Three-Dimensional Modeling of the Underground Mineral Extraction Process: A Dynamic Three-Dimensional Model of Underground Mining Space

Oleg Konovalov , Vladimir V. Krasnoproshin

Three-dimensional models of underground space are a core component of digital twins of mining enterprises. The fundamental requirement for such models is that they must be dynamic — accurately reflecting the current state of their physical counterpart at each moment in time. When developing large underground bedded mineral deposits (coal, potash), the mined horizon constitutes a continuously changing network of hundreds of openings with complex topology. Existing approaches based on sweep bodies with Boolean operations are critically resource-intensive for such scale, while loft representations based on vertical cross-sections suffer from shape distortion. This paper proposes a hybrid geometric representation that combines the accuracy of the sweep approach with the non-intersection property of the loft approach. The key idea is to decompose each excavation into a set of loft bodies corresponding to individual passes of the mining machine. An efficient analytical algorithm is developed for constructing vertical cross-sections of normal profile bodies (NP-bodies) without explicit 3D surface computation, exploiting the property that the projection of a helical sweep surface onto the horizontal plane is a circle for each fixed profile parameter. An inverse contour fitting algorithm based on gradient descent is proposed for recovering NP-body trajectory parameters from scanned cross-section data. Experimental validation using underground laser scanning data from a potash deposit demonstrates contour recovery accuracy of 0.05 m and surface deviation of 0.07 m, with gradient descent convergence in 14–32 iterations. The approach is suitable for most digital twin tasks including equipment placement, ventilation calculation, and transport route planning.