Abstract
Compared with two-dimensional (2D) contact cases, three-dimensional (3D) contact problems are more complicated in both contact geometry representation and contact detection. The entrance block theory proposed by Shi lays the foundation for solving contact problems in a uniform format. This paper presents a new contact detection approach for 3D polyhedral blocks with the use of entrance block theory. In this approach, contacts between 3D polyhedra were classified into three categories: finite-contact covers (face to face, edge to face, and parallel edge to edge), single-contact covers (vertex to face, crossing edge to edge, vertex to edge, and vertex to vertex), and basic-contact covers (vertex to face and crossing edge to edge). A finite-contact cover consists of several single-contact covers, and all single-contact covers can be identified as basic-contact covers. Thus, the contact detection process can be fulfilled in three phases: a rough search phase to form a potential contacting block list for all blocks, a delicate search phase to detect the four single-contact covers, and an identification phase to identify basic-contact covers from all single-contact covers. Because contacts happen on boundaries of blocks, which can be regarded as a union of boundaries of 3D block angles, the delicate search can be fulfilled through detection between boundaries of 3D block angles to increase its efficiency. After contact detection, a list of potential contact pairs based on the three contact categories was formed and solved based on two basic-contact covers (i.e., vertex-to-face and crossing edge-to-edge contact covers). The half-edge data structure was applied to represent angles, edges, and polygons in polyhedra. The contact detection algorithm was fulfilled in the framework of 3D discontinuous deformation analysis (DDA), using the object-oriented programming method. In this paper, examples are provided to verify the accuracy of the proposed algorithm in treating vertex-to-vertex, vertex-to-edge, parallel edge-to-edge, edge-to-face, and face-to-face contact types as well as its robustness in solving contacts of a large number of blocks.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This study is supported by the National Basic Research Program of China (973 Program) (2011CB710602, 2014CB046904, 2014CB047101), the National Natural Science Foundation of China (51479191), and the Key Research Program of the Chinese Academy of Sciences (KZZD-EW-05). The authors thank Genhua Shi for the new contact theory and his original 3D DDA code, which are important references for the authors. The first author is supported by the China Scholarship Council (CSC) during his study at the University of California, Berkeley.
References
Bao, H. R., and Zhao, Z. Y. (2010). “An alternative scheme for the corner-corner contact in the two-dimensional discontinuous deformation analysis.” Adv. Eng. Software, 41(2), 206–212.
Cundall, P. A. (1988). “Formulation of a three-dimensional distinct element model—Part I. A scheme to detect and represent contacts in a system composed of many polyhedral blocks.” Int. J. Rock Mech. Min. Sci., 25(3), 107–116.
Cundall, P. A. (2004). UDEC 4.0 manual—Theory and background.” ITASCA Consulting Group, Inc., Minneapolis.
Doolin, D. M., and Sitar, N. (2004). “Time integration in discontinuous deformation analysis.” J. Eng. Mech., 249–258.
Feng, Y. T., and Owen, D. R. J. (2004). “A 2D polygon/polygon contact model: Algorithmic aspects.” Eng. Comput., 21(2/3/4), 265–277.
He, L., An, X. M., and Zhao, Z. Y. (2014). “Development of contact algorithm for three-dimensional numerical manifold method.” Int. J. Numer. Methods Eng., 97(6), 423–453.
He, K. J., Dong, S. B., and Zhou, Z. Y. (2007). “Multigrid contact detection method.” Phys. Rev. E: Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., E, 75(3 Pt 2), 036710.
Jiang, Q. H., and Yeung, M. R. (2004). “A model of point-to-face contact for three-dimensional discontinuous deformation analysis.” Rock Mech. Rock Eng., 37(2), 95–116.
Jiao, Y. Y., Zhang, H. Q., Tang, H. M., Zhang, X. L., Adoko, A. C., and Tian, H. N. (2014). “Simulating the process of reservoir-impoundment-induced landslide using the extended DDA method.” Eng. Geol., 182, 37–48.
