Issue 27

X. Ran et alii, Frattura ed Integrità Strutturale, 27 (2014) 74-82; DOI: 10.3221/IGF-ESIS.27.09 76 E LASTIC - PLASTIC DAMAGE MODEL he effective shear strength parameters * c and *  is influenced by rock damage [13]. So the * c and *  is a function of damage state. When the effect of damage and pore pressure is involved, the Mohr-Coulomb failure criterion can be indicated as Eq. (1). * * tan 1 1 n n w p c            (1) where: -  is damage variable; - n  and n  are stresses on the failure surface; - w p is the pore pressure. In this paper, the internal frictional angle is deemed to be changeless. But the cohesion will decrease gradually with the accumulation of damage. Their relationship can be represented by a power-law function:   m m r p c c c c      (2) where: - m c is the cohesion of shale with no damage; - r c is the cohesion of shale with complete damage; -  is the material parameter, 0 1    . The elastic modulus of the damaged shale is:   0 1 E E    (3) where 0 E is elastic modulus of shale with no damage. According to (3), 0 E  when 1   . This does not match the actual reality. In fact, the rock also has a certain elastic modulus after damage. So, Eq. (3) needs to modify as:   0 0 r E E E E     (4) where r E is elastic modulus of shale with complete damage. D AMAGE EVOLUTION EQUATION f the stress exceeded rock strength at the condition of fluid-solid coupling, plastic deformation will be produced in wall rock. The equivalent plastic strain is:       2 2 2 1 2 2 3 3 1 2 3 p p p p p p p              (5) where 1 p  , 2 p  and 3 p  are the three principal plastic strains. In this paper, the damage variable is the first order index decay function of equivalent plastic strain which is as follows [14]: / 0 0 pn a A e B      (6) 0 1/ 1 1 a A e    ; 0 1/ 1 1 a B e     where pn  is normalized equivalent plastic strain; a is material parameter which can be measured by experiments. T I