Flow mechanisms and 3D IEZ evolution under multi-drawbell spacing in block caving using experiment, DEM and DBSCAN-a-shape

Abstract

How inter-drawbell spacing dictates three-dimensional flow interactions and the formation of stagnant pillars under uneven drawdown remains a critical, unquantified challenge in block caving. To resolve this scientific problem, a multi-scale kinematic framework was established. Large-scale (1:33) physical drawing tests were conducted and utilized to rigorously calibrate a Discrete Element Method (DEM) model, analyzing granular flow dynamics across varying drawbell spacings (4, 6, and 8 m). To quantitatively decode complex spatial interactions, a novel data-driven framework based on the DBSCAN-a-shape algorithm was introduced, enabling the precise 3D morphological reconstruction of the Isolated Extraction Zone (IEZ). The integrated analysis revealed that the mass of stagnant pillars increases quadratically with spacing, governed by a determinable static equilibrium limit. Furthermore, the non-linear morphological evolution of the IEZ was strictly quantified, transitioning from an initial constrained ellipsoid to an unconfined "inverted trumpet” geometry. Based on the site-specific fragmentation profile (predominant 200–300 mm in-situ fragment size), a 6 m spacing was quantitatively identified as the optimal configuration to balance maximum flow efficiency with pillar stability. This research provides a new analytical paradigm and precise design criteria for multi-drawbell extraction.

Keywords

Block caving / Drawpoint spacing of multi-drawbell / Extraction zone / 3D reconstruction / DBSCAN-a-shape

References

[1] Laubscher DH. Cave mining — the state of the art. J S Afr N Inst Min Metall 1994; 94(10):279-93.

[2] Brown ET. Block Caving Geomechanics. 2nd ed. Brisbane: Julius Kruttschnitt Mineral Research Centre, The University of Queensland;2007.

[3] Castro R, Oyarzo D, Gómez R, Suzuki K, Cifuentes M. Coupling geomechanical and gravity flow models to obtain more representative flow simulations and air—gap risk identification in caving mining. Num Anal Meth Geomechanics 2025; 49(1):376-90.

[4] Guo J, Huang WB, Feng GR, Bai JW, Li LR, Wang Z, et al. Stability analysis of longwall top—coal caving face in extra—thick coal seams based on an innovative numerical hydraulic support model. Int J Min Sci Technol 2024; 34(4):491-505.

[5] Zhang JW, Cheng DL, Wang JC, Yang SL, Wan XH, Li XY. Improving recovery in sublevel top coal caving mining by using partially reverse drawing technique. Int J Min Sci Technol 2024; 34(12):1655—76.

[6] Wang JC, Yu X, Huang Z, Li LH, Wang YB. Impact of surface irregularities on coal wall stability and support mechanisms: Insights from physical and numerical experiments. Int J Min Sci Technol 2025; 35(7):1019—35.

[7] Trueman R, Castro R, Halim A. Study of multiple draw—zone interaction in block caving mines by means of a large 3D physical model. Int J Rock Mech Min Sci 2008; 45(7):1044—51.

[8] Dai BB, Zhao XD, Zhu ZH, Tao GQ, Yin G. Feasibility of broken ore flow simulation in block caving mining method using attribute stochastic medium theory. Minerals 2022; 12(5):576.

[9] Melo F, Vivanco F, Fuentes C, Apablaza V. Kinematic model for quasi static granular displacements in block caving: Dilatancy effects on drawbody shapes. Int J Rock Mech Min Sci 2008; 45(2):248-59.

[10] Kvapil RK. Gravity flow of granular materials in hoppers and bins. Int J Rock Mech Min Sci Geomech Abstr 1965; 2(1):25-41.

[11] Heslop T. In: Understanding the flow of caved ore and its influence on ore recoveries and dilution in a block cave. Perth: Australian Centre for Geomechanics; 2010. p. 539-51.

[12] Jin AB, Sun H, Wu SC, Gao YT. Confirmation of the upside—down drop shape theory in gravity flow and development of a new empirical equation to calculate the shape. Int J Rock Mech Min Sci 2017; 92:91-8.

[13] Bridgwater J, Utsumi R, Zhang Z, Tuladhar T. Particle attrition due to shearing: The effects of stress, strain and particle shape. Chem Eng Sci 2003; 58(20):4649-65.

[14] Hashim M. Particle percolation in block caving mines. Doctoral dissertation. Sydney: UNSW Sydney; 2011.

[15] Song ZY, Wei WJ, Zhang JW. Numerical investigation of effect of particle shape on isolated extracted zone (IEZ) in block caving. Arab J Geosci 2018; 11(12):310.

[16] Sun H, Jin AB, Elmo D, Gao YT, Wu SC. A numerical based approach to calculate ore dilution rates using rolling resistance model and upside—down drop shape theory. Rock Mech Rock Eng 2020; 53(10):4639-52.

[17] Castro R, Cid P, Gómez R, Weatherley D. The influence of drawbell geometry on Hang—ups during ore extraction. Min Metall Explor 2023; 40(3):787-92.

[18] Pierce M. A model for gravity flow of fragmented rock in block caving mines. Doctoral dissertation. Brisbane: The University of Queensland; 2010.

[19] Hancock W, Weatherley D, Chitombo G. Large—scale simulations of gravity flow in block caving. Proceedings of the Second International Symposium on Block and Sublevel Caving. Australian Centre for Geomechanics, Perth, 2010: 553-566.

[20] Hancock WR. Gravity flow of rock in caving mines: Numerical modelling of isolated, interactive and non—ideal draw. University of Queensland Library, PhD Thesis 2013.

[21] Wang YZ, Wan W, Chen W, Zhao YL, Lian SL, Wu QH, et al. Multiscale PFC2D experimental assessment of progressive failure in variable—ratio coal—rock composites. J Mater Eng Perform 2026; 22.

[22] Ester M, Kriegel HP, Sander J, Xu XW. A density—based algorithm for discovering clusters in large spatial databases with noise. In: Proceedings of the Second International Conference on Knowledge Discovery and Data Mining. p. 226-31.

[23] MacQueen JB. Some methods for classification and analysis of multivariate observations. In: Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability. 1967; 1:281-97.

[24] Lloyd S. Least squares quantization in PCM. IEEE Trans Inf Theory 1982; 28(2):129-37.

[25] Edelsbrunner H, Mücke EP. Three—dimensional alpha shapes. ACM Trans Graph 1994; 13(1):43-72.