A Fractal and Numerical Simulation Coupled Study of Fracture Network during Coal Mining Excavation

A Fractal and Numerical Simulation Coupled Study of Fracture Network during Coal Mining Excavation Yanan Gao,1,2 Feng Gao,1,2 and Man-chu Ronald Yeung3 1School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, China 2State Key Laboratory of Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221116, China 3Department of Civil Engineering, California State Polytechnic University, Pomona, CA 91768, USA Received 7 November 2013; Accepted 12 January 2014; Published 23 February 2014 Academic Editor: Guangchen Wang Copyright © 2014 Yanan Gao 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. Abstract This paper features a numerical study that is carried out by using discontinuous deformation method (DDA) and fractal geometry. The configurations of rock strata calculated by DDA were imported into a code that is written by using VC++ called “Fractal” to calculate the fractal dimension of the rock strata. As illustrated, a long wall mining case in China was presented. The relationship of the fractal dimension, excavation length, stress, and movement of strata were discussed. The evolution of fractal dimension can be considered as an index of instability or failure. The method proposed in this paper can be employed to predict the period weighting in long wall mining engineering. 1. Introduction Numerical methods which are rapidly developing and have been widely employed in various engineering fields like geotechnical engineering, mining engineering, civil engineering, and so forth from the past decades [1, 2] can be used to study different geometry and time scales of engineering cases or lab tests and the results obtained by these methods can be repeated with ease. Enormous amount of information extracted from a numerical analysis includes almost all the physical parameters such as displacement, stress state, and energy. The advantages mentioned above rarely exit in theoretical or experimental methods. The important information obtained from a numerical analysis is displacements, stresses, and failure area. Besides, the evolution of fracture network can also be simulated by using discontinuous method, such as UDEC [3] software and DDA (discontinuous deformation method) [4, 5]. Study of fracture network is of great significance to underground engineering, such as deep mining, since stability of surrounding rock, the movement of strata, gas, and water flow are all associated with it. Wang et al. [6] set up a physical model to investigate the fracture network evolution of overburden rock mass. They pointed out in their study that there exists a strong relation between the ground pressure and evolution and configuration of the fracture network. Fractal dimension was employed as an index to study the evolution fracture network. The fractal theory was widely used to study the geomaterials, especially rocks, after the pioneer work of Xie and Chen [7]. However, compared to lab tests, which are used to study material properties, the relative larger scale problem such as overburden rock movement is rarely studied except the work of Wang et al. [6]. Inspired by the previous study, we attempt to explore more information based on numerical results and fractal dimension. 2. Methodology and Basic Theory Two tools are used in this study; one is the numerical method—DDA—and the other is the fractal theory and fractal dimension. 2.1. Basic Theory of DDA The DDA is a discrete element method following the definition by Cundall and Hart [3]. The method was developed by Shi [4, 5]; since then it has received considerable attention by the geoengineering community and has been under continuous development and application. The DDA is based on inverse analysis method inspired by an in situ rock block model experiment. It was developed to back-calculate the deformed geometry of the block model from experimentally measured displacements and deformations using a least-square formulation. The displacement function of DDA can be written as where and are the horizontal and vertical displacement of the rock block, respectively, and and () are unknowns. In DDA, the large deformation and displacement are calculated by accumulating the small deformation and displacement with a time matching scheme. Based on the definition of Cauchy strain, (1) can be written as where, the , , and are horizontal strain, vertical strain, and shear strain, respectively. Here, the deformation of the th block is assumed as []: We thus have the displacement as the following form: where is the rigid body displacement of centroid ; is rotation angle. Minimization of the potential energy of the system of blocks, following the FEM convention, results in the following equation: is made of 6 × 1 s (...truncated)