Fig 1.
Flowchart of the proposed block identification methodology, outlining the key steps from model construction through discontinuity cutting to block merging and final identification.
Fig 2.
Schematic diagrams illustrating the formation and classification of rock blocks, including finite/infinite types and their unified polyhedral representation.
(A) Rock mass model with discontinuities cutting to form potential blocks; (B) Block system showing classification into finite (B1, B2) and infinite blocks (B3); (C) System elements demonstrating unified polyhedral representation with directed faces and edges.
Fig 3.
Convention for defining edge directions in polygons, which is fundamental for geometric calculations.
(A) Direction of edges in a convex polygon (B) Direction of edges in a concave polygon.
Fig 4.
The topological rule showing the reversed direction of a shared edge between two adjacent faces in a polyhedron.
Table 1.
Building of convex polyhedron model.
Fig 5.
Edge-face direction relationship in a convex polyhedral model, illustrating how faces are composed of sequentially connected edges with orientations determined by the right-hand rule.
Fig 6.
Construction of a concave stope model by combining three convex sub-regions (M1, M2, M3).
(A) Final merged excavation geometry after eliminating virtual boundaries. (B) Display of sub-blocks of the combined slope.
Fig 7.
Sequence showing the merging of two overlapping faces with opposite orientations based on directed edge operations.
(A) Initial State: Two adjacent blocks with overlapping faces that have opposing orientation vectors. (B) Subdivision: Each face is subdivided by projecting the edges of the opposing face, creating multiple sub-faces. (C) Deletion: The overlapping sub-faces with opposite orientations are deleted according to Rule R1. (D) Final Merged Face: The remaining sub-faces are merged using Rules R2 and R3 to form a single composite face, while non-overlapping regions remain unchanged.
Fig 8.
Sequence illustrating the merging of two overlapping faces with the same orientations based on directed edge operations.
(A) Initial state with two adjacent blocks. (B) Illustration of edge directions within a face. (C) Subdivision of faces by edges (D) Final merged face forming a concave polyhedron.
Fig 9.
Sequential cutting of a rock mass model by discontinuities, demonstrating the block subdivision process.
(A) Initial intersection of discontinuity J1, dividing the rock mass into two distinct sections (A1 and A2). (B) Subsequent introduction of discontinuity J2, which further partitions the lower block while leaving the upper block unaffected.
Fig 10.
Sequential block identification process in a convex polyhedron model using a 2D analogy.
(A) Initial rock mass with discontinuities J1-J3, (B) Division after J1 cut, (C) Further division with J2 and J3 cuts, (D) Merge after J1 size restoration, (E) Additional merge after J2 restoration, (F) Final block configuration after J3 restoration.
Fig 11.
Block identification process in a concave polyhedron model through convex decomposition.
(A) Initial concave excavation geometry, (B) Division into convex sub-regions (A,C,D,E) with auxiliary faces (α,β,γ,λ), (C) Cutting by discontinuity J1, (D) Further division by J2, (E) Block merging after J1 shrinkage, (F) Additional merging after J2 shrinkage, (G) Elimination of auxiliary face α, (H) Final block configuration after removing all auxiliary faces.
Table 2.
Decomposition of the model.
Fig 12.
Three-dimensional model of the stope at the -40m horizontal level, showing the excavation geometry with convex polyhedra.
(A) -40m horizontal middle goaf model (B) Goaf model segmented into 7 convex parts (A-G), illustrating the initial rock mass division. (C) Three-dimensional view showing the convex decomposition (parts A-G) and attributes of the sub-regional face units.
Table 3.
The features of deterministic discontinuities.
Table 4.
The parameters of discontinuities in network simulation.
Fig 13.
Field measurement results of discontinuities using photogrammetry, showing the spatial distribution of distinct groups.
Table 5.
The key blocks information generated by deterministic discontinuities.
Fig 14.
Key blocks generated by deterministic discontinuities after mining phases.
(A) Distribution after the first mining phase, showing key blocks at stope 1# and 4#. (B) Additional key blocks identified after the second mining phase due to excavation-induced discontinuity growth.
Fig 15.
Key blocks formed by random discontinuities, showing distribution along deterministic discontinuities.