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

Yang Ping,Qiang Kou,Teng-Fei Ma,Shu-Chen Li,Shu-Cai Li,Lu-Chen Zhang

doi:10.1155/2014/315983

Abstract

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.

Highlights

The rock is a complex mixture composed of various mineral crystals, cements, and pore defects
Some numerical methods such as RFPA, DDA, meshless method, manifold method, boundary element method, and discrete element method were applied in the study on crack propagation, and good results have been achieved (Cundall [6], Liu et al [7], Harrison et al [8], Chen et al [9], Li et al [10], Tang et al [11,12,13,14], etc.)
Based on the manifold cover concept, this paper proposes a new discrete element numerical method, manifold particle discrete, to simulate the generation, propagation, and coalescence of rock crack from the macro-meso perspective, combined with the particle contact model and introduced concept of stress boundary

Summary

Introduction

The rock is a complex mixture composed of various mineral crystals, cements, and pore defects. For heterogeneous media that are not totally continuous or totally discrete, Doctor Shi created a new numerical calculation method, numerical manifold method, using the finite cover technique in manifold analysis based on his proposed discontinuous deformation analysis in the 1990s This method uniformly solves mechanics problems of continuous and discontinuous deformation. Based on the manifold cover concept, this paper proposes a new discrete element numerical method, manifold particle discrete, to simulate the generation, propagation, and coalescence of rock crack from the macro-meso perspective, combined with the particle contact model and introduced concept of stress boundary

MPD Model Unit

Balance Equation and Geometric Equation of the MPD Model

Numerical Results

Conclusion