A method for identifying three-dimensional rock blocks formed by curved fractures

Abstract Identifying blocks formed by various fractures is important in rock engineering. Most studies focus mainly on blocks formed by planar fractures whereas curved fractures are rarely considered. However, large fractures observed in the field are often curved. This paper presents a new method for identifying rock blocks formed by both curved and planar fractures based on the element-block-assembling approach, in which the study domain is divided into numerous tetrahedral subdomains under the constraint of curved fractures and the subdomains are further decomposed into element blocks by extended planar fractures. When the fractures are restored to finite dimensions, the element blocks are combined and the subdomains are assembled to form complex blocks. The combination of the two subdomains is skipped if and only if their common facet lies on a curved fracture. A computer program was implemented based on the method introduced in this study and the verification examples indicated that this method could effectively handle both convex and concave blocks.

[1]  N. Jones,et al.  Building solid models from boreholes and user-defined cross-sections , 2003 .

[2]  Marc Elmouttie,et al.  Polyhedral modelling of rock mass structure , 2010 .

[3]  John A. Hudson,et al.  Numerical methods in rock mechanics , 2002 .

[4]  J. A. Hudson,et al.  A NOVEL AUTOMATIC IDENTIFICATION SYSTEM FOR THREE‐DIMENSIONAL MULTI‐BLOCK SYSTEMS , 1992 .

[5]  Fernando Muge,et al.  Interpolation approach for 3D smooth reconstruction of subsurface objects , 2002 .

[6]  Jonathan Richard Shewchuk,et al.  Constrained Delaunay Tetrahedralizations and Provably Good Boundary Recovery , 2002, IMR.

[7]  Lanru Jing,et al.  Block system construction for three-dimensional discrete element models of fractured rocks , 2000 .

[8]  Zixin Zhang,et al.  Object-oriented modeling for three-dimensional multi-block systems , 2013 .

[9]  Marc Elmouttie,et al.  Robust algorithms for polyhedral modelling of fractured rock mass structure , 2013 .

[10]  D. Heliot.  Generating a blocky rock mass , 1988 .

[11]  Y. Estrin,et al.  Interlocking of convex polyhedra: towards a geometric theory of fragmented solids , 2004 .

[12]  Bernard A. Galler,et al.  An algorithm for equivalence declarations , 1961, CACM.

[13]  Yuting Zhang,et al.  Improvement of methodology for block identification using mesh gridding technique , 2012 .

[14]  Jonathan Richard Shewchuk,et al.  A condition guaranteeing the existence of higher-dimensional constrained Delaunay triangulations , 1998, SCG '98.

[15]  Jonathan Richard Shewchuk,et al.  Delaunay refinement algorithms for triangular mesh generation , 2002, Comput. Geom..

[16]  K. Gärtner,et al.  3D boundary recovery by constrained Delaunay tetrahedralization , 2011 .

[17]  Raimund Seidel,et al.  On the difficulty of triangulating three-dimensional Nonconvex Polyhedra , 1992, Discret. Comput. Geom..

[18]  Yuzo Ohnishi,et al.  A generalized procedure to identify three‐dimensional rock blocks around complex excavations , 2009 .

[19]  Marc Elmouttie,et al.  Polyhedral modelling of underground excavations , 2010 .

[20]  P. M. Warburton.  Applications Of A New Computer Model For Reconstructing Blocky Rock Geometry-Analysing Single Block Stability And Identifying Keystones , 1983 .

[21]  Nicholas Anthony Lanney,et al.  Statistical description of rock properties and sampling. , 1978 .

[22]  Liang-feng Zhu,et al.  Building 3D solid models of sedimentary stratigraphic systems from borehole data: An automatic method and case studies , 2012 .

[23]  Hossein Rahami,et al.  Developing an algorithm for reconstruction of blocky systems in discontinuous media: two-dimensional analysis , 2011 .

[24]  Michael J. Fischer,et al.  An improved equivalence algorithm , 1964, CACM.

[25]  Jun Lu,et al.  Systematic identification of polyhedral rock blocks with arbitrary joints and faults , 2002 .

[26]  H. Si.  Three Dimensional Boundary Conforming Delaunay Mesh Generation , 2008 .

[27]  A. Jafari,et al.  Developing an algorithm for reconstruction blocky systems in discontinuous media: three-dimensional analysis , 2013 .

[28]  Charles Fairhurst,et al.  GEOMETRICAL IDENTIFICATION OF THREE-DIMENSIONAL ROCK BLOCK SYSTEMS USING TOPOLOGICAL TECHNIQUES , 1987 .

[29]  Yuting Zhang,et al.  A new methodology for block identification and its application in a large scale underground cavern complex , 2010 .