On a statistical damage constitutive model for rock materials

• Published in: Computers & geosciences Vol. 37; no. 2; pp. 122 - 128
• Main Authors: Deng, Jian, Gu, Desheng
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.02.2011; Elsevier
• Subjects: Constitutive model; Constitutive relationships; Damage; Earth sciences; Earth, ocean, space; Engineering and environment geology. Geothermics; Engineering geology; Entropy; Exact sciences and technology; Mathematical models; Maximum entropy; Maximum entropy distribution; Rock; Rock materials; Strain softening; Strength; Weibull distribution; Maximum entropy distribution; Constitutive model; Rock materials; Weibull distribution; strain; experimental studies; damage; models; strength; data processing; metamorphic rocks; quartzites; entropy; confining pressure; triaxial compression; computers; theory
• ISSN: 0098-3004; 1873-7803
• DOI: 10.1016/j.cageo.2010.05.018

A statistical damage constitutive model for rocks with strain softening behaviour is put forward, using the theory of continuous damage mechanics together with statistical mesoscopic strength theory based on maximum entropy distribution. In statistical constitutive modelling, the probabilistic distribution of mesoscopic element strength in rocks is a critical piece of information, which was conventionally described by various empirical distributions among which the Weibull distribution was extensively used. In this paper, an alternative and universal distribution, i.e. maximum entropy distribution, is proposed to describe the statistical property of mesoscopic strength in rocks. By incorporating the entropy distribution information into a damage variable, the paper derives a new constitutive model, which is verified by conventional triaxial experiments and dynamic experiments on rock specimens. To illustrate suitability and flexibility, the new model is compared to the well-established Weibull-distribution-based models.