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Mathematical Problems in Engineering
Volume 2016 (2016), Article ID 4517360, 9 pages
http://dx.doi.org/10.1155/2016/4517360
Research Article

Numerical Analysis of Flattened Brazilian Disc Test Based on the Cusp Catastrophe Theory

Min Wang1,2 and Ping Cao1

1School of Resources and Safety Engineering, Central South University, Changsha, Hunan 410083, China
2Hunan Provincial Key Laboratory of Shale Gas Resource Utilization, Hunan University of Science and Technology, Xiangtan, Hunan 411201, China

Received 20 April 2016; Revised 11 June 2016; Accepted 26 June 2016

Academic Editor: Xiao-Qiao He

Copyright © 2016 Min Wang and Ping Cao. 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

The Brazilian disc test is a simple and useful technique to determine the tensile strength of rock materials. By using FLAC3D, 63 numerical simulations in total were performed when flattened Brazilian disc coefficient and Poisson’s ratio were different. Based on Griffith theory, the corresponding FISH language was compiled to record the Griffith equivalent stress. Through analysis of numerical simulation results, it is indicated that fracture plane was not the plane going through center of the Brazilian disc, which was in good agreement with the references. In addition, the flattened Brazilian disc coefficients had greater influence on tensile strength than Poisson’s ratio. Based on cusp catastrophe theory, the flattened Brazilian disc coefficient should not exceed 0.035 for the flattened Brazilian disc tests. Consequently, a tensile strength empirical formula considering flattened Brazilian disc coefficient by utilizing the flattened Brazilian disc test was established, which was , .