement and shape of rock blocks. Keywords Artificialintelligence . Discontinuity . Imageprocessingtechniques . Digitalimage processing . Computersimulation . Mathematica Introduction Rock masses are almost always associated with imperfections called discontinuities, such as joints, bedding planes, faults, among others, which shape the geometry of the rock mass and play an important role in the assessment of the stability of the rock mass (Nikoobakht et al. 2016; Azarafza et al. 2013), proportions of the dimension stone (Saliu and Idowu 2014), blasting patterns (Hamdi and du Mouza 2005), mine design (Alejano et al. 2007), open pit excavations (Yarahmadi et al. 2015) and size and volume of the block (Palmstrom 2005). Goodman (1989) reported that discontinuities cause massive changes in the engineering behaviour and characteristics of rock masses, specifically leading to nonlinear behaviour, anisotropy and reduced tensile strength to nearly zero. Since in most cases discontinuities are the main causes of the * Akbar Ghazifard a.ghazifard@sci.ui.ac.ir Mohammad Azarafza m.azarafza.geotech@gmail.com Haluk Akgün hakgun@metu.edu.tr Ebrahim Asghari-Kaljahi e-asghari@tabrizu.ac.ir 1 Department of Geology, University of Isfahan, Isfahan, Iran 2 Geotechnology Unit, Department of Geological Engineering, Middle East Technical University, Ankara, Turkey 3 Department of Earth Sciences, University of Tabriz, Tabriz, Iran Bulletin of Engineering Geology and the Environment https://doi.org/10.1007/s10064-018-1298-2