Jiao, Y. Y., Zhang, H. Q., Zhang, X. L., Li, H. B., and Jiang, Q. H. (2015). “A two-dimensional coupled hydromechanical discontinuum model for simulating rock hydraulic fracturing.” Int. J. Numer. Anal. Methods Geomech., 39(5), 457–481.
Jiao, Y. Y., Zhang, X. L., and Zhao, J. (2012). “A two-dimensional DDA contact constitutive model for simulating rock fragmentation.” J Eng Mech., 199–209.
Keneti, A. R., Jafari, A., and Wu, J. H. (2008). “A new algorithm to identify contact patterns between convex blocks for three-dimensional discontinuous deformation analysis.” Comput. Geotech., 35(5), 746–759.
Krishnasamy, J., and Jakiela, M. J. (1995). “A method to resolve ambiguities in corner-corner interactions between polygons in the context of motion simulations.” Eng. Comput., 12(2), 135–144.
Liu, X. L., and Lemos, J. V. (2001). “Procedure for contact detection in discrete element analysis.” Adv. Eng. Software, 32(5), 409–415.
Munjiza, A., and Andrews, K. R. F. (1998). “NBS contact detection algorithm for bodies of similar size.” Int. J. Numer. Methods Eng., 43(1), 131–149.
Nezami, E. G., Hashash, Y. M. A., Zhao, D. W., and Ghaboussi, J. (2004). “A fast contact detection algorithm for 3-D discrete element method.” Comput. Geotech., 31(7), 575–587.
Perkins, E., and Williams, J. R. (2001). “A fast contact detection algorithm insensitive to object sizes.” Eng. Comput., 18(1/2), 48–62.
Peters, J. F., Kala, R., and Maier, R. S. (2009). “A hierarchical search algorithm for discrete element method of greatly differing particle sizes.” Eng. Comput., 26, 621–634.
Shi, G. H. (2015). “Contact theory.” Sci. China Tech Sci., 58(9), 1450–1496.
Shi, G. H. (1988). “Discontinuous deformation analysis: A new numerical model for the statics and dynamics of block systems.” Ph.D. thesis, Univ. of California, Berkeley, CA.
Shi, G. H. (2001). “Three dimensional discontinuous deformation analyses.” Proc., 38th US Symp. on Rock Mechanics. American Rock Mechanics Association, Alexandria, VA.
UDEC [Computer software]. ITASCA Consulting Group, Inc., Minneapolis.
Williams, J. R., Perkins, E., and Cook, B. (2004). “A contact algorithm for partitioning N arbitrary sized objects.” Eng. Comput., 21(2/3/4), 235–248.
Wu, J. H., Juang, C. H., and Lin, H. M. (2005). “Vertex-to-face contact searching algorithm for three-dimensional frictionless contact problems.” Int. J. Numer. Methods Eng., 63(6), 876–897.
Wu, W., Zhu, H. H., Zhuang, X. Y., Ma, G. W., and Cai, Y. C. (2014). “A multi-shell cover algorithm for contact detection in the three dimensional discontinuous deformation analysis.” Theor. Appl. Fract. Mech., 72, 136–149.
Yeung, M. R., Jiang, Q. H., and Sun, N. (2007). “A model of edge-to-edge contact for three-dimensional discontinuous deformation analysis.” Comput. Geotech., 34(3), 175–186.
Zhang, H., et al. (2015). “Detection of contacts between three-dimensional polyhedral blocks for discontinuous deformation analysis.” Int. J. Rock Mech. Min. Sci., 78, 57–73.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 17 • Issue 5 • May 2017
Copyright
© 2016 American Society of Civil Engineers.
History
Received: Sep 14, 2015
Accepted: Apr 8, 2016
Published online: May 18, 2016
Discussion open until: Oct 18, 2016
Published in print: May 1, 2017
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.