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Mathematical Problems in Engineering
Volume 2018 (2018), Article ID 3080173, 11 pages
Research Article

A New Equivalent Statistical Damage Constitutive Model on Rock Block Mixed Up with Fluid Inclusions

State Key Laboratory of Disaster Prevention & Mitigation of Explosion & Impact, National Defense Engineering College, Army Engineering University of PLA, Nanjing 210000, China

Correspondence should be addressed to Hongfa Xu; moc.anis@1afgnohux

Received 31 October 2017; Revised 3 January 2018; Accepted 9 January 2018; Published 18 March 2018

Academic Editor: Michele Brun

Copyright © 2018 Xiao Chen 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.


So far, there are few studies concerning the effect of closed “fluid inclusions” on the macroscopic constitutive relation of deep rock. Fluid-matrix element (FME) is defined based on rock element in statistical damage model. The properties of FME are related to the size of inclusions, fluid properties, and pore pressure. Using FME, the equivalent elastic modulus of rock block containing fluid inclusions is obtained with Eshelby inclusion theory and the double M-T homogenization method. The new statistical damage model of rock is established on the equivalent elastic modulus. Besides, the porosity and confining pressure are important influencing factors of the model. The model reflects the initial damage (void and fluid inclusion) and the macroscopic deformation law of rock, which is an improvement of the traditional statistical damage model. Additionally, the model can not only be consistent with the rock damage experiment date and three-axis compression experiment date of rock containing pore water but also describe the locked-in stress experiment in rock-like material. It is a new fundamental study of the constitutive relation of locked-in stress in deep rock mass.