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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 315983, 13 pages
Research Article

Particle Discrete Method Based on Manifold Cover for Crack Propagation of Jointed Rock Mass

Geotechnical and Structural Engineering Research Center, Shandong University, Jinan, Shandong 250061, China

Received 15 December 2013; Accepted 8 March 2014; Published 10 April 2014

Academic Editor: Miaojuan Peng

Copyright © 2014 Yang Ping et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The rock mass can be assumed to be homogeneous material from a macroscopic view; however, it is the heterogeneous material in mesoscopic scale and its physicomechanical properties are discontinuous in space. The failure of jointed rock mass was usually caused by the initiation, propagation, and coalescence of new wing cracks derived from primary joint. In order to further study the rock fracture instability, we need to study the expansion of rock cracks under external loads from the macro-meso perspective. This paper, based on the manifold cover concept, proposes a new discrete element numerical method, manifold particle discrete (MPD), combined with the particle contact model and the introduced concept of stress boundary. The proposed method can easily simulate the crack generation, propagation, and coalescence of jointed rock mass from the macro-meso perspective. The whole process of rock fragmentation is thereafter reproduced. By analyzing the manifold cover and sphere particle model, this paper constitutes the sphere unit cover function of three-dimensional manifold cover, establishes tetrahedron units, and obtains the equilibrium equation and compatible equation of the MPD model. For rock-like brittle material, crack propagation process can be simulated, and it also verifies the accuracy of the proposed numerical method.