Application of a vertex chain operation algorithm on topological analysis of three-dimensional fractured rock masses

doi:10.1007/s11709-017-0391-0

Front. Struct. Civ. Eng.

2017, Vol. 11

Issue (2) : 187-208 https://doi.org/10.1007/s11709-017-0391-0

RESEARCH ARTICLE

Application of a vertex chain operation algorithm on topological analysis of three-dimensional fractured rock masses

Zixin ZHANG^1,^2,³, Jia WU^1,^2,⁴, Xin HUANG^1,²(

)

¹. Department of Geotechnical Engineering, School of Civil Engineering, Tongji University, Shanghai 200092, China
². Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Tongji University
³. State Key Laboratory for Geomechanics and Deep Underground Engineering, Xuzhou 221008, China
⁴. Shanghai?Tunnel?Engineering?&?Rail?Transit?Design?and?Research?Institute, Shanghai 200235, China

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Abstract

Identifying the morphology of rock blocks is vital to accurate modelling of rock mass structures. This paper applies the concepts of directed edges and vertex chain operations which are typical for block tracing approach to block assembling approach to construct the structure of three-dimensional fractured rock masses. Polygon subtraction and union algorithms that rely merely on vertex chain operation are proposed, which allow a fast and convenient construction of complex faces/loops. Apart from its robustness in dealing with finite discontinuities and complex geometries, the advantages of the current methodology in tackling some challenging issues associated with the morphological analysis of rock blocks are addressed. In particular, the identification of complex blocks with interior voids such as cavity, pit and torus can be readily achieved based on the number and the type of loops. The improved morphology visualization approach can benefit the pre-processing stage when analyzing the stability of rock masses subject to various engineering impacts using the block theory and the discrete element method.

Keywords morphology block assembling vertex operation discontinuities

Corresponding Author(s): Xin HUANG

Online First Date: 19 April 2017 Issue Date: 19 May 2017

Cite this article:

Zixin ZHANG,Jia WU,Xin HUANG. Application of a vertex chain operation algorithm on topological analysis of three-dimensional fractured rock masses[J]. Front. Struct. Civ. Eng., 2017, 11(2): 187-208.

URL:

https://academic.hep.com.cn/fsce/EN/10.1007/s11709-017-0391-0
https://academic.hep.com.cn/fsce/EN/Y2017/V11/I2/187

Fig.1 Illustration of two families of rock blocks identification algorithm: (a) the block tracing approach; (b) the block assembling approach

Fig.2 The procedure of the block detection algorithm

Fig.3 The internal data structure of the vertex class and the fracture class

Fig.4 Illustration of the definition of a boundary box

Fig.5 The internal data structure of the element face class and element block class

Fig.6 The internal data structure of the complex face class and the complex block class

Fig.7 The procedure of element block identification

Fig.8 Handling order of the fractures: (a) not sorted by the area; (b) sorted by the area

Fig.9 Four typical relationships between the boundary boxes of the element block and the fracture plane: (a) isolated; (b) intersecting; (c) EB1 and EB2 respectively located in the upper and the lower space of the fracture; (d) the fracture plane cuts through EB3

Fig.10 Determining the anticlockwise order of the vertex list

Fig.11 The procedure of fracture cutting element block

Fig.12 The union-find relationship judgment of the element block (dashed rectangular indicates the area of extended fracture plane while the solid ellipse represents the real area of the fracture plane): (a) two separate EBs; (b) two blocks that can be combined

Fig.13 The procedure of the union-find element blocks

Fig.14 An example for constructing complex blocks using the grouped element blocks (id number within the brackets indicates the id of the fracture plane that the EF is on)

Fig.15 Two typical cases of element face operations to generate complex faces

Fig.16 The problem of identification the loop of the complex face: (1) an outer loop with three inner loops; (2) two outer loops (an outer loop with two inner loops); (3) three outer loops (an outer loop with an inner loop)

Fig.17 Illustration of typical polygon subtraction

Fig.18 Three typical cases in which the polygons could be merged: (a) two successive vertexes in common; (b) more than two sequentially-numbered vertexes in common; (c) the common vertexes are discrete but at least two of these vertexes are in sequence

Fig.19 Combining one hollow element face with a solid element face: (a) The vertexes of the inner loop does not equal to the common vertexes; (b) The common vertexes are coincident with the vertexes of the inner loop of the subject polygon

Fig.20 Typical types of complex rock blocks: (a) convex; (b) concave; (c) containing cavity; (d) containing a pit; (e) containing a torus

Fig.21 Excavation of a complex block

Tab.1 Geological parameters of the boundary planes

Tab.2 Geological parameters of the fracture planes

Fig.22 Morphology analysis for a three-dimensional fractured rock mass prior to excavation: (a) generating the fracture network within the computational domain; (b) identifying the element blocks; (c) clustering the element blocks; (d) constructing the final complex blocks.

Fig.23 Morphology analysis for a three-dimensional fractured rock mass after excavation: (a) defining the excavation planes and identifying the affected complex blocks; (b) determining the newly-created element blocks; (c) deleting the element blocks in the excavation domain; (d) clustering the newly-created element blocks; (e) constructing the final complex blocks (4–12 are newly-generated complex blocks. The size of some blocks has been scaled down or scaled up for the ease of observation.)

Tab.3 Geological parameters of the excavation planes

Tab.4 The geometrical parameters of each complex block

Tab.5 Geological parameters of the boundary planes

Tab.6 Geological parameters of the fracture planes

Tab.7 Geological parameters of the excavation planes

Tab.8 The geometrical parameters of each complex block

Fig.24 Morphology analysis for a three-dimensional fractured rock mass after excavation of a circular tunnel

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