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Advances in Mathematical Physics
Volume 2017, Article ID 3807401, 10 pages
Research Article

A Statistical Damage Constitutive Model for Geomaterials under Plane-Strain Biaxial Stress State

1Key Laboratory of Deep Coal Resource Mining (CUMT), Ministry of Education of China, School of Mines, China University of Mining & Technology, Xuzhou 221116, China
2Department of Energy and Mineral Engineering, EMS Energy Institute and G3 Center, The Pennsylvania State University, University Park, PA 16802, USA

Correspondence should be addressed to Zhijun Wan; moc.621@nawjhz

Received 30 May 2017; Accepted 10 September 2017; Published 17 October 2017

Academic Editor: John D. Clayton

Copyright © 2017 Hongwei Zhang 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 mechanical behavior of geomaterials under plane-strain biaxial stress state (PSBSS, a special case of biaxial stress state) is often considered in geotechnical structures such as highwall and longwall coal pillars. In this study, a modified statistical damage constitutive model based on Weibull distribution was established to explain the mechanical behavior of rocks under the PSBSS. The modified Wiebols-Cook criterion, Drucker-Prager criterion, and extremum method were adopted in this model to estimate the peak strength of rock, the strength level of microscopic element, and the statistical parameters of model, respectively. Besides, laboratory tests for brittle and ductile geomaterials under PSBSS were conducted using the modified surface instability detection apparatus to validate the accuracy of the proposed statistical damage model. Finally, the relationships between mechanical parameters and statistical parameters were studied and discussed.